Generally, all such models are based on energy conservation principles which dictate that net radiation RN (W m-2) is balanced by the soil heat flux (G, W m-2), sensible heat flux (H, W m-2) and latent heat flux (LE, W m-2) at the surface:RN=G+H+LE(1)Figure 1.Schematic diagram of one-source thermal-based model for energy balance terms.Generally, it is assumed that RN may be easily computed, and G is parameterized in a straightforward fashion (as a simple proportion of RN). The two remaining terms, H and LE, are turbulent flux quantities and are the most difficult to estimate.In the study, net radiation was estimated as:RN=Rs(1?r)+?a��Ta4??s��Ts4(2)where Rs is the incoming short wave radiation (Wm-2) measured by pyranometers, �� is the Stefan-Boltzman constant (5.
67 10-8 Wsm-2K-4), �� is emissivity and T is the temperature (K) with the subscripts ��a�� and ��s�� for air and surface respectively; the surface albedo (r) is computed from the formulation proposed by Menenti in 1984 (see Table 1).Table 1.Vegetation parameters and vegetation indices analysed in the work.Soil heat flux was calculated by assuming that the ratio G/RN is related to the fractional vegetation cover [8]. For vegetated surfaces the term G/RN is less with respect to bare soil because of the partial extinction of net radiation by the vegetation cover. Because spectral vegetation indices (VIs) are proportional to the net radiation extinction by the canopy, the VI can be used as a linear scaling factor to estimate G/RN over vegetated fields [25].
In order to avoid the calibration of the relationship between G/RN and VIs, it is assumed here that G/RN is related to the fractional vegetation cover by Eq. 3. The fractional vegetation cover is estimated from LAI.(G/RN)=fv(G/RN)veg+(1?fv)?(G/RN)soil(3)with GSK-3 (G/RN)veg=0.05, (G/RN)soil=0.315, and fv estimated from LAI.The terms of Eq. (1) are modelled using a 1-D flux-gradient expression based on a convection analogue to Ohm’s law:H=��CpTs?Tarah(4)where �� is air density (Kg m-3), Cp is the specific heat of air at a constant pressure (J kg-1 K-1) and rah is the aerodynamic resistance for sensible heat (s m-1). Eq. 4 is a one-layer bulk transfer equation based on the assumption that the radiometric temperature measured by a thermal infrared radiometer is identical to aerodynamic temperature. In fact, in the case of full canopy cover, there is near-equivalence between these two temperatures and it is found that estimates of evapotraspiration using radiometric temperatures are in good agreement with observed values [10, 26-27].
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