On time-horizons based post-processing of flow forecasts

Post-processing raw stream flow forecasts are generally understood as estimating the univariate predictive density of stage or discharge values at selected future time steps, which is conditional on a single or multiple streamflow forecasts and observations up to the forecast start time to. The predictive density indicates to a forecaster in the most comprehensive way which flood level is likely to be expected. To this end, a variety of post-processing methods were proposed, which have respective strengths and weaknesses. These methods focus near-exclusively on the probabilistic forecast of the predictand at a single set future time ti, without addressing the predictive capability over the sequence of temporal sub-horizons (to, t1] ⊂ (to, t2] ⊂ … ⊂ (to, tk] nested into the overall forecast horizon. Here, we demonstrate the advantages of time-horizon dependent processing of streamflow forecasts, which evaluates the evolution of the predictive density over the sub-horizons by considering the temporal correlation among forecast ensemble members in addition to their cross-correlation with observations. The resulting probabilistic forecast consists of a multivariate distribution of stages and/or discharges at lagged forecasting times. These multivariate predictive distributions have the advantage of providing the likelihood of exceeding a critical threshold during the forecasting horizon while simultaneously offering valuable insights into the expected time of such exceedance. This approach supports not only decisions on issuing timely flood warnings but also the planing and roll-out of mitigating actions.