Single- and Dual-Surface Iterative Energy Balance Solutions for Reference ET

Abstract

The concept of a reference evapotranspiration (ETr) calculated from daily or hourly weather data, and multiplied by a crop coefficient (Kc) in order to estimate crop water use (ETc), is widely established in agricultural science and engineering. To find region- and variety-specific values of Kc from field-measured ETc values, the equation is inverted to: Kc = ETc/ETr. Forms of the Penman-Monteith (PM) formula for calculation of reference alfalfa or grass evapotranspiration (ETr and ETo, respectively) were promulgated by ASCE in 1990, FAO in 1998, and ASCE in 2005. The PM formulations are sensitive to climatic conditions, producing estimates of ETr and ETo that are more or less close to measured values depending on regional climate, and yielding values of Kc that vary from region to region and so are not transferrable. Theoretical shortcomings may be the basis of some of these problems, including the explicit nature of the calculation, which relies on the implied assumption that canopy and air temperatures are equal. We examined the ETr estimation of two surface energy balance formulations that stipulated different air and canopy temperatures: a two-layer (soil and canopy) approach, and a one-layer (big leaf) approach that included soil heat flux. Since canopy temperature is implicit in these formulations, they must be solved iteratively. Iterative solutions of ETr were compared with the ASCE PM formulation and against lysimeter-measured ETr. All three methods of ETr estimation produced ET values that compared very well with field-measured ET for alfalfa grown under reference ET conditions. Errors may occur with any of the three approaches to ETr estimation when stomatal resistance changes due to weather conditions; thus, assumptions of constant daytime and nighttime surface resistances cause mis-estimation of surface energy fluxes. It appears that a surface resistance value of 200 s m-1 at night for alfalfa grown under reference ET conditions is too large. It also appears that assuming constant daytime surface resistance of 30 s m-1 is probably not ideal, and that presenting daytime surface resistance as a function of vapor pressure deficit might improve ETr calculation.