An analysis of input errors in precipitation‐runoff models using regression with errors in the independent variables

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Abstract
Errors in runoff prediction caused by input data errors are analyzed by treating precipitation‐runoff models as regression (conditional expectation) models. Independent variables of the regression consist of precipitation and other input measurements; the dependent variable is runoff. In models using erroneous input data, prediction errors are inflated and estimates of expected storm runoff for given observed input variables are biased. This bias in expected runoff estimation results in biased parameter estimates if these parameter estimates are obtained by a least squares fit of predicted to observed runoff values. The problems of error inflation and bias are examined in detail for a simple linear regression of runoff on rainfall and for a nonlinear U.S. Geological Survey precipitation‐runoff model. Some implications for flood frequency analysis are considered. A case study using a set of data from Turtle Creek near Dallas, Texas illustrates the problems of model input errors.