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Study on Markov Joint Transition Probability and Encounter Probability of Rainfall and Reference Crop Evapotranspiration in the Irrigation District

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  • Jinping Zhang
  • Yong Zhao
  • Weihua Xiao

Abstract

Based on the markov theory, the first-order markov joint transition probability of rainfall and reference crop evapotranspiration is analyzed to reveal their joint transition laws. Then using copula function, the joint probability distribution of rainfall and reference crop evapotranspiration is built, and the conditional probabilities of rainfall and reference crop evapotranspiration are also presented. The results show that the first-order markov joint transition probability to rich-rich state and rich-poor state of rainfall and reference crop evapotranspiration is larger. The joint encounter frequency of rainfall and reference crop evapotranspiration in synchronous encounter situation is different with that in asynchronous encounter situation. The selected frank copula showing the joint probability distribution characteristics of rainfall and reference crop evapotranspiration is reasonable. When reference crop evapotranspiration is less than 1,865 mm, the sort of its conditional probability in different rainfall states is rich rainfall>normal rainfall>poor rainfall, which presents an opposite to the conditional probability of rainfall in different reference crop evapotranspiration states when rainfall is less than 1,105 mm. Copyright Springer Science+Business Media Dordrecht 2014

Suggested Citation

  • Jinping Zhang & Yong Zhao & Weihua Xiao, 2014. "Study on Markov Joint Transition Probability and Encounter Probability of Rainfall and Reference Crop Evapotranspiration in the Irrigation District," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 28(15), pages 5543-5553, December.
    • Handle: RePEc:spr:waterr:v:28:y:2014:i:15:p:5543-5553
    DOI: 10.1007/s11269-014-0821-x
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    References listed on IDEAS

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    1. Ali Tabrizi & Davar Khalili & Ali Kamgar-Haghighi & Shahrokh Zand-Parsa, 2010. "Utilization of Time-Based Meteorological Droughts to Investigate Occurrence of Streamflow Droughts," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 24(15), pages 4287-4306, December.
    2. Harris Vangelis & Mike Spiliotis & George Tsakiris, 2011. "Drought Severity Assessment Based on Bivariate Probability Analysis," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 25(1), pages 357-371, January.
    3. D. Fu & Y. Li & G. Huang, 2013. "A Factorial-based Dynamic Analysis Method for Reservoir Operation Under Fuzzy-stochastic Uncertainties," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 27(13), pages 4591-4610, October.
    4. Tong, Ling & Kang, Shaozhong & Zhang, Lu, 2007. "Temporal and spatial variations of evapotranspiration for spring wheat in the Shiyang river basin in northwest China," Agricultural Water Management, Elsevier, vol. 87(3), pages 241-250, February.
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    Cited by:

    1. Zhang, Yaling & Guo, Li & Liang, Chuan & Zhao, Lu & Wang, Junqin & Zhan, Cun & Jiang, Shouzheng, 2022. "Encounter risk analysis of crop water requirements and effective precipitation based on the copula method in the Hilly Area of Southwest China," Agricultural Water Management, Elsevier, vol. 266(C).
    2. Zhang, Jinping & Xiao, Honglin & Li, Jiayi & Shi, Xixi, 2021. "Study on the cointegration relationship between water supply and demand in the irrigation district with structural breaks," Agricultural Water Management, Elsevier, vol. 258(C).
    3. Zhang, Shuo & Kang, Yan & Gao, Xuan & Chen, Peiru & Cheng, Xiao & Song, Songbai & Li, Lingjie, 2023. "Optimal reservoir operation and risk analysis of agriculture water supply considering encounter uncertainty of precipitation in irrigation area and runoff from upstream," Agricultural Water Management, Elsevier, vol. 277(C).

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