Calibration of rainfall-runoff models in ungauged basins: A regional maximum likelihood approach

Parameter estimation for rainfall-runoff models in ungauged basins is a challenging task that is receiving significant attention by the scientific community. In fact, many practical applications suffer from problems induced by data scarcity, given that hydrological observations are often sparse or unavailable. This study focuses on regional calibration for a generic rainfall-runoff model. The maximum likelihood function in the spectral domain proposed by Whittle [40] is approximated in the time domain by maximising the fit of selected statistics of the river flow process, with the aim to propose a calibration procedure that can be applied at regional scale. Accordingly, the statistics above are related to the dominant climate and catchment characteristics, through regional regression relationships. The proposed technique is applied to the case study of 4 catchments located in central Italy, which are treated as ungauged and are located in a region where detailed hydrological, as well as geomorphologic and climatic information, is available. The results obtained with the regional calibration are compared with those provided by a classical least squares calibration in the time domain. The outcomes of the analysis confirm the potential of the proposed methodology and show that regional information can be very effective for setting up hydrological models.