## Applicability of the Penman Monteith Equation

The PM equation (5.2) can be utilized for the direct calculation of crop ET because the surface and aerodynamic resistances are crop specific. However, despite research, data are available only for a limited number of crops. Typical values for rl and rs are given in reviews by Garratt [29] and Allen etal. [10]. For zom and d and information on predicting LAI, see Allen et al. [10].

The computation of ra with Eqs. (5.4) and (5.5) for partial cover crops presents some problems relative to the predictive calculation of the roughness length zom and the zero plane displacement height d. For partial cover crops, it is necessary to treat the soil and the crop separately, thus considering two surface resistances [30, 31]. Shuttleworth and Wallace [32] developed a specific model for partial cover crops, which considers a more complex but rational separation of fluxes from the soil surface up to the canopy boundary layer. Good results have been obtained with that model [33]. The applicability of the "big leaf" approach to partial cover crops is questionable.

There is very little information on the early crop growth stages, when LAI is small. For the partial cover crops, approaches are still insufficient. Information is also scarce for fruit crops. For conditions of incomplete ground cover, other problems include the roughness of the surface and the variable albedo of the surface, which is now a combination of vegetation and soil, thus affecting the calculation of net radiation Rn.

Other difficulties concern the prediction of the surface resistance rs. There is relatively little information on bulk stomatal resistances rl characterizing a given crop; rl usually increases as a crop matures and begins to ripen. The use of prediction equations is difficult because of differences among varieties and in crop management. Information on stomatal conductance or stomatal resistances available in the literature is often oriented to physiological or ecophysiological studies and is not easy to use predictively with Eq. (5.6). There are also difficulties in measuring or estimating the LAI and plant height h over time [10].

It is well known that resistances r¡ and rs are influenced by climate and water availability to the crop. Influences change from one crop to another and different varieties can be affected differently. Surface resistance rs increases when the crop is water stressed or when soil water availability limits crop ET, when the VPD increases, and when ra is higher. On the contrary, rs decreases when energy available at the surface increases. However, all factors act together. The dependency of surface resistances on the climate is described by several authors [4, 11, 34-38]. It can be demonstrated [39] that rs varies according to

(- \ , x P cpVPD „ , rs = rJ -0 - 1 + (1 + 0) P p , (5.9)

where all parameters are defined as for the PM equation (5.2) and 0 is the Bowen ratio, 0 = H/kET. In this equation, 0 plays the role of a water stress indicator. This equation illustrates that weather variables interact and that their influences are interdependent. This brings into consideration the difficulties in appropriately selecting the rs to be utilized predictively, unless appropriate simplifications are assumed.

Despite these difficulties, many recent studies have advocated using the PM formulation for estimating ET. McNaughton and Jarvis [40], Sharma [41], Hatfield and Fuchs [42], and Burman and Pochop [43] considered the PM equation to be the most acceptable form of the combination equation for computing crop and reference ET. The PM approach is commonly utilized in field studies of crop evapotranspiration (e.g., [7, 44-48]). Several crop-water models use the PM equation predictively, as do environmental models (e.g., [49-51]). This equation also is utilized widely in hydrology, particularly to predict ET from forests [52].

The difficulties referred to earlier create challenges in applying the PM equation or other more complex multilayer resistance equations to directly estimate ET from complex crop canopies. The algorithms and equations needed to describe changes in resistances and net radiation require more than a few simple equations. Current work at research locations around the globe is focusing on improving our ability to directly apply the PM equation or multilayer ET models to specific agricultural crops. However, the research community is probably some 10 to 15 years away from producing one-step procedures that are consistent, predictable, and reliable. When these one-step procedures do become available, they will likely be in the form of relatively complex computer models. Meanwhile, at present, full advantage in irrigation practice can be taken of the PM equation only to compute the reference ET and to determine the crop ET through use of the crop coefficients.

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