Energy fluxes estimation at low spatial resolution: Application of the energy balance model SPARSE

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PhD motivation, objectives and methodological approach

The central question of my PhD thesis is the control of agrometeorological models by satellite data from optical and thermal sensors to monitor the crop water budget in semi-arid environments. The general objective of this work, entitled “Spatial estimation of actual evapotranspiration and irrigation volumes using water and energy balance models forced by optical remote sensing data (VIS/ NIR/TIR)”, is to develop and test methods for estimating the hydrological variables related to crop water budget, i.e. evapotranspiration, crop water requirements and irrigation volumes, at scales ranging from plot to regional level and for relatively long time periods (up to the agricultural season). The operational perspective is to provide tools for irrigation and watershed management. Our study area is the Kairouan semi-arid plain located in central Tunisia, occupied by irrigated agriculture and where most of the water is extracted from an overexploited aquifer.
The adopted approach combines field experimentation, modeling and the use of multi-sensor / multi-resolution remote sensing data. Both types of tools used to estimate hydrological variables (ET and irrigation volumes) are: i) a daily water balance model, SAMIR (Simonneaux et al., 2009), simulating water fluxes at a daily time step and ii) an instantaneous energy balance model, SPARSE (Boulet et al., 2015), which characterizes the water status at the satellite overpass time.
For this purpose, two main research focuses have been explored:
 The first was the development of methods to integrate in situ data and high-resolution (VIS-NIR) remote sensing data (SPOT imagery) in the SAMIR model to draw up the spatialized water balance of irrigated areas in the Kairouan plain during four agricultural seasons (2008-2009 and 2011-2014).
The model was calibrated using plot scale measurement of evapotranspiration (eddy correlation) and the control output variables, ET and irrigation volumes were assessed using field fluxes measurements by Extra Large Scintillometer XLAS and irrigation volumes obtained by field surveys, respectively.
 The second focus was to test the performance of the SPARSE energy balance model in monitoring the water status of a heterogeneous landscape in the Kairouan Plain and to determine whether the low-resolution data from Terra-MODIS and Aqua-MODIS satellites in the VIS-NIR and TIR domains were useful for spatializing the key variables of the energy balance in a semi-arid context, i.e. sensible and latent heat fluxes. Validation of the results was carried out by means of the XLAS sensible heat flux measurements. Special attention has been paid to the extrapolation of the instantaneous ET estimates to daily time step for hydrological applications.
This manuscript is organized in five chapters:
– The first chapter reviews general notions concerning the soil water balance components and the various methods to estimate them. A particular interest is given to ET and irrigation with a comparison between water balance and energy balance-based methods for ET modeling. The potential of multi-sensor/multi-resolution spatial remote sensing data in ET modeling is also discussed.
– The second chapter decribes the study area, the experimental set-up and the satellite datasets, as well as the pre-processing of the in situ data.
– The third chapter studies the possibility of using high-resolution VIS-NIR imagery in an agro-meteorological modeling scheme through the SAMIR model (after calibration for irrigated cereal-crops) in order to establish maps of daily ET and irrigation volumes at the scale of the irrigated perimeter for four agricultural seasons (2008-2009 and 2011-2014). Observed irrigation volumes at field, farm and perimeter scale were used to validate the modeled irrigation volumes, while ET derived from the XLAS scintillometer measurements (operated continuously for more than two years from March 2013 to June 2015) was used to validate the modeled ET of the last two seasons.
– In the fourth chapter, the parameterization of SAMIR model was revisited, since the comparison of daily modeled ET with the scintillometer derived ET shows shortcomings mainly attributed to the parameterization of the non calibrated crops (trees and vegetables). Also, the calibration for cereal crops was redone based on both ET (eddy covariance) and soil moisture measurements. Since no calibration was possible for trees and vegetables parameters, they were enhanced based on literature.
– In the last chapter, the operational use of the SPARSE model was tested and the accuracy of the modeled sensible heat flux (H) and of the modeled daily ET over a semi-arid land surface, in a context of high land cover complexity (i.e. trees, winter cereals, summer vegetables) was assessed. The validation was based on the comparison of modeled H and ET with the scintillometer measured H and derived ET, respectively.

Soil water balance components’ estimation methods

The determination of water fluxes at the soil-plant-atmosphere (SPA) interface is of fundamental interest for agro-hydrological management purposes. Information on water balance components under cropped soils is crucial for irrigation planning (Calera et al., 2017) and crop water stress monitoring (Ihuoma and Madramootoo, 2017) at field and regional scales. The water balance equation is usually applied to the unsaturated zone of the soil. Mass conservation is thus expressed for agricultural systems as:
where P is precipitation, I is irrigation, W is contribution from water table by capillary rise, ET is evapotranspiration, R is runoff, D is the deep percolation, Icp is interception and S is soil water storage variation within the time stept in the soil layer where the roots are active to supply water to the plant (between the surface and the root zone depth z in meter). All the term in equation 1.1 are expressed in rates (millimeters per unit time).
Since it is often very difficult to accurately measure all terms of Eq. (1.1), a number of simplifications are generally made. For application over flat terrain, condition that prevails in many agricultural regions, the runoff term R could be neglected (e.g. Holmes, 1984) but, actually, it depends on the occurrence and characteristics of precipitation (amount, duration and intensity) and can only be neglected for a particular type of soil (Jensen et al., 1990), i.e. coarse (sand and loamy sand) and moderately coarse (sandy loam) in absence of other factors such as the presence of crust, overland flow for gravity irrigation etc. On the other hand, deep percolation is a major unknown of equation (1.1). Some researchers suggest that it can be neglected in dry regions (e.g. Holmes, 1984), but actually it depends on the soil depth, slope, permeability and surface storage (Jensen et al., 1990) and needs to be checked in each particular case (Brutsaert, 2013), depending also on the climate and irrigation practices. For operational applications in irrigation management, the soil water balance equation can be expressed in its simplified form as follows:
The precipitation term can be estimated from a network of rainfall stations (rain gauge measurements) or weather radar data (Arkin and Xie, 1994), from satellite-based precipitation products like the Tropical Rainfall Measuring Mission (TRMM) (Huffman et al., 2007), the Global Satellite Mapping of Rainfall (Ushio et al., 2009), the Naval Research Laboratory blended-satellite rainfall technique (Turk et al., 2010) or from meteorological model outputs (Clark et al., 2016). Therefore, the evapotranspiration and irrigation terms become the key terms of the water balance equation.
Strictly speaking, crop water requirement refers to the water transpired by the plant, the water evaporated from the soil and the water stored by the plant for its metabolic processes. Since evaporation from soil (E) and transpiration by the plant (T) occur simultaneously, the term evapotranspiration (ET) is used to describe the total loss of water from vegetated land surfaces to the atmosphere. Furthermore, since the water used for the plant metabolism is substantially negligible as compared to E and T, the term crop water requirement is frequently alternative to evapotranspiration in standard/optimum conditions.
The crop ET under optimal conditions (unstressed crop), referred to as ETc (for “ET crop”), is the evapotranspiration from crops grown under standard management and environmental conditions. When cultivating crops in fields, the actual crop evapotranspiration, referred to as ETa, often deviates from ETc due to non-optimal conditions (pests and diseases, soil salinity, low soil fertility, water scarcity or water logging) that reduce the evapotranspiration rate.
The amount of water required to cover the theoretical water demand by the plant, e.g. ETc, is defined as crop water requirement (CWR). Although the values for ETc and CWR are identical, crop evapotranspiration refers to the amount of water that is evaporated and transpired while CWR refers to the amount of water that needs to be available in the soil for making such crop consumption possible. The CWR always refers to a crop grown under optimal conditions, i.e. a uniform crop, actively growing, completely shading the ground, free of diseases, and favorable soil conditions (including fertility and water). The crop thus reaches its full production potential under the given environment. CWR mainly depends on the weather conditions (major climatic factors influencing the CWR are solar radiation, air temperature and humidity and wind speed), the crop type and the phenological/growing stage of the crop. The influence of the climate on CWR is synthesized into the reference crop evapotranspiration (ETo) which is the evapotranspiration of an hypothetical reference grass cover (Allen et al., 1998). The CWR can be supplied to the crops by rainfall, by irrigation or by a combination of irrigation and rainfall. Efficient agricultural water management requires reliable estimation of the CWR (or ETc) and the corresponding irrigation requirement to meet CWR complementary to rainfall.

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Soil water storage

The water balance computation consists in describing the evolution of the stock of water available in the soil, i.e. the profile distribution of the water content in the various soil horizons.
In order to calculate the soil water budget, an estimate of the soil’s ability to store water is required. Available water capacity is the maximum amount of water a soil can provide to the plant. It is the water held between the soil field capacity (FC) and the permanent wilting point (WP) in the root zone. The FC or drained upper limit (Figure 1.2) is defined as the water content of a soil that has reached equilibrium with gravity after several days of drainage. The WP or lower limit of available water (Figure 1.2) is defined as the water content at which plants can no longer extract a sustainable quantity of water from the soil and begin to wilt. Typical suction values associated with the FC and WP are -3.3 kPa (-0.33 bars) and -1500 kPa (-15 bars) respectively. Like water content, FC and WP are defined as a volume of water per volume of soil. Given these two definitions, the water available for evapotranspiration after drainage i.e. the available water retention capacity is defined as the FC minus the WP.
There are different methods to provide these soil hydrodynamic properties, which are function of soil texture and organic content. They may be prescribed from literature values when available (Table 1.1 gives some typical values of available water retention capacity). The in situ measurement of these properties is costly and time consuming, in addition to implementation difficulties, linked to soil manipulation and data interpretation. Moreover, proxy data on the soil texture, structure, organic matter content, porosity or dry bulk density, can be used to find the hydrodynamic parameters of the soil by applying functional mathematical relationships i.e. pedotransfer functions or PTF. However, PTF performance is quite variable and depends on several factors such as the similarity between the application region and the database’s source region, climate, geology or measurement techniques (Wösten et al., 2001).
For soil water balance calculations, it is necessary to know the total available water retention capacity in a soil profile. This value is typically expressed in mm and can be obtained by integrating the available water-holding capacity over the effective depth of the soil, i.e the soil depth where the roots have access. If the initial soil moisture is unknown, which is usually the case, a soil moisture evolution model can be used to force the net change in soil moisture from the beginning to the end of a specified period (for which the soil moisture at the end can be considered similar to one at the beginning, e.g. an hydrological year), use the final moisture profile as the initial one and run the model again over the same period, and repeat the process until the first and the last profile of the period are similar (long-term equilibrium) according to a given precision (Ghosh, 2016); this method is called “spin-up”.
Wang-Erlandsson et al. (2016) described six approaches for the root zone water storage capacity estimation, and showed that remote sensing-based studies are generally based on field observations and look up tables (Sánchez et al., 2010; Sánchez et al., 2012).

Evapotranspiration

The evapotranspiration process involves a phase change of water from liquid to gaseous state, with latent heat requirement of about 2.47 MJ per kg of water evaporated. Most of the energy required in ET process comes from solar and atmospheric radiation. The large amount of energy involved in the processes of evaporation and transpiration means a coupling between the water and energy cycles. Actual ET (ETa)– or its energy equivalent, the total latent heat flux LE (E is the rate of evaporation of water [kg.m-2.s-1] and L is the latent heat of vaporization of water [J.kg-1]) – depends on three factors: weather, soil water availability and vegetation cover, which are highly variable in time and space. Depending on the application, an estimation of ETa is required at hourly (weather applications), daily (hydrology, agronomy) or monthly (surface-subsurface interactions) time steps (Lagouarde and Boulet, 2016).
Transpiration occurs through different organs, involving many processes. It is driven by the water vapor difference between the stomata cavity and the surrounding air: as water evaporates through the stomata, it creates a negative pressure (also called tension or suction) within the leaves and the xylem cells, which exerts a pulling force on the water in the soil to be absorbed by the roots and draws the water upward from the root system to the air system by the conductive system. Water is then disseminated in liquid form through the leaf intercellular spaces and stomata (small orifices of a few micrometers in diameter ensuring and regulating the gas exchange (CO2 and H2O) between the plant and the atmosphere); T includes the transfer towards the atmosphere through the boundary layer around the leaf.
In addition to the intrinsic specificities of the plant itself, root extraction depends on soil texture, soil moisture, and the climatic conditions. If the water is insufficiently abundant in the soil, the plant is under water stress and the leaf potential decreases. The critical leaf potential represents the water potential of the stomata under which the plant can no longer extract water to the atmospher. When this threshold is reached, the plant adapts its morphology to meet its needs, reducing for example the opening of the stomata, developing its root system or decreasing its leaf area.
The capability to predict levels of actual ET is a valuable asset for water resource managers, as it describes the water consumption from vegetation. ET can be either measured or estimated via modeling (even though most models require field measurements). Conventionally, if ET is quantified by the use of an instrument, it is ‘directly’ measured and when it is found by means of a relationship among several observations, it is ‘indirectly’ measured (Rana and Katerji, 2000). Conversely, ET is considered as ‘estimated’ if it is expressed by a model.

Direct measurements of ET

The ET measurement methods are based on concepts which can be critical under semi-arid and arid environments for several reasons: (i) representativeness (ii) instrumentation (iii) microclimate and (iv) applicability. Therefore, to establish the degree of accuracy of the obtained ET measurement and the validity of a method, it is necessary to consider all these parameters (Allen et al., 2011b).

Table of contents :

Chapter 1: Soil water balance components’ estimation methods
1.1 Soil water storage
1.2 Evapotranspiration
1.2.1 Direct measurements of ET
1.2.1.1 Hydrological approach: Weighing lysimeters
1.2.1.2 Plant physiology approaches
1.2.1.3 Micrometeorological approaches
1.2.2 Remote sensing based method for ET estimation
1.2.2.1 Surface energy budget methods
1.2.2.2 Soil water balance method: crop coefficient approach
1.2.2.3 Deterministic methods
1.2.2.4 Inter comparisons of ET estimation methods
1.3 Irrigation
1.3.1 How much water is given?
1.3.2 When water is given?
1.3.3 How often water is given?
1.3.4 Plant response to water stress
1.3.5 Irrigation efficiencies
1.4 Synthesis
Chapter 2: Study area and data processing
2.1 Study area description
2.1.1 Geographic location
2.1.2 Climat data
2.1.2.1 Rainfall
2.1.2.2 Temperature
2.1.2.3 Relative humidity
2.1.2.4 Wind conditions
2.1.3 Water Resources
2.1.3.1 Surface water resources
2.1.3.2 Groundwater resources
2.2 Land use maps
2.3 Observed irrigation data
2.4 Remote sensing data
2.4.1 High-resolution satellite imagery
2.4.2 Low-resolution satellite imagery
2.5 In situ data
2.5.1 Meteorological data
2.5.2 Flux and soil moisture data
2.5.3 Extra large aperture scintillomter (XLAS)
2.5.3.1 Scintillometer derived fluxes
2.5.3.2 XLAS footprint computation
2.5.3.3 XLAS derived latent heat flux
2.6 Synthesis
Chapter 3: Evapotranspiration and irrigation volumes estimation at high spatial resolution: application of the soil water balance model SAMIR
3.1 SAMIR model description
3.2 Irrigation volumes results validation at perimeter scale: Published results (article) 92
3.3 Unpublished results and additional analyzes
3.3.1 Irrigation volumes results validation at perimeter scale for the 2013-2014 season
3.3.2 Irrigation volumes results validation at field and farm scales
3.3.3 Evapotranspiration results validation using the XLAS data
3.4 Synthesis and partial conclusion
Chapter 4: Revisiting SAMIR parameters setting for evapotranspiration and irrigation spatialization
4.1 SAMIR model calibration
4.1.1 Second calibration on cereals fields
4.1.2 Calibration for the olive orchard
4.2 Model parameters setting
4.3 Validation of new modeled irrigation volumes at perimeter scale
4.4 New evapotranspiration results validation using the XLAS data
4.5 Synthesis and partial conclusion
Chapter 5: Energy fluxes estimation at low spatial resolution: Application of the energy balance model SPARSE
5.1 SPARSE model description
5.1.1 Input data
5.1.2 Algorithm
5.2 Validation of instantaneous and daily SPARSE model estimates using the XLAS data: Published results (article)
5.3 Synthesis and partial conclusion
General conclusion and perspectives
Major findings
Limitations of the methods and models
Perspectives and future plans

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