Complexity Analysis of Precipitation-Runoff Series Based on a New Parameter-Optimization Method of Entropy

Abstract

Different parameters of dimension m and tolerance threshold r in approximate entropy (ApEn) and sample entropy (SampEn) can cause inconsistency of complexity comparison in hydrologic time series. A new approach to determine the optimal common parameters m and r is presented to solve this inconsistency. Time series of runoff and precipitation during 1956–2010 in the Jinghe watershed of the Chinese Loess Plateau were analyzed. The optimal common parameters were determined to be m=2 and r=0.11 standard deviation of time series. The runoff and precipitation show significant decreasing trends, which are opposite of the significant increasing trends of ApEn and SampEn. The runoff and precipitation have close relationships with their corresponding complexity. The decreasing trend of precipitation has important influences on the increase of runoff complexity. The ApEn is better than the SampEn for describing the general trend of the time series, while the SampEn has a stronger capacity to identify the turning points in the time series. This new approach has wide applicability.