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The Investigation of Trends, Analysis and Modelling of Daily Rainfall In i The Investigation of Trends, Analysis and Modelling of Daily Rainfall in Australia Bright Emmanuel Owusu A Thesis Submitted in Fulfillment of the Requirements for the Degree of Doctor of Philosophy in Research Methodology Prince of Songkla University 2018 Copyright of Prince of Songkla University ii Thesis Title The Investigation of Trends, Analysis and Modelling of Daily Rainfall inAustralia Author Mr. Bright Emmanuel Owusu Major Program Research Methodology _____________________________________________________________________ Major Advisor: Examining Committee: ……………………………......... ………………….…..…… Chairperson (Emeritus Prof. Dr. Don McNeil) (Dr.Somporn Chuai-Aree) ………………………….…....... Co- advisor: (Emeritus Prof. Dr.Don McNeil) ………………………….…….. ………………………………... (Asst. Prof. Dr. Nittaya McNeil) (Asst. Prof. Dr. Nittaya McNeil) ………………………………….... (Asst. Prof. Dr. Suree Chooprateep) The Graduate School, Prince of Songkla University, has approved this thesis as fulfilment of the requirements for the Doctor of Philosophy Degree in Research Methodology. …….…………………………..……………. (Assoc. Prof. Dr. Damrongsak Faroongsarng) Dean of Graduate School iii This is to declare that the work here submitted is the result of the candidate investigations. Due acknowledgements have been made of any assistance received. ……………………………..Signature (Emeritus Prof. Dr. Don McNeil) Major Advisor ………………………….….Signature (Mr. Bright Emmanuel Owusu) Candidate iv I at this moment declare that this work has not been accepted in substance for any degree, and is not being currently submitted in candidature for any degree. …….………….…………Signature (Mr. Bright Emmanuel Owusu) Candidate v Thesis Title The Investigation of Trends, Analysis and Modelling of Daily Rainfall in Australia Author Mr. Bright Emmanuel Owusu Major Program Research Methodology Academic Year 2017 ABSTRACT Daily accumulated rainfall data obtained from observational stations in Australia over a period of 64 years were explored using statistical methods to determine the patterns. The thesis composed three studies. In the first study, daily rainfall during 1950-2013 for 92 observational stations was obtained from Australian Bureau of Meteorology. Rainfall variability over successive 5-day periods from 1950-2013 was examined. The first model uses factor analysis to classify the 92 stations of factors, which represent distinct geographical regions. Gamma generalised linear models were then fitted to describe the patterns in the 5-day non-zero rainfall amount in each factor region with period and year as the predictors. The factor analysis revealed eight factors in the data, which represent eight geographical regions. These regions comprise north, northeast, central east, northwest, central south, north southeast, southwest and south-southeast. The rainfall from each region exhibits different overall mean with various seasonal variations. The second study also uses daily accumulated rainfall from the 92 observational stations acquired from the Australian Bureau of Meteorology. Multiple linear regression and Gamma GLM models fitted to the 5-day rainfall observations were compared. A simple linear regression model was also fitted to explore the trends in the annual rainfall. The 5-day vi rainfall observations in successive periods were serially correlated, and this was minimised by using the AR(1) technique in fitting the models. The Gamma GLM and the multiple regression models fitted the data quite well in all the regions, particularly in delineating the periodic seasonal patterns. The patterns of the models were well marked mainly in the tropical regions (lower latitudes) where the internal atmospheric variability is small relative to the forced change. However, the multiple regression models did better than the Gamma generalised linear model in the north, northeast and the southwest regions. These models could be used to infill data in areas where rainfall records are inadequate. The linear regression model revealed substantial decreasing annual rainfall trends in the southwest and the north southeast regions. In contrast, significant increasing annual rainfall trends were found in the north and the northwest regions. The final study used daily accumulated rainfall from 105 observational stations acquired from the Australian Bureau of Meteorology. The 64 years data also span between 1950 and 2013. The stations were randomly selected to cover the whole of Australia. Logistic regression was then applied to develop a model to predict 5-day rainfall probability of occurrence or non-occurrence in each station, but nine stations were carefully chosen as a case study. The nine stations were carefully selected to capture the patterns observed in the data from all the stations and to capture most of the six climate classification by the Australian Bureau of Meteorology. The fitted logistic regression models predicted the occurrence and non-occurrence rainfall events quite well with good accuracies. The predictors significantly affected the models in all stations. Analysis of the levels of each of the predictors showed that vii the parameters of the 5-day period factors were more influential in all the models, particularly during the rainy season in most stations relative to that of the annual factors. viii Acknowledgements I would like to express my sincere appreciation to my advisor, Professor Dr. Don McNeil, my co-advisor Asst. Prof. Dr. Nittaya McNeil, and Asst. Prof. Dr. Chamnein Choonpradub for their advice and support throughout the study. I am most grateful to my thesis committee members whose valuable comments, suggestions and advice helped in transforming the thesis to the required format. My great thanks also go to lecturers and staff of the Department of Mathematics and Computer Science Prince of Songkla University Pattani Campus whose work directly or indirectly contributed to the completion of this thesis. I would like to thank the Graduate school Prince of Songkla University and the Presbyterian University College Ghana for their financial support and providing an enabling environment for the successful completion of this thesis. It is also my great thanks to my family and colleagues who have thrown their weight behind me throughout the study. Bright Emmanuel Owusu ix Contents ABSTRACT -------------------------------------------------------------------------------------- v Acknowledgements -------------------------------------------------------------------------- viii List of figures --------------------------------------------------------------------------------- xiii CHAPTER 1 ------------------------------------------------------------------------------------- 1 Introduction -------------------------------------------------------------------------------------- 1 1.1 Background and Rational ---------------------------------------------------------------- 1 1.2 Research Objective ----------------------------------------------------------------------- 4 1.3 Literature Review ------------------------------------------------------------------------- 4 1.4 Conceptual Framework ------------------------------------------------------------------ 9 1.5 Organisation of the Thesis ------------------------------------------------------------- 10 CHAPTER 2 ----------------------------------------------------------------------------------- 11 Methodology ----------------------------------------------------------------------------------- 11 2.1 Data Sources and Management ------------------------------------------------------- 11 2.1.1 Variables -----------------------------------------------------------------------------13 2.2 Study diagrams -------------------------------------------------------------------------- 14 2.3 Statistical methods ---------------------------------------------------------------------- 16 2.3.1 Serial Correlation -------------------------------------------------------------------16 2.3.2 The Correlogram -------------------------------------------------------------------17 2.3.3 Factor analysis ----------------------------------------------------------------------17 2.3.4 Linear regression analysis ---------------------------------------------------------19 2.3.6 Generalised Linear Models -------------------------------------------------------19 x 2.3.5 Multiple regression -----------------------------------------------------------------20 2.3.7 Logistic regression -----------------------------------------------------------------21 2.3.8 Evaluation of the fitted Models --------------------------------------------------22 2.3.9 Gamma generalised linear model ------------------------------------------------23 CHAPTER 3 ----------------------------------------------------------------------------------- 25 Preliminary Analysis of Data --------------------------------------------------------------- 25 3.1 The study area and data ---------------------------------------------------------------- 25 3.2 Summary of the daily rainfall data --------------------------------------------------- 25 CHAPTER 4 ----------------------------------------------------------------------------------- 32 Classification and the modelling of daily rainfall Amount in Australia ---------- 32 4.1 Factor analysis results ------------------------------------------------------------------ 32 4.2 Annual rainfall patterns ---------------------------------------------------------------- 34 4.3 Seasonal rainfall patterns -------------------------------------------------------------- 36 4.4 Annual rainfall trends in Australia
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