Rainfall Estimation for Hydrologic Modeling on Large Basins

Abstract

Accuracy of computer models for surface-water hydrology and surface-water quality on the watershed scale is crucially dependent on the quality of areal rainfall depth estimates. On large basins, such as the Christina Watershed (1462 km 2 ) located in northern Delaware and southeastern Pennsylvania, rainfall data quality is compromised by the sparseness of the rain gage network and reduced further because it is common for many gages to record only daily rainfall totals. Important information about rainfall rates is available from a limited number of gages that record hourly data. Watershed-scale computer models of hydrology and water quality such as HSPF and SWMM allow large watersheds to be divided into smaller subcatchments. Such models typically require a single rain gage to be associated with each subcatchment. The standard approach used by modelers is to assume that rainfall occurring at the rain gage closest to the subcatchment is representative. Since rain gage networks are often very sparse, large errors in rainfall depth estimates for a particular subcatchment can result. Five methods of estimating rainfall on the subcatchments of a large watershed are examined in this paper. One method used the rain gage closest to the area centroid of the subcatchment. The other four methods were weighted averages of the rainfall observations at the five gages. The first used a simple arithmetic mean of the rainfall observations at all gages, the second used weights obtained from multiquadric surface-fitting, the third employed weights obtained by reciprocal-distance weighting between gage locations and the subcatchment centroids, and the fourth used reciprocal-distance-squared. Rainfall and stream flow records for twenty-five rainfall events were analyzed for four subcatchments of the Christina Basin. These subcatchments ranged in size from 22.3 km 2 up to 828 km 2 . Base flows were removed from the streamflow data to obtain runoff volumes. Rainfall depths were correlated with runoff by using a linear model and a model employing a nonlinear NRCS-style runoff equation. Rainfall at the nearest gage had the highest correlation with runoff at three of the four stream gage locations for the linear model and the lowest error sum of squares at two of the four locations for the nonlinear model. With the exception of the arithmetic mean, results from the weighted averaging methods were about equal to those obtained from nearest gage rainfall. As might be expected for an average of several observations, errors fluctuated less with the weighted averaging methods. For the nonlinear runoff model, error sum of squares values for runoff predicted with all the weighted averaging methods, with the exception of arithmetic mean, were on average less than those for runoff estimates that used nearest gage rainfall. Of the weighting methods considered, the multiquadric method, reciprocal-distance-squared, and reciprocal-distance methods all gave results that were fairly similar in terms of error. The arithmetic mean of rainfall observations had a higher runoff prediction error than any of the other methods. Even though nearest gage rainfall gave good results for these watersheds and rainfall data, rainfall at a single gage can be an unreliable indicator of the average rainfall over a subcatchment. In many situations, better, more robust estimates of areal rainfall for hydrologic modeling applications can be obtained with a weighted average of rainfall observations.