Evaporation and cooling of a lake under unstable atmospheric conditions

Abstract

The problem involves turbulent diffusion of momentum, sensible heat, and water vapor in the lower atmosphere when a neutral, dry air mass encounters a warm, wet surface. The water surface temperature is specified, and the surface roughness is taken to be constant over land and water. The turbulent fluxes are formulated by a semiempirical turbulence theory with the Businger‐Dyer form of the Monin‐Obukhov similarity functions, a water vapor buoyancy term in the Obukhov stability length, and Blackadar's scaling height in the mixing length. The resulting solution of the equations of conservation shows that the stability discontinuity at the leading edge can greatly affect the mean rate of evaporation and that the vertical vapor flux can greatly contribute to the atmospheric stability. The solution is relatively insensitive to the exact form of the Monin‐Obukhov similarity functions or to the exactness of Reynolds' analogy or von Karman's constant. For large fetches and near‐neutral conditions the solution becomes similar to that obtained in Sutton's problem and with Harbeck's empirical formula.

Modelling hourly rates of evaporation from small lakes

“…An appropriate formulation of the transfer processes occurring in the advective boundary layer is required. This was demonstrated by Weisman and Brutsaert (1973), who applied analytical solutions to the advection problem over open water for the unstable case. Blanken et al (2000), in a study of evaporation over Great Slave Lake, showed that for daily periods, open water evaporation is governed by the wind speed and the vapour gradient over the water.…”

“…Hence, the model development proceeded from the relationship between wind speed and evaporation; this relationship was then modified to include in turn the effects of the land-lake temperature and lake-land humidity contrasts. Weisman and Brutsaert (1973) showed lake evaporation includes advection and that fetch distance, or the distance from the upwind shore is also significant; therefore the effect of the fetch distance was also included in each step of the development. Most lakes are not uniform in shape, so the fetch distance was determined as a function of the wind direction.…”

“…For these reasons, land surface data alone are insufficient to parameterize the lake evaporation; water surface data are also required. Weisman and Brutsaert's (1973) analysis demonstrated that in an advective situation, as is the case for open water, the evaporation rate is not uniform over the lake surface, but can increase or decrease from the leading edge. Their analytical solution provided for an evaporation rate that is a function of the distance from the upwind shore.…”

“…Mahrer and Assouline (1993), using a meso-scale model also demonstrated the horizontal variability of open water evaporation. Granger (2000), using lake evaporation observations made over Big Quill Lake, in Saskatchewan, showed that the analytical solutions developed by Weisman and Brutsaert (1973) can be applied when the boundary layer over the lake is unstable (temperature decreasing with height). For stable conditions, however, these analytical expressions did not work well; and an analysis of the advection under stable boundary layer conditions, such as those encountered over a lake during daytime heating of the adjacent land surface, is required.…”

“…There are limits to the lake size for which an approach such as that of Weisman and Brutsaert (1973) can be expected to apply. When a lake is large, meso-scale atmospheric effects such as the entrainment of higher-level air can become significant.…”