Abstract
It is very important to estimate the parameters of a risk prediction model in the case of small samples. This paper proposed an improved method for predicting water shortage risk in situations when insufficient data are available. The new method (maximum entropy estimation, MEE) does not require the data about water shortage risk but only a few data about the risk factors. Twelve simulations or experiments were made to evaluate the performance of MEE under different small sample size and compared with the maximum likelihood estimation (MLE) which requires a large amount of data about risk and its factors, and two models which require small samples about risk and risk factors. The result shows that MEE performs much better than MLE, and has an advantage over the two models. Water shortage risks in 2020 in all the districts or counties of Tianjin were predicted by using the new method. The result shows that the values of water shortage risk in most of the districts or counties of Tianjin are very high when the transferred and unconventional water are not used. After using the transferred and unconventional water, all the values of water shortage risk decline considerably.
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References
Bai C Z, Zhang R, Hong M, Qian L and Wang Z 2015 A new information diffusion modelling technique based on vibrating string equation and its application in natural disaster risk assessment; Int. J. Gen. Syst. 44(5) 601–614.
Brown C C 1982 On a goodness-of-fit test for the logistic model based on score statistics; Commun. Stat.-Theo. Meth. 11(10) 1087–1105.
Coron C, Calenge C, Giraud C and Julliard R 2018 Bayesian estimation of species relative abundances and habit preferences using opportunistic data; Environ. Ecol. Stat. 25(1) 71–93.
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.
Goldberg D E and Holland J H 1988 Genetic algorithms and machine learning; Mach. Learn. 2 95–99.
Guhathakurta P and Saji E 2013 Detecting changes in rainfall pattern and seasonality index vis-à-vis increasing water scarcity in Maharashtra; J. Earth Syst. Sci. 122(3) 639–649.
Huang C F 1997 Principle of information diffusion; Fuzzy Sets Syst. 91(1) 69–90.
Jia X L, Li C H, Cai Y P, Wang X and Sun L 2015 An improved method for integrated water security assessment in the Yellow River basin, China; Stoch. Environ. Res. Risk Assess. 29(8) 2213–2227.
Jones G A and Jones J M 2000 Information and coding theory; Springer-Verlag London Ltd., London.
Liu B and Gan H 2018 Evapotranspiration management based on the application of SWAT for balancing water consumption: A case study in Guantao, China; J. Earth Syst. Sci. 127 51.
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.
Qian L, Wang H, Dang S, Wang C, Jiao Z and Zhao Y 2018a Modelling bivariate extreme precipitation distribution for data scarce regions using Gumbel–Hougaard copula with maximum entropy estimation; Hydrol. Process. 32 212–227.
Qian L, Zhang R, Hou T and Wang H 2018b A new nonlinear risk assessment modeling technique based on an improved project pursuit; Stoch. Environ. Res. Risk Assess. 32(6) 1465–1478.
Singh V P 1997 The use of entropy in hydrological and water resources; Hydrol. Process. 11 587–626.
Tidwell V C, Cooper J A and Silva C J 2005 Threat assessment of water supply systems using Markov latent effects modeling; J. Water Resour. Plann. Manag. 131(3) 218–227.
Yan B W, Guo S L and Xiao Y 2007 Synchronous-asynchronous encounter probability of rich-poor precipitation between source area and water receiving areas in the Middle Route of South-North Water Transfer Project; J. Hydraul. Eng. 38(10) 1178–1185 (in Chinese).
Yan D, Weng B and Wang G et al. 2014 Theoretical framework of generalized watershed drought risk evaluation and adaptive strategy based on water resources system; Nat. Hazards 73(2) 259–276.
Yan D, Yao M and Ludwig F et al. 2018 Exploring future water shortage for large river basins under different water allocation strategies; Water Resour. Manag. 32(9) 3071–3086.
Yerel S and Anagun A S 2010 Assessment of water quality observation stations using cluster analysis and ordinal logistic regression technique; Int. J. Environ. Pollut. 42(4) 344–358.
Yu P S, Yang T C, Kuo C M and Wang Y T 2014 A stochastic approach for seasonal water-shortage probability forecasting based on seasonal weather outlook; Water Resour. Manag. 28(12) 3905–3920.
Zhang Q, Liang X and Fang Z et al. 2016 Urban water resources allocation and shortage risk mapping with support vector machine method; Nat. Hazards 81 1209–1228.
Zhang Q, Zhang J, Yan D and Bao Y 2013 Dynamic risk prediction based on discriminant analysis for maize drought disaster; Nat. Hazards 65 1275–1284.
Zheng J, Wu W and Hu X et al. 2011 Integrated risk governance-comprehensive energy and water resources risk in China; Science Press, Beijing (in Chinese).
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The study was supported by National Natural Science Foundation of China (Grant No. 51609254).
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Communicated by Subimal Ghosh
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Qian, L., Wang, Z., Wang, H. et al. An improved method for predicting water shortage risk in the case of insufficient data and its application in Tianjin, China. J Earth Syst Sci 129, 48 (2020). https://doi.org/10.1007/s12040-019-1299-y
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DOI: https://doi.org/10.1007/s12040-019-1299-y