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
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A new mathematical expression of water shortage loss was proposed in order to describe the random uncertainty and economic attributes of water resources.
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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.
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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.
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The potential water shortage losses for all the districts of Tianjin were predicated.
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References
Ayantobo O O, Li Y and Song S 2019 Copula-based trivariate drought frequency analysis approach in seven climatic sub-regions of mainland China over 1961–2013; Theor. Appl. Climatol. 137(3–4) 2217–2237.
Feng L H and Huang C F 2008 A risk assessment model of water shortage based on information diffusion technology and its application in analyzing carrying capacity of water resources; Water Resour. Manag. 22 621.
Frahm G, Junker M and Schmidt R 2005 Estimating the tail dependence coefficient: Properties and pitfalls; Insurance Math. Econom. 37(1) 80–100.
Fujinawa Y 1991 A method for estimating earthquake occurrence probability using first- and multiple-order Markov chain models; Nat. Hazards 4(1) 7–22.
Gan H, Wang L, Ni H and Zhang C 2008 Assessment on methods for calculating economic value of water; J. Hydraul. Eng. 39(11) 1160–1166 (in Chinese).
Gao X, Liu Y and Sun B 2018 Water shortage risk assessment considering large-scale regional transfers: A copula-based uncertainty case study in Lunan, China; Environ. Sci. Pollut. Res. 25(33) 23,328–23,341.
Goldberg D E and Holland J H 1988 Genetic algorithms and machine learning; Mach. Learn. 2 95–99.
Haimes Y Y 2009 On the complex definition of risk: A systems-based approach; Risk Anal. 29(12) 1647–1654.
Hashimoto T, Stedinger J R and Loucks D P 1982 Reliability, resiliency and vulnerability criteria for water resources system performance evaluation; Water Resour. Res. 18(1) 14–20.
Jiang R, Yu X, Xie J, Zhao Y, Li F and Yang M 2018 Recent changes in daily climate extremes in a serious water shortage metropolitan region, a case study in Jing-Jin-Ji of China; Theor. Appl. Climatol. 134(1–2) 565–584.
Li W, Feng C, Dai C, Li Y, Li C and Liu M 2016 An inexact risk management model for agriculture land-use planning under water shortage; Front. Earth Sci. 10(3) 419–431.
Ma M, Song S, Ren L, Jiang S and Song J 2012 Multivariate drought characteristics using trivariate Gaussian and Student t copulas; Hydrol. Process. 27(8) 1175–1190.
Qian L, Wang H, Bai C and Deng C 2019 A new method of parameter estimation for a logistic regression model of water shortage risk in the case of small sample numbers; Math. Geosci., https://doi.org/10.1007/s11004-019-09824-6.
Qian L, Wang H, Dang S, Wang C, Jiao Z and Zhao Y 2018 Modelling bivariate extreme precipitation distribution for data scarce regions using Gumbel–Hougaard copula with maximum entropy estimation; Hydrol. Process. 32 212–227.
Qian L, Wang H and Zhang K 2014 Evaluation criteria and model for risk between water supply and water demand and its application in Beijing; Water Resour. Manag. 28 4433–4447.
Qian L, Zhang R, Hong M, Wang H and Yang L 2016 A new multiple integral model for water shortage risk assessment and its application in Beijing, China; Nat. Hazards 80(1) 43–67.
Vergni L, Todisco F and Mannocchi F 2015 Analysis of agricultural drought characteristics through a two-dimensional copula; Water Resour. Manag. 29(8) 2819–2835.
Yang C C, Yeh C H and Ho C C 2015 Systematic quantitative risk analysis of water shortage mitigation projects considering climate change; Water Resour. Manag. 29(4) 1067–1081.
Yu P S, Yang T C, Kuo C M and Wang Y T 2015 A stochastic approach for seasonal water-shortage probability forecasting based on seasonal weather outlook; Water Resour. Manag. 28(12) 3905–3920.
Zhang D D, Yan D H, Lu F, Wang C Y and Feng J 2015 Copula-based risk assessment of drought in Yunnan province, China; Nat. Hazards 75(3) 2199–2220.
Zhang J, Lin X and Guo B 2016 Multivariate copula-based joint probability distribution of water supply and demand in irrigation district; Water Resour. Manag. 30(7) 2361–2375.
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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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.
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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