Long-Duration–Rainfall Intensity Equations

Abstract

Rainfall intensity-duration equations for long-duration rainfall (that is, for durations from 1 to 10 days) are developed using data from readily available isopluvial maps prepared by the National Weather Service (NWS) for four geographic regions: the contiguous United States, Alaska, Hawaii, and Puerto Rico and the U.S. Virgin Islands. NWS finds the ratio of n -day rainfall to 2-day rainfall depths in a geographic region to depend on the ratio of 10-day rainfall to 2-day rainfall. Dimensionless forms of four types of commonly used intensity-duration equations were then fit to 10 ratios of n - to 2-day rainfall depths for n = 1, 2, . . . , 10 for various 10-day–rainfall to 2-day–rainfall depth ratios. Optimal parameters for each equation type were found by an intensive pattern search covering the entire feasible range of each parameter. Parameters are graphed as functions of the 10-day–rainfall to 2-day–rainfall depth ratio for a specific return period for each geographic region covered by the isopluvial maps. The best equation for a particular region is found from a graph of the error sums of squares of each equation type as a function of the 10-day–rainfall to 2-day–rainfall depth ratio. The procedure presented here will be useful for developing precipitation patterns (that is, design storms) used in the hydrologic design of structures that control storm runoff and flooding.