On the bulk Richardson number and flux―profile relations in an atmospheric surface layer under weak wind stable conditions

摘要

For describing the surface fluxes in the atmospheric dispersion models, the commonly used linear universal similarity functions φ_m and φ_h for nondimensional wind and temperature profiles (J. Atmos. Sci. 28 (1971) 181; Boundary-Layer Meteorol. 7 (1974) 363) are analyzed under weak wind stable conditions. The stability parameter z/L (z is the height above the ground and L is the Obukhov length) is not known a priori. On the other hand, the bulk Richardson number (Ri_B) is readily available from profile measurements. Thus, a systematic mathematical analysis is carried out to analyze the applicability of the linear functions in terms of Ri_B. These linear functions are found to be valid as long as Ri_B is smaller than Pr_t γ/β~2 where Pr_t is the turbulent Prandtl number and β and γ are constants appearing in the linear functions of φ_m and φ_h. The linear functional forms for φ_m and φ_h underestimate the Obukhov length resulting in the large value of the stability parameter when Ri_B≥Pr-t γ/β~2 occurring in weak wind stable conditions. Using the data from plume validation field experiment conducted by Electric Power Research Institute at Kincaid, it is found that in 70% of the weak wind cases, the Ri_B is larger than Pr_t γ/β~2. The similarity functions proposed by Beljaars and Holtslag (J. Appl. Meteorol. 30 (1991) 327) are shown to perform well in weak wind stable conditions for all the values of Ri_B. The computed surface fluxes are also compared with those based on turbulence measurements taken in Cooperative Atmospheric Surface Exchange Study.