Analytical solution of the coupled 2-D turbulent heat and vapor transport equations and the complementary relationship of evaporation

In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier's archiving and manuscript policies are encouraged to visit: Keywords: Complementary relationship of evaporation Coupled turbulent heat and moisture transport equations Evaporation Evapotranspiration s u m m a r y The existence of a symmetrical complementary relationship (CR) in evaporation has been hypothesized in the hydrologic literature but the conditions required have not been investigated in much detail. In this study it is shown that under near-neutral atmospheric conditions and a constant energy term at the evaporating surface, the analytical solution of the coupled turbulent diffusion equations of heat and vapor transport across a moisture discontinuity of the surface yields a symmetrical CR between the evaporation rate of the uniform drying land upwind of the discontinuity and the mean evaporation rate of the wet area provided, the latter has a proper fetch (i.e., along-the-wind extent). This fetch is a function of the air stability parameter and the assumed uniform surface roughness value, and it is in the order of a 100 m for a smooth surface under near-neutral atmospheric conditions. The analytically derived mean evaporation rates of such a smooth wet surface compare well, i.e., within 10%, to the Penman equation estimates, most frequently employed within the CR framework. Introduction The complementary relationship (CR) of evaporation, first introduced by Bouchet (1963), is an important tool for the practicing hydrologist because it can estimate actual evaporation (E) from climatic variables that are regularly observed at standard meteorological stations. This is unique because other existing evaporation estimation methods require measurements (a) obtained at two different heights above the ground (Bowen-ratio instruments); (b) ta-ken by fast response sensors (eddy-covariance stations), or (c) by remote sensing platforms. Still others need information of the vegetation status of the land (Penman–Monteith equation (Monteith, 1973)) or depend on the choice of the soil-moisture tracking algorithm to maintain a book keeping of the incoming and outgoing water fluxes of the area in question within the confines of a lumped or distributed hydrologic model. 2009) combined with a controversy about the existence of a true complementary relationship between potential (E p) and actual motivated this study. It is aimed to look at how the increase in sensible heat flux over a drying land surface actually becomes transformed into …