Permutation Entropy and its Niche in Hydrology: A Review

Complexity is one of the most discriminating properties of complex systems. In principle, this property cannot be fully captured by any single model, although contemporary approaches strive to address this limitation. Current calculations of complexity by models indicate only trends of evolving the complex system. Another method of analysis complexity is using the information measures applied to time series obtained by measurements. Permutation entropy (PE) is one of those measures. This non-parametric information measure quantifies the degree of disorder or complexity within a time series by examining the order relations among its values. Its benchmark is the quality of simplicity, robustness, and very low computational cost. The advantages and drawbacks of PE are considered. The diverse applications of PE in hydrology categorizing the uses of PE across various subfields, examining its role in runoff prediction, streamflow analysis, water level forecasting, assessment of hydrological changes, measurement of statistical complexity, and the impact of infrastructure on hydrology, is reviewed.