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Necessary length of daily precipitation time series for different entropy measures

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Abstract

Entropy is a useful tool to measure the uncertainty of precipitation. However, the necessary length of the precipitation time series is not clear because of the highly spatial-temporal variability of precipitation and the quite different mechanisms of entropy indices. Thus, this study aims at exploring the relationship between necessary length of daily precipitation time series and the typical entropy indices, including information entropy and sample entropy, denoted as IE and SE respectively. Firstly, the probability distribution of the entropy calculated from data with the same length is identified using the K-S test. Based on the confidential interval of 95%, the threshold value and the necessary length are obtained. On the basis of the results calculated by 675 65-year-length daily precipitation time series in China, the spatial distributions of the minimum length and their influencing factors are uncovered. The main findings are manifested by the following aspects. Generally, the entropy calculated from data with the same length follows a normal distribution, from which the threshold value is obtained: coefficient of variance, CV, equaling to 0.025 on the basis of the 95% confidential interval. The average necessary length is 35 years for SE and 24 years for IE, with the range of 8–58 years and 5–60 years respectively. Spatially, the necessary length is mainly affected by the climatic conditions: smaller values observed in southern humid areas while the larger value in arid areas. The necessary length for SE, NLSE, is larger than the data length for IE, NLIE, in the southern areas. However, the NLSE is smaller than NLIE in part of extreme arid areas. The reason is mainly the different mechanism of the two entropy measures: a lower frequency of precipitation events in arid areas require a longer period to capture almost all of the rainfall intensity to make the probability distribution stable. These results would not only provide some useful references to determine the necessary data length when explore the temporal variability of SE with the climate change, but also provide a deeper insight into understanding the different entropy measures for precipitation time series.

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Acknowledgements

The research was supported by Science and Technology Funding of Guizhou Province (grant numbers LH [2017]7290), Science and Technology Funding of Water Resources Department of Guizhou Province (grant numbers KT201707), National Natural Science Foundation of China (grant number 41701558) and The first class subject foundation of Civil Engineering of Guizhou Province (QYNYL[2017]0013),.

Author contributions statement

Chunmin Zhang, the first author, was responsible for the calculating and the writing this manuscript; Xiangyang Zhou as the corresponding author proposed the idea of this study, and was responsible for collecting the data and revising the manuscript. Wenjuan Lei, the third author, searched the background of the hydrological effect of oasis and helped to revise this manuscript. All authors have read and approved the final manuscript.

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Authors and Affiliations

  1. College of Water Resource and Hydropower, Sichuan University, Chengdu, 610065, China

    Chunmin Zhang

  2. State Key Laboratory of Hydraulics and Mountain River Engineering, Sichuan University, Chengdu, 610065, China

    Chunmin Zhang & Xiangyang Zhou

  3. College of Resource and Environmental Engineering, Guizhou University, Guiyang, 550025, China

    Xiangyang Zhou

  4. College of Architecture & Environment, Sichuan University, Chengdu, 610065, China

    Wenjuan Lei

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  1. Chunmin Zhang
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  2. Xiangyang Zhou
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Correspondence to Xiangyang Zhou.

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Zhang, C., Zhou, X. & Lei, W. Necessary length of daily precipitation time series for different entropy measures. Earth Sci Inform 12, 475–487 (2019). https://doi.org/10.1007/s12145-019-00392-1

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