A Comparison of Modelling Generalized Extreme Value Distribution of Rainfall Volume in Eastern Thailand Provinces
Main Article Content
Abstract
This study aims to compare models for the generalized extreme value distribution suitable for annual maximum rainfall volume over 30 years from 1993 to 2022 in the eastern region of Thailand. The study area includes the provinces of Chanthaburi, Chonburi, Prachinburi, Rayong, Sa Kaew, and Trat. The investigation compares the generalized extreme values distribution under stationary and non-stationary processes. Eight models are considered, with parameters varying over time. The suitability of a model is assessed based on the goodness-of-fit tests and model selection criteria, considering Akaike's information criteria. The parameter estimation employs the maximum likelihood method. Additionally, the study examines the estimated recurrence levels of rainfall volumes for the return levels of 2, 5, 10, 20, and 100 years, providing a comprehensive analysis of the variability of extreme rainfall events. The results indicate that two provinces, namely Chanthaburi and Prachinburi, are suitable for the Frechet distribution, while Chonburi, Rayong, Sa Kaew, and Trat are suitable for the Gumbel distribution. The models of Chanthaburi and Trat are suitable for the constant parameters. Furthermore, the Chonburi, Prachinburi, Rayong, and Sa Kaew models are suitable for non-constant parameters that vary with time. When considering the return level of rainfall volume, it is found that Trat and Chanthaburi provinces have higher return levels than the others. There is a greater chance of experiencing the highest rainfall, which indicates that both provinces tend to experience severe flood disasters. Therefore, it is crucial to prioritize disaster prevention efforts for flood disasters in the Chanthaburi and Trat provinces more than others.
Article Details
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
The articles published are the opinion of the author only. The author is responsible for any legal consequences. That may arise from that article.
References
Office of the National Economic and Social Development Council. (2020, May). Eastern Development Plan (Review year 2017-2022). [Online]. (in Thai) Available: https:// www.nesdc.go.th/ewt_dl_link.php?nid=10196& filename=index
P. Busababodhin and A. Keawmun, “Extreme values statistics,” The Journal of KMUTNB, vol. 25, no. 2, pp. 55-65, 2015 (in Thai).
L. Rajaram, Statistical models in Environmental and Life Sciences. Florida : University of South Florida. 2006.
P. Khongthip, M. Khamkong, and P. Bookamana, “Modeling annual extreme precipitation in upper Northern region of Thailand,” Burapha Science Journal, vol. 18, no. 1, pp. 95-104, 2013 (in Thai).
P. Busababodhin, M. Siriboon, and A. Keawmun, “Modeling of extreme precipitation in upper Northeast of Thailand,” Burapha Science Journal, vol. 20, no. 1, pp. 106–117, 2015 (in Thai).
R. Riaman, S. Sukono, S. Supian, and N. Ismail, “Analysis the decision making for agricultural assessment: an application of extreme value analysis,” Decision Science Letters, vol. 10, pp. 351–360, 2021.
H. Tabari, “Extreme value analysis dilemma for climate change impact assessment on global flood and extreme precipitation,” Journal of Hydrology, vol. 593, pp. 1–16, 2021.
C. P. Pandey, V. Ahuja, L. K. Joshi, and H. Nandan, “Extreme value analysis of precipitation and temperature over western Indian Himalayan State, Uttarakhand,” Journal of Earth System Science, vol. 132, no. 48, pp. 1–20, 2023.
E. Gilleland and R. W. Katz, “extRemes 2.0: An extreme value analysis package in R,” Journal of Statistical Software, vol. 72, no. 8, pp. 1–39, 2016.
A.F. Jenkinson, “The frequency distribution of the annual maximum (or minimum) values of meteorological elements,” Quarterly Journal of the Royal Meteorological Society, vol. 81, pp. 158–171, 1955.
J. Galambos, The Asymptotic Theory of Extreme Order Statistics. New York: Wiley, 1978.
J. Beirlant, Y. Goegebeur, J. Segers, and J. L. Teugels, Statistics of Extremes: Theory and Applications. Wiley Series in Probability and Statistics. New York: John Wiley & Sons, 2004.
S. Coles, An Introduction to Statistical Modeling of Extreme Values. London: Springer-Varlag, 2001.
P. Guayjarernpanishk, T. Phupiewpha and P. Busababodhin, “Extreme value analysis: Nonstationary process,” The Journal of KMUTNB, vol. 32, no. 2, pp. 506–515, 2022 (in Thai).
J. Nocedal and S. J. Wright. Numerical Optimization. Springer, 1999.
M. A. Stephens, “Introduction to Kolmogorov (1933) On the Empirical Determination of a Distribution,” Breakthroughs in Statistics, pp. 93–105, 1992.
H. Akaike, “Information Theory and an Extension of the Maximum Likelihood Principle,” Proceedings of the 2nd International Symposium on Information Theory, Budapest, 1973, pp. 267–281.
S. Kullback and R. A. Leibler, “On information and sufficiency,” The Annals of Mathematical Statistics, vol. 22, pp. 79–86, 1951.
M. Ahsan-ul-Haq, H. M. Yousof and S. Hashmi, “A new five-parameter Frechet model for extreme value,” Pakistan Journal of Statistics and Operation Research, vol. 13, no. 3, pp. 617– 632, 2017.