Complexity analysis of rainfall and runoff time series based on sample entropy in different temporal scales

This study applied sample entropy (SampEn) to rainfall and runoff time series to investigate the complexity of different temporal scales. Rainfall and runoff time series with intervals of 1, 10, 30, 90, and 365 days for the Wu-Tu upstream watershed were used. Thereafter, SampEn was computed for the five rainfall and runoff time series. The results show that for the various temporal scales, comparisons of the complexity between the rainfall and runoff time series based on the SampEn are inconsistent. Calculating the dynamic SampEn further elucidated variations of the complexity in the rainfall and runoff time series. In addition, the results show that SampEn measures of the rainfall and runoff time series are typically higher than the approximate entropy measures of the rainfall and runoff time series for a specific temporal scale. The complexity increases when the sample size increases for a specific temporal scale. Furthermore, temporal scales with low complexity and high predictability are obtained from the variations of SampEn for the rainfall and runoff time series with different temporal scales, thereby providing a reference for determining the appropriate temporal scale for rainfall and runoff time series forecasting.