When is Rain Steady?

Abstract

By definition, steady rain should have a nearly constant rainfall rate. Thus far, however, the criteria for determining when rain is steady remain qualitative and arbitrary. The authors suggest a definition for steadiness that can be used to quantify the elusive notion of natural variability. In particular, the logical criteria for steadiness imply statistical stationarity and lack of correlation between raindrops in neighboring volumes, requirements identical to those for the drops being distributed according to a Poisson process at all scales. Hence, steady rain is Poissonian. Explicit equations for the variance σ2R of the rainfall rates are developed. They show that, in general, raindrop clustering enhances the variance beyond that for Poissonian rain (σ2P). It is also demonstrated by using observations that this enhancement is augmented further when the rain is statistically nonstationary. Identifying steady rain is important. To be specific, because steady rain is statistically stationary, the drop size distributions have physical, deterministic meanings independent of the measurement process. Observables such as the radar reflectivity factor and the rainfall rate are then steady and linearly related also. Techniques for determining when rain is steady are discussed. The ratio σ2R/σ2P is proposed as a useful quantitative measure of the steadiness of the rain. It is also shown that an estimate of the minimum possible standard deviation for steady rain is R/k where R and k are the mean rain rate and average number of drops per sample, respectively. Examples using video-disdrometer data are also presented.