Rainfall Patterns From Multiscale Sample Entropy Analysis

Abstract

Precipitation is a manifestation of many interacting complex processes. How to grasp its temporal pattern that would reveal underlain dominant contributing factors is the key objective of the study. For this, we explored the application of multiscale sample entropy (MSE) in describing the long-term daily precipitation. Sample entropy (SE) adds similarity measure over the conventional information entropy, and it has been used in quantifying changing complexity in chaotic dynamic systems. With the further incorporation of multiscale consideration, the MSE analysis gives the trend of SE changes with scale, and provides a rich description of participating factors. The daily precipitation time series studied were taken from 665 weather stations across China that have been recorded for about 50–61 years. The SE estimates are a function of the length of time series (n), the dimension of similarity (m), and the match threshold (r). These parameters are problem-dependent, and through simulation, this study has determined that m = 2, r = 0.15, and n ≈ 20,000 would be appropriate for estimating SE up to the 30-day scale. Three general patterns of MSE for precipitation time series are identified: (1) Pattern A, SE increases with scale; (2) Pattern B, SE increases then decreases and followed by increase; and (3) Pattern C, SE increases then decreases. The MSE is found capable of detecting differences in characteristics among precipitation time series. Matching MSE thus could serve as a metric to evaluate the adequacy of simulated precipitation time series. Using this metric, we have shown that to embody seasonal changes one needs to use different monthly two-parameter gamma distribution functions in generating simulated precipitation time series. Moreover, for dry seasons, one also needs to consider interannual fluctuations: it is inadequate to use just one single function for simulating multi-year precipitation data. Finally, for the study region, MSE patterns show coherence over the distance in that stations that are close, which range from 40 to 80 km, exhibit similar MSE trends. The MSE patterns obtained are also found to be reflective of the regional precipitation patterns—this has important implications on water resources management.