Olivier Merlin

Said Khabba

Mme Zohra

Lili Chabaane

Rapporteure M Kamal

Rapporteur M Ahmed Labbassi

Examinateur M Bahlaoui

Khadir El

Examinateur M Olivier Lakhal

Directeur Merlin

M De These

Said Khabba

Résumé

Une estimation précise de l'évapotranspiration (ET) à grand échelle est une priorité pour comprendre les interactions sol-atmosphère, particulièrement dans les zones semi-arides. La télédétection fournit des informations très pertinentes à grande échelle pour alimenter les modèles d'ET. Généralement, trois variables dérivées de la télédétection sont utilisées pour déterminer la distribution spatiale de l'ET : l'humidité du sol en surface (SM) dérivée des données micro-ondes, la température de surface (LST) dérivée des données infrarouges thermiques et les indices de végétation (ou fraction de couvert f c ,) issus des réflectances visible/proche infrarouge . Cependant, très peu d'études ont tenté de combiner les trois variables dans un même modèle ET. Dans ce contexte, l'objectif principal de cette thèse est d'améliorer l'estimation de l'ET en combinant la modélisation par télédétection optique /micro-ondes à multiples résolutions et la modélisation des échanges surface-atmosphère. Dans la première partie, le modèle de bilan d'énergie à double source (TSEB) basé sur les données de LST, f c et le coefficient de Priestley Taylor (αPT) qui relie l'ET au le rayonnement net est testé sur une zone hétérogène à Niamey, Niger (Wankama). Les prédictions du modèle en terme de flux de chaleur latente (LE) et sensible (H) sont comparées aux données acquises par un scintillomètre à grande ouverture (LAS) installé sur un transect d'environ 3,2 km couvrant trois types de végétation (mil, savane et jachère). Les résultats obtenus pour H et LE sont pertinents. Cependant, une surestimation des flux simulés à la fin de la saison est remarquée. Ce qui est principalement due à la valeur de αPT (fixé généralement à 1,26). Dans la 2 ème partie, un nouveau modèle appelé TSEB-SM dérivé du formalisme TSEB a été développé en utilisant, en plus des données LST et f c , les données de SM comme une contrainte supplémentaire sur l'évaporation du sol. Une calibration innovante est proposée pour extraire trois paramètres clés : le coefficient de Priestley Taylor (αPT) et les paramètres (a rss and, b rss ) de la résistance du sol. En pratique, a rss et b rss sont extraits à l'échelle saisonnière à partir des données SM et LST avec f c inférieur à un seuil donné f c,thres (f c,thres = 0.5), tandis que αPT est inversé à la échelle journalière à partir des données SM et LST pour f c > f c,thres . Le modèle TSEB-SM est testé sur une parcelle de blé inondée et 2 parcelles de blé irriguées en goutte-à-goutte en utilisant les données in-situ collectées lors de deux expériences expérimentales en 2002-2003 et en 2016-2017 dans le bassin versant du Tensift. L'insertion de la résistance du sol dans le modèle TSEB améliore l'estimation de l'évaporation du sol et, par conséquent, améliore la partition de l'ET. L'analyse de la série temporelle indique que αPT suit principalement la phénologie de la culture de blé, avec une valeur maximale correspondant au développement complet de la biomasse verte et une valeur minimale atteinte à la récolte. Finalement, TSEB-SM est appliqué à l'état réel en utilisant les données MODIS LST et f c à 1 km de résolution et les données SM issu de satellite SMOS (Soil Moisture and Ocean Salinity) désagrégées à l'aide d'un algorithme de désagrégation (DisPATCh) à 1 km de résolution. L'approche est validée sur une période de quatre ans (2014)(2015)(2016)(2017)(2018) sur une parcelle de blé pluvial dans le bassin du Tensift, au Maroc. La parcelle a été semée pour la saison agricole 2014-2015 (S1), 2016-2017 (S2) et 2017-2018 (S3), alors qu'elle n'était pas labouré (sol nu) pendant la saison 2015-2016 (B1). La contrainte appliquée sur l'évaporation du sol en utilisant le SM dérivé des données SMOS est l'un des principaux facteurs de contrôle de la fraction évaporative, ce qui permet de déterminer avec plus de précision la partition LE / H. (Word Bank, 2017). L'agriculture, qui contribue à l'économie nationale entre 14 et 20% du PNB (Produit National Brut) en fonction des précipitations de l'année [START_REF] Balaghi | La prédiction agrométéorologique des rendements céréaliers au Maroc[END_REF] et consomme environ 85% des ressources en eau mobilisées du pays [START_REF] Jarlan | Remote Sensing of Water Resources in Semi-Arid Mediterranean Areas: the joint international laboratory TREMA[END_REF], sera sans doute le secteur le plus touché par ce stress. Donc, la gestion des ressources hydriques deviendra ainsi un facteur limitant le développement du pays.

Dans ce contexte, une bonne gestion des ressources en eau est liée à la modélisation des flux hydrologiques, tels que l'infiltration des sols, le ruissellement et l'évapotranspiration (ET). ET est une composante cruciale du cycle de l'eau, particulièrement dans les zones semi-arides. À l'échelle du bassin versant, les pertes en eau par ET constituent généralement la partie la plus importante du bilan hydrique et peuvent être responsables de la dissipation de 60% de l'apport pluviométrique [START_REF] Oudin | Recherche d'un modèle d'évapotranspiration potentielle pertinent comme entrée d'un modèle pluie-débit global[END_REF]. De plus, une estimation précise de l'ET détermine les besoins en eau des cultures, ce qui permet par la suite d'améliorer la gestion de l'eau d'irrigation [START_REF] Allen | Crop evapotranspiration-Guidelines for computing crop water requirements-FAO Irrigation and drainage paper 56[END_REF]. Une grande variété de modèles et de mesures de l'ET ont été rapportés dans la littérature [START_REF] Allen | Evapotranspiration information reporting: I. Factors governing measurement accuracy[END_REF][START_REF] Olivera-Guerra | Estimation of real evapotranspiration and its variation in Mediterranean landscapes of central-southern Chile[END_REF][START_REF] Subedi | Crop Evapotranspiration (ET) Estimation Models: A Review and Discussion of the Applicability and Limitations of ET Methods[END_REF].

Cependant, l'estimation de l'ET sur des zones étendues comprenant différents biomes et climats est encore sujette à des incertitudes importantes [START_REF] Ershadi | Multi-site evaluation of terrestrial evaporation models using FLUXNET data[END_REF][START_REF] Pereira | The Priestley-Taylor parameter and the decoupling factor for estimating reference evapotranspiration[END_REF], bien que les principaux moteurs de l'ET, tels que la demande d'évaporation atmosphérique, le type de végétation, les stades de développement, les caractéristiques biophysiques de surface et la disponibilité en eau du sol [START_REF] Federer | Sensitivity of Annual Evaporation to Soil and Root Properties in Two Models of Contrasting Complexity[END_REF] sont maintenant bien identifiés. Une difficulté majeure dans la modélisation de ce processus réside dans le manque de données d'entrée pertinentes disponibles aux échelles d'espace et de temps souhaitées [START_REF] Allen | Evapotranspiration information reporting: I. Factors governing measurement accuracy[END_REF][START_REF] Pereira | Crop evapotranspiration estimation with FAO56: Past and future[END_REF]. La précision des estimations de l'ET à une échelle donnée représente donc un compromis entre complexité et réalisme du modèle, qui est généralement liée au: i) nombre de paramètres de modèle et de variables de forçage et ii) la disponibilité des données qui diminue généralement avec l'étendue spatiale [START_REF] Allen | Evapotranspiration information reporting: I. Factors governing measurement accuracy[END_REF][START_REF] Gharsallah | Comparison of six evapotranspiration models for a surface irrigated maize agro-ecosystem in Northern Italy[END_REF]. Quant à la disponibilité des données, les observations satellitaires sont en mesure de fournir des mesures intégrées à différentes échelles temporelles et spatiales et dans différentes bandes spectrales. La télédétection multi-spectrale fournit des outils puissants pour observer les surfaces continentales et les composants hydrologiques tels que l'humidité du sol (SM) à l'aide de satellites SMOS (Soil Moisture and Ocean Salinity, Kerr et al (2001)) et SMAP (Soil Active Passive Moisture, [START_REF] Entekhabi | The Soil Moisture Active Passive {(SMAP)} Mission[END_REF]). La température de surface (LST) dérivée de satellite MODIS (Moderate-Resolution Imaging Spectroradiometer) fournit également des informations sur l'état thermique des surfaces et sur les variations temporelles des flux hydrologiques [START_REF] Anderson | A Two-Source Time-Integrated Model for Estimating Surface Fluxes Using Thermal Infrared Remote Sensing[END_REF] à l'interface surface-atmosphère à travers les bilans énergétique et hydrique [START_REF] Anderson | A thermal-based remote sensing technique for routine mapping of land-surface carbon, water and energy fluxes from field to regional scales[END_REF][START_REF] Brunsell | Validating remotely sensed land surface fluxes in heterogeneous terrain with large aperture scintillometry[END_REF]Kustas et Anderson, 2009). En outre, l'indice de végétation normalisé (NDVI) et la fraction de végétation, qui sont des paramètres essentiels pour la modélisation de ET sur les couverts végétaux, peuvent être estimés à partir de données visibles proche-infrarouge fournies par MODIS. Généralement, ces observations (LST, SM, NDVI et f c ) de télédétection fournissent des informations très pertinentes pour l'alimentation des modèles ET. En effet, SM contrôle l'évaporation du sol, la transpiration des plantes et la partition des eaux de pluie en infiltration et ruissellement [START_REF] Chanzy | Significance of soil surface moisture with respect to daily bare soil evaporation[END_REF], f c constitue une contrainte structurelle essentielle pour la partition de l'évaporation / transpiration [START_REF] Allen | Evapotranspiration information reporting: I. Factors governing measurement accuracy[END_REF] et LST représente une signature de l'énergie disponible et de l'ET [START_REF] Norman | Source approach for estimating soil and vegetation energy fluxes in observations of directional radiometric surface temperature[END_REF]. Pour cette raison, des efforts ont été faits pour intégrer ces données en tant qu'informations supplémentaires et complémentaires pour l'estimation de l'ET [START_REF] Price | Using spatial context in satellite data to infer regional scale evapotranspiration[END_REF].

Cependant, l'utilisation efficace des observations satellitaires pour des applications agricoles et hydrologiques présente plusieurs limites. En particulier, la représentativité spatiale de la mesure, qui joue un rôle majeur dans la précision de cette mesure. Dans ce contexte, plusieurs algorithmes ont été développés afin désagréger les données satellites. On cite par exemple l'outil DisPATCh (DISaggregation based on Physical and Theoretical Scale Change, [START_REF] Merlin | Selfcalibrated evaporation-based disaggregation of SMOS soil moisture: An evaluation study at 3km and 100m resolution in Catalunya, Spain[END_REF], Malbeteau et al. 2016, Molero et al. 2016) qui permet de fournir des produits d'humidité avec une résolution d'1km comparable avec celle du MODIS.

Objectifs et méthodologie de la thèse

iii L'objectif essentiel de cette thèse est d'améliorer l'estimation de l'ET en combinant les observations satellitaires d'humidité du sol en surface (issue des données micro-ondes, SMOS) et de température de surface (issue des données optiques dont thermiques, MODIS).

La stratégie proposée consiste à estimer un indice de stress hydrique de la végétation dérivée de la transpiration. Cette dernière sera estimée à haute résolution spatiale en développant les trois axes suivants: la désagrégation des données d'humidité du SMOS (axe 1); l'estimation de l'évaporation du sol (axe 2) et la partition de l'évapotranspiration entre l'évaporation du sol et la transpiration des plantes (axe 3).

a. Désagrégation de données spatiales :

Un algorithme de désagrégation des données d'humidité DisPATCh [START_REF] Merlin | Selfcalibrated evaporation-based disaggregation of SMOS soil moisture: An evaluation study at 3km and 100m resolution in Catalunya, Spain[END_REF], Malbeteau et al. 2016, Molero et al. 2016) a été utilisé. Ce modèle permet d'améliorer la résolution spatiale des données SMOS de plusieurs ordres de grandeur. La méthode se base sur le lien spatial entre l'humidité du sol en surface inversée des données micro-ondes et l'efficacité évaporative du sol déduit des données optiques à plus haute résolution spatiale.

L'humidité désagrégée à haute résolution spatiale s'exprime comme un développement de Taylor d'un modèle d'efficacité évaporative du sol autour de l'humidité du sol observée à basse résolution (Section II.5 Chapitre II). La résolution en sortie de désagrégation est de 1 km avec les données MODIS (MODerate resolution Imaging Spectroradiometer). Le processeur C4DIS [START_REF] Molero | SMOS disaggregated soil moisture product at 1 km resolution: Processor overview and first validation results[END_REF]) est la version opérationnelle du prototype DisPATCh (Merlin et al. 2012 ;[START_REF] Merlin | Selfcalibrated evaporation-based disaggregation of SMOS soil moisture: An evaluation study at 3km and 100m resolution in Catalunya, Spain[END_REF]) appliqué aux données SMOS de niveau 3 (humidité CLF31A/D) et aux produits MODIS (température MOD11A1, MYD11A1 et NDVI MOD13Q2). Le processeur a été validé dans différentes régions en Espagne [START_REF] Merlin | Selfcalibrated evaporation-based disaggregation of SMOS soil moisture: An evaluation study at 3km and 100m resolution in Catalunya, Spain[END_REF], en Australie (Malbeteau et al. 2016, Molero et al. 2016) et aux Etats Unis (Molero et al. 2016). Dans le cadre de cette thèse, le processeur C4DIS a été appliqué à la tuile MODIS au Maroc afin de générer le produit d'humidité sur la période 2014-2018. Les SM désagrégées sont ensuite évaluées par les mesures in-situ des sites intensifs de l'observatoire Tensift (http://trema.ucam.ac.ma).

b. Estimation de l'évaporation du sol:

Les données d'humidité DisPATCh sont ensuite utilisées en entrée d'un modèle de l'évaporation du sol (section 3, chapitre II). Une revue complète et détaillée des méthodes pour estimer l'évaporation à partir des observations d'humidité du sol en surface est proposée par [START_REF] Mahfouf | Analysis of Soil Moisture from Near-Surface Parameters: A Feasibility Study[END_REF], [START_REF] Lee | Estimating the Soil Surface Specific Humidity[END_REF], Ye et al. (1993), Mihailovic et al. (1995), Dekic et al. (1995) et [START_REF] Cahill | Combined spatial and Kalman filter estimation of optimal soil hydraulic properties[END_REF]. Bien que de nombreuses formulations ont été proposées depuis les années 1960, il n'existe toujours pas de consensus sur une meilleure façon de modéliser l'évaporation sur de grandes étendues [START_REF] Desborough | Analysis of the relationship between bare soil evaporation and soil moisture simulated by 13 land surface schemes for a simple non-vegetated site[END_REF][START_REF] Sakaguchi | Effects of soil wetness, plant litter, and under-canopy atmospheric stability on ground evaporation in the Community Land Model (CLM3.5)[END_REF]. Néanmoins, la revue bibliographique de ces modèles nous permet de tirer les enseignements suivants: 1) les formulations existantes diffèrent selon quatre aspects: les valeurs limites basse et haute de l'humidité, la non-linéarité de la relation entre évaporation et humidité, les données d'entrée nécessaires autres que l'humidité et la profondeur des mesures d'humidité [START_REF] Merlin | An analytical model of evaporation efficiency for unsaturated soil surfaces with an arbitrary thickness[END_REF], 2) des expressions empiriques simples peuvent être plus précises et robustes que d'autres modèles à base physique (Dekic et al. 1995, Mihailovic et al. 1995), et 3) aucune de ces formulations n'a été évaluée dans ces conditions de sol et atmosphériques variées. Sur la base de ces résultats, un nouveau modèle développé par [START_REF] Merlin | Modeling soil evaporation efficiency in a range of soil and atmospheric conditions: A downward approach based on multi-site data[END_REF] a été utilisé pour estimer l'évaporation du sol (équation II.17, chapitre II). c. La partition de l'évapotranspiration entre l'évaporation du sol et la transpiration des plantes:

Un nouveau modèle de bilan énergétique pour la partition d'évaporation / transpiration est développé pour intégrer simultanément les données de télédétection LST et SM. Pour construire ce modèle à partir d'une modélisation état de l'art de l'ET, en tenant en compte les caractéristiques suivantes: i) modélisation à partir de données LST, ii) utilisation d'une représentation à deux sources permettant une séparation explicite de l'évaporation du sol et de la transpiration des plantes, et iii) paramétrer les flux de surface avec un réseau de résistances, plus directement liés au SM que les modèles à efficacité d'évaporation.

Nous choisissons donc le modèle TSEB [START_REF] Norman | Source approach for estimating soil and vegetation energy fluxes in observations of directional radiometric surface temperature[END_REF] car il satisfait ces trois critères.

La transpiration dans le modèle TSEB est basée sur l'approche Priestley Taylor (PT). Le coefficient PT noté αPT relie directement le flux de chaleur latente à l'énergie disponible en surface. En négligeant le terme de résistance aérodynamique inclus dans l'équation de Penman-Monteith (Monteith, 1965), la formulation du PT est relativement simple, nécessite moins de données d'entrée et s'est révélée remarquablement précise et robuste pour estimer l'ET potentielle dans un large éventail de conditions [START_REF] Fisher | Global estimates of the land-atmosphere water flux based on monthly AVHRR and ISLSCP-II data, validated at 16 FLUXNET sites[END_REF]. Il est donc bien adapté aux applications opérationnelles [START_REF] Mcaneney | Operational limits to the Priestley-Taylor formula[END_REF] et à grande échelle [START_REF] Anderson | A thermal-based remote sensing technique for routine mapping of land-surface carbon, water and energy fluxes from field to regional scales[END_REF]. Néanmoins, plusieurs études (Ait Hssaine et al., 2018a;[START_REF] Fisher | Global estimates of the land-atmosphere water flux based on monthly AVHRR and ISLSCP-II data, validated at 16 FLUXNET sites[END_REF][START_REF] Jin | Continental-scale net radiation and evapotranspiration estimated using MODIS satellite observations[END_REF][START_REF] Yang | Comparison of three dual-source remote sensing evapotranspiration models during the MUSOEXE-12 campaign: Revisit of model physics[END_REF] ont souligné que αPT varie selon les types de surface et les conditions atmosphériques entre 0.5 et 2.0 avec une valeur moyenne estimée autour de v 1,3 [START_REF] Fisher | Global estimates of the land-atmosphere water flux based on monthly AVHRR and ISLSCP-II data, validated at 16 FLUXNET sites[END_REF][START_REF] Jin | Continental-scale net radiation and evapotranspiration estimated using MODIS satellite observations[END_REF][START_REF] Yang | Comparison of three dual-source remote sensing evapotranspiration models during the MUSOEXE-12 campaign: Revisit of model physics[END_REF]. D'autres études [START_REF] Gonzalez-Dugo | Agricultural and Forest Meteorology A comparison of operational remote sensing-based models for estimating crop evapotranspiration[END_REF][START_REF] Long | A Two-source Trapezoid Model for Evapotranspiration (TTME) from satellite imagery[END_REF][START_REF] Morillas | Environmental factors affecting the accuracy of surface fluxes from a two-source model in Mediterranean drylands: Upscaling instantaneous to daytime estimates[END_REF] ont montré que l'approche PT peut surestimer l'ET du couvert, en particulier en cas de faible humidité du sol et / ou de faible couvert végétal, car elle n'inclut pas une réduction raisonnable de l'ET initiale dans des conditions de stress. Dans ce but, la modification du formalisme TSEB basé sur le PT (Kustas et al., 1999;[START_REF] Norman | Source approach for estimating soil and vegetation energy fluxes in observations of directional radiometric surface temperature[END_REF] a été étudiée en intégrant simultanément les données LST et SM (la version modifiée s'appelle TSEB-SM). Une procédure de calibration innovante a également été mise en oeuvre pour inverser les principaux paramètres d'évaporation du sol (résistance du sol) et de transpiration des plantes (αPT).

b. Le modèle TSEB-SM :

Le modèle TSEB-SM est basé sur le formalisme original de TSEB, ce qui signifie que le bilan énergétique de la végétation est identique à celui de TSEB utilisant la formule PT, bien que l'évaporation du sol est estimée en fonction de SM en utilisant une résistance du sol développée par [START_REF] Sellers | Relations between surface conductance and spectral vegetation indexes at intermediate (100m2 to 15km2) length scales[END_REF] (Figure II.2,chapitre II). L'utilisation de la formulation de résistance du sol est justifiée par le fait que ses paramètres principaux (a rss , b rss ) peuvent être ajustés en fonction des caractéristiques de texture du sol [START_REF] Merlin | Modeling soil evaporation efficiency in a range of soil and atmospheric conditions: A downward approach based on multi-site data[END_REF] ou en combinant les données de SM et de LST dans les conditions du sol nu ou partiellement couvert (Figure V.1,chapitre V et figure VI.4,chapitre VI). Les paramètres a rss et b rss sont déterminés en considérant que, lorsque f c est inférieure à un seuil donné (f c,thres ), la dynamique de ET total est principalement contrôlée par la variation temporelle de l'évaporation du sol. Cela signifie que les deux paramètres de sol sont estimés lorsque le coefficient PT est réglé sur une valeur constante. Une fois que la résistance du sol a été calibrée, le coefficient PT est récupéré à vi l'échelle journalière pour f c supérieure à f c,thres . En fait, une boucle itérative est exécutée sur les paramètres de sol et de végétation pour atteindre la convergence de tous les paramètres (Figure II.3,chapitre II). Les principales équations du modèle et de la procédure de calibration sont détaillées dans le chapitre II (pages 31-34). En pratique, les paramètres de résistance du sol sont extraits à l'échelle saisonnière à partir des données SM et LST avec f c ≤f c,thres (un seuil empirique permettant la séparation itérative des paramètres sol / végétation dans les estimations de ET), tandis que αPT est récupéré à l'échelle journalière à partir des données SM et LST pour f c > f c,thres . Le modèle TSEB-SM a été testé sur une parcelle de blé irrigué en gravitaire (R3) et 2 parcelles de blé irrigué en goutte-àgoutte (Une parcelle (Référence) qui a été irriguée en fonction des besoins en eau des cultures estimés selon la méthode FAO tous les 3-4 jours, et une autre parcelle (contrôlée) qui a été subie plusieurs périodes de stress lorsque l'irrigation est délibérément coupée, Chichaoua) en utilisant des données in-situ recueillies lors de deux expériences réalisées en 2002-2003 (R3) et en 2016-2017 (Chichaoua) (Chichaoua). La convergence des trois paramètres (a rss , b rss et αPT) est atteinte en 2 ou 3 itérations. Ce résultat confirme bien la robustesse d'appliquer la calibration selon un seuil de f c . La paire (a rss , b rss ) calibrée est respectivement (5.67, 1.40), (6.51, 3.82) et (9.47, 6.87) pour la parcelle de R3, et les deux de Chichaoua (contrôlée et référence). Les valeurs moyennes récupérées (7.2, 4.0) sont relativement proches de celles estimées par Sellers et al. (1992) (8.2, 4.3). La variabilité de a rss et b rss peut être expliquée par de nombreux facteurs tels que la texture du sol [START_REF] Merlin | Modeling soil evaporation efficiency in a range of soil and atmospheric conditions: A downward approach based on multi-site data[END_REF] et les conditions météorologiques [START_REF] Merlin | An analytical model of evaporation efficiency for unsaturated soil surfaces with an arbitrary thickness[END_REF]. Néanmoins, les paramètres récupérés sont significativement différents pour les deux sites de Chichaoua (référence et contrôlé), alors qu'ils sont situés à environ 200 m l'un de l'autre et ont une texture du sol et des conditions météorologiques similaires. Cela peut être expliqué par la compensation entre a rss et b rss ce qui révèle la nature empirique de la formulation r ss de Sellers et al. (1992). La valeur moyenne de αPT est respectivement 0,81, 0,88 et 1,24 pour la parcelle R3, contrôlée et référence. Cette valeur est très proche de la valeur théorique αPT pour la parcelle référence.

Néanmoins, elle est nettement inférieure à la valeur par défaut pour la parcelle R3 et contrôlée. Cela peut être associé à des conditions de stress pouvant survenir pendant la phase de développement du blé. Une analyse de la variation journalière de αPT indique que les valeurs inversées sur les deux parcelles de Chichaoua sont supérieures à celles inversées sur R3. Cela pourrait s'expliquer par la différence entre les pratiques agricoles de chaque parcelle

I.1. General context

Water makes up about 71% of the Earth's surface, 97% of all the Earth's water is contained within the oceans as salt water, while the remaining 3% is freshwater (Figure I.1). Glaciers and ice caps cover about 70% of the world's freshwater. Unfortunately, most of these resources are located far from human habitation and are not readily accessible for human use.

According to the United States Geological Survey (USGS), Groundwater is by far the most abundant and readily available source of freshwater, followed by lakes, reservoirs, rivers and wetlands. The groundwater represents over 90% of the world's readily available freshwater resource [START_REF] Boswinkel | International Groundwater Resources Assessment Centre (IGRAC)[END_REF]. About 1.5 billion people depend upon groundwater for their drinking water supply (WRI, UNEP, UNDP, World Bank, 1998). on the quality and quantity of available water as water plays a disproportionately powerful role through its impact on, among other things, food production and security, hygiene, sanitation and health and maintenance of ecosystem services."The water issue becomes a major concern for the majority of countries; especially because it covers a real complexity related to geopolitical, security, ecological, social and economical issues. As a result, the pressure on water resources is growing under the combined effects of anthropogenic pressure (population growth, urban development and the increase of water consumingby agriculture, industry and tourism) and climate changes (temperature increases, precipitation decreases especially in southern mediterranean, increase of drought frequency …).

In most regions of the world, over 70 percent of freshwater is used for agriculture (FAO, 2011). By 2050, the global water demand of agriculture is estimated to increase by a further 19% due to irrigational needs. Countries in the southern Mediterranean have only 1% of the world's freshwater resources and gather more than half of the water-poor population (namely an average less than 1000 m 3 per year per capita). This area is characterized by a strong spatio-temporal variability in precipitation associated with a marked seasonality of evaporative demand, resulting in a period of high water deficit in summer (Bolle, 2003). In this region, crop irrigation consumes up to 80-90% of the mobilized water (FAO, 2015), which makes the relationship between water availability and agricultural production for a continuously growing population more critical [START_REF] Vorosmarty | Global Water Resources: References Vulnerability from Climate Change and Population Growth[END_REF]. Mediterranean countries are already facing major problems of water stress, desertification, loss of biodiversity and extreme weather events such as floods and droughts. In particular, the Mediterranean area has been identified as a hot spot of climate change [START_REF] Giorgi | Climate change hot-spots[END_REF].

According to the International Panel on Climate Change (IPCC, 2014) a rise of temperatures of 2 to 3° C is expected in the Mediterranean region by 2050, and 3 to 5 ° C by 2100. The increase of the length of dry spell (days) is expected [START_REF] Schleussner | Differential climate impacts for policy-relevant limits to global warming: the case of 1.5 • C and 2[END_REF] and the decrease in precipitation, especially in summer and with important regional differences (IPCC, 2013). The general increase in water scarcity as a consequence of climate change is enhanced by the increasing demand for irrigated agriculture to stabilize production and to maintain food security [START_REF] Schwabe | Drought in Arid and Semi-Arid Regions[END_REF]. The irrigation demands in the region are projected to increase between 4 and 18% by the end of the century [START_REF] Cramer | Climate change and interconnected risks to sustainable development in the Mediterranean[END_REF].

Morocco is one of the 45 countries, in the world, most affected by water shortage, according to World Resources Institute water scarcity map (Figure I.2), which reveals Morocco's critical situation [START_REF] Bleu | Etat de l'environnement et du développement en méditerranée[END_REF]. A difficult situation for the population and, among others, agriculture. The latter is by far the largest water user of all human activities; accounting for 85% of the country's mobilized water resources [START_REF] Jarlan | Remote Sensing of Water Resources in Semi-Arid Mediterranean Areas: the joint international laboratory TREMA[END_REF]. Agriculture contributes to the national economy in the range 14-20 % of GNP depending on the rainfall of the year [START_REF] Balaghi | La prédiction agrométéorologique des rendements céréaliers au Maroc[END_REF]. According to the World Resources Institute report, Morocco will reach an extremely high level of water stress by 2040. Indeed, Morocco is expected to enter a situation of extreme water stress in less than 25 years (Word Bank, 2017). A shortage that could be mainly explained by the fast expansion the irrigated areas and the intensification of water consumption by the touristic and domestic sectors. • The National Irrigation Water Economics Program (PNEEI) with the objective of converting 550 000 ha to localized irrigation (2008)(2009)(2010)(2011)(2012)(2013)(2014)(2015)(2016)(2017)(2018)(2019)(2020), increasing productivity and water valuation, and sustainable management of water resources;

• The Irrigation Extension Program (PEI), aimed at making public investment in water resource mobilization (dams), creating nearly 60 000 permanent jobs, increasing farmers' incomes.

Monitoring water resources is therefore strongly linked to the modeling of hydrological fluxes, such as soil infiltration, runoff and evapotranspiration. Evapotranspiration (ET) is a crucial component of the water cycle, especially in semi-arid areas where it strongly impacts the water resource management, drought monitoring, and climate [START_REF] Littell | A review of the relationships between drought and forest fire in the United States[END_REF][START_REF] Molden | Improving agricultural water productivity: Between optimism and caution[END_REF]. At the watershed scale, water losses by ET are generally the most important part of the water balance, and can be responsible for the dissipation of 60% of the rainfall contribution [START_REF] Oudin | Recherche d'un modèle d'évapotranspiration potentielle pertinent comme entrée d'un modèle pluie-débit global[END_REF]. Furthermore, a precise estimate of ET determines the crop water requirements, which subsequently allow for optimizing water management practices and irrigation regimes [START_REF] Allen | Crop evapotranspiration-Guidelines for computing crop water requirements-FAO Irrigation and drainage paper 56[END_REF]. A large variety of ET models and measurements have been reported in the literature [START_REF] Allen | Evapotranspiration information reporting: I. Factors governing measurement accuracy[END_REF][START_REF] Olivera-Guerra | Estimation of real evapotranspiration and its variation in Mediterranean landscapes of central-southern Chile[END_REF][START_REF] Subedi | Crop Evapotranspiration (ET) Estimation Models: A Review and Discussion of the Applicability and Limitations of ET Methods[END_REF]. However, ET estimation over extended areas including different biomes and climates is still subject to significant uncertainties [START_REF] Ershadi | Multi-site evaluation of terrestrial evaporation models using FLUXNET data[END_REF][START_REF] Pereira | The Priestley-Taylor parameter and the decoupling factor for estimating reference evapotranspiration[END_REF].

Although the main drivers of ET, such as atmospheric evaporative demand, vegetation type, development stages and health, surface biophysical characteristics and soil water availability [START_REF] Federer | Sensitivity of Annual Evaporation to Soil and Root Properties in Two Models of Contrasting Complexity[END_REF], are now well identified. One major difficulty in modeling this process lies in a lack of relevant inputs data available at the desired space and time scales [START_REF] Allen | Evapotranspiration information reporting: I. Factors governing measurement accuracy[END_REF][START_REF] Pereira | Crop evapotranspiration estimation with FAO56: Past and future[END_REF]. The accuracy of ET estimates at a given scale thus currently represents a trade-off between model complexity and realism, which is usually related to: i) the number of model parameters and forcing variables and ii) the data availability that generally decreases with the spatial extent [START_REF] Allen | Evapotranspiration information reporting: I. Factors governing measurement accuracy[END_REF][START_REF] Gharsallah | Comparison of six evapotranspiration models for a surface irrigated maize agro-ecosystem in Northern Italy[END_REF].

Regarding data availability, satellite observations are able to provide integrated measurements at different temporal and spatial scales and in different spectral bands. Multi-spectral remote sensing provides powerful tools for observing continental surfaces and hydrologic components such as soil moisture using SMOS satellites (Soil Moisture and Ocean Salinity, Kerr et al (2001)) and SMAP ( Soil Active Passive Moisture [START_REF] Entekhabi | The Soil Moisture Active Passive {(SMAP)} Mission[END_REF]). Surface temperature from the thermal infrared also provides information on the state of the surfaces and on the temporal variations of the hydrological fluxes [START_REF] Anderson | A Two-Source Time-Integrated Model for Estimating Surface Fluxes Using Thermal Infrared Remote Sensing[END_REF] at the surfaceatmosphere interface through the energy balance and water balance [START_REF] Anderson | A thermal-based remote sensing technique for routine mapping of land-surface carbon, water and energy fluxes from field to regional scales[END_REF][START_REF] Brunsell | Validating remotely sensed land surface fluxes in heterogeneous terrain with large aperture scintillometry[END_REF][START_REF] Kustas | Advances in thermal infrared remote sensing for land surface modeling[END_REF]. Meteorological satellites, either geostationary (Geostationary Operational Environmental Satellites (GOES), Meteosat satellites) or polar (Global Precipitation Measurement (GPM), Tropical Rainfall Measuring Mission (TRMM)) can detect precipitation and estimate their intensity [START_REF] Hou | The Global Precipitation Measurement Mission[END_REF][START_REF] Huffman | The TRMM Multisatellite Precipitation Analysis (TMPA): Quasi-Global, Multiyear, Combined-Sensor Precipitation Estimates at Fine Scales[END_REF]. In addition, a number of space programs aim to create a multi-spectral synergy. A recent example of this motivation is the Sentinel satellite constellation. Visible and near infrared (VIS-NIR, Sentinel 2), thermal infrared (TIR, Sentinel 3) and C-band microwave (Sentinel 1) data are available with unprecedented spatio-temporal resolution.

These strategies are based on the development of a system of complementary observations in order to better characterize the continental surfaces. However, there are several limitations in the efficient use of remote sensing observations for agricultural and hydrological applications.

Especially, the spatial representativeness of the measurement, which plays a major role in the accuracy of this measurement. Spatial and temporal resolutions are of paramount importance to realistically integrate spatial observations into hydrological models, or even to model hydrological processes from satellite observations. The spatial resolution depends mainly on the sensitivity of the sensor to receive energy emitted by the surface. This sensitivity is strongly dependent on the wavelength domain and plays an important role since it determines the size of the region observed and the size of the objects that will be possible to characterize. For example, the radiometers have a coarse-scale resolution (about 40 km for SMOS and 50 km for AMSR-E) which is too wide to be directly integrated into agro-hydrological models, in contrary to measurements from the radar which have a finer resolution (about 10 m for Sentinel 1). The temporal resolution is the time required for the satellite to make a complete orbital cycle, ie to observe exactly the same scene again from the same point in space, it is related to the spatial resolution for a given wavelength domain because it depends on the orbit of the satellite. For example, in the thermal infrared, Landsat data have a spatial resolution of 100 m but a temporal resolution of 16 days whereas the MODIS data have a spatial resolution of 1 km but with a frequency of 1-2 days. Generally, spatial and temporal resolution must be chosen according to the objects observed and / or modelled (Figure I.3). Overall, remote sensing observations provide very relevant information to feed ET models such as vegetation indices (Normalized Difference Vegetation Index NDVI and vegetation fraction cover f c , VIS-NIR), land surface temperature (LST, TIR) and near-surface soil moisture (SM, microwave). More specifically, SM is one of the main controlling factors of soil evaporation [START_REF] Chanzy | Significance of soil surface moisture with respect to daily bare soil evaporation[END_REF], vegetation cover fraction (f c ) provides an essential structural constraint on evaporation/ transpiration partitioning [START_REF] Allen | Evapotranspiration information reporting: I. Factors governing measurement accuracy[END_REF] and LST is a signature of available energy and ET [START_REF] Norman | Source approach for estimating soil and vegetation energy fluxes in observations of directional radiometric surface temperature[END_REF]. For this reason, efforts have been made to integrate those data as additional and complementary information on ET [START_REF] Price | Using spatial context in satellite data to infer regional scale evapotranspiration[END_REF].

Many measurement devices are used to develop, calibrate and test important ET process models. A bibliographic review of the main methods of ET measurement at the plot scale is describedin the following sub-section.

I.2. In-situ measurements of Evapotranspiration a. Eddy covariance method

The Eddy correlation (EC) method is considered as a reference technic for several reasons [START_REF] Allen | Evapotranspiration information reporting: I. Factors governing measurement accuracy[END_REF]: it allows a direct measurement of the latent and sensible heat flux densities within atmospheric boundary layers at field scale. It introduces no artefact on the system it is measuring, it is quasi-continuous and represents a relatively large upwind extent.Early examples of eddy instrumentation were described by [START_REF] Tanner | Use Requirements for Bowen Ratio and Eddy Correlation Determination of Evapotranspiration[END_REF] and [START_REF] Tanner | Density Fluctuations and Use of the Krypton Hygrometer in Surface Flux Measurements[END_REF]. Since then, many advances in instrumentation have been made and this method is now widely used as described by [START_REF] Wilson | Energy Balance Closure at FLUXNET Sites[END_REF][START_REF] Baldocchi | Assessing the eddy covariance technique for evaluating carbon dioxide exchange rates of ecosystems: past, present and future[END_REF].

The EC method is based on the turbulent transport theory in the surface layer of the atmosphere. Indeed, the average vertical flux density (F x ̅̅̅ ) of a magnitude X (e.g. temperature,

water vapor or carbon dioxide) is proportional to the covariance of fluctuations between the vertical wind velocity and the concentration of that magnitude, at a specific point above the area of interest.

Turbulent fluxes (momentum, sensible heat, latent heat and gaseous concentration) can be expressed as the product of the fluctuations term of the vertical velocity and the fluctuations term of the magnitude considered. In particular, the sensible heat flux density H, is given by:

H ≈ ρc p w ′ T ′ ̅̅̅̅̅̅ (W. m -2 ) (I.1)
The vertical flux density of water vapor called latent heat or evapotranspiration is defined by:

LE ≈ ρw ′ q ′ ̅̅̅̅̅̅ (W. m -2 ) (I.2)
In general, the eddy correlation method requires personnel who are well-trained in electronics, turbulent theory, and biophysics. Instrumentation is relatively fragile and expensive.The footprint of the EC system, depends on wind speed, but doesn't exceed 100 m [START_REF] Ezzahar | On the application of scintillometry over heterogeneous grids[END_REF]. It uses complex calculations, and utilizes many assumptions. It has proposing perspectives for the future use in various natural sciences [START_REF] Allen | Evapotranspiration information reporting: I. Factors governing measurement accuracy[END_REF].

b. Lysimetry method

The lysimeter is a device, generally a tank or container, to define the water movement across a soil boundary [START_REF] Howell | History of Lysimeter Design and Use for Evapotranspiration Measurements[END_REF][START_REF] Prueger | Bowen-Ratio Comparisons with Lysimeter Evapotranspiration[END_REF][START_REF] Young | Monitoring Near-Surface Soil Water Storage in Turfgrass using Time Domain Reflectometry and Weighing Lysimetry[END_REF], and to quantify actual evaporation from a bare soil or actual ET from a soil covered by vegetation [START_REF] Kashyap | Evaluation of evapotranspiration estimation methods and development of crop-coefficients for potato crop in a sub-humid region[END_REF][START_REF] Parlange | Estimation of the diurnal variation of potential evaporation from a wet bare soil surface[END_REF].

Lysimeters of varying designs, sizes, shapes, and measurement systems have been built over the years [START_REF] Allen | Evapotranspiration information reporting: I. Factors governing measurement accuracy[END_REF][START_REF] Howell | History of Lysimeter Design and Use for Evapotranspiration Measurements[END_REF]. Thechnically, there are two main types of lysimeters: the drainage and the weighing types. In the first case, potential evaporation is obtained as the difference between added and drained water quantity. In the second case, changes in the total weight of the soil sample are measured, whereby the real ET during a short time period (10 min) can be estimated. Indeed, the actual ET measurements from weighing lysimeters have become one of the most accurate methodologies to study the return of water to the atmosphere by the combined processes of evaporation and transpiration [START_REF] Malone | Error analysis and quality improvement of the coshocton weighing lysimeters[END_REF], and are the standard method to directly measure the actual evapotranspiration (ET a ) [START_REF] Payero | Construction, installation, and performance of two repacked weighing lysimeters[END_REF][START_REF] Reicosky | Comparison of alfalfa evapotranspiration measured by a weighing lysimeter and a portable chamber[END_REF].

In connection with the additional measurement of deep percolation (DP) and precipitation (P), the actual ET a can easily be derived using the surface water balance:

ET a = P -DP ± ∆W (I.3)
Where ΔW is the change of soil water storage measured by the lysimeter.

c. The Energy Balance Bowen Ratio (EBBR) method

The Energy Balance Bowen Ratio (EBBR) method is a relatively simple technique based on net radiation, soil heat flux, and the air temperature and vapour pressure gradients measurements [START_REF] Allen | Evapotranspiration information reporting: I. Factors governing measurement accuracy[END_REF]. It is an indirect method, compared to the previous methods such as EC, which directly measures turbulent fluxes, or weighing lysimeters, which measures the mass change of an isolated volume of surface soil-vegetation. EBBR produces the 30 min estimates of the vertical fluxes of sensible and latent heat fluxes at the local surface. Many studies have investigated the use of the BR method to estimate the sensible and latent heat fluxes [START_REF] Aston | Heat storage in a young eucalypt forest[END_REF][START_REF] Black | Psychrometric apparatus for Bowen-ratio determination over forests[END_REF][START_REF] Euser | A new method to measure Bowen ratios using high-resolution vertical dry and wet bulb temperature profiles[END_REF][START_REF] Jara | Measurement of evapotranspiration and its components in a corn (Zea Mays L.) field[END_REF][START_REF] Peacock | Estimating evapotranspiration from a reed bed using the Bowen ratio energy balance method[END_REF]. The Bowen ratio can be determined as the ratio of the gradients of temperature and vapor pressure across two fixed heights above the surface [START_REF] Bowen | The Ratio of Heat Losses by Conduction and by Evaporation from any Water Surface[END_REF] or as the ratio of the sensible and latent heat flux:

β = H LE = ∆T ∆e (I.4)
The Bowen ratio is combined with the energy balance to yield the following expressions for H and LE:

LE = R n -G 1+β (I.5) H = β 1+β (R n -G) (I.6)

d. Scintillometry

A scintillometer is an optical instrument that consists of a light/radiation source (transmitter)

and receiver; it is used to measure small fluctuations of the refractive index of air caused by variations in temperature, humidity, and pressure. The transmitter emits electromagnetic radiation over a separation distance (or path length), which, depends on aperture size, effective height above the surface, and atmospheric stability. The receiver detects and evaluates the intensity fluctuations of the transmitted signal, called scintillation.

Scintillometer provides continuous measurements of sensible heat fluxes over path lengths from 100 m up to few kilometres. Several investigations have demonstrated the potential of using scintillometer to measure reliable averaged sensible heat fluxes over path lengths which are similar to satellite pixel scale [START_REF] Artogensis | Measuring areally-averaged sensible heat fluxes with a Large Aperture Scintillometer[END_REF][START_REF] De Bruin | The scintillation method tested over a dry vineyard area[END_REF][START_REF] Ezzahar | On the application of scintillometry over heterogeneous grids[END_REF][START_REF] Kohsiek | A Comparison between Line-Averaged Observation of Cn2 from Scintillation of a CO2 Laser Beam and Time-Averaged in situ Observations[END_REF][START_REF] Lagouarde | Scintillation measurements of sensible heat flux over heterogeneous surfaces[END_REF]. The scintillometer method is based on the measure of the structure parameter of refractive index (C n 2 ), which characterises the turbulence intensity within the atmosphere [START_REF] Ezzahar | On the application of scintillometry over heterogeneous grids[END_REF][START_REF] Ochs | A second-generation large-aperature scintillometer[END_REF]. By using the Monin-Obukhov Similarity Theory (MOST) and complementary parameters (meteorological conditions and site features such as vegetation height), C n 2 can be directly related to sensible heat flux. For more details on this method, the readeris invited to refer to [START_REF] Ezzahar | On the application of scintillometry over heterogeneous grids[END_REF].

I.3. Modeling approaches of Evapotranspiration

In-situ measurements are able to give only localized estimates of ET over relatively homogeneous areas. In addition, they cannot be extended at large scales due to the heterogeneity of the landscape and the complexity of hydrologic processes. In fact, the factors that conditioning the soil-vegetation-atmosphere exchanges (land surface temperature, wind, soil characteristics, type of crop..) are highly variable in space and time and are specific for each field. Therefore, none of the approaches mentioned before can adequately account for these variabilities. The spatial modelling has become a dominant means to estimate ET fluxes over regional and continental areas [START_REF] Anderson | A climatological study of evapotranspiration and moisture stress across the continental United States based on thermal remote sensing: 2. Surface moisture climatology[END_REF][START_REF] Fisher | The future of evapotranspiration: Global requirements for ecosystem functioning, carbon and climate feedbacks, agricultural management, and water resources[END_REF]. Different methods have been developed to use remote sensing data in surface flux estimation schemes.

It is always difficult to classify these methods, since their complexity depends on the balance between the empirical and physically based modules used.

An overview of existing ET modeling approaches is discussed below.

I.3.1. Empirical models

The empirical models are the most used approaches for spatializing ET through remote sensing. In this context, the empirical relationship between land surface temperature and air temperature observationswas used. This simplified method for estimating ET was firstly derived by [START_REF] Stocker | Wheat canopy temperature: A practical tool for evaluating water requirements[END_REF] at two different times of day at field scale and later modified by [START_REF] Seguin | Using midday surface temperature to estimate daily evaporation from satellite thermal IR data[END_REF] for mapping daily ET over large scales from LST measurements [START_REF] Courault | Review on estimation of evapotranspiration from remote sensing data: From empirical to numerical modeling approaches[END_REF][START_REF] Lagouarde | Suivi de l'evapotranspiration reelle journaliere a partir des donnees NOAA-AVHRR lors de la campagne Hapex-Mobilhy[END_REF]. This approach assumes that the daily ET is related to the instantaneous (LST -T a ) measurements obtained around mid-day:

ET d = R n d -B(LST -T a ) n (I.7)
Where B and n are the regression adjusted constants which depend respectively on surface roughness and atmospheric stability. LST can be obtained by observed in-situ or by thermal infrared remote sensing images.

This method assumes that the ratio H/R n is constant during the day, and that the daily variation of the heat flux in the soil is negligible (G = 0).

The main advantage of this empirical regression method is its simplicity and relatively high accuracy (1 mm / day) when calibrated in-situ dataset. However, the adjusted constants are site-specific (climate, vegetation, soil…), which may limit the application of this approach to other sites and heterogeneous surfaces [START_REF] Carlson | A new look at the simplified method for remote sensing of daily evapotranspiration[END_REF].

I.3.2. Mechanistic models

Estimation of ET can be based on more detailed and complex models such as Soil-Vegetation-Atmosphere transfer models (SVAT), which include a coupled energy balance and water balance model. Many SVAT models have been developed in the last 20 years for meteorological needs which explains their more detailed description of physical processes.

This approach gives access to simulate continuously the temporal evolution of surface states (LST, soil moisture, etc…) [START_REF] Deardorff | Efficient prediction of ground surface temperature and moisture, with inclusion of a layer of vegetation[END_REF][START_REF] Dickinson | Biosphere-atmosphere Transfer Scheme (BATS) for the NCAR Community Climate Model[END_REF][START_REF] Sellers | A Revised Land Surface Parameterization (SiB2) for Atmospheric GCMS. Part I: Model Formulation[END_REF], variables required in the partition of the surface into soil and vegetation energy balance. In addition, most of the transfer mechanisms at ground and/or vegetation coverlevelandsome physiological processesare based on the scale of the energy balance and the parameterization of different processesindependently of remote sensing data:

-Radiative transfers are modeled in general following a simple Beer-Lambert law of by using radiative transfer schemes within the plant cover [START_REF] Olioso | Simulation des échanges d'énergie et de masse d'un couvert végétal, dans le but de relier la transpiration et la photosynthèse aux mesures de réflectance et de température de surface[END_REF].

-Turbulent transfersaregenerally based on the resistive schemes [START_REF] Choudhury | Estimating evaporation and carbon assimilation using infrared temperature data:vistas in modeling[END_REF][START_REF] Deardorff | Efficient prediction of ground surface temperature and moisture, with inclusion of a layer of vegetation[END_REF].

-Heat and water transfers in the soil; in most models, a system with two soil reservoirs is used, one representing the root zone and the other one representing the first centimeters of the soil which are directly concerned by soil evaporation [START_REF] Carlson | Estimation of surface heat flux and an index of soil moisture using adjoint-state surface energy balance[END_REF][START_REF] Deardorff | Efficient prediction of ground surface temperature and moisture, with inclusion of a layer of vegetation[END_REF].

-Water transfers from the soil to the atmosphere, through the plants, based on an adequate description of stomatal regulation and water extraction by the roots [START_REF] Braud | A simple soilplant-atmosphere transfer model (SiSPAT) development and field verification[END_REF][START_REF] Taconet | Evaluation of a Surface/Vegetation Parameterization Using Satellite Measurements of Surface Temperature[END_REF].

-Photosynthesis in relation with water transfers, through stomatal regulation or water status of leaves [START_REF] Zur | A model for the water relations, photosynthesis, and expansive growth of crops[END_REF].

SVAT models are typically complex and highly parameterized, which can make their spatialization tricky when surfaces are poorly characterized. On the other hand, this approach is not dependent on remote sensing data, and relies solely on knowledge of radiative forcing, weather forcing, crop canopy architecture and physiology, and water supplies (rainfall and irrigation). The LST is not used as a forcing data, but is simulated by the model, as the resultant of energy balance, and can therefore possibly be corrected by assimilation methods [START_REF] Carlson | Estimation of surface heat flux and an index of soil moisture using adjoint-state surface energy balance[END_REF][START_REF] Coudert | An improved SVAT model calibration strategy based on the optimisation of surface temperature temporal dynamics[END_REF][START_REF] Crow | Multiobjective calibration of land surface model evapotranspiration predictions using streamflow observations and spaceborne surface radiometric temperature retrievals[END_REF][START_REF] Hain | An intercomparison of available soil moisture estimates from thermal infrared and passive microwave remote sensing and land surface modeling[END_REF][START_REF] Olioso | Seguin and Itier[END_REF].

Among SVAT models, it may be mentioned Suivi de l'Etat Hydrique des Surfaces (SEtHyS) [START_REF] Coudert | Contribution of Thermal Infrared Remote Sensing Data in Multiobjective Calibration of a Dual-Source SVAT Model[END_REF], Soil Biosphere-Atmosphere Interaction (ISBA) [START_REF] Noilhan | The ISBA land surface parameterisation scheme[END_REF] and Interactive CAnopy Radiation Exchange (ICARE) [START_REF] Gentine | Analysis of evaporative fraction diurnal behaviour[END_REF], Simple

Biosphere Model (SiB) [START_REF] Sellers | A Revised Land Surface Parameterization (SiB2) for Atmospheric GCMS. Part I: Model Formulation[END_REF] and Simple Soil-Plant-Atmosphere Transfer (SiSPAT) [START_REF] Braud | A simple soilplant-atmosphere transfer model (SiSPAT) development and field verification[END_REF].

SVAT models provide access to detailed plant cover and soil functioning, and not just to a limited number of variables such as ET, as it is the case for empirical or residual approaches.

However, a major disadvantage of these models is that they require the adjustment of many parameters related to the properties of the observed surfaces (soil textures, type of cover observed). They also rely on atmospheric (e.g. precipitation) and anthropogenic (e.g. irrigation) forcing. If such calibrations are possible at the plot scale, where the soils and varieties grown are known and can be considered homogeneous, they become particularly difficult to perform overareas with a certain spatial extent.

I.3.3. Surface Energy Balance (SEB) models

Surface Energy Balance (SEB) models are designed to be forced by the LST and focus on solving the SEB instantaneously. SEB can be represented, at any scale [START_REF] Brutsaert | Introduction[END_REF][START_REF] Mcnaughton | An evaluation of the Priestley and Taylor equation and the complementary relationship using results from a mixed-layer model of the convective boundary layer[END_REF] by:

H + LE = R n -G (I.8)
whereH HH is the sensible heat flux, LE __ is the latent heat flux,R n _is the net radiation absorbed by the earth's surface, and G_ is the heat flux into the soil. All components are usually in units

W/m 2 2_.
Additional energy flux components that could also be included are photosynthesis [START_REF] Stewart | Preliminary modelling of transpiration from the fife site in Kansas[END_REF] and vegetation canopy storage [START_REF] Shuttleworth | Evaporation from sparse crops-an energy combination theory[END_REF], but for short-term measurements, or for non-forested regions, these terms are negligible [START_REF] Brutsaert | Introduction[END_REF][START_REF] Stewart | Energy budgets in pine forest[END_REF]. The difference R n -G is the surface available energy, generally consumed by H and LE. G is classically expressed as a fraction of net radiation, (as an exemple, 0.05*R n for fully developed plant cover, and 0.5*R n for bare soil) [START_REF] Kustas | Use of remote sensing for evapotranspiration monitoring over land surfaces[END_REF] or as a variable fraction depending on different parameters such as canopy fraction and soil characteristics [START_REF] Bastiaanssen | A remote sensing surface energy balance algorithm for land (SEBAL). 1[END_REF][START_REF] Kustas | Instantaneous and Daily Values of the Surface Energy Balance over Agricultural Fields Using Remote Sensing and a Reference Field in an Arid Environment[END_REF][START_REF] Su | The Surface Energy Balance System (SEBS) for estimation of turbulent heat fluxes[END_REF].

The methods of resolution of SEB thus differ mainly on the partition of the available energy between the turbulent fluxes. In the review of ET estimation methods, several authors classified two categories of approach to describe the surface and its resistance network [START_REF] Kalma | Estimating land surface evaporation: A review of methods using remotely sensed surface temperature data[END_REF][START_REF] Overgaard | Land-surface modelling in hydrological perspective-a review[END_REF]:

 The "single-pixel" methods for which the fluxes are calculated independently for each pixel. Among these models, we can distinguish three models (i) Methods considering the surface as a homogeneous mixture of soil and vegetation without distinction between soil evaporation and transpiration of vegetation [START_REF] Monteith | Evaporation and the Environment[END_REF][START_REF] Penman | Natural evaporation from open water, bare soil and grass[END_REF]: (ii) Models taking into account vegetation and bare soil as two separate sources for energy transfers [START_REF] Shuttleworth | Evaporation from sparse crops-an energy combination theory[END_REF]; (iii) multi-source models, which are essentially extensions of the dual-source model.

 Contextual models based on the contrasts between hot and cold pixelswithin a given image, these models link surface temperature and other satellite data (reflectance, vegetation indices) to evapotranspiration by semi-empirical laws.

a. Single-source models

Single source models treat the land surface as one homogeneous surface, so that they cannot distinguish between soil evaporation and planttranspiration. Their simplicity and yet physically sound basis has made the mono-source models widely used. Although, singlesource energy balance models may provide reliable estimates of turbulent heat fluxes. They often need field calibration and hence may be unable to be applied over a diverse range of surface conditions. [START_REF] Kustas | Instantaneous and Daily Values of the Surface Energy Balance over Agricultural Fields Using Remote Sensing and a Reference Field in an Arid Environment[END_REF] have shown that single source model is not suitable for ET estimation over partially vegetated surfaces. Single-source energy balance models include Surface Energy Balance Algorithm for Land (SEBAL; [START_REF] Bastiaanssen | A remote sensing surface energy balance algorithm for land (SEBAL). 1[END_REF],

Simplified Surface Energy Balance Index (S-SEBI; [START_REF] Roerink | S-SEBI: A simple remote sensing algorithm to estimate the surface energy balance[END_REF], Surface Energy Balance System (SEBS; [START_REF] Su | The Surface Energy Balance System (SEBS) for estimation of turbulent heat fluxes[END_REF], Mapping ET at High Resolution with Internalized Calibration (METRIC; [START_REF] Allen | Satellite-Based Energy Balance for Mapping Evapotranspiration with Internalized Calibration (METRIC)-Applications[END_REF], and Operational Simplified Surface Energy Balance (SSEBop; [START_REF] Senay | Operational Evapotranspiration Mapping Using Remote Sensing and Weather Datasets : a New Parameterization for the Sseb Approach[END_REF][START_REF] Senay | A Coupled Remote Sensing and Simplified Surface Energy Balance Approach to Estimate Actual Evapotranspiration from Irrigated Fields[END_REF].

b. Double-source models

Over homogeneous areas, single source models can evaluate ET with relatively high accuracy. However, there is a strong need to develop a dual-source modeling to separate the heat and water exchange and interaction between soil and atmosphere and between vegetation and atmosphere, over partially vegetated areas. Considering contributions of energy fluxes from soil and vegetation components, dual source models have been proposed to more precisely depict water and heat transfers from sparse or heterogeneous canopies. Among the dual-source approaches, two typical configurations can be distinguished [START_REF] Boulet | Modelisation des changements d'echelle et prise en compte des heterogeneites de surface et de leur variabilite spatiale dans les interactionssol-vegetation-atmosphere[END_REF][START_REF] Lhomme | Comments on dual-source vegetation-atmosphere transfer models[END_REF]. One is the 'layer' (or coupled) approach in which each source of water and heat fluxes is superimposed and coupled. It has a more complicated model structure and performs better over homogeneous vegetated surfaces. The layer approach cannot distinguish the difference between evaporation from the soil under and between vegetation canopies, which may lead to significant errors when applied to surfaces with large heterogeneity in soil wetness. The other one is the patch (uncoupled) approach, which represents the soil and the canopy as two springs side by side, where water and heat fluxes from each source interact independently with the above atmosphere. This latter approach may be more appropriate for more clumped vegetation, when vegetation is agglomerated and surrounded by large areas of bare soil [START_REF] Blyth | Application of aggregation models to surface heat flux from the Sahelian tiger bush[END_REF]William P. Kustas and Norman, 1997;[START_REF] Norman | Source approach for estimating soil and vegetation energy fluxes in observations of directional radiometric surface temperature[END_REF]. It assumes that each component receives full radiation loading but neglects evaporation from under-canopy soil surfaces. Several models have been developed based on this approach, including the Two Source Energy Balance Model "TSEB" [START_REF] Norman | Source approach for estimating soil and vegetation energy fluxes in observations of directional radiometric surface temperature[END_REF], Mapping Evapotranspiration with Internalized

Calibration "METRIC" [START_REF] Allen | Satellite-Based Energy Balance for Mapping Evapotranspiration with Internalized Calibration (METRIC)-Applications[END_REF], and the Two-source Trapezoid Model for Evapotranspiration "TTME" [START_REF] Long | A Two-source Trapezoid Model for Evapotranspiration (TTME) from satellite imagery[END_REF].

c. Multi-source models

For surfaces with multiple types of vegetation, neither the single nor the dual source model can capture energy fluxes from the surface due to the different canopy resistances and structures among different vegetation types. The energy transfers within these areas are often represented by multi-source models. The first models of this kind were designed for sparse canopies to take into accountseparately the vegetation and soil contributions [START_REF] Shuttleworth | Evaporation from sparse crops-an energy combination theory[END_REF][START_REF] Shuttleworth | The theoretical relationship between foliage temperature and canopy resistance in sparse crops[END_REF]. Afterward, more complex representations were proposed to take into account the heterogeneous canopies with diverse components (main vegetation, herbaceous substrate, bare soil) [START_REF] Dolman | Monitoring wheat phenology and irrigation in Central Morocco: On the use of relationships between evapotranspiration, crops coefficients, leaf area index and remotely-sensed vegetation indices[END_REF][START_REF] Huntingford | An intercomparison of single and dualsource vegetation-atmosphere transfer models applied to transpiration from sahelian savannah[END_REF]. The multi-source models are generally represented by resistance networks, which combine surface and air resistances within the canopy. If vegetation or bare soil surfaces are large enough to allow different aerodynamic resistances to be defined for each patch, a patch (uncoupled) representation should be chosen. In the opposite case, if the different sources are close to each other and do not allow the definition of separate aerodynamic resistances, a layer approach should be preferred. To estimate ET, based on the layer model, Dolman.

(1993) distinguished the vegetation layer into upper-canopy and understory layers and estimated energy fluxes from each layer respectively. In addition, [START_REF] Williams | Effect of changes in water content on photosynthesis, transpiration and discrimination against 13CO2 and C18O16O in Pleurozium and Sphagnum[END_REF] separated the vegetation canopy into different horizontal, and the total flux from the entire canopy was calculated as the sum through the layers. More specifically, this model should also be considered as a multiple-source model, as vegetation layers at different heights receive different radiation laoding and have different canopy resistances.

d. Contextual models

Unlike the models described above, where the energy balance equation is explicitly solved for each pixel independently of the others, other approaches are based on the use of the spatial variability captured by satellite imagery (reflectance, vegetation indices) to derive the ET at the local and regional scales [START_REF] Gowda | ET mapping for agricultural water management: present status and challenges[END_REF]. These methods, known as contextual methods, are based on the simultaneous presence of hot and cold pixels due to the existence of wet and dry pixels on the same satellite image [START_REF] Chirouze | Intercomparison of four remote-sensing-based energy balance methods to retrieve surface evapotranspiration and water stress of irrigated fields in semi-arid climate[END_REF]. Roughly, the intermediate water status of a given temperature pixel is scaled between the hottest points considered the driest and the coldest points considered the wettest. The physical borderlines of LST corresponding to fully dry and fully wet conditions for both soil and vegetation are determined in the space defined by LST and NDVI (Jiang andIslam, 2001, 1999) and/or the space defined by LST and albedo [START_REF] Merlin | Selfcalibrated evaporation-based disaggregation of SMOS soil moisture: An evaluation study at 3km and 100m resolution in Catalunya, Spain[END_REF][START_REF] Roerink | S-SEBI: A simple remote sensing algorithm to estimate the surface energy balance[END_REF]. There are various models based on this method, such as SEBI (Surface Energy Balance Index, [START_REF] Menenti | Linear relationships between surface reflectance and temperature and their application to map actual evaporation of groundwater[END_REF], S-SEBI (Simpli_ed Surface Energy Balance Index, [START_REF] Roerink | S-SEBI: A simple remote sensing algorithm to estimate the surface energy balance[END_REF], SEB-1S

(Monosource Surface Energy Balance model, [START_REF] Merlin | Selfcalibrated evaporation-based disaggregation of SMOS soil moisture: An evaluation study at 3km and 100m resolution in Catalunya, Spain[END_REF]. More details about the contextual approach can be found in [START_REF] Kalma | Estimating land surface evaporation: A review of methods using remotely sensed surface temperature data[END_REF] and [START_REF] Li | Watershed allied telemetry experimental research[END_REF], who offer a summary of various existing contextual models.

I.4. Remote sensing of Evapotranspiration

Regarding the data availability over extended areas, remote sensing is the only viable technique that can provide very relevant information to feed ET models. It has shown a great potential for characterizing land surfaces (land use, vegetation coverage, soil moisture, water stress, etc.). Amongst the variety of remotely sensed variables, there are three in particular that are pertinent to the estimation of ET: vegetation cover index, land surface temperature and surface soil moisture. The approaches based on each variable are described below.

I.4.1. Models based on vegetation index

Vegetation indices (VI) have been available since the launch of the first satellites used for vegetation monitoring in the early 1970s [START_REF] Bannari | A review of vegetation indices[END_REF][START_REF] Bausch | spectral Inputs Improve Corn Crop Coefficients and Irrigation Scheduling[END_REF][START_REF] Huete | MODIS Vegetation Indices[END_REF][START_REF] Rouse | Monitoring vegetation systems in the Great Plains with ERTS[END_REF]. Nevertheless, the Normalized Difference Vegetation Index (NDVI) is the most common VI [START_REF] Tucker | Red and photographic infrared linear combinations for monitoring vegetation[END_REF]. NDVI computed from red and near infrared bands of the satellite can be considered as a useful indicator to study vegetation characteristics and consequently ET rates [START_REF] Norman | Source approach for estimating soil and vegetation energy fluxes in observations of directional radiometric surface temperature[END_REF]. Over the last two decades, several authors have confirmed the linear relationship between remote sensed vegetation indices and the vegetation photosynthesis by vegetation canopy [START_REF] Glenn | Relationship Between Remotelysensed Vegetation Indices, Canopy Attributes and Plant Physiological Processes: What Vegetation Indices Can and Cannot Tell Us About the Landscape[END_REF], between ET and NDVI [START_REF] Rossato | Evapotranspiration estimation in the Brazil using NDVI data[END_REF] and between NDVI and basal crop coefficient for irrigated agricultural fields [START_REF] Dolman | Monitoring wheat phenology and irrigation in Central Morocco: On the use of relationships between evapotranspiration, crops coefficients, leaf area index and remotely-sensed vegetation indices[END_REF]. Unlike complex and physically based models, FAO-56 is one of the simplest ET estimation approaches based on correlation of crop ET and NDVI [START_REF] Allen | Evapotranspiration information reporting: I. Factors governing measurement accuracy[END_REF][START_REF] Er-Raki | Combining Satellite Remote Sensing Data with the FAO-56 Dual Approach for Water Use Mapping In Irrigated Wheat Fields of a Semi-Arid Region[END_REF], 2007;[START_REF] Hunsaker | Estimating cotton evapotranspiration crop coefficients with a multispectral vegetation index[END_REF]. It requires fewer input data, and provides acceptable ET estimates [START_REF] Allen | Evapotranspiration information reporting: I. Factors governing measurement accuracy[END_REF][START_REF] Er-Raki | Combining FAO-56 model and ground-based remote sensing to estimate water consumptions of wheat crops in a semi-arid region[END_REF][START_REF] Rafi | Partitioning evapotranspiration of a drip-irrigated wheat crop: Inter-comparing eddy covariance-, sap flow-, lysimeter-and FAO-based methods[END_REF]. FAO-56 is based on the concepts of reference evapotranspiration ET 0 and crop coefficientsK c , which is a direct representation of actual crop growth conditions in the field. It has been introduced to separate the climatic demand from the plant response [START_REF] Allen | Crop evapotranspiration-Guidelines for computing crop water requirements-FAO Irrigation and drainage paper 56[END_REF]. This approach is mostly used for annual crops where VI dynamic defines well the phenological stages [START_REF] Glenn | Actual evapotranspiration estimation by ground and remote sensing methods: the Australian experience[END_REF][START_REF] Senay | Estimating basin scale evapotranspiration (ET) by water balance and remote sensing methods[END_REF]. However, in complex areas ( trees, herbaceous, degraded shrubs, etc…) the model must be adjusted with additional meteorological data [START_REF] Maselli | Operational monitoring of daily evapotranspiration by the combination of MODIS NDVI and ground meteorological data: Application and evaluation in Central Italy[END_REF] as the K c varies in space and time for a number of reasons including the land use pattern, irrigation management, natural variability of soil properties, vegetation amount and atmospheric boundary conditions (temperature, wind notably). No common relationship was found between ET and VI for different sites and climatic conditions.

I.4.2. Models based on Land Surface Temperature

The spatial modeling has become a dominant means to estimate ET fluxes over regional and continental areas [START_REF] Anderson | A climatological study of evapotranspiration and moisture stress across the continental United States based on thermal remote sensing: 2. Surface moisture climatology[END_REF][START_REF] Fisher | The future of evapotranspiration: Global requirements for ecosystem functioning, carbon and climate feedbacks, agricultural management, and water resources[END_REF]. One of the most widely used ET spatial models is the temperature-based approach as the land surface temperature (LST) is potentially a signature of both ET and the soil water availability via the surface energy balance. In recent decade, many efforts have been devoted to extract the LST from remote sensing data. Thermal sensors, on board satellites and aircrafts in the spectral range of the thermal infrared (between 8 and 14 μm) offer the possibility of obtaining spatially distributed LST data. ASTER (Advanced Space borne Thermal Emission), Landsat-8 and MODIS (Moderate-Resolution Imaging Spectroradiometer) provide images ranging from 90 m to 100 m and 1 km for applications in the Earth's surface processes [START_REF] Zhou | A new index for mapping built-up and bare land areas from Landsat-8 OLI data[END_REF]. Despite their low resolution, MODIS data are the most widely used because they cover the entire surface of the Earth every 1-2 days, whereas the revisit period for ASTER and Landsat is 16 days.

A variety of temperature-driven models with empirical and stronger physical basis have been described above (Section I.3). Among well-known temperature-driven energy flux models, the TSEB model proposed by [START_REF] Norman | Source approach for estimating soil and vegetation energy fluxes in observations of directional radiometric surface temperature[END_REF] has been showing high robustness for a wide range of landscapes [START_REF] Colaizzi | Two-source energy balance model estimates of evapotranspiration using component and composite surface temperatures q[END_REF]. This model has two key input variables, which can be derived from remote sensing data. The first one is the LST as it is used to estimate the sensible heat flux. The second is vegetation cover fraction (f c ) as it controls the partitioning of the energy between soil and vegetation. The TSEB model adopts an iterative procedure, in which an initial estimate of the plant transpiration is given by the Priestly-Taylor (PT) formulation [START_REF] Priestley | On the Assessment of Surface Heat Flux and Evaporation Using Large-Scale Parameters[END_REF]. This assumption is relatively simple, requires few input data and has proven to be remarkably accurate and robust for estimating potential ET in a wide range of conditions [START_REF] Fisher | Global estimates of the land-atmosphere water flux based on monthly AVHRR and ISLSCP-II data, validated at 16 FLUXNET sites[END_REF]. Recently, [START_REF] Boulet | The SPARSE model for the prediction of water stress and evapotranspiration components from thermal infra-red data and its evaluation over irrigated and rainfed wheat[END_REF] have developed the Soil-Plant-Atmosphere and Remote Sensing Evapotranspiration (SPARSE) model similar to the basic assumption of TSEB model. Nevertheless, SPARSE is solved in two modes: the prescribed and the retrieval mode to constrain the output fluxes. The former first generates equilibrium LST from the evaporationand the transpiration efficiencies estimates by assuming that their values are equal to 1. Then, LST is implemented in the SPARSE retrieval mode to circumscribe the output fluxes by both limiting cases (namely the fully stressed and potential conditions). In spite of the good retrieval performances of ET by this model, significant uncertainties are observed during the quasi-senescent vegetation period [START_REF] Boulet | The SPARSE model for the prediction of water stress and evapotranspiration components from thermal infra-red data and its evaluation over irrigated and rainfed wheat[END_REF].

I.4.3. Models based on Surface soil moisture

Over the past 50 years, several studies have documented that soil moisture (SM) status may be derived indirectly from thermal infrared data. [START_REF] Nemani | Developing Satellite-derived Estimates of Surface Moisture Status[END_REF] found a strong negative relationship between LST and NDVI across biomes with a distinct change in the slope between dry and wet days. In studies dedicated to SM the estimation [START_REF] Carlson | A new look at the simplified method for remote sensing of daily evapotranspiration[END_REF] and [START_REF] Gillies | Thermal Remote Sensing of Surface Soil Water Content with Partial Vegetation Cover for Incorporation into Climate Models[END_REF] have proved the previous idea, they developed a universal triangular method to explore relationships between SM, LST and NDVI. However, the atmospheric effects, the cloud cover as well as the effect of the vegetation have limited the development of these approaches.

While many bands in the electromagnetic spectrum are sensitive to changes in SM, the microwave domain is recognized as the most promising tool due to its independence to atmospheric conditions and is strongly related to water content in the first centimeters of soil [START_REF] Schmugge | Remote sensing in hydrology[END_REF]. Microwave sensors can be classified as either active (radars) or passive (radiometers). The radars have proved to be the most useful platforms for monitoring surface moisture at high spatial resolution [START_REF] Balenzano | Dense Temporal Series of C-and L-band SAR Data for Soil Moisture Retrieval Over Agricultural Crops[END_REF]. However, the impact of vegetation cover, its structure and soil roughness on the backscatter signal remains extremely difficult to model at high spatial resolution over large areas [START_REF] Satalino | C-Band SAR Data for Mapping Crops Dominated by Surface or Volume Scattering[END_REF]. Therefore, global SM products are generally derived from the radiometers such as the C-band Advanced

Microwave Scanning Radiometer (AMSR-E) [START_REF] Njoku | Soil Moisture Retrieval From AMSR-E[END_REF] on the Earth Observing System (EOS) Aqua satellite launched on May 2002. The AMSR-E instrument provides the SM at approximately 60 km resolution [START_REF]Aggregation scheme[END_REF][START_REF]Disaggregation model of SM data[END_REF][START_REF]Chapter II. Modeling approaches: Description and implimentation References[END_REF](7)(8). The first L-band mission dedicated to SM monitoring is the Soil Moisture and Ocean Salinity (SMOS) mission [START_REF] Kerr | The SMOS Mission: New Tool for Monitoring Key Elements of the Global Water Cycle[END_REF] launched in November 2009 that provides global maps of SM every three days at 40 km resolution (1.4 GHz). One difficulty is that microwave radiometry requires a large antenna to detect the signals emitted by the surface with sufficient sensitivity, which limits the resolution of the data to a few tens of km. The use of such coarse spatial resolution data is generally unsuitable or even incompatible with many hydrological and agricultural applications. To overcome the limitations linked to radars (higher spatial resolution and lower accuracy) and radiometers (higher accuracy and lower spatial resolution), the Soil Moisture Active and Passive (SMAP) mission [START_REF] Entekhabi | The Soil Moisture Active Passive {(SMAP)} Mission[END_REF] was expected to provide SM at a spatial resolution of 9 km at 3 days repeat intervals, by combining radar and radiometer measurements. However, the radar on broad SMAP stopped transmitting on July 2015 due to anomaly that involved the radar's high power amplifier, and since then SMAP has continued to work with data from radiometer only.

The brightness temperature from the radiometers and the backscattering coefficient from radars have a great potential for the SM estimation. Therefore, combining these two sensor observations can provide complementary information included in the land surface microwave signature. Several studies have attempted to combine passive and active microwave remote sensing observations for the SM estimation [START_REF] Njoku | Soil Moisture Retrieval From AMSR-E[END_REF][START_REF] Zhong | Large-Scale Microwave Remote Sensing of Retrieving Surface Multi-parameters Using Active and Passive Satellite Data: In the Tibetan Plateau Region of Maqu[END_REF].

Neverthless, satellite observations are provided at different overpass times which can be lead to some differences on land surface parameters especially SM [START_REF] Li | Comparison of two retrieval methods with combined passive and active microwave remote sensing observations for soil moisture[END_REF]. Other studies seek to estimate SM without the complementary information provided by active observations.

One such approach was to employ optical/thermal remote sensing data that provide finer resolution information to downscale passive microwave SM estimations [START_REF] Chauhan | Spaceborne soil moisture estimation at high resolution: A microwave-optical/IR synergistic approach[END_REF][START_REF] Merlin | An improved algorithm for disaggregating microwave-derived soil moisture based on red, near-infrared and thermalinfrared data[END_REF][START_REF] Piles | Downscaling SMOS-Derived Soil Moisture Using MODIS Visible/Infrared Data[END_REF]. The relationship between SM, LST and vegetation coverhas been commonly represented as a triangle [START_REF] Carlson | A method to make use of thermal infrared temperature and NDVI measurements to infer surface soil water content and fractional vegetation cover[END_REF] or trapezoidal pattern relationship [START_REF] Moran | Estimating Crop Water Deficit Using the Relation between Surface-Air Temperature and Spectral Vegetation Index[END_REF]. For instance, [START_REF] Piles | Downscaling SMOS-Derived Soil Moisture Using MODIS Visible/Infrared Data[END_REF] applied a new polynomial-fitting method based on the results of [START_REF] Chauhan | Spaceborne soil moisture estimation at high resolution: A microwave-optical/IR synergistic approach[END_REF], by linking coarse resolution SM from SMOS and MODIS products to provide SM data at 10km and 1km resolution. Another potential approach to estimate SM through the semi-empirical relationship between SM and soil evaporative efficiency (SEE, defined as a ratio of actual to potential soil evaporation) has been applied by several authors [START_REF] Fang | Soil moisture at watershed scale: Remote sensing techniques[END_REF]Merlin et al., 2012b[START_REF] Merlin | Towards deterministic downscaling of SMOS soil moisture using MODIS derived soil evaporative efficiency[END_REF]. These authors used finer resolution MODIS VI, LST and surface albedo to compute SEE based on the triangle approach to generate a disaggregated SMOS SM product up to 1 km resolution. Merlin et al. (2012a) improved the evaporationbased method developed in [START_REF] Merlin | Towards deterministic downscaling of SMOS soil moisture using MODIS derived soil evaporative efficiency[END_REF]. DisPATCh (DISaggregation based on Physical And Theoretical scale CHange) includes the effect of vegetation water stress [START_REF] Moran | Estimating Crop Water Deficit Using the Relation between Surface-Air Temperature and Spectral Vegetation Index[END_REF]) within a trapezoid-based approach by using a 1 st order Taylor series expansion of a SEE model. [START_REF] Merlin | Selfcalibrated evaporation-based disaggregation of SMOS soil moisture: An evaluation study at 3km and 100m resolution in Catalunya, Spain[END_REF] implemented a simple correction for elevation effects.

Multiple recent studies have used the SEE-based algorithm for validation of downscaled SM product from coarse-scale satellite ( AMSR-E, SMOS and SMAP) [START_REF] Chan | Assessment of the SMAP Passive Soil Moisture Product[END_REF]Colliander et al., 2017;[START_REF] Djamai | Evaluation of SMOS soil moisture products over the CanEx-SM10 area[END_REF][START_REF] Malbéteau | DisPATCh as a tool to evaluate coarse-scale remotely sensed soil moisture using localized in situ measurements: Application to SMOS and AMSR-E data in Southeastern Australia[END_REF][START_REF] Molero | SMOS disaggregated soil moisture product at 1 km resolution: Processor overview and first validation results[END_REF].

Alternatively to the use of LST as a proxy for ET, numerous studies have stressed that the SM plays a critical role in the partitioning of available energy into latent and sensible heat fluxes and is the prominent controlling factor of actual ET [START_REF] Boulet | The SPARSE model for the prediction of water stress and evapotranspiration components from thermal infra-red data and its evaluation over irrigated and rainfed wheat[END_REF][START_REF] Gokmen | Remote Sensing of Environment Integration of soil moisture in SEBS for improving evapotranspiration estimation under water stress conditions[END_REF]Kustas et al., 1999;[START_REF] Kustas | Combining optical and microwave remote sensing for mapping energy fluxes in a semiarid watershed[END_REF][START_REF] Li | Comparing the utility of microwave and thermal remote-sensing constraints in twosource energy balance modeling over an agricultural landscape[END_REF]. Several authors have revised the wellknown LST-based TSEB model and replaced the LST with microwave-derived SM to estimate daily ET [START_REF] Bindlish | Influence of near-surface soil moisture on regional scale heat fluxes: Model results using microwave remote sensing data from SGP97[END_REF][START_REF] Kustas | Combining optical and microwave remote sensing for mapping energy fluxes in a semiarid watershed[END_REF]Kustas et al., 1999;[START_REF] Li | Comparing the utility of microwave and thermal remote-sensing constraints in twosource energy balance modeling over an agricultural landscape[END_REF]. [START_REF] Bindlish | Influence of near-surface soil moisture on regional scale heat fluxes: Model results using microwave remote sensing data from SGP97[END_REF] found that the impact of SM on surface fluxes is strongly related to the vegetation cover. The impact is high for low fraction cover, and relatively weak for high cover fraction. Moreover, the soil evaporation is constrained by the SM through soiltexture dependent coefficients reported in [START_REF] Sellers | Relations between surface conductance and spectral vegetation indexes at intermediate (100m2 to 15km2) length scales[END_REF]. In the sameway, Li et al.

I.5. Objectives

Several studies agree with the view that combining both LST and SM information at a time would enhance the robustness and accuracy of ET estimates in various biomes and climates [START_REF] Gokmen | Remote Sensing of Environment Integration of soil moisture in SEBS for improving evapotranspiration estimation under water stress conditions[END_REF][START_REF] Kustas | Estimating subpixel surface temperatures and energy fluxes from the vegetation index-radiometric temperature relationship[END_REF][START_REF] Kustas | Combining optical and microwave remote sensing for mapping energy fluxes in a semiarid watershed[END_REF][START_REF] Li | Comparing the utility of microwave and thermal remote-sensing constraints in twosource energy balance modeling over an agricultural landscape[END_REF]. Nevertheless, few studies have simultaneously combined both observations in a unique energy balance model. One difficulty lies in developing a consistent representation of the soil evaporation (as constrained by SM, [START_REF] Chanzy | Significance of soil surface moisture with respect to daily bare soil evaporation[END_REF], the total ET (as constrained by LST, [START_REF] Norman | Source approach for estimating soil and vegetation energy fluxes in observations of directional radiometric surface temperature[END_REF] and the plant transpiration (as indirectly constrained by both LST and SM, Ait Hssaine et al., 2018a).

In this context, the objective of this thesis is to improve the estimation of ET by combining multi-resolution optical / microwave remote sensing and surface-atmosphere exchange modeling. The proposed strategy consists ini) disaggregating the microwave SM data ii) estimating soil evaporation, and iii) partitioning the ET between soil evaporation and plant transpiration. To realise these objectives:

1-We rely on the DisPATCh remote sensing algorithm (Merlin et al., 2012a) that combines the coarse scale microwave-retrieved SM with high-resolution optical/ thermal data within a downscaling relationship to produce SM at 1km resolution. The method is based on the spatial relationship between microwave SM data and the soil evaporative efficiency (SEE) derived from optical data (including thermal) at higher spatial resolution. DisPATCh converts the high-resolution optical-derived SEE fields into high-resolution SM fields given a semiempirical SEE model and a first-order Taylor series expansion around the SMOS observation.

As part of this thesis, the C4DIS processor has been applied to the MODIS tile in Morocco to generate the moisture product over the 2014-2018 period. The DisPATCh SM are then evaluated by the in-situ measurements of intensive sites of the Tensift Observatory (http://trema.ucam.ac.ma).

2-DisPATCh SM data are used as input to a soil evaporation model. Several methods for estimating evaporation from SM observations at the surface have been proposed by [START_REF] Cahill | Combined spatial and Kalman filter estimation of optimal soil hydraulic properties[END_REF], [START_REF] Dekić | A study of the sensitivity of bare soil evaporation schemes to soil surface wetness, using the coupled soil moisture and surface temperature prediction model[END_REF], [START_REF] Lee | Estimating the Soil Surface Specific Humidity[END_REF], and [START_REF] Mahfouf | Analysis of Soil Moisture from Near-Surface Parameters: A Feasibility Study[END_REF]. Although many formulations have been proposed since the 1960s, there is still no consensus on a better way of modeling soil evaporation over large areas [START_REF] Desborough | Analysis of the relationship between bare soil evaporation and soil moisture simulated by 13 land surface schemes for a simple non-vegetated site[END_REF][START_REF] Sakaguchi | Effects of soil wetness, plant litter, and under-canopy atmospheric stability on ground evaporation in the Community Land Model (CLM3.5)[END_REF]. Nevertheless, the bibliographic review of these models allows to draw the following conclusions: 1) the existing formulations differ in four aspects: the low and high limit values of SM, the non-linearity of the relation between evaporation and SM, need of input data other than SM and depth of SM measurements [START_REF] Merlin | An analytical model of evaporation efficiency for unsaturated soil surfaces with an arbitrary thickness[END_REF], 2) Simple empirical expressions may be more accurate and robust than other physically based models (Dekić et al., 1995;[START_REF] Mihailović | The validation of various schemes for parameterizing evaporation from bare soil for use in meteorological models: A numerical study using in situ data[END_REF] on LST data, ii) using dual source representation, allowing an explicit separation of soil evaporation and plant transpiration, and iii) parameterizing the surface fluxes with a network of resistances, more directly related to SM than models with evaporative efficiency. The TSEB model [START_REF] Norman | Source approach for estimating soil and vegetation energy fluxes in observations of directional radiometric surface temperature[END_REF] is selected because it satisfices these three criteria. The transpiration in TSEB model is estimated based on Priestley Taylor (PT) approach. Indeed, the PT assumption that empirically relates ET to net radiation [START_REF] Priestley | On the Assessment of Surface Heat Flux and Evaporation Using Large-Scale Parameters[END_REF] has shown a growing interest [START_REF] Anderson | A climatological study of evapotranspiration and moisture stress across the continental United States based on thermal remote sensing: 2. Surface moisture climatology[END_REF][START_REF] Kustas | Evaluation of soil and vegetation heat flux predictions using a simple two-source model with radiometric temperatures for partial canopy cover[END_REF][START_REF] Norman | Source approach for estimating soil and vegetation energy fluxes in observations of directional radiometric surface temperature[END_REF]. PT coefficient noted αPT directly relates latent heat flux to the energy available at the surface. By neglecting the aerodynamic resistance term included in the full Penman-Monteith equation [START_REF] Monteith | Evaporation and the Environment[END_REF], the PT formulation is relatively simple, requires less input data and has proven to be remarkably accurate and robust for estimating potential ET in a wide range of conditions [START_REF] Fisher | Global estimates of the land-atmosphere water flux based on monthly AVHRR and ISLSCP-II data, validated at 16 FLUXNET sites[END_REF]. It is therefore well suited for operational [START_REF] Mcaneney | Operational limits to the Priestley-Taylor formula[END_REF] and large scale [START_REF] Anderson | A thermal-based remote sensing technique for routine mapping of land-surface carbon, water and energy fluxes from field to regional scales[END_REF] applications. In addition, recent studies based on in-situ global data sets have reported a good robustness of the PT modelingapproach over a variety of biomes [START_REF] Ershadi | Multi-site evaluation of terrestrial evaporation models using FLUXNET data[END_REF]. Nevertheless, severalstudies (Ait Hssaine et al., 2018a;[START_REF] Fisher | Global estimates of the land-atmosphere water flux based on monthly AVHRR and ISLSCP-II data, validated at 16 FLUXNET sites[END_REF][START_REF] Jin | Continental-scale net radiation and evapotranspiration estimated using MODIS satellite observations[END_REF][START_REF] Yang | Comparison of three dual-source remote sensing evapotranspiration models during the MUSOEXE-12 campaign: Revisit of model physics[END_REF] have stressed that the PT coefficient varies under different types of surface and according to various atmospheric conditions in the range 0.5-2.0 with an average value estimated around 1.3 (above references). Other studies [START_REF] Gonzalez-Dugo | Agricultural and Forest Meteorology A comparison of operational remote sensing-based models for estimating crop evapotranspiration[END_REF]Long and[START_REF] Long | A Two-source Trapezoid Model for Evapotranspiration (TTME) from satellite imagery[END_REF][START_REF] Morillas | Environmental factors affecting the accuracy of surface fluxes from a two-source model in Mediterranean drylands: Upscaling instantaneous to daytime estimates[END_REF] reported that the PT approach may overestimate the canopy ET, especially for low soil wetness, and/or sparse vegetation cover, because it does not include a reasonable reduction of the initial canopy ET under stress conditions. For this purpose, the modification of the PT-based TSEB formalism (Kustas et al., 1999;Norman et al., 1995) was investigated by integrating LST and SM data simultaneously (the modified version is named TSEB-SM). An innovative calibration procedure was also implemented to retrieve the main parameters of soil evaporation (soil resistance) and plant transpiration (αPT).

The following text of this manuscript is structured in seven chapters:

 Chapter 2 presents a detailed description of the study sites, as well as the acquisition devices of field /remote sensing data necessary to extract the surface biophysical characteristics and climatic variables.

 Chapter 3 describes the used modeling approaches.

 Chapter 4 presents the validation results of TSEB model over sparse and heterogeneous vegetation in Sahel region (Niger).

 Chapter 5 discusses the improviement made on TSEB model by integrating SM data (TSEB-SM): a feasibility study using in-situ data over 3 sites in Morocco was investigated.

 Chapter 6: presents an application of TSEB-SM in real life using readily available satellite thermal and microwave data for estimationg ET at 1 km resolution.

 Chapter 7 offers general conclusions and future perspectives

II.1. Introduction

This chapter describes the main equations of both the original version of TSEB model [START_REF] Norman | Source approach for estimating soil and vegetation energy fluxes in observations of directional radiometric surface temperature[END_REF] and those of the new TSEB-SM model (Ait Hssaine et al., 2018b) are fully described. Note that the main difference between the two models concerns the treatment of soil evaporation, which is either estimated as a residual term in TSEB and explicitly represented through a soil resistance term in TSEB-SM. After that, the equations for calculating SM from DisPTACh algorithm and turbulent fluxes at large scale from flux aggregationmodelare briefly reproduced.

II.2. TSEB Model Description and Implementation

The TSEB model was presented and described by Norman et al., [START_REF] Norman | Source approach for estimating soil and vegetation energy fluxes in observations of directional radiometric surface temperature[END_REF]. It In TSEB, the directional radiometric temperature (T rad (θ)) is divided into its soil and vegetation cover fractions as seen by the radiometer, and is expressed as follows:

T rad (θ) = [f(θ) * T veg 4 + (1 -f(θ)) * T soil 4 ] 1/4 (II.1)
Where T veg and T soil are the vegetation and soil temperatures (K). The fraction of the field of view of the infrared radiometer occupied by canopy, f(θ), can be calculated by combining the view zenith angle θand the vegetation cover fraction f c considering vegetation with a spherical distribution of leaf angles (Kustas and Norman, 1997) :

f(θ) = 1 -exp ( -0.5 * LAI cos (θ) ) (II.2)
And f c is simply f(θ = 0), namely:

f c = 1 -exp (-0.5 * LAI) (II.3)
The LAI estimates were then used to derive the canopy height by the empirical equation:

Chapter II. Modeling approaches: Description and implimentation

h c = ( LAI-LAI min LAI max -LAI min ) (II.4)
Net radiation, R n , is the sum of incoming and outgoing short and long wave radiation fluxes:

R n = (1 -α)SW + ε s LW -(ε veg f c σT veg 4 + ε soil (1 -f c )σT sol 4 )) (II.5)
Where α is the surface albedo, SW is the incoming solar radiation and LW is the incoming long wave radiation (atmospheric radiation), ε s , ε veg and ε soil are the surface, soil and leaf emissivity, respectively.In this study, the soil emissivity and leaf emissivity were taken as constant values from the literature (0.95 and 0.97, respectively).σ is the Stefan-Boltzman constant (=5.6698 10-8 W.m -2 .K -4 ).

The double source energy balance corresponds to the simple source balance shared between the soil and vegetation components: where ρ (kg.m -3 ) is the density of air, c p (W.s -1 . kg -1 K -1 ) the specific heat capacity of air,T a the air temperature,T veg and T soil respectively the canopy and soil temperatures, r ah the aerodynamic resistance to heat transfer across the canopy-surface layer interface, and r s the resistance to heat flux in the boundary layer immediately above the soil surface.

The r ah is calculated from the adiabatically corrected log temperature profile equation [START_REF] Brutsaert | Introduction[END_REF] expressed as:

r ah = ( ln (z u -d) z m -Ψ m )( ln (z h -d) z m -Ψ h ) v kar 2 * U a (II.10)
Chapter II. Modeling approaches: Description and implimentation wherez u and z T are the height of wind speed measurement U a and air temperature measurement T a , respectively.dis the displacement of reference plan (d = 2/3*h c ), z m is the roughness length for momentum (z m = h c /8) , V kar is the von Karman constant taken to be 0.4, and Ѱ m and Ѱ H are the adiabatic correction factors for momentum and heat, respectively [START_REF] Brutsaert | Introduction[END_REF].

Although r s is rather complex as it depends on many factors, [START_REF] Sauer | Measurement of heat and vapor transfer coefficients at the soil surface beneath a maize canopy using source plates[END_REF] provided a reasonable approximation:

r s = 1 a+b * U s (II.11)
where a=0.004 m.s -1 , b=0.012, and U s is the wind speed at a height above the ground where the effect of soil roughness is minimal (typically between 0.05 and 0.2 m). Using the empirical relations from Campbell and Norman(1998):

U s = U h exp [a sc ( z h c -1)] (II.12)
With a sc being the leaf size expressed as:

a sc = 0.28LAI 2/3 h c 1/3 s -1/3 (II.13)
And U h the wind speed at the top of vegetation canopy given by:

U h = [ ln( h c -d z m ) ln( z u -d z m )-Ѱ m ] (II.14)
The surface soil heat flux is estimated as a fraction of R n,soil :

G = c G R n,soil (II.15)
where c G ~0.35 [START_REF] Choudhury | Analysis of an empirical model for soil heat flux under a growing wheat crop for estimating evaporation by an infrared-temperature based energy balance equation[END_REF].

The latent heat flux from the vegetated canopy is derived from the PT formula:

LE veg = α PT f g ∆ ∆+γ R n,veg (II.16)
where γ is the psychometric constant (≈67 Pa K -1 ), f g the fraction of leaf area index (LAI) that is green, Δ the slope of the saturation vapor pressure versus temperature curve, and α PT ~1.26

for TSEB model [START_REF] Priestley | On the Assessment of Surface Heat Flux and Evaporation Using Large-Scale Parameters[END_REF].

Chapter II. Modeling approaches: Description and implimentation

II.2.1. Algorithm for solving the energy balance and the equation system

The algorithmfor solving the energy balance and the equation systemis presented in the schematic diagramin figure II.1.

In order to solve the system that includes more unknowns than equations, an iterative process is used that closes on the Obukhov length (LMO). The algorithm starts by calculating the wind and turbulence variables (LMO,U * ,U s , and r ah expressed by the above equations).

The available energy and heat fluxes are then determined by calculating the net radiation (R n )

and its partition between the vegetation (R n,veg

II.2.2. Calibration procedure

The PT coefficient (PT) is one of the most sensitive parameters of TSEB, because it drives the vegetation latent heat flux. Most studies conducted with TSEB have used its generic value around 1.3 [START_REF] Anderson | A climatological study of evapotranspiration and moisture stress across the continental United States based on thermal remote sensing: 2. Surface moisture climatology[END_REF][START_REF] Bindlish | Influence of near-surface soil moisture on regional scale heat fluxes: Model results using microwave remote sensing data from SGP97[END_REF][START_REF] Colaizzi | AND ET: COMPARISON OF PRIESTLEY-TAYLOR AND PENMAN-MONTEITH FORMULATIONS AND TWO TIME SCALING METHODS[END_REF][START_REF] Kustas | Evaluation of soil and vegetation heat flux predictions using a simple two-source model with radiometric temperatures for partial canopy cover[END_REF][START_REF] Norman | Source approach for estimating soil and vegetation energy fluxes in observations of directional radiometric surface temperature[END_REF]. Other studies have identified different values of αPT depending on the vegetation fraction cover and particular forcing conditions. Notably, the PT coefficient was found to be smaller for dry surfaces and higher for humid conditions [START_REF] Eichinger | On the concept of equilibrium evaporation and the value of the Priestley-Taylor coefficient[END_REF]. Nevertheless, the relative stability of αPT in many conditions has led to set αPT constant. Consistent with this assumption, αPTis set to 1.26 in TSEB [START_REF] Priestley | On the Assessment of Surface Heat Flux and Evaporation Using Large-Scale Parameters[END_REF]. Moreover, as an auxiliary parameter in Equation (2.16), f g also needs to be calibrated. Kustas and Norman (1997) assumed that f g was generally equal to 1, by considering that vegetation keeps being fully green during the growing stage, which represents most of the agricultural season. Note that green vegetation indices such as NDVI Chapter II. Modeling approaches: Description and implimentation (Normalized Difference Vegetation Index) can provide a strong constraint on f g . However, it may be difficult to separate between senescent vegetation and soil from green vegetation indices only. In this context, [START_REF] Merlin | An imagebased four-source surface energy balance model to estimate crop evapotranspiration from solar reflectance / thermal emission data ( SEB-4S )[END_REF] combined NDVI and surface albedo to estimate the fractions of both senescent and green vegetation. For the purpose of the comparison between TSEB and TSEB-SM using in-situ data sets, and consistent with most studies using TSEB, herein f g is set to 1 all along the agricultural season.

II.3. TSEB-SM Model Description and Implementation

The TSEB formalism is modified to integrate SM as an additional constraint on modeled ET.

In practice, the energy balance for vegetation and soil in TSEB-SM is the same as in TSEB, but the soil evaporation is now explicitly represented as a function of SM via a soil resistance term. Note that Song et al. (2016) have recently introduced SM in TSEB using a formulation of soil evaporative efficiency. While there is partial equivalence between both formulations, the soil resistance formulation is preferred herein as its parameters can be calibrated either from soil texture information [START_REF] Merlin | Modeling soil evaporation efficiency in a range of soil and atmospheric conditions: A downward approach based on multi-site data[END_REF] or from a combination of LST and SM data under bare soil conditions [START_REF] Merlin | A phenomenological model of soil evaporative efficiency using surface soil moisture and temperature data[END_REF].

The soil latent heat flux is estimated as:

LE soil = ρc p γ (e s -e a )
r ah +r s +r ss (II.17)

Where e s is the saturated vapor pressure at the soil surface, e a is the air vapor pressure, and r ss is the resistance to vapor diffusion in the soil. r ss is expressed as follows [START_REF] Silans | Transferts de masse et de chaleur dans un sol stratifié soumis à une[END_REF]:

r ss =
F soil,k = (R n,soil,k -H soil,k -LE soil,k -G k ) 2 (II.20)
with k being a loop index. By using the Newton method formula: Given that soil evaporation and plant transpiration may compensate each other to result in similar total ET values, it is important to ensure that the calibration procedure is well defined, meaning that a unique triplet (a rss , b rss , αPT) is systematically obtained at the desired time scale. In order to do so, the calibration data set is divided into two regions with specific

F veg,k = (R n,veg,k -H veg,k -LE veg,k ) 2 (II.21) T soil,k+1 = T soil,k - F soil,k dF soil,k (
Chapter II. Modeling approaches: Description and implimentation behaviors: i) data with f c ≤ f c,thres for which ET is mainly controlled by soil evaporation and ii) data with f c > f c,thres (f c,thres is taken =0.5) for which ET is dominated by plant transpiration. In both data sets, soil evaporation and plant transpiration may occur simultaneously but the LST over the mixed surface is expected to be more sensitive to soil evaporation and plant transpiration for f c ≤ 0.5 and f c > 0.5, respectively (Merlin et al., 2012a;[START_REF] Moran | Estimating Crop Water Deficit Using the Relation between Surface-Air Temperature and Spectral Vegetation Index[END_REF].

The first calibration step initializes αPT =1.26 and inverts r ss at each time (30-min) step for data with f c ≤ 0.5. The r ss is first adjusted to minimize the following cost function:

F inst = (T surf,sim -T surf,

II.4. Aggregation scheme

The spatial aggregation is a method to bridge the model parameters controlling surface exchange at a patch scale with the areal average value of equivalent model parameters applicable at a larger scale in order to estimate grid scale surface fluxes using the same equations that govern the patch scale behaviour [START_REF] Chehbouni | Methods to aggregate turbulent fluxes over heterogeneous surfaces: application to SALSA data set in Mexico[END_REF]. In general, aggregation can be applied either to the input forcing of the evapotranspiration models, or to the fluxes derived from fine resolution input fields [START_REF] Ershadi | Effects of spatial aggregation on the multi-scale estimation of evapotranspiration[END_REF]. Here the first assumption is used to link between local and effective values of land surface parameters [START_REF] Chehbouni | Methods to aggregate turbulent fluxes over heterogeneous surfaces: application to SALSA data set in Mexico[END_REF][START_REF] Chehbouni | American Meteorological Society Approaches for Averaging Surface Parameters and Fluxes over Heterogeneous Terrain[END_REF]Ezzahar et al., 2009b;[START_REF] Lhomme | Estimating sensible heat flux from radiometric temperature over sparse millet[END_REF]. The chosen averaging approach is directly related to the considered variable. For albedo (α) and

Chapter II. Modeling approaches: Description and implimentation displacement height𝑑, a simple arithmetic average is used:

〈α〉 = ∑ f i α i i (II.28) 〈d〉 = ∑ f i d i i (II.29)
From the Stefan-Boltzmann law, the aggregated value of the land surface temperature LST can be obtained from:

〈LST〉 = [ ∑ f i ε i LST i 4 i 〈ε〉 ] 0.25 (II.30)
Where f i is the fraction of the surface covered by the patch i (with ∑ f i = 1 i ). Finally, the aggregation of the roughness length is obtained from a logarithmic average as follows:

ln〈z 0 〉 = ∑ f i ln(z 0 ) i (II.31)
Because of the absence of a soil occupation map for the Wankama study site, the aggregation schemeusing in-situ measurementsis done by weighted average of the estimated variables from the data of the threeEC stations. Following (Ezzahar et al., 2009b)

II.5. Disaggregation model of SM data

The DisPATCh remote sensing algorithm combines the coarse scale microwave-retrieved SM with high-resolution optical/thermal data within a downscaling relationship to produce SM at higher spatial resolution. A detailed description of the algorithm can be found in Merlin et al. (2012) and [START_REF] Malbéteau | DisPATCh as a tool to evaluate coarse-scale remotely sensed soil moisture using localized in situ measurements: Application to SMOS and AMSR-E data in Southeastern Australia[END_REF].

Briefly, the soil evaporation from the 0-5 cm soil layer and the vegetation transpiration from the root-zone soil layer are first decoupled by separating LST into its soil and vegetation components (Merlin et al., 2012). The optical-derived soil temperature is then used to estimate the soil evaporative efficiency (SEE, ratio of actual to potential soil evaporation), which is known to be relatively constant during the day on clear sky conditions. In our application, we applied DisPATCh to 40 km resolution SMOS level-3 SM and 1 km resolution MODIS optical/thermal data to produce SM at a 1 km resolution [START_REF] Molero | SMOS disaggregated soil moisture product at 1 km resolution: Processor overview and first validation results[END_REF]. The input dataset is generated by taking into account different combinations of SMOS SM (ascending 6 am and descending 6 pm) and MODIS (Terra overpass 10:30 am and Aqua 1:30 pm from one day before until one day after the SMOS overpass), as well as the GTOPO Chapter II. Modeling approaches: Description and implimentation Digital Elevation Model (DEM) used to correct LST for topographic effects [START_REF] Malbéteau | DisPATCh as a tool to evaluate coarse-scale remotely sensed soil moisture using localized in situ measurements: Application to SMOS and AMSR-E data in Southeastern Australia[END_REF][START_REF] Merlin | Selfcalibrated evaporation-based disaggregation of SMOS soil moisture: An evaluation study at 3km and 100m resolution in Catalunya, Spain[END_REF]. The characteristics of these data are described in Table II.1.

II.6. Conclusion

TSEB and TSEB-SM models described above are used to estimate the ET within different cultures. For this purpose, different data have been used as input to feed these two models. In particular, the two key inputs, LST and f c are used to force the TSEB model. While SM is used as an additional constrain of soil evaporation in TSEB-SM model. The three products (LST, f c and SM) are either measured at the field scale using in-situ measurements or extracted from thermal/microwave remote sensing images. In addition, the meteorological data including air temperature, solar radiation, relative humidity, and wind speed are also used to force TSEB and TSEB-SM. To achieve these objectives, the experiments carried out and the data collected (field and spatial) are presented in the following chapter.

Chapter

III.1. Introduction

The first part presents the study sites and the description of the in-situ experimental. Indeed, six sites; including 2 irrigated and 1 rainfed wheat in the Haouz plain of the Tensift watershed (centre of Morocco), and three rainfed fields (Millet, fallow, and degraded shrubs) in the Wankama basin (Niger), have been chosen to calibrate and test the modeling approaches developed in the previous chapter. While, the second section is devoted to the presentation of remote sensing data (Optic, thermal and microwave) used to feed the models. and spring (November-April). The average air humidity is 50% and the reference evapotranspiration ET 0 is estimated as 1600 mm/year [START_REF] Allen | Crop evapotranspiration-Guidelines for computing crop water requirements-FAO Irrigation and drainage paper 56[END_REF][START_REF] Jarlan | Remote Sensing of Water Resources in Semi-Arid Mediterranean Areas: the joint international laboratory TREMA[END_REF], which is greatly exceeding the annual rainfall.

III.2. Sites and in

In the Haouz plain, three sites; including 2 irrigated and 1 rainfed wheat are selected to test our model. In the following, several inputs (including LST, SM and f c ) are used to force the TSEB-SM. Turbulent fluxes from the EC system used to validate the model estimates are also described below. being the most widely used method [START_REF] Belaqziz | Irrigation scheduling of a classical gravity network based on the Covariance Matrix Adaptation-Evolutionary Strategy algorithm[END_REF][START_REF] Belaqziz | Caractérisation de la distribution des irrigations par l'utilisation de la télédétection pour les réseaux d'irrigation gravitaire "Agro-hydrology from space&quot[END_REF]. The irrigation is managing by regional agricultural office (Office Régional de Mise en Valeur Agricole du Haouz or ORMVAH) through a network of concrete channels directly connected to a dam. The irrigation scheduling is defined before the beginning of the cropping season according to the dam water level and is negotiated with the farmer's associations.

In the frame work of this PhD Thesis, the experimentation in R3 zone was carried out in experiment, one plot (called the reference field) was irrigated according to the crop water needs estimated by the FAO-56 method. For the other field, so called (controlled field), the wheat was stressed in some periods [START_REF] Rafi | Partitioning evapotranspiration of a drip-irrigated wheat crop: Inter-comparing eddy covariance-, sap flow-, lysimeter-and FAO-based methods[END_REF]. The seasonal water irrigation was 374 and 504 mm for the controlled, and reference fields, respectively.

III.2.1.3. Sidi Rahal area (Bour field)

This study site is located about 60 km eastern Marrakech city (see Figure

Climatic data

For each experiment, an automatic weather station was set up, near the three studied wheat fields (R3, Chichaoua and Sidi Rahal). This station is equipped with instruments to measure solar radiation, wind speed and direction, air temperature and air humidity and rainfall. These climate forcing data, available at a half-hourly time step, are either sent in real time by remote transmission to the LMI-TREMA server (at the Faculty of Semlalia Sciences) or stored on a central data logger, before to be processed and analysed.

III.2.1.4.2. Turbulent heat flux measurements

To quantify the exchanges between the canopy and the atmosphere, the three studied field were equipped by an eddy covariance (EC) tower to measure the latent (LE) heat and sensible (H) heat fluxes. EC systems included a CSAT3 3D sonic anemometer (Campbell scientific Chapter III. Sites and data used Ltd, Logan USA) which measures the fluctuations in the wind velocity components and temperature, a LICOR-7500 open-path infrared gas analyzer (Campbell scientific Ltd, Logan USA) installed over the R3 site and a Krypton hygrometer (KH20, Campbell Scientific Ltd, Logan USA) installed over both Chichaoua sites and Bour filed to measure the concentration of water vapour. The half-hourly fluxes were calculated off-line using the EC processing software 'ECpack', after performing all required corrections for planar fit correction, humidity and oxygen (KH20), frequency response for slow apparatus, and path length integration [START_REF] Dijk | The principles of surface flux physics: theory, practice and description of the ECPACK library[END_REF]. EC towers were also equipped with Kipp and Zonen CNR radiometers to measure net radiation (R n ) and heat flux plates (Campbell Scientific Ltd, Logan USA) to measure the soil heat flux (G). Analysis of the energy balance closure showed that the sum of latent and sensible heat flux measured independently by the EC systems was often lower than the available energy (R n -G). The relative closure was satisfied by about 88%, 64%, and 70% (of available energy) for the R3, controlled and reference sites, respectively and about 68%, 79%, 76%, and 79% for S1, B1, S2 and S3, respectively in the Bour field . This problem could not be explained neither by the mismatch in the spatial extent of flux measurements, nor by the uncertainties associated with the measurements of soil heat flux and net radiation (Ezzahar et al., 2009b;[START_REF] Hoedjes | Comparison of Large Aperture Scintillometer and Eddy Covariance Measurements: Can Thermal Infrared Data Be Used to Capture Footprint-Induced Differences?[END_REF][START_REF] Twine | Correcting eddy-covariance flux underestimates over a grassland[END_REF].

Correction was hence performed using the approach suggested by [START_REF] Twine | Correcting eddy-covariance flux underestimates over a grassland[END_REF]. Indeed, the daily (computed using 30-minute estimates between 9 am and 5 pm) Bowen ratio

Land surface temperature

Land surface temperature is measured at the EC station by using two Apogee IRTS-P infrared radiometers, oriented downward and measuring the surface leaving radiance between 8 to 14 µm, set up at a 2-m height above ground. An estimate of LST is obtained by averaging both measurements.

III.2.1.4.4. Vegetation data a. Leaf area index (LAI)

LAI is a dimensionless quantity that characterizes plant canopies. It is defined as the onesided green leaf area per unit ground surface area; it is an important structural property of vegetation. Because leaf surfaces are the primary border of energy and mass exchange,

Chapter III. Sites and data used important processes such as canopy interception, evapotranspiration, and gross photosynthesis are directly proportional to LAI. The most commonly method used for measuring LAI is 'The hemispheric photography technique', which relies on the acquisition and processing of hemispheric photographs [START_REF] Becker | Analysis of forest light environments part I. Computerized estimation of solar radiation from hemispherical canopy photographs[END_REF]. It consists on taking photos with a camera equipped with a FC_E8 Fish-eye lens (180° wide-angle lens). Several photos are taken in order to have a representative LAI value of the parcel (about 10 photos). The photos are taken under optimal lighting conditions to avoid the effects of shadow and overexposure phenomena that make the classification more delicate. The photos are then digitally processed to extract the value of the LAI. The principle treatment is as follows: 1) The photo is decomposed into a matrix, and a binary classification (soil / vegetation) is carried out based on thresholds in the green and red bands [START_REF] Khabba | Evaluation of Digital Hemispherical Photography and Plant Canopy Analyzer for Measuring Vegetation Area Index of Orange Orchards[END_REF].

2) The useful part of the matrix is extracted by masking the strong angles, which are outside the studied system. 3)

Extraction of vegetation cover rate on concentric rings associated with fixed viewing angles 4) Calculating the average directional LAI on photos taken in each parcel.

b. Vegetation cover fraction

The vegetation cover fraction (f c ) defined as the vegetated surface area projected on the ground at nadir, per soil surface area unit. It is dimensionless and varies between zero and one. In-situ methods of measuring the fraction of the canopy are very varied but the most widely used approach is the digital photography-based method. This is the same procedure as for the LAI. The vegetation cover fraction is then the ratio between the number of pixels of vegetation and the total number of pixels. Based on a comparison of the various techniques used to obtain field measurements of the f c , [START_REF] White | Measuring fractional cover and leaf area index in arid ecosystems: digital camera, radiation transmittance, and laser altimetry methods[END_REF] have argued that hemispheric photography is the simplest and most reliable technique.

Chapter III. Sites and data used

In our work, the f c is considered as a variable which controls the energy partitioning between surface vegetation and soil.

c. Surface soil moisture

Among many existing methods for measuring in-situ soil moisture, we find:

The gravimetric method, which is a direct method. The soil moisture content may be expressed by weight as the ratio of the mass of water present to the dry to the dry weight of the soil sample, or by volume as ratio of volume of water to the total volume of the soil sample. To determine any of these ratios for a particular soil sample, the water mass must be determined by drying the soil to constant weight and measuring the soil sample mass after and before drying. The water mass (or weight) is the difference between the weights of the wet and oven dry samples. The limits of this method are the destructive nature of the approach, the need to have a laboratory operator to perform the measurements and their low representativity, which is about only few centimeters. However, this method has the advantage of being simple and inexpensive.

The electromagnetic method, which is an indirect approach that measure an electric field in the ground. The idea is to use the quasi-linear relationship between the measured electric field and the soil moisture. However, this relationship depends on the type of soil. It is therefore necessary to calibrate, from the gravimetric measurements, the measurements for each type of soil in order to match the measurement (in mV) and the soil moisture. This approach has the advantage of being able to obtain measurements of soil moisture over a long period of time with a high temporal resolution and automatically, thanks to the data acquisition units. In addition, these electromagnetic techniques are non-destructive, non-radioactive and the sensors are not costly.

Two types of measuring devices are used in our study fields; the theta-probe devices that provide spatially point measurements and Time Domain Reflectometry (TDR) probes (model CS615, CS655) which are installed in a soil pit near the EC towers to measure soil water content at different soil depths of 5, 10, 20, 30, 50, 100 cm and 5, 15, 25, 35, 50, 80 cm and 5, 15, 30, 50, 80 cm and 5,10, 20, 30, 50, 70 cm for the flood-, controlled drip-and reference drip-irrigated wheat and Bour field, respectively.

Chapter III. Sites and data used

III.2.2.1. Site description

The region of interest is part of the Wankama catchment, which is located 70 km eastern the Niamey city, Niger (Figure III.5). It is situated between an upland at an altitude of 255 m and a pond at 200 m [START_REF] Boulain | Towards an understanding of coupled physical and biological processes in the cultivated Sahel -2. vegetation and carbon dynamics[END_REF]. This semi-arid site belongs to the AMMA-CATCH-Niger observatory [START_REF] Cappelaere | Un protocole expérimental pour l ' étude du couplage entre hydrologie et végétation en région centrale-sahélienne[END_REF], one of three meso-sites along the West African latitudinal transect [START_REF] Lebel | AMMA-CATCH studies in the Sahelian region of West-Africa: An overview[END_REF]. The climate is typically Sahelian with a short rainy season from June to September with an annual mean of 560 mm for the years 1905-2004, and very strong year-to-year and spatial variability. The site is characterized with high temperatures throughout the year with a daily average which ranges from 24°C to 35°C.

Additionally, the potential evapotranspiration is about 2500 mm/year [START_REF] Massuel | Integrated surface water-groundwater modelling in the context of increasing water reserves of a regional Sahelian aquifer[END_REF], greatly exceeding the annual rainfall. The soil is sandy (>90% sand) and poor in nutrients [START_REF] Rockström | Hillslope dynamics of on-farm generation of surface water flows: The case of rain-fed cultivation of pearl millet on sandy soil in the Sahel[END_REF]. The study area is covered by: (1) Millet fields cover 58% of the catchment's surface area. This rainfed crop is cultivated traditionally with little chemical fertilizer and no pesticides, being by far the main crop grown. ( 2) Fallow savannah fields represent 23% of the total surface area and they are no more than five years old and typical of the Niamey region. ( 3) Degraded shrubs occupy the remaining area [START_REF] Ramier | Towards an understanding of coupled physical and biological processes in the cultivated Sahel -1. Energy and water[END_REF].

Vegetation usually emerges after the first rainfall events occurring in June or early July, peaks around the end of the rainy season in early September and then dries out during the senescence phase.

b. Grid scale

A Large Aperture Scintillometer (LAS) was set up over a 3.2 km transect spanning the three ecosystem types, i.e., millet and fallow fields and the degraded shrubs. The LAS used in this study was developed and built by the Meteorology and Air Quality Group from the Wageningen University (Netherlands). This instrument was constructed according to the basic design described in Ochs and Wilson [START_REF] Ochs | A second-generation large-aperature scintillometer[END_REF]. It has an aperture size of 0.15 m and the transmitter operates at a wavelength of 0.94 µm. At the receiver, C n 2 is sampled at 1

Hz and averaged over 1 min intervals by a CR510 datalogger [START_REF] Meijninger | SCINTILLOMETER-BASED TURBULENT FLUXES OF SENSIBLE AND LATENT HEAT OVER A HETEROGENEOUS LAND SURFACE-A CONTRIBUTION TO LITFASS[END_REF]. The transmitter and the receiver were installed on 10 m towers with an altitude difference of approximately 46 m. The receiver was installed at the highest part of the basin (upland) whilst the transmitter was installed at the lowest part of the basin (Figure III.5). The direction of the Chapter III. Sites and data used resolution of about 40 km and an accuracy better than 0.04 m 3 /m 3 [START_REF] Kerr | The SMOS Soil Moisture Retrieval Algorithm[END_REF]. The revisiting time at the equator is every 3 days for both ascending and descending passes, which are sun synchronous at 6 am and 6 pm respectively. The SMOS level-3 1-day global SM product (MIR CLF31A\D, version 2.72 in reprocessing mode RE02) posted on the ~25 km Equal Area Scalable Earth (EASE) version 1.0 grid is used as input to DisPATCh algorithm.

III.3. Conclusion

Two different study sites, along with the remote sensing and meteorological data are described in this chapter. Thereafter, the Wankama Niger site will be used to validate the TSEB model (which provide estimates of evapotranspiration) over heterogeneous field.

While, Haouz plain sites (including irriagated fields (Chichaoua and R3) and rainfed field (Bour)) will be used to test the robustness of the new version of TSEB model (named TSEB-SM) which integrates LST, SM and f c simultaneously to retrieve the main parameters of soil evaporation (soil resistance) and plant transpiration (αPT). Then, DISPATCh SM and MODIS data will be integrated within the TSEB-SM to provide large-scale estimates of evapotranspiration.

Chapter IV. Validation of TSEB model over sparse and heteregeous vegetation in Sahel region (Niger)

IV.1. Introduction

Estimates of turbulent fluxes (i.e., sensible and latent heat fluxes H and LE) over heterogeneous surfaces is not an easy task. The heterogeneity caused by the contrast in vegetation, hydric and soil conditions can generate a large spatial variability in terms of surface-atmosphere interactions.

SEB model driven by MODIS (Moderate resolution Imaging Spectroradiometer) and MSG (Meteosat Second Generation) observations in conjunction with an aggregation scheme are used to derive area-averaged H and LE over a heterogeneous watershed in Niamey, Niger (Wankama catchment) [START_REF] Allies | Estimating evapotranspiration from remote sensing in West Africa: application of S-SEBI and Ts-VI triangle methods[END_REF][START_REF] Boulain | Towards an understanding of coupled physical and biological processes in the cultivated Sahel -2. Vegetation and carbon dynamics[END_REF]Ezzahar et al., 2009b;[START_REF] Ramier | Towards an understanding of coupled physical and biological processes in the cultivated Sahel -1. Energy and water[END_REF][START_REF] Velluet | Building a field-and model-based climatology of local water and energy cycles in the cultivated Sahel – annual budgets and seasonality[END_REF]. A spatial aggregation approach is conceived as a method which seeks to link the model parameters that control surface exchange (LST, α, d, 𝑧 0 , LAI, h c ) on a patch scale with the area-average value of equivalent model parameters applicable on a larger scale or grid-scale, assuming that the same equations are used to describe surface fluxes at both scales [START_REF] Ershadi | Effects of spatial aggregation on the multi-scale estimation of evapotranspiration[END_REF]Ezzahar et al., 2009bEzzahar et al., , 2009a;;[START_REF] Liu | Upscaling evapotranspiration measurements from multi-site to the satellite pixel scale over heterogeneous land surfaces[END_REF][START_REF] Long | How sensitive is SEBAL to changes in input variables, domain size and satellite sensor?[END_REF]. In general, aggregation scheme can be applied on the input requirements (Ezzahar et al., 2009b) or directly to predicted fluxes [START_REF] Saadi | Assessment of actual evapotranspiration over a semiarid heterogeneous land surface by means of coupled low-resolution remote sensing data with an energy balance model: comparison to extra-large aperture scintillometer measurements[END_REF]. Nevertheless, the efficiency of this approach lies on the evaluation of their outputs/performances against field observations, which requires the development of a measurement network at the local scale such as Eddy covariance systems [START_REF] Baldocchi | Measuring fluxes of trace gases and energy between ecosystems and the atmosphere -the state and future of the eddy covariance method[END_REF][START_REF] Baldocchi | Inter-annual variability of net and gross ecosystem carbon fluxes: A review[END_REF][START_REF] Baldocchi | Terrestrial Carbon Cycle Variability[END_REF][START_REF] Baldocchi | FLUXNET: A New Tool to Study the Temporal and Spatial Variability of Ecosystem-Scale Carbon Dioxide, Water Vapor, and Energy Flux Densities[END_REF]). Such a system is very costly, and man-power demanding with a competent staff for data processing and maintenance, as well as an important energy supply for operation. To overcome these difficulties, Large Aperture Scintillometer (LAS) is one of the alternative techniques employed to validate the satellite remote sensing H and LE estimates due to the comparable spatial resolutions. It has already been used in various contexts over complex topography and heterogeneous vegetation cover [START_REF] Brunsell | Validating remotely sensed land surface fluxes in heterogeneous terrain with large aperture scintillometry[END_REF]Ezzahar et al., 2009b;[START_REF] Liu | Measurements of evapotranspiration from eddy-covariance systems and large aperture scintillometers in the Hai River Basin, China[END_REF].

Consequently, LAS is becoming popular in hydro-meteorological studies because it is relatively cheap, robust, and easy to operate and maintain. Additionally, the LAS can be potentially used to improve the representation of surface heterogeneity in land-surfaceatmosphere models operating at large scales.

Chapter IV. Validation of TSEB model over sparse and heteregeous vegetation in Sahel region (Niger)

57

In this chapter, the thermal-based two-source energy balance (TSEB; [START_REF] Norman | Source approach for estimating soil and vegetation energy fluxes in observations of directional radiometric surface temperature[END_REF] has been chosen as it has been evaluated with success in different contexts including sparse canopy in semi-arid areas [START_REF] Diarra | Performance of the two-source energy budget (TSEB) model for the monitoring of evapotranspiration over irrigated annual crops in North Africa[END_REF][START_REF] Kustas | Evaluation of soil and vegetation heat flux predictions using a simple two-source model with radiometric temperatures for partial canopy cover[END_REF]. TSEB algorithm is described in detail in chapter 3. As far as we know, the TSEB model has never been tested over a heterogeneous Sahelian agro-ecosystem. Therefore, a validation at patch scale was firstly investigated using in-situ measurements from three eddy-covariance stations sampling

IV.2. Results and discussion

As a preliminary step, the quality of experimental data including EC and scintillometer underestimation of the turbulent fluxes by about 8%, 17%, and 20% for the millet, fallow and degraded shrubs, respectively. Several practical reasons preclude perfect closure [START_REF] Foken | Some aspects of the energy balance closure problem[END_REF], e.g. spatial scale discrepancies between measurements of energy balance components, and spatial heterogeneities; storage between measurement levels (canopy and superficial soil); so-called eddy flux losses (not measured here); difficulties with ground flux estimation [START_REF] Guyot | Combined analysis of References energy and water balances to estimate latent heat flux of a sudanian small catchment[END_REF][START_REF] Heusinkveld | Surface energy balance closure in an arid region: role of soil heat flux[END_REF]. Results reported in other experimental studies have shown that balance shortfalls commonly stand between 10% and 40 % of the available energy [START_REF] Foken | Some aspects of the energy balance closure problem[END_REF][START_REF] Mauder | Impact of post-field data processing on eddy covariance flux estimates and energy balance closure[END_REF]. As a conclusion, closure is quite satisfactory for our experiment, especially at the millet site which was more homogenous than fallow and degraded shrubs sites. during the entire study period. Note that the scintillometer only calculates H, and LE is derived as a residual term of the energy balance (LE LAS = R n -G -H LAS ). In this case, the available energy has been aggregated using the values measured at each instrumented field

(< R n -G > agg = ∑ f i (R n -G) i 3 1
). Stages 1, 2 and 3 present respectively the beginning of season (June 1 st -mid July), the growing stage which took place over two months (mid Julyto mid-September) and the senescence stage (from mid-September). Preliminary to the scintillometer data analysis, a comparison between H LAS against weighted EC fluxes was done for the wind direction interval 70° to 250°, because the footprint of the LAS covers the monitored sites where the EC systems were installed. The statistical results show a good agreement between the LAS sensible heat fluxes and those derived from the EC systems with a relative error of about 20% (Ezzahar et al., 2009b). The H LAS and LE LAS dynamics are almost stable throughout the season and LE LAS does largely dominate H LAS through the growing stage. Rainfall is rather regular between mid-July and mid-September, which ensured enough soil moisture to keep millet growing until mid-September. It can be seen that every rainfall event caused an immediate response with a significant energy shift between H and LE. LE LAS is around 200 W/m 2 and increases after each rain event, and peaks at the end of August with 315 W/m 2 , which corresponds to the LAI peak for Millet crop [START_REF] Boulain | Towards an understanding of coupled physical and biological processes in the cultivated Sahel -2. Vegetation and carbon dynamics[END_REF]. In the same period, soil moisture was high and reached its maximum. Some points produced a short period of albedo increase. During the rain events, albedo follows a very markedly decreasing general trend, with large fluctuations due to alternating dry and wet spells [START_REF] Ramier | Towards an understanding of coupled physical and biological processes in the cultivated Sahel -1. Energy and water[END_REF]. This assumption is supported by the observed positive bias of 0.03. The LST comparison shows a reasonable correlation of R=0.77 with an RMSE=3.8 K, and an underestimation of LST MODIS by -1.8 K on average. The RMSE is on the upper limit of the values reported in the literature that usually range between 2 and 4 K [START_REF] Yu | Evaluation of MODIS LST Products Using Longwave Radiation Ground Measurements in the Northern Arid Region of China[END_REF]. The observed scattering may also stem from the fact that the in-situ LST is not representative for the satellite LST. A finer look at the results highlights also a very contrasted bias between the two sites: over Millet that dominates the Wankama land use with 58% of the area, the bias is logically low (MBE=-0.5 K) while it reaches more than -4 K over the denser and thus colder vegetation of the fallow site.

degraded shrubs sites, respectively. Indeed, affected by the complexity of the physical processes that occur in the soil as well as the vegetation cover, soil heat flux is the most difficult parameter to estimate with great precision. Several studies have pointed out this difficulty in estimating G especially on sparse vegetation (Ezzahar et al., 2009b(Ezzahar et al., , 2009a[START_REF] Ezzahar | On the application of scintillometry over heterogeneous grids[END_REF]. In addition, measuring this parameter at 5 cm and in sparse vegetation represents a major challenge to get representative measurement. The installation of heat flux plates in the soil must take into account several criteria: the plates must be totally covered to ensure that it is not directly exposed to the sunlight especially when the soil is very sandy as in the Wankama catchment where sand represents 80 to 90% [START_REF] Verhoef | Spatio-temporal surface soil heat flux estimates from satellite data; results for the AMMA experiment at the Fakara (Niger) supersite[END_REF]. Additionally, heavy rainfall within a few hours, which is relatively common in the Sahel region, can uncover the plates and thus lead to exposing them to sunlight. Moreover, the use of the Brutsaert formula (developed for clear sky days by Brutsaert [START_REF] Brutsaert | On a derivable formula for long-wave radiation from clear skies[END_REF] for the incoming longwave radiation (that replaced the measurements when they were not available for this station, to estimate R n ) can create a significant dispersion for low radiation values in cloudy conditions [START_REF] Ezzahar | On the application of scintillometry over heterogeneous grids[END_REF].

The agreement between the measured and predicted turbulent fluxes is obviously lower than for the estimated available energy (see figures, IV. 4.d,IV.4.e and IV.4.f for H and IV.4.g,IV.4.h and IV.4.i for LE)but, despite a significant dispersion, correlation coefficients and RMSEs are encouraging (Table IV.1). The observed dispersion can be related to the footprint effect, as the footprint of the EC system is considerably larger than the representativity scale of the measured input variables (mainly α, LST and LAI). In addition, other parameters such as roughness length (z 0m ) and displacement height (d) were estimated as a fraction of the vegetation height using classical rules of thumb [START_REF] Shaw | Aerodynamic roughness of a plant canopy: A numerical experiment[END_REF][START_REF] Thom | Momentum absorption by vegetation[END_REF]). These equations have been established for homogeneous and dense covers while the study sites are heterogeneous and sparse. A further step to minimize dispersions would be to estimate these variables using EC data following [START_REF] Hoedjes | Comparison of Large Aperture Scintillometer and Eddy Covariance Measurements: Can Thermal Infrared Data Be Used to Capture Footprint-Induced Differences?[END_REF] and [START_REF] Lagouarde | Monitoring the Sensible Heat Flux over Urban Areas using Large Aperture Scintillometry: Case Study of Marseille City During the Escompte Experiment[END_REF]. Finally, several empirical and constant model parameters have been used in the TSEB model, which require calibration according to the specific conditions of the study area. Among them, the Priestley-Taylor parameter (αPT) directly relates latent heat flux to the available energy at the surface. Most studies driven by TSEB model have used its theoretical value of 1.26 [START_REF] Bindlish | Influence of near-surface soil moisture on regional scale heat fluxes: Model results using microwave remote sensing data from SGP97[END_REF][START_REF] Colaizzi | AND ET: COMPARISON OF PRIESTLEY-TAYLOR AND PENMAN-MONTEITH FORMULATIONS AND TWO TIME SCALING METHODS[END_REF][START_REF] Kustas | Evaluation of soil and vegetation heat flux predictions using a simple two-source model with radiometric temperatures for partial canopy cover[END_REF][START_REF] Norman | Source approach for estimating soil and vegetation energy fluxes in observations of directional radiometric surface temperature[END_REF]. Other studies have identified that it is variable under different surface and atmospheric conditions (varies in the range 0.5-2). In particular, the αPT was found to be smaller for dry surfaces and higher for humid conditions [START_REF] Eichinger | On the concept of equilibrium evaporation and the value of the Priestley-Taylor coefficient[END_REF]. In the same context, (Ait Hssaine et al.,

b. Using MODIS

An intercomparison between (R n -G) and turbulent fluxes measured by each station and the fluxes estimated by TSEB model using MODIS data is done and the error statistics are reported in Table IV.1. Overall, the discrepancies between the available energy estimated from TSEB model and measured one, for both sites (millet and fallow) is likely due to greater scatter between MODIS and measured α, and to the difference between MODIS and in-situ

LST. In all cases, LE does largely dominate H through the growing season (July-September), in particular for the fallow field. For the Millet site, the late start of the rainy season had significant adverse effects and the crop was not able to take advantage of the abundant rainfall because of insufficient plant development [START_REF] Boulain | Hydrologic and land use impacts on vegetation growth and NPP at the watershed scale in a semi-arid environment[END_REF]. For both sites, an overestimation of simulated LE compared to measured ones is recorded at the end of the season. Indeed, the saturation of TSEB in the higher range of LE is due to the fixed maximum value for αPT (equal to 1.26) (Ait Hssaine et al., 2018b). The structure of the model cannot accommodate large evaporative demand conditions and strong advective conditions (Song et al., 2016b). Moreover, the change in wind direction in monsoon periods strengthens advection

c. Using MODIS products

In this section, the effect of land cover heterogeneity on the estimated turbulent fluxes has been studied by combining TSEB model driven by Terra and Aqua remotely sensed data and an aggregation scheme, at Terra-MODIS and Aqua-MODIS overpass time. In a subsequent step, simulated LE was compared to the observed one using the three schemes described before. As shown in figure IV.8.d, the Scheme 1 overestimates LE with a relative error of about 58% (RMSE= 102 W/m 2 , R=0.85, MBE=73 W/m 2 ). That can be explained by the fact that LE is a residual term affected by errors in both available energy and sensible heat flux. Figures IV.8.e and IV.8.f plot simulated versus observed LE for the simple scheme 2 and scheme 3. TSEB provides satisfying results with a RMSE of 65 W/m 2 and 63 W/m 2 , and relative error of 39% and 35% for the second and third schemes, respectively. Based on the above results, the first scheme could not achieve satisfactorily the upscaling of turbulent fluxes over heterogeneous land surfaces. In fact, the method considers that all pixels belonging to the footprint of LAS contributes 100% of the pixel value, even for pixels of low contribution. This will obviously lead to large differences in LST, which is a key feature for determining the turbulent fluxes. October were available. Despite a significant scattering, both observed and simulated fluxes depict a similar behavior with a gradual switching of available energy from latent to sensible heat following the last rainfall around mid-September. An interesting feature is the underestimation of H by TSEB during the senescence while LE is overestimated for the same period. This could be attributed to the constant value of αPT equal to 1.26 used in this study.

Indeed, this value is usually accepted for semi-arid to sub-humid agricultural areas under irrigation regime [START_REF] Anderson | A climatological study of evapotranspiration and moisture stress across the continental United States based on thermal remote sensing: 2. Surface moisture climatology[END_REF][START_REF] Diarra | Performance of the two-source energy budget (TSEB) model for the monitoring of evapotranspiration over irrigated annual crops in North Africa[END_REF][START_REF] Norman | Source approach for estimating soil and vegetation energy fluxes in observations of directional radiometric surface temperature[END_REF] while it has been shown that lower αPT are obtained for dry areas such as in our region of study after the end of the rainy season. Finally, the obtained significant scattering, in particular after the last rainfall could also be related to the radiative properties of vegetation that are not well represented for dry vegetation.

IV.3. Summury and Conclusions

The main objective of this chapter is to estimate the turbulent fluxes over a path covering the three dominant crops (millet, fallow and degraded shrubs) in the Wankama basin by combining TSEB model, an aggregation method and satellite data (MODIS and MSG SEVIRI). The data used to validate this approach were collected within the framework of the AMMA project. Each site was equipped with meteorological stations and Eddy Covariance systems for monitoring the energy and water balance as well as the soil and vegetation characteristics. In addition, a large aperture scintillometer was installed over a transect of The results obtained at the station scale for H and LE are relevant, especially when using insitu data given the complexity of the study sites and in the range of what has been reported in the literature in terms of RMSE and correlation coefficient. Some scatter was noted, which is mainly related to the difference in footprints of the measuring instruments (about 100 m for EC systems with regard to less than 10 m for inputs variables such as LAI, albedo and LST), as well as to the fixed maximum value for αPT (equal to 1.26) during the entire season.

Despite this dispersion and as already underlined by several authors, TSEB provides with good performances for H and LE prediction at the station scale by using in-situ measured inputs or, to a lesser extent, MODIS derived inputs.

TSEB was then evaluated at the (1 km and 3 km) grid-scale along the scintillometer transect spanning a heterogeneous landscape. To this end, in-situ data were first aggregated to estimate the mean turbulent fluxes. In this ideal case where the major inputs are well known thanks to in-situ measurements on the dominant vegetation type, the predicted fluxes obviously showed a good agreement with the scintillometer observations with statistical metrics on the same order of values as those of the comparison at the station scale (RMSE=37 W/m 2 and 75 W/m 2 for H et LE, respectively) although some dispersions were observed. The latter were explained by the difference in the footprints of the measuring instruments as well as because LE LAS was calculated as a residual term of the energy balance using the average available energy values derived from measurements at each site. In a second step, TSEB is validated at the grid-scale but with remotely-sensed inputs. To this objective, MSG SEVIRI and MODIS sensors only offers a revisit time able to sample the high inter-and intra-daily variability of the SEB in semi-arid areas. The first assessment was performed by using the MSG SEVIRI LST at 3 km without explicit representation of the sub-pixel heterogeneity. The agreement between H and LE simulated by TSEB model and scintillometer observations is very poor, in particular in terms of temporal dynamic (R=0.39 and 0.2 for H and LE, respectively). This dispersion could be attributed to the large bias on MSG SEVIRI LST linked to the heterogeneity of land cover. In addition, this highlights the need to represent the sub-pixel heterogeneity. This was tested in a final step by using 1-km MODIS products as input of the TSEB model and 3 aggregation schemes. If the results with the simplest aggregation scheme consisting in averaging MODIS inputs independently of the footprint

V.1. Introduction

Data available from space can help in implementing the PT approach from three distinct perspectives: i) applying a constraint on vegetation transpiration using an a priori value for αPT [START_REF] Anderson | A thermal-based remote sensing technique for routine mapping of land-surface carbon, water and energy fluxes from field to regional scales[END_REF]Kustas et al., 1999;[START_REF] Norman | Source approach for estimating soil and vegetation energy fluxes in observations of directional radiometric surface temperature[END_REF], ii) applying a constraint on soil evaporation using SM data [START_REF] Bindlish | Influence of near-surface soil moisture on regional scale heat fluxes: Model results using microwave remote sensing data from SGP97[END_REF][START_REF] Yao | Differences in estimating terrestrial water flux from three satellite-based Priestley-Taylor algorithms[END_REF], or iii) retrieving the PT coefficient from vegetation indices [START_REF] Fisher | Global estimates of the land-atmosphere water flux based on monthly AVHRR and ISLSCP-II data, validated at 16 FLUXNET sites[END_REF][START_REF] Jin | Continental-scale net radiation and evapotranspiration estimated using MODIS satellite observations[END_REF][START_REF] Yao | Differences in estimating terrestrial water flux from three satellite-based Priestley-Taylor algorithms[END_REF] or from an interpretation of the LST-vegetation index feature space [START_REF] Jiang | Estimation of surface evaporation map over southern Great Plains using remote sensing data[END_REF][START_REF] Pérez | Satellite-based References method for estimating the spatial distribution of crop evapotranspiration: Sensitivity to the priestley-taylor coefficient[END_REF][START_REF] Wang | Estimation of evaporative fraction from a combination of day and night land surface temperatures and NDVI: A new method to determine the Priestley-Taylor parameter[END_REF]. While LST, vegetation indices and SM are alternatively used by satellite-based PT approaches, few studies have combined all three data types. In fact, most studies have compared LST-based versus SM-based ET models separately [START_REF] Gokmen | Remote Sensing of Environment Integration of soil moisture in SEBS for improving evapotranspiration estimation under water stress conditions[END_REF][START_REF] Kustas | Estimating subpixel surface temperatures and energy fluxes from the vegetation index-radiometric temperature relationship[END_REF][START_REF] Kustas | Combining optical and microwave remote sensing for mapping energy fluxes in a semiarid watershed[END_REF][START_REF] Li | Comparing the utility of microwave and thermal remote-sensing constraints in twosource energy balance modeling over an agricultural landscape[END_REF]. Given that SM controls the soil temperature (via the soil evaporation) and that LST integrates both soil and vegetation temperatures, the main issue to integrate simultaneously SM and LST into an unique model is to ensure a robust convergence of soil/vegetation temperatures [START_REF] Kustas | Estimating subpixel surface temperatures and energy fluxes from the vegetation index-radiometric temperature relationship[END_REF][START_REF] Li | Comparing the utility of microwave and thermal remote-sensing constraints in twosource energy balance modeling over an agricultural landscape[END_REF] and associated evaporation/transpiration fluxes. The recent studies of [START_REF] Li | Integrating soil moisture retrieved from L-band microwave radiation into an energy balance model to improve evapotranspiration estimation on the irrigated oases of arid regions in northwest China[END_REF] and Song et al. (2016b) combined LST and SM to better constrain ET but both approaches relied on a priori reduction coefficients of potential ET. Reduction coefficients of potential ET are equivalent to the soil evaporative efficiency (defined as the ratio of actual to potential evaporation, e.g. [START_REF] Merlin | Modeling soil evaporation efficiency in a range of soil and atmospheric conditions: A downward approach based on multi-site data[END_REF] and to the vegetation stress functions (defined as the ratio of actual to potential transpiration, e.g. [START_REF] Hain | Retrieval of an Available Water-Based Soil Moisture Proxy from Thermal Infrared Remote Sensing. Part I: Methodology and Validation[END_REF] for the soil and vegetation component, respectively. The point is there is no universal parameterization of both soil evaporation efficiency and vegetation stress functions. Alternatively, [START_REF] Sun | Three complementary methods for sensitivity analysis of a water quality model[END_REF] proposed an innovative assimilation method to calibrate the parameters of a SVAT (Soil Vegetation Atmosphere Transfer) model from available remote sensing variables including LST and SM. Assimilation results improved ET estimates but the retrieved parameters were mostly conceptual due to the simplicity of the surface model used.

First of all, the modification of the PT-based TSEB formalism [START_REF] Norman | Source approach for estimating soil and vegetation energy fluxes in observations of directional radiometric surface temperature[END_REF] to integrate LST and SM data simultaneously (the modified version is named TSEB-SM), as well as the calibration procedure of TSEB-SM to retrieve the main parameters of soil evaporation (soil resistance) and plant transpiration (αPT) are described in chapter 3. In the present chapter, the approach is tested over three irrigated wheat crops in the Tensift basin, by using in-situ data, central Morocco. In each case, the calibration procedure is tested and the Chapter V. Improving TSEB model by integrating SM data (TSEB-SM): a feasibility study using in-situ data (LST, fc and SM) TSEB-SM latent and sensible heat fluxes are evaluated and compared against the original TSEB simulations.

V.2. TSEB-SM Model Description and Implementation

The TSEB-SM is the modified version of TSEB model, by using in addition to LST and f c data, the near-surface soil moisture (SM) as an extra constraint on soil evaporation. A calibration procedure is proposed to retrieve three key parameters: αPT and the pair parameters Iteration 0 corresponds to default values. The convergence of all three parameters is very fast, requiring only 2 or 3 iterations for achieving a relative error better than 1%. This result confirms the appropriateness of separating the calibration range in f c intervals where one parameter has significantly more weight on simulation results (i.e. simulated LST and associated fluxes) than the others. The calibrated pair (a rss , b rss ) is (5.67, 1.40), (6.51, 3.82) and (9.47, 6.87) for the flood-, controlled drip-and reference drip-irrigated field, respectively.

The mean retrieved values (7.2, 4.0) are relatively close to those estimated in Sellers et al. (1992) (8.2, 4.3). The variability of a rss and b rss can be explained by numerous factors such as soil texture [START_REF] Merlin | Modeling soil evaporation efficiency in a range of soil and atmospheric conditions: A downward approach based on multi-site data[END_REF] and meteorological conditions [START_REF] Merlin | An analytical model of evaporation efficiency for unsaturated soil surfaces with an arbitrary thickness[END_REF].

Nevertheless, retrieved parameters are significantly different for both drip sites whereas they i) are located about 200 m apart only and ii) have similar soil texture and meteorological conditions. In fact, retrieved a rss is an increasing function of retrieved b rss due to compensation effects between a rss and b rss for a given SM and LST observation pair and regardless of soil properties and meteorological conditions. Such compensation reveals the empirical nature of the r ss formulation in [START_REF] Sellers | Relations between surface conductance and spectral vegetation indexes at intermediate (100m2 to 15km2) length scales[END_REF].

The mean value of αPT at the semi-hourly time scale (see Figure V.2) is 0.81, 0.88 and 1.24

for the flood-, controlled drip-and reference drip-irrigated wheat fields, respectively. Note that the mean value is very close to the theoretical αPT value for the reference drip-irrigated field case. It is suggested that f g generally equals 1 at the maximum of αPT (peak of ET), so that the maximum αPT value is directly comparable to its default value (1.26) corresponding to fully unstressed conditions [START_REF] Priestley | On the Assessment of Surface Heat Flux and Evaporation Using Large-Scale Parameters[END_REF]. Nonetheless, the mean αPT is significantly smaller than the default value for the flood-and controlled drip-irrigated cases.

Lower values can be associated with stress conditions that may have occurred during the crop development. practices of each field (sowing date, irrigation events, rainfall and fertilization) as well as uncertainties in retrieved αPT. Two effects are likely to explain the highly variable and excessively high retrieved αPT values over the drip irrigated site for the first few daily retrievals. First, it is reminded that αPT is retrieved for f c > 0.5. When f c is slightly larger than 0.5 (that is on the first few retrieval days of the season), large uncertainties in retrieved αPT are expected because the soil surface still plays a significant role in the observed LST. Little response is shown for the first two months over the flood irrigation field, because the flux measurements over this site started when wheat was already well developed (f c significantly larger than 0.5). Second, the R3 site is surrounded by homogeneous irrigated wheat fields while the drip irrigated fields are surrounded by dryland, which potentially reinforces advection effects, leading to enhanced retrieved αPT. Note that the retrieved αPT values above 2 and near 0 are due to the uncertainties in LST-derived daily estimates, especially during the periods when wheat is partially covering the soil.

As explained above, a smoothing function is applied to reduce uncertainties in daily αPT. The smoothing length (it is one parameter of the smoothing function) is set to 10% of the total time series, that is about 10-20 days. Such a smoothing procedure is justified by the fact that both biomass and root-zone soil moisture commonly change across the agricultural season with a characteristic time of 1 to 2 weeks [START_REF] Albergel | Place des petits barrages dans la mobilisation des eaux de surface et dans la lutte contre l'érosion au Maghreb et au Moyen-Orient, in: Efficacité de La Gestion de l'[END_REF]. Furthermore, Figure V.2 clearly

shows that the smoothing function removes all outliers while capturing significant patterns at the quasi daily scale. The smoothed αPT ranges from 0.03 to 1.22, 0.17 to 1.26 and 0.61 to 1.38 for the flood-, controlled drip-and reference drip-irrigated wheat, respectively.

V.3.3. Calibration 3th step

The normalization in Equation (3.27) of smoothed αPT between its assumed minimum value (0) and smoothed maximum value makes the calibrated daily αPT range from 0 to 1.22, 0 to with f c for comparison purposes. The maximum calibrated daily αPT is close to the theoretical value of 1.26 in each case. However, its temporal variability is found to be significant even during the growing stage of wheat. Calibrated daily αPT is more stable for the reference drip field than for both flood and controlled drip fields, with a relative change during the growing period of 8.08% compared to 26.94% and 22.66% for the other two fields, respectively. This result is consistent with the fact that the reference drip field had been irrigated according to the water needs estimated by the FAO-56 method while the other two fields (flood and controlled drip) had been under water deficit conditions for one or several periods during the growing stage. Note that the controlled-drip field has a special feature in terms of αPT daily dynamics. The maximum value is reached by the beginning of March, which is much earlier than the αPT peak observed at the reference drip (around late April) and flood (beginning of May) fields, although wheat was sowed on the same date as reference drip field. It is suggested that the controlled drip-irrigated wheat did not recover well from the first (relatively long) stress period from 22/02/2017 to 06/03/2017. The irrigation water supplied after mid-March was probably not sufficient for the wheat of controlled drip field to catch up with the reference drip-irrigated wheat, even if the amount of water used for irrigation after this period was approximately the same (about 166 mm). interpolates αPT peaks generally increases up to the maximum of VWC and then decreases as the green vegetation fraction starts to decline at the onset of senescence. Note that the maximum of VWC may not necessarily coincide perfectly with the maximum of αPT since αPT is also affected by soil water availability. In the case of controlled drip field, the maximum of αPT appears significantly sooner than the maximum of green biomass. This is explained by a lack of moisture in the soil in this crop field as depicted by the strong drop in the 30-cm soil moisture from early February. This can also be explained by the fact that fertilization (nitrogen) was provided to the plant via irrigation water. Hence, a deficit in irrigation had the dual effects of decreasing soil water availability and depleting the soil in nutrient compared to the reference drip field.

The qualitative analysis of αPT variability in relation to soil water availability and the amount of green biomass thus indicates that αPT cannot be considered as a constant. Large variations in this parameter are likely to occur during the agricultural season, especially under stress conditions. Water deficit may happen with flood irrigation when the frequency of water supplies (every 3 weeks on average over R3) is relatively low compared to the water demand under such semi-arid conditions. Indeed the water stress observed in the flood-irrigated wheat may be attributed to the increase in water depletion at the root zone through a removal of water by transpiration and percolation losses [START_REF] Er-Raki | Combining FAO-56 model and ground-based remote sensing to estimate water consumptions of wheat crops in a semi-arid region[END_REF]. Water stress may also happen with drip when the technique is not appropriately implemented or by applying regulated deficit irrigation.

metrics used to evaluate results comprise the determination coefficient (R 2 ), the root mean square error (RMSE) and the mean bias error (MBE) between simulated and observed fluxes. drip-irrigated field respectively. The determination coefficient between simulated and observed H is significantly improved from 0.61 to 0.67, from 0.37 to 0.75 and from 0.29 to 0.82, respectively when including calibrated parameters to TSEB-SM.

One can observe that the slope of the linear regression between TSEB and in-situ H is very low in all cases. The modeled H does not seem to be sensitive enough to changes in surface and atmospheric conditions during all three periods (f c ≤ 0.5, f c > 0.5 and senescence). The intercomparison between TSEB and TSEB-SM is finally undertaken by simulating the available energy, instead of forcing R n and G to their measured values as in Table V.1. Table V.2 reports the error statistics for the four energy fluxes separately. The larger discrepancies for LE estimated from TSEB-SM model in this case is likely due to greater scatter between modeled and measured R n , which is related to the difference between simulated and observed LST. Note also that the determination coefficient between simulated and measured G is about 0.4-0.5 for both TSEB and TSEB-SM and all three sites. This is linked in part to the relatively small magnitude and range in the observed values combined with the simplicity of the approach used to estimate G. Overall, the simulations of LE and H when modeling R n and G are fully consistent with those obtained when forcing R n and G to their measured values.

TSEB-SM still provides superior results to TSEB in terms of RMSE, R 2 and MBE between simulated and observed fluxes. Especially the sensible heat flux is significantly improved in all cases. V.5.

Summary and Conclusions

A new evapotranspiration model named TSEB-SM is derived from the TSEB formalism by explicitly representing soil evaporation using a soil resistance. An innovative calibration Chapter V. Improving TSEB model by integrating SM data (TSEB-SM): a feasibility study using in-situ data (LST, fc and SM)

VI.1. Introduction

The TSEB-SM model was tested in the previous chapter using in-situ measurements. The model provided an important improvement in terms of latent heat flux/sensible heat flux estimates compared to the classic TSEB all along the agricultural season, especially during the crop emergence and the senescence periods. Such improvements are attributed to stronger constraints exerted on the representation of soil evaporation (via SM data and the calibrated soil parameters) and plant transpiration (via the calibrated daily PT coefficient). It is reminded that TSEB-SM is based on the original TSEB formalism, meaning that the energy balance for vegetation is the same as in TSEB using the PT formula, while the soil evaporation is explicitly represented (contrary to TSEB) as a function of SM via a soil resistance term. The use of the soil resistance formulation is justified by the fact that its main parameters (a rss , b rss ) can be calibrated from soil texture information [START_REF] Merlin | Modeling soil evaporation efficiency in a range of soil and atmospheric conditions: A downward approach based on multi-site data[END_REF] or a combination of SM and LST data under bare [START_REF] Merlin | A phenomenological model of soil evaporative efficiency using surface soil moisture and temperature data[END_REF] or partially covered (Ait Hssaine et al., 2018b) soil conditions.

In this part, the TSEB-SM will be applied at 1km resolution using remote sensing data including thermal-derived LST and NDVI and DisPATCh SM in order to provide surface energy fluxes over a rainfed wheat field in the Tensift basin, central Morocco during four agricultural seasons.

VI.2. TSEB-SM Model improvements

Two improvements are made on the former of TSEB-SM, First, the calibration of αPT is bounded by a minimum (0) and maximum (2) acceptable physical value, in order to avoid unacceptable values of αPT that can be produced due to the uncertainties in LST-derived daily estimates. Such an upper bounding is especially needed when vegetation partially covers the soil. Second, the output fluxes are normalized using the LST-derived available energy.

Therefore, the new version of TSEB-SM uses both LST and SM data (in addition to vegetation cover fraction data) as forcing on a daily basis. In practice, the latent and sensible heat fluxes derived from the TSEB-SM model are re-computed using the TSEB-SM derived evaporative fraction (EF, defined as the ratio of latent heat to available energy) and the LSTderived available energy. The rationale is that numerous modelling studies have shown the regularity and constancy of EF during daylight hours in cloud-free days [START_REF] Gentine | The Diurnal Behavior of Evaporative Fraction in the Soil-Vegetation-Atmospheric Boundary Layer Continuum[END_REF] Chapter VI. Remote sensing application of TSEB-SM (combining DisPATCh SM and MODIS LST data for mapping ET at 1 km resolution)

92 [START_REF] Lhomme | Examination of evaporative fraction diurnal behaviour using a soil-vegetation model coupled with a mixed-layer model[END_REF][START_REF] Shuttleworth | FIFE: the variation in energy partition at surface flux sites[END_REF] and the EF has a strong link with SM availability [START_REF] Bastiaanssen | A new crop yield forecasting model based on satellite measurements applied across the Indus Basin, Pakistan[END_REF], which is an important factor for estimating latent heat flux. For that purpose, the LST data collected at the Terra and Aqua-MODIS overpass times are used separately to estimate the instantaneous R n and G. A ratio between the daily (obtained as an average value between Aqua and Terra overpass times) latent heat flux LE daily and the daily available energy (R n,daily -G daily ) is used to calculate an average daily EF:

EF = LE daily (R n,daily -G daily ) (VI.1)
The daily EF and the instantaneous available energy (calculated using Terra and Aqua MODIS LST, separately) are finally used to re-calculate the instantaneous TSEB-SM output of LE and H by the following formulas:

LE = EF * (R n -G) (VI.2) H = (1 -EF) * (R n -G) (VI.3)

VI.3. Accuracy of Remote Sensing data

The LST collected by MODIS at Terra and Aqua overpass times and the SM product derived at 1 km resolution from the DisPATCh algorithm applied to SMOS data, are used as input to TSEB and TSEB-SM models. Validation of TSEB and TSEB-SM input data prior to the evaluation of models output is an important issue, notably due to the scale mismatch existing between the spatial resolution (1 km) of MODIS/DisPATCh data and the footprint of the EC flux measurements that does not exceed 100 m [START_REF] Schmid | Source areas for scalars and scalar fluxes[END_REF].

Several studies have demonstrated the effectiveness of DisPATCh 1km resolution SM. respectively. The observed scatter may stem from the fact that the localized (1 or 2 m wide) in-situ LST is not fully representative of the 1 km resolution MODIS pixel (Ait Hssaine et al., 2018b;[START_REF] Yu | New scheme for validating remote-sensing land surface temperature productswith stationobservations[END_REF]. For all years (S1-3, B1), it can be seen that the MBE is negative.

Note that the MBE is the greatest when the temperatures are largest. Such a systematic error is probably due to the non-representativeness of the in-situ LST observations when compared to the corresponding scale of MODIS observations. 3). In fact the localized in-situ measurements may not be perfectly representative of the 1 km resolution satellite data. Note that the efficiency of DisPATCh is supposedly higher for low SM values [START_REF] Malbéteau | DisPATCh as a tool to evaluate coarse-scale remotely sensed soil moisture using localized in situ measurements: Application to SMOS and AMSR-E data in Southeastern Australia[END_REF], which is clearly illustrated during B1 season, while it is lower for high SM values (after rain events). This can be explained by the constraints of atmospheric and vegetation conditions on disaggregation results, as well as the saturation of SEE in the higher SM range. Another major issue that can lead to differences between DisPATCh and in-situ SM is that the ground SM sensors are buried at a depth of 5 cm while the penetration of the L-band wave varies between 2 and 5 cm depending on soil conditions (notably SM content, texture). For S2, the SM provided by DisPATCh underestimated field measurements, especially in the higher SM range. This particular behaviour could be explained by the particularly low precipitation amount during this year.

Especially, it is possible that the surrounding plots were not sown by neighbour farmers, resulting in a soil that dried quickly compared to our field, which retained the SM for a longer period of time. satellite data. The apparent scatter in retrieved r ss could be interpreted by the impact of the daily cycle of meteorological (evaporative demand) conditions or soil properties differences [START_REF] Merlin | An analytical model of evaporation efficiency for unsaturated soil surfaces with an arbitrary thickness[END_REF]2016;2018). The retrieved soil parameters also vary from year to year: the standard deviation is 0.39 and 1.69 for a rss and b rss , respectively. This can be explained by the compensation effects between a rss and b rss parameters which justifies the empirical nature of the r ss formulation in [START_REF] Sellers | Relations between surface conductance and spectral vegetation indexes at intermediate (100m2 to 15km2) length scales[END_REF]. Another major issue that can lead to these differences is the depth of SM measurements [START_REF] Merlin | An analytical model of evaporation efficiency for unsaturated soil surfaces with an arbitrary thickness[END_REF]. In [START_REF] Sellers | Relations between surface conductance and spectral vegetation indexes at intermediate (100m2 to 15km2) length scales[END_REF], the near-surface soil moisture is defined in the 0-5-cm soil layer, whereas in our field, SM measurements are made at 5-cm depth. Also, the sensing depth of SMOS observations is generally shallower than the in-situ surface measurements [START_REF] Escorihuela | Effective soil moisture References sampling depth of L-band radiometry: A case study[END_REF].

Moreover, the variability of a rss and b rss in Fig. 5b For this reason, no information linked to the variability of αPT can be derived during this season. The retrieved values are smoothed and superimposed with the rainfall events. It is clearly shown that the smoothed αPT for S1 and S2 have the same shape with a small variability, when comparing with the smoothed αPT using in-situ data, with a relative error (estimated as the RMSE divided by the mean αPT) of about 11 and 19 %, for S1 and S2

respectively. For S1 the maximum of smoothed αPT is reached at the same time as when using the in-situ data, with a value of about 1.38, while the maximum for S2 is reached 10 days before the maximum of the αPT derived from in-situ data with little response of αPT to rainfall Chapter VI. Remote sensing application of TSEB-SM (combining DisPATCh SM and MODIS LST data for mapping ET at 1 km resolution) 100 events. These differences may be linked to uncertainties in disaggregated SMOS SM, as well as to the weaker availability of satellite data. Because of the small number of data points (retrieved αPT) during S3, the smoothed αPT remains at a mostly constant value (~0.7) throughout the study period, with a significant relative difference of about 34 % when comparing with the αPT retrieved using in-situ data. the onset of senescence. In contrast, the maximum value of NDVI appears later than the maximum value of αPT for S2. This can be explained by the fact that rainfall at the beginning of the development phase satisfies the plant requirements, while the rainfall amount during the development stage is relatively low compared to the crop water needs [START_REF] Kharrou | Water use efficiency and yield of winter wheat under different irrigation regimes in a semi-arid region[END_REF]. Large variations in αPT occur during the agricultural season, as a result of the amount, frequency, and distribution of rainfall along the season. In general, the analysis of the αPT variability using satellite data illustrates the robustness of the proposed approach, which using the statistical results including R for bare soil surfaces. In fact, 1.26 is an optimum value for the potential transpiration rate (Agam et al., 2010a;[START_REF] Chirouze | Intercomparison of four remote-sensing-based energy balance methods to retrieve surface evapotranspiration and water stress of irrigated fields in semi-arid climate[END_REF]. In the case of TSEB-SM, biases are reduced thanks to the calibration of the r ss resistance. Additionally, according to TSEB-SM assumptions, αPT for f c ≤0.5 is set to the average value of the αPT retrieved for f c >0. The ability of TSEB-SM to estimate the sensible heat fluxes is also investigated.

VI.6.2. Using satellite data

In order to gain greater insight into how TSEB and TSEB-SM models respond to different surface conditions across a landscape, an analysis of the spatial distributions and the magnitude of the turbulent fluxes using remotely sensing data produced from the two models Chapter.VII.

Conclusion and perspectives

Improving the management of water resources in semi-arid areas requires accurate knowledge of the hydrological processes involved. ET is a critical component of the hydrologic cycle and a link between the energy, water, and carbon cycles. It strongly impacts the drought monitoring, the water resource management and climate [START_REF] Littell | A review of the relationships between drought and forest fire in the United States[END_REF][START_REF] Molden | Improving agricultural water productivity: Between optimism and caution[END_REF]. Furthermore, a precise estimate of ET determines the crop water requirements, which subsequently allow for optimizing water management practices and irrigation regimes [START_REF] Allen | Crop evapotranspiration-Guidelines for computing crop water requirements-FAO Irrigation and drainage paper 56[END_REF]. Three key remote sensing variables can be used to determine the spatial distribution of ET:

-microwave-derived surface (0-5 cm) soil moisture (SM), which is the main controlling factor of soil evaporation considering a given evaporative demand (e.g. [START_REF] Chanzy | Significance of soil surface moisture with respect to daily bare soil evaporation[END_REF],

-visible/near-infratred-derived vegetation cover fraction (f c ), which provides an essential structural constraint on the evaporation/transpiration partitioning (e.g. [START_REF] Allen | Evapotranspiration information reporting: I. Factors governing measurement accuracy[END_REF], and -thermal-derived land surface temperature (LST), which is a signature of both available energy and ET rate (e.g. [START_REF] Norman | Source approach for estimating soil and vegetation energy fluxes in observations of directional radiometric surface temperature[END_REF].

The aim of this thesis is to consistently integrate those independent and complementary information on total ET within an energy balance model. As a state-of-the-art and commonly used model, we chose the TSEB modelling as a basis for developments. In fact, there are two main limitations of the TSEB model. The first one is when considering the most common value of the Priestley-Taylor coefficient as a constant (1.26) meaning that vegetation has access to enough water in the root zone to transpire at a potential rate. This implies that the vegetation stress conditions are not properly taken into account. Indeed, several studies found that αPT is variable according to several parameters (LAI, vapour pressure deficit, and SM) [START_REF] Baldocchi | What limits evaporation from Mediterranean oak woodlands-The supply of moisture in the soil, physiological control by plants or the demand by the atmosphere?[END_REF][START_REF] Pereira | The Priestley-Taylor parameter and the decoupling factor for estimating reference evapotranspiration[END_REF], while αPT can reach values up to 2 under wettest SM conditions [START_REF] Baldocchi | Measuring and modelling carbon dioxide and water vapour exchange over a temperate broad-leaved forest during the 1995 summer drought[END_REF][START_REF] Baldocchi | An analytical solution for coupled leaf photosynthesis and stomatal conductance models[END_REF]. Agam et al. (2010) reported that over partially covered surfaces, αPT is more likely less than 1.26, as the soil evaporation decreases because of the drying of the top soil [START_REF] Stannard | Comparison of Penman-Monteith, Shuttleworth-Wallace, and Modified Priestley-Taylor Evapotranspiration Models for wildland vegetation in semiarid rangeland[END_REF]. She also stressed that αPT is a critical parameter for natural vegetation and sites with strong vapour pressure deficit values where the root zone moisture does not limit transpiration. The second limitation of the TSEB approach lies on the estimation of soil evaporation as a residual to the soil component energy The major limitation of the TSEB-SM model lies on the different resistances used to estimate the turbulent fluxes. Indeed, the soil resistance formulation r ss is impacted by soil texture and structure. Errors on a rss and b rss estimations reveal the empirical nature of the r ss . The soil surface resistance (r s ) is also difficult to characterize, because it depends on many factors including wind speed, roughness, and cover type [START_REF] Norman | Source approach for estimating soil and vegetation energy fluxes in observations of directional radiometric surface temperature[END_REF][START_REF] Sauer | Measurement of heat and vapor transfer coefficients at the soil surface beneath a maize canopy using source plates[END_REF]. In our work the simplified equation given by [START_REF] Norman | Source approach for estimating soil and vegetation energy fluxes in observations of directional radiometric surface temperature[END_REF] is used with its default coefficients (a and b) that are suitable for semi-arid regions. However, a sensitivity study of these two parameters shows their strong impact on the surface fluxes, which implies that a calibration procedure is necessary for each type of cover. There are two main limitations regarding the DisPATCh SM product used as input to TSEB-SM. The first one is linked to the temporal resolution (discussed in detail in [START_REF] Malbéteau | Toward a Surface Soil Moisture Product at High Spatiotemporal Resolution: Temporally Interpolated, Spatially Disaggregated SMOS Data[END_REF][START_REF] Malbéteau | DisPATCh as a tool to evaluate coarse-scale remotely sensed soil moisture using localized in situ measurements: Application to SMOS and AMSR-E data in Southeastern Australia[END_REF] and the second one is linked to the spatial resolution. The temporal resolution of DisPATCh data is constrained by the number of SMOS overpasses (a global coverage every 3 days) and by the gaps in MODIS images due to cloud cover. Moreover, the spatial resolution of 1 km is still coarse for applications and validation studies at the field scale. This is the main reason why the model is applied over a rainfed parcel located within a larger area occupied mostly by rainfed wheat ('Bour'). This field was chosen to be representative at a scale of 1 km, thus enabling the comparison between 1 km resolution satellite-derived and localized insitu measurements. Over irrigated areas however, wheat fields do not exceed 4 ha, and they are sowed and irrigated on different dates, which generate heterogeneity in SM as well as LST and NDVI fields within a 1 km resolution pixel, and result in systematic errors in the model predictions.

Overall, this thesis is based on a development of original methods exploiting optimally the synergy between different sensors. In particular, combining the microwave / optical data for the high spatial resolution estimation of root zone SM and appropriate partitioning of ET into transpiration and soil evaporation. These targeted researches respond to the needs of managing agencies by providing spatialized indicators of drought and crop water requirements. Based on the results obtained and the conclusions reached, several promising perspectives can be considered for improving this work.

Further efforts should be made to investigate the variability of αPT at the daily and finer time scales and to relate its variations to variables other than biomass and soil water availability.

Reciprocally, the retrieved αPT could serve as a basis for deriving a proxy for root zone soil moisture and crop water needs. The aim is to evaluate the modelling approaches for partitioning the ET at regional scale, while using very different physical constraints. Besides, modelling the transpiration schemes in a more physically and realistic way, hence obviating the semi-empirical formulation of PT, can provide valuable results. Several studies incorporate the canopy conductance model into the thermal-based TSEB model under various atmospheric and SM conditions [START_REF] Anderson | A thermal-based remote sensing technique for routine mapping of land-surface carbon, water and energy fluxes from field to regional scales[END_REF][START_REF] Anderson | An analytical model for estimating canopy transpiration and carbon assimilation fluxes based on canopy light-use efficiency[END_REF][START_REF] Zhan | A coupled model of land surface CO2 and energy fluxes using remote sensing data[END_REF].

Recently [START_REF] Gan | Estimating time series of land surface energy fluxes using optimized two source energy balance schemes : Model formulation , calibration , and validation[END_REF] In addition to SM and LST, other relevant remote sensing indicators could be used as input to the TSEB-SM approach. In particular, the Photochemical Reflectance Index (PRI) derived from narrow-band spectroradiometers is a spectral index based on the short term reversible xanthophyll pigment changes that accompany plant stress and associated photosynthetic activities. Strong relationships between PRI and LUE were shown at leaf and canopy scales and over a wide range of species [START_REF] Garbulsky | The photochemical reflectance index (PRI) and the remote sensing of leaf, canopy and ecosystem radiation use efficiencies: A review and meta-analysis[END_REF][START_REF] Peñuelas | Photochemical reflectance index (PRI) and remote sensing of plant CO2 uptake[END_REF]. Suárez et al. Lastly, it is important to note that TSEB-SM has not been specifically evaluated in terms of evaporation/transpiration partitioning, meaning using ground measurements separating both components simultaneously. Especially the derived evaporation/transpiration products should be validated using lysimeter and sap flow measurements instead of validating the total ET by eddy covariance system [START_REF] Rafi | Partitioning evapotranspiration of a drip-irrigated wheat crop: Inter-comparing eddy covariance-, sap flow-, lysimeter-and FAO-based methods[END_REF]). In addition, the evaluation of ET at large scale is missing. Spatialized measurements that could be collected by scintillometers installed at various points in the region would be a solution for that purpose.

III. 1 .

 1 Introduction ............................................................................................................... III.2. Sites and in-situ data description .............................................................................. III.2.1. Watershed of Tensift el Haouz ........................................................................... III.2.2. Wankama basin (Niger) ..................................................................................... III.2.3. Spatial data ......................................................................................................... III.3. Conclusion ................................................................................................................. Chapter.IV. Validation of TSEB model over sparse and heterogeneous vegetation in Sahel region (Niger) ............................................................................................................... IV.1. Introduction ............................................................................................................... IV.2. Results and discussion ............................................................................................... IV.2.1. Experimental data analysis ................................................................................. IV.2.2. Results of multi-Scale surfaces fluxes ............................................................... IV.3. Summury and Conclusions ........................................................................................ v

1 .

 1 Introduction Le Maroc est l'un des 45 pays du monde les plus affectés par la pénurie d'eau ((Figure I.2, chapitre I). Cette situation est le résultat de la double pressions climatique (augmentation de la température, diminution et irrégularité spatio-temporelle de la précipitation …) et anthropique (extension des zones irriguées, intensification de la consommation d'eau par les secteurs touristique et domestique ….). Selon le rapport du World Ressources Institute, le niveau de stress hydrique au Maroc sera extrêmement élevé d'ici 2040. En effet, le Maroc atteindra une situation de stress hydrique extrême dans moins de 25 ans

3 .

 3 Modèles utilisés a. Le modèle TSEB : Le modèle TSEB calcule deux bilans d'énergie distincts pour le sol et la végétation, puis estime l'évaporation comme terme résiduel du bilan d'énergie. Deux variables dérivées d'instruments de télédétection sont des éléments clés de modèle TSEB: LST, qui est utilisée dans l'estimation des flux de chaleur sensible, et f c , qui contrôle le partitionnement de l'énergie entre la végétation et le sol (Figure II.1, chapitre II). αPT est l'un des paramètres les plus sensibles de TSEB, car il pilote le flux de chaleur latent de la végétation. La plupart des études menées avec TSEB ont utilisé sa valeur générique autour de 1.3.

4 .

 4 Sites et dispositifs expérimentaux associés Nos approches ont été testées sur deux bassins versants (Tensift (Maroc), Wankama (Niger)) situées dans des régions caractérisées par un climat semi-aride, et une variabilité spatiale et temporelle marquée de précipitations. Différentes données ont été utilisées en entrée pour alimenter les deux modèles (Chapitre II). En particulier, les deux entrées clés, LST et f c , sont utilisées pour forcer le modèle TSEB. Alors que SM est utilisée comme contrainte supplémentaire de l'évaporation du sol dans le modèle TSEB-SM. Ces trois produits sont soit mesurés à l'échelle de la parcelle à l'aide des mesures in-situ, soit extraits d'images satellitaires thermique /optique et micro-ondes (Chapitre III). En plus de ces produits, les données météorologiques comprenant la température de l'air, le rayonnement solaire, l'humidité relative et la vitesse du vent sont également utilisées pour forcer TSEB et TSEB-SM. Le modèle TSEB classique a été testé entre 23 Juillet et 23 Octobre 2006 sur trois parcelles pluviales (mil, savane et jachère) dans le bassin de Wankama (Niger) (Chapitre IV). Des flux de chaleur sensible (H) et latente (LE) provenant des systèmes d'Eddy covariance (EC) et de scintillomètre ont été utilisés pour valider l'estimation du TSEB à l'échelle du patch et de la grille. Alors que le modèle TSEB-SM a été testé durant deux saisons agricoles 2002-2003 et 2016-2017 sur deux parcelles de blé irrigué en goutte à goutte (Chichaoua et R3) (Chapitre V) et durant quatre saisons 2014-2015, 2015-2016, 2016-2017 et 2017-2018 sur une parcelle de blé pluvial (Bour) (Chapitre VI) dans la plaine de Haouz du bassin versant du Tensift (centre du Maroc).

5 .

 5 Résultats a. Validation du TSEB classique : Dans un premier temps, le chapitre « Les résultats de la validation du modèle TSEB sur une végétation éparse et hétérogène dans la région du Sahel (Niger) » vise à tester le modèle TSEB piloté par des observations MODIS (Moderate resolution Imaging Spectroradiometer) en conjonction avec un schéma d'agrégation spatiale. Le but est d'estimer les flux de chaleur sensible à la surface (H) et latente (LE) sur un trajet de 3 km couvrant trois cultures dominantes dans le bassin de Wankama (Mil, Jachère et la savane). Les données qui ont servi à la validation de cette approche ont été collectées dans le cadre du projet AMMA. Chaque site a été équipé par des stations météorologiques et des systèmes d'Eddy Covariance ainsi qu'un scintillomètre à grande ouverture installé sur un trajet de 3 km afin de dériver les valeurs de H et LE moyens sur les trois champs. Premièrement, le modèle TSEB a été évalué à l'échelle du patch (Mil, Jachère et la Savane), et ensuite à l'échelle du grid qui est composé des trois champs, en utilisant les données in-situ (chaque 30 minutes), Météosat seconde génération (MSG) (3 km de résolution et à l'heure de passage MSG-SEVIRI) et MODIS (1 km de résolution et à l'heure de passage Terra et Aqua). En tenant compte de la complexité de chaque champ liée à la dispersion du couvert végétal, les résultats obtenus à l'échelle de la station pour H et LE sont pertinents, en particulier lors de l'utilisation de données in-situ. Quelques dispersions constatées sont principalement liées à la différence entre les footprints des systèmes de mesure, ainsi qu'à la valeur de αPT fixée à 1,26 durant toute la saison. TSEB a été ensuite évalué à l'échelle de grid. En général, les flux prédits par TSEB en utilisant les données in-situ concordent bien avec les observations par scintillomètre avec un RMSE de l'ordre de 37 et 75 W / m 2 pour H et LE, respectivement. L'accord entre H et LE simulés par TSEB forcé par les données MSG et les observations du scintillomètre est très médiocre, (R = 0,39 et 0,2 pour H et LE, respectivement). Cette dispersion peut être attribuée au fort biais sur les LST de MSG SEVIRI lié à l'hétérogénéité du site. Ce qui souligne la nécessité de représenter l'hétérogénéité des sous-pixels. Ceci a été testé en dernière étape en utilisant les produits MODIS à 1 km comme entrée du modèle TSEB en conjonction avec trois schémas d'agrégation de complexité croissante (une moyenne simple des entrées à l'échelle de résolution MODIS, une moyenne simple sans tenant en compte l'étendue du footprint du scintillomètre, et une moyenne pondérée des entrées en tenant en compte la fonction du footprint du scintillomètre). Les valeurs de H et LE simulées par la 3 ème méthode d'agrégation étaient plus précises que par les deux autres méthodes. Les valeurs des métriques statistiques obtenues sont R = 0,71, RMSE= 63 W/m 2 et MBE= -23 W / m 2 pour H et R = 0,82, RMSE = 88 W/m 2 et MBE = 45 W/m 2 pour LE. b. Intégration des données in-situ de SM au modèle TSEB : La deuxième partie de la thèse est dédiée à l'amélioration du modèle TSEB en intégrant les données SM (TSEB-SM) avec une étude de faisabilité utilisant des données in-situ (LST, f c et SM) ». Pour ce but, un nouveau modèle de calcul de ET appelé TSEB-SM est dérivé du formalisme TSEB en représentant explicitement l'évaporation du sol par une équation basée sur la résistance du sol. Pour contraindre la partition évaporation / transpiration de TSEB-SM, une approche de calibration innovante est également développée pour inverser les principaux paramètres d'évaporation du sol (résistance du sol, r ss ) et de transpiration des plantes (αPT).

( 1 .

 1 date de semis, épisodes d'irrigation, précipitations et fertilisation) ainsi que par les incertitudes concernant l'inversion de αPT. Une fonction de lissage est utilisée pour supprimer toutes les valeurs aberrantes tout en gardant des tendances significatives à l'échelle ix journalière. Les αPT lissés varient de 0.03 à 1.22, 0,17 à 1.26 et 0.61 à 1,38 respectivement, pour la parcelle R3, contrôlée et référence. Les αPT lissés sont ensuite normalisées entre une valeur minimale supposée (0) et une valeur maximale lissée. Les αPT calibrés varient alors de 0 à 1.22, de 0 à 1.26 et de 0 à 1.38 respectivement pour la parcelle R3, contrôlée et référence. En conclusion, l'intégration de la résistance du sol dans le modèle TSEB améliore l'estimation de l'évaporation du sol et, par conséquent, améliore la partition de l'ET. La série temporelle récupérée indique que αPT journalier suit la phénologie de la culture de blé d'hiver, avec une valeur maximale correspondant au développement maximal de la biomasse verte et une valeur minimale atteinte au moment de la récolte. Une analyse qualitative des variabilités de αPT en relation avec l'humidité du sol à 5 cm et à une profondeur de 30 cm indique que αPT ne peut pas être considéré comme une constante (Figure V.4, chapitre V). Des écarts importants par rapport à la valeur de 1,26 risquent de se produire pendant la saison agricole, en particulier en période sèche et de déficit en eau. En termes des flux turbulents H et LE, TSEB fournit des résultats satisfaisants pour le site R3, mais pas pour les deux autres sites de Chichaoua. La surestimation de LE par TSEB pendant la sénescence est associée à la valeur maximale fixée pour αPT (égale à 1,26). Cette limitation identifiée dans le formalisme TSEB semble être en partie résolue par l'approche TSEB-SM avec une pente de la régression linéaire est beaucoup plus proche de 1 dans tous les cas. Le RMSE (pour les trois sites) entre l'ET simulée par TSEB-SM et les mesures d'EC est de 67 W/m 2 (erreur relative de 24%), contre 108 W/m 2 (erreur relative de 38%) pour la version originale de TSEB utilisant le paramétrage par défaut (αPT = 1.26). c. Intégration des données SM-DisPATCh et des données MODIS (LST, 𝑓 𝑐 ) pour l'estimation de l'ET à une résolution de 1 km : Le 3 ème axe de la thèse « Combinaison de l'humidité du sol DisPATCh et des données MODIS (LST, f c ) pour cartographier l'ET à une résolution de 1 km » vise à évaluer la performance de TSEB-SM en conditions réelles en utilisant les LST et f c MODIS à 1 km de résolution et les données SM SMOS désagrégées à 1 km de résolution à l'aide de DisPATCh. L'approche est appliquée sur un champ de blé pluvial dans le bassin du Tensift, pendant une période de quatre ans (2014-2018). La parcelle a été semée pour la saison agricole 2014-2015 (S1), 2016-2017 (S2) et 2017-2018 (S3), alors qu'elle n'était pas labourée pendant la saison de blé 2015-2016 (B1) (sol nu) à cause du retard de la pluie. Malgré la différence d'échelle entre les données MODIS / DisPATCh et les mesures in-situ, les paramètres (a rss , b rss ) calculés tout au long de la période d'étude à l'aide des données satellitaires sont relativement proches x de ceux dérivés des mesures in situ. La deuxième étape de calibration consiste à inverser αPT pour f c > f c,thres à l'aide des données LST et SM. Les maximum αPT journaliers calibrés sont respectivement 1,38, 1,25 et 0,87 pour S1, S2 et S3. Ces valeurs correspondent aux quantités totales de précipitations, qui étaient respectivement de 608, 214 et 421 mm / saison de blé pour S1, S2 et S3. En effet, S1 et S2 ont la même tendance de αPT calibré à l'échelle journalière en comparaison avec le αPT récupéré à l'aide des données in-situ, tandis que αPT reste à une valeur constante (0.7) pendant toute la période d'étude S3 en raison de non disponibilité des produits MODIS pendant les jours nuageux. Comparé aux mesures d'EC, le modèle TSEB basé uniquement sur les données LST et f c surestime de manière significative les flux de chaleur latente pour les quatre saisons. Les MBE globaux sont d'environ 119, 181, 94 et 128 W / m 2 pour respectivement S1, B1, S2 et S3. La surestimation de LE peut s'expliquer par le fait que PT est fixé à 1,26 pendant toute la saison agricole, même en conditions de stresse. Cela provoque des erreurs plus importantes sur l'estimation du LE, en particulier pendant la phase de croissance. Les erreurs sont réduites lors de l'utilisation de TSEB-SM. En fait, la contrainte sur la transpiration de la plante, lors de l'inversion de la série temporelle de αPT, améliore les estimations de l'ET surtout en stade de croissance et en phase de sénescence, le biais important de LE est considérablement réduit. De plus, la contrainte sur l'évaporation du sol via les SM DisPATCh réduit clairement les valeurs de MBE pendant la période d'émergence (f c ≤ f c,thres ). Enfin, la contrainte appliquée aux flux de sortie TSEB-SM en utilisant l'énergie disponible dérivée de LST et la fraction évaporative dérivée de TSEB-SM (équation VI.1, chapitre VI) améliore les estimations de LE pour toute la période d'étude. Les MBE sont d'environ 39, 4, 7 et 62 W / m 2 pour respectivement S1, S2, S3 et B1. TSEB présente des erreurs systématiquement importantes sur l'estimation de H (Figure VI.10, chapitre VI), avec des valeurs de RMSE allant jusqu'à 98, 73, 56 et 66 W / m 2 pour respectivement S1, S2, S3 et B1. Le RMSE est amélioré avec l'utilisation de TSEB-SM, avec des valeurs d'environ 55, 41, 24 et 27 W / m 2 pour respectivement S1, S2, S3 et B1. En perspectives de ce travail, on propose d'estimer l'humidité en zone racinaire à une haute résolution spatiale car elle représente un enjeu important pour le suivi des ressources. Elle permet à la fois de détecter les périodes de stress hydrique et d'anticiper le besoin en eau des cultures. Ceci nécessite une répartition appropriée de l'ET en transpiration et évaporation du sol. Des efforts supplémentaires doivent être déployés pour étudier la variabilité de αPT à des échelles de temps journalières et plus fines et pour relier ses variations à des variables autres que la biomasse et la disponibilité de l'eau du sol. Input data of DisPATCh chain ............................................................................. 39 Table III. 1. Characteristics of the instruments equipping EC station. ................................... 50 Table IV. 1. Statistical metrics of the comparison between measured and estimated values of available energy and turbulent fluxes (H and LE) at patch and grid scale ............................... 65 Table V. 1. Error statistics (RMSE, R 2 and MBE) between modeled and measured sensible and latent heat fluxes for the flood, controlled drip-and reference drip-irrigated fields, and for TSEB and TSEB-SM model, separately (R n and G are forced to their measured value) ........ 87 Table V. 2. Error statistics (RMSE. R 2 and MBE) between modeled and measured net radiation, conductive flux, and sensible and latent heat fluxes for the flood, controlled dripand reference drip-irrigated fields, and for TSEB and TSEB-SM model, separately. ............. 88

FIGURESFigure I. 1 . 2 Figure I. 2 . 4 Figure I. 3 .Figure II. 1 .Figure II. 2 .Figure II. 3 .Figure II. 4 .Figure III. 3 .Figure III. 4 .Figure IV. 1 .Figure IV. 2 .Figure IV. 3 .Figure IV. 4 .Figure IV. 5 .Figure IV. 6 .Figure V. 1 .Figure V. 2 .Figure V. 3 .Figure V. 4 .Figure V. 5 .Figure V. 6 .Figure VI. 1 .Figure VI. 2 .Figure VI. 3 .Figure VI. 5 .Figure VI. 6 .

 1224312343412345612345612356 FIGURESFigure I. 1. Global world distribution of the water resource under different aspects "Source: www.consoglobe.com." ............................................................................................................. 2 Figure I. 2. Global water map. Source: World Resouces Institute ............................................ 4 Figure I. 3. Multi-sensor / multi-resolution remote sensing data for crop monitoring and agrohydrological applications (from Malbéteau, (2016)) ................................................................. 7 Figure II. 1. Schematic diagram of TSEB model .................................................................... 29 Figure II. 2. Schematic diagram of TSEB-SM model ............................................................ 32 Figure II. 3. Schematic diagram of the two-step calibration strategy of TSEB-SM model. ... 35 Figure II. 4. Footprint of the LAS, calculated using the footprint model of Horst and Weil, superposed with a LST/MODIS image on DOY 273. ............................................................. 37 Figure III. 1. Geographical situation of the Tensift watershed, its hydrographic network as well as the limit of the Haouz plain. ......................................................................................... 42 Figure III. 2. Location of the four study sites: (a) flood-irrigated wheat crop in the R3 zone (east of Marrakech), (b) rainfed wheat crop in Bour site (east of Marrakech) and (c) two (controlled and reference) drip-irrigated wheat crops near Chichaoua city (west of Marrakech) in the Tensift basin, central Morocco. (Flat area). ................................................................... 44 Figure III. 3. Example of the digital processing procedure for photos taken in rainfed wheat field ........................................................................................................................................... 46 Figure III. 4. Photograph of (a) TDR (Time Domain Reflectometry) and (b) Theta Probe instruments ............................................................................................................................... 48 Figure III. 5. (a) Map of the Wankama basin; (b) location of the three study sites (millet, fallow and (c) basin toposequence ........................................................................................... 49 Figure III. 6. (a) An overview of theWankama basin and the experimental setup, locations of LAS (T and R stand for transmitter and receiver, respectively) and three EC systems are shown (millet, fallow and degraded shrubs sites). Photos (EC system (b) and scintillometer (c)) were taken by J. Ezzahar as part of the ACN project. ....................................................... 51 Figure IV. 1. Time series of LAS latent and sensible heat fluxes (daily average between 9am and 5pm) ................................................................................................................................... 59 Figure IV. 2. Scatterplot of MODIS Ts (a), and α (b) versus in-situ data (only Millet and Fallow sites are considered) ..................................................................................................... 60 Figure IV. 3. Scatterplot of MODIS versus MSG SEVIRI LST ............................................. 61 Figure IV. 4. Scatterplot of simulated versus observed AE,H and LE for the (left) Millet, (middle) Fallow and (right) Degraded shrubs, respectively, using in-situ data. ...................... 64 Figure IV. 5. Scatterplot of simulated versus observed AE,H and LE for the (left) Millet, (middle) Fallow and (right) Degraded shrubs, respectively, using MODIS data. ................... 67

Figure VI. 8 .

 8 Figure VI. 8. Same as Fig VI.7 but for H fluxes. ..................................................................

Figure VI. 9 .

 9 Figure VI. 9. Same as Fig VI.7 but for satellite data. ........................................................... Figure VI. 10. Same as Fig VI.8 but for H fluxes and satellite data. ....................................

Figure I. 1 .

 1 Figure I. 1. Global world distribution of the water resource under different aspects "Source: www.consoglobe.com."

Figure I. 2 .

 2 Figure I. 2. Global water map. Source: World Resouces Institute

Figure I. 3 .

 3 Figure I. 3. Multi-sensor / multi-resolution remote sensing data for crop monitoring and agrohydrological applications (from Malbéteau, (2016))

  (2006) indicated that the model performance is sensitive to these two coefficients, and thus they proposed to average the output of LST-based TSEB and SM-based TSEB models, in order to provide more consistent results over a wide range of conditions. More recently, Yao et al. (2017) evaluated three satellite-based PT algorithms (ATI-PT, VPD-PT and SM-PT for apparent thermal inertia-, vapour pressure deficit-and SM-based formulations of the PT coefficients, respectively) to estimate terrestrial water flux in different biomes. Their finding showed that the SM-PT algorithm had relatively better results compared to those of ATI-PT and VPD-PT. However, all three models underestimated ET in irrigated crops, reflecting that these algorithms may not capture well the soil evaporation, notably through its (site-specific) parameterization with SM. In the same vein,[START_REF] Purdy | Remote Sensing of Environment SMAP soil moisture improves global evapotranspiration[END_REF] updated the PT Jet Propulsion Laboratory (PT-JPL) and incorporated the SM data derived from SMAP (Soil Moisture Active and Passive,[START_REF] Entekhabi | The Soil Moisture Active Passive {(SMAP)} Mission[END_REF] to constrain both evaporation and transpiration, separately. The model showed high improvements compared to the original PT-JPL, especially in dry conditions. However, the model relied on evaporation and transpiration reduction parameters, whose values were set a priori.

  solves two separate energy balances for the soil and vegetation and estimates evaporation as residual terms of the energy balance. This model adopts thePriestley-Taylor (PT) parameterization and an iteration procedure estimate the energy partitioning. Two main input variables of TSEB model are: i) the first is land surface temperature (LST), used for estimating the sensible heat flux and ii) the vegetation cover fraction (f c ), which controls partitioning of the surface energy between vegetation and underlying soil. These key variables (LST and f c ) are usually derived from remote sensing sensors.

  R n,soil = H soil + LE soil + G (II.6) R n,veg = H veg + LE veg (II.7) With R n,soil being the soil net radiation, H soil the soil sensible heat flux, LE soil the soil latent heat flux, R n,veg the vegetation net radiation, H veg the vegetation sensible heat flux and LE veg the vegetation latent heat flux.The surface sensible heat flux (H) is partitioned between the vegetated canopy and soil using the following relations:

Figure II. 1 .

 1 Figure II. 1. Schematic diagram of TSEB model

II. 3 . 1 .

 31 the soil moisture in the 0-5 cm soil layer, a rss and b rss are two empirical parameters and SM sat the soil moisture at saturation expressed as: SM sat = 0.1 * (-108 * f sand + 49.305) (II.19) withf sand is the percentage of sand in the soil. Algorithm for solving the energy balance and the equation system The flowchart of Figure II.2 summarizes the different steps followed to resolve the energy balance in TSEB-SM model. The algorithm is based on an iterative procedure that loops on the Monin-Obukhov length (LMO), which is a scale parameter that characterizes the degree Chapter II. Modeling approaches: Description and implimentation of instability or stability of the boundary layer. LMO is approximately the height at which aerodynamic shear, or mechanical energy, is equal to the buoyancy energy. In practice, LMO is used as correction factor to determine the aerodynamic resistance r ah . First, the algorithm starts by initializing the soil and vegetation temperatures, as well as sensible and latent heat fluxes. Then it calculates the available energy for the soil-vegetation-atmosphere interface by estimating the surface net radiation (R n ) and its partition between the vegetation and the soil, as well as the soil heat flux. The way soil and vegetation temperatures are estimated is in fact a specificity of the new model, which is based on the explicit resolution of the energy balance for soil and vegetation respectively. Component temperatures are obtained by minimizing cost functions F soil and F veg :

  Figure II. 2. Schematic diagram of TSEB-SM model

mes ) 2 (

 2 Figure II. 3. Schematic diagram of the two-step calibration strategy of TSEB-SM model.

  Figure II. 4. Footprint of the LAS, calculated using the footprint model of Horst and Weil, superposed with a LST/MODIS image on DOY 273.

Finally,

  DisPATCh converts the high-resolution optical-derived SEE fields into highresolution SM fields given a semi-empirical SEE model and a first-order Taylor series expansion around the SMOS observation. The downscaling relationship is expressed as: Chapter II. Modeling approaches: Description and implimentation SM HR = SM LR + ∂SM mod ∂SEE SEE LR (SEE HR -SEE LR ) (II.32) WhereSM HR represents the 1 km disaggregated SM, SM LR the SMOS observation, SM relative to SEE at LR, SEE HR the MODIS-derived SEE, and SEE HR its average within the SMOS pixel. The HR SEE is estimated as: max and T s,min are end-members temperatures estimated from the polygons obtained by plotting MODIS surface temperature against MODIS NDVI datasets as in Merlin et al. (2012a). Soil temperature is based on a linear decomposition of the surface temperature into its soil and vegetation components. Itis expressed as: MODIS being the 1 km resolution MODIS land surface temperature, f c the MODISderived vegetation cover fraction, and T v,HR the vegetation temperature. In this study, vegetation temperature is estimated using the approach proposed by Carlson et al. (1994). The vegetation cover fractionis written as: f c,HR = NDVI MODIS -NDVI s NDVI v -NDVI s (II.35) withNDVI MODIS being the 1 km resolution MODIS NDVI, NDVI s the NDVI corresponding to bare soil, andNDVI v the NDVI corresponding to full-cover vegetation. Minimum and maximum NDVI values are set to 0.15 and 0.90, respectively.

1 .

 1 Watershed of Tensift el HaouzThe Tensift catchment, located around Marrakech city, is one of the most important Moroccan watersheds(Figure III.1). It is characterized by a very contrasting relief and altitudes; between 0 and 4167 m. The catchment is surrounded by the the High Atlas Mountains on its south side, the small mountains called "Jbilet" on the north, by the watershed line on the east and the Atlantic Ocean on the west where the outlet is located. This Tensift watershed covers an area of about 20450 km². It consists of three main areas: Jbilet form a massif located north of the Tensift on a width of 20 to 30 km from north to south. Natural vegetation represents only a small area because of an intensive exploitation by overgrazing and deforestation for firewood and significant expansion of cultivated areas. The predominant agricultural activity in Jbilet zone is the rainfed cereal crop (wheat and barley), called Bour  The High Atlas is a large mountain range that limiting the Haouz plain on the south (800 km long and 70 km wide). It is the "water tower" of the region. It is the main source of water for crop irrigation in the plain. The water is transported to the plain either directly by hydraulic systems (dams and both modern and traditional canals) or indirectly by contributing to the aquifers recharge[START_REF] Abourida | Impact de la modernisation agricole sur l'évolution piézométrique de la nappe phréatique du Haouz (Maroc central) Impact de la modernisation agricole sur l'´ evolution piézométrique de la nappe phréatique du Haouz (Maroc central)[END_REF][START_REF] Boudhar | Analyse de la dynamique des surfaces enneigées du Haut Atlas marocain à partir des données SPOT-VEGETATION Article scientifique Analyse de la dynamique des surfaces enneigées du Haut Atlas marocain à partir des données[END_REF][START_REF] Chaponnière | A combined high and low spatial resolution approach for mapping snow covered areas in the Atlas mountains[END_REF]. The Haouz plain, which is the main area of our study, covers about 6000 km 2 of almost surface. The plain is crossed from the South to the North by several wadis draining the reliefs of the High Atlas and join the Wadi Tensift (main collector of the superficial waters of the basin). The relief of the Haouz plain is very little, marked with slopes not exceeding 5%. The altitude is about 900 m at the foothills of the Atlas Chapter III. Sites and data used mountain and gradually decreases towards the North, reaching about 300 m at the Wadi Tensift. The climate in the region is semiarid, with an average yearly precipitation of about 250 mm, of which approximately 75% falls during the winter

Figure III. 1 .

 1 Figure III. 1. Geographical situation of the Tensift watershed, its hydrographic network as well as the limit of the Haouz plain.

  wheat crop field of about 4 ha (Figure III.2), to monitor the energy and water balance as well as the soil and vegetation characteristics and conditions during the entire wheat growing cycle. The data set was collected from December 2002 to May 2003. site is located 70 km western Marrakech city. Data sets are collected during wheat season, from November 2016 to May 2017 over two wheat crops of about 1.5 ha each (Figure III.2). The plots are supplied by drip irrigation method. During the 2016-17

Figure III. 2 .

 2 Figure III. 2. Location of the four study sites: (a) flood-irrigated wheat crop in the R3 zone (east of Marrakech), (b) rainfed wheat crop in Bour site (east of Marrakech) and (c) two (controlled and reference) drip-irrigated wheat crops near Chichaoua city (west of Marrakech) in the Tensift basin, central Morocco. (Flat area).

  (called β =H/LE) and the 30-minute flux estimates are combined to derive the corrected 30

Figure III. 3 .

 3 Figure III. 3. Example of the digital processing procedure for photos taken in rainfed wheat field

Figure III. 4 .

 4 Figure III. 4. Photograph of (a) TDR (Time Domain Reflectometry) and (b) Theta Probe instruments

Figure III. 5 .

 5 Figure III. 5. (a) Map of the Wankama basin; (b) location of the three study sites (millet, fallow and (c) basin toposequence

Figure III. 6 .

 6 Figure III. 6. (a) An overview of theWankama basin and the experimental setup, locations of LAS (T and R stand for transmitter and receiver, respectively) and three EC systems are shown (millet, fallow and degraded shrubs sites). Photos (EC system (b) and scintillometer (c)) were taken by J. Ezzahar as part of the ACN project.

  the dominating canopy (millet, fallow and degraded shrubs) of the studied area. TSEB predictions of the convective fluxes are then evaluated at the scintillometer fooprint scale by aggregating the station scale predictions fed by the in-situ observations of albedo, LST and Leaf area index (LAI). In a second step, remote sensing products are used. A first evaluation is directly conducted at the scale of the scintillometer measurements by using 3 km LST observations from the MSG SEVIRI instrument. Finally, three aggregation schemes of MODIS products are tested to assess if a better representation of heterogeneity based on the 1-km products improves our large-scale estimates. Data collected in the context of the African Monsoon Multidisciplinary Analysis (AMMA) program

  surface fluxes and satellite products are assessed. In a second step, the TSEB predictions are evaluated at the station scale. Finally, the TSEB predictions of the convective fluxes are evaluated at the scale of the scintillometer fooprint: (1) by aggregating the station scale predictions using the in-situ observations of albedo, LST and LAI. This constitutes the ideal case (2) by using 3 km LST observations from the MSG SEVIRI instrument directly at the scale of the scintillometer measurements; and (3) by testing three aggregation schemes of MODIS products in order to assess if a better representation of heterogeneity based the 1The quality of EC measurements is usually assessed by assuming that the energy balance is closed. The comparison of the (R n -G) and the sum of the latent and sensible heat fluxes (LE EC + H EC ), measured independently by the EC systems (data not shown here), showed an

Figure IV. 1

 1 Figure IV.1 plots the time series of the average between 9 am and 5 pm of H LAS , and LE LAS

Figure IV. 1 .

 1 Figure IV. 1. Time series of LAS latent and sensible heat fluxes (daily average between 9am and 5pm)

  2018b) demonstrated, using a new TSEB-based evapotranspiration model (called TSEB-SM), that αPT cannot be considered as a constant because it varies in time according to several factors including LAI, green vetation cover fraction and soil water availability. In particular, it can take extreme values under dry, water deficit and advective conditions. Interestingly enough, the partition between latent and sensible heat fluxes is correctly reproduced for the degraded shrub site (mean biases lower than 0.92 W/m² and 11 W/m 2 for respectively, H and LE). Indeed the results of sensible heat flux over the millet crop matches perfectly with the results found by[START_REF] Lhomme | Estimating sensible heat flux from radiometric temperature over sparse millet[END_REF] (RMSE=43 W/m 2 ) who used a two layer model to estimate H from LST.[START_REF] Lhomme | Estimating sensible heat flux from radiometric temperature over sparse millet[END_REF] used an empirical relationship between LST and Ta (δT = a(LST -Ta) m ), m and a being statistically determined by adjusting the modelled to the H observed by the Bowen ratio method.

Figure IV. 5 .Figure

 5 Figure IV. 5. Scatterplot of simulated versus observed AE,H and LE for the (left) Millet, (middle) Fallow and (right) Degraded shrubs, respectively, using MODIS data.

Figure IV. 6 .

 6 Figure IV. 6. Sensible (a) and latent (b) heat fluxes scatterplots between LAS measurements and TSEB prediction feeded by aggregated in-situ data (at 30min time).

  scheme 1 (figure IV.8.b). The relative error was about 13%, the RMSE value was 65W/m 2 , and the linear regression forced through the origin yielded an R of 0.70 and the mean bias error was reduced to -30 W/m 2 instead of -48 W/m 2 for the first scheme. H simulated by using scheme 3 in figure IV.8.c is closer to the 1:1 line, providing a quite significant improvement with regards to the second scheme. The RMSE and the mean bias error between the simulated and measured values were 63 and -23 W/m 2 , respectively. The relative error of 10% indicates that the scheme 3 is very reliable in providing area-averaged sensible heat flux over heterogeneous surfaces.

Figure IV. 8 .

 8 Figure IV. 8. Sensible and latent heat fluxes scatterplots of the comparison between the LAS grid scale measurements and TSEB predictions based on MODIS products for a simple averaging (a,d), area weighted method (b,e) and footprint weighted method (c,f) ( at MODIS overpass time).

Figure IV. 9 .

 9 Figure IV. 9. Time series of the comparison between the LAS grid scale measurements (𝐻 𝐿𝐴𝑆 and 𝐿𝐸 𝐿𝐴𝑆 ) and TSEB predictions based on MODIS products (𝐻 𝑠𝑖𝑚 and 𝐿𝐸 𝑠𝑖𝑚 ) for footprint weighted method (at MODIS overpass time).

about 3 .

 3 2 km spanning the three dominant vegetation types (with contrasted energy balances and different fluxes behaviours) to derive the integrated H and LE values over this heterogeneous landscape. Our approach was organized into three steps. The experimental data including in-situ surface fluxes and remote sensing products were evaluated. The TSEB model was then evaluated at the station scale for the three study sites (millet, fallow and degraded shrubs) instrumented with EC systems. Finally, the TSEB prediction of surface Chapter IV. Validation of TSEB model over sparse and heteregeous vegetation in Sahel region (Niger) fluxes were evaluated at the grid-scale based on in-situ data (at the 30 min time), MODIS (at Terra and Aqua overpass time), and MSG products (at MDG-SEVIRI overpass time) and aggregation schemes.

(V. 3 . 1 .

 31 Figure V.1 plots the iterative values of a rss , b rss and mean αPT during calibration step 1.

Figure V. 1 .V. 3 . 2 .

 132 Figure V. 1. Iterative values of 𝑎 𝑟𝑠𝑠 ,(a), 𝑏 𝑟𝑠𝑠 (b) and mean value of retrieved αPT (c) for the flood-, controlled drip-and reference drip-irrigated wheat fields separately (calibration step 1).

Figure V. 2 .

 2 Figure V. 2. Time series of daily retrieved and smoothed αPT for the (a) flood-, (b) controlled dripand (c) reference drip-irrigated wheat fields, separately (calibration step 2).

1 .

 1 26 and 0 to 1.38 for the flood-, controlled drip-and reference drip-irrigated fields, respectively. Time series of calibrated daily αPT are presented in Figure V.3 superimposed

Figure V. 3 . 1 .

 31 Figure V. 3. Time series of calibrated daily αPT, superimposed with fc for the (a) flood-, (b) controlled drip-and (c) reference drip-irrigated wheat fields, separately. The red segments represent irrigations during the season.

Figure V. 5

 5 Figure V.5 plots simulated versus observed LE for the three sites separately. TSEB provides satisfying results for the flood site with a RMSE of 78 W/m 2 and a relative error (estimated as RMSE divided by mean observed LE) of 27%. However, two notable features are observed for the other two (controlled and reference drip) sites: i) the LE simulated by TSEB never exceeds 500 W/m 2 over the entire growing season (f c > 0.5) although observations reach 700 W/m 2 and ii) the overall MBE is about 29 W/m 2 and 66 W/m 2 for the controlled and reference drip field respectively, meaning that TSEB also overestimates LE in the lower ET range. To dig deeper, the performance of TSEB is now assessed by analyzing the metrics computed for three distinct periods of the agricultural season: the period for f c ≤ 0.5, for f c > 0.5 and the senescence stage. Note that the senescence period is defined herein as starting after the last peak observed on the calibrated daily αPT (becomes remarkable after about one week) and finishing when green fraction cover becomes zero, which corresponds to the last date of the three time series. Hence the senescence starts on 27/04/2003, 19/04/2017 and 15/04/2017 for the flood-, controlled drip-and reference drip-irrigated field, respectively. A visual assessment of scatter plots in Figure V.5 and the statistics presented in Table V.1 clearly indicate that TSEB underestimates LE fluxes at around the maximum of ET (well developed crop before senescence) while it overestimates LE fluxes during senescence until harvest. The saturation of TSEB in the higher range of ET is due to the fixed maximum value for αPT (equal to 1.26). The structure of the model cannot accommodate large evaporative demand conditions and strong advective conditions(Song et al., 2016a).

Figure V. 5 .

 5 Figure V. 5. Scatterplot of simulated versus observed LE for the (top) food-, (middle) controlled dripand (bottom) reference drip-irrigated fields and for (left) TSEB-SM and (right) TSEB models, respectively.

Figure V. 6 .Table V. 1 .

 61 Figure V. 6. Scatterplot of simulated versus observed H for the (top) food-, (middle) controlled dripand (bottom) reference drip-irrigated fields and for (right) TSEB and (left) TSEB-SM model, respectively.

Figure VI. 1 .

 1 Figure VI. 1. Scatter plots of MODIS versus in-situ LST at Sidi Rahal site for S1 (2014-2015), B1 (2015-2016), S2 (2016-2017) and S3 (2017-2018) agricultural seasons, separately, (red dashed line is the line(1:1)-black line is the regression line)

Figure VI. 2 .

 2 Figure VI. 2. Scatter plots of the 1 km resolution DisPATCh versus in-situ SM at Sidi Rahal site for S1(2014)(2015),B1 (2015-2016), S2 (2016-2017) and S3 (2017-2018) agricultural seasons, separately.

Figure VI.

  Figure VI. 3. NDVI image derived from Landsat data acquired on 17/04/2018. The experimental field

VI. 5 . 2 .

 52 Figure VI.5 illustrates the time series of daily retrieved αPT for each season separately, using satellite data. It can be seen that S1 and S2 have a very similar distribution of the retrieved αPT as compared to the retrieved αPT using in-situ data, respectively. For S3, only six retrieved αPT values are available because of the non-availability of MODIS products during cloudy days.

Figure VI. 5 .

 5 Figure VI. 5. Time series of daily retrieved and smoothed αPT (calibration step 2-using in-situ data, and satellite data) collected during S1, S2 and S3.

  Figure VI. 7. Scatterplot of simulated versus observed LE for (top) TSEB and (bottom) TSEB-SM models using in-situ data collected during S1, B1, S2 and S3, respectively.

  Figure VI. 8. Same as Fig VI.7 but for H fluxes.

  is conducted. The comparisons between TSEB/TSEB-SM versus observed LE over the four seasons are illustrated in Figure VI.9. A visual assessment of scatter plots in Figure VI.9 and the statistical results (TableVI.2) clearly indicates that TSEB overestimates LE fluxes. The overall MBE are about 119, 181, 94 and 128 W/m 2 for S1, B1, S2 and S3 respectively. The overestimation of LE fluxes can be explained by the fact that αPT is set to be 1.26 for the whole study period, including both stressed and unstressed conditions. This probably causes larger errors on the LE estimation especially during the growing stage. Indeed, the saturation of TSEB in the higher range of ET during the senescence period is precisely due to the fixed maximum value of αPT to 1.26. The errors are reduced when using TSEB-SM. In fact, the constraint on plant transpiration, while retrieving daily αPT values instead of using the theoretical value 1.26 significantly improves ET estimates especially for the growing stage.Moreover, the large bias of LE during the senescence stage is much reduced. It is suggested that the decrease in calibrated daily αPT integrates the drop in green vegetation fraction that takes place during senescence(Ait Hssaine et al., 2018b). Additionally, the constraint on the soil evaporation via the DisPATCh SM, clearly reduces the MBE values during the Chapter VI. Remote sensing application of TSEB-SM (combining DisPATCh SM and MODIS LST data for mapping ET at 1 km resolution)106 emergence period (f c ≤f c,thres ). Finally, the constraint applied on TSEB-SM output fluxes using LST-derived available energy and TSEB-SM-derived evaporative fraction (Equation6.1) improves the LE estimates for the whole study period. The MBE are about 39, 4, 7 and 62 W/m 2 for S1, S2, S3 and B1 respectively.

Figure VI. 9 .

 9 Figure VI. 9. Same as Fig VI.7 but for satellite data.

  Our initial proposal 'The validation results of TSEB model over sparse and heterogeneous vegetation in Sahel region (Niger)' aims to test the TSEB model, which operates the ET partitioning by using the LST, f c , and the Priestley Taylor (PT) assumption that relates transpiration to net radiation via a fixed PT coefficient (αPT). This study considers the issue of using TSEB driven by MODIS (Moderate resolution imaging spectroradiometer) observations in conjunction with an aggregation scheme to derive area-averaged sensible (H) and latent (LE) heat fluxes over an heterogeneous watershed in Niamey, Niger (Wankama catchment). Data collected in the context of the African Monsoon Multidisciplinary Analysis (AMMA) program, including a scintillometry campaign, are used to test the proposed approach. The model predictions of area-averaged turbulent fluxes are compared to data acquired by a Large Aperture Scintillometer (LAS) set up over a transect about 3.2 km-long and spanning three vegetation types (millet, fallow and degraded shrubs). First, H and LE fluxes are estimated at the MSG-SEVIRI grid scale by neglecting explicitly the subpixel heterogeneity. Next, the impact of upscaling the model's inputs is investigated using in-situ input data and three aggregation schemes of increasing complexity based on MODIS products: a simple averaging Chapter VII. Conclusion and perspectives of inputs at the MODIS resolution scale, another simple averaging scheme that considers the scintillometer footprint extent, and the weighted average of inputs based on the footprint weighting function. The results obtained for H and LE are relevant. However, an overestimation of simulated fluxes is recorded at the end of the season, mainly due to the fixed maximum value for αPT (equal to 1.26).

  budgets. This equation may contain biases from the net radiation, soil heat flux and sensible heat flux estimates. To overcome these limitations, data available from space can help in implementing the PT approach by applying a direct constraint on soil evaporation and plant transpiration simultaneously.The second part of the thesis is hence dedicated to 'Improving TSEB model by integrating SM data (TSEB-SM): a feasibility study using in-situ data (the land surface temperature, vegetation cover fraction and near-surface soil moisture) data'. For this purpose, a new ET model named TSEB-SM is derived from the TSEB formalism by explicitly representing soil evaporation using a soil resistance. To help constrain the evaporation/transpiration partition of TSEB-SM, an innovative calibration approach is also developed to retrieve the main parameters of soil evaporation (soil resistance, r ss ) and plant transpiration (αPT). In practice, the soil resistance parameters are retrieved at the seasonal time scale from SM and LST data with f c ≤f c,thres (an empirical threshold dedicated to iteratively separate the soil/vegetation parameters on ET estimates), while αPT is retrieved at the daily time scale from SM and LST data for f c > f c,thres . TSEB-SM model is tested over1 flood-and 2002-2003 and 2016-2017. The coupling of the soil resistance formulation with the TSEB formalism improves the estimation of soil evaporation, and consequently, improves the partitioning of ET. Analysis of the retrieved time series indicates that the daily α PT mainly follows the phenology of winter wheat crop with a maximum value coincident with the full development of green biomass and a minimum value reached at harvest. The temporal variations of α PT before senescence are attributed to the dynamics of both the root zone soil moisture and the amount of green biomass. These results encourage us to develop a parameter estimation method based on SM remote sensing.

  The third section 'Remote sensing application of TSEB-SM (Combining DisPATCh soil moisture and MODIS LST/𝐟 𝐜 data for mapping ET at 1 km resolution' aims to evaluate the performance of TSEB-SM in real-life using 1 km resolution MODIS LST and f c data and the 1 km resolution SM data disaggregated from SMOS (Soil Moisture and Ocean Salinity) observations by using DisPATCh. The approach is applied over a rainfed wheat field in the Tensift basin, central Morocco, during a four-year period (2014-2018). The field was seeded for the 2014-2015 (S1), 2016-2017 (S2) and 2017-2018 (S3) agricultural season, while it remained under bare soil conditions during the 2015-2016 (B1) wheat seasons. Compared to eddy covariance measurements, TSEB driven only by LST and f c data significantly overestimates latent heat fluxes for the four seasons. The overall mean bias values are 119, 94, 128 and 181 W/m 2 for S1, S2, S3 and B1 respectively. In contrast, these errors are much reduced when using TSEB-SM (SM and LST combined data) with the mean bias values estimated as 39, 4, 7 and 62 W/m 2 for S1, S2, S3 and B1 respectively. The constraint applied on the soil evaporation by using the SM derived from SMOS data is one of the main Chapter VII. Conclusion and perspectives controlling factors of the evaporative fraction, which helps to determine with more accuracy the LE/H partitioning.

  photosynthetically active radiation absorbed by the vegetative canopy) based model of canopy resistance within the TSEB model instead of using the PT based transpiration. Results show that LUE module improves the partitioning of the surface energy budget. It reflects its robustness to achieve appropriate reductions in canopy conductance in response to elevated midday vapour pressure deficits, which implicitly reduce the errors on flux predictions. These previous results are very encouraging, because they prove that the stomatal conductance can be a critical indicator for monitoring the water status/stress of crops.Parallel to ongoing work in a more realistic representation of canopy resistance, the resistance to soil evaporation also needs some improvements.[START_REF] Merlin | Modeling soil evaporation efficiency in a range of soil and atmospheric conditions: A downward approach based on multi-site data[END_REF] proposed a pedotransfer function to relate the main soil evaporation parameter to soil texture. To better constrain the soil evaporation using microwave / thermal data, a new formulation was developed in[START_REF] Merlin | A phenomenological model of soil evaporative efficiency using surface soil moisture and temperature data[END_REF] to correct the cyclic phenomenon of drying/rewetting of the top soil during daytime/night-time.Regarding the input data of TSEB-SM, a new method is being developed to apply DisPATCh to (Landsat-7 and Landsat-8) thermal infrared data in order to disaggregate SMOS and SMAP SM data to a spatial resolution of 100 m (Nitu Ojha's thesis). This spatial resolution of 100 m will allow the crop field size to be resolved and thus a finer and more precise estimate of SM and associated ET/water stress predictions. Alternatively, the use of active sensors recently launched, as Sentinel-1 that potentially provides the surface SM at resolutions of 20 m each 6 days. Such high spatio-temporal resolution is consistent with Sentinel-2 mission, which follows the characteristics of the canopy at resolution of 10 to 60 m with a repeat cycle of 5 days by combining both ascending and descending overpasses. The integration of these recent high-resolution products could improve the partitioning of evaporation/ transpiration and consequently provide a better estimate of ET at large scale. Recently, a new work developed in the framework of LMI/TREMA (Nadia Ouaadi thesis) demonstrates the sensitivity of the backscattering coefficient and the interferometric coherence (Sentinel-1) to SM variabilities and wheat crops growth. Nadia developed a new method to retrieve SM combining the interferometric coherence and C-band backscattering coefficient over irrigated wheat from sowing to harvest. The preliminary results are very encouraging. The proposed approach

(

  2008) found that PRI is well correlated to physiological indicators of water stress, such as stomatal conductance, stem water potential, and fluorescence over an olive orchard. Our challenge lies on developing a new formulation of stomatal conductance, which embed hydric stress information provided from the PRI index. In this context, the Earth Explorer -Fluorescence Explorer (FLEX) mission will be launched by 2022 to provide global maps of vegetation fluorescence, PRI, canopy temperature measurements and all the relevant variables (chlorophyll content, Leaf Area Index, etc.) needed to assess the actual physiological status of vegetation. In the same context, current work conducted in the framework of LMI/TREMA (Zoubair Rafi thesis) aims to analyse the PRI data collected over several irrigated wheat fields in Morocco by developing a new early water stress indicator that could be used in addition to LST-derived indices.

Table VI . 1 .

 VI1 Validation results of DisPATCh SM and MODIS LST at Sidi Rahal site. .

....... 94 Table VI. 2. Statistical

results (RMSE, R

Chapter.I. Introduction and state of art Chapter.I. Introduction and state of art ............................................................................. I

  .1. General context ............................................................................................................ I.2. In-situ measurements of Evapotranspiration ............................................................... I.3. Modeling approaches of Evapotranspiration ............................................................. I.3.1. Empirical models ................................................................................................ I.3.2. Mechanistic models ............................................................................................ SEB) models .............................................................. Objectives ..................................................................................................................

	I.3.3. Surface Energy Balance (I.4. Remote sensing of Evapotranspiration ......................................................................
	I.4.1.	Models based on vegetation index .....................................................................
	I.4.2.	Models based on Land Surface Temperature .....................................................
	I.4.3.	Models based on Surface soil moisture ..............................................................
	I.5.

  , and 3) none of these formulations are evaluated under different types of soil and variable atmospheric conditions. Based on these findings, a new model of evaporation developed by[START_REF] Merlin | Modeling soil evaporation efficiency in a range of soil and atmospheric conditions: A downward approach based on multi-site data[END_REF] have been used to estimate soil evaporation.

3-A new energy balance model for evaporation /transpiration partitioning is developed to simultaneously integrate remote sensing LST and SM data. To build this model from a stateof-the-art ET model, the following characteristics are taken into account: i) modeling based

Table II . 1 .

 II1 Input data of DisPATCh chain

	Product	Variable	Resolution	Projection	Format
	SMOS CLF31A/CLF31D	SM	25 km/ 3 days	EASE grid	NetCDF
		LST_day_Q
	MODIS MOD11A1/MYD11A2	C	1 km/ 1 day	USGS Sinusoidal	HDF
	MODIS MOD13A2	NDVI,QC	1 km/ 16 days USGS Sinusoidal	HDF
	GTOP030	MNT	0.01°	WGS84	GeoTIFF

  III. Sites and data used

	Chapter.III.	Sites and data used

Chapter.III. Sites and data used ....................................................................................... III.1. Introduction ............................................................................................................... III.2. Sites and in-situ data description .............................................................................. III.2.1. Watershed of Tensift el Haouz ........................................................................... III.2.2. Wankama basin (Niger) ..................................................................................... III.2.3. Spatial data ......................................................................................................... III.3. Conclusion .................................................................................................................

Table III . 1 .

 III1 Characteristics of the instruments equipping EC station.

	Site Instrument	Measurements	Height or depth
		Fluxes MAST
		Campbell CSAT3 sonic anemometer Wind direction and speed	5,1m (Millet) et 4,95m (Fallow)
		Li-Cor7500 IRGA	CO2 and H2O concentration	4,8m(Millet) et 4,65m (Fallow)
		CNR1 Kipp & Zonen radiometer	Shortwave and longwave incoming and outcoming radiation	2,5m(Millet) et 3,4m(Fallow)
	Millet and Fallow	Vaisala HMP45 Soil measurements Campbell CS616 water content	Air temperature and relative humidity Soil volumetric water content	2m -.1, -.5, -1, -1.5, -2
		reflectometer (x6)		and -2.5 m
		Campbell T108 temperature probe (X6)	Soil temperature	-.1, -.5, -1, -1.5, -2 and -2.5 m
		Hukseflux HFP01SC heat flux plates (x3)	Surface soil heat flux	-.05 m
		Flux MAST
		Solent R3-50 sonic anemometer	Wind direction and speed	5 m
		Kipp & Zonen CNR1 radiometer	Shortwave and longwave incoming and outcoming radiation	2 m
	Degraded shrubs	Vaisala WXT510 weather transmitter RIMCO tipping bucket raingauge	Air temperature, relative humidity, atmospheric pressure, wind speed, wind direction Rainfall amount, duration and intensity	2 m 0 m
		Soil measurements
		Campbell CS616 water content reflectometer (x2)	Soil volumetric water content	-.1, -.5 m
		Campbell T107 temperature probe (X2)	Soil temperature	-.1, -.5 m

Table IV . 1 .

 IV1 Statistical metrics of the comparison between measured and estimated values of available energy and turbulent fluxes (H and LE) at patch and grid scale

				n	R	MBE	RMSE
			Fluxes	(-)	(-)	(W/m 2 )	(W/m 2 )
			H	1442	0.81	26
		Millet	LE	1442	0.69	-17
			R n -G	1442	0.92	-23
	Patch-scale		H	1905	0.89	-21
	(using in-	Fallow	LE	1905	0.88	0.38
	situ data)		R n -G	1905	0.98	-37
			H	486	0.82	0.92
		Degraded-shrubs	LE R n -G	486 486	0.71 0.95	11 -42
			H	52	0.45	13
		Millet	LE	52	0.58	58
			R n -G	52	0.67	4
	Patch-scale		H	52	0.73	25
	(using	Fallow	LE	52	0.71	32
	MODIS		R n -G	52	0.79	23
	data)		H	-	-	-	-
		Degraded-	LE	-	-	-	-
		shrubs	R n -G	-	-	-
	Grid-scale		H	370	0.87	-21
	(using in-situ data)		LE	186	0.72	39
	Grid-scale		H	51	0.39	-19	65
	using MSG
	SEVIRI data		LE	51	0.2	32
	Grid-scale	Scheme 1	H LE	20	0.71 0.85	-48 73	102
	(using MODIS	Scheme 2	H LE	20	0.7 0.82	-30 49
	data)	Scheme 3	H LE	20	0.71 0.82	-23

Table V . 2 .

 V2 Error statistics(RMSE. R2 and MBE) between modeled and measured net radiation, conductive flux, and sensible and latent heat fluxes for the flood, controlled drip-and reference dripirrigated fields, and for TSEB and TSEB-SM model, separately.

				TSEB-SM			TSEB
			RMSE	R 2	MBE	RMSE	R 2	MBE
			(W/m 2 )	(-)	(W/m 2 )	(W/m 2 )	(-)	(W/m 2 )
		Flood	31	0.98	-25	18	0.99	-17
	Net	Controlled drip	27	0.98	-10	16	0.99	1
	radiation	Reference drip	50	0.95	-32	9	0.99	1
	(Rn)
		Flood	23	0.41	2	22	0.43	1
	Conductif	Controlled drip	20	0.5	9	25	0.48	12
	flux (G)	Reference drip	14	0.39	14	30	0.38	26
		Flood	27	0.66	34	78	0.61	-67
	Sensible	Controlled drip	61	0.82	8	118	0.38	-28
	heat flux
	(H)

  Figure VI.1 displays the scatter plots of MODIS LST (at Terra and Aqua overpass) versus insitu measurements for the four agricultural seasons separately. The obtained R 2 , RMSE, and MBE are reported inTable VI.1. The statistical comparison shows strong linear correlations

	(0.76 ≤ R 2 ≤ 0.90) for all years. The RMSE is around 4 K for S2 (2016-2017) and S3 (2017-
	2018) agricultural seasons while it reaches 6 K for S1 (2014-2015) and B1 (2015-2016),
	Malbéteau et al. (2016) compared DisPATCh SM data with the in-situ measurements of 38
	stations distributed within the Murrumbidgee catchment in Southeastern Australia. Their
	results showed that DisPATCh improved the spatial representation of SM at 1 km resolution
	(compared to the original 40 km resolution SMOS SM) independently from the temporal
	information provided by SMOS satellite, especially in semi-arid areas. Recently, Malbéteau et
	al. (2018) combined the DisPATCh SM over the entire year 2014 (Sidi Rahal-Morocco) with

the continuous predictions of a surface model in order to obtain a better estimate of daily SM at 1 km resolution. They found that the assimilation of DisPATCh data improved quasi systematically the dynamics of SM.

Table VI . 1 .

 VI1 Validation results of DisPATCh SM and MODIS LST at Sidi Rahal site. In order to evaluate the 1 km resolution SM during the study period, Figure VI.2 shows a comparison of DisPATCh SM with in-situ measurements for the four wheat agricultural seasons (S1, B1, S2 and S3) separately. The statistical results including the coefficient of determination (R 2 ), the root mean square error (RMSE), and the mean bias error (MBE) are reported in Table VI.1. The R 2 ranges from 0.27 to 0.55, the RMSE from 0.04 to 0.09 m 3 /m 3 and the MBE from -0.05 to -0.03 m 3 /m 3 . These results are encouraging considering the heterogeneous land use composed of rainfed wheat, bare soil, fallow and farm building (see Figure VI.

		Period	R 2	RMSE	MBE
		S1	0.80	6.4 (K)	-3.7 (K)
	LST	B1 S2	0.76 0.91	5.6 (K) 4.3 (K)	-4.6(K) -2.9 (K)
		S3	0.89	4 (K)	-2 (K)
		S1	0.55	0.07 m 3 /m 3	-0.04 m 3 /m 3
	SM	B1 S2	0.36 0.27	0.04 m 3 /m 3 0.09 m 3 /m 3	-0.03 m 3 /m 3 -0.05 m 3 /m 3
		S3	0.47	0.08 m 3 /m 3	-0.03 m 3 /m 3

  Chapter VI. Remote sensing application of TSEB-SM (combining DisPATCh SM and MODIS LST data for mapping ET at 1 km resolution)The soil resistance r ss is inverted for f c ≤ f c,thres , between 11 am and 2 pm and at Terra and Aqua overpass time step for in-situ and satellite data, respectively. The inverted r ss is then correlated to the ratio SM/SM sat to estimate a rss and b rss parameters. These latter are the intercept of the linear regression between the log (r ss ) and SM/SM sat relationship. The calibration process is applied for each season independently. Then a pair (a rss , b rss ) is calculated for the entire study period for in-situ and satellite data, respectively.Figures VI.4.a and VI.4.b plot the log (r ss ) versus in-situ SM/SM sat using in-situ and satellite data, respectively. The mean retrieved values (7.62, 2.43) and (7.32, 4.58) for in-situ and satellite data, respectively, are relatively close to the values estimated in Sellers et al. (1992) (8.2, 4.3) and in Ait Hssaine et al. (2018b) (7.2, 4). However, by comparing both figures (VI.4.a and VI.4.b), one notes that the use of in-situ data generates more scatter than with

	VI.4.	Retrieving (𝐚 𝐫𝐬𝐬 , 𝐛 𝐫𝐬𝐬 ) parameters

3. NDVI image derived from Landsat data acquired on 17/04/2018. The experimental field and the overlaying 1 km resolution MODIS pixel are superimposed

  2 , RMSE and MBE between simulated and observed fluxes.

	VI.6.1. Using in-situ data
	Figure VI.7 shows an intercomparison of simulated and observed LE for the 4 seasons
	separately. TSEB-SM clearly provides improved results compared to the original TSEB. The
	obtained values of RMSE by TSEB-SM are about 68 and 72 W/m 2 for S1 and S2
	respectively, which is significantly lower than those revealed by TSEB (109 and 86 W/m 2 ,
	respectively) (see Table VI.2). For B1 (season of bare soil), TSEB largely overestimates LE
	with a MBE of about 165 W/m 2 compared to TSEB-SM, which yields a MBE of 59 W/m 2 .
	This overestimation of TSEB is most probably related to an inadequate value of αPT (=1.26)

Table VI . 2

 VI2 As a further step, the intercomparison between TSEB and TSEB-SM is assessed by predicting R n and G fluxes instead of forcing them to their measured values. The statistical results of the comparison between simulated and observed R n , G, H and LE are listed in TableVI.3. The simulations of LE and H when modeling R n and G are consistent with those obtained when forcing R n and G to their measured values. The scattering obtained when comparing turbulent flux estimations to measurements is mainly related to the uncertainty in available energy estimates, mainly related to the uncertainty in soil heat flux estimates. Indeed, as reported in Table VI.3, R n is very well simulated for both TSEB and TSEB-SM. The R 2 between simulated and observed R n is about 0.99 during all seasons. Meanwhile G shows a poor correlation, with an R 2 varying from 0.05 to 0.45. This is mainly linked to the simplicity of the approach used to estimate G, which requires local calibration.[START_REF] Kustas | Combining optical and microwave remote sensing for mapping energy fluxes in a semiarid watershed[END_REF] hence indicated that the ratio G/R n,soil cannot be considered as a constant, because it is affected by different factors such as time of day, moisture conditions and soil texture and structure.

					TSEB			TSEB-SM
				RMSE	R 2	MBE	RMSE	R 2	MBE
			S1	109	0.39	76	68	0.59	10
		LE	B1	136	0.15	165	52	0.22	59
		(W/m 2 )	S2	86	0.22	30	72	0.16	-24
	Using in-		S3	103	0.53	71	98	0.29	-7
	situ data		S1	127	0.33	-41	68	0.70	-10
		H	B1	136	0.44	-165	52	0.91	-59
		(W/m 2 )	S2	112	0.47	1	72	0.63	24
			S3	103	0.38	-71	98	0.14	7
			S1	95	0.34	119	55	0.51	39
		LE	B1	66	0.07	181	27	0.01	62
	Using satellite data	(W/m 2 ) H	S2 S3 S1 B1	67 56 98 66	0.02 0.55 0.3 0.37	94 128 -104 -181	41 24 55 27	0.08 0.68 0.54 0.52	4 7 -39 -62
		(W/m 2 )	S2	73	0.33	-71	41	0.6	-4
			S3	56	0.28	-128	24	0.36	-7

. Statistical results (RMSE, R 2 and MBE) between modeled and measured sensible and latent heat fluxes for S1, S2, B1 and S3, and for TSEB and TSEB-SM model, separately (R n and G are forced to their measured value).

Table VI . 3 .

 VI3 Same as Table VI.2. but for simulated R n and G

					TSEB			TSEB-SM
				RMSE	R 2	MBE	RMSE	R 2	MBE
			S1	35	0.99	-38		0.99	-38
		R n (W/m 2 )	B1	14	0.99	12		0.99	12
			S2	20	0.99	9		0.99	9
			S3	7	0.99	-0.46	7	0.99	-0.46
			S1	19	0.32	17		0.32	17
		G	B1	19	0.05	12		0.05	12
		(W/m 2 )	S2	30	0.28	-13		0.28	-13
	Using in-		S3	26	0.44	9		0.44	8
	situ data		S1	87	0.35	27		0.58	-21
		LE (W/m 2 )	B1	141	0.12	174		0.16	60
			S2	91	0.23	35		0.22	-15
			S3	91	0.62	54		0.47	22
			S1	127	0.33	-44		0.73	34
		H	B1	145	0.43	-177		0.90	-60
		(W/m 2 )	S2	112	0.48	2		0.68	36
			S3	99	0.30	-64		0.30	-32
			S1	23	0.94	8		0.93	8
		R n (W/m 2 )	B1 S2	85 22	0.47 0.94	32 12		0.47 0.94	32 12
			S3	17	0.97	2		0.97	2
			S1	20	0.41	24		0.40	24
		G	B1	20	0	15		0	15
	Using satellite data	(W/m 2 ) LE (W/m 2 )	S2 S3 S1 B1 S2	25 22 103 151 101	0.12 0.08 0.24 0.02 0.07	-15 10 86 240 96		0.12 0.08 0.49 0.01 0.06	-15 10 28 65 28
			S3	83	0.47	74		0.69	14
			S1	112	0.34	-91		0.44	-45
		H	B1	150	0.16	-240		0.49	-61
		(W/m 2 )	S2	97	0.4	-56		0.52	-4
			S3	85	0.12	-83		0.28	-29

Note that despite the relative heterogeneity within the 1 km pixel (characterized by rainfed wheat in addition to bare soil and fallow), the comparison between field measurements and 1 km resolution satellite data reflects acceptable accuracies.

Figure V. 4. Time series of 𝛼 𝑃𝑇,𝑐𝑎𝑙,𝑑𝑎𝑖𝑙𝑦 superimposed with 5-cm/30-cm soil moisture (SM) and vegetation water content (VWC) for: (a) flood-, (b) controlled drip-and (c) reference drip-irrigated fields, respectively. For the flood-irrigated wheat, VWC is unavailable.

V.4.2. Surface fluxes

The ability of TSEB and TSEB-SM for partitioning the available energy into H and LE is assessed by forcing -in each case-R n and G to their measured values. Note that the calibration of TSEB-SM is still undertaken using observed LST, SM and fc whereas the validation of TSEB and TSEB-SM model output is undertaken using EC measurements of H and LE. The Chapter V. Improving TSEB model by integrating SM data (TSEB-SM): a feasibility study using in-situ data (LST, fc and SM)

LAS path was 250° from the north. At the receiver tower, a 2D anemometer (Wp200, R.M.

Young Company, Traverse City, MI, USA) to measure wind speed and direction at 10 m was also installed. Additionally, the air temperature and humidity were measured using Vaisala HMP45C probe.

III.2.3. Spatial data

III.2.3.1. MODIS and MSG data a. MODIS products

The MODIS instrument operates on both Terra and Aqua spacecraft. It has a viewing swath width of 2330 km and views the entire surface of the Earth every 1-2 days. Its detectors measure 36 spectral bands between 0.405 and 14.385 μm, and it acquires data at three spatial resolutions: 250 m, 500 m, and 1000 m. The MOD15A2 LAI is a 1 km global data product updated once every 8 days derived from the MODIS sensor on board TERRA. The MODIS LAI algorithms were developed jointly by personnel at Boston University, the University of Montana SCF and NASA GSFC. The algorithm consists of a main procedure based on the inversion of a 3D radiative transfer model thanks to a look-up-table. This algorithm exploits the spectral information content of MODIS surface reflectances at up to seven spectral bands. Should this main algorithm fail, a back-up algorithm is triggered to estimate LAI empirical relationships with vegetation indices. The LAI products in the collection version 5 are available from 2001 to present. The MCD43B3 α product is upscaled from MCD43A3 and provides both the white-sky-albedo (α) and the black-sky-α at 1-km resolution every 16 days.

Both Terra and Aqua data are used in the generation of this product. We were interested in a single integrated value over the entire solar emission spectrum (0.3-5.0 μm) called shortwave broadband α. The black-sky-α (directional hemispherical reflectance) is a directional α corresponding to 100% of direct light; it depends on the solar zenithal angle unlike the whitesky-α (bihemispherical reflectance) which corresponds to a completely diffuse light. The "blue sky" α used in this study is a weighted average between these two extreme values. The weighting depends essentially on the aerosol content of the atmosphere [START_REF] Lewis | Influence of the sky radiance distribution on various formulations of the earth surface albedo[END_REF]. In our case, we considered that we have 85% direct light and 15% diffuse, and the final α value is calculated as follows [START_REF] Lewis | Influence of the sky radiance distribution on various formulations of the earth surface albedo[END_REF]: α = 0.85 * α black-sky + 0.15 * α white-sky (III.1)

Chapter III. Sites and data used

The MOD11A1 and MYD11A1 at 1 km spatial resolution under clear-sky conditions are the daily land surface temperature (LST) products, derived from Terra and Aqua, respectively.

LST is derived from the brightness temperature using bands 31 and 32 through a generalized split-window algorithm. The daily level 3 MODIS LST (collection 5) were used in this study.

The MOD11A1 and MYD11A1 at 1 km spatial resolution under clear-sky conditions are the daily land surface temperature (LST) products, derived from Terra and Aqua, respectively.

LST is derived from the brightness temperature using bands 31 and 32 through a generalized split-window algorithm.

The MOD13A2 provides spatio-temporal coverage of vegetation conditions via several indices at 1 km resolution as a gridded level-3 product in the Sinusoidal projection.

b. SEVIRI Land Surface Temperature

The Spinning Enhanced Visible and InfraRed Imager (SEVIRI) aboard Meteosat Second Generation (MSG) is a multi-spectral sensor, imaging across the visible and near-IR, which provides data with a high temporal and spectral resolution every 15 min in 12 wavebands, and image spatial sampling scales of 3 km for nadir view. The land surface temperature is estimated from top of atmosphere (TOA) brightness temperatures of SEVIRI split-window channels, centered on 10.8 and 12.0 μm, using a generalized split-window (GSW) algorithm [START_REF] Wan | A Generalized Split-Window Algorithm for Retrieving Land-Surface Temperature from Space[END_REF] with the adoption of SEVIRI data [START_REF] Trigo | An assessment of remotely sensed land surface temperature[END_REF]. IR radiance is absorbed and scattered even by thin clouds and aerosols. Therefore, the retrieval of LST works only for completely cloud-free pixels and the quality of this product is automatically assessed by means of the accuracy of the parameters used in the LST algorithm. LST products used in this study are distributed by EUMETSAT through the Satellite Application Facility on Land Surface Analysis (LSA SAF).

III.2.3.2. SMOS data

The SMOS mission measures the natural (passive) microwave radiation around the frequency of 1. angle is enhanced with surface heterogeneities. In addition, LST was retrieved using one MSG SEVIRI window channel (10.8 µm), while the MODIS algorithm is based on two windows channel (11.03 µm and 12.02 µm). These dissimilarities related to the spectral characteristics of the two instruments can induce the observed differences in retrieved LST.

Finally, the positioning error of MSG that has been found to reach up to 8 pixels i.e. ~30 km [START_REF] Aksakal | Geometric Accuracy Investigations of SEVIRI High Resolution Visible (HRV) Level 1.5 Imagery[END_REF] could also explain this over-estimation, in particular if the pixel is shifted to the north of the area characterized by bare and hot soils.

IV.2.2. Results of multi-Scale surfaces fluxes

The TSEB predictions are evaluated at the station scale both using in-situ and MODIS derived products. Focus is then put on the evaluation of TSEB at the grid scale using in-situ, MODIS and MSG products.

IV.2.2.1. Station scale a. Using in-situ data

The available energy and turbulent fluxes predicted by the TSEB model are compared to those measured over the three eddy covariance stations at half-hourly time step. Table IV Chapter IV. Validation of TSEB model over sparse and heteregeous vegetation in Sahel region (Niger)

provides poor results (RMSE of 73 W/m 2 and 102W/m 2 for H and LE, respectively), the statistical metrics based on the two other aggregation schemes are encouraging. In particular, the scheme 2 considering the MODIS pixel included in the scintillometer footprint only but without weighting the values based on the footprint contribution as in the scheme 3, represents a good trade-off between accuracy and ease of implementation to map evapotranspiration over complex landscape.

In this chapter, LST has been extensively used to retrieve ET at a wide range of spatial resolutions. To improve these models to take into account the water stress conditions, TSEB formalism is modified (in the next chapter), to a new model named TSEB-SM, by using, in addition to LST and f c data, the near-surface soil moisture (SM) as an extra constraint on soil evaporation. An innovative calibration procedure of TSEB-SM is proposed to retrieve the main parameters of soil evaporation (soil resistance) and plant transpiration (αPT). approach is also developed to retrieve the main parameters of soil evaporation and plant transpiration via the soil resistance and αPT respectively. In practice the soil resistance parameters are retrieved at the seasonal time scale from SM and LST data with f c ≤ 0.5.

While αPT is retrieved at the daily time scale from SM and LST data for f c > 0.5. The performance of TSEB-SM and TSEB models is assessed in terms of LE and H partitioning using an in-situ data set collected over 1 flood-and 2 drip-irrigated wheat fields.

The convergence of the iterative calibration procedure on (a rss , b rss ) and αPT is successfully tested when all three parameters are estimated at the seasonal time scale, as well as when considering a daily variability of αPT. The maximum calibrated daily αPT is close to the theoretical value of 1.26 for all three sites. However, its temporal variability is found to be significant even during the growing stage of wheat. A qualitative analysis of αPT variabilities in relation to soil moisture at 5 cm and 30 cm depth and to VWC indicates that αPT cannot be considered as a constant in the conditions of the experiments. Large deviations about the 1.26 value are likely to occur during the agricultural season especially under dry, water deficit and advective conditions.

In terms of flux estimates, TSEB provides satisfying results for the flood site but not for the other two (controlled and reference drip) sites. The saturation of TSEB in the higher range of ET is due to the fixed maximum value for αPT (equal to 1.26). Moreover, the overestimation of LE by TSEB during senescence is associated with a very low sensitivity of simulated H to any surface/atmospheric conditions. Both limitations identified in the TSEB formalism seem to be partly solved by the TSEB-SM approach with a slope of the linear regression between simulated and observed LE/H much closer to 1 in all cases. Such an evapotranspiration model simultaneously constrained by LST, f c and SM seems to respond robustly in terms of LE/H partitioning for wheat crops under the conditions of the experiments. However, the calibrated daily αPT needed to be i) smoothed to reduce random uncertainties and ii) normalized between its two extreme values since the 0 value was not necessarily reached at harvest.

In the next chapter, the microwave-derived near-surface soil moisture (SM), in addition to the thermal-derived LST and fractional vegetation cover (f c ) will be used to investigate how remote sensing data can be used to derive the main parameters (a rss , b rss and αPT) of TSEB-SM model. In this purpose, TSEB-SM at 1 km resolution using MODIS (Moderate resolution imaging spectroradiometer) LST/ f c data and SMOS SM data will be applied. To make the SMOS data spatially consistent with MODIS data, the SMOS SM is disaggregated at 1 km.

VI.5. αPT variablities

The second calibration step consists in inverting the daily αPT when vegetation is covering a significant part of soil (f c > f c,thres ), for the three seasons of rainfed wheat (S1, S2 and S3), by using in-situ data and satellite data, separately. It is reminded that the daily αPT for f c ≤f c,thres is set to the mean daily αPT obtained for f c > f c,thres (Ait Hssaine et al., 2018b).

VI.5.1. Using in-situ data

VI.6. Surface fluxes

The robustness of TSEB and TSEB-SM for partitioning (R n -G) into H and LE is evaluated by considering several hypothesis.1) R n and G are forced to their measured values, for each season separately.

2) The calibration process of TSEB-SM is applied using in-situ and remotely sensed LST, SM and NDVI, separately, at the Terra and Aqua MODIS overpasses.

3) The validation of TSEB and TSEB-SM model output is assessed by using EC measurements (H and LE). The greater scatter between modeled and measured G from the two models reflect the fact that there is a major mismatch in scale between the area sampled by the soil heat flux sensors and

VI.7. Summary and Conclusions

The microwave-derived near-surface soil moisture (SM) from SMOS and thermal-derived land surface temperature (LST) from MODIS are integrated simultaneously within a calibration procedure to retrieve the main parameters of soil evaporation (soil resistance, r ss An analysis of the spatial distributions and the magnitude of the turbulent fluxes using remotely sensing data produced from the two models were conducted. TSEB exhibits larger errors on H and LE estimates. These uncertainties can be linked to the theoretical value of αPT, which is fixed to 1.26 for the whole study period, including both stressed and unstressed conditions, as well as to the scale mismatch between the 1 km resolution of MODIS LST and the footprint size (approximately 1 m) of the ground-based radiometer. The constraint applied on the soil evaporation represented explicitly as a function of SM via a soil resistance term reduces the errors when using TSEB-SM. In fact, the use of the SM derived from microwave data is one of the main controlling factors of the evaporative fraction, which helps to determine with more accuracy the LE/H partitioning.