Soil water balance components’ estimation methods

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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).


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 []) – 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).

Hydrological approach: Weighing lysimeters

Weighing lysimeters have been developed to give a direct measurement of ET. In general, it is a device, a tank or container, to define the water movement across a boundary (depth level of the soil). Lysimeters of many different designs, sizes, shapes, and measurement systems have been built over the years (Howell et al., 1991). The main advantage of the lysimeter in situ measurements is that water consumption of vegetation can be performed under approximately realistic field conditions. However, a lysimeter measurement requires elaborate preparation. Moreover it is typically limited to only few individual trees or a small surface area of agricultural crops (Verstraeten et al., 2008). A Major limitation of lysimeters is that capillary rise is not taken into consideration because the water table can be supposed to be at a considerable depth (Makkink, 1959); moreover, root extension is sometimes limited.

Plant physiology approaches

Methods based on plant physiology either measure the water loss from a whole plant or a group of plants. They may include methods such as tracer technique and porometry but here, only two of the most common methods will be analysed: the sap flow method and the chamber system.

Sap flow method

Sap flow measures only plant transpiration by means of simple accurate models; sap flow can be measured by two basic methods: (i) heat pulse and (ii) heat balance. The most popular sap flow method is the heat balance method, based on the concepts proposed by Čermák et al. (1973) and Steinberg et al. (1990). The plant transpiration can be estimated by determining the sap mass flow; this is done using gauges that are attached to or inserted in the plant stem. For the heat balance method, a heater element is placed around the plant stem to provide energy to the system. Thermocouples are used to determine how much heat is lost by conduction up, down and radially in the stem from the heater element. The difference between the heat input and these losses is assumed to be dissipated by convection with the sap flow up the stem and may be directly related to water flow (Kjelgaard et al., 1997). The mass flow rate F [g.t-1] is expressed by the relationship:
(1. 3) where Qh is input heat, Qv is vertical conductive heat, Qr is radial heat loss to environment, cw [J.g-1.K-1] is specific heat of water and δT is the temperature difference between the upstream and downstream thermocouples.
Direct measurements of actual transpiration can also be performed with the heat pulse-sap flow technique, which has been applied in vineyards (Yunusa et al., 2004) and olive groves (Testi et al., 2006; Williams et al., 2004). Sap flow method is a very good alternative to lysimeter experiments; however, operation of sap-flow sensors requires a vast technical input and maintenance effort.

Chambers system

The chamber system method was described for the first time by Reicosky and Peters, (1977). The first chambers system version was portable (by means of a tractor, for example) and the ET rate was calculated as a difference (latent heat storage) between two measurements by a psychrometer: one acquisition before the chamber was lowered on the plot and another one minute later. Chambers system is easier to implement than the weighing lysimeter (Reicosky et al., 1983), but it is not suitable for long term ET measurements. The most serious problem of almost all chambers is the microclimate modification (solar radiation balance; air temperature, wind speed) during the measurement period.

Micrometeorological approaches

ET consumes energy; this energy corresponds to what is required to transport water from the inner intercellular space in the leaves and plant organs to the atmosphere; it is therefore expressed as a flux density in [W.m-2].
Micrometeorological methods based on physical principles require accurate measurements of meteorological parameters on a small temporal scale (1 h or less). Their accuracy depends on the validity of some hypothesis such as the flux conservation, which implies that measurements are performed over a large flat area with uniform vegetation.


Aerodynamic method

Assuming that a flux density can be related to the gradient of the concentration in the atmospheric surface layer (ASL), the latent heat flux by the aerodynamic technique can be determined directly by means measurement of the vapour pressure at different heights above the crop. LE is then calculated by means of the scaling factors u* and q* (Grant, 1975; Saugier and Ripley, 1978):
where k=0.41 is the von Karman constant, d (m) is the zero plane displacement height, z0 (m) is the roughness length of the surface and ψm is the stability correction function for momentum transport. q* is determined similarly from the humidity profile measurement:
where q0 is the air humidity extrapolated at z=d+z0 and ψv is the stability correction function for latent heat transport.
The major difficulty with this technique is the correct measurement of the vapor pressure at different heights above the crop. For this reason, LE can also be derived indirectly by the energy balance (see section where the sensible heat flux can be determined by the flux-gradient relation for temperatures:
where cp [] is the specific heat of air at constant pressure, ρ [kg.m-3] is density of air and T*, the temperature scale, is deduced by the air temperature profile:
Under this form, the main advantage of the aerodynamic technique consists in avoiding complex high frequency humidity measurements. Nevertheless, the accuracy depends on the number of measurement levels for the wind speed and temperature profiles. In fact, equations (1.8) and (1.9) require at least three or four levels (Webb, 1965), but accuracy is improved when many more levels are used (Wiernga, 1993). This method showed good results (Pieri and Fuchs, 1990), when the stability correction functions of Dyer and Hicks (1970) and Paulson (1970) were used.

Eddy covariance

The transport of scalar (vapor, heat, carbon dioxide CO2) and vectorial amounts (i.e. momentum) in the lower atmosphere in contact with the canopies is mostly governed by air turbulence. In recent decades, methods for measuring turbulent flows have been been improved, both in terms of reliability and in terms of operationality. The eddy covariance method (EC) is considered as the standard method for measuring surface turbulent fluxes. The first complete scientific contributions to this topic were given by Dyer (1961) and Hicks (1970); extensive details of the theory can be found in Baldocchi, (2003), Falge (2017) and Stull (2012) .
EC method is a direct measurement of the turbulence in order to get the surface fluxes of sensible and latent heat and of CO2 with high accuracy.
The mean vertical flux density ( ) of a physical quantity (X, for example temperature, water vapor or CO2) in the turbulent layer is proportional to the covariance between the vertical velocity ( ) and the concentration of this quantity (Van Dijk, 2004). In general, the instantaneous vertical flux density ( ) per unit of time and surface can be written:
Using the Reynolds decomposition ( and ), the average flux ( )
can be approximated by the following formula:
By expanding this expression and using the fact that and the fluctuations mean is
zero, equation (1.10) becomes:
In a horizontal homogeneous boundary layer flow, the average vertical wind speed is zero
by definition (Brunet Y., 1995), hence .
Finally, for the flux density, we obtain:
Turbulent fluxes (momentum, sensible heat, latent heat and gas concentration) can be expressed as the product of the vertical wind speed fluctuations term by the considered quantity fluctuations term.
To measure ET directly by the EC method, vertical wind fluctuations have to be measured (by the sonic anemometer) and acquired synchronously to the vapour density fluctuations (by fast response hygrometer); both have to be acquired at a typical frequency of 10–20 Hz.
Despite problems linked to the correct management of the sensors, complex data processing, and the management of ‘closure error’ (the sum of measured LE+H does not equal measured Rn−G) of about 10-30% (Foken, 2008; Twine et al., 2000; Wilson et al., 2002), this method has very good performances both at hourly and daily scale, also in semi-arid environments. Examples of eddy correlation measurements can be found in Er-Raki et al. (2009), Hoedjes et al. (2007), Hoedjes et al. (2008), Liu et al. (2016) and Williams et al. (2004). The EC method has the advantage of allowing the measurement of the fluxes of all kinds of molecules other than water, and in particular CO2.


Large-scale turbulent fluxes are difficult to evaluate since the above methods are mostly valid only on small homogeneous surfaces. Indeed, the heterogeneity of most landscapes generates large flux variability, which is difficult to measure with the conventional techniques. Hence, indirect turbulent flow measurement techniques have been developed, the most promising is the scintillometery. Scintillometry has emerged as one of the most widely used tools to quantify average fluxes over heterogeneous land surfaces (Brunsell et al., 2011). Scintillometer operating at wavelengths λ of about 1μm are called optical scintillometer, whereas when λ is ranged between 1 and 10 mm these are called microwave scintillometers.
Scintillometer consists of a transmitter and a receiver at both ends of an atmospheric propagation path (measurement transect). Fluxes of sensible heat and momentum cause atmospheric turbulence close to the ground, and creates, with surface evaporation, refractive index fluctuations due mainly to air temperature and humidity fluctuations (Hill et al., 1980). The receiver detects and evaluates the intensity fluctuations of the transmitted signal, called scintillations, which are linked to surface fluxes of sensible and latent heat. The magnitude of the fluctuations in the refractive index is usually measured in terms of a structure parameter of the refractive index of air integrated along the optical
path [m-2/3] (Tatarskii, 1961). Scintillometers measure sensible and latent heat fluxes (H and LE) by relating to the structure parameter of temperature and the structure parameter of humidity , respectively, through the Monin Obukhov stability parameters. Temperature fluctuations given by are the dominant cause of scintillation in the optical wavelengths, and therefore optical scintillometers can be applied to measure H without making measurements of, or assumptions on, humidity fluctuations. Scintillometers can provide average H estimates over areas comparable to those observed by satellites (Hemakumara et al., 2003; Lagouarde et al., 2002) along a path length ranginge from a few hundred meters to 5 km (the case of large aperture scintillometers LAS) up to 10 km (the case of extra large aperture scintillometers XLAS).
Since the optical scintillometer provides spatially averaged H, LE can be computed as the energy balance residual term (LE =Rn-G-H) assuming 100% energy balance closure. The estimation of a representative value for the available energy (Rn-G) across the transect is therefore crucial for the accuracy of LE retrieved values.
Since the upwind area contributing to the flux (i.e. the flux footprint) varies according to wind direction and atmospheric stability, it must be estimated if one wants to compare scintillometer measurements to, say, pixel derived estimates of the flux (Brunsell et al., 2011). The footprint of a flux measurement defines the spatial context of the measurement, i.e. the source areas that influence the sensors. Assessing the upwind area contributing to the flux can be done using several footprint models (Horst and Weil, 1992; Leclerc and Thurtell, 1990). These models have been developed to determine what area is contributing the the flux. Contributions of upwind locations to the measurement depend on the height of the vegetation, height of the instrumentation, wind speed, wind direction, and atmospheric stability conditions (Chávez et al., 2005).
The scintillometry technique has been evaluated and analyzed over heterogeneous landscapes against EC measurements (Bai et al., 2009; Chehbouni et al., 2000; Ezzahar et al., 2009) and also against model outputs (Marx et al., 2008; Samain et al., 2012; Watts et al., 2000). Few studies dealt with extra large aperture scintillometer (XLAS) data (Kohsiek et al., 2006; Kohsiek et al., 2002; Moene et al., 2006). An historical survey, the theoretical rationale as well as recent works in applied research are reviewed in De Bruin and Wang (2017). Calculations of the sensible heat flux measured by scintillometry as well as the footprint computation are detailed in the next chapter (see section 2.5.3).

Table of contents :

Chapter 1: Soil water balance components’ estimation methods
.1 Soil water storage
.2 Evapotranspiration
.2.1 Direct measurements of ET
.2.1.1 Hydrological approach: Weighing lysimeters
.2.1.2 Plant physiology approaches
.2.1.3 Micrometeorological approaches
.2.2 Remote sensing based method for ET estimation
.2.2.1 Surface energy budget methods
.2.2.2 Soil water balance method: crop coefficient approach
.2.2.3 Deterministic methods
.2.2.4 Inter comparisons of ET estimation methods
.3 Irrigation
.3.1 How much water is given?
.3.2 When water is given?
.3.3 How often water is given?
.3.4 Plant response to water stress
.3.5 Irrigation efficiencies
.4 Synthesis
Chapter 2: Study area and data processing
.1 Study area description
.1.1 Geographic location
.1.2 Climat data
.1.2.1 Rainfall
.1.2.2 Temperature
.1.2.3 Relative humidity
.1.2.4 Wind conditions
.1.3 Water Resources
.1.3.1 Surface water resources
.1.3.2 Groundwater resources
.2 Land use maps
.3 Observed irrigation data
.4 Remote sensing data
.4.1 High-resolution satellite imagery
.4.2 Low-resolution satellite imagery
.5 In situ data
.5.1 Meteorological data
.5.2 Flux and soil moisture data
.5.3 Extra large aperture scintillomter (XLAS)
.5.3.1 Scintillometer derived fluxes
.5.3.2 XLAS footprint computation
.5.3.3 XLAS derived latent heat flux
.6 Synthesis
Chapter 3: Evapotranspiration and irrigation volumes estimation at high spatial resolution: application of the soil water balance model SAMIR
.1 SAMIR model description
.2 Irrigation volumes results validation at perimeter scale: Published results (article) 92
.3 Unpublished results and additional analyzes
.3.1 Irrigation volumes results validation at perimeter scale for the 2013-2014 season
.3.2 Irrigation volumes results validation at field and farm scales
.3.3 Evapotranspiration results validation using the XLAS data
.4 Synthesis and partial conclusion
Chapter 4: Revisiting SAMIR parameters setting for evapotranspiration and irrigation spatialization
.1 SAMIR model calibration
.1.1 Second calibration on cereals fields
.1.2 Calibration for the olive orchard
.2 Model parameters setting
.3 Validation of new modeled irrigation volumes at perimeter scale
.4 New evapotranspiration results validation using the XLAS data
.5 Synthesis and partial conclusion
Chapter 5: Energy fluxes estimation at low spatial resolution: Application of the energy balance model SPARSE
.1 SPARSE model description
.1.1 Input data
.1.2 Algorithm
.2 Validation of instantaneous and daily SPARSE model estimates using the XLAS data: Published results (article)


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