A New Two-Dimensional Physical Basis for the Complementary Relation between Terrestrial and Pan Evaporation

Abstract

Archived global measurements of water loss from evaporation pans constitute an important indirect measure of evaporative flux. Historical data from evaporation pans shows a decreasing trend over the last half century, but the relationship between pan evaporation and moisture-limited terrestrial evaporation is complex, leading to ambiguities in the interpretation of these data. Under energy-limited conditions, pan evaporation Epan and moisture-limited terrestrial evaporation E increase or decrease together, whereas in moisture-limited conditions these fluxes form a complementary relation (CR) in which increases in one rate accompany decreases in the other rate. This has led to debate about the meaning of the observed trends in the context of changing climate. Here a two-dimensional numerical model of a wet pan in a drying landscape is used to demonstrate that, over a wide range of realistic atmospheric and surface conditions, the influence that changes in E have on Epan 1) are complementary and linear, 2) do not depend upon surface wind speed, and 3) are strikingly asymmetrical, in that a unit decrease in E causes approximately a fivefold increase in Epan, as found in a recent analysis by Kahler and Brutsaert of daily evaporation from U.S. grasslands. Previous attempts to explain the CR have been based on one-dimensional diffusion and energy balance arguments, leading to analytic solutions based on Penman-type bulk difference equations. However, without acknowledging the spatially complex humidity and temperature fields around the pan and, specifically, how these fields change as the contrast between the wet pan and the drying land surface increases, such integrated bulk difference equations are a priori incomplete (they ignore important divergence terms), and thus these explanations must be considered physically incomplete. Results of this study improve the theoretical foundation of the CR, thus increasing the reliability with which it can be applied to estimate water balance and to understand the pan evaporation record of climate change.