Studies of the effect of averaging the continuity equation for soluble species over wet and dry periods of a precipitation cycle have shown that the effective scavenging rate which must be used in such averaged models is less than the classical value obtained by a simple average of the scavenging rate over a cycle. This is a consequence of the fact that for an intermittent loss process such as precipitation wet periods correspond to depressed and dry periods to enhanced soluble species concentration. There is thus an inherent negative correlation between departures from the mean of the scavenging rate and soluble species concentration which is not accounted for in the averaging process. This study shows that if the source of the soluble species is time dependent, then periods of positive correlation between scavenging rate and species concentration may also result from temporal averaging. This can result when the end of a precipitation period is coincident with the diminution or termination of the source. A specific example considered is the late afternoon rainout of nitric acid occurring just prior to the night time cessation of its chemical production. Under some assumed precipitation scenarios, the positive correlation may dominate, leading to an effective scavenging rate exceeding the classical value. A model is developed to take account of the effect of random precipitation times on the nitric acid scavenging rate. These calculations give effective scavenging rates about a factor of 2 to 3 greater than those of some other published models. For small wet fractional periods, typically less than 0.1, the effective scavenging rate may exceed the classical value slightly, although the details of this calculation depend on the mean precipitation period and on some of the model's statistical assumptions.