Rain scavenging of soluble gases by non-evaporating and evaporating droplets from inhomogeneous atmosphere

We suggest a one-dimensional model of precipitation scavenging of soluble gaseous pollutants by non-evaporating and evaporating droplets that is valid for arbitrary initial vertical distribution of soluble trace gases in the atmosphere. It is shown that for low gradients of soluble trace gases in the atmosphere, scavenging of gaseous pollutants is governed by a linear wave equation that describes propagation of a wave in one direction. The derived equation is solved by the method of characteristics. Scavenging coefficient and the rates of precipitation scavenging are calculated for wet removal of sulfur dioxide (SO2) and ammonia (NH3) using measured initial distributions of trace gases. It is shown that scavenging coefficient for arbitrary initial vertical distribution of soluble trace gases in the atmosphere is non-stationary and height-dependent. In case of exponential initial distribution of soluble trace gases in the atmosphere, scavenging coefficient for non-evaporating droplets in the region between the ground and the position of a scavenging front is a product of rainfall rate, solubility parameter, and the growth constant in the formula for the initial profile of a soluble trace gas in the atmosphere. This expression yields the same estimate of scavenging coefficient for sulfur dioxide scavenging by rain as field estimates presented in McMahon and Denison (1979). It is demonstrated that the smaller the slope of the concentration profile the higher the value of a scavenging coefficient.