From runoff to rainfall: inverse rainfall–runoff modelling in a high temporal resolution

Abstract. Rainfall exhibits a large spatio-temporal variability, especially in complex alpine terrain. Additionally, the density of the monitoring network in mountainous regions is low and measurements are subjected to major errors, which lead to significant uncertainties in areal rainfall estimates. In contrast, the most reliable hydrological information available refers to runoff, which in the presented work is used as input for an inverted HBV-type rainfall–runoff model that is embedded in a root finding algorithm. For every time step a rainfall value is determined, which results in a simulated runoff value closely matching the observed runoff. The inverse model is applied and tested to the Schliefau and Krems catchments, situated in the northern Austrian Alpine foothills. The correlations between inferred rainfall and station observations in the proximity of the catchments are of similar magnitude compared to the correlations between station observations and independent INCA (Integrated Nowcasting through Comprehensive Analysis) rainfall analyses provided by the Austrian Central Institute for Meteorology and Geodynamics (ZAMG). The cumulative precipitation sums also show similar dynamics. The application of the inverse model is a promising approach to obtain additional information on mean areal rainfall. This additional information is not solely limited to the simulated hourly data but also includes the aggregated daily rainfall rates, which show a significantly higher correlation to the observed values. Potential applications of the inverse model include gaining additional information on catchment rainfall for interpolation purposes, flood forecasting or the estimation of snowmelt contribution. The application is limited to (smaller) catchments, which can be represented with a lumped model setup, and to the estimation of liquid rainfall.