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Research on the joint probability distribution of rainfall and reference crop evapotranspiration

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Abstract

The relationship between rainfall and reference crop evapotranspiration (ET0) can be complex in an irrigation district. To reveal such complex and possibly a nonlinear relationship, rainfall and ET0 data were collected at the Xinxiang irrigation experiment station from the years 1961 to 2010. Marginal distributions of the two variables derived from fitting the Pearson Type III distribution were incorporated for the development of the joint probability distribution using a copula model. Subsequently, the joint probability as well as the return period of given specific rainfall and ET0 values can be computed. For the analysis of the variations in drought conditions over the 50 years, the copula-based joint probability is further decomposed into several subcomponents using the empirical mode decomposition method. The variations under distinct frequencies and over different time periods were observed. Our results showed that the joint probability distribution of rainfall and ET0 can facilitate the planning for drought resistance in an irrigation district.

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Abbreviations

ET0 :

Reference crop evapotranspiration

IDF:

Intensity–duration–frequency

P-III type:

Pearson Type III

EMD:

Empirical mode decomposition

XXIES:

Xinxiang irrigation experiment station

IMF:

Intrinsic mode function

SD:

Standard deviation

OLS:

Ordinary least squares

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Acknowledgments

This research is supported by the National Natural Sciences Foundation of China (Project No. 51309202), Outstanding Young Talent Research Fund of Zhengzhou University (Project No. 1521323002) and Fundamental Research Funds for the Central Universities (Project No. SWU115081).

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Authors and Affiliations

  1. School of Water Conservancy & Environment, Zhengzhou University, High-tech District, No. 100 Science Road, Zhengzhou, 450001, Henan, China

    Jinping Zhang

  2. State Key Laboratory of Simulation and Regulation of Water Cycle in River Basin, China Institute of Water Resources and Hydropower Research, Beijing, 100038, China

    Yong Zhao

  3. Tianjin Zhongshui Science and Technology Consulting Co., LTD, Tianjin, 300170, China

    Zhihong Ding

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  1. Jinping Zhang
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  2. Yong Zhao
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  3. Zhihong Ding
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Correspondence to Jinping Zhang.

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Zhang, J., Zhao, Y. & Ding, Z. Research on the joint probability distribution of rainfall and reference crop evapotranspiration. Paddy Water Environ 15, 193–200 (2017). https://doi.org/10.1007/s10333-016-0540-4

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  • DOI: https://doi.org/10.1007/s10333-016-0540-4

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