Multiscale error analysis, correction, and predictive uncertainty estimation in a flood forecasting system

River discharge predictions often show errors that degrade the quality of forecasts. Three different methods of error correction are compared, namely, an autoregressive model with and without exogenous input (ARX and AR, respectively), and a method based on wavelet transforms. For the wavelet method, a Vector-Autoregressive model with exogenous input (VARX) is simultaneously fitted for the different levels of wavelet decomposition; after predicting the next time steps for each scale, a reconstruction formula is applied to transform the predictions in the wavelet domain back to the original time domain. The error correction methods are combined with the Hydrological Uncertainty Processor (HUP) in order to estimate the predictive conditional distribution. For three stations along the Danube catchment, and using output from the European Flood Alert System (EFAS), we demonstrate that the method based on wavelets outperforms simpler methods and uncorrected predictions with respect to mean absolute error, Nash-Sutcliffe efficiency coefficient (and its decomposed performance criteria), informativeness score, and in particular forecast reliability. The wavelet approach efficiently accounts for forecast errors with scale properties of unknown source and statistical structure.