This work describes the derivation of a set of statistics, termed spatial moments of catchment rainfall, that quantify the dependence between rainfall spatial organization, basin morphology and runoff response. These statistics describe the spatial rainfall organisation in terms of concentration and dispersion along the flow distance coordinate. These statistics were derived starting from an analytical framework, and related with the statistical moments of the flood hydrograph. From spatial moments we also created an index quantifying catchment scale storm velocity. This index measures the overall movement of the rainfall system over the catchment, reflecting the filtering effect of its morphology. We also extended spatial moments to the hillslope system, developing a framework to evaluate the relevance of hillslope and channel propagation in the flood response to spatially variable rainfall fields. Data from six flash floods occurred in Europe between 2002 and 2007 are used to evaluate the information provided by the framework. High resolution radar rainfall fields and a distributed hydrologic model are employed to examine how effective are these statistics in describing the degree of spatial rainfall organisation, which is important for runoff modelling. The size of the study catchments ranges between 36 to 2586 km2. The analysis reported here shows that spatial moments of catchment rainfall can be effectively employed to isolate and describe the features of rainfall spatial organization which have significant impact on runoff simulation. Rainfall distribution was observed to play an important role in catchments as small as 50 km2. The description timing error was further improved by the inclusion in the framework of hillslope propagation. This development allows to compare scenarios of hillslope conditions, to evaluate the sensitivity of single basins or the effect of catchment scale. The analysis of catchment scale storm velocity showed a nonlinear dependence with basin scale. The values of velocity observed were however rather moderate, in spite of the strong kinematic characteristics of individual storm elements, and did not play a relevant effect on the flood analyzed
