Discharge and rainfall control the size and shape of alluvial fans

Alluvial fans are sedimentary deposits that form at the foot of mountain belts. Their surficial and internal structures are used to infer past tectonic or climatic events. They all share a characteristic conical shape with their apex forming at the mouth of a large river flowing from the mountain side. Their size varies widely and appears to be related to the size of their upstream catchment. Here we show that, contrary to the common assumption that fan size is controlled by basement subsidence, this relationship is a direct consequence of the control of discharge (and therefore rainfall) on the efficiency of sediment transport on the fan. We demonstrate this point by comparing morphometric data that we compiled on 69 fans of varied sizes and environments to an analytical solution derived from the most widely used model for sediment transport. We also show, using a two-dimensional numerical model, that fans are dynamical features that reach a quasi steady-state form where frequent avulsions control the distribution of deposition events along the main channel, whilst rainfall-driven erosion takes place elsewhere. Our findings provide a novel framework to interpret the record stored in fans stratigraphy in terms of climatic or tectonic signals.