Error-correction across gauged and ungauged locations: A data assimilation-inspired approach to post-processing river discharge forecasts

Abstract. Forecasting river discharge is essential for disaster risk reduction and water resource management, but forecasts of the future river state often contain errors. Post-processing reduces forecast errors but is usually only applied at the locations of river gauges, leaving the majority of the river network uncorrected. Here, we present a data-assimilation-inspired method for error-correcting ensemble simulations across gauged and ungauged locations in a post-processing step. Our new method employs state augmentation within the framework of the Local Ensemble Transform Kalman Filter (LETKF). Using the LETKF, an error vector representing the forecast residual is estimated for each ensemble member. The LETKF uses ensemble error covariances to spread observational information from gauged to ungauged locations in a dynamic and computationally efficient manner. To improve the efficiency of the LETKF we define new localisation, covariance inflation, and initial ensemble generation techniques that can be easily transferred between modelling systems and river catchments. We implement and evaluate our new error-correction method for the entire Rhine-Meuse catchment using forecasts from the Copernicus Emergency Management Service's European Flood Awareness System (EFAS). The resulting river discharge ensembles are error-corrected at every grid box but remain spatially and temporally consistent. A spatial cross-validation strategy is used to assess the ability of the method to spread the correction along the river network to ungauged locations. The skill of the ensemble mean is improved at almost all locations including stations both up- and downstream of the assimilated observations. Whilst the ensemble spread is improved at short lead-times, at longer lead-times the ensemble spread is too large leading to an underconfident ensemble. In summary, our method successfully propagates error information along the river network, enabling error correction at ungauged locations. This technique can be used for improved post-event analysis and can be developed further to post-process operational forecasts providing more accurate knowledge about the future states of rivers.