Occurrence of extreme rainfall has increased globally for couple of years, causing a lot of damages that affect the aspects of life such as, economic, environmental, social and physical. Different researchers have used different methods to model extreme rainfall around the globe. For example Generalized Extreme Value (GEV) and time series. This project focuses on modelling extreme rainfall in the areas Nyeri, Kericho Mombasa Nairobi and Kakamega. There are areas which are more prone to heavy rains, using rainfall data for the past 20 years to model extreme rainfall pattern in Kenya. We have used generalized Pareto distribution (GPD) to model extreme rainfall and have used time series to show the pattern and forecast the occurrence of extreme rainfall in Kenya.
From forecasted result, we found that for the year 2016-2018 monthly rainfall tend to increase and decrease randomly this could be as a result of changes in climate due to global warming.
Table of Contents
CHAPTER ONE
INTRODUCTION
1.1 Background
1.2 Statement of the problem
1.3 Objectives
1.3.1 General objectives
1.3.2 Specific objectives
1.4 Scope of the study
CHAPTER TWO
LITERATURE REVIEW
2.0 Introduction
2.1 Related study
CHAPTER THREE
RESEARCH METHODOLOGY
3.1 Introduction
3.2 Data collection
3.3 Methodology
3.3.1 Fitting a GPD to the rainfall series
3.3.2 Estimation of parameters.
3.3.3 Time series analysis.
3.3.4 Auto-Regressive Model – AR (p)
3.3.5 Moving average model - MA (q)
3.3.6 Auto-regressive moving average model - ARMA (p, q)
3.3.7 Box-Jenkins Approach
CHAPTER FOUR
4.0 DATA ANALYSIS AND REPRESENTATION
4.1 Introduction
4.2 DESCRIPTIVE ANALYSIS
4.3 GENERALIZED PARETO DISTRIBUTION
4.3.1 Parameter estimation
4.3.2 Goodness of fit
4.4 RAINFALL TIME SERIES PLOT FOR DIFFERENT REGIONS IN KENYA.
4.4.1 Stationarity and seasonality
4.4.2 Model identification
4.4.3 Identification of best fit ARIMA model
CHAPTER FIVE
5.1 SUMMARY OF FINDINGS, CONCLUSION AND RECOMMENDATION.
5.1.1 Summary of findings.
5.1.2 Conclusion.
5.1.3 Recommendation.
Research Objectives and Themes
This study aims to model patterns of extreme rainfall in five specific regions of Kenya—Nyeri, Kericho, Mombasa, Nairobi, and Kakamega—using secondary data from the past 20 years to improve disaster preparedness and infrastructure planning.
- Modelling extreme rainfall events using the Generalized Pareto Distribution (GPD).
- Application of Time Series Analysis (ARIMA models) to show rainfall patterns.
- Forecasting future rainfall occurrences to assist in water demand and risk management.
- Assessment of stationarity and seasonality in regional rainfall data.
- Diagnostic evaluation of statistical models to ensure fit and reliability.
Excerpt from the Book
3.3.1 Fitting a GPD to the rainfall series
Let X_1...X_n be a series of identically distributed random variables with unknown paremeter distribution F(x) denotes the monthly rainfall observations. We are estimating the behavior of rainfall over a given threshold μ and excess distribution defined F_μ(y) = P{X_i - μ ≤ y | X_i > μ} = (F(y + μ) - F(μ)) / (1 - F(μ)) equation 1
Where 0 ≤ y < rF - μ, and rF = inf{x : F(x) = 1} ≤ ∞ is the right tail of F(x). The excess distribution represents the probability that a heavy rainfall event that has the value X_i exceeds the threshold μ. The limit theorem about the asymptotic form of F_μ(y) as was first given by Balkema and De Haan (1974) and Pickands (1975).
For a large class of underlying distributions we can find a function β(μ) such that lim sup |F_μ(y) - G_ε,β(μ)(y)| = 0 equation 2
This is the generalized Pareto distribution with parameters β > 0 and x ≥ 0 when ε ≥ 0 and 0 ≤ x ≤ -β/ε, when ε < 0 where β is the scaling parameter and ε is the shape parameter of the distribution. Therefore, for the distribution F(x) as the threshold μ increases, the excess distribution F_μ(y) converges to a GPD.
Summary of Chapters
CHAPTER ONE: Provides an overview of climate change impacts in Kenya and the motivation for modelling extreme rainfall to address economic and social hazards.
CHAPTER TWO: Reviews existing literature on extreme value distributions and the application of various mathematical models like GEV, ARIMA, and GPD globally.
CHAPTER THREE: Details the research methodology, covering data collection, the mathematical fitting of the GPD, and the Box-Jenkins approach for time series modelling.
CHAPTER FOUR: Presents the analysis and interpretation of rainfall data, including descriptive statistics, model parameter estimation, and diagnostic checks for the selected regions.
CHAPTER FIVE: Summarizes the study's findings, provides conclusions regarding model efficiency, and offers recommendations for future meteorological research.
Keywords
Extreme Rainfall, Kenya, Generalized Pareto Distribution, GPD, Time Series Analysis, ARIMA, Forecasting, Climate Change, Global Warming, Stationarity, Parameter Estimation, Box-Jenkins, Rainfall Patterns, Statistical Modelling.
Frequently Asked Questions
What is the core focus of this research?
The research focuses on modelling and forecasting extreme rainfall patterns in five key regions of Kenya to mitigate economic and environmental damage.
Which areas in Kenya were studied?
The study analyzed rainfall data from Nyeri, Kericho, Mombasa, Nairobi, and Kakamega.
What is the primary objective of this work?
The primary objective is to model the patterns of extreme rainfall and forecast future occurrences using robust statistical methods.
What scientific methods were employed?
The researchers utilized the Generalized Pareto Distribution (GPD) for extreme values and ARIMA (Auto-Regressive Integrated Moving Average) models for time series forecasting.
What does the main body of the work cover?
It covers the mathematical derivation of GPD, data collection from the Kenya Meteorological Department, model identification using ACF/PACF plots, and forecasting results.
Which keywords define this study?
Key terms include Extreme Rainfall, GPD, ARIMA, Time Series Analysis, Forecasting, and Climate Change.
Why was the Generalized Pareto Distribution (GPD) used?
GPD was selected because it is highly effective for modelling exceedances over a threshold, which helps in identifying extreme weather events.
What was the conclusion regarding future rainfall?
Based on the return level plots, the study concludes that extreme rainfall levels are likely to continue increasing in the regions studied over the next few decades.
Were the models reliable for forecasting?
The models were found to be effective for general forecasting, although prediction intervals were sometimes influenced by correlated residuals.
- Citar trabajo
- MSC George Kingori Maina (Autor), Fredrick Muhindi (Autor), 2022, Modelling extreme rainfall in Kenya, Múnich, GRIN Verlag, https://www.grin.com/document/1223565
