Recursive and explicit combination-based energy balance equations for calculating reference evapotranspiration in relation to Bowen ratio measurements

Efficient use of water in agro-ecosystems requires accurate quantification of actual evapotranspiration (ET _a). The two-step approach, i.e., reference ET (ET _ref) adjusted with crop coefficients (K _c), is an extensively used approach to estimate ET _a. Explicit combination equations, i.e., Penman-type combination-based equations and their derivatives (e.g., Penman-Monteith, ASCE-EWRI Penman-Monteith), have been widely tested and used. These equations rely on an assumption to remove the surface temperature from the calculation, and the validity of this assumption has been questioned as likely underestimating ET, particularly in semiarid and arid climates. Information on the validity of this assumption in subhumid regions is rare. Recursive combination methods, based on an equation proposed by Budyko, make no assumptions for the surface temperature, but they require iteration to arrive at a solution. The objective of this research was to compare ET calculated by explicit and recursive combination equations with measured values from a Bowen ratio energy balance system (BREBS) for an irrigated grassland. Results indicated that both equations were very sensitive to the value used for the surface resistance (rs). For equivalent values of rs, the explicit and recursive combination equations performed nearly equally as well in predicting BREBS-measured ET on both hourly and daily time steps. A surface resistance value of 40 s m-1 provided the best fit between both the Budyko and ASCE-EWRI equation-estimated ET and the measured ET values. Root mean square difference (RMSD) using r _s = 40 s m ^-1 was 0.06 mm h _-1, and model efficiency and R ₂ were both greater than 0.90. The same value (r _s = 40 s m ^-1) also provided the best fit for nighttime ET estimates. Similarly, a daytime r _s of 40 s m ^-1 provided the best fit between the ASCE-EWRI equation estimate and measured ET. On a daily time step, a sum-of-hourly approach provided better agreements with the BREBS-measured ET for both explicit (R ² = 0.95, RMSD = 0.57 mm d ^-1) and recursive (R ² = 0.96, RMSD = 0.57 mm d ^-1) combination methods than calculating ET using a daily average approach (explicit: R ² = 0.82, RMSD = 0.64 mm d ^-1; recursive: R ² = 0.78, RMSD = 0.72 mm d ^-1). While the recursive combination equation may potentially provide more accuracy under some conditions (i.e., arid and semiarid regions), it was no more accurate than the explicit equation under these experimental conditions.