Validation of TSEB model over sparse and heterogeneous vegetation in Sahel region (Niger)

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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 (Allen et al., 2011). 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 (Aston, 1985; Black and McNaughton, 1971; Euser et al., 2014; Jara et al., 1998; Peacock and Hess, 2004). The Bowen ratio can be determined as the ratio of the gradients of temperature and vapor pressure across two fixed heights above the surface (Bowen, 1926) or as the ratio of the sensible and latent heat flux: β = H =LE ∆e ∆T (I.4).

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 (Brutsaert, 1982; Mcnaughton and Spriggs, 1989) by: H + LE = Rn − G (I.8).
where H is the sensible heat flux, LE is the latent heat flux,Rnis 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/m2 . Additional energy flux components that could also be included are photosynthesis (Stewart and Gay, 1989) and vegetation canopy storage (Shuttleworth and Wallace, 1985), but for short-term measurements, or for non-forested regions, these terms are negligible (Brutsaert, 1982; Stewart and Thom, 1973). The difference Rn − 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*Rn for fully developed plant cover, and 0.5*Rn for bare soil) (Kustas and Norman, 1996) or as a variable fraction depending on different parameters such as canopy fraction and soil characteristics (Bastiaanssen et al., 1998; Kustas et al., 1993; Su, 2002).
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 (Kalma et al., 2008; Overgaard et al., 2006):
• 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 (Monteith, 1965; Penman, 1948): (ii) Models taking into account vegetation and bare soil as two separate sources for energy transfers (Shuttleworth and Wallace, 1985); (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.

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, single-source 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. Kustas et al. (1990) 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; Bastiaanssen et al., 1998), Simplified Surface Energy Balance Index (S-SEBI; Roerink et al., 2000), Surface Energy Balance System (SEBS; Su, 2002), Mapping ET at High Resolution with Internalized Calibration (METRIC; Allen et al., 2007), and Operational Simplified Surface Energy Balance (SSEBop; Senay et al., 2013, 2001).

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 (Boulet, 1991; Lhomme and Chehbouni, 1999). 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 (Blyth and Harding, 1995; William P. Kustas and Norman, 1997; Norman et al., 1995). 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 » (Norman et al., 1995), Mapping Evapotranspiration with Internalized Calibration « METRIC » (Allen et al., 2007), and the Two-source Trapezoid Model for Evapotranspiration « TTME » (Long and Singh, 2012).

Models based on Land Surface Temperature

The spatial modeling has become a dominant means to estimate ET fluxes over regional and continental areas (Anderson et al., 2007; Fisher et al., 2017). 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 (Zhou et al., 2014). 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 Norman et al. (1995) has been showing high robustness for a wide range of landscapes (Colaizzi et al., 2012). 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 (fc) 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 (Priestley et al., 1972). 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 (Fisher et al., 2008). Recently, Boulet et al. (2015) 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 (Boulet et al., 2015).

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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. Nemani et al. (1993) 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 Carlson et al. (1995) and Gillies and Carlson, (1995) 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 (Schmugge et al., 2002). 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 (Balenzano et al., 2011). 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 (Satalino et al., 2014). Therefore, global SM products are generally derived from the radiometers such as the C-band Advanced Microwave Scanning Radiometer (AMSR-E) (Njoku et al., 2003) on the Earth Observing System (EOS) Aqua satellite launched on May 2002. The AMSR-E instrument provides the SM at approximately 60 km resolution (4-8 GHz). The first L-band mission dedicated to SM monitoring is the Soil Moisture and Ocean Salinity (SMOS) mission (Kerr et al., 2010) 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 (Entekhabi et al., 2010) 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.

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 (Merlin et al., 2016) or from a combination of LST and SM data under bare soil conditions (Merlin et al., 2018).

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 Malbéteau et al. (2016).
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.
Finally, DisPATCh converts the high-resolution optical-derived SEE fields into high- resolution SM fields given a semi-empirical SEE model and a first-order Taylor series expansion around the SMOS observation.

Table of contents :

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
I.3.3. Surface Energy Balance (SEB) models
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. Objectives
Chapter.II. Modeling approaches : Description and implementation
II.1. Introduction
II.2. TSEB Model Description and Implementation
II.2.1. Algorithm for solving the energy balance and the equation system
II.2.2. Calibration procedure
II.3. TSEB-SM Model Description and Implementation
II.3.1. Algorithm for solving the energy balance and the equation system
II.3.2. Calibration procedure
II.4. Aggregation scheme
II.5. Disaggregation model of SM data
II.6. Conclusion
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
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
Chapter.V. Improving TSEB model by integrating sm data (TSEB-SM): a feasibility study using in-situ data (LST, 𝐟𝐜and SM)
V.1. Introduction
V.2. TSEB-SM Model Description and Implementation
V.3. Retrieving (arss, brss) and αPT parameters
V.3.1. Calibration first step
V.3.2. Calibration 2nd step
V.3.3. Calibration 3th step
V.4. Results
V.4.1. Interpretation of αPT variabilities
V.4.2. Surface fluxes
V.5. Summary and Conclusions
Chapter.VI. Remote sensing application of TSEB-SM (combining DisPATCh SM and MODIS LST data for mapping ET at 1 km resolution
VI.1. Introduction
VI.2. TSEB-SM Model improvements
VI.3. Accuracy of Remote Sensing data
VI.4. Retrieving (arss, brss) parameters
VI.5. αPT variablities
VI.5.1. Using in-situ data
VI.5.2. Using satellite data
VI.5.3. Interpretation of αPT variabilities
VI.6. Surface fluxes
VI.6.1. Using in-situ data
VI.6.2. Using satellite data
VI.7. Summary and Conclusions
Chapter.VII. Conclusion and perspectives


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