Elasticity curves describe streamflow sensitivity to precipitation across the entire flow distribution

Abstract. Streamflow elasticity is a simple approximation of how responsive a river is to precipitation. It is represented as a ratio of the expected percentage change in streamflow for a 1 % change in precipitation. Typically estimated for the annual median streamflow, we here propose a new concept in which streamflow elasticity is estimated across the full range of streamflow percentiles in a large-sample context. This “elasticity curve” can be used to develop a more complete depiction of how streamflow responds to precipitation. We find three different elasticity curve types which characterize this relationship at the annual and seasonal timescales in the USA, based on two statistical modelling approaches, a panel regression which facilitates causal inference and a single catchment model which allows for consideration of static attributes. Type A describes catchments where low flows are the least and high flows are the most responsive to precipitation. The majority of catchments at the annual, winter, and fall timescales exhibit this behavior. Type B describes catchments where the response is relatively consistent across the flow distribution. At the seasonal timescale, many catchments experience a consistent level of response across the flow regime. This is especially true in snow-fed catchments during cold months, when the actual elasticity skews towards zero for all flow percentiles while precipitation is held in storage. Consistent response is also seen across the majority of the country during spring when streamflow is comparatively stable and in summer when evaporation demand is high and soil moisture is low. Finally, Type C describes catchments where low flows are the most responsive to precipitation change. These catchments are dominated by highly flashy low flow behavior. We show that the curve type varies separately from the magnitude of the elasticity. Finally, we demonstrate that available water storage is likely the key control which determines curve type.