VOL. 6, NO. 4 WATER RESOURCES RESEARCH AUGUST 1970 Implications a Type Empirical Evaporation Formula Lakes and Pans WILFRIED BRUTSAERT AND GOUR-TSYH YEH Cornell University, Ithaca, New York 14850 Abstract. Empirical mass transfer formulas for evaporation from lakes and from pans at ground level are compared with the theoretical solution based on semiempirical turbulent diffusion theory in conjunction with Reynolds' analogy and the power law for the wind pro- file. It was found that although the theory has its limitations, it is a useful tool for the study of evaporation, especially under conditions of lateral advection. The empirical formu- las should be adequate for many design problems. INTRODUCTION A complete study of the problemof evapora- tion in nature from a free water surface at ground level under conditionsof lateral advec- tion should deal with the three-dimensional simultaneous turbulent transfer of momentum, heat, and water vapor and with the interaction between each quantity and the other two. Be- cause of the physical and mathematical diffi- culties in the corresponding theoretical models, two very commonly usedassumptions are, first, that momentumtransfer is strictly vertical and can be represented by a one-dimensional wind profile equation with constant roughnessand atmospheric stability over the land and water surface; and second, that the temperature of the water surface is constant so ghat the heat and vapor fields are separable and each can be analyzed by itself. Similarly, because of the experimental difficulties involved in carrying out field measurements, most empiricalevapora- tion formulas are implicitly based on the same assumptions of uniformity of the surfacerough- ness,of the stability, and of the water surface temperature. Thus for their application,most of these formulas require wind speedand water temperature data which are suitably averaged over the water surface. It is clear that the above two conditions are almost never satisfied.Nevertheless, the study of this specialcase may be of sufficient interest because awaiting the complete solution it should provide some insight into certain aspects of three-dimensional turbulent transfer in the lower atmosphere, at least on a long-termbasis or for engineeringdesign purposes. In this paper Vhe solution of this casebased on two-dimensional semiempirical turbulent dif- fusion theory is examinedand compared with two available empirical formulas for lake and pan evaporation. These formulasare considered because unlike most other formulasthey take account of lateral advection by the inclusion of the effect of the size of the water surface. The theoretical solution is based on the addi- tional assumptions of the validity of Reynolds' analogy with constant shear stress and of the power law for the wind profile.It is well known that the power law can give only a rough ap- proximationin the lower atmosphere. Yet be- causeof its simplicity, it is probably the only functional form with which a complete analytical solution will be obtainable. Although power laws, togetherwith Reynolds' analogy, have been ap- pliedextensively in the padt, the values of the parameters to be used for actual turbulent dif- fusion calculations are not well known. On the other hand the two empirical equations are based on relatively few experiments sothat their validity or generality is largely unknown and often doubted (mostly by their originators). Therefore this papershould mainly provide first, someadmittedly limited theoreticaljustification for these two empirical equations to clarify their strong and weak pointsfor the hydrologic prediction of evaporation under conditionsof forced convection; and second, a discussion of some of the limitations of the theoretical model ß 1202