Jamaludin Suhaila

Characterisation of Drought Properties with Bivariate Copula Analysis

Drought severity and duration are usually modelled independently. However, these two characteristics are known to be related. To model this relationship, a joint distribution of drought severity and duration using a bivariate copula model is proposed and applied to daily rainfall data (1976–2007) of 30 rain gauge stations in Peninsular Malaysia. The drought characteristics are classified using the standardized precipitation index (SPI) and their univariate marginal distributions are further identified by fitting exponential, gamma, generalized extreme value, generalized gamma, generalized logistics, generalized pareto, gumbel max, gumbel min, log-logistic, log-pearson3, log-normal, normal, pearson 5, pearson 6 and weibull distributions. The three-parameter log-normal distribution is identified as the best fitting distribution for drought severity while the generalized pareto distribution is determined as the most appropriate distribution for drought duration with respect to the application of the Anderson-Darling procedure. The dependency among the drought properties is analysed using Kendall’s τ method. The maximum likelihood estimation of the univariate marginal distributions and the maximisation of the bivariate likelihood are employed to compute the Akaike Information Criterion (AIC) values in verifying the best fitting copula distribution. The Galambos distribution is recognised as the most appropriate copula distribution for describing the relationship between drought severity and duration. The conditional drought probability and drought return period are further described to explain the drought properties comprehensively. The probabilities of drought occurrences under certain circumstances with a specific seriousness or duration can be determined in order to verify the possibility of drought episodes. The return period of a recurrent drought has also been investigated to identify the time-interval for repeated drought occurrences under similar situation.

Spatial analysis of daily rainfall intensity and concentration index in Peninsular Malaysia

This study presents the spatial analysis of daily rainfall intensity and concentration index over Peninsular Malaysia. Daily rainfall data from 50 rainfall stations are used in this study. Due to the limited number of stations, the geostatistical method of ordinary kriging is used to compute the values of daily rainfall concentration and intensity and to map their spatial distribution. The resultant analysis of rainfall concentration indicated that the distribution of daily rainfall is more regular over the west, northwest and southwest regions compared to the east. Large areas of the eastern Peninsula display an irregularity in distribution of daily rainfall. In terms of number of rainy days, analysis of daily rainfall confirms that a large number of rainy days across the Peninsula arise from low-intensity events but only contribute a small percentage of total rain. On the other hand, a low frequency of rainy days with high-intensity events contributes the largest percentage of total rain. The results indicated that the total rain in eastern areas is mainly contributed by the high-intensity events. This finding explains the occurrence of a large number of floods and soil erosions in these areas. Therefore, precautionary measures should be taken earlier to prevent any massive destruction of property and loss of life due to the hazards. These research findings are of considerable importance in providing enough information to water resource management, climatologists and agriculturists as well as hydrologists for planning their activities and modelling processes.

Rainfall characterisation by application of standardised precipitation index (SPI) in Peninsular Malaysia

The interpretations of trend behaviour for dry and wet events are analysed in order to verify the dryness and wetness episodes. The fitting distribution of rainfall is computed to classify the dry and wet events by applying the standardised precipitation index (SPI). The rainfall amount for each station is categorised into seven categories, namely extremely wet, severely wet, moderately wet, near normal, moderately dry, severely dry and extremely dry. The computation of the SPI is based on the monsoon periods, which include the northeast monsoon, southwest monsoon and inter-monsoon. The trends of the dry and wet periods were then detected using the Mann–Kendall trend test and the results indicate that the major parts of Peninsular Malaysia are characterised by increasing droughts rather than wet events. The annual trends of drought and wet events of the randomly selected stations from each region also yield similar results. Hence, the northwest and southwest regions are predicted to have a higher probability of drought occurrence during a dry event and not much rain during the wet event. The east and west regions, on the other hand, are going through a significant upward trend that implies lower rainfall during the drought episodes and heavy rainfall during the wet events.

Bivariate copula in fitting rainfall data

The usage of copula to determine the joint distribution between two variables is widely used in various areas. The joint distribution of rainfall characteristic obtained using the copula model is more ideal than the standard bivariate modelling where copula is belief to have overcome some limitation. Six copula models will be applied to obtain the most suitable bivariate distribution between two rain gauge stations. The copula models are Ali-Mikhail-Haq (AMH), Clayton, Frank, Galambos, Gumbel-Hoogaurd (GH) and Plackett. The rainfall data used in the study is selected from rain gauge stations which are located in the southern part of Peninsular Malaysia, during the period from 1980 to 2011. The goodness-of-fit test in this study is based on the Akaike information criterion (AIC).

Clustering rainfall pattern in Malaysia using functional data analysis

Understanding rainfall pattern is important for planning and prediction in hydrology, meteorology, water planning and agriculture. There are two important features of rainfall: the rainfall amount and the probability of rainfall occurrence. The discrete raw data of rainfall precipitation was reconstructed into rainfall amount curves by using functional data analysis method. Hierarchical clustering method with complete-linkage method was used to search for natural similar groupings of rainfall amount curves. The functional clustering illustrated the four dominant patterns for rainfall amount curves. In additional, adaptive Neyman test showed that each clusters are significantly different with from each others.

Bivariate copula in Johor rainfall data

Copula is a probability distribution that allows a joint distribution function build from different univariate marginal distribution function. The climate in Malaysia is very humid, which cause the rainfall data is usually skewed. Gumbel, Clayton and skew t copula are distributions that good in analyze data that is extreme. Five rain gauge stations in Johor will be used in this study. The most suitable copula function that best suit the bivariate relation among the five stations will be studied. The Akaike information criterion and Bayesian information criterion will be the used as the moderators to decide the best suit copula function. Gumbel copula is the best suit copula function among the five rain gauge stations.

Temporal changes and variability in temperature series over Peninsular Malaysia

With the current concern over climate change, the descriptions on how temperature series changed over time are very useful. Annual mean temperature has been analyzed for several stations over Peninsular Malaysia. Non-parametric statistical techniques such as Mann-Kendall test and Theil-Sen slope estimation are used primarily for assessing the significance and detection of trends, while a nonparametric Pettitt’s test and sequential Mann-Kendall test are adopted to detect any abrupt climate change. Statistically significance increasing trends for annual mean temperature are detected for almost all studied stations with the magnitude of significant trend varied from 0.02°C to 0.05°C per year. The results shows that climate over Peninsular Malaysia is getting warmer than before. In addition, the results of the abrupt changes in temperature using Pettitt’s and sequential Mann-Kendall test reveal the beginning of trends which can be related to El Nino episodes that occur in Malaysia. In general, the analysis re...

Statistical analysis on mean rainfall and mean temperature via functional data analysis technique

Generally, the climate variable such as rainfall and temperature data are collected on daily, monthly and annual basis which is in the form of discrete observations. The purpose of this study is to build up a functional data object from these observations which could be used to represent the continuous rainfall-temperature process at each station. This study is interested in looking on how daily means for both temperature and rainfall fluctuate at each station over time. Smoothing technique such as Fourier series is used to capture the variations. Based on the fitted smoothing curve, a summary statistics on a typical weather patterns and variability in these rainfall and temperature patterns could be examined. Using the concept of functional analysis, the test results indicated that there exist significance differences in the functional means of rainfall and temperature between studied stations. Besides, a functional relationship between rainfall and temperature could also be established based on functional linear models.