An examination of the Priestley‐Taylor equation using a convective boundary layer model

Abstract

The effect of large‐scale parameters on the behavior of the Priestley‐Taylor coefficient is addressed by means of a simple analytical model of the convective boundary layer (CBL). In this model, surface and aerodynamic resistances are maintained constant throughout daytime, and the diurnal course of available energy is parameterized in the form of a parabolic curve. To account for entrainment of overlying air, the height of the CBL is assumed to grow as square root of time, and the water vapor saturation deficit in the undisturbed atmosphere above the CBL is represented by a simple linear profile. The Priestley‐Taylor coefficient is defined as the ratio of potential evaporation over equilibrium evaporation, and two different ways of defining potential evaporation are considered: (1) as the evaporation of an extensive saturated area (i.e., the whole region influencing the CBL) or (2) as the evaporation of a limited saturated area (small enough that the excess moisture does not modify the characteristics of the CBL). These two ways, called respectively Penman's and Morton's ways, are successively examined. Numerical simulations from the CBL model show that the Priestley‐Taylor coefficient (α) does not have a fixed and universal value (1.26) as it has been suggested by these authors. When based on Penman's concept of potential evaporation, α varies as a function of the conditions in the undisturbed atmosphere above the CBL (inversion strength) but also as a function of the characteristics of the surface (aerodynamic resistance). The additional energy implied by a coefficient greater than 1 has to be ascribed only to the entrainment effect. When based on Morton's concept, α depends upon the areal surface resistance and the external conditions above the CBL: The daily mean value of α increases asymptotically with areal surface resistance towards a limit value which grows with inversion strength. In this case the additional energy (implied by α > 1) has a double origin: the feedback of areal evaporation on local potential evaporation and the entrainment effect.