Runoff and Evapotranspiration Elasticities in the Western United States: Are They Consistent With Dooge's Complementary Relationship?

Many studies have examined how runoff (Q) responds to long-term changes in precipitation (P) and temperature (T), but the effects of potential evapotranspiration (PET) have received less attention. We examine observational data sets for P, T, and Q, along with PET estimated from observations, to determine the extent to which derived P and PET runoff elasticities (epsilon(P) and epsilon(PET), the fractional changes in runoff associated with given fractional changes in precipitation and PET, respectively) meet Dooge's complementary relationship (under certain conditions, epsilon(P) + epsilon(PET) = 1). We apply three statistical methods and two hydrologic models to estimate epsilon(P) and epsilon(PET) in 84 headwater river basins in California, Oregon, and Washington. We find that while the estimates of epsilon(P) are generally consistent across two statistical estimators and one model-based estimator, the estimates of epsilon(PET) using the statistical methods differ considerably (generally, they are much more negative) from the model-based estimates, and some appear to be implausible. The model-based estimates show better conformance to the complementary relationship (and in the median across sites, they sum to close to 1.0). We explore several factors that might explain the failure of the observation-based estimators, including interaction between P and PET and nonclosure of the water budget at annual time scales.