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Prediction of water shortage loss in situations with small samples based on an improved Gumbel copula

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Abstract

Prediction of water shortage losses is of great importance for water resources management. A new mathematical expression of water shortage loss was proposed in order to describe the random uncertainty and economic attributes of water resources. Then, Gumbel copula with a new method of parameter estimation was introduced to model the joint probabilistic characteristics for water supply and water use in situations when sufficient data is unavailable. The new parameter estimation method requires only the minimum and maximum values of two variables. The improved Gumbel copula was proved to be reliable based on the RMSEs (root mean square error) and AICs (Akaike information criterion), statistical tests and upper tail dependence tests. The potential water shortage losses for all the districts of Tianjin were predicated. The water shortage loss in the Urban district is highest (7.02 billion CNY), followed by the new district of Binhai and Wuqing district, while those in the Baodi district and Ji County are very small.

Highlights

  • A new mathematical expression of water shortage loss was proposed in order to describe the random uncertainty and economic attributes of water resources.

  • Gumbel copula with a new method of parameter estimation was introduced to model the joint probabilistic characteristics for water supply and water use in situations when sufficient data is unavailable.

  • The Gumbel copula was proved to be reliable based on the RMSEs (Root mean square error) and AICs (Akaike information criterion), statistical tests and upper tail dependence tests.

  • The potential water shortage losses for all the districts of Tianjin were predicated.

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Acknowledgements

The study was supported by the Open Research Fund of State Key Laboratory of Simulation and Regulation of Water Cycle in River Basin, China Institute of Water Resources and Hydropower Research, Grant No. IWHR-SKL-KF202009, National Natural Science Foundation of China (Grant Nos. 51609254 and 41875061), and NUPTSF (Grant Nos. NY219161 and NY220035).

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Contributions

The contribution of Longxia Qian is project design, model construction and case study. The contribution of Yong Zhao is project design and result analysis. The contribution of Hongrui Wang is algorithmic programming and model validation. The contribution of Suzhen Dang is data processing and parameter estimation.

Corresponding author

Correspondence to Yong Zhao.

Additional information

Communicated by Subimal Ghosh

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Qian, L., Zhao, Y., Wang, H. et al. Prediction of water shortage loss in situations with small samples based on an improved Gumbel copula. J Earth Syst Sci 130, 3 (2021). https://doi.org/10.1007/s12040-020-01490-1

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  • DOI: https://doi.org/10.1007/s12040-020-01490-1

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