Catherine Prigent

Carlos Jimenez

An evaluation of the synergy of satellite passive microwave observations between 1.4 and 36 GHz, for vegetation characterization over the Tropics published in Remote Sensing of Environment

An evaluation of the synergy of satellite passive microwave observations between 1.4 and 36 GHz, for vegetation characterization over the Tropics

Introduction

Vegetation distribution and its dynamics strongly affect the Earth water, energy, and carbon cycles, through complex biogeophysical and biogeochemical processes, at intricate time and spatial scales [Bonan, 2015]. Vegetation covers ∼20% of the globe, and large scale monitoring of its parameters is critical, to evaluate its response to anthropogenic pressure and climate changes.

Satellite observations provide a unique possibility to monitor the vegetation distribution and dynamics at global scales on a regular basis. Vegetation monitoring from satellites has been primarily based on visible-infrared observations, with the Normalized Difference Vegetation Index (NDVI) being one of the most popular satellite-derived environmental parameters, available for ∼4 decades with kilometric spatial resolution (see [Tucker, 1979] for pioneering work). NDVI is calculated from the difference in the reflectances of green vegetation between red and near-infrared wavelengths and is representative of the amount of photosynthetically active chlorophyll components of the vegetation. Different parameters such as the Leaf Area Index (LAI) or the Fraction of Absorbed Photosynthetically Active Radiation (FAPAR) have been calculated using similar observations to characterize the green elements of the vegetation. However, NDVI being derived from visible and infrared observations, it is not available, or is at least contaminated, under cloudy conditions. In addition, it tends to saturate for dense vegetation such as tropical forests, as it is only representative of the top layer of the vegetation. Nevertheless, the visible-infrared observations (along with all its derived vegetation metrics) remain a very valuable source of information for vegetation studies, at local to global scales, for multiple applications (e.g., agriculture, weather prediction, climate monitoring).

Microwave satellite remote sensing offers complementary information on the vegetation [Chukhlantsev, 2006]. First, it is partly insensitive to clouds and it can sense within or below the vegetation canopy with lower frequencies having a greater penetration depth. Second, microwave observations are primarily sensitive to the water presence in the vegetation. Water strongly affects the dielectric properties of the media, modifying the attenuation, emission, and scattering of vegetation and soil at microwave frequencies [START_REF] Ulaby | Microwave remote sensing: Active and passive. volume 1-microwave remote sensing fundamentals and radiometry[END_REF]Long, 2015]. As a consequence, contrarily to visible-infrared information, the microwave observations should be rep-resentative of both photosynthetic and non-photosynthetic above ground biomass, including trunk and branches. With increasing attenuation in the vegetation with increasing frequencies, it is expected that over a dense forest the lower microwave frequencies provide more information about the woody parts of the vegetation, whereas the higher microwave frequencies mostly sense the foliage in the canopy. Early works from [Choudhury et al., 1987, Paloscia andPampaloni, 1988] showed evidence of a relationship between the passive microwave observations and the vegetation at large scales, followed by more quantitative assessments of vegetation properties (e.g., the vegetation biomass in [START_REF] Wigneron | A simple algorithm to retrieve soil moisture and vegetation biomass using passive microwave measurements over crop fields[END_REF], the vegetation water content in [START_REF] Njoku | Retrieval of land surface parameters using passive microwave measurements at 6-18 ghz[END_REF], or the vegetation phenology in [START_REF] Shi | Microwave vegetation indices for short vegetation covers from satellite passive microwave sensor amsr-e[END_REF]). The Vegetation Optical Depth (VOD) calculated from passive microwave observations (e.g., [START_REF] Owe | A methodology for surface soil moisture and vegetation optical depth retrieval using the microwave polarization difference index[END_REF], Liu et al., 2011, Jones et al., 2011, Konings et al., 2016, Fernandez-Moran et al., 2017, Wigneron et al., 2021]) is typically based on the zeroth-order solution of the soil-vegetation radiative transfer equation (the tau-omega model), and it integrates the vegetation water content and structural effects. Several methods have been developed to calculate the VOD, using multi-polarizations, multi-angles, and/or multi-temporal observations depending on the possibilities offered by the instrument, with the help of ancillary data such as soil roughness, land surface temperature, and land cover classification (this later parameter possibly derived from NDVIrelated products). See the review by [START_REF] Frappart | Global monitoring of the vegetation dynamics from the vegetation optical depth (vod): A review[END_REF]. Recent developments in VOD calculation tend to limit the contribution of ancillary information for noise reduction, but still use some necessary external inputs [START_REF] Fernandez-Moran | A new calibration of the effective scattering albedo and soil roughness parameters in the smos sm retrieval algorithm[END_REF], Wigneron et al., 2021]. Vegetation biomass estimation from microwaves assumes that the vegetation water content to which microwaves are sensitive is tightly linked to the biomass of the plant and to its carbon content, especially at low microwave frequencies that penetrate deep in the vegetation with less influence of green non-woody plant components [START_REF] Liu | Global long-term passive microwave satellitebased retrievals of vegetation optical depth[END_REF], Brandt et al., 2018, Fan et al., 2019]. Benchmark forest carbon stocks have been mapped from the combination of in situ inventories and satellite data from lidar, from visible/infrared images, and from active microwave observations [START_REF] Saatchi | Benchmark map of forest carbon stocks in tropical regions across three continents[END_REF]. Significant correlation has been evidenced between the VOD at 1.4 GHz and large scale inventories of above ground carbon (for instance from [START_REF] Saatchi | Benchmark map of forest carbon stocks in tropical regions across three continents[END_REF]) and this relationship has been exploited to reveal recent carbon losses in African drylands [START_REF] Brandt | Satellite passive microwaves reveal recent climate-induced carbon losses in african drylands[END_REF], or to quantify the inter-annual dynamics of the total tropical forest carbon [START_REF] Fan | Satellite-observed pantropical carbon dynamics[END_REF]. VODs at higher frequencies have also been explored. For instance, [START_REF] Jones | Satellite passive microwave remote sensing for monitoring global land surface phenology[END_REF], Jones et al., 2014] showed the sensitivity of the VOD at 10 and 18 GHz to the vegetation phe-nology, overcoming limitations affecting satellite optical-infrared observations. Currently, the Soil Moisture and Ocean Salinity (SMOS) and the Soil Moisture Active Passive (SMAP) missions provide satellite observations at 1.4 GHz (L band), and measurements from 6 to 36 GHz (C, X, Ku, and Ka bands) are available from the Advanced Microwave Scanning Radiometer-2 (AMSR2).

The relative merit of passive microwave observations at different frequencies and their potential complementarity for vegetation characterization have been raised in several studies, from satellite observations (e.g., between 6 and 18 GHz [START_REF] Njoku | Retrieval of land surface parameters using passive microwave measurements at 6-18 ghz[END_REF], between 19 and 85 GHz [START_REF] Prigent | Joint characterization of vegetation by satellite observations from visible to microwave wavelengths: A sensitivity analysis[END_REF]) or from ground-based measurements (e.g., between 1.4 and 90 GHz [START_REF] Calvet | Sensitivity of passive microwave observations to soil moisture and vegetation water content: L-band to wband[END_REF]). More recently, [START_REF] Chaparro | Sensitivity of l-band vegetation optical depth to carbon stocks in tropical forests: a comparison to higher frequencies and optical indices[END_REF] compared the sensitivity of the VOD between 1.4 and 10 GHz to above ground carbon, as measured from airborne lidar in South American forests: although they showed that the 1.4 GHz band observations have a good potential for the quantification of the carbon stocks, they indicated the synergy of multi-frequency observations for an improved monitoring. [START_REF] Baur | Estimation of relative canopy absorption and scattering at l-, c-and x-bands[END_REF]] also analyzed VODs from 1.4 to 10 GHz, in an attempt to quantify the absorption and scattering losses as a function of vegetation type, and as a function of frequency. Their results showed that the VODs at 6 and 10 GHz are mostly sensitive to the leaf phenology, whereas the 1.4 GHz VOD variations are dominated by changes in the water content of stems and woody parts. [START_REF] Li | Global-scale assessment and inter-comparison of recently developed/reprocessed microwave satellite vegetation optical depth products[END_REF] inter-compared VOD at different frequencies, and showed that they have complementary capabilities in monitoring vegetation. All these studies suggest that the combined use of multiple microwave frequencies should allow new insights into the vegetation functioning.

The Copernicus Imaging Microwave Radiometer (CIMR) mission is currently being implemented by the European Space Agency (ESA) as a High Priority Expansion Mission. It partly inherits from previous studies conducted at ESA for the Multifrequency Imaging Microwave Radiometer (MIMR) [START_REF] Bernard | Mimr: Multifrequency passive microwave radiometer[END_REF]. CIMR is a conically scanning microwave radiometer imager in a sun-synchronous polar orbit that will provide, for the first time, simultaneous measurements at 1.4, 6.9, 10.65, 18.7, and 36.5 GHz [Kilic et al., 2018]. With its large deployable ∼8 m antenna, it will have a spatial resolution of ∼55 km at 1.4 GHz, ∼15 km at 6 and 10 GHz, and ∼5 km at 18 and 36GHz. For an extensive description of the mission, see https://cimr.eu/sites/cimr.met.no/files/documents/CIMR-MRD-v2.0-20190305-ISSUED0.pdf. The potential synergy of the CIMR frequencies for the characterization of vegetation is expected, but still needs to be quantified at large scales.

Analyzing the synergy of the CIMR frequencies for vegetation characterization could be based on radiative transfer model simulations between 1.4 and 36 GHz, using a set of vegetation and soil input parameters. That would suppose the existence of a reliable and consistent radiative transfer model from 1.4 to 36 GHz, along with representative and coherent vegetation and soil parameters, at least at regional scales. [START_REF] Njoku | Retrieval of land surface parameters using passive microwave measurements at 6-18 ghz[END_REF] insisted on the difficulty to model the interaction between the microwave radiation and the land surface, due to the large number of factors that affect the emission and scattering processes (soil and vegetation numerous physical properties, surface temperature, atmosphere), to the non-linearity and complexity of the processes, to the spatial heterogeneity of the surface properties, and to the lack of in situ measurements with coincident observations to constrain the problem. Despite significant efforts in radiative transfer model developments, primarily at 1.4 GHz in the framework of SMOS and SMAP (e.g., [START_REF] Ferrazzoli | Simulating l-band emission of forests in view of future satellite applications[END_REF], Wigneron et al., 2007]), a recent evaluation of state-of-the-art radiative transfer models at 1.4 GHz at ECMWF still shows discrepancies with satellite observations [de Rosnay et al., 2020]. At higher frequencies, the simulation results are not expected to be better: insuring a consistent agreement between radiative transfer simulations and observations over a large frequency range is usually very challenging, as most models are partly based on ad hoc parameterization for specific instrument observing conditions (such as frequency, polarization, incidence angle). As discussed in [START_REF] Baur | Estimation of relative canopy absorption and scattering at l-, c-and x-bands[END_REF], the retrieval of VOD from radiative transfer modeling often relies upon the assumption that several parameters, such as the effective physical temperature, the soil moisture at the penetration depth, or the effective surface roughness, are independent of the frequency, which is questionable when calculating the VODs at different frequencies, especially with the intent of comparing their potential. Exploiting the direct relationship between the satellite brightness temperatures and the geophysical variables is another solution that already proved efficient. For exemple for the estimation of soil moisture from passive microwave observations, a statistical neural network inverse model can be trained on coincident satellite observations and soil moisture model outputs at global scale [START_REF] Aires | Sensitivity of satellite microwave and infrared observations to soil moisture at a global scale: 2. Global statistical relationships[END_REF], Kolassa et al., 2013]. This methodology is currently applied at ECMWF for near-real time operational estimation of soil moisture with SMOS [START_REF] Rodriguez-Fernandez | Smos neural network soil moisture data assimilation in a land surface model and atmospheric impact[END_REF].

Here we propose an objective and direct analysis of the sensitivity of existing close-to-CIMR passive microwave observations from 1.4 to 36 GHz to the vegetation information over the Tropics. It consists in studying the direct statistical relationships between the satellite observations and veg-etation parameters, without relying on characterizing the vegetation and soil response by radiative transfer modeling. It involves an attempt to retrieve two complementary vegetation parameters from existing close-to-CIMR multi-frequency microwave observations, the first vegetation parameter mostly related to the foliage and the photosynthesis activity of the chlorophyll (NDVI), and the second vegetation parameter representative of the woody components and its carbon stock (the Above Ground Carbon (AGC) quantity estimated from [START_REF] Saatchi | Benchmark map of forest carbon stocks in tropical regions across three continents[END_REF]). Notice that at this stage, the goal is not to develop an optimal retrieval method, but to analyze the information content of the multi-frequency observations for vegetation characterization and to quantify their potential synergies.

The passive microwave satellite observations and the vegetation related datasets are presented in Section 1. The methodology is described in Section 2. The results are discussed in Section 3, first with a general analysis of the sensitivity of the passive microwave data to the vegetation parameters, and then with the inversion of the vegetation parameters with multi-frequency passive microwaves and the quantification of the frequency synergy. Section 4 concludes this study.

Data

A large dataset of passive microwave satellite observations has been collected, along with spatially and temporally coincident vegetation related parameters, derived from visible-infrared satellite observations (NDVI) and from maps of the Above Ground Biomass (AGB). Data have been systematically averaged over a 0.25 • x0.25 • regular grid. All data with daily or sub-daily variations have also been averaged on a 8-day period, following the temporal pattern selected by MODIS products. Data are prepared for 2015. With SMAP data starting in April, the analysis covers April to December 2015. The surface waters have been filtered out, following the monthly mean surface water extent at 0.25 • resolution, available from the Global Inundation Extent from Multi-Satellite version 2 (GIEMS2) [START_REF] Prigent | Satellite-derived global surface water extent and dynamics over the last 25 years (giems-2)[END_REF].

One key vegetation-related data set (the AGB reference map from [START_REF] Saatchi | Benchmark map of forest carbon stocks in tropical regions across three continents[END_REF]) is essentially available over the tropical area. As a consequence, this first analysis concentrates on the tropical region, from 22 • S to 22 • N. It nevertheless includes a large variety of environments, from semi-arid vegetation to tropical forests.

Satellite passive microwaves

The passive microwave signals over vegetated land surfaces are the complex result of soil properties (e.g., humidity, roughness), vegetation characteristics (e.g., fractional coverage within the field-of-view, water content, foliage structure), surface temperature (Ts), and atmospheric contribution. The atmospheric contribution (water vapor, clouds, and rain) decreases with decreasing frequencies, with rather limited contribution at 10 GHz and below. The presence of vegetation generally increases the surface emissivity, especially the horizontal polarization, and it tends to depolarize the soil contribution that can be rather specular. To reduce the impact of the surface temperature in the microwave signatures, MicroWave Indices (MWI) have been used very early [START_REF] Choudhury | Monitoring vegetation using nimbus-7 scanning multichannel microwave radiometer's data[END_REF]. Here, we calculated it as: MWI=100* (TBV-TBH)/(TBV+TBH), where TBV and TBH are, respectively, the brightness temperatures at vertical and horizontal polarizations. A factor 100 is used in this study as the (TBV-TBH)/(TBV+TBH) ratio is usually lower than 0.05 over vegetation. Neglecting the atmospheric contribution, the microwave brightness temperature TB can be written as TB=emissivity*Ts, and MWI then corresponds to the ratio of the emissivity polarization difference normalized by its sum.

In this study, we used passive microwave observations between 1.4 and 36 GHz. Only passive microwave observations at night or early morning are used, to further reduce the impact of the Ts diurnal variations. We are fully aware that passive microwaves are not only sensitive to the vegetation properties, and that the variability of many other parameters affects the variables (such as the soil moisture or roughness, especially at low frequency under sparse vegetation). MWI (as well as the emissivity polarization difference) is expected to decrease with vegetation density increase; over bare soils, it increases with soil moistures increase and decreases with soil roughness increase [START_REF] Ulaby | Microwave radar and radiometric remote sensing[END_REF].

The 1.4 GHz observations (L band)

The SMAP satellite, launched at the end of January 2015 by NASA, is equipped with a real aperture antenna of 6 m to observe the Earth surface at 1.4 GHz with a fixed 40 • incidence angle and a native spatial resolution of 36 km x 47 km [START_REF] Entekhabi | Smap handbook[END_REF]. We use the L1B 36 km L-band brightness temperature at vertical and horizontal polarizations from SMAP (https://nsidc.org/data/SPL1BTB/versions/4, [START_REF] Piepmeier | Smap l1b radiometer half-orbit timeordered brightness temperatures[END_REF]).

2.1.2 The 6 to 36 GHz observations (C, X, Ku, and Ka bands) AMSR2, on board the Japanese JAXA GCOM-W1 mission, provides observations at frequencies between 6 and 89 GHz, in both vertical and horizontal polarizations, with an incidence angle of 55 • . We explored the frequencies that are common to the CIMR project, i.e., the 6, 10, 18, and 36 GHz channels, with respective spatial resolutions of 48, 33, 18, and 9 km. The other channels are more affected by the atmosphere (at 23.8 and 89.0 GHz) or are rather redundant to already selected channels (i.e., at 7.3 GHz). The top of the atmosphere TBs are extracted from the JAXA data center (https://suzaku.eorc.jaxa.jp/GCOM W/index.html). The level L3 product is used [START_REF] Maeda | Gcom-w1 amsr2 level 1r product: Dataset of brightness temperature modified using the antenna pattern matching technique[END_REF], already projected on a 0.25 • x0.25 • regular grid.

Vegetation-related datasets

MODIS vegetation indices

MODIS vegetation indices are derived from 16-day composites of reflectances in the red, near-infrared, and blue wavelengths. Two major vegetation indices are provided from the atmospherically-corrected reflectances: NDVI, calculated as the difference of the red (645 nm) and near-infrared (858 nm) reflectances over their sum, and the Enhanced Vegetation Index (EVI) that also uses the reflectances in the blue (469 nm), to minimize canopy background variations and maintain sensitivity over dense vegetation conditions. See for instance [START_REF] Huete | Overview of the radiometric and biophysical performance of the modis vegetation indices[END_REF] and the very abundant NDVI and EVI literature. MODIS instruments from both Terra and Aqua satellites are combined to permit a higher temporal resolution product, especially in areas strongly affected by cloud coverage.

Here, the MOD13C1 (from Terra) and MYD13C1 (from Aqua) L3 products are both used (https://lpdaac.usgs.gov/products/mod13c1v006/), to provide vegetation estimates every 8 days (16-day composites produced alternatively every 8 days from the two satellites). The initial 0.05 • grid (∼5 km) are aggregated to the 0.25 • x0.25 • regular grid in this study, for comparison with the other data.

Above Ground Carbon stock

A reference map of total forest biomass in the tropical region has been produced by [START_REF] Saatchi | Benchmark map of forest carbon stocks in tropical regions across three continents[END_REF], based on field measurements, Geoscience Laser Altimeter System (GLAS) LIDAR data, and spatial imagery from visible-infrared and active microwave data. A large collection of calibra-tion plots (∼500) in coincidence with GLAS measurements is first analyzed, and the result is spatially extrapolated with MODIS, SRTM (Shuttle Radar Topography Mission), and QuikSCAT images. The benchmark map illustrates regional patterns at 1 km spatial resolution and provides methodologically comparable estimates of biomass, representative of circa 2000. Once the total biomass is estimated, it is commonly admitted that the carbon stock corresponds to 50% of the total biomass (e.g., [START_REF] Saatchi | Benchmark map of forest carbon stocks in tropical regions across three continents[END_REF], Brandt et al., 2018]). [START_REF] Brown | The storage and production of organic matter in tropical forests and their role in the global carbon cycle[END_REF] presents significant results, and some discussion is proposed in [START_REF] Elias | Assessing interand intra-specific variation in trunk carbon concentration for 32 neotropical tree species[END_REF] for instance.

Here, we will also adopt the 50% coefficient to convert the biomass into carbon stock.

For comparison purposes, the [START_REF] Avitabile | An integrated pan-tropical biomass map using multiple reference datasets[END_REF]] biomass map at 1 km spatial resolution is also tested in this study. It was obtained by merging in situ data from forest plots, with the [START_REF] Saatchi | Benchmark map of forest carbon stocks in tropical regions across three continents[END_REF] and the [START_REF] Baccini | Estimated carbon dioxide emissions from tropical deforestation improved by carbon-density maps[END_REF] maps, using machine-learning techniques. The merged dataset is representative of the 2000-2010 period.

Land cover dataset

GlobCover is an ESA initiative providing land cover maps derived from the 300 m MERIS sensor on board the ENVISAT satellite mission. It contains 22 land cover classes and is representative of December 2004 -June 2006. This land cover classification is adopted in this study: the initial high resolution product is aggregated onto the 0.25 • x0.25 • regular grid, by selecting the dominant land cover type.

Method

Contrarily to methods using radiative transfer modeling, a purely statistical analysis of the passive microwave observations was conducted, with no a priori assumptions about vegetation or soil characteristics that could interfere or bias the results.

First, the direct relationship between the passive microwave observations from 1.4 to 36 GHz and the two vegetation parameters (NDVI and AGC) were studied. The spatial correlations were analyzed, over the Tropics, for a given time of the year (June). Maps of the temporal correlations between the variables were then calculated over the full period covered by the dataset, over the same region. The variations of the microwave observations were also studied, per vegetation types and for different seasons.

Then, we analyzed the synergy of the multi-frequency microwave observations by testing a statistical retrieval of two complementary vegetation parameters, one representative of the foliage (NDVI) and one related to the carbon stock (AGC), for different combinations of the microwave frequencies. To conduct the retrieval tests, we propose an inversion method based on the direct statistical relationships between the satellite observations and the vegetation parameters to estimate, using artificial neural networks (NN). Compared to multilinear regressions, the NN can account for complex and non-linear relationships between the variables while maintaining the algorithm simple and quick to run. NN regressions have been successfully applied to many remote sensing problems (e.g., [START_REF] Aires | A new neural network approach including first guess for retrieval of atmospheric water vapor, cloud liquid water path, surface temperature, and emissivities over land from satellite microwave observations[END_REF], Jimenez et al., 2009, Rodriguez-Fernandez et al., 2019]). Multi Layered Perceptron (MLP) models [START_REF] Rumelhart | Learning internal representations by error propagation[END_REF]] were adopted. A NN is defined by the number of input neurons (the satellite information used for the retrieval), the number of outputs (the vegetation parameter to estimate) and the number of neurons in a hidden layer to control the complexity of the NN model. The MLP weights are assigned by a Marquardt-Levenberg backpropagation algorithm [START_REF] Hagan | Training feedforward networks with the marquardt algorithm[END_REF], with a validation method to monitor the evolution of the training error and avoid overfitting to the training data set. For each retrieval test, corresponding to a frequency combination and one of the two vegetation parameter, a new MLP of one input layer, one hidden layer with a sigmoidal activation function, and one output layer with a linear function was trained. The number of inputs depended upon the frequency selection. For each passive microwave frequency, two inputs are selected: the MWI and the TBH, as experiments demonstrated that the addition of the TBH to the MWI systematically improved the results.

Tests showed that one hidden layer with a sufficiently large number of neurons was sufficient. For a given output (NDVI or AGC), the NNs corresponding to the different frequency combinations were all trained on the same dataset, to insure fair comparisons. It corresponds to a subset of the initial dataset (one 8-day averaged period per season over a 9 month initial 8-day averaged dataset, i.e., ∼12% of the initial dataset), over the Tropical continental area (from 22 • S to 22 • N). Different training datasets were tested (more than one 8-day average per month, and changing the months), with very similar results. For NDVI, time coincident NDVI and passive microwave observations are considered. However, AGC from [START_REF] Saatchi | Benchmark map of forest carbon stocks in tropical regions across three continents[END_REF] being a static reference, the NNs to reproduce AGC are always trained on the same AGC values, regardless of the time period.

The retrievals were then tested on the original data set, excluding the data used to train the NNs. Two metrics assessed the quality of the re-trievals: the coefficient of determination R 2 (the square of the linear correlation coefficient R), and the Root Mean Square Error (RM SE) calculated from the difference between the retrieved value and the truth. Note that the systematic error (or bias) is expected to be 0 over the full dataset, by construction of the NNs, and as a consequence, RMSE is very close to the random error for this dataset. Comparisons of the metrics for the retrievals using the different frequency combinations made it possible to quantify the synergy between the frequencies.

Results

Large Scale Correlation Analysis

Figure 1 presents images of MWI at 1.4 GHz from SMAP, and at 6 and 18 GHz from AMSR2 over the Tropics, for June 2015, along with corresponding the MODIS NDVI image. The static AGC [START_REF] Saatchi | Benchmark map of forest carbon stocks in tropical regions across three continents[END_REF]] is also shown. MWI at 1.4 GHz shows a larger dynamical range than MWI at 6 or 18 GHz. This is particularly clear in the transition zone from the Sahara deserts southward to the equatorial forest in Africa or in South America, from the east to the west coast, along latitudes around 10 • S. The tropical forest around the equator in Africa, indicated by high NDVI and high AGC, is well delineated at 1.4 GHz, with low MWI showing spatial patterns similar to NDVI and AGC.

To characterize the relationship between the passive microwave observations and the vegetation parameters, the density plots of selected pairs of variables are presented in Figure2, along with the corresponding coefficient of determination (R 2 ), first with NDVI, second with AGC, for the region (the Tropics) and month (June) displayed in Figure 1. The relationship between NDVI and EVI is also presented as well as the link between AGC from [START_REF] Saatchi | Benchmark map of forest carbon stocks in tropical regions across three continents[END_REF] and from [START_REF] Avitabile | An integrated pan-tropical biomass map using multiple reference datasets[END_REF]. Deserts (following the GlobCover classification) and surface waters (following a monthly climatology calculated from [START_REF] Prigent | Satellite-derived global surface water extent and dynamics over the last 25 years (giems-2)[END_REF]) are excluded from the analysis. R 2 between MWI and NDVI increases between 1.4 and 6 GHz, but then decreases from 6 to 18 GHz (with similar results at 18 and 36 GHz, not shown). Note that the scatterplot of MWI at 1.4 GHz versus NDVI presents two branches for the same high values of MWI: even with rather high density of green vegetation (rather high NDVI), observations at 1.4 GHz can detect the soil moisture and can present high polarization differences (high MWI). R 2 between MWI and AGC strongly decreases from 1.4 to 6 GHz and keeps decreasing to 18 GHz, with similar R 2 at 18 and 36 GHz (not Figure 1: From top to bottom: the MicroWave Index (MWI) at 1.4 GHz (calculated from SMAP), at 6 and 18 GHz (calculated from AMSR2), the Normalized Difference Vegetation Index (NDVI) from MODIS, and the Above Ground Carbon (AGC) in Mg/ha from [START_REF] Saatchi | Benchmark map of forest carbon stocks in tropical regions across three continents[END_REF], for the Tropics, averaged over June 2015 for MWI and NDVI.

shown). The scatterplot of NDVI versus AGC shows that for low AGCs (<50 Mg/ha), the NDVI dynamics can be significant (from 0.1 to 0.8). This is likely representative of the photosynthesis activity of chlorophyll in rather low vegetation with limited trees (limited carbon content). For high NDVI (>0.75), AGC presents a rather large range of values that are expected to characterize a variety of dense forest areas with varying carbon contents. NDVI and EVI are strongly correlated (R 2 =0.85) but the amplitude of variation for EVI is clearly smaller than for NDVI. Contrarily to what is sometimes shown, EVI here tends to saturate over very dense vegetation and rarely exceeds 0.5 even over tropical forests. We checked that the correlation coefficient is always smaller between MWI and EVI than between MWI and NDVI. [START_REF] Saatchi | Benchmark map of forest carbon stocks in tropical regions across three continents[END_REF] used NDVI and not EVI to interpolate the biomass information among in situ AGB estimates to produce their benchmark biomass map, as well as several other studies related to dense vegetation (e.g., [START_REF] Brandt | Satellite passive microwaves reveal recent climate-induced carbon losses in african drylands[END_REF]). Our analysis here also tends to favor NDVI versus EVI, for the characterization of dense forests.

The previous analysis focused on the spatial correlations between the different variables for a given time of the year (June). The temporal correlations between NDVI and MWIs are presented in Figure 3 (statistical significance is tested, and pixels with p<0.05 are not displayed). It is calculated over April to December 2015, with SMAP not available before. The temporal correlations between NDVI and MWI at 1.4 GHz are dominantly positive, except in regions of very dense forests around the equator (where the correlation is negative or not statistically significant). For most locations, when NDVI increases, i.e., the 'green' vegetation grows, MWI at 1.4 GHz also increases, i.e., the emissivity polarization difference increases. 'Green' vegetation increases with available soil moisture for plant growth and correlation between NDVI and MWI is expected. The opposite prevails at 6 GHz and at higher frequencies (not shown), where negative correlations between NDVI and MWI time series are observed. The temporal correlations between MWI at 1.4 and 6 GHz are nevertheless mostly positive. The difference in behavior between 1.4 GHz and higher frequencies with respect to NDVI indicates some complementarity between the passive microwave frequencies that could be exploited, to better characterize the vegetation. The physical interpretation of these behaviors in the passive microwaves is due to different extinction in the vegetation as a function of frequency, related to both attenuation and scattering by the vegetation elements containing water. As already stressed by [START_REF] Baur | Estimation of relative canopy absorption and scattering at l-, c-and x-bands[END_REF] or [START_REF] Momen | Interacting effects of leaf water potential and biomass on vegetation optical depth[END_REF], the extinction is not only due to the absorption by the water in the vegetation, but also to the scattering of the microwave radiation by the canopy structure (trunk, branches, leaves), with their respective constituents and sizes. Except over dense forests, with increasing NDVI (due to vegetation chlorophyll activity or 'greenness'), the emissivity polarization difference at 6 GHz (and at higher frequencies) decreases with increasing extinction in the foliage. At 1.4 GHz, the vegetation extinction is lower than at higher frequencies: the effect of the soil moisture on the variability of the emissivity polarization difference can still be observed when the vegetation is not totally opaque.

Figure 4 presents cross-sections of MWI, NDVI, and AGC at two longitudes in Africa and in South America, for June and December. All the variables are normalized for an easier comparison (see the figure caption). Large gradients are observed for all variables in Africa, from the semi-arid regions north of 5 • N, to the dense forest around the equator, down to the shrubland and grassland southwards. In South America, the Amazon River and its associated floodplains induce very large values of MWIs (at ∼ 3 • S at 60 • W and ∼ 2 • S at 55 • W). The presence of standing water at the surface generates strong polarization differences in the microwave surface emissivity and this property has been exploited to derive the extent and dynamics of the surface water at global scale (e.g., [START_REF] Prigent | Satellite-derived global surface water extent and dynamics over the last 25 years (giems-2)[END_REF]). In the equatorial forest where AGC reaches its maximum values, in Africa as well as in South America, NDVI reaches high values whereas MWIs show their lowest values, as expected. Note that in these evergreen tropical forests, NDVI tends to vary during the year, although MWI values appear quite stable, regardless of the season. These temporal changes in NDVI over evergreen forests have already been documented at several occasions (e.g., [START_REF] Prigent | Joint characterization of vegetation by satellite observations from visible to microwave wavelengths: A sensitivity analysis[END_REF] ) and are essentially related to atmospheric contamination (water vapor and possibly clouds) in NDVI, with the contamination modulated by the displacement of the Inter Tropical Convective Zone with seasons. Over shrubland and grassland with low AGC, NDVI during summer can reach values of the same order as over very dense forests (see for instance the high values of NDVI in Africa in December around 10 • S). In these regions, the seasonal changes of MWI at 1.4 GHz is significant and much larger than at higher frequencies, with even opposite behavior as observed between 5 • S and 10 • S at longitude 25 • E (top right panel in Figure 4). An increase in soil moisture between June and December induces a vegetation increase (as indicated by the increase in NDVI). It results in an increase in the emissivity polarization difference (MWI) at 1.4 GHz, very sensitive to the soil moisture and not significantly attenuated by the vegetation, whereas at higher microwave frequencies, MWI decreases for increasing vegetation extinction. Depending on the vegetation parameters at a given time of the year and depending on the wavelength of observation, the soil and vegetation contribute differently to the signal, and these complementarities can be exploited to better characterize the vegetation with multi-frequency passive microwaves.

For selected vegetation types in Africa (following the GlobCover classification), Figure 5 presents the normalized histograms of NDVI and MWIs at 1.4, 6, 18 GHz for June and December, for two regions north and south of the equator. For each region and each vegetation type, the mean AGC [START_REF] Saatchi | Benchmark map of forest carbon stocks in tropical regions across three continents[END_REF] is indicated. For a given season, with increasing vegetation density from grassland to evergreen forest (and corresponding AGC increase), NDVI increases and MWIs tend to decrease, as expected. The temporal changes from June to December for a given vegetation type is more complex, as already observed in Figure 3 with positive or negative tempo-Figure 4: Cross-sections of AGC [START_REF] Saatchi | Benchmark map of forest carbon stocks in tropical regions across three continents[END_REF], NDVI (MODIS), MWI at 1.4 GHz (SMAP), and MWI at 6 and 36 GHz (AMSR2), for two different longitudes in Africa (top), and in South America (bottom), for two months (June as solid lines and December as dashed lines). Data are averaged over 2 • around the given longitude, and over the month for the dynamic variables. For each figure separately, AGC, NDVI, and MWIs are normalized by their maximum and minimum values over the two months (and over the three frequencies for MWIs). ral correlations between NDVI and MWIs, depending on the frequency and on the relative contribution of the soil and vegetation in the signal. The evergreen forest has stable signatures for both seasons and regions, for all variables except some changes for NDVI as already discussed.

Retrieval of the vegetation parameters and quantification of microwave observation synergy

So far, we analyzed the individual sensitivity of each passive microwave observation from 1.4 to 36 GHz to the vegetation parameters, through the use of a simple microwave index. Recently, several papers also studied the individual sensitivity of the VOD in the different frequency bands to the vegetation information (e.g., AGC in [START_REF] Chaparro | Sensitivity of l-band vegetation optical depth to carbon stocks in tropical forests: a comparison to higher frequencies and optical indices[END_REF] or the vegetation height in [START_REF] Baur | Estimation of relative canopy absorption and scattering at l-, c-and x-bands[END_REF]). Now, we propose to evaluate the synergy of the multi-frequency microwave observations by comparing the retrieval of NDVI and AGC, using different microwave frequency combinations. The analysis in the previous section showed that the spatial and temporal correlation patterns between MWIs and vegetation information (NDVI and AGC) could be rather complex and not necessarily linear, justifying the use of the NN retrieval method, compared to multi-linear regressions.

Tests are conducted, first using individual passive microwave frequencies to reproduce the vegetation information, second using their different combinations to analyze their synergy, including the combination that corresponds to CIMR. Ten different passive microwave combinations have been tested: first, each frequency separately (the 1.4 GHz alone corresponding to SMAP), then the 6, 10, 18, and 36 GHz combination corresponding to AMSR2, and finally the successive addition of frequencies to the 1.4 GHz, to reach the full combination of considered frequencies corresponding to the CIMR configuration. For each frequency, the MWI and the TBH are both used as inputs to the NNs. For each vegetation parameter and frequency combination, a new NN is trained: 20 NNs were thus trained, 10 for the NDVI retrieval and 10 for the AGC retrieval.

All NNs are trained on the same NDVI or AGC training dataset, for comparison purposes between the frequency combinations. The training dataset contains ∼140 000 combinations of the vegetation parameter and the passive microwave observations, for NDVI and AGB separately. For NDVI, time coincident NDVI and passive microwave observations are considered as previously mentioned. For AGC, the NN to reproduce AGC is trained on the same AGC values, regardless of the time period but we tested the train-Figure 5: Normalized histograms of NDVI and MWIs at 1.4, 6, and 18 GHz, for two regions in Africa, for selected vegetation types, as described by the GlobCover classification, for June (solid lines) and December (dashed lines). Top: north of the equator. Bottom: south of the equator. For each region and each vegetation type, the mean AGC from [START_REF] Saatchi | Benchmark map of forest carbon stocks in tropical regions across three continents[END_REF] is indicated.

ing of AGC retrieval by first averaging the microwave observations at the different time steps, and very similar results were obtained. The natural distribution of AGC shows two distinct peaks, one for low AGC at ∼30 Mg/ha and another one at high AGC at ∼120 Mg/ha (see Figure 2). The original training database distribution is resampled to avoid an under representation of medium AGC values. This procedure has already been applied with success at different occasions for similar problems (e.g., [START_REF] Prigent | Satellite-derived global surface water extent and dynamics over the last 25 years (giems-2)[END_REF]) and it has been systematically applied to the training of all the frequency combinations for the retrieval of AGC. NDVI distribution is smoother and this procedure has not been applied to the retrieval of this variable.

Figure 6 presents the results of the retrieval evaluation for both NDVI and AGC, for all the passive microwave combinations, as evaluated with the two selected metrics, the coefficient of determination R 2 , and the RM SE. The evaluation is performed on the remaining 8-day periods in the original dataset, excluding the four 8-day periods from the training dataset.

For the retrieval of NDVI, none of the frequency alone matches the performances obtained with the combination of at least two frequencies. 1.4 and 10 GHz, when used alone, tend to produce the best results. Note that the linear correlation of MWI at 1.4 GHz with NDVI was lower than at higher frequencies (see Figure 2). We checked that when using a multi-linear regression retrieval with the same inputs (MWI and TBH for each frequency), the retrieval results were poorer at 1.4 GHz than at higher frequencies (and significantly much poorer than with the NN for each frequency). The NN retrieval systematically outperforms the linear regression and manages to extract the complex non-linear information present in the observations. The coefficient of determination R 2 between retrieved and true NDVI reaches 0.84 when using all CIMR frequencies, with a RMSE of 0.07 (compared to 0.09 with the 1.4 GHz only). Compared to AMSR2, the CIMR frequency combination performs slightly better with respect to the two selected metrics for NDVI, but the improvement is not significant, especially when considering that the addition of 1.4 GHz to the frequencies from 6 to 36 GHz penalizes the spatial resolution of the retrieved product (with a spatial resolution of 55 km at 1.4 GHz compared to 15 km at 6 GHz with CIMR).

For the retrieval of AGC, 1.4 GHz is the frequency that has the highest information content, with significantly better performances than any other frequency alone. The coefficient of determination R 2 drops significantly from 1.4 to 6 GHz and gets worse at higher frequencies (Figure 6, top panel). That was already concluded by other studies analyzing the relationship between AGC and the VODs for the different frequencies (e.g., [START_REF] Chaparro | Sensitivity of l-band vegetation optical depth to carbon stocks in tropical forests: a comparison to higher frequencies and optical indices[END_REF]). In parallel, AGC retrieval error shows a sharp increase from 1.4 to 6 GHz and then a moderate increase for the higher frequencies. The addition of the higher frequencies to the 1.4 GHz channels improves the AGC retrieval results, with R 2 reaching 0.82 with CIMR (compared to 0.77 with SMAP 1.4 GHz alone), with a RMSE of 21 Ma/ha (compared to 24 Ma/ha with 1.4 GHz only).

Figure 7 shows the RMSE of the retrievals for each vegetation variable, as a function of the variable itself, for the SMAP, AMSR2, and CIMR configurations. For NDVI, CIMR and AMSR2 performances are close, regardless of the NDVI values. For AGC, CIMR performances closely follow the variations of the SMAP ones, as a function of AGC. However, from low to high NDVI or AGC, the CIMR frequency combination always provides the lowest error for both NDVI and AGC estimations. It is thus expected that CIMR will contribute to an improved and consistent estimation of both photosynthetic and non-photosynthetic above ground biomass.

A similar exercice has been applied to EVI (instead of NDVI) and to AGC estimated by [START_REF] Avitabile | An integrated pan-tropical biomass map using multiple reference datasets[END_REF] (instead of AGC from [START_REF] Saatchi | Benchmark map of forest carbon stocks in tropical regions across three continents[END_REF]). For these two variables, the performance of the retrievals is reduced, compared to NDVI and AGC from [START_REF] Saatchi | Benchmark map of forest carbon stocks in tropical regions across three continents[END_REF] (not shown). This is especially noticeable for EVI, regardless of the frequency combination. It could be interpreted as a reduced consistency between the passive microwave observations and EVI and AGC from [START_REF] Avitabile | An integrated pan-tropical biomass map using multiple reference datasets[END_REF], compared to what is existing with NDVI and AGC from [START_REF] Saatchi | Benchmark map of forest carbon stocks in tropical regions across three continents[END_REF]. [START_REF] Fan | Satellite-observed pantropical carbon dynamics[END_REF]] also tends to favor AGC from [START_REF] Saatchi | Benchmark map of forest carbon stocks in tropical regions across three continents[END_REF] compared to the one from [START_REF] Avitabile | An integrated pan-tropical biomass map using multiple reference datasets[END_REF] for comparison with VOD at 1.4 GHz. The saturation observed with EVI over the tropical forests, as compared to NDVI, can be responsible for the reduced performances of the EVI retrieval.

Conclusion

Satellite passive microwave observations from 1.4 to 36 GHz already showed sensitivity to vegetation parameters, primarily through the calculations of VODs at each frequency separately. Here we evaluated the synergy of this frequency range for vegetation characterization through the estimation of two vegetation parameters, the foliage photosynthesis activity as represented by NDVI, and the vegetation above ground carbon stock with AGC, using different combinations of channels in the considered frequency range. NN retrievals are trained on the two considered vegetation parameters, for several microwave channel combinations, including the CIMR configuration. [START_REF] Saatchi | Benchmark map of forest carbon stocks in tropical regions across three continents[END_REF]. Top: the coefficient of determination R 2 between the retrieval and the truth for NDVI (left axis) and AGC (right axis). Bottom: the retrieval error (RMSE) for NDVI (left axis) and AGC (right axis). This methodology avoids the use of any assumptions in the complex interaction between the surface (vegetation and soil) and the radiation, as well as any ancillary observations, to propose a genuine and objective evaluation of the information content of the passive microwave frequencies for vegetation characterization, without any a priori.

The performance of the NN vegetation retrievals is used to quantify the synergy of different frequency combinations. For the retrieval of NDVI, the coefficient of determination R 2 between retrieved and true NDVI reaches 0.84 when using the full 1.4 to 36 GHz range as will be measured by CIMR, with a retrieval error of 0.07. For the retrieval of AGC, the coefficient of determination R 2 reaches 0.82 with CIMR, with an error of 21 Mg/ha. This study also confirmed that 1.4 GHz observations have the highest sensitivity to AGC, as compared to other frequencies up to 36 GHz, at least under tropical environments.

CIMR will provide valuable ecological indicators to enhance our present global vegetation understanding. Considering both vegetation aspects together (foliage photosynthesis activity and carbon stocks) offers a more robust and consistent characterization and assessment of long-term vegetation dynamics at large scale.

Figure 2 :

 2 Figure 2: Density plots of MWI at 1.4, 6, and 18 GHz and vegetation related variables (NDVI, EVI, and AGC), calculated over the Tropics, for June 2015, as a function of NDVI (MODIS) for the two top rows, and as a function of AGC [Saatchi et al., 2011] for the two bottom rows. The colors indicate the number of pixels per bin. The coefficient of determination (R 2 ) is indicated. Deserts and surface water pixels are excluded from the statistics.

Figure 3 :

 3 Figure 3: Maps of the temporal correlations over the Tropics between NDVI (MODIS) and MWI at 1.4 GHz (SMAP) (top panel), between NDVI (MODIS) and MWI at 6 GHz (AMSR2) (middle panel), and between MWI at 1.4 GHz (SMAP) and at 6 GHz (AMSR2) (bottom panel). Pixels with p-values below 0.05 are not displayed.

Figure 6 :

 6 Figure 6: Performance of NDVI and AGC retrievals with different passive microwave combinations. True NDVI and AGC are respectively from MODIS and from[START_REF] Saatchi | Benchmark map of forest carbon stocks in tropical regions across three continents[END_REF]. Top: the coefficient of determination R 2 between the retrieval and the truth for NDVI (left axis) and AGC (right axis). Bottom: the retrieval error (RMSE) for NDVI (left axis) and AGC (right axis).

Figure 7 :

 7 Figure 7: Top: NDVI retrieval error (RMSE), as a function of NDVI, for SMAP, AMSR2, and CIMR frequency combinations. The normalized NDVI distribution is also indicated in dashed line (see left axis). Bottom: Same for AGC.

Acknowledgements

The authors would like to thank Jean-Pierre Wigneron for valuable discussions. They would also like to thank Craig Donlon and the ESA CIMR Mission Advisory Group. Comments from the editor and from three anonymous reviewers made it possible to significantly improve the initial manuscript.


Laureline Lecarme

Aurélie Niyongabo

Frédéric Lafolet

Fannie Alloin

Wayne Jones

come

RuII tris-bipyridine-modified electrode as a sensor for battery electrolyte

Figure S2 .

 S2 Figure S2. Cyclic voltammetry of the Ru II modified carbon electrode (Ф = 2mm) (after 20 cycles

Figure S3 .

 S3 Figure S3. Cyclic voltammetry of the Ru II modified carbon electrode (Ф = 2mm) (after 20 cycles at 100 mV.s -1 ) after transfer in CH3CN + 0.1 M LiClO4 (blue); + 0.1 M LiPF6 (red) or + 0.1 M

Supporting information

Ru II tris-bipyridine modified electrode as a sensor for battery electrolyte Lauréline Lecarme,* [a] , Aurélie Niyongabo, [b] Frédéric Lafolet, [c] Fannie Alloin, [a] Wayne E. Jones Jr., [b] Jean-Claude Leprêtre [a] [a] Univ. Grenoble Alpes, Univ. Savoie Mont Blanc, CNRS, Grenoble INP ⁕ , LEPMI, 38000 Grenoble, France.


Romain Authors

Palich

Marie Gardette

Cécile Bébéar

Éric Caumes

Sabine Pereyre

Gentiane Monsel

Dr Romain Palich
email: romain.palich@aphp.fr

Initial failure of pristinamycin treatment in a case of multidrug-resistant Mycoplasma genitalium urethritis eventually treated by sequential therapy

Keywords:

The initial failure of pristinamycin-based therapy was possibly linked to the presence of A2062T mutation, and the Mycoplasma genitalium infection was finally cured after secondary loss of this mutation.

INTRODUCTION

Mycoplasma genitalium (MG) is the most common cause of urethritis after Neisseria gonorrhoeae (NG) or Chlamydia trachomatis (CT). European treatment guidelines recommend azithromycin 1.5 g (500 mg followed by 250 mg daily for a total of 5 days) , and moxifloxacin (400 mg daily for 7-10 days) as second-line treatment or in case of uncomplicated macrolide resistant MG infection. [START_REF] Jensen | European guideline on Mycoplasma genitalium infections[END_REF] However in less than 10 years, more than 50% of strains have become macrolide resistant and 5-10% fluoroquinolone resistant, in some parts of the world. [START_REF] Fernández-Huerta | Mycoplasma genitalium and antimicrobial resistance in Europe: a comprehensive review[END_REF][START_REF] Machalek | Prevalence of mutations associated with resistance to macrolides and fluoroquinolones in Mycoplasma genitalium: a systematic review and meta-analysis[END_REF] Hence sequential antibiotic treatment following susceptibility testing was suggested for MG urethritis. [START_REF] Durukan | Resistance-Guided Antimicrobial Therapy Using Doxycycline-Moxifloxacin and Doxycycline-2.5 g Azithromycin for the Treatment of Mycoplasma genitalium Infection: Efficacy and Tolerability[END_REF][START_REF] Read | Outcomes of Resistance-guided Sequential Treatment of Mycoplasma genitalium Infections: A Prospective Evaluation[END_REF] Treatment began with doxycycline for 7 days meanwhile possible macrolide resistance was detected. According to susceptibility testing, patients then received azithromycin for 5 days or fluoroquinolones (sitafloxacin or moxifloxacin) for 7 days in case of macrolide resistance. The rationale of sequential therapy beginning with doxycycline is to reduce the bacterial load, to optimize the second antibiotic's effect while limiting the emergence of resistance.

We report a case of multidrug-resistant MG urethritis successfully cured by several sequential antibiotic treatments guided by susceptibility testing.

CASE REPORT

The patient was a 51-year-old Parisian man having sex with men, who had just started HIV preexposure prophylaxis (PrEP). He consulted a general practitioner about urethral symptoms (dysuria and discharge). After performing NG and CT nucleic acid amplification tests (NAATs) on urine specimen, he received empirical therapy combining 7 days oral cefixime plus 1 g single dose azithromycin (Table ). NG and CT NAATs were negative. His symptoms persisted 12 days later.

He was referred to a STI clinic, where the MG NAAT performed was positive. Moxifloxacin was given but stopped after 48 hours because the patient reported tendon pain in lower limbs, as a possible side effect of fluoroquinolones. He was given a sequential treatment with doxycycline for 7 days followed by pristinamycin for 14 days, during which symptoms decreased but relapsed afterwards.

Since his urethral discharge persisted, he was referred to our Infectious Diseases department, at Pitié-Salpêtrière hospital in Paris. MG NAAT remained positive. Amplification and Sanger sequencing of domain V of the 23S rRNA gene 6 identified two mutations. The first one was A2058T substitution (Escherichia coli numbering), known to be associated with macrolide resistance. The second one was A2062T substitution, possibly associated with pristinamycin resistance, as increased pristinamycin MICs were reported for in vitro Mycoplasma pneumoniae strains harboring substitutions at A2062 position. [START_REF] Pereyre | In vitro selection and characterization of resistance to macrolides and related antibiotics in Mycoplasma pneumoniae[END_REF] Amplification and sequencing of the parC gene didn't show any mutation associated with fluoroquinolone resistance.

The patient initially refused moxifloxacin despite his persistent symptoms, fearing a side effect.

He finally accepted a sequential treatment with doxycycline 200 mg daily for 7 days followed by moxifloxacin 400 mg daily for 14 days without complication. A new screening of resistance mutations performed during the moxifloxacin course found the previous A2058T mutation and a new S83I mutation in ParC, associated with fluoroquinolone resistance. The A2062T mutation was not detected anymore. He therefore received an additional sequential treatment with minocycline for 21 days followed by pristinamycin for 14 days.

His urethral symptoms slowly disappeared. MG NAAT performed as test of cure 3 months after completing the last sequential treatment was negative. The time period to obtain test of cure was due to the patient's reluctance to come back to the hospital. MG NAAT performed 10 days later remained negative, thus confirming microbial cure. Three-site NG and CT NAATs (urine, rectal and pharyngeal sites) were all negative throughout this year, as well as HIV and syphilis serologies. All sexual intercourse was protected by condom as reported by the patient.

DISCUSSION

As illustrated here, MG urethritis treatment can become very complex due to antibiotic resistance. International guidelines now recommend doxycycline for 7 days instead of 1 g single dose azithromycine as empirical therapy for urethritis and cervicitis, to preserve macrolide susceptibility in case of undetected MG infection. [START_REF] Read | Azithromycin 1.5g Over 5 Days Compared to 1g Single Dose in Urethral Mycoplasma genitalium: Impact on Treatment Outcome and Resistance[END_REF] For macrolide and fluoroquinolone-resistant MG strains, pristinamycin is the recommended option in Europe, 1 with a success rate averaging 75%. [START_REF] Read | Use of Pristinamycin for Macrolide-Resistant Mycoplasma genitalium Infection[END_REF] But in case of failure, there is hardly any alternative, with the possible exception of spectinomycin 10 though unavailable in Europe or minocycline, which cured71% of cases. [START_REF] Doyle | Nonquinolone Options for the Treatment of Mycoplasma genitalium in the Era of Increased Resistance[END_REF] Sequential treatment has also been suggested, consisting of doxycycline followed by an appropriate antibiotic chosen according to the detected resistance mutations. Although doxycycline cure failed in approximately 70% of cases, it could strongly decrease the bacterial load hence substantially increase the second antibiotic's efficacy. [START_REF] Read | Outcomes of Resistance-guided Sequential Treatment of Mycoplasma genitalium Infections: A Prospective Evaluation[END_REF] Here we successfully changed doxycycline for minocycline, which could be more effective on MG. [START_REF] Doyle | Nonquinolone Options for the Treatment of Mycoplasma genitalium in the Era of Increased Resistance[END_REF] Combination therapy may also be an alternative for treating highly resistant MG. Doyle et al.

reported 75% of therapeutic success with doxycycline and pristinamycine combination therapy in 73 macrolide-resistant MG cases. [START_REF] Doyle | Nonquinolone Options for the Treatment of Mycoplasma genitalium in the Era of Increased Resistance[END_REF] Durukan et al. reported 11/12 cured MG infections using doxycycline and sitafloxacine combination therapy, after pristinamycin failure. 12 However, sitafloxacine is not available in France.

Importantly, the first part of sequential treatment gives time to perform a resistance genotypic test, which requires a specialized molecular biology platform and takes several days. Since resistance may vary depending on antibiotic pressure, we demonstrated here the relevance of repeating the resistance screening. We described the A2062T mutation, possibly associated with resistance to pristinamycin. Although mutations at 2062 position are not detected by any commercial assays, the A2062T mutation has been reported a few times in MG, using 23S rRNA amplification and sequencing. [START_REF] Chrisment | Detection of macrolide resistance in Mycoplasma genitalium in France[END_REF][START_REF] Roy | French Prospective Clinical Evaluation of the Aptima Mycoplasma genitalium CE-IVD Assay and Macrolide Resistance Detection Using Three Distinct Assays[END_REF] So far, this mutation has never been associated with clinical resistance to pristinamycin in MG. However, we suggest it may be associated with pristinamycin resistance, as the A2062G substitution is associated with increased pristinamycin MICs for M. pneumoniae, the phylogenetically closest Mycoplasma species. [START_REF] Pereyre | In vitro selection and characterization of resistance to macrolides and related antibiotics in Mycoplasma pneumoniae[END_REF] Considering the difficulties to grow MG, more studies focusing on pristinamycin treatment failure with characterization of 23S rRNA mutations by Sanger sequencing are needed to confirm this hypothesis.

In conclusion, we assume that the A2062T mutation is associated with pristinamycin resistance in MG. We believe that the resistance profile of MG may vary over time, depending on the different antibiotics received, and that antibiotic efficacy also depends on the bacterial load.

Repeated screening for genotypic resistance, combined with the use of antibiotics with the highest antibacterial activity, could succeed in curing multidrug-resistant MG infections.

TABLE . Therapeutic management and microbiological outcomes of the MG urethritis.

 . NOTES. * Moxifloxacin was stopped due to tendon pain. a. NAAT, nucleic acid amplification test. b. Mutation in 23S rRNA associated with resistance to macrolides, Escherichia coli numbering. c. Mutation in 23S rRNA possibly associated with resistance to pristinamycin, Escherichia coli numbering. d. Mutation in ParC associated with resistance to fluoroquinolones, Mycoplasma genitalium numbering.

	Date	Day	Genito-	Treatment	MG	MG
			urinary		NAAT a	resistance
			symptoms			mutations
	08/23/2019	D0	Yes	Cefixime 200 mg 2/d 7 days
				AND azithromycin 1 g 1 day
	09/04/2019	D12	Yes		Positive
	09/07/2019	D15	Yes	Moxifloxacin 400 mg 1/d 2 days*
				THEN doxycycline 100 mg 2/d 7 days
				THEN pristinamycin 1 g 4/d 14 days
	10/11/2019	D49	Yes		Positive	A2058T b
						A2062T c
	05/12/2020	D243 Yes	Doxycycline 100 mg 2/d 7 days
				THEN moxifloxacin 400 mg 1/d 14 days
	05/30/2020	D281 Yes		Positive	A2058T b
						S83I d
	06/04/2020	D286 Yes	Minocycline 100 mg 2/d 21 days
				THEN pristinamycin 1 g 4/d 14 days
	09/10/2020	D384 No		Negative
	09/21/2020	D395 No		Negative

ACKNOWLEDGMENT

We thank Dr Armelle Wastiaux for proofreading this article prior to submission.

DECLARATION OF CONFICTING INTEREST

The authors declared no potential conflicts of interest with respect to the research, authorship and/or publication of this article.

FUNDING

The authors received no financial support for the research, authorship and/or publication of this article.


Lénaïg Cornanguer
email: lenaig.cornanguer@irisa.fr

Passive Learning of Timed Automata from Logs (Student Abstract)

We propose a novel algorithm to passively learn deterministic Timed Automata from events sequences associated with the delay occurring between them. This algorithm produces models that are more specific than State-of-the-Art algorithms and that has a better identification of the temporal constraints applying on the systems.

Introduction

Many systems save a history of the events occurring within it or linked to it. These timestamped events sequences are named logs and the main purposes of logging are to track the evolution of a process or to identify the cause when a problem is occurring. If each logging sequence informs us about one specific execution of the system, looking at the whole set of logs can give us an insight of the global functioning of the system. When the behavior of a system is time-dependant, this functioning can be complex, and obtaining its behavior model helps to understand it. One behavior model is the Timed Automaton (TA). Traditionally used to model electronic circuits and ensure their safety, TA are now used to model biological ecosystems, software, or industrial systems. The first strength of this modeling is its expressiveness: in addition to the classical automata expressiveness, TA support temporal constraints which can be verified with temporal logics such as TCTL [START_REF] Alur | Modelchecking for real-time systems[END_REF]. This expressiveness has lead to the development of numerous tools based on TA. Some of these tools were created to verify properties (e.g. safety specifications) of the represented system thanks to timed logical expressions. Other ones allow the generation of test case scenarios with the controller synthesis. Finally, TA's formalism can be translated into a state-transition diagram, which makes it easily interpretable.

Given timestamped event sequences, learning a TA modelling the sytem's behavior is a recent issue. We can distinguish two learning approaches, the active and the passive one. While active approaches require to query the system, passive approaches can learn TA only with labeled sequences. The existing algorithms that passively learn TA tend to lack precision due to their management of the time constraints or to produce too complex models, which reduce the interpretability.

We propose a novel algorithm named TAG that passively learns deterministic TA from timestamped event sequences and use a new strategy to obtain a good trade-off between the size of the models and their precision.

Background and State-of-the-Art Timed Automata

A Timed Automaton is a data structure to model the functioning of dynamic systems whose state is conditioned by the occurrence of discrete events at specific moments. The notion of time is supported by temporal variables named clocks that can be reset during the transition from one state to another (e.g., the clock "c0" on the transition from S1 to S0 in Figure 1) and whose value conditions the transition from a state to another (e.g., "c0 < 5" on the same transition as before). Formally, a Timed Automaton A is a 6-uple A = (Q, Σ, C, E, q 0 , F ) where Q is a finite set of states, Σ is a finite set of events or symbols, C is a finite set of clocks, E is a finite set of transitions, q 0 ∈ Q is the initial state and F ⊆ Q is a finite set of final states. A transition e ∈ E of A is a 5-uple e = (q, a, g, r, q ) where q and q are respectively the source state and the destination state of e, g is a guard i.e. a constraint on the value of a clock, and r is the set of clocks being reset on the transition.

Timed Automata Passive Learning Algorithms

Learning a TA is a NP-hard problem [START_REF] Verwer | A likelihood-ratio test for identifying probabilistic deterministic real-time automata from positive data[END_REF]. To reduce the complexity of the task, the existing approaches use approximations or learn a subclass of Timed Automata.

GenProgTA [START_REF] Tappler | Learning Timed Automata via Genetic Programming[END_REF]) is an algorithm that learns TA from positive timestamped event sequences based on genetic programming. This algorithm requires the user to give a lot of parameters such as the number of clocks or the relevant guards.

Timed k-Tail (Pastore, Micucci, and Mariani 2017) is an algorithm that learns TA from a positive set of operations and their duration. For each state of the initialized automaton, it compares the set of possible trajectories of k transitions starting from this state. This set is called the k-future of the state and the states with the same k-future are merged. One of the drawbacks of Timed k-Tail is that it learns an automaton that isn't deterministic in contrast to the algorithm we propose.

RTI+ (Verwer, de Weerdt, and Witteveen 2010) is an algorithm that learns Probabilistic Deterministic Real-Time Automata (PDRTA) from only positive timestamped event sequences. A PDRTA is a TA where the notions of clock and guards are reduced to intervals of acceptable delays between two successive events. It is also deterministic. RTI+ introduces the notion of transition division which permits to model the influence of time on the target state for the same event. However, its management of the temporal constraints leads to models not sensitive enough.

Contribution

We propose a novel algorithm named TAG for Timed Automata Generator, its strategy is in two phases.

After having initialized an automaton with an input sample of positive timestamped event sequences, it reduces its size by merging the states having the same k-future, like Timed k-Tail. However, if the merge induces a determinism issue, it also merges the problematic transitions and states until a deterministic solution.

The second phase attempts to capture the temporal dynamic of the system by realizing transition divisions. If the event occurring after a transition differs in function to the time value of passage, the transition and its target state are split into two paths. During this second phase, it also realizes state merging if needed, but always by favoring the transition divisions.

It finally returns a PDRTA consistent with the input sample, concise in terms of state number but capturing the temporal constraints of the system.

Experimentation Experimental Setup

In order to compare our new algorithm with algorithms of the State-of-the-Art, we choose to use an example of Gen-ProgTA (Figure 1). We generated a set of 1000 event sequences with the delay occurring between two events consistent with the model TA. 70% of this set was used to learn a TA with each algorithm. The 30% remaining were used to test the models by checking if they were accepted by it and compute the True Positive Rate (TPR). We also generated 300 sequences inconsistent with the model automaton to compute the False Positive Rate (FPR).

Algorithm

TPR FPR State number GenProgTA 0.94 0.00 5 RTI+ 1.00 0.22 6 TAG 1.00 0.00 5

Table 1: Validation scores of the learned models.

Results

We did not compute the TPR and the FPR of the TA learned by Timed k-Tail because it is not deterministic. This TA has 11 states. The TPR, FPR, and the state number of the TA learned by the other algorithms are presented in Table 1. The model learned by GenProgTA did not recognize all the sequences of the positive set of validation due to an error on a guard. However, it rejected all the sequences of the negative one on the contrary to RTI+'s model which accepted 66 negative sequences. The cause is a bad management of the temporal constraints leading to a model with guards too large. Finally, our algorithm TAG produced the exact same automaton as the target and therefore correctly accepts or rejects the sequences of the validation set.

Conclusion and Future Work

Learning passively TA from logs can be really interesting to model systems without having to know its functioning or having to interact with it.

We propose a novel algorithm that passively learns TA and achieves a trade-off between a model that would be too sensitive to the input data and a model that wouldn't be specific enough and accept wrong behaviors.

The next step of our work is to improve the validation of the resultant TA. A study about the distances between TA has to be done to consolidate the validation. An other step is the formal verification of the algorithm. Then, we would like to delete progressively the constraints on the learned automaton to obtain models fully exploitable by the model checking or controller synthesis tools.

Figure 1 :

 1 Figure 1: The model TA from GenProgTA used to generate the timestamped sequences of events.