Analytical formulas for the below-cloud scavenging coefficient of an irreversibly soluble gas: a quantitative evaluation for HNO<SUB align=right>3

Abstract

In the present paper, analytical expressions are derived for the below-cloud gas scavenging coefficient, considering various functions that can be found in the literature to describe raindrop populations and terminal velocities. Three primary cases have been identified where an analytical solution exists: (i) a raindrop size distribution described by a gamma function and raindrop terminal velocity by a power function of raindrop size; (ii) a raindrop size distribution described by a gamma function and raindrop terminal velocity by an exponential function; and (iii) a raindrop size distribution described by a log–normal function and raindrop terminal velocity by a power function. In addition, in case (i), the gas scavenging coefficient is expressed analytically as a function of rain intensity. The derived analytical expressions are subsequently used to compute the scavenging coefficients of HNO3 for different parameterizations of the raindrop size distribution and terminal velocity functions. In order to broaden the sensitivity test of HNO3 scavenging coefficients on parameterizations, scavenging coefficients of HNO3 are also computed numerically for the raindrop terminal velocity as a function of raindrop size and atmospheric conditions. The results show that there is a relative variation in the values of the gas scavenging coefficient up to 50% for the parameterization considered in this study, and that the overestimation given by the analytical formulas is not important for cut-off limits of raindrop spectra below 0.2 mm.