Spatial modelling of extreme rainfall amount in Kelantan - Noor Fadhilah, Ahmad Radi (2018)
The study on extreme rainfall modelling is very important to estimate the extreme rainfall process accurately and to generate a long series of synthetic extreme rainfall data in cases where data is limited. Assessing the behaviour of extreme events is quite challenging and requires the characterisation of the tail distribution. The extreme events require the modelling of spatial extreme data in order to analyse and characterise the regional behaviour in a study region. Hence, this study focuses on the univariate and multivariate spatial modelling of extreme rainfall data with application in Kelantan, Malaysia. Firstly, the identification of extreme rainfall data can be achieved using two methods, namely block maximum (BM) and peak over threshold (POT) methods. The difficulty arises in choosing the appropriate method to extract the extreme rainfall data. In most cases, the researcher will choose either POT or BM method in extracting extreme rainfall. Hence, for the case where univariate rainfall data are collected at the spatial locations, we proposed a new procedure of regional frequency analysis (RFA) by considering the BM and POT methods to extract extreme rainfall data. Secondly, we considered the case of spatial multivariate analysis where the dependence structures between the rainfall stations were taken into account using the max-stable model. A current practice on max-stable process is to model the dependence for spatial extremes using some constant thresholds and constant marginal models. In this study, we proposed a new procedure for max-stable model by considering different spatial threshold with marginal distribution that depends on covariates that suits well for large study regions. We also applied the max-stable model by regionalising the stations with similar characteristics using the RFA method. Three models from max-stable were considered namely Smith, Schlather and Brown-Resnick models. We also considered the case when the dependence structure does not converge to the max-stable limit using the inverted max-stable model. Thirdly, we considered another method to incorporate the spatial dependence of extreme rainfall using the copula model. The multivariate skew-t copula was constructed to model the spatial extreme of rainfall data. We have extended the bivariate case to the trivariate case of skew-t copula where three rainfall stations were considered. Fourthly, we considered the generation of synthetic extreme rainfall data that has similar characteristics to the observed data. Thus, in this study, we have proposed the generation of synthetic rainfall data that can complement the unavailability of the observed rainfall data using the best spatial model from the RFA, max-stable and copula methods. Lastly, we described and discussed the strengths of the extreme rainfall models that have been proposed in this study. We developed the spatial rainfall profile for Kelantan based on its spatial characteristics. The applications of all the models were illustrated using rainfall amount data of Kelantan. The results of the study shows that the RFA, max-stable and copula methods were successfully applied to the study region. By comparing the performance of all models used, it was found that there was no consistent pattern in the performance of each method and thus, no definite conclusion could be drawn on which method is the best or most appropriate. The choice of the best rainfall model is subjective depending on the purpose of the study itself. Different studies used different methods for rainfall estimation, which makes it difficult to draw a general conclusion. However, based on the results obtained, it was shown that the RFA, max-stable and copula methods can be used to model the extreme rainfall data in Kelantan when the spatial dependence is of the main concern. Nevertheless, all the proposed model that are RFA, copula and max-stable model perform well and able to demonstrate its usefulness on real data sets. The significant contribution of the study on spatial dependence in extreme rainfall modelling is important to reduce the uncertainties of the point estimates for the tail index. Also, the study is important as it provides an estimate of regional characteristics of extreme rainfall in Kelantan, Malaysia that is useful in flood estimation to support flood risk management as well as for engineering design.