On the impact of rainfall patterns on the hydrologic response

We study the influence exerted by space-time rainfall patterns on the hydrologic response to determine the scales for which the spatial heterogeneity of rainfall may play a significant role in shaping the hydrographs generated in basins of varying characteristics. We perform numerical experiments using models based on the geomorphological theory of the hydrologic response, in which the spatial resolution of the input rainfall fields is coarse grained from 100 m to 50 km. The variation in the resulting hydrographs shows that rainfall spatial variability does not significantly influence the flood response for basin areas up to about 3500 km2 in the cases considered, provided that the rainfall volume at each time interval is preserved. We then search for the physical interpretation of these results using the Jensen-Shannon divergence measure to characterize differences in travel time distributions sampled by real and idealized disk-shaped rainfall patterns of different size. Because the total residence time of a water parcel is often controlled by the travel time within hillslopes, we find that when typical hillslope size is smaller than the characteristic size of rainfall structures (say, a correlation length of rainfall intensity), the rainfall pattern effectively samples all possible residence times and the response of the catchment does not depend on the specific rainfall pattern. In larger basins (say, typically larger than 103 km2) the travel time in the channels is expected to be an important part of the total residence time. In this case the response of a catchment will also be controlled by the specifics of the spatial distribution of rainfall.