Modeling evapotranspiration in a spring wheat from thermal radiometry: crop coefficients and E/T partitioning

Abstract

Wheat is one of the crops occupying the largest areas in the world (218 million ha in 2013). Understanding the land–atmosphere energy exchanges over these croplands becomes important not only for agronomy but also for climatic and meteorological aspects. This study continues previous work on the estimation of actual evapotranspiration (ET) and the assessment of crop coefficients of sorghum, sunflower, or canola. Two variations of a simple two-source energy balance (STSEB) approach were used in combination with land surface temperature measurements to calculate hourly and daily values of surface fluxes and actual ET. An experiment was carried out during the spring season of 2014 in Las Tiesas experimental farm in Barrax, Spain. Soil and canopy temperature components together with meteorological variables and biophysical parameters were measured from planting to senescence. Comparison to lysimeter measurements showed calculation errors of ±0.11 mm h⁻¹ and ±0.8 mm day⁻¹ for hourly and daily ET values, respectively, whereas an underestimation no >4 % resulted from the entire campaign. Partition between soil and canopy components yielded a ratio of evaporation (E) to transpiration (T) of 36–64 %, respectively, for the total growing season. Dual crop coefficients were also calculated and compared to those proposed by FAO-56. Although separate E and T measurements were not available, similar results between the STSEB and FAO-56 models demonstrate the utility of the STSEB for investigating management strategies aimed at increasing crop water use efficiency.

Appendix

The original formulation of the simplified two-source energy balance model (STSEB) (Sánchez et al. 2008) used the measured temperature of both soil (T _s) and canopy (T _c) components to calculate the different terms of the energy balance equation:

$$R_{\text{n}} = H + {\text{ET}} + G$$

(1)

where R _n is the net radiation flux (W m⁻²), H is the sensible heat flux (W m⁻²), ET is the latent heat flux (W m⁻²), and G is the soil heat flux (W m⁻²).

According to the STSEB approach, the sum of the soil and canopy contributions (values per unit area of component) to the total sensible heat flux, H _s and H _c, respectively, are weighted by their respective partial areas as follows:

$$H = P_{\text{v}} H_{\text{c}} + (1 - P_{\text{v}} )H_{\text{s}}$$

(2)

where P _v is the vegetation cover fraction at nadir. In Eq. (2), H _s and H _c are expressed as:

$$H_{\text{c}} = \rho C_{\text{p}} \frac{{T_{\text{c}} - T_{\text{a}} }}{{r_{\text{a}}^{\text{h}} }}$$

(3a)

$$H_{\text{s}} = \rho C_{\text{p}} \frac{{T_{\text{s}} - T_{\text{a}} }}{{r_{\text{a}}^{\text{a}} + r_{\text{a}}^{\text{s}} }}$$

(3b)

where ρC _p is the volumetric heat capacity of air (J K⁻¹m⁻³), T _a is the air temperature at a reference height (h), $r_{\text{a}}^{\text{h}}$ is the aerodynamic resistance to heat transfer between the canopy and the reference height at which the atmospheric data are measured (s m⁻¹), $r_{\text{a}}^{\text{a}}$ is the aerodynamic resistance to heat transfer between the point z _0M + d (z _0M: canopy roughness length for momentum, d: displacement height) and the reference height (s m⁻¹), and $r_{\text{a}}^{\text{s}}$ is the aerodynamic resistance to heat flow in the boundary layer immediately above the soil surface (s m⁻¹). A summary of the expressions to estimate these resistances can be found in Sánchez et al. (2008). Equations (3a) and (3b) are taken from the parallel configuration of the TSEB model (Norman et al. 1995; Li et al. 2005), modified to take into account the distinction between $r_{\text{a}}^{\text{h}}$ and $r_{\text{a}}^{\text{a}}$ (Sánchez et al. 2008).

The partitioning of the net radiation flux, R _n, between the soil and canopy is proposed as follows:

$$R_{\text{n}} = P_{\text{v}} R_{\text{nc}} + (1 - P_{\text{v}} )R_{\text{ns}}$$

(4)

where R _nc and R _ns are the contributions (values per unit area of component) of the canopy and soil, respectively, to the total net radiation flux. They are estimated by establishing a balance between the long-wave and the short-wave radiation separately for each component:

$$R_{\text{nc}} = (1 - \alpha_{\text{c}} )S + \varepsilon_{\text{c}} L_{\text{sky}} - \varepsilon_{\text{c}} \sigma T_{\text{c}}^{4}$$

(5a)

$$R_{\text{ns}} = (1 - \alpha_{\text{s}} )S + \varepsilon_{\text{s}} L_{\text{sky}} - \varepsilon_{\text{s}} \sigma T_{\text{s}}^{4}$$

(5b)

where S is the solar global radiation (W m⁻²), α _s and α _c are soil and canopy albedos, respectively, σ is the Stefan–Boltzmann constant, and L _sky is the incident long-wave radiation (W m⁻²).

A similar expression is used to combine the soil and canopy contributions, ET_s and ET_c, respectively, to the total latent heat flux:

$${\text{ET}} = P_{\text{v}} ET_{\text{c}} + (1 - P_{\text{v}} ){\text{ET}}_{\text{s}}$$

(6)

According to this framework, a complete and independent energy balance between the atmosphere and each component of the surface is established from the assumption that all the fluxes act vertically. In this way, the component fluxes to the total latent heat flux can be written as:

$${\text{ET}}_{\text{c}} = R_{\text{nc}} - H_{\text{c}}$$

(7a)

$${\text{ET}}_{\text{s}} = R_{\text{ns}} - H_{\text{s}} - \frac{G}{{(1 - P_{\text{v}} )}}$$

(7b)

Finally, G can be estimated as a fraction (C _G) of the soil contribution to the net radiation (Choudhury et al. 1987):

$$G = C_{\text{G}} (1 - P_{\text{v}} )R_{\text{ns}}$$

(8)

where C _G can vary in a range of 0.2–0.5 depending on the soil type and moisture. A value of C _G = 0.35 was used in this work.

When the composed target temperature (T _R) is the only measurement available, the original formulation of the STSEB needs the inclusion of additional assumptions to calculate, for example, an initial estimate of canopy latent heat flux. In this STSEB-T_R approach, the Priestley–Taylor equation was used:

$${\text{ET}}_{\text{c}} = f_{\text{g}} \alpha \left[ {\frac{\varDelta }{\varDelta + \gamma }} \right]R_{\text{nc}}$$

(9)

where f _g is the fraction of the vegetation that is green, Δ is the slope of the water vapor saturation curve, α is the Priestley–Taylor (PT) parameter (Priestley and Taylor 1972), and γ is the psychrometric constant. A value of α = 1.26 was assumed in this study, according to the non-water-stressed conditions over this wheat field (French et al. 2007). Note that this value might need adjustment under water-stressed conditions.

An initial value of T _c is extracted by solving the equation resulting from the combination of (5a), (7a), and (9). Then, the corresponding value of T _s can be calculated from the equation (Sánchez et al. 2008):

$$\varepsilon T_{\text{R}}^{4} = P_{\text{v}} \varepsilon_{\text{c}} T_{\text{c}}^{4} + (1 - P_{\text{v}} )\varepsilon_{\text{s}} T_{\text{s}}^{4}$$

(10)

where ε _c and ε _s are the canopy and soil emissivities, respectively, ε is the effective surface emissivity. Once T _c and T _s values are estimated, Eqs. (2)–(8) can be applied.