Final project report of telesphore and vilany

“USING METEO DATA FOR RAINFALL PREDICTION IN RWANDA,
CASE STUDY: RWAMPARA SWAMP”
A PROJECT REPORT
Submitted by
NDACYAYISENGA Télesphore (REG.NO: GS 20111583)
And
BYUKUSENGE Vilany (REG.NO: GS 20111369)
Under the Guidance of
Mr. MAJORO Félicien
Submitted in partial fulfilment of the requirements for the award of
BACHELOR OF SCIENCE DEGREE
IN
WATER AND ENVIRONMENTAL ENGINEERING
DEPARTMENT OF CIVIL ENGINEERING AND ENVIRONMENTAL TECHNOLOGY
SCHOOL OF ENGINEERING
(Nyarugenge Campus)
COLLEGE OF SCIENCE AND TECHNOLOGY
P.O. Box: 3900 Kigali, Rwanda.
MAY 2014
PROJECT ID: WEE/2013-14/18

COLLEGE OF SCIENCE AND TECHNOLOGY
SCHOOL OF ENGINEERING
(Nyarugenge Campus)
P.O. Box: 3900 Kigali, Rwanda.
DEPARTMENT OF
CIVIL ENGINEERING AND ENVIRONMENTAL TECHNOLOGY
C E R T I F I C A T E
This is to certify that the Project Work entitled “using meteo data for rainfall prediction in
RWANDA, case study: RWAMPARA swamp” is a record of the original bonafide work done by
NDACYAYISENGA Telesphore
(REG. No: GS20111583 ) and BYUKUSENGE Vilany (REG.No:GS20111369) in partial
fulfilment of the requirement for the award of Bachelor of Science Degree in Water and
Environmental Engineering of College of Science and Technology under the University of
Rwanda during the Academic Year 2013-2014.
…………………………… ……………………………
SUPERVISOR HEAD OF DEPARTMENT
Mr. MAJORO Félicien Dr. G. S. KUMARAN
Submitted for the final Project Defense Examination held at School of Engineering (Nyarugenge Campus), College
of Science and Technology, on ………………………………..........................
ii

iii
DECLARATION
We, NDACYAYISENGA Telesphore (Reg. No: GS 20111583) and BYUKUSENGE Vilany
(Reg No: GS 20111369) declare that this project entitled” USING METEO DATA FOR
RAINFALL PREDICTION IN RWANDA, CASE STUDY: RWAMPARA SWAMP “is based
on an original work conducted by ourselves for the award of bachelor Science degree in WATER
AND ENVIRONMENTAL ENGINEERING at College of Science and Technology. It has never
been submitted in any other higher learning institution, at our best knowledge, for the same
academic purposes.
SIGNATURE................... SIGNATURE........................
Date: / /2014 Date: / /2014
NDACYAYISENGA Telesphore BYUKUSENGE Vilany
REG. No: GS 20111583 REG. No: GS 20111369

iv
DEDICATION
This project is dedicated to:
 Our parents;
 Families;
 Our brothers;
 Our sisters;
 Friends; and
 Our classmates;

v
ACKNOWLEDGEMENT
It is with profound joy and great happiness that we are deeply thankful to the almighty God who
guided and protected us through all this time. We equally thank our research project supervisor
Eng. Félicien MAJORO who consistently and coherently worked with us in order to help us
achieve our goals and GASANA Emelyne helped us to use SPSS.
We are pleased to thank our families and all family members for their support and advice. Our
special thanks are addressed to the government of Rwanda for its appreciable policy of
promoting education at all levels. Finally our sincere acknowledgements go to the entire
administration of UR-CST and the whole academic staff for providing to us quality academic
services throughout these four years.

vi
ABSTRACT
The field study was carried out at RWAMPARA swamp, located especially between
NYARUGENGE and KICUKIRO Districts, the agriculture is very important and play great role
in the community where has both insufficient and abundance water or rainfall affect crops
production such as beets, onions, carrots, small vegetations, maize, etc.
In this study, we use many theories of rainfall prediction and the factors affecting rainfall to
precipices on earth surface and their losses. There are many software and models used in rainfall
prediction such as SPSS, ACCESS, ANFIS, NWP, Neural Networks and Matrix Decomposition
Method used in different countries.
The use of SPSS software in prediction of rainfall was selected because it is the one of software
which is generate the simulation of model and analysis of output data or forecasts data in rainfall
prediction at Rwampara swamp using data from meteo-Rwanda Kigali AERO station of 42 years
from 1972 to 2013. Also we used CROPWAT and CLIMWAT to analyze crop water
requirement and irrigation needed in RWAMPARA.
The processing historical rainfall data in SPSS software are showing predicted rainfall for next
two years where Rainfall (1168.0mm for 2014 and 1194.7mm for 2015) = -121.021+3.669
Humidity+4.434 Temperature to facilitate the agricultural activities in study area. In this report,
there is crop patterned related to rainfall predicted and irrigation water requirement of
160.8mm/decade, effective rain of 200.2mm/decade, Crop Evapotranspiration of
328.6mm/decade needed for some crops such as small vegetations from April to July 2014 and
type of crops according to rainfall predicted and creation of agriculture patterns.

vii
TABLE OF CONTENTS
DECLARATION.............................................................................................................................. iii
DEDICATION ..................................................................................................................................iv
ACKNOWLEDGEMENT...................................................................................................................v
ABSTRACT .....................................................................................................................................vi
TABLE OF CONTENTS ..................................................................................................................vii
LIST OF TABLES ............................................................................................................................xi
LIST OF FIGURES ..........................................................................................................................xii
LIST OF APPENDICES ..................................................................................................................xiii
LIST OF ABREVIATION ............................................................................................................... xiv
CHAPTER I: INTRODUCTION .........................................................................................................1
1.1 BACKGROUND OF THE STUDY ......................................................................................1
1.2 PROBLEM STATEMENT ...................................................................................................2
1.3 OBJECTIVES OF THE PROJECT .......................................................................................2
1.3.1 General objective..........................................................................................................2
1.3.2 Specific objectives ........................................................................................................2
1.4 SCOPE OF THE PROJECT .................................................................................................3
1.5 JUSTIFICATION OF THE PROJECT ..................................................................................3
1.5.1 Research significance....................................................................................................3
1.5.2 Public and administrative significance ...........................................................................3
1.5.3 Academic significance ..................................................................................................3
CHAPTER II: LITERATURE REVIEW ..............................................................................................4
2.1 GENERALITIES ON HYDROLOGY ..................................................................................4
2.1.1 Water resources of Rwanda ...........................................................................................4
2.1.2 Hydrology and hydrologic cycle ....................................................................................4
2.1.3 Scope of hydrology.......................................................................................................6

2.2 PRECIPITATION................................................................................................................6
2.2.1 Types of precipitation ...................................................................................................7
2.2.2 Measurement of precipitation ........................................................................................7
2.2.3 Analysis of rainfall data ................................................................................................8
2.3 WATER LOSSES.............................................................................................................. 10
2.3.1 Definition of water losses ............................................................................................ 10
2.3.2 Evaporation and evapotranspiration ............................................................................. 10
2.3.3 Hydrometeorology...................................................................................................... 11
2.3.4 Infiltration.................................................................................................................. 11
2.4 SOIL-WATER-IRRIGATION RELATIONSHIP................................................................. 12
2.4.1 Definitions ................................................................................................................. 12
2.4.2 Crop water requirement............................................................................................... 12
2.4.3 Effect of rainfall ......................................................................................................... 13
2.4.4 Net irrigation requirement (NIR) ................................................................................. 13
2.5 FACTORS AFFECTING RAINFALL ................................................................................ 14
2.5.1 Weather and Meteorology ........................................................................................... 14
2.5.2 Evaporation and Evapotranspiration............................................................................. 14
2.6 USING SPSS SOFTWARE IN RAINFALL PREDICTION ................................................. 16
2.6.1 Definition................................................................................................................... 16
2.6.2 Types of software used in rainfall prediction ................................................................ 16
2.6.3 Types of time series data ............................................................................................. 16
2.6.4 Process used in SPSS software by box-Jenkins modeling .............................................. 17
2.6.5 Autocorrelation .......................................................................................................... 19
2.6.6 Stationary time series .................................................................................................. 20
2.6.7 Data that is non stationary in the mean ......................................................................... 20
2.6.8 Identifying potential model ......................................................................................... 21
2.6.9 Estimating the component of a time series using SPSS .................................................. 21
viii

2.6.10 Basic concepts in analysis of time series data................................................................ 22
2.6.11 Autoregressive (AR) model ......................................................................................... 24
2.6.12 Prediction interval ...................................................................................................... 26
2.6.13 Forecasting................................................................................................................. 26
CHAPIII: MATERIALS AND METHODOLOGY ............................................................................. 27
3.1 SITE DESCRIPTION ........................................................................................................ 27
3.1.1 Site localization .......................................................................................................... 28
3.1.2 Soil type .................................................................................................................... 28
3.1.3 Rainfall pattern........................................................................................................... 28
3.1.4 Meteo factors of study area ......................................................................................... 28
3.2 RESEARCH TOOLS ......................................................................................................... 29
3.2.1 Digital camera ............................................................................................................ 29
3.2.2 Global Positioning System (GPS) ................................................................................ 30
3.3 RESEARCH METHODOLOGY ........................................................................................ 31
3.3.1 Contour map of the study area ..................................................................................... 31
3.3.2 Questionnaire and interview ........................................................................................ 31
3.3.3 Meteo data collection .................................................................................................. 32
3.3.4 Use of Cropwat window 8.0 ........................................................................................ 32
3.3.5 Use of SPSS window 11.0 ........................................................................................... 32
3.3.6 Books and e-book ....................................................................................................... 34
CHAPITER IV: RESULTS AND DISCUSSIONS.............................................................................. 35
4.1 SURVEY MAP AND MAIN FEATURES OF SITE ............................................................ 35
4.2 INTERVIEW RESULTS.................................................................................................... 36
4.2.1 Rwampara site............................................................................................................ 36
4.2.2 RWANDA meteorology agency .................................................................................. 36
4.3 METEO DATA INFLUENCING RAINFALL PATTERNS AT RWAMPARA..................... 36
4.4 EVALUATION OF RAINFALL MODEL .......................................................................... 37
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4.4.1 Modeling procedures .................................................................................................. 37
4.4.2 Modeling and simulation............................................................................................. 37
4.4.3 Level of acceptance of the model ................................................................................. 40
4.4.4 Importance of the model ............................................................................................. 41
4.5 CROP WATER REQUIREMENT FOR DIFFERENT CROPS ............................................. 41
4.6 RAINFAL PREDICTION .................................................................................................. 42
4.6.1 Measurement of the accuracy ...................................................................................... 42
4.6.2 Rainfall pattern for agriculture of Rwampara swamp..................................................... 45
4.7 PLANTING CROPS AND SOWING DATE ....................................................................... 45
4.7.1 Planting crops............................................................................................................. 45
4.7.2 Sowing date ............................................................................................................... 46
CHAPTER V: CONCLUSION AND RECOMMENDATION............................................................. 48
5.1 CONCLUSION ................................................................................................................. 48
5.2 RECOMMENDATIONS.................................................................................................... 49
REFERENCES................................................................................................................................. 50
APPENDICES ................................................................................................................................. 52
x

LIST OF TABLES
TABLE 3.1: AVERAGE METEO DATA COLLECTION ............................................................................. 29
TABLE 4. 1: REGRESSION COEFFICIENTS ........................................................................................ 38
TABLE 4. 2: IRRIGATION WATER REQUIREMENT ................................................................................ 41
TABLE 4. 3: ERROR MEASUREMENT .................................................................................................. 43
TABLE 4. 4: RAINFALL FORECASTING RESULT FOR TWO YEARS......................................................... 44
TABLE 4. 5: SOWING DATE PROGRAM AND TYPES OF CROPS .............................................................. 47
xi

LIST OF FIGURES
FIGURE 2. 1: HYDROLOGICAL CYCLE ................................................................................................... 5
FIGURE 2. 3: SPSS MODELING PROCESS ............................................................................................ 18
FIGURE 2. 4: MODELING IDENTIFICATION PROCESS ........................................................................... 21
FIGURE 3. 1: CULTURE OF RWAMPARA SWAMP ................................................................................. 27
FIGURE 3. 2: DIGITAL CAMERA ......................................................................................................... 30
FIGURE 3. 3: GPS .............................................................................................................................. 30
FIGURE 3. 4: CONTOUR MAP OF RWAMPARA ..................................................................................... 31
FIGURE 4. 1: SURVEY MAP OF RWAMPARA........................................................................................ 35
FIGURE 4. 2: RAINFALL TIME PLOT MODEL ........................................................................................ 39
FIGURE 4. 3: FORECASTING MODEL ................................................................................................... 40
xii

xiii
LIST OF APPENDICES
APPENDIX 1: Meteo data
APPENDIX 2: Questionnaires
APPENDIX 3: Model output
APPENDIX 4: GPS Coordination

xiv
LIST OF ABREVIATION
UR: University of Rwanda
CST: College of Science and Technology
CEET: Civil Engineering and Environmental Technology
WEE: Water and Environmental Engineering
SPSS: Statistical Packages of Social Sciences
UHF: Ultra High Frequency
UCL: upper confidence limit
LCL: Lower confidence limit
NIR: Net Irrigation Requirement
SARIMA: seasonal autoregressive integrated moving average
ARIMA: autoregressive integrated moving average
SMA: seasonal moving average
MA: moving average
AR: autoregressive
ARMA: autoregressive moving average

xv
SWC: Soil Water Content
SAWC: Soil Available Water Capacity
SAS: Seasonal Adjusted series
SAF: Seasonal Adjusted Factor
STC: Seasonal Trends cycle
D: transformation Difference
Q: number of moving average values
P: number of autoregressive values
SIMSEM: Simulated structural equation Modeling
MINITERE: Ministry of foreign affairs
MINAGRI: Ministry of Agricultural
WMO: World Meteorology Organization
FAO: Food and Agriculture Organization

1
CHAPTER I: INTRODUCTION
1.1 BACKGROUND OF THE STUDY
Rwanda, officially the Republic of Rwanda, is a sovereign state in state in central and East
Africa of capital of Kigali. Located a few degrees south of the Equator for coordinate’s
latitude: 1º04’and 51’ south and 28º45’ and 31º15’ East. Rwanda is bordered by Uganda,
Tanzania, Burundi, and the Democratic Republic of the Congo. Rwanda has area of 26,338
kilometer square (km2) and 5.3% of water. Water generates in Rwanda is coming from the
precipitation related cycle which is use in agricultural activities. (Safaris, 2013)
The broad aim of this study was to develop objectives means of assessing the performance of
Meteo-RWANDA rainfall prediction used to support the agriculture cost due to unprepared
irrigation. Within this broad remit a more specific aim was to establish performance criteria to
be applied to the seasonal rainfall prediction, to the annually updates and announcing the
sowing date for cultivators.
A prediction or forecast is a statement about the way things will happen in the future, often
but not always based on experience or knowledge. While there is much overlap between
prediction and forecast, a prediction may be a statement that some outcome is expected, while
a forecast is more specific, and may cover a range of possible outcomes. (wiki,
http://en.wikipedia.org/wiki/Prediction, 2013) In our project, we have predicted rainfall
patterns for announcing sowing dates to save irrigation expenses.
The rainfall patterns are characterized by four seasons, a short rainy season from September to
November and a longer rainy season between March and May. Between these seasons are two
dry periods, a short one between December and February and a long one from June to August.
Rainfall ranges from about 900mm to 1500mm in the RWANDA areas.
Agriculture is a vital sector for the sustained growth of developing countries, especially
agriculture based in RWANDA. A significant portion of the Rwandan’s population 80
percent of rural inhabitants still depends on agriculture for employment and sustenance.
(EDPRS2, 09 April 2013)

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1.2 PROBLEM STATEMENT
The Rwanda Meteorological service does not have enough capacity to predict proper rainfall
because of insufficient materials or irresponsible laborers.
Whether Rwanda is in a drought or much less rains than expected, both scenarios will have a
serious impact on the agricultural sector with reduced harvest and potentially even a food
shortage.
Analysis of rainfall trends show that rainy seasons are tending to become shorter with higher
intensity. This tendency has led to decreases in agricultural production and events such as
droughts in dry areas (BUGESERA) such cause the cost of irrigation to increase; and floods
or landslides in areas experiencing heavy rains. Heavy rains have been being observed
especially in North and Western province.
These heavy rains coupled with a loss of ecosystems services resulting from deforestation
and poor agricultural practices have resulted in soil erosion ,rock falls, landslides and floods
which destroy crops, houses and other infrastructure (roads, bridges, hospitals and schools )
as well as loss of human and animal life .
1.3 OBJECTIVES OF THE PROJECT
1.3.1 General objective
The general objectives of this research is to produce a feasibility study of rainfall prediction
project to encourage the Rwampara swamp‘s farmers to use rainfall predicted for the future
season.
1.3.2 Specific objectives
 To identify various factors affecting rainfall,
 To analyze the effect of rainfall on agriculture,
 Collection of the rainfall data from Meteo-Rwanda Kanombe airport station,
 To use SPSS software to simulate rainfall prediction,
 Prediction of seasonal rainfall patterns and advising cultivators on sowing dates to
save irrigation expenses.

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1.4 SCOPE OF THE PROJECT
The scope of this study is about rainfall prediction and analyzing for agriculture activities in
RWAMPARA. In fact, this analysis will conduct to the prediction of seasonal rainfall patterns
and advising cultivators on sowing dates.
The detailed of soil analysis of the area will not be performed such as seepage and agronomic
of soil and exact sowing date of each crop because of loss of materials.
1.5 JUSTIFICATION OF THE PROJECT
1.5.1 Research significance
For final year students , it is very important to put the class theories into practice .This project
is also in line with requirements for them to get a bachelor’s degree will help us to get
bachelor degree.
1.5.2 Public and administrative significance
This project will improve the agriculture production, environmental sustainable and personal
activities such as irrigation during dry period and rainy period.
1.5.3 Academic significance
This study may be served as the reference by students interested in rainfall for agriculture
seasons prediction and hydrological information of Rwanda.

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CHAPTER II: LITERATURE REVIEW
2.1 GENERALITIES ON HYDROLOGY
Hydrology is a branch of Earth science. The importance of hydrology in the assessment,
development, utilization, and management of the water resources, of any region is being
increasingly realized at all levels. It was in view of this that the United Nations proclaimed the
period of 1965-1974 as the International Hydrological decade during which ,intensive efforts
in hydrologic education research ,development of analytical techniques and collection of
hydrological on a global basis ,were promoted in Universities ,Research Institutions ,
Government Organizations. (Roghunath, 2007)
2.1.1 Water resources of Rwanda
Rwanda is a country located in great Lakes Region of Africa .Its topography gradually rises
from the East at an average altitude of 1,250m to the North and West where it culminates in a
mountain range called “Congo-Nile Ridge ” varying from 2,200m to 3,000m and a volcano
formation, the highest volcano being 4,507m high.
The country is divided by a water divide line called “Congo-Nile Ridge”. To the west of this
line lies the Congo River basin which covers 33% of the national territory, which receives
10% of the total national waters. To the east lies the Nile River basin, whose area covering
67% of the Rwandan territory and delivers 90% of the national waters {Ministry of Lands,
Environment, Forests, Water and Mines (MINITERE, 2004)}.
2.1.2 Hydrology and hydrologic cycle
Hydrology is the science, which deals with the occurrence, distribution and disposal of water
on the planet earth; it is the science which deals with the various phases of the hydrologic
cycle. Hydrologic cycle is the water transfer cycle, which occurs continuously in nature; the
three important phases of the hydrologic cycle are: Evaporation and Evapotranspiration,
Precipitation and Runoff.
Evaporation from the surfaces ponds, lakes, reservoirs, dams, seas, oceans, and soon; and
transpiration from surface vegetation (plant leaves of cropped land and forests, and soon) take
place. These vapors rise to the sky and are condensed at higher altitudes by condensation
nuclei and form clouds, resulting in droplet growth.

The clouds melt and sometimes burst resulting in precipitation of different forms like rain,
sleet, snow, hail, mist, dew and front. A part of this precipitation flows over the land called
“runoff” after infiltrate into the soil which builds up the groundwater table. The surface runoff
joins the streams, rivers and other water is stored in reservoirs or dams. A portion of surface
runoff and groundwater flows back to oceans, lake, wells, and soon; again evaporation restarts
from the water surfaces and the cycle repeats.
Hydrologic engineering differs from hydrology primarily in that an engineering application is
implied. Thus engineering considerations deal mostly with estimating, predicting or
forecasting precipitation or streamflow. Of these three phases of hydrologic cycle, namely,
evaporation, precipitation and runoff, it is the “rainfall and runoff phase”, which is important
to a water and environmental engineer since he is concerned with the storage of surface runoff
and quantity of rainfall in the catchment area or watershed for crop water requirement and
design of storages capacity for irrigation, municipal water supply, hydropower, and soon.
(Roghunath, 2007)
(Geofreekz, 2010)
Figure 2. 1: hydrological cycle
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2.1.3 Scope of hydrology
The study of hydrology helps us to know:
a) The maximum probable rainfall that may occur at a given site and its frequency; this is
required for the crop water needed, irrigation requirement, safe design of drains and
culverts, dams and reservoirs, channels and other water regulation control structures.
b) The water yield from a basin or region, its occurrence, quantity and frequency, and
soon; this is necessary for the planning of irrigation program, crop needed, design of
dams, municipal water supply, water power, river navigation, and soon.
c) The groundwater development for which a knowledge of the hydrology of the area,
means that formation of soil, recharge facilities like streams and reservoirs, rainfall
pattern, climate, cropping pattern, and soon are required.
d) The maximum intensity of storm and its frequency for the design of drainage project
in the area. (Roghunath, 2007)
2.2 PRECIPITATION
Precipitation is the primary mechanism for transporting water from the atmosphere to the
surface of the earth. The main forms of precipitation include drizzle, rain, snow, graupel and
hail. In meteorology, precipitation (also known as one of the classes of hydrometeors, which
are atmospheric water phenomena) is any product of the condensation of atmospheric water
vapor that falls under gravity (wiki, 2013). Precipitation occurs when a local portion of the
atmosphere becomes saturated with water vapor, so that the water condenses and precipitates.
Thus, fog and mist are not precipitation but suspensions, because the water vapor does not
condense sufficiently to precipitate. Two processes, possibly acting together, can lead to air
becoming saturated: cooling the air or adding water vapor to the air. Generally, precipitation
should fall to the surface; an exception is virga which evaporates before reaching the surface.
The precipitation occurs when a local portion of the atmosphere becomes saturated with water
vapor, so that the water condenses and “precipitates” Thus, fog and mist are not precipitation
but suspensions, because the water vapor does not sufficiently to precipitate. (Roghunath,
2007)

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2.2.1 Types of precipitation
The precipitation may be due to:
 Thermal convection (convectional precipitation), this type of precipitation is in the
form of local whirling thunder storms and is typical of the tropics. The air close to
the warm earth gets heated and rises due to its low density, cools adiabatically to
form a cauliflower shaped cloud, which finally bursts into a thunder storm. When
accompanied by destructive winds, they are called “tornados”.
 Conflict between two air masses (frontal precipitation), when two air masses due to
contrasting temperatures and densities clash with each other, condensation and
precipitation occur at the surface of contact; this surface of contact is called a “front or
front surface”. If a cold air mass drives out a warm air mass, it is called a “warm
front”.
 Orographic lifting (orographic precipitation), the mechanical lifting of moist air over
mountain barriers, causes heavy precipitation on the windward side.
 Cyclonic (cyclonic precipitation), this type of precipitation is due to lifting of moist air
converging into a low pressure belt, i.e. due to pressure differences created by the
unequal heating of the earth’s surface. (Roghunath, 2007)
2.2.2 Measurement of precipitation
Rainfall may be measured by a network of rain gauges which may either be of non-recording
or recording type.
The non-recording rain gauge used in India is the Symon’s rain gauge. It consists of a funnel
with a circular rim of 12.7cm diameter and a glass bottle as a receiver. The cylindrical metal
casing is fixed vertically to the masonry foundation with the level rim 30.5cm above the
ground surface. The rain falling into the funnel is collected in the receiver and is measured in
a special measuring glass graduated in mm of rainfall; when full it can measure 1.25cm of
rain.
Recording rain gauge: this is also called “self-recording, automatic or integrating rain
gauge”. This type of rain gauge has an automatic mechanical arrangement consisting of

clockwork, a drum with a graph paper fixed around it and a pencil point, which draws the
mass curve of rainfall. From this mass curve, the depth of rainfall, in a given time, the rate or
intensity of rainfall at any instant during a storm, time of onset and cessation of rainfall, can
be determined. The gauge is installed on a concrete or masonry platform 45cm2 in the
observatory enclosure by the side of the ordinary rain gauge at a distance of 2-3m from it. The
gauge is so installed that the rim of the funnel is horizontal and at a height of exactly 75cm
above ground surface. The self-recording rain gauge is generally used in conjunction with an
ordinary rain gauge exposed close by, for use as standard, by means of which the readings of
the recording rain gauge can checked and if necessary adjusted. There are three types of
recording rain gauges like tipping bucket gauge, weighing gauge and float gauge.
Automatic-radio-reporting rain gauge: this type of rain gauge is used in mountainous areas,
which are not easily accessible to collect the rainfall data manually. As in the tipping bucket
gauge, when the buckets fill and tip, they give electric pulses equal in number to the mm of
rainfall collected which are coded into messages and impressed on a transmitter during
broadcast. At the receiving station, these coded signals are picked up by UHF receiver.
(Roghunath, 2007)
2.2.3 Analysis of rainfall data
Rainfall during a year, season or monthly (or a number of years) consists of several storms
.The characteristics of a rainstorm are:
i. Intensity(cm/hr)
ii. Duration (min , hr ,or days)
iii. Frequency(once in 5 years or once in 10, 20, 40, 60, or 100)
iv. Areal extent (i.e. area over which it is distributed).
Correlation of rainfall records: Suppose a number of years of rainfall records observed on
recording and non recording rain-gauges for a river basin are available; then it is possible to
correlate
8
 The intensity and duration of storms
 The intensity, duration and frequency of storms

If there are storms of different intensity and various durations, then a relation may be obtained
by plotting the intensities (i, or cm/h) against durations (t, min, or hr) of the respective storms
either on the natural graph paper ,or a double log(log-log) paper, and relations of the form
given below may be obtained :
9
i. 푖 = 푎
푡 +푏
.N. Talbot’s formula (for t=5-120min)……… (2.1)
ii. 푖 = 푘
푡푛 ………. (2.2)
iii. 푖 = 푘푡푥 ………. (2.3)
Where t= duration of rainfall or its part a, b, k, n and x are constants for a given region. Since
x is usually negative equations (2.2) and (2.3) are same and are applicable for duration t>2hrs.
On the other hand ,if there are rainfall records for 30 to 40 years ,the various storms during the
period of record may arranged in the descending order of their magnitude(of maximum
depth).
When arranged like this in the descending order, if there are a total number of n items and the
order number or rank of any particular storm(maximum depth or intensity) is m, then the
recurrence interval T (also known as return period ) of the storm magnitude is given by one of
the following equations:
1. California method (1923),T=
푛
푚
………………………(2.4)
2. Hazen’s method (1930), 푇 = 푛
1
2
푚−
..……………………(2.5)
3. Kimball’s method, (Weibull, 1939) 푇 = 푛+1
푚
…………………… (2.6)
And the frequency F (expressed as per cent of time) of that storm magnitude (having
recurrence interval T) is given by 퐹 = 1
푇
푋 100% …………………… (2.7)
(Roghunath, 2007)

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2.3 WATER LOSSES
2.3.1 Definition of water losses
The hydrologic equation states that: rainfall – losses =runoff ………. (2.8)
In the previous we discussed precipitation and its measurement. The various water losses that
occur in nature are enumerated below. If these losses are deducted from the rainfall, the
surface runoff can be obtained. Interception loss due to surface vegetation, i.e. held by plant
leaves.
Interception loss: the precipitation intercepted by foliage (plant leaves, forests) and buildings
and returned to atmosphere (by evaporation from plant leaves) without reaching the ground
surface is called interception loss. (Roghunath, 2007)
Effective rain = Rainfall – Interception loss …………………… (2.9)
2.3.2 Evaporation and evapotranspiration
Evaporation from water and soil surface and transpiration through plants can account for
significant volumes of water. Evaporation is the process during which a liquid changes into a
gas. The process of evaporation of water in nature is one of the fundamental components of
the hydrological cycle by which are one of the vapors through absorption of heat energy. This
is the only form of moisture transfer from land and oceans into the atmosphere.
Considerable quantity of water is lost by evaporation from the soil surface. Sunlight,
temperature, wind velocity and humidity are the main climate factors influencing the rate and
extent of evaporation. More the fine aggregates of black soil, more the heat absorbed resulting
in more loss of water.
The basic principle is to cover them with vegetation, mulching, keeping soil surface loose by
tillage operation, use of wind brake etc. That can help to reduce evaporation losses.

Evaporation may also directly affect soil moisture conditions. If there is too much moisture in
the soil, the farm machinery can get bogged down because it has to work too hard.
If the soil is too dry, however, the plants may be easily stressed due to the lack of available
water and crust may sometimes form on top of the soil. This crust may be so impermeable that
when it rains on top of the crusty soil, the rain runs right off rather than soaking in .Each plant
type has its own unique evapotranspiration rate. The combination of two separated processes
whereby water are lost on the one hand from the soil surface by evaporation and on the other
hand from the crop by transpiration is referred to as evapotranspiration (ET). (John A.
Roberson, 1997)
11
2.3.3 Hydrometeorology
Hydrometeorology is branch of meteorology that deals with problems involving the
hydrologic cycle, the water budget and the rainfall statics of storms. The boundaries of
hydrometeorology are not clear cut, and the problems of the hydrometeorologists overlap with
those of the climatologists, the hydrologist, the cloud physicist, and weather forecaster.
Considerable emphasis is placed on determining, theoretically or empirically, the relationships
between meteorological variables and the maximum precipitation reaching the ground.
These analyses often serve as the bases for the design of flood-control and water usage
structures, primarily dams and reservoirs. Other concerns of hydrometeorologists include the
determination of rainfall probabilities, the space and time distribution of rainfall and
evaporation, the recurrence interval of major storms, snow melt and runoff, and probable wind
tides and waves in reservoirs. The whole field of water quality and supply is of growing
importance in hydrometeorology.
2.3.4 Infiltration
Infiltration is the process by which water on the ground surface enters the soil. Infiltration is
governed by two forces which are gravity and capillary action. While smaller pores offer
greater resistance to gravity, very small pores pull water through capillary action in addition to
and even against the force of gravity.

Infiltration rate in soil science is a measure of the rate at which a particular soil is able to
absorb rainfall or irrigation. It is measured in inches per hour (inch/hr) or millimeters per hour
(mm/hr). The rate decreases as the soil becomes saturated.
If the precipitation rate exceeds the infiltration rate, runoff will usually occur unless there is
some physical barrier. (Roghunath, 2007)
2.4 SOIL-WATER-IRRIGATION RELATIONSHIP
2.4.1 Definitions
Soil-plant-water relationships describes those properties of soils and plants that affect the
movement, retention, and use of water essential to plant growth. It can be divided and treated
as: soil-plant relation, soil-water relation and plant-water relations.
2.4.2 Crop water requirement
It is defined as “the depth of water needed to meet the water loss through evapotranspiration
(ETcrop) of a disease free crop growing in large fields under non-restricting soil conditions
including soil water and fertility and achieving full production potential under the given
growing environment”. That is, it is the quantity of water required by the crop in a given
period to meet its normal growth under a given set of environmental and field conditions.
The determination of water requirements is the main part of the design and planning of an
irrigation system. The water requirement is the water required to meet the water losses
through:
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 Evapotranspiration (ET);
 Unavoidable application losses; and
 Other needs such as leaching and land preparation.
The water requirement of crops may be contributed from different sources such as irrigation,
effective rainfall, and soil moisture storage and groundwater contributions. (Charlotte, 2013)
Hence, WR = IR + ER + S + GW ………………………… (2.11)
Where, IR = Irrigation requirement, ER = Effective rainfall, S = carry over soil moisture in
the crop root zone, GW = groundwater contribution.

2.4.3 Effect of rainfall
The primary source of water for agricultural production, for large parts of the world and
Rwanda, is rainfall. Rainfall is characterized by its amount, intensity and distribution in time.
All crops need water to grow and to produce yields. The most important source of water for
crop growth is rainfall.
When rainfall is insufficient, irrigation water may be supplied to guarantee a good harvest.
One of the main problems of the irrigator is to know the prediction of rainfall and the amount
of water that has to be applied to the field to meet the water needs of crops; in other words the
irrigation requirement needs to be determined. Too little water during the growing season
causes the plants to wilt. Long periods during which the water supply is insufficient, result in
loss of yield. In addition, the irrigation requirement needs to be determined for proper design
of the irrigation system and for establishment of the irrigation schedules. (docrep,
Httt://www.fao.org/docrep/r4082e/4082e03.htm)
2.4.4 Net irrigation requirement (NIR)
Net irrigation water requirement (NIWR) is the quantity of water necessary for crop growth. It
is expressed in millimeters per year (mm/yr) or in cubic meters per hectare per year (m3/ha/yr)
{1mm= 10m3/ha}. It depends on the cropping pattern and the climate. Information on
irrigation efficiency is necessary to be able to transform NIWR into gross irrigation water
requirement (GIWR), which is the quantity of water to be applied in reality, taking into
account water losses. Multiplying GIWR by the area that is suitable for irrigation gives the
total water requirement for that area. In our study water requirements are expressed in
m3/month. In order to be able to do this at the scale of Area, assumptions have to be made on
the definition of areas to be considered homogeneous in terms of rainfall, potential
evapotranspiration, cropping pattern, cropping intensity and irrigation efficiency (docrep,
2014).
Net irrigation requirement depend on: Depth of water, exclusive of effective precipitation,
or groundwater, that is required for meeting crop evapotranspiration for production and other
related uses. Such uses may include water required for leaching, frost protection, cooling and
chemigation.
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2.5 FACTORS AFFECTING RAINFALL
Rain is liquid water in the form of droplets that have condensed from atmospheric water vapor
and precipitated that is, become heavy enough to fall under gravity. Rain is a major
component of the water cycle and is responsible for depositing most of the fresh water on the
earth.
It provides suitable conditions for many types of ecosystem, as well as water for
hydroelectric power plants and crop irrigation. Changes in rainfall and other forms of
precipitation will be one of the most critical factors determining the overall impact of climate
change. Rainfall is much more difficult to predict than temperature but there are some
statements that scientists can make with confidence about the future. (John A. Roberson, 1997)
2.5.1 Weather and Meteorology
Temperature and precipitation are two characteristics of weather most familiar to all of us.
Quantitatively, each is governed by energy given off by the sun and distribution and
absorption of that energy on the earth. All weather, and hence all precipitation, is governed by
movement of the air mass surrounding the earth. Motion of that air mass is unsteady and
turbulent.
2.5.2 Evaporation and Evapotranspiration
Evaporation from water and soil surfaces and transpiration through plants, can account for
significant volumes of water. The process of evaporation and evapotranspiration occurs at the
water surface and vegetations where molecules of water develop sufficient energy to escape
bonds with the water and become vapor molecules in the air. Evaporation from a water body
is a function of air and water temperatures, the moisture gradient at the water surface, and
wind. Wind moves the moisture away from the lake’s surface and, thus, increases the moisture
gradient, increasing the rate of evaporation.
a) Temperature
Higher temperatures affect the conditions for cloud formation and rainfall. Heavy rain
showers, such as summer thunderstorms, are influenced more by temperature than rain from

larger widespread rain systems. Heavy rain has far-reaching consequences for society, and
these could worsen at higher temperatures.
15
b) Wind
Wind is the movement of air caused by the uneven heating of the earth by the sun. It does not
have much substance you cannot see it or hold it but you can feel its force. It can dry our
cloves in summer, blow clouds and condense it and chill us to the bone in winter.
It is strong enough to carry sailing ships across the ocean and rip huge trees from the ground.
It is the great equalizer of the atmosphere, transporting heat, moisture, pollutants, and dust
great distances around the globe. Landforms, processes, and impacts of wind are called
Aeolian landforms, processes, and impacts.
c) Humidity
Humidity is the amount of water vapor in the air. Water vapor is the gaseous state of water
and is invisible. Humidity indicates the likelihood of precipitation, dew, or fog. Higher
humidity reduces the effectiveness of sweating in cooling the body reducing the rate of
evaporation of moisture from the skin and the leaves of crops. There are three main
measurement s of humidity: absolute, relative and specific.
 Absolute humidity is the water content of air;
 Relative humidity, expressed as a percent, measures the current absolute humidity
relative to the maximum for that temperature;
 Specific humidity is a ratio of the vapor content of the mixture to the total air content
on a mass basis.
There are other factors affecting rainfall which are climate, sunshine, topography, human
activities and vegetation cover.

2.6 USING SPSS SOFTWARE IN RAINFALL PREDICTION
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2.6.1 Definition
 SPSS is a statistical package used for conducting statistical analyses ,manipulating
and presenting data
 Acronym statistical packages for the social science but now it is known as predictive
analysis software
 Its statistical capabilities range from simple percentages to complex analyses including
multiple regressions and general linear models.
2.6.2 Types of software used in rainfall prediction
There is main software used in rainfall prediction:
 SPSS (Statistical Package for Social Sciences) software (PAKISTAN, Ethiopia, India)
 ANFIS (Adaptive Neuro-Fuzzy Inference System) ,THAILAND
 Satellite Rainfall Estimates (Remote Sensing and GIS )
 ACCESS (Australian Community climate and Earth-System Simulator), AUSTRALIA
 NWP (Numerical Weather Prediction), USA
 Matrix Decomposition method (UK)
 STATA(UK)
 Neural Networks (USA)
2.6.3 Types of time series data
Time series data can have two main forms i.e. continuous and discrete. A continuous time
series is one in which the variable being examined is defined continuously in time. Means
defined at each point in time. Examples: mean temperature at specific site, amount of rainfall
at specific site, the wind speed at specific site, air humidity, and weather condition. Many time
series are not defined at each point in time, but only at specific time (discrete time series).
Examples: seasonal production for crops, monthly rainfall, monthly mean temperature,
monthly air humidity, and maximum o r minimum daily temperature.

In most case data are not measured continuously, but measured at specific points in time (such
as hourly or daily). Sometimes, they are measured more frequently, and then applied average
to give say, average hourly wind speed or mean temperature or relative humidity or rainfall.
Forecasting in the time series means that we extend the historical data into the future where
the measurements are not available yet. If a time series can be predicted exactly, it is said to
be “deterministic”. However, most time series are stochastic (random) in that the future is
only partly determined by past data, so that exact predictions are impossible and must be
replaced by the ideal that future data have a probability distribution which are conditioned by
a knowledge of past data. Therefore, the subject matter of time series and forecasting main
objective is focused on “understanding the past and forecasting the future”.
2.6.4 Process used in SPSS software by box-Jenkins modeling
Box-Jenkins Modeling is made using time series analysis by several methods, one which is
the Autoregressive Integrated Moving Average (ARIMA) or Box-Jenkins method, being
called the (p, d, q) model, too (Box and Jenkins, 1976). In the (p, d, q) model, p denotes the
number of autoregressive values, d is the order of differencing, representing the number of
times required to bring the series to a kind of statistical station or equilibrium and q denotes
the number of moving average values. In ARIMA model, (p, d, q) is called non-seasonal part
of the model, p denotes the order of connection of time series with its past and q denotes the
connection of the series with factors effective in its construction. At the first stage, the
primary values of p, d and q are determined using the autocorrelation function (ACF) and
partial autocorrelation function (PACF).
A careful study of the autocorrelation and partial autocorrelation diagrams and their elements,
will provide a general view on the existence of the time series, its trend and characteristics.
This general view is usually a basis for selection of the suitable model. Also, the diagrams are
used to confirm the degree of fitness and accuracy of selection of the model. At the second
stage, it is examined whether p and q (representing the autoregressive and moving average
values, respectively) could remain in the model or must exit it. At the third stage, it is
evaluated whether the residue values are stochastic with normal distribution or not.
17

It is then that one can say the model has good fitness and is appropriate. If the time series is of
seasonal type, then the modeling has two dimensional states, and in principle, a part of the
time series variations belongs to variations in any season and another part of it belongs to
variations between different seasons. A special type of seasonal models that shows deniable
results in practice and coin sides with the general structure of ARIMA models is devised by
Box and Jenkins (1976), which is called multiplicative seasonal model. It is in the form of
ARIMA (p, d, q) (P, D, Q) then, for the model being ideal, the schemes must be used to test
the model and for the comparison purpose, so as the best model is chosen for forecasting:
푿풕 = 푿풕−ퟏ ± 푿풕−ퟐ ± 푿풕−ퟑ ± 푿풕−풏 ± 풁풕 ………… (2.12) (Arash Asadi, 2013)
18
Chart shows description of SPSS process
Figure 2. 2: SPSS modeling process

Time sequence plot: It is similar to X-Y graphs, and is used to display time versus value data
pairs. A time Plot data item consists of two data values which are the time and the value.
Which translate into the x and y- coordinates, respectively. Each data item is displayed as a
symbol, but you can add a line.
풏풊= ퟏ /√(풚풊 − 풚̅)ퟐ ………….. (2.15)
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2.6.5 Autocorrelation
Correlation (often measured as a correlation coefficient) indicates the strength and direction of
linear relationship between two random variables. Pearson correlation coefficient is given by
equations: 풓
푺풙풚
푺풙푺풚
풙풚=
…………… (2.13)
Where Sxy is the covariance between x and y, Sx and Sy are standard deviation for x and y
variables respectively.
푺풙풚=Σ (풙 풏풊
=ퟏ i-풙̅) (yi -풚̅) / (n-1) ......................... (2.14)
Therefore rxy can be given as Σ (풙풊−풙̅)(풚풊−풚̅)
√Σ (풙풊−풙̅)ퟐ 풏풊=ퟏ
It lies in the range [-1, 1] and measures the strength of the linear association between the two
variables. A value of +1 indicates that the variables move together perfectly; a value of -1
indicates that they move in opposite directions. The primary difference between time series
models and other types of models is that lag values of the target variable are used a predictor
variables, whereas other models use other variables as predictors. There, in time series, an
autocorrelation is the correlation between the target variable and lag values for the same
variable.
Autocorrelation measure the correlation if any, between observations at different apart and
provide useful descriptive information. It is also an important tool in model building and often
provides variable clues to a suitable probability model for a given set of data.
For time series data yt the autocorrelation coefficient at lag k is given by:
풓풌 = Σ (풚풕 − 풚̅풕)(풚풕 + 풌 − 풚̅풕)/Σ (풚풕 − 풚̅풕)ퟐ 푵풊
=ퟏ
푵−풌
풕= ퟏ ……………. (2.16)

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2.6.6 Stationary time series
A time series is said to be stationary if there is no systematic change in mean (no trend) and if
there is no systematic change in variance in which if strictly periodic variations have been
removed.
Therefore, a time series yt; t= 1, 2, is called to be stationary if its statistical properties do not
depend on time t.
A time series may be stationary in respect to one characteristic such the mean, but not
stationary in respect to other characteristics such as the variance. Stationary in variance can
sometimes be produced by taking logarithmic transformation.
2.6.7 Data that is non stationary in the mean
If the data are not stationary in the mean, then the data show some sort of “trend “or “cyclical”
fluctuation. Thus, allowing either a straight forward increase or decrease, or a cyclical up and
down movement. The presence of such non stationary is indicated firstly by a trend in the plot
of the data; secondly, it is indicated on the ACF by the autocorrelation “dying away” very
slowly.
The PACF will in this case show a partial auto correlation at lag 1 of nearly unity. A method
of dealing with such data is to take differences of the data. If this is the correct of choice of
degree of differencing, then one will be able to identify a model based on the ACF and PACF.
In some cases, it is necessary to difference the data twice, in which case the ACF and PACF
of the first differences will still show trend. Previous ARMA models can be extended in the
same way to data is non stationary,
And such models are called auto regressive integrated moving models ARIMA (p; d; q)
models. The p and q are as in the ARMA models, while the d indicates the degree of the
differencing used (d=1 for first difference, d=2 for second differences) In general, it is seldom
necessary to go above second differences.

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2.6.8 Identifying potential model
The identification of potential models is based on patterns of the autocorrelation (ACF) and
partial auto correlation (PACF) functions. These are plots of the autocorrelations and partial
autocorrelations at various lags, against the size of lag. Thus in the autocorrelation plot, the
size of the autocorrelation is more or less equal to the size of the data minus 2.
In model fitting the principle of parsimony is in general a rule to seek simplest models as
much as possible.
For example in time series, if neither AR (p) nor MA (q) models are plausible, it is natural to
try ARMA (p, q). And in accordance with the principle of parsimony, to use as small as p and
q as possible, starting therefore with p=q=1
Figure 2. 3: Modeling identification process
2.6.9 Estimating the component of a time series using SPSS
Using SPSS we can estimate the components of seasonal time series .This is called seasonal
decomposition in SPSS , and is done using Seasonal Decomposition from the time series
submenu of analyze.

To use this decomposition, the following conditions should be satisfied
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 The time series has annual seasonality
 The time series (or transformation of it) may be described adequately by an additive
model.
 The time variable sand periodicity has been defined in SPSS using defines dates.
Then SPSS give us the estimated factors. Here period is the period of the cycle which 12
months. Period to 12 are the months from January to December.
The estimated seasonal factors give us largest and lowest number which indicates the
seasonal peak and through, respectively. Note that the estimated seasonal factors sum to zero.
After this seasonal decomposition analysis, in the data view panel of the SPSS Data Editor,
the following four new variables will obtained: ERR_1, SAS_1, SAF_1, and STC_1.
1) SAS_1 (Seasonal Adjusted Series) contains seasonally adjusted series, which is
obtained by subtracting the estimated seasonal component (SAF_1) (Seasonal adjusted
Factor) from the time series. In seasonally adjusted time series (SAS_1), the
seasonality has been removed from the original time series, leaving the trend
component and irregular component.
2) STC_1 (Seasonal Trend Cycle) is a smoothed version of SAS_1; it is called the trend-cycle
component in SPSS. This name indicates that annual seasonality has been
removed, and that the trend and any cycles of period greater than one year remain.
3) ERR_1 (Error) is an estimate of the irregular component; it is equal to the seasonally
adjusted series minus the trend cycle component.
2.6.10 Basic concepts in analysis of time series data
The special feature analysis is the fact that successive observations are dependent and that the
analysis must take into account the time order of observations. When successive observations
are dependent, future values may be predicted from past observations. A time series is said to
be stationary if there is no systematic change in mean (no trend), if there is no systematic

change in variance and if there is no systematic change in variance and if strictly periodic
variations have been removed. Much of the probability theory of time series is concerned with
stationary time series, and for this reason time series analysis often requires one to transform a
non-stationary series into a stationary one so as to use this theory. Trend can defined as “a
long term change in the mean level”. The simplest type of trend is familiar “linear trend +
Error” for which the observation at time t is a random variable Xt, given by Xt = α+βt+Єt
where α and β are constants and Єt denotes a random error term with zero mean.
As we know special type of filtering, which is particularly useful for removing a trend is
simply to differentiate a given time series until it becomes stationary. This method is an
integral part of the so called “Box-Jenkins procedure”. For non-seasonal data, first order
differencing is usually sufficient to attain apparent stationary.
But occasionally, second order differencing may be required. The analysis of time series
which exhibit seasonal variation depends on whether one wants to:
23
 Measure the seasonal effect and/or
 Eliminate seasonality
For series showing little trend, it is usually adequate to estimate the seasonal effect for a
particular period (e.g.: April) by finding the average of each April observation divided minus
the corresponding yearly average in the additive case, or the April observation divided by the
yearly average in the multiplicative case. Generally, a time series analysis consists of two
steps:
1. Building a model that represents a time series; and
2. Using the model to predict future data or values.
If a time series has a regular pattern, then value of the series should be a function of previous
values. If Y is the target (rainfall) value that we are trying to model and predict, and Yt the
value of Y at time t, then the goal is to create a model of the form:
풀풕 = 풇(풀풕−ퟏ , 풀풕−ퟐ , 풀풕−ퟑ , … , 풀풕−풏) + 풆풕 ………………… (2.17)

Where Yt-1 is the value of Y for the previous observation, Yt -2 is the value two observations
ago, etc, and et represents error that does not follow a predictable pattern (this is called a
random shock). Values of variables occurring prior to the current observation are called lag
values.
The goal of building a time series model is the same as the goal for other types of predictive
models which is to create a model such that the error between the predicted value of the target
variable and the actual value is as small as possible.
The main objective in investigating time series is forecasting future values of the observed
series. This can be done through the model which adequately describes the behavior of the
observed variable and the required forecast. Time series data corresponds to the sequence of
values for a single variable in ordinary data analysis. Each case (row) in the data represents an
observation at a different time the observations must be taken at equally spaced time interval.
24
2.6.11 Autoregressive (AR) model
AR model is a common approach for modeling univariate time series. Therefore, with a
stationary series in place, a process yt is said to be an autoregressive process of order p
abbreviated as AR (p) is a process like:
yt =α+βt1yt-1+ β2yt-2 +Єt or Rainfall= α +β1T+β2H+ random Error ……….. (2.18)
Where α is the constant and β1and β2 are the coefficients of temperature and humidity.
This look like multiple regression model, but yt is regressed on past values of yt rather than on
separate predictor variables, this explains the prefix “auto”. This model describes the time
series, plus a random error in the process. A random error (Єt) is assumed to be independently
and identically distributed normally (Gaussian) with mean 0 and constant variance, is denoted
by Єt.
The simplest model is the Autoregressive model of order 1[AR (1) model], which uses only
lag 1 observation, defined as Yt = αyt-1+ Єt ……….. (2.19)

Where Yt is the current observation, Yt-1 is the previous observation, α the parameter to be
estimated, known as AR (1) parameter.
This process is sometimes called the Markov process, after the Russian A .A Markov. The
parameter in this model (α) should lies between +1 and -1; otherwise there are problems with
model. If the parameter estimate is close to +1, then one should be considering the model of
the form Yt=yt-1+ Єt or Yt - yt-1= Єt ………………… (2.20)
Thus one should be modeling not the raw data, but differences between the data. One can use
more than one log; therefore the general form of the model is AR (p) model, which uses p-lags
of the data (i.e. forecasting yt from yt -1; yt -2; …; yt -p). For most data series found in practice,
lag -2 is the highest order required, and for such complex models, the parameters do not
always lie between +1 and -1. Thus the model for AR (2) is given by Yt =α1yt-1+ α2yt-2 +Єt
…. (2.21)
Generally, in the discussion above, the model has been written as if the data were zero
average; of course data do not have a zero mean, but some other value. Therefore, the model
for AR (1) which including the mean becomes Yt =μ+ αyt-1+ Єt …………… (2.22)
Practically, the first model to be tested on the stationary series consists solely of an
Autoregressive term with lag 1. Therefore, the autocorrelation and partial autocorrelation
patterns will be examined for significant autocorrelation to see whether the error coefficients
are uncorrelated.
That is the coefficient Values are zero within 95% confidence limits and without apparent
pattern. When fitted values as close as possible to the original series values are obtained, the
sum of the squared residuals will be minimized, a technique called least squares estimation.
Alternative models are comparing the progress of these factors, favoring models which use as
few parameters as possible. Finally, when a satisfactory model has been established a forecast
procedure is applied.
25

26
2.6.12 Prediction interval
Prediction interval in regression analysis it is a range of values that estimate the value of the
dependent variable for given values of one or more independent variables. Comparing
prediction intervals with confidence intervals:
i. Prediction intervals estimate a random value, while confidence intervals estimate
population parameters.
ii. A prediction interval is an estimate of an interval in which future observations will
fall, with certain probability, given what has already been observed.
It usually consists of an upper and a lower limit between which the future value is expected to
lie with prescribed probability (1- α) %. As a result a methodology for outlier detection
involves in the rule that an observation is an outlier if it falls outside the prediction interval
computed.
2.6.13 Forecasting
One of the main objectives in investigating a time series is forecasting. This can be using
through the simplest model which adequately describes the behavior of the observed variable
and the required forecast. Besides, in most complex model the current value of the variable
can depend on past events, to forecast future data points before they are measured. Forecasting
is designed to help decision making and planning in the present for the future. It empowers
people because their use implies that we can modify variables now to alter (or be prepared for)
the future.
Therefore, prediction is an invitation to introduce change into a system. It is necessarily t to
understand the current situation when there is a time lag between data collection and
assessment. (Emelyne, 2013)

CHAPIII: MATERIALS AND METHODOLOGY
In chapter III, the methods, materials and equipment used including their origin and
specification in order to get information are explained in details.
27
3.1 SITE DESCRIPTION
After direct observation, personal interview, the researchers found that RWAMPARA Swamp
located in between NYARUGENGE and KICUKIRO Districts, the swamp covers 13.7 ha and
its soil is clayey silt where agriculture is carried out by the people of these surrounding
sectors. Maize, beans, green peppers, carrots, beets, tomatoes, cucumbers, eggplants, and
cabbages are rotated in the field.
Figure 3. 1: Culture of Rwampara swamp
The swamp meet flooding and drought problems leading to yield reduction that is why it
needs rainfall prediction for managing their agricultural activities and the type crops needed
according to season.

3.1.1 Site localization
It is found that RWAMPARA Swamp is located between KICUKIRO and NYARUGENGE
Districts, the swamp is bounded by three sectors of GIKONDO, NYARUGENGE and
NYAMIRAMBO .It covers an area of 151ha. The swamp has not enough production yet, it
has fertile soil and enough information of rainfall to minimize the cost of irrigation for best
preparing the future of their crops to know where irrigation are required or not required.
3.1.2 Soil type
The soil of Rwampara is characterized by clayey silt capable to save water in short dry season
of two months. This type of soil, it has natural fertility capable for cabbage, carrots,
cucumber, beets, tomatoes, eggplants, green papers and beans. The moisture content in that
soil is equal to sixty percent and decrease to ten percent in dry seasonal.
3.1.3 Rainfall pattern
The rainfall patterns of Rwampara is the same of all nation characterized by short rain season
or short wet season beginning from September to November, short dry season starting in
December to February, long rain season or long wet season starting from March to May and
long dry season starting from June to August.
3.1.4 Meteo factors of study area
The climate of Rwampara is characterized by the following data in the table 3.1; these data
were collected by Meteo-Rwanda, Kanombe airport station from 1972 to 2013. These
climatologically data were collected at altitude of 1490, latitude of 1.96*S and longitude of
30.11 *E.
28

Average rainfall, temperature, humidity, wind speed and wind from 1972 to 2013
Table 3.1: Average Meteo data collection
29
Monthly average
/Meteo data factors
Rainfall
Mm
Temperature
oC
Humidity
%
Wind speed
m/s
Wind
January 72.5 21.2 75.5 2.4 20.4
February 91.2 21.4 75.0 2.5 20.4
March 118.0 21.2 76.9 2.6 20.4
April 151.4 21.0 81.1 2.2 20.4
May 89.1 20.9 79.8 2.4 20.4
June 21.5 20.7 69.9 2.5 20.4
July 12.5 20.9 69.4 2.7 20.4
August 31.1 21.9 64.3 3.0 20.4
September 71.5 21.8 75.6 3.0 20.4
October 101.3 21.4 79.5 5.9 20.4
November 116.4 20.7 80.8 5.5 20.4
December 85.0 20.9 79.0 8.6 20.4
Annuals Average 82.4 21.2 75.6 3.4 20.4
3.2 RESEARCH TOOLS
The national meteorological services agency, Rwanda, is the responsible organization for the
collection and publishing of meteorological data. The monthly rainfall data from the period
January 1972 to December 2013 of Kigali AERO station of Kigali region were taken from
national meteorological service Agency (meteo Rwanda data in Appendix).
Te following equipments was used to collect data on the site:
3.2.1 Digital camera
A digital camera is a camera that takes video or still photographs, or both, digitally by
recording images via an electronic image sensor.

A digital camera is used to capture the photos of plants of Rwampara swamp.
Figure 3. 2: Digital camera
3.2.2 Global Positioning System (GPS)
The Global Positioning System (GPS) is a satellite based navigation system that consists of 24
orbiting satellites, each of which makes two circuits around the Earth every 24 hours. With
signals from three or more satellites, a GPS receiver can triangulate its location on the ground
(i.e. longitude and latitude) from the known position of the satellites. In addition, a GPS
receiver can provide on your speed and direction of travel. GPS was used as the leveling in
order to determine the elevation (1396m) and area (150.8ha) of Rwampara swamp.
Figure 3. 3: GPS
30

31
3.3 RESEARCH METHODOLOGY
3.3.1 Contour map of the study area
NYARUGENGE SECTOR
NYARUGENGE DISTRICT
NYAMIRAMBO SECTOR
NYARUGENGE DISTRICT
Figure 3. 4: Contour map of Rwampara
3.3.2 Questionnaire and interview
This research was conducted through the following steps:
GIKONDO SECTOR
KICUKIRO DISTRICT
 Information through different visits which are made of the sites such as MASAKA
swamp, RULINDO swamp, MULINDI swamp where irrigation is carried out with the
purpose of getting more information concerning rainfall prediction as applied in
Rwanda;
 The information through the visit of Rwanda meteorology service about rainfall
forecasting, factors affecting rainfall, and challenges;
 Production of the survey map and the contour map of the swamp showing the
different features of the swamp using COVADIS and AUTOCAD and production of
crop pattern of the swamp.

3.3.3 Meteo data collection
In this project, we use data collected by meteo-Rwanda Kigali AERO station from 1972 to
2013 of monthly rainfall, monthly mean temperature and monthly relative humidity. This
data, we are simulating in SPSS software to predict rainfall of two years.
3.3.4 Use of Cropwat window 8.0
CLIMWAT is a climatic database to be used in combination with the computer program
CROPWAT and allows the calculation of crop water requirement, irrigation needed and
irrigation scheduling according to rainfall precipitate for various crops for a range of
climatologically stations worldwide.
CLIMWAT 2.0 for CROPWAT is a joint publication of the water development and
management unit and the climate change and Bio energy unit of FAO.
Cropwat window is a program that was published by FAO (1992) penman-monteith method
for calculating reference crop evapotranspiration. These estimates are used in crop water
requirements calculation. Here is a briefly of how Cropwat windows operate:
 Enter monthly climate (ETO) data. You can double click-check entered data by using
the climate data. Table and /or the climate data graph.
 If rainfall is significant, enter monthly rainfall data and select the method of effective
32
rainfall calculation.
 Enter cropping pattern data
 You can see the results of crop water requirement calculations in crop water
requirements;
 Enter/ retrieve soil data;
 Save reports of input data results as required
3.3.5 Use of SPSS window 11.0
Statistical package for social sciences (SPSS) software time series analysis and forecasting
has become a major tool in hydrology, environmental management, and climatic fields. It is
used to modeling and forecasting rainfall data in literatures.

The rainfall prediction using regressive analysis is written as:
Rainfall= constant+ coefficient of temperature+ coefficient of relative humidity+ standard
error
As written in equation:
y=α+β1T+β2H+Є ……….. (3.1)
Where, y: rainfall predicted, T: temperature, H: relative humidity and the constant α and the
coefficients β1 and β2 Є: random error or standard error.
i. ARIMA Model
The ARIMA model is an extension of the ARMA model in the sense that by including auto-regression
and moving average it has an extra function for differencing the time series.
If a dataset exhibits long term variations such as trends, seasonality and cyclic components,
differencing a dataset in ARIMA allows the model to deal with them.
Two common process of ARIMA for identifying patterns in times series and forecasting are
auto-regression and moving Average.
33
ii. Autoregressive process
Most series consists of elements that are serially dependent in the sense that one can estimate
a coefficient or a set of coefficients that describe consecutive elements of the series from
specific, time-lagged (previous) elements.
Each observation of time series is made up of random error components (random shock, ἐ)
and a linear combination of prior observations.
iii. Moving average process
Independent from the autoregressive process, each element in series can also affected by the
past errors (or random shock) that cannot be accounted by the auto-regressive component.
Each observation of the time series is made up of random error components and linear
combination of prior random shocks.
iv. General form of non-seasonal and seasonal
ARIMA models are sometimes called Box-Jenkins models.

An ARIMA model is a combination of an auto-regressive (AR) process and a moving average
(MA) process applied to non- stationary data series.
As such, in the general non-seasonal, ARIMA (p; d; q) model, AR (p) refers to in order of the
autoregressive part, I (d) refers to degree of differencing involved and MA (q) refers to order
of the moving average part .The equation for the simplest ARIMA (p; d; q) model is Seasonal
ARIMA (SARIMA) is generalization and extension of the ARIMA method in which a pattern
repeats seasonally over time. In addition to the non-seasonal parameters, seasonal parameters
for a specified lag (established in the identification phase) need to be estimated. Analogous to
simple ARIMA parameters, these are: seasonal autoregressive (P), seasonal differencing (D),
and seasonal moving average parameters is usually determined during the identification phase
and must explicitly specified. In addition to the non-seasonal ARIMA (p; d; q) model
introduced above, we could identify SARIMA (P; D; Q) parameters for our data. The general
form of the SARIMA (p; d; q) x (P; D; Q) model using backshift notation is given by:
Four phases are involved in identifying patterns of time series data using non-seasonal and
seasonal ARIMA .These are: model identification, parameter estimation, diagnostic checking
and forecasting. The first step is to determine if the time series is stationary and if there is
significant seasonality that needs to be modeled.
3.3.6 Books and e-book
In this project we used Seasonal Autoregressive Integrated Moving Average (SARIMA)
model, proposed by Box and Jenkins (1976), for model building and forecasting for rainfall.
The box and Jenkins methodology is powerful approach to the solution of many forecasting
problems. It can provide extremely accurate forecasts of times series and offers a formal
structured approach to model building and analysis. There many quantitative methods of
model building and forecasting which are used in climatology and metrological studies.
With the development of the statistical software packages and its available, these techniques
have become easier, faster and more accurate to use. In this study, we employ seasonal
adjusted series (SAS) and SPSS software packages for the statistical data analysis.
The Box-Jenkins methodology assumes that the time series is stationary and serially
correlated. Thus, before modeling process, it is important to check whether the data under
study meets these assumptions or not.
34

CHAPITER IV: RESULTS AND DISCUSSIONS
In this chapter, the SPSS software is applied to model rainfall relationship using observed data
of RWAMPARA swamp located in KIGALI CITY from METEO RWANDA Kigali AERO
station. It was originally assumed that rainfall would be the best predominant factor in this
swamp. However, subsequent research strongly indicates that rainfall generally was the most
critical input. Numerous of runs of data were done to demonstrate the impact of various
trainings data inputs. Several of those runs presented in this chapter to demonstrate the
evolution of final model. For each run, an evaluation of the SPSS reliability is presented
Procedure is then presented for the systematic selection of inputs variables.
The SPSS is extremely versatile program offering a number of choices of data processing and
error criteria. These choices are discussed and crop water requirement needed by the maize,
beans, beets, cabbage and eggplant are discussed in this chapter using CLIMWAT and
CROPWAT software.
4.1 SURVEY MAP AND MAIN FEATURES OF SITE
Figure 4. 1: Survey map of Rwampara
35

36
4.2 INTERVIEW RESULTS
4.2.1 Rwampara site
We have seen that there are many characteristics of changes of precipitation due to climate
changes. In that area there is many crops which has been cultivated in long dry season to
avoid water pounding destroy crops caused by high quantity of rainfall in wet seasons such as
carrots, eggplants, beets, cabbages, cucumbers, tomatoes, green-peppers, etc; and they applied
the furrow and natural irrigation systems in that swamp, which produce high production
during that dry season because it irrigate the crops rather than wet season because the crops
need water regulated. So in wet season they are cultivating maize, beans and soybeans need
high quantity of water.
The management of that swamp is distributed by five cooperatives in order to produce high
quantity of production such as TECOCOKI (Terimbere Complex Cooperative Kigarama). The
management of that swamp followed three agriculture seasons, one of them is SEASON A
start in October until January, the second one is season B start in February until May, the last
one is season C start in June until September.
4.2.2 RWANDA meteorology agency
RWANDA meteorology agency have many rainfall forecast system used tropical models to
forecast data from GITEGA station, airport station, and other four station and satellite data in
hourly, daily, monthly, and season forecasting. For season forecasting, they are making it at
Nairobi/ Kenya station with eastern Africa region experts to predict it. At that station has not
capacity of predicting yearly prediction and also meteo Rwanda has not capacity of predicting
it because of materials. For seasonal prediction has advantage to agriculture activities purpose
like Rwampara swamp area and weather forecasting for aviation movement.
4.3 METEO DATA INFLUENCING RAINFALL PATTERNS AT RWAMPARA
There are many factors influencing rainfall patterns at Rwampara swamp favorite
precipitation to fall down. Those factors are temperature (minimum and maximum), air
pressure, wind speed, relative humidity, sunshine, wind direction, soil moisture, elevation, and
population density. So in our prediction, we have forty two years ago data precipitations,
temperature, and relative humidity.

4.4 EVALUATION OF RAINFALL MODEL
4.4.1 Modeling procedures
The historical measurement of precipitation, humidity and temperature are available for
RWAMPARA swamp. This is contrast to data on:
1) Soil characteristics;
2) Land use;
3) Initial soil moisture;
4) Infiltration; and
5) Groundwater characteristics those are usually scarce and limited.
A model could be developed using readily available data sources would be easy to apply in
practice. Because of this, the dependent variable (rainfall) has relation with independent
variables (temperature and humidity) are inputs selected for use in this model and predicted
rainfall is the output. The selection of training data to represent the characteristics of swamp
and meteorological patterns is critical modeling.
The period of time for historical data selected was from January, 1972 through December
2013 the total of 42 years; the period was selected because of minimization of errors and
increases the accuracy. It provides an adequate number of observations for SPSS as well as a
reasonable of extreme predicted observations.
4.4.2 Modeling and simulation
The modeling shows the type of model used in prediction and rainfall equation modeling in
the simulation of input data and analysis it in output results. The type of equation used is
detected using regression system for showing model equation, after this equation, we make
another simulation to select a type of model used related the results observed.
37

Model coefficients
Table 4. 1: regression coefficients
Model Unstandardized Coefficients
α and β1, 2 Std. Error
38
1 (Constant)
Humidity
Temperature
-195.563
3.384
1.363
74.542
0.285
3.071
So these coefficients show that modeling equation is:
푹 = 휶 + 휷ퟏ푯 + 휷ퟐ 푻 + Є …………………………… (4.1)
푹 = −ퟏퟗퟓ. ퟓퟔퟑ + ퟑ. ퟑퟖퟒ푯 + ퟏ. ퟑퟔퟑ푻 + ퟕퟒ. ퟓퟒퟐ + ퟎ. ퟐퟖퟓ푯 + ퟑ. ퟎퟕퟏ푻
Є = ퟕퟒ. ퟓퟒퟐ + ퟎ. ퟐퟖퟓ푯 + ퟑ. ퟎퟕퟏ푻
푹 = −ퟏퟐퟏ. ퟎퟐퟏ + ퟑ. ퟔퟔퟗ푯 + ퟒ. ퟒퟑퟒ푻
Where, R= rainfall forecast, H= relative humidity, T= temperature and Є= standard error.
The selection of rainfall model type, we must simulate time plot stationary and calibrating the
model available after transformation of different models related to the characteristics of results
showed. In our software, it has three different models for each has there characteristics related
to the results of previous models. Those model different models are:
1) ARIMA (Autoregressive Integrated Moving Average Model);
2) Exponential smoothing model;
3) Autoregression model; and
4) Seasonal decomposition model.

JAN 1990
39
Example of time plot of rainfall model-3
Date
JAN 1981
APR 1983
APR 1974
Transforms: dif ference (1)
OCT 2005
APR 2010
JUL 2012
OCT 2014
OCT 1996
JAN 1999
JUL 2003
JAN 2008
APR 2001
APR 1992
JUL 1994
OCT 1987
JUL 1985
OCT 1978
JUL 1976
RAINFALL
300
200
100
0
-100
-200
-300
-400
Figure 4. 2: rainfall time plot model
For this type of plot we can use ARIMA Model for suitability of analyzing the results
represented by model_3 above.
Example of ARIMA model plot
i. Model description
This model represents variable (rainfall), non seasonal differencing (1), seasonal differencing
(1), and the length of seasonal cycle (12).
ii. Model parameters
This model represents different parameters from original value estimation.
 AR1: Autoregressive;
 MA1: Moving Average;
 SMA1: Seasonal Moving Average; and
 Constant
Our model has ninety five percent (95%) of confidence intervals should be generated.

OCT 1996
APR 2001
OCT 1987
APR 1992
JUL 1994
40
iii. Model termination criteria
This model represents termination criteria such as:
 Parameter epsilon of 0.001;
 Maximum Marquardt constant of 1.00E+09;
 Maximum number of iterations of 10.
iv. Time plot of model_6
This plot illustrates the previous rainfall and forecast rainfall in the same plot.
Date
OCT 1978
JAN 1981
JUL 1985
APR 1974
Transforms: dif ference (1)
OCT 2005
APR 2010
JUL 2012
OCT 2014
JUL 2003
JAN 2008
JAN 1999
JAN 1990
APR 1983
JUL 1976
300
200
100
0
-100
-200
-300
-400
RAINFALL
Fit for RAINFALL f ro
m ARIMA, MOD_13 CON
Figure 4. 3: Forecasting model
4.4.3 Level of acceptance of the model
This research, the performance of the model is measured by difference between and predicted
values of dependent variables (rainfall) or the errors. Average error is the absolute value of the
actual values minus the predicted values divided by the number of patterns. Correlation is
measure of how the actual and predicted correlate to each other in terms of direction (i.e.,
when the actual value increases, does the predicted value increase and vice).

41
4.4.4 Importance of the model
 Computer modeling helps in taking decisions for implementation of various projects.
A model is decision support tool
 It is important in predicting for future in some areas.
 It is of great importance in different fields of science and engineering to develop
different application and procedures for management of systems.
 Modeling assists in taking measures for protection for agriculture crops
 It is important in understanding the functioning of complex scientific or engineering
projects.
 Computer models reduce chances of failure for scientific or engineering projects. A
good model was reflecting all the probable failures or successes of the project in
question.
4.5 CROP WATER REQUIREMENT FOR DIFFERENT CROPS
An irrigation requirement characteristic shows in the table below for small vegetations sowing
on fifteen April 2014 and harvest at eighteen July 2014.
Table 4. 2: Irrigation water requirement
Month Decade Stage Kc Etc Etc Eff. Rain Irr. Req.
Coeff. mm/day mm/dec mm/dec mm/dec
April 2 Initiation 0.70 2.47 14.8 25.2 0.0
April 3 Initiation 0.70 2.46 24.6 38.0 0.0
May 1 Development 0.72 2.55 25.5 34.0 0.0
May 2 Development 0.83 2.92 29.2 30.9 0.0
May 3 Development 0.95 3.46 38.0 24.3 13.7
June 1 Mid 1.04 3.90 39.0 16.0 23.1
June 2 Mid 1.04 4.04 40.4 9.0 31.3
June 3 Mid 1.04 4.17 41.7 8.8 32.9
July 1 Late 1.03 4.23 42.3 8.4 33.8
July 2 Late 0.97 4.13 33.0 5.6 26.0
Total 328.6 200.2 160.8

Where Kc: crop coefficient (dimensionless), ETc: crop evapotranspiration (mm/day), Eff.
Rain: effective rain (mm/decade) and Irr. Req.: irrigation requirement for crops.
Etc= Kc x ETo ………………… (4.3)
Where ETo= reference Crop evapotranspiration (mm/decade).
Note: seasonal crop coefficient (Kc) = (Kc initial season + Kc mid season + Kc end season)/3.
42
4.6 RAINFAL PREDICTION
4.6.1 Measurement of the accuracy
We have selected ARIMA model after checking. Now we proceed to compare their accuracy
performance using the various accuracy measures.
For this purpose we used observations from September 2012 to December 2013 of monthly
data for calculation of forecasting error using following equation:
Error = rainfall – rainfall forecast …………… (4.4)

Table 4. 3: Error measurement
DATE HUMIDITY TEMPERATURE RAINFALL RAINFALL
43
FORECAST
ERROR
Sep-12 75.6 22.1 61.3 81.6 -20.3
Oct-12 79.5 22.3 97.9 115.8 -17.9
Nov-12 80.8 21.2 170.6 120.3 50.3
Dec-12 79 21.7 74.3 98.3 -24
Jan-13 79.5 22.8 63.2 83.6 -20.4
Feb-13 77.4 22.2 72.4 104.3 -31.9
Mar-13 86.9 22.5 324.3 116.8 207.5
Apr-13 86.1 22.4 141.7 201.1 -59.4
May-13 81.7 21.5 35.4 120.8 -85.4
Jun-13 62.8 21.4 0 27.9 -27.9
Jul-13 52.3 22.2 0 16.3 -16.3
Aug-13 58.2 23.8 6.7 34.7 -28
Sep-13 75.6 21.7 77.4 66.9 10.5
Oct-13 79.5 23 96.2 110.9 -14.7
Nov-13 80.8 20.8 217.4 118.2 99.2
Dec-13 79 21.8 89.2 104.5 -15.3
AVERAGE 75.91875 22.0875 95.5 88.3 7.2
To measure the forecasting ability of the ARIMA model, we have estimated within sample
and out of sample forecasts. If the magnitude of the difference between the forecasted and
actual values is low, then the model has good forecasting performances. In this case, the
seasonal ARIMA (1; 1; 1) X (0; 1; 1) model has shown better results which is evident from
table 4.4.
Now the final model for forecasting of historical monthly rainfall series of Kigali AERO
station is as given below. The ARIMA model (1; 1; 1) x (0; 1; 1) can be written as:
푹풂풊풏풇풂풍풍 = −ퟏퟗퟓ. ퟔ + ퟑ. ퟒ푯풖풎풊풅풊풕풚 + ퟏ. ퟒ푻풆풎풑풆풓풂풕풖풓풆 + 푹풂풏풅풐풎 풆풓풓풐풓 Or
푹 = 휶 + 휷ퟏ 푯 + 휷ퟐ 푻 + Є . ………………… (4.5)
Є = 흁 + ∅ퟏ 푯 + ∅ퟐ 푻 ………… (4.6)

Rainfall predicted table from 2014 to 2015 in the table below:
Table 4. 4: Rainfall forecasting result for two years
DATE RAINFALL FORECAST (mm) UCL (mm) LCL (mm)
January 2014 88.3 181.9 0.0
February 2014 112.3 208.8 15.8
MARCH 2014 144.8 242.9 46.8
APRIL 2014 163.0 262.5 63.5
MAY 2014 107.9 208.9 7.0
JUNE 2014 35.8 138.2 0.0
JULY 2014 25.8 129.6 0.0
AUGUST 2014 45.0 150.3 0.0
September 2014 84.8 191.4 0.0
October 2014 123.1 231.1 15.0
November 2014 140.8 250.3 31.3
DECEMBER 2014 96.4 207.3 0.0
TOTAL 1168 2403.2 179.4
JANUARY 2015 90.9 204.2 0.0
February 2015 114.5 229.4 0.0
MARCH 2015 147.0 263.4 30.6
APRIL 2015 165.1 283.0 47.2
MAY 2015 110.1 229.5 0.0
JUNE 2015 38.0 158.9 0.0
JULY 2015 28.0 150.4 0.0
AUGUST 2015 47.2 171.1 0.0
September 2015 87.0 212.3 0.0
October 2015 125.3 252.1 0.0
November 2015 143.0 271.3 14.7
DECEMBER 2015 98.6 228.4 0.0
TOTAL 1194.7 2654 92.5
44

4.6.2 Rainfall pattern for agriculture of Rwampara swamp
Rwampara swamp is characterized by four patterns in that they have three agriculture seasons.
Those four seasons are short wet season, short dry season, long wet season, and long dry
season.
 Short wet season (winter) starting from September to November;
 Short dry season (spring) starting from December to January;
 Long wet season (autumn) starting from February to May; and
 Long dry season (summer) starting from June to August.
45
The three agriculture seasons are:
 Season A starting from October and end in January;
 Season B starting from February and end in May; and
 Season C starting from June and end in September.
In season A, they are cultivating maize, peppers, beets and cucumber; in season B, they are
cultivating beans, soybeans, eggplants, and cabbages; then in season C they are cultivating
tomatoes, carrots, lettuces, scallions, small vegetations and onions.
4.7 PLANTING CROPS AND SOWING DATE
4.7.1 Planting crops
The prediction of crop species depends on the time at which prediction is required. If for
example, a prediction of national yield is required shortly before harvest time, then the
agricultural statistics for the current year data may be available, and the approaches described
above are applicable.
One possible approach in this case is simply to assume that at a regional scale the change in
land use from one year to another is negligible. Such an assumption would be reasonable for a
region where single crop farming dominates and no major changes in economic or regulatory
factors have occurred.

A second possibility is to use declared intentions of farmers, where such information is
available. The Rwandan agricultural ministry (MINAGRI) policies involves asking farmers to
declare which crops they intend to cultivate in each field, for example: eastern province are
cultivating maize, soybeans, beans etc. A minor problem here is that climatic conditions may
lead to some changes in plan, for example: Bugesera district. A major difficulty is obtaining
this information, which is protected by privacy laws. The information is made available in
form of computer database, but this only concerns data aggregated by district and furthermore
there is considerable delay before this is done.
4.7.2 Sowing date
For past data one could simply seek to obtain the sowing date for each field, but this can be
very difficult for large numbers of fields. Even if one is willing to address direct inquiries to
each farmer many may not respond. Information that is generally available is a recommended
sowing period for each crop, each variety and each region. One also has in general climate
information and statistical information about farm structure and land use.
46
a. Predicting sowing date
Sowing dates could be based on the recommendations that exist for each variety in each
region, but within the possible sowing period the actual sowing date will depend on available
manpower, the state of the soil and climate conditions. This suggests two possibility
approaches, either using a fixed average sowing date or calculating a sowing date for each
field based on information about farm cooperatives and climate. An example of calculation of
sowing date is the SIMSEN model of sowing date proposed by Leenhardt and Lemaire
(2002).
Determining possible sowing days using a soil water model: The water balance model is
run at daily time step over the months of the sowing period to determine, for each soil type,
which days are possible sowing days. To determine if sowing is possible, a decision rule
based on soil water status and precipitation is used. The rule is :”If the soil water content
(SWC) is below x% of soil available water capacity (SAWC) , and if it does not rain more
than y mm this day, then the sowing can occur” Threshold values x and y were obtained, for
the study of RWAMPARA swamp, after analysis of the past sowing dates.

Determining the time required to sow crop: the other step of SIMSEM procedure is
primarily based on the information given by the farm typology (a classification according to
general type, especially in archaeology, psychology, or the social sciences): the type and area
of various crop soil associations for each farm type, the kind and size of its livestock, and the
amount of manpower available. However, complementary information (and very specific to
the region considered) was provided by experts from local technical institutes: the earliest
possible date for sowing the various summer crops, winter crops, autumn crops, and spring
crops; the priority between crops for sowing, the time necessary to sow for various soil types,
and estimations of daily working time.
b. Determination of available season and crops
Table 4. 5: Sowing date program and types of crops
year Season Rainfall (mm) Sowing date prediction Crops available per season
2014 B 420.8 February Beans ,soybeans, eggplants,
47
cabbages
C 156.6 June Tomatoes, carrots, lettuces,
scallions, small vegetations
A 381.7 October Peppers, beets, cucumber,
maize
2015 B 462.3 February Beans ,soybeans, eggplants,
cabbages
C 167.8 June Tomatoes, carrots, lettuces,
scallions
A 397.2 October Peppers, beets, cucumber,
maize

CHAPTER V: CONCLUSION AND RECOMMENDATION
48
5.1 CONCLUSION
After the completion of this research project entailed “USING METEO DATA FOR
RAINFALL PREDICTION IN RWANDA, CASE STUDY “RWAMPARA SWAMP”
located in between NYARUGENGE and KICUKIRO districts, it was found that average rain
water is 1181.4mm/year, the evapotranspiration of the small vegetations were
328.6mm/decade, effective rainfall was 200.2mm/decade and irrigation requirement of
160.8mm/decade for the year 2014.
In this project the use of SPSS software Box-Jenkins methodology has been shown historical
rainfall data. The estimation and diagnostic analysis results revealed that models’ are
adequately fitted to the historical data. In particular, the residual analysis which is important
for diagnostic checking confirmed that there is no violation of assumptions in relation to
model adequacy. Further comparison based on the forecasting accuracy of the models is
performed with the holdout some rainfall values. The point forecast results showed a very
closer match with the pattern of the actual data and better forecasting accuracy in validation
period.
The quality of data is also a major issue for creating rainfall forecasting model .The ARIMA
or SARIMA modeling required the data be cleaned of erroneous or missing elements. To do
this, every time there was a “no data available” report from any reporting station (METEO
RWANDA).
For this project, similarly cleaned data was used to be able to predict rainfall for the future
time of two years, in order reduce the expenses of money during irrigation. Although the
SPSS trained in this study can only be applied to the RWAMPARA swamp, the guidelines in
the selection of the data, training criteria, and the evaluation of SPSS reliability are based on
statistical rules. Therefore, they are independent of the application. These guidelines can be
used in any application.

Final project report of telesphore and vilany

Final project report of telesphore and vilany

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