On the information content of reservoirs’ storage and discharge for the predictability of one another

Mass balance equation is the fundamental governing equation that links reservoirs’ inflow, storage and discharge; yet, it remains unclear to what extent each component can be inferred from the others. This is particularly the case when considering large samples of reservoirs with wide range of capacities and operational purposes. Here, we use an entropy-based framework to investigate the predictability of reservoirs’ storage and discharge based on the information of content of one another. Using the time series data of inflow, storage, and discharge from 52 reservoirs across the globe, we treat mass balance with two parallel approaches. First, we examine how well discharge can be constrained by antecedent storage and inflow. Second, we assess the predictability of storage based on discharge and inflow. Marginal and conditional entropies are used to measure and quantify information flows from one variable to the other and to evaluate how much uncertainty is reduced when additional information is introduced. We apply this approach to observational data as well as simulated data obtained from reservoir algorithms. Our results reveal considerable variability in entropy measures across reservoirs and between the two approaches. The suggested framework can be considered as flexible and empirical means for assessing reservoir algorithms and for evaluating the role of data assimilation in improving reservoir simulations in hydrology and land-surface models.