Evaluation of an empirical equation for annual evaporation using field observations and results from a biophysical model

Abstract An empirical equation for annual evaporation (E) of the form, E=P/{1+(P/Rn)α}1/α, where P is the annual precipitation, Rn the water equivalent of annual net radiation, and α an adjustable parameter, is evaluated using field observations (water balance, and micrometeorologic measurements for areas ca. 1 km2) at eight locations having different types of vegetation, and results from a biophysical process-based model for four years (1987–1990) for ten river basins (areas larger than 106 km2). For the field observations, minimum value of the mean absolute error (MAE) was 33 mm (4% of the mean observed evaporation) obtained for α=2.6, and the empirical equation was able to explain 99% of the variance under linear least square regression, with a slope of 0.99, intercept of 16 mm, and standard error of estimate (SEE) of 46 mm. For evaporation from the river basins, minimum value of the MAE was 36 mm (5% of the mean evaporation) obtained for α=1.8, and the empirical equation was able to explain 97% of the variance, with linear regression slope of 1.01, intercept of −11 mm, and SEE of 45 mm. The effect of spatial variations in P and Rn in determining evaporation from the empirical equation is analyzed to develop an understanding of the differences in the value of α for the field observations and the river basins.