Abstract
A methodology to statistically analyze the function of runoff or flow regulations in a river basin and year-by-year change in its performance is proposed. The Shannon's information entropy is employed to evaluate the auto-entropies indicating temporal dispersion of occurrence of hydrological events ; rainfall in a catchment of a reservoir, inflow to the reservoir (i.e., runoff to the reservoir) and outflow from the reservoir. Using the Kullback-Leibler distance (often called the cross-entropy) to measure distance or discrepancy of a posterior distribution from a prior distribution, change in distribution between different two hydrological variables in rainfall-runoff process or in inflow-outflow process in analyzed. In order to investigate time-varying performance of hydrological regulation, each of these entropy statistics is expressed in a time evolutionary series. An emphasis is made that combined use of the auto-entropy and the cross-entropy is indispensable in a practical analysis. A sample application of the methodology is made to a dam reservoir and its catchment in Yasu River basin, Japan. The results suggest that during the last 50 years the runoff regulation function of the catchment has come to be regressive, and performance of the flow regulation in the reservoir has perceptibly been dependent on the skill of dam operators.
