The role of spatial rainfall variability for the emergence of heavy tails in streamflow distributions

Heavy-tailed probability distributions of streamflow are frequently observed in river basins. In case of right skewed distributions, the larger probability assigned to relatively high flows translates into an unneglectable chance of occurrence of extreme floods in a long-term hydrological response. Although the spatial variability of rainfall has been identified as an impactful driver of flood events, delineating its effects for the emergence of heavy tails of streamflow distributions is still challenging.

In this study we apply a simple stochastic approach to generate spatially various rainfall as the input of a well-established continuous hydrological model. The model embeds the soil water balance in hillslopes, the probability distributions of transit times in the hillslopes of subcatchments, and the response time distribution in channels derived from a geomorphological analysis of the river network. We investigate the role of spatially variable rainfall for the emergence of heavy tails in streamflow distributions by simulating a wide range of spatial rainfall variability in five catchments in Germany, and then put the modelling results into real world context by analyzing historical data in 175 catchments across the whole Germany.

We find that increasing spatial variability of rainfall determines heavier streamflow tails only beyond a certain increase threshold which depends on physiographic features of catchments. Small and elongated catchments are less resilient to increasing spatial rainfall variability, i.e., their streamflow distributions begin to exhibit heavier tails for smaller increments of the spatial variability of rainfall. The distribution of runoff-routing pathway is suggested to be an effective attribute of catchments in this process.