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Nov. 2010, Nanjing, CHINA

Uncertainty Analysis of Hydrological Model Using Multi-criteria Likelihood Measure Within the GLUE Method. Li Ru ZHANG 张利茹. Nanjing Hydraulics Research Institute 南 京 水 利 科 学 研 究 院. Nov. 2010, Nanjing, CHINA. Outlines 汇报提纲. 一、 Structure of XAJ Model 新安江模型简介 二、 Uncertainty Analysis

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Nov. 2010, Nanjing, CHINA

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  1. Uncertainty Analysis of Hydrological Model Using Multi-criteria Likelihood Measure Within the GLUE Method Li Ru ZHANG 张利茹 Nanjing Hydraulics Research Institute 南 京 水 利 科 学 研 究 院 Nov. 2010, Nanjing, CHINA

  2. Outlines 汇报提纲 一、Structure of XAJ Model 新安江模型简介 二、Uncertainty Analysis 不确定性研究 三、应用 A case study

  3. Outlines 汇报提纲 一、Structure of XAJ Model 新安江模型简介 二、Uncertainty Analysis 不确定性研究 三、应用 A case study

  4. P and EM E K B,WM IM RB R 1-FR FR UH Qs Rs SM UM EU W EX LM EL WU S C ED CI WL RI QI ∑Q WD KG KI CG RG QG Structure of XAJ Model,1960’s

  5. Mr. Hydrologist Parameter calibration Human-computer interactive（interaction of artificial debugging and Automatically optimazation algorithm） Simplex method, Rosenbrock method 5/27 2014/9/10

  6. = observations = simulated flows * Flow Hours Parameters Optimization Probability distribution to be maximized

  7. Outlines 汇报提纲 一、Structure of XAJ Model 新安江模型简介 二、Uncertainty Analysis 不确定性研究 三、应用 A case study

  8. Input data Model structure Model parameter Uncertainty Analysis Uncertainty Generalized error Fuzzy characteristics Objective existence Uncertainty in Hydrology Randomness Uncertainty Shortage of subjective cognizance Hydrological Phenomena +Model Uncertainty of nature Output Uncertainty Hydrological Model

  9. Uncertainty Analysis 95% 5% Uncertainty associated with parameters Total Uncertainty including structural Errors Flow Hours

  10. Methods of uncertainty analysis • GLUE(Generalized Likelihood Uncertainty Estimation) • BaRE (Bayesian Recursive Estimation) • Markov Chain Monte Carlo, MCMC • Multi-criteria GLUE methodology

  11. The GLUE Methodology GLUEis based on the BaRE(Bayesian Recursive Estimation): Where is a specified Prior Likelihood is a likelihood measure calculated with input vector Y is Posterior Likelihood indicates the observations is parameter vector is a scaling constant

  12. Procedure for GLUE (1) Choice of the likelihood objective function Nash-Sutcliffe (2) Ascertain the parameter ranges and prior distributed function (3) Model parameter uncertainty analysis(scatter plots) (4)Comparison of prediction limits for a selected period

  13. the multi-criteria GLUE methodology is Nash-sutcliffe coefficient is the peak forecast error is the runoff error is the peak time error

  14. Multi-criteria Referring in the book of “intelligence hydrological forecasting norms ”,the principle is as fellows: Where is the bigger the better and the other three the smaller the better.

  15. Outlines 汇报提纲 一、Structure of XAJ Model 新安江模型简介 二、Uncertainty Analysis 不确定性研究 三、应用 A case study

  16. A Case study Lianghui Basin Area:35.06km2 Input: • rainfall(mm) • evaporation(mm) • observed runoff(m3/s) • model parameters Distribution of hydrological station around LiangHui Reservoir Output: simulated runoff(m3/s)

  17. parameter Ranges and prior distributed function Parameter ranges: Prior distributed function: Homogenous distribution

  18. Statistics for S and M The total simulation is 10000, for S ,the number of effective simulation is 827;for M, the number is 488 . S:the single-objection likelihood measure; M:the multi-criteria likelihood measure

  19. Scatter plots for GLUE

  20. Scatter plots for GLUE For the GLUE method, parameter Ci, kg and ki are not more sensitive than parameters Cs, Sm and Wm.

  21. Scatter plots for multi-criteria GLUE

  22. Scatter plots for multi-criteria GLUE For the multi-criteria GLUE method, parameter Ci, kg and ki are not more sensitive than parameters Cs, Sm and Wm. This shows the same phenomena with the GLUE method.

  23. Compare with these two methods , it is found that the scatter plots are clearly different for the same parameter under two different conditions. For the same parameter, scatter plots get from multi-criteria GLUE are obviously less than the scatter plots get from GLUE. • From above two figs, the equifinal phenomenon is exist.

  24. the equifinal phenomenon

  25. conclutions • This Nash-Sutcliffe coefficient can’t show all the characters of hydrology at the same time, so the multi-criteria GLUE is proposed. • For the same parameter, scatter plots get from multi-criteria GLUE are obviously less than the scatter plots get from GLUE. that is to say, this multi-criteria GLUE can sharply decrease the parameter sets of “equivalent”, the uncertainty of parameters can also be cut down. Comparison conforms that this multi-criteria GLUE methodology is superior to the GLUE methodology.

  26. Thank You !

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