Runoff prediction errors and bias in parameter estimation induced by spatial variability of precipitation

Abstract

Spatial variability of precipitation causes inflated mean squared errors of prediction in precipitation‐runoff modeling. One component of these larger errors is a bias, which often takes the form of over‐prediction for large events and underprediction for small events. This problem is examined using an assumed stochastic structure for the spatial behavior of rainfall together with a form of the Green‐Ampt infiltration equation for prediction of storm runoff volume. The stochastic rainfall model incorporates the nonstationarity and spatial correlation exhibited by actual rainfall. The bias in runoff prediction causes parameter estimates obtained by least squares calibration to be asymptotically biased. The magnitude and direction of the bias depends on the interaction between the runoff prediction bias and the sensitivity of predicted runoff to changes in parameter values. Numerous climatic and hydrologic factors exercise an influence on this interaction.