Climate, soil water storage, and the average annual water balance

TLDR

The study tests the hypothesis that long‑term water balance is governed solely by local interactions of fluctuating precipitation and potential evapotranspiration, mediated by soil water storage. Using this hypothesis and idealized representations of input variability, the authors develop a simple model for a finite area with uniform climate, partitioning average annual precipitation into evapotranspiration and runoff based on seven dimensionless numbers (dryness index, soil water‑holding capacity ratio, mean precipitation events, gamma shape parameter, and seasonality measures of precipitation intensity, storm arrival rate, and potential evapotranspiration), and test it on the U.S. east of the Rockies without calibration.

Abstract

This paper describes the development and testing of the hypothesis that the long‐term water balance is determined only by the local interaction of fluctuating water supply (precipitation) and demand (potential evapotranspiration), mediated by water storage in the soil. Adoption of this hypothesis, together with idealized representations of relevant input variabilities in time and space, yields a simple model of the water balance of a finite area having a uniform climate. The partitioning of average annual precipitation into evapotranspiration and runoff depends on seven dimensionless numbers: the ratio of average annual potential evapotranspiration to average annual precipitation (index of dryness); the ratio of the spatial average plant‐available water‐holding capacity of the soil to the annual average precipitation amount; the mean number of precipitation events per year; the shape parameter of the gamma distribution describing spatial variability of storage capacity; and simple measures of the seasonality of mean precipitation intensity, storm arrival rate, and potential evapotranspiration. The hypothesis is tested in an application of the model to the United States east of the Rocky Mountains, with no calibration. Study area averages of runoff and evapotranspiration, based on observations, are 263 mm and 728 mm, respectively; the model yields corresponding estimates of 250 mm and 741 mm, respectively, and explains 88% of the geographical variance of observed runoff within the study region. The differences between modeled and observed runoff can be explained by uncertainties in the model inputs and in the observed runoff. In the humid (index of dryness <1) parts of the study area, the dominant factor producing runoff is the excess of annual precipitation over annual potential evapotranspiration, but runoff caused by variability of supply and demand over time is also significant; in the arid (index of dryness >1) parts, all of the runoff is caused by variability of forcing over time. Contributions to model runoff attributable to small‐scale spatial variability of storage capacity are insignificant throughout the study area. The consistency of the model with observational data is supportive of the supply‐demand‐storage hypothesis, which neglects infiltration excess runoff and other finite‐permeability effects on the soil water balance.