The role of evapotranspiration in streamflow modeling - An analysis using entropy

Informational entropy can be used to elucidate some important relationships between precipitation, evapotranspiration (ET), and discharge over a range of spatial and temporal scales. Entropy does not suffer from any a priori assumptions of linearity or distributional characteristics. In a study of the Southeastern United States, entropy and mutual information were used to identify relationships between hydrologic variables over spatial scales from a few hundred to several thousand km(2) and temporal scales from days to months. Two distinct ET data sets were compared- one based on a highly parameterized energy budget approach and the other based on a complex iterative solution and a modified Penman method. It was found that there was a considerable difference in uncertainty between the two methods and that, although they each contained some amount of explanatory information regarding streamflow the more complex approach contained the most shared information. Further, it was found that streamflow entropy, or uncertainty, increased with drainage area, indicating that larger basins have more uncertainty to be reduced, in that more information can possibly be gained through the knowledge of other variables. However, the knowledge of ET reduces a greater proportion of uncertainty in smaller basins (< 1500 km(2)), while larger basins have more unexplained variability.