Abstract
In the existing agricultural water management models under uncertainty, the mutual-correlation and their self-correlation of random variables (like precipitation (P), runoff (R), reference evapotranspiration (ET0), etc.) are often ignored. When expressing the fuzziness of socio-economic factors, fuzzy membership function is usually determined by the experience of decision-makers, which often brings some confusions. To solve the above questions, first, C-vine copula is introduced in this study to depict the multiple interdependence structures. Two kinds of three-dimensional copulas is constructed: \({CV}_{1}({R}_{t}, {P}_{t}, {R}_{t-1})\) and \({CV}_{2}({ET}_{0t}, {P}_{t}, {ET}_{0(t-1)})\), where t is at t-th month. Second, the cloud model, as a novel qualitative and quantitative transformation model, is chosen to describe the uncertainty of crop prices. Combining these two uncertainty-expressing methods, an agricultural water resources optimization model is built to gain maximum net benefit by allocating limited surface water and groundwater. Then this model was applied to a case study in northwestern China. Results show that the developed model could provide the decision-makers with not only the best or the optimum range of system net benefits but also the probability of obtaining a given benefit under complex uncertainties. For comparison, the ordinary models without consideration of dependence of variables as an independent were also built. When overlooking the mutual-correlation and self-correlation, the optimal water allocation and system net benefits would be higher in dry years with total water allocation higher by 4.5%. This unreasonable allocation results may cause excessive agricultural irrigation to squeeze water for other industries in dry years, which would exacerbate water shortages. The discussion and comparison results prove the necessity and effectiveness of this research.
Similar content being viewed by others
References
Aas K, Berg D (2009) Models for construction of multivariate dependence – a comparison study. Eur J Financ 15:639–659. https://doi.org/10.1080/13518470802588767
Aas K, Czado C, Frigessi A, Bakken H (2009) Pair-copula constructions of multiple dependence. Insur: Math Econ 44:182–198. https://doi.org/10.1016/j.insmatheco.2007.02.001
Ali M, Deo RC, Downs NJ, Maraseni T (2018) Cotton yield prediction with Markov Chain Monte Carlo-based simulation model integrated with genetic programing algorithm: a new hybrid copula-driven approach. Agric For Meteorol 263:428–448. https://doi.org/10.1016/j.agrformet.2018.09.002
Alizadeh H, Mousavi SJ, Ponnambalam K (2018) Copula-based chance-constrained hydro-economic optimization model for optimal design of reservoir-irrigation district systems under multiple interdependent sources of uncertainty. Water Resour Res 54:5763–5784. https://doi.org/10.1029/2017wr022105
Allen RG, Pereira LS, Raes D, Smith M (1998) Crop evapotranspiration-guidelines for computing crop water requirements-FAO Irrigation and drainage paper 56, vol 9. FAO, Rome
Bedford T, Cooke RM (2001) Probability density decomposition for conditionally dependent random variables modeled by vines. Ann Math Artif Intell 32:245–268. https://doi.org/10.1023/a:1016725902970
Bevacqua E (2017) CDVineCopulaConditional: Sampling from Conditional C- and D-Vine Copulas, R package version 0.1.0 edn
Bevacqua E, Maraun D, Hobæk Haff I, Widmann M, Vrac M (2017) Multivariate statistical modelling of compound events via pair-copula constructions: analysis of floods in Ravenna (Italy). Hydrol Earth Syst Sci 21:2701–2723. https://doi.org/10.5194/hess-21-2701-2017
Chen F, Huang GH, Fan YR, Wang S (2016) A copula-based chance-constrained waste management planning method: an application to the city of Regina. Sask, Can J Air Waste Manag Assoc 66:307–328. https://doi.org/10.1080/10962247.2015.1135837
Dadmand F, Naji-Azimi Z, Farimani NM, Davary K (2020) Sustainable allocation of water resources in water-scarcity conditions using robust fuzzy stochastic programming. J Clean Prod. https://doi.org/10.1016/j.jclepro.2020.123812
Deng W, Wang G (2017) A novel water quality data analysis framework based on time-series data mining. J Environ Manage 196:365–375. https://doi.org/10.1016/j.jenvman.2017.03.024
Dißmann J, Brechmann EC, Czado C, Kurowicka D (2013) Selecting and estimating regular vine copulae and application to financial returns. Comput Stat Data Anal 59:52–69. https://doi.org/10.1016/j.csda.2012.08.010
Fan Y, Chen Y, Li W, Wang H, Li X (2011) Impacts of temperature and precipitation on runoff in the Tarim River during the past 50 years. J Arid Land 3:220–230. https://doi.org/10.3724/sp.J.1227.2011.00220
Ghahraman B, Sepaskhah A-R (2002) Optimal allocation of water from a single purpose reservoir to an irrigation project with pre-determined multiple cropping patterns. Irrig Sci 21:127–137. https://doi.org/10.1007/s002710100040
Jiang Y (2017) Simulation analysis and optimal regulation for agro-hydrological processes and water use efficiency on multiple scales of the middle Heihe River basin. PhD Thesis, China Agricultural University, Bejing, Chinese
Joe H (1996) Families of $m$-variate distributions with given margins and $m(m-1)/2$ bivariate dependence parameters. In: Ruschendorf L, Schweizer B, Taylor MD (eds) Distributions with Fixed Marginals and Related Topics. Institute of Mathematical Statistics, Hayward. https://doi.org/10.1214/lnms/1215452614
Kong XM, Huang GH, Fan YR, Li YP (2014) Maximum entropy-Gumbel-Hougaard copula method for simulation of monthly streamflow in Xiangxi river. China Stoch Environ Res Risk Assess 29:833–846. https://doi.org/10.1007/s00477-014-0978-0
Kurowicka D, Cooke RM (2007) Sampling algorithms for generating joint uniform distributions using the vine-copula method. Comput Stat Data Anal 51:2889–2906. https://doi.org/10.1016/j.csda.2006.11.043
Li D, Du Y (2007) Artificial intelligence with uncertainty. CRC Press, Florida
Li D, Meng H, Shi X (1995) Membership clouds and membership cloud generators. J Comput Res Dev 32:15–20
Li D, Liu C, Gan W (2009) A new cognitive model: Cloud model. Int J Intell Syst 24:357–375. https://doi.org/10.1002/int.20340
Li D, Wang S, Li D (2015) Spatial data mining: theory and application. 2nd edn. Science Press, Beijing, pp 187–201. https://doi.org/10.1007/978-3-662-48538-5
Li M, Guo P, Singh VP, Yang G (2016) An uncertainty-based framework for agricultural water-land resources allocation and risk evaluation. Agric Water Manag 177:10–23. https://doi.org/10.1016/j.agwat.2016.06.011
Li M, Jiang Y, Guo P, Li J (2017) Irrigation water optimal allocation considering stakeholders of different levels transactions of the Chinese society for agricultural. Machinery 48:199–207
Li M, Fu Q, Singh VP, Ma M, Liu X (2017) An intuitionistic fuzzy multi-objective non-linear programming model for sustainable irrigation water allocation under the combination of dry and wet conditions. J Hydrol 555:80–94. https://doi.org/10.1016/j.jhydrol.2017.09.055
Li M, Fu Q, Singh VP, Liu D, Li J (2020) Optimization of sustainable bioenergy production considering energy-food-water-land nexus and livestock manure under uncertainty. Agric Syst 184:102900. https://doi.org/10.1016/j.agsy.2020.102900
Li M, Fu Q, Singh VP, Liu D, Li T, Zhou Y (2020) Managing agricultural water and land resources with tradeoff between economic, environmental, and social considerations: a multi-objective non-linear optimization model under uncertainty. Agric Syst 178:102685. https://doi.org/10.1016/j.agsy.2019.102685
Liao YJ, Zhao HT, Jiang Y, Ma YK, Luo X, Li XY (2019) An innovative method based on cloud model learning to identify high-risk pollution intervals of storm-flow on an urban catchment scale. Water Res 165:115007. https://doi.org/10.1016/j.watres.2019.115007
Liu C, Feng M, Dai X, Li D (2004) A new algorithm of backward cloud. J Syst Simul 16:2417–2420. https://doi.org/10.16182/j.cnki.joss.2004.11.014
Liu D et al (2014) A risk assessment method based on RBF artificial neural network - cloud model for urban water hazard. J Intell Fuzzy Syst 27:2409–2416. https://doi.org/10.3233/ifs-141210
Lu H, Ren L, Chen Y, Tian P, Liu J (2017) A cloud model based multi-attribute decision making approach for selection and evaluation of groundwater management schemes. J Hydrol 555:881–893. https://doi.org/10.1016/j.jhydrol.2017.10.009
Mahootchi M, Ponnambalam K, Tizhoosh HR (2010) Operations optimization of multireservoir systems using storage moments equations. Adv Water Resour 33:1150–1163. https://doi.org/10.1016/j.advwatres.2010.07.004
Monteith JL (1965) Evaporation and environment. Symp Soc Exp Biol 19:205–234
Nagler T, Schepsmeier U, Stoeber J, Brechmann EC, Graeler B, Erhardt T (2019) VineCopula: Statistical Inference of Vine Copulas, R package version 2.3.0 edn
Nelsen R (2006) An introduction to copulas. Springer, Berlin. https://doi.org/10.1007/0-387-28678-0
Pham MT, Vernieuwe H, Baets BD, Willems P, Verhoest NEC (2015) Stochastic simulation of precipitation-consistent daily reference evapotranspiration using vine copulas. Stoch Env Res Risk Assess 30:2197–2214. https://doi.org/10.1007/s00477-015-1181-7
Purkus A, Röder M, Gawel E, Thrän D, Thornley P (2015) Handling uncertainty in bioenergy policy design–A case study analysis of UK and German bioelectricity policy instruments. Biomass Bioenerg 79:64–79. https://doi.org/10.1016/j.biombioe.2015.03.029
Rezaeian-Zadeh M, Tabari H, Abghari H (2012) Prediction of monthly discharge volume by different artificial neural network algorithms in semi-arid regions. Arab J Geosci 6:2529–2537. https://doi.org/10.1007/s12517-011-0517-y
Saccon P (2018) Water for agriculture, irrigation management. Appl Soil Ecol 123:793–796. https://doi.org/10.1016/j.apsoil.2017.10.037
Singh P, Ramasastri KS, Kumar N, Arora M (2000) Correlations between discharge and meteorological parameters and runoff forecasting from a highly glacierized Himalayan basin. Hydrol Sci J 45:637–652. https://doi.org/10.1080/02626660009492368
Sklar A (1959) Fonctions de répartition á n dimensions et leurs marges. Publications de l’Institut de Statistique de L’Université de Paris, 8:229–231
Wang G, Xu C, Li D (2014) Generic normal cloud model. Inf Sci 280:1–15. https://doi.org/10.1016/j.ins.2014.04.051
Wang D et al (2016) A cloud model-based approach for water quality assessment. Environ Res 148:24–35. https://doi.org/10.1016/j.envres.2016.03.005
Xiang G (2011) Risk assessment and regulation of groundwater development in Zhangye Basin of the Middle Reaches of the Heihe River. Master Thesis, Lanzhou University, Lanzhou, Chinese
Xiang K, Li Y, Horton R, Feng H (2020) Similarity and difference of potential evapotranspiration and reference crop evapotranspiration – a review. Agric Water Manag 232:106043. https://doi.org/10.1016/j.agwat.2020.106043
Yang F, Shao D, Gu W, Xiao C, Tan X, Yangdong H (2012) Stochastic simulation of regional water requirement based on Copula function. Trans Chin Soc Agric Eng Trans of the CSAE 28:107–112. https://doi.org/10.3969/j.issn.1002-6819.2012.18.016
Yu L et al (2020) A copula-based fuzzy interval-random programming approach for planning water-energy nexus system under uncertainty. Energy 196:117063. https://doi.org/10.1016/j.energy.2020.117063
Yue Q, Zhang F, Zhang C, Zhu H, Tang Y, Guo P (2020) A full fuzzy-interval credibility-constrained nonlinear programming approach for irrigation water allocation under uncertainty. Agric Water Manag 230:105961. https://doi.org/10.1016/j.agwat.2019.105961
Zhang C, Guo P (2018) FLFP: A fuzzy linear fractional programming approach with double-sided fuzziness for optimal irrigation water allocation. Agric Water Manag 199:105–119. https://doi.org/10.1016/j.agwat.2017.12.013
Zhang C, Engel BA, Guo P, Liu X, Guo S, Zhang F, Wang Y (2018) Double-sided stochastic chance-constrained linear fractional programming model for managing irrigation water under uncertainty. J Hydrol 564:467–475. https://doi.org/10.1016/j.jhydrol.2018.07.024
Zhang S, Xiang M, Xu Z, Wang L, Zhang C (2020) Evaluation of water cycle health status based on a cloud model. J Clean Prod 245:118850. https://doi.org/10.1016/j.jclepro.2019.118850
Zhang F, Guo S, Liu X, Wang Y, Engel BA, Guo P (2020) Towards sustainable water management in an arid agricultural region: a multi-level multi-objective stochastic approach. Agric Syst 182:102848. https://doi.org/10.1016/j.agsy.2020.102848
Acknowledgements
This research was supported by the National Natural Science Foundation of China (No. 41871199)
Author information
Authors and Affiliations
Contributions
Conceptualization: BS; Methodology: BS, SG, YW; Data collection: BS, PG; Writing—original draft preparation: BS; Writing—review and editing: SG, YW, HL, PG; Funding acquisition: PG; Resources: PG.
Corresponding author
Ethics declarations
Conflicts of interest
We declare that we have no financial and personal relationships with other people or organizations that can inappropriately influence our work. There is no professional or other personal interest of any nature or kind in any product, service and/or company that could be construed as influencing the position presented in, or the review of, the manuscript entitled.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Supplementary information
Rights and permissions
About this article
Cite this article
Shan, B., Guo, S., Wang, Y. et al. Vine copula and cloud model-based programming approach for agricultural water allocation under uncertainty. Stoch Environ Res Risk Assess 35, 1895–1915 (2021). https://doi.org/10.1007/s00477-021-01985-3
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00477-021-01985-3