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TABLE OF CONTENTS
Title Page
ABSTRACT
TABLE OF CONTENTS
ABBREVIATIONS, UNITS AND SYMBOLS
CHAPTER ONE: INTRODUCTION
1.1 Background of the Study
1.2 Statement of Problems
1.3.Justification of the Study
1.4.Objectives of the Study
CHAPTER TWO: LITERATURE REVIEW
2.2 Periodicity in
Hydrology
2.3 Statistical
Terms
2.4 Frequency Analysis
of Rainfall
2.4.1 Random Variable
2.4.2 Probability relationship
2.5 Return Period
2.6 Climate Data
2.6.1 Uncertainty in model parameters
2.6.2 Rainfall and climate data under climate change scenario
2.7 Rainfall
Amount Models
2.7.1 Normal (Gaussian) distribution
2.7.2 Exponential distributions
2.7.3 Probability Log-normal distribution
2.8 Goodness of
Fit Tests
2.8.1 Kolmogorov-Smirnov Test
2.8.2 Anderson-Darling Test
2.8.3 Chi-Squared test
2.8.4 ANOVA Test
2.8.5 Paired t-Test
2.8.6 Expert Modeler
CHAPTER THREE: MATERIALS AND METHODS
3.1 Study Location
3.2 Data Assembly
3.2.1 Preliminary
Data Analysis Method
.2.2 Formulation of
Hypothesis
3.3 Fitting of
Probability Distributions
3.4 Rainfall
Prediction Strategy
3.5 Statistical
Analysis Framework
CHAPTER FOUR: RESULTS AND DISCUSSION
4.1 Preliminary
Analysis
4.2 Analysis of
Statistical Parameters
4.2.1 Chi-Square Test
4.2.2 Kolmogorov-Smirnov
and Anderson-Darling Tests Statistic
4.3 Comparison of
Observed Monthly Rainfall Amounts with Generated
4.3.1 Testing the
Normal Model with the Observed Value
4.3.2 Testing the
Log-normal Model with the Observed Value
4.3.3 Testing the
Exponential Model with the Observed Value
4.4 Analysis of Trend
4.5 Monthly Rainfall Generation based on the Selected Models
4.5 .1 Monthly Rainfall generation for different Return
Periods
CHAPTER FIVE: SUMMARY, CONCLUSION AND
RECOMMENDATIONS
5.1 Summary
5.2 Conclusion
5.3 Recommendations
REFERENCE
APPENDICES
ABSTRACT
Estimation of rainfall for a desired return period is one of
the pre-requisites for any design purpose at a particular site, which can be achieved
by probabilistic approach. This study is aimed at using the statistical
parameters of long-term observed rainfall data to generate monthly rainfall
depth and estimate rainfall values at different return periods for hydrological
and agricultural planning purposes. The daily rainfall data of 60 years from
1953 to 2012 were collected from the meteorological station situated at the
Institute for Agricultural Research (IAR), Ahmadu Bello University (ABU) Zaria.
In this work, the expected number of observations was 720.However, a sample
size of 431 being the months with rainfall amounts was used for the study.
Three probability distributions functions viz: normal, log normal and
exponential distribution were used for rainfall generation. The data was processed
to estimate the statistical parameters of the distributions for Probability
Density Functions (PDFs) selected. The two types of parameters estimated using
the methods of maximum likelihood via the statistical package called
EasyFitXL5.6 are the scale and location parameters. The parameters‟ estimates
were further used in various PDFs equations to generate new sets of rainfall
amounts. Five statistical goodness of fit test were used in order to select the
best fit probability distribution and are; Anderson-Darling, Chi-square and
Kolmogorov-Smirnov, ANOVA and Student t test. From the analysis of the data, it
was discovered that the normal PDF predicts correctly the monthly amount of
rainfall and specific return periods rainfall values followed by the log-normal
and exponential PDF, the least predictor. After carefully observing and testing
the three PDFs, it was discovered that the normal PDF estimated closely the
monthly amounts of rainfall compared with the log-normal and exponential PDFs
when considered generally for monthly and return periods rainfall values
estimation. Nevertheless, the normal PDFs have been found to predict well the
daily rainfall amounts in Samaru. This work should be made available to local
and immediate environments to Samaru through local and regional experts on
climatic information dissemination for use in planning and management of
specific rainfed crop(s) production.
CHAPTER ONE
INTRODUCTION
1.1. Background
of the Study
Synthetically generated daily or monthly rainfall data are
frequently necessary in data scarce environments as input into the planning and
design of water resources and soil conservation projects; simulation studies of
crop growth and yield; farming systems and field farm operations scheduling (
Jamaludin and Jemain 2007). Rainfall is the principal phenomenon driving many
hydrological extremes such as floods, droughts, landslides, debris and
mud-flows; its analysis and modelling are typical problems in applied
hydrometeorology. Rainfall exhibits a strong variability in time and space.
Hence, its stochastic modeling is not an easy task (De Michele and Bernardara,
2005).
A good understanding of the
pattern and distribution of rainfall is important for water resource management
of an area. Knowledge of rainfall characteristics, its temporal and spatial
distribution play a major role in the design and operation of agricultural
systems, telecommunications, runoff control, erosion control, as well as water
quality systems. Generated weather is needed to supplement existing weather
data, provide alternative weather realizations for a particular historical record,
or identify possible weather sequences for a seasonal climate forecast (Walpole
and Mayers, 1989)....
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