Adaptive filtering through detection of isolated transient errors in rainfall‐runoff models

Real‐time river discharge forecasting models operate under widely different wet and dry regimes, producing sequences of highly nonstationary prediction residuals. Errors in the mean areal precipitation estimation are often magnified due to model approximations and nonlinear behavior and result in significant effective input errors which propagate as transient signals through the system. Normal operation of a feedback scheme based on the Kalman filter with stationary error statistics cannot account for such discrepancies leading to local divergence between expected and observed prediction residuals. An adaptive filtering methodology which explicitly accounts for transient errors in the prediction due to errors in the estimation of the effective rainfall is presented. The filter operates normally under the assumption of only stationary or slowly varying noise, while a generalized likelihood ratio test is used to detect the presence of transient errors. When such errors are detected, estimates of their timing and magnitude are obtained, and the forecasts are appropriately corrected. An illustrative example of the procedure operation is given.