Entropy-Based Quantification of Hydrological Variability in Peninsular Indian River Basins

Hydrological variability in river basins arises from complex, non-linear interactions between climatic forcing and catchment characteristics that are often inadequately captured by conventional statistical measures. In hydro-climatically diverse regions such as Peninsular India, there is a need for scale-consistent and assumption-free approaches to quantify both variability and process interdependence. This study applies an information-theoretic framework to characterise hydrological variability and process connectivity across river basins in Peninsular India. Long-term hydrological data, including daily precipitation and streamflow data for a large number of catchments, were obtained from the CAMELS-IND dataset. Analyses were conducted at daily, monthly, and annual time scales to investigate scale-dependent behaviour. Prior to the information-theoretic analysis, trends of various hydrological processes were assessed using non-parametric methods, including the Mann–Kendall test, to identify potential temporal changes in hydrological regimes. Shannon entropy and mutual information measures were used to quantify the variability and uncertainty of various hydrological processes and process relationships across spatial and temporal scales. Trend analysis indicates spatially heterogeneous precipitation and streamflow behaviour across river basins of Peninsular India, with stations exhibiting increasing, decreasing, and non-significant trends. Precipitation entropy is generally higher than streamflow entropy across catchments, suggesting differences in variability between climatic inputs and runoff responses. Mutual information analysis further reveals scale-dependent variations in rainfall–runoff dependence across catchments. The results highlight the potential of information-theoretic metrics for characterising hydrological variability and rainfall–runoff relationships in data-scarce and hydro-climatically heterogeneous regions.