Françoise Prudhomme

Patricia Braconnier

Valérie Savornin

Anne-Marie Bouchon

Barry Gardiner

Lisa Wingate

Ajit Govind

Dominique Guyon

Jean-Pierre Lagouarde

Christophe Moisy

Tovo Rabemanantsoa

Guy Pracros

Alain Mollier

Sandra Debesa

Didier Garrigou

Clement Duffour

Damien Commandoire

Jean-Charles Samalens

Joana Jorly

Sylvio Laventure

Julien Kammer

Keywords: Soil moisture, Global-scale, Hydrology, Microwave remote sensing, SMOS, ASCAT, AMSR-E, Statistical evaluation Humidité du sol, Échelle globale, Hydrologie, Télédétection micro-ondes

INRA) in Bordeaux to pursue a Ph.D. This period

appliquée aux mesures de températures de brillance de AMSR-E (2003AMSR-E ( -2011)). Les coefficients de régression ont été calibrés avec les produits SSM issus de SMOS sur 2010-2011. Le produit SSM résultant, qui fusionne les observations SMOS et AMSR-E, a été évalué par comparaison avec un produit SSM AMSR-E et les produits SSM MERRA-Land sur 2007-2009. Ces résultats préliminaires montrent que la méthode de régression linéaire est une approche simple et robuste pour construire un produit SSM réaliste en termes de variations temporelles et de valeurs absolues. En conclusion, cette thèse a montré que le potentiel de synergie entre les systèmes micro-ondes passifs (AMSR-E et SMOS) et actifs (ASCAT) est très prometteur pour le développement et l'amélioration de longues séries temporelles SSM à l'échelle mondiale, telles que celles produites dans le cadre du programme CCI de l'ESA. Elle a également fourni de nouvelles idées sur la façon de fusionner les différents ensembles de données de SSM dans le but de produire une série CCI SSM (Phase 2) long terme (une série cohérente combinant SMOS et AMSR-E sur la période 2003-2014), qui va être évaluée dans le cadre de projets ESA en cours.

1.1

Background and Motivation

Soil moisture (SM) is a key variable in better understanding of the land-atmosphere interactions because it influences the partitioning of precipitation into infiltration and runoff and the partitioning of energy into sensible and latent heat [START_REF] Daly | A review of soil moisture dynamics: from rainfall infiltration to ecosystem response[END_REF][START_REF] Pielke | The Role of Landscape Processes within the Climate System[END_REF][START_REF] Western | Scaling of soil moisture: a hydrologic perspective[END_REF]. Spatio-temporal variabilities of SM are critical and have direct applications in hydrology, agronomy, water resources managing [START_REF] Blöschl | Report for Final report of the Visiting Scientist Activity to the Satellite Application Facility on Support[END_REF][START_REF] Dobriyal | A review of the methods available for estimating soil moisture and its implications for water resource management[END_REF], weather prediction and climate change studies [START_REF] Leese | GEWEX/BAHC international workshop on soil moisture monitoring analysis and prediction for hydrometeorological and hydroclimatological applications[END_REF][START_REF] Seneviratne | Investigating soil moisture-climate interactions in a changing climate: A review[END_REF], flood analyses and drought monitoring [START_REF] Bolten | Evaluating the Utility of Remotely Sensed Soil Moisture Retrievals for Operational Agricultural Drought Monitoring[END_REF][START_REF] Michele | On the derived flood frequency distribution: analytical formulation and the influence of antecedent soil moisture condition[END_REF], irrigation operation, and soil erosion studies [START_REF] Fu | The relationships between land use and soil conditions in the hilly area of the loess plateau in northern Shaanxi, China[END_REF][START_REF] Luk | Effect of antecedent soil moisture content on rainwash erosion[END_REF].

In addition, SM initial conditions are crucial for the quality of hydrological models and Numerical Weather Prediction (NWP) at all range, including short range, monthly, and seasonal forecasts [START_REF] Beljaars | The Anomalous Rainfall over the United States during July 1993: Sensitivity to Land Surface Parameterization and Soil Moisture Anomalies[END_REF][START_REF] De Rosnay | Extended Kalman Filter soil moisture analysis in the IFS. ECMWF Spring Newsletter[END_REF][START_REF] Drusch | Initializing numerical weather prediction models with satellite-derived surface soil moisture: Data assimilation experiments with ECMWF's Integrated Forecast System and the TMI soil moisture data set[END_REF]Koster et al., 2004a;[START_REF] Koster | GLACE: The Global Land-Atmosphere Coupling Experiment. Part I: Overview[END_REF][START_REF] Panegrossi | Impact of ASAR soil moisture data on the MM5 precipitation forecast for the Tanaro flood event of April 2009[END_REF].

Consequently, there have been broad efforts to estimate SM in numerous research areas. Researchers have tried to estimate SM as accurately as possible using in situ observations [START_REF] Dirmeyer | GSWP 2: Multimodel analysis and implications for our perception of the land surface[END_REF][START_REF] Robock | The Global Soil Moisture Data Bank[END_REF], land surface models (wherein the accuracy of SM estimates depends on the forcing datasets and construction of the model), and Remote Sensing. Remote Sensing with high spatio-temporal coverage overwhelms the limitations and weakness of the other sources of information. Remote Sensing is an interesting source of information about SM as it offers the opportunity to obtain global and repetitive surface SM (SSM) estimates derived from satellite-based microwave sensors (Bartalis et al., 2007a;[START_REF] Kerr | Soil moisture retrieval from space: the Soil Moisture and Ocean Salinity (SMOS) mission[END_REF][START_REF] Njoku | Soil moisture retrieval from AMSR-E. Geoscience and Remote Sensing[END_REF][START_REF] Owe | Multisensor historical climatology of satellitederived global land surface moisture[END_REF]. The main disadvantages of the remotely sensed datasets are their limitation to the top few centimeters of soil and the spatial and temporal gaps in dense vegetation and high surface roughness regions.

Two types of microwave sensors offer the opportunity to retrieve SSM information: radiometers (passive) and radar (active) sensors (scatterometers or SAR system). Radar and radiometers sensors measure surface backscatter and brightness temperatures (TB) signals, respectively, which are mainly determined by the soil dielectric constant, from which SSM can be derived [START_REF] Njoku | Observations of soil moisture using a passive and active lowfrequency microwave airborne sensor during SGP99[END_REF][START_REF] Ulaby | Radar mapping of surface soil moisture[END_REF]. Various radiometer and radar sensors have been used to measure SSM, and space-borne missions with new radiometer and radar sensors are presently being developed (Bartalis et al., 2007a;[START_REF] Entekhabi | The Soil Moisture Active Passive (SMAP) Mission[END_REF]Kerr et al., 2001;[START_REF] Njoku | Soil moisture retrieval from AMSR-E. Geoscience and Remote Sensing[END_REF]. Historically, passive microwave sensors were first used, starting with the Scanning Multichannel Microwave Radiometer (SMMR;6.6,10.7 ,18.0 21,and 37 GHz channels; [START_REF] Wang | Effect of vegetation on soil moisture sensing observed from orbiting microwave radiometers[END_REF]), which operated on Nimbus-7 between 1978 and 1987, then the Special Sensor Microwave Imager (SSM/I; 19.4, 22.2, 37.0, and 85.0 GHz channels) of the Defense Meteorological Satellite Program which started in 1987. Later passive sensors include: the microwave imager from the Tropical Rainfall Measuring Mission (TRMM; 10, 19 and 21 GHz channel; [START_REF] Bindlish | Soil moisture estimates from TRMM Microwave Imager observations over the Southern United States[END_REF][START_REF] Gao | Using TRMM/TMI to Retrieve Surface Soil Moisture over the Southern United States from 1998 to 2002[END_REF]), the Advanced Microwave Scanning Radiometer on Earth Observing System (AMSR-E; from 6.9 to 89.0 GHz; [START_REF] Njoku | Retrieval of land surface parameters using passive microwave measurements at 6-18 GHz[END_REF]) which operated on the AQUA satellite between [START_REF] Dingman | Physical Hydrology[END_REF]2011, andCoriolis Windsat which started in 2003 [START_REF] Parinussa | The impact of land surface temperature on soil moisture anomaly detection from passive microwave observations[END_REF]. More recently, the Soil Moisture and Ocean Salinity (SMOS) was launched on November 2, 2009 [START_REF] Kerr | The SMOS Soil Moisture Retrieval Algorithm[END_REF] and the upcoming SMAP (Soil Moisture Active/Passive) mission is scheduled for launch in November 2014 [START_REF] Entekhabi | The Soil Moisture Active Passive (SMAP) Mission[END_REF].

Besides passive microwave sensors, active microwave sensors are also useful to retrieve SSM including, but are not limited to, the European Remote Sensing (ERS-1) Scatterometer which is operated since 1992, and its copy on ERS-2 which started collecting data from March 1996, and the Advanced Scatterometer (ASCAT) on board the Meteorological Operational satellite programme (METOP), METOP-A was launched in 2006 (Bartalis et al., 2007a) followed by METOP-B in 2012.

The (European Space Agency) ESA's Programme on Global Monitoring of Essential

Climate Variables (ECV), known as the Climate Change Initiative (CCI), and the European Space Agency's Water Cycle Multi-mission Observation Strategy (WACMOS) merged several active and passive i.e. SMMR, SSM/I, TMI, AMSR-E, ERS-1/2, and ASCAT data [START_REF] Liu | Developing an improved soil moisture dataset by blending passive and active microwave satellite-based retrievals[END_REF] to produce long-term and consistent time series of SSM (1978SSM ( -2010)), with a spatial resolution of 0.25° x 0.25°. This product has been available since June 2012 and has been of interest for researchers to study the long-term trends of SSM (Albergel et al., 2013b;[START_REF] Seneviratne | Investigating soil moisture-climate interactions in a changing climate: A review[END_REF].

The SMOS satellite, among all the aforementioned passive microwave sensors, is the first ever satellite dedicated and specifically designed to measure SSM, over the land surfaces, and surface ocean salinity (SSS) at L-band on a global basis [START_REF] Kerr | The SMOS Mission: New Tool for Monitoring Key Elements ofthe Global Water Cycle[END_REF]. L-band (1.4 GHz), within the microwave bands protected for remote sensing applications, has been recognized to be well-suited to monitoring SSM owing to better penetration through vegetation and reduced atmospheric effects on their signals [START_REF] Kerr | Soil moisture retrieval from space: the Soil Moisture and Ocean Salinity (SMOS) mission[END_REF][START_REF] Njoku | Multifrequency Microwave Radiometer Measurements of Soil Moisture[END_REF][START_REF] Wang | An Empirical Model for the Complex Dielectric Permittivity of Soils as a Function of Water Content[END_REF]. As the attenuation effects of the vegetation layer overlaying the ground decrease with increasing wavelength, L-band is theoretically more optimal for sensing SSM than C-band (4-8 GHz) or higher frequencies. Furthermore, the effective SSM sampling depth at L-band (~0-3cm; [START_REF] Escorihuela | Effective soil moisture sampling depth of L-band radiometry: A case study[END_REF] is larger than at C-band (~0-1cm). In the literature, the compared capabilities of remote sensing at C-band and L-band to monitor SSM were established from in situ observations and theory [START_REF] Ulaby | Microwave Remote Sensing, Active and Passive[END_REF][START_REF] Wigneron | Microwave emission of vegetation: sensitivity to leaf characteristics[END_REF]. Therefore, it is likely the SMOS SSM products are useful and of high priority in most operational hydrologic models for agricultural applications, flood forecast and water quality management.

Two SSM products have been released since the launch of SMOS: (i) the Level 2 SMOS SSM products (SMOSL2), distributed by the ESA, which is derived from the multi-angular and fully polarized bi-polarization SMOS TB observations and provided as swathbased products and more recently (ii) the Level 3 SMOS SSM products (SMOSL3), distributed by the Centre Aval de Traitement des Données SMOS (CATDS), which is a gridded product computed from the SMOS TB observations [START_REF] Jacquette | SMOS CATDS level 3 global products over land[END_REF]. The general principle of the algorithm used to compute SSM in both SMOSL2 and SMOSL3 is almost similar [START_REF] Jacquette | SMOS CATDS level 3 global products over land[END_REF]. However, in the SMOSL3, the quality of SSM products is enhanced by using multi-orbit retrievals [START_REF] Kerr | The CATDS SMOS L3 soil moisture retrieval processor, Algorithm Theoretical Baseline Document[END_REF], and provided as global maps in a more friendly format (NetCDF) for the final users. Evaluation of both SMOSL2 and SMOSL3 SSM products, as for any remote sensing products, is needed to guide their correct use, and to improve our understanding of their strengths and weaknesses over a large spectrum of climate and environmental conditions across the world. Evaluation not only assesses the accuracy and reliability of the estimates and their scientific utility, but also defines possible limits of satellite instruments.

Several studies have evaluated SMOSL2 SSM products over different regions using in situ observations, model-based data, and remote sensing products at the local, continental, and global scales [START_REF] Al Bitar | Evaluation of SMOS Soil Moisture Products Over Continental U.S. Using the SCAN/SNOTEL Network[END_REF][START_REF] Albergel | A first assessment of the SMOS data in southwestern France using in situ and airborne soil moisture estimates : the CAROLS airborne campaign[END_REF][START_REF] Albergel | Evaluation of remotely sensed and modelled soil moisture products using global ground-based in situ observations[END_REF]Collow et al., 2012;[START_REF] Dall'amico | First Results of SMOS Soil Moisture Validation in the Upper Danube Catchment[END_REF][START_REF] Dente | Validation of SMOS Soil Moisture Products over the Maqu and Twente Regions[END_REF][START_REF] Jackson | Validation of Soil Moisture and Ocean Salinity (SMOS) Soil Moisture Over Watershed Networks in the U.S. Geoscience and Remote Sensing[END_REF][START_REF] Kaihotsu | First evaluation of SMOS L2 soil moisture products using in situ observation data of MAVEX on the Mongolian Plateau in 2010 and 2011[END_REF][START_REF] Lacava | A First Assessment of the SMOS Soil Moisture Product With In Situ and Modeled Data in Italy and Luxembourg[END_REF]Leroux et al., 2013a;Leroux et al., 2013b;[START_REF] Parrens | Comparing soil moisture retrievals from SMOS and ASCAT over France[END_REF][START_REF] Peischl | The AACES field experiments: SMOS calibration and validation across the Murrumbidgee River catchment[END_REF][START_REF] Pierdicca | Analysis of two years of ASCAT-and SMOS-derived soil moisture estimates over Europe and North Africa[END_REF][START_REF] Sanchez | Validation of the SMOS L2 Soil Moisture Data in the REMEDHUS Network (Spain)[END_REF][START_REF] Wigneron | First evaluation of the simultaneous SMOS and ELBARA-II observations in the Mediterranean region[END_REF]. Nevertheless, there is no evaluation was done to evaluate the newly re-processed SMOSL3 SSM products, due to their recentness, with the exception of [START_REF] Strangeways | Inter-comparison of microwave satellite soil moisture retrievals over[END_REF] who evaluated SMOSL3 with AMSR-E and ASCAT against in-situ observations from the Murrumbidgee Soil Moisture Monitoring Network for the 2010-09/2011 period.

At the local scale, for instance, [START_REF] Lacava | A First Assessment of the SMOS Soil Moisture Product With In Situ and Modeled Data in Italy and Luxembourg[END_REF] have assessed SMOSL2 SSM products through a comparison with modelled SSM and in situ observations from three sites situated in Luxemburg and Italy. Collow et al. (2012) and [START_REF] Jackson | Validation of Soil Moisture and Ocean Salinity (SMOS) Soil Moisture Over Watershed Networks in the U.S. Geoscience and Remote Sensing[END_REF] have performed an evaluation of the SMOSL2 SSM products over the central USA and four watersheds located in the USA, respectively. Leroux et al. (2013b) compared the SMOSL2 SSM products with AMSR-E, ASCAT, and the European Centre for Medium range Weather Forecasting (ECMWF) SSM products, for the year 2010, against in situ observations over four watersheds located in the USA. [START_REF] Sanchez | Validation of the SMOS L2 Soil Moisture Data in the REMEDHUS Network (Spain)[END_REF] and [START_REF] Wigneron | First evaluation of the simultaneous SMOS and ELBARA-II observations in the Mediterranean region[END_REF] have evaluated the SMOSL2 SSM products with SSM observations obtained from the REMEDHUS Network and the VAS (Valencia Anchor Station) site, respectively, located in Spain. [START_REF] Dente | Validation of SMOS Soil Moisture Products over the Maqu and Twente Regions[END_REF] have validated SMOSL2 SSM products over the Maqu region on the Tibetan Plateau in China and the Twente region in The Netherlands. [START_REF] Peischl | The AACES field experiments: SMOS calibration and validation across the Murrumbidgee River catchment[END_REF] have evaluated SMOSL2 SSM products with SSM observations obtained from the Australian Airborne Experiments for SMOS (AACES) located in South-East Australia. More recently, [START_REF] Kaihotsu | First evaluation of SMOS L2 soil moisture products using in situ observation data of MAVEX on the Mongolian Plateau in 2010 and 2011[END_REF] have evaluated SMOSL2 SSM products using in situ observations on the Mongolian Plateau for the 2010-2011 period. Most of these studies came to almost the same conclusion that SMOS had a Root Mean Square Error (RMSE) close to the accuracy requirement of SMOS i.e. 0.04 m 3 /m 3 , the SSM dynamics were well captured by SMOS, and the SMOS was a bit dryer than the other datasets. At the regional and continental scales, for instance, [START_REF] Albergel | Evaluation of remotely sensed and modelled soil moisture products using global ground-based in situ observations[END_REF] have evaluated the SMOSL2 SSM products, together with ASCAT and SM-DAS-2 SSM products (produced at ECMWF ) against in situ observations from several stations located in Australia, Africa, the USA, and Europe during 2010. [START_REF] Albergel | Evaluation of remotely sensed and modelled soil moisture products using global ground-based in situ observations[END_REF] concluded that ASCAT and SMOS had a an average correlation of 0.55 with in-situ datasets. [START_REF] Parrens | Comparing soil moisture retrievals from SMOS and ASCAT over France[END_REF] have compared SMOSL2 SSM products with land surface model simulations (ISBA LSM) over the whole of France. Al Bitar et al. (2012) have evaluated SMOSL2 SSM products using in situ observations obtained from the Soil Climate Analysis Network (SCAN) and the Snowpack Telemetry (SNOTEL) sites located in North America. More recently, [START_REF] Pierdicca | Analysis of two years of ASCAT-and SMOS-derived soil moisture estimates over Europe and North Africa[END_REF] have compared SMOSL2 SSM products with only ASCAT SSM products over Europe and extreme North Africa during the 2010 -03/2012 period. [START_REF] Pierdicca | Analysis of two years of ASCAT-and SMOS-derived soil moisture estimates over Europe and North Africa[END_REF] have demonstrated that the two products correlated fairly to each other and their consistency depends on season and surface land cover.

At the global scale, there is only, to date, one dedicated SSM study that has been conducted to evaluate the SMOSL2 SSM products. Leroux et al. (2013a) performed, at the global scale, a comparison between the SMOSL2 SSM products against AMSR-E and ASCAT SSM products taking ECMWF model simulations as a benchmark for the year 2010.

This study showed that SMOS was better in terms of RMSE values than ASCAT and AMSR-E datasets over Australia, North America, and Central Asia.

Four issues can be identified in the review of the existing evaluations of SMOS SSM products, summarized in the previous paragraphs:

(i)
The evaluations and comparisons were generally made with observations from in situ networks, which are limited in space and time. In the natural environment, there is a large spatio-temporal variability of SM, which depends on the combined influence of hydrometeorology, soil hydraulic properties, climate, and vegetation. In situ observations have a low spatial density so that point-based observations cannot represent accurately the spatial distribution of SSM [START_REF] Dorigo | The International Soil Moisture Network: a data hosting facility for global in situ soil moisture measurements[END_REF], therefore inadequate to carry out a global evaluation and draw global conclusions. In contrast, land-surface models are able to simulate global SSM products [START_REF] Dirmeyer | GSWP 2: Multimodel analysis and implications for our perception of the land surface[END_REF][START_REF] Georgakakos | Potential value of operationally available and spatially distributed ensemble soil water estimates for agriculture[END_REF] and their spatial resolutions are often in agreement with the resolution of the remotely sensed products. For instance, several global SSM datasets produced from modelling or assimilation approaches are becoming readily available (e.g., SM-DAS-2, MERRA-Land which is a NASA atmospheric reanalysis) in 2013. However, little is known about the reliability of those products at the global scale and how they compare to the remote sensing datasets (Draper et al., 2009b;[START_REF] Reichle | Comparison and assimilation of global soil moisture retrievals from the Advanced Microwave Scanning Radiometer for the Earth Observing System (AMSR-E) and the Scanning Multichannel Microwave Radiometer (SMMR)[END_REF][START_REF] Sabater | From Near-Surface to Root-Zone Soil Moisture Using Different Assimilation Techniques[END_REF]. Hence, more research is required to advance our understanding of the capabilities of SSM products from remote sensing and from models to assess the uncertainties associated with them.

(ii)

The evaluations and comparisons were only based on the SMOSL2 SSM retrievals. However, as already mentioned, new recently re-processed 1-day global SSM product i.e. SMOSL3 provided by the CATDS with enhancement of better SSM estimations at revisited locations and increasing of SMOS retrieval coverage [START_REF] Jacquette | SMOS CATDS level 3 global products over land[END_REF] has been released.

(iii) Most of the aforementioned studies addressed the evaluation only in the year 2010, evaluation should include longer period so that the temporal span can be more reasonable to draw any conclusive statistics.

(iv) None of the aforementioned studies compared the capabilities of remote sensing at C-band and L-band to monitor SSM at the global scale.

The motivation for this doctoral research work relies on the fact, discussed above, that there has been limited evaluation of the state of the art SMOS SSM product, using SSM products retrieved from other active or passive microwave sensors or simulated from land surface models. It is crucial to evaluate their accuracy at the global scale and for a range of climate and environmental conditions across the world before developing operational applications based on the SMOS observations, thereby improving the knowledge of errors in the satellite data across space and time. In addition, the inter-comparisons of SMOS SSM products with other satellite and model SSM products at the global scale help in understanding the similarities and differences between the various products and in learning the regions where they agree or differ. Moreover, a successful evaluation of the SMOS SSM datasets at the global scale would be a significant contribution to improving the prediction capability of hydrologic models, thus, leading to improvement in SM estimation through data assimilation [START_REF] Reichle | An adaptive ensemble Kalman filter for soil moisture data assimilation[END_REF].

Furthermore, SSM sensors do not deliver decadal homogeneous products. SMOS SSM products, for instance, are only available since 2010; whereas AMSR-E SSM products are only available from 2002 to 2011. Nevertheless, for several applications such as climate change trend analysis, flood analysis, and drought monitoring, a historical record is required.

The latest CCI program SSM product did not consider SMOS in its first phase programme, due to its recentness. However, SMOS presents an innovative interferometric antenna concept, dedicated for SSM monitoring, which is a promising technology for SSM retrievals.

Therefore, SMOS should be considered to be merged with the other existing microwave remotely sensed products to produce long-term SSM time series.

Dissertation objectives

The main science objectives in the context of the global evaluation of SMOS SSM products have been already raised in the motivation of this doctoral dissertation. Very little research has been done to evaluate the performance of the newly reprocessed SMOSL3 SSM retrievals at the global and regional scales. The overall goal of this doctoral dissertation is to complement the existing assessment and evaluations of the global SMOSL3 SSM estimates by carrying out a comprehensive evaluation using longer time series (2010)(2011)(2012) that also include modelling products. This study is expected to contribute to the evaluation/validation activities of SMOS SSM products via SM-DAS-2 and MERRA-Land SSM products. In connection to the above introduction, the following research objectives have been addressed in this doctoral dissertation: These objectives are accomplished as separate studies resulting in journal articles. A brief description of each paper follows in the next Section.

Dissertation outline

This doctoral dissertation consists of seven chapters, which are organized as follows:

Chapter I has just given brief background and the motivation, objectives, and scope of this research work.

Chapter II gives the theoretical background regarding SM. It covers aspects such as:

SM definition, its importance, different types of measurements (including in situ, remote sensing, models, and assimilation techniques).

Chapter III gives an overview on the SMOS mission and its products. It describes shortly the basics of the SSM retrieval algorithm and the main types of existing SMOS products. This chapter includes also a brief overview of the AMSR-E and ASCAT missions and their SSM products.

Chapter IV performs a comparative analysis of the SMOSL3 SSM products along with another SSM product derived from the observations of the AMSR-E at C-band (this latter product is referred to as AMSRM). The AMSRM product is to date the reference SSM product produced from passive microwave remotely-sensed sensors [START_REF] Owe | Multisensor historical climatology of satellitederived global land surface moisture[END_REF]. SM-DAS-2, a SSM product produced by ECMWF Land Data Assimilation System was used as an independent reference to monitor the quality of both SMOSL3 and AMSRM SSM products.

The present study was carried out from 03/2010 to 09/2011, a period during which both SMOS and AMSR-E products were available at the global scale. Three statistical metrics (considering both original SSM data and anomalies) used for the evaluation were the correlation coefficient (R), the Root Mean Squared Difference (RMSD), and the bias. In this chapter, the impact of the biome types and vegetation density on the performance of the SMOS and AMSR-E retrievals was analyzed at the global scale.

In Chapter V, the performance of the SMOSL3 dataset is further evaluated against SSM retrievals made by an active C-band system. This chapter performs a global-scale having its own introduction to conclusion, but they are all connected under the umbrella of SMOS SSM data evaluation. Some overlap exists between the Chapters IV-VI, this was unavoidable since each chapter is a self-explanatory based manuscript that has been or will be published in scientific journals.

Finally, Chapter VII concludes this dissertation and summarizes the results obtained from all the chapters. Limitations encountered in this research are discussed and some directions/recommendations for the future research are provided.

Chapter II

2. Soil moisture and its importance/measurements

2.1

Soil moisture and its importance

Soil moisture

The soil medium is often divided into three phases consisting of liquid, gaseous, and solid phases. Soil matter, the sum of the mineral matter and the organic matter, represents the solid phase amounting about to 50 % of the entire soil medium [START_REF] Hillel | Aggregate stability[END_REF]. Pore space represents the other 50 %, which consists of the liquid phase (i.e., the soil water) and the gaseous phase (i.e., the soil atmosphere) [START_REF] Hillel | Aggregate stability[END_REF]. The components of the soil medium are displayed in Fig. 2.1. Pore spaces between soil particles can be filled by air or water, the latter is often referred to as soil moisture and is also known as soil water content. In other words, the quantity of water that is present in the unsaturated zone, held in the soil between the surface and the groundwater level, is known as soil moisture. The soil water moves freely down by gravity and up by capillary force. It is then extracted by plant roots, evaporates at the surface, or recharges the groundwater [START_REF] Strangeways | Inter-comparison of microwave satellite soil moisture retrievals over[END_REF]. It is a small fraction of the world's fresh water supply [START_REF] Dingman | Physical Hydrology[END_REF], and it is generally expressed in gravimetric units (g/cm 3 ), volumetric units (m 3 /m 3 ; m 3 water per m 3 bulk soil volume) or percent (% vol.) [START_REF] Dingman | Physical Hydrology[END_REF][START_REF] Smith | Soil and Environmental Analysis -Physical Methods -Second Edition:Revised and Expanded[END_REF].

Soil is saturated when the pore spaces between the soil particles are totally filled by water without any air pockets (See Fig. 2.1). This water, within a day or longer, drains-with the exception if the water table is within the soil which occurs quite often-downwards and away under gravity and leaves the soil at the so called "field capacity" with certain quantity of water that holds against gravity [START_REF] Twarakavi | An objective analysis of the dynamic nature of field capacity[END_REF][START_REF] Veihmeyer | The moisture equivalent as a measure of the field capacity of soils[END_REF].

At this point, the spaces between the soil particles are filled with a mixture of water and air pockets (see Fig. 2.1). When the plants can no longer extract the necessary water for growth and therefore suffer and they start to wilt before dying, the soil is described as at "wilting point" (see also Fig. 2.1) [START_REF] Briggs | The Wilting Coefficient and Its Indirect Determination[END_REF].

Fig. 2 -1 Components of soil medium (After O'Geen, 2012).

The capacity of the soil to store water depends on the size, type, shape, the properties of the solid phase (in particular its electrical charges), and the continuity of the pores of the soil. Temporal variations and spatial distribution of soil moisture can be influenced by precipitation, soil texture, topography, organic matter content, porosity, soil structure, and vegetation and land cover. Soil texture (i.e. percentage of clay, sand, and silt) and soil structure control the water-holding capacity while topography (i.e. variations in slope and aspect) affects soil moisture distribution i.e. soil moisture movements. Table 2.1 presents the influence of the relief elements (aspect & slope) on the spatial distribution of soil moisture.

The soil moisture values represent the ratio of soil moisture on a slope and soil moisture on a flat surface with the same type of soil and vegetation for four aspects (North, South, East and West) and for four slope parts(upper, middle, lower and the foot of a slope) for summer period of the year [START_REF] Svetlitchnyi | Spatial distribution of soil moisture content within catchments and its modelling on the basis of topographic data[END_REF]. Soil, for instance, is dryer at flat surface than at foot of slop, and the slopes face west and south are dryer than the slopes which face east and north, this may be explained by the relatively high radiation exposure of the sun [START_REF] Svetlitchnyi | Spatial distribution of soil moisture content within catchments and its modelling on the basis of topographic data[END_REF]. The effects of north and south may be not equal in the Northern and Southern Hemisphere.

Vegetation (i.e. vegetation type and density) influences infiltration, runoff, and evapotranspiration, thus, influences the variations of soil moisture at different space and timescales [START_REF] English | The influence of soil texture and vegetation on soil moisture under rainout shelters in a semi-desert grassland[END_REF]. In addition, climate (i.e. precipitation, solar radiation, wind, and humidity) controls the dynamics of soil moisture. Precipitation is the most important climatic forcing for soil moisture content and its distribution, which induces along with evaporation the trends in aridity and saturation of soil [START_REF] D'odorico | Preferential states in soil moisture and climate dynamics[END_REF][START_REF] Koster | Observational evidence that soil moisture variations affect precipitation[END_REF].

General importance of soil moisture for the environment and our climate system

Water is a vital source of all life on Earth's climate system. It circulates continuously between oceans, the atmosphere, and land surface due to the solar energy. This circulation and conservation of the Earth's water, known as the water cycle (see Fig. 2.2), is a critical component for our climate system. Although the soil moisture only represents a small proportion (0.05 %) of the total of fresh water volume, as can be seen in Fig. 2.3 compared to the other components, its influence on the global water cycle is of great importance and it plays a major role in the water cycle.

Soil moisture is a key variable in the exchanges of water, energy, carbon between the land surface interface and the atmosphere. It is also an important factor in many fields: in atmospheric circulation [START_REF] Walker | Requirements of a global near-surface soil moisture satellite mission: accuracy, repeat time, and spatial resolution[END_REF], as soil moisture influences energy and mass transfer across the landscape boundary [START_REF] Arora | The Temporal Variability of Soil Moisture and Surface Hydrological Quantities in a Climate Model[END_REF][START_REF] Findell | Atmospheric Controls on Soil Moisture-Boundary Layer Interactions. Part I: Framework Development[END_REF], in water resources management, for instance in flood analyses and drought monitoring [START_REF] Michele | On the derived flood frequency distribution: analytical formulation and the influence of antecedent soil moisture condition[END_REF], in agricultural management, by defining appropriate irrigation amounts and intervals [START_REF] Hanson | Monitoring Soil Moisture Helps Refine Irrigation Management[END_REF], in soil science, it is a key parameter in ecology and biogeochemistry to determine potential land slide and can help in soil erosion's predictions in semi-arid areas [START_REF] Kiome | Soil and water conservation for improved soil moisture and crop production: an empirical and modelling study in semi arid Kenya[END_REF], and in plant biology, soil moisture is the key factor for plant water stress [START_REF] Veihmeyer | Soil Moisture in Relation to Plant Growth[END_REF].

More specifically, soil moisture can be of significant importance resource for plants as well as for human activities:

a)

The soil moisture of the root zone is a limiting factor for plant growth, and it is optimal when not too dry and not too wet over a long time period for plants to survive.

Therefore, information of the appropriate amount of soil water is essential for cultivation of plants and agriculture in general. This helps in irrigating crop fields more efficiently.

Furthermore, information of soil moisture patterns helps agronomist to enhance irrigation's scheduling and better crop yield predicting in arid and semi-arid areas [START_REF] Tao | Changes in agricultural water demands and soil moisture in China over the last half-century and their effects on agricultural production[END_REF].

b)

The soil moisture is a variable of major importance to assess the potential for risks in the case of extreme events. Soil moisture conditions (excessively saturated or dry) can be signs of warning of subsequent flooding (as the occurrence and intensity of flooding are strongly influenced by the soil's ability to take up a certain amount of water) or drought [START_REF] Dingman | Physical Hydrology[END_REF][START_REF] Richter | Modelling impacts of climate change on wheat yields in England and Wales: assessing drought risks[END_REF]. c) Soil moisture plays an important role in the hydrological models, as it controls the re-distribution of the precipitation into runoff and infiltration. Therefore, accurate observations of soil moisture are essential before estimating water fluxes [START_REF] Parajka | Assimilating scatterometer soil moisture data into conceptual hydrologic models at the regional scale[END_REF].

d)

Soil moisture plays an important role in meteorological and climate models, as its temporal variation and spatial distribution play a major role in the partitioning of the solar energy into sensible and latent heat fluxes at both global and local scales [START_REF] Robock | Evaluation of the AMIP soil moisture simulations[END_REF]. Soil moisture availability plays a significant role in the biases of surface temperature in climate models (Cheruy et al., submitted for publication). Accurate estimates of soil moisture are necessary for improving numerical weather predictions, whereas inaccurate soil moisture initialization leads to large errors in climate predictions [START_REF] Robock | Evaluation of the AMIP soil moisture simulations[END_REF][START_REF] Rowntree | Simulation of the atmospheric response to soil moisture anomalies over Europe[END_REF]).

e) Soil moisture spatio-temporal variations over land influence runoff, inflow, controls evaporation and transpiration, thus regulates the extent of groundwater recharges [START_REF] Mohanty | Spatio-temporal evolution and time-stable characteristics of soil moisture within remote sensing footprints with varying soil, slope, and vegetation[END_REF]. More generally, soil moisture influences the discharge which is the most accessible fresh water resource.

Measurements of soil moisture

There are different methods for soil moisture measurements employed for different applications. These include measurements techniques: (i) direct and indirect in-situ measurements (e.g. radiological methods, neutron attenuation, gamma absorption, soil-water dielectrics, microwave probe, etc.) and (ii) emerging technologies (remote sensing), and estimation techniques: (i) land surface models and (ii) integration of the previous methods in the so called assimilation. All these methods differ significantly by the accuracy, complexity, technique, and spatio-temporal scales. These methods are briefly presented in the following sections.

In-situ measurements

In-situ measurements methods have several common advantages including, but not limited to, relatively accurate for the sampling point and measurements of soil moisture could be taken at several depths. On the other hand, there are common disadvantages including, but not limited to, local scale and thus cannot be representative for larger scales, time consuming, and costly. Nevertheless, models and remote sensing up to date use in-situ measurements to calibrate and validate their predictions and observations, respectively.

Thermogravimetric method [START_REF] Marshall | Soil Physics[END_REF] is the most common classical method to measure volumetric water content. The equation used to compute the water content (∅ 𝑚𝑚 ) on a mass basis can be written as follows:

∅ 𝑚𝑚 = 𝑚𝑚 𝑤𝑤 𝑚𝑚 𝑠𝑠 2 -1
where:

𝑚𝑚 𝑤𝑤 is mass of water lost upon a sample 24 hour drying in an oven at 105 °C and 𝑚𝑚 𝑠𝑠 is a constant mass of the sample before drying.

Whereas the equation used to compute the water content on a volumetric basis (∅ 𝑣𝑣 ), most commonly used, can be written as follows [START_REF] Smith | Soil and Environmental Analysis -Physical Methods -Second Edition:Revised and Expanded[END_REF]:

∅ 𝑣𝑣 = ∅ 𝑚𝑚 𝜌𝜌 𝑏𝑏 𝜌𝜌 𝑤𝑤 2 -2
where:

𝜌𝜌 𝑏𝑏 is the dry bulk density of the soil (kg/m 3 ) and 𝜌𝜌 𝑤𝑤 is the density of the water (1000 kg/m 3 ).

If the volume of soil is known (sampled by coring), volumetric water content (∅ 𝑣𝑣 ) can be computed as follows [START_REF] Smith | Soil and Environmental Analysis -Physical Methods -Second Edition:Revised and Expanded[END_REF]:

∅ 𝑣𝑣 = 𝑚𝑚𝑚𝑚𝑠𝑠𝑠𝑠 𝑜𝑜𝑜𝑜 𝑤𝑤𝑤𝑤𝑤𝑤 𝑠𝑠𝑜𝑜𝑠𝑠𝑠𝑠-𝑚𝑚𝑚𝑚𝑠𝑠𝑠𝑠 𝑜𝑜𝑜𝑜 𝑑𝑑𝑑𝑑𝑑𝑑 𝑠𝑠𝑜𝑜𝑠𝑠𝑠𝑠 𝑠𝑠𝑜𝑜𝑠𝑠𝑠𝑠 𝑣𝑣𝑜𝑜𝑠𝑠𝑣𝑣𝑚𝑚𝑤𝑤 * 𝑤𝑤ℎ𝑤𝑤 𝑑𝑑𝑤𝑤𝑑𝑑𝑠𝑠𝑠𝑠𝑤𝑤𝑑𝑑 𝑜𝑜𝑜𝑜 𝑤𝑤ℎ𝑤𝑤 𝑤𝑤𝑚𝑚𝑤𝑤𝑤𝑤𝑑𝑑

-3

This method has several advantages being simple, reliable, inexpensive (but not for regional or global scales), and can be easily calculated. This method is, however, not free error as some clay soils still contain water after oven drying which leads to an underestimation of water content. Similarly, some organic soils loose some weight due to organic matter changes during heating, which leads to an overestimation of water content [START_REF] Smith | Soil and Environmental Analysis -Physical Methods -Second Edition:Revised and Expanded[END_REF].

Other indirect methods have been developed to overcome the limitations of thermogravimetric method with more advantages such as repetitiveity, quickness, and less disruption [START_REF] Schmugge | Survey of methods for soil moisture determination[END_REF]. The basic principle of these methods is that certain characteristics of the soil are functions of the soil moisture, thus monitoring these properties leads to soil moisture measurements [START_REF] Strangeways | Inter-comparison of microwave satellite soil moisture retrievals over[END_REF]. Some of these methods are briefly summarized in Table 2.2. [START_REF] Schmugge | Survey of methods for soil moisture determination[END_REF][START_REF] Smith | Soil and Environmental Analysis -Physical Methods -Second Edition:Revised and Expanded[END_REF]Walker et al., 2004;Zazueta & Xin, 1994)

Technique

Measurement of SM Strengths Weaknesses Thermogravimetric

This method involves taking a volume of soil, accurately weighing it, completely drying it out in an oven, re-weighing the dry sample, and calculating soil moisture percentage from the weight loss.

Accurate measurements -simple procedure to compute soil moisture-not costly -and not dependent on salinity and soil type. Time consuming and pain staking proceduredifficult and destructive sampling -inapplicable to repetitive measurements and to automatic controlmust know dry bulk density to transform data to volume moisture content-costly for regional and global scales.

Nuclear techniques (Neutron scattering)

Based on the relationship between the emitted neutrons with the hydrogen nuclei in the soil water.

Average soil moisture with depth can be obtained -reliable -automatic readings -nondestructive -water can be measured in any phase.

Poor depth resolution -costly -radiological safety procedures (radiation hazard) required -special measures necessary to deal with readings in surface soil -care required in access tube installation -must calibrate for different types of soils -access tubes must be installed and removed -measurement partially dependent on physical and chemical soil properties -depth probe cannot measure soil water near soil surface.

Soil dielectric method (1)Time Domain Reflectrometry (TDR)

This method involves measuring the dielectric constant which is a function of soil moisture.

Can be installed easily and at any depthapplicable for automatic monitoring -possible to perform long-term in situ measurementsportable -independent of soil texture, temperature, and salt content.

Small zone of influence of TDR probes -the electronics to control and interpret the measurements are rather costly -high cost of equipment -only sensitive to the moisture around the probe -attenuation of the signal caused by salinity or highly conductive heavy clay soils.

Soil dielectric method (2) Capacitance probes

This method involves measuring the dielectric constant which is a function of soil moisture (Probes are inserted into the soil to the required measurement depth and the measurement can either be displayed on a meter or can be recorded using a Rapid and easy measurements -very sensitive to small changes in soil moisture -readings are instantaneous -precise resolution -theoretically, can provide absolute soil water content -water content can be determined at any depth.

Small zone of influence for capacitance probeshigh sensitivity to air gaps and regions surrounding the probes -long-term stability questionable.

Technique

Measurement of SM

Strengths Weaknesses data logger).

Thermal conductivity

This method involves measuring the rate of heat dissipation which decreases with decreased water content.

-This is only possible in soils with extreme salinity.

Gamma ray attenuation

Based on the scattering and absorption of the radiation which is related to the density of the matter.

Not destructive -very good depth resolution with attenuation method but poor with backscatter techniques -can determine mean water content with depth -can be automated for automatic measurements and recording -can measure temporal changes in soil water.

Costly -difficulty of use -radiological safety procedures necessary -Gamma ray scanners of the gamma ray method are only used in laboratory situations -restricted to soil thickness of 2.54 cm or less -affected by soil bulk density changes.

Electrical

Conductivity Probes and resistance Blocks

Generally, soil conductivity decreases with decreasing soil moisture.

Resistance or gypsum block sensors measure soil conductivity.

Not costly and simple to use and install. Conductivity of the soil water is different in different soil types (alkaline or acid soils) and can change according to the sprays or fertilizers applied -resistance block sensors are generally used for trends in soil moisture changes onlysometimes requires calibration.

Tensiometer (Soil Suction technique)

This method involves measuring the water availability to plants and on the measurement of the capillary tension.

Easy to design, install, and maintain -low-costreadings are in units of negative pressure (suction) expressed as kilo Pascals -it is preferred for agriculture and irrigation of cropsprovide additional information (water table elevation -the direction of fluxes in soil profileand soil moisture tension) -operates for long periods if properly maintained, can be adapted to automatic measurement with pressure transducers -can be operated in frozen soil with ethylene glycol.

Indirect measurements -very weak instrumentonly measures soil water suctionpredetermination of soil water characteristics essential -inaccuracies due to hysteresis of water content/potential relationship -limit range of 0 to -0.8 bar not adequate for sandy soil -difficult to translate data to volume water content -automated systems costly and not electronically stable.

Hygrometric techniques

Based on the relationship between moisture content in porous materials and the relative humidity.

Low-cost -low maintenance -wide soil matric potential range -well suited for automated measurements and control of irrigation systems.

Declination of the sensing element through interactions with the soil components and a special calibration is required for the tested material.

It is noticed from Table 2.2 that whatever the method used to measure the soil moisture, the common issue is the high cost and effort of setting up the network stations and they are only point measurements. Several researchers attempted to gather all available in situ soil moisture measurements in one database such as the Global Soil Moisture Data Bank developed by [START_REF] Robock | The Global Soil Moisture Data Bank[END_REF] which was transferred and extended recently to the International Soil Moisture Network (ISMN; [START_REF] Dorigo | The International Soil Moisture Network: a data hosting facility for global in situ soil moisture measurements[END_REF] which is available at https://ismn.geo.tuwien.ac.at/. Fig. 2.4 shows the geographical distribution of the available in situ networks at ISMN. It can be seen that most of the network stations are located in the Northern Hemisphere. Consequently, they are not sufficient to study soil moisture at the global scale.

Remote sensing of soil moisture

Remote sensing techniques are being widely used to monitor most kinds of environmental issues, from local to original and global scales. Information about the land and water surfaces on Earth can be derived using images of the electromagnetic radiations acquired from space, reflected or emitted from the Earth's surface [START_REF] Campbell | Introduction to Remote Sensing[END_REF].

Information over large areas can be obtained rapidly and repetitively thanks to remote sensing techniques for making it possible to distribute information through sensors mounted on satellites, which operate in several spectral regions (from the optical to microwave regions) [START_REF] Jeyaseelan | Droughts & floods assessment and monitoring using Remote Sensing and GIS[END_REF]. A satellite, launched into special orbit, mostly takes a few days to explore the whole surface of the Earth and repeats its path at regular intervals [START_REF] Jeyaseelan | Droughts & floods assessment and monitoring using Remote Sensing and GIS[END_REF].

Most of the electromagnetic spectrum (e.g., optical, infrared and microwave, Fig. 2.5) has been used in recent years with different sensors which can provide unique information about properties of the surface of the Earth or subsurface soil layers (e.g., albedo, surface temperature, soil moisture, etc.).

Remote sensing is the most appropriate technique to provide global maps of soil moisture, and recently, has been providing soil moisture using various techniques [START_REF] Sandholt | A simple interpretation of the surface temperature/vegetation index space for assessment of surface moisture status[END_REF]. In general, soil moisture can be estimated from remote sensing data especially from: (i) visible/near-infrared remote sensing, (ii) thermal infrared remote sensing, and (iii) microwave remote sensing which includes both passive microwave remote sensing and active microwave RS. Table 2.3 summarizes the characteristics and advantages as well as the limitations of each category. For more information on the principles of estimating nearsurface soil moisture from remote sensing data, advantages and limitations, the reader is directed to [START_REF] Nichols | Review and evaluation of remote sensing methods for soil-moisture estimation[END_REF][START_REF] Wang | Satellite remote sensing applications for surface soil moisture monitoring: A review[END_REF][START_REF] Wang | A review: theories, methods and development of soil moisture monitoring by remote sensing[END_REF].

Fig. 2 -5

Electromagnetic spectrums (including the entire range of radiations, which are measured either as waves or frequencies) (From [START_REF] Bartalis | GMSM Kick-Off Meeting Conference[END_REF].

Optical remote sensing (Visible and near-infrared)

The visible/near-infrared remote sensing is mainly used to study land cover and vegetation at the present. Nevertheless, measurements of surface reflectance of radiation of the sun in the visible and near-infrared (from 350 nm to 800 nm) regions (Fig. 2.5) have been also used to retrieve surface soil moisture [START_REF] Gillies | A verification of the 'triangle' method for obtaining surface soil water content and energy fluxes from remote measurements of the Normalized Difference Vegetation Index (NDVI) and surface e[END_REF][START_REF] Kaleita | Relationship Between Soil Moisture Content and Soil Surface Reflectance[END_REF][START_REF] Whiting | Predicting water content using Gaussian model on soil spectra[END_REF]. The basic principle is that it was found that the reflectance at visible and infrared wavelengths increased as the moisture content decreased (wet soils are darker in color on the image than dry soils and reflectance values are generally low for wet surfaces and high for dry surfaces) [START_REF] Kaleita | Relationship Between Soil Moisture Content and Soil Surface Reflectance[END_REF][START_REF] Planet | Some comments on reflectance measurements of wet soils[END_REF][START_REF] Weidong | Relating soil surface moisture to reflectance[END_REF]. Nevertheless, retrieving soil moisture from these data has some limitations and difficulties, as the reflectance of a soil is not just a function of soil moisture but is strongly influenced by other soil factors (e.g., amount of organic matter, surface roughness, angle of incidence, color of soil elements, texture, and mineral composition) (Gascoin et al., 2009a;[START_REF] Gascoin | Sensitivity of bare soil albedo to surface soil moisture on the moraine of the Zongo glacier (Bolivia)[END_REF][START_REF] Muller | Modelling soil moisture-reflectance[END_REF]. In addition optical sensors can only be used to monitor soil moisture over bare soil, due to the low penetration depth of the signal through clouds. There are two independent problems: (i) clouds and (ii) bare soil only as vegetation reflects light before the soil does.

Thermal Infrared remote sensing

Thermal infrared remote sensing, operating in a wavelength region of approximately 3 to 14 μm (Fig. 2.5), measures the soil surface temperature which could be used to infer nearsurface soil moisture content [START_REF] Curran | Principles of Remote Sensing[END_REF][START_REF] Hain | Retrieval of an Available Water-Based Soil Moisture Proxy from Thermal Infrared Remote Sensing. Part I: Methodology and Validation[END_REF][START_REF] Rahimzadeh-Bajgiran | Estimation of soil moisture using optical/thermal infrared remote sensing in the Canadian Prairies[END_REF]. Several researchers found that land surface temperature, in the thermal infrared, is strongly dependent on the soil moisture as areas having higher soil moisture content are cooler during the day and warmer at night [START_REF] Hain | Retrieval of an Available Water-Based Soil Moisture Proxy from Thermal Infrared Remote Sensing. Part I: Methodology and Validation[END_REF][START_REF] Van De Griend | Partial area hydrology and remote sensing[END_REF], because cooler areas are the ones that evaporated more, and evaporation is water limited. Earlier studies have shown that the amplitude of the diurnal range of soil surface temperature has been found to have a good correlation with the near-surface soil moisture [START_REF] Schmugge | Survey of methods for soil moisture determination[END_REF]. Limitations to this type of measurement are due to effects of cloud cover, soil types, and vegetation and meteorological factors [START_REF] Wetzel | Soil moisture estimation using GOESVISSR infrared data: a case study with a simple statistical method[END_REF].

Microwave remote sensing

Microwave remote sensing systems use electromagnetic radiation in the frequency range of about 0.3 to 30 GHz, with wavelengths of about 1mm to 1m (Fig. 2.5). Satellites operating in the microwave domain have unique capabilities, over the higher frequencies, such as atmosphere transparency, cloud penetration, day and night capability (independency of solar illumination), vegetation semi-transparency, strong dependency on the dielectric properties of the soil (which is a function of the soil moisture), and soil penetration (to a certain extent) [START_REF] Schmugge | Remote sensing in hydrology[END_REF][START_REF] Ulaby | Microwave remote sensing fundamentals and radiometry[END_REF]. The microwave remote sensing is categorized into active and passive systems (see Fig. 2.6). Active sensors emit electromagnetic pulses and measure the radiation back-scattered from the surface, whereas passive systems (radiometers) record the natural radiation of the earth's surface. Fig. 2.6 illustrates the differences between passive and active microwave remote sensing.

Although active and passive systems have different recording techniques, there is a close connection using Kirchhoff's law of thermal radiation, which states that the emissivity of a body is equal to its absorptivity under thermodynamic equilibrium [START_REF] Schanda | Physical fundamentals of remote sensing[END_REF]. Passive microwave sensors do not directly measure the soil moisture but brightness temperatures (TB), which allows for retrieving bio-geophysical variables including the soil moisture. TB for a non-black body can be computed using the inverse of Planck function:

𝑇𝑇𝑇𝑇 = 𝐷𝐷 2 𝜆𝜆 𝑙𝑙𝑙𝑙 [1 + 𝐷𝐷 1 𝜆𝜆 5 𝐼𝐼 𝜆𝜆 ] 2 -4
where:

D 1 = 1.1911x10 8 [W m -2 sr -1 µm 5 ], D 2 = 1.4388x104 [K µm],
I λ is the measured intensity (radiance) [W m -2 sr -1 ], and λ is the s the wavelength [µm].

It should be noted that TB, in the infrared domain, is equal to kinetic temperature for a black body but for a natural material:

𝑇𝑇𝑇𝑇 4 = 𝑒𝑒 𝑝𝑝 𝑇𝑇 4 2 -5
where the emissivity (e p ) is a dimensionless value (0 < e <1) and a function of a number of factors.

Planck function in the microwave domain can be further simplified using the Rayleigh -Jeans approximation, which gives:

𝑇𝑇𝑇𝑇 = 𝑒𝑒 𝑝𝑝 𝑇𝑇 2 -6
The emissivity of a soil varies greatly according to its water content, which can be described as [START_REF] Njoku | Retrieval of land surface parameters using passive microwave measurements at 6-18 GHz[END_REF]:

𝑒𝑒 𝑝𝑝 = 1 -𝑟𝑟 𝑠𝑠𝑝𝑝 2 -7
where r sp is the surface reflectivity, which can be computed for smooth soil using

Fresnel laws [START_REF] Njoku | Retrieval of land surface parameters using passive microwave measurements at 6-18 GHz[END_REF]. The Fresnel reflection coefficients r bH and r bV at horizontal (H) and vertical (V) polarizations, respectively, can be written as:

𝑟𝑟 𝑠𝑠𝑠𝑠 (θ) = � cos(𝜃𝜃) -�𝜇𝜇 𝑠𝑠 𝜀𝜀 𝑏𝑏 -𝑠𝑠𝑠𝑠𝑙𝑙 2 (𝜃𝜃) cos(𝜃𝜃) + �𝜇𝜇 𝑠𝑠 𝜀𝜀 𝑏𝑏 -𝑠𝑠𝑠𝑠𝑙𝑙 2 (𝜃𝜃) � 2 2 -8 𝑟𝑟 𝑠𝑠𝑠𝑠 (θ) = � 𝜀𝜀 𝑏𝑏 cos(𝜃𝜃) -�𝜇𝜇 𝑠𝑠 𝜀𝜀 𝑏𝑏 -𝑠𝑠𝑠𝑠𝑙𝑙 2 (𝜃𝜃) 𝜀𝜀 𝑏𝑏 cos(𝜃𝜃) + �𝜇𝜇 𝑠𝑠 𝜀𝜀 𝑏𝑏 -𝑠𝑠𝑠𝑠𝑙𝑙 2 (𝜃𝜃) � 2 2 -9
where ε b is the complex soil dielectric constant, θ is the incidence angle, and b subscript stands for bare soil.

The basic concept for retrieving surface soil moisture from passive measurements is based on the large contrast of the dielectric constant values of the soil, which is ~4 for dry soil, ~80 for water, and from ~4 to ~40 for soil-water mixtures in the microwave region [START_REF] Njoku | Passive microwave remote sensing of soil moisture[END_REF][START_REF] Schmugge | Passive Microwave Soil Moisture Research[END_REF]. The dielectric constant is an electrical property of the material which is a measure of the response of a medium to an applied electric field. It is a complex number, consisting of a real part (determines the propagation characteristics of the passed energy into the soil) and an imaginary part (determines the energy loose) [START_REF] Schmugge | Passive Microwave Soil Moisture Research[END_REF]. In an inhomogeneous medium, such as the soil, the complex dielectric constant is a combination of the individual dielectric constants of its components (air, water, and stone). Fig. 2.7 illustrates the relationship between the dielectric constant of the soil and water content, which is almost linear.

Fig. 2 -7

Relationship between The real ɛ´ and imaginary ɛ´´ components of the dielectric coefficient for different types of soils and soil moisture [START_REF] Ulaby | Microwave Remote Sensing, Active and Passive[END_REF].

The dielectric constant can be measured in the ground using Capacitance or Timedomain reflectometer (TDR) probes. However, these probes are expensive and require specific and careful calibrations [START_REF] Dobriyal | A review of the methods available for estimating soil moisture and its implications for water resource management[END_REF]. Alternatively, several dielectric models have been developed to calculate the dielectric constant such as: semi-empirical model [START_REF] Dobson | Microwave Dielectric Behavior of Wet Soil-Part II: Dielectric Mixing Models[END_REF][START_REF] Peplinski | Dielectric properties of soils in the 0.3-1.3-GHz range[END_REF], the Wang & Schmugge empirical mixing model [START_REF] Wang | An Empirical Model for the Complex Dielectric Permittivity of Soils as a Function of Water Content[END_REF], and more recently the semi-physical model [START_REF] Mironov | Temperature-and Texture-Dependent Dielectric Model for Moist Soils at 1.4 GHz[END_REF], which is formally known as the Mineralogy-Based Soil Dielectric Model (MBSDM). It should be noted that all these models depend on frequency, soil texture, and soil moisture though they differ in analytical forms. Readers are directed to [START_REF] Mironov | Physically and Mineralogically Based Spectroscopic Dielectric Model for Moist Soils[END_REF] for more details about the description of these different models.

Similarly, active sensors do not directly measure the soil moisture but the radar scattering cross section (σ), measured in m 2 , from the surface which is mainly influenced by the soil moisture. The radar scattering cross section is a function of the angle of incidence, the frequency of operation, polarization, electrical properties of soil (e.g., dielectric constant and conductivity), and the physical properties (e.g., texture, surface type, etc.). The radar scattering cross section is given by the general radar equation (e.g. [START_REF] Ulaby | Microwave remote sensing fundamentals and radiometry[END_REF]:

𝜎𝜎 = (4𝜋𝜋) 3 𝑅𝑅 4 𝑃𝑃 𝑑𝑑 𝐺𝐺 2 𝜆𝜆 2 𝑃𝑃 𝑤𝑤 2 -10
where:

P r is the received power at receiver [W],

P t is the transmitted power [W], λ is the wavelength [m],
R is the range or distance of target [m], and G is the antenna power gain [-].

There are several active (ASCAT, etc.) and passive (SMOS, AMSR-E, etc.) microwave sensors, as already mentioned in the Introduction, that have been used to observe the Earth emissions and backscatter from various targets for several decades. However, several factors affect the sensitivity of these microwave sensors to soil moisture, that should be accounted for when retrieving soil moisture from microwave observations, including [START_REF] Choudhury | Effect of surface roughness on the microwave emission from soils[END_REF][START_REF] Choudhury | Reflectivities of selected land-surface types at 19 and 37 GHz from ssm/i observations[END_REF][START_REF] Ferrazzoli | Sensitivity to microwave measurements to vegetation biomass and soil moisture content: a case study[END_REF][START_REF] Njoku | Passive microwave remote sensing of soil moisture[END_REF][START_REF] Njoku | Retrieval of land surface parameters using passive microwave measurements at 6-18 GHz[END_REF][START_REF] Schmugge | Passive Microwave Soil Moisture Research[END_REF][START_REF] Schmugge | Remote Sensing of Soil Moisture[END_REF][START_REF] Ulaby | Microwave Remote Sensing, Active and Passive[END_REF][START_REF] Wang | Multifrequency Measurements of the Effects of Soil Moisture, Soil Texture, And Surface Roughness[END_REF][START_REF] Wigneron | Microwave emission of vegetation: sensitivity to leaf characteristics[END_REF][START_REF] Wigneron | Use of passive microwave remote sensing to monitor soil moisture[END_REF]:

• Microwave sensors have different soil penetration capabilities which depend on the frequency used. The performance of microwave sensors operating at low frequencies is less affected by the atmospheric effects. The frequencies above 30 GHz, for instance, are strongly affected by water clouds, whereas the effects are negligible for frequencies below 15 GHz. Also, the effect of intense rain is more pronounced for frequencies above 10 GHz [START_REF] Ulaby | Microwave remote sensing fundamentals and radiometry[END_REF].

• The penetration depth in the surface is strongly related to the frequency/ wavelength.

Microwave sensors operating at longer wavelengths penetrate deeper in the soil surface and/or vegetation canopy. Therefore, the C (λ ~ 3.8 -7.5 cm) and L-band (λ ~ 15 -30 cm) are commonly used for sensing soil moisture but L-band is more preferred as the sampling depth is larger, ~ 3 cm [START_REF] Escorihuela | Effective soil moisture sampling depth of L-band radiometry: A case study[END_REF].

• The signal of microwave sensors is also influenced by the incidence angle; it becomes less sensitive to soil moisture when the incidence angle increases. At lower incidence angles, the attenuation of vegetation and the effect of surface roughness are minimized. Therefore, lower incidence angles are optimal for sensing soil moisture [START_REF] Ulaby | Microwave Remote Sensing, Active and Passive[END_REF].

• Active and passive microwave sensors measure the backscatter and surface's emission, respectively, using different polarizations. Active sensors can measure backscatter in HH, VV, HV, and VH polarizations, whereas passive sensors measure the emission in V or H polarizations. The vertical polarization signal is less sensitive to the soil moisture than horizontal polarization [START_REF] Njoku | Retrieval of land surface parameters using passive microwave measurements at 6-18 GHz[END_REF].

• The surface roughness, which is a measure of the irregularities of the surface geometry, has a significant effect on the variation of backscatter and TB, as it increases the surface area. Passive microwave sensors are, in most cases, less sensitive to surface roughness than active microwave sensors [START_REF] Schmugge | Remote Sensing of Soil Moisture[END_REF]. However, a recent study found that the sensitivity of the passive observations to surface roughness was relatively similar for all the frequencies i.e. 1.4, 10.65, 23.8, 36.5, and 90 GHz (Montpetit et al., 2014).

• Vegetation cover attenuates the soil emission and its influence increases as the frequency increases [START_REF] Ferrazzoli | Sensitivity to microwave measurements to vegetation biomass and soil moisture content: a case study[END_REF][START_REF] Wigneron | Microwave emission of vegetation: sensitivity to leaf characteristics[END_REF].

• Other factors such as the soil temperature [START_REF] Raju | Soil moisture and temperature profile effects on microwave emission at low frequencies[END_REF], topography [START_REF] Mialon | Flagging the Topographic Impact on the SMOS Signal[END_REF], soil texture [START_REF] Mironov | Temperature-and Texture-Dependent Dielectric Model for Moist Soils at 1.4 GHz[END_REF], have a small influence on the microwave observations but should be taken into consideration [START_REF] Njoku | Passive microwave remote sensing of soil moisture[END_REF].

It can be summarized that the negative effects of these factors, generally, increase with increasing frequency [START_REF] Njoku | Passive microwave remote sensing of soil moisture[END_REF] within the microwave domain. Besides, atmosphere and ground penetration is deeper at lower frequencies. This makes the observations at low-frequency bands (1-3 GHz i.e. ~30-10 cm wavelength) more optimal for sensing soil moisture [START_REF] Kerr | Soil moisture retrieval from space: the Soil Moisture and Ocean Salinity (SMOS) mission[END_REF][START_REF] Njoku | Passive microwave remote sensing of soil moisture[END_REF][START_REF] Schmugge | Passive Microwave Soil Moisture Research[END_REF].

Table 2.4 shows passive sensor frequency allocations. Some of the passive sensors, such as the AMSR-E, operate in unprotected frequency bands i.e., 6.925 GHz (C-band), 10.65

GHz (X-band), and 18.7 GHz (K-band) which are used also in satellite communications, whereas other passive sensors, such as the SMOS and SMAP, operate in protected bands i.e.

1.4 GHz (L-band). Consequently, models vary in the level of complexity of details they use in representing the physical system, temporal and spatial scales, variation of the driving forces, and the number of soil layers used [START_REF] Schmugge | Survey of methods for soil moisture determination[END_REF].

All above dynamic models predict soil moisture among other components of the water cycle such as runoff, rainfall, and evapotranspiration. This is true for hydrological models (e.g. TOPMODEL, a TOPography based hydrological MODEL [START_REF] Beven | A physically based, variable contributing area model of basin hydrology / Un modèle à base physique de zone d'appel variable de l'hydrologie du bassin versant[END_REF])), and land surface models (LSMs), whether used alone or within weather or climate models.

Among the various state-of-the-art LSMs, one finds: the Interactions Soil-Biosphere-Atmosphere (ISBA; [START_REF] Noilhan | A Simple Parameterization of Land Surface Processes for Meteorological Models[END_REF])), ORCHIDEE (Organizing Carbon and Hydrology In Dynamic Ecosystems) (de [START_REF] De Rosnay | Modelling root water uptake in a complex land surface scheme coupled to a GCM[END_REF][START_REF] Krinner | A dynamic global vegetation model for studies of the coupled atmosphere-biosphere system[END_REF], MERRA-Land (NASA's Modern-Era Retrospective Analysis for Research and Applications) [START_REF] Reichle | Assessment and Enhancement of MERRA Land Surface Hydrology Estimates[END_REF], HTESSEL (Hydrology Tiled ECMWF Scheme for Surface Exchange over Land [START_REF] Balsamo | A revised hydrology for the ECMWF model: Verification from field site to terrestrial water storage and impact in the ECMWF-IFS[END_REF], etc. Note that the Global Soil Wetness Project (GSWP-2) [START_REF] Dirmeyer | The Second Global Soil Wetness Project, GSWP-2[END_REF] is aiming at producing a global soil moisture datasets from a multiland surface models ensemble to serve as a benchmark production. Readers are directed to [START_REF] Pitman | The evolution of, and revolution in, land surface schemes designed for climate models[END_REF][START_REF] Singh | Mathematical Modeling of Watershed Hydrology[END_REF] for a detailed review of land surface and distributed hydrological models, as this topic is beyond the scope of this doctoral dissertation.

As stated before, soil moisture plays a major role in the water cycle by influencing the soil-vegetation-atmosphere interactions through influencing water and energy exchanges. It can be said that the two fundamental equations for soil moisture modelling are represented by the water and energy balance equations as follows:

The water balance is commonly expressed as follows [START_REF] Dingman | Physical Hydrology[END_REF][START_REF] Schmugge | Remote sensing in hydrology[END_REF]:

∆𝑆𝑆 ∆𝑡𝑡 = 𝑃𝑃 -𝐸𝐸𝑇𝑇 -𝑄𝑄 2 -11
where the variables are expressed as volume of water per unit system area per unit

Q is the runoff [L 3 /T].
The energy balance is commonly expressed as follows [START_REF] Schmugge | Remote sensing in hydrology[END_REF]:

𝑅𝑅 𝑑𝑑 -𝐺𝐺 = 𝐻𝐻 + 𝐿𝐿𝐸𝐸 2 -12
Where:

R n is the net radiation [W/m 2 ], G is the soil heat flux [W/m 2 ], H is the sensible heat flux [W/m 2 ],
and

LE is the latent heat flux [W/m 2 ].
The quantity R n -G is the available energy for the turbulent fluxes (LE and H).

In hydrological models, ET is often expressed as a depth of water over daily (mm/day) or longer time scales [START_REF] Schmugge | Remote sensing in hydrology[END_REF]. It is often deduced from the so-called "reference evapotranspiration", ET0, which corresponds to ET from a well-watered "reference" grass (uniform short grass of 0.12 m, with a fixed surface resistance of 70 s m -1 and an albedo of 0.23), that would not suffer from any water stress, thus evaporate at its potential rate. In this framework, actual ET (AET), i.e. the amount of ET that actually occurs when the water is limited [START_REF] Ward | Environmental Hydrology[END_REF], can be deduced from a water stress factor multiplied to potential ET (PET), which can itself be deduced from ET0 by means of a crop coefficient, accounting for the differences in PET between the reference grass and the selected vegetation/crop. The Penman-Monteith equation [START_REF] Monteith | Evaporation and Environment. In:The state and movement of water in living organism[END_REF] ), and ρ is the atmospheric density (kg/m 3 ). Basically, the Penman-Monteith approach is a way to implicitly use the energy budget without explicitly solving it. It is used in most hydrological models, including TOPMODEL [START_REF] Beven | A physically based, variable contributing area model of basin hydrology / Un modèle à base physique de zone d'appel variable de l'hydrologie du bassin versant[END_REF].

In contrast, LSMs use the energy budget equation and diffusive equations to calculate E and H [START_REF] Barella-Ortiz | Potential evaporation estimation through an unstressed surface-energy balance and its sensitivity to climate change[END_REF]. LSMs use turbulent diffusive equations because of high time step required to solve it jointly with the surface energy budget, which needs to be small enough (typically half-hourly) to account for the pronounced diurnal cycle of the involved energy fluxes. A diffusive equation was introduced by [START_REF] Budyko | Heat Balance of the Earth's Surface[END_REF] to estimate PET:

𝑃𝑃𝐸𝐸𝑇𝑇 = ρ 𝑟𝑟 𝑚𝑚 [𝑞𝑞 𝑠𝑠 𝑇𝑇 𝑤𝑤 -𝑞𝑞 𝑚𝑚 ] 2 -14
where:

ρ is the air density, r a is the aerodynamic resistance, q s is the saturated specific humidity, T w is the virtual temperature, and q a is the specific humidity of the air.

MERRA-Land

MERRA-Land is an enhanced product to the hydrological fields in the NASA MERRA atmospheric reanalysis [START_REF] Reichle | Assessment and Enhancement of MERRA Land Surface Hydrology Estimates[END_REF]. MERRA uses Version 5.2.0 of the Goddard Earth Observing System model (GEOS-5) and its associated data assimilation system, covering the period 1979-present period [START_REF] Rienecker | MERRA: NASA's Modern-Era Retrospective Analysis for Research and Applications[END_REF]. The reader is directed to [START_REF] Rienecker | MERRA: NASA's Modern-Era Retrospective Analysis for Research and Applications[END_REF] for more details on MERRA reanalysis and products, which can be obtained from the M-DISC (http://disc.sci.gsfc.nasa.gov/mdisc/) [START_REF] Reichle | The MERRA-Land Data Product[END_REF].

MERRA-Land, which is a land-only ("off-line"), introduced some enhancements to MERRA including [START_REF] Reichle | Assessment and Enhancement of MERRA Land Surface Hydrology Estimates[END_REF]: (ii) enhancing the MERRA-Land precipitation forcing by merging MERRA precipitation with a gauge-based data product from the NOAA Climate Prediction Center and (ii) updating the catchment land surface model by using the "Fortuna-2.5" version instead of the "MERRA" version. These two changes were evaluated by [START_REF] Reichle | Assessment and Enhancement of MERRA Land Surface Hydrology Estimates[END_REF] and was found that these changes improved the quality model in various ways.

Other characteristics of MERRA-Land data include [START_REF] Reichle | The MERRA-Land Data Product[END_REF]: (i) this product can be freely obtained from the Goddard Earth Sciences (GES) Data and Information Services Center (DISC) (ii) this product is provided as hourly averages (iii) this product is described as a simulation product and there is no assimilation of model state variables (such as soil moisture or snow) (iv) Leaf area index and greenness in this product are prescribed as a monthly climatology based on AVHRR (Advanced Very High Resolution Radiometer) observations, and (v) this product is provided with a horizontal resolution of 1/2° latitude by 2/3° longitude. This is the same as in the standard MERRA product [START_REF] Reichle | The MERRA-Land Data Product[END_REF].

Fig. 2.8 displays the surface below each atmospheric column in GEOS-5 which consists of a set of tiles: Ocean, Land, (land) Ice, or Lake. A catchment model is used to simulate these sub-tile fractions, which vary with time [START_REF] Reichle | The MERRA-Land Data Product[END_REF]. For further details on the catchment model, the readers are directed to [START_REF] Ducharne | A catchmentbased approach to modeling land surface processes in a general circulation model: 2. Parameter estimation and model demonstration[END_REF][START_REF] Koster | A catchmentbased approach to modeling land surface processes in a general circulation model: 1. Model structure[END_REF].

Fig. 2 -8

Land surface representation in GEOS-5. Adapted from [START_REF] Reichle | The MERRA-Land Data Product[END_REF] The land surface water balance equation is described, in GEOS-5, as follows [START_REF] Reichle | The MERRA-Land Data Product[END_REF])

𝜕𝜕𝜕𝜕 𝜕𝜕𝑡𝑡 = 𝑃𝑃 𝑠𝑠 + 𝑃𝑃 𝑠𝑠 -𝐸𝐸 𝑠𝑠 -𝑅𝑅 𝑠𝑠 + 𝑅𝑅 𝑤𝑤 2 -15
where:

W is the total water held in all land surface reservoirs (comprising the soil, the interception reservoir, and the snowpack), P l the liquid rain, Ps "snowfall" rates, E l is the total evapotranspiration rate, R l is the total runoff-surface (or overland) plus baseflow, and R w is a spurious water source

The balance equation for total land surface energy is described, in GEOS-5, as follows [START_REF] Reichle | The MERRA-Land Data Product[END_REF]:

𝜕𝜕ɛ 𝜕𝜕𝑡𝑡 = 𝑆𝑆𝜕𝜕 𝑠𝑠 + 𝐿𝐿𝜕𝜕 𝑠𝑠 -𝑆𝑆𝐻𝐻 𝑠𝑠 -𝐿𝐿 𝑣𝑣 𝐸𝐸 𝑠𝑠 -𝐿𝐿 𝑜𝑜 ∆𝑆𝑆𝜕𝜕𝐸𝐸 + 𝑅𝑅 𝑠𝑠 2 -16
where: ɛ is the total heat content (in the soil, canopy, and snowpack) relative to liquid water SW l is the net shortwave radiation, LW l is the net long wave radiation, L v is the latent heat of vaporization (from liquid), E l is the total evaporation from the land surface, SH l is the sensible heat flux from the land surface,

L f is the latent heat of fusion,
R l is the spurious snow energy source , and ΔSWE is the change in the snow water equivalent.

Soil moisture data assimilation

Forecasts (predictions) are made using numerical models, and different models are used depending on the target forecasted variables. Forecast of state variables can be improved by optimally integrating model predictions with observations through data assimilation techniques. Soil moisture data assimilation has been applied in hydrology since the eighties and with a recent rapid progress thanks to remote sensing [START_REF] Ni-Meister | Recent Advances On Soil Moisture Data Assimilation[END_REF]. The recent availability of surface soil moisture from remote sensing enables, for instance, hydrologists to obtain more accurate values of the root zone soil moisture through data assimilation of remotely sensed near-surface soil moisture into land surface models (Draper et al., 2009b;[START_REF] Draper | Assimilation of passive and active microwave soil moisture retrievals[END_REF][START_REF] Hoeben | Assimilation of active microwave observation data for soil moisture profile estimation[END_REF][START_REF] Reichle | Comparison and assimilation of global soil moisture retrievals from the Advanced Microwave Scanning Radiometer for the Earth Observing System (AMSR-E) and the Scanning Multichannel Microwave Radiometer (SMMR)[END_REF][START_REF] Scipal | Assimilation of a ERS scatterometer derived soil moisture index in the ECMWF numerical weather prediction system[END_REF].

There are several data assimilation techniques in soil moisture fields: (i) the Kalman Filter [START_REF] Crosson | Assimilating remote sensing data in a surface flux-soil moisture model[END_REF][START_REF] Walker | One-Dimensional Soil Moisture Profile Retrieval by Assimilation of Near-Surface Measurements: A Simplified Soil Moisture Model and Field Application[END_REF], (ii) direct insertion method [START_REF] Heathman | Assimilation of surface soil moisture to estimate profile soil water content[END_REF][START_REF] Walker | One-Dimensional Soil Moisture Profile Retrieval by Assimilation of Near-Surface Measurements: A Simplified Soil Moisture Model and Field Application[END_REF], (iii) extended Kalman Filter (Reichle et al., 2002a), and (iv)

Ensemble Kalman Filter [START_REF] Reichle | Hydrologic Data Assimilation with the Ensemble Kalman Filter[END_REF]. The Ensemble Kalman Filter (EnKF) is the most widely used due to its strength in handling non-linear systems and computational efficiency [START_REF] Crow | The assimilation of remotely sensed soil brightness temperature imagery into a land surface model using Ensemble Kalman filtering: a case study based on ESTAR measurements during SGP97[END_REF]. More recently, satellite-based active microwave nearsurface soil moisture observations (0-2 cm) from the ASCAT have been integrated with land surface models (ECMWF) through land data assimilation system and produced SM-DAS-2 soil moisture product [START_REF] De Rosnay | A simplified Extended Kalman Filter for the global operational soil moisture analysis at ECMWF[END_REF]. This recent later product was used in this doctoral dissertation as a benchmark and it is briefly described in Chapter IV.

SM-DAS

Fig. 2 -10

The scheme of HTESSEL and the recent revisions in the land surface model. Adapted from [START_REF] Balsamo | Evolution of land surface processes in the IFS[END_REF] For each tile the energy balance, in HTESSEL, is calculated separately as follows [START_REF] Wipfler | Seasonal evaluation of the land surface scheme HTESSEL against remote sensing derived energy fluxes of the Transdanubian region in Hungary[END_REF]: The water balance (mm/d) at the land surface, in HTESSEL, is calculated as follows [START_REF] Wipfler | Seasonal evaluation of the land surface scheme HTESSEL against remote sensing derived energy fluxes of the Transdanubian region in Hungary[END_REF]:

(1 -𝛼𝛼𝑠𝑠)𝑅𝑅 𝑠𝑠 ↓ +↓ 𝑅𝑅 𝑠𝑠 -𝑅𝑅 𝑠𝑠 ↑ -𝐺𝐺 𝑠𝑠 = 𝐻𝐻 𝑠𝑠 + 𝜆𝜆𝐸𝐸 𝑠𝑠 2 -
∆𝜕𝜕 + ∆𝑆𝑆 = 𝑃𝑃 -𝐸𝐸 -𝑅𝑅 2

SMOS/ASCAT/AMSR-E Mission overview

This chapter gives an overview on the current state of the art in the SMOS, as well as shortly ASCAT and AMSR-E, mission. It also describes shortly the basics of surface soil moisture (SSM) retrievals from these sensors and the types of existing SSM products. The main characteristics of SMOS, ASCAT, and AMSR-E missions and their SSM products are listed in Table 3.3 at the end of this chapter.

SMOS

SMOS mission overview

The SMOS mission (see SMOS satellite in orbit in Fig. GHz). L-band provides the best sensitivity to variations in surface soil moisture (SSM) and ocean salinity contents as it is not much sensitive to perturbing factors from weather, atmosphere, and vegetation [START_REF] Kerr | Soil moisture retrieval from space: the Soil Moisture and Ocean Salinity (SMOS) mission[END_REF][START_REF] Njoku | Passive microwave remote sensing of soil moisture[END_REF][START_REF] Pellarin | Surface soil moisture retrieval from L-band radiometry: a global regression study[END_REF].

Fig. 3 -1 SMOS satellite with ascending (ASC) and descending (DESC) orbits. Source: [www.esa.int].

The SMOS mission has two primary objectives [START_REF] Kerr | Soil moisture retrieval from space: the Soil Moisture and Ocean Salinity (SMOS) mission[END_REF][START_REF] Kerr | The SMOS Mission: New Tool for Monitoring Key Elements ofthe Global Water Cycle[END_REF]:

(i)
To accurately provide space-borne brightness temperatures (TB) observations from which global maps of SSM and Sea Surface Salinity (SSS) can be retrieved, which in turn enhance the understanding of climate change, improve weather forecasts, and make better hydrological models predictions, and

(ii) To contribute to cryosphere studies by providing observations over snow and ice regions and improving snow mantle monitoring and multilayer ice structure.

A unique aspect of this mission is that the SMOS satellite carries a novel and innovative payload adopting a completely different approach in the field of remote sensing.

This technique is based on a new passive instrument which is capable of recording TB at 1.40-1.427 GHz frequencies (L-band) in two polarizations (H & V) and multi-angular angles [START_REF] Mcmullan | SMOS: The Payload[END_REF]. This new instrument is called the Microwave Imaging Radiometer by Aperture Synthesis (MIRAS), which is a two-dimensional passive microwave interferometry radiometer [START_REF] Mcmullan | SMOS: The Payload[END_REF], see Fig. 3.2. To achieve an adequate spatial resolution for passive imaging from space by SMOS at L band (= 21 cm), large rotating antenna (several meters) is required. However, it will be too big to be carried by a satellite and costly, therefore it is a major challenge. To overcome this problem, antenna apertures for which thinned arrays using synthetic aperture principles were adopted for SMOS mission [START_REF] Kerr | Soil moisture retrieval from space: the Soil Moisture and Ocean Salinity (SMOS) mission[END_REF].

The main characteristics and features of MIRAS, which has a Y-shaped deployable structure, are listed below [START_REF] Mcmullan | SMOS: The Payload[END_REF]:

I.
A central hub to which 3 straight arms are connected and are equally separated, 120°

apart each other with an arm length of 4.5 m and are spaced d = 0.875 wavelengths (Fig. 3.2). The Nyquist criterion is not satisfied here as for hexagonal sampling necessitates that the antenna separation should be d =1/√3 wavelengths to avoid aliasing in the unit circle [START_REF] Camps | The processing of hexagonally sampled signals with standard rectangular techniques: application to 2-D large aperture synthesis interferometric radiometers[END_REF]. Consequently the reconstructed 2-D TB images (i.e. the microwave radiation emitted from the Earth's surface) suffer from aliasing (see Fig. 3.3) [START_REF] Camps | Retrieving sea surface salinity with multiangular L-band brightness temperatures: Improvement by spatiotemporal averaging[END_REF].

II.

Each arm comprises three segments with six L-band radiometers on each segment III. 54 radiometers on the arms and 12 in the hub (a total of 66 radiometers).

IV.

3 noise injection radiometers (NIRs) placed in the central hub.

V. 69 small receivers and uniformly distributed antennas, the antennas are separated by a distance of 18.37 cm, with a diameter of each antenna of 165 mm, with a height of 19 mm and a weight of 190 grams.

Fig. 3 -2 MIRAS instrument configuration diagram (upper panel) and during its assembly and integration (bottom panel) (McMullan et al., 2008).

The MIRAS instrument, on-board the SMOS satellite, has been measuring the TB at L-band since 2010 within a wide field of view (FOV; see Fig. 3.3 (a)) and range of incidence angles spanning from 0° to 65°. Fig. 3.3 (a-c) shows the observation geometry of SMOS (a), which is a hexagon-like shape about 1000 km across called the "alias-free zone" (www.esa.int; [START_REF] Camps | Retrieving sea surface salinity with multiangular L-band brightness temperatures: Improvement by spatiotemporal averaging[END_REF], an example (b) over the Baltic Sea area in Northern Europe, and each pixel in the Alias-free-FOV (c) as it is seen at a different radiometric sensitivity, spatial resolution, and incidence angle [START_REF] Camps | Retrieving sea surface salinity with multiangular L-band brightness temperatures: Improvement by spatiotemporal averaging[END_REF]. The spatial resolution of the TB measurements depends on the incidence angle [START_REF] Kerr | The SMOS Mission: New Tool for Monitoring Key Elements ofthe Global Water Cycle[END_REF], which is maximum (~ 50 km; at incidence angles of 65) at the edge of the FOV and minimum (~ 35 km; at nadir) at the center of the FOV [START_REF] Maaß | Snow thickness retrieval over thick Arctic sea ice using SMOS satellite data[END_REF].

Fig. 3 -3 SMOS observation geometry (a), an example of the hexagon-like shaped 'alias free'

SMOS snapshot over the Baltic Sea area in Northern Europe (b), and incidence angle (dashed lines from 10 to 60, circles cantered at (0, 0)); spatial resolution (dash-dot lines from 40 to 80 km); and radiometric sensitivity (dotted lines from 4 to 6 K) (c). (www.esa.int; [START_REF] Camps | Retrieving sea surface salinity with multiangular L-band brightness temperatures: Improvement by spatiotemporal averaging[END_REF].

SMOS products overview

SMOS SSM datasets are produced and distributed in different levels (Level 0 to Level 4) according to different levels of processors (www.esa.int). Level 0 (L0) to Level 2 (L2) are produced and distributed by the ESA, whereas Level 3 (L3) and Level 4 (L4) are produced and distributed by national centers in France and Spain [START_REF] Jacquette | SMOS CATDS level 3 global products over land[END_REF]. SMOS products are classified as follows (www.esa.int;Jacquette et al., 2010):

1-L0 processor and L0 products: the L0 products are obtained by formatting the SMOS Payload raw data (i.e. sorted in their original format as received from the satellite) in source packets with added Earth Explorer product headers.

2-Level 1: the TB are constructed in this level which is subdivided into three levels:

(i) Level 1A (L1A) processor and L1A products: the L1A processor converts and calibrates all data coming from the spacecraft into engineering units.

L1A products are, scientifically, called "Calibrated visibilities".

(ii) Level 1B (L1B) processor and L1B products: the L1B processor converts the L1A products into Fourier components of the TB using the so-called image reconstruction process. The L1B products are arranged as snapshots and not geographically sorted.

(iii) Level 1C (L1C) processor and L1C products: the L1C processor reprocesses L1B products and provides swath-based maps of TB in the antenna polarization reference frame, which are geographically sorted as the so-called swath-based multi-angular TB maps. The L1C data are geolocated in the Icosahedral Snyder Equal Area projection (ISEA).

(iv) Level 1 (L1) near real time (NRT) processor and L1 NRT products: L1

NRT processor converts the extracted L0 data into TB swaths. These datasets are delivered to the users within three hours from sensing time and are used as inputs for weather models such as the ECMWF.

3-Level 2 (L2) processor and L2 products: the L2 processor applies the L-MEB (L-Band

Emission of the Biosphere) model, which is shortly described in the next Section, to composite products, and monthly averaged products [START_REF] Jacquette | SMOS CATDS level 3 global products over land[END_REF]. The CATDS center provides the SMOSL3 SSM products in the NetCDF format on the EASE (Equal Area Scalable Earth) grid with a ~25 km cylindrical projection [START_REF] Jacquette | SMOS CATDS level 3 global products over land[END_REF]. The SMOSL3 SSM products can be easily downloaded from the CATDS of the L3 processor and this reprocessed product will be tagged RE02.

5-Level 4 (L4) products: the L4 product is a combination of SMOS data with external datasets (from sensors or models) under development at the CATDS. The L4 products, include, for instance, root zone moisture (1 meter deep), enhanced resolution products through a combination of optical, thermal and microwave remote sensing products, thickness of the ice, and extreme event products and prevention of natural risks (e.g., global drought index, fire, and flood prediction).

SMOS SSM algorithm

The basic theory of passive microwave remote sensing has been described in detail by a number of researchers (e.g., [START_REF] Ulaby | Microwave Remote Sensing, Active and Passive[END_REF]. The general principal of the SMOS algorithm relies on the measurements of the TB, corresponding to various contributions, from the surface of the Earth [START_REF] Kerr | Soil moisture retrieval from space: the Soil Moisture and Ocean Salinity (SMOS) mission[END_REF]. The TB observations are largely determined by the physical temperature and the emissivity of the radiating object. [START_REF] Wigneron | Microwave emission of vegetation: sensitivity to leaf characteristics[END_REF][START_REF] Stoffelen | Toward the true near-surface wind speed: Error modeling and calibration using triple collocation[END_REF]2000) have demonstrated the possibility to perform 2-parameter retrievals (soil moisture and optical depth) from multi-angular TB observations. A theoretical representation of the TB is given by a radiation equation of the black body. The concept of a perfect emitter is only theoretical. At microwave wavelengths the Rayleigh -Jeans is valid, and the emissivity (e) can be expressed as the ratio between the TB (K) and the physical temperature [START_REF] Njoku | Passive microwave remote sensing of soil moisture[END_REF], as shown in Eq. (2.6) in Section 2.2.2 in Chapter II.

Input datasets

The SMOSL2 and SMOSL3 retrieval algorithms use, as inputs, the following datasets [START_REF] Kerr | The SMOS Soil Moisture Retrieval Algorithm[END_REF]:

(i)
The SMOS L1C TB observations.

(ii) Static datasets i.e. do not vary over time such as: the soil texture, the land cover (ECOCLIMAP), soil bulk density (the Global Gridded Surfaces of Selected Soil Characteristics), sand and clay fraction (the FAO datasets), the topography index, etc.

(iii) Dynamic datasets i.e. vary over time such as: the Leaf Area Index (LAI; the MODerate Resolution Imaging Spectroradiometer (MODIS)), initial soil moisture (ECMWF), snow, soil and surface temperatures, etc.

The SMOSL2 algorithm

A flow chart showing the entire algorithm of SMOSL2 is displayed in Fig. 3.4 (Kerr et al., 2012). The SMOSL2 algorithm, in general, is based on a forward model and iterative inversion process. The forward model simulates the TB emitted by land nodes of SMOS using initial estimates of soil moisture obtained from the ECMWF forecasts, auxiliary datasets, surface temperature, etc. The inversion process estimates the actual soil moisture by minimizing the Root Mean Square Difference ("Cost Function") between the forward model simulations and the measured multi-angular TB (L1C data) [START_REF] Kerr | The SMOS Soil Moisture Retrieval Algorithm[END_REF].

The L1c products are delivered on the icosahedral Snyder equal area Earth fixed (ISEA-4H9) grid known as the discrete global grid (DGG). Each DGG node is subdivided into discrete fine flexible grids (DFFG) of approximately 4 km 2 each (Kerr et al., 2013a). The collective contributions from these DFFG cells form the upwelling TB signal measured by the SMOS satellite (Kerr et al., 2013a). This upwelling TB is inversed using the L-Band

Microwave Emission of the Biosphere (L-MEB; [START_REF] Wigneron | L-band Microwave Emission of the Biosphere (L-MEB) Model: Description and calibration against experimental data sets over crop fields[END_REF] model. The L-MEB model, with the help of auxiliary datasets (e.g., soil texture, land cover), is able to simulate TB for all incidence angles. The L-MEB model is the output of a broad review of knowledge of the microwave emission of a variety of land cover types [START_REF] Wigneron | L-band Microwave Emission of the Biosphere (L-MEB) Model: Description and calibration against experimental data sets over crop fields[END_REF]. The L-MEB model is continuously improved based on several ground and air-borne L-band radiometer experimental campaigns over different regions (e.g., [START_REF] De Rosnay | SMOSREX: A long term field campaign experiment for soil moisture and land surface processes remote sensing[END_REF][START_REF] Grant | A field experiment on microwave forest radiometry: L-band signal behaviour for varying conditions of surface wetness[END_REF][START_REF] Saleh | Soil moisture retrievals at L-band using a two-step inversion approach (COSMOS/NAFE'05 Experiment)[END_REF]. until the distance between the TB observed by SMOS and simulated by L-MEB is minimized (Kerr et al., 2013a;[START_REF] Kerr | The SMOS Soil Moisture Retrieval Algorithm[END_REF].

The SMOS TB signal observed at the antenna, shown in Fig. 3.5, can be formulated in the general radiative transfer equation as follows [START_REF] Kerr | The SMOS Soil Moisture Retrieval Algorithm[END_REF]:

𝑇𝑇𝑇𝑇 𝑝𝑝 = 𝑇𝑇𝑇𝑇 𝑚𝑚𝑤𝑤𝑚𝑚𝑣𝑣 + 𝑇𝑇𝑇𝑇 𝑠𝑠𝑝𝑝 exp(-𝜏𝜏 𝑚𝑚𝑤𝑤𝑚𝑚𝑣𝑣 ) + (𝑇𝑇𝑇𝑇 𝑚𝑚𝑤𝑤𝑚𝑚𝑑𝑑 + 𝑇𝑇𝑇𝑇 𝑠𝑠𝑠𝑠 exp(-𝜏𝜏 𝑚𝑚𝑤𝑤𝑚𝑚𝑑𝑑 )) 𝑟𝑟 𝑠𝑠𝑝𝑝 𝑒𝑒𝑒𝑒𝑒𝑒(-𝜏𝜏 𝑚𝑚𝑤𝑤𝑚𝑚𝑣𝑣 ) 3 -1
where:

TB atmu is the up-welling atmospheric emission, TB atmd is the down-welling atmospheric emission reflected (scattered) at the surface, TB sp is the Earth's surface emission, attenuated by the atmosphere, TB sk is the cosmic background emission attenuated by the atmosphere, reflected /scattered at the surface, r sp is the surface reflectivity, τ atd is the downward path atmospheric opacity, τ atu is the upward path atmospheric opacity, which depends on the gaseous and liquid droplet attenuating constituents (primarily oxygen, water vapor, and clouds), p subscript indicates the polarization, and s subscript stands for a combination of surface and near surface layers.

Fig. 3 -5

Components of the general radiative transfer equation [START_REF] Kerr | The SMOS Soil Moisture Retrieval Algorithm[END_REF].

The SMOS satellite operates at L-band, so τ atu and τ atd can be considered equal. Also, the atmospheric radiation components (TB atmd and TB atmu ) are small and can be considered equal. The spatial resolution of the SMOS is about 45 km in average, so a pixel represents various surface types such as rural areas, snow, forests, bare fields, fallow land, woodland, ponds, etc. Therefore, the total TB is the sum of various classes of emitters, which are aggregated by the L-MEB model to obtain a composite TB (Kerr et al., 2013a;[START_REF] Kerr | The SMOS Soil Moisture Retrieval Algorithm[END_REF]. The most important classes are shortly presented in the following (Kerr et al., 2013a;[START_REF] Kerr | The SMOS Soil Moisture Retrieval Algorithm[END_REF]:

1-Bare soil:

The SMOS satellite operates at low frequency (L-band) so Rayleigh-Jeans approximation can be used. Therefore, the upwelling TB measured from the surface of bare soils is simply the product of the soil effective temperature, T g and the soil emissivity of the radiating body e p :

𝑇𝑇𝑇𝑇 𝑝𝑝 = 𝑇𝑇 𝑔𝑔 𝑒𝑒 𝑝𝑝 3 -2 P subscript stands for either vertical or horizontal polarization, e p can be further described as:

𝑒𝑒 𝑝𝑝 = 1 -𝑟𝑟 𝑠𝑠𝑝𝑝 3 -3
where r sp is the surface reflectivity, which can be computed for smooth soil using [START_REF] Mialon | Comparison of Dobson and Mironov dielectric models in the SMOS soil moisture retrieval algorithm[END_REF].

The effective soil temperature is computed following a simplified formulation developed by [START_REF] Wigneron | Estimating the Effective Soil Temperature at L-Band as a Function of Soil Properties[END_REF]:

𝑇𝑇 𝑔𝑔 = 𝑇𝑇 𝑠𝑠𝑜𝑜𝑠𝑠𝑠𝑠 𝑑𝑑𝑤𝑤𝑝𝑝𝑤𝑤ℎ + 𝐶𝐶 𝑤𝑤 �𝑇𝑇 𝑠𝑠𝑜𝑜𝑠𝑠𝑠𝑠 𝑠𝑠𝑣𝑣𝑑𝑑𝑜𝑜 -𝑇𝑇 𝑠𝑠𝑜𝑜𝑠𝑠𝑠𝑠 𝑑𝑑𝑤𝑤𝑝𝑝𝑤𝑤ℎ � 3 -4
where:

C t is a parameter depending mainly on frequency and SSM, T soil depth is the soil temperature at depth (between ~ 0.5 and 1m), and T soil surf is the surface soil temperature (between ~ 1 and 5 cm).

T soil depth and T soil surf can be obtained from land surface models. T soil depth and T soil surf in the SMOSL2 algorithm are obtained from the ECMWF. According to (Choudhury et al., 1982), C t is a constant (~ 0.246 at L-band) that depends only on frequency. However [START_REF] Wigneron | Estimating the Effective Soil Temperature at L-Band as a Function of Soil Properties[END_REF] found that C t depends also on soil moisture. When the soil is very dry, soil layers deeper than 1 m for dry sand contribute significantly to the soil emission, and the value of C t is lower than 0.5. When the soil is very wet, the soil emission originates mainly from layers at the soil surface, and C t ≈ 1. C t can be computed using a simplified formulation, which is used in the L-MEB model, developed by [START_REF] Wigneron | A simple parameterization of the L-band microwave emission from rough agricultural soils[END_REF]:

𝐶𝐶 𝑤𝑤 = � 𝑤𝑤𝑠𝑠 𝑤𝑤0 � 𝑏𝑏𝑤𝑤0 3 -5
where:

ws is the surface soil moisture at about 0-2 cm, and w0 and bw0 are semi-empirical parameters depending on specific soil characteristics (e.g., texture, structure, and density). The values w0 = 0.3 m 3 /m 3 and bw0 = 0.3 are used as default values in the L-MEB model.

When the bare surface is not flat, Fresnel law (Eqs (2.8) & (2.9) in Section 2.2.2 in Chap. II) should be corrected for surface roughness with a purpose to account for the effects of surface scattering as follows (Kerr et al., 2013a;[START_REF] Wigneron | L-band Microwave Emission of the Biosphere (L-MEB) Model: Description and calibration against experimental data sets over crop fields[END_REF][START_REF] Wigneron | First evaluation of SMOS observations and Level-2 products over agricultural sites in temperate regions[END_REF]:

𝑟𝑟 𝑔𝑔𝑝𝑝 (θ) = �(1 -𝑄𝑄)𝑟𝑟 𝑏𝑏𝑝𝑝 + 𝑄𝑄𝑟𝑟 𝑏𝑏𝑝𝑝 � exp�-𝐻𝐻(𝑆𝑆𝑆𝑆)𝑐𝑐𝑐𝑐𝑠𝑠 𝑁𝑁𝑁𝑁𝑝𝑝 (𝜃𝜃)� 3 -6
where:

r gp is the rough surface reflectivity, Q is a polarization coupling factor, H is an effective surface roughness dimensionless parameter which can be computed as:

H = (2 k σ) 2
where k is the wave number and σ is the surface root mean square height,

NRp is an integer (N=2) used to parameterize the dependence of the roughness effects on incidence angle, and rbq is the smooth surface reflectivity for alternate polarization.

Table 3.1 presents the values of the different parameters used for bare soils (Kerr et al., 2013a) in the SMOSL2 algorithm.

2-Low vegetation (grassland, crop):

The τ -ω model [START_REF] Mo | A model for microwave emission from vegetation-covered fields[END_REF][START_REF] Wigneron | L-band Microwave Emission of the Biosphere (L-MEB) Model: Description and calibration against experimental data sets over crop fields[END_REF] is used to approximate the effects of vegetation, which attenuates soil emission and contributes to the emitted radiation, on the satellite signal. This model is mainly based on the optical depth τ, to parameterize the vegetation attenuation properties, and the single scattering albedo ω, to parameterize the scattering effects within the canopy layer. According to the τ -ω model, the emission from soil and vegetation is the sum of three components: (i) the direct emission from vegetation, (ii) the direct emission from soil attenuated by the canopy, and (iii) the direct emission from vegetation reflected by the soil and attenuated by the canopy layer [START_REF] Mo | A model for microwave emission from vegetation-covered fields[END_REF][START_REF] Wigneron | L-band Microwave Emission of the Biosphere (L-MEB) Model: Description and calibration against experimental data sets over crop fields[END_REF]. This is formulated as follows:

𝑇𝑇𝑇𝑇 𝑝𝑝 = �1 -ω 𝑝𝑝 ��1 -γ 𝑝𝑝 ��1 + γ 𝑝𝑝 𝑟𝑟 𝑠𝑠𝑝𝑝 �𝑇𝑇 𝑐𝑐 + �1 -𝑟𝑟 𝑠𝑠𝑝𝑝 � γ 𝑝𝑝 𝑇𝑇 𝑔𝑔 3 -7
where:

T g is the effective soil temperature [K], T c is the effective vegetation temperatures [K],
r sp is the soil reflectivity, ω p is the single scattering albedo, and γ p is the vegetation attenuation factor (transmissivity), which can be estimated as follows:

γ 𝑝𝑝 = exp � -𝜏𝜏 𝑝𝑝 𝑐𝑐𝑐𝑐𝑠𝑠 𝜃𝜃 � 3 -8
where:

τ p is the vegetation optical depth and θ is the observation angle.

More details on the values of the parameters used for low vegetation and the τ -ω model can be found in (Kerr et al., 2013a;[START_REF] Wigneron | L-band Microwave Emission of the Biosphere (L-MEB) Model: Description and calibration against experimental data sets over crop fields[END_REF].

3-Forest (coniferous, evergreen, and deciduous):

An algorithm specific for forest is only applied when a large fraction of land is covered by forests. When a large fraction of land is covered by forests, TB is computed as follows [START_REF] Ferrazzoli | Simulating L-band emission of forests in view of future satellite applications[END_REF]:

𝑇𝑇𝑇𝑇 𝑝𝑝 = �1 -ω 𝑜𝑜 �(1 -γ)�1 + γ 𝑝𝑝 𝑟𝑟 𝑔𝑔𝑝𝑝 �𝑇𝑇 𝑐𝑐 + �1 -𝑟𝑟 𝑔𝑔𝑝𝑝 �γ 𝑇𝑇 𝑔𝑔 3 -9
where:

T g is the effective soil temperature [K], T c is the effective vegetation temperatures [K],
r gp is the soil reflectivity, ω F is the equivalent albedo, and γ p is the vegetation transmissivity, which can be estimated as follows:

γ = exp � -𝜏𝜏 𝑜𝑜 𝑐𝑐𝑐𝑐𝑠𝑠 𝜃𝜃 � 3 -10
where:

𝜏𝜏 𝑜𝑜 represents the contributions due to crown, litter, and understory.

The basic algorithm used for forests is, in general, similar to the one used for low vegetation with some differences:

• A simple 𝜏𝜏 𝑜𝑜 constant (in law vegetation), and

• ω f (in law vegetation) may be considered constant (i.e., independent on angle, polarization and time), with a value of 0.08.

4-Open water

Contributions from the extended water surfaces (e.g., ocean for coastal pixels, rivers, canals, lakes, ponds, flooding, etc.) are taken into account in the SMOSL2 SSM algorithm. The emission from water bodies is estimated using the Fresnel equations (Eqs.

(2.8) & (2.9) in Section 2.2.2 in Chap. II) with replacing the soil magnetic permeability by the water magnetic permeability. The real and imaginary parts of the complex dielectric constant are computed using the modified Debye equation (Kerr et al., 2013a;[START_REF] Ulaby | Microwave Remote Sensing, Active and Passive[END_REF]. For information on how other surface types such as saline water, dry sand, very dry soils, rocks, etc. are dealt with in the SMOSL2 algorithm, readers are directed to (Kerr et al., 2013a;[START_REF] Kerr | The SMOS Soil Moisture Retrieval Algorithm[END_REF].

The SMOSL3 SSM algorithm

The SMOSL3 algorithm, adopted at the CATDS, is based on the SMOSL2 SSM algorithm, described shortly in the previous Section. The main differences with the SMOSL2 are that SMOSL3 takes into account several revisits simultaneously in a multi-orbit retrieval and are produced as gridded (NetCDF) maps not swath-based maps as the SMOSL2 products.

The input datasets for the SMOSL3 algorithm are the same as these used for the SMOSL2 but on a different grid (EASE-Grid). This grid was preferred as it is mostly used by the community [START_REF] Jacquette | SMOS CATDS level 3 global products over land[END_REF].

The SMOSL3 SSM algorithm produces daily products using three multi-angular acquisitions during the synthesis period [START_REF] Jacquette | SMOS CATDS level 3 global products over land[END_REF]: One for the product date (the reference day), one before and one after the product date; the data are selected from a search period of 7 days centered on the reference day [START_REF] Kerr | The CATDS SMOS L3 soil moisture retrieval processor, Algorithm Theoretical Baseline Document[END_REF]. This approach increases the number of views available, hence, more nodes are considered for the retrieval, which results in a larger coverage and more geophysical parameters can be derived. An overview of the SMOSL3 SSM processing chain at CATDS is displayed in Fig. 3.6. For a detailed description of the different steps of the algorithm, readers are directed to [START_REF] Kerr | The CATDS SMOS L3 soil moisture retrieval processor, Algorithm Theoretical Baseline Document[END_REF].

Fig. 3 -6

Overview of the CATDS SMOSL3 SSM processing chain [START_REF] Kerr | The CATDS SMOS L3 soil moisture retrieval processor, Algorithm Theoretical Baseline Document[END_REF]. Processors steps are colored in blue and products are colored in green. UDP: User Data Product, DAP: Data Analysis Product, ADF: Auxiliary Data File, and DPGS: Data Processing Ground Segment.

SMOS RFI issues

The negative impact of RFI (Radio Frequency Interference) on the passive microwave radiometers data has been a serious problem in the last decades [START_REF] Njoku | Global Survey and Statistics of Radio-Frequency Interference in AMSR-E Land Observations[END_REF], which should be well identified and removed in order to maintain the science value of the spaceborne observations. Since the launch of the SMOS satellite, it was noticed that the quality of its TB observations is negatively impacted by unnatural emissions, the so-called RFI.

Although SMOS measures TB in a protected frequency window of ( • Low RFI emissions, which are similar to natural levels or below and are very challenging to detect leading to retrieve wrong SSM.

• Moderate RFI emissions, which can be easily detected and, thus, corrected. • Cooperate with the National Spectrum Management Authorities (NSMA) to advance the progress about the investigation of the RFI sources and tracking the illegal transmitters and switching them off.

• Report the detected RFI sources to the NSMA and request for their support to initiate investigations to increase the awareness at the international level to fulfil the ITU Radio-Regulations, aiming at prohibiting any emissions and respecting the maximum levels recommended for unwanted emissions in the passive band.

• Enhance the RFI flagging processes in the data products which prevent retrieving SSM from contaminated regions.

• Develop new RFI mitigation algorithms to filter or remove the RFI impact.

The ESA has made many efforts and succeeded to contact 45 administrations, mostly in Europe and Asia. As a result, 42% of the RFI sources were successfully identified and switched off [START_REF] Daganzo-Eusebio | SMOS Radiometer in the 1400-1427-MHz Passive Band: Impact of the RFI Environment and Approach to Its Mitigation and Cancellation[END_REF].

Finally, RFI detection algorithm is progressively improved, therefore, caution should be taken when working with SMOS products by considering the version of the product. In V5.01, for instance, a temperature threshold linked to the surface expected emissivity was considered to filter RFI; whereas in previous versions V4.00, a fixed 340 K threshold was used.

ASCAT

ASCAT mission overview

The Advanced Scatterometer (ASCAT) is an active microwave sensor that transmits electromagnetic pulses and measures the electromagnetic wave reflected by the surface [START_REF] Bartalis | ASCAT Soil Moisture Product Handbook[END_REF][START_REF] Wagner | The ASCAT Soil Moisture Product: A Review of its Specifications, Validation Results, and Emerging Applications[END_REF] [START_REF] Wagner | The ASCAT Soil Moisture Product: A Review of its Specifications, Validation Results, and Emerging Applications[END_REF]. The ASCAT is a real-aperture radar system, thus it has a lower spatial resolution (25-50 km) compared to other instruments such as the syntheticaperture radar [START_REF] Wagner | The ASCAT Soil Moisture Product: A Review of its Specifications, Validation Results, and Emerging Applications[END_REF]. The main purpose of ASCAT and its first application was to measure wind speed over the oceans [START_REF] Wagner | The ASCAT Soil Moisture Product: A Review of its Specifications, Validation Results, and Emerging Applications[END_REF]. Another application of the ASCAT was the SSM retrievals on the mainland, as many studies (Bartalis et al., 2007a;[START_REF] Naeimi | An Improved Soil Moisture Retrieval Algorithm for ERS and METOP Scatterometer Observations[END_REF] have shown that soil moisture can be related, expressed as percentage, relatively to the historically highest and lowest ASCAT backscatter measurements. See Table 3.3 for more information on the ASCAT and MetOp -A Platform.

ASCAT SSM algorithm

The Vienna University of Technology (TU-Wien) in Austria developed an algorithm to retrieve SSM data from active microwave backscatter measurements, which was initially introduced by (Wagner et al., 1999b) and later improved by [START_REF] Naeimi | An Improved Soil Moisture Retrieval Algorithm for ERS and METOP Scatterometer Observations[END_REF]. This algorithm relies on several assumptions [START_REF] Bartalis | ASCAT Soil Moisture Product Handbook[END_REF][START_REF] Wagner | The ASCAT Soil Moisture Product: A Review of its Specifications, Validation Results, and Emerging Applications[END_REF]):

(i) There is a linear relationship between the backscattered signal (σ 0 expressed in decibels) measured by ASCAT and the SSM, (ii) There is a strong dependency between the backscattered signal and the incidence angle, which is illustrated in Fig. 3.9, (iii) The surface roughness and land-cover patterns do not vary in time (static), and

(iv) The backscattered signal is affected by the vegetation phenology on a seasonal scale and vegetation cycle does not change from year to year. Fig. 3.9 shows the relationship between the σ0 and the soil moisture and vegetation (Wagner et al., 1999a), where the σ0 may increase or decrease when vegetation grows and there is an incidence angle where the σ0 is stable in spite of seasonal changes in above ground vegetation biomass [START_REF] Wagner | The ASCAT Soil Moisture Product: A Review of its Specifications, Validation Results, and Emerging Applications[END_REF].

Fig. 3 -9

Relationship between the backscatter coefficient (σ0) and the surface soil moisture and vegetation. Adapted from Wagner et al. (1999a).

The soil Water Retrieval Package (WARP) software, realized with the programming language IDL at TU-Wien, is used to generate the ASCAT SSM products. It uses the change detection method (Fig. 3.10) [START_REF] Wagner | The ASCAT Soil Moisture Product: A Review of its Specifications, Validation Results, and Emerging Applications[END_REF], to produce the SSM from the ASCAT σ0 observations at the global scale. Soil moisture retrieval form the ASCAT σ0 measurements involve several processing steps [START_REF] Bartalis | ASCAT Soil Moisture Product Handbook[END_REF]: resampling the ASCAT measurements, using a Hamming weighting function with radius 18 km, in orbit geometry to a fixed Discrete 𝑆𝑆𝑆𝑆𝑆𝑆𝑠𝑠𝑙𝑙𝑆𝑆𝑒𝑒𝑒𝑒 (𝑡𝑡) = 𝜎𝜎 0 (𝑡𝑡, 𝑠𝑠) -𝜎𝜎 𝑑𝑑𝑑𝑑𝑑𝑑 0 (𝑠𝑠)

𝜎𝜎 𝑤𝑤𝑤𝑤𝑤𝑤 0 (𝑠𝑠) -𝜎𝜎 𝑑𝑑𝑑𝑑𝑑𝑑 0 (𝑠𝑠) 3 -12
where 𝜎𝜎 0 (𝑡𝑡, 𝑠𝑠) is the measured backscatter, given in m 2 / m 2 or Decibels (dB), at time t and under incidence angle i (40) and is given by:

𝜎𝜎 0 � 𝑚𝑚 2 𝑚𝑚 2 � = 𝜎𝜎 𝐴𝐴 𝑐𝑐𝑟𝑟 𝜎𝜎 0 [𝑆𝑆𝑇𝑇] = 10𝑙𝑙𝑐𝑐𝑙𝑙𝜎𝜎 0 � 𝑚𝑚 2 𝑚𝑚 2 � 3 -13
where:

A is the geometric antenna area [m²] σ is the radar scattering cross section [m²], which can be found in Section 2.2.2.2 in Chap.II as Eq. (2.10).

Detailed information on these processing steps and mathematical formulations can be found in (Bartalis et al., 2007b;[START_REF] Bartalis | ASCAT Soil Moisture Product Handbook[END_REF].

This algorithm provides a standardized SSM index in a unit of degree of saturation (i.e., the SSM content expressed in percent of porosity [START_REF] Hillel | Introduction to Soil Physics[END_REF]). Multiplying the degree of saturation with the porosity gives a direct estimation of the volumetric water (m 3 /m 3 ) content. Readers are directed to [START_REF] Wagner | The ASCAT Soil Moisture Product: A Review of its Specifications, Validation Results, and Emerging Applications[END_REF] for more details on the physical concept of the TU-Wien SSM algorithm.

There are several versions of the WARP processor; WARP 5.5 is the latest software version available for the retrieval of SSM from ASCAT scatterometer data, which was used in Chap. V. A new version of the WARP processor (WARP 6.0) is to be released in the near future.

ASCAT Products

The ASCAT products, in general, are categorized into different levels [START_REF] Bartalis | ASCAT Soil Moisture Product Handbook[END_REF]):

• Level 0 (L0): raw instrument datasets (unprocessed) transmitted from the spacecraft to the ground stations in binary form,

• Level 1a: reformatted L0 datasets for the successive processing,

• Level 1b (L1b): backscatter coefficients are calibrated and geo-referenced and their quality is controlled in full resolution,

• Level 2 (L2): L1b data are converted to geophysical parameters (SSM), and

• Level 3: L2 data are resampled or gridded.

AMSR-E

AMSR-E mission overview

In June 2002, the Advanced Microwave Scanning Radiometer (AMSR-E) sensor was launched aboard the AQUA satellite by the National Aeronautics and Space Administration (NASA) (see Fig. 3.11), which, however, due to some problems with rotations of its antenna, stopped working in October 2011. The AQUA satellite is on a sun-synchronous orbit at 705 km equatorial altitude and inclination of 98.2 о , with an ascending overpass time around 13:30 hours local at the equator and descending overpass time around 01:30 [START_REF] Demarest | Ascent plan for Aqua (EOS-PM1) including phasing with Terra (EOS-AM1)[END_REF]JAXA, 2006). AMSR-E records TB at six frequencies: 6.9 (C-band), 10.65 (X-band), 18.7 (Kuband), 23.8 (K-band), 36.5 (Ka-band), and 89 (W-band) GHz (horizontal and vertical polarizations) at a single incidence angle of 55°, with a spatial resolutions of 56 km (6.9 and 10.65 GHz), 25 km (18.7 and 23.8 GHz), 15 km (36.5 GHz), and 5 km (89 GHz) (JAXA, 2006). This mission is further detailed on the website of NASA:

http://www.ghcc.msfc.nasa.gov/AMSR/index.html and in JAXA ( 2006), its main characteristics are summarized in Table 3.3 at the end of this chapter.

The AMSR-E TB observations are contaminated by RFI particularly in the C-band frequencies in North America and Japan [START_REF] Njoku | Global Survey and Statistics of Radio-Frequency Interference in AMSR-E Land Observations[END_REF]. The RFI problems at C-and Xband in AMSR-E have been already investigated [START_REF] Kidd | Radio frequency interference at passive microwave earth observation frequencies[END_REF][START_REF] Li | A preliminary survey of radio-frequency interference over the U.S. in Aqua AMSR-E data[END_REF][START_REF] Njoku | Global Survey and Statistics of Radio-Frequency Interference in AMSR-E Land Observations[END_REF]. More recently, [START_REF] Lacava | A Multitemporal Investigation of AMSR-E C-Band Radio-Frequency Interference[END_REF] implemented the Robust Satellite Techniques (RST) approach using AMSR-E data at C-band to identify RFI source locations over land at global scale. [START_REF] Lacava | A Multitemporal Investigation of AMSR-E C-Band Radio-Frequency Interference[END_REF] have confirmed previous studies that large parts of North America and several zones in India, South America, and Japan are mostly contaminated by the RFI.

There are several algorithms which have been developed in order to retrieve SSM from the AMSR-E TB measurements. The official and first product is the NSIDC (National Snow and Data Centre, [START_REF] Njoku | Soil moisture retrieval from AMSR-E. Geoscience and Remote Sensing[END_REF]), which was shown to be able to reproduce the dynamics of SSM [START_REF] Rüdiger | An Intercomparison of ERS-Scat and AMSR-E Soil Moisture Observations with Model Simulations over France[END_REF]. Along with the official product and other algorithms, the Vrije Universiteit Amsterdam (VUA) in cooperation with the NASA (VU-NASA) [START_REF] Owe | A methodology for surface soil moisture and vegetation optical depth retrieval using the microwave polarization difference index[END_REF] developed an algorithm to retrieve SSM, surface temperature, and optical thickness at X and C-bands (the former is used when the latter is contaminated by the RFI) [START_REF] Owe | A methodology for surface soil moisture and vegetation optical depth retrieval using the microwave polarization difference index[END_REF]. The product of this later algorithm was used in Chap. IV and it is briefly described in the following Section.

AMSR-E VU-NASA algorithm:

The VU-NASA algorithm implements the LPRM (Land Parameter Retrieval Model, [START_REF] Owe | A methodology for surface soil moisture and vegetation optical depth retrieval using the microwave polarization difference index[END_REF][START_REF] Owe | Multisensor historical climatology of satellitederived global land surface moisture[END_REF] model to the TB acquisitions from the AMSR-E sensor in order to retrieve the SSM. The diagram displayed in Fig. 3.12 represents the algorithm of the LPRM, which is based on a forward radiative transfer model. The LPRM algorithm consists in five main modules: dielectric mixing model, smooth surface reflectivity, rough surface emissions, vegetation, and radiative transfer model, which are described in details in the Algorithm Theoretical Baseline Document [START_REF] Chung | Evaluation of SMOS retrievals of soil moisture over the central United States with currently available in situ observations[END_REF]. These five components are used to simulate a TB which is then compared to the TB acquired by the AMSR-E sensor.

SSM is changed (input at the top of Fig. 3.12) until the difference between the TB modelled and observed is at its minimum (weighted measurement accuracy difference). The LPRM algorithm retrieves the SSM and vegetation optical depth (τ v ) simultaneously from the AMSR-E observations at C-and X-band frequencies using iterative optimization technique; whereas surface temperature is computed from the Ka-band frequency. The vegetation optical depth (τ v ) is computed using the Microwave Polarization Difference Index (MPDI) [START_REF] Chung | Evaluation of SMOS retrievals of soil moisture over the central United States with currently available in situ observations[END_REF].

The TB (Tb in Fig 3 .12) observations measured by AMSR-E in LPRM are described using a simple radiative transfer model [START_REF] Mo | A model for microwave emission from vegetation-covered fields[END_REF]:

𝑇𝑇𝑇𝑇 𝑠𝑠,𝑝𝑝 = 𝑇𝑇 𝑠𝑠 𝑒𝑒 𝑑𝑑,𝑝𝑝 Γ 𝑣𝑣 + (1 -ω)𝑇𝑇 𝑣𝑣 (1 -Γ 𝑣𝑣 ) + (1 -ω)�1 -𝑒𝑒 𝑑𝑑,𝑝𝑝 �𝑇𝑇 𝑣𝑣 (1 -Γ 𝑣𝑣 )Γ 𝑣𝑣 3 -14
where:

T s is the thermodynamic temperatures of the soil [K],

T v is the thermodynamic temperatures of the vegetation [K],

Γ v is the vegetation transmissivity, which is assumed to be equal for vertical and horizontal polarization, e r is the rough surface emissivity, TB u and TB d are the upwelling and downwelling atmospheric brightness temperatures [K],

respectively, and ω is the single scattering albedo.

The subscript p denotes either horizontal (H) or vertical (V) polarization.

e r is calculated in LPRM as follows [START_REF] Wang | Remote sensing of soil moisture content, over bare field at 1.4 GHz frequency[END_REF]:

𝑒𝑒 𝑑𝑑 = 1 -𝑄𝑄�𝑟𝑟 𝑠𝑠,𝑝𝑝2 + (1 -𝑄𝑄)𝑟𝑟 𝑠𝑠,𝑝𝑝1 �𝑒𝑒 -𝑠𝑠𝑐𝑐𝑜𝑜𝑠𝑠𝐻𝐻 3 -15
where: Q is the polarization mixing factor, H is the roughness height, and r s is the surface reflectivity and p1 and p2 are opposite polarizations (horizontal or vertical).

Γ 𝑣𝑣 = exp � -𝜏𝜏𝑣𝑣 𝑐𝑐𝑜𝑜𝑠𝑠𝐻𝐻 � 3 -16
where τ v is the optical depth and θ is the incidence angle. Finally, in the LPRM algorithm, the RFI is detected based on an index of vertically polarized TB at C-band to vertically TB at X-band [START_REF] Li | A preliminary survey of radio-frequency interference over the U.S. in Aqua AMSR-E data[END_REF]. Two important things have to be noted about the AMSR-E VU-NASA SSM datasets:

-The AMSR-LPRM retrieval does not rely on calibration to local site conditions -

The LPRM algorithm does not need ancillary datasets.

3.4

Pre-Processing

Satellite soil moisture retrieved from observed brightness temperature is subject to some factors (strong topography, water bodies, etc.) that can strongly perturb the observed brightness temperature. Brightness temperatures emitted by the Earth surface, as a natural emission, are also affected by artificial sources originating from man-made emissions (e.g.

satellite transmissions, FM broadcast, etc.), so called Radio Frequency Interference (RFI) [START_REF] Njoku | Global Survey and Statistics of Radio-Frequency Interference in AMSR-E Land Observations[END_REF][START_REF] Oliva | SMOS Radio Frequency Interference Scenario: Status and Actions Taken to Improve the RFI Environment in the 1400-1427-MHz Passive Band[END_REF]. Therefore, remotely sensed datasets are often associated with flags to filter these potential effects.

Quality control was applied to SMOSL3, AMSRM, and ASCAT prior to the evaluation based on quality flags associated with the remotely sensed datasets. For SMOSL3, Data

Quality IndeX (DQX), index related to the quality of the retrieved parameter and RFI were used in the data selection. SMOSL3 datasets were rejected when DQX > 0.06 m 3 /m 3 , DQX is equal to fill value (meaning the retrieval has failed), Percentage of RFI > 30% (which is a daily RFI indicator), and Probability of RFI > 30% (which was computed from a moving window average of RFI events over several months). For AMSRM, the soil moisture error (SME), based on error propagation analysis, related to the sensor characteristics and vegetation optical depth, was used in the data selection. AMSRM datasets were rejected when SME > 0.35 m 3 /m 3 . For ASCAT, a noise error (ERR), which is based on Gaussian error propagation related to the sensor characteristics and incidence angle uncertainty, an estimated standard deviation of the backscatter signal, was used in the data selection. ASCAT datasets were rejected when ERR > 14% [START_REF] Draper | Assimilation of passive and active microwave soil moisture retrievals[END_REF].

Furthermore, all the datasets were re-projected from their original coordinate systems onto a regular 0.25° × 0.25° grid using a nearest neighbor approach (e.g., [START_REF] Draper | Assimilation of ASCAT near-surface soil moisture into the SIM hydrological model over France[END_REF][START_REF] Rüdiger | An Intercomparison of ERS-Scat and AMSR-E Soil Moisture Observations with Model Simulations over France[END_REF][START_REF] Scipal | Assimilation of a ERS scatterometer derived soil moisture index in the ECMWF numerical weather prediction system[END_REF]. Finally, all the remotely sensed datasets (SMOSL3, AMSRM, and ASCAT) were screened, applying additional static masks, to remove grid cells [START_REF] Bolten | Evaluating the Utility of Remotely Sensed Soil Moisture Retrievals for Operational Agricultural Drought Monitoring[END_REF][START_REF] Daly | A review of soil moisture dynamics: from rainfall infiltration to ecosystem response[END_REF], water resources [START_REF] Dobriyal | A review of the methods available for estimating soil moisture and its implications for water resource management[END_REF], and the climate system. It is central to land-atmosphere interactions due to its positive control on evapotranspiration, with feedback loops that are usually negative on air temperature [START_REF] Cheruy | Combined influence of atmospheric physics and soil hydrology on the simulated meteorology at the SIRTA atmospheric observatory[END_REF], and still not well understood on rainfall [START_REF] Taylor | Afternoon rain more likely over drier soils[END_REF]. SM also influences the dynamics of all the above mentioned processes by buffering or memory effects, with consequences on the persistence of extreme events, climate and hydrologic predictability, and even anthropogenic climate change trajectories (Entekhabi et al., 1996;Koster et al., 2004a;[START_REF] Koster | Skill in streamflow forecasts derived from large-scale estimates of soil moisture and snow[END_REF][START_REF] Quesada | Asymmetric European summer heat predictability from wet and dry southern winters and springs[END_REF][START_REF] Seneviratne | Impact of soil moisture-climate feedbacks on CMIP5 projections: First results from the GLACE-CMIP5 experiment[END_REF][START_REF] Teuling | Contrasting response of European forest and grassland energy exchange to heatwaves[END_REF].

As a result, accurate SM initialization is crucial to the quality of most water-related environmental forecasts up to at least seasonal forecasts, including numerical weather predictions (NWP) [START_REF] Beljaars | The Anomalous Rainfall over the United States during July 1993: Sensitivity to Land Surface Parameterization and Soil Moisture Anomalies[END_REF][START_REF] De Lannoy | Global Calibration of the GEOS-5 L-Band Microwave Radiative Transfer Model over Nonfrozen Land Using SMOS Observations[END_REF][START_REF] De Rosnay | Extended Kalman Filter soil moisture analysis in the IFS. ECMWF Spring Newsletter[END_REF][START_REF] De Rosnay | A simplified Extended Kalman Filter for the global operational soil moisture analysis at ECMWF[END_REF][START_REF] Drusch | Assimilation of Screen-Level Variables in ECMWF's Integrated Forecast System: A Study on the Impact on the Forecast Quality and Analyzed Soil Moisture[END_REF][START_REF] Koster | GLACE: The Global Land-Atmosphere Coupling Experiment. Part I: Overview[END_REF].

In particular, it is important to achieve an accurate SM initialization at the scale of the forecast models, which can exceed 0.5° × 0.5° for NWP and climate models. In situ SM measurements can now be routinely achieved with an accuracy as high as 0.025 m 3 /m 3 (Walker et al., 2004).

However, considering the high spatial variability of SM and the poor density of in situ measurement sites, it is not possible to produce accurate large-scale estimate of SM from in situ measurement networks [START_REF] Dorigo | The International Soil Moisture Network: a data hosting facility for global in situ soil moisture measurements[END_REF][START_REF] Hollinger | A Soil Moisture Climatology of Illinois[END_REF][START_REF] Vivoni | Comparison of ground-based and remotely-sensed surface soil moisture estimates over complex terrain during SMEX04[END_REF].

A major alternative to estimate SM at the large scale is to rely on remote sensing satellites, using passive or active microwave sensors, which offer global coverage and good temporal repetitivity, but are only sensitive to a shallow layer of the soil. Historically, passive microwave sensors were first used, starting with the Scanning Multichannel Microwave Radiometer (SMMR; 6.6, 10.7, 18.0 21, and 37 GHz channels; [START_REF] Wang | Effect of vegetation on soil moisture sensing observed from orbiting microwave radiometers[END_REF]) which operated on Nimbus-7 between 1978 and 1987, then the Special Sensor Microwave Imager (SSM/I) which started in 1987. Later passive sensors include the microwave imager from the Tropical Rainfall Measuring Mission (TRMM; 10, 19 and 21 GHz channel; [START_REF] Bindlish | Soil moisture estimates from TRMM Microwave Imager observations over the Southern United States[END_REF][START_REF] Gao | Using TRMM/TMI to Retrieve Surface Soil Moisture over the Southern United States from 1998 to 2002[END_REF], the Advanced Microwave Scanning Radiometer on Earth Observing System (AMSR-E; from 6.9 to 89.0 GHz; [START_REF] Njoku | Retrieval of land surface parameters using passive microwave measurements at 6-18 GHz[END_REF]) which operated on the AQUA satellite between 2002 and 2011, and Coriolis Windsat which started in 2003 [START_REF] Parinussa | The impact of land surface temperature on soil moisture anomaly detection from passive microwave observations[END_REF].

More recently, the Soil Moisture and Ocean Salinity (SMOS; 1.4 GHz) was launched in 2009 [START_REF] Kerr | The SMOS Mission: New Tool for Monitoring Key Elements ofthe Global Water Cycle[END_REF] and the upcoming SMAP (Soil Moisture Active/Passive) mission, including a radiometer at L-band, was planned by the National Aeronautics and Space Administration (NASA) and scheduled for launch in 2014 [START_REF] Entekhabi | The Soil Moisture Active Passive (SMAP) Mission[END_REF]. Lowresolution active microwave sensors (scatterometers) have also been used (Bartalis et al., 2007a;[START_REF] Wagner | Operational readiness of microwave remote sensing of soil moisture for hydrologic applications[END_REF].

Among all these microwave sensors, SMOS is the first satellite dedicated and specifically designed to measure directly surface SM (SSM) and sea surface salinity on a global scale [START_REF] Kerr | The SMOS Mission: New Tool for Monitoring Key Elements ofthe Global Water Cycle[END_REF][START_REF] Kerr | The SMOS Soil Moisture Retrieval Algorithm[END_REF] owing to its polar-orbiting 2-D interferometric radiometer at L-band. The Level 2 SMOS SSM products (SMOSL2) are derived from the multi-angular and fully polarized L-band passive microwave measurements [START_REF] Kerr | The SMOS Soil Moisture Retrieval Algorithm[END_REF]. A new global Level 3 SSM dataset (referred to as SMOSL3; [START_REF] Jacquette | SMOS CATDS level 3 global products over land[END_REF]) has been released very recently. The general principle of the algorithm is similar to the one used for producing the standard Level 2 SSM products, but the quality of the SSM product is enhanced by using multi-orbit retrievals [START_REF] Kerr | The CATDS SMOS L3 soil moisture retrieval processor, Algorithm Theoretical Baseline Document[END_REF].

Another strategy to produce large-scale estimates of SM relies on modelling, either directly using multimodel SM means [START_REF] Dirmeyer | GSWP 2: Multimodel analysis and implications for our perception of the land surface[END_REF][START_REF] Georgakakos | Potential value of operationally available and spatially distributed ensemble soil water estimates for agriculture[END_REF], or via assimilation systems, which aim at optimally combining land surface models and SM related observations [START_REF] De Rosnay | Extended Kalman Filter soil moisture analysis in the IFS. ECMWF Spring Newsletter[END_REF][START_REF] Drusch | Assimilation of Screen-Level Variables in ECMWF's Integrated Forecast System: A Study on the Impact on the Forecast Quality and Analyzed Soil Moisture[END_REF]. This strategy has proved to be particularly fruitful and highlighted the need for accurate surface and root zone SM remotely sensed estimates [START_REF] De Rosnay | Extended Kalman Filter soil moisture analysis in the IFS. ECMWF Spring Newsletter[END_REF][START_REF] De Rosnay | A simplified Extended Kalman Filter for the global operational soil moisture analysis at ECMWF[END_REF]Draper et al., 2009b;[START_REF] Muñoz-Sabater | From Near-Surface to Root-Zone Soil Moisture Using Different Assimilation Techniques[END_REF][START_REF] Reichle | Comparison and assimilation of global soil moisture retrievals from the Advanced Microwave Scanning Radiometer for the Earth Observing System (AMSR-E) and the Scanning Multichannel Microwave Radiometer (SMMR)[END_REF]. The SM-DAS-2 analysis, for instance, is retrieved by assimilating ASCAT SSM products in the ECMWF (European Centre for Medium-Range Weather Forecasts) Land Data Assimilation System, and the resulting estimates of SM benefit from high quality analyzed atmospheric data (de [START_REF] De Rosnay | Extended Kalman Filter soil moisture analysis in the IFS. ECMWF Spring Newsletter[END_REF][START_REF] De Rosnay | A simplified Extended Kalman Filter for the global operational soil moisture analysis at ECMWF[END_REF][START_REF] Drusch | Towards a Kalman Filter based soil moisture analysis system for the operational ECMWF Integrated Forecast System[END_REF].

Whatever their origin, the evaluation of global SSM products is needed to guide their correct use, and to improve our understanding of their strengths and weaknesses over a large spectrum of climate and environmental conditions across the world. Several studies have evaluated SSM products based on passive microwave sensors against in situ measurements and modelled data over different regions [START_REF] Al Bitar | Evaluation of SMOS Soil Moisture Products Over Continental U.S. Using the SCAN/SNOTEL Network[END_REF][START_REF] Albergel | Evaluation of remotely sensed and modelled soil moisture products using global ground-based in situ observations[END_REF][START_REF] Brocca | Soil moisture estimation through ASCAT and AMSR-E sensors: An intercomparison and validation study across Europe[END_REF][START_REF] Dall'amico | First Results of SMOS Soil Moisture Validation in the Upper Danube Catchment[END_REF]Draper et al., 2009a;[START_REF] Jackson | Validation of Soil Moisture and Ocean Salinity (SMOS) Soil Moisture Over Watershed Networks in the U.S. Geoscience and Remote Sensing[END_REF][START_REF] Lacava | A First Assessment of the SMOS Soil Moisture Product With In Situ and Modeled Data in Italy and Luxembourg[END_REF][START_REF] Leroux | Estimating SMOS error structure using triple collocation[END_REF][START_REF] Mladenova | Validation of AMSR-E soil moisture using L-band airborne radiometer data from National Airborne Field Experiment[END_REF][START_REF] Sahoo | Evaluation of AMSR-E soil moisture results using the in-situ data over the Little River Experimental Watershed, Georgia[END_REF][START_REF] Su | The Tibetan Plateau observatory of plateau scale soil moisture and soil temperature (Tibet-Obs) for quantifying uncertainties in coarse resolution satellite and model products[END_REF].

Although consistent results were generally obtained from the remotely sensed and modelled data, disagreements or biases between the different sources of SSM data were noted depending on the particular regions or time periods. For instance, [START_REF] Albergel | Evaluation of remotely sensed and modelled soil moisture products using global ground-based in situ observations[END_REF] found that the SM-DAS-2 SSM estimates were closer to in situ measurements in terms of correlation than SMOS and ASCAT SSM products, in several stations situated in Africa, Australia, Europe, and the United States.

In this context, we present in this study a global evaluation of two SSM datasets retrieved from passive microwave observations (SMOSL3 and AMSRM, respectively based on SMOS and AMSR-E observations) against the SM-DAS-2 product, which is used here as a reference, because it is the most consistent SM product compared to in situ SM data [START_REF] Albergel | Evaluation of remotely sensed and modelled soil moisture products using global ground-based in situ observations[END_REF]. In doing so, we have two specific objectives. The first objective is to provide the first assessment of the SMOSL3 product at global scale. The second objective is to compare SSM products retrieved from passive microwave observations at two different frequency bands: L-band (~ 1.4 GHz) for SMOSL3 vs. C-band (~ 5 GHz) for AMSRM. Although the performances of L-band vs. C-band for SSM retrievals have been compared against experimental or simulated data sets [START_REF] Calvet | Sensitivity of Passive Microwave Observations to Soil Moisture and Vegetation Water Content: L-Band to W-Band[END_REF][START_REF] Wigneron | Microwave emission of vegetation: sensitivity to leaf characteristics[END_REF], no global study based on satellite data has yet been made, to our knowledge. L-band is generally considered to be the optimum frequency band for SM monitoring due to (i) lower attenuation effects by vegetation (ii) lower atmospheric effects and larger effective sampling depth (~ 0-3 cm; [START_REF] Escorihuela | Effective soil moisture sampling depth of L-band radiometry: A case study[END_REF]) than C-band.

The SSM datasets used and the methodology for their evaluation are described in Section 4.2. The results are then presented in Section 4.3. Finally, discussion and conclusions are given in Section 4.4.

Materials and methods

Global-scale soil moisture datasets

The main characteristics of the three SSM datasets considered in this study are summarized in Table 4. [START_REF] Kerr | Soil moisture retrieval from space: the Soil Moisture and Ocean Salinity (SMOS) mission[END_REF][START_REF] Kerr | The SMOS Mission: New Tool for Monitoring Key Elements ofthe Global Water Cycle[END_REF]. The SMOS mission aims to monitor SSM at a depth of about 3 to 5 cm and an accuracy of 0.04 m 3 /m 3 . SMOS provides global coverage with a 3-day revisit at the equator with a morning ascending orbit at 0600 h local time and an afternoon descending orbit at 1800 h [START_REF] Kerr | The SMOS Soil Moisture Retrieval Algorithm[END_REF].

The CATDS Centre (Centre Aval de Traitement des Données; http://catds.ifremer.fr/) recently provided re-processed global maps of SSM at different temporal resolutions: daily products, 3-day global products insuring a complete coverage of the Earth surface, 10-day composite products, and monthly average products, the so-called SMOS level 3 products (SMOSL3). These products are presented in the NetCDF format on the EASE grid (Equal Area Scalable Earth grid) with a spatial resolution of ~25 km × 25 km. The main principle of the algorithm used to retrieve SSM is the same as the one used by the ESA operational algorithm for producing the standard Level 2 SSM products [START_REF] Kerr | The SMOS Soil Moisture Retrieval Algorithm[END_REF]Wigneron et al., 2007). In both Level 2 (L2) and Level 3 (L3) products, multiangular observations are used to retrieve simultaneously SSM and vegetation optical depth at nadir (τ-NAD) using a standard iterative minimization approach of a cost function (Statistical Inversion Approach as discussed in [START_REF] Wigneron | Retrieving near-surface soil moisture from microwave radiometric observations: current status and future plans[END_REF]. The main difference with the L2 processing is the fact that the L3 processing takes into account over each pixel several revisits simultaneously in a multi-orbit retrieval approach [START_REF] Jacquette | SMOS CATDS level 3 global products over land[END_REF][START_REF] Kerr | The CATDS SMOS L3 soil moisture retrieval processor, Algorithm Theoretical Baseline Document[END_REF]. In the L2 algorithm, SSM and τ-NAD are retrieved from multiangular observations made using one SMOS overpass at 0600 or 1800 h local time. Conversely, in the L3 algorithm, SSM and τ-NAD are retrieved from multiangular observations made using several overpasses (3 at most) over a 7day window. Over the short 7-day window, it is considered that optical depth at nadir (τ-NAD) varies slowly in time. In the L3 processor, this is accounted for by assuming that the retrieved values of τ-NAD are correlated using a Gaussian auto-correlation function over the 7-day window (while the SM values are considered as uncorrelated). The multi-orbit retrieval approach was selected to produce the L3 product as it improves the SM retrieval [START_REF] Kerr | The CATDS SMOS L3 soil moisture retrieval processor, Algorithm Theoretical Baseline Document[END_REF]:

I.
Increasing the number of overpasses over a given node taking into account several revisits (multi-orbit approach) increases the number of observations available for a node.

As the number of observations increases, more nodes are considered in the retrieval process, resulting in a larger coverage. This is mostly significant at the edge of the swath for which a single overpass does not provide enough brightness temperature (TB) data for an accurate retrieval process [START_REF] Wigneron | Two-Dimensional Microwave Interferometer Retrieval Capabilities over Land Surfaces (SMOS Mission)[END_REF].

II.

Considering that the vegetation optical thickness is correlated over a given period of time adds more constraints in the retrieval process and the robustness of the retrieval is improved.

SMOSL3 (ascending and descending) datasets include flags that can be used to filter out the datasets [START_REF] Jacquette | SMOS CATDS level 3 global products over land[END_REF][START_REF] Kerr | The CATDS SMOS L3 soil moisture retrieval processor, Algorithm Theoretical Baseline Document[END_REF][START_REF] Kerr | CATDS SMOS L3 processor: Algorithm Theoretical Baseline Document for the soil moisture retrieval (ATBD)[END_REF]. More details on the flags used to filter SMOSL3 data are given in Section 4.3.

Note that new versions of the SMOSL3 data set will be produced based on reprocessing activities in the near future and will lead to improvements in the product accuracy.

The version of SMOSL3 used in the present study was the latest version available at CATDS.

The version of the processor is V2.48, corresponding to a Level-2 version higher than ~V5.0, although there is not a strict correspondence between Level-2 and Level-3 versions.

AMSRM

The Aqua satellite is operated by the National Aeronautics and Space Administration (NASA). It was launched in May-2002 and carries, among others, the AMSR-E radiometer providing passive microwave measurements at six frequencies (6. 925, 10.65, 18.7, 23.8, 36.5, and 89.0 GHz) with day-time ascending orbit at 1330 h and night-time descending orbit at 0130 h [START_REF] Owe | Multisensor historical climatology of satellitederived global land surface moisture[END_REF]. The datasets cover the period from June 2002 to October 2011. On this latter date, AMSR-E on board the NASA Aqua satellite stopped producing data due to a problem with the rotation of its antenna.

The AMSR-E sensor was one of the first sensors to target SSM as a standard product [START_REF] Njoku | Soil moisture retrieval from AMSR-E. Geoscience and Remote Sensing[END_REF][START_REF] Njoku | Vegetation and surface roughness effects on AMSR-E land observations[END_REF]. Various algorithms have been developed to retrieve SSM from the AMSR-E observations. The main ones were developed at (i) NASA which produced the standard AMSR-E-NASA algorithm [START_REF] Njoku | Soil moisture retrieval from AMSR-E. Geoscience and Remote Sensing[END_REF], (ii) the Japan Aerospace Exploration Agency [START_REF] Koike | Development of an advanced microwave scanning radiometer (AMSR-E) algorithm of soil moisture and vegetation water content[END_REF], and (iii) the "Vrije Universiteit Amsterdam" in collaboration with NASA, referred to as the NASA-VUA algorithm [START_REF] Owe | A methodology for surface soil moisture and vegetation optical depth retrieval using the microwave polarization difference index[END_REF][START_REF] Owe | Multisensor historical climatology of satellitederived global land surface moisture[END_REF]. The NASA-VUA algorithm uses a three-parameter retrieval approach (i.e., SSM, vegetation optical depth, and soil/canopy temperature are retrieved simultaneously) to convert multi-frequency TB measured by AMSR-E to SSM. The retrieved SSM products accuracy was shown to be 0.06 m 3 /m 3 for sparsely to moderately vegetated canopies [START_REF] De Jeu | Global Soil Moisture Patterns Observed by Space Borne Microwave Radiometers and Scatterometers[END_REF].

A range of studies [START_REF] Brocca | Soil moisture estimation through ASCAT and AMSR-E sensors: An intercomparison and validation study across Europe[END_REF]Draper et al., 2009a;[START_REF] Hain | An intercomparison of available soil moisture estimates from thermal infrared and passive microwave remote sensing and land surface modeling[END_REF] addressed the evaluation of the NASA-VUA SSM products based on combinations of observations made at different AMSR-E frequencies, mainly using C-band (6.925 GHz)

and/or X-band (10.65 GHz). Using in situ observations and/or modelled SM data as reference, these studies showed good performance of the NASA-VUA products in capturing the SSM variability at global scale.

In this paper a version (Level 3 gridded data) of the NASA-VUA product exclusively based on the AMSR-E C-band and descending orbit observations was used. It is referred hereafter to as AMSRM. Descending orbit (night time) SM products were shown in previous studies to be more accurate and less affected by temperature-related errors than ascending orbit (day time) products (Draper et al., 2009a;[START_REF] Jackson | Validation of Advanced Microwave Scanning Radiometer Soil Moisture Products[END_REF][START_REF] Kerr | A semiempirical model for interpreting microwave emission from semiarid land surfaces as seen from space[END_REF][START_REF] Su | The Tibetan Plateau observatory of plateau scale soil moisture and soil temperature (Tibet-Obs) for quantifying uncertainties in coarse resolution satellite and model products[END_REF]. The use of C-band (6.925 GHz) data, i.e. the lowest frequency available for the AMSR-E instrument, maximizes the soil sampling depth (~ 0-1 cm) of the retrieved product [START_REF] Owe | Multisensor historical climatology of satellitederived global land surface moisture[END_REF] and minimizes the sampling depth mismatch with the SMOSL3 product.

ECMWF soil moisture analysis

This study used the SM-DAS-2 SM analysis product as a reference. SM-DAS-2 is produced at ECMWF in the framework of the H-SAF project of EUMETSAT (Satellite Application Facility on support to operational Hydrology and water management; more information at http://hsaf.meteoam.it/). The SM-DAS-2 analysis uses the Hydrology Tiled ECMWF Scheme for Surface Exchanges over Land (HTESSEL; [START_REF] Balsamo | A revised hydrology for the ECMWF model: Verification from field site to terrestrial water storage and impact in the ECMWF-IFS[END_REF][START_REF] Van Den Hurk | The Torne-Kalix PILPS 2(e) experiment as a test bed for modifications to the ECMWF land surface scheme[END_REF]). HTESSEL is a multilayer model where the soil is discretized in four layers (thickness: 7, 21, 72 and 189 cm). SM-DAS-2 relies on a dedicated advanced Land Data Assimilation System: a simplified Extended Kalman Filter able to ingest information EUMETSAT and it benefits from the latest model and analysis developments from ECMWF. This is why it was selected as the benchmarking dataset for this study. However it is important to emphasize that, as shown by the validation statistics above, SM-DAS-2 does not represent the absolute truth. It was used as a reference in this paper because at the time of this study it was the product that best captures the SM dynamics. On the longer term, when the SM retrieval algorithms will be fully calibrated, it is likely that satellite products such as SMOS SM will be used as reference data sets for SM product comparison studies. SM-DAS-2 is a SM index product; however in this study it was converted to volumetric SM (in m 3 /m 3 ) using global soil texture and hydraulic soil properties derived from the Food and Agriculture

Organization digital (FAO) soil map as described in [START_REF] Balsamo | A revised hydrology for the ECMWF model: Verification from field site to terrestrial water storage and impact in the ECMWF-IFS[END_REF]. Hereafter, this product will be referred to as "DAS2".

Pre-processing

Quality control was applied to SMOSL3 and AMSRM prior to the evaluation based on quality flags associated with the remotely sensed datasets. The uncertainties associated with the NASA-VUA retrieval algorithm are based on error propagation analysis, related to the sensor characteristics and vegetation optical depth, as described in Parinussa et al. (2011c).

AMSRM SSM values with an estimated SSM uncertainty greater than 0.35 m 3 /m 3 were rejected. Flags such as Data Quality IndeX (DQX) and Radio Frequency Interferences (RFI) are also associated with the SMOSL3 data and were used in our data selection. The DQX is an index related to the quality of the retrieved parameter. It takes into account the uncertainties associated with the parameter retrievals, depending on the number of multiangular observations available, the surface conditions (dry or wet soil conditions, dense or sparse vegetation cover, etc.), the TB accuracy, etc. [START_REF] Kerr | The SMOS Soil Moisture Retrieval Algorithm[END_REF][START_REF] Wigneron | Two-Dimensional Microwave Interferometer Retrieval Capabilities over Land Surfaces (SMOS Mission)[END_REF].

The DQX value is provided in volumetric SSM moisture units between 0 and 0.1 m 3 /m 3 . In this study, we selected data with a value of DQX lower than 0.06, as we considered this ratio represents a good compromise between the need to keep sufficient data and the need to ensure data quality. Radio Frequency Interferences come from man-made emissions (e.g. satellite transmissions, aircraft communications, radar, TV radio-links, FM broadcast, and wireless camera monitoring systems). It perturbs the natural microwave emission emitted by the Earth surface and measured by passive microwave systems [START_REF] Njoku | Global Survey and Statistics of Radio-Frequency Interference in AMSR-E Land Observations[END_REF][START_REF] Oliva | SMOS Radio Frequency Interference Scenario: Status and Actions Taken to Improve the RFI Environment in the 1400-1427-MHz Passive Band[END_REF].

With the SMOS interferometric system (based on a three arm Y-shaped antenna array), RFI effects are complex and oscillating interference effects may happen [START_REF] Oliva | SMOS Radio Frequency Interference Scenario: Status and Actions Taken to Improve the RFI Environment in the 1400-1427-MHz Passive Band[END_REF]. These (iii) Probability of RFI (RFI Prob) > 30%, which was computed from a moving window average of RFI events over several months.

Fig. 4 -1 Probability of Radio Frequency Interference (RFI) occurrences in the L-band SMOS observations. The map represents the average probability of RFI occurrences for the period 2010-2012.

Within the NASA-VUA algorithm for AMSR-E, Radio Frequency Interference is detected according to the method of [START_REF] Li | A preliminary survey of radio-frequency interference over the U.S. in Aqua AMSR-E data[END_REF]. This method is based on absolute differences between the different frequencies. In the AMSRM product, the standard configuration of NASA-VUA was used and C-band observations were used generally. Only when an RFI threshold value was reached, NASA-VUA made a switch to X band observations [START_REF] Chung | Evaluation of SMOS retrievals of soil moisture over the central United States with currently available in situ observations[END_REF].

Based on flags, AMSRM and SMOSL3 data were also rejected in regions of strong topography or wetlands. AMSRM, SMOSL3, and the reference DAS2 dataset were provided on different grids and formats. So pre-processing was required to allow a comparison of all products on the same grid. All the datasets were re-projected from their original coordinate systems onto a regular 0.25° × 0.25° grid using a nearest neighbor approach (e.g., [START_REF] Draper | Assimilation of ASCAT near-surface soil moisture into the SIM hydrological model over France[END_REF][START_REF] Rüdiger | An Intercomparison of ERS-Scat and AMSR-E Soil Moisture Observations with Model Simulations over France[END_REF][START_REF] Scipal | Assimilation of a ERS scatterometer derived soil moisture index in the ECMWF numerical weather prediction system[END_REF].

Comparison metrics

Three statistical indicators were computed between pairs of the remotely sensed (SSM RS ) and reference SSM products (SSM REF ). We considered the Pearson correlation coefficient (R), the mean difference (Bias), and the Root Mean Squared Difference (RMSD)

between the remotely sensed (SSM RS ) and the reference SM products. The equations for the calculation of the three indicators are given as follows [START_REF] Brocca | Soil moisture estimation through ASCAT and AMSR-E sensors: An intercomparison and validation study across Europe[END_REF][START_REF] Cecr | Comprehensive Error Characterisation Report[END_REF]:

𝑅𝑅 = ∑ (SSM REF(i) -SSM REF )(SSM RS(i) -SSM RS ) 𝑑𝑑 𝑠𝑠=1 � ∑ (SSM REF(i) -SSM REF ) 2 ∑ (SSM RS(i) -SSM RS ) 2 𝑑𝑑 𝑠𝑠=1 𝑑𝑑 𝑠𝑠=1 4 -1 Bias = (SSM RS -SSM REF ) 4 -2 RMSD = � (SSM RS -SSM REF ) 2 4 -3
where the overbar denotes the mean operator, n is the number of SSM data, SSM RS is the satellite-based SSM product (SMOSL3 and AMSRM), and SSM REF is the reference SSM (DAS2). We used RMSD instead of RMSE (Root Mean Squared Error) because the reference SSM values may contain errors and cannot be considered as the "true" SSM values.

Regional-scale analyses

This regional study was made to compare the three different datasets for a variety of conditions. We compared the SSM time series from SMOSL3, AMSRM, and the reference (DAS2) over eight sites which were selected taking into consideration contrasting vegetation types and climate conditions (see Fig. 4.2). A summary of the main characteristics of the eight selected sites is given in Table 4.2. This evaluation was limited to only eight sites which cannot span the whole range of soil, vegetation, and climate conditions present at global scale. However, this evaluation allowed us to analyze and illustrate some major features of the three datasets. To compare the temporal dynamics of SSM between remotely sensed and reference observations, we removed the systematic differences by matching the remotely sensed time series to the reference time series as discussed by [START_REF] Dorigo | Error characterisation of global active and passive microwave soil moisture datasets[END_REF]. This was done by normalizing the original remotely sensed data (the data referred to as 'original' in the following) are the data extracted directly from the SMOSL3 or AMSRM data set and expressed in volumetric units (m 3 /m 3 ) SSM or so that they have the same mean and standard deviation as the reference SSM dataset SSM REF according to the following equation [START_REF] Brocca | ASCAT soil wetness index validation through in situ and modeled soil moisture data in central Italy[END_REF]Draper et al., 2009a):

SSM(t) = SSM REF + σ(SSM or ) σ(SSM REF ) �SSM or (t) -SSM or � 4 -4
Here, SSM(t) stands for the rescaled remotely sensed retrievals at time steps t = 1,…, n, where n is the total number of observations, �SSM or � 𝑎𝑎𝑙𝑙𝑆𝑆 σ(SSM or ) are the mean and standard deviation of the original remotely sensed retrievals, respectively, and SSM 𝑁𝑁𝑅𝑅𝑅𝑅 and σ(SSM REF ) are mean and standard deviation of the reference dataset, respectively. [START_REF] Chesworth | Biomes and their Soils[END_REF]. The boxes on the map indicate the sites which were selected to illustrate the main features of the SMOSL3, AMSRM and DAS2 products for a variety of vegetation and climatic conditions.

Fig. 4 -2 Distribution of major biomes

SSM seasonal anomalies

All the above statistics were calculated for original SSM values, expressed in volumetric units (m 3 /m 3 ). We also applied the above performance metrics to SSM anomalies.

The anomaly time-series were calculated in order to avoid seasonal effects that can unrealistically increase the degree of correlation [START_REF] Scipal | Assimilation of a ERS scatterometer derived soil moisture index in the ECMWF numerical weather prediction system[END_REF] and to analyze the ability of remotely sensed SSM products to capture the day-to-day variability in the SSM time series.

We computed the anomalies following the method described by [START_REF] Albergel | An evaluation of ASCAT surface soil moisture products with in-situ observations in Southwestern France[END_REF]. The anomalies SSM anom (t) were computed as the difference to the mean for a sliding window of 35 days, which was further scaled using the standard deviation in order to be dimensionless:

SSM anom (t) = SSM or (t) -SSM or (t -17 ∶ t + 17) σ[SSM or (t -17: t + 17)] 4 -5
where SSMor(t) is the original SSM value at time t obtained from the satellite sensor or reference datasets, the over-bar and σ symbols are the temporal mean and standard deviation operators, respectively, for a time window of 35 days corresponding to the time interval [t -17 days, t + 17 days]. The use of a ~ monthly window is a very common approach to compute SM anomalies [START_REF] Brocca | Soil moisture estimation through ASCAT and AMSR-E sensors: An intercomparison and validation study across Europe[END_REF][START_REF] Draper | Estimating root mean square errors in remotely sensed soil moisture over continental scale domains[END_REF]Draper et al., 2009b;[START_REF] Reichle | An adaptive ensemble Kalman filter for soil moisture data assimilation[END_REF].

Global-scale analyses

Global maps of (i) correlations (R), to assess the global consistency in the SSM variability at both long-(original) and short-term (anomaly) scales, (ii) RMSD, and (iii) bias between the reference and the two remotely sensed SMOSL3 and AMSRM SSM time series were computed. The performance indicators were computed for all common pixels on a daily basis. To analyze the effects of the vegetation and climatic conditions and to facilitate the interpretation of the results of the global comparison, the values of the three performance indexes were averaged for a variety of biomes. These biomes represent different bioclimatic conditions and contrasting vegetation types. In this study we used the classification made by [START_REF] Chesworth | Biomes and their Soils[END_REF], illustrated in Fig. 4.2, who distinguished: "tundra", "boreal semihumid", "boreal humid", "temperate semi-arid", "temperate humid", "Mediterranean cold", "Mediterranean warm", "desert tropical", "desert temperate", "desert cold", and "tropical humid" biomes.

The analysis of the results was also made accounting for the LAI (mean value computed over the pixel) to evaluate the link between the accuracy of the remotely sensed

Results

Comparison of SMOSL3 ascending and descending overpasses

Original SMOSL3 retrievals obtained from the ascending and descending overpasses were compared to the reference SSM data. In terms of correlation, a better performance of SMOSL3 for ascending orbits compared with descending orbits with respect to the reference can be clearly seen in Fig. 4.4. In much of the world (e.g., central USA, Europe, South America, and South Africa), ascending SMOSL3 retrievals were found to be better correlated to the reference datasets than descending SMOSL3 retrievals. This was expected because at dawn soil is often in near hydraulic equilibrium [START_REF] Jackson | Profile soil moisture from surface measurements[END_REF], and factors affecting SM retrieval, such as vertical soil-vegetation temperature gradients, are minimized. In some places, however, particularly in India, Eastern USA, Eastern Australia, and the Middle East, descending SMOSL3 retrievals were found to be closer to the reference than the ascending ones. This result could be partly explained by the fact that ascending retrievals over these regions are highly affected by RFI (see Fig. 4.1), which is the main source of errors in the SMOS SSM products [START_REF] Oliva | SMOS Radio Frequency Interference Scenario: Status and Actions Taken to Improve the RFI Environment in the 1400-1427-MHz Passive Band[END_REF]. As the SMOS antenna is tilted forward by 32°, there is an asymmetry in the patterns of RFI contaminations between ascending and descending passes for a given ground location. For instance, when considering ascending overpasses over a given point in the Central Plains in the USA, the SMOS has a trajectory from South to North. And because the antenna is tilted by 32° toward the North, it picks up RFI emission from the Defense Early Warning (DEW) system in Northern Canada (the DEW line can be seen through the lighter blue band around the USA-Canada border in Fig. 4.1).

Conversely, for descending overpasses over the same sites, the tilted antenna is looking in a more southerly direction and is not contaminated by these northern RFI sites. To get a global assessment of the differences between the SSM retrievals for the ascending and descending overpasses, we computed the global averaged value of the RMSD and R coefficient between the SMOSL3 data and the reference; we obtained for ascending: RMSD = 0.18 m 3 /m 3 and R = 0.44 and for descending: RMSD = 0.20 m 3 /m 3 and R = 0.41. Given that better performances were generally found for ascending retrievals, only SMOSL3 ascending overpasses will be considered in the following.

Comparison of the SSM time series over eight selected sites

The time series of the three SSM products (SMOSL3, AMSRM, and DAS2) are compared in Fig. 4.5 for the eight selected sites described in Table 4.2. The SSM time series were spatially averaged over the whole site and normalized to have the same mean and standard deviation using the method given in Eq. (4.4). The eight sites were selected to illustrate the SSM dynamics in the three products for a variety in vegetation, soil, and climatic conditions (see Fig. 4.2). In general, the seasonal dynamics of SSM for the three products were found to be similar. However, over the "tropical humid" site (Fig. 4.5a) the seasonal dynamic of the reference product is better reproduced by the SMOSL3 retrievals. Over this site, it can be seen that the seasonal trend in the AMSRM product is almost opposite to that of the two other products (SMOSL3 and DAS2): increasing trends in AMSRM correspond more or less to decreasing trends in both SMOSL3 and DAS2 and vice versa. Over the same site, it can be seen that there is a large plateau (~ six months from October to April) in the DAS2 values, which cannot be seen for the two other products.

Over the site in India (Fig. 4.5b), a plateau for high values of SSM during the monsoon season can also be seen for DAS2 and not for SMOSL3 and AMSRM, but it is shorter (~ three months) than over the site in the "tropical humid" biome. Also, the transition from wet to dry conditions after the monsoon season is more abrupt for DAS2 than for the remotely sensed SSM values. Over this region, ascending SMOSL3 data are highly impacted by RFI from Northern India and surrounding countries (see Fig. 4.1) but they still reproduce a SSM dynamic, which is in good agreement with the AMSRM and DAS2 datasets.

The site in Central Australia (Fig. 4.5c), is a desert area which has the advantage of being almost free of RFI contaminations at both L-(see Fig. 4.1) and C-bands [START_REF] Njoku | Global Survey and Statistics of Radio-Frequency Interference in AMSR-E Land Observations[END_REF] along with low vegetation and unfrozen conditions in general. In this area, both SMOSL3 and AMSRM were found to be very close to the reference and the very dry conditions were well depicted. There is generally good agreement between all three products in the detection of rain events over this desert area. It should be noted that during the wet season (May, June, July), the declining trend in the SSM time series based on SMOSL3 and DAS2 seems to be slightly steeper than the one retrieved from AMSRM. Also, during rain events, very high values of SSM can be seen for SMOSL3. Such results have already been noted in previous studies and could be explained by water ponding effects when soil is at saturation during intensive rain events [START_REF] Al Bitar | Evaluation of SMOS Soil Moisture Products Over Continental U.S. Using the SCAN/SNOTEL Network[END_REF][START_REF] Jackson | Validation of Soil Moisture and Ocean Salinity (SMOS) Soil Moisture Over Watershed Networks in the U.S. Geoscience and Remote Sensing[END_REF]Wigneron et al., 2012).

Over the two sites in the USA (Fig. 4.5d and e), and in the Sahel (Fig. 4.5f), there is generally good agreement between the three SSM products, but it can be clearly seen that there is a much larger scatter in the remotely sensed products than in the reference one (DAS2). During cold periods in the Great Basin Region in the USA (Fig. 4.5d) very low values can be seen (below 0.1 m 3 /m 3 ). These values can be explained by the effect of soil freezing. In DAS2, the SSM values do not account for the frozen soil water content and its SSM estimates correspond only to the liquid soil water content. These peak values corresponding to "very dry conditions" cannot be seen in SMOSL3 and AMSRM, as frozen soil conditions were flagged and excluded in the remotely sensed products. In the site in Sahel (Fig. 4.4f), there is quite a good agreement between the general seasonal trends of all three SSM products. However, some outliers can be noted for AMSRM, especially when it rains and at the end of the wet season, and the scatter in the SMOSL3 dataset is much larger than that of the two other products.

Finally, results for two sites in wet regions are illustrated in Fig. 4.5g (Central Europe)

and Fig. 4.5h (Argentina). Even if the seasonal trend is relatively low over these two sites (SSM varying between 0.3 and 0.4 m 3 /m 3 ), it can be seen that there is good general agreement between all three products. As was found in some previous figures, very high values in SMOSL3 SSM data can be seen in Fig. 4.5g during some rain events and very low values corresponding to freezing conditions can be seen in Fig. 4.5h for DAS2. In summary, all the three products behaved similarly over the different test sites considered in this study, each product having in some cases some caveats either irregular behavior or adversely affected by RFI effects.

Spatial analysis of SSM retrievals at global scale

To get a more global evaluation of the SMOSL3 and AMSRM products, maps of the calculated statistical indicators (correlation coefficient (R) for both original SSM values and anomalies, RMSD and Bias) described in Section 4.3.2 are shown in Fig. 4.6a-h at global scale. In these maps, SMOSL3 and AMSRM were evaluated against the reference dataset (DAS2) for the period 03/2010-09/2011 and only significant correlations are presented. In this study, we consider that the correlation is statistically significant when the p-value is less than the significance level of 0.05 (p-value < 0.05 meaning that the probability of observing such a correlation value by chance is lower than 5%) as considered in several studies in this field [START_REF] Albergel | Evaluation of remotely sensed and modelled soil moisture products using global ground-based in situ observations[END_REF]. In general, it can be seen that the three products have similar spatial patterns over most of the globe, although there are important differences between them in the amplitude of the temporal SSM variations. Fig. 4.6a and b shows that robust correlations between the global remotely sensed and the reference SSM products (R > 0.5) were found in the transition zones between wet and dry climates (e.g., Sahel), in the Great Plains (USA), Western Europe, Eastern Australia, India, South Africa, and the south-eastern region of Brazil. This can be explained by the strong seasonal annual cycle of SSM in these regions [START_REF] Koster | Regions of Strong Coupling Between Soil Moisture and Precipitation[END_REF].

Conversely, remotely sensed datasets exhibited weak correlations (R < 0.20) against the reference in arid regions (e.g., Sahara) due to the small range of variation in the SSM values, which corresponds roughly to the remotely sensed retrieval accuracy (~ 0.04 m 3 /m 3 ). Low correlations in high latitude regions can also be seen in A similar distribution of RMSD and bias values was found for both SMOSL3 and AMSRM products (Fig. 4.6e-h). Low RMSD and bias values were found in deserts and semiarid regions (e.g., the Sahara, the Arabian Peninsula, extreme South Africa, and Central Australia), while high RMSD and bias values were found in high latitude regions (e.g., in

Northern Canada, Alaska, Northern Europe, and Siberia). Large differences between the remotely sensed and the reference SSM products were also found in tropical regions. In Fig.

4.6g and h, relatively similar patterns can be noted for both SMOSL3 and AMSRM at global

scale but the values of the biases are quite different: a strong overestimation of the reference SSM values can be noted for AMSRM, especially in the high latitude and desert regions, while a strong underestimation can be noted for SMOSL3.

To better identify the spatial differences in the results obtained for SMOSL3 and AMSRM, Fig. 4.7a and b shows the areas where SMOSL3 correlates better with the reference than AMSRM (red), where AMSRM correlates better with the reference than SMOSL3

(green) and where the difference in the correlation coefficient (R) between both SMOSL3 and AMSRM is less than 0.05 (blue). The top panel shows results for the original SSM datasets, while the bottom panel shows results for anomalies, i.e. areas where either SMOSL3 or AMSRM better captured the short-term variability in the reference SSM values. In these maps only significant values are plotted (p-value < 0.05). In general, it can be seen that better correlations with DAS2 were obtained with SMOSL3 over regions with high to moderate vegetation density (e.g., in parts of Amazonia, Eastern Australia and the North-Central US).

These latter regions are known to be little contaminated by RFI effects (see Fig. 4.1). On the other hand, it can be seen that AMSRM shows better correlations with DAS2 than SMOSL3 in areas with low to moderate vegetation density and where there is a strong seasonality in the SSM variability (e.g., India, Western Australia, Sahara, and Arabian Peninsula). Poor results

were also obtained systematically for SMOSL3 in regions known to be strongly contaminated by RFI effects (Middle East, Southern Europe, China, and India).

When looking at anomalies, AMSRM and SMOSL3 have relatively similar performances over dry regions, but better correlations with the reference were obtained for SMOSL3 over most of the grid cells.

Biome influence

To investigate more in depth the dependence of the results shown in with relatively sparse vegetation covers ("Mediterranean warm", "Mediterranean cold", "temperate semi-arid", "tropical semi-arid", etc.), while the poorest results were found in Northern environments ("tundra", "boreal semi-arid", and "boreal humid"). Yet, the results are quite different for the "Tropical humid" biome, where performances of SMOSL3 were more coherent with DAS2 (R = 0.42) compared to the results found for AMSRM (R = 0.15). In Fig. 4.8c, confirming previous results, the poorest performances (corresponding to the largest RMSD values), were obtained again in Northern environments ("tundra", "boreal semi-arid", and "boreal humid") for both SMOSL3 and AMSRM, while the best results

(smallest RMSD values) were obtained in desert regions ("desert temperate", "desert tropical") and in semi-arid regions. As discussed previously, in desert areas, the range in the SSM values simulated in DAS2 is relatively small and this fact partly explains the low values of RMSD computed.

Finally, Fig. 4.8d shows that biases with respect to the reference dataset are opposite for SMOSL3 and AMSRM. In all biomes, AMSRM overestimates SSM DAS2 values while SMOSL3 underestimates them. Moreover, the bias between remotely sensed and reference SSM varies substantially across biomes. The bias is very large in northern environments for both SMOSL3 and AMSRM but it is also large in humid regions ("temperate humid", "tropical humid") for SMOSL3. The lowest biases were found in deserts ("desert temperate", "desert tropical", and "desert cold") and in semi-arid regions ("temperate semi-arid", "Mediterranean warm" and "Mediterranean cold") for both SMOSL3 and AMSRM.

Influence of leaf area index (LAI)

Previous results showed that vegetation plays a key role in the performance results of the SMOSL3 and AMSRM products. To analyze in more detail the effect of vegetation, we computed the distribution of the correlation values as a function of the LAI. We chose to focus our study on the R correlation indicator as correlation is of particular interest for many hydrologic and atmospheric applications [START_REF] Koster | On the Nature of Soil Moisture in Land Surface Models[END_REF]. In [START_REF] Dirmeyer | GSWP 2: Multimodel analysis and implications for our perception of the land surface[END_REF] shown in Fig. 4 (p-value < 0.05) are considered in the analysis.

.3. The percentage value (top of figure) provides the cover fraction (%) over continental surfaces corresponding to each LAI interval. Error bars represent mean ± standard deviation (SD) and only significant correlations

Discussion and conclusions

This study investigated the performances of two remotely sensed SSM products (SMOSL3 and AMSRM) with respect to a reference SSM product (DAS2) at global scale, with 0.25° spatial sampling and a daily time step. The study was made during the whole period of common availability of the SMOS and AMSR-E products, i.e. after the test periods during the commissioning phase of SMOS and before AMSR-E stopped producing data (03/2010-09/2011).

Both AMSRM and SMOSL3 generally showed a good agreement with the reference dataset and successfully captured the seasonal SSM variations present in the reference DAS2 product. For instance, SMOSL3 and AMSRM performed well (in terms of correlation) in the transition zones between wet and dry climates and over semi-arid regions (e.g., Indian subcontinent, Great Plains of North America, Sahel, Eastern Australia, and South-eastern regions of Brazil). It is particularly important that the two remotely sensed SSM products being compared give consistent and correct results in these areas, where SM has been recognized to exert a strong influence on the weather/climate (e.g., Koster et al., 2004a;[START_REF] Taylor | Afternoon rain more likely over drier soils[END_REF][START_REF] Teuling | Contrasting response of European forest and grassland energy exchange to heatwaves[END_REF]. Conversely, both SMOSL3 and AMSRM exhibited weak correlations with the reference data in dry regions (e.g. Sahara, Arabian Peninsula, and Central Australia). These results could be related to the low range of variations in SSM in these regions, which roughly corresponds to the expected retrieval accuracy of the remotely sensed products (~ 0.04 m 3 /m 3 ).

We found quite opposite results in terms of bias for SMOSL3 and AMSRM: over all biomes, AMSRM overestimated SSM compared to the reference, while SMOSL3 underestimated SSM. The analysis of the SSM anomaly time series, obtained by removing the seasonal cycle, showed that the short-term SSM dynamics were better captured by SMOSL3

than by AMSRM at global scale. In addition, considering a variety of biomes, both SMOSL3

and AMSRM showed lowest performances in northern environments ("tundra", "boreal semiarid", and "boreal humid"), while the best performances were found over biomes with relatively sparse vegetation covers ("Mediterranean warm", "Mediterranean cold", "temperate semi-arid", "tropical semi-arid", etc.). In the "tropical humid" biome, SMOSL3 was found to be much better correlated to DAS2 than AMSRM.

The results confirmed that vegetation plays a key role in the performance evaluation of the SMOSL3 and AMSRM SSM products. Over areas with sparse vegetation, with LAI values lower than 1, both SMOSL3 and AMSRM had relatively good and similar performances. However, for higher LAI values, SMOSL3 had a consistent performance, whereas the performance of AMSRM quickly deteriorated with the increase in foliar abundance.

The fact that better performances could be obtained with SMOS (operating at L-band) than with AMSR-E (operating at C-band) over vegetated areas is not surprising. However this study presents one of the first studies confirming this effect with observations from sensors in space. In the passive microwave domain, L-band has long been considered as an optimal frequency to monitor SSM. When a vegetation layer is present over the soil surface, it attenuates the soil emissions and adds its own contribution to the emitted radiation measured by passive microwave radiometers. The retrieval algorithm attempts to decouple the effects of soil and vegetation in order to provide an estimation of SSM. However, as vegetation effects increase with increasing frequency [START_REF] Calvet | Sensitivity of Passive Microwave Observations to Soil Moisture and Vegetation Water Content: L-Band to W-Band[END_REF], the correction for vegetation effects is more complex at C-band (~ 6.6 GHz for AMSR-E) than at L-band (~ 1.4 GHz for SMOS).

Moreover, SMOS has multi-angular capabilities which make it, theoretically, more efficient for decoupling the soil and vegetation effects than mono-angular spatial radiometers such as AMSR-E [START_REF] Wigneron | Two-Dimensional Microwave Interferometer Retrieval Capabilities over Land Surfaces (SMOS Mission)[END_REF]. The combination of both a L-band system and multiangular capabilities for SMOS compared to a C-band system and monoangular capabilities for AMSR-E might explain the better performance of SMOS over biomes with dense vegetation cover (e.g., "tropical humid") in Fig. 4.8a and b or for LAI values larger than 1 in Fig. 4.9a and b. However, it should be noted that AMSRM had comparable performances to SMOSL3

(better performances if we consider the original SSM data and slightly lower performances if we consider anomalies) over sparse vegetation covers (with LAI ≤ 1), which represent more than 50% of the pixels considered in this global study. Future works will address in more depth the possibilities to exploit the complementary capabilities of both SMOS and AMRS-E to retrieve SSM over a gradient of vegetation density and to produce a coherent long term SSM product based on passive microwave sensors.

Some other aspects should be considered in this evaluation. As noted in the Introduction Section, the effective SM sampling depth at L-band (~ 0-3 cm) is larger than at C-band (~ 0-1 cm). Over a shallower soil layer (0-1 cm) SSM is more prone to quick time variations, especially during drying-out periods, due to weather events (rainfall, wind, high insolation, etc.) than over deeper soils. This effect may lead to lower correlations with SSM measurements or retrievals, which are not made at the exact same time or over larger soil sampling depth. Moreover, in the present study, the sampling depth corresponding to the SMOSL3 SSM product (~ 0-3 cm) is closer to that of the reference (0-7 cm for DAS2), than the sampling depth of AMRSM. Therefore, the mismatch between the sampling depths of the different products considered in this study is more detrimental for AMRSM, though it is present for both satellite data sets.

The effect due to the mismatch between the sampling depths of the different products may have an impact in the statistical indicators used in this study but it cannot fully explain the large and contrasting biases found between both the AMRSM and SMOSL3 products and the DAS2 reference. The positive bias in the AMSRM retrievals can be partially explained by the absence of correction in the NASA-VUA algorithm for open water bodies. It can also be instance, [START_REF] Albergel | Evaluation of remotely sensed and modelled soil moisture products using global ground-based in situ observations[END_REF] pointed out some non-realistic representation of SM in ECMWF products in some regions of the world (e.g. the Tibetan plateau), due to shortcomings in the description of soil characteristics, in the pedotransfer functions employed, and the difficulty of representing soil spatial heterogeneity.

Chapter V

5. Global-scale comparison of passive (SMOS) and active (ASCAT) satellite based microwave soil moisture retrievals with soil moisture simulations (MERRA-Land)2

Introduction

Soil moisture is a key variable in land surface and atmospheric systems, and has been identified as one of the "Essential Climate Variables" (Global Climate Observing System, 2010). It plays a fundamental role in the partitioning of precipitation into infiltration and runoff and the partitioning of incoming radiation into sensible and latent heat [START_REF] Daly | A review of soil moisture dynamics: from rainfall infiltration to ecosystem response[END_REF][START_REF] Koster | Regions of Strong Coupling Between Soil Moisture and Precipitation[END_REF][START_REF] Western | Scaling of soil moisture: a hydrologic perspective[END_REF]. Knowledge about global spatialtemporal variability of soil moisture is thus fundamental to improve our understanding of the interactions between the hydrosphere, biosphere, and the atmosphere.

Until now, global-scale studies on this topic were mostly based on modeled data [START_REF] Seneviratne | Land-atmosphere coupling and climate change in Europe[END_REF][START_REF] Taylor | Afternoon rain more likely over drier soils[END_REF]. With the recent advances in global soil moisture retrievals from satellites in the past decade, we are now in the position to study the related processes based on observations. Global surface soil moisture (SSM) datasets have been produced based on active and passive microwave satellite observations, including the Soil Moisture and Ocean Salinity (SMOS) and the Advanced Scatterometer (ASCAT) SSM products (Bartalis et al., 2007a;[START_REF] Kerr | The SMOS Mission: New Tool for Monitoring Key Elements ofthe Global Water Cycle[END_REF][START_REF] Njoku | Soil moisture retrieval from AMSR-E. Geoscience and Remote Sensing[END_REF][START_REF] Owe | Multisensor historical climatology of satellitederived global land surface moisture[END_REF]. See also [START_REF] Kerr | Soil moisture from space: Where are we?[END_REF] and [START_REF] Wagner | Operational readiness of microwave remote sensing of soil moisture for hydrologic applications[END_REF] for a detailed review. SMOS is the first passive satellite specifically designed to measure SSM (and sea surface salinity) on a global scale [START_REF] Kerr | The SMOS Mission: New Tool for Monitoring Key Elements ofthe Global Water Cycle[END_REF][START_REF] Kerr | The SMOS Soil Moisture Retrieval Algorithm[END_REF][START_REF] Walker | One-Dimensional Soil Moisture Profile Retrieval by Assimilation of Near-Surface Measurements: A Simplified Soil Moisture Model and Field Application[END_REF].

Since its launch in November 2009, SMOS has been recording brightness temperatures at L-Band (1.4 GHz) with an average spatial resolution of 43 km. The SMOS SSM products are derived from the multi-angular and full-polarization brightness temperature observations, using multi-orbital retrieval techniques [START_REF] Kerr | The SMOS Soil Moisture Retrieval Algorithm[END_REF]. SMOS SSM is available either in global mode (referred here to as SMOSL3; [START_REF] Jacquette | SMOS CATDS level 3 global products over land[END_REF][START_REF] Kerr | The CATDS SMOS L3 soil moisture retrieval processor, Algorithm Theoretical Baseline Document[END_REF] or in swath mode from the European Space Agency (ESA) at the Data Processing Ground Segment (DPGS) (Level 2) (Kerr et al., 2013a). In this study, we used the SMOS level 3 (SMOSL3) as its projection (EASE grid) and format (NetCdf) simplified considerably the analysis while retaining all the level 2 characteristics. The ASCAT sensor is a C-band scatterometer (5.2 GHz) operating on-board the Metop since 2006. Wagner et al. (1999b) proposed a method to retrieve SSM from ERS-1/2 scatterometer backscatter measurements. Naeimi et al. (2009) later improved it and the method is now referred to as the Vienna University of Technology (TU-Wien) change detection algorithm, which is presently employed for ASCAT data.

Since these global SSM observations are relatively new, they have not yet been sufficiently evaluated and their accuracy is still unknown to some degree. It is therefore important (i) to investigate the consistency of the remote sensing products with independent SSM estimates, such as from land surface modelling, and (ii) to characterize their uncertainties. A better knowledge of the skill and uncertainties of the retrievals will help not only to improve the individual products, but also to optimize the fusion schemes adopted to create multi-sensor products, e.g. the essential climate variable (ECV) soil moisture product generated within ESA's Climate Change Initiative [START_REF] Dorigo | Evaluating global trends (1988-2010) in harmonized multi-satellite surface soil moisture[END_REF][START_REF] Liu | Developing an improved soil moisture dataset by blending passive and active microwave satellite-based retrievals[END_REF]Liu et al., 2012). This merged product has shown large potential for validating land surface models (Albergel et al., 2013a;[START_REF] Loew | Potential and limitations of multidecadal satellite soil moisture observations for selected climate model evaluation studies[END_REF] and studying land-atmosphere-biosphere interactions [START_REF] Barichivich | Temperature and Snow-Mediated Moisture Controls of Summer Photosynthetic Activity in Northern Terrestrial Ecosystems between 1982 and 2011[END_REF][START_REF] Miralles | El Niño-La Niña cycle and recent trends in continental evaporation[END_REF].

To date, the validation of the SMOS and ASCAT SSM products has been focused on different regions of the world, primarily by comparing to in situ observations, which are limited in space and time (e.g., Al Bitar et al., 2012;[START_REF] Albergel | An evaluation of ASCAT surface soil moisture products with in-situ observations in Southwestern France[END_REF][START_REF] Albergel | Evaluation of remotely sensed and modelled soil moisture products using global ground-based in situ observations[END_REF][START_REF] Brocca | ASCAT soil wetness index validation through in situ and modeled soil moisture data in central Italy[END_REF][START_REF] Brocca | Soil moisture estimation through ASCAT and AMSR-E sensors: An intercomparison and validation study across Europe[END_REF][START_REF] Leroux | Estimating SMOS error structure using triple collocation[END_REF][START_REF] Sanchez | Validation of the SMOS L2 Soil Moisture Data in the REMEDHUS Network (Spain)[END_REF][START_REF] Sinclair | A comparison of ASCAT and modelled soil moisture over South Africa, using TOPKAPI in land surface mode[END_REF][START_REF] Su | The Tibetan Plateau observatory of plateau scale soil moisture and soil temperature (Tibet-Obs) for quantifying uncertainties in coarse resolution satellite and model products[END_REF]. A few studies compared microwave based SSM products to model simulations over larger domains (Al-Yaari et al., 2014;[START_REF] Dorigo | Error characterisation of global active and passive microwave soil moisture datasets[END_REF][START_REF] Draper | Estimating root mean square errors in remotely sensed soil moisture over continental scale domains[END_REF][START_REF] Parrens | Comparing soil moisture retrievals from SMOS and ASCAT over France[END_REF], thereby improving the knowledge of errors in the anomalies, unbiased root mean square difference (ubRMSD), and mean bias, (ii) a space-time analysis using Hovmöller diagrams, and (iii) a triple collocation error (TCE) estimation to characterize the spatial distribution of errors in the SMOS and ASCAT retrievals.

The three SSM datasets and the statistical methods used for the evaluation are presented in Section 5.2, results are presented in Section 5.3, and discussion and the main conclusions are presented in Section 5.4.

5.2

Materials and methods

Surface soil moisture datasets

Table 5.1 summarizes the main characteristics of the three SSM datasets (i.e. ASCAT, SMOSL3, and MERRA-Land) considered in this study. ASCAT and SMOSL3 were evaluated with respect to MERRA-Land during the period (05/2010-12/2012).

Table 5 -1 The main characteristics of the ASCAT, SMOS, and MERRA-Land SSM products.

Soil

SMOSL3

The SMOS mission was launched in November 2009 to monitor SSM at a depth of about 3 cm, with an accuracy of at least 0.04 m 3 /m 3 at the global scale, and with a 3-day revisit at the equator [START_REF] Kerr | Soil moisture retrieval from space: the Soil Moisture and Ocean Salinity (SMOS) mission[END_REF][START_REF] Kerr | The SMOS Mission: New Tool for Monitoring Key Elements ofthe Global Water Cycle[END_REF]. SMOS operates at L-band, with ascending overpasses at 06:00 Local Solar Time (LST) and descending overpasses at 18:00 LST [START_REF] Kerr | The SMOS Soil Moisture Retrieval Algorithm[END_REF].

The SMOS level 3 (SMOSL3) SSM products, re-processed global maps of SSM at different temporal resolutions, 1-day, 3-day, 10-day, and monthly, have been recently released by the Centre Aval de Traitement des Données (CATDS; http://catds.ifremer.fr/). The daily SMOSL3 SSM products were used in this study. The main principle of the retrieval algorithm is the same as the one used by ESA for producing the operational level 2 SSM products [START_REF] Kerr | The SMOS Soil Moisture Retrieval Algorithm[END_REF][START_REF] Wigneron | L-band Microwave Emission of the Biosphere (L-MEB) Model: Description and calibration against experimental data sets over crop fields[END_REF], that is, multi-angular observations are used to simultaneously retrieve SSM (directly quantified in m 3 /m 3 ) and the vegetation optical depth at nadir (τ-NAD) based on a standard iterative minimization approach of a cost function [START_REF] Wigneron | Two-Dimensional Microwave Interferometer Retrieval Capabilities over Land Surfaces (SMOS Mission)[END_REF]. SMOSL3 ascending retrievals were selected in this study as they have generally been proven to be more accurate than SMOSL3 descending retrievals (Al-Yaari et al., 2014;[START_REF] Alyaari | Performances of SMOS and AMSR-E soil moisture retrievals against Land Data Assimilation system estimates[END_REF]. The SMOSL3 datasets provide flags that can be used to screen out questionable SSM retrievals [START_REF] Jacquette | SMOS CATDS level 3 global products over land[END_REF][START_REF] Kerr | The CATDS SMOS L3 soil moisture retrieval processor, Algorithm Theoretical Baseline Document[END_REF], in particular because of radio-frequency interferences (see Section 5.2.2 for more details).

It should be noted that, in the present study, we used the latest version available at CATDS. In the near future, new versions of the SMOSL3 products will be produced based on re-processing activities.

ASCAT

ASCAT is a real-aperture radar instrument that operates at C-band (5.255 GHz) onboard the Metop satellite since 2006, which crosses the equator at 21:30 LST for the ascending overpass and at 09:30 LST for the descending overpass.

In this study, we used SSM products generated with the WARP5.5 software provided by TU-Wien, which is the latest version of the algorithm used to produce this SSM dataset. As for SMOSL3, we only considered here morning overpasses, as previous findings indicated that the ascending ASCAT overpass retrievals are less accurate than the descending (i.e., morning)

ones (e.g., [START_REF] Brocca | ASCAT soil wetness index validation through in situ and modeled soil moisture data in central Italy[END_REF].

ASCAT SSM data are provided in terms of degree of saturation, that is, in relative units ranging between 0 (dry) and 100 (saturated). These extremes correspond, respectively, to the lowest and highest values of the observed backscatter over the first few centimeters of soil (< 3 cm). As the two other SSM products (SMOSL3 and MERRA-Land) used in this study are expressed in volumetric units, the ASCAT SSM index was converted to volumetric units (m 3 /m 3 ).

Multiplying the degree of saturation by the soil porosity (expressed in m 3 /m 3 ) gives a direct estimate of the volumetric SSM content in m 3 /m 3 . The value of the soil porosity was estimated from global soil texture and hydraulic soil properties derived, as described by [START_REF] Balsamo | A revised hydrology for the ECMWF model: Verification from field site to terrestrial water storage and impact in the ECMWF-IFS[END_REF], from the Food and Agriculture Organization digital (FAO) soil map (FAO, 2003;[START_REF] Su | The Tibetan Plateau observatory of plateau scale soil moisture and soil temperature (Tibet-Obs) for quantifying uncertainties in coarse resolution satellite and model products[END_REF]. The porosity map was provided at a resolution of 5′ × 5′ and it was interpolated to 25 km, which is consistent with the ASCAT soil moisture resolution. In the ASCAT product, several flags are provided along with the SSM values, including a noise value (ERR) quantifying the uncertainty associated with the retrieved SSM value and a flag associated with the wetland fraction or to the topographic complexity. Readers are directed to Wagner et al. (1999)and [START_REF] Naeimi | An Improved Soil Moisture Retrieval Algorithm for ERS and METOP Scatterometer Observations[END_REF] for more details on the TU-Wien algorithm and to [START_REF] Wagner | The ASCAT Soil Moisture Product: A Review of its Specifications, Validation Results, and Emerging Applications[END_REF] for a full review on the ASCAT SSM Product.

MERRA-Land

The Modern-Era Retrospective analysis for Research and Applications (MERRA) is a global atmospheric reanalysis data product that integrates information from a broad variety of in situ and remote sensing observations of the atmosphere [START_REF] Rienecker | MERRA: NASA's Modern-Era Retrospective Analysis for Research and Applications[END_REF]. MERRA-Land is a supplemental data product of land surface hydrological fields [START_REF] Reichle | Assessment and Enhancement of MERRA Land Surface Hydrology Estimates[END_REF].

The MERRA-Land product is a land-only, off-line, replay of a revised version of the MERRA land model component that benefits from (i) corrections to the precipitation forcing based on merging a gauge-based data product from the NOAA Climate Prediction Centre with MERRA precipitation and (ii) updated parameter values in the rainfall interception model.

These changes correct known limitations in the MERRA surface meteorological forcing and yield improved estimates of land surface conditions [START_REF] Reichle | Assessment and Enhancement of MERRA Land Surface Hydrology Estimates[END_REF][START_REF] Reichle | The MERRA-Land Data Product[END_REF].

MERRA-Land SSM is associated with the 0-2 cm (topmost) soil layer and is available hourly at a spatial resolution of 2/3° longitude by 1/2° latitude. The MERRA-land SSM simulations at 6 am and 9 am were averaged and considered as a reference for both SMOS and ASCAT.

We used the gridded SSM product expressed in volumetric units (m 3 /m 3 ).

Pre-processing

Prior to the evaluation, SMOSL3 and ASCAT were filtered based on associated quality flags. Several values are associated with the ASCAT SSM retrievals, as described by [START_REF] Naeimi | An Improved Soil Moisture Retrieval Algorithm for ERS and METOP Scatterometer Observations[END_REF]: a noise error (ERR), which is based on Gaussian error propagation and which is related to the sensor characteristics and incidence angle uncertainty, an estimated standard deviation of the backscatter signal, etc. The ASCAT data were screened out to remove observations with a noise error (ERR) greater than 14% [START_REF] Draper | Assimilation of passive and active microwave soil moisture retrievals[END_REF]. The SMOSL3 product provides a Data Quality indeX (DQX) and a probability of radio frequency interference (RFI). The DQX values, which are provided in volumetric SSM units, quantify the error in the SSM retrieval and the brightness temperature measurement accuracy. RFI originates, for example, from satellite transmissions, aircraft communications, radar, or TV radio-links and contaminates the passive microwave emissions from Earth [START_REF] Njoku | Global Survey and Statistics of Radio-Frequency Interference in AMSR-E Land Observations[END_REF][START_REF] Oliva | SMOS Radio Frequency Interference Scenario: Status and Actions Taken to Improve the RFI Environment in the 1400-1427-MHz Passive Band[END_REF]. ASCAT, SMOSL3, and the reference MERRA-Land dataset are distributed on different grids and formats. In this study, a nearest neighbor approach (e.g., [START_REF] Draper | Assimilation of ASCAT near-surface soil moisture into the SIM hydrological model over France[END_REF][START_REF] Rüdiger | An Intercomparison of ERS-Scat and AMSR-E Soil Moisture Observations with Model Simulations over France[END_REF] was used to re-project all the datasets onto a regular 0.25° × 0.25° grid. Finally, all the three SSM datasets were screened, applying additional static masks, to remove grid cells with (i) steep mountainous terrain, based on a topographic complexity flag (provided with the ASCAT data) greater than 10% [START_REF] Draper | Assimilation of passive and active microwave soil moisture retrievals[END_REF], (ii) open water, identified as having a wetland fraction (provided with the ASCAT data) greater than 5%, and

(iii) frozen soil conditions, identified as having soil temperatures (top layer) below 276 K, obtained from MERRA-Land.

It should be noted that all the statistical indicators were computed only when all the three SSM data were available from the different datasets and therefore the number of ASCAT and SMOSL3 SSM data used in the time series are identical, which is illustrated in Fig. 5.2.

Comparison using classical metrics

Three classical metrics were calculated between pairs of the remotely sensed (SSM RS )

and reference SSM products(SSM REF ): (i) Pearson correlation coefficient (R), (ii) bias, and

(iii) unbiased root mean squared difference (ubRMSD). The equations for the calculation of the three indicators are given as follows [START_REF] Albergel | Evaluation of remotely sensed and modelled soil moisture products using global ground-based in situ observations[END_REF][START_REF] Brocca | Soil moisture estimation through ASCAT and AMSR-E sensors: An intercomparison and validation study across Europe[END_REF][START_REF] Cecr | Comprehensive Error Characterisation Report[END_REF]:

𝑅𝑅 = ∑ (SSM REF(i) -SSM REF )(SSM RS(i) -SSM RS ) 𝑑𝑑 𝑠𝑠=1 � ∑ (SSM REF(i) -SSM REF ) 2 ∑ (SSM RS(i) -SSM RS ) 2 𝑑𝑑 𝑠𝑠=1 𝑑𝑑 𝑠𝑠=1 5 -1 Bias = (SSM RS -SSM REF ) 5 -2 RMSD = � (SSM RS -SSM REF ) 2 5 -3 unRMSD = � RMSD 2 -Bias 2 5 -4
where n is the number of SSM data pairs, the overbar represents the mean operator, SSM REF is the reference SSM (MERRA-Land), and SSM RS is the satellite-based SSM product (SMOSL3 or ASCAT). We use the term ubRMSD rather than ubRMSE (root mean squared error) since the MERRA-Land SSM values also contain errors and cannot be considered as the "true" SSM values [START_REF] Entekhabi | The Soil Moisture Active Passive (SMAP) Mission[END_REF].

All the above statistical indicators were computed for the original SSM values, expressed in volumetric units (m 3 /m 3 ), and for SSM monthly anomalies for the correlation indicators only. The anomaly time-series are designed to assess the impact of seasonal effects that can unrealistically increase the degree of correlation between two time series [START_REF] Scipal | Assimilation of a ERS scatterometer derived soil moisture index in the ECMWF numerical weather prediction system[END_REF] and to explore the ability of the ASCAT/SMOSL3 SSM products to capture the short-term variability in the SSM time series. Following [START_REF] Albergel | An evaluation of ASCAT surface soil moisture products with in-situ observations in Southwestern France[END_REF], the anomalies SSM anom (t) were calculated as the difference from the mean for a sliding window of 5 weeks, the difference was further scaled to the standard deviation:

SSM anom (t) = SSM or (t) -SSM or (t -17 ∶ t + 17) σ[SSM or (t -17: t + 17)] 5 -5
where the overbar and σ symbols denote the temporal mean and standard deviation operators, respectively, SSM or (t)is the original remotely sensed/reference SSM value at time t; for a sliding window of 5 weeks corresponding to the time interval [t -17 days, t + 17 days].

Global maps of R (original and monthly anomaly), ubRMSD, and bias were calculated for all common pixels on a daily basis between the reference and the SMOSL3 and ASCAT SSM time series. To investigate the effects of the vegetation and to simplify the interpretation of the correlation maps (original and anomalies), the metrics were also averaged according to the long-term mean leaf area index (LAI) values obtained from the Global Soil Wetness Project [START_REF] Dirmeyer | GSWP 2: Multimodel analysis and implications for our perception of the land surface[END_REF], displayed in Fig. 5.3.

Fig. 5 -3

Global distribution of the long term mean leaf area index (LAI) [START_REF] Dirmeyer | GSWP 2: Multimodel analysis and implications for our perception of the land surface[END_REF].

Comparison using Hovmöller diagrams (space-time distribution)

A Hovmöller diagram (HD) is a two-dimensional plot that shows the time-latitude variations of a longitudinally averaged variable [START_REF] Hovmöller | The Trough-and-Ridge diagram[END_REF]. Here, we used the HD method to compare the spatio-temporal patterns of SSM for SMOS, ASCAT and MERRA-Land at the global scale. The diagrams helped us to investigate the consistency and differences between the three SSM products.

Comparison using triple collocation error model

The triple collocation error model (TCE) is a powerful statistical tool to estimate the RMSD of a set of at least three linearly related data sources with uncorrelated errors. [START_REF] Stoffelen | Toward the true near-surface wind speed: Error modeling and calibration using triple collocation[END_REF] introduced the TCE model to evaluate wind vector datasets derived from a model, buoy measurements and scatterometer observations. [START_REF] Scipal | Assimilation of a ERS scatterometer derived soil moisture index in the ECMWF numerical weather prediction system[END_REF] later used the TCE to evaluate SSM datasets derived from models and satellites. Then, other where < > is the long-term mean, and the square root of the estimated ε i 2* are the triple collocation errors estimates.

The above derivation, and hence the validity of the TCE analysis, is based on the assumptions that the errors ε i of the three datasets are uncorrelated, and that the three datasets can be linearly modeled as in Eqs. (5.6), (5.7) and (5.8) [START_REF] Dorigo | Error characterisation of global active and passive microwave soil moisture datasets[END_REF][START_REF] Janssen | Error Estimation of Buoy, Satellite, and Model Wave Height Data[END_REF][START_REF] Scipal | Triple collocation -A new tool to determine the error structure of global soil moisture products[END_REF]. Because the three datasets are largely independent, TCE can be expected to perform well, but any residual error cross-correlations among the datasets would result in biased error estimates [START_REF] Yilmaz | The Optimality of Potential Rescaling Approaches in Land Data Assimilation[END_REF]. Finally, to obtain statistically reliable results we restricted our analysis to grid cells where at least 100 observations were available from each dataset.

Results

Spatial Analysis of SSM retrievals at the global scale

Fig. 5.4 shows global maps of the time series correlation coefficient R for original SSM values and monthly anomalies (with only significant correlations, i.e., p < 0.05), the ubRMSD, and the bias (Section 5.2.3). In these maps, SMOSL3 (right panels) and ASCAT (left panels) were evaluated against the MERRA-Land reference dataset at each pixel over the 05/2010-12/2012 period.

In general, the metrics for SMOSL3 and ASCAT show a similar spatial correspondence with the MERRA-Land SSM over most of the globe. Fig. 5.4a and b shows that strong correlations (R is generally greater than ~ 0.5) between the global remotely sensed and the reference SSM products are found in the transition zones between wet and dry climates (e.g., Sahel), in the Great Plains (USA), western Europe, Australia, India, Time series correlation values (R) computed for seasonal anomalies, as described in Section 5.2.3, are shown in Fig. 5.4c and d. The global spatial patterns are again relatively similar for both SMOSL3 and ASCAT, with a slightly better ability of SMOSL3 to capture the short-term SSM variability of the reference than ASCAT in Central America and Australia, while ASCAT was found to be slightly better in Europe, India, and parts of China.

For both datasets, rather high correlation values (R > 0.5) with the reference were found in eastern Australia, southern South Africa, Western Europe, and Central America, whereas low values were found in the northern Arabian Peninsula, North Africa, and tundra regions. Due to the model-specific nature of the long-term mean values of soil moisture [START_REF] Koster | On the Nature of Soil Moisture in Land Surface Models[END_REF], large mean differences (biases) between the remotely sensed and the reference SSM products can be expected. Furthermore, bias may be caused by a wrong estimation of SSM when the satellite footprint includes small water bodies, as was found by [START_REF] Bartsch | Soil Moisture from Metop ASCAT Data at High Latitudes[END_REF][START_REF] Gouttevin | A comparison between remotelysensed and modelled surface soil moisture (and frozen status) at high latitudes[END_REF][START_REF] Kerr | The SMOS Soil Moisture Retrieval Algorithm[END_REF]. In Fig. 5.4g and h, relatively similar bias patterns can be noted for both SMOSL3 and ASCAT at global scale. However, the values of the biases are quite different: in comparison with the MERRA-Land SSM values, higher SSM values can be noted for ASCAT, especially in the boreal regions, whereas lower SSM values can be noted for SMOSL3. The positive bias, found mainly at high latitude regions, in the ASCAT retrievals which is associated to wetter months (i.e. summer periods) can be partially explained by errors in the FAO database used to convert the ASCAT degree of saturation to volumetric water content where values for a few pixels in the northern hemisphere exceed 0.6 m 3 /m 3 . Fig. 5.5a and b compares the areas where SMOSL3 correlates better with the reference than ASCAT (red), and where ASCAT correlates better with the reference than SMOSL3 (green). Looking at original datasets, it can be seen that better correlations with MERRA-Land were obtained with ASCAT over regions with high to moderate vegetation density and in regions where there is a strong seasonality in the SSM variability (e.g., India, Eastern

Australia and the North-Central US, locations near the equator). On the other hand, SMOSL3

shows better correlations with MERRA-Land than ASCAT in areas with low to moderate vegetation density (e.g., Western Australia, Sahara, and North America). The latter regions are known to be slightly contaminated by RFI effects (see Fig. 5.1).

When looking at monthly anomalies (Fig. 5.5b), ASCAT shows higher correlations with the reference than with SMOSL3 over regions such as Central Europe, China and India, which are known to be highly contaminated by RFI effects (see Fig. 5.1). With the exception of these regions, SMOSL3 exhibits higher correlations with the reference over most of the grid cells.

Influence of leaf area index (LAI)

To analyze the effect of vegetation, we computed the average correlation coefficient as a function of the global long term mean LAI, using values of the Global Soil Wetness Project [START_REF] Dirmeyer | GSWP 2: Multimodel analysis and implications for our perception of the land surface[END_REF]. Note that the MERRA-Land simulations use the monthly LAI climatology from the Global Soil Wetness Project 2 (GSWP-2). The results for both the original SSM data (Fig. 5.6a) and the anomalies (Fig. 5.6b) show that the consistency of the remotely sensed SSM products with the reference (MERRA-Land) is strongly related to LAI.

In Fig. 5.6a, it can be seen that the values of R increase almost linearly with LAI for ASCAT, from R ≈ 0.18 to R ≈ 0.55 as LAI increases from about 1 to 7. For SMOSL3, on the other hand, R values remain relatively constant as LAI increases, with values between ~ 0.32 and 0.44. A decrease in R can be noted for SMOSL3 when LAI is higher than ~ 4, leading to higher correlation values to the reference with ASCAT, but this corresponds to a very low fraction of the total number of pixels considered here (less than 5%, after screening for uncertain retrievals). In contrast, SMOSL3 provides higher correlation values with the reference than ASCAT when LAI is lower than 1 (i.e. over sparse vegetation covers), which corresponds to almost 50% of the pixels considered in this global analysis, and similar correlation coefficients R are obtained for SMOSL3 and ASCAT for intermediate LAI values

(1 ≤ LAI ≤ 3).

In Fig. 5.6b, the same analysis is shown for monthly anomalies. As noted above, they exhibit lower correlations to the reference data (R ≈ 0.25) than the original data, for both SMOSL3 and ASCAT anomalies. The correlation differences between the two remotely sensed products are also much weaker than in Fig. 5.6a, even if SMOSL3/ASCAT remains better correlated to MERRA-Land for lower/higher values of the LAI.

Hovmöller diagrams

SSM strongly varies spatially and temporally, and this variability depends mainly on latitude and season [START_REF] Schlosser | A Model-Based Investigation of Soil Moisture Predictability and Associated Climate Predictability[END_REF]. It is therefore important to analyze the capability of both ASCAT and SMOSL3 to detect time evolution and spatial patterns of SSM simultaneously. To this end, we used Hovmöller diagrams to illustrate the seasonal variations of SSM for SMOSL3 and ASCAT. The time evolution of the SSM for SMOSL3, ASCAT, and MERRA-Land, averaged along the longitude range by latitude bands, is displayed in Fig. 5.7. Note that, for SMOSL3, many regions of Europe and Russia are screened out due to RFI contaminations (see Fig. 5.1), and so the values in the Northern Hemisphere are dominated by estimates from North America. Note also that frozen conditions were excluded from the analysis (see Section 5.2.2), so there is no-data at latitudes above 55°N in the winter time. The main difference between the three HDs is a difference in mean, with higher SSMs according to MERRA-Land. This is consistent with the negative biases of the remotely sensed frozen and very dry soil conditions as the real part of the permittivity for both conditions are very close (values of permittivity ~ 5; [START_REF] Wigneron | L-band Microwave Emission of the Biosphere (L-MEB) Model: Description and calibration against experimental data sets over crop fields[END_REF]. So, it is likely that frozen soil conditions were not correctly flagged and excluded in the SMOSL3 products, and that the screening based on MERRA-Land soil temperatures may not be sufficient. For the same reasons, unrealistically drier winter-time SSM conditions were also retrieved by ASCAT in the same northern regions, albeit to a lower extent than for SMOS, with SSM values close to 0.2 m 3 /m 3 . Conversely, MERRA-Land SSM includes both liquid and frozen water and therefore shows a more realistic increase in SSM during the winter. These results show that correctly detecting and screening frost and snow is still a big challenge.

Triple collocation error model

Global error maps for the remotely sensed SSM long-term anomalies (excluding the effect of the biases) are derived using the TCE method over the 2010-2012 period. As shown in Fig. 5.8a and b, the error estimates for both products are lowest in arid regions (e.g., Arabian Peninsula, Central Australia, and Egypt) due to low amounts of precipitation received leading to a low temporal variability of SSM in these regions. Higher TCE errors were found for both SMOSL3 and ASCAT over India and over locations near the Equator (e.g., South Sudan, Zambia) where MERRA-Land is much less reliable due to the paucity of precipitation gauges, particularly over most of the African continent.

Relatively high errors were obtained for ASCAT in some arid regions (e.g., Algeria, Libya, and Iran) which is a well-known phenomenon already noted in the previous Sections

(5.3.1 and 5.3.2). Fig. 5.9 shows the areas where SMOSL3 provided lower errors than ASCAT (red), where ASCAT provided lower errors than SMOSL3 (green). Note that the absolute magnitude of the estimated error depends on the TCE reference. In general, it can be seen that lowest errors were obtained with ASCAT over regions with high to moderate vegetation density, and in regions where there is a strong seasonality in the SSM variability (e.g., India, in parts of Amazonia, Central Europe, Eastern Australia and the North-Eastern USA). On the other hand lower errors were obtained with SMOSL3 in areas with low to moderate vegetation density (e.g., Western Australia, Sahara, and western US, Central Asia), confirming the results shown in the previous Section about the sensitivity to the vegetation effects. The analysis of the original data shows, in general, a good correspondence between the SMOSL3 and ASCAT derived SSM products with the MERRA-Land reference. For instance, SMOSL3 and ASCAT successfully captured the spatio-temporal dynamics of the MERRA-Land SSM product, as seen in the correlation analyses, in the transition zones between wet and dry climates (e.g., Great Plains of North America, Sahel), Eastern Australia, and South-eastern regions of Brazil. It is worth noting that the regions of good agreement between SMOSL3, ASCAT, and MERRA-Land are also regions of strong coupling between soil moisture and precipitation as demonstrated by [START_REF] Koster | Regions of Strong Coupling Between Soil Moisture and Precipitation[END_REF].

SMOSL3 and ASCAT exhibited weak correlations with the MERRA-Land reference data in tundra and arid regions (e.g., Sahara, Arabian Peninsula, and Central Australia).

ASCAT even exhibited negative correlations over some of the dry deserts (e.g., Sahara).

These low correlations may be explained by the small range of variation in the SSM values in these dry regions which corresponds roughly to the remotely sensed retrieval accuracy (~ 0.04 m 3 /m 3 , [START_REF] Kerr | Soil moisture retrieval from space: the Soil Moisture and Ocean Salinity (SMOS) mission[END_REF]. Issues with the ASCAT SSM retrievals in dry regions may be explained by (i) systematic errors in the retrieval algorithm due to different scattering mechanisms in dry soils [START_REF] Wagner | The ASCAT Soil Moisture Product: A Review of its Specifications, Validation Results, and Emerging Applications[END_REF] and (ii) changes in small-scale surface roughness, produced by wind-blown sand [START_REF] Frison | Monitoring global vegetation dynamics with ERS-1 wind scatterometer data[END_REF]. Anomaly time series correlations show, in general, similar spatial patterns compared to the correlations found using original datasets, but with lower R values, especially in the transition zones.

The global scale analysis of the bias and ubRMSD also confirmed these results.

However, opposite patterns were generally obtained in terms of bias: ASCAT is generally wetter than MERRA-Land (positive bias), while SMOSL3 is generally drier than MERRA-Land (negative bias).

Additional insights were provided by the Hovmöller diagrams, which visualize the time changes in SSM as a function of latitude. It is found that even though strong correlations are found between all three products at global scale, the spatio-temporal patterns shown in the HD may be quite different for SMOSL3, ASCAT and MERRA-Land in some latitudinal bands. For instance, SMOSL3 presents consistently dry SSM conditions (less than ~ 0.10 m 3 /m 3 ) at mid latitudes (between 10°N and 30°N). This could be partly explained by the impact of RFI as high RFI values increase the SMOS observed brightness temperatures (TB) resulting in lower SSM retrievals [START_REF] Oliva | SMOS Radio Frequency Interference Scenario: Status and Actions Taken to Improve the RFI Environment in the 1400-1427-MHz Passive Band[END_REF]. [START_REF] Wigneron | First evaluation of the simultaneous SMOS and ELBARA-II observations in the Mediterranean region[END_REF] have interpreted the bias as an effect of the underestimation of the default contribution to TB of the forested areas in mixed pixels.

Finally, results from the TCE method generally confirmed the above results and the spatial error patterns were found to be consistent with known performance issues of SMOS and ASCAT (Leroux et al., 2013a). In particular, larger errors were found for SMOSL3 in the presence of moderate to dense vegetation in tropical and temperate regions and in regions known to be highly contaminated by RFI effects (Western Europe, India, Southern Asia).

Higher errors were found for ASCAT over arid regions (North Africa, Central Australia, and Central Asia). Our findings are generally in agreement with the results obtained by previous studies analyzing spatial errors of ASCAT over 2007-2008(e.g., Dorigo et al., 2010) and SMOS over 2010 [START_REF] Leroux | Estimating SMOS error structure using triple collocation[END_REF], using products based on earlier versions of the retrieval algorithms.

A more in-depth analysis, using LAI as a parameter to quantify the vegetation effects, revealed higher R values for SMOSL3 than for ASCAT when LAI is less than 1 (which corresponds to almost 50% of the pixels considered in this study), similar R values for both products for intermediate LAI values between 1 and 3, and higher R values for ASCAT than for SMOS when LAI exceeds 3. This implies that vegetation plays a key role in the performance of the SMOSL3 and ASCAT SSM products, and that the two products have different sensitivities to vegetation. Generally, SMOS is more efficient at monitoring SSM than ASCAT over sparse vegetation, whereas ASCAT is more efficient over relatively dense vegetation (LAI > 3).

Discussion

These results may appear as surprising because microwave sensors should be more efficient to sense through moderate vegetation at L-band than at C-band (Al-Yaari et al., 2014): with increasing frequency (i) scattering and attenuation effects by vegetation elements (leaves, stems, trunks, branches, fruits, etc.) increase and (ii) the sampling depth in soil decreases. However, in this study, SMOS and ASCAT differ not only in terms of frequency but also in terms of microwave technology: SMOS is a radiometer (i.e. a passive microwave system), while ASCAT is a scatterometer (i.e. an active microwave system). Previous studies comparing SSM retrievals from radiometer and scatterometer systems [START_REF] Brocca | Soil moisture estimation through ASCAT and AMSR-E sensors: An intercomparison and validation study across Europe[END_REF][START_REF] Rüdiger | An Intercomparison of ERS-Scat and AMSR-E Soil Moisture Observations with Model Simulations over France[END_REF]) also found that SSM products retrieved from scatterometer data were less impacted by vegetation than those retrieved from radiometers data.

There are different ways of interpreting these results. First, the good performances of ASCAT over vegetation canopies could be due to higher-order surface-vegetation interaction effects [START_REF] Crow | The Impact of Radar Incidence Angle on Soil-Moisture-Retrieval Skill[END_REF], such as double bounce reflection [START_REF] Karam | A microwave polarimetric scattering model for forest canopies based on vector radiative transfer theory[END_REF] that may increase the sensitivity of active systems to SSM in comparison to passive systems. These higher-order effects are often neglected in the current models used for SSM retrievals from both active and passive systems. However, these interaction effects may become extremely important under some conditions and may, to a large extent, explain the sensitivity of ASCAT to soil moisture over vegetated regions even at high incidence angles [START_REF] Crow | The Impact of Radar Incidence Angle on Soil-Moisture-Retrieval Skill[END_REF].

Second, the scatterometer systems have been also found to be very sensitive to the seasonal vegetation dynamics. For instance, early studies which investigated signatures from ERS backscatter coefficients based on averaged observations on a monthly basis have shown that the time variations in the measured backscatter coefficient were in good agreement with the vegetation dynamics as monitored by optical vegetation indices [START_REF] Frison | Monitoring global vegetation dynamics with ERS-1 wind scatterometer data[END_REF].

It should be noted that, for some specific conditions, the increase in vegetation effects and the increase in SSM both lead to an increase in the backscatter coefficient (Wigneron et al., 1999a;Wigneron et al., 1999b), which may make the decoupling of the two effects difficult using an active system such as ASCAT. So, it is difficult to appreciate whether ASCAT is really monitoring the time variations in SSM or in the vegetation in regions where there is a natural high correlation between the vegetation dynamics and the increase in the SSM values.

The hypothesis that ASCAT may have difficulties in decoupling vegetation and SSM effects at the seasonal scale may be used to interpret the fact that the performances of ASCAT become closer to those of SMOSL3 for LAI > 3 when anomalies (taking off seasonal effects)

were used (Fig. 5.6a and b).

However, many results can be raised to contradict this hypothesis. For instance, in many climate regions (Mediterranean Climate regions for instance) where soil moisture and vegetation may be out of phase, ASCAT performed quite well. Moreover, the increase in vegetation density often leads to an increase in backscatter, but the opposite may also happen, depending on the soil moisture conditions. Eventually, considering anomalies, the performances of SMOS and ASCAT were very close (ASCAT slightly better) in terms of correlation values for LAI > 1. This latter result confirms the very good ability of active systems such as ASCAT in monitoring SSM over well-developed vegetation.

It is also important to keep in mind that MERRA-Land, although found to be very reliable in several instances (Albergel et al., 2013b;[START_REF] Yi | Evaluation of MERRA Land Surface Estimates in Preparation for the Soil Moisture Active Passive Mission[END_REF], cannot be considered to be "ground truth" (Albergel et al., 2013a). Consequently, the interpretation of the results depends on the accuracy of the MERRA-Land product itself. The skill of MERRA-Land soil moisture strongly depends on the accuracy of the precipitation forcing, which is derived by merging the MERRA reanalysis precipitation with measurements from a global network of gauges. The density of the gauge network varies tremendously, with good coverage in North America, Europe and many parts of Asia and South America. However, the gauge density is very sparse in Africa and at high latitudes. In these regions in particular, a lack of consistency between the remote sensing products and MERRA-Land SSM does not necessarily imply poor performance by the remote sensing estimates. Other factors that determine the skill of MERRA-Land soil moisture include the radiation forcing as well as the land model physics and associated model parameters, whose quality is similarly variable across the globe.

Looking ahead, improvements in the retrieval algorithms as well as in the LSM data can be expected. For the SMOSL3 product, this includes enhancements especially in terms of RFI filtering and dry bias correction. For ASCAT, the issues found over arid regions are currently under investigation. Finally, the next version of the MERRA reanalysis is currently in production and features improved precipitation forcing, the single most critical input to SSM estimates from models.

The results of the present study revealed that both the SMOSL3 and the ASCAT SSM Chapter VI 6. Testing simple regression equations to derive long-term global soil moisture datasets from satellite-based brightness temperature observations3

Introduction

Soil moisture (SM) is one of the key variables in the environment and the climate system as it influences the exchange of heat and water between the land surface and atmospheric processes [START_REF] Hupet | Intraseasonal dynamics of soil moisture variability within a small agricultural maize cropped field[END_REF][START_REF] Western | Spatial correlation of soil moisture in small catchments and its relationship to dominant spatial hydrological processes[END_REF]Wigneron et al., 1999a). In 2008, SM was recognized as an Essential Climate Variable (ECV) which is considered essential for IPCC (Intergovernmental Panel on Climate Change) requirements [START_REF] Wagner | Fusion of Active and Passive Microwave Observations to Create an Essential Climate Variable Data Record on Soil Moisture[END_REF]. Complete and consistent record of SM, as an ECV, is required for hydrological applications, flood prediction, drought monitoring, climate forecasts, etc.

Active and passive microwave sensors offer the opportunity to retrieve surface SM (SSM) information from their surface backscatter and brightness temperatures (TB) signals, respectively, which are mainly determined by the soil dielectric constant [START_REF] Njoku | Observations of soil moisture using a passive and active lowfrequency microwave airborne sensor during SGP99[END_REF][START_REF] Ulaby | Radar mapping of surface soil moisture[END_REF]. Active and passive microwave remote sensing particularly at low frequencies have been shown to provide useful SSM retrievals (Bartalis et al., 2007a;Kerr et al., 2001;[START_REF] Njoku | Soil moisture retrieval from AMSR-E. Geoscience and Remote Sensing[END_REF] with large spatial coverage and high temporal resolution and, hence, to be suitable for SSM monitoring at the global scale [START_REF] Griend | Microwave vegetation optical depth and inverse modelling of soil emissivity using Nimbus/SMMR satellite observations[END_REF][START_REF] Owe | A methodology for surface soil moisture and vegetation optical depth retrieval using the microwave polarization difference index[END_REF][START_REF] Wigneron | A simple algorithm to retrieve soil moisture and vegetation biomass using passive microwave measurements over crop fields[END_REF][START_REF] Wigneron | Use of passive microwave remote sensing to monitor soil moisture[END_REF][START_REF] Wigneron | Two-Dimensional Microwave Interferometer Retrieval Capabilities over Land Surfaces (SMOS Mission)[END_REF]. Nevertheless, these microwave sensors provide individually inconsistent SSM datasets. Therefore, the ESA's Programme on Global Monitoring of ECV known as the Climate Change Initiative (CCI), and the European Space Agency's Water Cycle Multi-mission Observation Strategy (WACMOS) [START_REF] Su | Earth observation Water Cycle Multi-Mission Observation Strategy (WACMOS)[END_REF], merged the different observations acquired by several microwave sensors in an attempt to produce the most complete and consistent long-term time series of SSM (1978SSM ( -2010) ) (http://www.esa-cci.org/) [START_REF] Liu | Trend-preserving blending of passive and active microwave soil moisture retrievals[END_REF]. These include the Scanning Multichannel Microwave Radiometer (SMMR; 6.6, 10.7 , 18.0 21, and 37 GHz channels; [START_REF] Wang | Effect of vegetation on soil moisture sensing observed from orbiting microwave radiometers[END_REF]), the Special Sensor Microwave Imager (SSM/I; 19.4, 22.2, 37.0, and 85.0 GHz channels) of the Defense Meteorological Satellite Program, the Advanced Microwave Scanning Radiometer on Earth Observing System (AMSR-E; from 6.9 to 89.0 GHz; [START_REF] Njoku | Retrieval of land surface parameters using passive microwave measurements at 6-18 GHz[END_REF]), and the Advanced Scatterometer (ASCAT) data [START_REF] Liu | Developing an improved soil moisture dataset by blending passive and active microwave satellite-based retrievals[END_REF].

This product has been available since June 2012 and has been of interest for researchers to study the long-term trends of SSM (Albergel et al., 2013b;[START_REF] Seneviratne | Investigating soil moisture-climate interactions in a changing climate: A review[END_REF].

The second phase of the upcoming CCI project aims at including a new innovation in space technology, namely the SMOS (Soil Moisture and Ocean Salinity) SSM datasets, in the long term CCI SSM datasets. The SMOS satellite, launched in November 2009, is the firstever satellite specifically dedicated to monitoring SSM with an accuracy of 0.04 m 3 /m 3 from space over the continental surfaces [START_REF] Kerr | The SMOS Mission: New Tool for Monitoring Key Elements ofthe Global Water Cycle[END_REF][START_REF] Kerr | The SMOS Soil Moisture Retrieval Algorithm[END_REF]. SMOS at L-band has been providing multi-angular microwave TB observations [START_REF] Kerr | The SMOS Soil Moisture Retrieval Algorithm[END_REF] since 2010.

Consequently, there is no prior record of SSM from SMOS. SSM is retrieved from the SMOS TB observations using several approaches such as the forward model inversion, neural networks, and statistical regressions, and readers are directed to [START_REF] Wigneron | Retrieving near-surface soil moisture from microwave radiometric observations: current status and future plans[END_REF] for a review. The operational retrieval method (i.e. forward model inversion) is time consuming and requires several auxiliary datasets (e.g., the land cover, soil texture, etc.). Besides, [START_REF] Wigneron | Soil moisture retrievals from biangular L-band passive microwave observations[END_REF] and [START_REF] Saleh | Semi-empirical regressions at L-band applied to surface soil moisture retrievals over grass[END_REF] have developed and evaluated semi-empirical regression equations between the SSM and microwave reflectivity (i.e. one minus emissivity)

based on the radiative transfer model (τ-ω model) [START_REF] Mo | A model for microwave emission from vegetation-covered fields[END_REF][START_REF] Wigneron | A simple algorithm to retrieve soil moisture and vegetation biomass using passive microwave measurements over crop fields[END_REF], which simulates the L-band TB from soil underlying a vegetation canopy. More specifically, regression equations using multiple configurations of bipolarized and multi-angular microwave TB observations were shown to be efficient for retrieving SSM [START_REF] Albergel | A first assessment of the SMOS data in southwestern France using in situ and airborne soil moisture estimates : the CAROLS airborne campaign[END_REF][START_REF] Calvet | Sensitivity of Passive Microwave Observations to Soil Moisture and Vegetation Water Content: L-Band to W-Band[END_REF][START_REF] Parrens | Comparing soil moisture retrievals from SMOS and ASCAT over France[END_REF][START_REF] Saleh | Semi-empirical regressions at L-band applied to surface soil moisture retrievals over grass[END_REF]. These regression methods have been used in several studies based on in situ, airborne, or space-borne (SMOS) observations [START_REF] Calvet | Sensitivity of Passive Microwave Observations to Soil Moisture and Vegetation Water Content: L-Band to W-Band[END_REF][START_REF] Parrens | Comparing soil moisture retrievals from SMOS and ASCAT over France[END_REF][START_REF] Pellarin | Surface soil moisture retrieval from L-band radiometry: a global regression study[END_REF]. For instance, [START_REF] Albergel | A first assessment of the SMOS data in southwestern France using in situ and airborne soil moisture estimates : the CAROLS airborne campaign[END_REF] applied these methods successfully to SMOS data over some sites in France, and the retrieval method was extended over the whole of France by [START_REF] Parrens | Comparing soil moisture retrievals from SMOS and ASCAT over France[END_REF].

To date, to our knowledge, no study has been performed to assess the potential of the The knowledge gained from this study is to be used to help the preparation of the upcoming CCI phase 2 SSM programme to provide guidelines for a seamless SSM record.

Materials and methods

Datasets

AMSR-E Level 3 brightness temperatures

The AMSR-E sensor measures dual-polarized TB at C-band (6.925 GHz) vertically and horizontally with a spatial resolution of ~ 56 km. In this study, the level 3 global daily gridded TB product, projected on a global (Equal Area Scalable Earth) EASE grid 25 km, provided by the National Snow and Ice Data Center (NSIDC) was used. C-band was preferred in our study for retrieving SSM, as it is more sensitive to SSM than higher frequency bands, and the closest to L-band.

Night-time surface temperatures are more stable than day-time, hence the vegetation temperature is closer to soil temperature as the temperature gradients between them is not strong [START_REF] Kerr | A semiempirical model for interpreting microwave emission from semiarid land surfaces as seen from space[END_REF], and therefore we limited our study to night-time data (corresponding to AMSR-E descending overpass-time 0130 hour local time)(e.g., Al-Yaari et al., 2014).

SMOS level 3 soil moisture products

The SMOS satellite provides SSM products with global coverage and a 3-day revisit at the equator with ascending and descending orbits at 0600 and 1800 hours local time, respectively, with a spatial resolution of 35-50 km [START_REF] Kerr | The SMOS Mission: New Tool for Monitoring Key Elements ofthe Global Water Cycle[END_REF].

CATDS (Centre Aval de Traitement des Données) recently provided daily reprocessed global gridded SSM products, projected on a global EASE grid 25 km, namely the SMOS level 3 (SMOSL3) products. SMOSL3 has an enhanced accuracy in the SSM data by using several revisits simultaneously and multi-orbit retrievals [START_REF] Jacquette | SMOS CATDS level 3 global products over land[END_REF].

SMOSL3 product is provided as volumetric soil water content (m 3 /m 3 ) and can be freely obtained from the CATDS website (http://catds.fr).

SMOSL3 retrievals at dawn, corresponding to SMOS descending overpass-time 0600 hour local time, were selected in this study (Al-Yaari et al., 2014) for better consistency with AMSR-E night-time data.

ECMWF Soil temperature

Given the unavailability of real physical surface soil temperature through direct ground measurement at the global scale, we used soil temperature estimates produced by the European Center for Medium range Weather Forecasting (ECMWF). This surface soil temperature product (0-7cm) was re-projected and resampled to the same projection and spatial resolution of both SMOSL3 and AMSR-E SSM and TB products, respectively.

ECMWF Soil temperature is available for the whole period concerned in this study (2003)(2004)(2005)(2006)(2007)(2008)(2009)(2010)(2011).

MODIS NDVI

The NDVI (Normalized Difference Vegetation Index) products were obtained from MODIS (Moderate-resolution Imaging Spectroradiometer), which is an EOS sensor mounted on the TERRA satellite launched [START_REF] King | EOS Reference Handbook: A Guide to NASA's Earth Science Enterprise and the Earth Observing System[END_REF] by NASA in 1999. The NDVI is produced globally over land at 1 km resolution and for 16-day composite periods. The NDVI was found to be sensitive to (a good estimator of) Leaf Area Index (LAI) [START_REF] Chen | Retrieving leaf area index of boreal conifer forests using Landsat TM images[END_REF][START_REF] Colombo | Retrieval of leaf area index in different vegetation types using high resolution satellite data[END_REF][START_REF] Fan | Investigating the relationship between NDVI and LAI in semi-arid grassland in Inner Mongolia using in-situ measurements[END_REF][START_REF] Law | Remote Sensing of Leaf Area Index and Radiation Intercepted by Understory Vegetation[END_REF][START_REF] Potithep | What is the actual relationship between LAI and VI in a deciduous broadleaf forest? International Archives of the Photogrammetry[END_REF], which was shown to have a strong control on the skill of SSM retrieved by passive sensors (Al-Yaari et al., 2014).

Methods

In this study, we used simplified statistical regressions, which were analytically derived from the L-Band Emission of the Biosphere model (L-MEB, described in detail in [START_REF] Wigneron | L-band Microwave Emission of the Biosphere (L-MEB) Model: Description and calibration against experimental data sets over crop fields[END_REF]), based on bi-polarization TB datasets [START_REF] Saleh | Semi-empirical regressions at L-band applied to surface soil moisture retrievals over grass[END_REF][START_REF] Wigneron | Soil moisture retrievals from biangular L-band passive microwave observations[END_REF]. More specifically, these methods have been numerically derived from the equations of the τ-ɷ model (a zero-order solution of the radiative transfer equations), which is a simple formulation derived from the general radiative transfer equation for non-scattering homogeneous media, assuming that the value of the single scattering albedo is negligible and that the values of optical depth are the same for both polarizations. So these methods are based on physical equations.

The equation developed by [START_REF] Saleh | Semi-empirical regressions at L-band applied to surface soil moisture retrievals over grass[END_REF], which was also applied by (Albergel et al., 2011;[START_REF] Calvet | Sensitivity of Passive Microwave Observations to Soil Moisture and Vegetation Water Content: L-Band to W-Band[END_REF] to bi-polarization TB observations made at an incidence angle θ, can be written as:

ln(𝑆𝑆𝑆𝑆𝑆𝑆) = 𝑏𝑏 2 ln�Γ 𝑠𝑠 (𝜃𝜃)� + 𝑏𝑏 1 ln�Γ 𝑠𝑠 (𝜃𝜃)� + 𝑏𝑏 0 (𝜃𝜃) 6 -1
where Γ (θ) is the surface reflectivity at polarization V or H, defined as:

Γ 𝑃𝑃 (𝜃𝜃) = 1 - 𝑇𝑇 𝐵𝐵𝑃𝑃 (𝜃𝜃) 𝑇𝑇 𝐺𝐺 6 -2
where T BP and T G are the brightness temperature at polarization p (H or V) and surface soil temperature, respectively. In this study, T G is obtained from ECMWF. [START_REF] Mattar | A Combined Optical&Microwave Method to Retrieve Soil Moisture Over Vegetated Areas[END_REF] have shown that vegetation effects may be accounted for by adding vegetation information such as the NDVI to the regression equation, which may in turn enhance the regressions analysis. According to [START_REF] Mattar | A Combined Optical&Microwave Method to Retrieve Soil Moisture Over Vegetated Areas[END_REF], the regression equation can be rewritten as:

ln(𝑆𝑆𝑆𝑆𝑆𝑆) = 𝑏𝑏 3 (𝑁𝑁𝐷𝐷𝑁𝑁𝐼𝐼) + 𝑏𝑏 2 ln�Γ 𝑠𝑠 (𝜃𝜃)� + 𝑏𝑏 1 ln�Γ 𝑠𝑠 (𝜃𝜃)� + 𝑏𝑏 0 (𝜃𝜃) 6 -3
The coefficients b 0 , b 1 , b 2 , and b 3 of the regression Eqs. (6.1) and ( 6.3) are assumed to be constant in time and have to be calibrated over each pixel.

Regression calibration

The coefficients b 0 , b 1 , b 2 , and b 3 of the regression Eqs. (6.1) and ( 6.3) are calibrated using the AMSR-E T BP at C-band (6.9 GHz) in both H and V polarizations. The calibration was made over the whole time period during which both AMSR-E TB observation and SMOSL3 products are simultaneously available (namely Jun. 2010 -Sept. 2011). In both equations (6.1 & 6.3), as a reference value for SSM, we used the most recent available reprocessed SMOSL3 SSM products. The NDVI values used in Eq. ( 6.3) were taken from MODIS products. This bi-polarization approach was used here as AMSR-E provides TB measurements at only one angle 55° and two polarizations (H & V). In both equations (6.1 & 6.3), the regression coefficients were computed for each grid cell. They implicitly depend on the surface characteristics in terms of soil texture and surface roughness, vegetation types, topographic features, etc. [START_REF] Saleh | Semi-empirical regressions at L-band applied to surface soil moisture retrievals over grass[END_REF]. Fig. 6.1 shows a flowchart representation of the regression calibration method (1&2), soil moisture retrieval (3), and the availability of the datasets used in time (bottom panel).

Fig. 6 -1

Flow chart of the regression calibration method using Eq. (6.1) ( 1) and Eq. ( 6.3) (2) and soil moisture retrievals using the computed regression coefficients (3). The bottom panel shows the dataset availability in time.

Producing SSM data

The computed regression coefficients can then be used to derive a long SSM time series in all the pixels for the (2003)(2004)(2005)(2006)(2007)(2008)(2009) period (see Fig. 6.1) using Eqs. (6.1) and (6.3). In this period, TB measurements are obtained from AMSR-E. During the calibration period, soil temperatures are obtained from ECMWF, NDVI are obtained from MODIS, and the calibrated regression coefficients and thus all the parameters in the regression Eqs. (6.1) and (6.3) are known except the SSM which is our target to retrieve.

Results and discussion

Regression calibration

Using the above defined methodology, the regression coefficients b 0 , b 1 , and b 2 in Eq. Fig. 6.6 shows the areas where the correlation between the regressed data without NDVI and the reference SMOSL3 SSM products (in red) are higher than the correlation between the regressed data with NDVI and the reference SMOSL3 SSM products (in blue), and the areas where the difference is lower than 0.05 (in green). In general, the green color is prevalent, several red points can be noted, and there is almost no blue color. This tells that the addition of NDVI did not improve the regression in terms of temporal dynamics, thus, neither in RMSD (m 3 /m 3 ) nor in the correlation values. These results are consistent with a recent study [START_REF] Miernecki | Comparison of SMOS and SMAP soil moisture retrieval approaches using tower-based radiometer data over a vineyard field[END_REF], which concluded that including the NDVI variable in the

Product comparison with original AMSR-E SSM product

A comparison between the SSM estimated from AMSR-E TB observations using the regression approach (referred to as AMSR-reg) and that retrieved from AMSR-E TB observations implementing the Land Parameter Retrieval Model (LPRM) model, developed at Vrije Universiteit Amsterdam in cooperation with the NASA (VU-NASA) [START_REF] Owe | A methodology for surface soil moisture and vegetation optical depth retrieval using the microwave polarization difference index[END_REF] (referred to as AMSR-VUE), has been also carried out. The comparison was performed at the global scale considering the 2007-2009 period. AMSR-VUE SSM products were used in this comparison, among other AMSR-E SSM retrievals, as they were shown to be the best [START_REF] Brocca | Soil moisture estimation through ASCAT and AMSR-E sensors: An intercomparison and validation study across Europe[END_REF]Draper et al., 2009a;[START_REF] Gruhier | Soil moisture active and passive microwave products: intercomparison and evaluation over a Sahelian site[END_REF]. Correlation (R) and RMSD (m 3 /m 3 )

indicators were selected to study the consistency of both SSM retrievals in time evolution and spatial patterns.

The temporal correlation between the AMSR-reg and AMSR-VUA is shown in Fig. Chapter VII

Conclusions and perspectives

studies confirming the different effects of vegetation on L and C-bands signals with observations from sensors in space. In the passive microwave domain, L-band has long been considered as an optimal frequency to monitor SSM. When a vegetation layer is present over the soil surface, it attenuates the soil emissions and adds its own contribution to the emitted radiation measured by passive microwave radiometers. The retrieval algorithm attempts to decouple the effects of soil and vegetation in order to provide an estimation of SSM.

However, as vegetation effects increase with increasing frequency, the correction for vegetation effects is more complex at C-band (~ 6.6 GHz for AMSR-E) than at L-band (~ 1.4 GHz for SMOS). Moreover, SMOS has multi-angular capabilities which make it, theoretically, more efficient for decoupling the soil and vegetation effects than mono-angular spatial radiometers such as AMSR-E. The combination of both a L-band system and multiangular capabilities for SMOS compared to a C-band system and monoangular capabilities for AMSR-E explains the improved performance of SMOS over biomes with dense vegetation cover and for LAI values larger than 1.

The second part (Chap. V) investigated the consistency between the passive SMOSL3 and the active ASCAT SSM products with respect to land surface model SSM from the MERRA-Land product. It was found that the SMOSL3 and ASCAT SSM retrievals were consistent with the temporal dynamics of modelled SSM (correlation R>0.70) in the transition zones between wet and dry climates, including the Sahel, the Indian subcontinent, the Great Plains of North America, Eastern Australia, and South-Eastern Brazil. Over relatively dense vegetation covers, a better consistency with MERRA-Land was obtained with ASCAT than with SMOSL3. However, it was found that ASCAT retrievals exhibit negative correlation versus MERRA-Land in some arid regions (e.g., the Sahara and the Arabian Peninsula), most likely because of scattering effects in the soil that are not correctly accounted for over very dry surfaces. In terms of anomalies, SMOSL3 better captures the short term SSM variability of the reference dataset (MERRA-Land) than ASCAT over regions with limited radio frequency interference (RFI) effects (e.g., North America, South America, and Australia). The seasonal and latitudinal variations of SSM, as revealed by Hovmöller diagrams, are relatively similar for the three products, although the MERRA-Land SSM values were generally higher and their seasonal amplitude is much lower than for SMOSL3 and ASCAT. Finally, both SMOSL3 and ASCAT had relatively comparable triple collocation errors with similar spatial error patterns: (i) lowest errors in arid regions (e.g., Sahara, and Arabian Peninsula) and Central America, and (ii) highest errors over most of the vegetated regions (e.g., northern

Australia, India, Central Asia, and South America). However, the ASCAT SSM product is prone to larger random errors in some regions (e.g., North-Western Africa, Iran, and southern South Africa). As in the comparison of SMOS and AMSR-E, vegetation density was again found to be a key factor to interpret the consistency with MERRA-Land between the two remotely sensed products (SMOSL3 and ASCAT) which provides complementary The AMSR-reg SSM retrievals were evaluated against the AMSR-VUA SSM products, for the 2010-2011 period, and the MERRA-Land SSM simulations (considered here as a reference) for the 2007-2009 period. The results showed that the regression approach is very promising as it produces realistic SSM climate record from the AMSR-E TB product in terms of absolute values and time variations. The R (mostly > 0.75) and RMSD (mostly < 0.04 m 3 /m 3 ) maps showed a good agreement between the AMSR-reg SSM retrievals and the AMSR-VUA SSM retrievals as well as the MERRA-Land SSM simulations particularly over Australia, Central USA, Central Asia, and the Sahel.

Main conclusions

Based on the results of the three Chapters (IV, V, & VI) of this Ph.D. thesis research, joint conclusions can be drawn:

(i) There is, in general, a good correspondence between the SMOSL3 and ASCAT (AMSR-E) derived SSM products with the MERRA-Land (SM-DAS-2) reference in the transition zones between wet and dry climates (e.g., Great Plains of North America, Sahel), Eastern Australia, and South-eastern regions of Brazil. It is worth noting that these regions are regions of strong coupling between soil moisture and precipitation, where accurate soil moisture values are crucial to accurate weather, climate, and probably hydrological modelling.

(ii)

The performance of SMOS satellite was the same whether it was compared with AMSR-E or ASCAT over the USA and Central Asia, as it correlated better to the reference datasets over these regions than AMSR-E and ASCAT.

(iii) Different performances of SMOS were noted when it was compared to AMSR-E and ASCAT over arid regions (e.g., the Arabian Peninsula) and regions with moderate vegetation (e.g., the Sahel). Over arid regions, for instance, SMOSL3

was closer to the reference than the ASCAT, whereas AMSR-E was closer to the reference than the SMOSL3. Over regions with moderate vegetation, SMOSL3

was closer to the reference than the AMSR-E, whereas ASCAT was closer to the reference than the SMOSL3. More specifically, higher (lower) correlations with the reference were obtained for SMOSL3 than for ASCAT (AMSR-E) when LAI is less than 1 (which corresponds to almost 50% of the pixels considered in this study). This implies that vegetation plays a key role in the performance of the SMOSL3 (as well as ASCAT and AMSR-E) SSM products, and the different satellite products have different sensitivities to vegetation. Generally, SMOS is more (less) efficient at monitoring SSM than ASCAT (AMSR-E) over sparse vegetation, whereas (AMSR-E) ASCAT is (less) more efficient over relatively dense vegetation (LAI >3). It should be noted that these conclusions are relative to the references used in these studies.

(iv) RFI contamination of SMOSL3 was found to be the key factor in the interpretation of the consistency between the SMOSL3 and the other two remotely sensed products (AMSR-E and ASCAT), with major issues over Europe, Middle East, and India, in particular.

(v)

The complementary performances between SMOSL3 and the other two remotely sensed datasets revealed a potential synergy between the passive (SMOS) at L-

Limitations

There are two main limitations that were encountered during this Ph.D. thesis research:

• The first limitation in our evaluation studies was that the SMOSL3, AMSR-E, and ASCAT remote sensing SSM products were provided with different spatial resolutions, acquisition times, sampling depths, techniques and limitations. This disparity among these different datasets might have influenced the statistical indicators used in the evaluation results, but it is difficult to say how much the impact was.

• The second limitation in our evaluation studies was the choice of land surface simulations and land data assimilation SSM estimates as references due to the limited availability of the in-situ observations at the global scale. We considered MERRA-Land and SM-DAS-2 SSM estimates, based on their reliability performances highlighted by previous studies, to perform the evaluations. But it is difficult to say which model is the best for this purpose and to determine which one is more reliable or 'true'. Therefore, MERRA-Land or SM-DAS-2 can be more detrimental for SMOS or the other two satellites. One must keep in mind that, when using them to evaluate other SSM products, the interpretation of the results is hampered by their own accuracy.

Perspectives

Researches on the exploitation and consolidation of the SMOS algorithm, products, and possible applications are far from complete. There are a number of possible ways to verify, refine, and develop the results analyzed in this Ph.D. thesis research, and also to continue the evaluations dealing particularly with issues left open at the end of this document.

Further research may attempt to go further in the following tasks:

1.

The evaluation of remote sensing products is a continuous task as datasets are continuously enlarged and new algorithms are available. We recommend investigating the performance of SMOS SSM products using longer datasets as the SMOS SSM product in this Ph.D. research work was evaluated for the period 2010-2011 and 2010-2012. It is expected that with the new processing campaign a 5 year coherent of SMOS dataset will be available in 2015. A continuous validation procedure can be imagined which automatically monitors SSM products at the global scale taking into account regional information and analysis as the ones presented in this Ph.D. research work.

2.

The quality of the current SMOS SSM retrieval algorithm, used to translate observed TB into SSM, was recently enhanced by the substitution of the Dobson dielectric model with the Mironov dielectric mixing model, and the new retrieved SSM products will be released soon. An attempt will be made to perform a first assessment of the improvements of the most recent SMOS reprocessing: in particular the impact of introducing the Mironov model. Also, there is room for improvement in the SMOS retrieval algorithm by enhancing the RFI filtering. Some regions such as Europe, China, India, etc. are severely contaminated by the RFI at L-band, which led to unreliable SMOS SSM retrievals over these regions. The RFI problems are common issues for most radiometers, and efforts should be pursued on international level to minimize them. Furthermore, alternative soil moisture algorithms in particular the use of neural networks and statistical regression analyses proposed in Chapter VI, should be considered, especially over regions where the forward algorithm fails to accurately retrieve the SSM. Using these methods will also help in retrieving SSM in real time as using the standard algorithm (forward modelling) takes one month to retrieve SSM for one year whereas the other methods take roughly no more than a few hours. Furthermore, the SMOS SSM algorithm should account for changes in vegetation optical thickness (τ) and roughness of the soil surface caused by farming practices (e.g. tillage) and planting activities, which may confuse the satellites [START_REF] Patton | Initial Validation of SMOS Vegetation Optical Thickness in Iowa[END_REF]. For instance, new approaches such as the one combining vegetation and roughness effects within one parameter (TR) [START_REF] Fernández-Morán | Evaluating the impact of roughness in soil moisture and optical thickness retrievals over the VAS area[END_REF]Parrens et al., 2014), which is retrieved simultaneously to SSM, may improve the SMOS SSM products. The evaluation procedure of these products can benefit from the analyses presented in the PhD and can be a common benchmark for them.

3.

Unfortunately, in the highly vegetated regions, in situ data are almost completely unavailable so that it was unfeasible at the moment to investigate in detail the quite surprising finding of SMOS performance against ASCAT data over these regions, where ASCAT was closer to the model in terms of correlation. However, in-situ measurements stations are growing and this issue can be further investigated. More generally, the validation of the SMOS SSM products will significantly benefit from the increasing number of in-situ soil moisture networks thanks to efforts like the International Soil Moisture Network initiative (http://www.ipf.tuwien.ac.at/insitu/) [START_REF] Dorigo | The International Soil Moisture Network: a data hosting facility for global in situ soil moisture measurements[END_REF]. In on incorporating SMOS SSM datasets with GRACE products, which may be of help to separate the GRACE TWS datasets. In addition, GRACE and other remotely sensed products for all components (i.e. precipitation, evapotranspiration, runoff, and water storage) of the water budget have been recently used to compute and evaluate the potential of water budget closure. [START_REF] Sheffield | Closing the terrestrial water budget from satellite remote sensing[END_REF], for instance, used the stream flow component as the water balance closure and was evaluated over the Mississippi River basin against stream flow measurements. Including SMOS datasets in these analyses by, for instance, closing the water budget using SSM and evaluating errors using the SMOS SSM datasets can be investigated in the near future.

5.

Many studies suggest the use of multi-sensors data to disaggregate SSM from microwave data [START_REF] Merlin | Towards deterministic downscaling of SMOS soil moisture using MODIS derived soil evaporative efficiency[END_REF][START_REF] Merlin | An improved algorithm for disaggregating microwave-derived soil moisture based on red, near-infrared and thermal-infrared data[END_REF][START_REF] Merlin | Disaggregation of SMOS Soil Moisture in Southeastern Australia[END_REF][START_REF] Merlin | Self-calibrated evaporation-based disaggregation of SMOS soil moisture: An evaluation study at 3 km and 100 m resolution in Catalunya, Spain[END_REF][START_REF] Piles | Downscaling SMOS-Derived Soil Moisture Using MODIS Visible/Infrared Data[END_REF]. Those methods deliver high spatial resolution soil moisture. Analyses similar to the ones done in this Ph.D. need to be done to compare those approaches over different climatic conditions.

6.

The SMOS, AMSR-E, and ASCAT missions have their own advantages and limitations as was shown throughout this Ph.D. research work. Some perform better over arid regions; others can be better for vegetated areas. It is recommended to make a product from these different sensors where spatially each sensor has a different weight. This will be achieved by, for instance, taking advantage of each sensor on different places while conserving spatial and temporal coherence. The integration procedures (simple weighting, the constrained linear method, the optimal interpolation method, and the neural network technique) developed by [START_REF] Aires | Combining Datasets of Satellite-Retrieved Products. Part I: Methodology and Water Budget Closure[END_REF] can be applied to optimally combine the multiple observation datasets to obtain a coherent dataset.

List of figures

Fig. 2 -10

The scheme of HTESSEL and the recent revisins in the land surface model.

Adapted from [START_REF] Balsamo | Evolution of land surface processes in the IFS[END_REF]

Fig. 2 -11

Water balance representation in HTESSEL. Adapted from [START_REF] Wipfler | Seasonal evaluation of the land surface scheme HTESSEL against remote sensing derived energy fluxes of the Transdanubian region in Hungary[END_REF].

Fig. 3 -5

Components of the general radiative transfer equation [START_REF] Kerr | The SMOS Soil Moisture Retrieval Algorithm[END_REF]. ...........

Fig. 3 -6

Overview of the CATDS SMOSL3 SSM processing chain [START_REF] Kerr | The CATDS SMOS L3 soil moisture retrieval processor, Algorithm Theoretical Baseline Document[END_REF].

  du sol (SM) contrôle les bilans d'eau et d'énergie des surfaces continentales et joue ainsi un rôle clé dans les domaines de la météorologie, l'hydrologie et l'écologie. La communauté scientifique en télédétection micro-ondes a fait des efforts considérables pour établir des bases de données globales de l'humidité du sol en surface (SSM) découlant d'instruments micro-ondes actifs et passifs. Parmi ces instruments, SMOS (Soil Moisture and Ocean Salinity), lancé en 2009, est le premier satellite passif conçu spécifiquement pour mesurer SSM à partir d'observations en bande L (1.4 GHz) à l'échelle globale. La validation des données SMOS SSM sur différentes régions climatiques et pour des conditions environnementales variées est une étape indispensable avant qu'elles soient utilisées de manière opérationnelle. En effet, une meilleure connaissance de la précision des estimations de SSM et des incertitudes associées permettra non seulement d'améliorer les produits SMOS SSM, mais aussi d'optimiser les approches de fusion de données utilisées pour créer des produits multi-capteurs long terme. De tels produits sont développés dans le cadre du programme Climate Change Initiative (CCI) de l'Agence spatiale européenne (ESA) pour l'ensemble des variables climatiques essentielles (ECV), dont SSM. A la suite des chapitres d'introduction I à III, les résultats de cette thèse sont présentés en trois chapitres. Le chapitre IV présente une comparaison des produits SSM issus des capteurs passifs SMOS (bande L) et AMSR-E (bande C) en prenant pour référence les estimations SSM du système d'assimilation SM-DAS-2 du Centre Européen pour les Prévisions Météorologiques à Moyen Terme (CEPMMT). Cette évaluation est menée sur la période d'observation commune à SMOS et AMSR-E (2010-2011), en utilisant des indicateurs classiques (corrélation, RMSD, vi Biais). En parallèle, le chapitre V présente une comparaison des produits SMOS SSM avec les produits SSM issus du capteur actif ASCAT en bande C en utilisant comme référence les simulations SSM d'un modèle des surfaces continentales (MERRA-Land), et en utilisant des indicateurs classiques, des méthodes statistiques avancées (triple collocation), et des diagrammes de Hovmöller sur la période 2010-2012. Ces deux évaluations ont montré que la densité de la végétation (paramétrée ici par l'indice foliaire LAI) est un facteur clé pour interpréter la cohérence entre le produit SMOS et les produits AMSR-E et ASCAT. Cet effet de la végétation a été quantifié pour la première fois à l'échelle globale pour les trois capteurs micro-ondes. Ces deux chapitres ont également montré que les trois capteurs SMOS, AMSR-E et ASCAT ont des performances complémentaires selon la densité de végétation et qu'il y a ainsi un potentiel intéressant en terme de fusion des jeux de données micro-ondes passifs et actifs. Dans le chapitre VI, avec l'objectif général d'étendre vers le passé les séries de données SSM de SMOSL3 et de développer un jeu de données SSM homogène sur 2003-2014, nous avons évalué l'utilisation d'une approche de régression linéaire multiple

  between SMOS (L-band) SSM products and other existing microwave passive (AMSR-E; C-band) and active (ASCAT; Cband) SSM products using models SSM simulations (MERRA-Land and SM-DAS-2) as benchmarks with the following purposes: a. A better understanding of the quality of the SSM products retrieved from passive and active techniques at L-and C-bands at the global scale. b. Evaluating their ability to capture the spatial and temporal dynamics of SSM at the global scale (where are the significant differences and consistencies in the performances between the different satellite SSM products?). c. Evaluating the effects of the biome types and vegetation density, parameterized here by the leaf area index (LAI), on the different SSM retrievals (how the accuracy of the SSM retrievals is impacted by vegetation?). (ii) Developing a global and a long record i.e. 2003-2014 of SSM dataset which is coherent across different sensors (more specifically: Are statistical regression approaches a good tool to merge the AMSR-E and SMOS SSM data to produce realistic and long term SSM time series in terms of variations and absolute values?).

  evaluation of the SMOSL3 SSM products and a satellite-based active microwave SSM datasets (ASCAT) with respect to modelled surface SSM simulated by MERRA-Land. The SSM time series retrieved from ASCAT is to date the reference product used in the CCI project. The evaluation period in Chapter IV was extended to 3 years(2010)(2011)(2012) in thisChapter. The relationship between the global-scale SSM products was studied using (1) a time series statistics (considering both original SSM data and anomalies), (2) a space-time analysis using Hovmöller diagrams, and (3) a triple collocation error model. Chapter IV and V both have in common that the remotely sensed data were compared to a land surface model. In Chapter VI, the complementary performances between AMSR-E and SMOS shown in Chapter IV motivated us to produce a merged SSM dataset. For that purpose, this Chapter investigates the use of physically based multiple-linear regressions to retrieve a global and long term SSM record based on a combination of bi-polarization (horizontal and vertical) TB observations from the AMSR-E and SMOS sensors. Chapters IV to VI address the three major research objectives mentioned earlier. Each chapter is considered as an independent study

Fig. 2 - 2

 22 Fig. 2 -2The Global Water Cycle. Adapted from[START_REF] Houser | Predicting Energy and Water Cycle Consequences of Earth System Variability and Change[END_REF].

Fig. 2 - 3

 23 Fig. 2 -3 Schematic diagram of the Earth's water cycle. Reservoir volumes (boxes) are stated in 10 3 km 3 , water fluxes (arrows) in 10 3 km 3 per year. Adapted from Oki (1999).

Fig. 2 - 4

 24 Fig. 2 -4 Overview of soil moisture in situ network stations available at ISM. Adapted from Ochsner et al. (2013).

Fig. 2 - 6

 26 Fig. 2 -6 Scheme of active and passive microwave remote sensing principles. Source: [http://pmm.nasa.gov/node/345].

  -2 SM-DAS-2 is a near real time (NRT) root zone soil moisture index generated by assimilating the ASCAT surface soil moisture index in the improved, Hydrologically, ECMWF HTESSEL (Tiled ECMWF Scheme for Surface Exchanges over Land, Balsamo et al., 2009) land surface model (PUM, 2012). SM-DAS-2 soil moisture product is assimilation product produced based on a simplified Extended Kalman Filter (EKF) to propagate the ASCAT surface soil moisture index observation towards the root region down to 2.89 m below surface (PUM, 2012). Fig. 2-9 shows SM-DAS-2 production chain based on the ECMWF HTESSEL land surface model.

Fig. 2 -

 2 Fig. 2 -9 SM-DAS-2 production chain. Adapted from (PUM, 2012).

  density of short wave (W/m 2 ) Rl is the flux density long wave radiation (W/m 2 ), the arrows refer to incoming (↓) and outgoing (↑) flux densities, 𝛼𝛼i is albedo, Hi is the sensible flux density of tile I (W/m 2 ) λEi is the latent flux density of tile I (W/m 2 ) Gi is the soil heat flux density of tile I (W/m 2 ) , 𝜆𝜆 is the specific latent heat of vaporization (J/kg), and E is the mass flux density of evaporation (kg /m 2 /s).

Fig. 2 -

 2 Fig. 2 -11Water balance representation in HTESSEL. Adapted from[START_REF] Wipfler | Seasonal evaluation of the land surface scheme HTESSEL against remote sensing derived energy fluxes of the Transdanubian region in Hungary[END_REF].

  3.1), known as the European Space Agency (ESA's) water mission, was proposed by the CESBIO (Centre d'Etudes Spatiales de la BIOsphère) -CNES (Centre national d'études spatiales) in 1993 and then to ESA in 1999 as a response to the needs of weather and climate modelling, where surface soil moisture (SSM) is involved in the water cycle. The ESA collaborated with the CNES and CDTI (the Centre for the Development of Industrial Technology) in Spain to conduct the SMOS satellite as part of its Living Planet program as the second of seven Earth Explorer missions[START_REF] Kerr | Soil moisture retrieval from space: the Soil Moisture and Ocean Salinity (SMOS) mission[END_REF][START_REF] Kerr | The SMOS Mission: New Tool for Monitoring Key Elements ofthe Global Water Cycle[END_REF]. The SMOS satellite was launched in November 2009 by a Rocket launcher in Northern Russia at 01:50 UTC. It is the first ever passive satellite specifically dedicated to monitor two geophysical variables (ocean salinity and soil moisture) at the global scale[START_REF] Kerr | Soil moisture retrieval from space: the Soil Moisture and Ocean Salinity (SMOS) mission[END_REF][START_REF] Kerr | The SMOS Mission: New Tool for Monitoring Key Elements ofthe Global Water Cycle[END_REF]. The SMOS satellite has a revisit frequency of ~ three days and has two overpass times, from South Pole to North Pole (the so-called ascending) at 06:00 local time and from North Pole to South Pole (the so-called descending) at 18:00, displayed in Fig.3.1. The SMOS satellite measures the Earth's emissions (brightness temperatures) that originate from the top 5 cm of soil at L-band(1.4

  derive the global SSM swath-based maps. Quality indicators such as theoretical uncertainties of adjusted parameters and flags are also computed by L2 processors. The version number of SMOS L2 (SMOSL2) SSM operational processor(e.g., v4.2, v5.00, v5.51, v6.0, etc.) deployed in the SMOS processing has changed several times. The latest and current stable version available version is V6.0 which implemented substantial corrections and improvements (e.g., improved RFI detection, the change of the dielectric constant model from the Dobson model (from v5.51 onward) to the Mironov formulation, etc.). More details on the SMOSL2 processor and products can be found in (Kerr et al., 2012), ARRAY (www.array.ca/smos), ESA (http://earth.esa.int/smos), or through the CESBIO blog (www.cesbio.upstlse.fr/SMOS_blog/). 4-Level 3 (L3) processor and L3 products: the SMOS L3 (SMOSL3) products are global gridded maps of SSM produced with improved characteristics through temporal and spatial resampling and processing. They are provided by the CATDS (Centre Aval de Traitement des Données SMOS) center, which is a ground segment developed by the CNES since June 2011. The SMOSL3 SSM products are provided at different temporal resolutions: daily products, 3 day (a complete coverage of the Earth surface), 10-day

Fig. 3 - 4

 34 Fig. 3 -4 Schematic diagram of the SMOSL2 SSM algorithm. Adapted from Kerr et al. (2012).

Fig. 3

 3 Fig. 3 -8 ASCAT on orbit and its geometry. Source: [the European Organization for the Exploitation of Meteorological Satellites (EUMETSAT) website (www.eumetsat.int)].

Fig. 3 -

 3 Fig. 3 -11 AMSR-E aboard AQUA satellite. Source: [http://aqua.nasa.gov/]

Fig. 3 -

 3 Fig. 3 -12 Schematic diagram of the entail methodology of LPRM model. Adapted from Chung et al. (2013).

Fig. 3 -

 3 Fig. 3 -13 The number of data elements considered for (a) SMOSL3 and AMSR-E in Chapt. 4, (b) SMOSL3 and ASCAT in Chapt.5.

1 .

 1 The evaluation was performed for the period 03/2010-09/2011, which corresponds to the full period of availability of the two satellite-based products: tests made during the SMOS commissioning phase ended in March 2010 while the AMSR-E spatial mission ended in October 2011.

  contained in observations close to the surface (temperature and relative humidity at 2 m) as well asASCAT SM retrieval (de Rosnay et al., 2013;[START_REF] Drusch | Towards a Kalman Filter based soil moisture analysis system for the operational ECMWF Integrated Forecast System[END_REF], which is used to correct the model SM prognostic variable. SM-DAS-2 analysis is available at a spatial resolution of about 25 km (Gaussian reduced grid T799). The first layer (0-7 cm) is considered only, to represent the relatively low sampled soil layer of the SSM estimates derived from microwave remote sensing sensors (~ 0-3 cm at L-band and ~0-1 cm at Cband). SM-DAS-2 was shown to represent SM variability well. For instance, Albergel et al. (2012) have used in situ measurements from more than 200 stations located in western Africa, Australia, Europe, and the United States to determine the reliability of SM-DAS-2 to represent SM over 2010. Correlation values with in situ data were found to be very satisfactory over most of the investigated sites located in contrasted biomes and climate conditions with averaged correlation (R) values of 0.70 and an estimate of the averaged error is about 0.07 m 3 /m 3 . SM-DAS-2 is produced in the framework of the H-SAF project from

  effects could not be systematically detected and the SMOS L3 product is still contaminated by RFI effects. To illustrate the spatial patterns of the probability of RFI occurrences on SMOS observations, a map is given in Fig.4.1. This map represents the three-year(i.e., 2010-2012) average of probability of RFI occurrences and shows the regions where the undetected RFI effects are the most likely. The RFI flags provided in the SMOSL3 data set are given in an attempt to filter out the most significant RFI effects. In the present study, SMOSL3 data were rejected if one of the following conditions was fulfilled:(i) DQX >0.06 and DQX is equal to fill value (meaning the retrieval has failed), (ii) Percentage of Radio Frequency Interference (RFI fraction) > 30%, which is a daily RFI indicator, and

  SSM products and the vegetation effects (in relation with vegetation density and biomass). To investigate this link, the global correlation results (original and anomalies) were averaged according to the global distribution of LAI values. The values of LAI were the long termmean LAI values taken from the Global Soil Wetness Project[START_REF] Dirmeyer | GSWP 2: Multimodel analysis and implications for our perception of the land surface[END_REF] illustrated in Fig.4.3.

Fig. 4 - 3

 43 Fig. 4 -3 Global map of the long term mean LAI in m 2 •m -2[START_REF] Dirmeyer | GSWP 2: Multimodel analysis and implications for our perception of the land surface[END_REF].

Fig. 4 - 4

 44 Fig. 4 -4 Spatio-temporal comparison between SMOSL3 ascending (ASC) and SMOSL3 descending (DESC) products in terms of correlation with respect to the reference (DAS2) product for the period 03/2010-09/2011. The map shows the areas where either SMOSL3 ASC (red) or SMOSL3 DESC (green) correlates better with the reference. Pixels where ASC and DESC have similar performances (differences in the values of R are lower than 0.05) are shown in blue. Only significant correlations (p-value < 0.05) are presented.

Fig. 4 - 5

 45 Fig. 4 -5 Comparison of the time series of the mean SSM (site averaged) derived from SMOSL3, AMSRM and DAS2 for the period 03/2010-09/2011 for the eight selected sites shown in Fig. 4.2.

Fig. 4 - 6

 46 Fig. 4 -6 Pairwise comparison between the AMSRM (left panel) and SMOSL3 (right panel) SSM products with respect to the reference DAS2 product in terms of the correlation coefficient (R) based on original SSM data (a and b), the correlation coefficient (R) based on SSM anomalies (c and d), RMSD (m 3 /m 3 ; e and f), and Bias (m 3 /m 3 ; g and h) for the period 03/2010-09/2011. Only significant correlations (p-value < 0.05) are presented.

  Fig. 4.6a and b, where correlation values (R) drop below 0.25. The significant differences between satellites and model products in high latitude regions may partly be explained by the effect of frozen soil conditions. Correlation values (R) computed on seasonal anomalies, as described in Section 4.3.4, are shown in Fig. 4.6c and d. It can be seen that the global spatial patterns are relatively similar for both SMOSL3 and AMSRM, with better ability of SMOSL3 to capture the shortterm SM variability than AMSRM. The highest values of the R coefficient were found in eastern Australia, extreme South Africa, Western Europe, and Central America while the lowest values were found in the northern tundra region.

Fig. 4 - 7

 47 Fig. 4 -7 Pairwise comparison between the SMOSL3 and AMSRM SSM products with respect to the reference DAS2 SSM product in terms of correlations based on the original SSM data (a) or on SSM anomalies (b) for the period 03/2010-09/2011. The map show the areas where either SMOSL3 (red) or AMSRM (green) correlates better with the reference. Pixels where SMOSL3 and AMSRM have similar performances (differences in the values of R are lower than 0.05) are shown in blue. Only significant correlations (p-value < 0.05) are presented.

  Fig. 4.6 and Fig. 4.7 on the vegetation and climatic conditions, the statistical indicators were averaged for the twelve types of biomes described in Section 4.3.5 and illustrated in Fig. 4.2. The results are shown in Fig. 4.8a-d in terms of correlation (R) for original SSM data and anomalies, RMSD, and bias. The distributions of the correlation (R) and RMSD values as a function of biome types are quite similar for both SMOSL3 and AMRSM (Fig. 4.8a-c). In terms of correlation values computed from the original SSM data (Fig. 4.8a), the best results were obtained for biomes

Fig. 4 .

 4 Fig. 4.8b shows that the mean correlation coefficients computed from the SSM

Fig. 4 - 8

 48 Fig. 4 -8 Distribution of the statistical indicators between SMOSL3 (red) and AMSRM (green) and the reference as a function of biome types for the period 03/2010-09/2011. Statistics in terms of correlation coefficient based on original SSM data (a), correlation coefficient based on SSM anomalies (b), RMSD (m 3 /m 3 ; c), and Bias (m 3 /m 3 ; d) are computed at each grid cell and then averaged by biome type. The biome types are defined from the classification given by Chesworth (2008) shown in Fig. 4.2. Error bars represent mean ± standard deviation (SD) and only significant correlations (p-value < 0.05) are considered in the analysis.

Fig. 4 .

 4 9a and b, the correlation values shown in Fig. 4.6a and b (for original and anomaly SSM data) were averaged according to the values of LAI illustrated in the global map shown in Fig. 4.3. The results for both original SSM data (Fig. 4.9a) and anomalies(Fig. 4.9b) show that the performance of the remotely sensed SSM products (i.e., SMOSL3 and AMRSM) is strongly related to the distribution of the LAI values. In Fig.4.9a, it can be seen that the values of the correlation coefficient (R) decrease almost linearly with the mean value of LAI for both SMOSL3 and AMSRM. The rate of the decrease is much larger for AMSRM than for SMOSL3. For AMSRM the value of R decreases from R ≈ 0.45 to negative correlation values (R ≈ -0.1) as LAI increased from about 1 to 7. For the same increase in LAI values, the decrease in R for SMOSL3 is more limited: from R ≈ 0.4 to R ≈ 0.3. However, it should be noted that AMSRM provides slightly better performances than SMOSL3 when LAI is lower than 1 (i.e. over sparse vegetation covers), which corresponds to almost 50% of the pixels considered in this global analysis.In Fig.4.9b, the same analysis is shown for anomalies. It can be seen that better performances were obtained for SMOSL3, whatever the range of LAI values. Moreover, for this latter product, the correlation values remain stable (R ≈ 0.3) as LAI values increase.Conversely, the values of the R coefficient decrease rapidly and continuously for AMSMR as LAI values increase: R ≈ 0.25 for LAI ≈ 1 down to R ≈ 0.03 for LAI ≈ 7.

Fig. 4 - 9

 49 Fig. 4 -9 Distribution of the correlation coefficient (R) between SMOSL3 (red), AMSRM (green) and the reference dataset (DAS2) for the original SSM data (a) and anomalies (b) as a function of LAI for the period 03/2010-09/2011. Statistics are computed at each grid cell and then averaged by LAI intervals. The values of LAI were extracted from the map of (Dirmeyer et al., 2006) shown in Fig. 4.3. The percentage value (top of figure) provides the cover fraction (%) over continental surfaces corresponding to each LAI interval. Error bars represent mean ± standard deviation (SD) and only significant correlations (p-value < 0.05) are considered in the analysis.

  Fig. 5 -1 Three year average (2010-2012) of probability of radio frequency interference occurrences in the SMOS observations.

Fig. 5 - 2

 52 Fig. 5 -2 Number of data used to compare the SMOSL3 and ASCAT datasets.

Fig. 5 - 4

 54 Fig. 5 -4 Pairwise comparison between the SMOSL3 (right panel) and the ASCAT (left panel) SSM datasets with respect to the reference MERRA-Land product in terms of the correlation coefficient (R) based on original SSM data (a and b), on SSM monthly anomalies (c and d), ubRMSD (m 3 /m 3 ; e and f), and bias (m 3 /m 3 ; g and h) during the 05/2010-12/2012 period. Only significant correlations (p < 0.05) were plotted.

Fig. 5 .

 5 Fig. 5.4e-h shows a similar distribution of ubRMSD and bias values for both

Fig. 5 - 5

 55 Fig. 5 -5 Pairwise comparison between the ASCAT and SMOSL3 SSM datasets with respect to the reference SSM product in terms of correlations based on the original SSM data (a) or on SSM monthly anomalies (b) during the 05/2010-2012 period. The maps show the areas where either ASCAT (green) or SMOSL3 (red) correlates better with the reference. Pixels where the difference in the values of R is lower than 0.05 appear in blue. Only significant correlations (p < 0.05) were plotted and white areas indicate that the correlation is not significant.

Fig. 5 - 6

 56 Fig. 5 -6 Distribution of the correlation coefficient (R) between ASCAT (green), SMOSL3 (red) and the reference product (MERRA-Land) for the original SSM data (a) and monthly anomalies (b) as a function of leaf area index (LAI) during the 05/2010-2012 period. Significant correlations (p < 0.05) were computed at each grid cell and then averaged by LAI intervals, which were extracted from the global distribution of LAI displayed in Fig. 5.3. The area coverage provides the cover fraction (%) over continental surfaces corresponding to each LAI interval.

  SSM products with respect to the MERRA-Land reference shown in Fig. 5.4g-h. Moreover, Fig. 5.7 reveals a common periodical behavior with time and latitude: the lowest values are comprised in two "parallel" sinusoidal bands around the equator reaching the minima around April. Hence, ASCAT and SMOSL3 capture the SSM seasonal variations in the inter-tropical area as simulated by MERRA-Land. The meridional shift of the Intertropical Convergence Zone (ITCZ) is well detected by all three datasets, but MERRA-Land presents higher seasonal cycle variations. The main differences in the SSM distribution are found in the Northern Hemisphere particularly related to the increase of SSM values during the summer period. Furthermore, very low SMOS SSM values (bright red color in Fig. 5.7c, i.e., SSM values close to 0.05 m 3 /m 3 ) can be noted north of ~ 50°N during the winter. It is likely these very low values can be explained by the effect of soil freezing: the SMOS sensor cannot distinguish between

Fig. 5 - 7

 57 Fig. 5 -7 Time-latitude variations of original surface soil moisture data (m 3 /m 3 ) for (a) ASCAT, (b) MERRA-L, (c) SMOSL3 and (d) number of data illustrated in Hovmöller diagrams.

  Fig. 5.8a and b illustrates the TCE errors (i.e. the square-root of the values obtained from Eqs. (5.13) and (5.14)) of SMOSL3 and ASCAT.In general, the spatial patterns of the TCE errors obtained with ASCAT and SMOS are similar with relatively low TCE errors, with a mean global error of 0.014 m 3 /m 3 for SMOSL3, and 0.015 m 3 /m 3 for ASCAT. Note that the mean global error found for SMOSL3 in our study is much lower than the one found by[START_REF] Leroux | Estimating SMOS error structure using triple collocation[END_REF] (~ 0.06 m 3 /m 3 ). The higher mean value obtained by Leroux et al. may be explained by the use of only one year (2010), while we used 3 years in the present analysis(2010)(2011)(2012). Also,[START_REF] Leroux | Estimating SMOS error structure using triple collocation[END_REF] did not exclude SSM data measured during the commissioning phase which might have increased the error for the SMOS dataset. Moreover, the way to handle data filtering using flags such as the data quality index and RFI percentage may be different in both studies.

Fig. 5 - 8

 58 Fig. 5 -8 Spatial TCE errors of (a) ASCAT and (b) SMOSL3 SSM estimates expressed in volumetric water content. White areas indicate areas for which less than 100 common observations were available.

Fig. 5 - 9 1

 591 Fig. 5 -9The areas in which either ASCAT (green) or SMOSL3 (red) shows the smallest TCE error value. Pixels where the difference in TCE error is less than 0.005 m 3 /m 3 appear in blue.White areas indicate areas for which less than 100 common observations were available.

  products are largely consistent with the model-based SSM estimates from MERRA-Land, and that the two remote sensing products complement each other. Vegetation density and RFI contaminations of SMOSL3 were found to be the key factors in the interpretation of the consistency between the two remotely sensed products (SMOSL3 and ASCAT) with MERRA-Land. The potential synergy between the passive and active microwave systems at global scale is very promising for the development of improved, long-term SSM time series at global scale, such as those pursued by the European Space Agency's Climate Change Initiative.

  statistical methods to retrieve SSM at the global scale. The objectives of this study are twofold (i) deriving a merged SSM product based on the AMSR-E TB observations over 2003-2009 which is coherent with the SMOS SSM products (2010-2014) in terms of absolute values and time variations and (ii) evaluating the quality of this merged product with respect to several global scale SSM.

(6. 1 )

 1 Fig. 6 -2 Regression coefficients of AMSR-E brightness temperature vs. SMOSL3 SSM in 2010-2011 with Eq. (6.1). b0 (bottom panel): intercept, b1 (middle panel): vertical polarization, and b2 (top panel): horizontal polarization. White areas over land indicate areas with dense vegetation, strong topography, or wetlands.

Fig. 6 - 3 Fig. 6 - 4

 6364 Fig. 6 -3 Regression coefficients of the AMSR-E TB vs. SMOSL3 SSM during the 2010-2011 period with Eq. (6.3). b 0 : intercept, b 1 : vertical polarization, b 2 : horizontal polarization, and b 3 : NDVI. White areas over land indicate areas with dense vegetation, strong topography, and wetlands.

Fig. 6 - 5

 65 Fig. 6 -5 Regression statistics of AMSR-reg with inclusion of NDVI vs. SMOSL3 SSM in 2010-2011 with Eq. (6.3): a) R (top panel) and b) RMSD (bottom panel, m 3 /m 3 ). Only significant correlations (p-value < 0.05) are presented. White areas over land indicate areas with dense vegetation, strong topography, and wetlands.

  regressions provided lower performances. Consequently, for retrieving the long record 2003-2009 SSM, the regression without the inclusion of the NDVI values is recommended to extend back the SMOSL3 SSM for the period 2003-2009.

Fig. 6 - 6

 66 Fig. 6 -6 Pairwise comparison between the AMSR-reg with NDVI and AMSR-reg without NDVI SSM products with respect to the reference SMOSL3 SSM product in terms of correlations based on the original SSM data during the 2010 -2011 period. The map shows the areas where either AMSR-reg without NDVI (red) or AMSR-reg with NDVI (blue) correlates better with the reference. Pixels where the AMSR-reg with NDVI and AMSR-reg without NDVI have similar performances (differences in the values of R lower than 0.05) are shown in green. Only significant correlations (p-value < 0.05) are presented. White areas over land indicate areas with dense vegetation, strong topography, and wetlands.

  6.7a. High temporal correlations (R>0.75) are obtained over, particularly, the Sahel, central USA, and Europe regions, whereas a small correlation (even negative) is mainly obtained in the tundra regions, where the remotely-sensed retrievals are affected by the permanent snow cover and frozen soil. Except for the tundra regions, the results reveal that almost all over the world the AMSR-VUA and AMSR-reg are consistent. Consistently, Fig.6.7b shows that high RMSD values are obtained over the tundra regions, but also over North-Eastern Australia, whereas small RMSD values have been mainly obtained over arid regions such as the Middle East, extreme South Africa, Western Australia, etc. High RMSD values over the Northern Australian region may be associated to the overestimation of the SSM values by the AMSRreg as the intercept coefficient was high over these regions, hence leading to high retrieved SSM values.

Fig. 6 - 7

 67 Fig. 6 -7 Maps of correlation between the AMSR-reg and the AMSR-VUA SSM products (top panel) and b) RMSD (m 3 /m 3 ) between the AMSR-reg and the AMSR-VUA SSM products (bottom panel). Only significant correlations (p-value < 0.05) are presented. White areas over land indicate areas with dense vegetation, strong topography, and wetlands.

Fig. 6 - 8

 68 Fig. 6 -8 Pairwise comparison between the AMSR-reg (left panels) and AMSR-VUA (right panels) SSM products with respect to the MERRA-Land reference product in terms of the correlation coefficient (R) based on original SSM data (a and b), RMSD (m 3 /m 3 ; c and d) during the 2007 -2009 period. Only significant correlations (p-value < 0.05) are presented. White areas indicate areas with dense vegetation, strong topography, and wetlands.

Fig. 6 .Fig. 6 - 9

 669 Fig.6.9 confirms that AMSR-reg better captured the long-term variability of the

  information on SSM. The correlation (R) values increase almost linearly with LAI for ASCAT, from R ≈ 0.18 to R ≈ 0.55 as LAI increases from about 1 to 7. For SMOSL3, on the other hand, R values remain relatively constant as LAI increases, with values between ~ 0.32 and 0.44. SMOSL3 provides higher correlation values with the reference than ASCAT when LAI is lower than 1 (i.e. over sparse vegetation covers) and similar R values are obtained for SMOSL3 and ASCAT for intermediate LAI values (1 ≤ LAI ≤ 3). The third part (Chap. VI) investigated the use of physically based multiple-linear regressions to retrieve a global and long term (e.g. 2003-2014) SSM record based on a combination of passive microwave remote sensing observations from the AMSR-E (2003 -2011) and SMOS (2010 -2014) sensors. The coefficients of these regression equations were calibrated using AMSR-E TB and SMOSL3 SSM (as a reference). This calibration process was carried out over the 2010-2011 period, over which both SMOS and AMSR-E observations coincide. Based on these calibrated coefficients, global SSM maps were computed from the AMSR-E TB observations over the whole 2003-2011 period (AMSR-reg).

7 .

 7 Further analyses are to be focused on the extraction of long-term trends from the 11 year time series (i.e. 2003-2010 from AMSR-reg and 2010-2014 from SMOS) SSM with a purpose to depict which areas have become wetter or drier between 2003 and 2014. Before doing the trend analyses, the homogeneities of the developed long-term SSM time series should be examined over the full period i.e. 2003 -2014. There are special algorithms/ways that could be used to detect the discontinuities, which may cause misinterpretation of the trends, in the SSM time series for the whole period (e.g., Easterling & Peterson, 1995; Loew et al., 2013; Moisselin J-M & O, 2002).8.The upcoming SMAP mission will provide continuity for L-band measurements of SMOS. At the end of this year (2014), the SMOS mission will have been in the space for 5 years, and the SMAP satellite would be just launched. A consolidated SSM product, that is suitable to fill climate change research gaps, can be obtained through data fusion between SMOS and SMAP SSM products. How to build seamless data record of SSM from SMOS to SMAP should be envisaged, with insights from the analyses performed in this Ph.D. research work.

Fig. 2 - 1

 21 Fig. 2 -1 Components of soil medium (After O'Geen, 2012). .................................................

Fig. 2 - 2

 22 Fig. 2 -2 The Global Water Cycle. Adapted from Houser et al. (2007). ................................

Fig. 2 - 3 Fig. 2 - 4

 2324 Fig. 2 -3 Schematic diagram of the Earth's water cycle. Reservoir volumes (boxes) are stated in 10 3 km 3 , water fluxes (arrows) in 10 3 km 3 per year. Adapted from Oki (1999). .......

Fig. 2 - 5 Fig. 2 - 6

 2526 Fig. 2 -5 Electromagnetic spectrums (including the entire range of radiations, which are

Fig. 2 - 7 Fig. 2 - 8

 2728 Fig. 2 -7 Relationship between The real ɛ´ and imaginary ɛ´´ components of the dielectric

  .......................................................................................

Fig. 3 - 1

 31 Fig. 3 -1 SMOS satellite with ascending (ASC) and descending (DESC) orbits. Source:

Fig. 3 - 2

 32 Fig. 3 -2 MIRAS instrument configuration diagram (upper panel) and during its assembly

Fig. 3 - 3 Fig. 3 - 4

 3334 Fig. 3 -3 SMOS observation geometry (a), an example of the hexagon-like shaped 'aliasfree'

  Processors steps are colored in blue and products are colored in green. UDP: User Data Product, DAP: Data Analysis Product, ADF: Auxiliary Data File, and DPGS: Data Processing Ground Segment. ...................................................................................................

Fig. 3 - 7

 37 Fig. 3 -7 probability of RFI occurrences for 20140427 ascending (bottom) and descending

Fig. 3 -

 3 Fig. 3 -10 TU-Wien change detection approach for SSM retrieval using radar backscatter

Fig. 3 -

 3 Fig. 3 -11 AMSR-E aboard AQUA satellite. Source: [http://aqua.nasa.gov/] .......................

Fig. 3 -

 3 Fig. 3 -12 Schematic diagram of the entail methodology of LPRM model. Adapted from

Fig. 4 - 1 Fig. 4 - 2 Fig. 4 - 3 Fig. 4 - 5 Fig. 4 - 6 Fig. 4 - 7 Fig. 4 - 8 Fig. 4 - 9 Fig. 5 - 1 Fig. 5 - 3 Fig. 5 - 4 Fig. 5 - 5 Fig. 5 - 6 Fig. 5 - 7 Fig. 5 - 9 Fig. 6 - 1 Fig. 6 - 3 Fig. 6 - 4 Fig. 6 - 5 Fig. 6 - 6 Fig. 6 - 7 Fig. 6 - 8 Fig. 6 - 9

 4142434546474849515354555657596163646566676869 Fig. 4 -1 Probability of Radio Frequency Interference (RFI) occurrences in the L-band

Table 2 -

 2 1 Typical effects of slope and aspect on soil moisture values (relative units) in the upper soil layer(After Svetlitchnyi et al., 2003)

	Relief elements	Convex slope (Aspect at)		Straight or concave slope (Aspect at)
		North East South West North	East South West
	Flat surface	1.00 1.00	1.00	1.00	1.00	1.00	1.00 1.00
	Upper part of a slope	1.10 1.10	0.95	0.95	1.00	0.83	0.56 0.61
	Middle part of a slope	1.00 1.00	0.79	0.79	1.00	1.00	0.80 0.80
	Lower part of a slope	1.00 1.00	0.63	0.66	1.17	1.17	1.00 1.00
	Foot of a slope	1.50 1.50	1.24	1.24	1.61	1.61	1.30 1.30

Table 2 -

 2 2 Types of in situ soil moisture measurement techniques

Table 2 -

 2 3 Comparison of different remote sensing techniques. Adapted from[START_REF] Kong | near-surface soil moisture retrieval at field and regional scales in the UK[END_REF].

	Sensor type	Wavelengths	Property	Sensors	Advantages	Limitations
			observed
	Visible	Red: 610 -700 nm	Soil albedo ;	NOAA	High /medium	Influenced by various factors:
		Orange: 590 -610 nm	Index of	AVHRR	resolution.	Cloud effects, soil texture,
		Yellow: 570 -590 nm	refraction	Landsat TM		structure, illumination
		Green: 500 -570 nm		Terra		geometry, and atmospheric
		Blue: 450 -500 nm		MODIS		conditions.
		Indigo: 430 -450 nm		Envisat
		Violet: 400 -430 nm		MERIS
				AATSR
				SPOT
	Infrared	Near Infrared (NIR): 0.7 to 1.5 µm.	Surface	GOES TIR	High /medium	Influenced by Cloud effects,
		Short Wavelength Infrared (SWIR): 1.5	temperature	NOAA	resolution	vegetation, topography, and
		to 3 µm.		AVHRR	Large swath	meteorological conditions.
		Mid Wavelength Infrared (MWIR): 3 to		Terra	Physics are well	Limited frequency of coverage;
		8 µm.		MODIS	understood.
		Long Wavelength Infrared (LWIR): 8 to		Landsat TM
		15 µm.		Envisat
		Far Infrared (FIR): longer than 15 µm.		AATSR
	Passive	L band: 1 -2 GHz (15 -30 cm)	Brightness	SMMR	Penetrate cloud,	Low spatial resolution;
	microwave	S band: 2 -4 GHz (7.5 -15 cm)	temperature;	SSM/I	rain, smoke and	Influenced by roughness,
		C band: 4 -8 GHz (3.8 -7.5 cm)	Dielectric	AMSR-E	smog;	vegetation cover, and soil
		X band: 8 -12.5 GHz (2.4 -3.8 cm)	properties;	SMOS	Vegetation	temperature.
		Ku band: 12.5 -18 GHz (1.7 -2.4 cm)	Soil	AMSR2	semi-
		K band: 18 -26.5 GHz (1.1 -1.7 cm)	temperature	AQURIES	transparent;
		Ka band: 26.5 -40 GHz (0.75 -1.1 cm)		WindSat	Measurements
				SMAP	are directly
					sensitive to

Table 2 -

 2 4 Passive sensor frequency allocations (GHz). Adapted from[START_REF] Ulaby | Microwave remote sensing fundamentals and radiometry[END_REF].

	Protected

for radio astronomy -no transmitters allowed Shared primary use for services having transmitters Shared secondary use for services having transmitters

	0.404-0.406	1.6605-1.6684	1.370-1.400
	1.400-1.427	2.690-2.700	2.640-2.600
	10.68-10.70	10.60-10.68	4.2-4.4
	15.35-15.40	21.2-21.4	4.80-4.99
	23.6-24.0	31.5-31.8	6.425-7.250
	31.3-31.5	36-37	15.20-15.35
	89.92	50.2-50.4	18.6-18.8
	-	-	22.21-22.5
	2.2

.3 Soil moisture modelling

	In order to overcome the limitations of ground based measurement, several dynamic
	models can be used to predict and model the spatio-temporal variations of soil moisture over
	large areas. Models have the advantage, in comparison to in situ, that they can provide soil
	moisture in different spatial and temporal resolutions from local to global and from hours to
	days, respectively. Notwithstanding, models require knowledge of other estimated or
	measured parameters and have a disadvantage of requiring several dynamic and statics inputs
	(e.g., a digital terrain model, soil type, soil texture, land cover, climate forcings, etc.), due to
	the complexity of the hydrologic cycle and the heterogeneity of the land surface.

  website (http://catds.fr). This product was used throughout this Ph.D. research work. The SMOSL3 has, similar to the SMOSL2, several changes in the products for each update of the version and this depends on the period: SMOSL3 version v2.45 and v2.4X is from Jan. 2010 to Oct. 2012, SMOSL3 version v2.5X is from Nov 2012 to June 2013, SMOSL3 version v2.6 is from July 2013 to Dec. 2013, and SMOSL3 version 2.7X is from Jan. 2014 (corresponding to SMOSL2 V6) onwards. All SMOSL3 SSM products produced at CATDS from 2010 to 2013 are tagged RE01. However, a complete reprocessing is being done at the CATDS to produce a homogeneous time series (2010 -present) and this will be released very soon with the latest version 2.72

Table 3 -

 3 1 Bare soil parameters(Kerr et al., 2013a).

	Surface TB of bare soil	Input	Parameter Name	Range	Units
		S	Sand fraction	0-100	%
		C	Clay fraction	0-100	%
		ρb	Dry bulk soil density	0.5-2.5	g 3 /cm
	Dobson or Mironov model to	ρ s	Soil particle density	2-3	g 3 /cm
	compute soil dielectric constant : εb	SM	Soil moisture	0-0.5	m 3 /m
	Note: Mironov model does not require S, ρb , ρ s	Sal	Soil salinity	0-12	Ppt
		F	Frequency	1.4	Ghz
		Tg	Effective surface-deep soil temperature	250-350	K
	Fresnel equations to compute the
	εb Bare soil dielectric constant
	[F/m]
	specular reflectivity H &

V for smooth air-soil boundary rbp

•

  Strong RFI emissions, which influence larger areas. Strong RFI sources distort the whole snapshot's TB and lead to very high TB values, which exceed the naturally observed TB emitted by the Earth's surface. This TB cannot be used to retrieve SSM.A clear RFI was noticed in the first SMOS products[START_REF] Camps | Rfianalysis in smos imagery[END_REF]; consequently the development of effective approaches to mitigate and detect the RFI has been priority since the launch of SMOS. Several algorithms have been and are being developed to deal most effectively with the problems caused by the RFI contamination[START_REF] Camps | Rfianalysis in smos imagery[END_REF][START_REF] Oliva | SMOS Radio Frequency Interference Scenario: Status and Actions Taken to Improve the RFI Environment in the 1400-1427-MHz Passive Band[END_REF]. A first and simple detection method for the RFI was applied on SMOSL2 Several short, medium, and long-term actions and strategies were done since the launch of SMOS to deal most effectively with RFI issues[START_REF] Daganzo-Eusebio | SMOS Radiometer in the 1400-1427-MHz Passive Band: Impact of the RFI Environment and Approach to Its Mitigation and Cancellation[END_REF]

	Oliva et al., 2012):
	2013):
	𝑒𝑒 =	NRFIX + NRFIY NSNAP𝑒𝑒	3 -11
	where:
	NRFIX are the number of TBs detected as contaminated on X antenna polarization,
	NRFIY are the number of TBs detected as contaminated on Y antenna polarization, and
	NSNAP p is the total number of observed TBs.
		Fig. 3.7 displays the latest available worldwide probability of RFI occurrences maps
	for 24-04-2014 ascending and descending (http://www.cesbio.ups-tlse.fr/SMOS_blog/). It can

which relies mainly on excluding all unreasonable TB values. A natural physical temperature times the emissivity gives directly reasonable TB, so with knowing the ranges of this reasonable TB, other non-natural TB values can be isolated. 338 K is the maximum physical temperature that was ever recorded, so BTs values higher than 340 K originate from manmade transmitters

[START_REF] Daganzo-Eusebio | SMOS Radiometer in the 1400-1427-MHz Passive Band: Impact of the RFI Environment and Approach to Its Mitigation and Cancellation[END_REF]

. These conditions enable to build a global probability of RFI occurrences, for a specific time period, based on (Daganzo-Eusebio et al., be seen that RFI is not uniformly distributed, with particularly strong RFI over Europe, Japan, India, China, and the Middle East. Nevertheless, there is no or little RFI over most of America, Australia and south Africa, whereas the ocean is almost free of RFI with the exception of some cases of interferences coming from emitting ships

[START_REF] Daganzo-Eusebio | SMOS Radiometer in the 1400-1427-MHz Passive Band: Impact of the RFI Environment and Approach to Its Mitigation and Cancellation[END_REF]

. Fig. 3 -7 probability of RFI occurrences for 20140427 ascending (bottom) and descending (top). Source: [http://www.cesbio.ups-tlse.fr/SMOS_blog/].

  . It was launched in October 2006, following the

	European Remote-Sensing Satellites 1 and 2 (ERS 1 and 2) launched in 1991 and 1995,
	respectively, aboard the Meteorological Operational Platforms (METOP-A; Fig. 3.8) and

METOP-B since 2012 . METOP-A has a sun-synchronous orbit which crosses the equator at 09:30 and 21:30 local solar time for descending and ascending orbits, respectively

(Wagner et al., 2013)

. The ASCAT instrument operates at C-band (5.3 GHz, wavelength = 5.7 cm) in vertical vertical (VV) polarization, which inherits and continues the role of the ERS1 & 2 scatterometers

Table 3 -

 3 2 Values of the different parameters used in LPRM for the different frequencies. Adapted from[START_REF] Chung | Evaluation of SMOS retrievals of soil moisture over the central United States with currently available in situ observations[END_REF].

			X-band (~10.8	Ku-band (~19
	Parameter	C-band (~6.9 GHz)
			GHz)	GHz)
	τv	0.01	0.01	0.05
	ω	0.05	0.06	0.06
	H	0.09	0.18	0.13
	Q	0.115	0.127	0.14

Table 3 -

 3 3 The main characteristics of SMOS,ASCAT, and AMSR-E missions and SSM products used in this Ph.D. research work.

	Mission	SMOS	ASCAT	AMSR-E
	Satellite/ Spacecraft	SMOS	METOP -A & B	AQUA
	Agency	ESA/CNES	EUMETSAT/ESA	NASA
	Sensor	Passive MIRAS	Active ASCAT	Passive AMSR-E
	Launch	2nd, Nov. 2009	19th, Oct. 2006	4th, May 2002-1st, Oct. 2011
	Design life	Minimum 3 years	5 years	6 years
	End of data availability	ongoing	ongoing	09/2011
	Orbit	Polar (Sun-synchronous, dawn/dusk, quasi-circular orbit.	Polar (orbit at an angle of 98.7° to the equator, Sun-synchronous)	Polar (Sun-synchronous, near-polar orbit
	Equator crossing time (local solar time)	6.00 am for ascending and 18.00 pm for descending	21:30 pm for ascending and 09:30 am for descending	13:30 pm for ascending 01:30 am for descending
	Altitude (km)	763	817	705
	Spacecraft operations control center	CNES, Toulouse, France	European Meteorological Satellite Organization (EUMESAT)	National Space Development Agency of Japan (NASDA)
	Centre frequency (GHz)	1.413 (L-band; 21cm)	5.255 (C-band, 5.7 cm)	6.925 10.65 18.7 23.8	36.5 89.0
	Band width (MHz)	24	Microwave radar	350 100 200 400	1000 3000
	Polarization	H & V (polarimetric mode optional)	VV	H & V
			25-53° (mid-beam);
	Incidence angle	0-55 °	34-64° (fore-and at	55 °
			beams)
	Swath width (km)	1000	2* 520	1445

Table 4 -

 4 1 Main characteristics of the surface soil moisture datasets used in this study. Note that all products are daily and global products re-sampled to 0.25° (~ 25 km).

	Soil moisture datasets	Incidence angle (°)	Data type and frequency	Sampling depth and unit	Temporal coverage	Reference
			Remotely
	SMOS level 3 (SMOSL3)	0-55	sensed (L-band,	~ 0-3 cm (m 3 /m 3 )	2010-present	(Jacquette et al., 2010)
			passive)
	AMSR-E,		Remotely
	NASA-VUA Algorithm	55	sensed (C-band,	~ 0-1 cm (m 3 /m 3 )	2002-2011	(Owe et al., 2008)
	(AMSRM)		passive)
	ECMWF SM-DAS-2 (DAS2)	-	Land Data Assimilation System	0-7 cm (m 3 /m 3 )	2010-present	(de Rosnay et al., 2013; Drusch et al., 2009)
	4.2.1.1 SMOSL3

The SMOS satellite was launched in November 2009 and is operated by the European Space Agency (ESA), as part of its Living Planet Programme, and the Centre National d'Etudes Spatiales (CNES) in France. SMOS operates at L-band with a spatial resolution of 35-50 km

Table 4 -

 4 2 Locations and type of biome of the eight sites selected to evaluate the SSM time series (Fig.4.2). All sites have the same surface area (i.e., ~ 360,000 km 2 ).

		Coordinates		Köppen-
	Region	(center) (longitude-	Biome (vegetation)	Geiger climate
		latitude)		classification
	Brazil, Amazon Basin	(-53° W to -8° S)	Tropical humid (evergreen rain forest)	Af & Am
	Deccan Plateau Region of India	(78° E-21° N)	Tropical semi-arid (Isolated trees and bush in open grassland)	BSk, Aw, & BSh
	Central Australia	(133° E to -23° S)	Desert temperate	BWh
	North-West America,
	Great Basin Region (Nevada, Utah, Idaho	(-114° W-40° N)	Desert temperate	BWh & BWk
	and Washington)
	North-East America,
	Interior Plains Region		Temperate humid
	(Iowa, Illinois,	(-94° W-43° N)	(forest, grass land,	Aw & Dfa
	Minnesota, and		agriculture)
	Wisconsin)
	Sahel, Savanna Region of Nigeria, Cameroon, Republic and Chad Central African	(18° E-89° N)	Tropical semi-arid in open grassland) (isolated trees and bush	Aw
	Central Europe		Temperate forest
	(Austria, France,	(4° E-47° N)	(Deciduous broadleaf	Cfb
	Germany and Italy)		forest)
	Argentina, Pampas Region	(-53° W to -26°S)	Temperate humid (grass land)	Cfa

This chapter has been published as: A. Al-Yaari, J.-P. Wigneron, A. Ducharne, Y. Kerr, P. de Rosnay, R. de Jeu, A. Govind, A. Al Bitar, C. Albergel, J. Muñoz-Sabater, P. Richaume, A. Mialon, Global-scale evaluation of two satellite-based passive microwave soil moisture datasets (SMOS and AMSR-E) with respect to Land Data Assimilation System estimates, Remote Sensing of Environment, Volume 149, June

2014, Pages 181-195, ISSN 0034-4257, http://dx.doi.org/10.1016/j.rse.2014.04.006.

This chapter has been published as: A. Al-Yaari, J.-P. Wigneron, A. Ducharne, Y.H. Kerr, W. Wagner, G. De Lannoy, R. Reichle, A. Al Bitar, W. Dorigo, P. Richaume, A. Mialon, Global-scale comparison of passive (SMOS) and active (ASCAT) satellite based microwave soil moisture retrievals with soil moisture simulations (MERRA-Land), Remote Sensing of Environment, Volume 152, September 2014, Pages 614-626, ISSN 0034-4257, http://dx.doi.org/10.1016/j.rse.2014.07.013.

This chapter has been partially published as: Amen Al-Yaari, Jean-Pierre Wigneron, Agnes Ducharne, Yann H. Kerr, Patricia de Rosnay, Richard de Jeu, Ajit Govind, Ahmad Al Bitar, Clement Albergel, Joaquin Muñoz-Sabater, Philippe Richaume, Arnaud Mialon: Merging two passive microwave remote sensing (smos and amsr_e) datasets to produce a long term record of soil moisture. Geoscience and Remote Sensing Symposium (IGARSS), 2014 IEEE International 13-18 July 2014. The whole chapter is to be submitted.

Zazueta, F.S. & Xin, J. (1994). Soil Moisture Sensors. Florida Cooperative Extension Service, Institute of Food and Agriculture Sciences, University of Florida, Buletin 292

Three years have passed since my arrival at the Institut National de la Recherche Agronomique .D... I also dedicate this Ph.D. thesis to my two lovely children, Yousef and Fatima who are the pride and joy of my life. Finally, this Ph.D. research work was financially supported by a Merit Scholarship Programme for High Technology, the Islamic Development Bank (IDB) -Saudi Arabia. * =< (𝛳𝛳 1 * -𝛳𝛳 3 * ) (𝛳𝛳

Chapter I

Introduction

with (i) steep mountainous terrain (> 10%), (ii) wetland fraction ( > 5%) [START_REF] Draper | Assimilation of passive and active microwave soil moisture retrievals[END_REF], and (iii) frozen soil conditions (soil temperatures < 276 K).

In Chapters 4 and 5, we perform global-scale comparisons of three SSM datasets (AMSRM, SMOSL3, and SM-DAS-2 in Chapter 4, and ASCAT, SMOSL3, and MERRA-Land in Chapter 5). In each 0.25° × 0.25° pixel, the selected statistical indicators, detailed in Chapters 4 and 5, were computed only when the compared three SSM products were simultaneously available. Therefore, the number of SSM data elements used in the time series of Chapter 4 was identical for AMSRM and SMOSL3, and the number of SSM data elements used in the time series of Chapter 5 was identical for ASCAT and SMOSL3. This number of data elements is illustrated in Fig. 3.13. caused by a wrong estimation of the effective temperature in NASA-VUA algorithm over northern regions, leading to positive bias in satellite retrievals [START_REF] Owe | Multisensor historical climatology of satellitederived global land surface moisture[END_REF]. In contrast, the negative bias found in SMOSL3 is consistent with the results obtained in previous studies [START_REF] Al Bitar | Evaluation of SMOS Soil Moisture Products Over Continental U.S. Using the SCAN/SNOTEL Network[END_REF][START_REF] Albergel | Evaluation of remotely sensed and modelled soil moisture products using global ground-based in situ observations[END_REF][START_REF] Dall'amico | First Results of SMOS Soil Moisture Validation in the Upper Danube Catchment[END_REF][START_REF] Jackson | Validation of Soil Moisture and Ocean Salinity (SMOS) Soil Moisture Over Watershed Networks in the U.S. Geoscience and Remote Sensing[END_REF][START_REF] Lacava | A First Assessment of the SMOS Soil Moisture Product With In Situ and Modeled Data in Italy and Luxembourg[END_REF][START_REF] Sanchez | Validation of the SMOS L2 Soil Moisture Data in the REMEDHUS Network (Spain)[END_REF] comparing SMOS retrievals with in situ measurement networks in different regions of the world which all relied on the first release of the SMOS retrieval algorithm. RFI may increase the brightness temperatures (TB) measured by SMOS, leading to smaller retrieved SSM values and, thus, to a negative bias [START_REF] Oliva | SMOS Radio Frequency Interference Scenario: Status and Actions Taken to Improve the RFI Environment in the 1400-1427-MHz Passive Band[END_REF]. However, [START_REF] Wigneron | First evaluation of the simultaneous SMOS and ELBARA-II observations in the Mediterranean region[END_REF] showed that, even though no bias could be observed in the measured TB data over the VAS site in Spain, a strong negative bias could be noted in the SMOS SSM retrievals. Thus, the negative bias found in the SMOS SSM products (Fig. 4.8d) is likely to be related to some issues in the retrieval algorithm (e.g., accounting for pixel heterogeneity, use of auxiliary data, etc.) or in the L-MEB (L-band Microwave Emission of the Biosphere) forward modelling. For instance, recent results showed that the use of the dielectric soil model developed by [START_REF] Mironov | Temperature-and Texture-Dependent Dielectric Model for Moist Soils at 1.4 GHz[END_REF], instead of the model of [START_REF] Dobson | Microwave Dielectric Behavior of Wet Soil-Part II: Dielectric Mixing Models[END_REF] led to improved results (the bias decreased by about 0.04 m 3 /m 3 at global scale) and the New L2 SSM shows almost no negative bias. Moreover, improvements will be made by better accounting for the effects of litter, surface roughness, effective soil temperature, etc. [START_REF] Grant | A field experiment on microwave forest radiometry: L-band signal behaviour for varying conditions of surface wetness[END_REF][START_REF] Saleh | Soil moisture retrievals at L-band using a two-step inversion approach (COSMOS/NAFE'05 Experiment)[END_REF].

Finally, it should be noted that even though the reference product used in this study (SM-DAS-2 from ECMWF) was found to be very reliable according to some recent studies [START_REF] Albergel | Evaluation of remotely sensed and modelled soil moisture products using global ground-based in situ observations[END_REF], estimates of SSM from LDAS cannot be considered as "ground truth" (Albergel et al., 2013a). One must keep in mind that when using them to evaluate other SSM products, the interpretation of the results is hampered by their own accuracy (the accuracy of LDAS itself and its required inputs such as the atmospheric forcing, observations, etc.). For satellite data across space and time. At the global scale, there is only, to date, one dedicated SM study that has been conducted to evaluate the SMOS level 2 (SMOSL2) against ASCAT SSM products. Leroux et al. (2013a) performed, at the global scale, a comparison between the SMOSL2 SSM products against the Advanced Microwave Scanning Radiometer for EOS (AMSR-E) and ASCAT SSM products taking the European Centre for Medium-Range Weather Forecasts (ECMWF) model simulations as a benchmark for the year 2010. This study showed that SMOS provided best results over Australia, North America, and Central Asia in terms of triple collocation errors.

Here, we investigate the consistency of the latest SMOS and ASCAT products, against each other and compared to an independent reference, based on land surface SSM simulations. The analysis is conducted at the global scale, using newly re-processed SSM products, and for the period 05/2010-12/2012. SSM data from the supplemental land surface analysis of the Modern-Era Retrospective analysis for Research and Applications (MERRA-Land) are used as the reference in this study. MERRA-Land data are suitable due to their global availability and their ability to capture the SSM spatial and temporal variability [START_REF] Reichle | Assessment and Enhancement of MERRA Land Surface Hydrology Estimates[END_REF]. In addition, Albergel et al. (2013a) and [START_REF] Yi | Evaluation of MERRA Land Surface Estimates in Preparation for the Soil Moisture Active Passive Mission[END_REF] showed very good performance of MERRA-Land in comparison with other reanalysis products and in situ data.

The objectives of this study are (i) to compare distinct SSM retrieval products derived from satellite-based microwave observations at two different frequency bands, L-band (~ 1.4 GHz) for the passive SMOSL3 product and C-band (~ 5 GHz) for the active ASCAT product, (ii) to characterize the global error structure of the SMOSL3 and ASCAT SSM products, and (iii) to understand the spatio-temporal variability of SSM over a variety of biomes and climate regimes at global scale. To achieve these objectives this paper presents (i) a classical time series analysis using a temporal correlation analysis of original SSM and cycle of SSM in these regions [START_REF] Koster | Regions of Strong Coupling Between Soil Moisture and Precipitation[END_REF].

Conversely, remotely sensed datasets exhibited weak correlations (R is generally less than 0.15) against the reference in arid regions due to the small range of natural variation in the SSM values. The correlations can even be negative between the ASCAT and MERRA-Land data pairs in some arid sites (e.g., Saudi Arabia and North Africa; patterns with low values over moderate vegetation (e.g., the Sahel, India, West USA, etc.), whereas high values are found over arid regions (e.g., extreme South Africa, Central and Western Australia, the western United States, etc.).

Regression's quality and new AMSR-E SSM products

The three regression coefficients from Eq. (6.1) obtained during the calibration period (2010)(2011) were then used in the same empirical relationship equation (Eq. 6.1) to estimate SSM from AMSR-E TB data for the same period of calibration. Note that this step does not correspond to a validation exercise, as the comparison between the retrieved SSM values and the reference SSM values (SMOSL3) was made over the period of calibration (2010 -2011). So, our objective here was merely to check whether realistic and coherent retrieved SSM values could be produced from the regression Eq. (6.1). The accuracy of the estimated SSM based on the bi-polarization approach (referred here to as AMSR-reg), in terms of the Root Mean Square Difference (RMSD; bottom panel) and correlation coefficient (R; top panel) values against SMOSL3, is shown in Fig. 6.4.

In Fig. 6.4 (b), the spatial patterns of the RMSD are similar to the vegetation distribution with a global mean of 0.05 and high RMSD (~ 0.1) over regions with high to moderate vegetation to low RMSD (< 0.04) over arid regions. In Fig. 6.4 (top panel), only the significant correlations between the reference and the retrieved SSM estimate obtained from Eq. (6.1) (p-value<0.05) are plotted. The reference generally correlates well with the AMSRreg over most of the globe with a global mean of 0.60 with the highest R values (R > 0.75) over Australia, the United States, West Africa, etc.

Similarly, the four regression coefficients from Eq. ( 6.3) obtained during the calibration period (2010-2011) were then used in the same empirical relationship equation (Eq. 6.3) to estimate SSM from AMSR-E TB data for the same period of calibration. The accuracy of the estimated SSM based on the bi-polarization approach with the addition of NDVI vegetation index Eq. ( 6.3), in terms of the RMSD (bottom panel) and the correlation coefficient (top panel) values is illustrated in Figs. 6.5. It can be seen that the RMSD values

Product evaluation against a reference (MERRA-Land)

As it is difficult to draw a concrete conclusion from the comparison between the AMSR-reg and AMSR-VUA about the performance of the regressed SSM data, both the AMSR-reg and AMSR-VUA retrievals were evaluated against independent land surface model simulations. To this end, we used the SSM product MERRA-Land obtained from the MERRA (Modern-Era Retrospective analysis for Research and Applications) reanalysis over the 2007-2009 period. MERRA-Land has been recently developed from MERRA as a supplemental and improved product of land surface hydrological fields [START_REF] Reichle | Assessment and Enhancement of MERRA Land Surface Hydrology Estimates[END_REF].

Figs. 6.8a-d show that the large-scale spatial patterns are relatively similar for both AMSR-reg and AMSR-VUA, with a slightly better ability of AMSR-VUA to capture the long-term MERRA-Land SSM variability than AMSR-reg. Figs. 6.8 a and b show that strong correlations between the global remotely sensed and the reference SSM products are found in the transition zones between wet and dry climates (e.g., Sahel), in the Great Plains (USA), and India with R greater than 0.5. This can be explained by the strong seasonal annual cycle of SSM in these regions [START_REF] Koster | Regions of Strong Coupling Between Soil Moisture and Precipitation[END_REF]. However, AMSR-VUA datasets exhibit pronounced negative correlations against the reference over all the tundra (high latitude) regions, whereas AMSR-reg datasets exhibited moderate, and negative correlations over some parts, against the reference over the same regions.

Figs. 6.8c-d show a similar distribution of RMSD values for both AMSR-reg and AMSR-VUA products. For both products, the RMSD show a clear spatial distribution: low RMSD values were found over deserts (e.g., the Sahara, the Arabian Peninsula, extreme South Africa, and Central Australia), whereas high values of RMSD are found for both instruments over locations near the Equator, Southern Eastern Australia for only AMSR-reg, over boreal regions particularly for AMSR-VUA. Looking at the correlation and RMSD maps, AMSR-VUA have a serious problem over boreal and tundra regions as negative

Summary and conclusions

The potential of a physically-based simple regression algorithm to retrieve SSM from space-borne TB observations was investigated in this study at the global scale. This regression algorithm has the advantage of requiring only surface temperature as an auxiliary dataset. In a first step, regression coefficients (with and without the inclusion of NDVI values) were computed for the period 2010-2011 using SMOSL3 SSM, as a reference, and the AMSR-E TB observations. The spatial patterns of the regression coefficients were, in general, in agreement with the land cover type. The use of NDVI information did not improve the regression quality in terms of correlation and RMSD. So regression coefficients without the NDVI information were used for the subsequent step of this work. As a second phase, the computed regression coefficients were used to produce a SSM product from the AMSR-E TB measurements for the 2003-2009 period (AMSR-reg). The AMSR-reg SSM retrievals were evaluated against the AMSR-VUA SSM products and against the MERRA-Land SSM simulations (considered here as a reference) for the 2007-2009 period. This first evaluation results showed that the regression approach is very promising as it produces realistic SSM climate record from the AMSR-E TB product in terms of absolute values and time variations.

Further studies are required to improve the regression approach, within the upcoming CCI programme phase 2 of the ESA, including (i) analyzing more in depth the link between the maps of the calibrated coefficients in relation to the soil physical properties (soil texture, structure, etc.), (ii) using other vegetation information such as the LAI or the other vegetation indices, (iii) evaluating AMSR-reg SSM retrievals against in situ sites at the local scale, (iv) investigating the temporal consistency of AMSR-reg (2003-2009) and SMOSL3 (2010[START_REF] Aires | Combining Datasets of Satellite-Retrieved Products. Part I: Methodology and Water Budget Closure[END_REF] SSM time series, and (v) doing a trend analysis using the developed time series (2003)(2004)(2005)(2006)(2007)(2008)(2009) and the SMOS time series (2010-2014) with a purpose to depict which areas have become wetter or drier between 2003 and 2014.

Summary

A new level of the SMOS surface soil moisture (SSM) products has been released, namely the SMOS level 3 SSM products (SMOSL3). The SMOSL3 product is recent and thus currently subject to validation. In this context, the overall objective of this Ph.D. research work was investigating possible similarities and/or discrepancies and possible fusion of SMOSL3 SSM products with other existing microwave satellite datasets as an extension of preceding efforts to evaluate the SMOS SSM products.

In the first part of this Ph.D. thesis research (Chap. IV), a comparative analysis of SMOSL3, at L-band, with the AMSR-E SSM, at C-band, was presented. SM-DAS-2 SSM products were used to monitor both SMOSL3 and AMSR-E SSM from 03/2010 to 09/2011, a period during which both SMOS and AMSR-E products were available at the global scale. It was shown that both SMOSL3 and AMSR-E captured well the spatio-temporal variability of SM-DAS-2 for most of the biomes. In terms of correlation values, the SMOSL3 product was found to better capture the SSM temporal dynamics in highly vegetated biomes ("tropical humid", "temperate humid", etc.) while best results for AMSR-E were obtained over arid and semi-arid biomes ("desert temperate", "desert tropical", etc.). Finally, we showed that the accuracy of the remotely sensed SSM products is strongly related to the Leaf Area Index (LAI): (i) both the SMOSL3 and AMSR-E (marginally better) SSM products correlated well with the SM-DAS-2 product over regions with sparse vegetation for values of LAI ≤ 1, (ii) in regions where LAI >1, SMOSL3 showed better correlations with SM-DAS-2 than AMSR-E, and (iii) SMOSL3 had a consistent performance up to LAI = 6, whereas the AMSR-E performance deteriorated with increasing values of LAI. This section reveals that SMOS and AMSR-E complement one another in monitoring SSM over a wide range of conditions of vegetation density and that there are valuable satellite observed SSM data records over more than 10 years, which can be used to study land-atmosphere processes. This is one of the first this Ph.D. research work we also found that passive L-band microwave (e.g. SMOS) proved to be performant in semi-arid areas, where RFI is low, compared to active C-band sensors (e.g. ASCAT). These areas are subject to high stress in terms of water resources and satellite based SSM datasets are very useful to monitor this stress. For instance, specific studies need to be developed in semi-arid areas (like Yemen). The combination of multi-sensors (SMOS, the upcoming SMAP mission, AMSR-E) supported by in-situ monitoring station, to be installed in Yemen, is envisioned in the near future.

4.

As said previously, one of the limitations of this Ph.D. research was using Land Surface Models simulations as benchmarks, which are commonly used for evaluating the remotely sensed SSM at larges scales. Much less attention has been paid to the use of other space-borne datasets such as the Gravity Recovery and Climate Experiment (GRACE) satellite, which has been providing information on total water storage change (TWS) since 2002. This limitation can be overcome, in the future, by integration of GRACE data, for instance, into the validation of SMOS SSM datasets. Possibilities and benefits of relating the SMOS SSM products to TWS provided by the GRACE should be investigated. [START_REF] Abelen | Relating satellite gravimetry data to global soil moisture products via data harmonization and correlation analysis[END_REF] compared GRACE data, for instance, against ASCAT SSM products using correlation analysis between change in SSM from ASCAT and change in TWS from GRACE. This can be done using also SMOS SSM products to identify regions where the change of TWS is in agreement with SSM, thus, the regions where SMOS datasets may be useful for the understanding of TWS and vice-versa. On the other hand, GRACE is only able to provide the TWS but not to determine the individual contribution of each variable in the observed TWS integral signal. Further research shall focus [START_REF] Schmugge | Survey of methods for soil moisture determination[END_REF][START_REF] Smith | Soil and Environmental Analysis -Physical Methods -Second Edition:Revised and Expanded[END_REF]Walker et al., 2004;Zazueta & Xin, 1994)

List of tables

Statement of Co-Authorship

The manuscripts for chapters