An analytical model of the effects of catchment elevation on the flood frequency distribution

The effect of temperature on the flood frequency distribution in mountainous basins is examined through a minimalist analytical model. The conceptual hypothesis on which the model is grounded is the existence of a subtractive mechanism that reduces the basin-contributing area in flood formation to the fraction of basin laying below the freezing elevation at the time of occurrence of each precipitation event. This fraction depends on the watershed hypsometric curve and on the seasonal evolution of temperatures. Under this hypothesis, the probability distribution of the annual maximum discharge is analytically derived, based on simple assumptions on the stochastic process of precipitation. The shape and the moments of this distribution explicitly relate to basin hypsometry and to the seasonality of temperatures. Qualitative results show that the simple causative mechanisms can explain the attenuation of flood quantiles in high-elevation basins. Model application to 57 watersheds in the Northwestern Italian Alps effectively demonstrates the role of the hypsography in explaining the spatial variability of the mean of the flood distribution.