International Journal of Mathematics Trends and Technology
Volume 69 | Issue 1 | Year 2023 | Article Id. IJMTT-V69I1P511 | DOI : https://doi.org/10.14445/22315373/IJMTT-V69I1P511
| Received | Revised | Accepted | Published |
|---|---|---|---|
| 05 Dec 2022 | 07 Jan 2023 | 18 Jan 2023 | 31 Jan 2023 |
Flood events are very difficult to predict early, this is because the value of the amount of rainfall that occurs for each month in the next few years cannot be properly estimated, of course, will result in difficulty estimating the strength of the dam in holding back the flow rate water, in addition to the difficulty in estimating the size of the ditch as a rain reservoir for the next few years. This event will continue to occur every year along with an increased amount of rainfall. Amount rainfall variables can be determined using short-scale rainfall such as hourly obtained using storm theory. This study focuses on using hourly rainfall data to be modeled using several probability distribution models such as Gamma, Weibull, and Log Normal. Once the best model can be determined, the parameters will be modified by increasing every 10% so that it reaches 50% and using the quantile function the Amount of rainfall data simulation based on parameter modification will be carried out and the two characteristics of the simulated data such as the mean and maximum amount values will be compared to show the effect of increasing storm amount rainfall. In this study, it was found that the log-normal distribution model was the best and an increase in parameter values would affect the increase in the mean and maximum amount of rainfall for each year.
[1] R.D. Reiss, and M. Thomas, Statistical Analysis of Extreme Values: With Applications to Insurance, Finance, Hydrology and Other Fields, Birkhauser, 1997.
[2] 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
[3] 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
[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] Barry J. Adams et al., “Meteorological Data Analysis for Drainage System Design,” Journal of Environmental Engineering, vol. 112, no. 2, pp. 827-848, 1986. Crossref, https://doi.org/10.1061/(ASCE)0733-9372(1986)112:5(827)
[6] 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. 3421-3431, 1998. Crossref, https://doi.org/10.1029/98WR02448
[7] 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
[8] Sheng Yue, “Joint Probability Distribution of Annual Maximum Storm Peaks and Amounts as Represented by Daily Rainfalls,” Hydrologial Sciences Journal, vol. 45, no. 2, pp. 315–326, 2000. Crossref, https://doi.org/10.1080/02626660009492327
[9] 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, pp. 1307. 2002. Crossref, https://doi.org/10.1029/2002WR001343
[10] 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
[11] 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
[12] 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
[13] 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
[14] 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
[15] 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)
[16] 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
[17] 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)
[18] N.T. Ison, A.M. Feyerherm, and L.Dean Bark, “Wet Period Precipitation and the Gamma Distribution,” Journal of Applied Meteorology and Climatology, vol. 10, no. 4, pp. 658-665, 1971. Crossref, https://doi.org/10.1175/1520-0450(1971)010%3C0658:WPPATG%3E2.0.CO;2
[19] Richard W. Katz, “Precipitation as a Chain-Dependent Process,” Journal of Applied Meteorology and Climatology, vol. 16, no. 7, pp. 671-676, 1977. Crossref, https://doi.org/10.1175/1520-0450(1977)016%3C0671:PAACDP%3E2.0.CO;2
[20] T. A. Buishand, “Stochastic Modeling of Daily Rainfall Sequences,” Medidlingen Agricultural College Wageningen, vol. 77, no. 3, 1977.
[21] E.D. Waymire, and Vijay K. Gupta, “The Mathematical Structure of Rainfall Representations: 1. A Review of the Stochastic Rainfall Models,” Water Resources Research, vol. 17, no. 5, Pp. 1261-1272, 1981. Crossref, https://doi.org/10.1029/WR017i005p01261
[22] Paul W. Mielke, “Another Family of Distributions for Describing and Analyzing Precipitation Data,” Journal of Applied Meteorology and Climatology, vol. 12, no. 2, pp. 275-280, 1973. Crossref, https://doi.org/10.1175/1520-0450(1973)012%3C0275:AFODFD%3E2.0.CO;2
[23] Jose Rolda’n, and David A. Woolhiser, “Stochastic Daily Precipitation Models: I. A Comparison of Occurrence Processes,” Water Resources Research, vol. 18, no. 5, pp. 1451-1459, 1982. Crossref, https://doi.org/10.1029/WR018i005p01451
[24] Van-Thanh-Van Nguyen, and Alfred Mayabi, “Probabilistic Analysis of Summer Daily Rainfall for the Montreal Region,” Canadian Water Resources Journal, vol. 16, no. 1, pp. 65-80, 1991. Crossref, https://doi.org/10.4296/cwrj1601065
[25] 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
[26] 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-V68I12P511
Halimah Tun Satdiah, Rado Yendra, Muhammad Marizal, Ari Pani Desvina, Rahmadeni, "The Effect of Simulation Storm Amount Hourly Rainfall Based on Increase Various Rates Parameters to Mean and Maximum by Using Best Distribution Model," International Journal of Mathematics Trends and Technology (IJMTT), vol. 69, no. 1, pp. 71-78, 2023. Crossref, https://doi.org/10.14445/22315373/IJMTT-V69I1P511
PDF 
Abstract 
Keywords 
References 
Citation