Theoretical framework to estimate spatial rainfall averages conditional on river discharges and point rainfall measurements from a single location: an application to western Greece

Abstract. We focus on the special case of catchments covered by a single rain gauge and develop a theoretical framework to obtain estimates of spatial rainfall averages conditional on rainfall measurements from a single location, and the flow conditions at the catchment outlet. In doing so we use (a) statistical tools to identify and correct inconsistencies between daily rainfall occurrence and amount and the flow conditions at the outlet of the basin; (b) concepts from multifractal theory to relate the fraction of wet intervals in point rainfall measurements and that in spatial rainfall averages, while accounting for the shape and size of the catchment, the size, lifetime and advection velocity of rainfall-generating features and the location of the rain gauge inside the basin; and (c) semi-theoretical arguments to assure consistency between rainfall and runoff volumes at an inter-annual level, implicitly accounting for spatial heterogeneities of rainfall caused by orographic influences. In an application study, using point rainfall records from the Glafkos river basin in western Greece, we find the suggested approach to demonstrate significant skill in resolving rainfall–runoff incompatibilities at a daily level, while reproducing the statistics of spatial rainfall averages at both monthly and annual time scales, independent of the location of the rain gauge and the magnitude of the observed deviations between point rainfall measurements and spatial rainfall averages. The developed scheme should serve as an important tool for the effective calibration of rainfall–runoff models in basins covered by a single rain gauge and, also, improve hydrologic impact assessment at a river basin level under changing climatic conditions.