impacts of urbanization on kaduna river flooding and … of... · 2015-09-16 · danube river,...
TRANSCRIPT
IMPACTS OF URBANIZATION ON KADUNA RIVER FLOODING AND STREAMFLOW MODELING
BY
ALAYANDE, ADEGOKE WAHEED
PG/PhD/07/42567
THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS OF THE DEGREE OF
DOCTOR OF PHILOSOPHY IN CIVIL ENGINEERING
TO THE
DEPARTMENT OF CIVIL ENGINEERING FACULTY OF ENGINEERING
UNIVERSITY OF NIGERIA NSUKKA, NIGERIA
APRIL 2010
ii
CERTIFICATION
Alayande Adegoke Waheed, a Post-Graduate student of Civil Engineering Department with
Registration Number PG/PhD/07/42567 has satisfactorily completed the requirements for the
research work for the Degree of Doctor of Philosophy (Ph.D) in Civil Engineering. The work
embodied in this thesis is original and has not been submitted in part or full for any other
Diploma or Degree of this or any other University.
____________________________ _____________________
Engr. Prof. J.C. Agunwamba Date Supervisor
___________________________ _____________________
Engr. Prof. J.C. Agunwamba Date Head of Department
___________________________ _____________________
Engr. Prof. I. L. Nwaogazie Date External Examiner
iii
DEDICATION
This work is dedicated to the Almighty God, Who has made it possible for me to go through this
course.
iv
ACKNOWLEDGEMENT
I acknowledge the contributions of my supervisor, Professor J. C. Agunwamba whose
words of encouragement and untiring support serve as a source of strength that has made my
completion of this course possible. I am also grateful to Engr. Dr. O. A. Bamgboye most
especially for providing materials supports that enhanced the quality of this research work.
My appreciation also goes to the entire members of staff of the Civil Engineering
Department of the University of Nigeria Nsukka for providing me with amiable environment that
facilitated my stay in the University.
Above all, I am very grateful to my wife, Folake Alake Alayande for her support and
prayer throughout the period of this study.
Alayande Adegoke Waheed
v
TABLE OF CONTENTS
Certification ii
Dedication iii
Acknowledgement iv
Table of Contents v
List of Figures viii
List of Plates ix
List of Tables x
Abstract xi
CHAPTER ONE INTRODUCTION 1
1.0 Background 1
1.1 Problem Definition. 2
1.2 Objectives 3
1.3 Location of Project Area 3
1.4 Project Justification 5
1.5 Project Scope 6
1.6 Contribution of Research to Knowledge 7
CHAPTER TWO LITERATURE REVIEW 8
2.0 The Kaduna River Basin 8
2.1 Climate 9
2.2 River Floods and Flooding in Nigeria 10
2.3 The Saint Venant Equation 12
2.4 Hydrologic and Hydraulic Flood Modeling Studies 14
2.5 Flood Simulation Tools and Models 17
2.6 River Channel Planform Classification and Flooding Potentials 19
CHAPTER THREE METHODOLOGY 23
3.1 Data Collection 23
3.2 Analysis of Rainfall Data 23
vi
3.3 Analysis of Streamflow Data 29
3.4 Flow Duration Analysis 32
3.5 Regeneration of the Kaduna 2003 Flood Disaster 34
3.6 Flood Frequency Analysis 36
3.7 Field Investigation and Data Collection 38
3.8 Geomorphic Characterization and Channel Classification 39
3.9 Topographical Characteristics of the Studied Segments 41
3.9.1 Longitudinal Profile 41
3.9.2 Cross Sectional Views 42
3.9.3 Planform 42
3.10 Classification Result 43
3.11 Geomorphology and River Mechanics 50
3.11.1 Meandering and Bends 50
3.11.2 Bifurcations 51
3.11.3 Braided Reaches 51
3.11.4 Tributaries and Confluence Points 52
3.12 Impacts of Urbanization on Kaduna River Channel 52
3.12.1 Floodplain Encroachment 52
3.12.2 Flood Inundation Risk Zone 55
3.12.3 Decreased Floodplain Vegetation Density 55
3.12.4 Increase Bank Erosion 57
CHAPTER FOUR MODEL FORMULATION AND DEVELOPMENT 58
4.1 Model Description and Modification 58
4.2 Numerical Solution of Model Equations 61
4.3 Finite Difference Formulation 62
4.4 The Double Sweep Solution Technique 67
4.5 Applications of the Saint Venant Equation to Kaduna River 70
4.5.1 Model Boundary Limits 71
4.5.2 Model Computerization 71
4.5.3 Model Calibration 71
vii
4.5.4 Steady Run for Extreme Flows 72
4.5.4.1 Boundary Conditions 72
4.5.4.2 Model Run and Verification 73
4.5.5 Unsteady Run for Normal Flows 74
4.5.5.1 Boundary Conditions 74
4.5.4.2 Model Initialization and Model Run 78
4.6 Model Computerization User’s Guide 79
4.6.1 Flow Chart 79
4.6.2 Programs 80
CHAPTER FIVE RESULTS AND DISCUSSION 89
5.1 Results 89
5.2 Discussion 90
CHAPTER SIX CONCLUSION AND RECOMMENDATIONS 92
6.1 Conclusion 92
6.2 Recommendations 92
REFERENCES 93
APPENDIX 96
viii
LIST OF FIGURES
2.1 Map of the Kaduna River Basin 9
2.2 Longitudinal, Cross- sectional, and Plan views of major stream types 22
2.3 Classification Key for Natural Rivers 22
3.1 Variations in Maximum Rainfall Over Kaduna River Basin 1955 to 2004 28
3.2 Total Annual Rainfall over Kaduna Basin Measured at Kaduna
Airport 1955 to 2004 28
3.3 Max Daily Flow of Kaduna River at Kaduna South 1967 to 2004 31
3.4 Max 5-days Moving Avgerage flow of Kaduna River at Kaduna
South 1967 to 2004 31
3.5 Max 7-days Moving Average Flow of Kaduna River at Kaduna
South 1967 to 2004 31
3.6 Average Daily Flow of Kaduna River at Kaduna South 1967 to 2004. 31
3.7 Period of Record Flow Duration Curve for Kaduna River at Kaduna
South Waterworks 1967 to 2004 32
3.8 Flow Duration Curve for Kaduna River at Kaduna South
Waterworks 1967 to 2004 33
3.9 Discharge Rating Curve at Kaduna South Waterworks 35
3.10 Section of the Kaduna River and Locations of the Surveyed Cross Sections 40
3.11 Longitudinal Profile of Kaduna River Main Channel 41
4.1 Finite difference Scheme for the Implicit Method 62
4.2 Comparison of Predicted and Measured Water Stages for 5yr Flood 76
4.3 Comparison of Predicted and Measured Water Stages for 10yr Flood 76
4.4 Comparison of Predicted and Measured Water Stages for 25yr Flood 76
4.5 Comparison of Predicted and Measured Water Stages for 50yr Flood 76
4.6 Comparison of Predicted and Measured Water Stages for 100yr Flood 77
4.7 Comparison of Predicted and Measured Water Stages for Year 2003 Flood 77
4.8 Comparison of Predicted Discharge and Measured Discharge at
the Kaduna South Waterworks 78
i,j
ix
LIST OF PLATES
I The Satellite Imagery of the Project Area 6
II Reaches 1, 2 and 3. 46
III General Conditions of Reach 1 May and June 2009 47
IV General Conditions of Reach 2 May and June 2009 48
V General Conditions of Reach 3 February and March 2009 49
VI Survey Data Overlaid with Topographical Map of Project Area. 54
VII Existing Flood Protection Efforts. 56
VIII River Bank Cuttings along the Studied Reaches. 57
x
LIST OF TABLES
3.1 Summary of Rainfall Analysis over Kaduna 1955 to 2004 26
3.2 Flow Regime of Kaduna River at Kaduna South 1967 to 2004 30
3.3 Flow Duration of Kaduna River at Kaduna South Waterworks
1967 to 2004 Based on Log Cycle Interval 33
3.4 Rating Table Kaduna River at Kaduna South Waterworks 35
3.5 Flood Frequency Analysis for Kaduna River at Kaduna South
Waterworks Log Pearson Type III Skew Coefficients 37
3.6 Flood Frequency Analysis for Kaduna River at Kaduna South
Waterworks Log Pearson Type III Estimated Flood Flows (m3/sec) 37
3.7 Flood Frequency Analysis of Rainfall at Kaduna Airport
Log Pearson Type III Skew Coefficients 37
3.8 Flood Frequency Analysis of Rainfall at Kaduna Airport Log Pearson
Type III Estimated Rainfall (mm). 37
3.9 Characteristics of the Longitudinal Profiles of Kaduna River 41
3.10 Summary of Gemorphological Parameters 43
3.11 Geomorphological Characterization of Reach 1 Kaduna River 44
3.12 Geomorphological Characterization of Reach 2 Kaduna River 44
3.13 Geomorphological Characterization of Reach 3 Kaduna River 45
3.14 Summary of Bends Analysis. 50
3.15 Distribution of Bifurcated Reaches 51
3.16 Braided Reaches and type of Bars 52
3.17 Distribution of Tributaries along the Kaduna River 52
3.18 Extent of Kaduna River Floodplain Development Analysis 53
4.1 Linearization of Upstream Boundary condition 73
4.2 Linearization of Downstream Boundary condition 73
4.3 Linearization of Upstream Boundary Condition for Unsteady Model Run 74
4.4 Linearization of Downstream Boundary condition for Unsteady Model Run 75
4.5 Comparison of Predicted and Measured Discharge at the Kaduna
South Waterworks Gauging Station 78
xi
ABSTRACT
Population growth, urbanization and expansion of structural developments into flood prone areas
of urban settlements of Nigeria are challenges requiring dynamic predictions of inundation areas;
development of models for the propagation of flood waves on the floodplain; and the
development of a rapid response and flood warning systems. Hydrologic and hydraulics
modeling provide a veritable tool to investigate the spatial and temporary impact of the existing
and future landuse changes in the floodplain on the water surface elevation, velocity, and flow
patterns within the river reach. In this study the Saint Venant hydrodynamic equations were
modified for floodplain development index and applied to investigate the spatial and temporary
impact of the existing and future landuse changes on the water surface elevation, and flow
patterns along the Kaduna River floodplain. Results obtained indicated that the Kaduna River
floodplain is increasingly urbanized with a maximum encroachment rate of 85.31%, 68.47% and
67.54% respectively in Reach 2, Reach 3 and Reach 1, respectively over the period 1962 and
2009. The result also shows that the 5yr, 10yr, 25yr, 50yr, and 100yr floods when occur, the
level of floodplain inundation could be as much as 82.53% to 94.48% of the width of the
floodplain with Kigo extension, Sardauna Crescent, Kabala Doki, Living Faith Church area and
parts of Ungwan most vulnerable.
1
CHAPTER ONE
INTRODUCTION
1.1 BACKGROUND
Many cities developed independently along a number of river valleys throughout
the world because rivers supplied a continuous if not always dependable flow of water for
domestic, agricultural, industrial, navigational and waste disposal purposes. These cities
includes Kaduna, the capital city of Kaduna State Nigeria along the Kaduna River, Cairo
along the Nile River, New York along the Hudson River, Washington D.C. the capital of
the United States along the Potomac River, Dresden (Germany) along the Elbe River,
Madrid the capital of Spain along the Manzanares River, London the capital of Great
Britain, along the Thames River, Wien (Vienna) the capital city of Austria along the
Danube River, Berlin the capital of Germany along the Spree and Havel rivers, Paris the
capital of France along the Seine River, Moscow the capital of Russia along the Moskva
River, Istanbul the largest city in Turkey on both sides of the Bosporus River etc. These
rivers along with climate, vegetation, geography, and topography shaped the
development of these cities and inspired new technological and economic developments
to meet population increases.
On several occasions these rivers overflow their banks and spills flood waters into
the adjoining properties on their floodplain, Kaduna river in 2003; Elbe River in 2003,
2005 and 2007, River Sokoto in 2006, River Ogun in 2007, etc. Consequently flooding,
an associated natural hazard with floodplain developments is a major problem these cities
had to contend with and develop policy, legislative and technical measures to control.
In Nigeria, floods and flooding of urban settlements are becoming annual
occurrences especially during the raining seasons and the attendant damages to structural
2
and infrastructural systems as well as social and economic impact on the people calls for
a more pragmatic approach to flood and floodplain management. Population growth,
urbanization and expansion of structural developments into traditional flood prone areas
of urban settlements of Nigeria are challenges requiring dynamic predictions of
inundation areas; development of models for the propagation of flood waves on the
floodplain; and the development of a rapid response and flood warning systems.
Hydrologic and hydraulics modeling provide a veritable tool to investigate the spatial and
temporary impact of the existing and future landuse changes in the floodplain on the
water surface elevation, velocity, and flow patterns within the river reach.
1.1 Problem Definition.
On Friday September 6th 2003 Kaduna river overflows its banks thus spilling
flood waters into properties within its floodplains along the city of Kaduna. The water
stages in the channel were unprecedented and rose up to the bottom level of the railway
bridge across it in Kaduna south. The damages were equally unprecedented and
properties worth about N500 million ($3.9m) were destroyed while thousands of people
were rendered homeless in the State by the ravaging flood which lasted for three
consecutive days before the flood waters recedes. Affected by the flood are Mamman
Kotangora Estate, Kigo Road extension, Kabala Doki area and parts of Malali Estate.
During the flood, agricultural crops and household items including food items,
rugs, television sets, fridges, chairs, tables and other expensive electronics were damaged
when water from the river submerged most of the houses. Several mechanic workshops,
grocery stores and pharmaceutical shops were also submerged. At Kigo extension, apart
from household items, maize and sugar cane farms were also destroyed. In addition, such
3
structures as churches, mosques and private buildings were affected during the flood. The
new Makarfi City, an extension of the Kaduna City is planned on the eastern flank of
Kaduna within the study area. This will further exert more pressure on the resources of
the Kaduna River and increase the potentials for flooding.
1.2 OBJECTIVES
The objectives of the study are to:
1. Determine the magnitude and immediate causes of the 2003 flood event;
2. Develop a hydraulic model based on the modified St. Vennant hydrodynamic
flow equations to reconstruct the 2003 flood event and;
3. Calibrate and verify the model; and
4. Use the generated hydrograph as input into the hydraulic model to predict water
stages, flows and extent of flooded areas corresponding to the floods of various
frequencies 200, 100, 50, 10, 5 and 2 years recurrence interval passing the reaches
under investigation.
1.3 LOCATION OF PROJECT AREA
The project area covers the reaches of the Kaduna River extending between the
confluences with the Kangimi and Rigasa Rivers located upstream and downstream
Kaduna city respectively. For the purpose of this study, the parts of the Kaduna city
adjoining the Kaduna River as it flows past the city is divided into three distinct reaches
as described below. Plate I shows the location of the project area on satellite imagery.
4
1.3.1 Upper Reach.
The upper reach extends between the confluence of the Kaduna river with the
Kangimi to just upstream of the Kaduna Eastern Bye Pass Bridge at Malali. Important
settlements along this reach include Raafin Gusa, Angwan Dosa, part of Malali and the
Makarfi new town. The Kaduna North waterworks is the only industry within this reach
and mining of fine aggregates in the main channel and floodplain farming was dominant
activities in the floodplain. A weir constructed at the intake of the waterworks raise the
water levels in the river at low flows. The Kaduna basin especially upstream of this reach
has a large concentration of small to medium scale dams for water supply and irrigation
and which regulates the flows into this reach and with the potential to generate flash
floods during rainy season. The Galma River, one of the major tributary discharges into
the Kaduna River some 30km upstream of this reach has two major dams on its main
channel. The Kangimi reservoir is about one kilometer upstream of this reach and
releases its flow into the Kaduna river to augment the flow in the main channel during the
low flow period.
1.3.2 Middle Reach.
The middle reach extends between the Eastern Bye Pass bridge at Malali to the
Kaduna South Waterworks. The reach is the most developed of the three reaches in terms
of physical developments in the floodplain and host to the Kaduna South waterworks,
Ahmadu Bello Statdium, Angwan Rimi GRA, Kigo, Living Faith Church, Kabala Doki
and Barnawa. The 2003 flood has its devastating impacts concentrated in this reach. A
weir constructed to raise the water levels at the waterworks in addition to the railway
5
bridge, the old bridge linking the northern and southern parts of the town are the only
hydraulic structures within this reach.
1.3.3 Lower Reach
The lower reach extends downstream of the Kaduna South Waterworks to the
confluence of the Kaduna river with the Rigasa river. This reach adjoins the Zango,
Kudenda Industrial layout, Kakuri, Nasarawa, Moslem burial ground. Hydraulic
structures along this reach include three intake pumping stations belonging to the
Nigerian Breweries Plc, the United Nigerian Textile and Arewa Textiles while the
Western Bypass Expressway Bridge crosses the Kaduna River within this reach.
The lower reach is usually characterized by very low flow and almost dry situation
at the peak of the dry season and many industrial effluents are discharged into this
segment of the river. Physical development activities are fast emerging in the floodplain
within this reach especially around Kinkino extension of Angwan Muazu, Kakuri, and
Kudenda industrial layout. The reach profile is characterized by visible rock rapids
causing braiding and flow bifurcations at various segments of the reach.
1.4 PROJECT JUSTIFICATION.
The reaches of Kaduna River under investigation are very important to the socio-
economic development of the City. Important industries, two waterworks, Stadium
Complex, Children Play grounds, churches, and three bridge crossings which are vital
communication links linking the two major parts of the town on one hand and linking
Kaduna to the other parts of the North on the other. Repeated flooding of these areas
could have a damaging effect to socio-economic development of the State in particular
and Nigeria in general. The serviceability of the three bridge crossings over the Kaduna
6
river could be impaired if overtopped by flood waters, a situation capable of disrupting
the socio-economic activities the City.
The magnitude of the 2003 flood, extent of damages and the fact that absolute
safety against flooding cannot be guaranteed, it would therefore be necessary to carryout
an in-depth study of the affected reaches of the Kaduna River to identify the causes,
understand the dynamics of the flood through the development and application of
hydraulic models to develop strategic action plan to control a re-occurrence. The choice
of the hydraulic modeling was informed by the urban nature of the flooding and the need
to put into better perspectives the impact of the floodplain developments on the evolution
of the hydraulic geometry of the Kaduna river channel within the affected reaches.
Plate I The Satellite Imagery of the Study Area.
1.5 PROJECT SCOPE.
The scope of the study is limited to the investigation of the evolution of the
hydraulic geometry and geomorphological characteristics of the Kaduna river at the
7
reaches under investigation through the use of satellite imageries, topographical maps and
field measurements. A hydraulic model based on St. Vennant hydrodynamic flow
equations was constructed to evaluate the impacts of urbanization on the propagation of
flood wave on the floodplain.
1.6 CONTRIBUTION OF RESEARCH TO KNOWLEDGE.
The following contributions to knowledge have been made by the project:
1. An existing model was modified for the term “entrenchment ratio” which is an
index of floodplain development consequent to urbanization.
2. The model was applied to the Kaduna River with flood of various frequencies to
generate future scenarios of floodplain inundation upon which strategic action
plans can be developed to reduce the risks of flooding.
3. The study equally delineated zones under high risks of flooding and methods for
determining these risk zones. Government can use this to reclaim such high risk
zone for agricultural and recreational developments.
4. A hydraulic geometric database of the Kaduna River constituted in the course of
the study can form the reference database upon which impact of future
development within the floodplain is measured.
8
CHAPTER TWO
LITERATURE REVIEW
2.0 THE KADUNA RIVER BASIN
The word Kaduna is an Hausa word meaning “crocodiles”. The Kaduna river
took its source on the Jos Plateau, flows northwest across the Kaduna plains cutting
several gorges through rugged terrain between Kaduna and Zungeru. Finally, the river
flows southwards through the broad, level Niger valley, and enters the Niger River near
Wuya in Niger State having drained about 70,200 square kilometers of land area in a
550km long main river course (MNS Encarta, 2007) covering Kaduna, Niger, FCT, parts
of Plateau, Nasarawa, and Kano States. Major tributaries joining the Kaduna River along
its course include rivers Karami, Galma,Tubo, Sarkin Pawa and Mariga in that order from
source. Kaduna is the only state capital the main channel passes through and Shiroro
hydropower reservoir is the only major dam across the main.
Great seasonal fluctuations characterize the Kaduna's water flow; peak discharges
occur between July and September. Vegetation in the Kaduna’s 70,200 square kilometers
drainage basin is moist savanna. Dense rain forests line the lower course of the river,
where moisture is more abundant. Maize (corn), sorghum, yams, cowpeas, and cotton are
grown in this region, mostly on small, hand-tilled farms. Fishing is of local importance,
especially along the lower Kaduna. Figure 2.1 presents the map of the Kaduna river
basin.
9
2.1 CLIMATE
The dominant features of rainfall in Northern Nigeria are its seasonal character
and variability from year to year. Long term average annual rainfall in the Kaduna basin
ranges between 1000mm and 1200mm and is delivered by the northward movement of
the moisture laden South West Trade Winds bringing rainfall to the basin between April
and October each year. The dry months over the basin are characterized by southward
movement of the North East Trade Winds bringing dry and dusty harmattan winds to the
basin between November and March. Figure 2.2 presents the long term monthly rainfall
in the Kaduna basin.
Figure 2.1 Map of the Kaduna River Basin
10
2.2 RIVER FLOODS AND FLOODING IN NIGERIA.
There have been several cases of floods in Nigeria mostly resulting from heavy
rainfall and excess releases from dams whose operational capacities could not cope with
excessive inflows into their reservoir areas. In most cases these releases are made mainly
to safe the dams whose failure could be more catastrophic than the consequences of the
releases. In all cases, houses, property, farm produce and animals were destroyed running
into billions of naira each year (Vanguard, 2007; The Punch, 2003; Vanguard, 2005).
Managing flood and other disasters focuses on palate measures and reducing the socio-
economic impacts of these disasters through mobilizing relief materials with little
investments onto research efforts aiming at understanding the dynamics of these natural
events and reducing the impacts of future flood events. In fact a standing National
Emergency Management Agency (NEMA) was established by government at the federal
level and State Emergency Management Agency (SEMA) at State levels to rapidly
respond to the plight of the people in the cases of disasters including flooding. Flood
simulations are rarely used in disaster preparations and management either at policy
making or implementation levels.
Etiosa (2006) in a discussion paper on “Dams are unrenewable” reported that over
26 villages including Galadima Kogo, Gofa, Kusasun, Pai, Lagado, Nakpinda and Karai
in Kede, Lakpma and Shiroro Local Government in Niger State were flooded by the
waters from Rivers Niger and Kaduna. The flood which struck in the early hours of
Saturday 11th September, 2003 resulted from a heavy rainfall and the release of excess
water from the Shiroro Hydro-Electric Dam by the National Electric Power Authority
(NEPA). The flood displaced about 10,000 persons in Ketsho in Kede Local
Government, while other 13,500 persons in Lakpam and Shiroro were rendered homeless
11
(This Day, September 16, 2003). Similarly, in 1999 at least seven local government
districts in the state were flooded when water from the Shiroro Dam was released. Etiosa
(2006) also reported that the Obudu Dam spillway was damaged by storm in July 2003
which resulted in fatal disaster that claimed over 200 houses, several farmlands,
settlements and business concerns. Besides the release of excess water from Lagdo Dam,
expert attributed the disaster to intensive and non-stop rainfall in Obudu on the fateful
day for 16 hours. The rainfall recorded at the Obudu Dam meteorological station was
314.5mm, more than 15 years average rainfall for the peak months of July and
September, which was not anticipated for when the dam was constructed.
The 2006 Gusau flood disaster occurred on Saturday, September 30 2006 when a
section of the barrage across the River Sokoto on the outskirts of Gusau collapsed after a
heavy storm which had fallen for the previous two days. The incident occurred after
sluice gates failed to function, causing the water to overwhelm the dam. Lives were lost,
thousands of people became homeless, a number of farmlands that were almost due for
harvest were devastated and hundreds of livestock were killed. Furthermore, wells on
which the people depended for drinking water became polluted by the floodwaters.
In a research findings on the Gusau 2006 flood event, the National Water
Resources Institute (NWRI, 2008) found that a maximum precipitation of 182.9mm was
recorded over Gusau on the 14th August 2006 forty seven days before the 2006 flood
which is nearer to the probable maximum precipitation of 190mm calculated for the
Sokoto basin and concluded that the Gusau barrage and indeed the Sokoto river basin
actually experienced its “limiting storm” in September 2006 which sets in on the 14th
August 2006. However the non operational of the barrage overflow gates and the
inadequate capacity of the relief spillway of 17.273m3/sec can obviously not be able to
12
cope with the incoming flood waters into the reservoir hence the collapse of the barrage
in September 30, 2006 forty days after the basin storm sets in.
The Ogun Osun river systems on which we have Oyan and Ikere Gorge dams are
characterized by annual flood occurrences, flooding Abeokuta and Lagos each year.
River Benue is also not left out of flooding washing away the bridge at Jimeta in 2005.
2.3 The Saint Venant Equation
The basic equations that describe the propagation of a wave in an open channel
are the Saint Venant’s equation (Chow, 1985), consisting of the continuity and
momentum equations presented in Equations (2.1) and (2,2), respectively. In differential
form the governing equations are written as:
Continuity equation:
0=−∂∂
+∂∂ q
tA
xQ
(2.1)
Momentum:
( ) 0)(/2
=−+∂∂
+∂
∂+
∂∂
xf SSxhgA
xAQ
tQ
(2.2)
Where Q the flow through the section is, A is the flow area, x is the longitudinal
distance, t time, xS channel bottom slope, q is lateral inflow into the channel and fS
friction slope. The term 0)( =− xf SSgA is the kinematic wave; 0)( =−+∂∂
xf SSxhgA is
the diffusion wave and dynamic wave represented by the complete momentum equation.
The range of conditions over which these equations remain valid is constrained by
the following assumptions made in its derivation:
13
1. The flow is one dimensional such that the velocity is constant over a cross section
and the water level is horizontal;
2. The vertical component of the acceleration of the fluid is negligible so that the
pressure variation with the depth is hydrostatic;
3. Friction and turbulence can be represented using the same empirical laws that
govern steady state flow (such as the Manning’s equation); and
4. The bed slope is small resulting in the cosine of the angle between the bed level
and the horizontal being approximately unity.
There are other ways of representing the Saint Venant equations which are based
upon the same hypothesis but are expressed in terms of a different set of dependent
variables. Some of the more commonly used alternatives Cunge et al. (1980) for general
cross sections are presented as follows:
1. Using Q and h
01=
∂∂
+∂∂
tQ
Bth
(2.3)
( ) 0)(/2
=−+∂∂
+∂
∂+
∂∂
xf SSxhgA
xAQ
tQ
(2.4)
2. Using Q and y, where y is the surface elevation (y = h + z).
01=
∂∂
+∂∂
tQ
Bth
(2.5)
( ) 0/2
=+∂∂
+∂
∂+
∂∂
fgASxhgA
xAQ
tQ
(2.6)
3. Using u and h
14
0tan
=
∂∂
+∂∂
+∂∂
+∂∂
= tconshxA
Bu
xhu
xu
BA
th
(2.7)
0)( =−+∂∂
+∂∂
+∂∂
of SSgxhg
xuu
tu
(2.8)
4. Using u and y
0)(tan
=
∂∂
++∂∂
+∂∂
+∂∂
= tconsho x
ABuS
xyu
xu
BA
ty
(2.9)
0=+∂∂
+∂∂
+∂∂
fgSxyg
xuu
tu
(2.10)
It may be more appropriate to deal with one particular form of the equations than the
other depending on the particular problem under consideration and the numerical
techniques used.
2.4 HYDROLOGIC AND HYDRAULIC FLOOD MODELING STUDIES
Hydraulic modeling and geomorphic analysis had been used to solve floods and
flood related problems by engineers and scientists all over the world. Ayres Associates
(2002) use hydraulic modeling and geomorphic analysis to investigate the potential long-
term impact of reducing maintenance to the existing revetment on the Sacramento River
at County Road 29 combined with planned riparian restorations. As part of the analysis
two primary concerns were considered. The first concern is the effect on the operation of
the flood relief structures for controlling overbank flows into the Butte Basin, and the
second is the effect of potential changes in river alignment that could occur in
downstream reaches of the river. The results indicated that a meander bend cutoff at Road
29 through Kimmelshue Bend will have a small effect on the distribution of flood flows
15
between the Butte Basin and the flood control levees on the Sacramento River; the
modeled riparian restoration scenarios show moderate increases in water surface
elevations within the area for the given restoration conditions and that there is a moderate
probability that a major flood can produce a neck cutoff of Kimmelshue Bend at Road 29.
Hydraulic Modelling Services Ltd (HMSL 2007) on behalf of Environment
Waikato (EW) developed a hydraulic model for the Wentworth River and Moanaanuanu
Estuary to assess the predicted impact of flood hazard for various scenarios relating to the
presence or removal of mangroves from Moanaanuanu Estuary, and the associated
sedimentation levels on the future Wentworth River flood hazard area in Whangamata
The presence of mangroves in the Moanaanuanu Estuary and the associated
sedimentation were observed to likely reduce the hydraulic capacity of the river/estuarine
system.
The results produced by the hydraulic model indicated that the Wentworth River
current flood hazard is generally limited to land that is not subject to urban land-use and
that the extent of the future Wentworth River flood hazard would be reduced if the
mangroves are removed. The hydraulic model predicted that a number of properties
would be affected by the Wentworth River flood hazard by 2080. Hence, flood hazard
reduction within Whangamata would be necessary in the future regardless of the
mangroves removal, which could be achieved by a combination of different methods
including planning controls, flood control works, catchment and river management and
improvement work and mangroves removal and/or control.
Richard Taylor (2003) use hydrologic and hydraulic modeling via ArcView GIS
software in conjunction with the HEC-GeoRas and Geoprocessing extensions as a tool to
identify flooding problems at streams, culverts and bridges under the existing land use
16
conditions in the City of Griffin Georgia USA. The types of problems identified include
structural flooding, nonstructural flooding, areas that could potentially erode, undersized
or deteriorated drainage infrastructure, and roadway overtopping by floodwaters. The
results were used to develop comprehensive stormwater management priorities;
prioritized stream crossings in the watershed and identified Capital Improvement Project
locations based on the Level of Service.
Due to several large and damaging flood events in the state of California during
the 1980’s and 1990’s, most notably the January 1997 event, a Flood Emergency Action
Team was assembled. The team developed recommendations on how the impacts of
future flood events could be reduced and ecosystems restored. As part of the solution to
develop comprehensive plans for flood control the U. S. Army Corps of Engineers
developed hydrologic and hydraulic models of the river systems in the Sacramento and
San Joaquin River basins which were used by the Sacramento District for planning
purposes and making basin wide flood operation decisions on a real-time basis during
flood episodes.
In a river restoration study of the Middle Rio-Grande River, Susan (2006)
quantifies spatial and temporal trends in hydraulic geometry of the river. The study which
focuses on the post dam trends in the Cochiti reach discovered a declining trend in the
width, width / depth ratio and cross sectional area following reduced annual peak flow
rates into its downstream reaches. The planform also changes from braided to single
thread meandering channel between 1918 and 2004.
Swiatek (2007) modifies the St. Venant equations with retention effects of the
vegetated areas on flood wave conveyance to develop an unsteady 1D flow model for a
channel with vegetated floodplains. The model was applied to a 50 km long double
17
trapezoidal channel and contrary to the traditional approach, where floodplains are
considered as storage areas, the model computes velocities, discharges and friction
factors for the floodplains and the main channel depending on the type of vegetation and
allow for the computation of the variations of water level and discharges in the main
channel as well as on the floodplains.
2.5 FLOOD SIMULATION TOOLS AND MODELS
The resolution of river hydraulics issues always requires prediction of one or
more flow parameters; water stage or water surface elevation; velocity, or rate of
sedimentation. USACE (1993) presents the techniques and procedures used for flood
investigations and river engineering analysis and associated data requirements based on
past experiences. Research efforts in flood simulations have led to the development of
hydraulic software that enable the flood behavior of water across complex landscape to
be simulated. Notable among them are MIKE II, TELEMAC, HEC-RAS, WMS, HEC-
PrePro etc.
MIKE II is a one dimensional model developed by the Danish Hydraulic Institute
(DHI), and simulates one dimensional channel flow by solving the fully dynamic de
Saint-Venant equations while offering different modules for modeling flows, sediment
transport, water quality. It also provides an option where bed resistance (Manning’s n)
can be calculated as a function of hydraulic parameters such as water depth, hydraulic
radius, and flow velocity.
TELEMAC-2D is a two dimensional model developed by the National Hydraulics
and Environment Laboratory (LNHE) which solves the de Saint-Venant equations in two
dimensions. The simulation modules are based on solving partial differential equation
18
systems through the finite element method using a mesh structure consisting of triangles.
The simulation results produce water depth and average velocity at each node of the
computational mesh.
HEC-RAS - 1D hydraulic water surface profile model for steady and unsteady
flow for a full network of natural and constructed channels The program was developed
by the US Department of Defense, Army Corps of Engineers in order to manage the
rivers, harbors, and other public works under their jurisdiction. It has found wide
acceptance by many others since its public release in 1995. The Hydrologic Engineering
Center (HEC) in Davis, California developed the River Analysis System (RAS) to aid
hydraulic engineers in channel flow analysis and floodplain determination. It includes
numerous data entry capabilities, hydraulic analysis components, data storage and
management capabilities, and graphics and reporting capabilities.
Watershed Modeling System (WMS) is a GIS Watershed model interface for
HEC-1,HEC-RAS, HEC-HMS developed by the Environmental Modeling Research
Laboratory of Brigham Young University in cooperation with the U.S. Army Corps of
Engineers Waterways Experiment Station. WMS merges information obtained from
terrain models and GIS with lumped parameter hydrologic analysis models such as HEC-
1 and TR-20.
HEC-PrePro is a system of scripts and controls developed by the Centre for
Research in Water Resources at the University of Texas that allows the use of hydrologic,
topographic, and topologic information from digital spatial data to prepare input file
called the basin file containing the hydrologic and hydraulic data that can be read by
HEC-HMS (Olivera et al., 1998). The use of HEC-PrePro makes the calculation of the
19
parameters required by HEC-HMS easier and faster and thereby improving the efficiency
of the modeling system.
Ramirez Jorge and David Raff (2005) developed mathematical model for hillslope
hydrological process based on mathematical and numerical scheme presented by Fieldler
and Ramirez (2005). The model couples the Richards equation for one dimensional
infiltration to overland flow equation and a physically based sediment detachment and
transport component. The model captures effectively the interactions between overland
flow, infiltration, and erosion and sediment transport.
2.6 RIVER CHANNEL PLANFORM CLASSIFICATION AND FLOODING
POTENTIALS
The channel planform can be classified as straight, meandering and braiding or
anastomosing and variation from one class to another can occur from one reach to
another on the same stream. Braiding is typically referred to as the splitting of channels
around bars or islands, which are contained within a dominant pair of floodplain banks.
The main characteristic of the braided reach is the repeated division and joining of
channels and their associated flow patterns, referred to as zones of confluence and
diffluence.
Anastomosing refers to a type of channel splitting where the channel segments are
divided by stable, often vegetated islands that are large relative to channel widths.
Anastomosed channels typically remain divided at bankfull flows, often referred to as the
formative discharge that equals or barely exceeds the top of a river’s banks.
The concept of channel planform classification is based on empirical relationship
expressing the hydraulic geometry (width, depth and slope) of alluvial channels as a
20
separate function of dominant or channel forming discharge. The empirical relationship
were developed by, among others, Blench (1957) and Simons and Albertson (1963).
More recent developments and applications in hydraulic modeling include USACE
(1993), HMSL (2007), Richard Taylor (2003), Susan Novalk (2006), and Ayres
Associates (2002).
The hydraulic geometry regime of a River is a measure of its response to
hydrologic and environmental factors and generally describes the way in which the
channel properties changes with streamflow Channel geometry and characteristics of
streamflow are inherently related and over time changes in the geometric characteristics
of river channels are consequences of human developmental activities and associated
climatic changes in the basin. These changes which are manifested in the hydraulic
geometry, channel planform, cross sectional boundaries, longitudinal profiles and bed
topography ultimately affects the carrying capacities of the channel with wider
implications to the flood dynamics and propagation into the adjoining floodplains. For
example a river flowing full in a straight reach and running into a meander will have a
backwater effect at inlet into the meander channel section and water stages in the channel
raised. If braided sections exists in the meander channel, this will further reduces the
carrying capacities of the channel and eventually leads to channel overflow and spilling
flood waters into the floodplain.
Rosgen (1996) stream classification systems are widely used in the study of
stream morphology. The classification is a four-level classification based on a
“continuum of physical variables”. Level-I classification, otherwise referred to as
geomorphic characterization, takes into account channel slope (longitudinal profile),
shape (plan view morphology, cross-sectional geometry), and patterns to classify streams
21
into seven major categories labeled A-G. The Level-II morphological delineative criteria
include landform/soils, entrenchment ratio, width/depth ratio, sinuosity, channel slope,
and channel materials. The 42 subcategories of Level-II streams are labeled with a letter
and a number, A1-G6 (Rosgen 1996). Level-III designations are primarily used in
specific studies or in restoration projects to assess the quality and/or progress of a specific
reach. Level-IV classifications may be used to verify results of specific analyses used to
develop empirical relationships (such as a roughness coefficient) (Rosgen, 1996). The
level-I and level-II Rosgen classification systems based on the morphological relations
associated with stream types are as presented in Figures 2.2 and 2.3 which form the basis
for the classification of the reaches of Kaduna River in this study.
The morphological relations used for the classifications include:
1. The channel sinuosity which is an index of channel pattern, determined from a ratio of
stream length divided by valley length; or estimated from a ratio of valley slope
divided by channel slope. For a channel that is parallel to the valley (essentially
straight) sinuosity equals to 1. Gravel-bed River tends to have sinuosities ranging
from about 1.2 to 1.8, with lower values generally at higher slopes.
2. The entrenchment ratio (ER) is the ratio of the flood-prone area width (Wfpa
) divided
by bankfull channel width (Wbkf
).
3. The width to depth ratio (W/D) is the ratio of the bankfull width to the mean depth of
the stream channel at bankfull stage elevation.
The bankfull width (Wbkf
) is the width of the stream channel at the bankfull stage
elevation in a riffle section. The mean depth (dbkf
) is the depth of the stream channel at
the bankfull stage elevation in a riffle section. The maximum depth (dmbkf
) is the depth of
22
the bankfull channel cross-section, or vertical distance between the bankfull stage and
Thalweg elevations, in a riffle section. The flood-prone area width (Wfpa
) is measured at
an elevation that is twice the maximum depth at the location that the maximum depth was
determined.
Figure 2.2 longitudinal, cross-sectional, and plan views of major stream types
Figure 2.3 Classification Key for Natural Rivers
23
CHAPTER THREE
METHODOLOGY
3.1 DATA COLLECTION.
Long term, adequate and reliable time series data on hydrological variables, either real or
constructed, is an important prerequisite for any reliable forecasts of extreme events in
hydrology. Kaduna River is gauged at Kaduna South Waterworks located in reach number three
under consideration and the Power Holding Company of Nigeria uses the same station for
discharge measurement to estimate inflow into Shiroro Hydropower reservoir located some
100km downstream.
Long term daily rainfall data collected by Nigerian Meteorological Agency at Kaduna
Airport and Zaria College of Aviation Technology were available for the period 1955 to 2007
and 1980 to 2007, respectively. The Nigerian Meteorological Agency collects climatological
data for Aviation Control use with the best of instrumentations and well trained staff. The data
were used as collected except for correction to the metric system of the pre 1970 record. Rainfall
data collected by the Kaduna State Water Board at Kaduna South for the period 1958 to 2007
were available as monthly summary in many cases. Efforts to obtain daily rainfall records were
unsuccessful. Monthly summary data is not ideal for the study under consideration and this set of
data were not considered for subsequent analysis.
3.2 ANALYSIS OF RAINFALL DATA
Floods are catchment response to rainfall events on the basin and its magnitude and
frequencies are affected by the physical properties of the catchment and hydraulic
characteristics of the river channels. Statistical analyses of the rainfall data were carried out on
24
Microsoft EXCEL to create the following extreme rainfall database in an attempt to identify
the causes of the flood. The following database of extreme rainfall events were generated from
available rainfall data at Kaduna Airport and Zaria:
a. Maximum daily rainfall for each month;
b. Maximum five consecutive days total rainfall;
c. Maximum seven consecutive days total rainfall; and
d. Maximum annual rainfall.
The analyses of the resultant databases are presented as follows:
1. Maximum daily rainfall measured at Kaduna Airport for each month of the year 1955 to
2004 were computed and a maximum rainfall of 68.7mm was recorded on 19th September
2003 as against 17.6mm on the 6th September 2003, the day of the Kaduna 2003 flood.
Rainfall of 31.4mm, 4mm and 62.6mm were recorded earlier on 5th, 4th and 2nd September
2003. Upstream rainfall station at Zaria on the Galma River, a major tributary of Kaduna
River recorded its maximum daily rainfall of 60.8mm on 1st October 2003 long after the
2003 flood disaster in Kaduna. The implications of these are that the 2003 flood event was
not as a result of one single event of rainfall because the value of 68.7mm ranked 20th
maximum daily rainfall for the period 1955 to 2004. The nineteen maximum daily rainfalls
were with no incidences of floods.
2. Maximum five consecutive days total rainfall measured at Kaduna Airport for the period
1955 to 2004 were computed and and whereas a maximum 5-days consecutive days
rainfall of 122.6mm was recorded for the year 2003 on the 16th July 2003 and 115.6mm on
September 6th 2003 at Kaduna. The values 122.6mm and 115.6mm recorded at Kaduna
were ranked 21st and 29th, respectively maximum 5-days consecutive rainfall for the period
25
1955 to 2004. For the period 1980 to 2007, Zaria recorded a maximum 5-days consecutive
total rainfall of 126.8mm on 15th August 2003 and 65.1mm on 6th September 2003.
3. Maximum seven consecutive days total rainfall measured at Kaduna Airport for the period
1955 to 2004 were computed. Maximum 7-days consecutive days’ rainfall of 157mm was
recorded for the year 2003 on the 22nd August and 115.6mm on September 6th 2003. The
values 157mm and 115.6mm were ranked 23rd and 52nd, respectively maximum 7-days
consecutive rainfall for the period 1955 to 2004. For the period 1980 to 2007, Zaria
recorded a maximum 7-days consecutive total rainfall of 155.8mm on 13th August 2003
and 113.9mm on 6th September 2003.
4. Total annual rainfall measured at Kaduna Airport for the period 1955 to 2004 indicated the
year 2003 annual rainfall of 1459.4mm was the third historical maximum annual rainfall
coming after 1691.34mm and 1674.88mm of 1955 and 1957 respectively while the period
average annual rainfall was 1,218.59mm. This interestingly revealed that the year 2003
was the third wettest year for the period 1955 and 2004 and the month of August 2003 was
fifth wettest month in history. There was no information that the Kaduna River overflew
its banks in 1955 and 1957 but it is obvious that the level of urbanization in 2003and hence
encroachment into the Kaduna River floodplain is higher in 2003 than any of the 1955 and
1957. The graphical presentations of the rainfall analysis as presented in Figures 3.1 and
3.2 indicated a downward trend in annual rainfall. This further explains that the 2003 flood
was not as a result of peak rainfall alone but that in 2003 the Kaduna basin recorded its
third maximum rainfall within the study period and the resulting runoff overwhelms the
channel carrying capacities of the Kaduna River channel at several sections of the river
adjoining the Kaduna Capital City. The channel carrying capacities is a function of the
26
channel geometry which over the years obviously suffered degradation arising from
urbanization and bed siltation.
The summary of analysis of rainfall is presented in Table 3.1 and Figures 3.1 and 3.2.
Details of rainfall analysis are presented in Appendix I-Rainfall. The overall analysis of
rainfall indicated that the Kaduna 2003 flood which occurred on the 6th September 2003 was
caused by high rainfall as indicated by the analysis of the annual series.
Table 3.1 Summary of Rainfall Analysis over Kaduna 1955 to 2004 Year Max 5-day
Rainfall (mm)
Max 7-day Rainfall (mm)
Total Rain-Days
Total Annual Rainfall (mm)
Max Daily Rainfall (mm) Rainfall Date of Occurrence
1955 160.02 195.83 119.00 1,691.39 79.756 11th Sep 1955 1956 105.16 108.97 89.00 1,031.24 64.77 6th Sep 1956 1957 111.76 134.62 124.00 1,674.88 67.818 8th Sep 1957 1958 103.63 123.95 100.00 1,047.50 44.196 14th Sep 1958 1959 141.22 158.50 89.00 1,149.86 52.832 10th Sep 1959 1960 126.49 126.49 103.00 1,245.11 60.452 10th July 1960 1961 104.90 118.87 89.00 1,038.61 77.724 11th Aug 1961 1962 123.19 145.80 113.00 1,286.76 50.038 2nd Sept 1962 1963 120.40 140.97 115.00 1,360.17 59.944 17th July 1963 1964 127.25 159.26 96.00 1,211.07 90.678 17th Sept 1964 1965 151.13 174.50 108.00 1,243.33 101.092 25th July 1965 1966 145.54 154.18 111.00 1,378.97 55.88 30th Aug 1966 1967 109.98 110.24 101.00 1,141.98 97.79 21st May 1967 1968 95.00 132.84 105.00 1,360.17 76.962 29th July 1968 1969 129.54 153.92 110.00 1,423.19 77.978 11th Apr 1969 1970 117.86 134.37 92.00 1,038.61 48.768 18th Aug 1970 1971 96.90 133.10 103.00 1,263.32 68 16th Aug 1971 1975 105.10 146.10 106.00 1,307.13 52.1 26th May 1975 1977 119.30 124.10 76.00 968.50 74.3 8th Sep 1977 1978 116.00 138.00 114.00 1,414.61 65.1 18th Sep 1978 1979 163.80 199.10 105.00 1,445.93 79.2 28th Aug 1979 1980 121.10 131.00 82.00 1,210.48 77.9 16th May 1980 1981 104.90 158.40 93.00 1,228.06 55.1 10th Aug 1981 1982 152.60 191.60 67.00 1,061.00 58.3 29th Aug 1982 1983 115.60 126.90 70.00 899.60 86.6 16th Sept 1983 1984 103.70 116.20 91.00 1,184.59 53.2 28th July 1984 1985 118.40 136.80 96.00 1,215.60 60.6 29th Mar 1985 1986 133.30 148.90 79.00 1,090.30 57.6 13th Sep 1986 1987 189.10 222.50 85.00 1,200.10 108.1 5th June 1987 1988 186.30 260.50 84.00 1,176.80 132.1 13th Aug 1988 1989 104.20 134.00 98.00 1,012.80 45.9 10th Aug 1989 1990 101.50 137.50 93.00 1,022.00 55.8 11th Sep 1990 1991 238.80 263.00 104.00 1,408.10 118.6 5th Aug 1991 1992 149.20 158.10 88.00 1,118.80 59.6 4th Aug 1992
27
1993 161.60 191.20 96.00 1,223.90 86 21st Aug 1993 1994 111.00 142.90 117.00 1,109.10 52 9th Aug 1994 1995 124.90 140.10 95.00 1,159.16 78.5 8th Sept 1995 1996 119.60 138.40 102.00 1,214.60 58 30th Jul 1996 1997 102.80 121.00 101.00 1,320.00 48.3 14th Jun 1997 1998 92.50 118.40 105.00 1,081.30 60.4 28th Aug 1998 1999 144.10 177.90 95.00 1,282.80 72.5 21st Jul 1999 2000 127.90 178.50 92.00 779.93 83.9 12th Aug 2000 2001 115.60 133.50 88.00 1,186.70 58.3 31st Jul 2001 2002 97.20 141.60 100.00 1,307.50 57.9 29th Aug 2002 2003 122.60 157.00 95.00 1,459.40 68.7 19th Sep 2003 2004 127.20 161.60 102.00 1,380.40 70.1 10th Sep 200
Average 126.95 152.20 97.52 1,218.59 69.77 Std Dev 28.47 34.38 12.36 179.84 19.29
28
0.00
50.00
100.00
150.00
200.00
250.00
300.00
1950 1960 1970 1980 1990 2000 2010
Figure 3.1 Variations in Maximum Rainfall Over Kaduna River Basin 1955 to 2004Max Daily Max 5-day Max 7-day
0.00
200.00
400.00
600.00
800.00
1,000.00
1,200.00
1,400.00
1,600.00
1,800.00
1950 1960 1970 1980 1990 2000 2010
Figure 3.2 Total Annual Rainfall over Kaduna Basin Measured at Kaduna Airport 1955 to 2004
Total Annual Rainfall Linear (Total Annual Rainfall)
29
3.3 ANALYSIS OF STREAMFLOW DATA.
Daily Streamflow data for the period 1967 to 1992 and daily water stages record for the
period 1993 to 2004 were available for Kaduna River at Kaduna South Waterworks and both
data sets are characterized by several months of missing records due to gauge not operational or
washed away by flood. No discharge measurements were conducted at the station for the period
1993 to 2007 because of obsolete equipment and the data for these periods were converted to
discharge using the 1994 rating curve. Available data were examined for “spurious peak” and
suspicious record verified.
The Kaduna River was completely ungauged for the year 2003, a situation that made it
impossible to retrieve the river discharge values corresponding to the days of the 2003 flood
disaster. In order to understand the flow regime in the Kaduna River during the period under
investigation, the following database of extreme flow events were created and via Microsoft
EXCEL.
a. Maximum daily flow for each month;
b. Maximum five consecutive days moving average flows; and
c. Maximum seven consecutive days moving average flows.
The analyses of the resultant databases indicated that the months of August and
September are the wettest months producing the maximum daily yearly flow for ten and
fifteen months respectively during the period under investigation. The historical maximum
daily flow of 2,926.31m3/sec was recorded on the 18th September 1994 followed by
2,871.75m3/sec and 2,579.50m3/sec for 1986 and 1992 respectively. Maximum five
consecutive days moving average flow of 1,845.93m3/sec was recorded in 1998 followed
closely by maximum five days moving average flow of 1,774.98m3/sec and 1,765.62m3/sec in
30
1987 and 1994, respectively. The maximum seven days moving average flows of
1,686.62m3/sec, and 1,675.79m3/sec and 1,591.03m3/sec were recorded at the Kaduna South
Waterworks gauging station in 1992, 1998 and 1975, respectively. Table 3.2 and Figures 3.3
to Figure 3.6 presents the maximum flow regime at Kaduna South Waterworks for each month
of the year 1967 to 2004.
Table 3.2 Flow Regime of Kaduna River at Kaduna South 1967 to 2004 Year Avg Daily
Flow (m3/sec)
Max 5-days Flow (m3/sec)
Max 7-days Flow (m3/sec)
Max Daily Flow Parameters Discharge m3/sec
Water Stage (m)
Date of occurrences
1967 821.81 1,169.43 1,095.09 1,469.64 6.12 10th Sep 1967 1968 650.93 938.60 893.97 2,270.70 6.89 21st June 1968 1972 760.01 1,553.46 1,372.96 2,296.52 6.92 11th July 1972 1973 725.97 1,218.93 1,112.16 1,441.33 6.07 1st Sept 1973 1974 941.38 1,413.01 1,301.85 1,795.29 6.45 19th Sept 1974 1975 1,015.94 1,723.48 1,591.03 2,362.50 6.97 21st Sept 1975 1976 475.33 672.58 629.67 814.50 4.95 26th Sept 1976 1977 500.73 879.62 815.82 1,005.40 5.39 9th Sept 1977 1979 699.12 893.28 835.19 1,068.11 5.57 25th Sept 1979 1980 541.40 767.10 713.42 1,066.41 5.57 2nd Sept 1980 1981 750.15 1,440.22 1,125.74 1,192.14 5.16 8th Sept 1981 1982 492.32 947.20 953.63 1,251.04 5.79 7th Aug 1982 1983 395.69 597.60 561.28 700.56 4.68 1st Aug 1983 1984 233.77 316.29 302.26 422.49 3.79 2nd Oct 1984 1985 522.75 764.24 716.52 1,100.82 5.58 15th Aug 1985 1986 501.82 1,489.74 1,169.03 2,871.75 7.96 22nd Jul 1986 1987 623.50 1,774.98 1,298.34 2,370.38 6.98 21st June 1987 1988 536.00 1,497.67 1,112.96 2,072.57 6.78 25 and 26th Jun 1988 1989 67.02 94.91 93.28 126.20 2.38 15th Aug 1989 1990 658.06 1,258.47 1,124.76 1,440.94 5.67 19th Sep 1990 1991 853.71 1,274.04 1,163.84 1,460.45 5.70 28th Aug 1991 1992 1,093.47 1,755.53 1,686.62 2,579.50 7.14 1st Sept 1992 1994 828.40 1,765.62 1,523.63 2,926.31 7.39 18th Sept 1994 1995 550.09 766.87 727.30 862.01 5.08 10th Aug 1995 1996 643.89 862.77 838.28 1,151.79 5.67 12th Sept 1996 1997 668.08 918.65 867.41 1,013.98 5.41 20th Aug 1997 1998 960.22 1,845.93 1,675.79 2,395.85 7.00 10th Sept 1998 1999 923.92 1,373.41 1,269.23 2,488.34 7.07 4th Sept 1999 2000 831.71 1,001.33 958.29 1,083.83 5.55 25th Aug 2000 2001 NA 906.56 869.56 1,055.51 5.50 26th Aug 2001 2004 655.85 868.99 812.71 1,370.77 5.99 23rd Aug 2004
31
0
500
1,000
1,500
2,000
2,500
3,000
3,500
0 10 20 30 40
Dis
char
ge m
3 /se
c
Year
Figure 3.3 Max Daily Flow of Kaduna River at Kaduna South 1967 to 2004
Max Daily Flow
0
500
1,000
1,500
2,000
1960 1970 1980 1990 2000 2010
Dis
char
ge m
3 /se
c
Year
Figure 3.4 Max 5-days Moving Avgerage flow of Kaduna River at Kaduna South 1967 to 2004
Max 5-days Moving Avg
0200400600800
1,0001,2001,4001,6001,800
1960 1970 1980 1990 2000 2010
Dis
char
ge m
3 /se
c
Year
Figure 3.5 Max 7-days Moving Avgerage Flow of Kaduna River at Kaduna South 1967 to 2004
Max 7-days Moving Avg
0
200
400
600
800
1,000
1,200
1960 1970 1980 1990 2000 2010D
isch
arge
m3 /
sec
Year
Figure 3.6 Avg Daily Flow of Kaduna River at Kaduna South 1967 to 2004
Avg Daily Flow
32
3.4 FLOW DURATION ANALYSIS
The flow duration curve is a plot that shows the percentage of time that flow in a stream is
likely to equal or exceed some specified value of interest. The curve characterizes the ability of the
basin to provide flows for various magnitudes and this information is particularly important for flood
studies. The flow duration curve for Kaduna River at Kaduna South Waterworks was prepared based
on the average daily flow for the period 1967 to 2004 using the log cycle class interval because the
probability of choosing appropriate interval spacing is higher than other methods of selecting class
intervals. The analysis results are presented in Table 3.3 and Figure 3.7.
0
2000
4000
6000
8000
10000
12000
0 500 1000 1500 2000 2500 3000 3500 4000CUM
ULA
TIV
E N
O O
F D
AYS
WIT
H
DIS
CHA
RGE
LESS
TH
AN
OR
EQU
AL
TO
STA
TED
VA
LUES
DISCHARGE CUBIC METRES PER SECOND (MID-CLASS)FIGURE 3.7 PERIOD OF RECORD FLOW DURATION CURVE FOR KADUNA RIVER AT KADUNA
SOUTH WATERWORKS 1967 TO 2004
33
Table 3.3 Flow Duration of Kaduna River at Kaduna South Waterworks 1967 To 2004 Based on Log Cycle Interval S/N Flow Class Bound Flow Mid Class Cumulative
No of Days %Time flow NOT Exceeded
%Time Flow Equaled or Exceeded
1 10 – 14 12 4,450 43.75 56.25 2 15-19 17 4,765 46.84 53.16 3 20 – 29 25 5,081 49.95 50.05 4 30 – 39 35 5,392 53.01 46.99 5 40 – 49 45 5,648 55.52 44.48 6 50 – 59 55 5,863 57.64 42.36 7 60 – 69 65 6,070 59.67 40.33 8 70 – 99 85 6,449 63.40 36.60 9 100 - 149 125 7,008 68.90 31.10
10 150 - 199 175 7,422 72.97 27.03 11 200 - 299 250 8,084 79.47 20.53 12 300 - 399 350 8,575 84.30 15.70 13 400 - 499 450 8,926 87.75 12.25 14 500 - 699 550 9,599 94.37 5.63 15 700 - 999 850 10,017 98.48 1.52 16 1000 - 1499 1,250 10,136 99.65 0.35 17 1500 - 1999 1,750 10,149 99.77 0.23 18 2000 - 2999 2,500 10,171 99.99 0.01 19 3000 - 3999 3,500 10,172 100.00 0.00
0.00
10.00
20.00
30.00
40.00
50.00
60.00
0 500 1,000 1,500 2,000 2,500 3,000 3,500 4,000
% O
F TI
ME
DIS
CHA
RGE
IS E
QU
ALL
ED O
R EX
CEED
ED S
TATE
D V
ALU
ES
DISCHARGE CUBIC METRES PER SECOND (MID-CLASS)
FIGURE 3.8 FLOW DURATION CURVE FOR KADUNA RIVER AT KADUNA SOUTH WATERWORKS 1967 TO 2004
34
The flow duration curve indicated that the period average daily flow of 164.59m3/sec was
equaled for 72.97% and exceeded for 27.03% of the period under investigation. Kaduna River
within the reach under investigation is a regulated stream with dry season flow augmented by
releases from Kaingimi dam on a tributary of Kaduna River just upstream Kaduna City. Average dry
season flow range between less than 10m3/sec to less than 40m3/sec are sustainable for 53.01% of
the period investigated. Flows in the range 700m3/sec to 2926.31m3/sec (maximum flow ever
recorded) are rare flows which were exceeded for an insignificant period of 1.52% of the period
investigated. This points to the fact that floods in the Kaduna basin can only be expected to be rain-
induced
3.5 REGENERATION OF THE KADUNA 2003 FLOOD LEVEL
The Kaduna River was completely ungauged during the 2003 flood and therefore no data is
available on the amount of flow during the disaster. However eye witness account by the author and
interview made during the field survey indicated that stage record data corresponding to 2003 flood
level marks at the Kaduna Railway Bridge is 0.61m below the top of the central pier of the bridge.
The top level of the bridge is at 574.55m above mean sea level (amsl) and the top of the pier is 0.65m
to the top level of the bridge. Therefore the 2003 flood level measured at the railway bridge is
(574.55-0.65-0.61)m or 573.29m amsl. Rating table is available for the gauging station at Kaduna
South from 1955 to 2004 as presented in table 3.4 and data extracted from it to construct the rating
curve presented in Figure 3.9.
35
Table 3.4 Rating Table Kaduna River at Kaduna South Waterworks
Elevation amsl
GH (m)
Q m3/sec
Elevation amsl
GH (m)
Q m3/sec
563.71 0.00 0.00 568.71 5.00 831.81 564.01 0.30 0.17 569.01 5.30 962.06 564.32 0.61 0.71 569.38 5.67 1,151.79 564.62 0.91 2.61 569.68 5.97 1,355.67 564.90 1.19 7.39 569.71 6.00 1,378.32 565.23 1.52 18.29 570.02 6.31 1,661.49 565.51 1.80 42.48 570.32 6.61 1,961.65 565.81 2.10 75.04 570.63 6.92 2,301.45 566.12 2.41 131.67 570.93 7.22 2,686.56 566.42 2.71 188.36 570.96 7.25 2,726.20 566.73 3.02 245.28 570.99 7.28 2,765.85 567.03 3.32 302.20 571.03 7.32 2,813.99 567.34 3.63 378.74 571.06 7.35 2,862.13 567.67 3.96 486.34 571.09 7.38 2,910.26 567.82 4.11 528.82 571.12 7.41 2,958.40 568.13 4.42 616.60 571.15 7.44 3,006.54 568.43 4.72 729.87 571.18 7.47 3,054.68
With a right bank valley slope of 0.042% and distance of 905m to the cross section at the Kaduna
South Waterworks, the corresponding level at this cross section is 573.29-0.042%*905 or 572.91m
amsl. Extending the rating curve at Kaduna South Water Works to 572.91m gives the corresponding
discharge as 3,485.31m3/sec.
563.00564.00565.00566.00567.00568.00569.00570.00571.00572.00
0 500 1000 1500 2000 2500 3000 3500
Gau
ge H
eigh
t (m
sl)
Discharge (Cubic metres per sec)Figure 3.9 Discharge Rating Curve Kaduna at Kaduna South Waterworks
36
3.6 FLOOD FREQUENCY ANALYSIS.
The analysis of data in previous sections indicated that flooding in Kaduna River basin are
rainfall induced and the river channel are expected to be on higher risks of flooding when the channel
is flowing bankfull capacity coincides with high rainfall. Consequently, the foregoing flood
frequency analysis was carried out separately on the maximum daily flow and all the rainfall database
considered by fitting the Log Pearson Type III distribution into the database to determine floods
levels for 200, 100, 50, 20, 10, 5 and 2 years annual recurrence intervals floods which were used as
the basis for the proposed degrees of alert and protection against floods.
The Log-Pearson Type III distribution is a statistical technique for fitting frequency
distribution data to predict the design flood for a river at some site. The Log-Pearson Type III
distribution is calculated using the general equation:
xKxx logloglog σ+= (3.1)
where x is the flood discharge value of some specified probability, xlog is the average of the log x
discharge values, K is a frequency factor, and is the standard deviation of the log x values. The
frequency factor K is a function of the skewness coefficient and return period and can be found
using the frequency table. The flood magnitudes for the various return periods were found by
solving the general equation on Microsoft EXCEL. The analysis results are presented in Tables 3.5
to 3.9.
37
Table 3.5 Flood Frequency Analysis for Kaduna River at Kaduna South Waterworks Log Pearson Type III Skew Coefficients
Return Period (years) Skew Coef 2 5 10 25 50 100 200 Max Daily Q 0.244391999 -0.04245 0.826664 1.305449 1.835238 2.187916 2.512038 2.814715 Max 5days Q -2.386973563 0.342303 0.737176 0.815874 0.850832 0.859571 0.862441 0.86431 Max 7 days Q -2.579112505 0.361671 0.707867 0.718519 0.786943 0.791734 0.792734 0.793525
Table 3.6 Flood Frequency Analysis for Kaduna River at Kaduna South Waterworks Log Pearson Type III Estimated Flood Flows (m3/sec)
Return Period (years) 2 5 10 25 50 100 200 Max Daily Q 1,578.60 2,181.72 2,607.43 3,175.96 3,621.59 4,086.07 4,573.47 Max 5days Q 1,218.57 1,535.55 1,607.96 1,641.22 1,649.64 1,652.41 1,654.22 Max 7 days Q 1,108.94 1,343.03 1,350.97 1,403.08 1,406.81 1,407.59 1,408.20
Table 3.7 Flood Frequency Analysis of Rainfall at Kaduna Airport Log Pearson Type III Skew Coefficients Main Data Return Period (years) Skew
Coefficient 2 5 10 25 50 100 200
Max Daily -0.138312886 0.02687 0.848467 1.262598 1.693793 1.966072 2.206352 2.424014 Max 5-day -0.25107411 0.041317 0.851468 1.25164 1.661897 1.918091 2.141795 2.34201 Max 7-day -0.534662859 0.093454 0.856653 1.205546 1.541519 1.739758 1.905997 2.04789 Annual Rainfall -1.463316484 0.230503 0.829432 1.032563 1.18296 1.250558 1.295256 1.325688
Table 3.8 Flood Frequency Analysis of Rainfall at Kaduna Airport Log Pearson Type III Estimated Rainfall (mm) Return Period (years) 2 5 10 25 50 100 200 Max Daily 67.73 75.20 79.27 83.75 86.70 89.40 91.91 Max 5-day 124.78 134.11 138.97 144.14 147.47 150.43 153.14 Max 7-day 150.20 160.53 165.49 170.41 173.38 175.91 178.10 Annual Rainfall 1,235.79 1,317.84 1,346.89 1,368.80 1,378.77 1,385.40 1,389.93
38
3.7 FIELD INVESTIGATION AND DATA COLLECTION
The field investigation and topographic surveys were organized in three distinct reaches
of the Kaduna River principally to collect project related data on:
a. Geomorphology and River Mechanics; and
b. Cross section surveys and collection of channel hydraulic geometric data.
Efforts were made to interact with the local inhabitants on extents of historical spilling and
flooding especially the 2003 flood. Instrumentation mobilized for these activities includes eTrex
Garmin GPS for positioning and distance measurements; Total Station Instrument for spot
heights and positions, and digital camera for picture documentation on existing conditions. The
entire activities were carried out by traversing the river course while assessing the river and its
floodplains for changes in river morphology and hydraulic geometry. The following information
was collected and would be presented in sections where they were required:
1. Locations; boundaries; and dimensions of existing natural features and man-made
structures in the floodplain using handheld Global Position System.
2. Spot elevation at closely scattered locations for the purpose of generating the Digital
Elevation Model (DEM) of the floodplain.
3. Cross section surveys of the river channel spaced at 250m intervals for the purpose of
determining the hydraulic geometrical characteristics of the main river channel.
4. Extent of the 2003 flood through interviews of local farmers and inhabitants who
witnessed the flood.
5. Geomorphological characteristics and River mechanics.
6. General conditions of the floodplain channel related to the following were assessed for
the purpose of estimating the Manning’s roughness coefficients.
a. Uniformity and smoothness of channel,
b. Surface irregularity,
c. Variation in shape and size of channel cross section,
d. Obstructions,
e. Vegetation and flow conditions and
f. Meandering of channel.
All field generated data were analysed through a combination of software that facilitated
the management of the information collected and include Microsoft Excel 2007, Surface
39
Mapping System Software (Surfer Version 8.01) and AUTOCAD 2007. Raw field survey data
collected are presented as Figure 3.10.
3.8 GEOMORPHIC CHARACTERIZATION AND CHANNEL CLASSIFICATION.
The geomorphology of a river or stream – its shape, depth, channel materials – affects the
movement of flood flows through it. Stream morphology is directly influenced by eight major
variables including channel width, depth, velocity, discharge, channel slope, roughness of
channel materials, sediment load and sediment size (Leopold et al., 1964). A change in one
variable causes a series of channel adjustments which lead to changes in the other variables,
resulting in channel pattern alterations and the manner the channel respond to flood flows
flowing through it. The Google Earth web site presents the digital earth resources images of the
earth based on a mosaic of QUICK Bird satellite images acquired on different dates. The portion
of the Kaduna River under investigation was downloaded for this study from the Google Earth
web site for the determination of spatial and temporal changes in the channel geometry and
geomophology.
In order to understand the existing and potential consequences of urbanization on the
morphology of the Kaduna river, the Rosgen Channel Morphology Classification method was
used to broadly classify the Kaduna main channel (Rosgen, 1996). The Data for the classification
were largely based on observed channel patterns, topographic map, and stream geometry data
collected during field surveys. The classification provides a baseline record from which the
changes in geomorphology of Kaduna River arising from anthropological changes were
evaluated.
40
41
3.9 TOPOGRAPHICAL CHARACTERISTICS OF THE STUDIED SEGMENTS
3.9.1 Longitudinal Profile
The Thalweg were extracted from each river cross section surveyed as the elevation of
the lowest point in each cross section and plotted on Microsoft Excel as presented in figure 3.11.
The elevations of the right and left banks were also extracted to plot the longitudinal profiles for
both banks. Analysis of the profiles data shows that the average main channel slope is 0.0416%
while the longitudinal slope for both banks is 0.042%. The river is steeper in Reach 3 and
relatively flatter in Reach 1as indicated in Table 3.9.
Table 3.9 Characteristics of the Longitudinal Profiles of Kaduna River. Identification Characteristics Left Bank Channel Right
Bank Combined Reaches
Valley / Channel Slope (%) 0.0420 0.0416 0.0420 Valley / Channel Length 50,835.52 50,531.95 49,311.69
Reach 1 Valley / Channel Slope (%) 0.0370 0.0306 0.0376 Valley / Channel Length 20,622.44 20,898.43 21,097.14 Stream Power (N/m/s) 2.41
Reach 2 Valley / Channel Slope (%) 0.0641 0.0507 0.0515 Valley / Channel Length 24,708.42 24,032.93 22,483.18 Stream Power (N/m/s) 1.49
Reach 3 Valley / Channel Slope (%) 0.1403 0.1573 0.1143 Valley / Channel Length 4,561.13 4,650.63 4,802.10 Stream Power (N/m/s) 2.67
560.00
565.00
570.00
575.00
580.00
585.00
590.00
0.00 10,000.00 20,000.00 30,000.00 40,000.00 50,000.00 60,000.00
Chan
nel B
ed E
leva
tion
Abo
ve M
ean
Sea
Leve
l (m
)
Distance from Confluence with Kangimi River (m)
Figure 3.11 Longitudinal Profile of Kaduna River Main Channel
42
3.9.2 Cross Sectional Views
The survey of the river cross sections were carried out using the Total Station instrument
and canoe was used to carry the reflector across sections of the river where water was flowing at
the time of survey. A total of fifty nine cross sections were surveyed 21 in reach 1, 25 in Reach 2
and 13 in Reach 3. The cross sections were spaced in a manner to capture the geomorphological
changes along the channel. The channel geometric parameters related to bankfull and flood
dimensions and flows were calculated at each cross section and averaged over each of the three
reaches to determine the channel profiles parameters and stream power for each reach. The cross
sections are presented as APPENDIX III.
3.9.3 Planform
The Google Earth images of non vegetated reaches of Kaduna River under investigation
are presented as Plate II and were employed for the channel plan form description. In Reach 1
which is the uppermost portions under investigation the river channel exhibits a regular sinuous
meanders at its downstream portion. In the uppermost portion of the reach, the channel exhibits
braiding and mild meanders with several aggregation and degradation points. Commercial
mining of good quality aggregates for infrastructural development in Kaduna City has been
going on for years in this reach and still a daily activity today.
Reach 2 is the most urbanized of the three reaches and the river channel is multi
channeled characterized by heavy braiding and heavy anastomosing occasioned by heavy
concentration of rock outcrops all across the river length and cross section. The river width and
its flood plain is greatest in this reach most especially between Malali and Kigo road extension
where the 2003 flood unleashed the most devastating effect on the city. Two other left side
tributaries confluence with the Kaduna main channel within this reach which makes this reach
very critical for this study. The river and its floodplain narrowed to just 269.13m at its exit into
Reach 3 due to construction of fences by properties owner around.
The Kaduna river flow into Reach 3 with a very sharp U shaped meanders around the
Moslem burial ground and characterized by heavy braiding and major flow bifurcations
occasioned by occurrences of two vegetated bars just downstream the Kaduna South Waterworks
Intake. Two other intakes belonging to Nigerian Breweries Plc and United Nigeria Textiles are
located in this stretch. The left bank of this reach is the most developed.
43
3.10 CLASSIFICATION RESULT.
Table 3.10 presents the summary of the geomorphological parameters of the three
Reaches while the detailed parameters are presented in Table 3.11 to Table 3.13. On the average
the reaches investigated are stream B segment defined as moderately entrenched, moderate
gradient, riffle dominated channel with infrequently spaced pools; very stable plan and
profile. Rosgen (1996) further described the landforms and soils features associated with this
class of stream as moderate relief, colluvial deposition and / or structural. Moderate
entrenchment, and width-to-depth ratio. Narrow, gently sloping valleys; rapids
predominates with scour pools. Some of the photographs of the reach features taken during the
field surveys are presented as Plate III to Plate V.
Table 3.10 Summary of Gemorphological Parameters Parameter Reach 1 Reach 2 Reach 3
Channel Plan View Single Threaded Multi Threaded Single Threaded Average water surface slope (S) m/m 0.000109671 8.45557E-05 0.000306698 Stream or channel length (SL) m 21,097.14 24,032.93 4,650.63 Stream or Channel Slope 0.00038 0.00051 0.00157
Valley length (VL) m Left Bank 20,898.43 24,708.42 4,561.13 Right Bank 21,097.14 22,483.18 4,802.10
Valley slope (VS) m/m Left Bank 0.000306281 0.00064 0.00140 Right Bank 0.000375634 0.000515 0.001142501
Sinuosity (VS/SL) 0.907686209 1.13997 0.809256879 Sinuosity (SL/VL) 1.004731857 1.018525 0.993382274 Entrenchment ratio (Wfpa/Wbfl) 2.057847328 1.795573 1.936598257 Width / Depth Ratio 103.074 221.600 142.171 Stream Type Classification
44
Table 3.11 Geomorphological Characterization of Reach 1 Kaduna River
Table 3.12 Geomorphological Characterization of Reach 2 Kaduna River
PARAMETER X-SEC-14
X-SEC-21
X-SEC-22
X-SEC-15
X-SEC-16
X-SEC-23
X-SEC-17
X-SEC-24
X-SEC-18
X-SEC-19
X-SEC-25
X-SEC-20
X-SEC-26
X-SEC-27
X-SEC-37
X-SEC-28
X-SEC-29
X-SEC-30
X-SEC-35
X-SEC-31
X-SEC-34
X-SEC-32
X-SEC-36
X-SEC-33
X-SEC-38
Eastern Bye Pass
Bankfull Dimensions 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22
X-section area (m.sq.) 484.29 162.42 1,130.9 637.66 404.27 345.14 559.07 1,686.1 1,635.9 2,311.1 394.64 1,643.9 866.56 861.44 1,769.3 1,382.7 860.68 444.11 994.64 407.97 577.63 367.75 885.43 758.33 345.21 877.78
Width (m) 145.89 167.36 341.85 277.70 204.88 223.82 279.34 422.58 480.88 873.41 593.02 794.61 464.79 606.12 640.76 663.18 249.20 216.28 279.12 189.34 210.01 240.81 337.32 323.27 169.37 276.70
Mean depth (m) 1.30 1.15 2.97 2.10 0.84 1.20 1.76 3.94 3.14 2.43 0.46 2.09 1.57 0.83 2.38 1.93 3.51 1.81 2.87 1.81 2.28 1.29 2.19 2.10 2.86 1.99
Max depth (m) 2.74 2.13 5.18 3.35 3.96 2.13 3.66 6.71 5.79 3.96 3.05 3.35 5.18 4.27 4.88 3.35 6.10 3.35 4.57 3.05 3.96 2.44 3.66 3.35 5.18 4.27
Flood Dimensions Flood prone area Width (Wfpa) m 262.22 283.43 364.80 379.19 247.98 238.47 552.32 464.13 553.89 1,083.5 982.20 1,568.3 649.01 648.23 758.05 683.10 691.05 765.21 388.04 264.59 249.44 294.24 480.42 405.72 275.25 137.39
Width Left Floodplain 209.75 158.19 106.40 106.40 232.04 483.35 471.82 541.59 404.04 243.09 694.80 248.31 122.95 111.13 87.50 251.31 725.39 727.54 398.14 382.22 434.02 470.00 419.23 449.35 604.69 589.98 Width Left Floodplain Encroached (m) 144.10 124.08 106.40 106.40 206.18 457.19 303.79 406.38 373.22 77.06 461.77 126.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
Width Right Floodplain 499.95 492.86 439.41 437.02 571.30 494.42 654.69 639.57 767.86 936.59 863.31 1,033.3 915.16 616.47 788.36 598.78 816.22 595.96 467.05 517.47 477.68 488.50 437.50 437.50 415.81 638.44 Width Right Floodplain Encroached (m) 480.68 409.96 386.89 395.87 544.63 479.89 553.93 624.72 723.89 885.15 796.04 595.89 750.56 571.50 743.47 560.45 693.33 442.91 425.34 470.28 438.46 432.50 391.50 391.50 343.50 599.85
Low bank height 571.50 570.89 572.41 571.80 573.02 574.55 573.94 572.11 572.11 576.07 575.77 576.68 575.77 577.90 578.82 579.12 580.03 579.42 581.25 580.03 581.56 583.39 583.08 582.78 579.12 584.00
Max riffle depth 568.76 570.59 569.98 569.98 570.59 573.02 570.89 570.89 571.50 572.11 573.94 575.77 572.72 575.77 575.77 577.90 577.29 577.60 580.03 578.82 580.95 580.95 580.95 580.95 579.12 579.73 Bank height ratio (LBH/max riffle depth) 1.0048 1.0005 1.0043 1.0032 1.0043 1.0027 1.0053 1.0021 1.0011 1.0069 1.0032 1.0016 1.0053 1.0037 1.0053 1.0021 1.0048 1.0032 1.0021 1.0021 1.0010 1.0042 1.0037 1.0031 1.0000 1.0074 Flood prone area Elevation (ELfpa) m 574.24 574.85 580.34 576.68 578.51 577.29 578.21 584.30 583.08 580.03 580.03 582.47 583.08 584.30 585.52 584.61 589.48 584.30 589.18 584.91 588.87 585.83 588.26 587.65 589.48 588.26 Maximum Level in the Cross Section 573.94 573.94 575.16 575.46 574.85 575.46 576.68 577.90 577.60 578.51 581.25 581.86 578.82 590.40 589.48 581.25 589.18 585.22 587.04 581.86 585.22 585.22 591.31 587.04 588.87 591.62
PARAMETER X-S-39 X-S-40 X-S-41 X-S-42 X-S-43 X-S-44 X-S-45 X-S-46 X-S-47 X-S-48 X-S-49 X-S-50 X-S-51 X-S-52 X-S-53 X-S-54 X-S-55 X-S-56 X-S-57 X-S-58 X-S-59
Bankfull Dimensions 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1
X-Stion area (m.sq.) 1,609.87 759.46 344.47 899.81 660.35 493.24 417.78 421.74 945.65 827.25 1,432.26 1,544.96 281.40 1,161.15 777.42 261.88 259.22 53.92 608.76 1,057.14 973.25
Width (m) 506.70 295.11 288.53 374.72 232.47 234.76 233.18 263.25 285.94 241.89 376.10 321.36 185.89 402.62 243.59 336.11 162.38 87.04 236.16 390.54 362.72
Mean depth (m) 2.41 2.10 1.10 1.76 2.35 2.07 1.69 1.57 2.90 3.08 3.93 4.92 1.24 3.31 2.99 0.63 1.27 0.78 2.11 2.91 2.30
Max depth (m) 3.96 3.35 1.83 3.35 3.96 3.66 3.05 2.74 4.88 5.49 7.01 8.23 2.13 6.10 4.88 1.22 2.13 1.52 3.96 4.88 4.27
Flood Dimensions
Flood prone area Width (Wfpa) m 679.37 609.31 419.46 641.30 523.00 466.25 564.01 567.23 755.67 760.43 642.49 708.90 376.96 693.71 1,042.71 423.78 470.38 614.95 563.19 655.66 840.72
Width Left Floodplain 657.66 549.66 539.87 468.76 396.00 442.71 381.74 1,065.17 1,134.11 1,046.92 1,054.50 1,018.51 583.09 458.99 541.85 775.19 537.94 843.29 827.62 271.50 492.07
Width Left Floodplain Encroached (m) 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
Width Right Floodplain 444.84 642.01 615.79 474.50 838.50 840.38 680.39 400.51 331.84 552.68 331.50 384.71 400.55 601.13 758.07 454.59 912.56 701.57 372.92 598.00 351.43
Width Right Floodplain Encroached (m) 379.78 692.57 606.27 324.48 659.00 807.36 419.71 352.38 279.45 413.64 249.00 298.61 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
Low bank height 583.39 582.78 581.86 584.00 583.08 584.00 583.39 585.22 585.52 583.08 584.91 583.39 584.91 585.52 584.61 585.22 586.13 587.04 586.13 586.74 587.96
Max riffle depth 581.86 581.56 580.95 582.17 582.78 582.17 581.86 583.69 582.78 582.78 580.64 580.64 583.69 582.78 583.39 584.00 585.22 587.04 583.08 584.91 586.13
Bank height ratio (LBH/max riffle depth) 1.0026 1.0021 1.0016 1.0031 1.0005 1.0031 1.0026 1.0026 1.0047 1.0005 1.0073 1.0047 1.0021 1.0047 1.0021 1.0021 1.0016 1.0000 1.0052 1.0031 1.0031
Flood prone area Elevation (ELfpa) m 589.79 588.26 584.61 588.87 590.70 589.48 587.96 589.18 592.53 593.75 594.66 597.10 587.96 594.97 593.14 586.44 589.48 590.09 591.01 594.66 594.66
Maximum Level in the Cross Section 586.13 587.65 584.00 585.52 590.70 591.62 594.36 587.65 589.48 590.09 590.40 589.48 593.45 589.79 589.18 590.09 590.40 592.23 590.70 591.31 593.75
45
Table 3.13 Geomorphological Characterization of Reach 3 Kaduna River
PARAMETER X-SEC-1 X-SEC-2 X-SEC-3 X-SEC-4 X-SEC-5 X-SEC-6 X-SEC-7 X-SEC-8 X-SEC-9 X-SEC-10 X-SEC-11 X-SEC-12 X-SEC-13
Bankfull Dimensions 59 58 57 56 55 54 53 52 51 50 49 48 47
X-section area (m.sq.) 353.77 421.49 515.20 240.70 79.18 319.64 1,206.16 52.77 152.21 186.55 160.29 1,080.69 380.05
Width (m) 182.44 157.06 175.95 144.08 102.35 196.28 337.38 42.21 125.52 141.64 124.73 190.00 233.20
Mean depth (m) 1.68 2.26 2.37 1.60 0.61 1.70 0.43 1.52 1.22 1.52 1.02 3.65 1.75
Max depth (m) 3.35 3.96 4.27 2.74 4.57 3.35 5.49 3.05 1.83 3.05 1.83 8.40 3.05
Flood Dimensions
Flood prone area Width (Wfpa) m 474.65 470.35 272.76 311.75 476.65 406.54 653.38 252.23 241.57 386.05 376.05 581.94 487.37
Width Left Floodplain 287.50 206.68 328.71 345.90 247.70 281.50 144.00 198.98 221.91 412.51 211.13 220.28 88.20
Width Left Floodplain Encroached (m) 162.00 102.42 301.30 269.50 170.31 205.00 143.00 158.59 154.71 214.16 203.27 220.28 36.80
Width Right Floodplain 321.00 300.26 196.00 226.00 255.62 150.00 321.39 221.21 310.68 218.92 424.03 335.27 339.33
Width Right Floodplain Encroached (m) 143.50 104.00 131.50 130.84 0.00 0.00 18.50 315.60 161.52 174.08 79.16 0.00 88.12
Low bank height 571.20 569.06 569.37 569.67 574.24 573.94 573.02 569.98 570.59 572.11 570.89 571.01 572.11
Max riffle depth 567.84 567.23 566.01 568.15 573.33 570.89 570.59 569.98 570.28 572.11 570.28 563.71 569.98
Bank height ratio (LBH/max riffle depth) 1.0059 1.0032 1.0059 1.0027 1.0016 1.0053 1.0043 1.0000 1.0005 1.0000 1.0011 1.0129 1.0037
Flood prone area Elevation (ELfpa) m 574.55 575.16 574.55 573.63 582.47 577.60 581.56 576.07 573.94 578.21 573.94 580.51 576.07
Maximum Level in the Cross Section 574.85 575.46 573.63 574.55 579.73 583.39 578.82 574.85 574.85 577.90 576.99 581.86 575.46
46
Above : Reach 1
Middle : Reach 2
Reach 3
Plate II Reaches 1, 2 and 3.(Source Google Earth, 2008)
47
(a) Kaduna River at Eastern Byepass Bridge
(b) Flow bifurcation by vegetated bars
© Farming activities along the floodplain
(d) Floodplain Width reduction by property fence.
(e) Residential housing development in the floodplain
(f) Bank Erosion activity in Reach 1.
Plate III General Conditions of Reach 1 May and June 2009
48
(a) Residential developments close to the river bank
(b) Flow divides by Rock outcrops and vegetated island
(c) Anastomosing channel condition
(d) Channel overgrown by vegetation
(e) Channel bank ersosion
(f) Rock outcrops in the middle of river channel
Plate IV General Conditions of Reach 2 May and June 2009
49
(a) Kaduna River at Western Byepass Bridge at
Nasarawa
(b) Low flow condition in Reach 3
© Depth measurements during the survey
(c) General view of Reach 3
(d) Rocky channel bed
(e) Right bank erosion at Nigerian Brewries Intake
Plate V General Conditions of Reach 3 February and March 2009
50
3.11 GEOMORPHOLOGY AND RIVER MECHANICS
Kaduna River which flows past Kaduna City has partitioned the City into two major parts
namely Kaduna North and South Communities on the right and left banks respectively with the
main channel alignment on east-west direction. The upper reach of the study area extends
20.898.43km between the confluence with Kaingimi River to the new Eastern byepass bridge at
Malali; the middle reach extends 24.032.93km between the eastern byepass bridge to the
Ahmadu Bello Stadium bridge; and the third reach extends 4.650.63km between Ahmadu Bello
stadium bridge and the Western byepass at Nasarawa, all measured along the stream channel.
3.11.1 Meandering and Bends.
Meandering can be described as single winding channel, usually with well defined banks
and consisting of a series of bends, generally alternating in direction and at times connected by
straight reaches so that the river appear to be made up of series of S- curves. Channels shifts
mainly due to erosion by undercutting on outside of bends, causing the outward growth and
down valley migration of meanders. “Cutoffs” can occur at the base of a meander loop leaving
crescent shaped ‘Oxbow Lakes’. Three shapes of bends were observed in this survey are as
follows:
i. S- bend
ii. Concave or Convex shaped bends (C- bend)
iii. U-bends
The Kaduna river course is characterized by several meander and bend reaches throughout the
surveyed length investigated and summary of bends analysis is presented in Table 3.14.
Table 3.14 Summary of Bends Analysis.
REACH NO OF BENDS
TYPE OF BEND S U C
1 3 2 1 2 1 1 3 2 2
51
3.11.2 Bifurcations.
Bifurcated reaches are divided flow reaches formed naturally by continual migration of
the bendway channels followed closely by growth of point bars on the opposite bank. Such
bendway channel eventually lengthens and may deteriorate to a point where it does not have the
channel capacity required at medium to high flow, chute then develops across the point bars
which eventually carries a large percentage of the higher flows. As stages recede, the depth in the
chute channel decreases. At low stages the deep and narrow bendway channel is more efficient
for the transport of water and sediment and the greatest percentage of the flow returns to the
bendway channels. Bifurcated lengths observed in this report vary in length from 100m to
1.393km long. The bifurcated reaches are characteristically overgrown with forested vegetation,
or shrubs. The soils in the bars are consolidated eroded materials from the catchments. The
distribution of the bifurcated reaches along the surveyed length is presented in Table 3.15.
Table 3.15 Distribution of Bifurcated Reaches.
LOCATION
EASTING NORTH
32P34479 1172980 REACH1
32P337827 1172111 REACH1
32P334154 1170557 REACH1
32P334449 1168143 REACH1
32P327247 1161436 REACH3
3.11.3 Braided Reaches.
Braiding is a characteristic feature of the alluvial river and such reaches are characterized
by multiple or chaotic arrays of channel divided by bars of sediments or highland which can be
submerged depending upon water stages in the channel. The Kaduna river channel develops into
several low, medium and high flow braided reaches along the surveyed sections and unlike the
divided flow reaches, braided reaches are formed by rock outcrops in the middle of channel or
non-cohesive soil materials which are bare or vegetated with either shrubs or trees in most cases.
52
The location of the braided reaches and types of bars forming the braiding are presented in Table
3.16.
Table 3.16 Braided Reaches and type of Bars.
CHAINAGE LEVEL OF BRAIDING TYPE OF BAR 5+340 Heavy Point Bar 12+000 Heavy Mid Channel 20+770 Moderate Rock Outcrop The entire REACH 2 is highly braided by rock outcrops causing flow bifurcation
32+732 Heavy Mid Bar
3.11.4 Tributaries and Confluence Points.
A total of nineteen tributaries comprising eleven left side and eight right side tributaries
were identified along the Kaduna River within the reaches investigated. This amount to a
tributary density of 1.93 tributaries per kilometer. The distributions of tributaries along the
Kaduna River investigated are presented in Table 3.17.
Table 3.17 Distribution of Tributaries along the Kaduna River.
LOCATION LENGTH (KM)
TRIBUTARIES DENSITY (NO/KM) FROM CHG TO CHG NO ON LHS NO ON RHS
0+000 21+850 21.85 5 5 2.185 21+850 31+950 10.1 4 2 1.683 31+950 36+740 4.79 2 1 1.597
3.12 IMPACTS OF URBANIZATION ON KADUNA RIVER CHANNEL. 3.12.1 Floodplain Encroachment
Urban expansion in all of the communities located near the main stream channel of the
Kaduna River has caused floodplain areas to be developed. A high rise block wall fence has been
placed to allow the use and development of areas that originally provided zones for natural
floodwater storage and conveyance. As a result, channel floodway zones have become
constrained most especially in the middle reach where the 2003 has caused severe damages.
Consequences of these developments are many for instance flood passage through these areas
may results in higher stages than normal and a shortage of flood attenuation potential. In other
reaches, encroachment may impede the downstream progression of the floodwave such that
backwater effects may cause high local flood levels.
53
To determine the extent of encroachments the surveyed cross section data was overlaid
with the topographical map of the area as shown in Plate 4.5. The two extremities of the cross
sections are limits of floodplain development as at the time of surveys March 2009.
The limit of the floodplain as delineated by contour elevations 1900ft and 1950ft were
compared with the width of the cross section surveyed to quantitatively give the extent of
floodplain development / encroachment between 1962 and 2009 as presented in Table 3.18.
From Table 3.18 it is clear that the Kaduna River floodplain is increasingly urbanized with a
maximum encroachment rate of 85.31%, 68.47% and 67.54% respectively in Reach 2, Reach 3
and Reach 1 respectively over the period 1962 and 2009. These regions of the floodplain
corresponds to Ahmadu Bello Stadium, Kigo Extension, Angwan Rim and Malali in Reach 1;
Parts of Nasarawa, Kakuri and Railway Station areas adjoining the Kaduna River in Reach 3;
and Malai, Federal Government College Malali, Ungwan Dosa and Rafin Gusa in Reach 1.
The Kaduna 2003 flood disaster has more devastating effects in Ahmadu Bello Stadium,
Kigo Extension, Angwan Rim and Malali areas of Reach 1, which by this analysis is the most
developed part of the Kaduna River floodplain. In the years to come this rate is expected to be
higher unless an aggressive policy shift is pursued to reverse the rural-urban migration.
Table 3.18 Extent of Kaduna River Floodplain Development Analysis Reach 3 Reach 2 Reach 1* Left Right Left Right Left Right Area of floodplain (m2) 1,244,142.25 1,304,776.38 3,885,514.50 4,554,825.38 4,534,588.00 4,062,025.75 Perimeter (m) 9,528.04 11,348.90 22,111.32 18,512.11 17,568.91 18,987.66 Developed Area (m2) 851,864.63 360,413.26 680,562.63 3,885,514.50 0.00 2,743,513.75 1962 (%) 68.47 27.62 17.52 85.31 0.00 67.54 % Reach Floodplain Area
33.42 14.14 8.06 46.04 0.00 31.91
Perimeter (m) 8,945.94 5,873.21 7,821.00 18,479.77 0.00 18,817.17 Undeveloped Area (m2) 392,277.62 944,363.12 3,204,951.87 669,310.88 4,534,588.00 1,318,512.00 1962 (%) 31.53 72.38 82.48 14.69 100.00 32.46 *Measured to Rafin Gusa (Limit of Kaduna City)
54
Plate VI Survey Data Overlaid with Topographical Map of Project Area.
55
3.12.2 Flood Inundation Risk Zone The flood risk zones were determined by comparing the floodprone area elevation with
the maximum elevation in the cross section. Where maximum elevation in the cross section is
less than the floodprone area elevation, there is the risk of flooding. The analysis indicated that
39 out of 59 cross sections are under the risk of overbank spills of flood waters into the adjoining
properties with Reach 2, the most vulnerable having 21 cross sections susceptible to overbank
spills out of 21 cross sections. Plate VII shows the existing flood protection structures along the
reaches. These floodwalls made of hollow bricks are quite inadequate in capacities to floods as
they can be pulled down under severe flooding. Also these walls are not continuous a situation
that can lead to flood water flowing through unprotected sections to inundates properties.
3.12.3 Decreased Floodplain Vegetation Density
Floodplain vegetation along the Kaduna River has changed dramatically due in part to
changes in the flow regime and substantially due to urbanization. Urbanization in this case led to
cutting down of the trees for fuel wood and absolute removal for infrastructural development.
The latter also lead to planting of alien vegetation within the properties. Another noticeable
effect of urbanization on the vegetation is the cultivation of the floodplain for grains and sugar
cane which is apparent all along the floodplain. The floodplain cultivation has made an all year
round cultivation possible through the use of the river water for irrigation using surface pumps
and tube wells dug within the plain. The overall effect is the removal of native vegetation mostly
hard wood for shrubs.
56
(a) Property located at a bend
(b) Property fence near the river bank
© Property fence a few metres from right bank
(c) Floodplain width reduction by property fences
(d) Typical flood protection in study area.
(e) Residential development right inside floodway
Plate VII Existing Flood Protection Efforts.
57
3.12.4 Increased Bank Erosion
Changes in watershed conditions are causing the channel to adjust to the new influencing
factors. Most notably are an increase in channel sinuosity and an increase in the length of
channel banks that are actively cutting into previously uneroded banks. This increased activity in
channel bank cutting not only provides additional sediment for transport through the basin but
also gradually undermines the foundations of the protective “flood walls” built around properties
in the floodplain and making the properties increasingly vulnerable. Active channel banks
cutting are evident at several sections of surveyed reaches as presented in Plate VIII.
(a) Bank erosion Reach 3
(b) Bank erosion in Reach 2
© Bank erosion Reach 1
(c) Erosion activity in Reach 1
Plate VIII River Bank Cuttings along the
studied Reaches.
58
CHAPTER FOUR
MODEL FORMULATION AND DEVELOPMENT
4.1 MODEL DESCRIPTION AND MODIFICATION.
Unsteady flow in natural rivers is usually treated as a one-dimensional flow in practice,
and is based on St. Venant equations. The St. Venant equations consist of the equations of
continuity and conservation of momentum and had been presented in different sets of dependent
variables as shown in section 2.3. When water discharge, Q and water level, h are dependent
variables, these equations are written in the form, presented in Equations (4.1) and (4.2),
respectively (Chow, 1976). The derivations of these equations are available in literatures
(Nwaogazie, 1987, 2008) and need not be repeated in this work.
0=−∂∂
+∂∂ q
tA
xQ (4.1)
( ) 0)(/2
=−+∂∂
+∂
∂+
∂∂
xf SSxhgA
xAQ
tQ (4.2)
Where Qthe flow through the section is, A is the flow area, xis the longitudinal distance, t
time, xS channel bottom slope, q is the lateral inflow into the channel and fS friction slope.
0)( =− xf SSgA is the kinematic wave; 0)( =−+∂∂
xf SSxhgA is the diffusion wave and dynamic
wave represented by the complete momentum equation. Equations (4.1) and (4.2) form the basis
of applications in this study.
In the process of applying the Saint venant equations to practical problems several
researchers have found the need to modify the original equations to take into considerations
additional factors which in their own opinion are not properly considered in the
derivationAmong these efforts, as quoted in Chow (1985), are the Leap frog explicit method
(Liggett and Woolhiser, 1967); the two steps Lax-Wendroff explicit method (e.g., Liggett and
59
Woolhiser, 1967); the Amein four point implicit difference method; and the fixed-mesh
characteristics method (Baltzer and Lai, 1968). In order to deal with overbank or flow in the
floodplain, Fread (1975, 1976, and 1982) quoted in (Chow, 1985) presents a modified form of
the St. Venant equations as presented in Equations (4.3) and (4.3).
( ) 0=∂+∂
+∂∂
tAA
xQ o 4.3
0)(2
=++∂∂
+
∂∂
+∂∂
ef SSxzgA
AQ
xtQ
4.4
Where Ais the active cross-sectional area of flow, oA the inactive or off channel cross sectional
area, and eS the expansion and contraction slope.
However, in this application and especially as it affects the flow of a natural river flowing
through urban settlement where all along its banks are a combination of agricultural activities
and structural developments which modifies the flow in addition to channel meandering and off-
channel storages. It can be argued that as the flood wave moves through the valley, the wave
front is horizontal extending the entire width of both banks. It is only when this linearity is
broken that the flood waters starts to spill into the adjoining areas. Consequently, it can be said
that “Encroachment into the floodplain obviously reduces the floodplain width and raise the
water level in the floodplain by a proportion equal to the entrenchment ratio defined as the ratio
of the flood-prone area width (Wfpa
) to the bankfull channel width (Wbkf
) at the cross section
under consideration”. The overall impacts of urbanization is manifested in the reduction of
floodplain area through encroachments for structural development especially buildings, resulting
in reduction of the width of the floodplain relative to the top width of bankfull channel and
obvious rise in the water surface. In the case of Kaduna River floodplain, developers build their
60
properties around floodwalls in the form of block wall fences which push back floodwaters into
adjacent properties. The resulting contraction and expansion of the entrenchment ratio as the
river flows downstream influences the water surface elevation.
Consequently, to accurately model flood levels in a river channel flowing through an
urban settlement, the Saint Venant equations need to be modified to consider the impact of
expansion of property development in the floodplain on the linearity wave front. With these
considerations, the Saint Venant equations become modified to the form presented in Equations
(4.5) and (4.6).
0=∂∂
+∂∂
tA
WW
xQ
bkf
fpa (4.5)
( ) 0)(/2
=+∂∂
+∂
∂+
∂∂
fSxzgA
xAQ
tQ (4.6)
Writing the continuity equation (equation 4.5) using the gravity oriented coordinates, we have
0=∂∂
∂∂
+∂∂
tz
zA
WW
xQ
bkf
fpa
(4.7)
Taking the channel top width as zAB∂∂
= the continuity becomes
0=∂∂
+∂∂
tzB
WW
xQ
bkf
fpa
(4.8)
The momentum equation is given by Equation (4.9)
( ) 0)(/2
=+∂∂
+∂
∂+
∂∂
fSxzgA
xAQ
tQ 4.9
where: t = time (sec); x = longitudinal distance along the channel (m); Q = flow discharge; z =
the surface level of water in the channel (m)above a datum; A is the area of flow consisting of
61
bankfull area and flood prone area ( )fpabkf AA + , Wfpa
is the flood-prone area width , Wbkf
is the
bankfull channel width and fS is friction slope given by
3/42
2
RAQQn
S f = (4.10)
Put 3/2AR
nk =in the frictional slope Equation (4.9) and the momentum equation can be written
as presented in equation 4.11.
( ) 0)(/ 22
=+∂∂
+∂
∂+
∂∂ QQk
xzgA
xAQ
tQ
(4.11)
Equations 4.8 and 4.11 form the model equations applied in this study.
4.2 NUMERICAL SOLUTION OF MODEL EQUATIONS.
The continuity and momentum equations cannot be solved analytically but finite
difference provides a numerical integration procedure of solving the two equations. The finite
difference schemes are one of the practical methods used to deal with natural channels, where the
river channel is simulated by a series of cross sections at intervals corresponding to the space
step, ∆x and the solution is carried forward in time by a series of discrete time step, ∆t. and
values of discharge and depth for each succeeding time interval can be calculated based on
previously computed values for discharge and depth.
The applications of finite difference method require that the reach topography be
constituted into a regular grid system of equal spatial and temporal steps of ∆x and ∆t,
respectively and the computation of the discharge and depth of flow is accomplished at the
nodes. In order not to lose the accuracies provided by the field data so that they can be used as
collected rather than regenerating the cross section at each interval, thus the weighted four point
62
implicit scheme has be adopted in this application i.e. ∆x is not constant thus the grid used in this
analysis is of irregular step length and located at the surveyed cross section as we move along the
river channel. However each points in the scheme are identified or referenced by row and
column (i,j) with i representing the distance between the cross sections along the longitudinal
axis of flow while j represent the time step.
4.3 FINITE DIFFERENCE FORMULATION
In the weighted four-point implicit scheme solution process, the spatial derivatives 𝜕𝜕𝜕𝜕𝜕𝜕𝜕𝜕
and
𝜕𝜕(𝜕𝜕2
𝐴𝐴 )
𝜕𝜕𝜕𝜕 as well as the variables other than the derivatives were approximated between adjacent time
lines by finite difference quotients proportioned according to the weighting factors θ and (1-θ). θ
= 0.55 is used after Fread (1978). Considering the schematic x-t solution plane in Figure 4.1, the
finite difference approximations for the terms in Equations (4.8) and (4.11) for estimation of Q
and h are derived as follows using the forward difference approximations:
Figure 4.1 Finite difference Scheme for the Implicit Method .
t
x
i,j+1 i,j
i+1,j+1 i+1, j
i,j
63
( ) ( )
i
ji
jij
ij
i
ji
ji
i
ji
jij
ij
ij
ij
i
i
ji
ji
i
ji
ji
x
xQQ
xQQ
x
xQQQQ
x
xQQ
xQ
∆
−+
∆∆−∆
=
∆−
−∆
−+
∆∆+−∆+
=
∆
−−+
∆−
=
∂∂
++
++
++
++++
11
11
11
1111 )1(
θ
θθ
θθ
(4.12)
( ) ( )
i
ji
jij
ij
i
ji
ji
i
ji
jij
ij
ij
ij
i
i
ji
ji
i
ji
ji
x
zz
xzz
xzz
x
zz
xyzzz
xzz
xzz
xz
∆
−+
∆∆−∆
=
∆−
−∆
−+
∆∆+−∆+
=
∆−
−+∆−
=
∂∂
++
++
++
+++
+
11
11
11
111
1 )1(
θ
θθ
θθ
(4.13)
( ) ( ) ( ) ( ) ( )
( ) ( )( ) ( ) ( )( )[ ] ( ) ( )[ ]( ) ( )[ ]
( ) ( )[ ] ( ) ( )[ ]iiiii
ji
ji
ji
jii
jii
ji
i
i
ji
ji
i
ji
ji
AQAQx
AQAQx
AQAQx
AQAQx
AQAQAQAQx
xAQAQ
xAQAQ
xAQ
21
2121
2
21
2
21
22211
21
2
21
21211
22
1
1
)1(
−∆
+∆−∆∆
=
−∆−
−∆
+∆+−∆+∆
=
∆−
−+∆−
=
∂
∂
++
+
+++
+
++
+
θ
θ
θ
θθ
(4.14)
And the time derivatives as follows:
( )( )
( )( )
tQQ
QQQQQQt
QQQQtt
Q
ii
jii
ji
jii
ji
ji
ji
ji
ji
∆∆+∆
=
−∆++−∆+∆
=
−+−∆
=
∂∂
+
+++
++
++
2
)(21
)(21
1
111
11
11
(4.14)
64
( )( )
( )( )
tAA
AAAAAAt
AAAAtt
A
ii
jii
ji
jii
ji
ji
ji
ji
ji
∆∆+∆
=
−∆++−∆+∆
=
−+−∆
=
∂∂
+
+++
++
++
2
)(21
)(21
1
111
11
11
(4.15)
( )( )
( )( )
tzz
zzzzzzt
zzzztt
z
ii
jii
ji
jii
ji
ji
ji
ji
ji
∆∆+∆
=
−∆++−∆+∆
=
−+−∆
=
∂∂
+
+++
++
++
2
)(21
)(21
1
111
11
11
(4.16)
and all non derivative terms are estimated as weighted averages between two adjacent time lines
as follows:
( )
22
2)1(
2
2)1(
2
11
111
111
1
iiii
ji
ji
ji
jii
ji
ji
ji
ji
ji
AAgAAg
AAgAAAAg
AAgAAggA
++
∆+∆=
+−+
∆++∆+=
+−+
+=
++
+++
+++
+
θ
θθ
θθ
(4.17)
2)1(
21
11
1
j
ibkf
fpa
j
ibkf
fpa
j
ibkf
fpa
j
ibkf
fpa
bkf
fpa
BWW
BWW
BWW
BWW
BWW
+
−+
+
=
+
++
+ θθ
+
−
+
+
∆+
+
∆+
=
++
+++
ibkf
fpa
j
ibkf
fpa
ibkf
fpa
j
ibkf
fpa
ibkf
fpa
j
ibkf
fpa
ibkf
fpa
j
ibkf
fpa
BWW
BWW
BWW
BWW
BWW
BWW
BWW
BWW
11
111
221
2
θ
θ
+
+
∆+
∆=
++ ibkf
fpa
j
ibkf
fpa
ibkf
fpa
ibkf
fpa BWW
BWW
BWW
BWW
1121
2θ
(4.18)
65
Similarly
( ) ( ) ( ) ( )
( ) ( )( ) ( ) ( )( )[ ]i
j
ii
j
i
j
i
j
i
j
i
j
i
QQAkQQAkQQAkQQAkg
QQgAkQQgAkQQgAkQQgAkQQgAk
221
21
2
21
2121
12
2
2
2)1(
2
∆++∆+=
+−+
+=
++
+
++
+
θ
θθ
( ) ( )[ ] ( ) ( )[ ]ji
j
i
j
i
j
iQQAkQQAkgQQAkQQAkg 2
122
12
22+−++
++
θ
( ) ( )[ ] ( ) ( )[ ]ji
j
iiiQQAkQQAkgQQAkQQAkg 2
122
12
22++∆+∆=
++
θ (4.19)
The finite difference form of the continuity equation is derived by substituting the finite
difference form of the derivatives and non derivatives of Equation (4.8) as follows:
02
21
21
1
111 =
∆∆+∆
+
+
∆+
∆
+∆
−+
∆∆−∆ +
+
+++
tzz
BWW
BWW
BWW
BWW
x
xQQ ii
ibkf
fpa
j
ibkf
fpa
ibkf
fpa
ibkf
fpa
i
ji
jij
ij
i
θ
θ ( 4.20)
Multiply through by ∆x
( ) ( )ii
ibkf
fpa
j
ibkf
fpa
ibkf
fpa
ibkf
fpa
ji
ji
ji
ji zz
BWW
BWW
BWW
BWW
txQQQQ ∆+∆
+
+
∆+
∆
∆∆
+
−+∆−∆= +
+
+
++ 1
1
1
11
21
2
2
θ
θ (4.21)
Where:
∆Qi+1 = change in flow at location (i+1) over time increment ∆t
∆Qi = change in flow at location (i) over time increment ∆t
∆zi+1 = change in depth of flow at location (i+1) over time increment ∆t
∆zi = change in flow at location (i) over time increment ∆t
66
Equation (5.21) can be written in simplified form in terms of unknown ∆Qi+1, ∆Qi, ∆zi+1, and ∆zi
C1∆Qi+1 +C2∆Qi + C3∆zi+1 + C4∆zi+C5 = 0 (4.22)
Where C1 = θ = 0.55
C2 = -θ = -0.55
+
+
∆+
∆
∆∆
==
+
+
ibkf
fpa
j
ibkf
fpa
ibkf
fpa
ibkf
fpa
BWW
BWW
BWW
BWW
txCC
1
1
43
21
2
2
θ
C5 = ji
ji QQ −+1
Similarly the finite difference form of the momentum equation is derived by substituting the
finite difference form of the derivatives and non derivatives of Equation (4.11) as follows:
( ) ( )[ ] ( ) ( )[ ]
( ) ( )[ ] ( ) ( )[ ]ji
j
iii
i
ji
jij
ij
ij
ij
ij
ii
iiiii
ii
QQAkQQAkgQQAkQQAkg
x
zz
xzzAAgAAg
AQAQx
AQAQxt
21
221
2
1111
21
2121
21
22
22
12
++∆+∆+
∆
−+
∆∆−∆
++
∆+∆+
−
∆+∆−∆
∆+
∆∆+∆
++
++++
+++
θ
θθ
θ
5.2
( )( ) ( ) ( )
( ) ( )
( )( )
( )( )
( )( )
( )( )
++
∆+
∆+
−∆+
∆−
∆
∆+
−
++
∆+∆
∆+∆−∆
++
∆+∆
∆+
∆∆+∆
=
++++
++
++
+
++
j
i
j
ij
i
j
iji
ji
i
ji
i
ji
jij
ij
i
jiij
ij
iji
ji
jiiii
QQAk
QQAkg
QQAk
QQAkg
AQ
AQxAQ
AQx
zzAA
AAx
gzzAA
AAx
gt
2
12
2
12
2
12
12
12
11
11
1
11
221
222
θθ
θθθ
(4.23)
Where:
∆Qi+1 = change in flow at location (i+1) over time increment ∆t
67
∆Qi = change in flow at location (i) over time increment ∆t
∆zi+1 = change in depth of flow at location (i+1) over time increment ∆t
∆zi = change in flow at location (i) over time increment ∆t
Equation (4.15) can be written in simplified form in terms of unknown ∆Qi+1, ∆Qi, ∆zi+1, and ∆zi
C6∆Qi+1 +C7∆Qi + C8∆zi+1 + C9∆zi+C10 = 0 (4.24)
Where θ = 0.55
t
CC∆
==21
76
( )( )
++
∆+∆
∆=
+
+
ji
ji
jii
AAAA
xgC
1
18 2
θθ
( )( )
++
∆+∆
∆−=
+
+
ji
ji
jii
AAAA
xgC
1
19 2
θθ
( )( ) ( ) ( )
( )( )( )
( )( )
( )( )
++
∆+
∆+
−∆+
∆−
∆
∆+−
++
∆+∆
∆+=
++
+++
+
+
j
i
j
ij
i
j
i
ji
ji
i
ji
i
ji
jij
ij
i
jii
QQAk
QQAkg
QQAk
QQAkg
AQ
AQxAQ
AQx
zzAA
AAx
gC
2
12
2
12
2
12
12
12
11
110
22
12
θ
θθ
4.4 THE DOUBLE SWEEP SOLUTION TECHNIQUE
The implicit scheme is a numerical process that is stable for any magnitude of time
increment ∆t. The two resulting systems of linear algebraic equations of continuity and momentum
must be solved at every computational point for every time step ∆t. Linearizing the boundary
conditions in terms of ∆Q and ∆z, the systems of equations can be solved by several numerical
methods (using several methods for solutions of linear equations such as the Gaussian elimination,
Gauss-Sidel etc.). These methods involve a computational process that is cumbersome and high
memory requirement for programming on a computer.
68
The double sweep is a method for transferring a one-point boundary condition by means of
a differential or difference equation corresponding to the given equation and is used for solving
boundary value problems. It provides a more efficient approach in terms of computational
operations and memory requirements for the computer programming. In the double sweep solution
technique, it is assumed that at any point, n there is a linear relationship between discharge
increment ∆Q and stage increment ∆z of the form in Equation (4.25).
∆Qn = mn∆zn + Kn (4.25)
Similar relationship exist for the point (n+1)
∆Qn+1 = mn+1∆zn+1 + Kn+1 (4.26)
So that for the reach (n, n+1) the momentum Equation (4.24) can be written as in Equation (4.27)
010918716 =+∆+∆+∆+∆ ++ nnnnnnnnn CZCZCQCQC (4.27)
Substitute Equation (4.25) in Equation (4.27) gives:
0)( 10918716 =+∆+∆++∆+∆ ++ nnnnnnnnnnn CZCZCKZmCQC (4.28)
0109187716 =+∆+∆++∆+∆ ++ nnnnnnnnnnnnn CZCZCKmCZmCQC (4.29)
0)( 101879716 =+∆+++∆+∆ ++ nnnnnnnnnnnn CZCKmCCmCZQC (4.30)
nnn
nnnnnnnnn CmC
CZCKmCQCZ97
1018716 )(+
+∆++∆−=∆ ++ (4.31)
Equation (4.31) can be written as in Equation (4.32) as:
nnnnnn SQRZPZ +∆+∆=∆ ++ 11 (4.32)
Where:
Pn = C8n / Fn
Rn = C6n / Fn
Sn = (C7nKn + C10n) / Fn
Fn = -(C7nmn + C9n)
69
Similarly, writing the continuity Equation for reach (n, n+1), we have
05413211 =+∆+∆+∆+∆ ++ nnnnnnnnn CZCZCQCQC (4.33)
Substitute Equations (4.25) and (4.32) in (4.33) yields:
0)(])([ 51141311211 =++∆+∆+∆+++∆+∆+∆ ++++++ nnnnnnnnnnnnnnnnnnn CSQRZPCZCKSQRZPmCQC (4.34)
0)( 54141413211211 =++∆+∆+∆+++∆+∆+∆ ++++++ nnnnnnnnnnnnnnnnnnnnnn CSCQRCZPCZCKCSQRZPmCQC (4.35)
05414141322121211 =++∆+∆+∆+++∆+∆+∆ ++++++ nnnnnnnnnnnnnnnnnnnnnnnnnn CSCQRCZPCZCKCSmCQRmCZPmCQC (4.36)
0)()()( 542243214211 =++++++∆+++∆ ++ nnnnnnnnnnnnnnnnnnnnnn CSCKCSmCPCCPmCZRCRmCCQ (4.37)
Equation (4.37) can be written in the form presented in Equation (4.38)
1111 ++++ +∆=∆ nnnn KZmQ (4.38)
Where
14321 /)( ++ ++= nnnnnnnn TPCCPmCm
154221 /)( ++ +++= nnnnnnnnnn TCSCKCSmCK
)( 4211 nnnnnnn RCRmCCT ++−=+
Equations (4.32) and (4.38) provide the means of computing the next value of water surface elevation
Zt+∆t and Qt+∆t for all the modeled points n=1 to n = r-1 when all the boundary conditions are linearized
locally. This requires that the boundary conditions should be of the form:
a. At the boundary n=1, the relationship between Q and H or as in this application Q and Z
presented by Equation (5.38) must be known so that the coefficient m1 and K1 can be
determined.
b. At the downstream boundary n = r, the change in water surface elevation ∆z must be known so
that the coefficient mr and Kr can be determined.
70
4.5 APPLICATIONS OF THE SAINT VENANT EQUATION TO KADUNA RIVER
The solution of the St. Venant equations for the reaches of the Kaduna River under
investigation is accomplished by solving Equations (4.1) and (4.2) using Equations (4.32) and (4.38).
In the solution process, the terms “forward sweep” and “backward sweep” are used to describe two
independent procedures whereby the upstream and downstream boundary conditions are transferred
from one point to another by means of difference Equation (4.32) and (4.38).
The solution technique starts at the upstream boundary (section n =1) whereby the coefficients
mn and Kn are specified by the upstream boundary condition. In the forward sweep procedure the
Equation (4.38) is written for section n+1 and the coefficients mn+1 and Kn+1 determine by combining
Equations (4.32) and (4.38) such that:
)]()(([/)]()([97
64
97
621
97
843
97
821
nnn
nn
nnn
nnnn
nnn
nnn
nnn
nnnn CmC
CCCmC
CmCCCmC
CCCCmC
CmCm+
−+
+−
+−+
−++
+−
=+ (4.39)
)]()(([/)]))(())(([(97
64
97
6215
97
10742
97
10721
nnn
nn
nnn
nnnnn
nnn
nnnnnn
nnn
nnnnnn CmC
CCCmC
CmCCCCmCCKCCKC
CmCCKCmCK
+−
++
−+−+
++−
++++−
=+ (4.40)
The coefficients mn+1 and Kn+1 are thus completely specified in terms of parameters determined
from known conditions at the previous section n. With this, the equation of continuity Equation (4.38)
can be written for all model points n = r, in which case we have two unknowns ∆Q and ∆Z at each
point.
The backward sweep, starting from the downstream boundary section n = r to upstream section n=1,
provides a sequential solution for the set of equations formed during the forward sweep. The value of
∆zr is known from downstream boundary condition. The flows and water stages for each time, n∆t, are
then computed at each section by adding the incremental changes ∆Q and ∆Z to the previous values of
the flow and stage, Q and Z.
4.5.1 Model Boundary Limits.
71
In selecting the two extremities of the modeled reach consideration is given to points with
control section such as bridges and gauged section such that the flow across which can be estimated
with some degree of accuracy. To this effect, the upstream boundary is taken at the Eastern Byepass
Bridge at Malali while the downstream boundary is taken as X-Section-1 located at the Western
Bypass Bridge downstream the Kaduna South Waterworks gauging station. The model is to run over
the cross section at the Kaduna South Waterworks to serve as control. The cross section diagrams for
the modeled points are presented in Appendix III. The rating curve was generated for each cross
section using the Manning’s formula and n=0.035. The rating curves for each cross section are
presented in Appendix IV.
4.5.2 Model Computerization
The numerical solution of the model equations as presented in Equation (4.32) and (4.38) is
programmed using the Microsoft Excel. For the purpose of calculating the area, wetted perimeter
and floodprone area width at every cross section, the following relationship were established:
1. The area of flow is approximated by )(2 11 ++ +∆
+=∆+= hhhhh bbhAAAA
2. The wetted perimeter is approximated by hPPPP hhh ∆+=∆+=+ 21
3. The width of flood prone area is approximated equal to the top width of flow.
Also because of the effect of the floodplain development, the surcharge flow above the bankfull is
assumed to be rectangular in shapes.
4.5.3 Model Calibration
The variables in the model equations consisted essentially of water stage, discharge and
Mannings roughness coefficient and other channel geometry parameters which were previously
determined through cross section survey. In the Kaduna 2003 flood reconstruction, the approach is
72
to utilise the known stage and discharge of the 2003 flood to calibrate Manning’s n within the
model and this value of Manning’s n can then be used to constrain estimates for Kaduna river
floods of greater magnitude at each cross sections. Stage record data corresponding to 2003 flood
level marks at the Kaduna Railway Bridge is 0.61m below the top of the central pier of the bridge.
The top level of the bridge is at 574.55m amsl and the top of the pier is 0.65m to the top level of the
bridge. Therefore the 2003 flood level measured at the railway bridge is (574.55-0.65-0.61)m or
573.29m amsl. With a right bank valley slope of 0.042% and distance of 905m to the cross section
at the Kaduna South Waterworks, the corresponding level at this cross section is573.29-
0.042%*905 or 572.91m amsl. Extending the rating curve at Kaduna South Water Works to
572.91m gives the corresponding discharge as 3,485.31m3/sec.
4.5.4 Steady Run for Extreme Flows
4.5.4.1 Boundary Conditions
The flood flows for 2yr, 10yr, 25yr, 50yr, and 100yr return periods and the year 2003 flood
flow were used as boundary conditions at the upstream and downstream end of the modeled reach.
These data were adopted from rating curve based on recorded measurement at Eastern Bye Pass
Bridge and Western Bye Pass Bridge cross sections. In order to compute the successive values of
water surface elevation ∆H and ∆Q for all the modeled points from upstream to downstream
locations, all the boundary conditions must be linearized locally. The linearization of the boundary
conditions at the boundaries was accomplished using the function slope and intercept in Microsoft
Excel to determine the coefficient m1 and K1 at the upstream and mr and Kr at the downstream as in
Equations (4.39) and (4.40). Tables 4.1 and 4.2 present the computations for the upstream and
downstream boundaries.
Table 4.1 Linearization of Upstream Boundary condition
73
Return Period Q H ∆Q ∆H
2yr 1578.60 581.85
5yr 2181.72 582.19 603.12 0.34 Slope 1674.435
10yr 2607.43 582.39 425.71 0.20 Intercept -0.03289 25yr 3175.96 582.65 568.53 0.26
50yr 3485.31 582.79 309.35 0.14 2003 3621.59 582.85 136.28 0.05 100yr 4086.07 583.03 464.48 0.19 200yr 4573.47 583.23
Table 4.2 Linearization of Downstream Boundary condition Return Period Q H ∆Q ∆H
2yr 1578.60 570.79
5yr 2181.72 571.19 603.12 0.41 Slope 1336.24
10yr 2607.43 571.48 425.71 0.29 Intercept 0.00527 25yr 3175.96 571.93 568.53 0.45
50yr 3485.31 572.19 309.35 0.26 2003 3621.59 572.28 136.28 0.09
100yr 4086.07 572.58 464.48 0.31 200yr 4573.47 572.83
4.5.4.2 Model Run and Verification
The model was initialized with the 2yr flood and run for other floods of 5yr, 10yr, 25yr,
50yr, and 100yr year annual recurrence interval and the year 2003 flood. The slope and intercept
values were entered into the model as m and k at columns 30 and 31 as well as the differential flow
and stages between the initial flow (2yr-flood) and other floods in columns 35 and 36 of Appendix
VI_IB for the upstream location and the differential water stage levels (∆H) between the initial
flow (2yr-flood) and other floods in columns 36 of Appendix VI_IB for the downstream location.
The successive change in values of water surface elevation ∆Q and ∆H for all the modeled points
from downstream to upstream locations were subsequently calculated in a backward sweep and
presented as italics numbers under columns 35 and 36. The actual discharge and water surface
elevation at each model point presented in columns 37 and 38, respectively are the sum of
74
differential model results and the initial values for that cross section. The model results were
verified by comparing the modeled flood stages at each cross sections with the measured water
stages. The comparison of the modeled and predicted water surfaces are presented in Figures 4.2 to
4.7 and model computations presented in Appendix VI_1A to Appendix VI_6B.
Table 4.3 Linearization of Upstream Boundary condition for Unsteady Model Run
Q H
∆Q ∆H 0.00 579.73
0.00 0.00
Slope 2433.66
45.76 580.34
45.76 0.61
Intercept -36.62 404.41 580.95
358.65 0.61
1077.46 581.56
673.05 0.61 1578.60 581.85
501.14 0.29
2126.85 582.17
548.25 0.32 2181.72 582.19
54.87 0.03
2607.43 582.39
425.71 0.20 3175.96 582.65
568.53 0.26
3450.82 582.78
274.86 0.13 3485.31 582.79
34.49 0.01
3621.59 582.85
136.28 0.05 4086.07 583.03
464.48 0.19
4573.47 583.23
487.40 0.19 4975.88 583.39
402.41 0.16
7080.75 584.00
2104.87 0.61 9452.72 584.61
2371.96 0.61
12729.44 585.22
3276.72 0.61
4.5.5 Unsteady Run for Normal Flows
4.5.5.1 Boundary Conditions
The unsteady model run was carried out for the range of flows measured at the cross
sections considered and local boundary conditions were linearized. Using the entire data range from
the rating curve based on recorded measurement at the upstream and downstream boundaries. The
linearization of the boundary conditions at the boundaries was accomplished using the function
slope and intercept in Microsoft Excel to determine the coefficient m1 and K1 at the upstream and
75
mr and Kr at the downstream as in Equations (4.39) and (4.40). Tables 4.3 and 4.4 represent the
computations for the upstream and downstream boundaries.
Table 4.4 Linearization of Downstream Boundary condition
for Unsteady Model Run Q H ∆Q ∆H
0.00 567.84
Slope 2034.934 0.81 568.15 0.81 0.30 Intercept -49.7432
10.52 568.45 9.71 0.30 50.15 568.76 39.63 0.30 181.11 569.06 130.96 0.30 333.68 569.37 152.57 0.30 531.47 569.67 197.79 0.30 734.65 569.98 203.18 0.30 1082.26 570.28 347.61 0.30 1349.25 570.59 266.99 0.30 1578.60 570.79 229.35 0.20 1697.84 570.89 119.24 0.10 2181.72 571.19 483.88 0.30 2187.66 571.20 5.94 0.00 2607.43 571.48 419.77 0.29 2634.95 571.50 27.52 0.02 3039.06 571.80 404.11 0.30 3175.96 571.93 136.90 0.13 3369.75 572.11 193.79 0.18 3485.31 572.19 115.56 0.08 3621.59 572.28 136.28 0.09 3825.61 572.41 204.02 0.14 4086.07 572.58 260.46 0.17 4293.76 572.72 207.69 0.14 4573.47 572.83 279.71 0.11 5063.60 573.02 490.13 0.19 5858.27 573.33 794.66 0.30 6634.99 573.63 776.72 0.30 7784.21 573.94 1149.22 0.30 9163.39 574.24 1379.18 0.30 10827.70 574.55 1664.32 0.30 12723.66 574.85 1895.96 0.30 12723.66 574.85 0.00 0.00
76
560.00
565.00
570.00
575.00
580.00
585.00
1 3 5 7 9 11 13 15 17 19 21 23 25 27
Wat
er S
urfa
ce E
leva
tion
am
sl
Station Number from Upstream Boundary
Figure 4.2 Comparison of Predicted and Measured Water Stages for 5yr Flood
Hmeasured Hmodeled
555.00
560.00
565.00
570.00
575.00
580.00
585.00
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29Wat
er S
urfa
ce E
leva
tion
am
sl
Station Number from Upstream Boundary
Figure 4.3 Comparison of Predicted and Measured Water Stages for 10yr Flood
Hmeasured Hmodeled
555.00
560.00
565.00
570.00
575.00
580.00
585.00
590.00
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29
Wat
er S
urfa
ce E
leva
tion
am
sl
Station Number from Upstream Boundary
Figure 4.4 Comparison of Predicted and Measured Water Stages for 25yr Flood
Hmeasured Hmodeled
560.00
565.00
570.00
575.00
580.00
585.00
590.00
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29Wat
er S
urfa
ce E
leva
tion
am
sl
Station Number from Upstream Boundary
Figure 4.5 Comparison of Predicted and Measured Water Stages for 50yr Flood
Hmeasured Hmodeled
77
560.00
565.00
570.00
575.00
580.00
585.00
590.00
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29Wat
er S
urfa
ce E
leva
tion
am
sl
Station Number from Upstream Boundary
Figure 4.6 Comparison of Predicted and Measured Water Stages for 100yr Flood
Hmeasured Hmodeled
560.00
565.00
570.00
575.00
580.00
585.00
590.00
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29
Wat
er S
urfa
ce E
leva
tion
am
sl
Station Number from Upstream Boundary
Figure 4.7 Comparison of Predicted and Measured Water Stages for Year 2003 Flood
Hmeasured Hmodeled
78
4.5.4.2 Model Initialization and Model Run
The model was initialized with the flow of 500m3/sec and the slope and intercept values in
Tables 4.3 and 4.4 were entered into the model as m and k at columns 30 and 31 as well as the
differential flow and stages between the initial flow (500m3/sec) and other flows in the hydrograph
generated for this run. The successive change in values of discharge and water surface elevation
(∆Q and ∆H) for all the modeled points from downstream to upstream locations were subsequently
calculated in a backward manner. The comparisons of the predicted and measured discharges at the
Kaduna South Waterworks gauging station are presented in Table 4.5 and Figures 4.8.
Table 4.5 Comparison of Predicted and Measured Discharge at the Kaduna South Waterworks
Gauging Station
Time 2 3 4 5 6 7 8 9 10 11 12 QInput 531.5 567.4 625.8 685.4 736.7 786.0 885.6 1077.5 1234.1 1732.3 2133.1 Qmodel Out 513.8 549.8 608.4 668.2 719.5 768.9 868.6 1060.8 1217.7 1716.6 2117.8
Time 13 14 15 16 17 18 19 20 21 22 23 24 QInput 1973.2 1872.2 1617.3 1537.3 1287.9 1128.7 1088.7 980.7 878.2 778.8 687.7 554.7 Qmodel Out 1957.6 1856.6 1601.4 1521.3 1271.6 1112.1 1072.0 963.9 861.2 761.7 670.4 537.1
0
500
1000
1500
2000
2500
0 5 10 15 20 25 30
Dis
char
ge (m
3/se
c)
Time (hrs)
Figure 4.8 Comparison of Predicted Discharge and Measured Discharge at the Kaduna South Waterworks
QInput Qmodel Out
79
4.6 MODEL COMPUTERIZATION USER’S GUIDE 4.6.1 Flow Chart
START
Set Boundaries Conditions (Initial & Interior)
Linearize Boundaries Condition
Compute Model Coefficients Using Ms Excel Commands & Functions
Input Hydraulic Geometric Data for all Cross Sections
Run Model (by Computing ∆Q and ∆H using forward and backward sweeps operations)
Compute Model (Q ,H)
Use Model Q at each cross section to extract computed H from the Rating Curve for the
same Cross Section
STOP
Set First Model Run Boundary Condition
(Initial & Interior)
More Flood Flows to Run?
YES
NO
Set Next Model Run Boundary Condition
(Initial & Interior)
80
4.6.2 Programs 4.6.2.1 Excel Program for Input Channel Hydraulic Geometric Data For All Cross Sections MS EXCEL COMMAND / FUNCTION / ENTRY REMARKS OPEN A NEW EXCEL WORKSHEET ‘Setout the column headers SET CELL B12 as “Field Label”; SET CELL C12 as “ ∆x”; SET CELL D12 as “Station”; SET CELL E12 as “Zfpa”; SET CELL F12 as “Ztalweg”; SET CELL G12 as “So”; SET CELL H12 as “Wfpa Max”; SET CELL I12 as “Wbkf”; SET CELL J12 as “Qinit”; SET CELL K12 as “Top Wflow”; SET CELL L12 as “hflow”; SET CELL M12 as “Zws”; SET CELL N12 as “A”; SET CELL O12 as “R”; SET CELL P12 as “Wfpa*B/Wbkf”; SET CELL Q12 as “k=(n/AR2/3))”; SET CELL R12 as “Ak2Q|Q|”; SET CELL S12 as “Q2/A”; SET CELL T12 as “C1”; SET CELL U12 as “C2”; SET CELL V12 as “C3”; SET CELL W12 as “C4”; SET CELL X12 as “C5”; SET CELL Y12 as “C6”; SET CELL Z12 as “C7”; SET CELL AA12 as “C8”; SET CELL AB12 as “C9” SET CELL AC12 as “C10”; SET CELL AD12 as “m”; SET CELL AE12 as “ k”; SET CELL AF12 as “P”; SET CELL AG12 as “R”; SET CELL AH12 as “S”; SET CELL AI12 as “∆Q”; SET CELL AJ12 as “∆H” SET CELL AK12 as “H” SET CELL AL12 as “Q”; SET CELL AM12 as “Field Label”; SET CELL AN12 as “Hmeasured”; SET CELL AO12 as “Hmodeled”; SET CELL AP12 as “∆H” SET CELL A14 TO A42 as Serial numbering of the cross section location from upstream downstream of
model reach. SET CELL B14 TO B42 as Field label of the cross section SET CELL C14 TO C42 as ∆x, longitudinal distance between two immediate cross sections moving along
the talweg. SET CELL D14 TO D42 as Station Distance from the upstream location to the target cross section.
81
SET CELL E14 TO E42 as “Zfpa” Flood prone area elevation above the mean sea level for the cross section. SET CELL F14 TO F42as Ztalweg Elevation of Talweg above mean sea level for the cross section. SET CELL G14 TO G42as So Channel bed slope at the cross section for the cross section. SET CELL H14 TO 42 as Wfpa Max Channel with at maximum flood prone area elevation for the cross
section. SET CELL I14 TO I42as Wbkf Channel width at bank full elevation for the cross section.
4.6.2.2 Excel Program for Setting Initial Boundary Conditions This represents the conditions at the cross sections ijn the model at the beginning of the model computations or before the model run. The 2yr flood i.e 1,578.6m3/sec as computed in the flood frequency analysis and its corresponding water stage and water surface above the mean sea level (amsl) at the upstream, interior and downstream boundaries were adopted as the initial conditions at all the cross sections before the model computations, such that on the Excel Worksheet:
1. For Upstream boundary: MS EXCEL COMMAND / FUNCTION / ENTRY REMARKS SET CELL B5 as “Initial Boundary Condition” SET CELL C5 as “Qm3/sec” SET CELL D5 as “hflow” SET CELL E5 as “hws” SET CELL C6 = 1,578.6 SET CELL D6 = 2.12; “Water stage at Q=1,578.6m3/sec at Upstream boundary
cross section” SET CELL E6 = 581.85; “Water surface elevation amsl at Q=1,578.6m3/sec at
upstream boundary cross section”
2. For Downstream boundary: MS EXCEL COMMAND / FUNCTION / ENTRY REMARKS SET CELL C7 = 1,578.6 SET CELL D7 = 2.94; “Water stage at Q=1,578.6m3/sec at Downstream boundary cross section” SET CELL E7 = 570.79; “Water surface elevation amsl at Q=1,578.6m3/sec at Downstream
boundary cross section”
3. For Interior boundaries cross sections MS EXCEL COMMAND / FUNCTION / ENTRY REMARKS SET CELL J14 TO J42 = 1,578.6 SET CELL K14 TO K42 = WQ=1578.6; “Top width of flow at Q=1,578.6m3/sec from
Appendix V at each interior cross sections” SET CELL L14 TO L42 = hQ=1578.6; “Normal depth of flow at Q=1,578.6m3/sec from
Appendix V at each interior cross sections” SET CELL M14 TO M42 = ZQ=1578.6; “Water surface elevation amsl at
Q=1,578.6m3/sec from Appendix V at each interior cross sections”
SET N14 TO N42 = AQ=1578.6; “Area of flow at Q=1,578.6m3/sec from Appendix V at each interior cross sections”
SET O14 TO O42 = RQ=1578.6; “Hydraulic Radius of flow at Q=1,578.6m3/sec from Appendix V at each interior cross sections”
82
SET P14 = H14*K14/I14 ; ” Wfpa*B/Wbkf Ratio of product of flood prone area width and Top width to bank full width”
COPY CELL P14 INTO P16 TO P42; ” Wfpa*B/Wbkf Ratio of product of flood prone area width and Top width to bank full width”
SET Q14 = 0.035/(N14*POWER(O14,(2/3))); ” k=(n/AR2/3))” COPY CELL Q14 INTO CELL Q15 TO Q42; “ k=(n/AR2/3))” SET R14 =N15*POWER(Q14,2)*J14*ABS(J14); “Ak2Q|Q|” COPY CELL R14 INTO CELL R15 TO R42; “Ak2Q|Q|” SET CELL S14 =POWER(J14,2)/N14; “Q2/A” COPY CELL S14 INTO CELL S15 TO S42; “Q2/A”
4.6.2.3 Excel Program for Setting Model Run Boundary Condition The model was run for steady flows represented by the floods with 5yr, 10yr, 25yr, 50yr and 100yr recurrence intervals and the 2003 flood flow as presented in Table 4.5. The unsteady state run was carried out for all the range of flows measured at the upstream cross section (Eastern Byepass bridge) using Tables 4.3 and 4.4. Table 4.5 Steady Flow Floods Return Period (years) 2 5 10 25 50 100 200 Year
2003 Qmax Daily
1,578.60 2,181.72 2,607.43 3,175.96 3621.59 4086.07 4573.47 3,485.60
MS EXCEL COMMAND / FUNCTION / ENTRY REMARKS
SET CELL I5 as “Model Run Boundary Condition” SET CELL L5 as “Qm3/sec” SET CELL M5 as “hflow” SET CELL N5 as “hws” SET CELL O5 as “∆Q” SET CELL P5 as “∆H” SET CELL I6 as “Upstream” SET CELL I7 as “Downstream” SET CELL I8 as “∆t” SET CELL J8 as “1hr”
1. For 5yr Flood
MS EXCEL COMMAND / FUNCTION / ENTRY REMARKS SET CELL L6 = 2,181.72 “5yr flood flow” SET CELL M6 = 2.46; “Water stage at Q=2,181.72m3/sec at Upstream boundary
cross section from Appendix V at each this cross sections” SET CELL N6 = 582.19; “Water surface elevation amsl at Q=2,181.72m3/sec at
upstream boundary cross section from Appendix V at each this cross sections”
83
SET CELL O6 = 603.12; “Differential flow (∆Q) between initial Condition an Model Run Condition at Upstream boundary cross section from Appendix V at each this cross sections”
SET CELL P6 = 0.34; “Differential water level (∆HQ) between initial Condition an Model Run Condition at Upstream boundary cross section from Appendix V at each this cross sections”
SET CELL L7 = 2,181.72 “5yr flood flow” SET CELL M7 = 2.95; “Water stage at Q=2,181.72m3/sec at Downstream
boundary cross section from Appendix V at each this cross sections”
SET CELL N7 = 571.19; “Water surface elevation amsl at Q=2,181.72m3/sec at Downstream boundary cross section from Appendix V at each this cross sections”
SET CELL O7 = 603.12; “Differential flow (∆Q) between initial Condition an Model Run Condition at Downstream boundary cross section from Appendix V at each this cross sections”
SET CELL P7 = 0.40; “Differential water level (∆HQ) between initial Condition an Model Run Condition at Downstream boundary cross section from Appendix V at each this cross sections”
2. For 10yr Flood
MS EXCEL COMMAND / FUNCTION / ENTRY REMARKS SET CELL L6 = 2,607.43 “10yr flood flow” SET CELL M6 = 2.46; “Water stage at Q=2,607.43m3/sec at Upstream boundary
cross section from Appendix V at each this cross sections” SET CELL N6 = 582.39; “Water surface elevation amsl at Q=2,607.43m3/sec at
upstream boundary cross section from Appendix V at each this cross sections”
SET CELL O6 = 1028.83; “Differential flow (∆Q) between initial Condition an Model Run Condition at Upstream boundary cross section from Appendix V at each this cross sections”
SET CELL P6 = 0.54; “Differential water level (∆HQ) between initial Condition an Model Run Condition at Upstream boundary cross section from Appendix V at each this cross sections”
SET CELL L7 = 2,607.43 “10yr flood flow” SET CELL M7 = 3.34; “Water stage at Q=2,607.43m3/sec at Downstream
boundary cross section from Appendix V at each this cross sections”
SET CELL N7 = 571.48; “Water surface elevation amsl at Q=2,1607.43m3/sec at Downstream boundary cross section from Appendix V at each this cross sections”
SET CELL O7 = 1028.83; “Differential flow (∆Q) between initial Condition an Model Run Condition at Downstream boundary cross section from Appendix V at each this cross sections”
84
SET CELL P7 = 0.69; “Differential water level (∆HQ) between initial Condition an Model Run Condition at Downstream boundary cross section from Appendix V at each this cross sections”
3. For 25yr Flood
MS EXCEL COMMAND / FUNCTION / ENTRY REMARKS SET CELL L6 = 3,175.96 “25yr flood flow” SET CELL M6 = 2.92; “Water stage at Q=3,175.96m3/sec at Upstream boundary
cross section from Appendix V at each this cross sections” SET CELL N6 = 582.65; “Water surface elevation amsl at Q=3,175.96m3/sec at
upstream boundary cross section from Appendix V at each this cross sections”
SET CELL O6 = 1597.36; “Differential flow (∆Q) between initial Condition an Model Run Condition at Upstream boundary cross section from Appendix V at each this cross sections”
SET CELL P6 = 0.80; “Differential water level (∆HQ) between initial Condition an Model Run Condition at Upstream boundary cross section from Appendix V at each this cross sections”
SET CELL L7 = 3,175.96 “25yr flood flow” SET CELL M7 = 4.09; “Water stage at Q=3,175.96m3/sec at Downstream boundary
cross section from Appendix V at each this cross sections” SET CELL N7 = 571.93; “Water surface elevation amsl at Q=3,175.96m3/sec at
Downstream boundary cross section from Appendix V at each this cross sections”
SET CELL O7 = 1597.36; “Differential flow (∆Q) between initial Condition an Model Run Condition at Downstream boundary cross section from Appendix V at each this cross sections”
SET CELL P7 = 1.14; “Differential water level (∆HQ) between initial Condition an Model Run Condition at Downstream boundary cross section from Appendix V at each this cross sections”
4. For 50yr Flood
MS EXCEL COMMAND / FUNCTION / ENTRY REMARKS SET CELL L6 = 3,621.59 “50yr flood flow” SET CELL M6 = 3.12; “Water stage at Q=3,621.59m3/sec at Upstream boundary
cross section from Appendix V at each this cross sections” SET CELL N6 = 572.28; “Water surface elevation amsl at Q=3,621.59m3/sec at
upstream boundary cross section from Appendix V at each this cross sections”
SET CELL O6 = 2042.99; “Differential flow (∆Q) between initial Condition an Model Run Condition at Upstream boundary cross section from Appendix V at each this cross sections”
SET CELL P6 = 1.00; “Differential water level (∆HQ) between initial Condition an Model Run Condition at Upstream boundary cross section from Appendix V at each this cross sections”
85
SET CELL L7 = 3,621.59 “50yr flood flow” SET CELL M7 = 4.44; “Water stage at Q=3,621.59m3/sec at Downstream
boundary cross section from Appendix V at each this cross sections”
SET CELL N7 = 572.28; “Water surface elevation amsl at Q=3,175.96m3/sec at Downstream boundary cross section from Appendix V at each this cross sections”
SET CELL O7 = 2042.99; “Differential flow (∆Q) between initial Condition an Model Run Condition at Downstream boundary cross section from Appendix V at each this cross sections”
SET CELL P7 = 1.49; “Differential water level (∆HQ) between initial Condition an Model Run Condition at Downstream boundary cross section from Appendix V at each this cross sections”
5. For 100yr Flood
MS EXCEL COMMAND / FUNCTION / ENTRY REMARKS SET CELL L6 = 4,086.07 “100yr flood flow” SET CELL M6 = 3.30; “Water stage at Q=4,086.07m3/sec at Upstream boundary
cross section from Appendix V at each this cross sections” SET CELL N6 = 583.03; “Water surface elevation amsl at Q=4,086.07m3/sec at
upstream boundary cross section from Appendix V at each this cross sections”
SET CELL O6 = 2507.47; “Differential flow (∆Q) between initial Condition an Model Run Condition at Upstream boundary cross section from Appendix V at each this cross sections”
SET CELL P6 = 1.18; “Differential water level (∆HQ) between initial Condition an Model Run Condition at Upstream boundary cross section from Appendix V at each this cross sections”
SET CELL L7 = 4,086.07 “100yr flood flow” SET CELL M7 = 4.74; “Water stage at Q=4,086.07m3/sec at Downstream
boundary cross section from Appendix V at each this cross sections”
SET CELL N7 = 572.58; “Water surface elevation amsl at Q=4,086.07m3/sec at Downstream boundary cross section from Appendix V at each this cross sections”
SET CELL O7 = 2507.47; “Differential flow (∆Q) between initial Condition an Model Run Condition at Downstream boundary cross section from Appendix V at each this cross sections”
SET CELL P7 = 1.79; “Differential water level (∆HQ) between initial Condition an Model Run Condition at Downstream boundary cross section from Appendix V at each this cross sections”
6. For Year 2003 Flood
MS EXCEL COMMAND / FUNCTION / ENTRY REMARKS SET CELL L6 = 3,485.31 “2003 flood flow”
86
SET CELL M6 = 3.06; “Water stage at Q=3,485.31m3/sec at Upstream boundary cross section from Appendix V at each this cross sections”
SET CELL N6 = 582.79; “Water surface elevation amsl at Q=3,485.31m3/sec at upstream boundary cross section from Appendix V at each this cross sections”
SET CELL O6 = 1906.71; “Differential flow (∆Q) between initial Condition an Model Run Condition at Upstream boundary cross section from Appendix V at each this cross sections”
SET CELL P6 = 0.94; “Differential water level (∆HQ) between initial Condition an Model Run Condition at Upstream boundary cross section from Appendix V at each this cross sections”
SET CELL L7 = 3,485.31 “2003 flood flow” SET CELL M7 = 4.34; “Water stage at Q=3,485.31m3/sec at Downstream boundary cross
section from Appendix V at each this cross sections” SET CELL N7 = 572.18; “Water surface elevation amsl at Q=3,485.31m3/sec at Downstream
boundary cross section from Appendix V at each this cross sections”
SET CELL O7 = 1906.71; “Differential flow (∆Q) between initial Condition an Model Run Condition at Downstream boundary cross section from Appendix V at each this cross sections”
SET CELL P7 = 1.40; “Differential water level (∆HQ) between initial Condition an Model Run Condition at Downstream boundary cross section from Appendix V at each this cross sections”
4.6.2.4 Excel Program for Linearization of Boundaries Condition Enter, in Ms Excel Worksheet, the regression parameters for the linearization of the ∆Q and ∆H of rating table for the upstream and downstream cross sections presented in Tables 4.1 and 4.2. MS EXCEL COMMAND / FUNCTION / ENTRY REMARKS
SET CELL S4 as “Linearization Boundary Conditions” SET CELL S5 as “Upstream” SET CELL S6 as “Slope(m)” SET CELL S7 as “Intercept (C)” SET CELL S8 as “f(z)=∆H*m+C” SET CELL S9 as “k=f(∆H)-Q∆H” SET CELL V5 as “Downstream” SET CELL V6 as “Slope(m)” SET CELL V7 as “Intercept (C)” SET CELL V8 as “f(z)=∆H*m+C” SET CELL V9 as “(∆H)” SET CELL T6 = 1674.44 “Intercept as in Table 4.1” SET CELL T7 = -0.03289 “Slope as in Table 4.1” SET CELL W6 = 1674.44 “Intercept as in Table 4.2” SET CELL W7 = -0.03289 “Slope as in Table 4.2”
87
SET CELL T8 = P6*T6+T7 SET CELL T9 =T8-(L6-C6) SET CELL W8 =P7*W6+W7 SET CELL W9 =P7
4.6.2.5 Excel Program for Computing Model Coefficients 1. Computations of C1, C2, C3, C4, C5, C6, C7, C8, C9 and C10 Parameters C1 to C10 are computed for all the model points for cell addresses T14 to AC42 by writing valid Excel formula and using the copy command to copy the formula in the addresses T14 through AC42 to T15 through AC42. MS EXCEL COMMAND / FUNCTION / ENTRY REMARKS SET CELL T14 = 0.55; “C1 = θ = 0.55” COPY CELL T14 INTO CELLS T15 TO T42; “C1 = θ = 0.55” SET CELL U14 = -0.55; “C2 = -θ = -0.55” COPT CELL U14 INTO CELLS U15 TO U42 “C2 = -θ =-0.55” SET CELL V14 =C14*(0.55*((P14-P13)+(P15-P14))+0.5*(P14+P13))/(2*3600); “C3” COPY CELL V14 INTO CELLS V15 TO V42; “C3” SET W14 =C14*(0.55*((P14-P13)+(P15-P14))+0.5*(P14+P13))/(2*3600); “ C4” COPY CELL W14 INTO CELLS W15 TO W42; “ C4” SET CELL X14 = J14-J13; “C5” COPY CELL X14 INTO CELLS X15 TO X42; “C5” SET CELL Y14 =1/(2*J8); “C6“ COPY CELL Y14 INTO CELLS Y15 TO Y42; “C6“ SET CELL Z14 =1/(2*J8); “C7” COPY CELL Z14 INTO CELLS Z15 TO Z42; “C7” SET CELL AA14 = 0.55*9.81*(0.55*((N14-N13)+(N15-N14))+(N14+N13))/(2*C14); “C8” COPY CELL AA14 INTO CELLS AA15 TO AA42; “C8” SET CELL AB14 =-0.55*9.81*(0.55*((N14-N13)+(N15-14))+(N14+N13))/(2*C14); “C9” COPY CELL AB14 INTO CELLS AB15 TO AB42; “C9” SET CELL AC14 =AA14*(M14-M13)+(0.55/C14)*((S15-S14)-(S14-S13))+(1/C14)*(S14-
S13)+(9.81*0.55/2)*((R15-R14) +(R14-R13))+(9.81/2)*(R14+R13); “C10” COPY CELL AC14 INTO CELLS AC15 TO AC42; “C10” 2. Computations of “m, k, P, R, and S MS EXCEL COMMAND / FUNCTION / ENTRY REMARKS
SET CELL AD14 = T6; “m” SET CELL AE14 = T9; “k” SET CELL AF14 =AA14/-(Z14*AD14+AB14) “P” SET CELL AG14 =Y14/-(Z14*AD14+AB14) “R” SET CELL AH14 =(Z14*AE14+AC14)/-(Z14*AD14+AB14) “S” SET AD15 CELL =(U14*AD14*AF14+V14+W14*AF14)/-(T14+U14*AE14*AG14+W14*AG14) “m” SET CELL AE 15 =(U14*AD14*AH14+U14*AE14+W14*AH14+X14)/-
(T14+U14*AD14*AG14+W14*AG14 “k” COPY CELL AD15 INTO CELLS AD16 TO AD42; “m”
88
COPY CELL AE15 INTO CELLS AD16 TO AD42 “k” COPY CELL AF14 INTO CELLS AF14 TO AD42; “P” COPY CELL AG14 INTO CELLS AG16 TO AD42 “R” COPY CELL AH14 INTO CELLS AH16 TO AD42 “S”
4.6.2.6 Excel Program for Model Run The model run was executed by computing ∆Q and ∆H in a forward and backward sweeps operations MS EXCEL COMMAND / FUNCTION / ENTRY REMARKS SET CELL AI14 =O6 “∆Q” SET CELL AJ14 =P6 “∆H” SET CELL AK14 =AJ14+M14 “H” SET CELL AL14 = L6 “Q” SET CELL AJ42 = W9 “∆H” SET CELL AI2 =AD42*AJ42+AE42 “∆Q” SET CELL AJ41 =(AF41*AJ42+AG41*AI42+AH41) “∆H” SET CELL AI41 =AD41*AJ42+AE41 “∆Q” COPY CELL AI41:AJ41 UNTO CELLS AI40:AJ15 “∆Q, ∆H” SET CELL AK15 =AJ15+M15 “H” SET CELL AL15 =$AL$14+AI15 “Q” COPY CELL AK15:A15 UNTO CELLS AK16:AL42 “Q, H” 4.6.2.7 Excel Program for Comparison of Model H and Measured H MS EXCEL COMMAND / FUNCTION / ENTRY REMARKS SET CELL AM14 =B14 “Field Label” COPY CELL AM14 UNTO CELLS AM15:AM42 “Field Label” USE AL15:AL42 (Modelled Q) in Appendix V to obtain corresponding Measured H and ENTER Results in CELLS AN15:AN42 SET CELL AO15 =AK15 “Hmodeled” COPY CELL AO15 UNTO CELLS AO16:AO42 “Hmodeled” SET CELL AP15 =AN15-AO15 “∆H” COPY CELL AP15 UNTO CELLS AP16:AP42 “∆H”
89
CHAPTER FIVE
RESULTS AND DISCUSSION
5.1 RESULTS
Hydrological analysis of rainfall data of 1955 to 2004 revealed that for the year 2003 annual
rainfall of 1459.4mm was the third historical maximum annual rainfall coming after 1691.34mm
and 1674.88mm of 1955 and 1957, respectively while the period average annual rainfall was
1,218.59mm. Also the month of August 2003 was fifth wettest month during the period. The
analyses of streamflow data for the period 1967 and 2004 indicated that the months of August and
September are the wettest months producing the maximum daily yearly flow for ten and fifteen
months, respectively during the period under investigation. The historical maximum daily flow of
2,926.31m3/sec was recorded on the 18th September 1994 followed by 2,871.75m3/sec and
2,579.50m3/sec for 1986 and 1992 respectively.
Analysis of 5-days and 7-days consecutive rainfall and average daily flows did not show any
significant pointer to the occurrence of flooding. The flow duration analysis indicated that the
period average daily flow of 164.59m3/sec was equaled for 72.97% and exceeded for 27.03% of the
period under investigation while flows in the range of 700m3/sec to 2926.31m3/sec (maximum flow
ever recorded) are rare flows which were exceeded for an insignificant period of 1.52% of the
period investigated. The flood frequency analysis shows that the basin’s 2yr, 5yr, 10yr, 25yr, 50yr,
100yr and 200yr floods are respectively 1,578.6m3/sec, 2,181.72 m3/sec, 2,607.43 m3/sec, 3,175.86
m3/sec, 3,621.59 m3/sec, 4,086.07 m3/sec and 4,573.47 m3/sec, respectively (see Table 3.6) and
what we experienced in 2003 could be as much as 3,485.31m3/sec .
The geomorphologic characterization classify the reaches investigated as class B stream
segment defined as moderately entrenched, moderate width-to-depth ratio, moderate gradient, riffle
dominated channel with gently sloping valleys; rapids predominates with scour pools infrequently
90
spaced; very stable plan and profile. The average main channel slope is 0.0416% while the
longitudinal slope for both banks is 0.042%. The Kaduna River channel develops into several low,
medium and high flows braided reaches and five bifurcated reaches characteristically overgrown
with forested vegetation, or shrubs while the soils in the bars are consolidated eroded materials
from the catchments. Nineteen tributaries flow into the main Kaduna channel with a tributary
density of 1.93 tributaries per kilometer.
Impact analysis of urbanization shows that the Kaduna River floodplain is increasing
urbanized with a maximum encroachment rate of 85.31%, 68.47% and 67.54% respectively in
Reach 2, Reach 3 and Reach 1, respectively over the period 1962 and 2009. The flood risk zones
analysis indicated that 39 out of 59 cross sections are under the risk of overbank spills of flood
waters into the adjoin properties with Reach 2 the most vulnerable having 21 cross sections
susceptible to overbank spills out of 21 cross sections. Flood protection structures along the reaches
are essentially floodwalls made of hollow bricks built to no standard.
The comparison of the top width of flow for the 2yr, 5yr, 10yr, 25yr, 50yr, and 100yr model
run and the maximum width of the flood prone area measured for each cross sections indicated that
the 5yr, 10yr, 25yr, 50yr, and 100yr floods when occur, the level of floodplain inundation could be
as much as 82.53% to 94.48% with Kigo extension, Sardauna Crescent, Kabala Doki, Living Faith
Church area and parts of Ungwan most vulnerable.
5.2 DISCUSSION
Available record did not indicated occurrence of flood in the basin in 1955 and 1957 but
what is certain is that the level of urbanization and encroachment into the Kaduna River floodplain
in form of structural developments is higher in 2003 than in 1955 and 1957. From the hydrological
point of view, the Kaduna 2003 was rainfall-induced or as a result of high rainfall aggravated by
91
indiscriminate structural developments in the floodplain that progressively reduces the width of the
floodplain.
The geomorphology of the river within the reaches investigated indicated that the Kaduna
River floodplain is moderately encroached and if the current level of development is sustained, the
floodplain may become severely encroached and the vertical containment capacities of the channel
to contain floodwaters may become eroded. The implication of this situation includes, among
others, increased frequencies of flooding in the floodplain and government shall continue to
mobilize relief materials while social economic power of the affected people may be on the decline.
Existing floodwalls made of hollow bricks are quite inadequate in capacities for flood
control as they can be pulled down under severe flooding. Also these walls are not continuous a
situation that can lead to flood water flowing through unprotected sections to inundates properties,
hence the need for urgent action.
92
CHAPTER SIX
CONCLUSION AND RECOMMENDATIONS
6.1 CONCLUSION
The Saint Vennat hydrodynamic equations had been modified for applications into modeling
impact of urbanization on the flow of flood waters onto the floodplains. The modified model was
applied to the section of the Kaduna River adjoin the Kaduna City and the results from this study
indicated that urbanization is progressively modifying the Kaduna River floodplain and its flow.
This situation if persisted without proper flood protection works will endanger both lives and
properties in the floodplain. Existing flood protection measures cannot and will never put to check
the menace of flooding along Kaduna River. A concerted effort in the form holistic approach
towards controlling the flood is urgently required.
6.2 RECOMMENDATIONS
It is therefore recommended that the Kaduna State Government should immediately put in
place a policy to regulate infrastructural development along the Kaduna floodplain as a short term
measure and construct dyke along the banks to shield already developed area from flood water as a
long term measure.
Zones under high risks of flooding delineated under this study can be reclaimed by the
Kaduna State Government for agricultural and recreational developments.
The hydraulic geometric database of the Kaduna River constituted in the course of the study
can equally form a reference database upon which impact of future development within the
floodplain is measured.
93
REFERENCES
Ayres Associates (2002). Hydraulic Modeling and Geomorphic Analysis of Sacramento
River, RM 184 to RM 194 Glenn and Butte Counties, California.
Baltzer, R. A., and Lai, C., (1968). Computer Simulations of Unsteady Flows in
Waterways. Proceedings of the American Society of Civil Engineers, Journal of
Hydraulics Division, Volume 94, no. HY 4, July 1968, pp. 717-731.
Blench, T. (1957). Regime Behaviour of Canals and Rivers. London Butterworths
Scientific Publications. 138pp.
Brigham Young University (1998), Engineering Computer Graphics Laboratory. WMS
Watershed Modeling System, Reference Manual.
Chow V. T., (1985), Open-channel hydraulics. McGraw-Hill Book Company, New
York.
Christopher N. D., Cameron T. A., James D., and Tom E., (2003), Hydrologic Modeling
for the Sacramento and San Joaquin Basins Using GeoHMS.
Chow, V. T. (1959). Open Channel Hydraulics. McGeaw-Hill Inc., New York, N. Y.
Cunge J, Holly F. and Verwey A. (1980). Practical Aspects of Computational River
Hydraulics, Pitman Publishing Ltd.
Dinand A. (2007). Flooding Simulations Still Rarely used in Disaster Preparation. ITC
News No. 4.
Etiosa U., (2006). Dams are Unrenewable. A Discussion Paper on Community Research
and Development Centre Nigeria March 2006. Community Research and
Development Centre (CREDC), Benin City, Nigeria.
Fread, D. L., (1975), Discussion of Comparison of Four Numerical Methods for Flood
Routing,” by R. K. Price, Proceedings of the American Society of Civil Engineers,
Journal of Hydraulics Division, Volume 101, no. HY 3, pp. 565-567.
Fread, D. L., (1976). Flood Routing in Meandering Rivers with Flood Plains,
Proceedings Rivers, Third Symposium of Waterways, Harbours and Coastal
Engineering Division, American Society of Civil Engineers, Volume 1, pp.16-35.
Fread, D. L., (1982). DAMBRK: The NWS Dam Break Flood Forecasying Model, Office
of Hydrology, National Weather Service, Silver Spring, Md.,
Google Earth (2008) googleearth-win-plus-4.3.7284.3916
94
Hydraulic Modelling Services Ltd (2007). Wentworth River Flood Hazard Assessment
Environment Waikato Technical Report 2007/16. www.ew.govt.nz
Hydrologic Engineering Centre. (1997),HEC-RAS River Analysis System, Program
User’s Manual. U.S. Army Corps of Engineers, Davis, California.
Lane., E. W. (1957),. “A study of the shape of channels formed by natural streams
flowing in erodible material.” Missouri River Division Sediment Series No. 9,
U.S. Army Engineering Division Missouri River, Corps of Engineers, Omaha,
Nebraska.
Leopold., L. B. and Wolman, M. G. (1957), “River channel patterns: braided, meandering
and straight.” US Geological Survey Professional Papers, 262B, 39-85.
Leopold, L. B. and Maddock, T. Jr. (1964). The Hydraulic Geometry of Stream Channels
and som Physiographic Implications. USGS Professional Paper 252, 57pp.
Liggett, J. A., and Woolhiser, D. A., (1967)., “Difference Solution of Shallow-Water
Equations,” Proceedings of the American Society of Civil Engineers, Journal of
the Engineering Mechanics Division, vol. 93, no EM2, April 1967, pp.39-71.
MNS Encarta 2007. Microsoft Encarta One Microsoft Way, Redmond, WA 98052-6399.
U.S.A.
Nwaogazie, I. L. (1987), “Comparative Analysis of Some Explicit-Implicit Streamflow
Models” Advance Water Resources, Vol 10, pp 69-77.
Nwaogazie, I. L. (2008), Finite Element Modeling of Engineering Systems, with
emphasis in Water Resources, 2nd
Edition, University of Port Harcourt Press, Port
Harcourt Nigeria, 452pp.
NWRI, (2008), The Gusau 2006 Flood Studies, A research work by the Land and Water
Division, National Water Resources Institute, Kaduna.
Olivera, F., Reed, S. and Maidment, D., (1998), HEC-PrePro v. 2.0: An ArcView
Preprocessor for HEC’s Hydrologic Modeling Systems. Centre for Research in
Water Resources, Austin, Texas.
Ramirez, J. A. and David A. R. (2005). A physical Mechanistic and fully Coupled
Hillslope Hydrology Model. International Journal for Numerical Methods in
Fluids 2005; 49:1193-
95
Richard., T. (2003), Hydraulic & Hydrologic Floodplain Mapping City of Griffin
Stormwater Utility Department, Griffin, GA Proceedings of the 2003 Georgia
Water Resources Conference, held April 23-24, 2003, at the University of
Georgia. Kathryn J.
Rosgen, D. (1996). Applied River Morphology. Pagosa Springs, CO: Wildland
Hydrology, pp 360.
Simons, D. B. and Albertson, M. I. (1963). Uniform Water Conveyance Channels in
Alluvial Material. Transactionof the American Society of Civil Engineers. Paper
No. 3399 Vol. 128, Part I. pp65-107.
Surfer Version 8.01, (2002), Surface Mapping System Software, Golden Software Inc.
809 14th
Street Golden Colorado, 80401-1866.
Susan J. N. (2006), Hydraulic Modeling Analysis of the Middle Rio Grande River from
Cochiti Dam to Galisteo Greek, New Mexico. MSc Thesis, Department of Civil,
Colorodao State University. Fort Collins, Colorado.
Swiatek D., (2007). Unsteady 1D Flow Model of Natural Rivers with Vegetated
Floodplain, Institute of Polish Academy of Science, E-7 (401), 2007.
The Punch Newspapers 2nd
September (2003). Flood: NEMA to spend N120m in 11
States. Pg. 5.
USACE (1993). River Hydraulics Engineers Manual 110-2-1416, 15 October,
Department of the Army U.S. Army Corps of Engineers Washigton D.C. 20314-
1000.
Vanguard Newspapers18th
October (2007). Flood Ogun need N6 billion to repair
damaged infrastructures Pg. 9.
Vanguard Newspapers 21st September (2005). Flood Submerges 5,508 houses in eight
Local Governments in Bauchi. Pg. 12.
96
APPENDIX
A-1
APPENDIX I – RAINFALL
A-2
APPENDIX IA Maximum Daily Rainfall Recoded at Kaduna Airport 1955 to 2004 Rainfall
Year Jan. Feb. Mar. April May June July Aug. Sept Oct Nov Dec Max Daily
Date
1955 0.00 0.00 24.89 34.80 29.97 28.45 59.94 57.40 79.76 36.32 0.00 0.00 79.76 11th Sep 1955 1956 0.00 0.00 57.15 44.45 17.02 28.19 30.48 38.10 64.77 23.37 0.25 0.76 64.77 6th Sep 1956 1957 0.00 0.00 2.79 17.78 67.56 31.24 45.21 38.61 28.96 67.82 7.11 0.00 67.82 8th Sep 1957 1958 1.52 0.00 0.00 38.61 15.24 37.08 35.05 39.88 44.20 31.75 2.54 0.00 44.20 14th Sep 1958 1959 0.00 0.00 11.18 24.38 52.83 31.24 44.45 44.45 39.88 7.11 0.00 0.00 52.83 10th Sep 1959 1960 0.00 0.00 0.00 53.09 19.56 36.32 60.45 24.38 55.37 1.52 3.81 0.76 60.45 10th July 1960 1961 14.48 0.00 1.02 30.23 15.24 57.91 31.24 77.72 70.61 12.95 0.00 0.00 77.72 11th Aug 1961 1962 0.00 0.00 0.51 20.32 32.26 26.67 44.20 38.10 50.04 36.58 12.45 0.76 50.04 2nd Sept 1962 1963 0.00 5.84 1.27 11.18 31.50 28.70 59.94 33.02 40.64 33.02 0.00 0.76 59.94 17th July 1963 1964 0.00 0.00 16.51 19.30 36.83 28.96 77.72 43.69 90.68 31.75 0.00 0.00 90.68 17th Sept 1964 1965 0.00 6.60 5.84 19.05 52.07 48.01 101.09 56.64 29.97 12.45 0.00 0.76 101.09 25th July 1965 1966 0.00 0.00 0.00 50.55 47.24 30.48 21.59 55.88 42.67 10.92 0.00 0.76 55.88 30th Aug 1966 1967 0.00 0.00 5.33 28.45 97.79 32.00 45.21 24.89 33.02 22.86 0.00 0.00 97.79 21st May 1967 1968 0.00 0.00 16.26 45.47 49.78 42.42 76.96 44.45 37.08 18.29 1.52 0.00 76.96 29th July 1968 1969 0.00 0.00 0.00 77.98 37.59 26.16 64.26 64.26 50.55 25.15 11.18 0.00 77.98 11th Apr 1969 1970 0.00 0.00 12.19 0.51 25.91 35.31 27.43 48.77 26.42 22.86 0.00 0.76 48.77 18th Aug 1970 1971 0.00 0.00 2.30 32.50 26.40 52.60 30.00 68.00 51.50 26.40 0.00 0.00 68.00 16th Aug 1971 1972 1973 1974 1975 0.00 0.00 3.80 49.30 52.10 42.70 43.70 47.70 39.10 4.60 0.00 0.03 52.10 26th May 1975 1976 1977 0.00 0.00 0.00 2.50 28.00 38.40 25.20 51.30 74.30 10.10 0.00 0.00 74.30 8th Sep 1977 1978 0.00 0.00 2.30 23.30 49.50 47.00 31.10 50.20 65.10 24.20 0.00 0.00 65.10 18th Sep 1978 1979 0.00 0.00 0.00 45.10 40.50 42.30 50.90 79.20 35.70 25.00 31.70 0.03 79.20 28th Aug 1979 1980 0.00 0.00 2.00 2.10 77.90 46.00 56.80 71.00 26.80 14.20 0.00 0.00 77.90 16th May 1980 1981 0.00 0.00 0.00 34.80 48.20 53.30 47.90 55.10 36.10 15.20 0.00 0.00 55.10 10th Aug 1981 1982 0.00 0.00 0.00 46.60 33.90 35.70 52.60 58.30 25.80 0.00 0.00 0.00 58.30 29th Aug 1982 1983 0.00 0.00 0.00 17.90 35.40 24.20 43.80 40.70 86.60 0.00 0.00 0.00 86.60 16th Sept 1983 1984 0.00 0.00 2.90 29.20 33.50 45.50 53.20 51.80 45.10 40.80 0.00 0.00 53.20 28th July 1984 1985 0.00 0.00 60.60 2.60 46.80 31.40 60.10 49.40 23.00 19.20 0.00 0.00 60.60 29th Mar 1985 1986 0.00 0.00 7.30 11.10 40.10 21.40 55.60 56.40 57.60 10.40 0.00 0.00 57.60 13th Sep 1986
A-3
1987 0.00 0.00 29.70 6.80 14.40 108.10 39.10 41.40 45.40 41.60 0.00 0.00 108.10 5th June 1987 1988 0.00 11.80 0.10 26.70 19.80 28.80 25.20 132.10 59.00 5.70 0.00 0.00 132.10 13th Aug 1988 1989 0.00 0.00 0.00 37.00 34.40 26.80 38.40 45.90 22.60 36.10 0.00 0.00 45.90 10th Aug 1989 1990 0.00 0.00 0.00 8.00 32.60 18.80 38.60 38.60 55.80 16.80 0.00 0.00 55.80 11th Sep 1990 1991 0.00 0.00 2.00 16.80 49.10 56.30 43.10 118.60 30.40 28.50 0.00 0.00 118.60 5th Aug 1991 1992 0.00 0.00 2.30 19.40 15.40 20.60 38.10 59.60 46.40 40.90 1.30 0.00 59.60 4th Aug 1992 1993 0.00 0.00 0.30 12.60 28.20 36.60 86.00 83.50 38.00 12.60 0.00 0.00 86.00 21st Aug 1993 1994 0.00 0.00 0.00 20.10 16.30 32.90 50.80 52.00 42.50 37.20 0.00 0.00 52.00 9th Aug 1994 1995 0.00 0.00 3.10 38.00 28.30 29.10 37.60 34.50 78.50 14.10 0.00 0.00 78.50 8th Sept 1995 1996 0.00 0.00 0.00 2.20 27.60 41.90 58.00 30.20 52.40 35.80 0.00 0.00 58.00 30th Jul 1996 1997 0.00 0.00 25.50 42.70 36.00 48.30 30.20 42.80 35.20 19.00 1.10 0.00 48.30 14th Jun 1997 1998 0.00 0.00 0.00 25.80 16.60 28.20 26.90 60.40 39.50 25.50 0.00 0.00 60.40 28th Aug 1998 1999 0.00 0.00 11.40 17.70 24.50 46.10 72.50 50.70 58.60 28.50 0.00 0.00 72.50 21st Jul 1999 2000 0.00 0.00 0.00 0.67 28.60 42.80 38.20 83.90 80.80 5.30 0.00 0.03 83.90 12th Aug 2000 2001 0.00 0.00 0.00 39.70 28.00 34.40 58.30 39.90 56.60 5.60 0.00 0.00 58.30 31st Jul 2001 2002 0.00 0.00 15.50 34.40 31.90 37.80 54.20 57.90 56.80 23.40 0.00 0.00 57.90 29th Aug 2002 2003 0.00 0.00 0.00 28.00 40.50 27.40 60.80 49.70 68.70 32.50 0.00 0.00 68.70 19th Sep 2003 2004 0.00 0.00 0.00 21.00 21.20 40.10 59.00 43.20 70.10 15.70 0.00 0.00 70.10 10th Sep 200
A-4
APPENDIX IB Max 5-day Total Rainfall Recoded at Kaduna Airport 1955 to 2004 Rainfall
Year Jan. Feb. Mar. April May June July Aug. Sept Oct Nov Dec Max 5-day
1955 0.00 0.00 24.89 72.14 47.75 56.90 147.57 101.35 160.02 84.33 2.29 0.00 160.02 1956 0.00 0.00 57.15 44.45 17.02 62.74 54.86 54.36 105.16 56.13 0.25 0.76 105.16 1957 0.00 0.00 2.79 23.62 111.76 92.96 67.82 79.76 90.17 103.63 7.11 0.00 111.76 1958 1.52 0.00 0.00 47.24 25.15 67.06 55.37 72.14 103.63 40.13 2.54 0.00 103.63 1959 0.00 0.00 11.18 41.40 69.85 46.74 87.63 141.22 127.76 7.11 0.00 0.00 141.22 1960 0.00 0.00 0.00 126.49 24.64 94.74 90.42 74.42 88.39 9.91 3.81 0.76 126.49 1961 14.48 0.00 1.02 49.28 32.77 72.39 78.99 101.85 104.90 13.21 0.00 0.00 104.90 1962 0.00 0.00 0.51 33.27 49.28 49.02 59.44 74.93 123.19 103.12 19.05 0.76 123.19 1963 0.00 5.84 1.27 17.78 36.07 59.94 120.40 69.09 111.00 112.01 0.00 0.76 120.40 1964 0.00 0.00 16.51 33.53 57.66 46.74 115.82 71.63 127.25 31.75 0.00 0.00 127.25 1965 0.00 6.60 5.84 30.99 92.96 60.20 151.13 139.45 90.68 33.78 0.00 0.76 151.13 1966 0.00 0.00 0.00 57.66 69.09 69.09 49.02 145.54 112.27 24.13 0.00 0.76 145.54 1967 0.00 0.00 5.33 48.26 109.98 60.96 70.61 58.17 80.26 43.18 0.00 0.00 109.98 1968 0.00 0.00 16.26 67.56 88.65 63.75 95.00 95.00 95.00 18.29 1.52 0.00 95.00 1969 0.00 0.00 0.00 97.28 54.61 55.63 85.60 129.54 84.58 56.13 14.48 0.00 129.54 1970 0.00 0.00 12.19 0.51 30.48 53.34 54.10 117.86 107.19 40.13 0.00 0.76 117.86 1971 0.00 0.00 2.30 32.50 46.70 89.20 74.90 92.90 96.90 50.50 0.00 0.00 96.90 1972 1973 1974 1975 0.00 0.00 3.80 93.20 78.70 78.80 94.00 104.70 105.10 5.80 0.00 0.03 105.10 1976 1977 0.00 0.00 0.00 2.50 49.00 61.90 47.10 119.30 101.70 23.40 0.00 0.00 119.30 1978 0.00 0.00 3.60 32.10 103.00 98.00 69.00 116.00 104.70 41.60 3.60 0.00 116.00 1979 0.00 0.00 0.00 50.70 64.90 43.20 82.70 163.80 130.60 49.00 42.10 0.03 163.80 1980 0.00 0.00 2.00 4.10 105.60 64.80 92.10 121.10 50.10 24.50 14.20 0.00 121.10 1981 0.00 0.00 0.00 44.80 69.30 104.90 83.90 103.30 77.80 18.16 0.00 0.00 104.90 1982 0.00 0.00 0.00 81.50 33.90 44.10 84.40 150.20 152.60 1.10 0.00 0.00 152.60 1983 0.00 0.00 0.00 17.90 63.00 50.20 44.90 74.60 115.60 0.00 0.00 0.00 115.60 1984 0.00 0.00 2.90 29.20 53.80 66.20 80.90 103.70 102.70 55.60 0.00 0.00 103.70 1985 0.00 0.00 61.10 60.60 88.10 56.00 114.60 118.40 89.00 57.50 0.00 0.00 118.40
A-5
1986 0.00 0.00 7.30 12.50 45.60 41.50 81.50 133.30 96.70 60.10 2.60 0.00 133.30 1987 0.00 0.00 29.70 6.80 24.10 189.10 73.30 94.90 78.20 75.40 0.00 0.00 189.10 1988 0.00 11.80 0.10 50.70 34.80 76.20 44.60 186.30 90.10 23.40 0.00 0.00 186.30 1989 0.00 0.00 0.00 37.00 45.00 53.30 67.00 104.20 39.80 71.90 0.00 0.00 104.20 1990 0.00 0.00 0.00 8.00 56.30 41.90 70.40 90.70 101.50 58.20 0.00 0.00 101.50 1991 0.00 0.00 2.00 21.60 72.90 85.00 67.10 238.80 58.60 59.80 0.00 0.00 238.80 1992 0.00 0.00 2.30 34.70 21.60 35.30 68.50 149.20 74.90 58.40 1.30 0.00 149.20 1993 0.00 0.00 0.50 12.60 55.00 67.40 161.60 114.80 99.70 18.50 0.00 0.00 161.60 1994 0.00 0.00 0.00 27.10 28.60 63.80 62.20 111.00 70.60 74.40 0.00 0.00 111.00 1995 0.00 0.00 3.10 41.50 49.30 72.20 76.30 52.20 124.90 26.00 0.00 0.00 124.90 1996 0.00 0.00 0.00 2.20 50.90 74.00 119.60 96.00 109.50 41.60 0.00 0.00 119.60 1997 0.00 0.00 25.50 84.40 44.00 89.20 47.20 91.00 102.80 63.10 1.10 0.00 102.80 1998 0.00 0.00 0.00 50.80 24.90 65.20 43.90 92.50 90.00 57.60 0.00 0.00 92.50 1999 0.00 0.00 11.40 17.70 37.20 98.60 135.90 82.30 144.10 63.00 0.00 0.00 144.10 2000 0.00 0.00 0.00 0.96 53.10 54.60 56.90 123.00 127.90 9.10 0.00 0.03 127.90 2001 0.00 0.00 0.00 39.70 52.00 78.90 104.80 104.80 115.60 12.60 0.00 0.00 115.60 2002 0.00 0.00 15.50 38.30 32.90 66.20 97.20 88.80 71.00 60.60 0.00 0.00 97.20 2003 0.00 0.00 0.00 35.10 107.90 96.50 122.60 114.60 108.80 41.20 0.00 0.00 122.60 2004 0.00 0.00 0.00 21.00 47.80 69.40 127.20 94.40 121.40 48.00 0.00 0.00 127.20
A-6
APPENDIX IC Max 7-day Total Rainfall Recoded at Kaduna Airport 1955 to 2004 Rainfall
Year Jan. Feb. Mar. April May June July Aug. Sept Oct Nov Dec Max 7-day
1955 0.00 0.00 24.89 73.41 57.40 68.07 165.35 123.44 195.83 87.63 28.96 0.00 195.83 1956 0.00 0.00 57.15 44.45 17.02 67.56 83.06 86.11 108.97 56.13 0.25 0.76 108.97 1957 0.00 0.00 2.79 24.13 126.24 107.95 82.55 84.33 117.35 134.62 10.92 0.00 134.62 1958 1.52 0.00 0.00 62.23 28.70 81.79 55.37 72.39 123.95 58.67 2.54 0.51 123.95 1959 0.00 0.00 11.18 52.32 92.20 51.56 106.68 158.50 155.19 7.11 0.00 0.00 158.50 1960 0.00 0.00 0.00 126.49 28.19 109.73 95.50 107.44 116.08 59.94 3.81 0.76 126.49 1961 14.48 0.00 1.02 50.55 46.99 84.33 110.24 114.55 118.87 13.21 0.51 0.00 118.87 1962 0.00 0.00 0.51 33.27 64.26 55.63 85.09 81.79 134.37 145.80 22.10 0.76 145.80 1963 0.00 5.84 1.27 27.94 50.55 64.01 135.64 93.98 111.00 140.97 0.00 0.76 140.97 1964 0.00 0.00 16.51 33.53 57.66 57.40 159.26 90.17 147.32 42.16 0.00 0.00 159.26 1965 0.00 6.60 5.84 33.02 107.70 74.42 174.50 154.69 144.27 35.05 0.00 0.76 174.50 1966 0.00 0.00 0.00 62.48 89.15 81.79 59.94 154.18 140.72 55.37 0.00 0.76 154.18 1967 0.00 0.00 5.33 48.26 110.24 78.99 103.38 68.33 109.47 53.34 0.00 0.00 110.24 1968 0.00 0.00 18.29 76.96 102.62 80.26 108.46 132.84 104.39 18.29 1.52 0.00 132.84 1969 0.00 0.00 0.00 97.28 54.61 71.37 92.20 153.92 112.27 82.80 46.48 0.00 153.92 1970 0.00 0.00 12.19 0.51 40.89 59.69 54.10 134.37 130.81 40.13 0.00 0.76 134.37 1971 0.00 0.00 2.30 32.50 48.00 92.00 90.90 110.70 133.10 53.30 0.00 0.00 133.10 1972 1973 1974 1975 0.00 0.00 3.80 102.80 83.80 84.80 107.80 129.50 146.10 25.70 0.00 0.03 146.10 1976 1977 0.00 0.00 0.00 2.50 57.90 79.50 56.20 124.10 121.30 51.70 0.00 0.00 124.10 1978 0.00 0.00 3.60 37.90 117.50 107.20 121.90 138.00 130.10 43.20 41.60 0.00 138.00 1979 0.00 0.00 0.00 50.70 67.50 50.30 94.90 169.40 199.10 72.00 42.10 0.03 199.10 1980 0.00 0.00 2.00 4.10 105.90 79.20 105.50 131.00 126.90 26.40 14.20 0.00 131.00 1981 0.00 0.00 0.00 52.60 77.10 117.60 98.10 158.40 107.40 22.20 0.30 0.00 158.40 1982 0.00 0.00 0.00 86.70 48.40 51.30 96.80 165.80 191.60 1.10 0.00 0.00 191.60 1983 0.00 0.00 0.00 17.90 65.60 75.70 44.90 97.80 126.90 30.20 0.00 0.00 126.90 1984 0.00 0.00 2.90 29.20 63.80 73.90 102.50 116.20 113.50 67.00 0.00 0.00 116.20 1985 0.00 0.00 61.10 61.10 90.00 61.70 136.80 129.00 99.50 62.00 0.00 0.00 136.80 1986 0.00 0.00 7.30 12.50 45.60 48.30 89.30 148.90 133.30 60.70 2.60 0.00 148.90
A-7
1987 0.00 0.00 29.70 6.80 27.20 222.50 81.90 107.70 89.20 89.30 0.00 0.00 222.50 1988 0.00 11.80 0.10 56.80 35.00 81.90 60.60 260.50 142.90 28.30 0.00 0.00 260.50 1989 0.00 0.00 0.00 37.00 54.80 55.00 75.10 134.00 52.40 87.90 0.00 0.00 134.00 1990 0.00 0.00 0.00 13.70 69.00 48.40 84.40 112.90 137.50 60.30 0.00 0.00 137.50 1991 0.00 0.00 3.60 21.60 73.70 131.40 72.80 263.00 87.10 65.40 0.00 0.00 263.00 1992 0.00 0.00 2.30 34.70 21.60 35.30 91.20 158.10 98.90 60.10 1.30 0.00 158.10 1993 0.00 0.00 0.50 12.60 64.20 67.40 191.20 134.60 112.60 23.20 0.00 0.00 191.20 1994 0.00 0.00 0.00 27.10 28.60 67.30 73.40 142.90 79.50 85.00 7.90 0.00 142.90 1995 0.00 0.00 3.10 42.30 59.40 91.40 84.90 62.50 140.10 31.30 0.00 0.00 140.10 1996 0.00 0.00 0.00 2.20 54.40 86.30 138.40 133.50 130.10 108.60 0.00 0.00 138.40 1997 0.00 0.00 26.10 84.40 85.20 91.60 60.10 121.00 116.20 63.10 1.20 0.00 121.00 1998 0.00 0.00 0.00 52.00 34.30 73.30 51.30 118.40 92.80 64.00 0.00 0.00 118.40 1999 0.00 0.00 11.40 20.60 50.50 116.00 144.00 91.50 177.90 90.00 0.00 0.00 177.90 2000 0.00 0.00 0.00 1.01 53.10 62.10 56.92 178.50 146.90 12.20 0.02 0.03 178.50 2001 0.00 0.00 0.00 54.00 57.00 110.70 105.30 125.70 133.50 30.20 0.00 0.00 133.50 2002 0.00 0.00 15.50 60.60 34.30 95.60 141.60 119.40 85.40 83.80 0.00 0.00 141.60 2003 0.00 0.00 0.00 48.40 108.70 114.10 154.40 157.00 112.60 43.90 0.00 0.00 157.00 2004 0.00 0.00 0.00 21.00 69.00 73.70 161.60 108.80 157.90 50.40 0.00 0.00 161.60
A-8
APPENDIX ID Monthly Total Rainfall Recoded at Kaduna Airport 1955 to 2004 Rainfall
Year Jan. Feb. Mar. April May June July Aug. Sept Oct Nov Dec Total Annual
1955 0.00 0.00 34.29 129.79 120.40 164.34 373.89 288.29 391.67 188.72 0.00 0.00 1,691.39 1956 0.00 0.00 97.79 57.66 43.43 176.28 176.53 163.83 258.57 56.13 0.25 0.76 1,031.24 1957 0.00 0.00 3.30 34.54 357.12 261.62 216.92 263.91 345.44 183.64 8.38 0.00 1,674.88 1958 1.52 0.00 0.00 108.20 59.44 153.92 117.86 168.40 338.58 94.74 4.83 0.00 1,047.50 1959 0.00 0.00 13.97 58.67 167.13 110.74 207.01 259.33 325.88 7.11 0.00 0.00 1,149.86 1960 0.00 0.00 0.00 238.51 39.12 218.69 249.94 213.87 278.13 2.29 3.81 0.76 1,245.11 1961 14.48 0.00 1.02 52.32 65.02 206.76 247.14 187.96 243.59 20.32 0.00 0.00 1,038.61 1962 0.00 0.00 0.51 51.05 143.26 121.41 166.62 266.19 325.63 188.72 22.61 0.76 1,286.76 1963 0.00 5.84 2.29 36.58 85.60 192.02 274.07 285.50 267.21 210.31 0.00 0.76 1,360.17 1964 0.00 0.00 16.51 60.96 80.01 134.62 311.91 231.90 339.60 35.56 0.00 0.00 1,211.07 1965 0.00 6.60 5.84 40.13 122.17 187.20 343.41 347.22 169.67 20.32 0.00 0.76 1,243.33 1966 0.00 0.00 0.00 93.98 178.82 165.35 140.46 424.94 347.47 27.18 0.00 0.76 1,378.97 1967 0.00 0.00 5.33 114.55 130.81 179.07 240.79 184.91 256.54 29.97 0.00 0.00 1,141.98 1968 0.00 0.00 18.29 119.13 196.34 228.35 254.00 322.83 196.09 23.62 1.52 0.00 1,360.17 1969 0.00 0.00 0.00 111.76 94.49 155.73 255.78 358.39 310.64 124.97 11.43 0.00 1,423.19 1970 0.00 0.00 21.34 0.51 89.92 145.29 128.27 387.60 224.79 40.13 0.00 0.76 1,038.61 1971 0.00 0.00 2.30 36.60 122.30 181.90 250.20 321.77 284.70 63.55 0.00 0.00 1,263.32 1972 1975 0.00 0.00 3.80 103.60 172.20 184.60 242.20 297.50 294.80 8.40 0.00 0.03 1,307.13 1976 1977 0.00 0.00 0.00 2.50 97.00 219.70 107.20 279.00 238.70 24.40 0.00 0.00 968.50 1978 0.00 0.00 3.60 72.90 205.10 275.90 201.81 283.90 248.50 122.90 0.00 0.00 1,414.61 1979 0.00 0.00 0.00 68.10 177.20 142.50 291.70 397.40 264.20 62.70 42.10 0.03 1,445.93 1980 0.00 0.00 2.00 4.10 288.50 164.28 221.70 380.50 103.60 45.80 0.00 0.00 1,210.48 1981 0.00 0.00 0.00 67.70 129.00 181.80 259.30 357.10 217.60 15.56 0.00 0.00 1,228.06 1982 0.00 0.00 0.00 108.10 62.20 124.00 291.80 332.00 142.90 0.00 0.00 0.00 1,061.00 1983 0.00 0.00 0.00 28.50 122.10 202.80 108.50 207.50 230.20 0.00 0.00 0.00 899.60 1984 0.00 0.00 2.90 55.57 141.82 218.90 193.30 202.10 262.40 107.60 0.00 0.00 1,184.59 1985 0.00 0.00 70.50 2.60 140.00 125.40 323.80 281.30 236.10 35.90 0.00 0.00 1,215.60 1986 0.00 0.00 7.30 22.50 91.20 117.50 213.70 306.10 319.00 13.00 0.00 0.00 1,090.30 1987 0.00 0.00 29.70 6.80 52.30 260.50 221.50 319.90 207.30 102.10 0.00 0.00 1,200.10 1988 0.00 11.80 0.10 63.10 58.10 189.00 140.90 454.70 253.40 5.70 0.00 0.00 1,176.80
A-9
1989 0.00 0.00 0.00 37.70 106.70 146.10 165.00 264.90 155.50 136.90 0.00 0.00 1,012.80 1990 0.00 0.00 0.00 15.90 121.80 106.20 172.90 312.20 275.50 17.50 0.00 0.00 1,022.00 1991 0.00 0.00 3.60 32.00 219.20 226.40 185.80 548.80 130.50 61.80 0.00 0.00 1,408.10 1992 0.00 0.00 2.30 46.70 52.80 84.90 241.00 372.20 232.10 85.50 1.30 0.00 1,118.80 1993 0.00 0.00 0.50 14.70 145.40 169.10 393.00 285.90 177.50 37.80 0.00 0.00 1,223.90 1994 0.00 0.00 0.00 55.80 54.20 166.40 127.00 292.20 239.90 173.60 0.00 0.00 1,109.10 1995 0.00 0.00 3.10 55.26 139.50 159.00 239.40 202.30 330.40 30.20 0.00 0.00 1,159.16 1996 0.00 0.00 0.00 2.20 162.10 147.80 331.60 186.20 307.50 77.20 0.00 0.00 1,214.60 1997 0.00 0.00 41.30 95.50 88.70 238.80 126.20 334.20 319.00 75.20 1.10 0.00 1,320.00 1998 0.00 0.00 0.00 61.60 71.80 184.20 137.00 338.60 157.00 131.10 0.00 0.00 1,081.30 1999 0.00 0.00 11.40 30.50 89.00 209.20 272.40 170.90 407.40 92.00 0.00 0.00 1,282.80 2000 0.00 0.00 0.00 1.81 68.34 118.02 112.72 256.38 205.41 17.22 0.00 0.03 779.93 2001 0.00 0.00 0.00 81.10 82.20 208.80 268.80 209.50 326.00 10.30 0.00 0.00 1,186.70 2002 0.00 0.00 19.60 65.00 58.90 228.10 320.80 273.60 228.00 113.50 0.00 0.00 1,307.50 2003 0.00 0.00 0.00 78.20 125.30 109.30 387.60 404.20 283.70 71.10 0.00 0.00 1,459.40 2004 0.00 0.00 0.00 37.10 122.80 178.10 358.70 310.70 347.40 25.60 0.00 0.00 1,380.40
A-10
APPENDIX II-STREAMFLOW ANALYSIS
A-11
Average Daily Flow River Kaduna at Kaduna South
Year Jan. Feb. Mar. April May June July Aug. Sept Oct Nov Dec
1967 5.21 36.04 83.09 339.87 601.30 821.81 292.66 49.34 16.58
1968 8.67 6.19 5.20 20.30 69.89 269.77 438.34 650.93 549.01 148.44 33.21 11.78
1972 5.78 59.57 114.46 288.03 760.01 560.50 186.00 34.76 10.33
1973 5.47 1.80 1.44 4.01 8.86 61.38 148.81 725.97 660.44 125.11 22.14 8.00
1974 4.06 1.65 4.69 7.53 70.07 70.04 337.30 531.28 941.38 298.74 39.91 11.79
1975 6.35 3.11 1.59 12.22 91.29 88.19 296.89 717.27 1,015.94 232.86 45.47 16.09
1976 7.12 1.64 1.20 6.28 41.34 109.72 325.34 441.51 475.33 369.15 24.52 24.84
1979 9.38 12.98 1.25 20.53 56.10 107.92 367.48 536.64 699.12 210.14 46.24 9.82
1980 3.76 2.40 3.26 2.84 61.15 146.75 336.39 541.40 423.59 132.11 32.55 8.70
1981 3.17 1.58 1.34 1.59 56.74 101.67 243.17 473.35 750.15 390.94 35.70 8.65
1982 3.30 1.34 1.55 4.82 17.29 57.39 245.46 492.32 427.42 188.57 27.81 8.05
1983 2.74 1.67 1.40 1.95 18.25 129.96 222.83 374.41 395.69 66.66 13.72 2.83
1984 1.32 1.16 2.96 12.83 33.09 82.44 149.42 210.45 233.77 130.01 11.91 3.02
1985 1.61 1.13 1.54 6.12 21.34 132.63 287.41 522.75 408.91 83.63 9.64 2.80
1986 1.42 0.93 2.09 2.75 34.98 59.89 410.61 450.05 501.82 336.23 22.94 9.09
1987 3.37 2.57 2.53 2.02 3.26 410.11 201.54 623.50 448.56 155.51 0.00 0.00
1988 3.46 3.24 2.47 1.84 3.45 371.97 118.82 493.25 536.00 130.41 9.93 3.14
1990 0.00 2.29 1.46 2.28 45.06 53.12 185.02 598.17 658.06 53.85 17.76 6.89
1991 2.50 2.27 2.91 4.84 101.20 118.16 258.54 853.71 3.63 2.35 1.59 1.17
1992 2.42 1.59 1.95 6.97 15.74 104.07 313.94 708.62 1,093.47 94.06 20.81 8.65
1994 0.72 0.50 1.40 0.59 33.08 135.70 207.56 610.31 828.40 345.70 63.82 19.48
1995 4.92 21.88 96.24 203.39 513.18 550.09 160.55
1996 122.71 164.24 385.02 541.24 643.89 264.74
1997 84.67 59.14 188.86 283.43 625.68 668.08 267.10 109.13 23.95
1998 11.35 1.95 11.00 52.62 155.23 286.27 664.28 960.22 437.88 57.25 17.92
1999 7.08 3.10 3.22 6.39 48.49 180.76 430.83 469.55 923.92 426.60 59.25 7.64
2000 3.40 1.99 2.77 2.93 39.66 243.79 305.04 797.55 831.71 313.75 21.30 7.43
2004 3.70 2.47 2.94 4.12 57.26 301.06 369.32 655.85 161.85 23.93
A-12
Max Daily Flow River Kaduna at Kaduna South
Year Jan. Feb. Mar. April May June July Aug. Sept Oct Nov Dec Max
Daily
Flow
Water
Stage
Date
1967 0.00 0.00 0.00 27.18 210.54 557.56 719.81 836.48 1,469.64 832.52 103.92 39.87 1,469.64 6.1230 10th Sep 1967
1968 11.10 7.79 8.18 125.44 258.33 2,270.70 766.25 1,090.20 835.91 315.00 67.82 15.77 2,270.70 6.8920 21st June 1968
1972 0.00 0.00 0.00 26.33 207.14 313.27 2,296.52 2,098.28 959.94 279.97 64.42 15.40 2,296.52 6.9150 11th July 1972
1973 8.58 1.93 1.64 18.83 17.41 217.39 559.26 1,441.33 3,121.76 338.24 47.57 17.05 1,441.33 6.0720 1st Sept 1973
1974 5.49 2.56 5.86 19.60 246.38 232.74 4,377.78 1,192.14 1,795.29 720.95 69.09 18.38 1,795.29 6.4530 19th Sept 1974
1975 8.75 4.98 7.90 57.40 167.80 172.90 852.40 1,567.80 2,362.50 559.80 74.60 31.70 2,362.50 6.9740 21st Sept 1975
1976 17.00 2.80 1.20 57.40 119.70 285.20 695.60 628.80 814.50 551.30 42.20 42.20 814.50 4.9520 26th Sept 1976
1977 0.00 0.00 0.00 5.90 96.85 267.65 262.00 640.10 1,005.40 430.50 47.10 7.30 1,005.40 5.3900 9th Sept 1977
1979 13.76 146.93 4.76 484.82 136.20 232.48 611.64 837.05 1,068.11 515.65 110.15 15.40 1,068.11 5.5700 25th Sept 1979
1980 6.14 6.99 4.05 3.68 162.82 275.99 656.38 744.73 1,066.41 200.89 106.19 13.04 1,066.41 5.5660 2nd Sept 1980
1981 5.13 2.29 1.65 3.17 176.70 268.02 540.57 794.57 1,192.14 3,172.62 76.17 13.85 1,192.14 5.1600 8th Sept 1981
1982 5.13 2.13 4.27 18.16 49.27 215.68 383.41 3,152.94 669.98 549.66 94.86 13.36 1,251.04 5.7910 7th Aug 1982
1983 3.62 2.58 1.83 3.98 148.66 615.75 1,224.70 700.56 681.30 206.58 86.61 4.32 700.56 4.6800 1st Aug 1983
1984 1.97 1.97 13.91 59.47 58.33 272.00 234.69 329.75 380.01 422.49 25.20 4.27 422.49 3.7900 2nd Oct 1984
1985 2.27 1.74 1.82 34.26 133.94 299.92 454.91 1,100.82 712.88 269.75 16.49 3.75 1,100.82 5.5800 15th Aug 1985
1986 1.97 3.82 4.05 8.26 94.86 119.21 2,871.75 923.84 836.34 2,549.56 45.31 48.45 2,871.75 7.9600 22nd Jul 1986
1987 4.45 3.14 3.41 3.38 16.06 2,370.38 732.35 1,090.47 1,097.69 406.85 0.01 0.00 2,370.38 6.9810 21st June 1987
1988 5.35 6.79 4.28 4.01 30.24 2,072.57 399.76 1,576.77 1,397.57 563.90 25.96 4.43 2,072.57 6.7800 25 and 26th Jun 1988
1990 0.00 4.15 2.07 7.40 110.01 131.05 490.97 1,171.66 1,440.94 108.61 27.51 9.68 1,440.94 5.6700 19th Sep 1990
1991 4.26 3.60 3.86 12.38 453.04 253.21 588.58 1,460.45 5.16 3.52 1.81 1.40 1,460.45 5.7000 28th Aug 1991
1992 3.99 2.51 10.14 38.70 39.38 253.21 607.33 1,460.45 3,176.72 212.48 32.99 12.08 2,579.50 7.1400 1st Sept 1992
1994 1.62 2.30 1.78 9.27 194.06 237.69 460.86 1,004.54 2,926.31 801.61 165.65 156.22 2,926.31 7.3900 18th Sept 1994
1995 10.43 0.00 0.00 0.00 48.14 271.84 324.90 862.01 707.21 324.90 0.00 0.00 862.01 5.0800 10th Aug 1995
1996 0.00 0.00 0.00 0.00 190.26 302.20 722.32 933.75 1,151.79 520.32 75.04 0.00 1,151.79 5.6700 12th Sept 1996
1997 0.00 0.00 0.00 146.77 163.76 455.19 661.91 1,013.98 1,009.26 395.73 317.37 40.58 1,013.98 5.4100 20th Aug 1997
1998 14.19 0.00 3.11 49.08 205.44 285.12 1,055.51 966.78 2,395.85 588.28 143.00 26.43 2,395.85 7.0000 10th Sept 1998
1999 12.77 3.31 6.35 13.85 186.46 703.44 646.81 631.70 2,488.34 831.81 93.92 10.43 2,488.34 7.0700 4th Sept 1999
2000 11.03 2.53 3.31 27.38 222.51 317.37 514.66 1,083.83 1,055.51 551.47 61.36 10.43 1,083.83 5.5500 25th Aug 2000
2001 7.65 2.38 3.11 61.36 232.00 398.56 869.56 1,055.51 0.00 0.00 0.00 0.00 1,055.51 5.5000 26th Aug 2001
2004 5.13 5.13 4.15 19.31 271.84 390.06 596.78 1,370.77 378.74 48.14 0.00 0.00 1,370.77 5.9900 23rd Aug 2004
A-13
Max 5-days Moving Average Flow River Kaduna at Kaduna South
Year Jan. Feb. Mar. April May June July Aug. Sept Oct Nov Dec
1967 0.00 0.00 0.00 12.50 77.11 291.38 551.78 724.46 1,169.43 767.39 104.04 22.54
1968 10.40 6.94 6.84 71.87 173.44 666.52 587.69 938.60 798.15 314.02 60.03 16.35
1972 0.00 0.00 0.00 16.35 172.82 225.52 695.82 1,553.46 1,445.29 301.12 86.17 16.32
1973 7.95 2.51 1.67 12.02 14.57 112.68 339.55 1,218.93 998.34 490.53 53.24 10.27
1974 5.21 2.78 5.74 13.39 200.91 151.34 1,131.91 1,243.79 1,413.01 756.97 74.95 18.40
1975 8.26 4.43 4.86 38.06 131.04 123.78 595.18 1,107.66 1,723.48 683.52 88.74 26.44
1976 15.00 3.84 1.20 17.62 104.98 176.10 594.48 548.68 672.58 558.12 345.32 39.62
1977 0.00 0.00 0.00 4.20 62.61 236.05 198.37 559.77 879.62 375.64 53.94 7.54
1979 12.43 56.52 2.94 100.52 99.89 209.21 552.57 675.75 893.28 655.20 93.53 17.06
1980 5.59 4.14 4.64 3.48 128.39 196.30 567.41 694.44 767.10 243.27 108.11 13.72
1981 4.42 2.35 1.62 2.33 141.55 226.95 393.03 716.87 1,134.03 1,440.22 83.31 14.01
1982 4.88 2.20 3.20 12.23 27.61 138.73 333.92 947.20 640.24 344.98 110.04 12.02
1983 3.46 2.53 1.66 3.33 79.14 201.70 365.02 471.37 597.60 304.46 31.21 4.67
1984 1.83 1.94 4.79 36.00 47.46 206.93 194.51 288.52 316.29 313.27 31.43 4.75
1985 1.94 1.67 1.76 22.81 53.58 252.12 376.42 764.24 649.90 277.84 19.28 3.61
1986 1.87 1.38 3.12 5.77 59.58 99.14 719.04 720.98 606.86 1,489.74 41.91 18.57
1987 4.43 3.13 3.00 3.05 7.79 1,774.98 521.48 934.71 953.73 353.72 21.81 0.00
1988 5.10 5.66 3.57 2.83 12.44 1,497.67 210.82 811.72 1,092.39 370.68 29.54 5.04
1990 0.00 3.56 2.07 6.14 75.70 98.96 392.49 923.34 1,258.47 254.85 30.29 10.86
1991 3.99 3.41 3.66 9.04 344.23 234.33 414.96 1,274.04 1,153.43 3.16 1.84 1.42
1992 3.73 2.53 6.17 23.95 36.01 199.65 578.87 1,148.67 1,755.53 248.90 61.55 12.75
1994 1.36 1.69 1.67 2.06 97.05 206.95 331.14 898.63 1,765.62 579.65 181.55 52.39
1995 6.52 0.00 0.00 0.00 38.70 217.59 249.83 766.87 647.18 411.58 36.82 0.00
1996 0.00 0.00 0.00 0.00 141.13 223.28 617.55 752.14 862.77 569.40 90.14 0.00
1997 0.00 0.00 0.00 67.74 123.74 390.62 483.22 886.36 918.65 509.00 262.01 47.57
1998 13.46 0.00 2.77 36.25 106.59 227.82 503.90 815.01 1,845.93 558.83 168.70 27.19
1999 11.77 3.31 5.37 10.70 138.76 545.20 603.54 579.98 1,373.41 759.32 131.31 10.37
2000 5.34 2.65 3.31 8.40 133.99 287.02 399.17 1,001.33 952.44 564.31 76.83 10.31
2001 6.43 2.50 3.01 61.36 181.57 314.60 655.49 906.56 433.39 0.00 0.00 0.00
2004 4.34 4.27 3.96 13.70 206.33 365.99 507.30 868.99 406.85 91.18 0.00 0.00
A-14
Max 7-days Moving Average Flow River Kaduna at Kaduna South
Year Jan. Feb. Mar. April May June July Aug. Sept Oct Nov Dec
1967 0.00 0.00 0.00 10.98 66.20 223.18 516.90 698.33 1,095.09 734.46 109.02 24.03
1968 10.16 7.17 6.41 60.24 157.58 543.72 557.24 893.97 806.59 354.24 62.24 16.81
1972 0.00 0.00 0.00 13.50 149.50 204.37 546.88 1,334.25 1,372.96 327.79 91.89 16.80
1973 7.79 2.76 1.67 10.95 13.81 101.97 290.90 1,112.16 932.43 497.09 55.30 10.57
1974 5.12 2.85 5.67 11.88 180.65 138.03 870.05 989.09 1,301.85 775.88 85.17 18.97
1975 8.05 4.50 3.81 33.99 114.61 121.49 544.09 1,033.80 1,591.03 747.90 93.80 27.17
1976 13.67 4.06 1.20 13.91 92.24 171.06 567.70 529.29 629.67 599.96 351.76 38.09
1977 0.00 0.00 0.00 3.70 53.57 201.50 178.20 530.64 815.82 368.54 56.30 7.66
1979 12.18 42.10 2.48 72.94 97.18 199.31 545.75 657.36 835.19 756.71 84.44 18.05
1980 5.37 3.41 4.38 3.40 113.59 176.86 546.15 664.60 713.42 252.83 108.37 14.14
1981 4.22 2.38 1.61 2.06 121.54 216.58 372.84 693.36 1,098.17 1,125.74 88.96 14.03
1982 4.62 2.26 2.98 11.73 26.53 134.94 300.22 953.63 647.12 325.96 96.08 12.21
1983 3.32 2.49 1.69 3.03 59.68 187.64 294.22 435.28 561.28 301.37 25.44 5.10
1984 1.54 1.77 4.51 26.66 44.86 194.25 178.27 274.13 302.26 285.38 35.96 4.58
1985 1.88 1.42 1.71 18.53 54.41 220.70 354.57 716.52 626.15 272.60 20.45 4.16
1986 1.81 1.28 2.96 4.70 52.22 86.93 908.98 661.70 597.95 1,169.03 40.65 16.35
1987 4.33 3.22 2.99 2.95 7.74 1,298.34 443.02 892.56 911.35 339.03 24.97 0.00
1988 4.88 5.10 3.27 2.60 9.62 1,112.96 706.03 724.81 955.96 322.64 31.37 5.33
1990 0.00 3.47 2.14 5.39 67.92 86.66 373.98 835.93 1,124.76 272.16 31.28 11.36
1991 3.86 3.34 3.60 8.16 297.74 277.78 383.72 1,163.84 1,038.88 3.04 1.86 1.43
1992 3.61 2.49 5.29 19.98 33.96 185.36 554.34 1,019.22 1,686.62 277.34 63.59 13.13
1994 1.24 1.31 1.68 1.54 77.14 196.51 312.84 863.36 1,523.63 556.63 196.51 45.92
1995 5.60 0.00 0.00 0.00 35.46 184.68 233.09 727.30 660.02 414.74 43.96 0.00
1996 0.00 0.00 0.00 0.00 135.19 230.11 580.46 674.99 838.28 563.87 97.42 0.00
1997 0.00 0.00 0.00 48.38 113.06 365.36 411.71 850.82 867.41 541.94 234.75 49.08
1998 13.04 0.00 1.99 33.44 88.95 206.02 461.26 804.71 1,675.79 549.85 201.97 28.32
1999 11.38 3.36 5.30 9.83 112.20 442.71 562.78 584.48 1,269.23 758.52 151.13 10.61
2000 4.79 2.70 3.31 6.97 115.19 281.60 364.96 958.29 917.97 646.13 106.80 9.93
2001 5.71 2.51 2.92 54.08 174.87 240.63 618.46 869.56 570.01 0.00 0.00 0.00
2004 4.29 3.92 3.95 11.29 183.11 338.82 458.63 812.71 500.22 94.39 0.00 0.00
A-15
APPENDIX III RIVER CROSS SECTIONS AT MODELLED POINTS
A-16
578.00
580.00
582.00
584.00
586.00
588.00
590.00
592.00
594.00
0 200 400 600 800
Gro
un
d E
leva
tio
n A
bo
ve M
ean
Se
a Le
vel (
m)
Distance From Extreme End of left Flood Plain (m)
Kaduna River at Eastern Byepass Bridge Upstream Boundary
Left Abutmen Right Abutmen
Roundaboutmax depth below bridge bottom = 11.89m
578.00
580.00
582.00
584.00
586.00
588.00
590.00
0 50 100 150 200 250 300Gro
un
d E
leva
tio
n A
bo
ve M
ean
Se
a Le
vel (
m)
Distance From Extreme End of left Flood Plain (m)
Kaduna River Cross Section No 0038 Reach 2
Fence
580.00
581.00
582.00
583.00
584.00
585.00
586.00
587.00
588.00
0 100 200 300 400 500Gro
un
d E
leva
tio
n A
bo
ve M
ean
Se
a Le
vel (
m)
Distance From Extreme End of left Flood Plain (m)
Kaduna River Cross Section No 0033 Reach 2
Fence
580.00
582.00
584.00
586.00
588.00
590.00
592.00
0 200 400 600 800Gro
un
d E
leva
tio
n A
bo
ve M
ean
Se
a Le
vel (
m)
Distance From Extreme End of left Flood Plain (m)
Kaduna River Cross Section No 0036 Reach 2
Fence
A-17
580.50
581.00
581.50
582.00
582.50
583.00
583.50
584.00
584.50
585.00
585.50
0 100 200 300 400
Gro
un
d E
leva
tio
n A
bo
ve M
ean
Se
a Le
vel (
m)
Distance From Extreme End of left Flood Plain (m)
Kaduna River Cross Section No 0032 Reach 2
Fence
580.50
581.00
581.50
582.00
582.50
583.00
583.50
584.00
584.50
585.00
585.50
0 50 100 150 200 250 300Gro
un
d E
leva
tio
n A
bo
ve M
ean
Se
a Le
vel (
m)
Distance From Extreme End of left Flood Plain (m)
Kaduna River Cross Section No 0034 Reach 2
Fence
578.00
579.00
580.00
581.00
582.00
583.00
584.00
0 100 200 300
Gro
un
d E
leva
tio
n A
bo
ve M
ean
Se
a Le
vel (
m)
Distance From Extreme End of left Flood Plain (m)
Kaduna River Cross Section No 0031 Reach 2
Fence
579.00
580.00
581.00
582.00
583.00
584.00
585.00
586.00
587.00
588.00
0 100 200 300 400 500Gro
un
d E
leva
tio
n A
bo
ve M
ean
Se
a Le
vel (
m)
Distance From Extreme End of left Flood Plain (m)
Kaduna River Cross Section No 0035 Reach 2
Fence
A-18
577.00
578.00
579.00
580.00
581.00
582.00
583.00
584.00
585.00
586.00
0 200 400 600 800 1000
Gro
un
d E
leva
tio
n A
bo
ve M
ean
Se
a Le
vel (
m)
Distance From Extreme End of left Flood Plain (m)
Kaduna River Cross Section No 0030 Reach 2
Road
577.50
578.00
578.50
579.00
579.50
580.00
580.50
581.00
581.50
582.00
582.50
0 200 400 600 800Gro
un
d E
leva
tio
n A
bo
ve M
ean
Se
a Le
vel (
m)
Distance From Extreme End of left Flood Plain (m)
Kaduna River Cross Section No 0028 Reach 2
574.00
576.00
578.00
580.00
582.00
584.00
586.00
588.00
590.00
592.00
0 200 400 600 800 1000 1200
Gro
un
d E
leva
tio
n A
bo
ve M
ean
Se
a Le
vel (
m)
Distance From Extreme End of left Flood Plain (m)
Kaduna River Cross Section No 0037 Reach 2
Fence
574.00
576.00
578.00
580.00
582.00
584.00
586.00
588.00
590.00
592.00
0 200 400 600 800 1000Gro
un
d E
leva
tio
n A
bo
ve M
ean
Se
a Le
vel (
m)
Distance From Extreme End of left Flood Plain (m)
Kaduna River Cross Section No 0027 Reach 2
A-19
572.00
573.00
574.00
575.00
576.00
577.00
578.00
579.00
580.00
0 100 200 300 400 500 600 700Gro
un
d E
leva
tio
n A
bo
ve M
ean
Se
a Le
vel (
m)
Distance From Extreme End of left Flood Plain (m)
Kaduna River Cross Section No 0026 Reach 2
Fence
575.00
576.00
577.00
578.00
579.00
580.00
581.00
582.00
583.00
0 500 1000 1500 2000Gro
un
d E
leva
tio
n A
bo
ve M
ean
Se
a Le
vel (
m)
Distance From Extreme End of left Flood Plain (m)
Kaduna River Cross Section No 0020Reach 2
Fence Fence
573.00574.00575.00576.00577.00578.00579.00580.00581.00582.00
0 200 400 600 800 1000 1200
Gro
un
d E
leva
tio
n A
bo
ve M
ean
Se
a Le
vel (
m)
Distance From Extreme End of left Flood Plain (m)
Kaduna River Cross Section No 0025 Reach 2
Fence
571.00
572.00
573.00
574.00
575.00
576.00
577.00
578.00
579.00
0 200 400 600 800 1000 1200
Gro
un
d E
leva
tio
n A
bo
ve M
ean
Se
a Le
vel (
m)
Distance From Extreme End of left Flood Plain (m)
Kaduna River Cross Section No 0019 Reach 2
Fence
Fence
A-20
571.00
572.00
573.00
574.00
575.00
576.00
577.00
578.00
0 100 200 300 400 500 600Gro
un
d E
leva
tio
n A
bo
ve M
ean
Se
a Le
vel (
m)
Distance From Extreme End of left Flood Plain (m)
Kaduna River Cross Section No 0018 Reach 2
Fence
Fence
570.00
571.00
572.00
573.00
574.00
575.00
576.00
577.00
578.00
579.00
0 100 200 300 400 500
Gro
un
d E
leva
tio
n A
bo
ve M
ean
Se
a Le
vel (
m)
Distance From Extreme End of left Flood Plain (m)
Kaduna River Cross Section No 0024 Reach 2
Fence
Fence
570.00
571.00
572.00
573.00
574.00
575.00
576.00
577.00
0 100 200 300 400 500 600Gro
un
d E
leva
tio
n A
bo
ve M
ean
Se
a Le
vel (
m)
Distance From Extreme End of left Flood Plain (m)
Kaduna River Cross Section No 0017 Reach 2
Fence
Fence
572.50
573.00
573.50
574.00
574.50
575.00
575.50
576.00
0 50 100 150 200 250 300
Gro
un
d E
leva
tio
n A
bo
ve M
ean
Se
a Le
vel (
m)
Distance From Extreme End of left Flood Plain (m)
Kaduna River Cross Section No 0023 Reach 2Fence
Fence
A-21
570.00
570.50
571.00
571.50
572.00
572.50
573.00
573.50
574.00
574.50
575.00
575.50
0 50 100 150 200 250 300
Gro
un
d E
leva
tio
n A
bo
ve M
ean
Se
a Le
vel (
m)
Distance From Extreme End of left Flood Plain (m)
Kaduna River Cross Section No 0016 Reach 2
Fence
Fence
569.00
570.00
571.00
572.00
573.00
574.00
575.00
576.00
0 100 200 300 400
Gro
un
d E
leva
tio
n A
bo
ve M
ean
Se
a Le
vel (
m)
Distance From Extreme End of left Flood Plain (m)
Kaduna River Cross Section No 0015 Reach 2
Fence
Fence
569.00
570.00
571.00
572.00
573.00
574.00
575.00
576.00
0 100 200 300 400
Gro
un
d E
leva
tio
n A
bo
ve M
ean
Se
a Le
vel (
m)
Distance From Extreme End of left Flood Plain (m)
Kaduna River Cross Section No 0022Reach 2Fence
Fence
570.00
570.50
571.00
571.50
572.00
572.50
573.00
573.50
574.00
574.50
0 50 100 150 200 250 300G
rou
nd
Ele
vati
on
Ab
ove
Me
an S
ea
Leve
l (m
)Distance From Extreme End of left Flood Plain (m)
Kaduna River Cross Section No 0021Reach 2
Fence
Fence
A-22
568.00
569.00
570.00
571.00
572.00
573.00
574.00
575.00
0 50 100 150 200 250 300
Gro
un
d E
leva
tio
n A
bo
ve M
ean
Se
a Le
vel (
m)
Distance From Extreme End of left Flood Plain (m)
Kaduna River Cross Section No 0014 Reach 2
Fence
Fence
569.00
570.00
571.00
572.00
573.00
574.00
575.00
576.00
0 100 200 300 400 500 600Gro
un
d E
leva
tio
n A
bo
ve M
ean
Se
a Le
vel (
m)
Distance From Extreme End of left Flood Plain (m)
Kaduna River Cross Section No 0013 Reach 3
Fence
Fence
560.00
565.00
570.00
575.00
580.00
585.00
0.00 100.00 200.00 300.00 400.00 500.00 600.00 700.00
Gro
un
d E
leva
tio
n A
bo
ve
Me
an S
ea
Leve
l (m
)
Distance From Extreme End of left Flood Plain (m)
Kaduna River Cross Section No 0012 Reach 3
Gauge Location (LB)RB
569.00
570.00
571.00
572.00
573.00
574.00
575.00
576.00
577.00
578.00
0 100 200 300 400 500 600Gro
un
d E
leva
tio
n A
bo
ve M
ean
Se
a Le
vel (
m)
Distance From Extreme End of left Flood Plain (m)
Kaduna River Cross Section No 0011 Reach 3
A-23
570.00
571.00
572.00
573.00
574.00
575.00
576.00
0 100 200 300 400Gro
un
d E
leva
tio
n A
bo
ve M
ean
Se
a Le
vel
(m)
Distance From Extreme End of left Flood Plain (m)
Kaduna River Cross Section No 009 Reach 3
566
567
568
569
570
571
572
573
574
575
576
0 50 100 150 200 250 300Gro
un
d E
leva
tio
n A
bo
ve M
ean
Se
a Le
vel (
m)
Distance From Extreme End of left Flood Plain (m
Kaduna River Cross Section No 008 Reach 3
570.00
571.00
572.00
573.00
574.00
575.00
576.00
577.00
578.00
579.00
580.00
0 200 400 600 800
Gro
un
d E
leva
tio
n A
bo
ve M
ean
Se
a Le
vel
(m)
Distance From Extreme End of left Flood Plain (m)
Kaduna River Cross Section No 007 Reach 3
570.00
572.00
574.00
576.00
578.00
580.00
582.00
584.00
586.00
0 100 200 300 400 500 600G
rou
nd
Ele
vati
on
Ab
ove
Me
an S
ea
Leve
l (m
)
Distance From Extreme End of left Flood Plain (m)
Kaduna River Cross Section No 006 Reach 3
A-24
572
573
574
575
576
577
578
579
580
581
0 100 200 300 400 500 600
Gro
un
d E
leva
tio
n A
bo
ve M
ean
Se
a Le
vel
(m)
Distance From Extreme End of left Flood Plain (m)
Kaduna River Cross Section No 005 Reach 3
567
568
569
570
571
572
573
574
575
0 100 200 300 400
Gro
un
d E
leva
tio
n A
bo
ve M
ean
Se
a Le
vel (
m)
Distance From Extreme End of left Flood Plain (m)
Kaduna River Cross Section No 004 Reach 3
LB (89,569.67)RB (234,570.89)
566
567
568
569
570
571
572
573
574
575
576
0 100 200 300 400 500
Gro
un
d E
leva
tio
n A
bo
ve M
ean
Se
a Le
vel (
m)
Distance From Extreme End of left Flood Plain (m)
Kaduna River Cross Section No 002 Reach 3
LB (119, 571.2)
RB (276,560.06)
567
568
569
570
571
572
573
574
575
576
0 100 200 300 400 500
Gro
un
d E
leva
tio
n A
bo
ve M
ean
Se
a Le
vel (
m)
Distance From Extreme End of left Flood Plain (m)
Kaduna River Cross Section No 001 Reach 3 Downstream Boundary
A-25
Kaduna River By Malali New Bridge
581.50
582.00
582.50
583.00
583.50
584.00
584.50
585.00
585.50
586.00
586.50
0 100 200 300 400 500 600 700 800Gro
un
d E
leva
tio
n A
bo
ve M
ean
Sea
Lev
el
(m)
Distance From Extreme End of left Flood Plain (m)
Kaduna River Cross Section No 0039 Reach 1
Fence
Right Bank
Left Bank
571.00
572.00
573.00
574.00
575.00
576.00
577.00
578.00
0 100 200 300 400 500 600
Gro
un
d E
leva
tio
n A
bo
ve M
ean
Sea
Lev
el
(m)
Distance From Extreme End of left Flood Plain (m)
Kaduna River Cross Section No 0018 Reach 2
Fence Living Faith Church
Fence
Kaduna River by Kabala Doki / Shooting Range
574.00
576.00
578.00
580.00
582.00
584.00
586.00
588.00
590.00
592.00
0 200 400 600 800 1000 1200
Gro
un
d E
leva
tio
n A
bo
ve M
ean
Sea
Le
vel (
m)
Distance From Extreme End of left Flood Plain (m)
Fence & Transformer
Cross Section Downstream NB Plc / UNTL Intake
570.00
572.00
574.00
576.00
578.00
580.00
582.00
0.00 50.00 100.00 150.00 200.00 250.00 300.00 350.00 400.00 450.00 500.00
Gro
und
Elev
atio
n A
bove
Mea
n Se
a Le
vel
(m)
Distance from Extreme End Right Floodplain (m0
Left BankRight Bank
A-26
APPENDIX IV : RATING CURVE FOR SELECTED MODELLED CROSS SECTION
A-27
579.00
580.00
581.00
582.00
583.00
584.00
585.00
586.00
0 2000 4000 6000 8000 10000 12000 14000
Gau
ge H
eig
hts
(m
)
Discharge (Cubic metres per sec)
Discharge Rating Curve Kaduna River at Eastern Byepass Bridge Reach 2
580.00
581.00
582.00
583.00
584.00
585.00
586.00
587.00
588.00
0 5000 10000 15000 20000
Gau
ge H
eig
hts
(m
)
Discharge (Cubic metres per sec)
Discharge Rating Curve Kaduna River at Cross Section 33 Reach 2
577.00
578.00
579.00
580.00
581.00
582.00
583.00
584.00
585.00
0 5000 10000 15000
Gau
ge H
eig
hts
(m
)
Discharge (Cubic metres per sec)
Discharge Rating Curve Kaduna River at Cross Section 30 Reach 2
570.00
572.00
574.00
576.00
578.00
580.00
582.00
584.00
0 20000 40000 60000 80000 100000 120000
Gau
ge H
eig
ht
(m)
Discharge (Cubic metres per sec)
Discharge Rating Curve Kaduna River at Cross Section 12 Reach 3 Kaduna South Water Works Gauging Station
A-28
569.00
570.00
571.00
572.00
573.00
574.00
575.00
576.00
577.00
578.00
0 5000 10000 15000 20000 25000 30000 35000
Gau
ge h
eig
ht
(m)
Discharge (Cubic metres per sec)
Discharge Rating Curve Kaduna River at Cross Section 11 Reach 3
570.00
570.50
571.00
571.50
572.00
572.50
573.00
573.50
574.00
574.50
0 1,000 2,000 3,000 4,000 5,000 6,000 7,000
Gau
ge H
eig
hts
(m
)
Discharge (Cubic metres per sec)
Discharge Rating Curve Kaduna River at Cross Section 9 Reach 3
566.00
567.00
568.00
569.00
570.00
571.00
572.00
573.00
574.00
575.00
576.00
0 2000 4000 6000 8000 10000 12000
Gau
ge H
eig
ht
(m)
Discharge (Cubic metres per sec)
Discharge Rating Curve Kaduna River at Cross Section 8 Reach 3
570.00
572.00
574.00
576.00
578.00
580.00
582.00
584.00
586.00
0 20000 40000 60000 80000
Gau
ge H
eig
hts
(m
)
Discharge (Cubic metres per sec)
Discharge Rating Curve Kaduna River at Cross Section 6 Reach 3
A-29
567.00
568.00
569.00
570.00
571.00
572.00
573.00
574.00
575.00
0 2,000 4,000 6,000 8,000 10,000 12,000 14,000
Gau
ge H
eig
hts
(m
)
Discharge (Cubic metres per sec)
Discharge Rating Curve Kaduna River at Cross Section 4 Reach 3
566.00
567.00
568.00
569.00
570.00
571.00
572.00
573.00
574.00
575.00
0 1,000 2,000 3,000 4,000 5,000 6,000 7,000
Gau
ge H
eig
hts
(m
)
Discharge (Cubic metres per sec
Discharge Rating Curve Kaduna River at Cross Section 2 Reach 3
567.00
568.00
569.00
570.00
571.00
572.00
573.00
574.00
575.00
576.00
0 2,000 4,000 6,000 8,000 10,000 12,000 14,000
Gau
ge H
eig
hts
(m
)
Discharge (Cubic metres per sec
Discharge Rating Curve Kaduna River at Cross Section 1 Reach 3
A-30
APPENDIX V : Rating Tables and Channel Dimensions for Modeled Cross Sections.
A-31
Width h delta H delta A A P delta P delta A delta Q Q H ∆Q ∆H
cross-59 556.83 3.24 0.11 83.24 529.75 278.46 1.32 83.24 878.40 1578.60 589.37 603.12 0.14 slope 2917.1415
cross-59 559.13 3.38 0.14 12.42 591.35 279.63 0.38 12.42 84.13 2181.72 589.51 425.71 0.14 Intercept -0.0123009
cross-59 563.00 3.52 0.14 62.87 654.22 281.56 1.94 62.87 425.71 2607.43 589.65 568.53 0.17 cross-59 567.16 3.69 0.06 14.55 729.28 283.65 0.22 14.55 158.80 3175.96 589.82 309.35 0.06 cross-59 568.00 3.75 0.03 28.34 757.62 284.08 0.43 28.34 309.35 3485.31 589.88 136.28 0.03 cross-59 568.37 3.78 0.09 12.49 770.11 284.26 0.19 12.49 136.28 3621.59 589.91 464.48 0.09 cross-59 569.64 3.87 0.09 42.56 812.66 284.91 0.64 42.56 464.48 4086.07 590.00
cross-59 571.53 3.98 0.01 7.67 861.23 285.86 0.34 7.67 41.02 4573.47 590.11
Width h delta H delta A A P delta P delta A delta Q Q H ∆Q ∆H
cross-58 392.14 4.21 0.86 255.42 733.85 196.12 40.06 255.42 690.12 1578.60 589.12 cross-58 454.89 4.90 0.02 10.74 990.77 227.51 0.22 10.74 66.27 2181.72 589.81 603.12 0.69 slope 524.0624
cross-58 457.69 5.05 0.15 69.23 1060.00 228.92 1.41 69.23 425.71 2607.43 589.96 425.71 0.15 Intercept -0.1655825
cross-58 461.43 5.25 0.20 93.12 1153.12 230.80 1.88 93.12 568.53 3175.96 590.17 568.53 0.20 cross-58 463.46 5.37 0.11 50.99 1204.10 231.82 1.02 50.99 309.35 3485.31 590.28 309.35 0.11 cross-58 464.36 5.41 0.05 22.53 1226.64 232.27 0.45 22.53 136.28 3621.59 590.32 136.28 0.05 cross-58 467.41 5.58 0.17 77.12 1303.76 233.80 1.54 77.12 464.48 4086.07 590.49 464.48 0.17 cross-58 470.61 5.75 0.17 81.47 1385.23 235.42 1.61 81.47 487.40 4573.47 590.66
Width h delta H delta A A P delta P delta A delta Q Q H
cross-57 452.93 5.93 0.28 351.21 1355.05 252.50 37.51 351.21 1370.40 4573.47 589.01 cross-57 426.26 5.66 0.26 124.91 1230.14 239.16 13.34 124.91 487.40 4086.07 588.74 cross-57 400.84 5.39 0.08 119.04 1111.10 226.45 12.71 119.04 464.48 3621.59 588.48 cross-57 393.38 5.32 0.14 34.93 1076.17 222.72 3.73 34.93 136.28 3485.31 588.40 cross-57 373.63 5.12 0.52 21.81 992.48 212.84 3.27 21.81 67.88 3175.96 588.20 cross-57 318.91 4.59 0.02 182.62 809.86 185.48 27.37 182.62 568.53 2607.43 587.68 cross-57 286.77 4.19 0.22 22.96 686.01 169.40 3.36 22.96 72.55 2181.72 587.27 cross-57 239.66 3.51 0.46 35.13 509.80 145.84 3.18 35.13 153.21 1578.60 586.59
A-32
Width h delta H delta A A P delta P delta A delta Q Q H
cross-55 491.47 4.93 0.25 87.06 1139.30 245.81 6.49 87.06 487.40 4573.47 590.15 cross-55 478.50 4.71 0.22 54.46 1052.25 239.32 4.06 54.46 304.92 4086.07 589.93 cross-55 459.75 4.46 0.09 38.97 940.60 229.94 4.54 38.97 136.28 3621.59 589.68 cross-55 450.67 4.37 0.21 83.23 901.63 225.40 10.31 83.23 309.35 3485.31 589.58 cross-55 430.07 4.15 0.39 148.87 818.39 215.10 18.94 148.87 568.53 3175.96 589.37 cross-55 392.19 3.76 0.30 104.38 669.52 196.16 14.18 104.38 425.71 2607.43 588.97 cross-55 363.83 3.46 0.41 133.00 565.15 181.97 19.82 133.00 595.06 2181.72 588.68 cross-55 324.04 3.04 0.30 83.35 430.87 162.07 5.07 83.35 534.99 1578.60 588.26
Width h delta H delta A A P delta P delta A delta Q Q H
cross-54 628.34 3.41 0.06 35.30 1129.91 314.23 1.04 35.30 186.10 4573.47 587.41 cross-54 625.13 3.29 0.06 56.53 1057.94 312.62 0.88 56.53 464.48 4086.07 587.29 cross-54 623.38 3.20 0.09 16.59 1001.41 311.74 0.26 16.59 136.28 3621.59 587.20 cross-54 622.87 3.17 0.03 37.65 984.82 311.49 0.58 37.65 309.35 3485.31 587.17 cross-54 621.71 3.11 0.06 38.45 947.17 310.90 0.60 38.45 315.93 3175.96 587.11 cross-54 618.53 2.97 0.08 69.70 867.35 309.30 1.69 69.70 425.71 2607.43 586.96 cross-54 615.16 2.83 0.14 46.01 797.65 307.62 1.11 46.01 280.97 2181.72 586.83 cross-54 608.85 2.61 0.18 86.13 687.52 304.45 2.78 86.13 436.97 1578.60 586.61
Width h delta H delta A A P delta P delta A delta Q Q H
cross-53 826.74 6.02 0.38 150.33 1662.80 413.43 23.65 150.33 487.40 4573.47 589.40 cross-53 779.44 5.75 0.27 143.26 1512.47 389.78 22.54 143.26 464.48 4086.07 589.13 cross-53 734.35 5.49 0.26 42.03 1369.22 367.24 6.61 42.03 136.28 3621.59 588.87 cross-53 721.13 5.41 0.08 95.41 1327.19 360.62 15.01 95.41 309.35 3485.31 588.80 cross-53 691.10 5.24 0.17 175.35 1231.77 345.61 27.59 175.35 568.53 3175.96 588.63 cross-53 635.92 4.92 0.32 24.79 1056.43 318.02 3.90 24.79 80.38 2607.43 588.31 cross-53 506.91 4.43 0.47 164.95 853.89 253.51 46.32 164.95 365.39 2181.72 587.82 cross-53 371.82 3.64 1.20 323.47 569.86 185.96 79.17 323.47 886.62 1578.60 587.03
A-33
Width h delta H delta A A P delta P delta A delta Q Q H
cross-52 721.14 7.17 0.36 225.02 1782.84 360.65 31.51 225.02 487.40 4573.47 589.94 cross-52 658.13 6.81 0.34 202.32 1557.82 329.15 30.02 202.32 464.48 4086.07 589.59 cross-52 598.09 6.47 0.10 54.31 1355.50 299.12 8.81 54.31 136.28 3621.59 589.25 cross-52 580.47 6.37 0.23 119.38 1301.19 290.31 20.00 119.38 309.35 3485.31 589.15 cross-52 540.48 6.14 0.05 23.41 1181.80 270.32 4.14 23.41 64.03 3175.96 588.92 cross-52 474.12 5.63 0.15 55.36 990.33 237.13 7.73 55.36 162.84 2607.43 588.41 cross-52 425.38 5.20 0.29 213.96 841.71 212.76 38.18 213.96 603.12 2181.72 587.97 cross-52 349.02 4.53 0.67 182.73 627.75 174.58 32.61 182.73 515.10 1578.60 587.31
Width h delta H delta A A P delta P delta A delta Q Q H
cross-51 440.11 4.33 0.24 830.62 1123.01 262.33 112.99 830.62 3572.12 4573.47 588.02 cross-51 409.28 4.09 0.23 113.33 1009.67 246.91 15.42 113.33 487.40 4086.07 587.78 cross-51 379.90 3.86 0.07 108.00 901.67 232.22 14.69 108.00 464.48 3621.59 587.55 cross-51 371.28 3.79 0.15 31.69 869.98 227.91 4.31 31.69 136.28 3485.31 587.49 cross-51 351.71 3.64 0.28 71.93 798.05 218.13 9.78 71.93 309.35 3175.96 587.33 cross-51 315.75 3.36 0.21 132.20 665.85 200.14 17.98 132.20 568.53 2607.43 587.05 cross-51 288.82 3.15 0.10 98.99 566.86 186.68 13.47 98.99 425.71 2181.72 586.84 cross-51 252.80 2.70 0.26 88.64 429.81 168.66 11.44 88.64 394.94 1578.60 586.39
Width h delta H delta A A P delta P delta A delta Q Q H
cross-50 324.19 6.02 0.08 45.99 988.98 162.25 1.03 45.99 487.40 4573.47 586.66 cross-50 322.17 5.87 0.15 24.35 942.99 161.22 0.54 24.35 258.09 4086.07 586.51 cross-50 318.82 5.69 0.10 18.91 889.99 159.54 0.75 18.91 136.28 3621.59 586.33 cross-50 317.33 5.62 0.07 38.38 871.08 158.79 1.53 38.38 276.59 3485.31 586.27 cross-50 314.04 5.47 0.01 68.18 828.77 157.14 2.18 68.18 568.53 3175.96 586.12 cross-50 309.71 5.22 0.26 9.23 760.59 154.96 0.29 9.23 77.00 2607.43 585.86 cross-50 302.79 4.95 0.23 20.10 692.23 151.49 1.08 20.10 118.54 2181.72 585.60 cross-50 276.23 4.36 0.51 169.24 548.65 138.20 16.74 169.24 664.14 1578.60 585.01
A-34
Width h delta H delta A A P delta P delta A delta Q Q H cross-49 429.60 6.77 0.24 159.34 1279.66 214.92 24.98 159.34 487.40 4573.47 587.41 cross-49 379.64 6.32 0.44 81.49 1120.32 189.94 12.78 81.49 249.26 4086.07 586.97 cross-49 344.64 5.93 0.17 31.75 988.69 172.43 3.00 31.75 136.28 3621.59 586.57 cross-49 338.65 5.82 0.11 72.08 956.94 169.44 6.80 72.08 309.35 3485.31 586.47 cross-49 325.06 5.58 0.24 132.46 884.86 162.64 12.50 132.46 568.53 3175.96 586.23 cross-49 300.09 5.14 0.44 78.75 752.40 150.14 7.43 78.75 337.99 2607.43 585.78 cross-49 282.30 4.81 0.23 61.49 656.97 141.24 4.80 61.49 285.90 2181.72 585.45 cross-49 262.70 4.31 0.04 9.11 530.53 131.43 0.72 9.11 45.58 1578.60 584.95
Width h delta H delta A A P delta P delta A delta Q Q H
cross-48 340.72 4.16 0.11 36.51 679.86 170.43 1.55 36.51 487.40 4573.47 586.93 cross-48 337.63 4.02 0.13 17.16 643.35 168.88 0.73 17.16 229.12 4086.07 586.80 cross-48 334.46 3.89 0.07 35.32 607.53 167.28 1.63 35.32 445.63 3621.59 586.67 cross-48 333.46 3.85 0.04 24.52 596.73 166.78 1.13 24.52 309.35 3485.31 586.63 cross-48 331.20 3.75 0.10 24.60 572.21 165.65 1.14 24.60 568.53 3175.96 586.53 cross-48 319.80 3.50 0.16 153.09 509.20 159.94 18.21 153.09 1028.83 2607.43 586.28 cross-48 304.74 3.24 0.26 89.75 445.85 152.41 10.68 89.75 603.12 2181.72 586.02 cross-48 283.40 2.87 0.37 104.51 356.11 141.73 12.43 104.51 1237.78 1,578.60 585.65
Width h delta H delta A A P delta P delta A delta Q Q H
cross-47 701.19 5.58 0.09 47.91 1256.16 350.70 2.20 47.91 353.44 4573.47 588.36 cross-47 584.27 5.29 0.41 191.65 1088.02 292.23 116.48 191.65 277.32 4086.07 588.07 cross-47 350.40 4.82 0.06 43.12 878.26 175.30 1.09 43.12 445.63 3621.59 587.60 cross-47 349.74 4.78 0.04 29.93 865.07 174.97 0.76 29.93 309.35 3485.31 587.55 cross-47 348.24 4.68 0.10 34.62 835.14 174.21 0.87 34.62 568.53 3175.96 587.46 cross-47 342.40 4.45 0.19 60.80 770.20 171.28 3.23 60.80 330.30 2607.43 587.23 cross-47 334.26 4.21 0.25 73.34 695.80 167.20 3.93 73.34 439.33 2181.72 586.99 cross-47 311.15 3.77 0.42 110.05 567.70 155.64 16.78 110.05 359.76 1578.60 586.55
A-35
Width h delta H delta A A P delta P delta A delta Q Q H
cross-45 528.58 4.65 0.23 28.11 923.86 264.35 0.71 28.11 487.40 4573.47 586.51 cross-45 527.17 4.59 0.06 6.98 895.75 263.64 0.18 6.98 120.96 4086.07 586.45 cross-45 498.20 4.40 0.18 30.08 812.97 249.16 5.68 30.08 136.28 3621.59 586.26 cross-45 486.85 4.33 0.07 25.08 782.89 243.48 4.73 25.08 113.66 3485.31 586.19 cross-45 481.31 4.19 0.21 87.42 735.03 235.94 8.14 87.42 568.53 3175.96 586.06 cross-45 455.51 3.98 0.02 5.93 647.61 227.80 0.61 5.93 42.44 2607.43 585.84 cross-45 410.71 3.68 0.02 7.19 545.38 205.40 1.75 7.19 30.75 2181.72 585.54 cross-45 282.08 3.01 0.88 153.45 310.22 141.09 28.68 153.45 1077.40 1578.60 584.87
Width h delta H delta A A P delta P delta A delta Q Q H
cross-44 428.31 6.71 0.34 137.56 1431.99 211.52 8.10 137.56 487.40 4573.47 588.88 cross-44 406.59 6.37 0.27 104.84 1294.43 203.42 6.46 104.84 388.54 4086.07 588.54 cross-44 391.83 6.04 0.09 35.35 1189.26 196.03 1.67 35.35 136.28 3621.59 588.21 cross-44 388.50 5.95 0.21 79.26 1153.91 194.36 3.79 79.26 309.35 3485.31 588.12 cross-44 380.94 5.73 0.39 141.88 1074.65 190.57 6.96 141.88 568.53 3175.96 587.90 cross-44 367.03 5.34 0.30 100.83 932.76 183.61 5.21 100.83 425.71 2607.43 587.51 cross-44 356.62 5.05 0.17 54.73 831.93 178.40 2.98 54.73 242.93 2181.72 587.21 cross-44 339.07 4.57 0.61 184.72 682.87 169.61 11.39 184.72 863.18 1578.60 586.74
Width h delta H delta A A P delta P delta A delta Q Q H
cross-43 415.27 3.91 0.05 55.63 880.24 207.70 2.15 55.63 487.40 4573.47 586.69 cross-43 410.98 3.76 0.15 39.40 824.62 205.55 1.52 39.40 345.19 4086.07 586.54 cross-43 405.72 3.61 0.05 68.72 766.82 202.92 4.17 68.72 445.63 3621.59 586.38 cross-43 403.17 3.55 0.06 47.71 745.81 201.64 2.89 47.71 309.35 3485.31 586.32 cross-43 397.38 3.41 0.13 20.84 698.10 198.75 1.26 20.84 1468.32 3175.96 586.19 cross-43 393.51 3.25 0.10 32.18 644.50 196.80 0.67 32.18 425.71 2,607.43 586.03 cross-43 392.18 3.16 0.10 35.84 612.32 196.13 0.75 35.84 474.08 2,181.72 585.93 cross-43 378.19 2.93 0.49 153.80 534.98 189.13 25.54 153.80 526.71 1578.60 585.71
A-36
Width h delta H delta A A P delta P delta A delta Q Q H
cross-42 548.49 4.47 0.10 65.64 1326.90 274.32 1.47 65.64 487.40 4573.47 586.64 cross-42 545.57 4.34 0.13 38.91 1261.26 272.85 0.87 38.91 288.87 4086.07 586.51 cross-42 535.42 4.16 0.11 42.10 1168.10 267.77 3.27 42.10 136.28 3621.59 586.33 cross-42 528.88 4.08 0.08 58.20 1125.99 264.50 4.52 58.20 188.38 3485.31 586.25 cross-42 513.69 3.88 0.23 111.74 1030.87 256.90 8.88 111.74 348.72 3175.96 586.05 cross-42 485.75 3.51 0.16 76.38 854.77 242.93 5.61 76.38 242.20 2607.43 585.68 cross-42 473.83 3.30 0.05 68.28 757.61 236.96 1.18 68.28 603.12 2181.72 585.47 cross-42 471.50 3.13 0.17 34.55 689.33 235.79 0.60 34.55 305.20 1578.60 585.30
Width h delta H delta A A P delta P delta A delta Q Q H
cross-40 435.09 3.03 0.01 46.38 676.02 217.58 2.68 46.38 487.40 4573.47 584.59 cross-40 429.75 2.92 0.12 44.19 629.65 214.91 2.55 44.19 464.48 4086.07 584.48 cross-40 424.65 2.81 0.11 12.97 585.45 212.36 0.75 12.97 136.28 3621.59 584.37 cross-40 423.16 2.78 0.03 13.63 572.49 211.61 0.79 13.63 143.27 3485.31 584.34 cross-40 418.77 2.69 0.05 64.34 540.06 209.42 4.81 64.34 568.53 3175.96 584.25 cross-40 409.15 2.53 0.17 34.42 475.72 204.60 2.58 34.42 304.12 2607.43 584.09 cross-40 401.99 2.40 0.04 67.72 427.65 201.02 5.01 67.72 603.12 2181.72 583.95 cross-40 391.98 2.18 0.21 16.03 359.93 196.01 1.19 16.03 142.77 1578.60 583.74
W h delta H delta A A P delta P delta A delta Q Q H
cross-39 610.04 3.22 1.35 46.48 605.15 206.44 1.75 46.48 368.01 4573.47 585.0846 cross-39 522.12 2.97 0.08 60.84 543.04 204.07 2.42 60.84 464.48 4086.07 584.8347 cross-39 502.91 2.67 0.30 17.85 482.19 201.65 0.71 17.85 136.28 3621.59 584.5372 cross-39 497.27 2.59 0.09 40.52 464.34 200.94 1.61 40.52 309.35 3485.31 584.4499 cross-39 484.48 2.39 0.20 74.47 423.82 199.33 2.96 74.47 568.53 3175.96 584.2517
cross-39 460.96 2.02 0.36 39.98 349.34 196.37 1.59 39.98 305.23 2607.43 583.8875
cross-39 408.01 1.78 0.05 48.67 299.64 194.59 0.94 48.67 603.12 2181.72 583.6421 cross-39 402.60 1.53 0.25 119.60 250.97 193.66 2.30 119.60 1482.12 1578.60 583.392
A-37
W h delta H delta A A P delta P delta A delta Q Q H ∆H
E_Bye 195.75 2.12 0.32 57.15 270.36 97.90 6.00 57.15 501.14 1578.60 581.85
E_Bye 209.86 2.46 0.20 5.58 338.46 104.97 0.49 5.58 603.12 2181.72 582.19 0.34 slope 1674.4
35
E_Bye 217.50 2.66 0.26 43.27 381.73 108.79 3.83 43.27 425.71 2607.43 582.39 0.20 Interc
ept
-0.0328
89 E_Bye 227.70 2.92 0.13 101.06 439.52 113.90 8.93 101.06 994.24 3175.96 582.65 0.26
E_Bye 233.20 3.06 0.05 3.38 470.83 116.65 0.28 3.38 34.49 3485.31 582.79 0.14 E_Bye 235.43 3.12 0.19 13.35 484.19 117.77 1.12 13.35 136.28 3621.59 582.85 0.05 E_Bye 243.04 3.30 0.19 45.51 529.70 121.58 3.81 45.51 464.48 4086.07 583.03 0.19 E_Bye 251.02 3.50 0.16 47.76 577.45 125.58 4.00 47.76 487.40 4573.47 583.23
Width h delta H delta A A P delta P delta A delta Q Q H ∆Q ∆H
cross-38 173.48 4.35 0.22 9.99 460.59 101.00 0.08 9.99 487.40 4573.47 583.47 cross-38 173.38 4.30 0.06 4.98 450.61 100.92 0.04 4.98 242.92 4086.07 583.42 cross-38 172.60 4.20 0.07 23.47 433.96 100.51 0.75 23.47 445.63 3621.59 583.32 cross-38 172.15 4.16 0.04 16.30 426.78 100.28 0.52 16.30 309.35 3485.31 583.28 cross-38 171.14 4.06 0.09 17.19 410.48 99.77 0.55 17.19 568.53 3175.96 583.18 cross-38 167.40 3.84 0.12 30.26 372.73 97.88 1.97 30.26 356.38 2607.43 582.96 cross-38 158.88 3.58 0.08 35.02 330.40 93.61 6.68 35.02 201.18 2181.72 582.70 cross-38 138.22 3.06 0.29 1.49 253.66 83.27 0.13 1.49 14.33 1578.60 582.18
Width h delta H delta A A P delta P delta A delta Q Q H ∆Q ∆H
cross-33 315.55 2.71 0.04 77.77 592.21 204.02 3.20 77.77 951.88 4573.47 583.65 cross-33 312.28 2.58 0.13 37.95 552.39 202.38 1.56 37.95 464.48 4086.07 583.53 cross-33 309.16 2.46 0.12 5.74 514.44 200.82 0.24 5.74 136.28 3621.59 583.41 cross-33 308.05 2.42 0.02 83.15 502.45 200.26 4.27 83.15 877.88 3485.31 583.37
A-38
cross-33 305.04 2.32 0.10 53.85 473.15 198.75 2.77 53.85 568.53 3175.96 583.27 cross-33 299.52 2.14 0.18 3.24 419.30 195.99 0.17 3.24 425.71 2607.43 583.09 cross-33 297.26 2.04 0.10 43.58 387.77 194.85 1.49 43.58 603.12 2181.72 582.99 cross-33 294.29 1.89 0.15 18.39 344.20 193.36 0.63 18.39 254.52 1578.60 582.84
Width h delta H delta A A P delta P delta A delta Q Q H ∆Q ∆H
cross-31 216.15 3.17 0.18 26.36 461.98 150.70 3.22 26.36 234.64 4573.47 581.98 cross-31 209.05 2.99 0.05 20.60 424.41 147.14 0.62 20.60 464.48 4086.07 581.81 cross-31 207.82 2.89 0.10 6.04 403.81 146.52 0.18 6.04 136.28 3621.59 581.71 cross-31 207.45 2.87 0.03 13.72 397.77 146.33 0.42 13.72 309.35 3485.31 581.68 cross-31 206.63 2.80 0.07 11.77 384.05 145.92 0.36 11.77 265.43 3175.96 581.62 cross-31 203.35 2.64 0.11 29.99 350.92 144.27 1.82 29.99 425.71 2607.43 581.45 cross-31 199.72 2.49 0.15 10.28 320.93 142.45 0.62 10.28 145.98 2181.72 581.30 cross-31 185.38 2.16 0.27 6.00 258.37 135.27 0.75 6.00 52.46 1578.60 580.98
Width h delta H delta A A P delta P delta A delta Q Q H ∆Q ∆H
cross-30 402.86 3.70 3.01 88.53 924.01 241.98 13.08 88.53 487.40 4573.47 581.30 cross-30 376.70 3.55 0.15 84.37 835.48 228.90 12.47 84.37 464.48 4086.07 581.14 cross-30 351.77 3.40 0.15 24.75 751.11 216.43 3.66 24.75 136.28 3621.59 581.00 cross-30 344.45 3.36 0.04 56.19 726.36 212.77 8.30 56.19 309.35 3485.31 580.95 cross-30 327.85 3.26 0.10 103.27 670.16 204.47 15.26 103.27 568.53 3175.96 580.86 cross-30 297.33 3.08 0.18 77.33 566.89 189.21 11.43 77.33 425.71 2607.43 580.68 cross-30 274.48 2.95 0.13 109.55 489.57 177.79 16.19 109.55 603.12 2181.72 580.54 cross-30 242.11 2.76 0.19 8.75 380.01 161.60 1.29 8.75 48.16 1578.60 580.35
Width h delta H delta A A P delta P delta A delta Q Q H ∆Q ∆H
cross-29 470.01 7.57 0.35 150.19 1714.23 275.14 8.94 150.19 487.40 4573.47 584.86 cross-29 452.14 7.23 0.34 143.13 1564.03 266.19 8.52 143.13 464.48 4086.07 584.52 cross-29 435.10 6.91 0.32 42.00 1420.90 257.67 2.50 42.00 136.28 3621.59 584.20
A-39
cross-29 430.10 6.81 0.10 95.33 1378.91 255.17 5.68 95.33 309.35 3485.31 584.10 cross-29 418.76 6.60 0.22 175.20 1283.58 249.49 10.43 175.20 568.53 3175.96 583.89 cross-29 397.91 6.20 0.40 44.93 1108.38 239.06 2.68 44.93 145.80 2607.43 583.49 cross-29 312.80 5.56 0.23 22.61 878.66 196.50 2.68 22.61 46.38 2181.72 582.85 cross-29 223.10 4.27 0.30 0.62 521.59 126.46 0.08 0.62 1.22 1578.60 581.56
Width h delta H delta A A P delta P delta A delta Q Q H ∆Q ∆H
cross-28 645.39 3.15 0.10 132.45 1055.95 390.64 8.90 132.45 663.80 4573.47 581.05 cross-28 528.53 2.84 0.10 115.40 874.92 332.20 54.03 115.40 158.50 4086.07 580.74 cross-28 474.38 2.64 0.04 48.56 771.96 305.13 1.61 48.56 389.77 3621.59 580.54 cross-28 473.26 2.60 0.08 16.98 754.98 304.57 0.56 16.98 136.28 3485.31 580.51 cross-28 470.71 2.52 0.08 38.54 716.44 303.29 1.28 38.54 309.35 3175.96 580.42 cross-28 465.28 2.36 0.13 34.90 641.51 300.57 1.40 34.90 247.18 2607.43 580.26 cross-28 460.48 2.23 0.10 60.11 581.40 298.16 2.40 60.11 425.71 2181.72 580.13 cross-28 455.18 2.07 0.24 30.19 505.26 295.51 0.82 30.19 277.73 1578.60 579.97
Width h delta H delta A A P delta P delta A delta Q Q H ∆Q ∆H
cross-37 288.65 2.36 0.07 45.21 516.38 238.13 3.72 45.21 487.40 4573.47 578.13 cross-37 281.22 2.21 0.16 20.65 471.17 234.41 1.70 20.65 222.58 4086.07 577.97 cross-37 272.13 2.03 0.10 15.02 423.86 229.86 1.60 15.02 136.28 3621.59 577.80 cross-37 268.93 1.98 0.06 34.09 408.84 228.26 3.64 34.09 309.35 3485.31 577.75 cross-37 261.67 1.85 0.13 6.24 374.74 224.62 0.67 6.24 56.60 3175.96 577.62 cross-37 249.93 1.62 0.21 23.81 315.26 218.75 2.33 23.81 228.91 2607.43 577.39 cross-37 239.92 1.43 0.10 49.19 268.44 213.74 5.73 49.19 420.67 2181.72 577.19 cross-37 224.36 1.13 0.09 47.74 199.48 205.96 4.96 47.74 440.67 1578.60 576.90
Width h delta H delta A A P delta P delta A delta Q Q H ∆Q ∆H
A-40
cross-26 281.67 4.85 0.22 6.79 934.58 178.52 0.22 6.79 54.93 4573.47 577.57 cross-26 277.75 4.64 0.06 60.23 874.34 176.54 1.97 60.23 487.40 4086.07 577.36 cross-26 271.71 4.39 0.08 50.73 805.49 173.51 2.44 50.73 317.85 3621.59 577.11 cross-26 269.62 4.31 0.04 21.75 783.74 172.47 1.05 21.75 136.28 3485.31 577.03 cross-26 266.53 4.15 0.19 30.76 742.38 170.91 1.04 30.76 242.93 3175.96 576.87 cross-26 253.59 3.78 0.13 45.85 646.25 164.43 4.78 45.85 171.47 2607.43 576.50 cross-26 245.19 3.52 0.17 33.18 581.19 160.22 0.89 33.18 306.46 2181.72 576.24 cross-26 229.38 3.09 0.04 61.34 478.36 152.29 6.81 61.34 219.87 1578.60 575.81
Width h delta H delta A A P delta P delta A delta Q Q H ∆Q ∆H
cross-20 1067.39 2.14 0.30 6.95 622.89 554.24 0.18 6.95 243.51 4573.47 577.91 cross-20 768.76 2.00 0.14 123.11 514.38 404.93 180.77 123.11 295.64 4086.07 577.76 cross-20 404.61 1.80 0.03 9.87 379.04 222.85 1.05 9.87 136.28 3621.59 577.56 cross-20 402.50 1.77 0.03 22.40 369.17 221.80 2.39 22.40 309.35 3485.31 577.54 cross-20 397.73 1.72 0.06 41.17 346.77 219.41 4.38 41.17 568.53 3175.96 577.48 cross-20 388.97 1.61 0.10 30.83 305.60 215.03 3.28 30.83 425.71 2607.43 577.38 cross-20 382.40 1.53 0.08 3.71 274.77 211.74 0.40 3.71 51.25 2181.72 577.30 cross-20 373.16 1.42 0.11 72.81 231.19 207.12 7.72 72.81 1007.98 1578.60 577.18
Width h delta H delta A A P delta P delta A delta Q Q H ∆Q ∆H
cross-25 552.47 2.99 0.36 50.87 746.51 304.78 8.72 50.87 951.88 4573.47 576.93 cross-25 528.33 2.93 0.06 48.47 695.65 296.06 8.31 48.47 600.76 4086.07 576.87 cross-25 505.33 2.88 0.05 14.22 647.17 287.75 2.44 14.22 445.63 3621.59 576.82 cross-25 498.58 2.86 0.02 32.28 632.95 285.31 5.53 32.28 877.88 3485.31 576.80 cross-25 483.26 2.83 0.04 59.33 600.67 279.78 10.17 59.33 715.54 3175.96 576.77 cross-25 455.10 2.76 0.07 15.34 541.33 269.61 2.63 15.34 425.71 2607.43 576.70 cross-25 436.16 2.65 0.09 82.15 488.03 261.14 12.63 82.15 603.12 2181.72 576.59 cross-25 410.92 2.46 0.19 10.27 405.87 248.51 1.58 10.27 75.42 1578.60 576.40
Width h delta H delta A A P delta P delta A delta Q Q H ∆Q ∆H
cross-19 743.44 2.39 0.04 16.24 581.30 399.58 3.36 16.24 487.40 4573.47 574.50 cross-19 705.11 2.27 0.13 15.48 565.05 396.22 3.20 15.48 464.48 4086.07 574.38
A-41
cross-19 668.58 2.14 0.12 4.54 549.58 393.01 0.94 4.54 136.28 3621.59 574.25 cross-19 657.87 2.11 0.04 10.31 545.03 392.07 2.13 10.31 309.35 3485.31 574.22 cross-19 633.54 2.03 0.08 18.95 534.73 389.94 3.92 18.95 568.53 3175.96 574.14 cross-19 588.83 1.88 0.15 6.05 515.78 386.01 1.25 6.05 181.48 2607.43 573.99 cross-19 507.65 1.71 0.12 89.25 449.05 351.31 49.20 89.25 359.18 2181.72 573.82 cross-19 390.70 1.42 0.11 75.70 318.81 292.83 17.13 75.70 450.47 1578.60 573.53
Width h delta H delta A A P delta P delta A delta Q Q H ∆Q ∆H
cross-18 470.30 4.27 0.00 142.41 1044.22 450.60 3.10 142.41 1859.30 4573.47 575.77 cross-18 367.75 3.83 0.17 48.33 864.48 399.32 6.04 48.33 196.89 4086.07 575.33 cross-18 349.48 3.58 0.05 26.48 774.80 390.18 1.25 26.48 207.01 3621.59 575.08 cross-18 347.84 3.53 0.11 17.44 757.36 389.36 0.82 17.44 136.28 3485.31 575.03 cross-18 344.13 3.42 0.06 39.58 717.78 387.50 1.86 39.58 309.35 3175.96 574.92 cross-18 317.83 3.06 0.01 96.86 598.66 374.35 12.11 96.86 394.48 2607.43 574.56 cross-18 271.83 2.64 0.21 26.76 478.06 351.34 1.77 26.76 166.56 2181.72 574.14 cross-18 262.35 2.33 0.20 28.50 394.05 346.59 1.08 28.50 257.67 1578.60 573.83
Width h delta H delta A A P delta P delta A delta Q Q H ∆Q ∆H
cross-24 257.67 2.78 0.04 69.88 494.19 178.07 3.56 69.88 1216.61 4573.47 573.67 cross-24 252.44 2.65 0.13 22.33 462.27 176.06 1.52 22.33 320.48 4086.07 573.54 cross-24 248.76 2.53 0.04 32.36 429.92 173.86 2.20 32.36 464.48 3621.59 573.42 cross-24 247.69 2.49 0.05 9.49 420.42 173.21 0.65 9.49 136.28 3485.31 573.38 cross-24 243.89 2.39 0.22 11.81 396.14 171.17 1.19 11.81 130.29 3175.96 573.28 cross-24 233.49 2.17 0.04 51.52 344.62 165.96 5.21 51.52 568.53 2607.43 573.06 cross-24 221.95 1.97 0.15 35.42 299.71 160.19 4.81 35.42 320.89 2181.72 572.86 cross-24 206.31 1.68 0.16 30.31 237.04 152.37 3.43 30.31 309.92 1578.60 572.57
Width h delta H delta A A P delta P delta A delta Q Q H ∆Q ∆H
cross-16 223.50 4.03 0.06 56.25 456.87 123.69 12.24 56.25 419.95 4086.07 574.61 cross-16 205.19 3.78 0.07 38.19 404.05 114.53 5.98 38.19 355.21 3621.59 574.36
A-42
cross-16 200.60 3.71 0.05 14.65 389.40 112.23 2.29 14.65 136.28 3485.31 574.29 cross-16 191.20 3.54 0.19 21.59 357.48 107.53 3.09 21.59 213.22 3175.96 574.13 cross-16 176.75 3.25 0.20 18.35 303.07 100.30 2.07 18.35 212.49 2607.43 573.83 cross-16 168.67 3.04 0.25 1.42 266.70 96.25 0.11 1.42 21.07 2181.72 573.63 cross-16 162.42 2.79 0.05 40.51 226.19 93.12 3.13 40.51 603.12 1578.60 573.38
Width h delta H delta A A P delta P delta A delta Q Q H ∆Q ∆H
cross-15 257.53 3.99 0.27 8.02 847.12 186.10 0.88 8.02 37.20 4573.47 573.97 cross-15 261.20 3.82 0.14 38.28 802.00 184.26 1.00 38.28 464.48 4086.07 573.80 cross-15 263.17 3.67 0.15 4.28 763.72 183.26 0.11 4.28 51.90 3621.59 573.65 cross-15 264.86 3.61 0.05 44.70 747.25 182.41 2.70 44.70 309.35 3485.31 573.59 cross-15 270.25 3.45 0.17 24.89 702.55 179.71 1.50 24.89 172.22 3175.96 573.42 cross-15 288.09 3.08 0.28 8.04 599.93 170.79 0.77 8.04 41.01 2607.43 573.05 cross-15 297.58 2.85 0.20 30.58 532.34 166.03 2.05 30.58 197.56 2181.72 572.82 cross-15 294.46 2.54 0.20 31.20 442.70 160.38 1.91 31.20 214.25 1578.60 572.52
Width h delta H delta A A P delta P delta A delta Q Q H ∆Q ∆H
cross-14 157.63 3.05 0.00 49.29 273.82 92.65 3.64 49.29 1494.13 4573.47 571.80 cross-14 146.12 2.75 0.01 22.04 228.60 86.89 2.80 22.04 464.48 3621.59 571.51 cross-14 151.72 2.89 0.15 23.32 250.64 89.69 2.97 23.32 491.55 4086.07 571.65 cross-14 138.27 2.47 0.03 22.51 188.30 82.95 2.18 22.51 568.53 2607.43 571.22 cross-14 142.63 2.62 0.16 12.25 210.81 85.14 1.19 12.25 309.35 3175.96 571.38 cross-14 144.99 2.71 0.09 4.64 223.06 86.33 0.45 4.64 117.27 3485.31 571.47
cross-14 130.96 2.29 0.16 19.12 165.38 79.30 3.29 19.12 329.72 2181.72 571.05 cross-14 119.63 2.02 0.19 13.43 131.24 73.63 2.11 13.43 245.92 1578.60 570.78
Width h delta H delta A A P delta P delta A delta Q Q H ∆Q ∆H
cross-13 261.98 3.48 0.13 46.24 585.58 166.86 1.95 46.24 669.45 4573.47 573.46
A-43
cross-13 259.15 3.35 0.00 33.66 551.91 165.43 1.42 33.66 487.40 4086.07 573.33 cross-13 257.41 3.25 0.03 26.82 524.98 164.56 0.87 26.82 462.86 3621.59 573.22 cross-13 256.90 3.22 0.07 7.90 517.09 164.30 0.26 7.90 136.28 3485.31 573.19 cross-13 255.75 3.15 0.10 17.92 499.17 163.72 0.58 17.92 309.35 3175.96 573.12 cross-13 249.94 2.98 0.23 17.49 456.09 160.81 2.08 17.49 127.01 2607.43 572.95 cross-13 235.91 2.74 0.30 1.52 397.33 153.79 0.21 1.52 10.10 2181.72 572.71 cross-13 214.44 2.36 0.22 17.43 312.25 143.05 1.55 17.43 153.36 1578.60 572.33
Width h delta H delta A A P delta P delta A delta Q Q H ∆Q ∆H
cross-12 493.73 4.30 0.03 132.57 905.25 254.59 1.55 132.57 3777.99 4573.47 575.50 cross-12 493.34 4.27 0.00 17.10 888.15 254.39 0.20 17.10 487.40 4086.07 575.46 cross-12 458.97 4.07 0.06 94.03 792.90 237.20 17.17 94.03 429.69 3621.59 575.26 cross-12 448.09 4.00 0.04 29.82 763.08 231.76 5.44 29.82 136.28 3485.31 575.20 cross-12 384.62 3.77 0.11 77.81 666.68 200.03 28.34 77.81 224.41 3175.96 574.96 cross-12 301.48 3.31 0.26 12.06 510.64 158.45 3.15 12.06 43.45 2607.43 574.51 cross-12 256.53 2.95 0.20 25.32 410.48 135.97 2.95 25.32 156.18 2181.72 574.14 cross-12 226.95 2.50 0.07 55.87 302.69 121.18 8.75 55.87 282.87 1578.60 573.70
Width h delta H delta A A P delta P delta A delta Q Q H ∆Q ∆H
cross-11 222.26 2.44 0.00 71.87 329.59 144.09 13.93 71.87 376.90 1578.60 572.72 cross-11 328.00 3.01 0.27 9.74 481.27 196.97 4.75 9.74 27.59 2181.72 573.30 cross-11 355.14 3.22 0.18 45.69 552.86 210.54 6.51 45.69 294.09 2607.43 573.50 cross-11 369.32 3.40 0.04 18.79 615.22 217.63 0.66 18.79 309.35 3175.96 573.68 cross-11 370.63 3.45 0.05 8.28 634.02 218.29 0.29 8.28 136.28 3485.31 573.73 cross-11 371.20 3.47 0.02 28.22 642.30 218.58 0.98 28.22 464.48 3621.59 573.75 cross-11 373.17 3.55 0.08 29.61 670.51 219.56 1.03 29.61 487.40 4086.07 573.83 cross-11 375.22 3.63 0.08 11.85 700.12 220.59 0.41 11.85 195.00 4573.47 573.91
Width h delta H delta A A P delta P delta A delta Q Q H ∆Q ∆H
A-44
cross-9 199.37 2.29 0.16 29.47 281.84 116.99 3.33 29.47 221.70 1578.60 572.57 cross-9 219.00 2.69 0.25 11.86 364.66 126.81 1.44 11.86 84.80 2181.72 572.97 cross-9 225.09 2.87 0.13 40.27 405.06 129.86 2.27 40.27 481.09 2607.43 573.15 cross-9 230.10 3.07 0.03 20.95 451.25 132.38 0.86 20.95 309.35 3175.96 573.35 cross-9 231.81 3.16 0.09 9.23 472.20 133.24 0.38 9.23 136.28 3485.31 573.44 cross-9 232.57 3.20 0.04 31.46 481.43 133.62 1.29 31.46 464.48 3621.59 573.48 cross-9 235.13 3.34 0.14 3.31 512.88 134.91 0.14 3.31 48.91 4086.07 573.62 cross-9 237.99 3.48 0.13 42.23 546.65 136.34 1.80 42.23 608.09 4573.47 573.76
Width h delta H delta A A P delta P delta A delta Q Q H ∆Q ∆H
cross-8 174.59 3.43 0.22 66.17 354.43 96.06 6.59 66.17 328.00 1578.60 570.36 cross-8 186.67 3.92 0.04 49.04 442.06 102.12 2.22 49.04 411.85 2181.72 570.85 cross-8 189.22 4.14 0.13 32.71 482.06 103.42 0.97 32.71 364.54 2607.43 571.06 cross-8 193.69 4.44 0.13 34.27 541.22 105.68 1.52 34.27 291.17 3175.96 571.37 cross-8 196.35 4.62 0.06 8.71 574.57 107.02 0.25 8.71 99.99 3485.31 571.54 cross-8 197.01 4.68 0.20 11.87 586.43 107.35 0.34 11.87 136.28 3621.59 571.60 cross-8 199.33 4.88 0.30 1.17 627.25 108.53 0.06 1.17 9.22 4086.07 571.81 cross-8 205.46 5.19 0.29 1.08 688.81 111.58 0.03 1.08 12.72 4573.47 572.12
Width h delta H delta A A P delta P delta A delta Q Q H ∆Q ∆H
cross-7 210.81 1.96 0.13 37.68 253.88 114.78 2.68 37.68 385.47 1578.60 572.54 cross-7 226.23 2.29 0.15 34.55 325.96 122.50 5.06 34.55 218.56 2181.72 572.87 cross-7 248.45 2.58 0.14 39.97 396.48 133.61 6.73 39.97 230.25 2607.43 573.17 cross-7 283.73 2.96 0.22 23.33 497.54 151.26 4.17 23.33 129.20 3175.96 573.55 cross-7 298.00 3.13 0.08 18.80 545.73 158.39 2.24 18.80 136.28 3485.31 573.72 cross-7 302.48 3.19 0.06 48.72 564.53 160.64 5.81 48.72 353.13 3621.59 573.78 cross-7 318.18 3.40 0.05 70.13 629.28 168.49 8.91 70.13 487.40 4086.07 573.99 cross-7 336.00 3.62 0.21 13.44 699.41 177.40 1.71 13.44 93.41 4573.47 574.20
Width h delta H delta A A P delta P delta A delta Q Q H ∆Q ∆H
A-45
cross-6 158.73 2.65 0.21 13.92 204.50 84.73 2.97 13.92 68.47 1578.60 573.54 cross-6 195.82 3.22 0.18 25.30 306.44 103.28 2.51 25.30 207.46 2181.72 574.11 cross-6 214.56 3.54 0.18 25.67 370.76 112.66 4.52 25.67 143.59 2607.43 574.43 cross-6 238.86 3.92 0.26 10.13 457.16 124.81 1.27 10.13 70.89 3175.96 574.81 cross-6 251.35 4.11 0.14 20.67 503.46 131.06 2.84 20.67 136.28 3485.31 575.00 cross-6 257.03 4.19 0.08 19.97 524.12 133.90 2.75 19.97 131.68 3621.59 575.08 cross-6 272.19 4.43 0.16 39.11 587.79 141.49 4.33 39.11 297.86 4086.07 575.32 cross-6 285.51 4.65 0.08 65.04 650.16 148.15 6.51 65.04 529.96 4573.47 575.54
Width h delta H delta A A P delta P delta A delta Q Q H ∆Q ∆H
cross-5 161.88 1.93 0.11 33.02 185.47 110.55 8.76 33.02 140.48 1578.60 575.26 cross-5 185.21 2.37 0.24 12.35 261.95 122.23 0.83 12.35 131.47 2181.72 575.70 cross-5 222.97 2.76 0.01 41.43 339.81 141.12 1.90 41.43 568.53 2607.43 576.09 cross-5 226.75 2.94 0.18 22.54 381.23 143.01 1.03 22.54 309.35 3175.96 576.27 cross-5 228.80 3.04 0.10 1.78 403.77 144.05 0.08 1.78 24.46 3485.31 576.37 cross-5 230.09 3.09 0.04 39.85 415.15 144.69 2.33 39.85 464.48 3621.59 576.42 cross-5 234.74 3.26 0.17 21.60 455.00 147.02 1.26 21.60 251.79 4086.07 576.59 cross-5 353.15 3.67 0.01 107.92 569.28 206.23 10.31 107.92 907.44 4573.47 576.99
Width h delta H delta A A P delta P delta A delta Q Q H ∆Q ∆H
cross-4 203.27 3.18 0.13 35.46 330.96 113.37 5.09 35.46 227.21 1578.60 571.33 cross-4 227.15 3.60 0.24 13.63 420.46 125.32 1.73 13.63 94.83 2181.72 571.74 cross-4 234.48 3.79 0.13 41.48 464.31 128.99 2.66 41.48 454.22 2607.43 571.93 cross-4 242.58 4.02 0.06 37.80 519.75 133.05 3.76 37.80 309.35 3175.96 572.17 cross-4 250.09 4.17 0.15 16.65 557.56 136.81 1.66 16.65 136.28 3485.31 572.32 cross-4 253.40 4.24 0.07 6.95 574.21 138.47 0.69 6.95 56.84 3621.59 572.39 cross-4 274.29 4.51 0.24 16.03 646.49 148.91 2.39 16.03 100.02 4086.07 572.66 cross-4 286.71 4.72 0.15 43.86 706.05 155.13 3.85 43.86 390.25 4573.47 572.87
A-46
Width h delta H delta A A P delta P delta A delta Q Q H ∆Q ∆H
cross-3 140.67 2.54 0.10 28.72 233.11 83.89 2.43 28.72 261.52 1578.60 568.55 cross-3 153.36 3.02 0.27 4.86 302.66 90.25 0.47 4.86 40.68 2181.72 569.03 cross-3 159.84 3.29 0.24 9.87 345.75 93.50 0.72 9.87 99.37 2607.43 569.30 cross-3 171.42 3.68 0.02 35.05 410.38 99.31 3.11 35.05 309.35 3175.96 569.69 cross-3 177.63 3.88 0.20 14.25 445.42 102.42 1.27 14.25 125.78 3485.31 569.89 cross-3 180.32 3.97 0.01 47.43 460.74 103.76 3.60 47.43 464.48 3621.59 569.98 cross-3 187.50 4.23 0.26 7.71 508.17 107.37 0.59 7.71 75.48 4086.07 570.24 cross-3 192.62 4.45 0.18 23.76 550.64 109.94 1.36 23.76 281.55 4573.47 570.46
Width h delta H delta A A P delta P delta A delta Q Q H ∆Q ∆H
cross-2 187.29 3.67 0.29 1.92 412.31 110.68 0.14 1.92 11.71 1578.60 570.90 cross-2 203.58 4.20 0.07 47.27 515.96 118.84 4.06 47.27 258.80 2181.72 571.43 cross-2 217.98 4.58 0.30 1.72 596.15 126.05 0.17 1.72 8.62 2607.43 571.81 cross-2 240.01 5.07 0.11 46.42 709.23 137.08 4.49 46.42 234.68 3175.96 572.30 cross-2 250.10 5.31 0.10 31.15 766.51 142.13 2.52 31.15 177.23 3485.31 572.54 cross-2 253.98 5.40 0.09 23.95 790.46 144.07 1.94 23.95 136.28 3621.59 572.63 cross-2 268.58 5.73 0.06 63.45 875.40 151.38 5.57 63.45 342.21 4086.07 572.96 cross-2 291.31 6.10 0.30 1.12 979.44 162.75 0.11 1.12 5.57 4573.47 573.33
Width h delta H delta A A P delta P delta A delta Q Q H ∆Q ∆H
cross-1 168.68 2.94 0.20 17.37 285.64 89.72 2.25 17.37 119.24 1578.60 570.79 cross-1 182.32 3.35 0.30 0.66 356.55 96.55 0.06 0.66 5.94 2181.72 571.19 603.12 0.41 slope 1336.2406
cross-1 193.99 3.64 0.29 3.54 411.15 102.40 0.38 3.54 27.52 2607.43 571.48 425.71 0.29 Intercept 0.0052708
cross-1 224.94 4.09 0.13 40.66 505.41 117.88 9.10 40.66 193.79 3175.96 571.93 568.53 0.45 cross-1 249.65 4.34 0.08 23.33 565.85 130.23 3.85 23.33 136.28 3485.31 572.19 309.35 0.26 cross-1 257.34 4.44 0.09 34.92 589.17 134.08 5.76 34.92 204.02 3621.59 572.28 136.28 0.09 cross-1 286.83 4.74 0.17 38.54 672.42 148.83 7.17 38.54 207.69 4086.07 572.58 464.48 0.31 cross-1 308.08 4.99 0.11 60.29 745.37 159.46 6.06 60.29 490.13 4573.47 572.83
A-47
APPENDIX VI
MODEL COMPUTATION TABLES
A-48
Appendix VI_1A Model Run for 5yr Flood
Initial
Condition
Q
(m3/sec hflow Zws
Boundary Condition
Q
(m3/sec hflow Zws ∆Q ∆H
Upstream
Downstream
Upstream 1578.60 2.12 581.85
Upstream
2181.72 2.46 582.19 603.12 0.34
slope(m) 1674.44
slope(m) 1336.24
Downstream 1578.60 3.35 570.79
Downstream
2181.72 2.95 571.19 603.12 0.40
Intercept (C) -0.03289
Intercept (C) 0.00527
∆t = 1hr
f(z)=∆H*m+C 570.09 f(z)=∆H*m+C 536.51
k=f(∆H)-Q∆H -33.03
∆H= 0.40 from rating table
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
Field Label ∆x Station Zfpa Ztalweg So Wfpa Max Wbkf Qinit
Top
Wflow hflow Zws A R Wfpa*B/Wbkf k=(n/AR2/3)) Ak2Q|Q| Q2/A
X-SEC-39 315.00
589.79 581.86 0.000969 679.37 506.70 1578.60 402.60 1.53 583.39 250.97 1.30 539.79 0.00012 8.61 9929.45
1 Eastern Bye
Pass 456.00 0.00 588.26 579.73 0.00467 313.90 276.70 1578.60 209.86 2.46 582.19 338.46 3.22 238.07 0.00005 1.89 7362.70
2 X-SEC-38 617.36 617.36 589.48 579.12 0.00444 275.25 169.37 1578.60 158.88 3.58 582.70 330.40 3.53 258.20 0.00005 1.72 7542.42
3 X-SEC-33 701.49 1318.85 587.65 580.95 0.00261 405.72 323.27 1578.60 297.26 2.04 582.99 387.77 1.99 373.07 0.00006 3.14 6426.42
4 X-SEC-31 788.22 2532.39 584.91 578.82 0.00588 264.59 189.34 1578.60 199.72 2.49 581.30 320.93 2.25 279.10 0.00006 3.22 7764.88
5 X-SEC-30 1074.98 3841.75 584.30 577.60 0.00290 765.21 216.28 1578.60 274.48 2.95 580.54 489.57 2.75 971.14 0.00004 1.62 5090.17
6 X-SEC-29 1023.17 4864.92 589.48 577.29 0.00030 691.05 249.20 1578.60 312.80 5.56 582.85 878.66 4.47 867.41 0.00001 0.47 2836.12
7 X-SEC-28 726.63 5591.55 584.61 577.90 0.00084 683.10 663.18 1578.60 460.48 2.23 580.13 581.40 1.95 474.31 0.00004 2.16 4286.18
8 X-SEC-37 418.51 6010.06 585.52 575.77 0.00510 758.05 640.76 1578.60 239.92 1.43 577.19 268.44 1.26 283.84 0.00011 8.39 9283.32
9 X-SEC-26 1276.49 7817.67 583.08 572.72 0.00409 649.01 464.79 1578.60 245.19 3.52 576.24 581.19 3.63 342.37 0.00003 0.94 4287.75
10 X-SEC-20 258.62 8076.29 582.47 575.77 0.01179 1,568.27 794.61 1578.60 382.40 1.53 577.30 274.77 1.30 754.72 0.00011 7.85 9069.44
11 X-SEC-25 381.42 8457.71 580.03 573.94 0.00479 982.20 593.03 1578.60 436.16 2.65 576.59 488.03 1.87 722.38 0.00005 2.72 5106.22
12 X-SEC-19 322.63 8780.34 580.03 572.11 0.00567 1,083.56 873.41 1578.60 507.65 1.71 573.82 449.05 1.28 629.79 0.00007 4.90 5549.48
13 X-SEC-18 478.58 9258.92 583.08 571.50 0.00127 553.89 480.88 1578.60 271.83 2.64 574.14 478.06 1.36 313.10 0.00006 4.24 5212.72
14 X-SEC-24 86.82 9345.75 584.30 570.89 0.00702 464.13 422.58 1578.60 221.95 1.97 572.86 299.71 1.87 243.78 0.00008 4.42 8314.65
15 X-SEC-16 1036.71 11146.44 578.51 570.59 0.00894 247.98 204.88 1578.60 168.67 3.04 573.63 266.70 2.77 204.15 0.00007 2.94 9343.71
16 X-SEC-15 437.56 11584.00 576.68 569.98 0.00139 379.19 277.70 1578.60 297.58 2.85 572.82 532.34 3.21 406.34 0.00003 1.21 4681.15
17 X-SEC-14 415.20 12361.91 574.24 568.76 0.03484 262.22 145.89 1578.60 130.96 2.29 571.05 165.38 2.09 235.39 0.00013 6.93 15067.87
18 X-SEC-13 322.32 12684.23 576.07 569.98 0.00378 487.37 233.20 1578.60 235.91 2.74 572.71 397.33 2.58 493.02 0.00005 2.17 6271.87
19 X-SEC-12 459.84 13144.08 574.85 571.20 0.00265 353.11 190.00 1578.60 256.53 2.95 574.14 410.48 3.02 476.75 0.00004 1.70 6070.82
20 X-SEC-11 61.85 13205.93 573.94 570.28 0.01478 376.05 124.73 1578.60 222.26 2.44 572.72 329.59 2.29 670.07 0.00006 3.07 7560.94
21 X-SEC-9 743.66 13949.59 573.94 570.28 0.00458 241.57 125.52 1578.60 199.37 2.29 572.57 281.84 2.41 383.69 0.00007 3.35 8841.97
22 X-SEC-8 119.93 14069.53 576.07 569.98 0.00254 252.23 42.21 1578.60 174.59 3.43 570.36 354.43 3.69 1043.30 0.00004 1.51 7030.86
23 X-SEC-7 297.76 14367.29 581.56 570.59 0.00205 653.38 337.38 1578.60 210.81 1.96 572.54 253.88 2.21 408.26 0.00008 4.17 9815.66
24 X-SEC-6 391.72 14759.01 577.60 570.89 0.00078 406.54 196.28 1578.60 158.73 2.65 573.54 204.50 2.41 328.75 0.00010 4.61 12185.52
25 X-SEC-5 633.94 15392.95 582.47 573.33 0.00385 476.65 102.35 1578.60 161.88 1.93 575.26 185.47 1.68 753.87 0.00013 8.26 13435.92
26 X-SEC-4 959.79 16352.74 573.63 568.15 0.00540 311.75 144.08 1578.60 203.27 3.18 571.33 330.96 2.92 439.82 0.00005 2.21 7529.63
27 X-SEC-3 267.60 16620.34 574.55 566.01 0.00797 272.76 175.95 1578.60 140.67 2.54 568.55 233.11 2.78 218.08 0.00008 3.35 10689.97
28 X-SEC-2 428.77 17049.11 575.16 567.23 0.00284 470.35 157.06 1578.60 187.29 3.67 570.90 412.31 3.73 560.88 0.00004 1.28 6043.87
29 X-SEC-1 236.97 17286.08 574.55 567.84 0.00257 474.65 182.44 1578.60 168.68 2.94 570.79 285.64 3.18 438.85 0.00006 2.28 8724.13
A-49
Appendix VI_1B Model Run for 5yr Flood
20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42
C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 m k P R S ∆Q ∆H H Q Field Label Hmeasured Hmodeled ∆H
0.55 -0.55
X-SEC-39
0.55 -0.55 14.82 14.82 0.00 0.50 0.50 3.75 -3.75 26.12 1674.44 -33.03 -0.004494 -0.0006 -0.01152 603.12 0.34 582.53 2181.72 Eastern Bye Pass
0.55 -0.55 27.64 27.64 0.00 0.50 0.50 3.04 -3.04 21.77 -35.64 -26.16 0.1457947 0.023969 0.416706 -30.01 -0.16988 582.53 2151.71 X-SEC-38 582.67 582.53 0.14
0.55 -0.55 31.87 31.87 0.00 0.50 0.50 2.74 -2.74 29.03 -22.17 -20.25 0.1982921 0.03616 1.367108 -25.13 0.107992 583.09 2156.59 X-SEC-33 582.98 583.09 -0.11
0.55 -0.55 71.71 71.71 0.00 0.50 0.50 2.62 -2.62 21.59 -19.29 -33.30 0.2134443 0.040777 0.402859 -36.03 0.21988 581.52 2145.69 X-SEC-31 581.29 581.52 -0.23
0.55 -0.55 141.64 141.64 0.00 0.50 0.50 2.80 -2.80 11.90 -21.15 -13.18 0.2095616 0.037371 0.396967 -5.23 0.141175 580.69 2176.49 X-SEC-30 580.54 580.69 -0.14
0.55 -0.55 91.80 91.80 0.00 0.50 0.50 3.74 -3.74 20.10 -28.42 -10.85 0.2083877 0.027854 0.817753 -4.74 -0.37591 582.47 2176.98 X-SEC-29 582.84 582.47 0.37
0.55 -0.55 35.31 35.31 0.00 0.50 0.50 4.17 -4.17 27.60 -34.89 -26.48 0.193112 0.023129 0.664259 -41.25 -0.21497 579.92 2140.47 X-SEC-28 580.12 579.92 0.20
0.55 -0.55 17.82 17.82 0.00 0.50 0.50 5.48 -5.48 31.17 -26.90 -28.04 0.2893478 0.026413 0.90613 -41.55 0.423133 577.62 2140.17 X-SEC-37 577.17 577.62 -0.44
0.55 -0.55 101.43 101.43 0.00 0.50 0.50 1.80 -1.80 42.91 -19.09 -31.86 0.1589109 0.044069 2.37738 -23.79 0.501999 576.74 2157.93 X-SEC-26 576.23 576.74 -0.51
0.55 -0.55 27.21 27.21 0.00 0.50 0.50 8.39 -8.39 56.70 -20.58 -51.73 0.449247 0.026759 1.650021 -41.03 -0.42331 576.88 2140.69 X-SEC-20 577.29 576.88 0.42
0.55 -0.55 35.49 35.49 0.00 0.50 0.50 6.07 -6.07 35.54 -21.83 -58.21 0.3574982 0.029433 0.378909 -68.75 -0.51999 576.07 2112.97 X-SEC-25 576.57 576.07 0.50
0.55 -0.55 20.21 20.21 0.00 0.50 0.50 7.79 -7.79 19.87 -20.68 -25.67 0.4296486 0.027578 0.387677 -36.41 0.483017 574.30 2145.31 X-SEC-19 573.80 574.30 -0.50
0.55 -0.55 17.22 17.22 0.00 0.50 0.50 4.76 -4.76 48.32 -22.57 -18.55 0.2968181 0.031158 2.433311 -4.63 0.518956 574.66 2177.09 X-SEC-18 574.14 574.66 -0.52
0.55 -0.55 2.64 2.64 0.00 0.50 0.50 20.55 -20.55 35.25 -18.53 -55.87 0.6893498 0.016769 0.245431 -55.56 -0.61707 572.25 2126.16 X-SEC-24 572.84 572.25 0.59
0.55 -0.55 45.12 45.12 0.00 0.50 0.50 1.81 -1.81 26.80 -10.34 -44.28 0.2589238 0.07165 0.667264 -50.75 -0.01666 573.61 2130.97 X-SEC-16 573.60 573.61 0.00
0.55 -0.55 19.59 19.59 0.00 0.50 0.50 4.58 -4.58 35.71 -10.54 -13.90 0.4650704 0.05074 2.91859 -11.81 0.625538 573.45 2169.91 X-SEC-15 572.82 573.45 -0.63
0.55 -0.55 21.25 21.25 0.00 0.50 0.50 4.05 -4.05 34.92 -16.25 -44.47 0.3326583 0.041059 1.041674 -43.37 -0.19883 570.85 2138.35 X-SEC-14 571.03 570.85 0.18
0.55 -0.55 22.25 22.25 0.00 0.50 0.50 5.84 -5.84 27.61 -12.90 -31.24 0.4751836 0.040697 0.975652 -29.66 -0.06779 572.64 2152.06 X-SEC-13 572.69 572.64 0.05
0.55 -0.55 13.76 13.76 0.00 0.50 0.50 3.46 -3.46 12.13 -16.80 -26.27 0.2920595 0.04215 -0.08482 -24.21 -0.12228 574.02 2157.51 X-SEC-12 574.13 574.02 0.11
0.55 -0.55 4.49 4.49 0.00 0.50 0.50 29.19 -29.19 8.56 -11.77 -8.22 0.8321669 0.014254 0.126753 5.30 -0.89246 571.83 2187.02 X-SEC-11 573.30 571.83 1.47
0.55 -0.55 75.62 75.62 0.00 0.50 0.50 2.27 -2.27 26.41 -20.06 -8.37 0.1843947 0.040659 1.80705 -4.47 -1.14818 571.42 2177.25 X-SEC-9 572.97 571.42 1.54
0.55 -0.55 12.11 12.11 0.00 0.50 0.50 13.97 -13.97 1.18 -24.03 -39.57 0.5375467 0.019245 -0.7163 -71.80 -0.19444 570.17 2109.92 X-SEC-8 570.80 570.17 0.64
0.55 -0.55 13.76 13.76 0.00 0.50 0.50 4.76 -4.76 55.21 -21.40 -3.49 0.3080546 0.03233 3.45694 -10.34 1.341165 573.88 2171.38 X-SEC-7 572.86 573.88 -1.02
0.55 -0.55 30.39 30.39 0.00 0.50 0.50 2.90 -2.90 61.48 -20.46 -65.57 0.2207267 0.038086 2.185849 -68.49 0.320121 573.86 2113.23 X-SEC-6 574.07 573.86 0.21
0.55 -0.55 53.04 53.04 0.00 0.50 0.50 1.96 -1.96 55.77 -12.85 -59.50 0.2333757 0.059671 3.104898 -49.82 0.142945 575.41 2131.90 X-SEC-5 575.67 575.41 0.27
0.55 -0.55 40.28 40.28 0.00 0.50 0.50 1.53 -1.53 31.15 -11.83 -53.03 0.2049488 0.067187 0.622952 -46.69 -0.75362 570.57 2135.03 X-SEC-4 571.71 570.57 1.14
0.55 -0.55 14.70 14.70 0.00 0.50 0.50 6.14 -6.14 3.53 -9.56 -15.79 0.5621503 0.045795 -0.39962 -18.86 -0.53538 568.02 2162.86 X-SEC-3 569.01 568.02 1.00
0.55 -0.55 30.43 30.43 0.00 0.50 0.50 4.24 -4.24 28.36 -15.99 -0.48 0.3466603 0.040854 2.297368 -6.90 0.320898 571.22 2174.82 X-SEC-2 571.42 571.22 0.20
0.55 -0.55 6.30 6.30 0.00 0.50 0.50 5.36 -5.36 -1.75 -24.40 -41.99 0.3053671 0.028463 -1.29475 -51.79 0.40 571.19 2129.93 X-SEC-1 571.16 571.19 -0.03
A-50
Appendix VI_2A Model Run for 10yr Flood
Initial
Condition
Q
(m3/sec hflow Zws
Boundary Condition
Q
(m3/sec hflow Zws ∆Q ∆H
Upstream
Downstream
Upstream 1578.60 2.12 581.85
Upstream
2607.43 2.46 582.39 1028.83 0.54
slope(m) 1674.44
slope(m) 1336.24
Downstream 1578.60 2.94 570.79
Downstream
2607.43 3.34 571.48 1028.83 0.69
Intercept (C)
-
0.03289
Intercept (C) 0.00527
f(z)=∆H*m+C 904.16 f(z)=∆H*m+C 1082.36
k=f(∆H)-Q∆H -124.67
∆H= 0.69 from rating table
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
Field Label ∆x Station Zfpa Ztalweg So Wfpa Max Wbkf Qinit
Top
Wflow hflow Zws A R Wfpa*B/Wbkf k=(n/AR2/3)) Ak2Q|Q| Q2/A
X-SEC-39 315.00
589.79 581.86 0.000969 679.37 506.70 1578.60 408.01 1.78 583.64 299.64 1.54 547.05 0.00009 5.73 8316.66
1 Eastern Bye
Pass 456.00 0.00 588.26 579.73 0.00467 313.90 276.70 1578.60 217.50 2.66 582.39 381.73 3.51 246.74 0.00004 1.50 6528.12
2 X-SEC-38 617.36 617.36 589.48 579.12 0.00444 275.25 169.37 1578.60 167.40 3.84 582.96 372.73 3.81 272.04 0.00004 1.38 6685.79
3 X-SEC-33 701.49 1318.85 587.65 580.95 0.00261 405.72 323.27 1578.60 299.52 2.14 583.09 419.30 2.14 375.91 0.00005 2.64 5943.24
4 X-SEC-31 788.22 2532.39 584.91 578.82 0.00588 264.59 189.34 1578.60 203.35 2.64 581.45 350.92 2.43 284.17 0.00006 2.66 7101.23
5 X-SEC-30 1074.98 3841.75 584.30 577.60 0.00290 765.21 216.28 1578.60 297.33 3.08 580.68 566.89 3.00 1051.99 0.00003 1.25 4395.84
6 X-SEC-29 1023.17 4864.92 589.48 577.29 0.00030 691.05 249.20 1578.60 397.91 6.20 583.49 1108.38 4.64 1103.43 0.00001 0.36 2248.30
7 X-SEC-28 726.63 5591.55 584.61 577.90 0.00084 683.10 663.18 1578.60 465.28 2.36 580.26 641.51 2.13 479.25 0.00003 1.73 3884.58
8 X-SEC-37 418.51 6010.06 585.52 575.77 0.00510 758.05 640.76 1578.60 249.93 1.62 577.39 315.26 1.44 295.68 0.00009 5.95 7904.60
9 X-SEC-26 1276.49 7817.67 583.08 572.72 0.00409 649.01 464.79 1578.60 253.59 3.78 576.50 646.25 3.93 354.10 0.00002 0.76 3856.06
10 X-SEC-20 258.62 8076.29 582.47 575.77 0.01179 1,568.27 794.61 1578.60 388.97 1.61 577.38 305.60 1.42 767.68 0.00009 6.25 8154.46
11 X-SEC-25 381.42 8457.71 580.03 573.94 0.00479 982.20 593.03 1578.60 455.10 2.76 576.70 541.33 2.01 753.76 0.00004 2.23 4603.40
12 X-SEC-19 322.63 8780.34 580.03 572.11 0.00567 1,083.56 873.41 1578.60 588.83 1.88 573.99 515.78 1.34 730.50 0.00006 4.02 4831.47
13 X-SEC-18 478.58 9258.92 583.08 571.50 0.00127 553.89 480.88 1578.60 317.83 3.06 574.56 598.66 1.60 366.09 0.00004 2.73 4162.62
14 X-SEC-24 86.82 9345.75 584.30 570.89 0.00702 464.13 422.58 1578.60 233.49 2.17 573.06 344.62 2.08 256.44 0.00006 3.34 7230.99
15 X-SEC-16 1036.71 11146.44 578.51 570.59 0.00894 247.98 204.88 1578.60 176.75 3.25 573.83 303.07 3.02 213.94 0.00006 2.31 8222.53
16 X-SEC-15 437.56 11584.00 576.68 569.98 0.00139 379.19 277.70 1578.60 288.09 3.08 573.05 599.93 3.51 393.38 0.00003 0.95 4153.82
17 X-SEC-14 415.20 12361.91 574.24 568.76 0.03484 262.22 145.89 1578.60 144.99 2.71 571.47 223.06 2.58 260.61 0.00008 3.86 11171.97
18 X-SEC-13 322.32 12684.23 576.07 569.98 0.00378 487.37 233.20 1578.60 249.94 2.98 572.95 456.09 2.84 522.35 0.00004 1.67 5463.78
19 X-SEC-12 459.84 13144.08 574.85 571.20 0.00265 353.11 190.00 1578.60 301.48 3.31 574.51 510.64 3.22 560.29 0.00003 1.26 4880.09
20 X-SEC-11 61.85 13205.93 573.94 570.28 0.01478 376.05 124.73 1578.60 222.26 2.44 572.72 329.59 2.29 670.07 0.00006 3.07 7560.94
21 X-SEC-9 743.66 13949.59 573.94 570.28 0.00458 241.57 125.52 1578.60 199.37 2.29 572.57 281.84 2.41 383.69 0.00007 3.35 8841.97
22 X-SEC-8 119.93 14069.53 576.07 569.98 0.00254 252.23 42.21 1578.60 174.59 3.43 570.36 354.43 3.69 1043.30 0.00004 1.51 7030.86
23 X-SEC-7 297.76 14367.29 581.56 570.59 0.00205 653.38 337.38 1578.60 210.81 1.96 572.54 253.88 2.21 408.26 0.00008 4.17 9815.66
24 X-SEC-6 391.72 14759.01 577.60 570.89 0.00078 406.54 196.28 1578.60 158.73 2.65 573.54 204.50 2.41 328.75 0.00010 4.61 12185.52
25 X-SEC-5 633.94 15392.95 582.47 573.33 0.00385 476.65 102.35 1578.60 161.88 1.93 575.26 185.47 1.68 753.87 0.00013 8.26 13435.92
26 X-SEC-4 959.79 16352.74 573.63 568.15 0.00540 311.75 144.08 1578.60 203.27 3.18 571.33 330.96 2.92 439.82 0.00005 2.21 7529.63
27 X-SEC-3 267.60 16620.34 574.55 566.01 0.00797 272.76 175.95 1578.60 140.67 2.54 568.55 233.11 2.78 218.08 0.00008 3.35 10689.97
28 X-SEC-2 428.77 17049.11 575.16 567.23 0.00284 470.35 157.06 1578.60 187.29 3.67 570.90 412.31 3.73 560.88 0.00004 1.28 6043.87
29 X-SEC-1 236.97 17286.08 574.55 567.84 0.00257 474.65 182.44 1578.60 168.68 2.94 570.79 285.64 3.18 438.85 0.00006 2.28 8724.13
A-51
Appendix VI_2B Model Run for 10yr Flood
20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40.00 41 42
C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 m k P R S ∆Q ∆H Hmodeled Qmodeled Field Label Hmeasured Hmodeled ∆H
0.55 -0.55
X-SEC-39
0.55 -0.55 15.56 15.56 0.00 0.50 0.50 4.27 -4.27 16.80 1674.44 -124.67 -0.00513 -0.0006 0.05467 1028.83 0.54 582.39 2607.43 Eastern Bye Pass 582.39 582.39 0.00
0.55 -0.55 28.33 28.33 0.00 0.50 0.50 3.39 -3.39 18.57 -40.44 -17.44 0.14349 0.02118 0.41749 -15.03 -0.2347 582.72 2592.40 X-SEC-38 582.95 582.72 0.23
0.55 -0.55 32.21 32.21 0.00 0.50 0.50 3.00 -3.00 24.00 -26.30 -18.94 0.18576 0.03096 0.899863 -30.39 -0.05964 583.03 2577.04 X-SEC-33 583.08 583.03 0.05
0.55 -0.55 76.84 76.84 0.00 0.50 0.50 2.91 -2.91 16.23 -21.86 -26.27 0.21045 0.03611 0.22339 -33.60 0.435242 581.89 2573.83 X-SEC-31 581.44 581.89 -0.45
0.55 -0.55 167.02 167.02 0.00 0.50 0.50 3.35 -3.35 8.12 -24.84 -9.13 0.21238 0.03171 0.225553 3.91 0.335156 581.01 2611.34 X-SEC-30 580.68 581.01 -0.33
0.55 -0.55 108.39 108.39 0.00 0.50 0.50 4.53 -4.53 21.83 -34.20 -7.29 0.20925 0.02312 0.840821 6.97 -0.52494 582.96 2614.40 X-SEC-29 583.49 582.96 0.53
0.55 -0.55 35.03 35.03 0.00 0.50 0.50 4.88 -4.88 13.65 -42.88 -31.79 0.18533 0.019 -0.08514 -55.30 -0.41698 579.85 2552.13 X-SEC-28 580.25 579.85 0.40
0.55 -0.55 18.52 18.52 0.00 0.50 0.50 6.18 -6.18 16.26 -29.65 -7.51 0.29435 0.0238 0.59503 -22.81 0.548371 577.93 2584.62 X-SEC-37 577.38 577.93 -0.56
0.55 -0.55 103.62 103.62 0.00 0.50 0.50 2.02 -2.02 32.37 -26.42 -18.02 0.13268 0.03283 1.533567 -8.34 0.516183 577.02 2599.09 X-SEC-26 576.49 577.02 -0.52
0.55 -0.55 28.04 28.04 0.00 0.50 0.50 9.33 -9.33 46.46 -27.89 -43.15 0.40077 0.02148 1.06912 -29.51 -0.36639 577.01 2577.92 X-SEC-20 577.37 577.01 0.36
0.55 -0.55 39.22 39.22 0.00 0.50 0.50 6.81 -6.81 27.08 -27.33 -47.31 0.33255 0.02442 0.167211 -57.69 -0.48909 576.21 2549.74 X-SEC-25 576.69 576.21 0.48
0.55 -0.55 23.70 23.70 0.00 0.50 0.50 9.10 -9.10 6.48 -26.71 -18.72 0.4053 0.02226 -0.1281 -32.05 0.379985 574.37 2575.38 X-SEC-19 573.98 574.37 -0.39
0.55 -0.55 19.11 19.11 0.00 0.50 0.50 5.75 -5.75 37.46 -30.04 -3.83 0.27686 0.02407 1.711246 13.74 0.498959 575.06 2621.17 X-SEC-18 574.57 575.06 -0.49
0.55 -0.55 2.74 2.74 0.00 0.50 0.50 24.26 -24.26 14.56 -27.32 -44.82 0.63973 0.01319 -0.20706 -43.64 -0.58467 572.48 2563.79 X-SEC-24 573.05 572.48 0.57
0.55 -0.55 44.71 44.71 0.00 0.50 0.50 2.05 -2.05 21.11 -15.49 -26.73 0.20937 0.05105 0.790582 -26.55 -0.04298 573.79 2580.88 X-SEC-16 573.82 573.79 0.03
0.55 -0.55 20.01 20.01 0.00 0.50 0.50 5.30 -5.30 20.68 -15.59 -17.38 0.40456 0.0382 0.915722 -16.28 -0.0118 573.04 2591.15 X-SEC-15 573.04 573.04 0.00
0.55 -0.55 22.95 22.95 0.00 0.50 0.50 4.83 -4.83 17.92 -18.80 -21.77 0.33955 0.03513 0.494053 -23.54 -0.07054 571.40 2583.89 X-SEC-14 571.22 571.40 -0.18
0.55 -0.55 24.90 24.90 0.00 0.50 0.50 7.01 -7.01 21.53 -19.28 -16.53 0.42097 0.03003 0.796815 -16.98 0.094163 573.05 2590.45 X-SEC-13 572.94 573.05 -0.10
0.55 -0.55 16.33 16.33 0.00 0.50 0.50 4.21 -4.21 11.45 -25.37 -23.13 0.24909 0.0296 -0.0068 -23.73 0.0236 574.53 2583.70 X-SEC-12 574.48 574.53 -0.05
0.55 -0.55 4.45 4.45 0.00 0.50 0.50 31.16 -31.16 2.14 -16.93 -8.65 0.78633 0.01262 -0.05513 7.73 -0.79634 571.92 2615.16 X-SEC-11 573.51 571.92 1.58
0.55 -0.55 75.62 75.62 0.00 0.50 0.50 2.27 -2.27 26.41 -22.93 -5.53 0.16515 0.03642 1.722095 1.54 -0.9673 571.60 2608.97 X-SEC-9 573.15 571.60 1.55
0.55 -0.55 12.11 12.11 0.00 0.50 0.50 13.97 -13.97 1.18 -26.41 -41.19 0.51396 0.0184 -0.71453 -72.46 -0.30817 570.05 2534.97 X-SEC-8 571.03 570.05 0.98
0.55 -0.55 13.76 13.76 0.00 0.50 0.50 4.76 -4.76 55.21 -21.69 -3.48 0.30524 0.03203 3.425785 -10.98 1.183789 573.72 2596.45 X-SEC-7 573.16 573.72 -0.56
0.55 -0.55 30.39 30.39 0.00 0.50 0.50 2.90 -2.90 61.48 -20.53 -65.50 0.22012 0.03798 2.182608 -73.28 0.345922 573.89 2534.15 X-SEC-6 574.37 573.89 0.48
0.55 -0.55 53.04 53.04 0.00 0.50 0.50 1.96 -1.96 55.77 -12.88 -59.54 0.23296 0.05956 3.097055 -50.56 0.379293 575.64 2556.87 X-SEC-5 576.06 575.64 0.42
0.55 -0.55 40.28 40.28 0.00 0.50 0.50 1.53 -1.53 31.15 -11.85 -53.00 0.20477 0.06713 0.624208 -42.90 -0.69734 570.63 2564.53 X-SEC-4 571.92 570.63 1.29
0.55 -0.55 14.70 14.70 0.00 0.50 0.50 6.14 -6.14 3.53 -9.57 -15.81 0.56195 0.04578 -0.40052 -17.09 -0.85251 567.70 2590.34 X-SEC-3 569.29 567.70 1.59
0.55 -0.55 30.43 30.43 0.00 0.50 0.50 4.24 -4.24 28.36 -15.99 -0.48 0.3467 0.04086 2.297829 -11.51 0.133355 571.03 2595.92 X-SEC-2 571.80 571.03 0.77
0.55 -0.55 6.30 6.30 0.00 0.50 0.50 5.36 -5.36 -1.75 -24.40 -41.99 0.30537 0.02846 -1.29483 -58.83 0.69 571.48 2548.60 X-SEC-1 571.44 571.48 -0.03
A-52
Appendix VI_3A Model Run for 25yr Flood
Initial
Condition
Q
(m3/sec hflow Zws
Boundary
Condition
Q
(m3/sec Zws ∆Q ∆H
Upstream Downstream
Upstream 1578.60 2.12 581.85
Upstream
3175.96 2.92 582.65 1597.36 0.80
slope(m) 1674.44 slope(m) 1336.24
Downstream 1578.60 2.94 570.79
Downstream
3175.96 4.09 571.93 1597.36 1.14
Intercept (C) -0.03289
Intercept
(C) 0.00527
∆t = 1hr
f(z)=∆H*m+C 1342.08
k=f(∆H)-Q∆H -255.28 ∆H= 1.14
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
Field Label ∆x Station Zfpa Ztalweg So Wfpa Max Wbkf Qinit Top Wflow hflow Zws A R Wfpa*B/Wbkf k=(n/AR2/3)) Ak2Q|Q| Q2/A
X-SEC-39 315.00
589.79 581.86 0.000969 679.37 506.70 1578.60 460.96 1.53 583.39 250.97 1.30 618.05 0.00012 8.61 9929.45
1 Eastern Bye Pass 456.00 0.00 588.26 579.73 0.00467 313.90 276.70 1578.60 227.70 2.92 582.65 439.52 3.86 258.31 0.00003 1.15 5669.81
2 X-SEC-38 617.36 617.36 589.48 579.12 0.00444 275.25 169.37 1578.60 171.14 4.06 583.18 410.48 4.11 278.12 0.00003 1.13 6070.82
3 X-SEC-33 701.49 1318.85 587.65 580.95 0.00261 405.72 323.27 1578.60 305.04 2.32 583.27 473.15 2.38 382.84 0.00004 2.03 5266.82
4 X-SEC-31 788.22 2532.39 584.91 578.82 0.00588 264.59 189.34 1578.60 206.63 2.80 581.62 384.05 2.63 288.76 0.00005 2.19 6488.71
5 X-SEC-30 1074.98 3841.75 584.30 577.60 0.00290 765.21 216.28 1578.60 327.85 3.26 580.86 670.16 3.28 1159.95 0.00002 0.94 3718.46
6 X-SEC-29 1023.17 4864.92 589.48 577.29 0.00030 691.05 249.20 1578.60 418.76 6.60 583.89 1283.58 5.14 1161.25 0.00001 0.27 1941.43
7 X-SEC-28 726.63 5591.55 584.61 577.90 0.00084 683.10 663.18 1578.60 470.71 2.52 580.42 716.44 2.36 484.85 0.00003 1.35 3478.26
8 X-SEC-37 418.51 6010.06 585.52 575.77 0.00510 758.05 640.76 1578.60 261.67 1.85 577.62 374.74 1.67 309.56 0.00007 4.12 6649.85
9 X-SEC-26 1276.49 7817.67 583.08 572.72 0.00409 649.01 464.79 1578.60 266.53 4.15 576.87 742.38 4.34 372.17 0.00002 0.58 3356.75
10 X-SEC-20 258.62 8076.29 582.47 575.77 0.01179 1,568.27 794.61 1578.60 397.73 1.72 577.48 346.77 1.58 784.98 0.00007 4.78 7186.25
11 X-SEC-25 381.42 8457.71 580.03 573.94 0.00479 982.20 593.03 1578.60 483.26 2.83 576.77 600.67 2.15 800.39 0.00004 1.83 4148.69
12 X-SEC-19 322.63 8780.34 580.03 572.11 0.00567 1,083.56 873.41 1578.60 633.54 2.03 574.14 534.73 1.37 785.97 0.00005 3.75 4660.29
13 X-SEC-18 478.58 9258.92 583.08 571.50 0.00127 553.89 480.88 1578.60 344.13 3.42 574.92 717.78 1.85 396.38 0.00003 1.87 3471.76
14 X-SEC-24 86.82 9345.75 584.30 570.89 0.00702 464.13 422.58 1578.60 243.89 2.39 573.28 396.14 2.31 267.87 0.00005 2.52 6290.60
15 X-SEC-16 1036.71 11146.44 578.51 570.59 0.00894 247.98 204.88 1578.60 191.20 3.54 574.13 357.48 3.32 231.42 0.00004 1.72 6971.04
16 X-SEC-15 437.56 11584.00 576.68 569.98 0.00139 379.19 277.70 1578.60 270.25 3.45 573.42 702.55 3.91 369.02 0.00002 0.71 3547.06
17 X-SEC-14 415.20 12361.91 574.24 568.76 0.03484 262.22 145.89 1578.60 142.63 2.62 571.38 210.81 2.48 256.35 0.00009 4.32 11820.96
18 X-SEC-13 322.32 12684.23 576.07 569.98 0.00378 487.37 233.20 1578.60 255.75 3.15 573.12 499.17 3.05 534.49 0.00003 1.38 4992.29
19 X-SEC-12 459.84 13144.08 574.85 571.20 0.00265 353.11 190.00 1578.60 384.62 3.77 574.96 666.68 3.33 714.81 0.00002 0.92 3737.90
20 X-SEC-11 61.85 13205.93 573.94 570.28 0.01478 376.05 124.73 1578.60 222.26 2.44 572.72 329.59 2.29 670.07 0.00006 3.07 7560.94
21 X-SEC-9 743.66 13949.59 573.94 570.28 0.00458 241.57 125.52 1578.60 199.37 2.29 572.57 281.84 2.41 383.69 0.00007 3.35 8841.97
22 X-SEC-8 119.93 14069.53 576.07 569.98 0.00254 252.23 42.21 1578.60 174.59 3.43 570.36 354.43 3.69 1043.30 0.00004 1.51 7030.86
23 X-SEC-7 297.76 14367.29 581.56 570.59 0.00205 653.38 337.38 1578.60 210.81 1.96 572.54 253.88 2.21 408.26 0.00008 4.17 9815.66
24 X-SEC-6 391.72 14759.01 577.60 570.89 0.00078 406.54 196.28 1578.60 158.73 2.65 573.54 204.50 2.41 328.75 0.00010 4.61 12185.52
25 X-SEC-5 633.94 15392.95 582.47 573.33 0.00385 476.65 102.35 1578.60 161.88 1.93 575.26 185.47 1.68 753.87 0.00013 8.26 13435.92
26 X-SEC-4 959.79 16352.74 573.63 568.15 0.00540 311.75 144.08 1578.60 203.27 3.18 571.33 330.96 2.92 439.82 0.00005 2.21 7529.63
27 X-SEC-3 267.60 16620.34 574.55 566.01 0.00797 272.76 175.95 1578.60 140.67 2.54 568.55 233.11 2.78 218.08 0.00008 3.35 10689.97
28 X-SEC-2 428.77 17049.11 575.16 567.23 0.00284 470.35 157.06 1578.60 187.29 3.67 570.90 412.31 3.73 560.88 0.00004 1.28 6043.87
29 X-SEC-1 236.97 17286.08 574.55 567.84 0.00257 474.65 182.44 1578.60 168.68 2.94 570.79 285.64 3.18 438.85 0.00006 2.28 8724.13
A-53
Appendix VI_3B Model Run for 25yr Flood
20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40.00 41 42
C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 m k P R S ∆Q ∆H H Q Field Label Hmeasured Hmodeled ∆H
0.55 -0.55
X-SEC-39
0.55 -0.55 15.91 15.91 0.00 0.50 0.50 4.60 -4.60 20.54 1674.44 -255.28 -0.00553 -0.0006 0.12863 1597.36 0.80 582.65 3175.96
Eastern
Bye Pass 582.65 582.65 0
0.55 -0.55 28.87 28.87 0.00 0.50 0.50 3.80 -3.80 15.13 -45.85 -21.94 0.142026 0.01871 0.155837 -16.36 -0.33612 582.85 3159.60 X-SEC-38 583.18 582.85 0.33
0.55 -0.55 32.77 32.77 0.00 0.50 0.50 3.34 -3.34 19.08 -27.78 -13.12 0.19398 0.02902 0.726723 -25.37 -0.12175 583.15 3150.59 X-SEC-33 583.26 583.15 0.11
0.55 -0.55 83.55 83.55 0.00 0.50 0.50 3.30 -3.30 11.03 -24.61 -21.67 0.21172 0.03203 0.01235 -32.19 0.440924 582.06 3143.77 X-SEC-31 581.61 582.06 -0.45
0.55 -0.55 179.79 179.79 0.00 0.50 0.50 3.89 -3.89 5.12 -28.85 -3.58 0.21226 0.0273 0.18185 10.55 0.427315 581.28 3186.51 X-SEC-30 580.86 581.28 -0.42
0.55 -0.55 112.16 112.16 0.00 0.50 0.50 5.22 -5.22 22.89 -40.15 -6.37 0.20632 0.01977 0.779025 12.80 -0.49004 583.40 3188.76 X-SEC-29 583.90 583.40 0.50
0.55 -0.55 35.79 35.79 0.00 0.50 0.50 5.57 -5.57 2.41 -49.31 -33.74 0.184285 0.01654 -0.47855 -59.21 -0.47757 579.95 3116.75 X-SEC-28 580.41 579.95 0.46
0.55 -0.55 19.49 19.49 0.00 0.50 0.50 7.13 -7.13 3.85 -32.70 7.26 0.303547 0.0213 0.318454 -5.70 0.516682 578.14 3170.26 X-SEC-37 577.62 578.14 -0.52
0.55 -0.55 106.79 106.79 0.00 0.50 0.50 2.33 -2.33 23.58 -35.07 -5.89 0.117226 0.02517 1.038887 3.66 0.396239 577.27 3179.62 X-SEC-26 576.87 577.27 -0.39
0.55 -0.55 29.24 29.24 0.00 0.50 0.50 10.55 -10.55 36.35 -36.62 -36.04 0.365517 0.01733 0.635089 -24.26 -0.2723 577.21 3151.70 X-SEC-20 577.48 577.21 0.27
0.55 -0.55 42.02 42.02 0.00 0.50 0.50 7.43 -7.43 21.48 -33.78 -36.42 0.30559 0.02056 0.134642 -45.58 -0.32176 576.44 3130.38 X-SEC-25 576.76 576.44 0.32
0.55 -0.55 25.58 25.58 0.00 0.50 0.50 10.03 -10.03 -0.22 -33.16 -15.70 0.376982 0.01879 -0.30307 -26.23 0.271399 574.41 3149.73 X-SEC-19 574.13 574.41 -0.28
0.55 -0.55 20.35 20.35 0.00 0.50 0.50 6.63 -6.63 31.53 -35.30 3.38 0.2731 0.02059 1.368403 24.20 0.317789 575.23 3200.16 X-SEC-18 574.93 575.23 -0.31
0.55 -0.55 2.91 2.91 0.00 0.50 0.50 28.45 -28.45 -6.56 -33.53 -38.39 0.629216 0.01106 -0.56954 -43.20 -0.58972 572.69 3132.76 X-SEC-24 573.26 572.69 0.57
0.55 -0.55 43.96 43.96 0.00 0.50 0.50 2.40 -2.40 16.42 -20.04 -11.39 0.193191 0.04025 0.863425 -9.98 0.143267 574.27 3165.98 X-SEC-16 574.12 574.27 -0.15
0.55 -0.55 19.08 19.08 0.00 0.50 0.50 6.04 -6.04 21.53 -21.22 -19.45 0.362655 0.03003 0.709006 -17.55 -0.07039 573.35 3158.41 X-SEC-15 573.41 573.35 0.06
0.55 -0.55 23.28 23.28 0.00 0.50 0.50 5.21 -5.21 15.79 -20.93 -22.06 0.332242 0.0319 0.30359 -24.88 -0.08926 571.29 3151.08 X-SEC-14 571.37 571.29 0.08
0.55 -0.55 28.99 28.99 0.00 0.50 0.50 8.04 -8.04 21.15 -20.74 -13.67 0.436706 0.02716 0.777277 -13.72 0.134714 573.26 3162.24 X-SEC-13 573.12 573.26 -0.14
0.55 -0.55 21.23 21.23 0.00 0.50 0.50 5.24 -5.24 12.97 -30.25 -23.63 0.257156 0.02455 0.056898 -23.70 0.00225 574.96 3152.26 X-SEC-12 574.94 574.96 -0.02
0.55 -0.55 4.38 4.38 0.00 0.50 0.50 34.22 -34.22 -11.37 -22.27 -10.24 0.754483 0.01102 -0.36346 5.74 -0.76047 571.96 3181.70 X-SEC-11 573.68 571.96 1.72
0.55 -0.55 75.62 75.62 0.00 0.50 0.50 2.27 -2.27 26.41 -25.64 0.56 0.15029 0.03314 1.768999 13.09 -0.71741 571.85 3189.05 X-SEC-9 573.36 571.85 1.50
0.55 -0.55 12.11 12.11 0.00 0.50 0.50 13.97 -13.97 1.18 -29.26 -44.96 0.488422 0.01749 -0.74503 -72.82 -0.48831 569.87 3103.14 X-SEC-8 571.33 569.87 1.46
0.55 -0.55 13.76 13.76 0.00 0.50 0.50 4.76 -4.76 55.21 -21.68 -3.56 0.305359 0.03205 3.42443 -11.91 0.952107 573.49 3164.05 X-SEC-7 573.54 573.49 0.05
0.55 -0.55 30.39 30.39 0.00 0.50 0.50 2.90 -2.90 61.48 -20.50 -65.48 0.220389 0.03803 2.185798 -80.82 0.385188 573.93 3095.14 X-SEC-6 574.76 573.93 0.83
0.55 -0.55 53.04 53.04 0.00 0.50 0.50 1.96 -1.96 55.77 -12.87 -59.54 0.233087 0.0596 3.09846 -51.68 0.748008 576.01 3124.28 X-SEC-5 576.25 576.01 0.24
0.55 -0.55 40.28 40.28 0.00 0.50 0.50 1.53 -1.53 31.15 -11.84 -52.99 0.204843 0.06715 0.624717 -37.05 -0.61052 570.72 3138.91 X-SEC-4 572.15 570.72 1.43
0.55 -0.55 14.70 14.70 0.00 0.50 0.50 6.14 -6.14 3.53 -9.57 -15.81 0.562003 0.04578 -0.40062 -14.29 -1.34648 567.21 3161.67 X-SEC-3 569.69 567.21 2.48
0.55 -0.55 30.43 30.43 0.00 0.50 0.50 4.24 -4.24 28.36 -15.99 -0.48 0.346716 0.04086 2.29796 -18.70 -0.15933 570.74 3157.26 X-SEC-2 572.29 570.74 1.55
0.55 -0.55 6.30 6.30 0.00 0.50 0.50 5.36 -5.36 -1.75 -24.40 -41.99 0.30537 0.02846 -1.29486 -69.81 1.14 571.93 3106.15 X-SEC-1 571.87 571.93 -0.06
A-54
Appendix VI_4A Model Run for 50yr Flood
Initial
Condition
Q
(m3/sec hflow Zws
Boundary
Condition
Q
(m3/sec Zws ∆Q ∆H
Upstream Downstream
Upstream 1578.60 2.12 581.85
Upstream
3621.59 3.12 582.85 2042.99 1.00
slope(m) 1674.44 slope(m) 1336.24
Downstream 1578.60 2.94 570.79
Downstream
3621.59 4.44 572.28 2042.99 1.49
Intercept (C) -0.03289
Intercept
(C) 0.00527
∆t = 1hr
f(z)=∆H*m+C 1668.28
k=f(∆H)-Q∆H -374.71 ∆H= 1.49
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
Field Label ∆x Station Zfpa Ztalweg So Wfpa Max Wbkf Qinit Top Wflow hflow Zws A R Wfpa*B/Wbkf k=(n/AR2/3)) Ak2Q|Q| Q2/A
X-SEC-39 315.00
589.79 581.86 0.000969 679.37 506.70 1578.60 502.91 2.67 584.54 482.19 2.39 674.28 0.00004 1.98 5168.03
1 Eastern Bye Pass 456.00 0.00 588.26 579.73 0.00467 313.90 276.70 1578.60 235.43 3.12 582.85 484.19 4.11 267.08 0.00003 0.96 5146.73
2 X-SEC-38 617.36 617.36 589.48 579.12 0.00444 275.25 169.37 1578.60 172.60 4.20 583.32 433.96 4.32 280.50 0.00003 1.00 5742.43
3 X-SEC-33 701.49 1318.85 587.65 580.95 0.00261 405.72 323.27 1578.60 309.16 2.46 583.41 514.44 2.56 388.01 0.00004 1.69 4844.04
4 X-SEC-31 788.22 2532.39 584.91 578.82 0.00588 264.59 189.34 1578.60 207.82 2.89 581.71 403.81 2.76 290.41 0.00004 1.96 6171.13
5 X-SEC-30 1074.98 3841.75 584.30 577.60 0.00290 765.21 216.28 1578.60 351.77 3.40 581.00 751.11 3.47 1244.57 0.00002 0.77 3317.72
6 X-SEC-29 1023.17 4864.92 589.48 577.29 0.00030 691.05 249.20 1578.60 435.10 6.91 584.20 1420.90 5.51 1206.57 0.00001 0.22 1753.80
7 X-SEC-28 726.63 5591.55 584.61 577.90 0.00084 683.10 663.18 1578.60 474.38 2.64 580.54 771.96 2.53 488.63 0.00002 1.15 3228.10
8 X-SEC-37 418.51 6010.06 585.52 575.77 0.00510 758.05 640.76 1578.60 272.13 2.03 577.80 423.86 1.84 321.95 0.00005 3.19 5879.29
9 X-SEC-26 1276.49 7817.67 583.08 572.72 0.00409 649.01 464.79 1578.60 271.71 4.39 577.11 805.49 4.64 379.40 0.00002 0.49 3093.74
10 X-SEC-20 258.62 8076.29 582.47 575.77 0.01179 1,568.27 794.61 1578.60 404.61 1.80 577.56 379.04 1.70 798.54 0.00006 3.97 6574.39
11 X-SEC-25 381.42 8457.71 580.03 573.94 0.00479 982.20 593.03 1578.60 505.33 2.88 576.82 647.17 2.25 836.95 0.00003 1.60 3850.57
12 X-SEC-19 322.63 8780.34 580.03 572.11 0.00567 1,083.56 873.41 1578.60 668.58 2.14 574.25 549.58 1.40 829.45 0.00005 3.55 4534.36
13 X-SEC-18 478.58 9258.92 583.08 571.50 0.00127 553.89 480.88 1578.60 349.48 3.58 575.08 774.80 1.99 402.54 0.00003 1.58 3216.29
14 X-SEC-24 86.82 9345.75 584.30 570.89 0.00702 464.13 422.58 1578.60 248.76 2.53 573.42 429.92 2.47 273.23 0.00004 2.12 5796.41
15 X-SEC-16 1036.71 11146.44 578.51 570.59 0.00894 247.98 204.88 1578.60 205.19 3.78 574.36 404.05 3.53 248.35 0.00004 1.41 6167.48
16 X-SEC-15 437.56 11584.00 576.68 569.98 0.00139 379.19 277.70 1578.60 263.17 3.67 573.65 763.72 4.17 359.35 0.00002 0.60 3262.94
17 X-SEC-14 415.20 12361.91 574.24 568.76 0.03484 262.22 145.89 1578.60 146.12 2.75 571.51 228.60 2.63 262.64 0.00008 3.68 10901.02
18 X-SEC-13 322.32 12684.23 576.07 569.98 0.00378 487.37 233.20 1578.60 257.41 3.25 573.22 524.98 3.19 537.97 0.00003 1.24 4746.76
19 X-SEC-12 459.84 13144.08 574.85 571.20 0.00265 353.11 190.00 1578.60 458.97 4.07 575.26 792.90 3.34 852.99 0.00002 0.77 3142.87
20 X-SEC-11 61.85 13205.93 573.94 570.28 0.01478 376.05 124.73 1578.60 222.26 2.44 572.72 329.59 2.29 670.07 0.00006 3.07 7560.94
21 X-SEC-9 743.66 13949.59 573.94 570.28 0.00458 241.57 125.52 1578.60 199.37 2.29 572.57 281.84 2.41 383.69 0.00007 3.35 8841.97
22 X-SEC-8 119.93 14069.53 576.07 569.98 0.00254 252.23 42.21 1578.60 174.59 3.43 570.36 354.43 3.69 1043.30 0.00004 1.51 7030.86
23 X-SEC-7 297.76 14367.29 581.56 570.59 0.00205 653.38 337.38 1578.60 210.81 1.96 572.54 253.88 2.21 408.26 0.00008 4.17 9815.66
24 X-SEC-6 391.72 14759.01 577.60 570.89 0.00078 406.54 196.28 1578.60 158.73 2.65 573.54 204.50 2.41 328.75 0.00010 4.61 12185.52
25 X-SEC-5 633.94 15392.95 582.47 573.33 0.00385 476.65 102.35 1578.60 161.88 1.93 575.26 185.47 1.68 753.87 0.00013 8.26 13435.92
26 X-SEC-4 959.79 16352.74 573.63 568.15 0.00540 311.75 144.08 1578.60 203.27 3.18 571.33 330.96 2.92 439.82 0.00005 2.21 7529.63
27 X-SEC-3 267.60 16620.34 574.55 566.01 0.00797 272.76 175.95 1578.60 140.67 2.54 568.55 233.11 2.78 218.08 0.00008 3.35 10689.97
28 X-SEC-2 428.77 17049.11 575.16 567.23 0.00284 470.35 157.06 1578.60 187.29 3.67 570.90 412.31 3.73 560.88 0.00004 1.28 6043.87
29 X-SEC-1 236.97 17286.08 574.55 567.84 0.00257 474.65 182.44 1578.60 168.68 2.94 570.79 285.64 3.18 438.85 0.00006 2.28 8724.13
A-55
Appendix VI_4B Model Run for 50yr Flood
20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40.00 41 42
C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 m k P R S ∆Q ∆H H Q Field Label Hmeasured Hmodeled ∆H
0.55 -0.55
X-SEC-39
0.55 -0.55 16.09 16.09 0.00 0.50 0.50 5.56 -5.56 3.06 1674.44 -374.71 -0.00669 -0.0006 0.2216 582.85 1.00 582.85 3621.59
Eastern
Bye Pass 582.85 582.85 0.00
0.55 -0.55 29.18 29.18 0.00 0.50 0.50 4.08 -4.08 13.16 -53.17 -5.10 0.13318 0.0163 0.345839 4.86 -0.22975 583.09 3626.45 X-SEC-38 583.32 583.09 0.23
0.55 -0.55 33.10 33.10 0.00 0.50 0.50 3.58 -3.58 16.56 -34.50 -15.31 0.17201 0.024 0.427526 -33.78 -0.18721 583.22 3587.81 X-SEC-33 583.40 583.22 0.18
0.55 -0.55 88.71 88.71 0.00 0.50 0.50 3.59 -3.59 8.10 -27.19 -17.05 0.20881 0.0291 -0.02459 -29.45 0.535252 582.25 3592.14 X-SEC-31 581.70 582.25 -0.54
0.55 -0.55 189.82 189.82 0.00 0.50 0.50 4.30 -4.30 3.64 -32.42 -1.91 0.20974 0.02438 0.130923 15.97 0.456003 581.45 3637.56 X-SEC-30 581.00 581.45 -0.45
0.55 -0.55 115.08 115.08 0.00 0.50 0.50 5.76 -5.76 24.42 -44.86 -5.03 0.20426 0.01774 0.777215 18.08 -0.55161 583.65 3639.67 X-SEC-29 584.21 583.65 0.56
0.55 -0.55 36.44 36.44 0.00 0.50 0.50 6.11 -6.11 -4.70 -54.39 -36.77 0.18334 0.01501 -0.69336 -68.97 -0.51531 580.03 3552.62 X-SEC-28 580.52 580.03 0.50
0.55 -0.55 20.07 20.07 0.00 0.50 0.50 7.83 -7.83 -2.78 -34.70 16.67 0.31089 0.01986 0.220813 4.63 0.59206 578.39 3626.22 X-SEC-37 577.80 578.39 -0.59
0.55 -0.55 108.64 108.64 0.00 0.50 0.50 2.55 -2.55 18.88 -42.07 0.40 0.10798 0.02121 0.808955 13.26 0.347144 577.45 3634.85 X-SEC-26 577.11 577.45 -0.34
0.55 -0.55 30.19 30.19 0.00 0.50 0.50 11.45 -11.45 30.38 -43.12 -31.81 0.3468 0.01515 0.438617 -20.22 -0.30578 577.26 3601.37 X-SEC-20 577.56 577.26 0.30
0.55 -0.55 44.22 44.22 0.00 0.50 0.50 7.92 -7.92 18.04 -38.43 -30.11 0.29194 0.01843 0.110105 -42.99 -0.26873 576.55 3578.60 X-SEC-25 576.81 576.55 0.26
0.55 -0.55 26.63 26.63 0.00 0.50 0.50 10.59 -10.59 -3.24 -37.91 -13.54 0.35855 0.01692 -0.33881 -25.87 0.335382 574.59 3595.72 X-SEC-19 574.25 574.59 -0.34
0.55 -0.55 20.61 20.61 0.00 0.50 0.50 7.09 -7.09 28.91 -38.74 6.38 0.26805 0.01889 1.212889 32.95 0.325331 575.41 3654.54 X-SEC-18 575.09 575.41 -0.31
0.55 -0.55 3.05 3.05 0.00 0.50 0.50 31.10 -31.10 -18.36 -36.48 -35.27 0.6303 0.01013 -0.72966 -37.25 -0.68563 572.73 3584.34 X-SEC-24 573.41 572.73 0.68
0.55 -0.55 44.37 44.37 0.00 0.50 0.50 2.65 -2.65 14.32 -22.66 -3.23 0.18942 0.03577 0.909082 0.97 0.054291 574.42 3622.56 X-SEC-16 574.36 574.42 -0.05
0.55 -0.55 18.94 18.94 0.00 0.50 0.50 6.60 -6.60 17.85 -25.06 -20.69 0.34521 0.02613 0.392019 -22.92 -0.18527 573.46 3598.67 X-SEC-15 573.64 573.46 0.18
0.55 -0.55 23.60 23.60 0.00 0.50 0.50 5.59 -5.59 10.82 -22.53 -17.23 0.33187 0.02966 0.130936 -23.26 0.08881 571.59 3598.33 X-SEC-14 571.50 571.59 -0.10
0.55 -0.55 32.46 32.46 0.00 0.50 0.50 8.90 -8.90 20.24 -23.21 -8.77 0.43413 0.02438 0.772882 -4.42 0.267913 573.49 3617.17 X-SEC-13 573.22 573.49 -0.27
0.55 -0.55 25.63 25.63 0.00 0.50 0.50 6.05 -6.05 14.98 -35.71 -24.07 0.25294 0.02092 0.12311 -17.38 -0.18755 575.07 3604.21 X-SEC-12 575.25 575.07 0.18
0.55 -0.55 2.53 2.53 0.00 0.50 0.50 29.99 -29.99 -93.07 -27.20 -12.57 0.68803 0.01147 -2.27893 -16.67 0.151036 572.87 3604.92 X-SEC-11 573.75 572.87 0.88
0.55 -0.55 16.44 16.44 0.00 0.50 0.50 1.57 -1.57 18.72 -22.12 43.89 0.12416 0.0396 3.220441 -54.22 4.435638 577.01 3567.37 X-SEC-9 573.47 577.01 -3.54
0.55 -0.55 8.41 8.41 0.00 0.50 0.50 10.85 -10.85 -46.73 -81.55 -40.40 0.21021 0.00968 -1.2964 33.53 -0.90658 569.45 3655.12 X-SEC-8 571.62 569.45 2.16
0.55 -0.55 6.39 6.39 0.00 0.50 0.50 3.76 -3.76 19.55 -23.16 43.94 0.24501 0.03261 2.707524 -14.90 2.540846 575.08 3606.69 X-SEC-7 573.77 575.08 -1.31
0.55 -0.55 8.08 8.08 0.00 0.50 0.50 2.20 -2.20 21.13 374.71 -23.53 -0.01189 -0.0027 -0.05056 -5.47 0.048192 573.59 3616.12 X-SEC-6 575.08 573.59 1.48
0.55 -0.55 31.85 31.85 0.00 0.50 0.50 1.19 -1.19 43.43 -21.15 -21.16 0.10096 0.0425 2.792311 -40.62 0.919742 576.18 3580.97 X-SEC-5 576.40 576.18 0.22
0.55 -0.55 24.54 24.54 0.00 0.50 0.50 1.17 -1.17 18.87 -15.11 -55.49 0.13401 0.05731 -1.01754 -41.93 -0.89714 570.43 3579.66 X-SEC-4 572.37 570.43 1.94
0.55 -0.55 3.26 3.26 0.00 0.50 0.50 3.87 -3.87 -4.59 -7.81 1.19 0.49789 0.06429 -0.51302 2.49 -0.16564 568.39 3624.08 X-SEC-3 569.98 568.39 1.59
0.55 -0.55 16.13 16.13 0.00 0.50 0.50 3.27 -3.27 10.20 -9.79 4.38 0.40013 0.06127 1.518354 9.29 -0.50159 570.40 3630.88 X-SEC-2 572.64 570.40 2.24
0.55 -0.55 6.30 6.30 0.00 0.50 0.50 5.36 -5.36 -1.75 -17.79 -16.20 0.37624 0.03507 -0.69075 -42.70 1.49 572.28 3578.89 X-SEC-1 572.25 572.28 -0.03
A-56
Appendix VI_5A Model Run for 100yr Flood
Initial
Condition
Q
(m3/sec hflow Zws
Boundary
Condition
Q
(m3/sec Zws ∆Q ∆H
Upstream Downstream
Upstream 1578.60 2.12 581.85
Upstream
4086.07 3.30 583.03 2507.47 1.18
slope(m) 1674.44 slope(m) 1336.24
Downstream 1578.60 2.94 570.79
Downstream
4086.07 4.74 572.58 2507.47 1.79
Intercept (C) -0.03289
Intercept
(C) 0.00527
∆t = 1hr
f(z)=∆H*m+C 1979.16
k=f(∆H)-Q∆H -528.31 ∆H= 1.79
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
Field Label ∆x Station Zfpa Ztalweg So Wfpa Max Wbkf Qinit Top Wflow hflow Zws A R Wfpa*B/Wbkf k=(n/AR2/3)) Ak2Q|Q| Q2/A
X-SEC-39 315.00
589.79 581.86 0.000969 679.37 506.70 1578.60 522.12 2.97 584.83 543.04 2.66 700.04 0.00003 1.52 4588.98
1 Eastern Bye Pass 456.00 0.00 588.26 579.73 0.00467 313.90 276.70 1578.60 243.04 3.30 583.03 529.70 4.36 275.71 0.00002 0.81 4704.54
2 X-SEC-38 617.36 617.36 589.48 579.12 0.00444 275.25 169.37 1578.60 173.38 4.30 583.42 450.61 4.46 281.76 0.00003 0.92 5530.27
3 X-SEC-33 701.49 1318.85 587.65 580.95 0.00261 405.72 323.27 1578.60 312.28 2.58 583.53 552.39 2.73 391.92 0.00003 1.45 4511.26
4 X-SEC-31 788.22 2532.39 584.91 578.82 0.00588 264.59 189.34 1578.60 209.05 2.99 581.81 424.41 2.88 292.13 0.00004 1.75 5871.61
5 X-SEC-30 1074.98 3841.75 584.30 577.60 0.00290 765.21 216.28 1578.60 376.70 3.55 581.14 835.48 3.65 1332.77 0.00002 0.65 2982.69
6 X-SEC-29 1023.17 4864.92 589.48 577.29 0.00030 691.05 249.20 1578.60 452.14 7.23 584.52 1564.03 5.88 1253.81 0.00001 0.18 1593.30
7 X-SEC-28 726.63 5591.55 584.61 577.90 0.00084 683.10 663.18 1578.60 528.53 2.84 580.74 874.92 2.63 544.40 0.00002 0.96 2848.23
8 X-SEC-37 418.51 6010.06 585.52 575.77 0.00510 758.05 640.76 1578.60 281.22 2.21 577.97 471.17 2.01 332.69 0.00005 2.55 5288.96
9 X-SEC-26 1276.49 7817.67 583.08 572.72 0.00409 649.01 464.79 1578.60 277.75 4.64 577.36 874.34 4.95 387.83 0.00001 0.41 2850.12
10 X-SEC-20 258.62 8076.29 582.47 575.77 0.01179 1,568.27 794.61 1578.60 768.76 2.00 577.76 514.38 1.27 1517.25 0.00006 4.31 4844.61
11 X-SEC-25 381.42 8457.71 580.03 573.94 0.00479 982.20 593.03 1578.60 528.33 2.93 576.87 695.65 2.35 875.04 0.00003 1.40 3582.25
12 X-SEC-19 322.63 8780.34 580.03 572.11 0.00567 1,083.56 873.41 1578.60 705.11 2.27 574.38 565.05 1.43 874.77 0.00005 3.37 4410.16
13 X-SEC-18 478.58 9258.92 583.08 571.50 0.00127 553.89 480.88 1578.60 367.75 3.83 575.33 864.48 2.16 423.59 0.00002 1.26 2882.63
14 X-SEC-24 86.82 9345.75 584.30 570.89 0.00702 464.13 422.58 1578.60 252.44 2.65 573.54 462.27 2.63 277.26 0.00004 1.82 5390.69
15 X-SEC-16 1036.71 11146.44 578.51 570.59 0.00894 247.98 204.88 1578.60 223.50 4.03 574.61 456.87 3.69 270.52 0.00003 1.17 5454.43
16 X-SEC-15 437.56 11584.00 576.68 569.98 0.00139 379.19 277.70 1578.60 261.20 3.82 573.80 802.00 4.35 356.66 0.00002 0.54 3107.21
17 X-SEC-14 415.20 12361.91 574.24 568.76 0.03484 262.22 145.89 1578.60 151.72 2.89 571.65 250.64 2.79 272.71 0.00007 3.09 9942.56
18 X-SEC-13 322.32 12684.23 576.07 569.98 0.00378 487.37 233.20 1578.60 259.15 3.35 573.33 551.91 3.34 541.60 0.00003 1.11 4515.15
19 X-SEC-12 459.84 13144.08 574.85 571.20 0.00265 353.11 190.00 1578.60 493.34 4.27 575.46 888.15 3.49 916.85 0.00002 0.65 2805.82
20 X-SEC-11 61.85 13205.93 573.94 570.28 0.01478 376.05 124.73 1578.60 222.26 2.44 572.72 329.59 2.29 670.07 0.00006 3.07 7560.94
21 X-SEC-9 743.66 13949.59 573.94 570.28 0.00458 241.57 125.52 1578.60 199.37 2.29 572.57 281.84 2.41 383.69 0.00007 3.35 8841.97
22 X-SEC-8 119.93 14069.53 576.07 569.98 0.00254 252.23 42.21 1578.60 174.59 3.43 570.36 354.43 3.69 1043.30 0.00004 1.51 7030.86
23 X-SEC-7 297.76 14367.29 581.56 570.59 0.00205 653.38 337.38 1578.60 210.81 1.96 572.54 253.88 2.21 408.26 0.00008 4.17 9815.66
24 X-SEC-6 391.72 14759.01 577.60 570.89 0.00078 406.54 196.28 1578.60 158.73 2.65 573.54 204.50 2.41 328.75 0.00010 4.61 12185.52
25 X-SEC-5 633.94 15392.95 582.47 573.33 0.00385 476.65 102.35 1578.60 161.88 1.93 575.26 185.47 1.68 753.87 0.00013 8.26 13435.92
26 X-SEC-4 959.79 16352.74 573.63 568.15 0.00540 311.75 144.08 1578.60 203.27 3.18 571.33 330.96 2.92 439.82 0.00005 2.21 7529.63
27 X-SEC-3 267.60 16620.34 574.55 566.01 0.00797 272.76 175.95 1578.60 140.67 2.54 568.55 233.11 2.78 218.08 0.00008 3.35 10689.97
28 X-SEC-2 428.77 17049.11 575.16 567.23 0.00284 470.35 157.06 1578.60 187.29 3.67 570.90 412.31 3.73 560.88 0.00004 1.28 6043.87
29 X-SEC-1 236.97 17286.08 574.55 567.84 0.00257 474.65 182.44 1578.60 168.68 2.94 570.79 285.64 3.18 438.85 0.00006 2.28 8724.13
A-57
Appendix VI_5B Model Run for 100yr Flood
20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40.00 41 42
C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 m k P R S ∆Q ∆H H Q Field Label Hmeasured Hmodeled ∆H
0.55 -0.55
X-SEC-39
0.55 -0.55 16.33 16.33 0.00 0.50 0.50 6.05 -6.05 0.03 1674.44 -528.31 -0.007274 -0.0006 0.317771 2507.47 1.18 583.03 4086.07
Eastern
Bye Pass 583.03 583.03 0.00
0.55 -0.55 29.38 29.38 0.00 0.50 0.50 4.34 -4.34 11.58 -62.70 -2.84 0.1215644 0.01401 0.284575 9.69 -0.24232 583.17 4095.76 X-SEC-38 583.42 583.17 0.24
0.55 -0.55 33.37 33.37 0.00 0.50 0.50 3.80 -3.80 14.70 -37.77 -13.66 0.1675954 0.02204 0.34695 -35.87 -0.19995 583.33 4050.20 X-SEC-33 583.52 583.33 0.19
0.55 -0.55 94.09 94.09 0.00 0.50 0.50 3.88 -3.88 5.65 -29.25 -15.08 0.2095051 0.02703 -0.10244 -29.28 0.588122 582.40 4056.79 X-SEC-31 581.80 582.40 -0.59
0.55 -0.55 200.27 200.27 0.00 0.50 0.50 4.73 -4.73 2.48 -35.32 0.85 0.2114013 0.02232 0.129475 21.79 0.485452 581.63 4107.86 X-SEC-30 581.15 581.63 -0.48
0.55 -0.55 122.17 122.17 0.00 0.50 0.50 6.38 -6.38 26.57 -49.24 -5.13 0.2059063 0.01613 0.774356 21.56 -0.59283 583.93 4107.63 X-SEC-29 584.54 583.93 0.61
0.55 -0.55 39.61 39.61 0.00 0.50 0.50 6.82 -6.82 -11.18 -59.59 -40.04 0.1863295 0.01365 -0.85195 -77.86 -0.54202 580.20 4008.21 X-SEC-28 580.64 580.20 0.44
0.55 -0.55 20.49 20.49 0.00 0.50 0.50 8.67 -8.67 -8.84 -38.16 25.77 0.3125571 0.01802 0.145987 14.04 0.634571 578.61 4100.11 X-SEC-37 577.98 578.61 -0.63
0.55 -0.55 179.38 179.38 0.00 0.50 0.50 2.89 -2.89 17.52 -50.40 6.26 0.1030088 0.0178 0.734952 21.79 0.307504 577.66 4107.86 X-SEC-26 577.37 577.66 -0.30
0.55 -0.55 43.84 43.84 0.00 0.50 0.50 13.46 -13.46 32.12 -54.52 -35.12 0.3305568 0.01228 0.35767 -22.23 -0.30804 577.45 4063.84 X-SEC-20 577.75 577.45 0.30
0.55 -0.55 44.65 44.65 0.00 0.50 0.50 8.76 -8.76 17.39 -51.49 -31.39 0.2537865 0.01449 0.049175 -47.86 -0.23634 576.64 4038.21 X-SEC-25 576.87 576.64 0.23
0.55 -0.55 28.08 28.08 0.00 0.50 0.50 11.32 -11.32 -6.69 -43.64 -12.97 0.3415311 0.01509 -0.39754 -25.30 0.319763 574.70 4060.77 X-SEC-19 574.37 574.70 -0.33
0.55 -0.55 21.31 21.31 0.00 0.50 0.50 7.74 -7.74 27.36 -42.42 10.16 0.267358 0.01727 1.120724 41.15 0.282441 575.61 4127.22 X-SEC-18 575.36 575.61 -0.25
0.55 -0.55 3.21 3.21 0.00 0.50 0.50 34.26 -34.26 -32.88 -40.46 -33.64 0.6287106 0.00918 -0.91217 -37.22 -0.73061 572.81 4048.85 X-SEC-24 573.53 572.81 0.72
0.55 -0.55 45.73 45.73 0.00 0.50 0.50 2.88 -2.88 13.06 -25.65 6.03 0.1832569 0.03184 1.023546 13.72 0.088577 574.70 4099.79 X-SEC-16 574.62 574.70 -0.08
0.55 -0.55 19.13 19.13 0.00 0.50 0.50 7.06 -7.06 13.98 -29.83 -23.60 0.321306 0.02275 0.099469 -27.64 -0.29961 573.50 4058.43 X-SEC-15 573.79 573.50 0.29
0.55 -0.55 24.01 24.01 0.00 0.50 0.50 5.95 -5.95 6.82 -23.86 -12.16 0.3326225 0.02797 0.041394 -19.46 0.135646 571.79 4066.61 X-SEC-14 571.65 571.79 -0.14
0.55 -0.55 34.09 34.09 0.00 0.50 0.50 9.65 -9.65 19.73 -25.81 -5.18 0.427843 0.02216 0.759696 -0.27 0.306115 573.64 4085.80 X-SEC-13 573.33 573.64 -0.31
0.55 -0.55 27.66 27.66 0.00 0.50 0.50 6.67 -6.67 16.34 -40.00 -24.40 0.2502249 0.01874 0.155307 -16.80 -0.19001 575.27 4069.27 X-SEC-12 575.46 575.27 0.19
0.55 -0.55 2.50 2.50 0.00 0.50 0.50 31.86 -31.86 -102.12 -30.37 -14.27 0.6772663 0.01063 -2.32228 -21.68 0.244025 572.96 4064.39 X-SEC-11 573.82 572.96 0.86
0.55 -0.55 16.44 16.44 0.00 0.50 0.50 1.57 -1.57 18.72 -23.49 48.73 0.1177496 0.03755 3.235876 -63.82 4.790716 577.36 4022.25 X-SEC-9 573.60 577.36 -3.76
0.55 -0.55 8.41 8.41 0.00 0.50 0.50 10.85 -10.85 -46.73 -123.63 -41.27 0.1493418 0.00688 -0.92703 43.56 -0.68614 569.67 4129.63 X-SEC-8 571.84 569.67 2.16
0.55 -0.55 6.39 6.39 0.00 0.50 0.50 3.76 -3.76 19.55 -25.94 44.74 0.2246215 0.02989 2.506349 -14.87 2.298358 574.84 4071.20 X-SEC-7 573.98 574.84 -0.86
0.55 -0.55 8.08 8.08 0.00 0.50 0.50 2.20 -2.20 21.13 -2044.71 -23.27 0.0021488 0.00049 0.009266 -6.90 -0.00801 573.54 4079.17 X-SEC-6 575.32 573.54 1.78
0.55 -0.55 31.85 31.85 0.00 0.50 0.50 1.19 -1.19 43.43 -18.77 -21.12 0.1123529 0.0473 3.109371 -39.76 0.993397 576.26 4046.31 X-SEC-5 576.57 576.26 0.32
0.55 -0.55 24.54 24.54 0.00 0.50 0.50 1.17 -1.17 18.87 -14.04 -56.10 0.1427625 0.06106 -1.12131 -42.42 -0.97375 570.35 4043.65 X-SEC-4 572.63 570.35 2.28
0.55 -0.55 3.26 3.26 0.00 0.50 0.50 3.87 -3.87 -4.59 -7.41 2.11 0.5109761 0.06598 -0.46605 2.56 -0.06032 568.49 4088.63 X-SEC-3 570.24 568.49 1.75
0.55 -0.55 16.13 16.13 0.00 0.50 0.50 3.27 -3.27 10.20 -10.18 4.43 0.3907627 0.05984 1.485951 11.61 -0.70565 570.19 4097.68 X-SEC-2 572.97 570.19 2.77
0.55 -0.55 6.30 6.30 0.00 0.50 0.50 5.36 -5.36 -1.75 -17.98 -16.13 0.3737181 0.03483 -0.68395 -48.32 1.79 572.58 4037.75 X-SEC-1 572.55 572.58 -0.02
A-58
Appendix VI_6A Model Run for Year 2003 Flood
Initial
Condition
Q
(m3/sec hflow Zws
Boundary
Condition
Q
(m3/sec Zws ∆Q ∆H
Upstream Downstream
Upstream 1578.60 2.12 581.85
Upstream
3485.31 3.06 582.79 1906.71 0.94
slope(m) 1674.44 slope(m) 1336.24
Downstream 1578.60 2.94 570.79
Downstream
3485.31 4.34 572.19 1906.71 1.40
Intercept (C) -0.03289
Intercept
(C) 0.00527
∆t = 1hr
f(z)=∆H*m+C 1577.07
k=f(∆H)-Q∆H -329.64 ∆H= 1.40
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
Field Label ∆x Station Zfpa Ztalweg So Wfpa Max Wbkf Qinit Top Wflow hflow Zws A R Wfpa*B/Wbkf k=(n/AR2/3)) Ak2Q|Q| Q2/A
X-SEC-39 315.00
589.79 581.86 0.000969 679.37 506.70 1578.60 497.27 2.59 584.45 464.34 2.31 666.73 0.00004 2.15 5366.72
1 Eastern Bye Pass 456.00 0.00 588.26 579.73 0.00467 313.90 276.70 1578.60 233.20 3.06 582.79 470.83 4.04 264.55 0.00003 1.01 5292.69
2 X-SEC-38 617.36 617.36 589.48 579.12 0.00444 275.25 169.37 1578.60 172.15 4.16 583.28 426.78 4.26 279.77 0.00003 1.04 5839.02
3 X-SEC-33 701.49 1318.85 587.65 580.95 0.00261 405.72 323.27 1578.60 308.05 2.42 583.37 502.45 2.51 386.61 0.00004 1.78 4959.67
4 X-SEC-31 788.22 2532.39 584.91 578.82 0.00588 264.59 189.34 1578.60 207.45 2.87 581.68 397.77 2.72 289.91 0.00005 2.02 6264.90
5 X-SEC-30 1074.98 3841.75 584.30 577.60 0.00290 765.21 216.28 1578.60 344.45 3.36 580.95 726.36 3.41 1218.69 0.00002 0.82 3430.79
6 X-SEC-29 1023.17 4864.92 589.48 577.29 0.00030 691.05 249.20 1578.60 430.10 6.81 584.10 1378.91 5.40 1192.71 0.00001 0.23 1807.21
7 X-SEC-28 726.63 5591.55 584.61 577.90 0.00084 683.10 663.18 1578.60 473.26 2.60 580.51 754.98 2.48 487.48 0.00003 1.21 3300.70
8 X-SEC-37 418.51 6010.06 585.52 575.77 0.00510 758.05 640.76 1578.60 268.93 1.98 577.75 408.84 1.79 318.16 0.00006 3.43 6095.28
9 X-SEC-26 1276.49 7817.67 583.08 572.72 0.00409 649.01 464.79 1578.60 269.62 4.31 577.03 783.74 4.54 376.49 0.00002 0.52 3179.60
10 X-SEC-20 258.62 8076.29 582.47 575.77 0.01179 1,568.27 794.61 1578.60 402.50 1.77 577.54 369.17 1.66 794.40 0.00007 4.19 6750.15
11 X-SEC-25 381.42 8457.71 580.03 573.94 0.00479 982.20 593.03 1578.60 498.58 2.86 576.80 632.95 2.22 825.77 0.00003 1.67 3937.09
12 X-SEC-19 322.63 8780.34 580.03 572.11 0.00567 1,083.56 873.41 1578.60 657.87 2.11 574.22 545.03 1.39 816.15 0.00005 3.61 4572.15
13 X-SEC-18 478.58 9258.92 583.08 571.50 0.00127 553.89 480.88 1578.60 347.84 3.53 575.03 757.36 1.95 400.66 0.00003 1.66 3290.33
14 X-SEC-24 86.82 9345.75 584.30 570.89 0.00702 464.13 422.58 1578.60 247.69 2.49 573.38 420.42 2.43 272.04 0.00005 2.23 5927.30
15 X-SEC-16 1036.71 11146.44 578.51 570.59 0.00894 247.98 204.88 1578.60 200.60 3.71 574.29 389.40 3.47 242.81 0.00004 1.49 6399.51
16 X-SEC-15 437.56 11584.00 576.68 569.98 0.00139 379.19 277.70 1578.60 264.86 3.61 573.59 747.25 4.10 361.66 0.00002 0.62 3334.86
17 X-SEC-14 415.20 12361.91 574.24 568.76 0.03484 262.22 145.89 1578.60 138.27 2.47 571.22 188.30 2.27 248.52 0.00011 5.43 13233.80
18 X-SEC-13 322.32 12684.23 576.07 569.98 0.00378 487.37 233.20 1578.60 256.90 3.22 573.19 517.09 3.15 536.91 0.00003 1.28 4819.24
19 X-SEC-12 459.84 13144.08 574.85 571.20 0.00265 353.11 190.00 1578.60 448.09 4.00 575.20 763.08 3.29 832.76 0.00002 0.82 3265.69
20 X-SEC-11 61.85 13205.93 573.94 570.28 0.01478 376.05 124.73 1578.60 222.26 2.44 572.72 329.59 2.29 670.07 0.00006 3.07 7560.94
21 X-SEC-9 743.66 13949.59 573.94 570.28 0.00458 241.57 125.52 1578.60 199.37 2.29 572.57 281.84 2.41 383.69 0.00007 3.35 8841.97
22 X-SEC-8 119.93 14069.53 576.07 569.98 0.00254 252.23 42.21 1578.60 174.59 3.43 570.36 354.43 3.69 1043.30 0.00004 1.51 7030.86
23 X-SEC-7 297.76 14367.29 581.56 570.59 0.00205 653.38 337.38 1578.60 210.81 1.96 572.54 253.88 2.21 408.26 0.00008 4.17 9815.66
24 X-SEC-6 391.72 14759.01 577.60 570.89 0.00078 406.54 196.28 1578.60 158.73 2.65 573.54 204.50 2.41 328.75 0.00010 4.61 12185.52
25 X-SEC-5 633.94 15392.95 582.47 573.33 0.00385 476.65 102.35 1578.60 161.88 1.93 575.26 185.47 1.68 753.87 0.00013 8.26 13435.92
26 X-SEC-4 959.79 16352.74 573.63 568.15 0.00540 311.75 144.08 1578.60 203.27 3.18 571.33 330.96 2.92 439.82 0.00005 2.21 7529.63
27 X-SEC-3 267.60 16620.34 574.55 566.01 0.00797 272.76 175.95 1578.60 140.67 2.54 568.55 233.11 2.78 218.08 0.00008 3.35 10689.97
28 X-SEC-2 428.77 17049.11 575.16 567.23 0.00284 470.35 157.06 1578.60 187.29 3.67 570.90 412.31 3.73 560.88 0.00004 1.28 6043.87
29 X-SEC-1 236.97 17286.08 574.55 567.84 0.00257 474.65 182.44 1578.60 168.68 2.94 570.79 285.64 3.18 438.85 0.00006 2.28 8724.13
A-59
Appendix VI_6B Model Run for Year 2003 Flood
20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40.00 41 42
C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 m k P R S ∆Q ∆H H Q Field Label Hmeasured Hmodeled ∆H
0.55 -0.55
X-SEC-39
0.55 -0.55 16.01 16.01 0.00 0.50 0.50 5.41 -5.41 4.11 1674.44 -329.64 -0.006504 -0.0006 0.193207 1906.71 0.94 582.79 3485.31
Eastern
Bye Pass 582.79 582.79 0
0.55 -0.55 29.09 29.09 0.00 0.50 0.50 4.00 -4.00 13.68 -50.76 -5.91 0.1361011 0.01702 0.365085 3.24 -0.21672 583.06 3488.55 X-SEC-38 583.28 583.06 0.22
0.55 -0.55 33.01 33.01 0.00 0.50 0.50 3.51 -3.51 17.26 -33.49 -15.83 0.173389 0.02468 0.461411 -32.74 -0.18023 583.19 3452.57 X-SEC-33 583.36 583.19 0.17
0.55 -0.55 87.13 87.13 0.00 0.50 0.50 3.50 -3.50 8.93 -26.54 -17.83 0.2088282 0.02981 0.000744 -29.54 0.505124 582.19 3455.77 X-SEC-31 581.67 582.19 -0.51
0.55 -0.55 186.75 186.75 0.00 0.50 0.50 4.18 -4.18 4.05 -31.51 -2.76 0.2095132 0.02509 0.13413 13.83 0.441439 581.40 3499.14 X-SEC-30 580.96 581.40 -0.44
0.55 -0.55 114.19 114.19 0.00 0.50 0.50 5.59 -5.59 23.90 -43.52 -5.10 0.2044533 0.01828 0.780748 16.64 -0.52639 583.58 3501.95 X-SEC-29 584.11 583.58 0.54
0.55 -0.55 36.24 36.24 0.00 0.50 0.50 5.94 -5.94 -2.65 -52.98 -35.98 0.1832151 0.01542 -0.63649 -65.92 -0.49951 580.01 3419.39 X-SEC-28 580.49 580.01 0.48
0.55 -0.55 19.87 19.87 0.00 0.50 0.50 7.60 -7.60 -0.92 -34.10 14.01 0.3084066 0.02028 0.246876 2.17 0.565128 578.31 3487.48 X-SEC-37 577.75 578.31 -0.56
0.55 -0.55 108.01 108.01 0.00 0.50 0.50 2.47 -2.47 20.15 -39.89 -1.37 0.110367 0.0223 0.868225 10.41 0.347101 577.37 3495.72 X-SEC-26 577.03 577.37 -0.34
0.55 -0.55 29.90 29.90 0.00 0.50 0.50 11.16 -11.16 32.18 -41.12 -32.94 0.3518732 0.01576 0.495151 -21.90 -0.29553 577.24 3463.41 X-SEC-20 577.54 577.24 0.29
0.55 -0.55 43.55 43.55 0.00 0.50 0.50 7.77 -7.77 19.03 -37.02 -32.02 0.2957113 0.01902 0.114703 -44.17 -0.2684 576.53 3441.14 X-SEC-25 576.80 576.53 0.26
0.55 -0.55 26.31 26.31 0.00 0.50 0.50 10.42 -10.42 -2.36 -36.44 -14.13 0.363854 0.01746 -0.32912 -25.24 0.328124 574.55 3460.07 X-SEC-19 574.21 574.55 -0.33
0.55 -0.55 20.55 20.55 0.00 0.50 0.50 6.96 -6.96 29.60 -37.71 5.51 0.2694613 0.01937 1.253421 31.30 0.304934 575.34 3516.61 X-SEC-18 575.04 575.34 -0.29
0.55 -0.55 3.01 3.01 0.00 0.50 0.50 30.31 -30.31 -14.82 -35.62 -36.10 0.6298915 0.01039 -0.68311 -39.45 -0.68378 572.69 3445.86 X-SEC-24 573.37 572.69 0.67
0.55 -0.55 44.16 44.16 0.00 0.50 0.50 2.58 -2.58 14.85 -21.89 -5.63 0.1904374 0.03698 0.890107 -5.78 0.094219 574.39 3479.53 X-SEC-16 574.29 574.39 -0.10
0.55 -0.55 18.56 18.56 0.00 0.50 0.50 6.33 -6.33 25.84 -23.88 -20.21 0.346312 0.02737 0.86149 -21.56 0.006784 573.59 3463.75 X-SEC-15 573.58 573.59 -0.02
0.55 -0.55 23.15 23.15 0.00 0.50 0.50 5.26 -5.26 18.63 -21.68 -27.10 0.3265483 0.03106 0.315365 -31.94 0.056392 571.28 3453.37 X-SEC-14 571.46 571.28 0.18
0.55 -0.55 31.97 31.97 0.00 0.50 0.50 8.55 -8.55 22.93 -19.98 -15.84 0.4611895 0.02697 0.809884 -10.68 0.22301 573.42 3474.63 X-SEC-13 573.19 573.42 -0.23
0.55 -0.55 24.99 24.99 0.00 0.50 0.50 5.85 -5.85 14.61 -31.43 -25.46 0.2712191 0.02318 0.087121 -17.35 -0.25816 574.94 3467.96 X-SEC-12 575.19 574.94 0.25
0.55 -0.55 4.33 4.33 0.00 0.50 0.50 36.11 -36.11 -20.91 -25.07 -11.56 0.7423165 0.01028 -0.54863 -11.56 -0.28502 572.72 3473.75 X-SEC-11 573.73 572.72 1.01
0.55 -0.55 75.62 75.62 0.00 0.50 0.50 2.27 -2.27 26.41 -26.95 4.87 0.1440252 0.03176 1.831961 4.87 0.287693 572.57 3490.18 X-SEC-9 573.45 572.57 0.87
0.55 -0.55 12.11 12.11 0.00 0.50 0.50 13.97 -13.97 1.18 -30.93 -47.63 0.4745687 0.01699 -0.76931 -47.63 -0.21923 570.36 3437.68 X-SEC-8 571.52 570.36 1.16
0.55 -0.55 13.76 13.76 0.00 0.50 0.50 4.76 -4.76 55.21 -21.59 -3.63 0.3061776 0.03213 3.431363 -3.63 1.289215 572.54 3481.68 X-SEC-7 573.71 572.54 1.17
0.55 -0.55 30.39 30.39 0.00 0.50 0.50 2.90 -2.90 61.48 -20.46 -65.49 0.2207553 0.03809 2.189124 -65.49 -0.12331 573.54 3419.82 X-SEC-6 574.96 573.54 1.41
0.55 -0.55 53.04 53.04 0.00 0.50 0.50 1.96 -1.96 55.77 -12.85 -59.54 0.2332957 0.05965 3.101568 -59.54 -0.20232 575.26 3425.77 X-SEC-5 576.35 575.26 1.09
0.55 -0.55 40.28 40.28 0.00 0.50 0.50 1.53 -1.53 31.15 -11.83 -53.00 0.204944 0.06719 0.624793 -53.00 -0.61083 571.33 3432.31 X-SEC-4 572.29 571.33 0.97
0.55 -0.55 14.70 14.70 0.00 0.50 0.50 6.14 -6.14 3.53 -9.56 -15.81 0.562098 0.04579 -0.40048 -15.81 -0.84723 568.55 3469.50 X-SEC-3 569.88 568.55 1.33
0.55 -0.55 30.43 30.43 0.00 0.50 0.50 4.24 -4.24 28.36 -15.99 -0.48 0.3467186 0.04086 2.297943 -22.86 1.067572 570.90 3462.45 X-SEC-2 572.52 570.90 1.62
0.55 -0.55 6.30 6.30 0.00 0.50 0.50 5.36 -5.36 -1.75 -24.40 -41.99 0.3053724 0.02846 -1.29487 -41.99 1.40 570.79 3443.32 X-SEC-1 572.16 570.79 1.37
A-60