Derived Distributions of Storm Depth and Frequency Conditioned on Monthly Total Precipitation: Adding Value to Historical and Satellite-Derived Estimates of Monthly Precipitation

Abstract

The stochastic precipitation model in which storms arrive as a Poisson process and have gamma-distributed depths previously has been shown to display useful aggregation properties. Here the disaggregation properties of this model are explored. Specifically, derived distributions and Bayes?s theorem are used to find analytical expressions for the conditional arrival rate and conditional depth distribution for a given realization of monthly total precipitation. 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 storm depths? The method is useful as a disaggregation tool in those situations for which knowledge of storm or interstorm characteristics is required (e.g., for driving hydroecological and rainfall?runoff models), but only monthly precipitation totals are available or reliable. This condition exists in many historical, satellite-derived, and model-generated precipitation datasets. The derivations are tested using 45 yr of hourly precipitation data from humid (Boston, Massachusetts) and semiarid (Los Angeles, California) sites.