1.Presenter: Siti Musliha binti Mat Rasid Members: Pm. Dr. Zalina Mohd DAud Dr. Norzaida Abas International Conference on Computing, Mathematics and Statistics 2013 Date : 28th-29th August 2013 A REGIONALIZED SPATIAL TEMPORAL MODEL FOR HOURLY RAINFALL PROCESS

2. CONTENT Introduction and Background of the Study Methodology Result Discussion Conclusion 3. INTRODUCTION 4. Why we need rainfall model? Rainfall model are needed towards better planning, design and operation of the hydrologic system. Predicting flood, landslide and drought risk. Forecasting real-time flood or flood warning. Designing irrigation schemes and managing agricultural. Designing bridges. Designing sewers and urban drainage system. 5. Generating Synthetic Data - ungauge sites or sites with limited historical data. - missing or insufficient record length of rainfall data. Historical Data Hydrologist Developed Model Solve water- related problems in society. 6. The Objective Of The Study To fit a regionalized model To generate sequence of hourly rainfall data in Peninsular Malaysia based on a stochastic spatial temporal model. 7. METHODOLGY 8. REGIONALIZATION Regionalization can be defined as the transfer of information from one catchment to another (Bloschl and Sivapalan, 1995). Regionalization approaches was by optimising parameters representing certain catchment characteristics is applicable in other catchments with similar characteristics (Dave L. E. H. Deckers and Martijn J. Booij , 2010) 9. Figure 1 : Schematic representation of regionalization procedure (T. Wagener and H.S. Wheater, 2006) 10. Spatial Temporal-Neyman Scott Rectangular Pulse Model (ST- NSRP) Spatial temporal model allowed rainfall series to be simulated independently at any site within the study region. 11. Time Intensity Variable Distribution Parameter Arrival rate of storm origin Poisson Waiting time for each cell origin after the storm occur Exponenti al Mean number of cells generated by each storm Poison Duration of cells Exponenti al Intensity of rain cell Mix- Exponenti al , , : STORM ORIGIN : RAIN CELL : DURATION OF RAIN OCCUR 12. Time Totalintensity The total intensity at any point in time is the sum of the intensities of all active rain cells at that point 13. Spatial Temporal Model catchment rain cell where 14. Table 1: Statistical structure of the ST-NSRP model with nine parameters. Physical process Distribution Parameter PDF Arrival rate of storm origin Poisson Waiting time for each cell origin after the storm occur Exponential Mean number of cells generated by each storm Poison Duration of cells Exponential Radius of cell Exponential Number of cell per unit area Poisson Mean intensity of heavy cell Mix Exponential Mean intensity of light cell Mixing probability of cell intensity 15. Mathematical properties of the ST-NSRP model have been derived by Cowpertwait (1995): Where 16. The third moment function also was derived and given as follows where the functions and are given by: 17. Dimensionless statistics were calculated based on the merging of rainfall data across the sites and across the years; and scaling the data at each site according to month. The sample mean is first calculated for each site-month as follows Dimensionless statistical for each month k by pooling all available data (across sites and years). Variance : 18. Coefficient of Variation : Lag-k autocorrelation: Coefficient of Skewness : Cross correlation: 19. Parameter estimation process of the ST- NSRP model is executed using the method of moments that involved objective function (SS) as below: 20. In this study involved - Cross correlation between two site for 16 rainfall stations Shuffle Complex Evolution (SCE-UA) optimization technique help towards minimized the objective function . Simulation process was divided into two period - Calibration period (2001-2010) - Validation period (2011-2012) Simulation series represented by box plots was compared with historical data. 21. Code Station Number Station Name District State S1 6019004 Rumah Kastam Rantau Panjang Kelantan S2 5524001 Kg. La Besut Terengganu S3 4726001 Gunung Gagau Gua Musang Kelantan S4 5331048 Stor JPS Kuala Terengganu K. Terengganu Terengganu S5 4234109 JPS Kemaman Kemaman Terengganu S6 3930012 Sg. Lembing PCCL Mill Kuantan Pahang S7 3533102 Rumah Pahang Tua Pekan Pahang Table 2: 17 study sites in Peninsular Malaysia (continued..) STUDIED REGION 22. Table 2: 17 study sites in Peninsular Malaysia (continued..) Code Station Number Station Name District State S8 6103047 Stor JPS Alor Star Kedah S9 5504035 Lahar Ikan Mati Kepala Batas Pulau Pinang S10 5210069 STN. Pemeriksaan Hutan Lawin Hulu Perak Perak S11 4207048 Pejabat JPS Sitiawan Manjung Perak S12 3710006 Rumah Pam JPS Bagan Terap Selangor S13 3117070 JPS Ampang Kuala Lumpur Wilayah Persekutuan S14 2719001 Stor JPS Sikamat Seremban Negeri Sembilan S15 2025001 Pintu Kawalan Tg. Agas Muar Johor S16 1534002 Pusat Kemajuan Per. Pekan Nanas Pulai Johor S17 5320038 Dabong Dabong Kelantan 23. Figure 2: Position of 17 rainfall stations in Peninsular Malaysia. 24. RESULT 25. Table 3: Dimensionless statistical of 16 sites in Peninsular for the period 10 years (2001-2010). Jan 9.130 0.325 29.731 3.209 0.254 Feb 11.34 0.337 27.905 3.844 0.251 Mar 8.522 0.311 18.604 2.617 0.176 Apr 8.778 0.318 16.999 2.441 0.098 May 9.402 0.285 18.481 2.520 0.078 June 9.411 0.481 18.699 2.570 0.086 July 9.110 0.274 18.834 2.480 0.047 Aug 9.410 0.296 25.490 2.571 0.080 Sept 8.270 0.393 16.919 2.236 0.078 Oct 7.174 0.293 14.911 2.043 0.152 Nov 6.334 0.312 16.142 1.984 0.214 Dec 6.763 0.322 18.540 2.314 0.221 26. Fadhilah (2008) performed a study on hourly rainfall sequence and discovered the following relationship between values of , and as follows: 27. Jan 0.0202 0.0096 1.0565 2.0457 29.2194 0.1030 0.0033 0.65 0.4165 Feb 0.0191 0.0054 1.0041 1.6673 27.6781 0.1671 0.0045 0.65 0.4469 Mac 0.0408 0.0082 1.0686 1.9258 18.1757 0.1528 0.0040 0.65 1.0481 Apr 0.0475 0.0014 1.1108 1.9876 9.5635 0.1186 0.0025 0.65 0.2505 May 0.0730 0.0015 1.0085 3.4684 8.1621 0.1352 0.0029 0.65 0.2505 Jun 0.0281 0.0012 1.0691 1.0011 7.6770 0.1443 0.0035 0.65 0.9552 Jul 0.1032 0.0015 1.0222 3.9329 11.3009 0.1261 0.0026 0.65 0.2523 Aug 0.0429 0.0010 1.0600 2.9433 14.4387 0.2566 0.0111 0.65 0.3004 Sep 0.1087 0.0013 1.0017 5.7030 18.9747 0.1833 0.0054 0.65 0.9914 Oct 0.0818 0.0027 1.0017 2.1421 14.1189 0.1930 0.0059 0.65 0.2541 Nov 0.0717 0.0012 1.0822 2.5258 14.3491 0.2117 0.0077 0.65 0.2508 Dec 0.0710 0.0011 1.0058 3.3635 19.5305 0.1656 0.0044 0.65 0.2504 Table 5: Parameter estimation of Regionalized ST-NSRP model in Peninsular Malaysia 28. Simulation Result 29. Comparison between statistics of simulated hourly series (boxplots) and observed series (dotted diamond) at Dabong, Kelantan for 10 years period (2001-2010) 30. Comparison between statistics of simulated hourly series (boxplots) and observed series (solid diamond) at Dabong, Kelantan for 10 years period (2001-2010) (continued...) 31. Spatial temporal model is an appropriate technique to describe rainfall process particularly in Peninsular Malaysia which experience different rainfall pattern from the west to the east coast. Simulation result show statistical characteristics of simulated series sequences match the observed data fairly well. However, the model has the tendency to underestimate the hourly covariance and lag one autocorrelation. Considering that spatial variability of rainfall is high within the studied region, this model is able to capture the trend of rainfall process. 32. 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