A Stochastic Model Relating Rainfall Intensity to Raindrop Processes

The temporal variability of rainfall and raindrop processes is examined at time scales ranging from less than 1 minute to 1 hour. Raindrop processes are represented in terms of drop arrival rate, mean diameter and coe cient of variation of drop diameter and modeled as time-varying stochastic processes. It is shown that rainfall rate and accumulated rainfall have simple and accurate representations in terms of raindrop processes. Using these results the temporal variability of rainfall rate is examined in terms of temporal variability of raindrop processes. It is shown that the temporal variability of rainfall rate varies systematically across a range of climatic settings and, more importantly, that these climatic contrasts in rainfall rate can be related to contrasting properties of raindrop processes. Two statistical models of rainfall rate and raindrop processes are examined in detail: a lognormal model with xed parameters and a lognormal model with parameters that vary from storm to storm. Temporal correlation structure of rainfall rate exhibits qualitatively di erent behaviour under the two models. Lognormal models of rainfall rate are extended to models in which dependence on the averaging time interval is explicitly represented. Scale properties of rainfall rate are examined empirically for averaging time intervals ranging from 1 minute to 30 minutes. Empirical analyses are based on drop-size data from North Carolina, New Jersey, Oregon, Alaska, and the Marshall Islands. 2