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Rainfall Estimation for Hydrologic Modeling on Large Basins
Published by the American Society of Agricultural and Biological Engineers, St. Joseph, Michigan www.asabe.org
Citation: Paper number 012128, 2001 ASAE Annual Meeting. (doi: 10.13031/2013.7312) @2001
Authors: Carmine C. Balascio, Kendall B. Wilson
Keywords: areal rainfall estimation, hydrologic modeling, waterquality, runoff depth
Accuracy of computer models for surfacewater hydrology and surfacewater 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. Watershedscale 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 surfacefitting, the third employed
weights obtained by reciprocaldistance weighting between gage locations and the subcatchment centroids, and the
fourth used reciprocaldistancesquared. Rainfall and stream flow records for twentyfive 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 NRCSstyle 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, reciprocaldistancesquared, and reciprocaldistance 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.
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