For describing the surface fluxes in the atmospheric dispersion models, the commonly used linear universal similarity functions m and 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 (RiB) 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 RiB. These linear functions are found to be valid as long as RiB is smaller than Prt γ/β2 where Prt is the turbulent Prandtl number and β and γ are constants appearing in the linear functions of m and h. The linear functional forms for m and h underestimate the Obukhov length resulting in the large value of the stability parameter when RiBPrt γ/β2 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 RiB is larger than Prt γ/β2. 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 RiB. The computed surface fluxes are also compared with those based on turbulence measurements taken in Cooperative Atmospheric Surface Exchange Study.