Fadhilah Yusof

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.

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.

Volatility modeling of rainfall time series

Networks of rain gauges can provide a better insight into the spatial and temporal variability of rainfall, but they tend to be too widely spaced for accurate estimates. A way to estimate the spatial variability of rainfall between gauge points is to interpolate between them. This paper evaluates the spatial autocorrelation of rainfall data in some locations in Peninsular Malaysia using geostatistical technique. The results give an insight on the spatial variability of rainfall in the area, as such, two rain gauges were selected for an in-depth study of the temporal dependence of the rainfall data-generating process. It could be shown that rainfall data are affected by nonlinear characteristics of the variance often referred to as variance clustering or volatility, where large changes tend to follow large changes and small changes tend to follow small changes. The autocorrelation structure of the residuals and the squared residuals derived from autoregressive integrated moving average (ARIMA) models were inspected, the residuals are uncorrelated but the squared residuals show autocorrelation, and the Ljung–Box test confirmed the results. A test based on the Lagrange multiplier principle was applied to the squared residuals from the ARIMA models. The results of this auxiliary test show a clear evidence to reject the null hypothesis of no autoregressive conditional heteroskedasticity (ARCH) effect. Hence, it indicates that generalized ARCH (GARCH) modeling is necessary. An ARIMA error model is proposed to capture the mean behavior and a GARCH model for modeling heteroskedasticity (variance behavior) of the residuals from the ARIMA model. Therefore, the composite ARIMA–GARCH model captures the dynamics of daily rainfall in the study area. On the other hand, seasonal ARIMA model became a suitable model for the monthly average rainfall series of the same locations treated.

A comparative study of mixed exponential and Weibull distributions in a stochastic model replicating a tropical rainfall process

A stochastic rainfall model is presented for the generation of hourly rainfall data in an urban area in Malaysia. In view of the high temporal and spatial variability of rainfall within the tropical rain belt, the Spatial–Temporal Neyman–Scott Rectangular Pulse model was used. The model, which is governed by the Neyman–Scott process, employs a reasonable number of parameters to represent the physical attributes of rainfall. A common approach is to attach each attribute to a mathematical distribution. With respect to rain cell intensity, this study proposes the use of a mixed exponential distribution. The performance of the proposed model was compared to a model that employs the Weibull distribution. Hourly and daily rainfall data from four stations in the Damansara River basin in Malaysia were used as input to the models, and simulations of hourly series were performed for an independent site within the basin. The performance of the models was assessed based on how closely the statistical characteristics of the simulated series resembled the statistics of the observed series. The findings obtained based on graphical representation revealed that the statistical characteristics of the simulated series for both models compared reasonably well with the observed series. However, a further assessment using the AIC, BIC and RMSE showed that the proposed model yields better results. The results of this study indicate that for tropical climates, the proposed model, using a mixed exponential distribution, is the best choice for generation of synthetic data for ungauged sites or for sites with insufficient data within the limit of the fitted region.

Application of Self-Organizing Map (SOM) in Missing Daily Rainfall Data in Malaysia

organizing map (SOM) is applied to deal with missing daily rainfall data with different rainfall patterns in Peninsular Malaysia. In this study, stations from Damansara and Kelantan are focused and aimed to evaluate the effectiveness of SOM in clustering and imputation of missing data. The missing data that are imputed by SOM are evaluated by computing the mean square error (MSE) and coefficient correlation(R). Besides, the effects of the imputed data to the mean and variance of the rainfall data is also been observed. The clustering analysis showed that all the stations in Damansara are grouped distinctively, and having a good and even distribution of rain intensity as compared to Kelantan. Meanwhile it is also found that SOM is an excellent tool in estimation of missing data. Keywords-organizing map (SOM); missing values Recently, the impact of climatic change causes the varying of rainfall patterns in Peninsular Malaysia. The high frequency of flood due to monsoon and non-monsoon seasons will have significant influence to the existence of missing rainfall data. Therefore, this study will use the SOM algorithm in treating this missing data problem. Besides, the clustering analysis by SOM on the two river basins namely Damansara and Kelantan, Malaysia also will be examined. The results will be discussed in Section 4.

Optimal design of rain gauge network in Johor by using geostatistics and particle swarm optimization

This study proposes particle swarm optimization (PSO) approach to determine the optimal number and locations for the optimal rain gauge network in Johor state. The existing network of 84 rain gauges in Johor is also restructured into new locations by using daily rainfall, humidity, solar radiation, temperature and wind speed data collected during the monsoon season (November - February) of 1975 until 2008. This study used the combination of geostatistics method (variance-reduction method) and particle swarm optimization as the algorithm of optimization during the restructured proses. The numerical result shows that the new rain gauge location provides minimum value of estimated variance. This shows that the proposed method can serve as an analysis tool for a decision making to assist hydrologist in the selection of prime sites for the installation of rain gauge stations.

The Modelled Raindrop Size Distribution of Skudai, Peninsular Malaysia, Using Exponential and Lognormal Distributions

This paper presents the modelled raindrop size parameters in Skudai region of the Johor Bahru, western Malaysia. Presently, there is no model to forecast the characteristics of DSD in Malaysia, and this has an underpinning implication on wet weather pollution predictions. The climate of Skudai exhibits local variability in regional scale. This study established five different parametric expressions describing the rain rate of Skudai; these models are idiosyncratic to the climate of the region. Sophisticated equipment that converts sound to a relevant raindrop diameter is often too expensive and its cost sometimes overrides its attractiveness. In this study, a physical low-cost method was used to record the DSD of the study area. The Kaplan-Meier method was used to test the aptness of the data to exponential and lognormal distributions, which were subsequently used to formulate the parameterisation of the distributions. This research abrogates the concept of exclusive occurrence of convective storm in tropical regions and presented a new insight into their concurrence appearance.

Statistical Analysis of Electrical Tree Inception Voltage, Breakdown Voltage and Tree Breakdown Time Data of Unsaturated Polyester Resin

This paper presents a statistical approach to analyze electrical tree inception voltage, electrical tree breakdown voltage and tree breakdown time of unsaturated polyester resin subjected to AC voltage. The aim of this work was to show that Weibull and lognormal distribution may not be the most suitable distributions for analysis of electrical treeing data. In this paper, an investigation of statistical distributions of electrical tree inception voltage, electrical tree breakdown voltage and breakdown time data was performed on 108 leaf-like specimen samples. Revelations from the test results showed that Johnson SB distribution is the best fit for electrical tree inception voltage and tree breakdown time data while electrical tree breakdown voltage data is best suited with Wakeby distribution. The fitting step was performed by means of Anderson-Darling (AD) Goodness-of-fit test (GOF). Based on the fitting results of tree inception voltage, tree breakdown time and tree breakdown voltage data, Johnson SB and Wakeby exhibit the lowest error value respectively compared to Weibull and lognormal.

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).

Disaggregation of daily rainfall data using Bartlett Lewis Rectangular Pulse model: a case study in central Peninsular Malaysia

Short duration rainfall data are required for certain hydrological risk assessments. However, short timescale rainfall intensity records are still scarce due to the high cost and low reliability of the monitoring systems. One way to solve this problem is by disaggregating rainfall data using stochastic methods. This study used the Bartlett Lewis Rectangular Pulse model to disaggregate daily rainfall into hourly rainfall for ten stations in the central region of Peninsular Malaysia. The performance of the model was evaluated on its ability to reproduce statistical properties, namely the mean and standard deviation, derived from the historical records over the disaggregated rainfall. The disaggregation of daily to hourly rainfall produced daily and hourly means that closely matched the historical records. However, the standard deviations of the disaggregated daily rainfall were lower than the historical values. Despite the significant differences in the standard deviation, both data series exhibit similar patterns and the model adequately preserved the trends of all the statistical properties used in evaluating its performance.