LH-Moments of the Wakeby Distribution applied to Extreme Rainfall in Thailand

Busababodhin Piyapatr, Chiangpradit Monchaya, Phoophiwfa Tossapol, Jeong-Soo Park, Do-ove Manoon, Guayjarernpanishk Pannarat


This article applies the Wakeby distribution (WAD) with high-order L-moments estimates (LH-ME) to annual extreme rainfall data obtained from 99 gauge stations in Thailand. The objectives of this study investigate to obtain appropriate quantile estimates and return levels for several return periods, 2, 5, 10, 25 and 50 years. The 95% confidence intervals for the quantiles determined from the WAD are derived using the bootstrap technique. Isopluvial maps of estimated design values that correspond to selected return periods are presented. The LH-ME results are better than estimates from the more primitive L-moments method for a large majority of the stations considered.


L-Moments; LH-Moments; Wakeby Distribution; Higher-Order Statistics; Bootstrap Resampling

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Busababodhin, P., Siriboon, M., Keawmun, K. 2015. Modeling of Extreme Precipitation in Upper Northeast of Thailand. Burapha Science Journal, 20(1), 1-10. (in Thai)

Busababodhin, P., Seo, Y.A., Park, J.S., Kumphon, B. 2015. LH-moment estimation of Wakeby distribution with hydrology applications. Stochastic Environmental Research and Risk Assessment, 1-11.

Deka, S., Borah, M., Kakaty, S.C. 2009. Distribution of annual maximum rainfall series of north-east India. European Water, 3-14.

Dunn, P.K. 2001. Bootstrap confidence intervals for predicted rainfall quantiles. International Journal of Climatology, 21(1), 89-94, doi:10.1002/ joc.596.

Huff, F.A., Angel, J.R. 1992. Rainfall frequency atlas of the midwest Illinois State water survey. Bulletin, 71, Chanpaign, IL.

Khamkong, M. 2012. Statistical modeling of annual monthly maximum rainfall in upper northern region of Thailand, Proceeding of International Days of Statistics and Economics, Prague.

Keawmun, K., Busababodhin, P., Budchamruei, P. 2015. Modeling Monthly Precipitation in Central Northeast of Thailand. KKU Science Journal, 43(1), 137-147. (in Thai)

Keawmun, K., Rattanawan, S., Busababodhin, P., Kumphon, B. 2015. Modeling for extreme rainfall in lower Northeastern of Thailand. The Journal of Applied Science, 13(2), 55-65. (in Thai)

Khongthip, R., Khamkong, M., Bookamana, P. 2013. Modeling annual extreme precipitation in upper northern region of Thailand. Burapha Science Journal, 18, 95-104. (in Thai).

Landwehr, J.M., Matalas, N.C., Wallis, J.R. 1980. Quantile estimation with more or less floodlike distribuitoion. Water Resources Research, 16(3), 547-555, doi:10.1029/WR016i003p00547.

Matalas, N.C., Slack, J.R., Wallis, J.R. 1975. Regional skew in search of a parent. Water Resources Research, 11, 815-826, doi:10.1029/WR011i006 p00815.

Oztekin, T. 2007. Wakeby distribution for representing annual extreme and partial duration rainfall series. Meteorological Applications, 14(4), 381-387, doi:10.1002/met.37.

Park, J.S., Jung, H.S., Kim, R.E., OH, J.H. 2001. Modelling summer extreme rainfall over the Korean peninsula using Wakeby distribution. Internaltional Journal of Climatology, 21(11), 1371-1384, doi:10.1002/joc.701.

Press, W.H., Teukolsky, S.A., Vetterling, W.T., Flannery, B.P. 1996. Numerical Recipes in Fortran 77.

The Art of Scientific Computing (2nd edn). Cambridge University Press: New York.

Rahman, A., Zaman, M.A., Haddad, K., Adlouni, S.E., Zhang, C. 2015. Applicability of Wakeby distribution in flood frequency analysis: a case study for eastern Australia. Hydrological Processes, 29(4), 602-614, doi:10.1002/hyp.10182.

Ross, S.M. 1990. A Course in Simulation. Macmillan Publishing Co: New York.

Seckin, N., Haktanir, T., Yurtal, R. 2011. Flood frequency analysis of Turkey using L-moments method. Hydrological Processes, 25(22), 3499-3505, doi:10.1002/hyp.8077.

Soukissian, T. 2013. Use of multi-parameter distributions for offshore wind speed modeling: The Johnson SB distribution. Applied Energy, 111(0), 982-1000, doi:10.1016/j.apenergy.2013.06.050.

Su, B., Kundzewicz, Z.W., Jiang, T. 2009. Simulation of extreme precipitation over the Yangtze River Basin using Wakeby distribution. Theoretical and Applied Climatology, 96(3-4), 209-219, doi:10.1007/s00704-008-0025-5.

Thai Meteorological Department, 2014. Annual weather summary over Thailand in 2014.

Thai Meteorological Department, 2016. Annual weather summary over Thailand in 2016.

Thai Meteorological Department, 2017. Annual weather summary over Thailand in 2017.

Thai Meteorological Department, 2019. Annual weather summary over Thailand in 2019.

Wang, Q.J. 1997. LH moments of Statistical analysis of extreme events. Water Resources Research, 33, 2841-2848.

Wilks, D.S., McKay, M. 1996. Extreme-value statistics for snowpack water equivalent in the northeastern United States using the cooperative observer network. Journal of Applied Meteorology, 35, 706-713.

Yao, Z., Wei, H., Lui, H., Li, Z. 2013. Statistical vehicle specific power profiling for urban freeways. Procedia - Social and Behavioral Sciences, 96: 2927-2938, doi:10.1016/j.sbspro.2013.08.324.

Zalina, M.D., Desa, M.N.M., Nguyen, V.T.V., Kassim, A.H.M. 2002. Selecting a probability distribution for extreme rainfall series in Malaysia. Water Science and Technology, 45(2),63-68.

http://www.tmd.go.th/programs%5Cuploads Varadhan R, 2012 R-package “alabama” constrained nonlinear optimisation. http://cran.r-project.org/web/ packages/alabama/index.html.

DOI: https://doi.org/10.11113/mjfas.v17n2.2005


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