Abstract
A hydrologic model consists of several parameters which are usually calibrated based on observed hydrologic processes. Due to the uncertainty of the hydrologic processes, model parameters are also uncertain, which further leads to the uncertainty of forecast results of a hydrologic model. Working with the Bayesian Forecasting System (BFS), Markov Chain Monte Carlo simulation based Adaptive Metropolis method (AM-MCMC) was used to study parameter uncertainty of Nash model, while the probabilistic flood forecasting was made with the simulated samples of parameters of Nash model. The results of a case study shows that the AM-MCMC based on BFS proposed in this paper is suitable to obtain the posterior distribution of the parameters of Nash model according to the known information of the parameters. The use of Nash model and AM-MCMC based on BFS was able to make the probabilistic flood forecast as well as to find the mean and variance of flood discharge, which may be useful to estimate the risk of flood control decision.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bayes T R, 1763. An essay towards solving a problem in the doctrine of chances. Philosophical Transactions of the Royal Society of London, 53: 370–418.
Beven K J, Binley A, 1992. The future of distributed models: Model calibration and uncertainty prediction. Hydrological Processes, 6(3): 270–298. DOI: 10.1002/hyp.3360060305
Beven K J, Kirkby M J, 1979. A physically based variable contributing area model of basin hydrology. Hydrological Science Bulletin, 24(1): 43–69.
Burnash R J C, Ferral R L, McGuire R A, 1973. A generalied streamflow simulation system: Conceptual modeling for digital computers (technical report). Sacramento: Joint Federal and State River Forecast Center, U.S. National Weather Service and California Department of Water Resources, 204.
Crawford N H, Linsley R K, 1966. Digital simulation in hydrology: Stanford Watershed Model IV (technical report No. 39). Stanford: Department of Civil Engineering, Stanford University, 210.
Direcu S, Reis J, Jery R S, 2005. Bayesian MCMC flood frequence analysis with historical information. Journal of Hydrology, 313(1–2): 97–116. DOI: 10.1016/j.jhydrol.2005.02.028.
Gelman A G, Roberts G O, Gilks W R, 1996. Efficient Metropolis jumping rules. In: Bernardo J M et al. (eds.). Bayesian Statistics V. Oxford: Oxford University Press, 599–608.
Gelman A, Rubin D B, 1992. Inference from iterative simulation using multiple sequences. Statistics Science, 7(4): 457–511.
Haario H, Saksman E, Tamminen J, 1999. Adaptive proposal distribution for random walk Metropolis algorithm. Computing Statistics, 14, 375–395.
Haario H, Saksman E, Tamminen J, 2001. An adaptive metropolis algorithm. Bernoulli, 7(2): 223–242.
Hasting W K, 1970. Monte carlo sampling methods using markov chain and their applications. Biomertrika, 57: 97–109.
Henry D H, Krzysztofowicz R, 2010. Bayeisan ensemble forecast of river stages and ensemble size requirements. Journal of Hydrology, 387(3–4): 151–164. DOI: 10.1016/j.jhydrol.2010.02.024.
Kelly K S, Krzysztofowicz, 2000. Precipitation uncertain processor for probabilistic river stage forecasting. Water Resources Research, 36(9): 2643–2653. DOI: 10.1029/2000WR900061
Krzysztofowicz R, 1985. Bayesian models of forecasted time series. Water Resources Bulletin, 21(5): 805–814. DOI: 10.11-11/j.1752-1688.1985.tb00174.x
Krzysztofowicz R, 1999. Bayesian theory of probabilistic via deterministic hydrologic model. Water Resources Research, 35(9): 2739–2750. DOI: 10.1029/1999WR900180
Krzysztofowicz R, 2002. Bayesian system for probabilistic river stage forecasting. Journal of Hydrology, 268(1–4): 16–40. DOI: 10.1016/s0022-1694(02)00106-3
Krzysztofowicz R, Drzal W J, Drake T R et al., 1993. Probabilistic quantitative precipitation forecasts for river basin. Weather Forecasting, 8(4): 424–439.
Krzysztofowicz R, Herr H D, 2001. Hydrologic uncertainty processor for probabilistic river forecasting: precipitation dependent model. Journal of Hydrology, 249(1–4): 46–48.
Krzysztofowicz R, Kelly K S, 2000. Hydrologic uncertainty processor for probabilistic river stage forecasting. Water Resources Research, 36(11): 3265–3277. DOI: 10.1029/2000WR-900108
Krzysztofowicz R, Maranzano C J, 2004. Hydrologic uncertainty processor for probabilistic stage transition forecasting. Journal of Hydrology, 293(1–4): 57–73. DOI: 10.1016/j.jhydrol.2004.01.003
Metropolis N, Rosenbluth A W, Rosebluth M L et al., 1953. Equation of state calculations by fast computing machines. Journal of Chemistry and Physics, 21: 1087–1092.
Nash J E, 1958. The form of instantaneous unit hydrograph. International Association of Scientific Hydrology, 51: 546–557.
Wang Jianping, Cheng Shutian, Jia Haifeng, 2006. Markov Chain Monte Carlo Scheme for parameter uncertainty analysis in water quality model. Chinese Journal of Environment Science, 27(1): 24–30. (in Chinese)
Xing Zhenxiang, Rui Xiaofang, Cui Haiyan, 2007. Bayesian probabilistic flood forecasting based on AM-MCMC. Journal of Hydraulic Engineering, 38(12): 1500–1506. (in Chinese)
Zhao R J, 1980. The Xin’anjiang model, proceedings oxford symposium. International Association of Hydrological Science Prediction in Ungauged Basin, 129: 351–356.
Author information
Authors and Affiliations
Corresponding author
Additional information
Foundation item: Under the auspices of National Natural Science Foundation of China (No. 50609005), Chinese Postdoctoral Science Foundation (No. 2009451116), Postdoctoral Foundation of Heilongjiang Province (No. LBH-Z08255), Foundation of Heilongjiang Province Educational Committee (No. 11451022)
Rights and permissions
About this article
Cite this article
Xing, Z., Rui, X., Fu, Q. et al. Nash model parameter uncertainty analysis by AM-MCMC based on BFS and probabilistic flood forecasting. Chin. Geogr. Sci. 21, 74–83 (2011). https://doi.org/10.1007/s11769-010-0433-1
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11769-010-0433-1