Research Article | OPEN ACCESS
Modeling of Annual Maximum Storm Intensity with Bayesian Markov Chain Monte Carlo (MCMC) and L-moment
1Rado Yendra, 1Ari Pani Desvina, 1Rahmadeni, 2Kuseiri, 3Abdul Aziz Jemain and 4Ahmad Fudholi
1Department of Mathematics, Faculty of Science and Technology, Universitas Islam Sultan Syarif Kasim (UIN Suska), 28293 Pekanbaru, Riau, Indonesia
2Department of Mathematics and Science Education, Faculty of Education and Teacher Training, Islamic State University of Sunan Ampel, Surabaya, Indonesia
3School of Mathematical Sciences, Faculty of Science and Technology
4Solar Energy Research Institute, Universiti Kebangsaan Malaysia, 43600 Bangi, Selangor, Malaysia
Research Journal of Applied Sciences, Engineering and Technology 2016 4:283-294
Received: July 13, 2015 | Accepted: August 30, 2015 | Published: August 15, 2016
Abstract
This study presents the best fitting distribution to describe the siries MSI based on hourly rainfall form 1970 to 2008 for three rain gauge stations in Peninsular Malaysia namely Bertam, Dungun and Pekan. Two three-parameter extreme value distributions which are considered are Generalized Extreme Value (GEV) and Generalized Logistic (GL). The parameters of these distributions are determined using the Bayesian MCMC with non-informative prior distribution and L-moments (LMOM) method. The Goodness-Of-Fit (GOF) between empirical data and theoretical distributions are then evaluated for each stations. The result show that the majority of the stations are found that the L-moment method can give the best modelling for MSI, specified for GEV distribution. Based on the model that has been identified, we can reasonably predict the risks associated the MSI for various return periods.
Keywords:
AMSE , Bayesian MCMC , MSA , MSD , MSI,
References
-
Adams, B.J., H.G. Fraser, C.D.D. Howard and M.S. Hanafy, 1986. Meteorological data analysis for drainage system design. J. Environ. Eng., 112(5): 827-848.
CrossRef Direct Link
-
Adams, B.J. and F. Papa, 2000. Urban Stormwater Management Planning with Analytical Probabilistic Models. Wiley, New York.
-
Bernado, J.M. and A.F.M. Smith, 1994. Bayesian Theory. Wiley, New York, USA.
CrossRef PMid:7516051
-
Carlin, B.P. and T.A. Louis, 1996. Bayes and Empirical Bayes Method for Data Analysis. Chapman & Hall, London.
-
Coles, S.G. and E.A. Powell, 1996. Bayesian methods in extreme value modelling: A review and new developments. Int. Stat. Rev., 64(1): 119-136.
CrossRef Direct Link
-
Eagleson, P.S., 1972. Dynamics of flood frequency. Water Resour. Res., 8(4): 878-898. http://onlinelibrary.wiley.com/doi/10.1029/WR008i004p00878/abstract.
CrossRef Direct Link
-
Gelman, A., J.B. Carlin, H.S. Stern and D.B. Rubin, 1995. Bayesian Data Analysis. Chapman & Hall, London, UK.
-
Guo, Y. and B.J. Adams, 1998a. Hydrologic analysis of urban catchments with event-based probabilistic models: 2. Peak discharge rate. Water Resour. Res., 34(12): 3433-3443. http://onlinelibrary.wiley.com/doi/10.1029/98WR02448/abstract.
CrossRef Direct Link
-
Guo, Y. and B.J. Adams, 1998b. Hydrologic analysis of urban catchments with event-based probabilistic models: 1. Runoff volume. Water Resour. Res., 34(12): 3421-3431. http://onlinelibrary.wiley.com/doi/10.1029/98WR02449/full.
CrossRef Direct Link
-
Hosking, J.R.M. and J.R. Wallis, 1997. Regional Frequency Analysis: An Approach based on L-moments. Cambridge University Press, London, pp: 224.
CrossRef
-
Jeffreys, H., 1961. Theory of Probability. 3rd Edn., Clarendon Press, Oxford, UK.
PMCid:PMC1929700
-
Kuczera, G. and E. Parent, 1998. Monte Carlo assessment of parameter uncertainty in conceptual catchment models: The metropolis algorithm. J. Hydrol., 211(1-4): 69-85. http://www.sciencedirect.com/science/article/pii/S002216949800198X.
CrossRef Direct Link
-
Palynchuk, B. and Y. Guo, 2008. Threshold analysis of rainstorm depth and duration statistics at Toronto, Canada. J. Hydrol., 348(3-4): 535-545. http://www.sciencedirect.com/science/article/pii/S0022169407006166.
CrossRef Direct Link
-
Restrepo-Posada, P.J. and P.S. Eagleson, 1982. Identification of independent rainstorms. J. Hydrol., 55(1-4): 303-319.
CrossRef Direct Link
-
Rivera, P., J. Gironás, J.P. Montt and B. Fernández, 2005. An analytical model for hydrologic analysis in urban watersheds. Proceeding of the 10th International Conference on Urban Drainage. Copenhagen, Denmark.
-
Suhaila, J., Suhaila, J., M.D. Sayang, W.Z.W. Zin and A.A. Jemain, 2010a. Spatial patterns and trends of daily rainfall regime in Peninsular Malaysia during the southwest and northeast monsoons: 1975-2004. Meteorol. Atmos. Phys., 110(1): 1-18.
CrossRef
-
Suhaila, J., S.M. Deni, W.Z.W. Zin and A.A. Jemain, 2010b. Trends in Peninsular Malaysia rainfall data during the southwest monsoon and northeast monsoons seasons: 1975-2004. Sains Malays., 39(4): 533-542.
Direct Link
-
Vogel, R.M. and N.M. Fennessey, 1993. L moment diagrams should replace product moment diagrams. Water Resour. Res., 29(6): 1745-1752. http://onlinelibrary.wiley.com/doi/10.1029/93WR00341/abstract.
CrossRef Direct Link
-
Zawiah, W.Z.W., A.A. Jemain, K. Ibrahim, J. Suhaila and M.D. Sayang, 2009. A comparative study of extreme rainfall in Peninsular Malaysia: With reference to partial duration and annual extreme series. Sains Malays., 38(5): 751-760.
Direct Link
-
Zin, W.Z.W., A.A. Jemain and K. Ibrahim, 2009. The best fitting distribution of annual maximum rainfall in Peninsular Malaysia based on methods of L-moment and LQ-moment. Theor. Appl. Climatol., 96(3): 337-344.
CrossRef Direct Link
-
Zin, W.Z.W., J. Suhaila, S.M. Deni and A.A. Jemain, 2010. Recent changes in extreme rainfall events in Peninsular Malaysia: 1971-2005. Theor. Appl. Climatol., 99(3): 303-314. https://www.researchgate.net/publication/225439528_Recent_changes_in_extreme_rainfall_events_in_Peninsular_Malaysia_1971-2005.
CrossRef
Competing interests
The authors have no competing interests.
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This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
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