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

Abstract

Abstract. This paper presents a novel technique to calculate mean areal rainfall in a high temporal resolution of 60 min on the basis of an inverse conceptual rainfall–runoff model and runoff observations. 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. The most reliable hydrological information available refers to runoff, which in the presented work is used as input for a rainfall–runoff model. Thereby a conceptual, HBV-type model is embedded in an iteration algorithm. For every time step a rainfall value is determined, which results in a simulated runoff value that corresponds to the observation. To verify the existence, uniqueness and stability of the inverse rainfall, numerical experiments with synthetic hydrographs as inputs into the inverse model are carried out successfully. The application of the inverse model with runoff observations as driving input is performed for the Krems catchment (38.4 km2), situated in the northern Austrian Alpine foothills. Compared to station observations in the proximity of the catchment, the inverse rainfall sums and time series have a similar goodness of fit, as the independent INCA rainfall analysis of Austrian Central Institute for Meteorology and Geodynamics (ZAMG). Compared to observations, the inverse rainfall estimates show larger rainfall intensities. Numerical experiments show, that cold state conditions in the inverse model do not influence the inverse rainfall estimates, when considering an adequate spin-up time. The application of the inverse model is a feasible approach to obtain improved estimates of mean areal rainfall. These can be used to enhance interpolated rainfall fields, e.g. for the estimation of rainfall correction factors, the parameterisation of elevation dependency or the application in real-time flood forecasting systems.