Estimation of the uncertainty in water level forecasts at ungauged river locations using quantile regression

River water level forecasts play an essential role in operational river management, and uncertainty estimates in the forecasts can support and influence decision-making. Currently, uncertainty estimates in the water level forecasts are commonly available at forecast locations where water level measurements are available, but are lacking at the remaining ungauged forecast locations. In the research presented in this paper, we investigate the combined use of (i) spatial interpolation of the errors (or residuals) in water level forecasts to ungauged locations, and (ii) quantile regression, which is a widely used technique to estimate the quantiles of a distribution, in this case, the error distribution around water level forecasts. The methodology was applied to the IJssel River in the Netherlands, using seven measurement locations and 5 years of hindcasted water levels. We applied a simple inverse-distance interpolation of the residuals in the water level forecasts, and carried out quantile regression on the interpolated residuals. Validation of the methodology showed that the estimated quantiles represented the observations to about 5% accuracy for forecast lead times of 24 h and greater. For shorter lead times, the accuracy varied per station, but was generally poorer due to the relatively greater spread of the interpolated residuals around the true residuals for shorter lead times. For delta rivers such as the IJssel River, the presented methodology is an easy-to-implement and (for lead times of 24 h or greater) accurate technique to augment river level forecasts at ungauged locations with uncertainty estimates. Improvement of the method would be supported by further research into interpolation techniques that take into account additional factors such as proximity of a tributary, influence of wind, or the proximity of a model boundary.