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Modelling Rainfall Occurrence Using First Order Markov Chain Model: A Case Study Of Okitipupa, Ondo State, Nigeria

Type Project Topics (docx)
Faculty Sciences
Course Statistics And Data Sciences
Price ₦4,000
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Key Features:
Year: 2000-2019
Pages: 48
Format: Ms word
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Abstract:
The research applied the first order Markov chain model to daily rainfall observations recorded over Okitipupa, Ondo state, Nigeria, in other to determine the sequences of rainfall occurrences. The model relies on 20 years of historical rainfall data obtained from the archive of the Nigerian Meteorological Agency, Abuja and modeled to forecast future occurrences based on whether a rainy day followed a rainy daily or a rainy day followed a dry day or vice versa. The analysis reveals a total of 3,956 rain days and 3,349 dry days over the study period, with 2,664 rain-to-rain sequences and 2,095 dry-to-dry sequences. Results on monthly basis further revealed varying rainfall sequences, with a clear peak in rainy season months. Transition probabilities calculated from the model highlight the likelihood of transitions between different states (rainy or dry days). This predictive approach provides a useful tool for addressing the region's agricultural and water resource challenges. The model demonstrates how accurate rainfall predictions can mitigate the risks of crop failures and inefficient water usage, enhancing food security and resource management. The study emphasizes the importance of understanding climate variability and its effects on rainfall patterns, especially as regions like Okitipupa face the growing threat of climate change. Findings from the model support decision-making processes that help local farmers and authorities plan more effectively, ensuring that agricultural activities and water resource management are aligned with predictable weather conditions. The project concludes that a first-order Markov chain model is a practical and effective method for modeling rainfall in tropical regions. Its ability to predict transitions between wet and dry periods has significant implications for agricultural productivity and water conservation. The study’s approach lays the foundation for further exploration, incorporating more environmental factors to refine and improve rainfall forecasting models.
Table of Content:
TITLE PAGE i
DECLARATION ii
DEDICATION iii
CERTIFICATION iv
ACKNOWLEDGEMENT v
ABSTRACT vi
TABLE OF CONTENTS vii
LIST OF TABLES ix
LIST OF FIGURES x

CHAPTER ONE 1
1.0 BACKGROUND TO THE STUDY 1
1.1 AIM OF THE STUDY 2
1.2 OBJECTIVE OF THE STUDY 2
1.3 SIGNIFICANCE OF THE STUDY 3
1.4 SCOPE AND LIMITATION OF THE STUDY 4
1.4.1 SCOPE 4
1.4.2 LIMITATIONS 4
1.5 AREA OF STUDY 5
1.6 RESEARCH QUESTIONS 7



CHAPTER TWO 8
2.1 MARKOV CHAIN MODELLING 8


CHAPTER THREE 14
3.1 RESEARCH DESIGN 14
3.2 DESCRIPTION OF THE AREA OF STUDY 14
3.3 MODEL SPECIFICATION 14
3.3.1 STOCHASTIC PROCESS 15
3.3.2 MARKOV PROCESS 15
3.3.3 CONVERGENCE 17
3.4 MARKOV CHAIN 18
3.5 FIRST ORDER MARKOV CHAIN 19
3.6 DEPENDENCEY TEST 20
3.7 TRANSFORMING A PROCESS INTO A MARKOV CHAIN 20
3.8 CHAPMAN-KOLMOGOROV EQUATIONS 21
3.8.1 CHAPMAN-KOLMOGOROV EQUATIONS 21
3.8.2 REMARKS 22
3.8.3 PROOF OF C-K EQUATIONS 22
3.9 ‘R’ LANGUAGE 23

CHAPTER FOUR 25
4.1 ANALYSIS AND RESULTS 25
4.2 DESCRIPTIVE ANALYSIS 29

CHAPTER FIVE 34
5.1 SUMMARY 34
5.2 CONCLUSION 34
5.3 RECOMMENDATIONS 34
REFERENCES 36
Introduction:
Rainfall is a natural phenomenon that occurs when water vapor in the atmosphere condenses and falls to the ground, nourishing our planet and shaping our environment. This incredible process is crucial for maintaining the delicate balance of our ecosystem, supporting biodiversity, and influencing the global climate, (Wikipedia).
Gobena (2010) conducted a study for selected three catchments of Upper Awash Sub Basin using two models namely AWBM and SMAR models among five lumped conceptual models nested in Rainfall-Runoff library. Automatic calibration and verification of the models were performed using Genetic Algorithm optimization method together with Nash Sutcliffe criteria and runoff difference as primary and secondary objectives respectively. A comparison of observed and simulated flow as well as comparison of performance of the two models were conducted. Both AWBM and SMAR models predict the flows fairly well with overall Nash Sutcliffe criteria of 0.6 to 0.85 for both calibration and verification periods.
The water cycle, also known as the hydrologic cycle, is the continuous process by which water is circulated between the Earth and the atmosphere. Rainfall is the most significant component of this cycle, accounting for approximately 70% of the world's freshwater supply. It is estimated that over 5,000 cubic miles of water fall on Earth as rainfall every year, with an average annual global rainfall of around 30 inches (760 mm). This staggering amount of water is distributed unevenly across the globe, with some regions experiencing heavy rainfall while others face drought and aridity.
Rainfall plays a vital role in sustaining human life and economic development. It provides drinking water for millions of people worldwide, especially in areas without access to alternative sources. Agriculture, the backbone of global food security, relies heavily on rainfall to irrigate crops and support livestock. Rainfall also drives hydroelectric power generation, a clean and renewable energy source that reduces our reliance on fossil fuels.
In addition to its practical applications, rainfall has a profound impact on our environment and ecosystems. It replenishes groundwater, lakes, rivers, and reservoirs, ensuring a steady water supply for various purposes. Rainfall maintains healthy ecosystems, supporting biodiversity and the intricate web of life. It shapes our landscape, carving out valleys, creating waterfalls, and forming wetlands that provide habitat for countless species.
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