Derived distributions of storm depth and frequency conditioned on monthly total precipitation: Adding value to historical and satellite-derived estimates of monthly precipitation

The stochastic precipitation model in which storms arrive as a Poisson proc ess and have gamma-distributed depths previously has been shown to display useful aggregation properties. Here the disaggregation properties of this m odel are explored. Specifically, derived distributions and Bayes's theorem are used to find analytical expressions for the conditional arrival rate an d conditional depth distribution for a given realization of monthly total p recipitation. The conditioning procedure yields answers to questions of the following nature. If the precipitation in a given month is twice the mean, what is the likelihood that it rained more frequently and/or with larger s torm depths? The method is useful as a disaggregation tool in those situati ons for which knowledge of storm or interstorm characteristics is required (e.g., for driving hydroecological and rainfall-runoff models): but only mo nthly precipitation totals are available or reliable. This condition exists in many historical, satellite-derived, and model-generated precipitation d atasets. The derivations are tested using 45 yr of hourly precipitation dat a from humid (Boston, Massachusetts) and semiarid (Los Angeles, California) sites.