Climate, interseasonal storage of soil water, and the annual water balance

The effects of annual totals and seasonal variations of precipitation and potential evaporation on the annual water balance are explored. It is assumed that the only other factor of significance to annual water balance is a simple process of water storage, and that the relevant storage capacity is the plant-available water-holding capacity of the soil. Under the assumption that precipitation and potential evaporation vary sinusoidally through the year, it is possible to derive an analytic solution of the storage problem, and this yields an expression for the fraction of precipitation that evaporates (and the fraction that runs off) as a function of three dimensionless numbers: the ratio of annual potential evaporation to annual precipitation (index of dryness); an index of the seasonality of the difference between precipitation and potential evaporation; and the ratio of plant-available water-holding capacity to annual precipitation. The solution is applied to the area of the United States east of 105°W, using published information on precipitation, potential evaporation, and plant-available water-holding capacity as inputs, and using an independent analysis of observed river runoff for model evaluation. The model generates an areal mean annual runoff of only 187 mm, which is about 30% less than the observed runoff (263 mm). The discrepancy is suggestive of the importance of runoff-generating mechanisms neglected in the model. These include intraseasonal variability (storminess) of precipitation, spatial variability of storage capacity, and finite infiltration capacity of land.