Regionalization of Climate Elasticity Preserves Dooge's Complementary Relationship

Abstract Climate elasticity of streamflow represents a nondimensional measure of the sensitivity of streamflow to climatic factors. Estimation of such elasticities from observational records has become an important alternative to scenario‐based methods of evaluating streamflow sensitivity to climate. Nearly all previous elasticity studies have used a definition of elasticity known as arc elasticity, which measures changes in streamflow about mean values of streamflow and climate. Using observational records in the western U.S., our findings reveal that elasticity definitions based on power law models lead to both regional and basin specific estimates of elasticity which are physically more realistic than estimates based on arc elasticity. Evaluating the ability of arc and power law elasticity estimators in reproducing Dooge's complementary relationship (DCR) between potential evapotranspiration and precipitation elasticities reveal that power law elasticities estimated from at‐site, panel, and hierarchical statistical models reproduce DCR, whereas corresponding estimators based on arc elasticity cannot reproduce DCR. Importantly, our regional elasticity formulations using panel and hierarchical formulations led to estimates of both regional and basin specific estimates of elasticities, enabling and contrasting streamflow sensitivity to climate across both basins and regions.