Volume 69 | Issue 1 | Year 2023 | Article Id. IJMTT-V69I1P512 | DOI : https://doi.org/10.14445/22315373/IJMTT-V69I1P512
Received | Revised | Accepted | Published |
---|---|---|---|
07 Dec 2022 | 09 Jan 2023 | 20 Jan 2023 | 31 Jan 2023 |
Storm amount (SA), storm intensity (SI), and storm duration (SD) are three external measurements that can be used to describe short-scale rainfall modeling based on storm process. This study displays the distribution that fits the SI series the best, which is based on hourly rainfall data from 1970 to 2008 at the Alor Setar station in Peninsular Malaysia. Gamma, Weibull, and Log Normal distributions with two parameters are taken into consideration. The Bayesian Maximum Likelihood (MLE) approach is used to determine these distributions' parameters. Then it is determined how well theoretical data and model distributions fit one another (GOF). The outcome demonstrates that the stations discovered that the MLE method may provide the best SI modeling, specifically for Log-Normal distribution. We can reliably forecast the future risks associated with the SI based on the stated model.
[1] Barry J. Adams et al., “Meteorological Data Analysis for Drainage System Design,” Journal of Environmental Engineering, vol. 112, no. 5, pp. 827-848, 1986. Crossref, https://doi.org/10.1061/(ASCE)0733-9372(1986)112:5(827)
[2] Barry J. Adams, and Fabian Papa, Urban Stormwater Management with Analytical Probabilistic Model, Jhon Wiley and Sons Inc., Toronto, Ontario, 2000.
[3] William H. Asquith et al., Statistical Characteristics of Storm Interevent Time, Depth, and Duration for Eastern New Mexico, Oklahoma, and Texas, U.S. Geological Survey Publication, 2006. Crossref, https://doi.org/10.3133/pp1725
[4] P.S. Eagleson, “Dynamics of Flood Frequency,” Water Resources Research, vol. 8, no. 4, pp. 878-897, 1972. Crossref, https://doi.org/10.1029/WR008i004p00878
[5] Yiping Guo, and Barry J. Adams, “Hydrologic Analysis of Urban Catchments with Event-based Probabilistic Models: 2. Peak Discharge Rate,” Water Resources Research, vol. 34, no. 12, pp. 3433-3443, 1998. Crossref, https://doi.org/10.1029/98WR02448
[6] Yiping Guo, and Barry J. Adams, “Hydrologic Analysis of Urban Catchments with Event-based Probabilistic Models: 1. Runoff Volume,” Water Resources Research, vol. 34, no. 12, pp. 3421-3431, 1998. Crossref, https://doi.org/10.1029/98WR02449
[7] N.K. Goel et al., “A Derived Flood Frequency Distribution for Correlated Rainfall Rainfall Intensity and Duration,” Journal of Hydrology, vol. 228, no. 1-2, pp. 56-67, 2000. Crossref, https://doi.org/10.1016/S0022-1694(00)00145-1
[8] C. De Michele, and G. Salvadori, “A Generalized Pareto Intensity–duration Model of Storm Rainfall Exploiting 2-Copulas,” Journal of Geophysical Research, vol. 108, no. D2, 2003. Crossref, https://doi.org/10.1029/2002JD002534
[9] P. Rivera et al., “An Analytical Model for Hydrologic Analysis in Urban Watersheds,” Proceedings of the 10th International Conference on Urban Drainage, Copenhagen, Denmark, 2005.
[10] Shih-Chieh Kao, and Rao S. Govindaraju, “Probabilistic Structure of Storm Surface Runoff Considering the Dependence Between Average Intensity and Storm Duration of Rainfall Events,” Water Resources Research, vol. 43, no. 6, 2007. Crossref, https://doi.org/10.1029/2006WR005564
[11] L. Zhang, and Vijay P. Singh, “Bivariate Rainfall Frequency Distributions Using Archimedean Copulas,” Journal of Hydrology, vol. 332, no. 1–2, pp. 93–109, 2007. Crossref, https://doi.org/10.1016/j.jhydrol.2006.06.033
[12] Barry Palynchuk, and Yiping Guo, “Threshold Analysis of Rainstorm Depth and Duration Statistics at Toronto, Canada,” Journal of Hydrology, vol. 348, no.3–4, pp. 535–545, 2008. Crossref, https://doi.org/10.1016/j.jhydrol.2007.10.023
[13] A.C. Favre, A. Musy, and S. Morgenthaler, “Two-Site Modeling of Rainfall Based on the Neyman–Scott Process,” Water Resources Research, vol. 38, no. 12, 2002. Crossref, https://doi.org/10.1029/2002WR001343
[14] S. Yue, T.B.M.J. Ouarda, and B. Bobee, “A Review of Bivariate Gamma Distributions for Hydrological Application,” Journal of Hydrology, vol. 246, no. 1–4, pp. 1–18, 2001. Crossref, https://doi.org/10.1016/S0022-1694(01)00374-2
[15] Sheng Yue, “The Bivariate Lognormal Distribution for Describing Joint Statistical Properties of a Multivariate Storm Event,” Environmetrics, vol. 13, no. 8, pp. 811–819, 2002. Crossref, https://doi.org/10.1002/env.483
[16] J.T. Shiau, “Return Period of Bivariate Distributed Extreme Hydrological Events,” Stochastic Environmental Research and Risk Assessment, vol. 17, pp. 42–57, 2003. Crossref, https://doi.org/10.1007/s00477-003-0125-9
[17] Sheng Yue, “Joint Probability Distribution of Annual Maximum Storm Peaks and Amounts as Represented by Daily Rainfalls,” Hydrological Sciences Journal, vol. 45, no. 2, pp. 315–326, 2000. Crossref, https://doi.org/10.1080/02626660009492327
[18] Shih-Chieh Kao, and Rao S. Govindaraju, “Trivariate Statistical Analysis of Extreme Rainfall Events via the Plackett Family of Copulas,” Water Resources Research, vol. 44, no. 2, 2008. Crossref, https://doi.org/10.1029/2007WR006261
[19] C. De Michele, and G. Salvadori, “A Generalized Pareto Intensity–duration Model of Storm Rainfall Exploiting 2-Copulas,” Journal of Geophysical Research, vol. 108, no. D2, 2003. Crossref, https://doi.org/10.1029/2002JD002534
[20] C. De Michele et al., “Bivariate Statistical Approach to Check Adequacy of Dam Spillway,” Journal of Hydrological Engineering, vol. 10, no. 1, p. 50, 2005. Crossref, https://doi.org/10.1061/(ASCE)1084-0699(2005)10:1(50)
[21] G. Salvadori, and C. De Michele, “Frequency Analysis via Copulas: Theoretical Aspects and Applications to Hydrological Events,” Water Resources Researach, vol. 40, no. 12, 2004. Crossref, https://doi.org/10.1029/2004WR003133
[22] L. Zhang, and V.P. Singh, “Bivariate Flood Frequency Analysis Using the Copula Method,” Journal of Hydrological Engineering, vol. 11, no. 2, p. 150, 2006. Crossref, https://doi.org/10.1061/(ASCE)1084-0699(2006)11:2(150)
[23] Anne-Catherine Favre et al., “Multivariate Hydrological Frequency Analysis Using Copulas,” Water Resources Research, vol. 40, no. 1, 2004. Crossref, https://doi.org/10.1029/2003WR002456
[24] B. Renard, and M. Lang, “Use of a Gaussian Copula for Multivariate Extreme Value Analysis: Some Case Studies in Hydrology,” Advances in Water Resources, vol. 30, no. 4, pp. 897–912, 2007. Crossref, https://doi.org/10.1016/j.advwatres.2006.08.001
[25] Pedro J. Restrepo-Posada, and Peter S. Eagleson, “Identification of Independent Rainstorms,” Journal of Hydrology, vol. 55, no. 1–4, pp. 303–319, 1982. Crossref, https://doi.org/10.1016/0022-1694(82)90136-6
[26] Anisha Putri Ramadhani et al., “The Modelling Number of Daily Death Covid 19 Data Using Some of Two and One Parameter Distributions in Indonesia,” International Journal of Mathematics Trends and Technology, vol. 68, no. 12, pp. 106–111, 2022. Crossref, https://doi.org/10.14445/22315373/IJMTT-V68I12P512
[27] Vinny Anugrah et al., “Applied Some Probability Density Function for Frequency Analysis of New Cases Covid-19 in Indonesia,” International Journal of Mathematics Trends and Technology, vol. 68, no. 12, pp. 100–105, 2022. Crossref, https://doi.org/10.14445/22315373/IJMTT-V68I12P51
Lisa Rahayu, Rado Yendra, Muhammad Marizal, Ari Pani Desvina, Rahmadeni, "The Short Scale (Hourly) Rainfall Modelling For Intensity Based On Strom Analysis Events (SEA) Using Some Probability Distributions," International Journal of Mathematics Trends and Technology (IJMTT), vol. 69, no. 1, pp. 79-85, 2023. Crossref, https://doi.org/10.14445/22315373/IJMTT-V69I1P512