Predicting Streamflow Elasticity Based on Percolation Theory and Ecological Optimality

Abstract

How much terrestrial precipitation is used by vegetation and how much runs off, represents central issues in hydrologic science, ecology, climate change, and even geopolitics. We present a theory for the water balance to predict the fractional change in streamflow due to given fractional changes in temperature and precipitation. The theory involves a single parameter whose value is derived under the conditions of neither energy- nor water-limitations and, therefore, is not an adjustable parameter. By comparison with extensive data for precipitation elasticity ϵ_p at global scale, we find that the theory captures the key trends of the variations of the median value of ϵ_p with the aridity index A_I. In contrast to a shortcoming of the classical Budyko phenomenology, namely, convergence to ϵ_p = 4 for large A_I, our theory yields a value of 2 for the median value of ϵ_p for all A_I > 1, in accord with the data for major river basins, as well as with the median value of summaries of global and continental data sets. Incorporating in the theory the effects of annual changes in water storage leads to the ability to predict the range of observed values of the elasticity as a function of the aridity index, or its inverse, the humidity index, as well as the run-off ratio. When changes in storage are neglected, the theory yields more accurate predictions for major river drainages than for small watersheds, particularly if the large basin spans various climate regimes and, as such, an integration over climates tends to reduce relative changes in the storage.