Neyman Scott Rectangular Pulse Modeling for Storm Rainfall Analysis in Peninsular Malaysia

The objective of this study is to evaluate the application Neyman-Scott Rectangular Pulse (NSRP) modeling in describing the storm rainfall in Peninsular Malaysia. Hourly rainfall data for the periods of 1970 to 2008 from 50 rain-gauge stations in Peninsular Malaysia is used in this study. The rain-gauge stations are divided into four sub regions, namely northwest, west, southwest and east. The goodness of fit of the NSRP model to the observation is tested first before further application of the model. The results showed the NSRP model is able to represent the rainfall data in Peninsular Malaysia.


INTRODUCTION
The issues of climatic change and global warming receive considerable attention from various researchers nowadays, particularly with regard to the effect of the behavior of the storm rainfall to the community.In relation to that, the analysis of storm rainfall is becoming important in many areas, particularly in water-related sectors such as agriculture, hydrology and water resource management.With the expansion of irrigated agriculture, coupled with the development of industrialization and the rapid growth of population, such analysis can be utilized in rainfall forecasting and eventually, decision making.Studies in storm rainfall such as the intensity of rainfall, extreme rainfall, total rainfall and heavy rains have attracted much attention from scientists throughout the world, such as researches carried out by Lana et al. (2004), Martinez et al. (2007), Aravena and Luckman (2009), Sen Roy (2009), Turkes et al. (2008) and Burgueño et al. (2004Burgueño et al. ( , 2005Burgueño et al. ( , 2010)).
There have been a few published works on the behavior of storm rainfall in Peninsular Malaysia.Among them are works on detecting trends in dry and wet spells over the Peninsula during monsoon seasons (Deni et al., 2008(Deni et al., , 2010a(Deni et al., , 2010b)), changes in extreme rainfall events (Zin et al., 2010), changes in daily rainfall during monsoon seasons (Suhaila et al., 2010) and analysis of rainfall variability (Wong et al., 2009).
In these studies, various objectives and approaches have been highlighted in describing the characteristics of rainfall in this area.

DATA AND METHODOLOGY
Peninsular Malaysia is situated in the tropics at between 1 and 7 north of the equator.In general, the country experiences a wet and humid tropical climate throughout the year, characterized by high annual rainfall, humidity and temperature.Peninsular Malaysia has a uniform temperature of 25.5-32 o C throughout the year.Normally, annual rainfall is between 2,000 and 4,000 mm, while the annual number of wet days ranges from 150 to 200.The climate of Peninsular Malaysia is described two monsoons separated by two intermonsoons.The Southwest Monsoon (SWM) occurs from May to September and the Northeast Monsoon (NEM) occurs from November to March.The two inter-monsoons occur in April (FIM) and October (SIM).In Peninsular Malaysia, the Main Range Mountains, known locally as Banjaran Titiwangsa, run southward from the Malaysia-Thai border in the north, spanning a distance of 483 km and separating the eastern and western parts of the Peninsula.During the NEM season, exposed areas in the eastern part of the Peninsula receive heavy rainfall.In contrast, areas sheltered by the Main Range (Fig. 1), are more or less free from its influence.
In this study, hourly rainfall data from 48 rain gauge stations were used.The data was obtained from the Malaysian Meteorological and Drainage and Irrigation Departments for the period of 1970-2008.The 48 stations are then divided into four categories in this study.The segregation of the stations into categories are based on studies done by Dale (1959) and Deni et al. (2008).Dale (1959) has delineated five rainfall regions in Peninsular Malaysia to northwest, west, Port Dickson-Muar coast, southwest and east.In this study, however, the stations located on the Port Dickson-Muar coast were combined with those in the southwest region.The list of the 48 stations with their respective regions is provided in Table 1 and geographical regions and the selected 48 stations can be depicted as in the Fig. 1.
The Neyman-Scott Rectangular Pulse (NSRP) modeling is used to model the rainfall amount at each station Peninsular Malaysia.The single-site NSRP model is characterized by a flexible structure in which the model parameters broadly relate to the underlying physical features observed in rainfall events.In theory, the NSRP model assumes that the storm origins follow a Poissonian process with parameter λ.Then, a random number of cell E(C) origins are displaced from the storm origins by exponentially distributed distances with parameter β.A rectangular pulse, with duration and intensity expressed by other two independent random variables, assumed to be exponentially distributed with parameters η and E(X) respectively, is associated at each cell origin.The total intensity at any point in time is given by the sum of all the active cell intensities at that particular point.The NSRP model therefore has a total of five parameters that can be estimated by minimizing an objective function, evaluated as sum of normalized residuals between the statistical properties of the observed and their theoretical expressions (Rodriguez-Iturbe et al., 1987a, 1987b;Cowpertwait, 1991;Cowpertwait et al., 1996).This model is able to produce statistics estimation values close to the observed values (Cowpertwait et al., 1996).
The main feature of the NSRP model can be summarized as follows: • Every storm arrival, represented by l i , i = 1, 2, 3,… is exponentially distributed in poisson process with parameter λ. • Every rain cells, c ij , i = storm index of i, j = rain cell index of storm-i, has poisson or geometry distribution with mean of E(C).• Every waiting time for cells after the storm origin, b ik , i = index storm of i, k = time of rain cell at storm-i, will be exponentially distributed with mean β. • In every rain cell, there are two other parameters forming cluster as rain cell intensity x jh , j = jth cell, h = intensity at j th cell, which is exponentially distributed with mean E(X) and the duration of rain t js , j = jth cell, s = duration at jth cell, is exponentially distributed with mean η.These four conditions can be depicted as in the Fig. 2.
Hourly data from each station is fitted with NSRP and the resulting NSRP parameters ( , ( ), ( ), and ) are recorded on monthly basis.To check on how well the NSRP model obtained is able to represent the actual rainfall data, the mean of the 1-hour rainfall and the probabilities of the 1 and 24hour rainfall estimated from the model are compared with these statistics values calculated from the observed data.

RESULTS
Table 2 shows contain the estimated parameters of the NSRP model for the 48 stations in the November and December.Rainfall data is generated based on the NSRP model with parameters identified for each station and several statistics values, in particular, the mean and probability values of the 1 and 24-hour rainfall amount are then calculated.These statistics are chosen for their ability to describe the condition of a data set.
To check on how well the NSRP model obtained able to represent the actual rainfall data, the mean of the     3.It can be seen that there are no major differences between the estimated and the observed values of the statistics of interest.

CONCLUSION
The results of this study proved that the Neyman-Scott Rectangular Pulse (NSRP) model is able to imitate the pattern of actual rainfall in Peninsular Malaysia by comparing the parameters as well as the spatial distribution of the means and probabilities of 1 and 24-hour rain.Thus, results from the NSRP model fitting for each station are valid to be used in further analysis that is to evaluate the behavior of storm rainfall.research would not have been possible without the sponsorship from Universiti Kebangsaan Malaysia.This research was funded by UKM-DIP-2012-15.

Fig. 1 :
Fig. 1: Geographical regions and the selected 48 stations in Peninsular Malaysia

Fig. 2 :
Fig. 2: NSRP modelling l i storm arrival time, c ij of rain cell, b ik waiting time of rain cell, t js duration of rain cell and x jh intensity of rain cell (observed data), ME = mean of 1-hour rainfall (NSRP model), KO = probability of 1-hour rainfall (observed data), KE = probability of 1-hour rainfall (NSRP model), KO2 = probability of 24-hour rainfall (observed data, KE2 = probability of 24-hour rainfall (NSRP model) 1-hour rainfall and the probabilities of the 1 and 24hour rainfall estimated from the model are compared with these statistics values calculated from the observed data.Part of the results, focusing on the month of November and December only, is displayed in Table

Table 1 :
The list of 48 rain gauges stations with their respective regions and geographical coordinates

Table 2 :
List NSRP parameter for the 48 rain gauges stations

Table 3 :
Comparison between the statistics estimated from the NSRP model with the statistics obtained from the observed data for the 48 rain gauges stations