The effect of the spatial and temporal variations of rainfall on runoff from small semiarid watersheds.

Abstract

A procedure for estimating runoff from convective storms in the semiarid Southwest is needed for the design of small hydraulic structures. The aim of this study was to develop and test rainfall and runoff relationships based on the analysis of 12 years of hydrologic data for an 18-square mile experimental watershed. rhe experimental area is divided into four subwatersheds ranging in size from 0.5 to 7.8 square miles, Vegetation and soils are typical of what is encountered in the valley floors of southern Arizona. Rainfall is measured at 29 locations. Isohyetal maps were prepared for all of the storms which lead to the development of a rainfall model that describes the distribution of rainfall in space. An exponential relationship was found to adequately represent the spatial variation of each storm. A single equation for all storms was developed by using a parameter that is related to the storm center depth. The Kolmogorov-Smirnov procedure was used to test the hypothesis that storm center location is governed by chance in areas not influenced by topographic changes. It was found that the assumption which states that convective storm cells are randomly located within valley floors is acceptable. An equation was derived for calculating point rainfall probabilities from raingage network data, The results were based on the random location of storm centers and on an extremal distribution function fitted to storm center depths. The calculated probabilities were found to be significantly higher than the observed probabilities determined from a nearby, long-term U. S. Weather Bureau station. The volume of runoff from small, semiarid watersheds was found to be a function primarily of mean rainfall. In a multiple linear regression model, mean rainfall accounted for 67 to 82 percent of the variance. The use of a time distribution factor which includes the maximum 15-minute intensity reduced the unexplained variance to 11 to 16 percent. Inserting a space distribution variable into the model indicated that storm center location on the watershed was not a significant factor in predicting runoff. An antecedent rainfall index did not produce any significant correlation with runoff from convective storms. For winter frontal storms, however, a four-day antecedent rainfall index was found to be an important factor in oxplaining runoff. It appears that the commonly used Soil Conservation Service method underestimates convective storm runoff for most storm center depths below about three inches. A direct comparison with the multiple regression equation was not possible as this method does not take into account the variability of convective rainfall in time and space. As a means for estimating runoff volumes for ungaged watersheds, a runoff coefficient was defined as the ratio of runoff to effective rainfall (mean rainfall less initial abstractions). It appears that as a first approximation, the runoff coefficient can be considered as being equal to the coefficient in the well known rational formula. There is some evidence to the belief that the runoff coefficient is affected by a storm's time distribution factor. It was demonstrated that runoff volume recurrence intervals can be determined adequately from the rainfall and runoff relationships developed in this study.