Improvement of rank histograms for verifying the reliability of extreme event ensemble forecasts

Ensemble forecasting is becoming increasingly popular as a hydrological forecasting tool because of its advantages of not only predicting the most likely outcome of a hydrological event, but also providing related uncertainty information. Rank histogram is one of the most widely used metrics for verifying the reliability of ensemble forecasts. This study proposed an improved rank histogram method, the Rank Polar Diagram (Rpolar diagram), for evaluating the reliability of ensemble forecasts of extreme events. The conventional rank histogram provided a simple evaluation of the reliability of an ensemble forecast, which could not differentiate the reliability of the forecasts of extreme events such as heavy storms, high flows and low flows. Rpolar diagrams were able to verify not only the overall reliability but also the partial reliability over different flow intervals, including extremes. In Rpolar diagram, forecast intervals could be set according to user preference or uniform intervals automatically. This study evaluated the effectiveness of the Rpolar diagram using two typical sets of simulation ensembles and actual streamflow/precipitation ensembles. Both streamflow and precipitation application results exhibited the suitability of the Rpolar diagrams for verifying the reliability of extreme events.