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Water Resources Management

, Volume 33, Issue 3, pp 1203–1215 | Cite as

Upper and Lower Bound Interval Forecasting Methodology Based on Ideal Boundary and Multiple Linear Regression Models

  • Wei LiEmail author
  • Jianzhong Zhou
  • Lu Chen
  • Kuaile Feng
  • Hairong Zhang
  • Changqing Meng
  • Na Sun
Article
  • 111 Downloads

Abstract

The uncertainty research of hydrological forecast attracts the attention of a host of hydrological experts. Prediction Interval (PI) is a convinced method that can ensure the forecasting accuracy meanwhile take uncertainty range into consideration. While the existed Prediction Interval methods need algorithm optimization and are susceptible to local optima, so it is particularly urgent to provide an efficient Prediction Interval (PI) model with excellent performance. This paper proposes a novel upper and lower bound interval estimation model to rapidly define the PI and reduce the amount of calculation to implement convenient and high precise hydrological forecast. Above all, the ideal upper and lower bounds are defined according to the relative width or absolute width. Then, the proposed model is utilized to forecast interval runoff via least square method and multiple linear regression methods. The estimated interval inclusion ratio, interval width, symmetry, and root-mean-square error which are popular used to judge the precision serve as accuracy evaluation indexes. The measured discharge data from five hydrological stations which located upstream of the Yangtze River is applied for interval forecasting. Compared with the results of neural network-based upper and lower bound interval estimation model, the proposed method yields higher forecasting accuracy, meanwhile, the ideal upper and lower bounds successfully minimize the number of processes which require a mass of parameter searching and optimization.

Keywords

Interval hydrological forecasting The ideal boundary Multiple linear regression models Upper and lower bound estimation 

Notes

Acknowledgements

This work was supported by the State Key Program of National Natural Science of China of Major Research Projects (No. 91547208), 2017 research project of ChongQing Municipal Education Commission “The cross-sectional study of optimal hydraulics in rural irrigation canals of Chongqing Three Gorges Reservoir Region” (KJ1735447), High-level talent introduction fund of Chongqing Water Resources and Electric Engineering Colleage in the year 2016-2017 (No.:KRC201702): Study on the Bearing Capacity of Region Water Resources—by Taking the YongChuan District in ChongQing City as an Example.

Compliance with Ethical Standards

Conflict of Interest

None.

References

  1. Abdi A, Hassanzadeh Y, Ouarda TBMJ (2017) Regional frequency analysis using growing neural gas network. J Hydrol 550:92–102CrossRefGoogle Scholar
  2. Alemu ET, Palmer RN, Polebitski A, Meaker B (2010) Decision support system for optimizing reservoir operations using ensemble streamflow predictions. J Water Resour Plan Manag 137(1):72–82CrossRefGoogle Scholar
  3. Blasone RS, Vrugt JA, Madsen H et al (2008) Generalized likelihood uncertainty estimation (GLUE) using adaptive Markov chain Monte Carlo sampling[J]. Adv Water Resour 31(4):630–648CrossRefGoogle Scholar
  4. Bogner K, Pappenberger F, Cloke HL (2012) Technical note: the normal quantile transformation and its application in a flood forecasting system. Hydrol Earth Syst Sci 16(4):1085–1094.  https://doi.org/10.5194/hess-16-1085-2012 CrossRefGoogle Scholar
  5. Carpenter TM, Georgakakos KP (2006) Intercomparison of lumped versus distributed hydrologic model ensemble simulations on operational forecast scales[J]. J Hydrol 329(1):174–185CrossRefGoogle Scholar
  6. Chen X, Yang T, Wang X, Xu C-Y, Yu Z (2013) Uncertainty intercomparison of different hydrological models in simulating extreme flows. Water Resour Manag 27(5):1393–1409CrossRefGoogle Scholar
  7. D’Oria M, Mignosa P, Tanda MG (2014) Bayesian estimation of inflow hydrographs in ungauged sites of multiple reach systems. Adv Water Resour 63:143–151.  https://doi.org/10.1016/j.advwatres.2013.11.007 CrossRefGoogle Scholar
  8. Fan FM, Schwanenberg D, Alvarado R, dos Reis AA, Collischonn W, Naumman S (2016) Performance of deterministic and probabilistic hydrological forecasts for the short-term optimization of a tropical hydropower reservoir. Water Resour Manag 1–17Google Scholar
  9. Golian S, Saghafian B, Maknoon R (2010) Derivation of probabilistic thresholds of spatially distributed rainfall for flood forecasting. Water Resour Manag 24(13):3547–3559CrossRefGoogle Scholar
  10. Guo J, Zhou J, Zou Q, Liu Y, Song L (2013) A novel multi-objective shuffled complex differential evolution algorithm with application to hydrological model parameter optimization. Water Resour Manag 27(8):2923–2946CrossRefGoogle Scholar
  11. Hassanzadeh Y, Abdi A, Talatahari S, Singh VP (2011) Metaheuristic algorithms for hydrologic frequency analysis. Water Resour Manag 25(7):1855–1879CrossRefGoogle Scholar
  12. Herr HD, Krzysztofowicz R (2010) Bayesian ensemble forecast of river stages and ensemble size requirements. J Hydrol 387(3–4):151–164.  https://doi.org/10.1016/j.jhydrol.2010.02.024 CrossRefGoogle Scholar
  13. Herr HD, Krzysztofowicz R (2015) Ensemble Bayesian forecasting system part I: theory and algorithms. J Hydrol 524:789–802.  https://doi.org/10.1016/j.jhydrol.2014.11.072 CrossRefGoogle Scholar
  14. Kasiviswanathan KS, Sudheer KP (2016) Comparison of methods used for quantifying prediction interval in artificial neural network hydrologic models. Model Earth Syst Environ 2(1).  https://doi.org/10.1007/s40808-016-0079-9
  15. Krzysztofowicz R (2014) Probabilistic flood forecast: exact and approximate predictive distributions. J Hydrol 517:643–651.  https://doi.org/10.1016/j.jhydrol.2014.04.050 CrossRefGoogle Scholar
  16. Li H, Xu C-Y, Beldring S, Tallaksen LM, Jain SK (2016) Water resources under climate change in Himalayan basins. Water Resour Manag 30(2):843–859CrossRefGoogle Scholar
  17. Li M, Yang D, Chen J, Hubbard SS (2012) Calibration of a distributed flood forecasting model with input uncertainty using a Bayesian framework. Water Resour Res 48(8).  https://doi.org/10.1029/2010WR010062
  18. Liu Z, Guo Y, Wang L, Wang Q (2015) Streamflow forecast errors and their impacts on forecast-based reservoir flood control. Water Resour Manag 29(12):4557–4572CrossRefGoogle Scholar
  19. Marshall L, Nott D, Sharma A (2004) A comparative study of Markov chain Monte Carlo methods for conceptual rainfall-runoff modeling. Water Resour Res 40(2):n/a-n/a.  https://doi.org/10.1029/2003wr002378
  20. Montanari A (2007) What do we mean by ‘uncertainty’? The need for a consistent wording about uncertainty assessment in hydrology. Hydrol Process 21(6):841–845CrossRefGoogle Scholar
  21. Sang Y-F (2013) Improved wavelet modeling framework for hydrologic time series forecasting. Water Resour Manag 27(8):2807–2821CrossRefGoogle Scholar
  22. Taormina R, Chau K-W (2015) ANN-based interval forecasting of streamflow discharges using the LUBE method and MOFIPS. Eng Appl Artif Intell 45:429–440.  https://doi.org/10.1016/j.engappai.2015.07.019 CrossRefGoogle Scholar
  23. Wu J, Lu G, Wu Z (2014) Flood forecasts based on multi-model ensemble precipitation forecasting using a coupled atmospheric-hydrological modeling system. Nat Hazards 74(2):325–340CrossRefGoogle Scholar
  24. Ye L, Zhou J, Gupta HV, Zhang H, Zeng X, Chen L (2016) Efficient estimation of flood forecast prediction intervals via single- and multi-objective versions of the LUBE method. Hydrol Process 30(15):2703–2716.  https://doi.org/10.1002/hyp.10799 CrossRefGoogle Scholar
  25. Yu P-S, Yang T-C, Kuo C-M, Wang Y-T (2014) A stochastic approach for seasonal water-shortage probability forecasting based on seasonal weather outlook. Water Resour Manag 28(12):3905–3920CrossRefGoogle Scholar
  26. Zarghami M, Abdi A, Babaeian I, Hassanzadeh Y, Kanani R (2011) Impacts of climate change on runoffs in East Azerbaijan, Iran. Glob Planet Chang 78(3–4):137–146CrossRefGoogle Scholar
  27. Zhang H, Zhou J, Ye L, Zeng X, Chen Y (2015) Lower upper bound estimation method considering symmetry for construction of prediction intervals in flood forecasting. Water Resour Manag 29(15):5505–5519.  https://doi.org/10.1007/s11269-015-1131-7 CrossRefGoogle Scholar
  28. Zhao T, Cai X, Yang D (2011) Effect of streamflow forecast uncertainty on real-time reservoir operation. Adv Water Resour 34(4):495–504.  https://doi.org/10.1016/j.advwatres.2011.01.004 CrossRefGoogle Scholar
  29. Zhao T, Zhao J, Yang D, Wang H (2013) Generalized martingale model of the uncertainty evolution of streamflow forecasts. Adv Water Resour 57:41–51.  https://doi.org/10.1016/j.advwatres.2013.03.008 CrossRefGoogle Scholar

Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  • Wei Li
    • 1
    • 2
    Email author
  • Jianzhong Zhou
    • 2
    • 3
  • Lu Chen
    • 2
    • 3
  • Kuaile Feng
    • 2
    • 3
  • Hairong Zhang
    • 2
    • 3
  • Changqing Meng
    • 2
    • 3
  • Na Sun
    • 2
    • 3
  1. 1.Chongqing Water Resources and Electric Engineering CollegeChongqingChina
  2. 2.School of Hydropower and Information EngineeringHuazhong University of Science and TechnologyWuhanChina
  3. 3.Hubei Key Laboratory of Digital Valley Science and TechnologyWuhanChina

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