Performance and robustness of probabilistic river forecasts computed with quantile regression based on multiple independent variables

Abstract. This study applies quantile regression (QR) to predict exceedance probabilities of various water levels, including flood stages, with combinations of deterministic forecasts, past forecast errors and rates of water level rise as independent variables. A computationally cheap technique to estimate forecast uncertainty is valuable, because many national flood forecasting services, such as the National Weather Service (NWS), only publish deterministic single-valued forecasts. The study uses data from the 82 river gauges, for which the NWS' North Central River Forecast Center issues forecasts daily. Archived forecasts for lead times of up to 6 days from 2001 to 2013 were analyzed. Besides the forecast itself, this study uses the rate of rise of the river stage in the last 24 and 48 h and the forecast error 24 and 48 h ago as predictors in QR configurations. When compared to just using the forecast as an independent variable, adding the latter four predictors significantly improved the forecasts, as measured by the Brier skill score and the continuous ranked probability score. Mainly, the resolution increases, as the forecast-only QR configuration already delivered high reliability. Combining the forecast with the other four predictors results in a much less favorable performance. Lastly, the forecast performance does not strongly depend on the size of the training data set but on the year, the river gauge, lead time and event threshold that are being forecast. We find that each event threshold requires a separate configuration or at least calibration.