ABSTRACT
It is widely accepted that water supply will be a pressing issue in this century. Thus, position of adequate rainfall in the development of human and natural resources is a worthwhile research work. The data used in this project work was monthly amount of rainfall in Enugu city within the period of (2000- 2012).A preliminary inspection on the data revealed that the data has no trend but consist of multiplicative seasonal movements. Furthermore, the monthly data was also found to be stationary and serially uncorrelated by the Augmented Dickey Fuller test of unit root and the Autocorrelation test for serial correlation of the error term respectively.
The exponential smoothing procedures were adopted for the construction of the best fit model for the prediction of future rainfall pattern in Enugu. This was achieved by algorithms aimed at smoothing out all irregular components inherent in the series. The best fit model parameters were used to predict monthly rainfall distribution for 2013. The result suggested heavy rainfall in general for the year in question with its amplitude in the month of October.

CHAPTER ONE
General Introduction
Water resources are essential renewable resources that are the basis for existence and development of a society. Proper utilization of these resources requires assessment and management of the quantity and quality of the water resources both partially and temporally. Water crises cause by shortages, floods and diminishing water quality, among other, are increasing in all parts of the world. The growth of population demands for increased domestic water supplies and are the same time, results with a higher consumption of water due to expansion in agriculture and industry. Mismanagement and lack of knowledge about existing water resources and the changing climatic conditions have consequences of an imbalance of supply and demand of water. The problem is pronounced in semi-arid and arid areas where the resources are limited.
Surface water being easy, direct and therefore less expensive to exploit in compassion to other sources like ground water or desalination makes it the major source of water supply for irrigation, industry and domestic uses. The surface water, in form of lakes and river discharge (runoff) is predoming obtained from rainfall after being generated by the rainfall runoff processes.
The primary source of water agricultural production for most of the world is rainfall. Three main characteristics of rainfall are its amount, frequency and intensity, the value of which way from place to place, day to day, month to month and also year to year. Precise knowledge of these three main characteristics is essential for planning its full utilization.
Information of the amount, intensity and distribution of monthly or annually rainfall for the most important places in the world is generally available. Long-term records of daily rainfall have been compiled for years, norm and standard deviations have been worked out, floods and droughts have been defined and climate zones of potential evaporation less precipitation have been mapped from rainfall pattern and crop studies. Investigation using electronic computer are continuous in progress and effective are being made to predict future trend in order for refine planning.
Most rain water is used in agriculture for crop production. Therefore, the first point which arises is whether the available rainfall adequate and well distributed for crop-raining. This njew water rate structure encourages water conservation. Preliminary calculations done by city staff confirmed the advantages of the new billing system. However, a specific water forecast model is required for a more precise estimation of the influence of the new rate structure on water consumption and on revenue collection. Such a model will allow testing of different rate structures and different conditions affecting water use and therefore revenue (water price, conservation programs, and weather conditions).
The water forecasting system is very powerful decision support tool. The precise estimation of the future water consumption is essential for determining the water management policy including the efficient water use and for the water purchase planning. The revenue projections are necessary for budget preparation. The knowledge of the future water production is indispensable for utility planning and management.
1.1 Method of Measuring Rainfall
Rainfall is usually measured by first collecting it in a rain gauge. These special drums are then used to record the depth of the water inside. Rain gauge is usually about 50 cm tall and is place on the ground just high enough to avoid splashes. Rain water that is caught in a funnel on top runs down into a measuring cylinder below where it can be recorded.
1.2 Method of Data Collection
The information (Data) collected for the analysis of this project work is purely secondary data that is, already made data. The data on the monthly amount of rainfall (2000-2012), were collected from Nigeria Meteorological Agency Enugu state. The data are recorded on daily basis so that at the end of each month the overall total will be calculated.
1.3 Objectives of the Study
Having known that rainfall is important in the development of the nation and nation’s wealth. This research work is specifically aim at;
o Conduct a preliminary check on the data obtained to gain sight on the on the pattern of trend and seasonal components that constitutes monthly amount of rainfall in Enugu City during the period covered.
o To investigate whether the sample obtained comes from the normal population.
o To conduct the unit root test on the data obtained using the Autocorrelation test, (ACF at lag k), and the Augmented Dickey Fuller test.
o To determine the seasonal adjustment factor using the twelve (12) point multiplicative moving average approach.
o To establish the best fit model for the observations using the exponential smoothing method.
o To forecast monthly amount of rainfall in Enugu using the best fit model parametres for the year 2013.
o To make recommendation based on our findings.
1.4 Scope of the Study
This project work/research is restricted to Nigeria Meteorological Agency in Enugu State. The study covers a period of twelve (12) years (2000-2012). It takes into consideration of the monthly amount of rainfall in Enugu City.
1.5 Statement of the Problem
The researcher has the interest in knowing about the problems of rainfall in Enugu city. The objective is to provide answers to:
Does climatic change affects the monthly amount of rainfall?
Has there been any significant difference in the monthly amount of rainfall from 2000-2012.
Does the trend of monthly amount of rainfall decrease yearly from 2000-2012?
Does seasonal variations affects the monthly amount of rainfall in Enugu city.
1.6 Limitations of the Study
As already stated in the purpose of study, this research was specifically carried out to analyses the monthly amount of rainfall in Enugu City, however the work is only limited to twelve years figures (2000-2012). Hence the expected precision may not be so much. This is because the larger the number of observation, the greater the efficiency of the estimate made from the statistical data.
Another limitation is on data collection. Data collection is not an easy task to carry out as a result of the confidentiality of data. This effect presented some problems in gathering enough facts as regard to this study.
This scope of this research has been limited to lack of adequate and relevant information from the Nigeria Meteorological Agency, financial constraint to transport, and photocopy of some relevant material and to browse for more information on the internet.
There is also the inadequate of materials in the libraries that deals or discuss more on the topic. Lastly, the time limit or duration also constituted considerable limitation because the project work was being done at the time normal lectures were going on.
1.7 Definition of Terms
Time Series
A time series is a time ordered set of observations made on a variable at different period of time. E.g Total annual production of crude oil in Nigeria, Number of yearly accident in a factory e.t.c.
Uses of Time Series
o It helps in understanding part behavior, by observing data over a period of time.
o It helps in planning future operation plans for the future cannot be made without forecasting events and relationship they with have.
o It helps in evaluating current accomplishment. The actual performance can be compared with the expected performance and the cause of variation analyzed.
o It facilitates comparison. Difference time series are often compared and important conclusion drawn therefore.
1. Time series analyses uses historical data of the variable being forecasted to developed a model for predicting future values.
Component of Time Series Data
The time series data are made up of the following components:
Trend
The trend is the long-run trending of the time series data. It helps us to asset whether there is a rise (up-ward trend) a fall (downward trend) or no change (steady trend) in the series data.
The Seasonal Variation
Seasonal movements are variation in the time series that are periodic in nature and occur more or less regular within a period of one year or less due to the effect of the season. The seasonal variation are not restricted to only the effect of the seasons of the years (dry/rainy season) festivities (Christmas/Sallah/Independence) but also to such other favorable/ unfavorable condition that affect out time data.
The Cyclical Variation
These are fluctuation noticeable in time series data, but they cover longer periods of time than the seasonal variation, which means that the length of cycle is more than one year. The length of the cycle is not constant and they are less predictable.
Example of such business cycle or periods of prosperity recession, depression and recovery etc.
Erration (Irregular) Variation
This refers to variations in time series, which cannot be accounted for by either secular, cyclical or seasonal factors; this irregular variation is random in nature, and is strikes, earthquakes, floods, droughts, changes in government armed conflict, fire disasters sampling error and measurement errors.
Fore-Casting
Forecasting can be said to be a statement about what will happen in the future based on the information or data that is available now.