An information-theoretic approach for evaluating catchment scale process relationships

Hydrological responses of a catchment evolve due to the complex interactions between various climate inputs and landscape characteristics. Such interactions and the resulting hydrological processes need to be adequately understood to explicitly describe the catchment’s behaviour and process dynamics. Hydrological modelling serves as a powerful tool to strengthen the understanding of such complex process interactions. Conventional hydrological modelling practices focus on calibrating the model outputs with an aim only to match the observed discharge at stream gauge locations. This procedure might not adequately capture the process interactions and the underlying causalities, especially in catchments exhibiting strong non-linear hydrological process relationships. While getting the streamflow right, there is a chance that the other hydrological processes may be wrongly captured, i.e., getting the right calibration results for the wrong reasons. In this study, information-theoretic measures such as Shannon Entropy, Mutual Information and Transfer Entropy are used to understand the process relationships simulated using a physically based hydrological model. The grid-based Variable Infiltration Capacity (VIC) model is employed at a spatial resolution of 0.25 x 0.25-degree over the Cauvery river basin in peninsular India at a daily time scale. Entropy measures are applied to the major hydrological processes such as rainfall, surface runoff, actual evapotranspiration and baseflow, which are simulated using the model, and their relationships are evaluated using non-linear correlation metrics. The study also proposes an entropy-based calibration framework for improving the model efficiency in simulating the catchment water balance. This work highlights the advantages of using information-theoretic measures over conventional methods in evaluating hydrological process relationships, especially in catchments manifesting strong non-linear hydrological behaviour.