Abstract
Multiscale entropy is a popular and valuable methodology for analyzing hydrological complexity. However, some errors and limitations remain in its use and interpretation. This study identified three key issues, incorrect mapping of entropy values with frequency signals, an insufficient time scale range, and an unclear relationship between features in the multiscale entropy curve and hydrological interpretation. To address these issues, we focused on the sediment concentration and runoff in the Yanhe Watershed and conducted in-depth explorations using refined composite multiscale entropy (RCMFE) and three other methods, power spectrum density analysis, wavelet transform, and surrogate analysis.The results indicate that the entropy at each scale is influenced by signals with time scales equal to or greater than its own scale and that its variation is controlled by the overall signal dispersion. The RCMFE method demonstrated suitability for the complexity analysis of sediment and runoff sequences with short-length data. To effectively capture hydrological complexity, attention to the scale range issue is crucial, ensuring that the richness of complex features at larger scales in multiscale entropy curves is not overlooked. Interpretation of the local minima and maxima in the multiscale entropy curve is highlighted. Local minima signify high periodic patterns and predictability, whereas the first peak, typically occurring at approximately 2–3 months, is a valuable indicator of the overall complexity of the hydrological series. Linear characteristics were found to contribute significantly to the hydrological complexity, with stronger linear correlations resulting in an overall increase, lower local minima, and increased volatility in the multiscale entropy curve. The notable reduction in the hydrological complexity of the Yanhe Watershed calls for ecological sustainability and sustainable soil and water conservation efforts.
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