IDEAS home Printed from https://ideas.repec.org/a/spr/waterr/v35y2021i11d10.1007_s11269-021-02921-4.html
   My bibliography  Save this article

Analytical Water Shortage Probabilities and Distributions of Various Lead Times for a Water Supply Reservoir

Author

Listed:
  • Jenq-Tzong Shiau

    (National Cheng Kung University)

Abstract

Reducing the negative impacts of water shortages is the primary concern of water supply reservoir operation. This study aims to propose a theoretical framework of water shortage probabilities and distributions of various future lead times for a water supply reservoir based on the supply–demand relationship. Reservoir supply ability is represented by the water availability, which is the sum of storage and inflow. The water availability distribution is obtained by the convolution of storage and inflow distributions since both are random variables. The water shortage probability is thus the probability that the water availability is insufficient to meet the known demand. The water shortage distribution is a flip of the water availability distribution with a right-shifted amount of demand and truncating the infeasible negative water shortage. The Nanhua Reservoir located in southern Taiwan is used as an example to illustrate the proposed methodology. The water shortage probabilities and distributions of various initial storage amounts in any month for future 1- to 6-month lead times are constructed based on the fitted inflow distribution and known monthly demand. Apparently different water shortage probabilities in various months are attributed to the initial storage and inherently different inflow distributions in low- or high-inflow months. Low initial storage induces greater water shortage probabilities in low-inflow months, but approximate null probabilities are noted in high-inflow months due to abundant inflow. The effects of future lead times on water shortage probabilities and distribution also reflect the characteristics of inflow distributions of the current and lead-time months under consideration.

Suggested Citation

  • Jenq-Tzong Shiau, 2021. "Analytical Water Shortage Probabilities and Distributions of Various Lead Times for a Water Supply Reservoir," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 35(11), pages 3809-3825, September.
    • Handle: RePEc:spr:waterr:v:35:y:2021:i:11:d:10.1007_s11269-021-02921-4
    DOI: 10.1007/s11269-021-02921-4
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11269-021-02921-4
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11269-021-02921-4?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Jenq-Tzong Shiau & Yen-Ning Hung & Huei-Er Sie, 2018. "Effects of Hedging Factors and Fuzziness on Shortage Characteristics During Droughts," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 32(5), pages 1913-1929, March.
    2. Moursi, Hossam & Kim, Daeha & Kaluarachchi, Jagath J., 2017. "A probabilistic assessment of agricultural water scarcity in a semi-arid and snowmelt-dominated river basin under climate change," Agricultural Water Management, Elsevier, vol. 193(C), pages 142-152.
    3. Israel R. Orimoloye & Johanes A. Belle & Adeyemi O. Olusola & Emmanuel T. Busayo & Olusola O. Ololade, 2021. "Spatial assessment of drought disasters, vulnerability, severity and water shortages: a potential drought disaster mitigation strategy," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 105(3), pages 2735-2754, February.
    4. Cherubini, Umberto & Mulinacci, Sabrina & Romagnoli, Silvia, 2011. "A copula-based model of speculative price dynamics in discrete time," Journal of Multivariate Analysis, Elsevier, vol. 102(6), pages 1047-1063, July.
    5. Giuseppe Rossi & Antonino Cancelliere, 2013. "Managing drought risk in water supply systems in Europe: a review," International Journal of Water Resources Development, Taylor & Francis Journals, vol. 29(2), pages 272-289, June.
    6. Qian Zhang & Xiujuan Liang & Zhang Fang & Tao Jiang & Yubo Wang & Lei Wang, 2016. "Urban water resources allocation and shortage risk mapping with support vector machine method," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 81(2), pages 1209-1228, March.
    7. Jenq-Tzong Shiau & Hsu-Hui Wen & I-Wen Su, 2021. "Comparing Optimal Hedging Policies Incorporating Past Operation Information and Future Hydrologic Information," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 35(7), pages 2177-2196, May.
    8. Andreas Nicolaidis Lindqvist & Rickard Fornell & Thomas Prade & Linda Tufvesson & Sammar Khalil & Birgit Kopainsky, 2021. "Human-Water Dynamics and their Role for Seasonal Water Scarcity – a Case Study," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 35(10), pages 3043-3061, August.
    9. Ruckdeschel, Peter & Kohl, Matthias, 2014. "General Purpose Convolution Algorithm in S4 Classes by Means of FFT," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 59(i04).
    10. Qian Zhang & Xiujuan Liang & Zhang Fang & Tao Jiang & Yubo Wang & Lei Wang, 2016. "Urban water resources allocation and shortage risk mapping with support vector machine method," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 81(2), pages 1209-1228, March.
    11. Longxia Qian & Ren Zhang & Mei Hong & Hongrui Wang & Lizhi Yang, 2016. "A new multiple integral model for water shortage risk assessment and its application in Beijing, China," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 80(1), pages 43-67, January.
    12. Pao-Shan Yu & Tao-Chang Yang & Chen-Min Kuo & Yi-Tai Wang, 2014. "A Stochastic Approach for Seasonal Water-Shortage Probability Forecasting Based on Seasonal Weather Outlook," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 28(12), pages 3905-3920, September.
    13. Sel Ly & Kim-Hung Pho & Sal Ly & Wing-Keung Wong, 2019. "Determining Distribution for the Product of Random Variables by Using Copulas," Risks, MDPI, vol. 7(1), pages 1-20, February.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Irfan Ahmed Shaikh & Aimrun Wayayok & Munir Ahmed Mangrio & Ziyad Ali Alhussain & Farman Ali Chandio & Zaheer Ahmed Khan & Waseem Asghar Khan & Mogtaba Mohammed & Murtada K. Elbashir & Jamshaid Ul Rah, 2022. "Optimizing Approach of Water Allocation to Off-Takes During Reduced Flows," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 36(3), pages 891-913, February.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. A. S. Giannikopoulou & F. K. Gad & E. Kampragou & D. Assimacopoulos, 2017. "Risk-Based Assessment of Drought Mitigation Options: the Case of Syros Island, Greece," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 31(2), pages 655-669, January.
    2. Qiang Zhang & Tianyao Qi & Vijay Singh & Yongqin Chen & Mingzhong Xiao, 2015. "Regional Frequency Analysis of Droughts in China: A Multivariate Perspective," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 29(6), pages 1767-1787, April.
    3. Richard L. Warr & Cason J. Wight, 2020. "Error Bounds for Cumulative Distribution Functions of Convolutions via the Discrete Fourier Transform," Methodology and Computing in Applied Probability, Springer, vol. 22(3), pages 881-904, September.
    4. Meghan Klasic & Amanda Fencl & Julia A. Ekstrom & Amanda Ford, 2022. "Adapting to extreme events: small drinking water system manager perspectives on the 2012–2016 California Drought," Climatic Change, Springer, vol. 170(3), pages 1-25, February.
    5. Wenjing Xie & João Paulo Vieito & Ephraim Clark & Wing-Keung Wong, 2020. "Could Mergers Become More Sustainable? A Study of the Stock Exchange Mergers of NASDAQ and OMX," Sustainability, MDPI, vol. 12(20), pages 1-25, October.
    6. Bambo Bayo & Shakeel Mahmood, 2023. "Geo-spatial analysis of drought in The Gambia using multiple models," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 117(3), pages 2751-2770, July.
    7. Francis Liu & Natalie Packham & Meng-Jou Lu & Wolfgang Karl Härdle, 2023. "Hedging cryptos with Bitcoin futures," Quantitative Finance, Taylor & Francis Journals, vol. 23(5), pages 819-841, May.
    8. José Edmundo de-Almeida-e-Pais & Hugo D. N. Raposo & José Torres Farinha & Antonio J. Marques Cardoso & Svitlana Lyubchyk & Sergiy Lyubchyk, 2023. "Measuring the Performance of a Strategic Asset Management Plan through a Balanced Scorecard," Sustainability, MDPI, vol. 15(22), pages 1-19, November.
    9. Kim-Hung Pho & Tuan-Kiet Tran & Thi Diem-Chinh Ho & Wing-Keung Wong, 2019. "Optimal Solution Techniques in Decision Sciences A Review," Advances in Decision Sciences, Asia University, Taiwan, vol. 23(1), pages 114-161, March.
    10. Carmen Hervás-Gámez & Fernando Delgado-Ramos, 2019. "Drought Management Planning Policy: From Europe to Spain," Sustainability, MDPI, vol. 11(7), pages 1-26, March.
    11. Glenn Baxter & Panarat Srisaeng & Graham Wild, 2019. "An Assessment of Airport Sustainability: Part 3—Water Management at Copenhagen Airport," Resources, MDPI, vol. 8(3), pages 1-24, July.
    12. Roman Matkovskyy, 2019. "Extremal Economic (Inter)Dependence Studies: A Case of the Eastern European Countries," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 17(3), pages 667-698, September.
    13. Sel Ly & Kim-Hung Pho & Sal Ly & Wing-Keung Wong, 2019. "Determining Distribution for the Product of Random Variables by Using Copulas," Risks, MDPI, vol. 7(1), pages 1-20, February.
    14. Guido Antonetti & Matteo Gentilucci & Domenico Aringoli & Gilberto Pambianchi, 2022. "Analysis of landslide Susceptibility and Tree Felling Due to an Extreme Event at Mid-Latitudes: Case Study of Storm Vaia, Italy," Land, MDPI, vol. 11(10), pages 1-21, October.
    15. Jenq-Tzong Shiau & Hsu-Hui Wen & I-Wen Su, 2021. "Comparing Optimal Hedging Policies Incorporating Past Operation Information and Future Hydrologic Information," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 35(7), pages 2177-2196, May.
    16. Wei Li & Jianzhong Zhou & Huaiwei Sun & Kuaile Feng & Hairong Zhang & Muhammad Tayyab, 2017. "Impact of Distribution Type in Bayes Probability Flood Forecasting," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 31(3), pages 961-977, February.
    17. Valeriy A. Naumov & Yuliya V. Gaidamaka & Konstantin E. Samouylov, 2020. "Computing the Stationary Distribution of Queueing Systems with Random Resource Requirements via Fast Fourier Transform," Mathematics, MDPI, vol. 8(5), pages 1-9, May.
    18. Ruqayah Mohammed & Miklas Scholz, 2017. "Impact of Evapotranspiration Formulations at Various Elevations on the Reconnaissance Drought Index," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 31(1), pages 531-548, January.
    19. Soyeon Lim & Seungyub Lee & Donghwi Jung, 2021. "Identifying the Drought Impact Factors and Developing Drought Scenarios Using the DSD Model," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 35(14), pages 4809-4823, November.
    20. Sel Ly & Kim-Hung Pho & Sal Ly & Wing-Keung Wong, 2019. "Determining Distribution for the Quotients of Dependent and Independent Random Variables by Using Copulas," JRFM, MDPI, vol. 12(1), pages 1-27, March.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:waterr:v:35:y:2021:i:11:d:10.1007_s11269-021-02921-4. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.