Prediction of Rainfall in Saudi Arabia

118 Pages·2015·2.2 MB·English

by  University Libraries

Prediction of Rainfall in Saudi Arabia

A THESIS
SUBMITTED TO THE GRADUATE EDUCATIONAL POLCIES COUNCIL
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS

For the degree
MASTER OF SCIENCE

By
Hadi Obaid M Alshammari

Adviser Dr. Rahmatullah Imon

Ball State University
Muncie, Indiana
May 2015
ACKNOWLEDGEMENTS

I would like to gratefully and sincerely thank my supervisor Professor Dr. Rahmatullah Imon for
the patient guidance, encouragement and advice he has provided throughout my time as his
student. I have been extremely lucky to have a supervisor who cared so much about my work,
and who responded to my questions and queries so promptly. His mentorship was paramount in
providing a well-rounded experience consistent my long-term career goals. For everything
you’ve done for me Dr. Imon, thank you. I would like also to thank the rest of my thesis
committee: Dr. Rich Stankewitz and Dr. Yayuan Xiao for their encouragement, insightful
comments and patience.

Finally, I would like to thank my family: my mother, my brothers and sisters, for supporting me
throughout my life.

Hadi Obaid M Alshammari

March, 30, 2015
Table of Contents
CHAPTER 1 4
INTRODUCTION 4
1.1 Saudi Arabia Climate Data 5
1.2 Outline of the Study 10

CHAPTER 2 12
ESTIMATION OF MISSING VALUES IN SAUDI ARABIA CLIMATE DATA
2.1 Imputation Methods 12
2.2 Expectation Maximization Algorithm 14
2.3 Estimation with Trend Models 15
2.4 Estimation with Smoothing Techniques 17
2.5 Robust Methods 18
2.6 Nonparametric Bootstrap 21
2.7 Estimation of Missing Values for Saudi Arabia Climate Data 24
2.8 Trend of Climate Data for Saudi Arabia 32

CHAPTER 3 34
MODELING AND FITTING OF DATA USING REGRESSION AND MEDIATION METHODS 34
3.1 Classical Regression Analysis 34
3.2 Mediation 42
3.3 Accuracy Measures 43
3.4 A Comparison of Regression and Mediation Fits for Gizan 45

CHAPTER 4 48
FORECASTNG WITH ARIMA MODELS 48
4.1 The Box-Jenkins Methodology 48
4.2 Stationary and Nonstationary Time Series 49
4.3 Test for Significance of a White Noise Autocorrelation Function 52
4.4 ARIMA Models 54
4.5 Estimation and Specification of ARIMA Models 60
4.6 Diagnostic Checking 62
4.7 Computing a Forecast 63
4.8 Fitting of the ARIMA Model to Saudi Arabia Rainfall Data 69

CHAPTER 5 79
EVALUATION OF FORECASTS BY REGRESSION, MEDIATION AND ARIMA
MODELS 77
5.1 Cross Validation in Regression and Time Series Models 79
5.2 Evaluation of Forecasts for Rainfall Data 81

CHAPTER 6 86
CONCLUSIONS AND AREAS OF FUTURE RESEARCH 86
6.1 Conclusions 86
6.2 Areas of Future Research 87
REFERENCES 88

APPENDIX A 91
Saudi Arabia Climate Data
List of Tables
Chapter 2

Table 2.1: Trend of Complete Climate Data for Saudi Arabia 32

Chapter 3

Table 3.1: Actual and Predicted Fits of Rainfall for Gizan 45
Table 3.2: Accuracy Measures for Regression and Mediation Fits of Rainfall for Gizan 47

Chapter 4

Table 4.1: Specification of ARIMA Models 62
Table 4.2: ACF and PACF Values of Rainfall Data for Gizan 70

Chapter 5

Table 5.1: Rainfall Forecast for Gizan 82
Table 5.2: MSPE of Regression, Mediation and ARIMA Forecasts of Rainfall for Gizan 83
Table 5.3: Predicted Trend of Rainfall in Saudi Arabia 84
List of Figures
Chapter 1
Figure 1.1 Major Cities of Saudi Arabia 5
Figure 1.2: Time Series Plot of Total Number of Rainy Days in Gizan 7
Figure 1.3: Time Series Plot of Yearly Temperature of Gizan 7
Figure 1.4: Time Series Plot of Maximum Temperature in Gizan 7
Figure 1.5: Time Series Plot of Minimum Temperature in Gizan 8
Figure 1.6: Time Series Plot of Wind Speed in Gizan 8
Figure 1.7: Time Series Plot of Rainfall in Gizan 8
Figure 1.8: Individual Value Plot of Rainy Days vs Rainfall in Gizan 9
Chapter 2
Figure 2.1: Time Series Plot of Total Number of Rainy Days in Gizan with Complete Data 26
Figure 2.2: Time Series Plot of Yearly Temperature of Gizan with Complete Data 27
Figure 2.3: Time Series Plot of Maximum Temperature in Gizan with Complete Data 28
Figure 2.4: Time Series Plot of Minimum Temperature in Gizan with Complete Data 29
Figure 2.5: Time Series Plot of Wind Speed in Gizan with Complete Data 30
Figure 2.6: Time Series Plot of Rainfall in Gizan with Complete Data 31

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Chapter 3
Figure 3.1: Normal Probability Plot of Rainfall vs Rainy Days in Gizan 40
Figure 3.2: Normal Probability Plot of Rainfall vs Different Climate Variables in Gizan 41
Figure 3.3: Time Series Plot of Original and Predicted Rainfall for Gizan 41
Figure 3.4: Regression vs Mediation Analysis 43
Figure 3.5: Time Series Plot of Actual and Predicted Fits of Rainfall for Gizan 46

Chapter 4
Figure 4.1: ACF and PACF of Rainfall Data for Gizan 70
Figure 4.2: ACF and PACF of Rainfall Data for Hail 70
Figure 4.3: ACF and PACF of Rainfall Data for Abha 71
Figure 4.4: ACF and PACF of Rainfall Data for Al Ahsa 71
Figure 4.5: ACF and PACF of Rainfall Data for Al Baha 71
Figure 4.6: ACF and PACF of Rainfall Data for Arar 72
Figure 4.7: ACF and PACF of Rainfall Data for Buriedah 72
Figure 4.8: ACF and PACF of Rainfall Data for Dahran 72
Figure 4.9: ACF and PACF of Rainfall Data for Jeddah
73
Figure 4.10: ACF and PACF of Rainfall Data for Khamis Mashit 73
Figure 4.11: ACF and PACF of Rainfall Data for Madinah 73
Figure 4.12: ACF and PACF of Rainfall Data for Mecca 74
Figure 4.13: ACF and PACF of Rainfall Data for Quriat 74
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Figure 4.14: ACF and PACF of Rainfall Data for Rafha 74
Figure 4.15: ACF and PACF of Rainfall Data for Riyadh 75
Figure 4.16: ACF and PACF of Rainfall Data for Sakaka 75
Figure 4.17: ACF and PACF of Rainfall Data for Sharurah 75
Figure 4.18: ACF and PACF of Rainfall Data for Tabuk 76
Figure 4.19: ACF and PACF of Rainfall Data for Taif 76
Figure 4.20: ACF and PACF of Rainfall Data for Turaif 76
Figure 4.21: ACF and PACF of Rainfall Data for Unayzah 77
Figure 4.22: ACF and PACF of Rainfall Data for Wejh 77
Figure 4.23: ACF and PACF of Rainfall Data for Yanbu 77
Figure 4.24: ACF and PACF of Rainfall Data for Bishah 78
Figure 4.25: ACF and PACF of Rainfall Data for Najran 78
Chapter 5

Figure 5.1: Time Series Plot of Rainfall Forecast for Gizan
83

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CHAPTER 1
INTRODUCTION
Prediction of rainfall is still a huge challenge to the climatologists. It is the most important
component of a climate system. Most of the burning issues of our time like global warming, floods,
draught, heat waves, soil erosion and many other climatic issues are directly related with rainfall.
Every country should have a better understanding and prediction of its weather to avoid
environmental issues in the future. In Saudi Arabia, we have little rain and snow comparing with
other western countries. However, Saudi Arabia has a lot of damages if the weather becomes
rainy or snowy. Since we do not have enough studies regarding environmental issues in Saudi
Arabia, we usually face problems with that. As a desert country, people think that we do not need
to deal seriously with weather damages, but the reality is different. Our government spends a lot
of money to fix the damages which are caused by environmental change. In 2011, Jeddah
Municipality made a session to discuss the causes of environmental issues. “Nowadays, the
environmental change is major problem in Saudi Arabia, and we need to forecast the damages
before it happened”. (Eng. Alzahrani 2011). In this session, all speakers agree that we should
have a lot of studies about our future weather to be able to avoid the problems and damages of it.
In that year (2011), Prince Khaled Al-Feisal employed more than 9 companies to deal with
environmental issues just in Jeddah. (Okaz newspaper, 2011). Saudi Arabia has been suffering
with lots of kinds of environmental issues. Since the population is increasing, the need for
solving these issues becomes very significant. We are interested to study the weather of Saudi
Arabia and its environmental issues. In this study, we will forecast the future rainfall of Saudi
Arabia, and try to know the reasons that cause rainfall. We will employ appropriate statistical
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