Parameters Uncertainty Analysis in Estimating Probable Maximum Flood in Bakhtiary Dam Basin by Monte Carlo Method

Document Type : Research Paper


1 Department of Water Resources Engineering, Faculty of Agriculture and Natural Resources, Ahvaz Branch, Islamic Azad University (IAU), Ahvaz, Iran.

2 Professor of Hydrology and Water Resources Engineering Department, Collage of Water Sciences Engineering, Shahid Chamran University of Ahvaz, Ahvaz, Iran.

3 Assistant prof, Hydrology and Water Resource Engineering, faculty of Water Sciences Engineering, Shahid Chamran Univrsity, Ahvaz, Iran.


The reliability and validity of extreme floods, especially the probable maximum flood (PMF), requires to consider uncertainty sources in flood estimation. Parameters uncertainty of rainfall-runoff models are the main sources of uncertainty in flood estimation. In this paper, the Monte Carlo method has been used to estimate the PMF hydrograph uncertainty due to uncertainty in the calibration parameters of the rainfall-runoff model in Bakhtiary Basin in southwestern of Iran. The HEC-HMS hydrologic model was used to estimate the PMF hydrograph resulted by the probable maximum precipitation (PMP). The SCS curve number, Clark's unit hydrograph and Muskingum methods were used to model losses, rainfall-runoff transform and river flood routing, respectively. The results show that the uncertainty in peak discharge and volume of PMF hydrograph due to the uncertainty of all parameters are 17.13 and 6.79%, respectively. The results showed that the uncertainty in peak discharge and PMF hydrograph volume due to uncertainty of all parameters are 17.13 and 6.79 percent respectively. The uncertainty in peak discharge of PMF hydrograph due to curve number, initial losses, concentration time, Clark's storage coefficient, Muskingum K and Muskingum X parameters are 5.05, 0.4, 3.78, 3.85, 4.05 and 0.01 percent respectively. Also, the uncertainty in the PMF hydrograph volume due to the uncertainty of the curve number, initial losses, concentration time, Clark's storage coefficient, Muskingum K and Muskingum X parameters were 4.46, 0.332, 0.328, 1.6, 0.08 and 0.0002 percent respectively. Therefore, in order to reduce the uncertainty in estimating PMF hydrograph, it is necessary to be more precise in estimating the parameters of curve number, Muskingum K, Clark's storage coefficient and concentration time, respectively.


Abrahart, R., Kneale, P. E. and See, L. M. (2004). Neural networks for hydrological modeling. CRC Press, 316p
Australian Bureau of Meteorology (1996). Development of the generalized southeast Australia, Method for estimating probable maximum precipitation, Hydrology Report Series, HRS, R., No.4.
Beauchamp, J., Leconte, R., Trudel, M., & Brissette, F. (2013). Estimation of the summer‐fall PMP and PMF of a northern watershed under a changed climate. Water Resources Research, 49(6), 3852-3862.
Bhavsar, P.N. and Patel, J.N., 2018. Event-based rainfall–run-off modeling and uncertainty analysis for lower Tapi Basin, India. ISH Journal of Hydraulic Engineering, pp.1-10.
Dotto, C. B., Kleidorfer, M., Deletic, A., Rauch, W., McCarthy, D. T., & Fletcher, T. D. (2011). Performance and sensitivity analysis of stormwater models using a Bayesian approach and long-term high resolution data. Environmental Modelling & Software, 26(10), 1225-1239.
Eckhardt, K., Breuer, L., & Frede, H. G. (2003). Parameter uncertainty and the significance of simulated land use change effects. Journal of Hydrology, 273(1-4), 164-176.
FathAbadi, A., Ruohani, H., Seyedian, S. M. (2018). The efficiency of nonparametric methods based on residual analizes and parametric method to estimate hydrological model uncertainty. Iran Water and Soil Research Journal, 49(2), 281-292. (In Farsi)
Gangrade, S., Kao, S. C., Naz, B. S., Rastogi, D., Ashfaq, M., Singh, N., & Preston, B. L. (2018). Sensitivity of probable maximum flood in a changing environment. Water Resources Research, 54(6), 3913-3936.
Gao, G. Y., Fu, B. J., Lü, Y. H., Liu, Y., Wang, S., & Zhou, J. (2012). Coupling the modified SCS-CN and RUSLE models to simulate hydrological effects of restoring vegetation in the Loess Plateau of China. Hydrology and Earth System Sciences, 16(7), 2347-2364.
Hydrologic Engineering Center. (2018). Hydrologic modeling system HEC-HMS: User manual and Applications Guide: Version 4.3, U.S. Army Corps of Engineers, Davis, CA.
Iran Power and Water Resources Development Company (2006a). Review Report of Probable Maximum Precipitation (PMP) Studies, Bakhtiari Dam and Power Plant Design, Iranian Water and Power Resources Development Company, 175 p.  (In Farsi)
Iran Power and Water Resources Development Company (2006b). Review Report of Probable Maximum Flood (PMF) Studies, Bakhtiari Dam and Power Plant Design, Iranian Water and Power Resources Development Company, 110 p. (In Farsi)
Kabir, A., Bahremand, A. R. (2013). Study uncertainty of parameters of rainfall-runoff model (WetSpa) by Mont Carlo method. J. of Water and Soil Conservation, Vol. 20(5), pp: 97-81.  (In Farsi)
Kahe, M.S., Javadi, S. and Roozbahani A. (2017). Uncertainty Assessment of Hydraulic Conductivity Parameter in MODFLOW Model Using Monte Carlo and RPEM Methods (Case Study: Ali Abad Plain of Qom). Iran Water Resources Research, 14(2):23-35 (In Farsi)
Karami cheme, E. and Mazaheri, M. (2018). Determine of the importance of longitude dispersion coefficient on solute transport in rivers using the Monte Carlo simulation. Iran Water and Soil Research Journal, 50(4), 763-776. (In Farsi)
Karimi, Sh., Jabbarian Amiri, B. and Malekian, A. (2018). Modeling the Impact of Watershed Physical Attributes on Surface Water Quality and Uncertainty Assessment of the Models Using the Monte Carlo Simulation. Iran Water Resources Research, 14(3):304-317 (In Farsi)
Klein, I. M., Rousseau, A. N., Frigon, A., Freudiger, D., & Gagnon, P. (2016). Evaluation of probable maximum snow accumulation: Development of a methodology for climate change studies. Journal of hydrology, 537, 74-85.
Kumar, R., Chatterjee, C., Lohani, A.K., Kumar, S., and Singh, R.D. (2002). Sensitivity analysis of the GIUH based Clark model for a catchment. Water Resources Management, 16, 263–278.
Kunkel, K. E., Karl, T. R., Easterling, D. R., Redmond, K., Young, J., Yin, X., & Hennon, P. (2013). Probable maximum precipitation and climate change. Geophysical Research Letters, 40(7), 1402-1408.
Liu, Y. R., Li, Y. P., Huang, G. H., Zhang, J. L., & Fan, Y. R. (2017). A Bayesian-based multilevel factorial analysis method for analyzing parameter uncertainty of hydrological model. Journal of hydrology, 553, 750-762.
Maskey, S., Guinot, V., & Price, R. K. (2004). Treatment of precipitation uncertainty in rainfall-runoff modelling: a fuzzy set approach. Advances in water resources, 27(9), 889-898.
Maskey, S., Price, R. K. (2003). Uncertainty Issues in flood forecasting. Flood Events: Are We Prepared? Proceeding of the OSIRIS Workshop, March 2003, Berlin. 123–136.
Micovic, Z., Schaefer, M. G., & Taylor, G. H. (2015). Uncertainty analysis for probable maximum precipitation estimates. Journal of Hydrology, 521, 360-373.
Moffat, R.J. (1982). Contributions to the Theory of Single-Sample Uncertainty Analysis. Journal of Fluids Engineering, 104, 250-258.
Mostafazadeh R, Mirzaei S, Esmali Ouri A and Zabihi M (2018) Sensitivity analysis of the flow hydrograph components due to changes in Clark's time-area model in Mohammad-Abad watershed, Gloestan Province. J. of Water and Soil Conservation, Vol. 49(1), pp: 91-99. (In Farsi)
Nash, J. E. and Sutcliffe, J. V. (1970). River flow forecasting through conceptual models; part I: A discussion of principles. Journal of Hydrology 10:282-290
Rastogi, D., Kao, S. C., Ashfaq, M., Mei, R., Kabela, E. D., Gangrade, S. ... & Anantharaj, V. G. (2017). Effects of climate change on probable maximum precipitation: A sensitivity study over the Alabama‐Coosa‐Tallapoosa River Basin. Journal of Geophysical Research: Atmospheres, 122(9), 4808-4828.
Rousseau, A. N., Klein, I. M., Freudiger, D., Gagnon, P., Frigon, A., & Ratté-Fortin, C. (2014). Development of a methodology to evaluate probable maximum precipitation (PMP) under changing climate conditions: Application to southern Quebec, Canada. Journal of Hydrology, 519, 3094-3109.
Stratz, S. A., & Hossain, F. (2014). Probable maximum precipitation in a changing climate: Implications for dam design. Journal of Hydrologic Engineering, 19(12), 06014006.
Vrugt, J. A., Ter Braak, C. J., Clark, M. P., Hyman, J. M., & Robinson, B. A. (2008). Treatment of input uncertainty in hydrologic modeling: Doing hydrology backward with Markov chain Monte Carlo simulation. Water Resources Research, 44(12).
Wang, H., Wang, C., Wang, Y., Gao, X., & Yu, C. (2017). Bayesian forecasting and uncertainty quantifying of stream flows using Metropolis–Hastings Markov Chain Monte Carlo algorithm. Journal of hydrology, 549, 476-483.
Zimmermann, H.-J. 1997a. a Fresh Perspective on Uncertainty Modelling: Uncertainty vs. Modelling. In Uncertainty Analysis in Engineering and Sciences: Fuzzy Logic, Statistics, and Neural Network Approach, Kluwer Academic Publisher, pp. 353-364.
Zimmermann, H.-J. 1997b. Uncertainty Modelling and Fuzzy Sets. In Uncertainty: Models and Measures. Mathematical Research, 99, Akademie Verlag, pp. 84-100.
Zischg, A. P., Felder, G., Weingartner, R., Quinn, N., Coxon, G., Neal, J. ... & Bates, P. (2018). Effects of variability in probable maximum precipitation patterns on flood losses. Hydrology and earth system sciences, 22(5), 2759-2773.