Predicting Streamflow Elasticity Based on Percolation Theory and Ecological Optimality

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 e(p) at global scale, we find that the theory captures the key trends of the variations of the median value of e(p) with the aridity index A(I). In contrast to a shortcoming of the classical Budyko phenomenology, namely, convergence to e(p) = 4 for large A(I), our theory yields a value of 2 for the median value of e(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.

Automated summary

The utilization of precipitation and the amount of runoff are key issues in hydrologic science, ecology, climate change, and geopolitics. We propose a theory for water balance that predicts changes in streamflow due to changes in temperature and precipitation. The theory incorporates a single parameter, derived under certain conditions, that is not adjustable. By comparing the theory with global data on precipitation elasticity, we find that it accurately captures the trends of median precipitation elasticity variations. Unlike the classical Budyko phenomenology, our theory yields a median precipitation elasticity value of 2 for all aridity indices greater than 1.