Wan Zawiah Wan Zin

Analysis of drought condition and risk in Peninsular Malaysia using Standardised Precipitation Index

Contrary to the belief that Peninsular Malaysia experiences wet condition throughout the year, prolonged dry condition has lately become a recurrent phenomenon in this region. As a result, countrys agricultural sector and water resources have been under severe constraints from this situation. To get a clearer picture of the dry condition in Peninsular Malaysia, the Standardised Precipitation Index, based on the data of monthly rainfall from 50 stations, is derived. Spatial analysis is used to illustrate the percentage of occurrences of dry and very dry events. To evaluate the potential risk due to the dry conditions, we modelled the joint distribution of severity and duration of dry condition by means of bivariate copula. Several copula models were tested, and the model, which best represents the relationship between severity and duration, is determined using Akaike information criterion. Based on the results, the return period for the drought severity, based on the longest duration of drought at each station, can be estimated. This enables the drought risk to be calculated, thus planning on the measures to minimise the impact of a prolonged drought to the societies, which can be done by the relevant authorities.

Generating Synthetic Rainfall Total Using Multivariate Skew-t and Checkerboard Copula of Maximum Entropy

This study aims to test the appropriateness of multivariate skew-t copula and checkerboard copula of maximum entropy in generating monthly rainfall total data. The generation of synthetic data is important, as it provides hypothetical data in areas for which data availability remains limited. Three selected meteorological stations in Kelantan, Malaysia, Stesen Pertanian Melor, Rumah Pam Salor, and Ladang Lepan Kabu, are considered in this study. Monthly rainfall total data for the driest and wettest months in the year are tested in this study. For these three stations, the identified month with the least total of rainfall received (driest) is May, while the month with the highest total of rainfall received (wettest) is November. The data is fitted to gamma distribution with the corresponding parameters estimated. The observed data will be transformed to be in unit uniform using the gamma marginal. The resulting data is compared to simulated uniform data generated using multivariate skew-t copula and checkerboard copula of maximum entropy models based on the correlation values of the observed and simulated data. Next, the Kolmogorov-Smirnov test is used to assess the fit between the observed and generated data. The results show that the values of simulated correlation coefficients do not differ much for gamma distribution, multivariate skew-t, and maximum entropy approaches. This implies that the multivariate skew-t and maximum entropy may be used to generate monthly rainfall total for cases in which actual data is unavailable.

Modelling of extreme rainfall events in Peninsular Malaysia based on annual maximum and partial duration series

In this study, two series of data for extreme rainfall events are generated based on Annual Maximum and Partial Duration Methods, derived from 102 rain-gauge stations in Peninsular from 1982-2012. To determine the optimal threshold for each station, several requirements must be satisfied and Adapted Hill estimator is employed for this purpose. A semi-parametric bootstrap is then used to estimate the mean square error (MSE) of the estimator at each threshold and the optimal threshold is selected based on the smallest MSE. The mean annual frequency is also checked to ensure that it lies in the range of one to five and the resulting data is also de-clustered to ensure independence. The two data series are then fitted to Generalized Extreme Value and Generalized Pareto distributions for annual maximum and partial duration series, respectively. The parameter estimation methods used are the Maximum Likelihood and the L-moment methods. Two goodness of fit tests are then used to evaluate the best-fitted distribut...

Methods on handling missing rainfall data with Neyman-Scott rectangular pulse modeling

Rainfall data from rain-gauge stations suffers the risk of being missing due to factors such as human negligence, faulty equipment and disasters. In this paper, complete monthly rainfall data from 1985 to 1992 in Payakangsar station is used as the base data to determine the appropriate method for handling missing data. A portion of this complete data is then omitted at random by as much as 5%, 10% and 15% of the total number of data. Three methods of missing data replacement are considered that is, replacement of the missing data with zero (NR), single imputation (SI) and multiple imputation (MI) methods. The Neyman-Scott Rectangular Pulse (NSRP) rainfall stochastic model is then fitted to the resulting data from these three methods. Data from the month of October and November are selected for further analysis as these two months represent the months with highest rainfall amount received. To assess the performance of these three methods, a goodness-of-fit test based on the mean absolute error is applied. ...

On the comparison of the interval estimation of the Pareto parameter under simple random sampling and ranked set sampling techniques

Ranked set sampling (RSS) is recognized as a useful sampling scheme for improving the precision of the parameter estimates and increasing the efficiency of estimation. This type of scheme is appropriate when the variable of interest is expensive or time consuming to be quantified, but easy and cheap to be ranked. In this study, the estimation of the shape parameter of the Pareto distribution of the first type when the scale is known is studied for the data that are gathered under simple random sampling (SRS), RSS, and selective order statistics based on the maximum (SORSS(max)). The confidence intervals for the shape parameter of Pareto distribution under the sampling techniques considered are determined. A simulation study is carried out to compare the confidence intervals in terms of coverage probabilities (CPs) and expected lengths (ELs). When the coverage probabilities and expected lengths for the confidence intervals of the shape parameter of Pareto distribution determined based on the different samp...

Bayesian extreme rainfall analysis using informative prior: A case study of Alor Setar

Bayesian analysis is an alternative approach in statistical inferences. The inclusion of other information regarding the parameter of the model is one of analysis capabilities. In the area of extreme rainfall analysis, expert opinion can be used as prior information to model the extreme events. Thus, considering previous or expert knowledge about the parameter of interest would reduce the uncertainty of the model. In this study, the annual maximum (AM) rainfall data of Alor Setar rain gauge station is modeled by the Generalized Extreme Value (GEV) distribution. A Bayesian Markov Chain Monte Carlo (MCMC) simulation is used for parameter estimation. Comparison of the outcomes between non-informative and informative priors is our main interest. The results show that there is a reduction in estimated values, which is due to informative priors.

Probability distribution of extreme share returns in Malaysia

The objective of this study is to investigate the suitable probability distribution to model the extreme share returns in Malaysia. To achieve this, weekly and monthly maximum daily share returns are derived from share prices data obtained from Bursa Malaysia over the period of 2000 to 2012. The study starts with summary statistics of the data which will provide a clue on the likely candidates for the best fitting distribution. Next, the suitability of six extreme value distributions, namely the Gumbel, Generalized Extreme Value (GEV), Generalized Logistic (GLO) and Generalized Pareto (GPA), the Lognormal (GNO) and the Pearson (PE3) distributions are evaluated. The method of L-moments is used in parameter estimation. Based on several goodness of fit tests and L-moment diagram test, the Generalized Pareto distribution and the Pearson distribution are found to be the best fitted distribution to represent the weekly and monthly maximum share returns in Malaysia stock market during the studied period, respect...

A preliminary study on drought events in Peninsular Malaysia

In this research, the Standard Precipitation Index (SPI) is used to represent the dry condition in Peninsular Malaysia. To do this, data of monthly rainfall from 75 stations in Peninsular Malaysia is used to obtain the SPI values at scale one. From the SPI values, two drought characteristics that are commonly used to represent the dry condition in an area that is the duration and severity of a drought period are identified and their respective values calculated for every station. Spatial mappings are then used to identify areas which are more likely to be affected by longer and more severe drought condition from the results. As the two drought characteristics may be correlated with each other, the joint distribution of severity and duration of dry condition is considered. Bivariate copula model is used and five copula models were tested, namely, the Gumbel-Hougard, Clayton, Frank, Joe and Galambos copulas. The copula model, which best represents the relationship between severity and duration, is determined using Akaike information criterion. The results showed that the Joe and Clayton copulas are well-fitted by close to 60% of the stations under study. Based on the results on the most appropriate copula-based joint distribution for each station, some bivariate probabilistic properties of droughts can then be calculated, which will be continued in future research.In this research, the Standard Precipitation Index (SPI) is used to represent the dry condition in Peninsular Malaysia. To do this, data of monthly rainfall from 75 stations in Peninsular Malaysia is used to obtain the SPI values at scale one. From the SPI values, two drought characteristics that are commonly used to represent the dry condition in an area that is the duration and severity of a drought period are identified and their respective values calculated for every station. Spatial mappings are then used to identify areas which are more likely to be affected by longer and more severe drought condition from the results. As the two drought characteristics may be correlated with each other, the joint distribution of severity and duration of dry condition is considered. Bivariate copula model is used and five copula models were tested, namely, the Gumbel-Hougard, Clayton, Frank, Joe and Galambos copulas. The copula model, which best represents the relationship between severity and duration, is determine...

Empirical Bayes estimation for Markov chain models of drought events in Peninsular Malaysia

This study employs empirical Bayes method to estimate the transition probability matrix of Markov chain. The transition probability is used to determine drought characteristics for 35 rainfall stations in Peninsular Malaysia. The result reveals that non-drought condition is more persistent than the other drought conditions. The result also shows that the middle area of Peninsular Malaysia experiences longer non-drought condition with higher probability compared to other regions. Meanwhile, western area experiences moderate drought condition, more frequent with shorter duration.

Assessment of the intensity-duration-frequency (IDF) curves for storms in Peninsular Malaysia based on the generalized extreme value distribution

Rainfall characteristics can be analyzed by using storm events with storms representing actual rainfall events instead of rainfall amounts in fixed time frames. One of the most commonly used methods in rainfall analysis is the construction of intensity-duration-frequency (IDF) curves. IDF curves help in designing hydraulic structures by providing a mathematical relationship between storm intensity, duration and return period. In Peninsular Malaysia, these curves are often built using the generalized extreme value (GEV) distribution to represent annual maximum storm intensity. The mathematical formula for the curves is usually taken from either known empirical equations or from quantile functions of probability distributions. However, there is no research which compares and analyzes the differences between the curves obtained for storms in Peninsular Malaysia based on the empirical and quantile functions. Thus, the aim of this study is to build IDF curves for storms in Peninsular Malaysia using typical emp...