chemeda's thesis feb 2014 final

i

RAINFALL INTENSITY-DURATION-FREQUENCY ANALYSIS

UNDER CHANGING CLIMATE SCENARIO IN SELECTED STATIONS

OF THE CENTRAL HIGHLAND OF ETHIOPIA

MSc THESIS

CHEMEDA NURGI

JANUARY 2014

HARAMAYA UNIVERSITY




A Thesis Submitted to School of Graduate Studies Through

School of Natural Resources and Environmental Engineering

HARAMAYA UNIVERSITY

In Partial Fulfilment of the Requirements for the Degree of

MASTER OF SCIENCE IN SOIL AND WATER ENGINEERING

(Soil and Water Conservation Engineering)

By

Chemeda Nurgi ([email protected])

January 2014

Haramaya University

i

SCHOOL OF GRADUATE STUDIES

HARAMAYA UNIVERSITY

As the thesis research advisor, I hereby certify that I have read and evaluated this thesis

prepared, under my guidance, by Chemeda Nurgi, entitled ‘Rainfall Intensity-

Duration-Frequency Analysis under Changing Climate Scenario in Selected

Stations of the Central Highland of Ethiopia’. I recommend that it can be

submitted as fulfilling the MSc thesis partial requirement.

Prof. Shoeb Quraishi (Dr. Eng) _______________ _________________

Major Advisor Signature Date

As member of the Board of Examiners of the MSc thesis Open Defense Examination, we

certify that we have read, evaluated the thesis prepared by Chemeda Nurgi and examined the

candidate. We recommended that the thesis can be accepted as fulfilling the thesis

requirement for the Degree of Master of Science in Master of Science in Soil and Water

Engineering (Soil and Water Conservation Engineering stream).

Dr. Asfaw Kebede (PhD.) _________________ ______________

Chair Person Signature Date

Dr. Kibebew Kiberet (PhD.) _________________ ______________

Internal Examiner Signature Date

Dr. Awdenegest Moges (PhD.) _________________ ______________

External Examiner Signature Date

DEDICATION

This thesis manuscript is dedicated to my family for nursing me with love and affection and

for their dedication to support me for the success of my life as well as to my children

(Etsubdink, Minase, Tsinat and Dibora Chemeda) to whom the future Ethiopia belongs.

iii

BIOGRAPHICAL SKETCH

The author was born in west Shewa zone of Oromia region, Gindeberet woreda on April 23,

1971. He attended elementary school and high school in Gindeberet woreda at Kere Dobi

elementary school and Gindeberet Secondary School (Kachisi) respectively. He joined the

then Alemaya University of Agricultural (Haramaya University) in September 1989 and

graduated in July 1994 with BSc degree in Agricultural Engineering.

After the completion of his training, Chemeda has worked in different organizations at

different capacities for about 20 years. From December 1994 to December 2000 he was

employed by International Crop Research Institute for the Semi-Arid Tropics (ICRISAT) in

the capacity of research assistant, from January 2001 to June 2003 in Ethiopian

Environmental NGO (EENGO) as project officer for agricultural development, natural

resource conservation and management and rural potable water supplies development

programs, from June 2003 to April 2005 in Oromia Pastoralist Area Development

Commission as infrastructural development engineer and from May 2005 to July 2006 in

Ministry of Water Resources of Ethiopia in the capacity of drainage engineer and irrigation

project coordinator. Moreover, Chemeda has worked for UNICEF Ethiopia as Water,

Sanitation and Hygiene (WASH) consultant from July 2006 to January 2012 and from

February 2012 to date he is working in UNICEF Ethiopia as WASH Programme officer for

Oromia region.

In July 2010, he joined the School of Graduate Studies of Haramaya University in the summer

programme to pursue his MSc study in Soil and Water Engineering (Soil and Water

Conservation Engineering stream). Chemeda is married to Saba Gebre and have four children

(a son and three daughters).

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STATEMENT OF THE AUTHOR

I declare that this thesis is my genuine work and that all sources of materials used for thesis

have been duly acknowledged. This thesis has been submitted in partial fulfillment of the

requirements for an MSc degree at Haramaya University and is deposited at the University

library to be made available to borrowers under rules of the library. I declare that this thesis is

not submitted to any other institution anywhere for the award of any academic degree,

diploma, or certificate.

Brief quotations from this thesis are allowable without special permission provided that

accurate acknowledgement of sources is made. Requests for permission for extended

quotation from or reproduction of this manuscript in whole or in part may be granted by the

Head of the major department or the Dean of the School of Graduate Studies when in his or

her judgment the proposed use of the material is in the interest of scholarship. In all other

instances, however, permission must be obtained from the author.

Chemeda Nurgi Signature:

Haramaya University, Haramaya

January 2014

v

ACKNOWLEDGMENT

The knowledge of God is the beginning of wisdom. First of all, I would like to praise my

GOD, who gave me the courage, health, the resources to continue the study and helped me

changing the adversities to opportunity to complete the course.

My sincere gratitude goes to my major advisor Prof. Shoeb Quraishi (Dr. Eng) for his

encouragement, intellectual stimulation, moral support as well as constructive and helpful

comments from the inception of proposal development to the completion of thesis work.

I would like to extend my grateful thanks to National Meteorological Services Agency staff

members who provided me with numerous valuable meteorological data free of charge and

for their hospitality. I would like to thank also Haramaya University for giving me the chance

to pursue the MSc study in Soil and Water Engineering (Soil and Water Conservation

Engineering stream).

I would like to extend my grateful thanks to my friend Gashaye Chekol, for his

encouragement from scratch and continuous guidance to enroll as a student and for his sweet

advice. I would like to thank also Dr. Teklu Erkossa, Dereje Abdeta, Dr. Daniel Galan,

Elizabeth Girma, Awoke Moges and Gebreegziabeher Lemma for their continuous

encouragement and provision of the necessary materials for my study. The deep loves they

have shown me will be always the constant sources of my strength and hope in every aspect

of my life. I am very grateful to Tesfaye Asgele for his support on the data analysis

(especially use of SDSM and MIDUSS software). Without his support, this document

wouldn’t have been realized at this time. I would like to thank also Abeba Tesfaye, for her

constructive advice and materials support and Tigist Alemu for her support in data entry. In

addition, the generous support and contribution of all my colleagues, friends, families and

relatives through their pray are deeply acknowledged and emphasized in all cases of my

future life.

Last not the least, I would like to thank my spouse Saba Gebre for the support and

encouragement she has provided to me as well as for her proper management and taking care

of the household during my study.

vi

LIST OF ABBREVIATIONS AND ACRONYMS

ACCRA Africa Climate Change Resilience Alliance

AOGCM Atmosphere-Ocean Global Circulation Models

AR4 Fourth Assessment Report

CGCM1 Canadian Centre of Climate Modelling and Analysis

CGD Centre for Global Development

CICS Canadian Institute for Climate Studies

EXACT Executive Action Team

EVI Extreme Value Type I Distribution

GCM Global Circulation Model

GHG Greenhouse Gases

HadCM3 Hadley Centre Coupled Model version 3

HadCM3A2a Hadley Centre Coupled Model, version 3, for the A2a emission scenario

HadCM3B2a Hadley Centre Coupled Model, version 3, for the B2a emission scenario

IDF Intensity Duration Frequency

IPCC Intergovernmental Panel on Climate Change

KT Frequency factor

MIDUSS Microcomputer Interaction Design of Urban Stormwater Systems

MuDRain Multivariate Disaggregation of Rainfall

NCEP National Centre for Environmental Prediction

NMSA National Meteorological Service Agency of Ethiopia

NSE Nash and Sutcliffe coefficient

RCM Regional Circulation Model

SDSM Statistical Downscaling Model

SRES Special Report on Emission Scenarios

TGCIA Task Group on Scenarios for Climate and Impact Assessment

UNESCO United Nations Educational, Scientific and Cultural Organization

UNFCCC United Nation Framework Convention on Climate Change

WMO World Meteorological Organization

vii

TABLE OF CONTENTS

BIOGRAPHICAL SKETCH iii

STATEMENT OF THE AUTHOR iv

ACKNOWLEDGMENT v

LIST OF ABBREVIATIONS AND ACRONYMS vi

LIST OF TABLES ix

LIST OF FIGURES x

LIST OF TABLES IN THE APPENDIX xi

LIST OF FIGURES IN THE APPENDIX xii

ABSTRACT xiii

1. INTRODUCTION 1

2. LITERATURE REVIEW 4

2.1. Climate Change 4 2.2. Climate Models 4

2.3. Defining Climatic Baseline 5 2.4. Methods for Generating Regional Climate Information 6

2.4.1. Statistical downscaling model 7 2.4.2. Dynamical downscaling 7

2.5. Climate Change Scenarios 8 2.5.1. Construction of climate change scenarios 9

2.5.2. Emissions scenarios 9 2.6. Climate Change in Ethiopia 11

2.7. Characteristics of Rainfall Event 12 2.8. Daily Rainfall Disaggregation Methods 12

2.8.1. The hyetos model 12 2.8.2. Rainfall ratio method 14

2.9. Rainfall Intensity Duration Frequency Analysis 14 2.9.1. Normal distribution 16

2.9.2. Log-normal distribution 16 2.9.3. Gumbel extreme value distribution 17

2.9.4. Log-pearson type III distribution 18 2.9.5. Frequency factor 20

2.9.6. Probability plotting position 22 2.10. Intensity Duration Frequency Relationships 23

2.10.1. Mathematical form of IDF 23 2.10.2. Parameter estimation methods 24

2.10.3. Evaluation of model 26

3. MATERIALS AND METHODS 28

3.1. Description of the Study Area 28 3.2. Data Collection and Quality Control 30

viii

TABLE OF CONTENTS Continue …

3.2.1. Filling missing data 30 3.2.2. Consistency of data 30

3.3. Building Climate Change Scenarios for Rainfall 31 3.3.1. Climate Change Scenarios 31

3.3.2 General circulation model (GCM) 31 3.3.3. Statistical downscaling model (SDSM) 32

3.4. Daily Rainfall Disaggregation Model 36 3.5. Rainfall Intensity Duration Frequency Analysis 38

3.5.1. Fitting the probability distribution function 38 3.5.2. Testing the goodness of fit of data 39

3.5.3. Computation of extreme value (XT) 40 3.5.4. Calculation of intensity of rainfall 40

3.5.5. Estimation of intensity duration frequency curve coefficients 41 3.5.6. Parameter performance testing 41

3.6. Comparison of Intensity Duration Frequency Results 42

4. RESULTS AND DISCUSSIONS 43

4.1. Rainfall Variability and Trend 43 4.2. Climate Change Scenarios of Rainfall 44

4.2.1. Predictor variables selected 44 4.2.2. Calibration and validation 45

4.2.3. Performance evaluation of the model 46 4.2.4. Scenarios developed for the future (2010-2099) 49

4.3. Disaggregation of daily rainfall 55 4.4. Selection of the Probability Distribution Functions 55

4.4.1. Extreme rainfall values (XT) 56 4.4.2. Rainfall intensity (I) 58

4.4.3. Estimation of the IDF Parameters 63 4.4.4. Sensitivity of the IDF parameters 65

4.4.5. Comparison of IDF curve under climate change with historic IDF 66

5. SUMMARY, CONCLUSION AND RECOMMENDATIONS 73

5.1. Summary and Conclusions 73

5.2 Recommendations 74

6. REFERENCES 75

7. APPENDICES 84

7.1. Appendix Tables 85 7.2 Appendix Figures 98

ix

LIST OF TABLES

Table Page

2.1. Plotting position formula 22 3. 1. Locations of Meteorological Stations 29

3.2. The rainfall pattern of the study area 29

3.3 Relationship of observed and disaggregated rainfall at Addis Ababa station 37

4.1. Summary of annual rainfall statistics of the meteorological stations 43 4.2.Selected predictor variables for the three stations 45

4.3. Calibration and validation statistics of rainfall for the three stations. 45

4.4.The statistical comparison of observed and generated monthly rainfall values 46 4.5 Seasonal percentage change from the base for Addis Ababa station 51

4.6. Seasonal percentage change from the base for Fiche station 53

4.7. Seasonal percentage change from the base for Kachisi station 55

4.8. Comparisons of R2 values of the selection of probability distributions 55

4.9. Summaries of Chi Square value 56

4.10. Summary of computed XT for Addis Ababa stations under A2a Scenario 57

4.11. Summary of computed XT for Addis Ababa stations under B2a Scenario 57 4.12. Computed rainfall intensities (mm/hr) using XT and IDF parameters at Addis Ababa

station for 2020s (A2a scenario) 60

4.13. Computed rainfall intensities (mm/hr) using XT and IDF parameters at Addis Ababa station for 2050s (A2a scenario) 60

4.14. Computed rainfall intensities (mm/hr) using XT and IDF parameters at Addis Ababa


4.15. Computed rainfall intensities (mm/hr) using XT and IDF parameters at Addis Ababa station for 2020s (B2a scenario) 61

4.16. Computed rainfall intensities (mm/hr) using XT and IDF parameters at Addis Ababa

station for 2050s (B2a scenario) 62 T4.17. Computed rainfall intensities (mm/hr) using XT and IDF parameters at Addis Ababa

station for 2080s (B2a scenario) 62

4.18. the computed IDF parameters at Addis Ababa station for various frequencies 63

4.19. the computed IDF parameters at Fiche station for various frequencies 64

4.20. the computed IDF parameters at Kachisi station for various frequencies 64

4.21. Percentage change between historic rainfall intensity and climate change under A2a scenario for Addis Ababa 67

4.22. Percentage change between historic rainfall intensity and climate change

under B2a scenario for Addis Ababa 68 4.23. Percentage change between historic rainfall intensity and climate change

under A2a scenario for Fiche 69

4.24. Percentage change between historic rainfall intensity and climate change

under B2a scenario for Fiche 70 4.25. Percentage change between historic rainfall intensity and climate change

under A2a scenario for Kachisi 71

4.26. Percentage change between historic rainfall intensity and climate change under B2a scenario for Kachisi 72

x

LIST OF FIGURES

Figure Page

3.1. Location map of the study area 28

3.2 The gird box for downloading predictor variables for the study area 33

3.3. Relationship between observed and disaggregated 12hr rainfall at

Addis Ababa station. 38

4.1. Annual rainfall trend of the stations for the period of 1987-2009. 44

4.2 The daily mean of observed and NCEP output for Fiche station. 46

4.3. Average monthly rainfall pattern for the base period (1970-99) at Addis

Ababa station 47

4.4. Average monthly rainfall pattern for the base period (1986-2001) at Fiche station 48

4.5. Average monthly rainfall pattern for the base period (1987-2001) at Kachisi station 49

4.6. Average monthly rainfall change in the future at Addis Ababa station for A2a

scenario. 50

4.7. Average monthly rainfall change in the future at Addis Ababa station for B2a

scenario. 51

4.8. Average monthly rainfall change in the future at Fiche station for A2a scenario. 52

4.9. Average monthly rainfall change in the future at Fiche station for B2a scenario. 52

4.10. Average monthly rainfall change in the future at Kachisi station for A2a scenario. 54

4.11. Average monthly rainfall change in the future at Kachisi station for B2a scenario. 54

xi

LIST OF TABLES IN THE APPENDIX

Appendix Table Page

1. Annual rainfall of the study area 85

2. Mean Monthly rainfall of the three stations 86

3. The monthly variability of rainfall of the study area 86

4. Calibration and validation results for Addis Ababa Station 87

5. Calibration and validation results for Fiche Station 88

6. Calibration and validation results for Kachisi Station 88

8. Summary of extreme rainfall values ( XT) for Fiche stations under B2a Scenario 89

9. Summary of extreme rainfall values ( XT) for Kachisi stations under A2a Scenario 90

10. Summary of extreme rainfall values ( XT) for Kachisi stations under B2a Scenario 90

11. Computed rainfall intensities (mm/hr) using XT and IDF parameters at Fiche












17. Computed rainfall intensities (mm/hr) using XT and IDF parameters at Kachisi












23. IDF parameters for historic rainfall at Addis Ababa, Fiche and Kachisi stations) 97

24. Historic rainfall intensities of Addis Ababa, Fiche and Kachisi stations 97

xii

LIST OF FIGURES IN THE APPENDIX

Appendix Figure Page

1. Double mass curve for Addis Ababa station ...................................................................... 98

2. Double mass curve for Fiche station ................................................................................. 98

3. Double mass curve for Kachisi station .............................................................................. 98

4. IDF curves for Fiche Station under climate change A2a Scenario .................................... 99

5. IDF curves for Fiche Station under climate change B2a Scenario ................................... 100

xiii




ABSTRACT

The rainfall Intensity-Duration-Frequency (IDF) relationship is one of the most imperative

tools used in water resource systems planning, designing and operation. Annual extreme

historic rainfall is fitted to a theoretical probability distribution from which rainfall

intensities, corresponding to particular durations, are obtained. In the use of this procedure,

an assumption was made that historic hydro meteorological conditions could be used to

characterize the future (i.e., the historic record was assumed to be stationary). However, this

assumption is not valid under changing climatic conditions which may bring shifts in the

magnitude and frequency of extreme rainfall. The objective of this study was to assess the

change in IDF curves for some selected stations (Addis Ababa, Fiche and Kachisi) in central

highland of Ethiopia under changing climatic conditions. The historic daily rainfall data of

the satiations were collected from National Meteorological Service Agency (NMSA) of

Ethiopia, and Statistical Downscaling model (SDSM) Version 4.2, was used to downscale

climate information from coarse resolution of Global Circulation Model (HadCM3 coupled

atmosphere-ocean GCM model for the A2 and B2 emission scenarios) to local or site level to

produce the future rainfall scenario for three future climate periods of 30 years from 2010 to

2099. The future daily rainfalls of the stations were obtained by multiplying the historic

rainfall by the change fields. The results of the future daily rainfall were disaggregated into

hourly value using rainfall ratio method to simulate future IDF relationships. Scenarios were

generated for the base period and for the future times. IDF curves under climate scenarios

were developed for the stations for return periods of 2, 5, 10, 25, 50 and 100 years, and for

durations of 1, 2, 3, 6, 12 and 24 hours and comparisons were made with the historic IDF

curves. The results of Special Report on Emission Scenario (SRES) under A2a indicate that

the magnitude of annual rainfall will decrease at Addis Ababa and Fiche stations while at

Kachisi it will increase in 2020s and 2050s. Under B2a emission scenario the annual rainfall

will decrease at Addis Ababa while it will increase at Fiche and Kachisi stations for all

periods compared to the base period. The comparison between the historic IDF curves and

IDF curve under climate change scenario shows a difference that ranges between: 0.52% -

45.6% with average value of approximately 24% increase of rainfall intensity for Addis

Ababa station, 0.7% - 35.7% with average value of approximately 14% increase of rainfall

intensity for Fiche station and 11.52% - 44% with average value of approximately 29%

increase of rainfall intensity for Kachisi station. The result of the study indicates that climate

change is real; hence, the national climatic change adaptation programme of Ethiopia should

be strengthened. The IDF relationships established in this study could be used for water

resource systems design in the area provided that verification with other GCM model outputs

are made to minimize uncertainty of cost implication.

1

1. INTRODUCTION

Rising fossil fuel burning and land use changes have emitted, and are continuing to emit,

increasing quantities of greenhouse gases (GHG) into the earth’s atmosphere. These GHGs

include carbon dioxide (CO2), methane (CH4) and nitrogen dioxide (N2O), and a rise in these

gases has caused a rise in the amount of heat from the sun withheld in the earth’s atmosphere,

heat that would normally be radiated back into space. This increase in heat has led to the

greenhouse effect, resulting in climate change. The main characteristics of climate change are

increase in average global temperature (global warming); changes in cloud cover and

precipitation particularly over land; melting of ice caps and glaciers and reduced snow cover;

and increases in ocean temperatures and ocean acidity due to seawater absorbing heat and

carbon dioxide from the atmosphere (Rosenzweig et al., 2007).

Climate change has the potential to affect many sectors in which water resource managers

have to play an active role. The major drivers are changing temperature and rainfall regimes,

and increasing global sea level and associated impacts. Rainfall changes are expected to differ

across the country, with some areas receiving more and others receiving less, as suggested by

the model simulations. There may also be changes in seasonal patterns and extremes of

rainfall. Depending on location, these possible changes have led to concerns that droughts and

floods, defined relative to past experiences, will occur more frequently and (or) be more

severe under future climate conditions (IPCC, 2007b).

As a result of global warming, the type, frequency and intensity of extreme events, such as

tropical cyclones (including hurricanes and typhoons), floods, droughts and heavy

precipitation events, are expected to rise even with relatively small average temperature

increases. Changes in some types of extreme events have already been observed, for example,

increases in the frequency and intensity of heat waves and heavy precipitation events (Meehl

et al., 2007).

The growing evidence from the Intergovernmental Panel on Climate Change (IPCC) that

climate will change as greenhouse gases accumulate (IPCC, 2007a) has added urgency to the

need to understand the consequences of warming. Initial studies of climate change, using a

2

variety of methods, identified Africa as one of the most vulnerable locations on the planet to

climate change because it is already hot and dry, a large fraction of the economy is tied to

agriculture, and the farming methods are relatively primitive (Carter et al., 2007).

In Ethiopia, the distribution and occurrence of rainfall is not uniform; rather it has got spatial

as well as temporal variation. Mean annual minimum temperature and annual rainfall

variability and trend observed over the country in the period 1951-2006 reveals that there has

been a warming trend in the annual minimum temperature over the past 56 years. It has been

increasing by about 0.370C every ten years. The country has also experienced both dry and

wet years over the same period. The trend analysis of annual rainfall shows that rainfall

remained more or less constant when averaged over the whole country (NMSA, 2007).

According to NMSA (1996) analysis, the mean value of annual rainfall varies from about 100

mm in the north-eastern part to 2800 mm over the south-western parts. It is this variation in

the rainfall distribution over space and time that creates serious hydrological extremes, such

as floods and droughts.

The rainfall characteristics (intensity, duration and frequency) relate with each other in many

hydrologic design problems. The intensity-duration-frequency curves (IDF) are used to

estimate peak run-off rates as these are used in the rational formula. The curves are also used

as input to rainfall-runoff models that are used to create large floods for bridge and spillway

designs. Soil-erosion prevention practices and irrigation-management procedures also are

based on reliable predictions of rainfall intensities. The IDF relationship is an important

hydrologic tool which will bridge the gap between the design need and the unavailability of

design information mainly in water resources projects. Due to lack of these IDF relationships,

the planning and design of water resource development, irrigation and drainage schemes, soil

conservation programs and other projects are based on some assumption and empirical data

from other countries (Nhat et al., 2006).

In the highland of Ethiopia (area more than 1500 meter above sea level), which covers 40% of

the land mass of the country but account for 95% of the cultivated land, accommodating 88%

of human population and 70% of livestock population (Constable, 1984), due to limited

availability of IDF curve under climate change, the planning and design of water resource

3

development, irrigation and drainage schemes, soil conservation programs and other similar

projects are based on historic climate information and empirical data from other countries.

Hence, investigating how the climate change impacts on IDF is necessary.

Recently numerous studies have been made: Abeba (2012) developed IDF curves under

changing climate for Chiro and Hurso stations of Oromia region, Tesfaye (2011) developed

IDF curves under changing climate for Eastern Haraghe Zone, Elias (2010) produced IDF

curves and parameters for Ilubabor zone, Shimelis (2008) produced IDF curves and

parameters for Eastern Oromia, and Chali (2008) developed regional IDF curves for the

Oromia Region for some given durations and frequencies, which are now still in use for the

stations. Assefa (2008) also developed IDF curve for southern Nation, Nationalities and

people’s region. However, in central highland of Ethiopia due to limited availability of IDF

curve under climate change scenario, the design standards of most hydraulic structures are

based on historic climate information and required level of protection from natural

phenomena. With changing climate, it is necessary to methodically review the current design

standards for water management infrastructures and present information in order to prevent

the possibility of failure of infrastructure performing below its designed guideline and high

cost implication due to over design.

Therefore, the overall objective of this study was to analyse the rainfall intensity-duration-

frequency under changing climate scenario for design and their modifications of hydraulic

structures in order to take into consideration the likely impact of changing climatic conditions

for Addis Ababa, Fiche and Kachisi stations of central Highland of Ethiopia by assessing the

change in IDF curves for two climate scenarios (A2 and B2). The specific objectives of the

study were:

To analyze climate change scenarios (rainfall) for some selected stations (Addis

Ababa, Fiche and Kachisi) in central highland of Ethiopia.

To develop rainfall IDF relationships for some selected stations in central highland of

Ethiopia under changing climate conditions and compare with the existing rainfall

intensity duration frequency relationship.

4

2. LITERATURE REVIEW

2.1. Climate Change

Climate change is one of the hottest topics (literally, if we talk about global warming) of

current literature on climate. The most prominent publication on this topic is by the

Intergovernmental Panel on Climate Change (IPCC), which releases a vast and

comprehensive overview on climate change every 6 years, with the Fourth Assessment Report

(AR4) published in 2007 (IPCC, 2007a).

In the AR4 and other "Climate Change" reports, most attention is focused on the changes in

temperature and rainfall. Climate change in the IPCC usage refers to any change in climate

over time, whether due to natural variability or as a result of human activity. Also in the

United Nation Framework Convention on Climate Change (UNFCCC), climate change refers

to a change of climate that is attributed directly or indirectly to human activity that alters the

composition of the global atmosphere and that is in addition to natural climate variability

observed over comparable time periods (IPCC, 2007b).

Climate change has the potential to affect many sectors in which water resource is a major

one. The major drivers are changing temperature and rainfall regimes, and increasing global

sea level and associated impacts. Rainfall changes are expected to differ across the country,

with some areas receiving more and others receiving less, as suggested by the model

simulations. There may also be changes in seasonal patterns and extremes of rainfall.

Depending on location, these possible changes have led to concerns that droughts and floods,

defined relative to past experiences, will occur more frequently and (or) be more severe under

future climate conditions (IPCC, 2007b).

2.2. Climate Models

Currently, one of the best ways to study the effects of climate change is to use global

circulation models (GCM). These models are the current state of the art in climate science.

The aim is to describe the functioning of the climate system through the use of Physics, Fluid

5

Mechanics, Chemistry, as well as other sciences. All global circulation models discretize the

planet and its atmosphere into a large number of three dimensional cells (Kolbert, 2006) to

which relevant equations are applied.

Climate models relate basic representations of the physical laws leading mass and energy

interactions in the ocean-atmosphere system enabling us to better understand and predict the

outcome of greenhouse gas (GHG) emissions. The mathematical models generally used to

approximate the present climate and project future climate with forcing by GHG and aerosols

are commonly referred to as Global Circulation Model (GCM). The most difficult climate

models, termed coupled atmosphere-ocean universal circulation models (AOGCM), absorb

pairing comprehensive three-dimensional Atmospheric General Circulation Models (AGCMs)

with Ocean General Circulation Models (OGCMs), with sea-ice models, and with models of

land-surface processes. For AOGCMs, in sequence about the state of the atmosphere and the

ocean closest to, or at the sea surface, is used to compute interactions of heat, wetness and

energy between the two equipment (McAvaney et al., 2001).

In majority, GCMs simulate global and continental level processes and give a reasonably

exact symbol of the normal environmental climate. Regional Climate Models (RCMs)

simulate sub-GCM grid-scale climate features dynamically using time-varying atmospheric

conditions supplied by a GCM bounding a specified area. The most recent models may

contain representations of aerosol processes and the carbon cycle. The improvement of these

extremely difficult joined models goes hand in hand with the accessibility of constantly larger

and quicker computers to run the models. Climate simulations involve the largest, most

capable computers available (Baede et al., 2001).

2.3. Defining Climatic Baseline

A baseline period is needed to define the observed climate with which climate change

information is usually combined to create a climate scenario. When using climate model

results for scenario construction, the baseline also serves as the reference period from which

the modeled future change in climate is calculated. Availability of the required climate data

6

governs the choice of baseline period. There may be climatologically reasons to favour earlier

baseline periods over later ones. In this regard, the “ideal” baseline period would be in the 19

century when anthropogenic effects on global climate were negligible. Most impact

assessments; however, seek to determine the effect of climate change with respect to “the

present”, and therefore recent baseline periods such as 1961 to 1990 are usually preferential.

Advantage of using 1961 to 1990 is that observational climate data coverage and availability

are generally better for this period compared to earlier ones (Mearns et al., 2001).

2.4. Methods for Generating Regional Climate Information

Atmosphere-Ocean General Circulation Models (AOGCMs) constitute the primary tool for

capturing the global climate system behaviour. They are used to investigate the processes

responsible for maintaining the general circulation and its natural and forced variability, to

assess the role of various forcing factors in observed climate change and to provide

projections of the response of the system to scenarios of future external forcing. As AOGCMs

seek to represent the whole climate system, clearly they provide information on regional

climate and climate change and relevant processes directly. For example, the skill in

simulating the climate of the last century when accounting for all known forcings

demonstrates the causes of recent climate change and this information can be used to

constrain the likelihood of future regional climate change. Because of their significant

complexity and the need to provide multi-century integrations, horizontal resolutions of the

atmospheric components of the AOGCMs in the Multi-Model Data set (MMD) range from

400 to 125 km. Generating information below the grid scale of AOGCMs is referred to as

downscaling (Christensen et al., 2007a).

Downscaling techniques have emerged as a way of connecting meso-scale atmospheric

variables to grid and sub-grid scale surface variables. There are two main approaches for

deriving information on local or regional scales from the global climate scenarios generated

by GCMs (Wilby and Wigley, 1999). Numerical downscaling (also known as dynamic

downscaling) involving a nested regional climate model (RCM) and statistical downscaling

employing statistical relationship between the large-scale climatic state and local variations

derived from historical data records.

7

2.4.1. Statistical downscaling model

Empirical statistical downscaling methods use cross-scale relationships that have been derived

from observed data, and apply these to climate model data. Statistical downscaling methods

have the advantage of being computationally inexpensive, able to access finer scales than

dynamical methods and applicable to parameters that cannot be directly obtained from the

RCM outputs. They require observational data at the desired scale for a long enough period to

allow the method to be well trained and validated (Christensen et al., 2007a). The main

drawbacks of SD methods are that they assume the statistical relationships identified for the

current climate will remain valid under changes in future conditions (Giorgi et al., 2001).

Moreover, it cannot take account of small-scale processes with strong time-scale

dependencies e.g., land-cover changes (Christensen et al., 2007a).

The statistical downscaling model (SDSM) enables the construction of climate change

scenarios for individual sites at daily time-scales using grid resolution of GCM output, and is

the first tool of this type offered to the broader climate change impacts community. The

statistical relationship between large scale climatic factors (predictors) and local variables

(predictands) is firstly established, then local change information can be simulated and

climate change scenarios in the future can be obtained. According to Wilby and Wigley

(1999), the following assumptions are involved in statistical downscaling: (i) suitable

relationships can be derived between large scale and small scale predictor variables (ii) these

observed empirical relationships are valid under future climate conditions and (iii) the

predictor variables and their change are well characterized by GCMs. A diverse range of

statistical downscaling techniques have been developed over the past few years and each

method generally lies in one of the three categories, namely regression(transfer function)

methods , stochastic weather generators and weather typing schemes.

2.4.2. Dynamical downscaling

Dynamical downscaling uses high-resolution climate models to represent global or regional

sub-domains, and uses either observed or lower-resolution AOGCM data as their boundary

conditions. Dynamical downscaling has the potential for capturing meso scale nonlinear

effects and providing coherent information among multiple climate variables. These models

8

are formulated using physical principles and they can credibly reproduce a broad range of

climates around the world, which increases confidence in their ability to downscale

realistically future climates (Christensen et al., 2007a). Dynamical downscaling involves the

nesting of a higher resolution Regional Climate Model (RCM) within a coarser resolution of

GCM They can resolve smaller–scale atmospheric features such as aerographic rainfall or

low–level jets better than the host GCM. Furthermore, RCMs can be used to explore the

relative significance of different external forcing’s such as terrestrial–ecosystem or

atmospheric chemistry changes (O'Hare et al., 2005). The main drawbacks of dynamical

models are their computational cost and that in future climates the parameterization schemes

they use to represent sub-grid scale processes may be operating outside the range for which

they were designed (Christensen et al., 2007a).

2.5. Climate Change Scenarios

Among the wide range of GCM models HadCM3 (Hadley Centre for Climate Prediction and

Research, England), ECHAM4 (Max Plank Institute, Hamburg, Germany), CGCM2

(Canadian Centre of Climate Modelling and Analysis), GFDL_R30 (Geophysical Fluid

Dynamics Laboratory & NOAA), and CCSR/NIES (Centre for Climate Systems Research &

Japanese National Institute for Environmental Studies) are commonly used. The results of

these models are made available on websites for impact studies by the scientific community.

Each model has a unique approach to modelling these complex systems, differing in their

levels of resolution and degree of specificity. Very recent GCMs are coupled models that

include four principal components: atmosphere, ocean, land surface, and sea ice. The GCMs

also make use the future forcing scenarios to produce the ranges of the climate change. These

scenarios represent a set of assumptions about population growth, economic and technological

development, and socio-political globalization. Special Report on Emission Scenarios (SRES)

recommends choosing among the following six emission scenarios: A1F1, A1T, A1B, A2,

B1, and B2 (details are discussed in section 2.5.2).

Scenarios are neither predictions nor forecasts of future conditions. Rather they describe

alternative possible futures that conform to sets of circumstances or constraints within which

9

they occur (Mearns et al., 2001). There are two types of scenario developments: climatic and

non-climatic (IPCC-TGCIA, 1999). It is a probable and often simplified representation of the

future climate, based on an internally consistent set of climatological relationships that has

been constructed for explicit use in investigating the potential consequences of anthropogenic

climate change, often serving as input to impact models. Climate projections often serve as

the raw material for constructing climate scenarios, but climate scenarios usually require

additional information such as about the observed current climate. A climate change scenario

is the difference between a climate scenario and the current climate (IPCC, 2007a).

2.5.1. Construction of climate change scenarios

The true purpose of scenarios is to illuminate uncertainty and to represent future climate that

has been constructed for explicit use in investigating the potential impacts of anthropogenic

climate change. Such representation should account for both human-induced climate change

and natural climate variability. Climate scenario is distinguishable from a climate projection,

which refers to a description of the response of the climate system to a scenario of greenhouse

gas and aerosol emissions, as simulated by a climate model. Climate projections alone rarely

provide sufficient information to estimate future impacts of climate change; hence they make

use of climate projections by manipulating model outputs and combining them with observed

climate data. The types of climate variables needed for quantitative impacts studies vary

widely. The six main variables commonly required are: maximum and minimum temperature,

rainfall, incident solar radiation, relative humidity, and wind speed (Mearns et al., 2001).

2.5.2. Emissions scenarios

Future emissions of GHG and aerosols into the atmosphere depend very much on factors such

as population and economic growth and energy use. In third assessment report, the IPCC

(2001) commissioned a special report on emissions scenarios (SRES), in which about forty

different emissions scenarios were developed. These could be classified into four families,

depending on whether or not the scenarios had a global or regional development focus or were

driven by environmental rather than economic considerations. The starting point for each

projection was a ‘‘storyline’’, telling the way world population, economies, political structure

10

and lifestyles may evolve over the next few decades. The storylines were grouped into four

scenario families and led in the end to the construction of six SRES marker scenarios (one of

the families has three marker scenarios, the others one each). The four families can be briefly

characterized as follows (Nakicenovic and Swart, 2000):

A1: Very rapid economic growth with increasing globalization, global population that peaks

in mid-century and declines thereafter, an increase in general wealth, with convergence

between regions and reduced differences in regional per capita income. Materialist-

consumerist values predominant with rapid technological change. Three variants within this

family make different assumptions about sources of energy for this rapid growth: fossil

intensive (A1FI), non-fossil fuels (A1T) or a balance across all sources (A1B). Balanced is

defined as not relying too heavily on one particular energy source, on the assumption that

similar improvement rates apply to all energy supply and end use technologies.

B1: Same population growth as A1, but development takes a much more environmentally

sustainable pathway with global-scale cooperation and regulation. Clean and efficient

technologies are introduced. The emphasis is on global solutions to achieving economic,

social and environmental sustainability.

A2: Heterogeneous, market-led world, with less rapid economic growth than A1, but more

rapid population growth due to less convergence of fertility rates. The underlying theme is

self-reliance and preservation of local identities. Economic growth is regionally oriented, and

hence both income growth and technological change are regionally diverse.

B2: Population increases at a lower rate than A2 but at a higher rate than A1 and B1, with

development following environmentally, economically and socially sustainable locally

oriented pathways. In terms of climate forcing, B1 has the least effect, followed by B2. The

greatest forcing is caused by the fossil fuel-intensive A1F1 scenario, followed by A2 (IPCC,

2001).

11

2.6. Climate Change in Ethiopia

Ethiopia is the second most populous country in Africa just next to Nigeria (List of African

countries by population, 2013), 85% of the people depend mainly on agriculture for their

livelihoods. Due to social, economic and environmental factors, Ethiopia is extremely

vulnerable to the impacts of climate change. In particular, high levels of poverty, rapid

population growth, a high level of reliance on rain-fed agriculture, high levels of

environmental degradation, chronic food insecurity and frequent natural drought cycles

increase climate change vulnerability in this country (NMSA, 2007).

In correlation with the global trends, an analysis of Ethiopian metrological data from 1951-

2005 showed a temperature increase of around 0.37oC every ten years. This trend is set to

increase with predictions indicating a further 1oC increase by 2020 and between 2-4

oC

increases by the 2080s. Whilst historical variability makes it harder to trace trends on rainfall.

Both climate science projections and community perceptions highlight the likelihood that

rainfall patterns will change (ACCRA, 2011). Similarly, (NMSA, 2007) stated the notable

impact of climate change on Ethiopia’s temperature and precipitation: average annual

temperatures nationwide are expected to rise 3.1° C by 2060, and 5.1°C by 2090. In addition,

precipitation is projected to decrease from an annual average of 2.04 mm/day (1961-1990) to

1.97 mm/day (2070-2099), for a cumulative decline in rainfall by 25.5 mm/year. The

vulnerability of Ethiopia to climate change impact is a function of several biophysical and

socioeconomic factors. Although the name ‘’Water Tower of Africa’’ has been given to

Ethiopia, agriculture is overwhelmingly dependent on the timely onset, amount, duration, and

distribution of rainfall.

According to Centre for Global Development (CGD, 2011) report, Ethiopia is ranked 11th

of

233 countries and other political jurisdictions in terms of its vulnerability to physical climate

impacts, and 9th

in terms of overall vulnerability, which are physical impacts adjusted for

coping ability.

12

2.7. Characteristics of Rainfall Event

The characteristics of rainfall that are important to hydrologic design problems are its

intensity, duration and frequency of occurrence. Intensity is defined as the time rate of rainfall

depth and is commonly given in the units of millimetres per hour. The greater the intensity of

rainfall, the shorter is the duration of the rainfall. In other words, very intense storms occur for

a short duration, and as the duration of a storm increases, its intensity decreases. Further, a

storm of any given duration will have a large intensity if its return period is large. In many

design problems related to watershed management it is necessary to know the rainfall

intensities of different durations and different return periods (Arora, 2002).

All precipitation is measured as the vertical depth of water that would accumulate on a flat

level surface if all the precipitation remained where it fell. A variety of rain gauges have been

devised to measure precipitation. All first-class weather stations utilize gauges that provide

nearly continuous records of accumulated rainfall with time. These data are typically reported

in either tabular form or as automatically recorded rainfall charts. Three rainfall

characteristics are important and interact with each other in many hydrologic design

problems. For use in design, the three characteristics are combined, usually graphically into

the Intensity-Duration-Frequency (IDF) curve. Rainfall intensity is graphed as the ordinate

and duration as the abscissa. One curve of intensity versus duration is given for each

exceedence frequency. It is general characteristics of the rainfall that as the rainfall duration

increases, the intensity decreases and vice versa. On contrast, the rainfall intensity increases

with increase in return period and vice versa (Suresh, 2005).

2.8. Daily Rainfall Disaggregation Methods

2.8.1. The hytos model

The Hyetos model disaggregates daily rainfall data at a single site into hourly data based only

on a temporal stochastic disaggregation scheme. It uses the Bartlett–Lewis rainfall model as a

background stochastic model for rainfall generation. Then it uses a repetit ion scheme to

derive a synthetic rainfall series, which resembles the given series at the daily time scale, and,

13

subsequently, the proportional adjusting procedure, to make the generated hourly series fully

consistent with given daily series (Santos et al.,1992).

The understanding of hydrological processes that occur in nature is one of the most important

tasks for both hydrologists and civil engineers for the design of almost all hydrological

applications and civil engineering works. Rainfall is the main input to all hydrological

systems, and a wide range of hydrological analyses, for flood alleviation schemes,

management of water catchments, water quality or ecological studies, require quantification

of rainfall inputs at both daily and hourly time scales (Koutsoyiannis, 2001).

The uniform method of daily rainfall distribution involves no stochastic methodology except

dividing the daily rainfall amount into 24 equal hourly values, the univariate (Hyetos) and

Multivariate Disaggregation of Rainfall (MuDRain) models involve procedures that are more

complicated. Disaggregation techniques have the ability to increase the time or spatial

resolution of certain processes, such as rainfall and runoff while simultaneously providing a

multiple scale preservation of the stochastic structure of the hydrologic processes. This

definition of disaggregation distinguishes it from downscaling, which aims at producing

hourly data with the required statistics but that do not necessarily add up to the observed

hourly data (Koutsoyiannis and Onof, 2000).

More recently, Koutsoyiannis (2001) studied the problem of multiple site rainfall

desegregations as a means for simultaneous spatial and temporal disaggregation at a fine time

scale and investigated the possibility of using available hourly information at one rain gage to

generate spatially and temporally consistent hourly rainfall information at several

neighbouring sites with significant cross-correlation coefficients between the rain gages. The

combination of spatial correlation and available single site hourly rainfall information enables

more realistic generation of the synthesized hyetographs that is the synthetic series generated

will resemble the actual one.

14

2.8.2. Rainfall ratio method

Based on studies of a large number of rainfall gauges in East Africa, the Rainfall Ratio

Method (Transport and Road Research Laboratory, Department of Environment, TRRL

Laboratory Report 623); was developed for the prediction of Storm Rainfall in East Africa by

Fiddes et al. (1974). The Rainfall Ratio Method is used to estimate the rainfall depth to be

distributed at required duration based on a 24 hour rainfall (Ethiopian road authority drainage

design manual 2002). For the rainfall ratio method, the following relationship was developed:

n

ttb

btRR

24

2424

(2.1)

where: Rt is rainfall in a given duration ‘t’ (hr), R24 Rainfall in 24 hours, t: time (hr), n and b

are constant. Based on studies of a large number of rainfall gauges in East Africa, the average

value of b was found to be 0.3 and n value ranges from 0.78 to 1.09. Assuming that the

diurnal variations of these constants (b and n) are constant, the daily rainfall can be converted

into smaller hours using rainfall ratio method. Rainfall ratio method is widely used in Ethiopia

where there are limitations of rainfall intensity records (Nigatu, 2011).

2.9. Rainfall Intensity Duration Frequency Analysis

An IDF curve is a tool that characterizes an area’s rainfall pattern. By analyzing past rainfall

events, statistics about rainfall re-occurrence can be determined for various standard return

periods. Intensity duration frequency (IDF) analysis is used to capture the essential

characteristics of point rainfall for shorter durations. The IDF relationships are used to

calculate design rainfall required in many practical applications such as in planning, designing

and evaluation of water resource systems, drainage works, etc. In developing these

relationships, the estimates of rainfall intensity for a given duration (expressed in minutes or

hours) and frequency (or return period expressed in years) can be obtained from frequency

analysis employing various probability distributions. Once this basic information is obtained,

the magnitude of various frequencies can be easily estimated. The analysis of rainfall

intensities will be expressed using different methods. These are the IDF mathematical form

equation, and families of IDF curve (Adamowski and Bougadis, 2003).

15

Analysis of gauged data permits an estimate of the peak rainfall in terms of its probability or

frequency of exceedence at a given site. The purpose of frequency of an annual series is to

obtain a relation between the magnitudes of the event and its probability of exceedence. The

probability analysis may be made either by empirical or by analytical methods. The simple

empirical procedures give good results for small extrapolations only, as extrapolation

increases, the error also increases. However, for obtaining better result for larger extrapolation

theoretical probability distributions have to be used. In general, the greater the number of

parameters, the better is the fit that can be obtained to a single data series. But this does not

necessarily mean that the underlying population distribution is better represented. A

probability distribution can also be characterized by its mean (μ), variance (σ2) and coefficient

of skewness (γ). For some distributions, these statistics are identical to the parameters in the

probability density function.

The study of extreme events involves the selection of largest or smallest value from historical

observations or records. For instance study of IDF curve utilizes, the largest extreme value of

rainstorms observed during the specified duration in each year at a given station out of so

many thousands of observations. Future floods cannot be predicted with certainty. Therefore,

their magnitude and frequency are treated using probability concepts. In a similar way, the

analysis of rainfall data for computation of expected rainfall of a given frequency is

commonly done by utilizing different probability distributions. Thus, for determining extreme

flood events, specific extreme value distributions are assumed, and the required statistical

parameters are determined from the available data from which the flood magnitude for any

specific return period can be determined. The basic statistical equation is given by:

X = X + Kσ (2.2)

where X is any variable, X is means of variate, σ is standard deviation of the variate and K is

frequencies factor (a constant). This equation has been shown by Chow (1992) to be

governing equation for almost all theoretical frequency distribution functions.

The choice of frequency distribution is influenced by many factors, such as methods of

discrimination between distributions, methods of parameters estimation, the availability of

16

data, etc. Generally, there is no general global agreement as to a preferable technique of

model choice and no single one distribution accepted universally. However, the most

commonly employed probability distributions for the predictions of extreme storm values are

(Haan, 1977):

i. Normal distribution

ii. Log-nomal distribution

iii. Gumbelʼs Extreme Value Type I (EVI) distribution and

iv. Log Pearson Type III distribution

2.9.1. Normal distribution

The normal distribution is a classical mathematical distribution commonly used in the

analysis of natural phenomena. The normal distribution has a symmetrical, unbounded, bell-

shaped curve with the maximum value at the central point and extending from - ∞ to + ∞. For

the normal distribution, the coefficient of skewness is zero. The probability density function

(PDF) of this distribution model according to Suresh (2005) is given by:

5.0

2

)2()(

2

2

S

eXf

S

XX

X (2.3)

Note that only two parameters are necessary to describe the normal distribution: the mean

value, ( X ) and the standard deviation, (S).

One disadvantage of the normal distribution is that it is unbounded in the negative direction

whereas most hydrologic variables are bounded and can never be less than zero. For this

reason and the fact that many hydrologic variables exhibit a pronounced skew, the normal

distribution usually has limited applications.

2.9.2. Log-normal distribution

The log-normal distribution has the same characteristics as the normal distribution except that

the dependent variable, X, is replaced with its logarithm (Y = log(X)). The characteristics of

17

the log-normal distribution are that it is bounded on the left by zero and it has a pronounced

positive skew. These are both characteristics of many of the frequency distributions that result

from an analysis of hydrologic data. The logarithmic transformation of the normal distribution

is given as:

5.0

2

)2()(

2

2

Y

S

YY

XS

eXf

Y

0X (2.4)

where Y = log(X), Y and SY are the mean and standard deviation of the sample.

The log-normal distribution has advantage over the normal distribution that it is bounded as x

> 0 and the log transformation tends to reduce the positive skewness.

2.9.3. Gumbel extreme value distribution

The Gumbel extreme value frequency distribution also referred to as the Gumbel extreme

value type I distribution (EVI) is the most widely used probability distribution model for

extreme values in hydrologic and meteorological studies and has received the highest

application for estimating large events in various part of the world. This distribution has been

used for rainfall depth-duration-frequency studies (Garg, 1999).

The Gumbel extreme value type I asymptotic distribution for maximum or minimum events is

the limiting mode for the distribution of the maximum or minimum of ‘n’ independent values

from an initial distribution whose right or left tails is unbounded and is an exponential type.

According to Reddi (2002) theory of maximum events, the probability of occurrence of an

event equal to or larger than a value Xo is:

Yeo eXXP

1)( (2.5)

where )( XY is called the reduced variate. The mean and standard deviation of the

variable μ and δ are related to its parameters through the following equations (Reddi, 2002):

18

28255.1 (2.6a)

45005.0 (2.6b)

where α and β are called the parameters of the distribution. The cumulative distribution

function is given by:

XeXF

Xe

)( (2.7)

YeeXF

)( (2.8)

It may be noted that β is the mode of the distribution point of maximum probability density

and ‘X’ is the variant (historically observed data).

Simplifying and solving equation (2.4) for Y gives:

)(

1lnln

XFY (2.9.a)

Substituting F(X) of equation (2.8) into equation (2.4) yields:

PXF 1)(

1lnln

1

1lnln

T

T

PYT (2.9.b)

Therefore, for the extreme value distribution, XT is related to YT as follows:

XY TT XY (2.10)

Hence,

XTTT

T SKXXY

X

(2.11)

2.9.4. Log-pearson type III distribution

Log-Pearson type III distribution is a logarithmic transformation of the Gamma distribution. If

log x follows a Pearson Type III distribution, then x is said to follow a log-Pearson

distribution. It has a special feature that when log x is symmetric about its mean; the log-

19

Pearson distribution will be reduced to normal distribution. This distribution is the standard

distribution for frequency analysis of annual maximum floods and has got also wide

application in the analysis of rainfall intensities. The fit of the distribution to data can be

checked using the chi-square test or by probability plotting. The probability density function

is given by (Apipattanavis et al., 2005):

xx

eyxf

y

log)(

)()(

1

(2.12)

where λ, β, and ε are the scale, shape and location parameters of the distribution and y = log x,

)1()( ,

yS

,

2

)(

2

yCS

and ySy assuming the skewness CS (y) is

positive. The skew coefficient (CS (y)) is determined using the expression:

321)( 1

3

nnn

yyn

yC

n

iS (2.13a)

where n is number of observations and the parameters λ, β, and ε are used to compute the

mean μy, standard deviation δy, and coefficient of skew CS of sample estimates of the

population as follows:

μy = ε+ λ β, y , and 2)( yCS (2.13b)

This is referred to as the three parameter fit. Due to its performance in stochastic hydrology,

Log-Pearson type III distribution has been adopted in a number of countries as a standard

distribution for flood frequency analysis.

From the following general equation for any distribution form which the T-year event

magnitude can be computed:

XT = μ + KδX (2.14)

Where XT is event magnitude of the record, μ and δX are mean and standard deviation of the

series and K is the frequency factor defined by a specific distribution, is a function of the

probability level of X.

20

The log-Pearson type III distribution differs from most of the distributions discussed above in

that three parameters (mean, standard deviation, and coefficient of skew) are necessary to

describe the distribution. By judicious selection of these three parameters, it is possible to fit

just about any shape of distribution.

2.9.5. Frequency factor

For given distribution, a relationship can be determined between the frequency factor (K) and

the return period (T). This relationship can be expressed in mathematical terms or given by

table. The value of XT of a hydrologic event may be represented by the mean (μ) plus

departure of the variate (Δ XT) from the mean (Garg, 1999).

XT = μ + Δ XT (2.15.a)

Assuming the departure to be equal to the product of the standard deviation (δ) and the

frequency factor KT (i.e. Δ XT = δ KT) then, XT becomes:

XT = μ + KT δ (2.15.b)

The value ΔXT and KT are functions of the return period (T) and the type of probability

distribution to be used in the analysis. If the relationship of the data analysis is in the form of

Y = log X, the same style is applied to the statistics for the logarithm of the data using, YT = Y

+ KTSY and the required value of XT is found by taking the antilog of YT.

The relationship between the frequency factor (KT) and the return period (T) is given for

different type of distribution as follows (Suresh, 2005):

For normal distribution

T

T

XK (2.16)

where KT is the same as the standard normal value Z.

21

For lognormal distribution, the following formula will be used for determining the

frequency factor (KT) (U.S. Army Corps of Engineers, 1994; Bhakar et al., 2006):

)0013.01893.04328.11(

)0103.08028.0516.2(32

2

www

wwwzKT

(2.17)

where w is intermediate variable and p is probability of exceedence; w will be calculated

using the following formula:

21

2

1ln

pw (0 < p ≤ 0.5) (2.18)

when p > 0.5, 1- p is substituted for p and the value of z is computed by equation (2.17) is

given a negative sign.

For Gumbel Extreme Value type I distribution, the frequency factor (KT) will be

computed by using the following formula (Das, 2004):

(2.19)

where YT, μy, and δy are log transfer of the variable, the mean, and the standard deviation

respectively. The value of the reduced variate YT for a given return period T is given as:

(Reddi, 2002).

1lnln

T

TYT (2.20)

For log-Pearson type III distribution: the frequency factor corresponding to the annual

maximum rainfall magnitude as (Suresh, 2005; Adeboye and Alatise, 2007).

(2.21)

(2.22)

where KT is frequency factor used for Log Pearson type III distribution, Cs is the coefficient

of skewness, and z is standard normal variable or frequency factor (when Cs= 0, then KT = z).

y

yT

T

YK

5432232

31)1()6(

31)1( kzkkzkzzkzzKT

6Csk

22

2.9.6. Probability plotting position

Probability plotting position refers to the probability value assigned to each pieces of data to

be plotted. The main purpose of probability frequency analysis is to obtain a relation between

the magnitude of a storm and its probability of occurrence. A number of different formulas

have been proposed for computing plotting position probabilities, with no agreement on the

preferred method. The simplest technique is arranging the event in descending order of

magnitude and assigning the rank number (m) to each event. The severest event will be placed

at the top with its ranking as 1. The lightest event will be placed at the last place and its

ranking will also be n. The one most commonly used formula is the Weibull formula given by

(Cordes and Hotchkiss, 1993):

m

nT

n

mXXP m

1

1)(

(2.23)

where m is rank number, n number of observation and T is return period.

The lists of plotting position formulas proposed by different hydrologists are presented in

Table 2.1. (Garg, 1999, and UNESCO, 2005).

Table 2.1. Plotting position formula

Method Formula

California m / n

Weibull m / (n+1)

Gringorten (m-0.44) / (n+0.12)

Hazen (m-0.5) / n

Cunnane (m-0.4)/(n+0.2)

Blom (m-3/8) / (n+1/4)

Chegodayev (m-0.3) / (n+0.4)

23

2.10. Intensity Duration Frequency Relationships

Intensity Duration Frequency relationship provides essential information for planning,

designing and evaluation of water resource systems, drainage works etc. The IDF

relationships enable estimation of intensity of rainfall corresponding to any required rainfall

duration and frequency. Once this basic information is obtained the magnitude of various

frequencies can be easily estimated. The intensity of rainfall decreases with the increase in

storm duration. Further a storm of any given duration will have a larger intensity if its return

period is large (Subramanya, 1994). The analysis of rainfall intensities will be expressed using

different methods. These are the IDF mathematical form equation, and families of IDF curves.

2.10.1. Mathematical form of IDF

IDF curves are mathematical equations which express the relation between intensity, duration

and return period of rainfall. The setting up of IDF curves takes place in three stages:

extraction of maxima time series for several rainfall durations, fitting of a distribution in each

maxima time series and finally estimation of the IDF curve parameters. For return period

exceeding the size of the sample, the annual maximum rainfall values can be extrapolated

either from the frequency distribution graph or estimated using either equation 2.11 or 2.15.b.

The IDF relationship can be expressed in the form of empirical equation rather than reading

the rainfall intensities from graphs or maps. From the mathematical relationship, the IDF

parameter can be estimated. The empirical formula is given in the following form (WMO,

1994):

n

r

T

TbaPi

)1(

)(log

(2.24)

where Pi is the maximum mean rainfall intensity for duration of T, Tr is the return period and

a, b and n are parameters that vary from station to station with selected frequency of

occurrence. In addition to this formula, Koutsoyiannis et al., (1998) also provided another

equation of the form:

24

dI (2.25)

Where ω, ν, θ and η are non-negative coefficients with νη ≤ 1 and θ and η are to be estimated

and d is rainfall duration.

Another generalized mathematical relationship of IDF for a given frequency was given by

Desa et al., (2006) as follows:

ev bd

aI

(2.26)

where a, b, e and v are non-negative coefficients with ν = 1 and e = 1 and a and b are to be

estimated and d is rainfall duration. Simplified form of the above equation was given by

adopting either one or two of the coefficients ν = 1, e = 1 and b = 0. Therefore, taking ν to be

1, the above equation is reduced to the following form (Nhat et al., 2006):

ebd

aI

(2.27)

Where I is intensity of rainfall (mm/hr), d is the duration (minutes); a, b and e are the constant

parameters depending on return period.

2.10.2. Parameter estimation methods

There are two methods of parameter estimation suggested by Koutsoyiannis et al., (1998).

These are the robust estimation and the one-step least squares methods based on optimization

technique. The second method estimates all parameters (θ, η and ω) in one step, by

minimizing the total square error of the fitted IDF relationship to the data. The minimization

of the total error can be performed using the embedded solver tools of the MS-Excel spread

sheet by a trial and error procedure.

There are also various IDF Curve-Fit software developed to solve the parameters (a, b, and c)

from a set of pairs of data values of an intensity-duration equation of the general form

(EXACT, 2006):

25

c

d bT

aI

(2.28)

where I is rainfall intensity (mm/hr), Td is time duration (minute), a is coefficient with the

same unit as I, b is time constant (minute) and c is an exponent usually less than 1.

Generally, equation (2.28) is identical to equation (2.27) which indicates the parameters d and

e in equation (2.27) are equivalent to Td and c of equation (2.28).

According to Bhakar et al., (2006), Chi-square (X2) test is a commonly used test for

determining the goodness of fit and is expressed as follows:

)(

))()(( 2

1

2

xip

xipxifnX s

m

i

c (2.29)

where m is the number of intervals, n fs(xi) is the observed number of occurrences in interval i

and n p (xi) is the corresponding expected numbers of occurrences in interval i.

According to Haan (1997) the number of classes should be 5 – 20 classes and also the class

interval should not exceed one-fourth to one-half of the standard deviation of the data. Hence,

the resulting calculating values of chi-square( cX 2 ) can be compared with a probability

distribution statistical (tabulated) values of chi-square( 12 ,vX ). In the test, the degree of

freedom ν is given by ν = m-p-1 (where ‘m’ is the number of intervals and ‘p’ is the number

of parameters used in fitting the proposed distribution which depending on that of the

distribution fitted. A confidence level is chosen for the test. It is often expressed as 1-α, where

‘α’ is termed as the significant level. A typical value for the confidence level is 95 percent.

The null hypothesis for the test is that the proposed probability fits the data adequately. This

hypothesis is rejected if the value of cX 2 (calculated) is larger than a limiting value, 12 ,vX

(tabulated) which is determined from the X2 distribution with ν degree of freedom at 5 % level

of significance. Otherwise it is accepted.

26

2.10.3. Evaluation of model

Model simulations can be evaluated by using regression coefficient (R2). The regression

coefficient (R2) is the square of the Pearson product–moment correlation coefficient and

describes the proportion of the total variance in the observed data that can be explained by the

model. The closer the value of R2 to 1, the higher is the agreement between the simulated and

the measured values. The coefficient of determination (R2) is used to check the accuracy of

the model output which is given by Krause (2005):

2

1

2

1

2

12

n

i

i

n

i

i

n

i

ii

PPOO

PPOO

R

(2.30)

where n is number of compared values, O is observed data, O is observed mean, P is

simulated data and P is simulated mean.

The range for R2 is from zero to one. The closer R

2 is to one, the better the regression

equation “fits” the data. Since 0 ≤ R2 ≤ 1, then -1 ≤ R ≤ 1. In fact, R is commonly called the

correlation coefficient which is a measure of the degree of linear association between

observed and predicted observations (Haan, 1977).

Nĕmec (1973) provided the values of coefficient of correlation as:

R = 1 Direct correlation

0.6 < R < 1 Good direct correlation

0 < R < 0.6 Insufficient direct correlation

R = 0 No correlation

-0.6 < R < 0 Insufficient reciprocal correlation

-1 < R < -0.6 Good reciprocal correlation

R = -1 Reciprocal linear correlation

The Nash and Sutcliffe coefficient (NSE) was used to evaluate the measure of efficiency that

relates the goodness-of- fit of the model to the variance of measured data. NSE can range

from - ∞ to 1 and an efficiency of 1 indicates a perfect match between observed and simulated

values (Moriasi et al., 2007). Optional for monthly time steps that NSE values between 0.75

27

and 1 is very good and NSE-value between 0.65 and 0.75 is good. The NSE is defined as one

minus the sum of the absolute squared differences between the predicted and observed values

normalized by the variance of the observed values during the period under investigation (Nash

and Sutcliffe, 1970).

N

i i

N

i ii

NS

OO

POE

2

2

)(

)(1

(2.31)

where n is number of compared values, O is observed data, O is observed mean, P is

simulated/ predicted data.

The regression coefficient (R2), and the Nash and Suttcliffe (1970) simulation efficiency (ENS)

can be checked in accordance to (Santhi et al., 2001) recommendation (R² >0.6 and ENS >

0.5).

28

3. MATERIALS AND METHODS

3.1. Description of the Study Area

The study was carried out in Addis Ababa, Fiche and Kachisi Meteorological Stations which

are parts of central highland of Ethiopia. Central highland of Ethiopia is characterized by

undulating topography and mountainous terrain. The highlands of Ethiopia are known as

most intense population density and of greatest livestock density. The area is also known as

the greatest land degradation. The Ethiopian highlands reclamation study (EHRS) concluded

that water erosion (sheet and rill) was the most important process and erosion rates were

estimated at 130 tons/ha/yr for cropland and 35 tons/ha/yr average for all land in the highlands

(FAO, 1986). The current rate of deforestation is estimated at 62,000 ha/yr (World Bank

2001). Forests in general have shrunk from originally covering 65% of the country and 90%

of the highlands to 16% and 20% in 1950s respectively. The forest coverage further reduced

to 2.2% of the country and 5.6% of the highlands in 2000 (Leonard, 2003).

Figure3.1. Location map of the study area

The geographical locations of the meteorological stations are shown in Figure 3.1 and Table

3.1. Addis Ababa Meteorological Station (Tikur Anbesa National Observatory) is located at a

longitude of 38.75o E, latitude of 9.02

o N and altitude of 2386 masl. Fiche, the capital of north

29

Shewa zone of Oromia region is located at a longitude of 38.73o E, latitude of 9.77

o N and

altitude of 2784 masl on the main road from Addis Ababa to Bahirdar. Kachis, the capital of

Gindeberet woreda is found in west Shewa zone of Oromia region, located at a longitude of

37.86o E, latitude of 9.61

o N and altitude of 2557 masl.

Table3. 1. Locations of Meteorological Stations

No. Station

Name

Longitude

( 0E )

Latitude

( 0N )

Altitude

(meters)

Daily rainfall

data Available Remarks

1

Addis Ababa

(Tikur Anbesa) 38.75 9.02 2386 1970-2009 40 years

2 Fiche 38.73 9.77 2784 1986-2009 24 years

3 Kachisi 37.86 9.61 2557 1987-2009 23 years

Source: National Meteorological Service Agency (NMSA) of Ethiopia.

The rainfall pattern of central highland of Ethiopia experiences three seasons (tri-modal type)

with two rainfall peaks (where one peak is more prominent than the other), a small peak in

April and maximum peak in August (NMSA, 1996). The main rainy season (kremt) lies

during the months of June to September and another rain (belg) during the months of March

to May. The analysis of historical rainfall records (1970-2009 for Addis Ababa, 1986-2009

for Fiche and 1987-2009 for Kachisi) reveals that the mean monthly minimum and maximum

rainfall of 8mm and 290.7mm, 7.6mm and 340.6mm and 15mm and 404.5 mm for Addis

Ababa, Fiche and Kachisi respectively (Appendix Table 2) with annual mean rainfall of 1214,

1141.6 and 1787.7mm. The contributions of the seasonal rainfall for the stations are indicated

in Table 3.2 below. The “kiremt” rain (JJAS) contributes more than 70% of the annual rainfall

followed by “Belg” (MAM) which accounts for about 20%. July and August are the months

with maximum annual rainfall for the study sites. The monthly variability of the rainfall of the

study area is shown in Appendix Table 3.

Table3.2. The rainfall pattern of the study area

Station Mean Annual

rainfall (mm)

Seasonal Rainfall (mm)

Seasonal Percentage (%)

Belg

(MAM)

Kiremt

(JJAS)

Bega

(ONDJF)

Belg

(MAM)

Kiremt

(JJAS)

Bega

(ONDJF)

Addis Ababa 1214.0 239.3 864.1 110.6 20 71 9

Fiche 1141.6 180.6 869.9 91.0

16 76 8

Kachisi 1787.7 276.7 1335.2 175.8 15 75 10

30

3.2. Data Collection and Quality Control

The rainfall data of the three stations (Addis Ababa, Fiche and Kachisi) were collected from

National Meteorological Service Agency (NMSA) of Ethiopia. The stations were selected

based on the assumptions that the stations are first class (automatic recording) with long years

of rainfall data which were required for climate change study and minimum missing records.

Global Circulation Model (GCM) data for the selected models were downloaded from

www.pcmdi.llnl.gov/ipcc/about_ipcc.php website.

3.2.1. Filling missing data

Only Kachisi station has a missing value for which only one neighbouring meteorological

station (Harodoyo station) is available. Hence, normal ratio method (NR) was used to estimate

the missing values. The missing value (P) was computed using the universal formula (Chow

et al., 1988):

(3.1)

where, Wi is the weighted for the rainfall depth Pi, and Pi is rainfall at gauging i (neighbouring

station/ Harodoyo). The weighting factor (wi) is computed by:

(3.2)

where, Ai is the average annual normal catch at gauging station i (neighbouring station), Ax is

the average annual normal catch at station x (where data is missing) and n is the number of

neighbouring stations.

3.2.2. Consistency of data

Double mass curve method was used to carryout data quality analysis and to test the

homogeneity of rainfall data. The mass curves for three of the stations were found to be nearly

∑

Wi

http://www.pcmdi.llnl.gov/ipcc/about_ipcc.php

31

straight line (with R2 = 0.998 for Addis Ababa and R2 = 0.999 for Fiche and Kachisi)

indicating the consistency of the data.(Appendix Figures 1-3).

3.3. Building Climate Change Scenarios for Rainfall

3.3.1. Climate Change Scenarios

The climate change scenarios produced for this study were based on the outputs of GCM

results that were established on the SRES emission scenarios. As the objective was to get

indicative future climate ensembles, the scenarios were developed only for precipitation

values. The rest of the climate variables were assumed to be constant. The outputs of

HadCM3 GCM model for the A2 and B2 emission scenarios were used to produce the future

scenarios. The SDSM was adopted to downscale the global scale outputs of the HadCM3

model into the study site scale.

The future time scales from the year 2010 until 2099 were divided into three periods of 30

years and their respective changes were determined as percentages (for precipitation)

difference from the base period values. The details of all the methodologies used are

explained in the following sections.

3.3.2 General circulation model (GCM)

Very recent GCMs are coupled models that include four principal components: atmosphere,

ocean, land surface, and sea ice. The GCMs also make use the future forcing scenarios to

produce the ranges of the climate change. These scenarios represent a set of assumptions

about population growth, economic and technological development, and socio-political

globalization. SRES recommends choosing among the following six emission scenarios:

A1F1, A1T, A1B, A2, B1, and B2 (details were discussed in section 2.5.2).

For this study among the different GCM models, HadCM3 (Hadley Centre for Climate

prediction and Research, England) was used. Although, it is recommended to use the

Ensemble of different GCM model output to minimize the uncertainties, however, in this

study, due to limitations of time the output of only one GCM model (HadCM3) was used. The

32

model was selected because it was broadly functional in many climate change impact studies,

and it provides large scale daily predictor variables which could be used for Statistical

Downscaling Model (Wilby and Dawson, 2007).The model results were available for the A2

(medium-high emissions) and B2 (medium-low emission) emission scenarios and the results

were used to produce the future scenarios. Moreover, the A2 and B2 emission scenarios may

better represent the Ethiopia condition because it is in a medium range. For the two of these

emission scenarios three ensemble members (a, b, and c) are available where each refer to

different initial point of climate perturbation along the control run (Lijalem, 2006).

Currently data for ensemble ‘a’ only were available at the Canadian climate research Centre

therefore only A2a and B2a scenarios were considered in this study.

3.3.3. Statistical downscaling model (SDSM)

Due to their very coarse resolution, GCM model outputs cannot be directly applied for impact

studies at a watershed level. The temporal and spatial resolution disparity between the outputs

of the GCM models and the data needed for such impact studies could be adjusted by using

the so called “downscaling” technique (Palmer et al., 2004).

SDSM Version 4.2, was used to downscale climate information from coarse resolution of

GCMs to local or site level for rainfall scenario generation for the study area. The methods

outlined by Lines and Barrow (2002) and that was described in the SDSM ‘User’s Manual’,

which was downloaded from the SDSM website (http://www.aff.lboro.ac.uk/~cocwd/sdsm.html)

was adopted. SDSM uses linear regression techniques between predictor and predictand to

produce multiple realizations (ensembles) of synthetic daily weather sequences. The predictor

variables provide daily information about large scale atmosphere condition, while the

predictand describes the condition at the site scale. The SDSM software was used for data

quality control, screening of predictor variables, model calibration, weather generation,

statistical analysis, graphing model out puts and scenario generation.

http://www.aff.lboro.ac.uk/~cocwd/sdsm.html

33

3.3.3.1. Statistical downscaling model inputs

The SDSM predictor data files were downloaded from the Canadian Institute for Climate

Studies (CICS) website (http://www.cics.uvic.ca/scenarios/sdsm/select.cgi). Even though,

there was a possibility of selecting predictors from different available GCMs like (HadCM3

and CGCM1), only the HadCM3 GCM data files were downloaded. The predictor variables of

HadCM3 are provided on a grid box by grid box basis of size 2.5°N latitude x 3.75°E

longitude (275km X 412km). For this study, the three meteorological stations completely fall

in between 9.02°N to 9.77°N latitude and 37.86°E to 38.55°E longitude (Table 3.1). Hence,

predictor variables in the nearest grid box whose centre is 10°N latitude and 37.5°E longitude

represented by BOX_11X_31Y was downloaded for the HadCM3 GCM model data files,

which represents the study area.

Figure 3.2 The gird box for downloading predictor variables for the study area

http://www.cics.uvic.ca/scenarios/sdsm/select.cgi

34

3.3.3.2 Setting of the model parameter

Year Length: For the observed and the NCEP data the year length was set to be the default

366 days), which allows 29 days in February in leap years. However, as HadCM3 have model

years that do only consist of 360 days, the default value was changed to 360 days. Moreover,

the default base period of the model (1/1/961 to 31/12/1990) was changed to 1/1/1970-

31/12/1999, 1/1/1986-31/12/2001 and 1/1/1987-31/12/2001 for Addis Ababa, Fiche and

Kachisi stations respectively.

Threshold Value: for daily precipitation calibration the parameter was fixed to 0.1 mm/day

because the rainfall data of the stations were available to one decimal place. That means rainy

days below this threshold value was traced as dry days.

Variance Inflation: For the daily precipitation, the range of variation of the downscaled daily

weather parameters can be controlled by fixing the variance inflation. This parameter changes

the variance by adding/reducing the amount of “white noise” applied to regression model

estimates of the local process. The default value, which is 12 produces approximately normal

variance inflation (prior to any transformation). In calibrating the model the default variance

inflation which is 12 was kept constant to compensate by the change in the bias correction.

Bias Correction: Compensates for any tendency to over or under estimate the mean of

conditional processes by the downscaling model (e.g., mean daily rainfall totals). The default

value is 1.0, indicating no bias correction. The model was calibrated by varying the bias

correction from zero to two. The process stops when the graph of the statistical parameters of

the observed and the generated data have of the same pattern.

3.3.3.3. Predictor variables selection

The first step in the downscaling procedure using SDSM is to set up the empirical

relationships between the predictand variables (rainfall collected from stations) and the

predictor variables obtained from the National Centre for Environmental Prediction (NCEP)

re-analysis data for the current climate. Predictor variables selection involves the

identification of appropriate predictor variables that have strong correlation with the

predictand variable. This is the most challenging part of the work due to the temporal and

35

spatial variation of the explanatory power of each predictor (Wilby and Dawson 2007). The

selection was done at most care as the behaviour of the climate scenario completely depends

on the type of the predictors selected.

Annual analysis period was used which provided the predictor-predictand relationship all

along the months of the year. The parameter which tests the significance of the predictor

predictand relationship, significance level, was set to be equal to the default value (p<0.05).

Moreover, the process type that identifies the presence of an intermediate process in the

predictor-predictand relationship was defined. For daily precipitation, because of its

dependence on other intermediate process like on the occurrences of humidity, cloud cover,

and/or wet-days; the conditional process was selected.

Accordingly, identification of gridded predictors and single site predictands (observed data)

was done using seasonal correlation analysis, partial correlation analysis, and scatterplots.

Based on the criterion set for screening of appropriate predictors for the given site, of the

twenty-six predictor variables derived from the NCEP reanalysis data sets, predictor variables

that gave better correlation results at p<0.05 were chosen. As the strength of individual

predictors often varies markedly on a month by month basis, personal judgment was also

added in selecting the appropriate combination(s) of predictor(s) for a given season and

predictand.

3.3.3.4. GCM model calibration, validation and weather generator

The calibration process was carried out based on the outputs of the selection of the predictor

variables that used the NCEP data base of the selected grid box. The mathematical relation

between a specific predictand and the selected predictor variables was estimated and the

parameters of a multiple linear regression equation were determined. The temporal resolution

of the downscaling model was selected by choosing the model type (monthly, seasonal, or

yearly). In Monthly models, model parameters were estimated for each month of the year.

Hence, for this study, the calibration was done for the period of 20 years (1970-1989), 10

years (1986-95) and 10 years (1987-96) for Addis Ababa, Fiche and Kachisi respectively at a

monthly model type in order to see the monthly temporal variations. The result of the weather

36

generator was used to validate the calibrated model using independent observed data not used

during the calibration procedure. Accordingly the validation was done with the data from

1990-1999 (10 years), 1996-2001 (6 years) and 1997-2001 (5 years) for Addis Ababa, Fiche

and Kachisi respectively.

3.3.3.5. Scenario generation

SDSM has scenario generator which was used to downscale GCM (HadCM3) predictors in

grid box containing the study area for the A2 and B2 SRES emission scenarios to the stations.

Hence for this study, the HadCM3A2a and HadCM3B2a were the two GCM output files used

for the scenario generation. Finally scenario was generated for rainfall predictand variables,

both for base and future periods, using HadCM3 GCM model output for the two emission

scenarios (A2 and B2 SRES emission scenarios) for the stations. The future scenarios was

developed by dividing the future time series into three periods of 30 years the 2020s (2010-

2039), the 2050s (2040-2069), and the 2080s (2070-2099). The period from 1970-1999, 1986-

2001 and 1987-2001 were taken as a base period for Addis Ababa, Fiche and Kachisi stations

respectively with which the comparison was made.

Climate change scenarios were developed using SDSM to formulate the historic daily record

at the three stations under study. The change fields for the climate change scenarios were

computed using the SDSM outputs as the percent difference from the baseline case of

monthly rainfall averaged for all years of output. The historic daily rainfalls at the three

stations were modified by multiplying rainfall data with the monthly percentage change

values previously obtained. This means that if the change field for the month of June is +10%,

then all June values in the historic record are multiplied by 1.10; similarly, if the change field

is -5% for the same month, all historic data is multiplied by 0.95 (Prodanovic and Simonovic,

2009).

3.4. Daily Rainfall Disaggregation Model

The future climate will continue to change as the greenhouse gas concentrations is being

altered in the atmosphere, ignoring any future change in greenhouse gas emissions. To

37

maintain seasonality in rainfall distribution, the downscaled daily rainfall outputs were

proposed to be disaggregated into hourly values using the method of Hyetos Temporal

Rainfall Disaggregation model. The Hyetos model require long time (at least 10 years)

continuous record of rainfall intensity data of the sites for the estimation of parameters which

would be used for disaggregating the daily rainfall into hours. However, for the study sites,

the rainfall intensity data collected from National Meteorological Agency (NMA) had a lot of

monthly and yearly missing values. Moreover, some of the existing rainfall intensity data

were not the same with daily rainfall data both in amount and date. Hence, the Hyetos model

could not be used. Consequently, the Rainfall Ratio Method (Equation 2.1) was adopted to

convert 24hrs rainfalls into rainfall depths of different small durations’ required in

constructing IDF curves. During calibration of the model, the value of n for the stations was

found to be 0.87 which was used for the disaggregation of the daily rainfall into smaller

hours. Hence value of n as 0.87 was used in this study. Figure 3.3 shows that there had been

good relationship between the observed and disaggregated for 12hrs rainfall with correlation

coefficient of 0.995. During calibration, the relationship obtained between observed and

disaggregated rainfall at Addis Ababa station was indicated below (Table 3.3 and Figure 3.3).

Table3.3 Relationship of observed and disaggregated rainfall at Addis Ababa station

No Observed Disaggregated

6hr 12hr 24hr 6hrs 12hrs 24hrs

1 66.6 73.6 74.0 59.9 66.9 74.0

2 15.0 16.1 16.1 13.0 14.6 16.1

3 28.6 28.6 30.7 24.8 27.8 30.7

4 19.2 20.9 20.9 16.9 18.9 20.9

5 20.4 21.5 24.5 19.8 22.1 24.5

6 24.0 29.5 30.7 24.8 27.7 30.7

7 29.6 30.8 33.0 26.7 29.8 33.0

8 29.3 29.3 29.3 23.7 26.5 29.3

9 23.9 26.6 26.6 21.5 24.1 26.6

The disaggregated hourly rainfall data were next used to generate intensity duration frequency

curves for the generated scenarios to create different realizations of future climate using

different GCM responses. Finally, the annual maximum rainfalls for 1, 2, 3, 6, 12 and 24 hour

durations was selected to fit to probability distribution function for calculating return periods.

38

Figure 3.3. Relationship between observed and disaggregated 12hr rainfall at Addis Ababa

station.

3.5. Rainfall Intensity Duration Frequency Analysis

The annual maximum rainfall data formulated by climate change scenario at the three stations

were analysed using the method of frequency analysis and applying mathematical

relationships. Data analysis and fitting the theoretical probability distribution to the observed

data as well as numerical computation of the extreme rainfall magnitude (XT) were made for

the required durations and frequencies based on the selected probability distribution function.

The procedures and methods followed are outlined in the following subsections.

3.5.1. Fitting the probability distribution function

The extracted annual maximum rainfall data were arranged in descending order to fit to the

probability distribution functions. The maximum rainfall depths at the durations of 1, 2, 3, 6,

12 and 24 hours were fitted to Gumbel Extreme Value type I (EVI), lognormal and Log

Pearson type III using frequency analysis techniques to select the best fitting model. The

reason for selecting these distributions for analysis was due to the fact that they were being

commonly used in rainfall and flood studies (Chowdhury et al., 1991; Vogel and McMartin,

1991 and Takara and Stedinger, 1994).

0

10

20

30

40

50

60

70

80

1 2 3 4 5 6 7 8 9

Rai

nfa

ll (

mm

)

Rainfall Records

12 hr Observed 12 hr Disaggregated

39

In fitting the data to the probability distributions, the most commonly used plotting position

formula, the Weibull formula (Takara and Stedinger, 1994), was used to identify the best

fitting probability distributions. The method of fitting the annual maximum rainfall data to the

EVI, lognormal and Log Pearson Type III probability distributions are presented below.

A. Fitting the data to Gumbel Extreme Value Type I (EVI) distribution function:

This was achieved by plotting the rainfall data to the probability distribution function

and YT (reduced variate) as abscissa. YT was calculated from the relationship given in

Equation 2.9b. Weibull plotting positions was used in the computation.

B. Fitting the data to lognormal distribution function: The standard normal variable,

z, corresponding to the return periods of the ranked annual maximum rainfall was

determined using equation 2.17 (Suresh, 2005; Bhakar et al., 2006; Adeboye and

Alatise, 2007). Weibull plotting positions was used in the computation.

C. Fitting the data to Log Pearson type III distribution function: To fit the data to

Log Pearson type III distribution, the frequency factors, KT, corresponding to the

annual maximum rainfall magnitude was determined using equation 2.21 (Adeboye

and Alatise, 2007). Weibull plotting positions was used in the computation.

3.5.2. Testing the goodness of fit of data

For each probability distribution (EVI, lognormal and log Pearson III) the chi-square

goodness of fit test (equation 2.29) was used to see whether the data are fitting the theoretical

frequency distributions for annual maximum rainfall values of all durations and stations under

consideration.

40

3.5.3. Computation of extreme value (XT)

For the computation of extreme values (XT) comparisons were made among the most

common probability distributions for hydrological analysis (Gumbel’s extreme value type I,

log normal and Log Pearson type III distributions) to select the best fitting one. Then once

the probability distribution of the observed data was known, the extreme rainfall events (XT)

for the selected return periods were estimated numerically. For instance, in the Log Pearson

type III and Log normal distribution, the natural values of variate was converted into

logarithmic form and the computations were performed (Haan, 1977; Suresh, 2005). The

expected extreme rainfall (XT) exceeding the observed values were calculated by using

Equation:

XT = X + KTSy, (3.1)

where XT is the reduced variate, X and Sy are the mean and standard deviation of data series,

respectively, and KT is frequency factor. The selection of the return period for the design was

based on the relative importance of the facility to be designed, cost (economics), desired level

of protection, and damages resulting from a failure. The commonly used return periods as 2,

5, 10, 25, 50 and 100 years were considered in this study as suggested by Bhakar et al.,

(2006).

3.5.4. Calculation of intensity of rainfall

The calculation of rainfall intensity was made by dividing the computed extreme rainfall

value based on return period by the individual durations. Hence, intensity was calculated

using the following expression:

ιD

ΤX

(hr)duration Τime

(mm)depth RainfallΙ (3.2)

where XT is extreme rainfall depth (mm) and Di duration (hr)

41

3.5.5. Estimation of intensity duration frequency curve coefficients

Finally, using either extreme rainfall values (XT) or the intensity values (I) as inputs for the

IDF Curve Fit Software (MIDUSS version 2.25) the IDF parameters (a, b and c) were

estimated using Equation (3.3) as:

Cb)(d

aΙ

(3.3)

where I is rainfall intensity (mm/hr), d is rainfall duration (minute), a is coefficient with the

same unit as I, b is time constant (minute) and c is an exponent usually less than 1.

The IDF Curve Fit Software (MIDUSS version 2.25) manipulates data describing an

Intensity-Duration-Frequency relation for a particular geographical location and used:

i. To compute the ‘a’, ‘b’, and ‘c’ parameters that most closely approximates a set of

observed rainfall data.

ii. To compute the IDF curve for user-supplied values of the three coefficients and

compare this with observed data.

The value of the ‘a’ coefficient depends on the return interval in years of the storm and the

system of units being used.

The constant ‘b’ in minutes was used to make the log-log correlation as linear as possible. A

value of zero for b parameter represents a special case of the IDF equation where poor

agreement between observed values of intensity and duration are represented.

The ‘c’ exponent is usually less than 1.0 and is obtained in the process of fitting the data to

the power expression. Its values are usually in the range of 0.75 to 1.0.

3.5.6. Parameter performance testing

The coefficient of determinations R2 and Nash and Sutcliffe simulation efficiency ENS were

used for performance testing between the computed and observed intensities were calculated

using equations (2.30 and 2.31).

42

3.6. Comparison of Intensity Duration Frequency Results

An IDF curve developed under climate change scenarios (rainfall intensity) were compared

with IDF curves developed by using historic observed data for the stations. Relative

differences between the curves were determined using the following relationship (Prodanovic

and Simonovic, 2008, and Slobodan and Angela, 2010):

X100

2

)2

X1

(X2

X-1

XDifference

(3.4)

where X1 is historic rainfall intensity and X2 is rainfall intensity under climate change

scenario.

The difference between the two IDF curves may have special significance on ways in which

current and future water management infrastructures are designed, operated and maintained.

43

4. RESULTS AND DISCUSSIONS

4.1. Rainfall Variability and Trend

The knowledge of the rainfall variation is useful for planning and management of water

resource intervention. Accordingly, the analysis of the historic (observed) rainfall data

(Appendix Table 1) of the study area indicates that the coefficient of variation (CV) values for

Addis Ababa, Fiche and Kachisi stations were 13.0%, 10.3% and 12.1% respectively (Table

4.1 and Appendix Table 3). According to Hare (1983) classification, rainfall is considered as

less variable, moderately variable, and highly variable when coefficient of variation (CV) is

less than 20%, 20% to 30% and greater than 30%, respectively.

Table4.1. Summary of annual rainfall statistics of the meteorological stations

Station name

Minimum

Rainfall

(mm)

Maximum

Rainfall

(mm)

Mean

Rainfall

(mm)

Standard

deviation

(mm)

Coefficient of

Variation

(%)

Addis Ababa 917.8 1567.9 1214.0 157.7 13.0

Fiche 982.6 1539.3 1141.6 118.0 10.3

Kachisi 1377.9 2214.2 1787.7 215.5 12.1

When we look at the CV of the annual values (Table 4.1 and Figure 4.1), it seems that the

rainfall of the area is less variable. However, the monthly values (Appendix Table 3) indicate

that the rainfall of the stations are highly variable except July and August (for the three

stations) and June for Kachisi are moderately variable. Which indicate that for the study sites,

the monthly variability of rainfall is more important to be considered than the annual

variability for practical application. On the other hand, the monthly variability was not

reflected in the annual rainfall because there was rainfall extremes variability (flood and

drought) among the months. Thus, the monthly rainfall extremes variability records in the last

40, 24 and 23 years for Addis Ababa, Fiche and Kachisi stations respectively might be an

evidence of variation in the rainfall distribution and a sequential climatic change which

indicate the seasonal fluctuations in the study area. However, as can be seen from Figure 4.1,

the mean annual rainfall of the study area for the periods of 1987-2009 shows slight an

increasing trend for Addis Ababa and Fiche stations and decreasing trend for Kachisi station,

This is in contrast to McSweeney et al, (2010) who reported from the study of 42

44

meteorological stations all over the country, that there was no any statistically significant

trend in observed mean rainfall in any season in Ethiopia between 1960 and 2006. For

instance, decreases in JAS rainfall observed in the 1980s have shown recovery in the 1990s

and 2000s.

Figure 4.1. Annual rainfall trend of the stations for the period of 1987-2009.

4.2. Climate Change Scenarios of Rainfall

For the analyse of climate change scenarios of rainfall, the selected predicator variables,

calibration and validation statistics, performance evaluation of the model and climate change

scenarios of the future (2010 – 2099) are discussed as follow.

4.2.1. Predictor variables selected

Based on the criterion set for screening of appropriate predictors for the given site of the

twenty-six predictor variables derived from the NCEP reanalysis data sets, predictor variables

that gave better correlation results at p<0.05 were chosen. Table 4.2 shows, the predictor

variables that had the strongest association with local rainfall at the three stations once the

influence of all other predictors were removed.

Addis: y = 2.0776x - 2918.8 Fiche: y = 0.899x - 652.95

Kachisi: y = -2.5703x + 6923

700

900

1100

1300

1500

1700

1900

2100

2300

198

7

198

8

198

9

199

0

199

1

199

2

199

3

199

4

199

5

199

6

199

7

199

8

199

9

200

0

200

1

200

2

200

3

200

4

200

5

200

6

200

7

200

8

200

9

Annual

rain

fall

(m

m)

Year Addis Ababa Fiche Kachisi

Linear (Addis Ababa) Linear (Fiche) Linear (Kachisi)

45

Table4.2.Selected predictor variables for the three stations

Stations

Name

Predictor

variable Predictors Description Partial r*

Addis Ababa P_zaf Surface vorticity 0.051

r850af Relative humidity at 850 hPa height 0.076

Fiche P_zhaf Surface divergence 0.11

P8_uaf 850 hpa zonal velocity 0.085

Kachisi

mslpaf Mean sea level pressure 0.098

P_faf Surface air flow strength -0.099

P8_uaf 850 hpa zonal velocity 0.131

* The partial correlation coefficient(r) shows the explanatory power that is specific to each

predictor. hPa is a unit of pressure, 1 hPa = 1 mbar = 100 Pa = 0.1 kpa.

4.2.2. Calibration and validation

The calibration and validation statistics of predictand variables (rainfall) for the three stations

are shown in Table 4.3.

Table 4.3. Calibration and validation statistics of rainfall for the three stations.

Station Calibration

R2

Standard error of

the model (SE) Validation R

2

Standard error of

the model (SE)

Addis Ababa 0.023 0.450 0.039 0.446

Fiche 0.083 0.421 0.036 0.405

Kachisi 0.062 0.429 0.115 0.406

As can be seen from Table 4.3, during calibration for rainfall the model showed 0.023, 0.083

and 0.062 R2

values for Addis Ababa, Fiche and Kachisi stations respectively, which indicates

that statistically the simulated precipitation at the three stations have poor agreement with the

observed data. However, the SDSM manual (Wilby and Dawson 2007), states that the user

shouldn’t be discouraged with low values of R2 during calibration and validation of

precipitation. Because precipitation is affected by external forcing which are not included in

the gridded predictors. There is no cut off points set to reject from using the model based on

R2 values. For that reason, in most of the literatures, the R

2 values are hardly mentioned.

However, when the observed and downscaled are compared, it shows a comparable results

(Figure 4.2)

46

Figure 4.2 The daily mean of observed and downscaled output for Fiche station.

4.2.3. Performance evaluation of the model

For the performance evaluation of the model, the observed values and the generated

(downscaled) values of the base periods were averaged to a monthly time step and

comparisons were made.

Table4.4.The statistical comparison of observed and generated monthly rainfall values

Station Monthly Rainfall Maximum Minimum Mean Standard

deviation

Addis

Ababa

Observed 426.5 0 99.9 102.6

Average of 20 Ensembles

(A2a Scenario) 286.4 6.0 102.4 94.0


(B2a Scenario) 284.0 5.3 102.5 93.4

Fiche

Observed 496.0 0.0 95.4 120.0


(A2a Scenario) 359.2 8.0 102.9 122.8


(B2a Scenario) 355.6 7.1 100.2 119.9

Kachisi

Observed 552.9 0.0 150.7 151.8


(A2a Scenario) 414.2 4.8 142.5 136.9


(B2a Scenario) 417.4 4.4 143.5 138.8

0

2

4

6

8

10

12

0

2

4

6

8

10

12

1986-2001Observed: Mean

1986-2001Downscaled: Mean

Observed Vs Downscaled output

47

The comparison statistics for the observed and the downscaled values of the stations are

shown in Table 4.4.The comparisons result indicates that the observed and generated mean

monthly rainfall values are similar but SDSM is less skilful in simulating extreme rainfall

events (maximum and minimum rainfall). As shown in Figures 4.3 to 4.5, SDSM is able to

simulate all except the extreme rainfall events. The model underestimates or overestimates the

farthest values in both extremes and keeps more or less similar with average events. This lack

of replicating the extreme values was also observed by (Abeba, 2012 and Wilby, 2005) and

they described it as “the model is less skilful at replicating the frequency of events”.

4.2.3.1. Addis Ababa station

Comparison of observed and generated mean monthly rainfall for the base period (1970-1999)

at Addis Ababa station indicate that the generated values for A2a and B2a scenarios are

slightly underestimated in the months of July and overestimated in the months of April, June

and October. On the other hand, the comparison between the generated values of A2a and B2a

scenarios reveals that A2a’s monthly values are slightly more in the months of March, July

and August while the B2a scenario values are slightly more in the months of April, June and

September. For the rest of the months (January, February, May, October, November and

December) A2a and B2a scenarios have almost equal values (Figure 4.3).

Figure4.3. Average monthly rainfall pattern for the base period (1970-1999) observed Vs

downscaled at Addis Ababa station

0.0

50.0

100.0

150.0

200.0

250.0

300.0

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

Mea

n M

on

thly

Rai

nfa

ll (m

m)

Months Addis Observed Addis H3A2a Addis H3B2a

48

4.2.3.2. Fiche station

For Fiche station the comparison of observed and generated mean monthly rainfall for the

base period (1986-2001) indicate that the generated values for A2a and B2a scenarios are

slightly overestimated in the months of July, August and September. The comparison between

the generated values of A2a and B2a scenarios also reveals that A2a’s monthly values are

slightly more in the months of July, August and September compared to B2a values. For the

rest of the months, the observed, A2a and B2a monthly values are almost have equal values

(Figure 4.4).

Figure4.4. Average monthly rainfall pattern for the base period (1986-2001) at Fiche station

4.2.3.3. Kachisi station

Comparison of observed and generated mean monthly rainfall for the base period (1987-2001)

at Kachisi station indicate that the generated values for A2a and B2a scenarios are slightly

underestimated in the months of June, July, August, September, November and December

while overestimated in the months of March, April, May and October. That means, during the

main rainy season (kiremt) the observed values are slightly more than the generated values

while during ‘belg’ (March, April and May) the generated scenarios are more. On the other

hand, the comparison between the generated values of A2a and B2a scenarios reveals that

A2a’s monthly values are slightly less in the months of June, July, August and September. For

the rest of the months both A2a and B2a scenarios have almost equal values.

0.0

50.0

100.0

150.0

200.0

250.0

300.0

350.0

400.0


Me

an

mo

nth

ly r

ain

fall

(mm

)

Months

Fiche Observed Fiche H3A2a Fiche H3B2a

49

Figure4.5. Average monthly rainfall pattern for the base period (1987-2001) at Kachisi

station

In general, SDSM is able to simulate all the mean monthly rainfall of the three stations except

for the months in main rainy season (JJAS) where the model a slightly underestimates or

overestimates which might be due to the existence of extreme rainfall (high rainfall) during

those months. This indicates that SDSM is less skillful in capturing extreme rainfall values.

This lack of replicating the extreme values was also observed by (Wilby, 2005) and he

described it as “the model is less skilful at replicating the frequency of events”. However, the

result is taken as suitable, due to conditional nature of precipitation in which an intermediate

state variable governs the relationship between regional forcing and local weather.

4.2.4. Scenarios developed for the future (2010-2099)

For the three stations of study sites, future climate scenarios were developed from statistical

downscaling using the GCM predictor variables for the two emissions scenarios for a period

of 2010 to 2099 years based on the mean of 20 ensembles (default) and the analysis was done

based on three 30 years periods centred on the 2020s (2010–2039), 2050s (2040–2069) and

2080s (2070–2099).

0.0

50.0

100.0

150.0

200.0

250.0

300.0

350.0

400.0

450.0


Me

an m

on

thly

ra

infa

ll (m

m)

Months

Kachisi Observed Kachisi H3A2a Kachisi H3B2a

50

4.2.4.1 Future scenario on monthly basis (2010-2099)

Addis Ababa Station

Under A2a scenario in all future time horizons, the rainfall amount will decrease in the

months of January, February and September while it shows an increase in the months of

April, May and December. Moreover, under the same scenario in 2050 and 2080s the rainfall

will decrease in March and increase in August. The rainfall amounts will decrease in the

months of October and November for the years in 2020 and 2080’s while it will increase in

2050’s (Figure 4.6).

Figure4.6. Average monthly rainfall change in the future at Addis Ababa station for A2a

scenario.

Under B2a scenario for Addis Ababa station in all future time horizons, the rainfall amount

will decrease in the months of March, June, August and December while it shows an increase

in the months of January, February and November. Moreover, in 2020 and 2050s the

projected rainfall amount is expected to decrease in April and increase in July. (Figure4.7).

For the analysis of seasonal variation, the monthly change values for the seasons are added

together. Accordingly, the analysis of the future rainfall in seasonal time scale for Addis

Ababa indicates an increasing trend by 7% for ‘belg’(MAM) from the base period level for

A2a scenario and decreasing during main rainy season /‘kiremt’ (JJAS) and dry season

(October to February) in all future time horizons. Moreover, under B2a scenario the seasonal

rainfall will decrease except ‘bega’/ dry season (ONDJF)) in which the amount of rainfall will

increase by13.5% and 5.1% in 2020s and 2080s respectively compared to the base period. The

-30.00

-25.00

-20.00

-15.00

-10.00

-5.00

0.00

5.00

10.00

15.00

20.00


Ch

ange

fro

m t

he

bas

e (%

)

Months

Add2020s A2a Add2050s A2a Add2080s A2a

51

amount of annual rainfall also show a decreasing trend under both A2a and B2a scenarios

from the base period (Table 4.5)

Figure4.7. Average monthly rainfall change in the future at Addis Ababa station for B2a scenario.

As can be seen from (Table 4.5) under both scenarios (A2a and B2a), the amount of future

annual rainfall for Addis Ababa will be less compared to the base period. Hence, to meet the

water demand (for domestic consumption, industry, agriculture and others) of Addis Ababa

population from rainfall, effective water conservation and managements has to be in place.

Table 4.5 Seasonal percentage change from the base for Addis Ababa station

Season A2a Scenario Addis

B2a Scenario Addis

2020s 2050s 2080s

2020s 2050s 2080s

Belg (MAM) 5.1 6.4 7.0 -22.3 -14.4 -8.9

Kiremt (JJAS) -11.5 -5.3 -9.3

-1.2 -2.8 -0.1

Bega (ONDJF) -50.3 -12.1 -41.0

13.5 -9.9 5.1

Annual -11.7 -3.5 -8.9 -4.1 -5.8 -1.4

Fiche station

At Fiche station, under A2a scenario in all future time horizons, the projected rainfall amount

will decrease in the months of March, June, September and November (with very significant

decrease in November) while it shows an increase in the months of April and May. Moreover,

-25.0

-20.0

-15.0

-10.0

-5.0

0.0

5.0

10.0

15.0

20.0


Ch

ange

fro

m t

he

bas

e (

%)

Months

Add2020s B2a Add2050s B2a Add2080s B2a

52

in 2020 and 2050s the amount of rainfall will increase in January, February and November

while the reverse is true in the months of August and October (Figure 4.8).

Figure4.8. Average monthly rainfall change in the future at Fiche station for A2a scenario.

As shown in (Figure4.9), under B2a scenario at Fiche station, in all future time horizons, the

projected rainfall amount will decrease in the months of February, March and October while

it shows an increase in the months of April, May, July and December (with very significant

increase in May and December). January, June, August, September and November shows a

slight increasing and decreasing trends.

Figure 4.9. Average monthly rainfall change in the future at Fiche station for B2a scenario.

-22.0

-17.0

-12.0

-7.0

-2.0

3.0

8.0


Ch

ange

fro

m t

he

bas

e (

%)

Months

Fiche 2020s A2a Fiche 2050s A2a Fiche 2080s A2a

-15.0

-10.0

-5.0

0.0

5.0

10.0

15.0

20.0


Ch

ange

fro

m t

he

bas

e (%

)

Months

Fiche 2020s B2a Fiche 2050s B2a Fiche 2080s B2a

53

For Fiche station the analysis of the future rainfall in seasonal time scale indicates an increase

of 5.1%, 4.1% and 0.6% for ‘belg’ season under A2a scenario and an increase of 5.7%, 4.9%

and 16.3% under B2a scenario for the periods of 2020s, 2050s and 2080s respectively. The

amount of ‘kiremt’ (JJAS) and Bega (ONDJF) rainfall will decrease compared to the base

period. Under A2a scenario the annual rainfall will decrease by 7.6%, 12.2% and 2.2% in

2020s, 2050s and 2080s respectively. However, under B2a scenario the amount of annual

rainfall will increase by 1%, 3.5% and 9.6% for the periods of 2020s, 2050s and 2080s

respectively (Table 4.6).

Table4.6. Seasonal percentage change from the base for Fiche station

Season A2a Scenario Fiche

B2a Scenario Fiche

2020s 2050s 2080s

2020s 2050s 2080s

Belg (MAM) 5.1 4.1 0.6 5.7 4.9 16.3

Kiremt (JJAS) -11.0 -15.5 -0.3

-1.5 4.0 11.6

Bega (ONDJF) -1.4 -13.6 -25.3

14.3 -4.8 -22.6

Annual -7.6 -12.2 -2.2 1.0 3.5 9.6

Taking into consideration the future seasonal change of rainfall pattern at Fiche station,

effective water conservation and managements has to be in place to meet the water demand

(for domestic consumption, industry, agriculture and others) of the area from rainfall. Water

demand will increase with increase of population; hence, business as usual may not be an

option.

Kachisi station

At Kachisi station, under A2a scenario, the projected rainfall amount will decrease in the

months of January, March, April, May, August and October while it shows an increase in the

months of February, June, July, September and December. On the other hand, in November

the rainfall amount will increase in 2020 and 2080s and will decrease in 2050s. (Figure4.10).

Under B2a scenario at Kachisi station, the projected rainfall amount will decrease in the

months of January, April, May, August and October while it shows a significant increase in

the months of November and December. Moreover, February, July and September will show

a trend of an increase of rainfall amount in the year 2050 and 2080s. (Figure4.11).

54

Figure4.10. Average monthly rainfall change in the future at Kachisi station for A2a scenario.

Figure4.11. Average monthly rainfall change in the future at Kachisi station for B2a scenario.

The future seasonal rainfall analysis of Kachis station indicates an increase of 7.1%, 10.6%

and 2.6% for ‘kiremit’ season (JJAS) under A2a scenario and an increase of 5.7%, 4.9% and

16.3% for ‘belg’ season under B2a scenario for the periods of 2020s, 2050s and 2080s

respectively for both scenarios. The amount of annual rainfall will increase by 2.9% and 3.3

for the period of 2020s and 2050s under A2a scenario and will decrease by 1.3% in 2080s.

However, under B2a scenario the amount of annual rainfall will increase by 1.2%, 3.3% and

8.9% for the period of 2020s, 2050s and 2080s compared to the base period (Table 4.7).

-25.0

-20.0

-15.0

-10.0

-5.0

0.0

5.0

10.0

15.0

20.0

25.0


Ch

ange

fro

m t

he

bas

e (

%)

Months

Kach 2020s A2a Kach 2050s A2a Kach 2080s A2a

-20.0

-10.0

0.0

10.0

20.0

30.0

40.0


Ch

ange

fro

m t

he

bas

e (%

)

Months

Kach 2020s B2a Kach 2050s B2a Kach 2080s B2a

55

Table4.7. Seasonal percentage change from the base for Kachisi station

Season A2a Scenario Kachisi

B2a Scenario Kachisi

2020s 2050s 2080s

2020s 2050s 2080s

Belg (MAM) -21.1 -22.3 -35.7 5.7 4.9 16.3

Kiremt (JJAS) 7.1 10.6 2.6

-1.5 4.0 11.6

Bega (ONDJF) 6.9 -13.1 21.0

14.3 -4.8 -22.6

Annual 2.9 3.3 -1.3 1.2 3.3 8.9

4.3. Disaggregation of daily rainfall

Based on historic data, the daily rainfall scenarios generated using SDSM were disaggregated

into the required hourly rainfall (1hr, 2hr, 3hr, 6hr, 12hr and 24hr) using the rainfall ratio

method. Then from each duration of the daily rainfall, the maximum annual rainfall value was

selected to develop the future IDF curves for the stations.

4.4. Selection of the Probability Distribution Functions

For the computation of extreme rainfall values (XT) for certain duration, comparisons were

made among the most common probability distributions for hydrological analysis (Gumbel’s

extreme value type I, log normal and Log Pearson type III distributions) to select the best

fitting one. The values of coefficient of determination (R2) are shown in (Table 4.8).

Table4.8. Comparisons of R2 values of the selection of probability distributions

Station Types of Probability

distribution

R2 values for the indicated duration (hr)

1 2 3 6 12 24

Addis

Ababa

EVI 0.971 0.971 0.971 0.971 0.971 0.971

Log-normal 0.935 0.935 0.935 0.935 0.935 0.935

Log Pearson 0.934 0.978 0.937 0.978 0.978 0.978

Fiche

EVI 0.956 0.956 0.956 0.956 0.956 0.956

Log-normal 0.880 0.880 0.880 0.880 0.880 0.880

Log Pearson 0.900 0.970 0.912 0.970 0.970 0.970

Kachisi

EVI 0.960 0.960 0.960 0.960 0.960 0.960

Log-normal 0.946 0.946 0.946 0.946 0.946 0.946

Log Pearson 0.949 0.957 0.957 0.957 0.957 0.957

The closer the value of R2 to 1, the higher is the agreement between the simulated and the

measured values (Krause, 2005). Accordingly, based on R2

values, Gumbel’s Extreme Value

Type I (EVI) distribution was selected among the probability distributions for the three

56

stations. Further, chi-square test was used to confirm the suitability of probability distribution

function for all durations of the three stations (Table 4.9). Results of the chi-square test

indicate that for all durations the calculated chi-square values are less than the tabulated

values at 95% confidence level for the EVI distribution functions for all stations. Therefore,

the EVI (Gumbel) distribution functions can be used to explain the rainfall data of the

stations.

Table4.9. Summaries of Chi Square value

Station Calculated Chi Square Tabulated

chi-square 1h 2h 3h 6h 12h 24h

Addis Ababa 7.11 7.10 7.12 7.11 7.11 7.10 15.51

Fiche 6.18 6.16 6.12 6.10 6.11 6.11 14.07

Kachisi 3.56 3.53 3.56 3.50 3.482 3.46 12.59

4.4.1. Extreme rainfall values (XT)

The extreme rainfall values (XT) for the required return periods were computed using

(equation 3.1) and the frequency factor using (equation 2.19). The extreme rainfall values

(XT) for the return periods of (2, 5, 10, 25, 50 and 100 years) for Addis Ababa station was

computed using the proposed probability distribution (Gumble EVI) to form the IDF curves

under changing climate for both (A2a and B2a scenarios) are indicated in Table 4.10 and

4.11. Similarly XT values for Fiche and Kachisi stations are given in Appendix Table 7 to 10.

The extreme rainfall values for all return periods will increase for the durations of 2020s and

2050s for Addis Ababa station under A2a scenario then it decrease in 2080s. Under B2a

scenario it shows a slight decreasing trend for all duration from 2020s – 2080s. However, for

Fiche and Kachisi stations, the extreme rainfall values under A2a scenario shows an opposite

trend to that of Addis Ababa station. Under B2a scenario, the extreme rainfall values at Fiche

station shows an increasing trend for all durations from 2020s to 2080s while at Kachisi

station it increases from 2020s to 2050s then it decrease in 2080s.

57

Table4.10. Summary of computed XT for Addis Ababa stations under A2a Scenario

T (years) 1hr 2hr 3hr 6hr 12hr 24hr

A. (2010-2039)

2 27.29 33.22 36.40 41.48 46.35 51.26

5 36.69 44.67 48.94 55.77 62.32 68.93

10 42.92 52.25 57.25 65.24 72.90 80.63

25 50.78 61.83 67.75 77.20 86.26 95.41

50 56.62 68.93 75.53 86.07 96.18 106.38

100 62.41 75.99 83.26 94.87 106.02 117.26

B. (2040-2069)

2 27.51 33.49 36.69 41.81 46.72 51.68

5 36.86 44.88 49.17 56.03 62.61 69.25

10 43.05 52.42 57.43 65.44 73.13 80.88

25 50.88 61.94 67.87 77.34 86.42 95.59

50 56.68 69.01 75.61 86.16 96.28 106.49

100 62.45 76.03 83.30 94.92 106.07 117.32

C. (2070-2099)

2 27.09 32.99 36.14 41.18 46.02 50.90

5 36.22 44.09 48.31 55.05 61.52 68.04

10 42.26 51.45 56.37 64.23 71.78 79.39

25 49.89 60.74 66.55 75.83 84.74 93.73

50 55.55 67.63 74.10 84.44 94.36 104.36

100 61.17 74.47 81.60 92.98 103.90 114.92

Table 4.11. Summary of computed XT for Addis Ababa stations under B2a Scenario


a. 2020s (2010-2039)

2 27.55 33.54 36.75 41.88 46.80 51.76

5 36.91 44.93 49.23 56.10 62.69 69.34

10 43.10 52.48 57.50 65.52 73.22 80.98

25 50.93 62.01 67.94 77.42 86.51 95.69

50 56.74 69.08 75.69 86.25 96.38 106.60

100 62.50 76.10 83.38 95.01 106.17 117.43

b. 2050s (2040-2069)

2 27.46 33.43 36.63 41.74 46.64 51.59

5 36.55 44.49 48.75 55.55 62.08 68.66

10 42.56 51.82 56.78 64.70 72.30 79.97

25 50.17 61.08 66.92 76.26 85.22 94.25

50 55.81 67.94 74.45 84.83 94.80 104.85

100 61.41 74.76 81.91 93.34 104.31 115.37

c. 2080s (2070-2099)

2 27.14 33.04 36.20 41.25 46.10 50.99

5 36.58 44.53 48.79 55.60 62.13 68.72

10 42.83 52.14 57.13 65.10 72.74 80.46

25 50.72 61.75 67.66 77.10 86.15 95.29

50 56.58 68.88 75.47 86.00 96.10 106.29

100 62.39 75.96 83.23 94.84 105.98 117.21

58

4.4.2. Rainfall intensity (I)

Once XT values of the rainfall data are known, the intensity (I) in (mm/hr) is computed

dividing the XT values by their respective durations (equation 3.2). The rainfall intensities

calculated using equation 3.2 was compared with the rainfall intensities calculated using

equation 3.3 using MIDUSS software with XT as an input. The rainfall intensity values

obtained using both equation for Addis Ababa station is shown in Table 4.12 to 4. 17 for

future climate change scenarios for both A2a and B2a for discussion. The degree of linear

association between the two rainfall intensities were evaluated using the correlation

coefficient (R2) and Nash and Sutcliffe coefficient (ENS). For the three stations the R

2 and

NSE values are greater than 0.999. The closer R2 to 1, the better the regression equation fit the

data (Haan, 1977). ENS value of 1 indicates perfect match and values between 0.75 to 1 is very

good match between observed and simulated values (Moriasi et al., 2007). Further, Santhi et

al., (2001) recommended that R² >0.6 and ENS > 0.5 are acceptable. Hence, it can be said that

the intensity values obtained by using the IDF parameters would adequately describe the data

and the parameter estimation model performs very well. The rainfall intensities for Fiche and

Kachisi stations are tabulated in Appendix Table 11 to 22.

The rainfall intensities for all return periods will increase for the durations of 2020s and 2050s

for Addis Ababa station under A2a scenario then it decrease in 2080s. Under B2a scenario it

shows a slight decreasing trend for all duration from 2020s – 2080s. However, for Fiche and

Kachisi stations, the rainfall intensities under A2a scenario shows an opposite trend to that of

Addis Ababa station but under B2a scenario, the rainfall intensity at Fiche station shows an

increasing trend for all durations from 2020s to 2080s while at Kachisi station it increases

from 2020s to 2050s then it decrease in 2080s. The trend of rainfall intensities at Fiche and

Kachis stations are almost similar while at Addis Ababa it is different which might be

attributed due to the length of data period used. For Addis Ababa 30 years rainfall data was

used while for Fiche and Kachisi 16 and 15 years data were used respectively. However, the

classical period for climate is 30 years as defined by World Meteorological Organization

(IPPC, 2001).

59

As can be seen from Tables (4.12 to 4.17) below, for the given return periods, the values of

the rainfall intensities decrease as the rainfall duration increase, however, the rainfall intensity

increases with an increase in return period for each duration at all stations. This is in

agreement with Arora (2002) which states, the greater the intensity of the rainfall, the shorter

its duration. In other words, as the duration of storm increase, its intensity decreases. Further,

a storm of any given duration will have a large intensity if its return period is large.

60

Table4.12. Computed rainfall intensities (mm/hr) using XT and IDF parameters at Addis Ababa station for 2020s (A2a scenario)

Time

(min)

2 years return periods 5 years return periods 10 years return periods

25 years return

periods 50 years return periods

100 years return

periods

RI. Using

XT values*

RI. Using

IDF

parameters.

**

RI. Using

XT values

RI. Using

IDF

parameters.

RI. Using

XT values

RI. Using

IDF

parameters

RI. Using

XT values

RI. Using

IDF

parameters

RI. Using

XT values

RI. Using

IDF

parameters

RI. Using

XT values

RI. Using

IDF

parameters

60 27.29 27.28 36.69 36.72 42.92 42.95 50.78 50.79 56.62 56.62 62.41 62.42

120 16.61 16.61 22.33 22.33 26.13 26.12 30.92 30.91 34.47 34.47 37.99 37.99

180 12.13 12.14 16.31 16.31 19.08 19.08 22.58 22.58 25.18 25.18 27.75 27.75

360 6.91 6.91 9.3 9.29 10.87 10.87 12.87 12.87 14.35 14.34 15.81 15.81

720 3.86 3.86 5.19 5.19 6.08 6.07 7.19 7.19 8.02 8.01 8.84 8.83

1440 2.14 2.14 2.87 2.87 3.36 3.36 3.98 3.98 4.43 4.43 4.89 4.89

R2 1.000 1.000 1.000 1.000 1.000 1.000

ENS 1.000 1.000 1.000 1.000 1.000 1.000

* The rainfall intensities (RI.) calculated using equation 3.2,

** The rainfall intensity computed using IDF parameters (equation 3.3 (using MIDUSS software)


Time

(min)

2 years return periods 5 years return periods

10 years return

periods

25 years return


100 years return

periods

RI. Using XT values

RI. Using

IDF parameters

RI. Using XT values

RI. Using

IDF parameters

RI. Using XT values

RI. Using

IDF parameters

RI. Using XT values

RI. Using

IDF parameters

RI. Using XT values

RI. Using

IDF parameters

RI. Using XT values

RI. Using

IDF parameters

60 27.51 27.52 36.86 36.86 43.05 43.07 50.88 50.91 56.68 56.66 62.45 62.45

120 16.75 16.74 22.44 22.44 26.21 26.2 30.97 30.96 34.51 34.51 38.01 38.01

180 12.23 12.23 16.39 16.39 19.14 19.14 22.62 22.61 25.2 25.21 27.77 27.77

360 6.97 6.97 9.34 9.34 10.91 10.9 12.89 12.88 14.36 14.36 15.82 15.82

720 3.89 3.89 5.22 5.22 6.09 6.09 7.2 7.2 8.02 8.02 8.84 8.84

1440 2.15 2.15 2.89 2.89 3.37 3.37 3.98 3.98 4.44 4.44 4.89 4.89

R2 1.000 1.000 1.000 1.000 1.000 1.000

ENS 1.000 1.000 1.000 1.000 1.000 1.000

61


Time

(min)


10 years return

periods

25 years return

periods

50 years return

periods

100 years return

periods

RI. Using

XT values

RI. Using

IDF

parameters

RI. Using

XT values

RI. Using

IDF

parameters

RI. Using

XT values

RI. Using

IDF

parameters

RI. Using

XT values

RI. Using

IDF

parameters

RI. Using

XT values

RI. Using

IDF

parameters

RI. Using

XT values

RI. Using

IDF

parameters

60 27.09 27.11 36.22 36.2 42.26 42.28 49.89 49.9 55.55 55.55 61.17 61.17

120 16.5 16.49 22.05 22.05 25.73 25.72 30.37 30.37 33.81 33.81 37.24 37.24

180 12.05 12.04 16.1 16.11 18.79 18.78 22.18 22.18 24.7 24.7 27.2 27.2

360 6.86 6.86 9.18 9.18 10.71 10.7 12.64 12.64 14.07 14.07 15.5 15.5

720 3.84 3.83 5.13 5.13 5.98 5.98 7.06 7.06 7.86 7.86 8.66 8.66

1440 2.12 2.12 2.84 2.83 3.31 3.31 3.91 3.91 4.35 4.35 4.79 4.79

R2 1.000 1.000 1.000 1.000 1.000 1.000

ENS 1.000 1.000 1.000 1.000 1.000 1.000

Table4.15. Computed rainfall intensities (mm/hr) using XT and IDF parameters at Addis Ababa station for 2020s (B2a scenario)

Time (min)


10 years return

periods

25 years return


100 years return

periods

RI. Using

XT values

RI. Using

IDF

parameters

RI. Using

XT values

RI. Using

IDF

parameters

RI. Using

XT values

RI. Using

IDF

parameters

RI. Using

XT values

RI. Using

IDF

parameters

RI. Using

XT values

RI. Using

IDF

parameters

RI. Using

XT values

RI. Using

IDF

parameters

60 27.55 27.54 36.91 36.92 43.10 43.11 50.93 50.95 56.74 56.76 62.5 62.54

120 16.77 16.77 22.47 22.46 26.24 26.24 31.00 31.00 34.54 34.54 38.05 38.04

180 12.25 12.25 16.41 16.41 19.17 19.16 22.65 22.64 25.23 25.22 27.79 27.78

360 6.98 6.98 9.35 9.35 10.92 10.92 12.9 12.9 14.38 14.37 15.84 15.83

720 3.90 3.90 5.22 5.22 6.10 6.10 7.21 7.21 8.03 8.03 8.85 8.85

1440 2.16 2.16 2.89 2.89 3.37 3.37 3.99 3.99 4.44 4.44 4.89 4.89

R2 1.000 1.000 1.000 1.000 1.000 1.000

NSE 1.000 1.000 1.000 1.000 1.000 1.000

62


Time

(min)


10 years return

periods

25 years return

periods

50 years return

periods

100 years return

periods

RI. Using XT values

RI. Using

IDF parameters

RI. Using XT values

RI. Using

IDF parameters

RI. Using XT values

RI. Using

IDF parameters

RI. Using XT values

RI. Using

IDF parameters

RI. Using XT values

RI. Using

IDF parameters

RI. Using XT values

RI. Using

IDF parameters

60 27.46 27.45 36.55 36.56 42.56 42.58 50.17 50.2 55.81 55.79 61.41 61.43

120 16.72 16.72 22.25 22.24 25.91 25.91 30.54 30.53 33.97 33.98 37.38 37.38

180 12.21 12.21 16.25 16.25 18.93 18.92 22.31 22.3 24.82 24.82 27.30 27.30

360 6.96 6.96 9.26 9.26 10.78 10.78 12.71 12.71 14.14 14.14 15.56 15.55

720 3.89 3.89 5.17 5.17 6.03 6.02 7.10 7.10 7.90 7.90 8.69 8.69

1440 2.15 2.15 2.86 2.86 3.33 3.33 3.93 3.93 4.37 4.37 4.81 4.81

R2 1.000 1.000 1.000 1.000 1.000 1.000

ENS 1.000 1.000 1.000 1.000 1.000 1.000


Time (min)


10 years return

periods

25 years return


100 years return

periods

RI. Using

XT values

RI. Using IDF

parameters

RI. Using

XT values

RI. Using IDF

parameters

RI. Using

XT values

RI. Using IDF

parameters

RI. Using

XT values

RI. Using IDF

parameters

RI. Using

XT values

RI. Using IDF

parameters

RI. Using

XT values

RI. Using IDF

parameters

60 27.14 27.12 36.58 36.58 42.83 42.81 50.72 50.74 56.58 56.61 62.39 62.36

120 16.52 16.52 22.26 22.27 26.07 26.07 30.88 30.87 34.44 34.43 37.98 37.99

180 12.07 12.07 16.26 16.26 19.04 19.05 22.55 22.55 25.16 25.15 27.74 27.75

360 6.88 6.88 9.27 9.27 10.85 10.85 12.85 12.85 14.33 14.33 15.81 15.81

720 3.84 3.84 5.18 5.18 6.06 6.06 7.18 7.18 8.01 8.01 8.83 8.83

1440 2.12 2.12 2.86 2.86 3.35 3.35 3.97 3.97 4.43 4.43 4.88 4.88

R2 1.000 1.000 1.000 1.000 1.000 1.000

NSE 1.000 1.000 1.000 1.000 1.000 1.000

63

4.4.3. Estimation of the IDF Parameters

The computed IDF parameters (a, b & c) for the three stations of various return periods are

summarized in Tables 4.18 to 4.20.

Table4.18. the computed IDF parameters at Addis Ababa station for various frequencies

Range of

years Parameters

Return periods (years)

2 5 10 25 50 100

A2a

(2020s)

a 1213.28 1612.32 1885.96 2246.39 2504.22 2760.71

b 18.1741 17.6848 17.6819 17.9655 17.9655 17.9655

c 0.87062 0.86895 0.86894 0.86988 0.86985 0.86987

A2a

(2050s)

a 1213.78 1630.66 1899.58 2235.80 2519.58 2762.69

b 17.8548 17.9655 17.8548 17.6869 18.1743 17.9655

c 0.86954 0.8699 0.86952 0.86894 0.87058 0.86991

A2a

(2080s)

a 1190.58 1613.52 1860.65 2202.03 2457.27 2705.95

b 17.6869 18.2655 17.7639 17.8703 17.9655 17.9655

c 0.86894 0.8709 0.86923 0.86957 0.86988 0.86989

B2a

(2020s)

a 1225.56 1627.50 1904.07 2247.86 2502.29 2751.60

b 18.2097 17.8328 17.9117 17.8703 17.8359 17.7639

c 0.87068 0.86944 0.86968 0.86956 0.86945 0.86919

B2a

(2050s)

a 1221.70 1612.49 1876.35 2208.79 2479.10 2707.77

b 18.2097 17.8548 17.8277 17.7639 18.1466 17.8328

c 0.87071 0.86952 0.86939 0.86921 0.87048 0.86943

B2a

(2080s)

a 1208.84 1618.05 1905.69 2237.81 2491.08 2491.08

b 18.264 17.966 18.210 17.855 17.764 17.764

c 0.8709 0.870 0.871 0.870 0.869 0.869

From the Tables 4.18 to 4.20 a general trend of the following was observed. The “a”

parameter increases with an increase in return period and also in time for duration of 2020s

and 2050s then it decline for Addis Ababa and Kachisi stations. The “b” constant and the “c”

exponent generally increase or decrease with increase or decrease of the “a” coefficient with

exception of Fiche station where there is no generalized pattern between the parameters. In

general, the “b”and“c” parameters slightly varied with an increase or decrease of return period

and duration. Nigatu (2011) has reported similar results using A1B emission scenario

(balanced energy source) for the upper Blue Nile basin. In general, the estimated IDF

parameters are different for time intervals of 2020s-2080s which indicates that the IDF

parameters for stations are not fixed in magnitude. Hence, depending on more rainfall record

availability, the global phenomena on climate change and parameter estimation techniques;

64

the IDF parameters shall be updated at some intervals of time to end up with preferable and

reliable results of IDF relationships.

Table4.19. the computed IDF parameters at Fiche station for various frequencies

Range of

years Parameters


2 5 10 25 50 100

A2a

(2020s)

a 1100.77 1441.96 1664.80 1957.74 2187.36 2379.50

b 17.764 17.822 17.764 17.966 18.319 17.966

c 0.8692 0.8694 0.8692 0.8699 0.8711 0.8699

A2a

(2050s)

a 1101.54 1439.05 1666.55 1953.10 2301.83 2365.54

b 18.181 17.966 17.966 17.966 20.563 17.764

c 0.87056 0.86988 0.86993 0.8699 0.87856 0.8692

A2a (2080s)

a 1121.76 1468.67 1685.78 1963.46 2174.74 2406.47

b 17.966 18.181 17.966 17.833 17.854 18.265

c 0.8699 0.8706 0.8699 0.8694 0.8695 0.8709

B2a (2020s)

a 1131.75 1462.79 1698.04 1987.25 2213.67 2403.92

b 18.266 17.764 17.966 17.966 18.181 17.764

c 0.87094 0.86926 0.86986 0.86986 0.87062 0.86921

B2a

(2050s)

a 1135.58 1490.70 1697.69 1995.17 2209.59 2443.32

b 18.210 18.328 17.682 17.855 17.833 18.181

c 0.8707 0.8711 0.8690 0.8695 0.8694 0.8706

B2a

(2080s)

a 1142.72 1503.01 1737.72 2065.16 2271.98 2493.70

b 17.855 17.870 17.764 18.328 17.966 17.966

c 0.8695 0.8695 0.8692 0.8711 0.8699 0.8699

Table4.20. the computed IDF parameters at Kachisi station for various frequencies

Range of

years Parameters


2 5 10 25 50 100

A2a

(2020s)

a 1441.96 1783.73 2030.61 2292.53 2503.63 2706.78

b 17.822 17.870 18.328 17.870 17.870 17.7639

c 0.8694 0.8696 0.8711 0.8695 0.8695 0.8692

A2a

(2050s)

a 1445.16 1768.00 1979.80 2256.15 2479.42 2657.18

b 18.174 17.966 17.828 17.855 18.181 17.764

c 0.8706 0.8699 0.8694 0.8695 0.8706 0.8692

A2a (2080s)

a 1436.02 1783.17 2003.50 2288.83 2499.17 2701.69

b 17.685 17.905 17.821 17.854 17.867 17.764

c 0.8689 0.8697 0.8694 0.8696 0.8695 0.8692

B2a

(2020s)

a 1431.41 1755.27 1978.38 2262.14 2451.56 2694.16

b 17.966 17.764 17.854 17.966 17.682 18.305

c 0.8699 0.8692 0.8695 0.8699 0.8690 0.8710

B2a

(2050s)

a 1452.51 1774.16 1993.62 2270.73 2495.63 2688.74

b 18.1756 17.8675 17.8548 17.8548 18.1808 17.9655

c 0.8706 0.86957 0.86953 0.86949 0.87057 0.86989

B2a

(2080s)

a 1413.18 1739.04 1957.18 2246.79 2421.8 2627.38

b 17.8277 17.8328 17.8703 18.194 17.6869 17.7639

c 0.86944 0.86942 0.86958 0.87064 0.86893 0.86923

65

Based on the values of parameters (a, b and c), rainfall intensity of each station for all

durations can easily be calculated with the general equation of the form:

Cd)(b

aΙ

I = exp[(ln(a) – c* ln(b + d))]

For intensity calculations each station has six different equations for different return period.

For example the six equations for the IDF relationships at Fiche station for 2020s under A2a

scenario is listed below.

For 2 Year return period, I = exp [7.004 - 0.8692*ln(17.764+d)]



For 25 Year return period, I = exp [7.580 - 0.8699*ln (17.966+d)]



Where I = rainfall intensity for the given duration and d = duration in minute

Similar equation can be written for all the 3 stations using the parameter values in Table 4.18

to 4.20 for different return periods. Rainfall Intensity values generated using the parameter

values (a, b, and c) shown in Table 4.18 to 4.20 for different return periods are tabulated in

Table 4.12 to 4.17 for Addis Ababa and in Appendix Table 11 to 22 for Fiche and Kachisi

stations.

IDF curves were plotted for the future duration of 2020s, 2050s and 2080s for each station

using the computed rainfall intensities for both A2a and B2a scenarios on a double logarithmic

scale. The IDF Curve Fit Tool (MIDUSS version 2.25) was used to plot the IDF curves using

the duration (d), as abscissa (x-axis) and the intensity (I), as ordinate (y-axis). As a sample the

IDF curves of Fiche station is shown in Appendix Figure 4 and 5.

4.4.4. Sensitivity of the IDF parameters

Results of the sensitivity analysis showed that an increase of “a” by 10% resulted 10%

increase of intensity while similar increase in “b” and “c” resulted in a decrease of intensity

66

by 0.11 to 1.95% and 31.52 to 46.9% respectively. A decrease of “c” by 10% also resulted in

an increase of the intensity by 46%- 88% which shows that the “c” exponent is the most

sensitive parameter. This is a good indication that care has to be taken in determining the “c”

exponent.

4.4.5. Comparison of IDF curve under climate change with historic IDF

Comparison was made between IDF curves developed under climate change scenarios and

historic rainfall IDF. The historic rainfall IDF parameters developed for the study area and the

corresponding rainfall intensities for different return periods are tabulated in Appendix Table

23 and 24 respectively. Relative differences between the curves were determined using

equation 3.4.

4.4.5.1. Addis Ababa station

For Addis Ababa station the comparisons made between historic rainfall intensity (Appendix

Table 24) and climate change rainfall intensity (Table 4.12 to 4.17) data set for specified

return periods are indicated in Table 4.21 and 4.22 below. The results of both SERS emission

scenarios (A2a and B2a) indicate that the rainfall magnitude will be different in the future.

The comparison between the historic IDF curves and IDF curve under climate change

scenario for Addis Ababa station shows a difference (an increase) that ranges between 0.52

and 45.6% with average value of approximately 24%. This is in agreement with McSweeney

et al. (2010) who reported an increase in the proportion of total rainfall that falls in ‘heavy’

events, with annual changes ranging from ‐1 to +18% in Ethiopia. The increase in rainfall

intensity will have major implications on ways in which current (and future) municipal water

management infrastructure is designed, operated, and maintained. However, the annual

rainfall of the Addis Ababa station shows a decreasing trend for all future periods under both

A2a and B2a emission scenarios (Table 4.5).

67

Table4.21. Percentage change between historic rainfall intensity and climate change under

A2a scenario for Addis Ababa

Time (hr.) Return period (years)

2 5 10 25 50 100

A. 2020s 1 1.40 5.66 7.04 17.12 21.71 25.94

2 5.95 12.16 16.50 21.78 25.86 29.23

3 9.33 15.35 20.42 24.54 28.41 31.54

6 13.75 19.96 25.25 29.23 32.82 35.93

12 17.32 23.93 28.58 33.81 37.31 40.61

24 20.66 27.54 31.28 38.44 41.84 45.60

B. 2050s

1 0.52 6.04 7.32 17.35 21.78 25.99

2 6.73 12.65 16.80 21.94 25.98 29.28

3 10.06 15.83 20.73 24.67 28.52 31.61

6 14.61 20.49 25.52 29.30 32.96 35.99

12 18.09 24.50 28.90 33.95 37.43 40.72

24 21.13 28.22 31.57 38.44 42.06 45.60

C. 2080s

1 2.02 4.23 5.47 15.36 19.83 23.95

2 5.23 10.90 14.96 20.04 23.96 27.28

3 8.50 14.12 18.85 22.77 26.52 29.59

6 13.02 18.78 23.69 27.46 30.97 34.01

12 16.55 22.78 27.11 32.04 35.48 38.74

24 19.73 26.16 29.82 36.73 40.10 43.64

68


B2a scenario for Addis Ababa


2 5 10 25 50 100

A. 2020s 1 0.45 6.20 7.42 17.43 21.96 26.13

2 6.91 12.74 16.95 22.07 26.06 29.36

3 10.23 15.95 20.83 24.80 28.56 31.65 6 14.75 20.60 25.70 29.46 33.02 36.06

12 18.34 24.50 29.06 34.08 37.55 40.83

24 21.58 28.22 31.57 38.69 42.06 45.60 B. 2050s

1 0.78 5.22 6.18 15.96 20.25 24.37

2 6.61 11.76 15.70 20.56 24.45 27.64

3 9.90 14.98 19.59 23.31 27.00 29.95 6 14.46 19.64 24.43 28.00 31.45 34.33

12 18.09 23.55 27.77 32.59 35.97 39.07

24 21.13 27.19 30.41 37.22 40.54 44.04 C. 2080s

1 1.99 5.28 6.72 17.02 21.70 25.85

2 5.41 11.89 16.31 21.66 25.75 29.23

3 8.75 15.04 20.26 24.40 28.29 31.54 6 13.31 19.75 25.06 29.08 32.75 35.93

12 16.81 23.74 28.41 33.68 37.31 40.61

24 19.73 27.19 30.99 38.20 41.84 45.41

4.4.5.2. Fiche station

For Fiche station the comparisons made between historic rainfall intensity (Appendix Table

24) developed by Chali (2008) and rainfall intensity under climate change scenario set for

specified return periods are indicated in Table 4.23 and 4.24 below. The results of both SERS

emission scenarios (A2a and B2a) indicate that the rainfall magnitude will be different in the

future. The comparison between the historic IDF curves and IDF curve under climate change

scenario for Fiche station shows a difference (an increase of rainfall intensity) that ranges

between 0.7 and 35.7% with average value of approximately 14%. This is in agreement with

McSweeney et al. (2010) who reported an increase in the proportion of total rainfall that falls

in ‘heavy’ events, with annual changes ranging from ‐1 to +18% in Ethiopia. The change in

rainfall intensity will have major practical implications on planning, design and evaluation of

water resources systems, drainage works etc.

69


A2a scenario for Fiche


2 5 10 25 50 100

A. 2020s 1 10.08 5.87 5.64 3.40 7.36 11.22

2 2.85 0.70 3.86 8.12 11.64 14.54

3 0.47 3.89 7.82 10.90 14.25 16.92

6 5.00 8.51 12.73 15.60 18.77 21.41 12 8.70 12.61 16.11 20.22 23.31 26.16

24 11.94 16.24 18.81 24.80 27.99 31.19

B. 2050s 1 11.04 6.45 6.07 3.15 6.71 11.14

2 3.64 0.15 3.51 7.86 11.64 14.42

3 0.35 3.40 7.46 10.65 14.39 16.75 6 4.21 8.03 12.31 15.33 18.93 21.26

12 7.86 12.18 15.74 20.06 23.16 26.16

24 10.92 15.86 18.48 24.80 27.48 31.19

C. 2080s 1 8.69 4.96 4.91 4.05 7.97 11.55

2 1.35 1.70 4.68 8.71 12.10 15.00

3 1.99 4.91 8.65 11.51 14.66 17.37 6 6.41 9.59 13.46 16.22 19.17 21.84

12 10.10 13.68 16.85 20.85 23.87 26.68

24 13.45 17.40 19.48 25.65 28.50 31.65

70


B2a scenario for Fiche


2 5 10 25 50 100

A. 2020s 1 8.61 4.29 4.18 4.90 8.90 12.74

2 1.22 2.25 5.41 9.63 13.13 16.02

3 2.16 5.46 9.35 12.41 15.70 18.36 6 6.72 10.07 14.28 17.09 20.27 22.85

12 10.10 14.10 17.59 21.79 24.86 27.70

24 13.45 17.78 20.47 26.49 29.51 32.80 B. 2050s

1 8.06 3.84 3.48 5.56 9.62 13.31

2 0.70 2.84 6.01 10.25 13.75 16.70 3 2.69 6.06 9.94 13.01 16.33 19.05

6 7.19 10.78 14.79 17.70 20.82 23.56

12 10.66 14.74 18.31 22.40 25.41 28.33 24 13.95 18.16 21.13 27.05 30.01 33.25

C. 2080s

1 6.55 1.83 1.35 7.81 12.04 15.88

2 0.77 4.74 8.15 12.64 16.20 19.22 3 4.09 7.93 12.06 15.40 18.79 21.57

6 8.56 12.64 17.00 20.10 23.28 26.00

12 12.30 16.61 20.46 24.69 27.87 30.81 24 15.43 20.42 23.06 29.24 32.47 35.70

4.4.5.3. Kachisi station

For Kachisi station the comparisons made between historic rainfall intensity and rainfall

intensity under climate change for specified return periods are indicated in Table 4.25 and

4.26 below. Results of both SERS emission scenarios (A2a and B2a) indicate that the rainfall

magnitude will be different in the future. The comparison between the historic IDF curves and

IDF curve under climate change scenario for Kachisi station shows a difference (an increase

of rainfall intensity) that ranges between 11.52 and 44% with average value of approximately

29%. This is in agreement with McSweeney et al. (2010) who reported an increase in the

proportion of total rainfall that falls in ‘heavy’ events, with annual changes ranging from ‐1 to

+18% in Ethiopia. This change in rainfall intensity will have major practical implications on

planning, design and evaluation of water resources systems, drainage works etc. On the other

hand, using the same climate change scenario for Chiro station, Abeba (2012) reported

10.92% higher rainfall intensity than that of historic rainfall in 2020s, while in 2050s and

71

2080s climate scenario produces values up to 43.31% and 55.93% less than that of historic

rainfall respectively.


A2a scenario for Kachisi

Time (hr) Return period (years)

2 5 10 25 50 100

A. 2020s 1 16.75 15.23 12.75 19.38 21.94 24.50

2 23.96 21.77 22.35 24.03 26.03 27.75

3 27.20 24.94 26.29 26.78 28.56 30.06

6 31.59 29.55 31.02 31.41 33.02 34.45 12 35.18 33.45 34.35 35.94 37.55 39.18

24 38.18 36.91 36.90 40.59 42.06 44.04

B. 2050s 1 16.08 14.12 11.52 17.84 20.18 22.69

2 23.37 20.68 20.99 22.49 24.37 25.95

3 26.66 23.83 24.87 25.23 26.92 28.25 6 31.12 28.39 29.66 29.83 31.38 32.69

12 34.55 32.42 33.13 34.48 35.85 37.40

24 37.43 35.99 35.80 38.93 40.32 42.44

C. 2080s

1 16.69 15.11 12.71 19.24 21.77 24.32

2 23.86 21.65 22.17 23.87 25.86 27.57 3 27.07 24.77 26.05 26.60 28.41 29.88

6 31.59 29.36 30.85 31.26 32.82 34.26

12 35.18 33.28 34.20 35.81 37.43 39.07 24 38.18 36.91 36.90 40.36 41.84 44.04

In general, even though, the three stations (Addis Ababa, Fiche and Kachisi) are located in the

same gird box, the effects of climate change at the stations are different. This may be due to

other intermediate state variables (the occurrences of humidity, cloud cover, wet-days and/or

dry-days) between regional forcing and local weather. Wilby and Dawson (2007) reported

that precipitation depends on conditional process in which an intermediate state variable

governs the relationship between regional forcing and local weather. From the result of the

three stations it can be concluded that the future rainfall is different and climate change is real.

Hence, the climate change national adaptation programme of action of Ethiopia (NMSA,

2007) needs to be strengthened.

72


B2a scenario for Kachisi

Time (hr) Return period (years)

2 5 10 25 50 100

A. 2020s 1 15.65 13.92 11.39 17.78 20.33 22.67

2 22.92 20.43 20.84 22.45 24.37 26.05

3 26.19 23.56 24.77 25.19 26.92 28.43 6 30.64 28.20 29.57 29.83 31.38 32.81

12 34.13 32.08 32.98 34.48 35.97 37.51

24 37.05 35.68 35.53 38.93 40.54 42.44

B. 2050s 1 16.56 14.71 12.14 18.48 20.84 23.34

2 23.86 21.25 21.60 23.12 25.03 26.64

3 27.14 24.39 25.51 25.83 27.59 28.98 6 31.59 28.97 30.26 30.51 32.07 33.38

12 35.18 32.94 33.74 35.15 36.58 38.07

24 38.18 36.60 36.35 39.64 40.97 43.04

C. 2080s 1 14.72 12.82 10.25 16.55 19.11 21.55

2 21.96 19.37 19.75 21.30 23.17 24.82

3 25.22 22.49 23.63 24.05 25.72 27.11 6 29.68 27.12 28.45 28.69 30.20 31.53

12 33.28 31.04 31.90 33.27 34.74 36.37

24 36.28 34.74 34.42 37.71 39.43 41.22

73

5. SUMMARY, CONCLUSION AND RECOMMENDATIONS

5.1. Summary and Conclusions

This paper presents indicative study on IDF relationships which were developed for

selected stations in central highland of Ethiopia under the emerging climate scenarios. The

daily rainfall of the selected three stations (Addis Ababa, Fiche and Kachisi) were

collected from NMSA and scenario data were downloaded from websites. The quality of

all the collected data was checked in order to make it ready for analysis work. The

coefficient of determination (R2) was used in order to select the best probability

distribution. SDSM was used to downscale climate information from coarse-resolution of

GCMs to local or site level and were applied here to downscale the rainfall for the study

area. The HadCM3A2a and HadCM3B2a were the two GCM SRES emission scenarios

output files used for the scenario generation. The base period and future climate change

scenarios were generated by using SDSM to simulate the impacts of climate changes on

the IDF curves of the three stations. The change fields for the climate change scenarios

were computed using the SDSM outputs as the percent difference from the baseline case

of monthly rainfall averaged for all years of output. The historic daily rainfall at the

stations was modified by multiplying rainfall data with the monthly percentage change

values. Using this modified historic daily rainfall data; the rainfall intensity-duration-

frequency (IDF) relationships were developed and compared with the historic one. For the

establishment of IDF relationship, disaggregation of the daily rainfall for all stations were

done using rainfall ratio method. Using IDF curve fit tool, estimation of IDF parameters

was done and based on the estimated parameters IDF curves were drawn for the selected

stations of the three time segments of 30 years period.

The IDF-relationships give an idea about the frequency or return period of rainfall

intensity or rainfall volume that can be expected within a certain period, i.e. the storm

duration. The IDF curves are therefore critical in the design of hydraulic structures (such

as bridges and culverts) to ensure that they are built economically and safely. Hence,

accurate and reliable rainfall IDF establishments are needed to ensure that appropriately

safe and economical designs are achieved.

74

Estimation of IDF parameters was done and mathematical equations for IDF curves under

climate change were developed for each of three stations for different return periods. The

comparison between the historic IDF curves and IDF curve under climate change scenario

shows a difference that ranges between: 0.52 % - 45.6% with average value of

approximately 24% for Addis Ababa station, 0.7 % - 35.7% with average value of

approximately 14% for Fiche station and 11.52 % - 44% with average value of

approximately 29% for Kachisi station. In general, the impacts of climate change were

observed by increasing the magnitude of rainfall intensity for a range of durations and

return periods. Both SERS emission scenarios (A2a and B2a) indicate that the rainfall

magnitude will likely to increase in the future which indicate that climate change is real.

The increase in rainfall intensity and magnitude will have major implications on ways in

which current (and future) hydrological water management infrastructure is designed,

operated and maintained.

The seasonal analysis of the rainfall data of the stations shows that the rainfall will likely

to decrease in ‘kiremt’ (JJAS) at Addis Ababa and Fiche stations while ‘belg’ rainfall

(MAM) will likely to decrease at Kachisi station.

5.2 Recommendations

The study result is based on only one GCM model output (HadCM3), hence, to

minimize uncertainty, before revising the IDF curve of the study site to reflect the

potential impact of the climate change, it is recommended to verify it with other

GCM model outputs.

An economic analysis should be performed to justify the necessary investment that

the change in IDF will require.

The impacts of monthly and seasonal variation of rainfall pattern under climate

change scenario on soil and water conservation and other development activities

like agriculture require further investigation.

Results of any impact studies are highly dependent on the quality of input data.

Therefore, increasing the number of meteorological stations with improved

databases is very important.

75

6. REFERENCES

Abeba Tesfaye, 2012. Development of Rainfall Intensity-Duration and Frequency Curves

Under Changing Climate for Chiro and Hurso Stations of Oromia Region. MSc. Thesis.

Haramaya University. Haramaya, Ethiopia.

ACCRA (Africa Climate Change Resilience Alliance), 2011. Understanding the Influence

of Development Interventions on Adaptive Capacity at Local Level in Ethiopia. Africa

Climate Change Resilience Alliance (ACCRA) Ethiopia Synthesis Report.

Adamowski, K., and J. Bougadis, 2003. Hydrological Processes. University of Ottawa,

Ontario, Canada, Department of Civil Engineering. Hydro. Process. 17, 3547-3560.

Adeaboye, O.B., and M.O. Alatis, 2007. Performance of Probability Distribution and

Plotting Positions in Estimating the Flood of River Osun at Apoje Sub-basin, Nigeria.

Agricultural Engineering International: the CIGR journal. Department of Agricultural

Engineering, Federal University of Technology, Akure, Ondo State, Nigeria. Vol. IX: 1-

21.

Apipattanavis, S., B. Rajagopalan, and U. Lall, 2005. Local Polynomial Technique for

Flood Frequency Analysis. Journal of Hydrology. Colorado.

Arora, K.R., 2002. Irrigation, Water Power and Water Resources Engineering. Standard

Publishers Distributors. Delhi.

Assefa Kebede, 2008. Development of Rainfall Intensity-Duration-Frequency Curves for

Selected Stations in Southern Nation, Nationalities and People Region of Ethiopia. An

MSc. Thesis Submitted in Haramaya University. Haramaya, Ethiopia.

Baede, A.P., M.E. Ahlonsou, Y. Ding and D. Schimel, 2001. The Climate System, An

Overview. In: Climate Change 2001: The Scientific Basis. Contribution of Working

Group I to the Third Assessment Report of the Intergovernmental Panel on Climate

Change [Houghton, J.T.,Y. Ding, D.J. Griggs, M. Noguer, P.J. vander Linden, X. Dai, K.

Maskell, and C.A. Johnson (eds.)]. Cambridge University Press, Cambridge, United

Kingdom and New York, NY, USA.

76

Bhakar, S.R., A.K. Bansal, N. Chhajed and R.C. Purohit, 2006. Frequency Analysis of

Consecutive Days Maximum Rainfall at Banswara, Rajasthan, India. Department of Soil

and Water Engineering, Udaipur, Rajasthan, India. Vol.1, No.3.

Carter, T.R., R.N. Jones, X. Lu, S. Bhadwal, C. Conde, L.O. Mearns, B.C. O’Neill,

M.D.A. Rounsevell and M.B. Zurek, 2007: New Assessment Methods and the

Characterisation of Future Conditions. Climate Change 2007: Impacts, Adaptation and

Vulnerability. Contribution of Working Group II to the Fourth Assessment Report of the

Intergovernmental Panel on Climate Change, M.L. Parry, O.F. Canziani, J.P. Palutikof,

P.J. van der Linden and C.E. Hanson, Eds., Cambridge University Press, Cambridge, UK,

133-171.

CGD (Centre for Global Development), 2011. Map and Vulnerability Ranking. Available:

http://www.cgdev.org/section/topics/climate_change/mapping_the_impacts_of_climate_c

hange [Accessed 24 June 2013].

Chali Edesa, 2008. Regional Rainfall Intensity-Duration-Frequency Analysis for Oromia

Region. MSc. Thesis. Arba Minch University. Arba Minch, Ethiopia.

Chow V.T., D.R. Maidment and L.W.Mays, 1988, “Applied Hydrology”, McGraw- Hill.

Chow, V.T. 1992. Hydrologic Determination of Waterway Areas for Drainage Structures

in Small Drainage Basins. Bulletin No.462, Engineering Experimental Station, University

of Illinois, Urbana.

Chowdhury, J.U., J.R. Stedinger and L.H. LU, 1991. Goodness-of-fit Test for Regional

GEV Flood Distribution. Water Resource Research 27, 1765 – 1776.

Christensen, J.H., B. Hewitson, A. Busuioc, A. Chen, X. Gao, I. Held, R. Jones, R.K.

Kolli, W.-T. Kwon, R. Laprise, V. Magaña Rueda, L. Mearns, C.G. Menéndez, J.

Räisänen, A. Rinke, A. Sarr and P. Whetton, 2007a: Regional Climate Projections. In:

Climate Change 2007: The Physical Science Basis. Contribution of Working Group I to

the Fourth Assessment Report of the Intergovernmental Panel on Climate Change

[Solomon, S., D. Qin, M. Manning, Z. Chen, M. Marquis, K.B. Averyt, M. Tignor and

H.L. Miller (eds.)]. Cambridge University Press, Cambridge, United Kingdom and New

York, NY, USA.

http://www.cgdev.org/section/topics/climate_change/mapping_the_impacts_of_climate_change

http://www.cgdev.org/section/topics/climate_change/mapping_the_impacts_of_climate_change

77

Constable M., 1984. Resource for Rural Development in Ethiopia. Working Paper 17.

FAO/ Ministry of Agriculture Ethiopia, Addis Ababa

Cordes, K.E., and R.H. Hotchkiss, 1993. Design Discharge of Culverts. University of

Nebrask-Lincoln, Nebrask. 110p

Das, G., 2004. Hydrology and Soil Conservation Engineering. Prentice-Hall of India

Private Limited. New Delhi.

Desa, M.N.M., M.Z.M. Amin, M.L. Asnor, and F. Mohamed, 2006. Developing a Low

Return Period Regional IDF Relationship Using Generalized Pareto (GPA) Distribution.

The Regional Humid Tropics Hydrology and Water Resources Center. For Southeast Asia

and the Pacific. Jalan Leading off Jln Duta, Kuala Lumpur. No. 2.

Elias Jamal, 2010. Intensity-Duration-Frequency (IDF) Analysis of Point Rainfall for

Selected Meteorological Stations in Illu Aba Borra Zone, Oromia Region. MSc. Thesis.

Haramaya University. Haramaya, Ethiopia.

EXACT (Executive Action Team), 2006. Middle East Water Data Banks Project.

Application of Methods for Analysis of Rainfall Intensity in Areas of Israeli, Jordanian,

and Palestinian Interest. Water resources of Palestinian, Jordanian, and Israeli Interest.

FAO 1986. Highlands Reclamation Study Ethiopia Final Report. Vol. I & II. Rome, Italy

Fiddes, D., J. A. Forsgate, and A. O. Grigg, 1974. The Prediction of Storm Rainfall In East

Africa. Transport and Road Research Laboratory, Department of Environment, TRRL

Laboratory Report 623. Crowthorne, Berkshire.

Garg, S.K., 1999. Irrigation Engineering and Hydraulics Structures. Khanna Publisher.

New Delhi.

Giorgi, F., B.C. Hewitson, C. Christensen, R. Fu and R.G. Jones, Eds., 2001: Regional

climate information: evaluation and projections. Climate Change 2001: The Scientific

Basis. Contribution of Working Group I to the Third Assessment Report of the

Intergovernmental Panel on Climate Change, J.T. Houghton,Y. Ding, D.J. Griggs,M.

Noguer, P.J. van der Linden, X. Dai, K. Maskell and C.A. Johnson, Eds., Cambridge

University Press, Cambridge, 583-638.

78

Haan, C.T., 1997. Statistical Methods in Hydrology, IOWA State University Press.

Hare, F.K., 1983. Climate and Desertification. Revised Analysis. (WMO-UNDP) WCP-

44.

IPCC, 2001: Climate Change 2001. The Scientific Basis. Contribution of Working Group

I to the Third Assessment Report of the Intergovernmental Panel on Climate Change

[Houghton, J.T.,Y. Ding, D.J. Griggs, M. Noguer, P.J. van der Linden, X. Dai, K. Maskell,

and C.A. Johnson (eds.)]. Cambridge University Press, Cambridge, United Kingdom and

New York, NY, USA, 881pp.

IPCC, 2007a: Climate Change 2007: The Physical Science Basis. Contribution of

Working Group I to the Fourth Assessment Report of the Intergovernmental Panel on

Climate Change [Solomon, S., D. Qin, M. Manning, Z. Chen, M. Marquis, K.B. Averyt,

M. Tignor and H.L. Miller (eds.)]. Cambridge University Press, Cambridge, United

Kingdom and New York, NY, USA, 996 pp.

IPCC, 2007b: Climate Change 2007: Impacts, Adaptation and Vulnerability. Contribution

of Working Group II to the Fourth Assessment Report of the Intergovernmental Panel on

Climate Change, M.L. Parry, O.F. Canziani, J.P. Palutikof, P.J. van der Linden and C.E.

Hanson, Eds., Cambridge University Press, Cambridge, UK, 976pp.

IPCC-TGCIA, 1999. Guidelines on the Use of Scenario Data for Climate Impact and

Adaptation Assessment. Version 1. Prepared by Carter, T.R., M. Hulme, and M. Lal,

Intergovernmental Panel on Climate Change, Task Group on Scenarios for Climate Impact

Assessment, 69pp.

Kolbert, E., 2006. Field notes from a catastrophe: man, nature, and climate change.

Bloomsbury Publishing, New York.

Koutsoyiannis, D., 2001. Coupling stochastic models of different time scales, Water

Resource, 37(2), 379-392.

Koutsoyiannis, D., and C. Onof, 2000. A computer program for temporal rainfall

disaggregation using adjusting procedures, XXV General Assembly of European

Geophysical Society, Nice, Geophys. Res. Abstracts, 2 (on line at

http://www.itia.ntua.gr/e/docinfo/59/

79

Koutsoyiannis, D., D. Kozonis, and A. Manetas. 1998. A Mathematical Framework for

Studing Rainfall Intensity-Duration-Frequency Relationships. Journal of Hydrology 206,

118-135. Athens.

Krause. P., D.P. Boyle, and F. Bäse, 2005. Comparison of different efficiency criteria for

hydrological model assessment. Advances in Geosciences. Department for

Geoinformatics, Hydrology and Modelling, Friedrich-Schiller-University, Jena, Germany.

5, 89–97

Leonard Berry, 2003. Land Degradation in Ethiopia: Its Extent and Impact. Accessed at

ftp://ftp.fao.org/agl/agll/ladadocs/ETHIOPIA_LD_CASE_STUDIES.doc on 20 June 2013.

Lijalem Zeray Abraham, 2006. Climate Change Impact on Lake Ziway Watershed Water

Availability, Ethiopia. MSc. Thesis. University of Applied Sciences Cologne. Germany.

Lines, G.S. and E.M. Barrow, 2002. Regional Climate Change Scenarios in Atlantic

Canada Utilizing Downscaling Techniques: Preliminary Results. AMS Preprint, 13-17

January 2002, Orlando FL, USA.

List of African countries by population, 2013. Available:

http://en.wikipedia.org/wiki/List_of_African_countries_by_population [Accessed 12

January 2014].

Malone E.L. 2009. Vulnerability and Resilience in the Face of Climate Change: Current

Research and Needs for Population Information. PNWD-4087.

McAvaney, B.J., C. Covey, S. Joussaume, V. Kattsov, A. Kitoh, W. Ogana, A.J. Pitman,

A.J. Weaver, R.A. Wood and Z.-C Zhao, 2001. Model Evaluation. In Climate Change

2001: The Scientific Basis. Contribution of Working Group I to the Third Assessment

Report of the Intergovernmental Panel on Climate Change [Houghton, J.T.,Y. Ding, D.J.

Griggs, M. Noguer, P.J. van der Linden, X. Dai, K. Maskell, and C.A. Johnson (eds.)].

Cambridge University Press, Cambridge, United Kingdom and New York, NY, USA.

McSweeney, C., New, M. & Lizcano, G. 2010. UNDP Climate Change Country Profiles:

Ethiopia. Available: http://country-profiles.geog.ox.ac.uk/ [Accessed 10 October 2013].

ftp://ftp.fao.org/agl/agll/ladadocs/ETHIOPIA_LD_CASE_STUDIES.doc

http://en.wikipedia.org/wiki/List_of_African_countries_by_population

http://country-profiles.geog.ox.ac.uk/

80

Mearns, L.O., M. Hulme, T.R. Carter, R. Leemans, M. Lal and P. Whetton, 2001. Climate

Scenario Development. In: Climate Change 2001: The Scientific Basis. Contribution of

Working Group I to the Third Assessment Report of the Intergovernmental Panel on

Climate Change [Houghton, J.T.,Y. Ding, D.J. Griggs, M. Noguer, P.J. van der Linden, X.

Dai, K. Maskell, and C.A. Johnson (eds.)]. Cambridge University Press, Cambridge,

United Kingdom and New York, NY, USA, 881pp.

Meehl, G.A., T.F. Stocker, W.D. Collins, P. Friedlingstein, A.T. Gaye, J.M. Gregory, A.

Kitoh, R. Knutti, J.M. Murphy, A. Noda, S.C.B. Raper, I.G. Watterson, A.J. Weaver and

Z.-C. Zhao, 2007: Global Climate Projections. In: Climate Change 2007: The Physical

Science Basis. Contribution of Working Group I to the Fourth Assessment Report of the

Intergovernmental Panel on Climate Change [Solomon, S., D. Qin, M. Manning, Z. Chen,

M. Marquis, K.B. Averyt, M. Tignor and H.L. Miller (eds.)]. Cambridge University Press,

Cambridge, United Kingdom and New York, NY, USA.

Moriasi, N.D., J. G. Arnold, W.M. VanLiew, LR. Bingner, D.R. Veithand and T.

L.Harmel, 2007. Model Evaluation Guidelines For Systematic Quantification of Accuracy

in Watershed Simulations. American Society of Agricultural and Biological Engineers,

Vol. 50(3): 885-900.

Nakicenovic, N., and R. Swart, 2000. IPCC Special Report on Emissions Scenarios,

Intergovernmental Panel on Climate Change. Cambridge University Press, Cambridge,

United Kingdom.

Nĕmec, J., 1973. Engineering Hydrology. McGraw-Hill Publishing Company Limited.

New Delhi.

Nhat, M.L.,Y. Tachikawa and K. Takara, 2006. Establishment of Intensity-Duration-

Frequency Curves for Precipitation in the Monsoon Area of Vietnam. Graduate School of

Urban and Environment Engineering, Kyoto University, 49: 93-103.

Nigatu Merra, 2011. Rainfall Intensity Duration Frequency (RIDF) Relationships under

the Changing climate (Case study on Upper Blue Nile River Basin, Ethiopia). MSc.

Thesis. Addis Ababa University. Addis Ababa, Ethiopia.

81

NMSA (National Meteorological Service Agency), 1996. Assessment of Drought in

Ethiopia. No.2. Addis Ababa, Ethiopia.

NMSA (National Meteorological Agency of Ethiopia), 2007. Climate Change National

Adaptation Programme of Action of Ethiopia.

O'Hare, G., J. Sweeney and R. Wilby, 2005. Weather, Climate and Climate Change:

Human Perspectives. 403.

Palmer, Richard N., Erin Clancy, Nathan T. Van Rheenen, and Matthew W. Wiley, 2004.

The Impacts of Climate Change on the Tualatin River Basin Water Supply: An

Investigation into Projected Hydrologic and Management Impacts, Draft Report.

Department of Civil and Environmental Engineering, University of Washington, 67pp.

Prodanovic, P. and S.P. Simonovic, 2009. Revision of Intensity-Duration-Frequency under

Changing Climatic Conditions. 5th

International Symposium on Flood Defense: Managing

Flood Risk, Reliability and Vulnerability, Toronto, Ontario, Canada.

Reddi, P.J., 2002. A Text Book of Hydrology. Laxmi Publications Pvt. Ltd. New Delhi.

Ruttan, J.A., 2001. Guidelines on Flood Frequency Analysis. Alberta Transportation,

Transport and Civil Engineering Division, Civil Project Branch, Canada. 84p

Rosenzweig, C., G. Casassa, D.J. Karoly, A. Imeson, C. Liu, A. Menzel, S. Rawlins, T.L.

Root, B. Seguin, P. Tryjanowski, 2007: Assessment of observed changes and responses in

natural and managed systems. Climate Change 2007: Impacts, Adaptation and

Vulnerability. Contribution of Working Group II to the Fourth Assessment Report of the

Intergovernmental Panel on Climate Change, M.L. Parry, O.F. Canziani, J.P. Palutikof,

P.J. van der Linden and C.E. Hanson, Eds., Cambridge University Press, Cambridge, UK,

79-131.

Santos, E. G. and J. D. Salas, 1992. Stepwise disaggregation scheme for synthetic

hydrology, Journal of Hydraulic Engineering, 118(5), 765-784.

Santhi, C., J.G. Arnold, J.R. Williams, W.A. Dugas, R. Srinivasan, and L.M. Hauck, 2001.

Validation of the SWAT Model on a Large River Basin with Point and Non point Sources,

Journal of the American Water Resources Association, 1169-1188.

82

Shimelis Berhanu, 2008. Rainfall Intensity-Duration-Frequency Analysis for Parts of

Eastern Oromia. MSc. Thesis. Haramaya University. Haramaya, Ethiopia.

Slobodan P. S. and Angela, P., 2010. Updated rainfall intensity duration frequency curves

for the City of London under the changing climate. Department of Civil and

Environmental Engineering, The University of Western Ontario. London, Ontario,

Canada.

Smith, A.A., 2004. Microcomputer Interaction Design of Urban Storm water Systems

(MIDUSS), Tutorial Manual, Version, 2, Ontario, Canada.

Subramanya, K., 1994. Engineering Hydrology. TATA McGraw-Hill. New Delhi.

Suresh, R., 2005. Watershed hydrology: Principles of Hydrology. Standard Publishers

Distributors. Delhi.

Takara, K.T. and J.R. Stedinger, 1994. Recent Japanese Contribution to Frequency

Analysis and Quantile Lower Bound Estimators. Stochastic and Statistical Methods.

Hydrology and Environmental Engineering 1, 217-234. Kluwer Academic, Netherlands.

Tesfaye Morka, 2011. Development of Rainfall Intensity-Duration-Frequency Curves for

Some Selected Stations Under Changing Climate, Eastern Hararghe Zone, Oromia . MSc.

Thesis. Haramaya University. Haramaya, Ethiopia.

UNESCO and WL/Delft Hydraulics, 2005. Water Resources Systems Planning and

Management: An Introduction to Methods, Models and Applications. UNESCO

Publishing. Paris.

U.S. Army Corps of Engineers, 1994. Engineering and Design: Flood-Runoff Analysis.

Engineer Manual 1110-2-1417. Washington, DC.

Vogel, R.M. and D.E. McMartin, 1991. Probability plot Goodness-of-fit and Skewness

Estimation Procedures for the Pearson Type 3 Distribution. Water Resource Research 27,

3149- 3158.

Wilby, R. L. and T. M. L. Wigley, 1999. Precipiation Predictors for Downscaling:

Observed and General Circulation Model Relationships. International journal of

climatology,74 (2009) 106– 115.

83

Wilby, R.L. and C.W. Dawson, 2007. SDSM 4. A decision support tool for the assessment

of regional climate change impacts, User Manual.

Wilby, R. L., 2005. A framework for assessing uncertainties in climate change impacts:

Lowflow scenarios for the River Thames, UK. Water resources research.

World Bank. 2001. African Development Indicators. Washington.

World Bank, 2010. Ethiopia: Economics of Adaptation to Climate Change. Addis Ababa,

World Bank.

World Meteorological Organisation, 1994. Guide to Hydrological Practices. Data

Acquisition and Processing, Analysis, Forecasting, and Other Applications. WMO-No.

168. 5th Edition. Geneva, Switzerland.

84

7. APPENDICES

85

7.1. Appendix Tables

Appendix Table1. Annual rainfall of the study area

Year Addis Ababa Fiche Kachisi

1970 1421.6

1971 1181.2

1972 978.3

1973 1269.3

1974 1140.6

1975 917.8

1976 1124.4

1977 1471.6

1978 1046.9

1979 1314.4

1980 1219.9

1981 1176.4

1982 1210.3

1983 1192.0

1984 1128.6

1985 1190.4

1986 1234.4 1101.8

1987 1317.9 1001.9 2119.2

1988 1202.6 1145.4 1623.9

1989 1321.3 1140.9 1729.4*

1990 1124.6 1195.3 1878.4*

1991 1153.5 1060.3 1512.7

1992 1101.4 1130.6 1966.3

1993 1567.9 1205.9 2105.8*

1994 1042.5 1018.4 1756.7*

1995 1145.6 1152.8 1544.5*

1996 1548.5 1539.3 1817.8

1997 952.4 1099.5 1862.5

1998 1337.7 1139.2 1734.7

1999 929.4 1208.3 1864.1*

2000 1191.1 1150.0 1956.5

2001 1452.0 1028.9 1660.7

2002 1016.1 1060.3 1377.9

2003 1173.3 1176.6 1602.0

2004 1158.5 1103.3 1669.2

2005 1383.2 982.6 1975.5

2006 1341.2 1349.3 1902.1

2007 1308.6 1138.6 1767.4

2008 1330.7 1046.5 2214.2

2009 1240.6 1221.5 1475.0

*estimated values

86

Appendix Table2. Mean Monthly rainfall of the three stations

Station J F M A M J J A S O N D Total

Addis Ababa 18.4 35.8 64.7 86.3 88.3 132.7 269.0 290.7 171.7 37.8 8.0 10.7 1214.0

Fiche 21.3 33.8 62.0 70.4 48.3 84.5 330.2 340.6 114.6 20.2 7.6 8.0 1141.6

Kachisi 15.4 17.2 81.5 76.3 118.8 284.1 398.2 418.3 234.5 101.9 25.1 16.3 1787.7

Appendix Table3. The monthly variability of rainfall of the study area

Month Addis Ababa Fiche Kachisi

Min. Max. Mean SDv. CV. Min. Max. Mean SDv. CV. Min. Max. Mean SDv. CV.

J 0 127.9 18.4 25.2 137.2 0.0 77.3 21.3 20.9 98.1 0.0 60.8 15.4 16.5 107.0

F 0 155.9 35.8 33.6 93.9 0.0 106.6 33.8 33.9 100.1 0.0 75.1 17.2 18.3 106.6

M 0 248.9 64.7 60.4 93.3 0.0 253.7 62.0 52.7 85.1 0.9 175.8 81.5 52.9 64.8

A 8.4 197.6 86.3 48.7 56.4 1.9 133.0 70.4 38.1 54.1 8.1 190.8 76.3 41.9 54.9

M 0.5 241.3 88.3 60.4 68.4 2.1 151.4 48.3 35.6 73.7 8.4 284.2 118.8 70.1 59.0

J 31.9 258.5 132.7 45.8 34.5 12.9 209.1 84.5 44.7 52.9 136.8 439.5 284.1 72.1 25.4

J 180.1 428 269.0 53.4 19.9 107.1 486.5 330.2 87.7 26.6 209.9 524.3 398.2 80.1 20.1

A 137.3 426.5 290.7 63.2 21.8 212.5 496.0 340.6 66.4 19.5 305.7 552.9 418.3 72.0 17.2

S 88.4 294.2 171.7 53.3 31.1 39.9 216.8 114.6 45.5 39.7 142.3 413.3 234.5 79.4 33.8

O 0 272.5 37.8 49.2 130.3 0.0 79.9 20.2 22.6 111.9 0.9 314.5 101.9 78.8 77.4

N 0 79.4 8.0 18.4 229.7 0.0 58.6 7.6 12.8 167.5 0.0 180.4 25.1 40.2 160.4

D 0 65 10.7 17.8 167.3 0.0 42.4 8.0 12.4 154.3 0.0 74.9 16.3 21.2 130.2

Annual 917.8 1567.9 1214.0 157.7 13.0 982.6 1539.3 1141.6 118.0 10.3 1377.9 2214.2 1787.7 215.5 12.1

87

Appendix Table4. Calibration and validation results for Addis Ababa Station

a. Calibration b. Validation

88

Appendix Table5. Calibration and validation results for Fiche Station


Appendix Table6. Calibration and validation results for Kachisi Station


89

Appendix Table7. Summary of extreme rainfall values ( XT) for Fiche stations under A2a

Scenario


A. (2010-2039)

2 25.00 30.43 33.35 38.00 42.46 46.96

5 32.71 39.82 43.63 49.72 55.56 61.45

10 37.81 46.03 50.44 57.47 64.22 71.03

25 44.26 53.88 59.04 67.27 75.18 83.15

50 49.04 59.71 65.42 74.55 83.30 92.14

100 53.79 65.49 71.76 81.76 91.37 101.06

B. (2040-2069)

2 24.78 30.17 33.06 37.67 42.10 46.56

5 32.53 39.61 43.40 49.45 55.26 61.12

10 37.67 45.86 50.24 57.25 63.98 70.76

25 44.15 53.75 58.89 67.11 74.99 82.94

50 48.96 59.61 65.31 74.42 83.16 91.98

100 53.73 65.42 71.68 81.68 91.27 100.95

C. (2070-2099)

2 25.36 30.88 33.83 38.55 43.08 47.65

5 33.03 40.22 44.07 50.21 56.11 62.06

10 38.11 46.40 50.84 57.93 64.74 71.60

25 44.53 54.21 59.40 67.69 75.64 83.66

50 49.29 60.01 65.75 74.92 83.72 92.60

100 54.02 65.76 72.05 82.11 91.75 101.48

Appendix Table8. Summary of extreme rainfall values ( XT) for Fiche stations under B2a

Scenario


A. (2010-2039)

2 25.40 30.92 33.88 38.60 43.14 47.71

5 33.22 40.44 44.31 50.49 56.42 62.40

10 38.39 46.74 51.21 58.36 65.21 72.13

25 44.93 54.70 59.94 68.30 76.32 84.42

50 49.79 60.61 66.41 75.68 84.57 93.53

100 54.60 66.48 72.84 83.00 92.75 102.58

B. (2040-2069)

2 25.53 31.08 34.06 38.81 43.37 47.97

5 33.41 40.68 44.57 50.78 56.75 62.77

10 38.63 47.03 51.53 58.71 65.61 72.57

25 45.22 55.05 60.32 68.73 76.81 84.95

50 50.11 61.00 66.84 76.17 85.11 94.14

100 54.96 66.91 73.32 83.54 93.36 103.26

C. (2070-2099)

2 25.90 31.54 34.56 39.38 44.00 48.67

5 34.06 41.47 45.44 51.78 57.86 64.00

10 39.47 48.05 52.65 59.99 67.04 74.15

25 46.29 56.36 61.75 70.37 78.63 86.97

50 51.36 62.53 68.51 78.06 87.24 96.49

100 56.38 68.64 75.21 85.70 95.77 105.93

90

Appendix Table9. Summary of extreme rainfall values (XT) for Kachisi stations under A2a

Scenario T (years) 1hr 2hr 3hr 6hr 12hr 24hr

A. (2010-2039)

2 32.71 39.82 43.63 49.72 55.56 61.45

5 40.41 49.20 53.91 61.43 68.64 75.92

10 45.51 55.41 60.71 69.18 77.30 85.50

25 51.95 63.25 69.30 78.97 88.25 97.61

50 56.73 69.07 75.68 86.24 96.37 106.59

100 61.48 74.85 82.01 93.45 104.43 115.50

B. (2040-2069)

2 32.51 39.58 43.37 49.42 55.22 61.08

5 39.97 48.66 53.31 60.75 67.89 75.09

10 44.90 54.67 59.90 68.25 76.27 84.36

25 51.14 62.26 68.22 77.74 86.87 96.08

50 55.77 67.90 74.39 84.77 94.73 104.78

100 60.36 73.49 80.52 91.75 102.53 113.41

C. (2070-2099)

2 32.68 39.79 43.59 49.67 55.51 61.40

5 40.36 49.14 53.84 61.35 68.55 75.82

10 45.44 55.33 60.62 69.07 77.19 85.37

25 51.87 63.15 69.19 78.84 88.10 97.44

50 56.63 68.95 75.55 86.08 96.20 106.40

100 61.36 74.71 81.86 93.27 104.23 115.28

Appendix Table10. Summary of extreme rainfall values ( XT) for Kachisi stations under B2a

Scenario


A. (2010-2039)

2 32.36 39.40 43.17 49.19 54.97 60.80

5 39.87 48.54 53.19 60.61 67.72 74.91

10 44.84 54.60 59.82 68.16 76.17 84.25

25 51.13 62.25 68.20 77.71 86.84 96.05

50 55.79 67.92 74.42 84.80 94.76 104.81

100 60.42 73.55 80.59 91.83 102.62 113.50

B. (2040-2069)

2 32.67 39.78 43.59 49.66 55.50 61.38

5 40.20 48.94 53.62 61.10 68.28 75.52

10 45.18 55.01 60.27 68.68 76.74 84.88

25 51.47 62.67 68.67 78.24 87.44 96.71

50 56.14 68.35 74.89 85.34 95.37 105.48

100 60.78 74.00 81.08 92.39 103.24 114.19

C. (2070-2099)

2 32.05 39.02 42.75 48.71 54.44 60.21

5 39.44 48.02 52.61 59.95 67.00 74.10

10 44.34 53.98 59.15 67.40 75.31 83.30

25 50.52 61.51 67.40 76.80 85.82 94.92

50 55.11 67.10 73.52 83.78 93.62 103.54

100 59.67 72.65 79.60 90.70 101.35 112.10

91

Appendix Table 11. Computed rainfall intensities (mm/hr) using XT and IDF parameters at Fiche station for 2020s (A2a scenario)

Time (min)

2 years 5 years 10 years 25 years 50 years 100 years

RI. Using

XT values

RI. Using

IDF

parameters

RI. Using

XT values

RI. Using

IDF

parameters

RI. Using

XT values

RI. Using

IDF

parameters

RI. Using

XT values

RI. Using

IDF

parameters

RI. Using

XT values

RI. Using

IDF

parameters

RI. Using

XT values

RI. Using

IDF

parameters

60 25 25.01 32.71 32.72 37.81 37.83 44.26 44.26 49.04 49.01 53.79 53.8

120 15.22 15.21 19.91 19.91 23.01 23.01 26.94 26.94 29.85 29.86 32.74 32.74

180 11.12 11.11 14.54 14.54 16.81 16.81 19.68 19.68 21.81 21.82 23.92 23.92

360 6.33 6.33 8.29 8.28 9.58 9.58 11.21 11.21 12.43 12.43 13.63 13.63

720 3.54 3.54 4.63 4.63 5.35 5.35 6.26 6.26 6.94 6.94 7.61 7.61

1440 1.96 1.96 2.56 2.56 2.96 2.96 3.46 3.46 3.84 3.84 4.21 4.21

R2 1.000 1.000 1.000 1.000 1.000 1.000

NSE 1.000 1.000 1.000 1.000 1.000 1.000


Time

(min)


RI. Using

XT values

RI. Using

IDF

parameters

RI. Using

XT values

RI. Using

IDF

parameters

RI. Using

XT values

RI. Using

IDF

parameters

RI. Using

XT values

RI. Using

IDF

parameters

RI. Using

XT values

RI. Using

IDF

parameters

RI. Using

XT values

RI. Using

IDF

parameters

60 24.78 24.77 32.53 32.53 37.67 37.67 44.15 44.15 48.96 48.69 53.73 53.76

120 15.09 15.09 19.81 19.8 22.93 22.93 26.88 26.87 29.81 29.86 32.71 32.7

180 11.02 11.02 14.47 14.47 16.75 16.75 19.63 19.63 21.77 21.85 23.89 23.88

360 6.28 6.28 8.24 8.24 9.54 9.54 11.19 11.18 12.4 12.45 13.61 13.61

720 3.51 3.51 4.61 4.61 5.33 5.33 6.25 6.25 6.93 6.93 7.61 7.61

1440 1.94 1.94 2.55 2.55 2.95 2.95 3.46 3.46 3.83 3.82 4.21 4.21

R2 1.000 1.000 1.000 1.000 1.000 1.000

NSE 1.000 1.000 1.000 1.000 1.000 1.000

92


Time (min)


RI. Using

XT values

RI. Using

IDF

parameters

RI. Using

XT values

RI. Using

IDF

parameters

RI. Using

XT values

RI. Using

IDF

parameters

RI. Using

XT values

RI. Using

IDF

parameters

RI. Using

XT values

RI. Using

IDF

parameters

RI. Using

XT values

RI. Using

IDF

parameters

60 25.36 25.36 33.03 33.02 38.11 38.11 44.53 44.55 49.29 49.31 54.02 53.98

120 15.44 15.44 20.11 20.11 23.2 23.2 27.1 27.1 30 30 32.88 32.89

180 11.28 11.28 14.69 14.69 16.95 16.95 19.8 19.8 21.92 21.91 24.02 24.03

360 6.42 6.42 8.37 8.37 9.65 9.65 11.28 11.28 12.49 12.48 13.69 13.69

720 3.59 3.59 4.68 4.68 5.39 5.39 6.3 6.3 6.98 6.98 7.65 7.65

1440 1.99 1.99 2.59 2.59 2.98 2.98 3.49 3.49 3.86 3.86 4.23 4.23

R2 1.000 1.000 1.000 1.000 1.000 1.000

NSE 1.000 1.000 1.000 1.000 1.000 1.000

Appendix Table 14. Computed rainfall intensities (mm/hr) using XT and IDF parameters at Fiche station for 2020s (B2a scenario)

Time

(min)


RI. Using

XT values

RI. Using

IDF

parameters

RI. Using

XT values

RI. Using

IDF

parameters

RI. Using

XT values

RI. Using

IDF

parameters

RI. Using

XT values

RI. Using

IDF

parameters

RI. Using

XT values

RI. Using

IDF

parameters

RI. Using

XT values

RI. Using

IDF

parameters

60 25.4 25.38 33.22 33.24 38.39 38.39 44.93 44.93 49.79 49.77 54.6 54.63

120 15.46 15.46 20.22 20.22 23.37 23.37 27.35 27.35 30.31 30.31 33.24 33.23

180 11.29 11.3 14.77 14.77 17.07 17.07 19.98 19.98 22.14 22.14 24.28 24.27

360 6.43 6.44 8.41 8.41 9.73 9.73 11.38 11.38 12.61 12.62 13.83 13.83

720 3.6 3.59 4.7 4.7 5.43 5.43 6.36 6.36 7.05 7.05 7.73 7.73

1440 1.99 1.99 2.6 2.6 3.01 3.01 3.52 3.52 3.9 3.9 4.27 4.28

R2 1.000 1.000 1.000 1.000 1.000 1.000

NSE 1.000 1.000 1.000 1.000 1.000 1.000

93

Appendix Table15. Computed rainfall intensities (mm/hr) using XT and IDF parameters at Fiche station for 2050s (B2a scenario)

Time (min)


RI. Using

XT values

RI. Using

IDF

parameters

RI. Using

XT values

RI. Using

IDF

parameters

RI. Using

XT values

RI. Using

IDF

parameters

RI. Using

XT values

RI. Using

IDF

parameters

RI. Using

XT values

RI. Using

IDF

parameters

RI. Using

XT values

RI. Using

IDF

parameters

60 25.53 25.52 33.41 33.39 38.63 38.66 45.22 45.23 50.11 50.13 54.96 54.94

120 15.54 15.54 20.34 20.34 23.51 23.51 27.52 27.52 30.5 30.5 33.46 33.46

180 11.35 11.36 14.86 14.86 17.18 17.17 20.11 20.1 22.28 22.28 24.44 24.44

360 6.47 6.47 8.46 8.47 9.78 9.78 11.46 11.45 12.69 12.69 13.92 13.93

720 3.61 3.61 4.73 4.73 5.47 5.47 6.4 6.4 7.09 7.09 7.78 7.78

1440 2 2 2.62 2.61 3.02 3.03 3.54 3.54 3.92 3.92 4.3 4.3

R2 1.000 1.000 1.000 1.000 1.000 1.000

NSE 1.000 1.000 1.000 1.000 1.000 1.000

Appendix Table16. Computed rainfall intensities (mm/hr) using XT and IDF parameters at Fiche station for 2080s (B2a scenario)

Time

(min)


RI. Using

XT values

RI. Using

IDF

parameters

RI. Using

XT values

RI. Using

IDF

parameters

RI. Using

XT values

RI. Using

IDF

parameters

RI. Using

XT values

RI. Using

IDF

parameters

RI. Using

XT values

RI. Using

IDF

parameters

RI. Using

XT values

RI. Using

IDF

parameters

60 25.9 25.91 34.06 34.07 39.47 39.49 46.29 46.26 51.36 51.36 56.38 56.38

120 15.77 15.77 20.74 20.73 24.02 24.02 28.18 28.19 31.26 31.26 34.32 34.32

180 11.52 11.52 15.15 15.14 17.55 17.54 20.58 20.59 22.84 22.84 25.07 25.07

360 6.56 6.56 8.63 8.63 10 10 11.73 11.73 13.01 13.01 14.28 14.28

720 3.67 3.67 4.82 4.82 5.59 5.59 6.55 6.55 7.27 7.27 7.98 7.98

1440 2.03 2.03 2.67 2.67 3.09 3.09 3.62 3.62 4.02 4.02 4.41 4.41

R2 1.000 1.000 1.000 1.000 1.000 1.000

NSE 1.000 1.000 1.000 1.000 1.000 1.000

94

Appendix Table17. Computed rainfall intensities (mm/hr) using XT and IDF parameters at Kachisi station for 2020s (A2a scenario)

Time

(min)


RI. Using

XT values

RI. Using

IDF

parameters

RI. Using

XT values

RI. Using

IDF

parameters

RI. Using

XT values

RI. Using

IDF

parameters

RI. Using

XT values

RI. Using

IDF

parameters

RI. Using

XT values

RI. Using

IDF

parameters

RI. Using

XT values

RI. Using

IDF

parameters

60 32.71 32.72 40.41 40.42 45.51 45.48 51.95 51.96 56.73 56.75 61.48 61.51

120 19.91 19.91 24.6 24.6 27.7 27.71 31.63 31.62 34.53 34.53 37.42 37.42

180 14.54 14.54 17.97 17.97 20.24 20.25 23.1 23.1 25.23 25.22 27.34 27.33

360 8.29 8.28 10.24 10.24 11.53 11.53 13.16 13.16 14.37 14.37 15.57 15.57

720 4.63 4.63 5.72 5.72 6.44 6.44 7.35 7.35 8.03 8.03 8.7 8.7

1440 2.56 2.56 3.16 3.16 3.56 3.56 4.07 4.07 4.44 4.44 4.81 4.81

R2 1.000 1.000 1.000 1.000 1.000 1.000

NSE 1.000 1.000 1.000 1.000 1.000 1.000


Time

(min)


RI. Using

XT values

RI. Using

IDF

parameters

RI. Using

XT values

RI. Using

IDF

parameters

RI. Using

XT values

RI. Using

IDF

parameters

RI. Using

XT values

RI. Using

IDF

parameters

RI. Using

XT values

RI. Using

IDF

parameters

RI. Using

XT values

RI. Using

IDF

parameters

60 32.51 32.5 39.97 39.97 44.9 44.92 51.14 51.16 55.77 55.75 60.36 60.39

120 19.79 19.79 24.33 24.33 27.33 27.33 31.13 31.13 33.95 33.95 36.74 36.74

180 14.46 14.46 17.77 17.77 19.97 19.96 22.74 22.74 24.8 24.8 26.84 26.83

360 8.24 8.24 10.13 10.12 11.38 11.37 12.96 12.95 14.13 14.13 15.29 15.29

720 4.6 4.6 5.66 5.66 6.36 6.36 7.24 7.24 7.89 7.89 8.54 8.54

1440 2.55 2.54 3.13 3.13 3.52 3.52 4 4 4.37 4.36 4.73 4.73

R2 1.000 1.000 1.000 1.000 1.000 1.000

NSE 1.000 1.000 1.000 1.000 1.000 1.000

95


Time

(min)


RI. Using

XT values

RI. Using

IDF

parameters

RI. Using

XT values

RI. Using

IDF

parameters

RI. Using

XT values

RI. Using

IDF

parameters

RI. Using

XT values

RI. Using

IDF

parameters

RI. Using

XT values

RI. Using

IDF

parameters

RI. Using

XT values

RI. Using

IDF

parameters

60 32.68 32.7 40.36 40.37 45.44 45.46 51.87 51.89 56.63 56.65 61.36 61.4

120 19.9 19.89 24.57 24.57 27.67 27.66 31.58 31.57 34.47 34.47 37.35 37.35

180 14.53 14.52 17.95 17.94 20.21 20.2 23.06 23.06 25.18 25.18 27.29 27.28

360 8.28 8.28 10.22 10.22 11.51 11.51 13.14 13.14 14.35 14.34 15.54 15.54

720 4.63 4.63 5.71 5.71 6.43 6.43 7.34 7.34 8.02 8.02 8.69 8.69

1440 2.56 2.56 3.16 3.16 3.56 3.56 4.06 4.06 4.43 4.43 4.8 4.81

R2 1.000 1.000 1.000 1.000 1.000 1.000

NSE 1.000 1.000 1.000 1.000 1.000 1.000

Appendix Table20. Computed rainfall intensities (mm/hr) using XT and IDF parameters at Kachisi station for 2020s (B2a scenario)

Time

(min)


RI. Using

XT values

RI. Using

IDF

parameters

RI. Using

XT values

RI. Using

IDF

parameters

RI. Using

XT values

RI. Using

IDF

parameters

RI. Using

XT values

RI. Using

IDF

parameters

RI. Using

XT values

RI. Using

IDF

parameters

RI. Using

XT values

RI. Using

IDF

parameters

60 32.36 32.36 39.87 39.89 44.84 44.86 51.13 51.13 55.79 55.83 60.42 60.38

120 19.7 19.7 24.27 24.27 27.3 27.29 31.13 31.12 33.96 33.95 36.78 36.78

180 14.39 14.39 17.73 17.72 19.94 19.94 22.73 22.73 24.81 24.8 26.86 26.88

360 8.2 8.2 10.1 10.1 11.36 11.36 12.95 12.95 14.13 14.13 15.31 15.31

720 4.58 4.58 5.64 5.64 6.35 6.35 7.24 7.24 7.9 7.9 8.55 8.55

1440 2.53 2.53 3.12 3.12 3.51 3.51 4 4 4.37 4.37 4.73 4.73

R2 1.000 1.000 1.000 1.000 1.000 1.000

NSE 1.000 1.000 1.000 1.000 1.000 1.000

96

Appendix Table21. Computed rainfall intensities (mm/hr) using XT and IDF parameters at Kachisi station for 2050s (B2a scenario)

Time (min)


RI. Using

XT values

RI. Using

IDF

parameters

RI. Using

XT values

RI. Using

IDF

parameters

RI. Using

XT values

RI. Using

IDF

parameters

RI. Using

XT values

RI. Using

IDF

parameters

RI. Using

XT values

RI. Using

IDF

parameters

RI. Using

XT values

RI. Using

IDF

parameters

60 32.67 32.66 40.2 40.21 45.18 45.2 51.47 51.49 56.14 56.12 60.78 60.79

120 19.89 19.89 24.47 24.47 27.5 27.5 31.33 31.33 34.17 34.18 37 37

180 14.53 14.53 17.87 17.87 20.09 20.09 22.89 22.88 24.96 24.97 27.03 27.03

360 8.28 8.28 10.18 10.18 11.45 11.44 13.04 13.04 14.22 14.23 15.4 15.4

720 4.63 4.63 5.69 5.69 6.39 6.4 7.29 7.29 7.95 7.95 8.6 8.6

1440 2.56 2.56 3.15 3.15 3.54 3.54 4.03 4.03 4.39 4.39 4.76 4.76

R2 1.000 1.000 1.000 1.000 1.000 1.000

NSE 1.000 1.000 1.000 1.000 1.000 1.000

Appendix Table 22. Computed rainfall intensities (mm/hr) using XT and IDF parameters at Kachisi station for 2080s (B2a scenario)

Time

(min)


RI. Using

XT values

RI. Using

IDF

parameters

RI. Using

XT values

RI. Using

IDF

parameters

RI. Using

XT values

RI. Using

IDF

parameters

RI. Using

XT values

RI. Using

IDF

parameters

RI. Using

XT values

RI. Using

IDF

parameters

RI. Using

XT values

RI. Using

IDF

parameters

60 32.05 32.06 39.44 39.45 44.34 44.35 50.52 50.5 55.11 55.15 59.67 59.7

120 19.51 19.51 24.01 24.01 26.99 26.99 30.75 30.76 33.55 33.54 36.33 36.32

180 14.25 14.25 17.54 17.53 19.72 19.71 22.47 22.47 24.51 24.5 26.53 26.52

360 8.12 8.12 9.99 9.99 11.23 11.23 12.8 12.8 13.96 13.96 15.12 15.11

720 4.54 4.54 5.58 5.58 6.28 6.28 7.15 7.15 7.8 7.8 8.45 8.45

1440 2.51 2.51 3.09 3.09 3.47 3.47 3.95 3.95 4.31 4.32 4.67 4.67

R2 1.000 1.000 1.000 1.000 1.000 1.000

NSE 1.000 1.000 1.000 1.000 1.000 1.000

97

Appendix Table23. IDF parameters for historic rainfall at Addis Ababa, Fiche and Kachisi

stations)

Parameters Return period (year)

2 5 10 25 50 100

a 1285.1 1731.17 1671.89 2489.19 2701.69 3043.58

b 8.697 10.91 4.146 16.323 17.473 19.944

c 0.9075 0.9175 0.8969 0.9374 0.9387 0.9467

Source: (Chali, 2008)

Appendix Table24. Historic rainfall intensities of Addis Ababa, Fiche and Kachisi stations

Time

(min)

Return period (years)

2 5 10 25 50 100

60 27.66 34.70 40.03 42.78 45.53 48.09

120 15.65 19.77 22.14 24.84 26.58 28.30

180 11.06 13.99 15.54 17.65 18.92 20.19

360 6.02 7.60 8.43 9.59 10.30 10.99

720 3.24 4.08 4.55 5.11 5.49 5.85

1440 1.74 2.18 2.45 2.70 2.90 3.07

Adapted from: (Chali, 2008)

98

7.2 Appendix Figures

Appendix Figure1. Double mass curve for Addis Ababa station

Appendix Figure 2. Double mass curve for Fiche station

Appendix Figure3. Double mass curve for Kachisi station

y = 1.0282x + 944.9 R² = 0.9976

0

10000

20000

30000

40000

50000

0 10000 20000 30000 40000 50000An

nual

cum

mula

tive

rain

fall

of

Add

is A

bab

a (m

m)

Annual cummulative rainfall for near by satations (mm)

y = 1.270x - 68.07 R² = 0.999

0

5000

10000

15000

20000

25000

30000

0 5000 10000 15000 20000

Cum

mula

tive

annual

rai

nfa

ll o

f F

iche

(m

m)

Cummulative annuall rainfall of near by station (mm)

y = 1.2237x - 293.56 R² = 0.9997

0.0

5000.0

10000.0

15000.0

20000.0

25000.0

30000.0

35000.0

40000.0

0.0 5000.0 10000.0 15000.0 20000.0 25000.0 30000.0 35000.0

Cum

mula

tive

annual

rai

nfa

ll o

f K

achis

i (m

m)

Cummulative annual rainfall of nearby station (mm)

99

Appendix Figure4. IDF curves for Fiche Station under climate change A2a Scenario

100

Appendix Figure5. IDF curves for Fiche Station under climate change B2a Scenario

chemeda's thesis feb 2014 final

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