A simplified framework for assessing the impact of rainfall spatial variability on the hydrologic response

The spatial distribution of rainfall is recognized to play a fundamental role in determining the hydrological response of river basins. Factors which dampen or enhance its role, while extensively discussed in previous literature, have not been fully assessed. We propose an analytical approach to investigate how basin hydrograph depends on the heterogeneity of a spatially distributed unit pulse of excess-rainfall. Catchment response is assumed to be completely described for a uniform input by the time-invariant distribution of travel times, derived through a geomorphological approach. Excess-rainfall field is represented as a stationary and isotropic random process, defined by its variance and integral scale. The uncertainty of the hydrologic response due to rainfall spatial variability is evaluated computing the variance of the generated hydrograph as function of the properties of both drainage basin and excess-rainfall field. Results suggest that hydrograph variability is negligible in the asymptotic conditions when the integral scale of the excess-rainfall field is much smaller or much larger than basin drainage area. For intermediate conditions, rainfall heterogeneity may still produce relevant effects; these have been investigated (i) deriving the analytical solution for the simple case of a rectangular sloping plane and (ii) performing numerical simulations on a real basin. Results appear to be of general interest, all the approximations notwithstanding.

► We study hydrologic response uncertainty due to excess-rainfall spatial variability.
► Uncertainty is analytically derived as a function of basin and rainfall properties.
► Negligible uncertainty for rain integral scale much smaller/larger than basin area.
► In other cases hydrograph uncertainty can be relatively large.
► For small hillslope velocities the role of hillslopes prevails.