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

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.

Framework for Understanding Structural Errors (FUSE): A modular framework to diagnose differences between hydrological models

“…When the annual available energy, expressed as potential evapotranspiration, is greater than the annual precipitation, the annual evaporation is limited by the annual supply of water. Conversely, when the available energy is less than the available precipitation, the annual evaporation is limited by the annual supply of energy [Milly, 1994;Milly and Dunne, 2002]. Evaporation in the French Broad River is constrained by the annual supply of energy, but in the Guadalupe River the annual supply of energy and water is approximately equal.…”

Comparison of future runoff projections using Budyko framework and global hydrologic model: conceptual simplicity vs process complexity

“…In terms of their changes, the CCR of surface storage increased from 39% to 46%, while that of soil moisture decreased from 54% to 50%. Hence the process-based hydrologic model suggested more contribution from quick response-type surface runoff as the soil moisture storage approached an upper limit with the increase of precipitation in the future (Milly, 1994). On the contrary, constant n parameter in the Budyko equation assumed no change in the runoff generating mechanism.…”

Comment on “Antiphasing between Rainfall in Africa's Rift Valley and North America's Great Basin”

“…There is no obvious benefit to pursuing the issue further in this direction; with increasing numbers of degrees of freedom, the problem becomes proportionately unconstrained. It may be noted, however, that the theory presented by Milly (1994) provides a framework for generalizing (1) and (2) for changing seasonality of climate.…”