A theoretical basis for the Priestley-Taylor coefficient

• Published in: Boundary-layer meteorology Vol. 82; no. 2; pp. 179 - 191
• Main Author: LHOMME, J.-P
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer 01.02.1997; Springer Nature B.V
• Subjects: Atmospheric boundary layer; Boundaries; Coefficients; Convection, turbulence, diffusion. Boundary layer structure and dynamics; Earth, ocean, space; Evaporation; Exact sciences and technology; External geophysics; Flux; Forests; Humidity; Mathematical models; Meteorology; Moisture; Surface resistance; Theory; Theoretical study; Convective layer; Potential evaporation; Atmospheric boundary layer
• ISSN: 0006-8314; 1573-1472
• DOI: 10.1023/a:1000281114105

The relationship between potential evaporation and arealevaporation is assessed using a closed-box model of the convectiveboundary layer (CBL). Potential evaporation is defined as theevaporation that would occur from a hypothetical saturated surface,with radiative properties similar to those of the whole area, and smallenough that the excess moisture flux does not modify thecharacteristics of the CBL. It is shown that the equilibrium rate ofpotential evaporation is given by Ep0=aE0,where E0 is the equilibrium evaporation (radiative termof the Penman formula), and a is a coefficient similar to thePriestley-Taylor coefficient. Its expression is $$\alpha = 1 + \left[ {1/(\varepsilon + 1)} \right]\left( {\left\langle {r_s } \right\rangle /r_a } \right)$$, where $$\left\langle {r_s } \right\rangle $$ is the areal surface resistance, r sub(a) is the localaerodynamic resistance, and e is the dimensionless slope of thesaturation specific humidity at the temperature of the air. Itscalculated value is around 1 for any saturated surface surrounded bywater, about 1.3 for saturated grass surrounded by well-watered grassand can be greater than 3 over saturated forest surrounded by forest.The formulation obtained provides a theoretical basis to the overallmean value of 1.26, empirically found by Priestley and Taylor for thecoefficient a. Examining, at the light of this formulation, thecomplementary relationship between potential and actual evaporation(as proposed by Bouchet and Morton), it appears that the sum ofthese two magnitudes is not a constant at equilibrium, but depends onthe value of the areal surface resistance.