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

Forecasting river discharge is essential for disaster risk reduction and water resource management, but forecasts of future river states 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 Localised Ensemble Transform Kalman Filter (LETKF) to estimate an error vector 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 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 Rhine-Meuse catchment using ensemble 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. Leave-one-out cross validation is used to evaluate the skill of the ensembles at proxy-ungauged locations to assess the ability of the method to spread the correction along the river network. 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 reliability is decreased. 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.