The probability mass function of peak streamflow from a given catchment is derived from the density functions for climatic and catchment variables by using the functional relationships provided by the kinematic wave method of hydrograph forecasting. The exceedance probability for a flood peak of given magnitude is then related to the annual exceedance recurrence interval of this flood. The resulting theoretical flood frequency relation shows a changing form with change in catchment and climate parameters and agrees well with observations from three Connecticut catchments. It provides a theoretical basis for estimating flood frequency in the absence of streamflow records and for extrapolating empirical estimates based on short records. Because of the explicit appearance of physically meaningful catchment parameters it also allows quantitative estimates of the effect on flood frequency of changes in average land use. The flood frequency relation for a given catchment is averaged across the population of catchments of given size to provide a theoretical regional flood frequency function that compares favorably with observations of mean annual floods on 44 Connecticut catchments.
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