The Restoration of the Nile River and Its Delta, Egypt. Numerical Modeling Basim Mohammed Naseef Al-Zaidi

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Fall 2018 The Restoration of the Nile River and Its Delta, Egypt. Numerical Modeling Basim Mohammed Naseef Al-Zaidi

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Recommended Citation Naseef Al-Zaidi, B.(2018). The Restoration of the Nile River and Its Delta, Egypt. Numerical Modeling. (Doctoral dissertation). Retrieved from https://scholarcommons.sc.edu/etd/5003

This Open Access Dissertation is brought to you by Scholar Commons. It has been accepted for inclusion in Theses and Dissertations by an authorized administrator of Scholar Commons. For more information, please contact [email protected]. THE RESTORATION OF THE NILE RIVER AND ITS DELTA, EGYPT. NUMERICAL MODELING

Basim Mohammed Naseef Al-Zaidi

Bachelor of Science University of Mosul, 2004

Master of Science University of Mosul, 2008

Submitted in Partial Fulfillment of the Requirements

For the Degree of Doctor of Philosophy in

Civil Engineering

College of Engineering and Computing

University of South Carolina

2018

Accepted by:

Enrica Viparelli, Major Professor

Ahmed Moussa, Major Professor

M. Hanif Chaudhry, Committee Member

Jasim Imran, Committee Member

ii DEDICATION

To Almighty God “ALLAH”,

My parents, siblings, and precious nephews,

And all my teachers and friends.

iii ACKNOWLEDGMENTS

The completion of my doctoral degree was made possible by several years of graduate training. Many people have contributed to this goal, and without the support of these people, the goal would not have been possible. At this point, I would like to express my deepest gratitude individually to all of them.

First, I wish to express my profound sense of gratitude and sincerest appreciation to my major Professor Dr. Viparelli for her advice, the valuable discussions, and her comments. I am very indebted and grateful to Prof. Dr. A. Moussa for his advice, discussions, comments, and for his kind cooperation in making available data and other published information. I would like to express my appreciation and thanks to my dissertation committee members: Prof. Dr. M. Hanif Chaudhry and Prof. Dr. Jasim Imran for their continued advice and valuable suggestions during our weekly water resources group meetings. Special thanks for Dr. Zeyad Sulaiman for his kind cooperation. Also, I gratefully acknowledge the support by the Ministry of Higher Education and Scientific

Research (MoHESR), Iraq.

I am very thankful and grateful to my dear father who greatly supported me in my study during his life, and my thanks to my dear mother, Aliyah, for her prayers for me to succeed and for being very patient during my absence for study abroad. Finally, I wish to thank and acknowledge all my brothers, sisters, and nephews for their unending support and encourages during my study. Basim M. Al-Zaidi // November 8, 2018

iv ABSTRACT

The construction of the High Aswan Dam significantly reduced the flood flows and the sediment supply to the Egyptian portion of the Nile River. Consequences of this changes in river hydrology are diffuse channel bed erosion in the upstream part of the river, in- channel sedimentation in the downstream part of the system, delta recession, habitat deterioration, wetlands loss, water pollution, and environmental problems. The feasibility of a Nile River-Delta restoration project with controlled flow releases and sediment augmentations at Aswan is here investigated with the aid of site-specific one-dimensional morphodynamic models. The water source for the restoration project, based on previous estimates of water availability in Egypt, is an average annual volume of ~10 billion cubic meters that can be saved by improving the Egyptian irrigation system. Sediment can be mined from High Aswan Dam Reservoir upstream of the High Aswan Dam, where a delta is naturally forming and gradually reducing the volume of the reservoir. The mined sediment can be transported at Aswan with slurry pipes. The design of the pipeline goes beyond the scope of this study. This work is organized in two parts, river modeling, and delta modeling. The river modeling aims to quantitatively characterize the morphodynamic impact of the controlled flow releases and sediment augmentations at

Aswan on the Nile River in terms of navigation and flood control. The results of the river modeling show that the ongoing erosion of the Nile River channel in the upstream part of the model reach can be controlled with the proposed sand augmentations, the controlled

v flow releases from the Aswan Dam do not represent a threat for navigation and flood control at engineering time scales, and increase in the volumes of water and sediment delivered to the delta. The delta modeling presented herein consists the development of a

1D model to capture delta growth and the associated changes in channel geometry. The model is validated against field data collected in the High Aswan Dam Reservoir delta, and it is then applied to investigate the effects of sea level rise, subsidence, and wave action on the geometry of the channelized portion of the delta top. Future developments of this work, not reported in the present dissertation, consist in the application of the validated delta model to quantify the impacts of the proposed restoration project on the

Nile delta in terms of shoreline position and geometry of the delta top.

vi TABLE OF CONTENTS

DEDICATION ...... iii

ACKNOWLEDGMENTS ...... iv

ABSTRACT…...... v

LIST OF TABLES ...... ix

LIST OF FIGURES ...... x

LIST OF SYMBOLS ...... xv

CHAPTER 1: INTRODUCTION ...... 1

1.1 OBJECTIVES AND SCOPE OF THE STUDY ...... 1

1.2 RESTORATION PROJECTS OF LARGE DELTAS ...... 3

1.3 ORGANIZATION OF THE DISSERTATION ...... 5

CHAPTER 2: PRELIMINARY MORPHODYNAMIC RESULTS ON THE IMPACT OF THE HIGH ASWAN DAM ON THE NILE RIVER, EGYPT ...... 6

2.1 ABSTRACT ...... 6

2.2 INTRODUCTION ...... 7

2.3 NUMERICAL MODEL ...... 10

2.4 RESULTS ...... 17

2.5 CONCLUSIONS ...... 23

CHAPTER 3:MODELING THE IMPACT OF CONTROLLED FLOW AND SEDIMENT RELEASES FOR THE RESTORATION OF THE NILE RIVER, EGYPT ...... 29

3.1 INTRODUCTION ...... 29

3.2 THE EGYPTIAN NILE RIVER ...... 34

vii 3.3 THE NUMERICAL MODEL ...... 39

3.4 MODEL ZEROING ...... 46

3.5 MODEL APPLICATIONS FOR RESTORATION OF THE NILE RIVER ...... 53

3.6 CONCLUSIONS ...... 60

CHAPTER 4 : CONCURRENT MODELING OF DELTA GROWTH AND CHANNEL GEOMETRY IN THE HIGH ASWAN DAM RESERVOIR, SUDAN- EGYPT ...... 74

4.1 INTRODUCTION ...... 74

4.2 THE HAD RESERVOIR AND ITS DELTA ...... 76

4.3 MODEL DESCRIPTION ...... 80

4.4 MODEL VALIDATION ...... 87

4.5 MODEL MODIFICATION ...... 89

4.6 CONCLUSIONS ...... 94

CHAPTER 5: SUMMARY AND CONCLUSIONS ...... 113

5.1 SUMMARY AND CONCLUSIONS...... 113

5.2 FUTURE WORK ...... 116

REFERENCES ...... 119

viii LIST OF TABLES

Table 2.1 Input model parameters. Data source is the Nile Research Institute (NRI) database...... 24

Table 3.1 Nile River model parameters, data are from the Nile Research Institute (NRI) database. Where subreach 1 starts at the downstream end of the bedrock and ends at the Isna Barrage, subreach 2 goes from the Isna Barrage to the Nag Hammadi Barrage, subreach 3 starts at the Nag Hammadi Barrage and ends at the Asyut Barrage, and subreach 4 goes from the Asyut Barrage to the Delta Barrage (Figure 3.1)……………………………………………………………….………………62

Table 3.2 The comparison between the results of model simulations in the cases of sand diverted at the barrages and those in which it is assumed that the sand was not delivered upstream of the barrages. The symbol ∆ indicates to the difference in the elevation in meter between the two cases……………………………………63

Table 4.1 Summary of input parameters for the delta model during model validation, data are from Nile Research Institute (NRI) database...... ……….…………………96

ix LIST OF FIGURES

Figure 2.1 Nile River with location of the main infrastructures in the study reach, Egypt. Image is from Google Earth …..…………………………………………………25

Figure 2.2 Model results on the impact of the High Aswan Dam on the long profile of the Nile River.  represents the bed elevation and o is the pre-dam equilibrium bed elevation. The black dot line represents a condition of no net erosion and no net deposition …..……………………………………………………………………26

Figure 2.3 Effects of reductions in channel width, flow and flow and sand load on the long term evolution of the modeled reach at 60 years after dam closure – 2024 of Figure 2.2…..…………………………………………………….………………27

Figure 2.4 Effects of reductions in channel width, flow and flow and sand load on the long term evolution of the modeled reach at mobile bed equilibrium………...…27

Figure 2.5 Effects of the barrages on the long term evolution of the modeled reach at 60 years after dam closure – 2024 of Figure 2.2……………………………….……28

Figure 2.6 Effects of the barrages on the long term evolution of the modeled reach at mobile bed equilibrium …………………….……………………………………28

Figure 3.1 Map of the Nile River with location of the main infrastructures relevant for this study, Egypt. Image of the African continent is from Google Earth…..……64

Figure 3.2 The mean monthly hydrographs of pre- and post-High Aswan Dam at Aswan, upstream end of the study reach (Nile Research Institute database). The hydrograph with grey columns and thick borders represent the post-dam flow regime. The dashed columns represent the pre-dam flow regime………….……65

Figure 3.3 Figure A represents a comparison between pre-dam mean annual suspended sand load in the study reach. The black line represents model results, and the

x black diamonds are measurement data from Nile Research Institute. Error bars denote ± 5% of the measured value. The grey circle identifies the aggradation wave. Figure B represents the predicted pre-dam longitudinal profile of the Nile River, and black triangles represent the elevations at the barrages……………...66

Figure 3.4 Post-dam changes in longitudinal profiles in the study reach. ηc denotes the channel bed elevation at the generic time t and ηo is the pre-dam channel bed elevation. The black triangles represent the location of the main barrages. The black dotted line indicates a condition of no net erosion (or no net deposition). The continuous black and grey lines are respectively model results in 1984 and 2084, i.e., 20 and 120 years after the closure of the High Aswan Dam. The dashed black line represents the net change in bed elevation at post-dam mobile bed equilibrium. The black points are the available field data……………………….67

Figure 3.5 Comparison between measured (grey circles) and predicted (black triangles) suspended sand loads in time period range between 2008 and 2015, i.e., ~47 years after the closure of the High Aswan Dam, a) at Rkm 162 to Rkm 180, b) at Rkm 340 to 356, and c) at Rkm 520 to 552. Error bars denote ±10% of the measured value…..……………………………………………………….…………………68

Figure 3.6 Imposed flow hydrographs for the restoration project at Aswan; a) Scenario I; and b) for scenario II. The grey bars indicate the current mean monthly flow releases at Aswan, and the black bars are the proposed mean monthly flows released at Aswan during the restoration project……………………...…………69

Figure 3.7 Water discharge at Aswan and at the Delta Barrage for a) the pre-restoration, and b) and c) for the river restoration scenarios I and II respectively. Grey columns represent the discharges at Aswan, and black ones are at the Delta Barrage…..……………………………………………………….………………70

Figure 3.8 The longitudinal profiles of the channel bed of the river restoration project where (a) is for the scenario I, and (b) is for scenario II. The thin black line represents the initial condition of the bed elevation, the grey line represents the bed elevation at 300 years after the beginning of the restoration project, the dotted line represents the bed elevation at mobile bed equilibrium, the thick black line is the maximum water surface elevation, the dashed black line is the minimum water surface elevation, and the black points are the allowable water surface elevation from field measurements…..……………………………..………………………71

Figure 3.9 The net change in channel bed elevation of the river restoration scenarios. a) is restoration scenario I, and b) is the scenario II. The black dash line represents

xi model results at 50 years, the continues grey line represents model results at 100 years, the dash grey line represents the result at 200 years, and the continues black line is the result at 300 years of the restoration project……………….…………72

Figure 3.10 Mean annual sand load at the delta of the river restoration scenarios and without restoration. Grey line represents the post-dam scheme, dashed black is for the scenario I, and the black line one on the top is for the scenario II……….…..73

Figure 4.1 The location map of the HAD Reservoir showing the cross sections of the field data of the new Nile delta upstream High Aswan Dam. Images are from Google Earth …..…………………………………………………………………………97

Figure 4.2 The monthly average water levels upstream of the HAD from 1964 to 2014 above mean sea level, the red line represents the simplified water level used in the simulations, the data from Nile Research Institute (NRI). The yellow circle indicates the drought period…..………….………………………………………98

Figure 4.3 Longitudinal profiles of the new Nile delta in the High Aswan Dam reservoir (HAD delta), all elevations are above mean sea level (M.S.L). HAD delta profiles are courtesy of the Nile Research Institute (NRI)……………………………..…99

Figure 4.4 Streamwise variation of floodplain width along the modeled reach, Cross Section 23 is at 0Rkm (i.e., the upstream end of the modeled reach). The red points represent the field data, where the blue points represent the predicted data using the Google Erath during the study time. The black line with circle marks represents the bed elevation at 2006……………………………………………100

Figure 4.5 Interpretation of the cross-section measurements to determine bankfull geometry, the comparison between cross sections 23 and 3 in different years...101

Figure 4.6 Downstream fining on the delta top. The data were collected in 2006 by the Nile Research Institute (NRI). The red dots represent the median diameter D50 of the sediment samples. The black line with circle marks represents the bed elevation at 2006…..………………..……………………………………..……102

Figure 4.7 Geometry of channel-floodplain cross-section of the model, and schematic of delta progradation profile with the relevant model parameters…………...……103

xii Figure 4.8 Comparison between numerical predictions of channel bed elevation (blue lines) and average elevation of the delta top (black line) and measured data. The red dots represent measurements of channel bed elevation. Cross section 23 is at 0Rkm (i.e., the upstream end of the modeled reach)………………...…………104

Figure 4.9 Comparison between the predicted location of the shoreline (blue line) and the field data (black triangles), the model captures delta progradation in HAD Reservoir (error bars 15%). Data source is the Nile Research Institute (NRI). The red circle represents the drought period, and the yellow circle in initial part represents the model adjustment to the initial conditions………………………105

Figure 4.10 Comparison of bankfull channel geometry between the predicted and interpreted field data along the modeled reach for different time periods…...…106

Figure 4.11 The longitudinal profiles of delta with a constant floodplain width scenario at 320 years under the effect of sea rise, subsidence, and wave action, where A) represents the average channel floodplain elevation, and B) is the channel bed elevation. The black line represents the base case where no effect, the dashed black line is the sea level rise, the grey line is the subsidence, and the dashed grey line is for the wave effect…..……………………………………...……………107

Figure 4.12 The effect of the sea level rise, subsidence, and wave action on channel geometry at 320 years in the case of the constant floodplain width scenario, where A) is the bankfull water depth, and B) the bankfull channel width…………….108

Figure 4.13 Change in delta progradation at 320 years in the case of constant floodplain width under the effect of sea rise, subsidence, and the wave action, where A) is in terms of the shoreline position, (B) is the delta migration rate. The black line represents the base case, the dashed black line represents the sea level rise, the grey line is for the subsidence, and the dashed grey line is the wave action…...109

Figure 4.14 The longitudinal profiles of the delta with a variable floodplain width scenario at 320 years under the effect of sea rise, subsidence, and wave action, where A) represents the average channel floodplain elevation, and B) is the channel bed elevation. The black line represents the base case where no effect, the dashed black line is the sea level rise, the grey line is the subsidence, and the dashed grey line is for the wave effect……………………………….…………110

xiii Figure 4.15 The effect of the sea level rise, subsidence, and wave action on channel geometry at 320 years in the case of the variable floodplain width scenario, where A) is the bankfull water depth, and B) the bankfull channel width……….……111

Figure 4.16 Change in delta progradation at 320 years in the case of the variable floodplain width under the effect of sea rise, subsidence, and the wave action, where A) is in terms of the shoreline position, (B) is the delta migration rate. The black line represents the base case, the dashed black line represents the sea level rise, the grey line is for the subsidence, and the dashed grey line is the wave action…..………………………………………………………..………………112

xiv LIST OF SYMBOLS

A Constant in entrainment relation (1);

B Channel width (L);

Bbf Bankfull channel width (L);

Bf Delta plain width (L);

Cf Non-dimensional friction coefficient (1);

1/2 Cz Chezy resistance coefficient (L /T);

1/2 Czbf Chezy resistance coefficient at bankfull flow (L /T);

C5 Volumetric suspended sediment concentration at a distance equal to 5% of the flow depth above the channel bed (1);

D Grain size diameter (L);

D50 Median diameter of bed material (L);

D90 Grain diameter for which 90% of the bed material is finer (L);

퐷∗ Non-dimensional characteristic grain size of bed material (1);

E Specific energy (L);

Es Non-dimensional entrainment rate of sediment in suspension (1);

Fr Froude Number (1); g Acceleration of gravity (LT-2);

H Flow depth (L);

Hb Height of breaking waves (L);

xv Hbf Bankfull water depth (L); hb Breaker depth (L);

Hd Water depth at the last computational node (L);

I Integral in the direction normal to the channel bed of the product between the velocity and the volumetric suspended sediment concentration (1);

If Flood intermittency (1);

Is Storm intermittency (1); j Generic characteristic flow rate in the hydrograph (1); kc Composite roughness height (1); ks Roughness height associated with skin friction (1);

L Length of modeled reach (L);

M Number of the computational nodes (1); m Constant represents exponent in the bankfull Shields relation (1);

N Number of discharges in the hydrograph (1); n Constant represents exponent in the bankfull Shields relation (1);

푛푅 Constant represents exponent of the relation for dimensionless Chezy coefficient (1); pj Fraction of time in which the flow is in a given discharge (1);

3 qs Seaward directed sediment flux (L /T); qt Total (suspended and bedload) volumetric bed material load per unit channel width (L2/T);

2 qw Water discharge per unit channel width (L /T);

3 Qbm Total volumetric bed material transport capacity (L /T);

3 Qbm,b Volumetric bedload transport capacity (L /T);

3 Qbm,s Volumetric suspended bed material (L /T);

xvi 3 Qtbf Volumetric bed material load (sand) at bankfull flow (L /T);

3 Qtsbf Volumetric bed material load that delivered to the brink of the foreset (L /T);

3 Qw Water discharge (L /T);

3 Qwbf Bankfull water discharge (L /T);

R Submerged specific gravity (1);

Rp Particle Reynolds number (1);

S Channel bed slope (1);

Sa Slope of delta front (1);

Sb Slope of delta bottomset (1);

Sf Friction slope (1);

Sfbf Bankfull friction slope (1);

Ss Bed slope of the fluvial region at the topset-foreset break (1);

푆푏̇ Speed of migration rate of the forest-basement break (L/T);

푆푠̇ Speed of migration rate (L/T); t Time (T);

U Depth-averaged (mean) flow velocity (L/T);

Ubf Bankfull mean flow velocity (L/T);

Ud Mean flow velocity at the last computational node (L/T);

Uom Nearbed velocity of the shoaling waves (L/T);

푢∗ Shear velocity (L/T);

푢∗푠푘 Shear velocity due to skin friction (L/T); vs or Particle settling velocity (L/T); Ws Sediment fall velocity (L/T); x Streamwise coordinate (L);

xvii

X Non-dimensional entrainment parameter of sediment (1); xb Coordinate of the topset-foreset point of the delta profile (L); xs Coordinate of the foreset-bottomset point on the delta profile (L);

ZR Rouse number (1);

 Parameter accounts for stratification effects associated with suspended sediment transport (1);

훼푅 Coefficient of the relation for dimensionless Chezy coefficient (1);

 A calibration parameter in the relations of entrainment in Chapter 3 and Engelund and Hansen usedin Chapter 2, and a constant in delta model (1);

cA calibration parameter of Engelund and Hansen relation used in Chapter 4 (1);

b Breaker index which represents the ratio between the height of breaking waves and the breaker depth (L);

ss Efficiency of suspended sediment transport (1);

η Post-dam bed elevation above the datum (L);

ηav Average elevation of the channel and floodplain complex above the datum (L);

ηc Channel bed elevation above the datum (L);

ηf Delta plain (floodplain) elevation above the datum (L);

ηo Pre-dam equilibrium bed elevation above the datum (L);

ηs Bed elevation at the topset-foreset break (L);

κ Von Karman constant (1);

λp Bed material porosity (1);

 A ratio represents fraction of mud deposited per unit sand deposit (1); v kinematic viscosity of water (L2 T-1);

ξ Water surface elevation (L);

xviii ζ Mean sea level (or base level) rise rate (L/T);

휉푑 Water surface elevation at the downstream end (L);

ρ Fluid density (M L-3);

-3 ρs Sediment density (M L );

 Subsidence rate (L/T);

τ* Nondimensional shear stress (Shields stress) (1);

-1 -2 휏푏 Bed shear stress (M L T );

-1 -2 휏푏푠푘 Bed Shear stress due to skin friction (M L T );

∗ 휏푏푓 Nondimensional bankfull shear stress (Shields stress) (1);

∗ 휏푠푘 Shear stress due to skin friction (1);

Ω Channel sinuosity (1).

xix CHAPTER 1

INTRODUCTION

1.1 OBJECTIVES AND SCOPE OF THE STUDY

The closure of the High Aswan Dam significantly modified the flow and the sediment transport regimes in the Egyptian portion of the Nile River. Water diversions at the barrages further reduce the flow rate reaching the Nile delta. Consequences of the flow regulation are changes in river morphology along the Egyptian reach. Further, due to the flow diversion at the barrages and the associated decline in sediment transport capacity, the sediment load delivered to the Mediterranean Sea is negligible compared to pre-dam conditions. The reduction in sediment supply to the delta associated with the changes in hydrology resulted in delta wide wetland losses, shoreline retreat, widespread pollution, and several environmental problems.

Egypt depends on the Nile River-Delta system to support the development and growth of its population and economy. However, wetland losses, coastal erosion, and habitat deterioration clearly demonstrate that the current management practices in the

Egypt coast, are not sustainable. Determining sustainable strategies to restore the Nile

River-delta system to support the Egyptian population and economy is the research objective of this study.

1 The first comprehensive studies by the Nile Research Institute (NRI) on the impacts of the High Aswan Dam on the Egyptian Nile River are that of Galay et al.

(1990) and Abdelbary (1992a). These studies reported measurements of cross sections and longitudinal profiles collected by the Nile Research Institute ~20 years after the closure of the High Aswan Dam. The comparison between pre-and post-dam longitudinal profiles shows that the Egyptian Nile River is experiencing channel bed aggradation in its downstream part and erosion in the upstream part.

The main objective of this study is to identify sustainable strategies to restore the

Nile River-Delta system. This work focuses on a river-delta restoration project characterized by controlled flow and sediment releases at Aswan. This restoration project has the following specific objectives: 1) control river bed erosion in the upstream portion of the study reach, 2) control in-channel sediment deposition in the downstream part of the system, and 3) supply the Nile Delta with a sufficient amount of fresh water and sediment to help reduce coastal erosion and wetland deterioration. To achieve this goal, the stated problem is divided into three main studies as following:

1) Preliminary morphodynamic results on the impact of the High Aswan Dam on the

Nile River, Egypt;

2) Modeling the impact of controlled flow and sediment releases for the restoration

of the Nile River, Egypt;

3) Modeling of delta growth and channel geometry in the High Aswan Dam

Reservoir, Sudan-Egypt.

2 1.2 RESTORATION PROJECTS OF LARGE DELTAS

A delta may be defined as the downstream most reach of a river and it is made of the sediment that is deposited into a body of standing water such as an ocean, sea, lake, or even another river (Volker et al., 1993). Many factors such as input of fluvial water and sediment, changes in sea level, subsidence, waves, tides, sediment size, influence delta evolution, including human activities. Changes to any of these factors can effect the delta evolution (Stanley and Ware,1993; Day et al., 2007; Syvitski and Saito, 2007; Syvistik et al., 2009; Tessler et al., 2015).

More than 85% of river deltas around the world have shrunk in recent years due to sediment capture and flow regulation in the upstream parts of their river basins

(Syvistik et al., 2009). Thus, delta restoration has emerged as increasingly important strategy to improve water quality and habitat conditions, restore wetlands, and sustain human and natural environments in deltaic settings (Briggs et al., 1998; Pitt, 2001; All,

2006; Paola et al., 2011).

The idea of delta restoration has been introduced to study the possibility of reducing or reversing wetland loss and shoreline retreat in the Mississippi River Delta,

Louisiana, USA (Kim et al., 2009; Paola et al., 2011). The restoration project proposed for the Mississippi River Delta was characterized by one or two engineered diversion structures to capture water and sediment (sand) from the Mississippi River main channel, and transport them with artificial distributary channels to drowned areas, where the natural delta-building process will result in the formation of new delta lobes (Kim et al.,

2009; Paola et al., 2011).

3 Withdrawals for intensive agriculture and hydrocarbon production, the rapidly growing population with the development of industrial areas, and the construction of dams on the Yellow River have resulted in ecosystem deterioration, wetland losses, and shoreline erosion on the Yellow River Delta (Yonggui et al., 2013). A combination of restoration measurements, such as stabilization of the river course, sediment diversion and/or dredging and increased flow releases have been implemented to restore the Yellow

River Delta by reducing wetland losses and ecosystem deterioration (Syvitski, 2008; Cui et al., 2009).

The Colorado River dries up before reaching the sea during normal years due to upstream water diversions and dam construction (Carriquiry et al., 2001; All John, 2006), so that, the Colorado Delta in the Gulf of California, Mexico, has been extensively altered with considerable land losses and ecosystem deterioration (Glenn et al., 1996;

Briggs et al., 1999; Gerlak et al., 2013). The Colorado River-Delta Restoration Project and the Colorado River Ecosystem Sediment Augmentation have been recently initiated to reverse the deterioration of the Colorado Delta (Briggs et al.,1999; Randle et al.,

2007).

Briggs et al., (1999) note that proper management of the existing water resources in the Colorado River basin can be used to generate, flood flows at a sufficient rate to cause overbank flooding and flush pollutants from the system. Briggs et al., (1999) identified drainage water and wastewater as a potential source of flood water for the

Colorado Delta. Furthermore, sand and fine sediment could be delivered to the Colorado

River below the dam through slurry pipelines, the most efficient sediment conveyance

4 method for large quantities of sediment over long distances (Randle et al., 2007;

Paterson, 2012).

1.3 ORGANIZATION OF THE DISSERTATION

This dissertation is organized as follows: Chapters 2 and 3 focus on the quantification of the impacts of the proposed restoration project on the Nile River from Aswan to Cairo city. A very simplified 1D morphodynamic model is used in Chapter 2 to determine if the proposed restoration project was able to control the changes in the Nile River longitudinal profile. A quantitative study performed with a site-specific 1D morphodynamic model is presented in chapter 3. The objective of this study was to estimate the impacts of the proposed restoration on navigation and flood control. The last study represents the first step of the delta restoration is presented in Chapter 4. This study focuses on the verification at field scale of 1D morphodynamic model of delta growth that predicts the changes in depth and width of the channelized portion of the delta top.

The effects of the wave action, subsidence, and sea level rise, which are important controls on the morphodynamics of the Nile delta, is also explored. Finally, the summary and conclusions of the completed phases of these studies, in addition to suggestions for future works are presented in Chapter 5.

CHAPTER 2

PRELIMINARY MORPHODYNAMIC RESULTS ON THE IMPACT OF

THE HIGH ASWAN DAM ON THE NILE RIVER, EGYPT1

2.1 ABSTRACT

The construction of the High Aswan Dam significantly altered the flow and sediment transport regimes in the Egyptian reach of the Nile River. In this study, a one- dimensional model of river morphodynamics was developed and validated at field scale.

The field scale model validation was used in constraining a sand budget for the Nile

River, which is the first and necessary step to investigate the feasibility of a river restoration project. Here we present preliminary modeling runs specifically designed to 1) investigate the impacts of the High Aswan Dam and of the river barrages on the observed morphodynamic evolution on the study reach, 2) quantify the volumes of sediment that are needed to control channel bed erosion in the upstream part of the modeled domain, and 3) explore the impacts of the barrages on the sediment deposition observed in the downstream portion of the Egyptian Nile.

1 Basim M. Al-Zaidi, A. Moussa, and E. Viparelli, published in River Flow 2016 Conference-the 8th International Conference of Fluvial Hydraulic, St. Louis, MO, USA; River Flow 2016- Constantinescu, Garcia and Hanes (Eds),  2016 Taylor & Francis Group, London, UK, ISBN 978-1-138-02913-2, pp 1166-1174.

2.2 INTRODUCTION

The Nile River is one of the longest rivers in the world, it is more than 6700 km long, and it is the main source of water for 11 countries. In this study, we focus on the Egyptian portion of the Nile River, i.e., from the Egypt-Sudan borders to the apex of the Nile Delta located downstream of Cairo. The study reach is represented in Figure 2.1, where we report the location of the Aswan Dams and of the main barrages on the Nile.

With a rapidly growing of population and its corresponding growing water demand, the Egyptian annual share of Nile water has been fixed at 55.5 BCM. This volume is stored in Lake Nasser upstream of the High Aswan Dam with total capacity of

162 BCM (Abdel- Fattah et al., 2004; Abdelgawad et al., 2010).

The annual volume of flood flows of the Nile River in Egypt prior to the construction of the High Aswan Dam varied between 43 and 150 billion cubic meters

(Moussa et al., 2001) with a total (sand and mud) mean annual suspended load of about

124 million tons per year (El-Mottassem et al., 2005). The closure of the High Aswan

Dam in 1964 significantly altered the flow and sediment transport regimes in the

Egyptian portion of the Nile River. The long- term annual monthly peak discharges has been reduced from 8430 m3/s to 2550 m3/s, corresponding to the maximum flow release from the dam, and nearly 98% of the sediment is trapped upstream in Lake Nasser

(Shalash, 1980).

In addition, the construction of barrages for irrigation, domestic and industrial water usage and generation of electric power further modified the hydrology and the sediment transport regime in the Egyptian Nile River.

The prediction and quantification of the impacts of the regulated flow and sediment transport regimes on the Egyptian Nile River is a long studied and still poorly constrained problem (Fathy, 1956; Mostafa, 1957; Shalash, 1980). This is partially due to the complexity of the system and partially to the lack of detailed field data.

The first comprehensive study known to the authors on the impacts of the High

Aswan Dam on the Egyptian Nile River is that of Galay et al. (1990), who reported measurements of cross sections and longitudinal profiles collected by the Nile Research

Institute between the 1965 and the 1982. The comparison between pre-and post-dam longitudinal profiles shows that the Egyptian Nile River is experiencing both channel bed aggradation and degradation in different locations and at different rates. In the streamwise coordinate system defined by Galay et al., which will be used throughout this paper, river km (Rkm) 0 corresponds to the Old Aswan Dam, and Rkm 954 corresponds to the Delta Barrage downstream of Cairo.

In particular, Galay et al. divided the Egyptian Nile River into four reaches.

Reach 1 from the Old Aswan Dam to the Isna Barrage – Rkm 0 to Rkm 167, Reach 2 from the Isna Barrage to Nag Hammadi Barrage at Rkm 359, Reach 3 from Nag

Hammadi Barrage to Asyut Barrage at Rkm 545, and Reach 4 from the Asyut Barrage to the Delta Barrage (Figure 2.1).

The upstream 154 Rkm are bedrock controlled. In this reach, erosion of the channel bed alluvial cover was observed during the construction of the High Aswan Dam between 1963 and 1965, while about 0.5 m of in-channel deposition was measured from

1964 to 1985. The causes of this unexpected sediment deposition are unclear. It could be caused by windblown sand or to changes in cross sectional geometry. Channel bed

degradation was observed in Reach 2 with maximum erosion downstream of the Isna

Barrage of about 6 m, three of which were attributed to channel bed degradation, and the other three were associated to changes in channel geometry and meandering pattern.

Significant changes in channel bed elevation were not observed in Reach 3, while diffuse channel bed aggradation was measured in Reach 4. Making reliable prediction of the future changes in Nile River channel geometry, however, remains a problem that requires further investigation.

In the 954 km-long reach of Nile River in Egypt numerous barrages control water diversions for agriculture and municipal uses, navigation and are used for the production of hydroelectric power. The quantification of the impacts of these barrages on the longitudinal river profile is still uncertain due to the combined effects of localized changes in channel geometry, and reductions of the flow rate, and thus of the sediment transport capacity, in the streamwise direction.

In this study, we present a preliminary quantification of the morphodynamic impacts of the High Aswan Dam and of the barrages on the Nile River channel. We developed a one-dimensional model of river morphodynamics, and we studied the combined impacts of the regulated flow and sediment transport regime and of the barrages on the Nile River channel.

The model is zeroed under the assumption that the pre-High Aswan Dam Nile

River was close to equilibrium conditions, as commonly done for field scale applications of morphodynamics models (e.g., Viparelli et al., 2015). We validate the model by comparing measured and numerical changes in channel bed elevation after the construction of the High Aswan Dam. Preliminary predictions of the impacts of the

barrages on the longitudinal river profile are done by modeling the structures as localized reductions in channel depth. Each barrage is associated with a change in flow rate. Field measurements to constrain the amount of suspended bed material diverted at the barrages are not available, and so we hypothesize and test different sediment diversion scenarios.

It is important to mention here that due to the increasing Egyptian population, the water demand - and thus the lateral outflow at each barrage - is also increasing. It is thus necessary to quantify the impacts of these lateral outflows on the morphology of the Nile

River main channel to identify adequate and sustainable river management strategies

(Vella, 2012; Elba et al., 2014).

2.3 NUMERICAL MODEL

The model governing equations are the shallow water equations of open channel flow

(Chaudhry, 2008) and the Exner equation of conservation of bed material, i.e., sand (e.g.,

De Vries, 1965). As in previous models of river morphodynamics, the problem is simplified with the following assumptions and approximations:

1) the study reach is modeled as a sediment feed flume analog wherein the total

amount of sediment is allowed to change in time, because we are interested in the

spatial and temporal changes in channel bed elevation;

2) the volumetric bed material load is assumed to be orders of magnitude smaller

than the flow rate so that the quasi-steady approximation holds (De Vries, 1965);

3) the channel cross section is assumed to be rectangular with constant effective

width to model sediment transport B;

4) the bed material is modeled as uniform sand with characteristic grain size D;

5) flow resistances are modeled with a Chezy formulation;

6) the lateral sediment fluxes associated with channel migration and changes in

channel width are not accounted for. Thus, the washload, i.e., the fraction of the

sediment load in the silt and clay size ranges, is not accounted for in the

morphodynamic calculations;

7) the flow is assumed to be always Froude subcritical; and

8) the interannual variability of flow discharge is simplified in terms of a

characteristic flood flow Qw and a flow intermittency factor If that represents the

fraction of time that the river is morphologically active (Paola et al., 1992).

2.3.1 Flow Equations

The 1D shallow water equations of conservation of flow mass and streamwise momentum respectively take the form (Chaudhry, 2008)

휕퐻 휕푈퐻 + = 0 (2.1) 휕푡 휕푥

휕푈퐻 휕푈2퐻 휕퐻 + = −푔퐻 + 푔퐻푆 − 퐶 푈2 (2.2) 휕푡 휕푥 휕푥 푓 where t and x respectively denote the temporal and the downchannel coordinates, H is the flow depth, U is the mean flow velocity, g is the acceleration of gravity, S is the channel

-2 slope, and Cf is a friction coefficient equal to Cz , where Cz is the non-dimensional Chezy coefficient. Dropping the time dependence in equations (2.1) and (2.2), the equation of mass conservation is reduced to qw = UH, with qw= Qw/B and the momentum equation

(2.2) is reduced to the backwater form

휕퐻 푆 − 푆 = 푓 (2.3) 휕푥 1 − 퐹푟2

0.5 where Fr is the Froude number defined as U/(gH) and Sf is the friction slope equal to

2 Cf Fr . Equation (2.3) is integrated in the upstream direction with a predictor corrector scheme (Chaudhry, 2008), and the downstream boundary condition is expressed in terms of a known water surface elevation  = d.

2.3.2 Bed Material Equations

The equation of conservation of channel bed material – Exner equation – takes the form

휕휂 휕푞 (1 − 휆 ) 푐 = −퐼 푡 (2.4) 푝 휕푡 푓 휕푥

where p = bulk porosity of the bed, c = channel bed elevation (m), If is the flood intermittency, and qt is the volumetric bed material load per unit channel width. We compute the total bed material (sand) load with a calibrated form of the Engelund and

Hansen (1967) (Engelund and Hansen, 1967) relation

0.05 ∗ 2.5 푞푡 = 훽√푅푔퐷 퐷 (휏 ) (2.5) 퐶푓 where R is the submerged specific gravity of the sediment (1.65); 휏∗ is the Shields number and  is an adjustment factor of the load relation that is calibrated during the model zeroing. The Shields Number 휏∗ is defined as (Parker, 2004):

휏푏 휏∗ = (2.6) 휌푅푔퐷

2 where ρ denotes fluid density; and b is the boundary shear stress computed as CfU .

2.3.3 Filed Site and Input Parameters

The 954 km long study reach is the portion of the Nile River from the Aswan High Dam to the Delta Barrage, where significant changes in sediment supply and flows occurred in the past 50 years. Beside the Aswan dams, several barrages have been constructed in

Egyptian reach of the Nile River. The four main Barrage structures shown in Figure 2.1 are the Isna Barrage at Rkm 167, the Nag Hammadi Barrage at Rkm 359, the Asuit

Barrage at Rkm 454, and the Delta Barrage at Rkm 954, which corresponds to the end of the study reach. These structures were built between the 1830s and the 1930s to control navigation and water diversions.

There are two types of characteristic barrage structures, bridge type (old structures), i.e., transverse structures with multiple openings, and dam type for the generation of electricity (new structures) characterized by a continuous transverse structure with a lateral channel. It is reasonable to expect that the old and the new barrage structures have a significantly different morphodynamic impact on the Nile River, due to their different trapping efficiency of sand. In the simulations presented herein, the old type of structures (i.e., bridge type) are considered and modeled as a localized reduction in effective channel width associated with a reduction in flow discharge. In the numerical runs discussed below the discharge diverted from the Nile River main channel upstream of each barrage is based on mean monthly averages at the barrages gauging stations from

1969 to 1988. The mean monthly diverted discharges are 1795 m3/s, 1635 m3/s, and 1307 m3/s respectively at barrages stations of Isna, Nag Hammadi, and Asyut (Abdelbary,

1992b).

Due to the lack of information on the amount of suspended sand diverted at each barrage from the main channel, we consider two limiting cases, 1) no sand is diverted upstream of each barrage, and 2) the amount of sand diverted as each barrage is proportional to the amount of lateral outflow, i.e., if 20% of the flow is diverted upstream of one barrage, 20% of the sand load is also diverted to from the main channel.

The Egyptian Nile River is a large, low slope sand bed river with an average pre-

High Aswan Dam (pre-dam in the continuing of the text) bed slope of about 0.072 m/km.

Due to channel bed degradation in the upstream portion of the modeled reach and to in- channel sediment deposition in its downstream part, the post High Aswan Dam (post-dam in the continuing to the paper) average bed slope decreased to 0.056 m/km in about 20 years (Galay et al., 1990; Abdelbary, 1992b). In addition, Shawki et al. (2005) report significant changes in channel width that occurred after the closure of the High Aswan

Dam. Between the 1950 and the 1987 the top channel width decreased of about 30% from Aswan to the Nag Hammadi Barrage (from about 850 m to about 600 m in Reaches

1 and 2), of about 38% in Reach 3 (from 920 m to 570 m) and of about 54% in reach 4

(from 1000 m to 540 m). Based on these data, in the simulations presented herein, we assume a constant pre-dam top channel width of 850 m and a post-dam top channel width of 583 m. The top channel widths of Shawki et al. represent the distance from bank to bank along the river. However, as commonly done in the engineering practice, we further assume that the effective channel width to model sediment transport, B, can be approximated by the 70% of the top width (e.g., Mooney, 2008), which results in a pre- dam effective width B of 600 m and in a post-dam effective width equal to 410 m.

In large scale preliminary morphodynamic calculations the river is assumed to be morphologically active during floods, and the flow regime is described in terms of a characteristic flood flow Qw (e.g., Parker 2004 and references therein). The characteristic pre-dam flood flow was determined based on flow measurements performed at the

Dongola gauging station in Sudan, i.e., about 780 km upstream of the High Aswan Dam, where monthly flow discharge have been recorded since 1964. The absence of main tributaries between the Dongola station and the Mediterranean Sea guarantees that the monthly averages at Dongola are reasonably representative of the pre-dam flow regime in the Egyptian part of the Nile River.

The Dongola flow measurements show that the flood season in the pre-dam

Egyptian Nile River started in August, peaked in September and ended in October with an average value of 560 – 605 Mm3/day corresponding to a flood flow of 6500 – 7000 m3/s (Sharaf El Din, 1977; Shalash, 1980; Abdelbary, 1992b; Stanley et al., 1998; Shawki et al., 2005; Raslan and Salama, 2015). Thus, the pre-dam Egyptian Nile River was, on average, in flood for three months, and this corresponds to an intermittency factor If of

0.25.

The construction of the High Aswan Dam eliminated the flood flows in the

Egyptian Nile River. The peak flows correspond to the maximum releases from the dam, i.e., 2550 m3/s based on ten-day-mean discharge measured at the Aswan Dam gauging station. Due to the Egyptian water needs the maximum flow releases last on average three months per year, which corresponds to a post-dam intermittency factor If of 0.25 (i.e.,

Shalash, 1980; Abdelbary, 1992a; Shawki et al., 2005; Raslan and Salama, 2015).

Previous studies estimated a pre-dam mean annual sediment load in the Egyptian

Nile River of 124 Mt/yr, 30% of which were made of fine sand with characteristic grain size of about 0.25 mm. This corresponds to a pre-dam mean annual bed material load of

37.2 Mt/yr. The 54% of the pre-dam washload, i.e., the fraction of the sediment load that is not present in the channel bed, was in the silt range and the rest was made of clays

(Abdel-Aziz and De Smedt, 1992; El Moattassem and Nordin, 1992; Makary, 1992;

Abdel-Aziz and Attia, 2003; El-Moattassem et al., 2005). Noting that close to 98% of the

Nile River sediment is trapped in Lake Nasser, the post-dam sediment load at the upstream end of the modeled reach was estimated to be 2.5 Mt/yr, with fractions of sand, silt, and clay respectively equal to 30%, 40% and 30% (Abdel-Aziz and De Smedt, 1992;

El Moattassem and Nordin, 1992; Makary, 1992; El-Moattassem et al., 2005).

The input model parameters, i.e., channel width, sediment size, characteristic flood flow, mean annual bed material load, and friction coefficient are summarized in

Table 2.1. Some of these input parameters are taken as an average value of the model of the study reach. The value of the friction coefficient corresponds to a non-dimensional bankfull Chezy coefficient of 10-11, which is a reasonable estimate for a sand bed stream

(Wilkerson & Parker, 2011). The numerical model is written in Python and the spatial and temporal intervals used in the simulations respectively varied between 2 km and 5 km and 0.01 years and 0.5 years.

2.4 RESULTS

2.4.1 Model Zeroing

The model zeroing is the first phase of a field scale application of a morphodynamic model to quantify the impact of anthropogenic activities on river morphodynamics.

Depending on data availability, model formulation and type of application a model is zeroed for different purposes. For example, in studies to quantify the impacts of dams on fluvial systems, Viparelli et al. (2011) and Nittrouer & Viparelli (2014) zeroed their models to calibrate the relation to compute the bed material load under the assumption that the pre-disturbance study reaches were close to mobile bed equilibrium. To study the feasibility of a delta restoration project in the Mississippi River delta, the model zeroing consisted of the comparison between sand loads at low and high flows to determine if the implemented formulations reasonably reproduced the bed material load (Viparelli et al.,

2015).

Due to the lack of sufficient field data to thoroughly characterize the pre- disturbance morphodynamics of the studied reaches, morphodynamic models are generally zeroed under the assumption that the undisturbed reach was close to conditions of mobile bed equilibrium, i.e., steady and uniform flow and sediment transport conditions (Lauer & Parker, 2008).

Here, as in Nittrouer & Viparelli (2014), the model zeroing is performed to calibrate the  value in the Engelund and Hansen bed material load relation – equation

(2.5). Under the assumption of pre-dam and pre-barrages mobile bed equilibrium conditions, equation (2.3) reduces to the Chezy relation for normal flow. Given the pre- dam slope, characteristic flood flow, and channel width, the Chezy relation is used to

estimate the average pre-dam flood flow water depth, H = 11.6 m, and Shields number,

∗ 휏 f,pre = 2.04. At mobile bed equilibrium, equation (2.4) reduces to If qt = Qtf,pre /B, with

Qtf,pre denoting the pre-dam volumetric mean annual bed material load, and it is used to determine qt, i.e., the pre-dam transport capacity of the characteristic flood flow. Finally, equation (2.5) is solved to estimate the paramter  and thus calibating the equations to compute the bed material load. In particular, the estimated value of the paramter  of the model is 5.2.

2.4.2 Post-Dam Runs

The initial condition for the post-dam runs is the pre-dam and pre-barrages equilibrium channel profile with constant slope of 0.072 m/km and downstream water surface elevation at Delta barrage equal to 15 m above mean sea level (Abdelbary, 1992b). The start date of the post-dam runs is the closure of the High Aswan Dam in 1964. In other words, based on the work by Stanley et al. (1998), we assume that prior to the construction of the High Aswan Dam the control structures of the Nile River did not significantly altered the flow and the sediment transport regimes, and thus the morphodynamics, of the Egyptian portion of the Nile River.

The post-dam runs are performed in two phases, we first neglect the presence of the barrages to identify the impacts of the regulated flow and sediment transport conditions, and then we account for the presence of the barrages. For simplicity and lack of field data, the pre-dam impact of the barrages on the Nile River morphodynamics is neglected in the simulations presented herein, i.e., the initial condition for the post-dam model runs with barrages is the pre-dam and pre-barrages profile with a constant slope of

0.072 m/km. We hope to release this assumption in the near future when new field data will become available.

2.4.2.1 Impacts of the Regulated Flow and Sediment Transport Regime

The long-term evolution of the Egyptian Nile River profile under the regulated flow and sediment transport regime is presented in Figure 2.2 in terms of changes in bed elevation

 – o, where o represents the pre-dam equilibrium bed profile and  the post-dam bed profile. For reference, the grey triangles on the horizontal axis represent the locations of the four main barrages.

Model results are presented for the alluvial reach, i.e., from Rkm 154 to the Delta

Barrage, with continuous lines 20 and 60 years after the closure of the High Aswan Dam, i.e., in 1984 and 2024, after 800 years from the dam closure, and at mobile post-dam equilibrium. The grey dot represents the only available field measurement, i.e., 3 m of channel bed degradation downstream of the Isna barrage ~20 years after the closure of the High Aswan Dam, i.e., in 1984 (Galay et al., 1990).

In agreement with the work by Galay et al. (1990) after 20 years of regulated flow and sediment transport regime (1984) the model does not predict significant changes in channel bed elevation in Reach 2 and 3, and it predicts 0.5 m – 1 m of in-channel deposition in Reach 4, i.e., upstream of the Delta Barrage. According to our model results, the Egyptian reach of the Nile River is evolving towards a new condition of mobile bed equilibrium characterized by an average channel slope of 0.016 m/km

(dashed grey line) with a characteristic water depth during floods H = 12.6 m. This evolution is characterized by the streamwise migration of a wave of channel bed

degradation (continuous grey lines), which is associated with temporary deposition in the downstream most ~100 Rkm. The maximum channel bed degradation is expected to occur in the upstream portion of the domain, and it is on the order of 40 m, the value that is comparable to previous estimates (Fathy, 1956). The maximum transient in-channel sediment deposition is estimated to be on the order of ~6.5 m.

The predicted channel bed erosion in the modeled domain is clearly unsustainable. The simplified numerical runs presented in Figure 2.2 show that channel bed degradation in the Egyptian Nile River is partially due to a deficit of sediment downstream of the High Aswan Dam. In other words, the sediment transport capacity of the regulated flow is higher than the sediment input rate into the modeled reach, and this results in the erosion of the channel bed.

The black dash-dot line in Figure 2.2 represents the net changes in channel bed elevation at mobile bed equilibrium in the case of a sand augmentation project characterized by the present flow regime associated with an input rate of sand in the modeled reach of 6.5 Mt/yr of sand. This equilibrium condition is characterized by a maximum channel bed erosion of ~3 m at the Isna Barrage and ~7 m of deposition at the

Delta Barrage, with a final equilibrium slope of 0.06 m/km and a flood depth H = 8 m.

The predicted in-channel deposition will not be associated with flooding because the water surface elevations are contained within the pre-dam channel cross section.

The discussion of the feasibility of this sand augmentation project goes beyond the scope of this paper. It is necessary to mention here, however, that we are working on the feasibility study of a sand augmentation project characterized by sediment mining in

Lake Nasser delta, i.e., the delta that is naturally forming upstream of the High Aswan

Dam. This sediment will be conveyed downstream of the High Aswan Dam by slurry pipelines, as commonly done in large mining projects (e.g., Paterson, 2012).

2.4.2.2 Impacts of the Barrages

The impact of the barrages on the morphodynamics of the lowermost 954 km of the Nile

River is modeled as a streamwise reduction in flow rate and sand load associated with a localized reduction in channel width. In particular, based on the design of the old barrages we assume that the effective width for sediment transport at the barrage locations is equal to 25% of the effective post-dam channel width (Abu-Zeid, 1995; Attia et al., 2005).

The effects of the reductions in 1) channel width, 2) flow rate and 3) flow rate and sediment load on the transient – 60 years after dam closure - and the equilibrium profiles of the modeled reach, are presented in Figures 2.3 and 2.4 with grey, red and green lines respectively in terms of bed elevation changes from the pre-dam equilibrium profile. For reference, the black lines represent the results of the post-dam simulations discussed in

Figure 2.2.

The results of (Figs 2.3, 2.4) show that the morphodynamic effect of a localized change in channel width is not a change in the overall slope of the fluvial reach. It is a local scour hole, whose geometric details have to be modeled with detailed 2D or 3D formulations (grey line).

A reduction in flow rate (green and red lines), which is associated with a reduction in sand transport capacity, results in in-channel deposition downstream of the diversion structure (see also Viparelli et al., 2015). In particular, 60 years after dam

closure (Figure 2.3) this in-channel deposition downstream of the barrages in the upstream part of the domain is largest in the simulations with a reduction in flow rate only (red line). In the downstream most ~300 Rkm the in-channel deposition at the barrages is largest when the reduction in flow rate and channel width is associated with a reduction in sand load (green line in Figure 2.3). At mobile bed equilibrium, the upstream channel erosion is smallest in the run with flow reduction only - ~35 m. While in-channel deposition in the downstream part of the modeled reach is highest in the runs with no reduction in sand load.

The results of Figure 2.3 are necessary to interpret the model output in the runs with reductions in channel width and flow rate presented in Figure 2.5, where the grey lines represent the post-dam simulation results obtained for the case of reduction in channel width only. The blue line of Figure 2.5 pertains to simulations with reductions in channel width and flow rate at the barrages, while the gold lines represent model results with streamwise reductions in channel width, flow rate and sand load.

The large scale effects of the barrages presented in Figure 2.5 and 2.6 are in agreement with the model results of (Figs 2.3, 2.4). The predicted erosion in the upstream part of the modeled reach is highest if the barrages are modeled as localized water and sand diversions (gold line), and the deposition in the downstream part of the domain at equilibrium is highest when the streamwise reduction in flow rate is accounted for in the calculations. Recalling that the post-dam equilibrium slope of the modeled reach in absence of flow and sediment diversions is 0.016 m/km, the overall post-dam slope of the system increases to 0.021 m/km when the barrages are modeled as localized water diversions, and to 0.0165 m/km if the barrages are modeled as water and sand diversions.

Finally, it is interesting to note that the model predicts localized scour depths at the barrages 60 years after dam closure of ~3.5 m at the Isna Barrage, ~2.7 m at the Nag

Hammadi Barrage and of ~2.5 m at the Asyut Barrage. These scour depths, as well as the deposition in the reached downstream of the barrages, are of the same order of magnitude of those reported in the literature (Galay, 1983; Galay et al., 1990; and Abdelbary,

1992a).

2.5 CONCLUSIONS

In this study, we developed and implemented a model of river morphodynamics that is able to account for the presence of bridge-type of barrages. The model is applied to study the effect of the controlled flow and sediment transport regime on the post High Aswan

Dam 954 km long Egyptian reach of the Nile River. Preliminary model results show that

1) the Nile River is experiencing diffuse channel bed degradation that can be

controlled with sand augmentations;

2) the long term effect of the water diversions at the barrages is a reduction of

channel bed erosion in the upstream part of the modeled reach associated with

higher in-channel deposition in the lower ~250 Rkm;

3) the morphodynamic effect of barrages modeled as localized changes in channel

width is a scour hole downstream of the structure.

Table 2.1 Input model parameters. Data source is the Nile Research Institute (NRI) database.

Parameter Definition Value (s) unit

3 Qw,pre Pre-dam water discharge 7000 m /s

3 Qw,post Post-dam water discharge 2550 m /s

If Flood intermittency 0.25 ---

Bpre Effective channel width (pre-dam) 600 m

Bpost Effective channel width (post-dam) 410 m

S Pre-dam bed slope 0.072 m/km

Qtf,pre Bed material load (pre-dam) 124 Mt/yr

Qtf,post Bed material load (post-dam) 2.5 Mt/yr

Cf Friction coefficient 0.0083 ---

D Grain size diameter 0.25 mm

Mediterranean Sea

Nile Delta

Delta Barrage

Nile River

Asyut Barrage

Nag Hammadi Barrage Isna Barrage

Old Aswan Dam High Aswan Dam ³ Lake Nasser 0 km 520 SUDAN Study Area

Figure 2.1. Nile River with location of the main infrastructures in the study reach, Egypt. Image is from Google Earth.

Figure 2.2. Model results on the impact of the High Aswan Dam on the long profile of the Nile River.  represents the bed elevation and o is the pre-dam equilibrium bed elevation. The black dot line represents a condition of no net erosion and no net deposition.

4 Depostion

(m) 0 o

 Erosion -  No barrages -4 Width reduction

Flow reduction

-8 Flow and load reduction

Reach 1 Reach 2 Reach 3 Reach 4 -12 0 200 400 600 800

Downchannel distance from the Old Aswan Dam (km)

Figure 2.3. Effects of reductions in channel width, flow and flow and sand load on the long term evolution of the modeled reach at 60 years after dam closure – 2024 of Figure 2.2.

5 Depostion

-5 (m) Erosion

o Depostion 

- -15 No barrages  Width reduction -25 DepostionErosion Flow reduction Flow and load reduction -35

ReachDepostionErosion 1 Reach 2 Reach 3 Reach 4 -45 0 200 400 600 800 Downchannel distance from the Old Aswan Dam (km) DepostionErosion

Figure 2.4. Effects Erosionof reductions in channel width, flow and flow and sand load on the long term evolutionDepostion of the modeled reach at mobile bed equilibrium.

DepostionErosion

Erosion 27

4 Depostion

(m) 0

o Depostion

 -

 Erosion -4 Width reduction Depostion Erosion Width and flow reduction Width, flow and load reduction -8 Depostion Erosion Reach 1 Reach 2 Reach 3 Reach 4 -12 Depostion 0 Erosion 200 400 600 800

Downchannel distance from the Old Aswan Dam (km) Erosion

Erosion Figure 2.5. Effects of the barrages on the long term evolution of the modeled reach at 60 years after dam closure – 2024 of Figure 2.2. Erosion

Erosion

5 Depostion

(m) -5 Erosion

o Depostion  -  -15 Erosion Width reduction Depostion

-25 Width and flow reduction Erosion Depostion -35 Width, flow and load reduction

Reach 1 Reach 2 Reach 3 Reach 4 -45 Erosion Depostion 0 200 400 600 800 Downchannel distance from the Old Aswan Dam (km) Erosion Depostion

Erosion Figure 2.6. Effects ofDepostion the barrages on the long term evolution of the modeled reach at mobile bed equilibrium . Erosion Depostion

Erosion 28

CHAPTER 3

MODELING THE IMPACT OF CONTROLLED FLOW AND SEDIMENT RELEASES FOR THE RESTORATION OF THE NILE RIVER, EGYPT1

3.1 INTRODUCTION

The Nile River, which is the main source of water for Egypt, has been intensely regulated since the 1800s. Barrages were constructed in the 1830s to divert water for agricultural and municipal uses and to control navigation (Volker et al., 1993; Conniff et al., 2012).

The Old Aswan Dam was built in the early 1900s to sustain irrigation by storing water during the flood season and releasing it during the low flow season (Shahin, 1993; Abu-

Zeid, 1995; Cook, 2013). The construction and operation of these structures, however, did not dramatically modify the Nile River hydrology and sediment transport regime.

Seasonal floods occurred every year for about three months, fertile silt was deposited on the agricultural fields, saltwater intrusion and channel siltation in the Nile delta were naturally controlled, flood water and sediment were delivered to the delta shoreline

(Shalash, 1980; Stanely et al., 1998; El Banna and Frihy, 2009).

The closure of the High Aswan Dam and the impoundment of Lake Nasser in the

1960s for multi-year water storage and hydropower generation dramatically impacted the

Egyptian Nile River and the delta. The system is shown in Figure 3.1, where the control

1 Basim M. Al-Zaidi, Ahmed Moussa, Zeyad A. Sulaiman, and E. Viparelli. To be submitted to Water Resources Research.

structures relevant for this study, i.e., the Aswan dams (High and Old) and four main barrages (Isna Barrage, Nag Hammadi Barrage, Asyut Barrage, and Delta Barrage) are indicated. Streamwise distances are measured in river kilometers (Rkm) downstream of the Old Aswan Dam. In this reference system, the Isna Barrage is at Rkm 167, the Nag

Hammadi Barrage at Rkm 359, the Asyut Barrage at Rkm 545, and the Delta Barrage at

Rkm 954 (Hammad, 1972; Galay et al., 1990; Abdelbary, 1992a).

The closure of the High Aswan Dam eliminated the annual floods, and high flow releases occur when the water demand is highest, not during the natural flood season.

Further, ~98% of the sediment load is trapped in the High Aswan Dam Reservoir.

Consequences of the dam closure have been widespread channel erosion associated with changes in channel morphology in the upstream part of the Egyptian Nile River, wetland loss and shoreline retreat in the delta (Simaika, 1970; Hammad, 1972; Shalash, 1980;

Galay et al., 1990; Abdelbary, 1992a; Abu Zeid et al.,1997; Stanely and Warne, 1998).

The Egyptian annual share of Nile River water is set by international treates at

55.5 billion of meter cubes, which is not sufficient to fulfill the current Egyptian water needs (Mohie El-Din and Moussa, 2016), and thus only a small amount of water is currently delivered to the Egyptian coast (Stanley, 1996; Milliman, 1997).

The paucity of fresh water in the Nile River delta associated with the high population density (Syvitski and Saito, 2007; Syvitski, 2008; Syvitski et al., 2009), the development of industrial areas, intensive agriculture (El-Raey, 1997; Zeydan, 2005) and water reuse for irrigation (El-Din, 2013) has resulted in widespread delta pollution, reduction soil quality, salination of cultivated land, wetland losses, and saltwater intrusion (Abdel-Shafy, 2002; El Banna and Frihy, 2009).

Due to the absence of floods and deposition of fertile silt on the agricultural fields, the use of fertilizers and pesticides lead to aquatic weed growth with consequent blockage of the waterways, sediment trapping, increased water losses for evapotranspiration (Milliman, 1997; Zeydan, 2005; El Ella et al., 2016), and groundwater contamination (Zeydan, 2005).

In summary, the Nile River and its delta present severe water-related problems that directly affect the Egyptian population and the natural environment (Aleem, 1972;

El-Raey, 1997; Abdel-Shafy et al., 2002; El Ella, 2016).

The idea of delta restoration was introduced to reduce/reverse wetland loss and shoreline retreat in the Mississippi River delta, Louisiana, USA (Kim et al., 2009; Paola et al., 2011). The restoration project proposed by Kim et al. (2009) for the Mississippi

River delta was characterized by a system of engineered, land-building diversion structures to transport water and sediment from the Mississippi River main channel to drowned areas, where natural delta-building process may result in the formation of new delta lobes (Paola et al., 2011). This restoration strategy is appropriate for the restoration of the Mississippi River delta because the Mississippi River flow regime and the sand supply did not significantly change in recent times and will likely remain constant in the near future (Nittrouer and Viparelli, 2014). Land-building diversions, on the other hand, are clearly inapplicable to control wetland losses and shoreline retreat in the Nile River delta, where only a very limited amount of water is available for restoration purposes.

Here we present modeling results on the impacts of a restoration project for the

Nile River-delta system downstream of Lake Nasser (Figure 3.1) characterized by controlled flow releases combined with sediment augmentations at Aswan. The

controlled flow releases will restore a semi-natural hydrograph in the Nile River, and the sediment augmentations will control the ongoing channel bed degradation in the upstream portion of the Egyptian part of the Nile River.

Our long term objective is to assess the feasibility of a restoration project for the

Nile River and its delta. This paper summarizes the first part of the feasibility study, which consisted in the quantification of 1) the changes in channel bed elevation and slope associated with the proposed restoration project, 2) the flow rates delivered to the delta apex, and 3) the corresponding mean annual bed material (sand) load supplied to the delta. These calculations allowed us to constrain a sand budget for the Nile River and to determine if the proposed controlled flow releases and sediment augmentations will induce flooding in urban areas and ensure safe navigation. Throughout this paper, the bed material is defined as the portion of the sediment load that is found in the channel bed and on the lower part of the banks, and that controls the channel slope and width (Paola,

2001; Church, 2006).

3.1.1 Water and Sediment Availability for the Proposed Restoration Project

Previous estimates of water availability in Egypt suggest that an average annual water volume of ~10 billions of cubic meters can be saved by improving the irrigation system and reducing the water losses in urban networks (Waterbury, 1997; Stanley and Warne,

1998; AsusAID, 2011). The agricultural sector uses between 80-85 % of Nile River water and the prevalent irrigation system is surface irrigation with less than 70% water efficiency (Stanley, 1996; Nicholas, 1999; Zeydan, 2005; Bohannon, 2010; AusAID,

2011; Mohie El-Din and Moussa, 2016).

The volume of water saved with the improvement of the Egyptian irrigation system is used here as water source for the restoration project. We propose to use the 10 billions of cubic meters of water to increase the water discharge during the natural flood season, i.e., from August to October, and restore a semi-natural hydrograph for the Nile

River and its delta. Thus, there are no proposed changes in the total annual volume of water released from the High Aswan Dam, which will also be operated as a flow control structure to re-establish the interannual variability of flow discharges in the Nile River.

The hydrographs used in the numerical simulations presented below should be considered averages over many years (Wong and Parker, 2006). The hydrograph released each year will depend on water availability, that is, during droughts less water will be available for restoration purposes, while large volumes of water can be used for river- delta restoration in wet years (e.g., Viparelli et al., 2011). Finally, we do not consider the impact of climate change on the Nile River hydrology because different climate change scenarios result in opposite predictions of the future Nile River flow regime (El-Din,

2013).

The proposed controlled flow releases are characterized by flows that are higher than the present releases from August to October, this will likely result in accelerated rates of channel erosion in the upstream part of the study reach, compared to the erosion rates that have already been observed. We thus propose to combine the controlled flow releases with sand augmentations to reduce/reverse the upstream erosion of the channel bed.

Sand can be mined from the High Aswan Dam Reservoir, where a delta is naturally forming and gradually shortening the life of the reservoir. This sediment can be

conveyed downstream of the Old Aswan Dam with slurry pipelines, commonly used in large-scale mining projects (e.g., Paterson, 2012). Noting that the mean annual sand load deposited in the High Aswan Dam Reservoir is larger than the mean annual sand load used for the restoration project and that the flood flows downstream of the High Aswan

Dam will be smaller than those entering the High Aswan Dam Reservoir, sand availability is not expected to be a problem.

A similar restoration approach has been proposed for the Colorado River delta in the Gulf of California, Mexico (Briggs et al., 1999; Randle et al., 2007), where the water resources in the Colorado River basin can be managed to generate flood flows at a sufficient rate to induce overbank flooding and to flush pollutants from the delta. The source of this flood water can be secured by the surplus water and waste flows from agriculture (Briggs et al., 1999). For the sediment management, it has been shown that sand and fine sediment can be delivered to the Colorado River downstream of the dams with slurry pipelines (Randle et al., 2007), which is the most efficient sediment conveyance method for large quantities of sediment over long distances (Randle et al.,

2007; Paterson, 2012).

3.2 THE EGYPTIAN NILE RIVER

The Nile Research Institute (NRI) is the Egyptian agency responsible for the protection and development of the Nile River, and provided the field data for this study. Our study reach originates at the Old Aswan Dam and ends at the Delta Barrage, which corresponds to the delta apex located North of Cairo city (Figure 3.1).

3.2.1 Barrages

The original barrage structures were characterized by multiple waterway openings, and the flow was regulated with gates. These barrages are being substituted by dam-type structures for hydropower generation. The original barrages had a fairly limited ability to trap sand (Galay et al., 1990; Abdelbary, 1992a; Sattar and Raslan, 2014), while the sand trapping efficiency of the modern dam-type barrages is expected to be considerably larger. However, due to the scale of the modeling exercises, the lack of details on the design and operation of the dam-type barrages and on the dates of completion of the renovation works, we model the four main barrages in terms of specified elevations of the channel bed and of the water surface associated with local reductions in water discharge and sand load.

3.2.2 Hydrology

The hydrology of the Egyptian portion of the Nile River is described in terms of monthly flow discharges based on the ten-day-mean discharge recorded at the Old Aswan Dam.

The mean monthly hydrographs are presented in Figure 3.2, where dashed columns represent the pre-High Aswan Dam (pre-dam, measurement period 1938 - 1963) mean monthly hydrograph, and the light grey columns with thick borders are the post-High

Aswan Dam (post-dam, measurement period 1969 - 2009) mean monthly hydrograph.

As shown in Figure 3.2, the pre-dam monthly hydrograph was characterized by a three month-long flood season, which started in August, peaked in September and ended in October (Shalash, 1980; Borsch, 2000; Shawki et al., 2005). The average maximum

monthly discharges varied between 560-605 Mm3/day corresponding to flood flows of

6500-7000 m3/s (Shalash, 1980; Abdelbary, 1992a).

Since the closure of the High Aswan Dam, the maximum Nile River flows occurred in the season of highest water demand, from June to August, with maximum monthly discharges that of ~2560 m3/s. This corresponds to a flood flow reduction of more than 60% from the natural condition. Due to the dam operation policy, the post-dam minimum monthly discharges have increased to ensure navigation and to fulfill the

Egyptian water demand (Shalash, 1980; Abdelbary, 1992a; Saad, 2002; Shawki et al.,

2005; Syvitski et al., 2007; Raslan et al., 2015).

The only available data to quantify the Nile River flow reduction at the barrages is the mean annual diverted volume. Here, for simplicity, we assume that the mean monthly flow diverted at each barrage does not change from one month to the other. More complex and realistic scenarios can be considered if new data will become available or if this study will move to a more advanced and applied phase. The mean monthly discharges diverted at the barrages are 1795 m3/s, 1635 m3/s, and 1307 m3/s respectively at Isna, Nag Hammadi, and Asyut (Hammad, 1972; Abdelbary, 1992b; El-Nefary, 2010).

Water diversion at the Delta Barrage, which is the downstream end of the study reach, is not accounted for in this study.

3.2.3 Sediment Load

The pre-dam mean annual sediment load to the Egyptian reach of the Nile River was estimated to be 124 Mt/yr (Shalash, 1980; El-Mottassem et al., 2005) with a volume fraction content of sand equal to 0.3 and corresponding mean annual sand load of about

37.2 Mt/yr (Simaika, 1970; Hammad, 1972; Shahin, 1985). The median grain size (D50) of the Nile River sand in Egypt was about 0.25 mm (Simaika, 1970; Hammad, 1972;

Gaweesh and Gasser, 1991; Saad, 2002). The volume fraction content of pre-dam wash load in the silt range was 70%, and the rest was clay (Simaika, 1970; Abdel-Aziz et al.,

1992; El Moattassem et al., 2005).

The post-dam sediment load at the Old Aswan Dam is estimated to be 2.5 Mt/yr, and the fractions of sand, silt, and clay are 0.3, 0.4, and 0.3 respectively (Inman et al.,

1985; Abdel-Aziz et al., 1992; El Moattassem et al., 1992; Makary, 1992; El Moattassem et al., 2005). The D50 of the post-dam sand is 0.25 mm, and D90, diameter such that 90% of the sediment is finer, is 0.67 mm (Saad, 2002; Abdel-Fattah et al., 2004). The bed material grain size does not vary significantly from the Old Aswan Dam to the delta

(Simaika, 1970; Saad, 2002) and, since the closure of the High Aswan Dam in 1964, the bed materials has become more uniform (Gaweesh and Gasser, 1991; Abdelbary, 1992b;

Saad, 2002).

3.2.4 Channel Geometry and Longitudinal Profile

Significant changes in channel geometry and longitudinal profile have been documented on the Egyptian Nile River since the closure of the High Aswan Dam. The average pre- dam slope was ~0.072 m/km (Simaika, 1970; Hammad, 1972; Gaweesh and Gasser,

1991; Abdelbary, 1992b). About 20 years after the High Aswan Dam closure, the water surface slope at a discharge of 2000 m3/s decreased from ~0.072 m/km to an average value of 0.056 m/km (Galay et al., 1990; Abdelbary, 1992b; Saad, 2002).

The average pre-dam channel width was ~870 m between the Old Awan Dam and the Isna Barrage, ~800 m between the Isna Barrage and the Nag Hammadi Barrage, ~920 m from the Nag Hammadi Barrage to the Asyut Barrage, and ~1000 m between the Asyut

Barrage and the Delta Barrage. The post-dam average channel width of the Nile River is

~635 m from the Old Aswan Dam to the Isna Barrage, 570 m from the Isna Barrage to the Nag Hammadi Barrage, 590 m from the Nag Hammadi Barrage to the Asyut Barrage, and 540 m from the Asyut Barrage to the Delta Barrage. These values represent the top channel widths.

Field measurements performed ~20 years after the High Aswan Dam closure showed that 1) about 3 m of channel bed degradation occurred downstream of the Isna

Barrage (Rkm 167), 2) between 0.5 m – 1 m of in-channel deposition occurred upstream of the Delta Barrage (Rkm 954), 3) significant changes in channel bed elevation were not observed in the central part of the study reach, and 4) no net change in bed elevation was measured near the Old Aswan Dam due to the presence of exposed bedrock (Galay et al.,

1990; Abdelbary, 1992a). This bedrock reach extended for about 154 km downstream the dam and is not modeled in the present study.

The average water surface elevation (above mean sea level) is equal to 78.6 m at the Isna Barrage, 65.4 m at the Nag Hammadi Barrage, 49.5 m at the Assuit Barrage, and

~15 m at the Delta Barrage, i.e., at the end of the study reach (Abdelbary, 1992b; El-

Nefary, 2010).

3.3 THE NUMERICAL MODEL

The model governing equations are the shallow water equations of open channel flow

(Chaudhry, 2008) and the equation of conservation of bed material, i.e., the Exner equation (De Vries, 1965; Parker, 2004). These equations are simplified with the following assumptions and approximations for the 1D morphodynamic modeling of the

~950 km long reach of the Nile River presented herein:

1) the volumetric bed material load is orders of magnitude smaller than the flow

discharge so that the quasi-steady approximation holds (De Vries, 1965);

2) the bed material is modeled as uniform sand with characteristic grain size D =

D50, as commonly done in simplified morphodynamic models (e.g., Viparelli et

al., 2015);

3) the flow is assumed to be always Froude subcritical, as appropriate for large, low-

slope sand bed systems (e.g., Wright and Parker, 2004a, b);

4) the channel cross-section is assumed to be rectangular with constant effective

width, B (e.g., Galay et al., 1990; Abdelbary, 1992a; Wright and Parker, 2005;

Moussa, 2016). This effective width is approximated by the 70% of the top width,

i.e., the distance from the top one bank to the top of the other river bank (Mooney,

2008);

5) while in-channel sediment transport processes are explicitly modeled, the

exchange of sediment between the river channel and the floodplain is not

accounted for, i.e., the overbank deposition of suspended sediment during floods

is assumed to be minimal and bank erosion and deposition for channel migration

are assumed to be equal (Viparelli et al., 2015).

The numerical model is written in Python. The model domain is divided into M-1 intervals bounded by M computational nodes. The temporal and spatial intervals used in the simulations respectively varied between 3.5 days and 73 days, and 2 km and 4 km (M is set equal to 477 and 238).

3.3.1 Flow Equations

In the case of a rectangular cross section, the 1D shallow water equations of mass continuity and streamwise momentum conservation take the form (Chaudhry, 2008).

휕퐻 휕푈퐻 + = 0 (3.1) 휕푡 휕푥

휕푈퐻 휕푈2퐻 휕퐻 + = −푔퐻 + 푔퐻푆 − 퐶 푈2 (3.2) 휕푡 휕푥 휕푥 푓

where H is the flow depth, U is the depth-averaged flow velocity, Cf is the bed friction coefficient, g is the acceleration of gravity, S is the channel slope, t and x respectively denote a temporal and a streamwise (downchannel) coordinate. The time derivatives in equations (3.1) and (3.2) are dropped for the quasi-steady approximation, so that the equation of mass conservation reduces to qw = UH, with qw denoting the flow rate per unit channel width, and the momentum equation simplifies in

휕푈 휕퐻 푈퐻 + 푔퐻 − 푔퐻푆 = −퐶 푈2 (3.3) 휕푥 휕푥 푓

Dividing equation (3.3) by gH and recalling that the bed slope S is defined as

S  c / x , with c denoting the channel bed elevation, equation (3.3) is rewritten as

휕퐸 = −푆 (3.4) 휕푥 푓

2 where E denotes the specific energy 퐸 = 휂푐 + 퐻 + 푈 /2푔 and Sf represents the friction

2 slope defined as CfFr , with Fr being the Froude number 퐹푟 = 푈⁄√푔퐻. The downstream boundary condition for equation (3.4) is expressed in terms of a known water surface elevation at the downstream boundary, d :

휉푑(푡) = 휂푐|푑 + 퐻|푑 (3.5)

where the subscript d denotes the downstream boundary, 휂푐|푑 and 퐻|푑 are respectively the channel bed elevation and water depth at the downstream end of each model subreach. The time dependence of d in equation (3.5) indicates that the model can explicitly account for temporal changes of the downstream water surface elevation.

Flow resistances are computed with the Wright and Parker (2004a, b) formulation for large, low slope alluvial rivers. In this formulation, the friction coefficient Cf is defined as

1 푈 8.32 퐻 ⁄6 −1/2 (3.6) 퐶푓 = = ( ) 푢∗ 훼 푘푐

0.5 where 푢∗ denotes the shear velocity which defined as (b/) with b denoting the bed shear stress and  the water density,  is a parameter that accounts for stratification

effects associated with suspended sediment transport and kc is the composite roughness height, which accounts for the presence of bedforms.

To implement the Wright and Parker formulation in a gradually varyied flow model, the bed slope of the original formulation has to be substituted with the friction slope Sf (Viparelli et al., 2015). Thus, the relation to compute the parameter  takes the form

퐶 0.77 퐶 1 − 0.06 ( 5) 𝑖푓 5 ≤ 10 푆 푆 훼 = 푓 푓 (3.7) 퐶5 퐶5 0.67 − 0.0025 ( ) 𝑖푓 > 10 { 푆푓 푆푓

with C5 denoting the suspended sediment concentration at a distance equal to five percent of the flow depth above the channel bed.

In equilibrium conditions, C5 is equal to the non-dimensional entrainment rate of sediment in suspension Es. Due to the lack of predictors for C5 under disequilibrium conditions, we assume that C5 = Es under slowly varying disequilibrium conditions

(Parker, 2004; Viparelli et al., 2015). In the Wright and Parker formulation, the relation to compute Es takes the form

훽퐴푋5 퐸 = 푠 훽퐴 (3.8) 1 + 푋5 0.3 where A is a constant equal to 7.8×10-7 (Wright and Parker, 2004b),  is a calibration parameter to be determined in the model zeroing (e.g., Nittrouer and Viparelli, 2014), and

X is the non-dimensional parameter defined as a representative of bed shear stress and defined in equation (3.9) as

푢∗푠푘 0.6 0.08 푋 = ( 푅푝 ) 푆푓 (3.9) 푠

with 푢∗푠푘 denoting the shear velocity associated with skin friction, vs the particle settling

0.5 velocity and Rp the particle Reynolds number defined as (RgD) D/. Here R denotes the submerged specific gravity of the sediment (1.65) and  is the kinematic viscosity of water.

0.5 The shear velocity associated with skin friction 푢∗푠푘 is equal to (bsk/) , with

bsk denoting the bed shear stress associated with skin friction (Parker, 2004). The Wright and Parker (2004b) relation to partition the flow resistances between skin friction and form drag takes the form

∗ ∗ 0.7 0.8 휏푠푘 = 0.05 + 0.7(휏 퐹푟 ) (3.10)

∗ ∗ where 휏 denotes the Shields number and 휏푠푘 is the Shields number associated with skin

∗ ∗ friction, i.e., 휏 and 휏푠푘 are non-dimensional bed shear stresses respectively defined as the ratio between the bed shear stresses b and bsk divided by RgD (Parker, 2004).

Equations (3.6), (3.7), (3.8) and (3.10) represent a system of four equations in the five unknowns Cf, , Es, 푢∗푠푘, and kc. Thus, one more equation is needed to close the problem. The fifth equation describes how the ratio between the composite roughness height kc and the roughness height associated with skin friction, ks, vary as a function of the ratio between b and bsk. This relation takes the form (Wright and Parker, 2004b)

∗ 4 푘푐 휏 = ( ∗ ) (3.11) 푘푠 휏푠푘

where the roughness height associated with skin friction ks is taken equal to 3D90, with

D90 denoting the diameter such that 90% of the bed material is finer.

Equation (3.4) is integrated in the upstream direction with a first order, finite difference scheme. We divide the modeled reach into the four subreaches of Figure 3.1, i.e., from the downstream end of the bedrock reach to the Isna Barrage (subreach 1), from the Isna Barrage to the Nag Hammadi Barrage (subreach 2), from the Nag Hammadi

Barrage to the Asyut Barrage (subreach 3), and from the Asyut Barrage to the Delta

Barrage (subreach 4).

Equation (3.4) with the boundary condition given in equation (3.5) proceeds for each subreach as follows. Given the water surface elevation at the downstream end of the modeled subreach, the water depth at the last computational node, Hd, is computed with equation (3.5) and the mean flow velocity Ud is computed with the equation of conservation of mass as qw/Hd. Equations (3.6)-(3.11) are then iteratively solved to compute the friction slope Sf, and then equation (3.4) is integrated to compute the specific energy E one node upstream. When the specific energy E is known in a computational node, U and H are iteratively computed using the definition of specific energy, the equation of conservation of mass, and by assuming Froude subcritical flow conditions.

Equations (3.6)-(3.11) are then iteratively solved, and the specific energy E is then computed at the next computational node upstream.

3.3.2 Bed Material Equations

The change in channel bed elevation is computed with the equation of conservation of bed material, i.e., the Exner equation (De Vries, 1965; Parker, 2004)

휕휂 휕푞 (1 − 휆 ) 푐 = − 푡 (3.12) 푝 휕푡 휕푥

where p is the bulk porosity of the bed, c is channel bed elevation, and qt is the total

(suspended plus bedload) volumetric mean annual bed material load per unit channel width. In each modeled subreach, equation (3.12) is integrated in time with a first order, finite difference scheme with a specified upstream sediment load as boundary condition.

The total mean annual bed material load, Qt, is computed as the average over the cycled hydrograph of the bed material transport capacities for the different flow rates considered in the simulations, that is

12 푄푏푚 = ∑ (푄푏푚,푏,푗 + 푄푏푚,푠,푗)푝푗 (3.13) 푗=1 where 12 represents the number of monthly flows in the annual hydrograph, the subscript j denotes the generic monthly flow Qj, pj is the average fraction of the time in which the flow is equal to Qj (1/12 in this study), Qbm,b and Qbm,s denote respectively the bedload and suspended sand transport capacities of the flow.

The volumetric bedload transport capacity is computed with the Ashida and

Michiue (1972) relation

∗ ∗ 푄푏푚,푏 = 17√푅푔퐷퐷퐵(휏푠푘 − 0.05)(√휏푠푘 − √0.05) (3.14)

where Qbm,b denotes the volumetric bed material load, and B is the channel width.

The volumetric suspended bed material transport capacity is computed using the

Wright and Parker (2004b) formulation as

1 9.7 퐻 ⁄6 푄푏푚,푠 = 퐶5푢∗퐻퐵 ( ) 퐼 (3.15) 훼 푘푐 where I denotes the integral in the direction normal to the channel bed of the product between the flow velocity and the volumetric suspended sediment concentration. Here I is computed with the following approximate equation, which approximates the integral within about 10% (Wright and Parker, 2004b)

0.679푒푥푝(−2.23푍푅) 푓표푟 푍푅 ≤ 1 퐼 ≅ { −1.44 (3.16) 0.073푍푅 푓표푟 푍푅 > 1

where ZR is the Rouse number defined as

푠 푍푅 = (3.17) 훼휅푢∗ with being the von Karman constant set equal to 0.4 in the simulations presented herein.

3.4 MODEL ZEROING

The model zeroing was performed in two phases, pre-dam and post-dam zeroing. The pre-dam zeroing was done to calibrate the relation for the entrainment of sand in suspension, equation (3.8), which was not derived with data collected in the Nile River basin (Wright and Parker, 2004a, b) and to determine a reasonable pre-dam longitudinal profile to perform the post-dam calculations. The objective of the post-dam zeroing was to verify that the morphodynamic model with the calibrated equation (3.8) reasonably captured the post-dam changes in channel bed elevation, and the measurements of

suspended sand load along the modeled reach. Model parameters used in the zeroing runs are summarized in Table 3.1.

3.4.1 Pre-dam Zeroing

Field data on the total (sand plus mud) suspended load of the pre-dam Nile River suggest that the Egyptian reach of the Nile River might not have been in equilibrium prior to the construction of the High Aswan Dam. Hassan (1997) and Shalash (1980) reported estimates of aggradation rates of the Nile River channel on the order of 1 mm/yr for the past ~4000 years. Abdelbary (1992b) showed a ~25% decline of the pre-dam total suspended load between Aswan and the Delta Barrage (Figure 3.1), but information on the spatial changes in the grain size of the suspended load is not available. In other words, we do not know if the reported ~25% decrease in total suspended load was associated with preferential deposition of sand in the channel, preferential deposition of mud on the floodplain or a combination of the two.

Recalling that ~30% of the pre-dam Nile River suspended load was composed of sand (Simaika, 1970; Hammad, 1972), we used this value to estimate the pre-dam suspended sand loads within the modeled reach of the Nile River. Thus, we assumed that everywhere in the modeled reach the volume fraction content of suspended sand was 0.3, and that in the pre-dam Nile River there was a ~25% decrease in suspended sand load between Aswan and the Delta Barrage.

We performed the pre-dam model zeroing in two steps, 1) calibration of the entrainment relation under the assumption of equilibrium, and 2) model simulations to estimate a non-equilibrium, pre-dam longitudinal profile of the study reach. It is

important to mention here that due to lack of field data prior to the construction of the

High Aswan Dam we did not account for the presence of the barrages during the pre-dam model zeroing (e.g., Galay et al., 1990), i.e., the modeled reach was not divided into the subreaches of Figure 3.1.

Under the assumption that the pre-dam Egyptian portion of the Nile River was in equilibrium, we estimated the value of the parameter in the equation (3.8) such that, given the pre-dam average hydrograph (Figure 3.2) and mean annual sand load (37.2

Mt/yr), the reach-averaged pre-dam bed slope of the modeled reach of the Egyptian Nile

River was equal to 0.072 m/km (Simaika, 1970; Hammad, 1972; Waterbury, 1977;

Abdelbary, 1992b; Saad, 2002), and the channel bed elevation at the barrage locations were close to the measured values of 71.5 m, 65.5 m, 43.8 m, and 10 m above mean sea level respectively at the Isna Barrage, Nag Hammadi Barrage, Asyut Barrage, and Delta

Barrage.

The calibrated value of the parameter  was 15.4. In other words, the entrainment model calibration suggests that there is an order of magnitude difference between the pre- dam suspended sand loads and the suspended sand load predicted with the Wright and

Parker formulation (2004a, b).

A difference of one order of magnitude between the suspended bed material load measured in the field and predicted with an empirical relation is not unusual. For example, one order of magnitude difference between bed material transport rates measured in the field and predicted with the Engelund and Hansen (1967) model was observed on the Yellow River in China (Ma et al., 2017). Ma et al. (2017) attributed this difference to the very fine bed material of the Yellow River (~0.07 mm) and the different

bedform regime between the lower Yellow River and other sand bed rivers. Field data to perform a more detailed calibration of the entrainment relation based on the bedform regime and the size distribution of the suspended load in the pre-dam Egyptian Nile River are unfortunately not available.

The second step in the pre-dam zeroing consisted in the performance of model simulations to reconstruct a pre-dam longitudinal profile of the modeled reach that was representative of non-equilibrium conditions, i.e., that was associated with a 25% decrease of the mean annual sand load in the streamwise direction an aggradation rate of

1 mm/yr and had a reasonable elevation of the channel bed at the barrages.

Non-equilibrium results of morphodynamic models are dependent on the initial conditions (Parker and Wilcock, 1993). For the non-equilibrium pre-dam model zeroing the initial average bed slope was set equal to 0.061 m/km in the entire modeled reach.

With this initial condition, the model predicted aggradation rates of 0.92 mm/yr and a

25% decrease in suspended sand load between Aswan and the Delta Barrage and reasonable bed elevation at the barrages after 200 years of simulated time.

The comparison between numerical and predicted suspended sand loads is presented in Figure 3.3a where the line represents the numerical results, and the diamonds represent the suspended sand load estimates with ±5% error bars. The drop in the predicted suspended sand load at streamwise distance of ~750 km (grey circle in

Figure 3.3a) represents a downstream migrating wave of bed aggradation associated with the arbitrary initial condition of the simulations. The average predicted pre-dam bed slope is ~0.07 m/km, which is within the range of reported pre-dam water surface slopes

(0.068 m/km - 0.073m/km) for flow rates ranging between 1000 and 2500 m3/s

(Abdelbary,1992b). Figure 3.3b represents the predicted pre-dam longitudinal profile of the Nile River, and black triangles represent the elevations at the barrages after 200 years, a reasonable agreement of the barrages elevation between the model predictions and field measurements is achieved.

3.4.2 Post-dam Zeroing

The longitudinal profile of Figure 3.3b was obtained in the pre-dam model zeroing was the initial condition for the post-dam model zeroing, i.e., it was assumed to be representative of the longitudinal profile of the Nile River in 1964, when the High Aswan

Dam was closed.

Model upstream boundary conditions for the post-dam zeroing calculations were the post-dam hydrograph of Figure 3.2 and the post-dam sand load of 2.5 Mt/yr (see

Table 3.1). The barrages are modeled in terms of specified water surface elevation

(section 3.2.3) and of a diverted flow rate (section 3.2.2).

Due to the lack of information on the amount of sand derived at the main flow diversion structures upstream of the barrages we modeled the impact of the barrages on the sand load in two ways that should bracket almost on the reasonable conditions. We assumed that 1) the sand partition between the Nile River main channel and the diversion canal was proportional to the flow discharges, so that if 20% of the Nile River water was diverted upstream of a barrage, 20% of the sand load was also diverted to the diversion canal, and 2) no sand was diverted to the diversion canals. Results of the calculations with the sand partition between the Nile River main channel and the diversion canal are presented in Figures 3.4 and 3.5.

The predicted post-dam changes in channel bed elevation are presented in Figure

3.4 with o denoting the bed elevation in 1964 and c denoting the bed elevation 20 years

(continuous black line) and 120 years (continuous grey line) after the dam closure, and at mobile bed equilibrium (dashed black line). The horizontal dotted line at c - o = 0 denotes no change in mean bed elevation. When c - o > 0, the model predicts channel bed aggradation, if c - o < 0 the model predicts channel bed erosion. The black triangles on the horizontal axis of Figure 3.4 denote the position of the four main barrages. The localized deposition at the barrage locations is associated with the imposed changes in flow discharge and sand load. Due to the strongly non-linear dependence of the sand load on the flow discharge expressed in equations (3.8) - (3.11) and (3.14) -

(3.17) the reduction of, e.g., 20% in flow rate corresponds to the reduction of sand transport capacity greater than 20%, and thus sediment deposition in a morphodynamic model.

The black points in Figure 3.4 represent field measurements of bed elevation change ~20 years after dam closure. The comparison between numerical predictions and field observations shows that the model was able to reasonably capture the changes in bed elevation caused by the closure of the High Aswan Dam. The long-term prediction of bed level change, i.e., 120 years and at equilibrium, are in agreement with model predictions of the Nile Research Institute (Fathy, 1956; Shalash, 1980).

The comparison between the results of the simulations presented in Figure 3.4 and those in which it is assumed that the sand was not diverted upstream of the barrages are summarized in Table 3.2 in terms of differences between net elevation changes 20 years and 120 years after the closure of the High Aswan Dam and at equilibrium. The

maximum predicted difference between bed level changes 120 years after dam closure

(engineering time scale) is 40 cm downstream of Isna Barrage, an almost negligible difference gives the problem scale and simplifications. At equilibrium, i.e., after 1200 years of simulated time, the difference between model predictions are everywhere smaller than 40 cm, but downstream of the Asyut Barrage, this large difference is likely due to high water diversion at this barrage. Due to the small differences between model predictions and the results of the simulations with a proportional reduction in water discharge and sand load at the barrages are presented and discussed in the continuing of this chapter.

The comparison of measured and modeled suspended sand loads at different locations along the study reach is presented in Figure 3.5 where the black triangles are model results, and measured suspended sand loads are represented with grey points. The measurements were collected between 2009 and 2015, i.e., between 45 and 51 years after the dam closure in cross sections located at 162 km-180 km downstream of the Old

Aswan Dam (Figure 3.5a), 340 km - 356 km downstream of the Old Aswan Dam (Figure

3.5b), and 520 km - 552 km downstream of the Old Aswan Dam (Figure 3.5c). The error bars in Figure 3.5 indicate a ±10 % interval around the modeled values and, given the model simplifications, the results of Figure 3.5 show that the morphodynamic model with the calibrated entrainment relation reasonably captures the suspended sand loads measured in different sections of the Nile River.

3.5 MODEL APPLICATIONS FOR RESTORATION OF THE NILE RIVER

The proposed restoration project is characterized by controlled flow releases combined with sediment augmentations at Aswan. The flow releases are modeled with a flow hydrographs created by modulating the current releases from the High Aswan Dam with a volume of 10 billion cubic meters of water saved with the improvement of the irrigation system. This volume of water (10 billion cubic meters) will be stored in the High Aswan

Dam reservoir (Lake Nasser), and thus the High Aswan Dam will be used as flow control structure to reshape the flow hydrographs.

In the calculation of the post-restoration water balance, it is assumed that the irrigation requirements in the months of high water demands for agriculture, i.e., from

February through September, are reduced by ~30% because the efficiency of the current irrigation system is ~70%. Noting that, 80% - 85% of the monthly volume of water released from the High Aswan Dam, VHD, from February through September is used for agriculture, the monthly volume of water saved with the improvement of the irrigation system is estimated to be 0.3·0.8·VHD.

Similarly, to estimate the volume of water diverted at the barrages during the restoration project it is assumed that 80% of the water diverted at each barrage is used for agriculture and that the future agricultural need is equal to 70% of the present value for the improvement of the irrigation system. Thus, the water diverted at each barrage in the restoration scenarios discussed below is estimated as 0.7·0.8·VB, with VB denoting the average volume of water currently diverted at each barrage. The monthly releases from the Old Aswan Dam from October through January, when the agricultural water demand is smallest, are equal to the present releases.

Two different scenarios (Scenario I and II) are considered to model the proposed controlled flow release from the Old Aswan Dam and are represented in Figure 3.6 in terms of mean monthly flows. The grey bars in Figure 3.6 represent the mean monthly releases at Aswan, and the black bars are the proposed mean monthly flows released at

Aswan during the restoration project.

In Scenario I (Figure 3.6a), the 10 billion cubic meters used for restoration are distributed over the months of August, September, and October characterizing the pre- dam flood season, with 5 billion cubic meters released in September, i.e., the month in which the natural flood peak occurred, and 5 billion cubic meters released with equally distributed over August and October.

In Scenario II the hydrograph is characterized by a shorter flood season compared to the pre-dam Nile River hydrology but a higher flood flow compared to Scenario I with the 10 billion cubic meters released in September.

The comparison between the monthly flows released at Aswan (grey) and the monthly flows at the Delta barrage (black) are presented in Figure 3.7, where Figure 3.7a illustrates the present situation, and Figures 3.7b and 3.7c represent the monthly hydrographs for Scenario I and Scenario II respectively. In the proposed restoration scenarios the flow rate at the Delta Barrage and to the delta is higher than present when higher flows are released at Aswan, i.e., from August to October in the scenario I and in

September in scenario II.

The flow hydrographs of Figure 3.6 are combined with sand augmentations to reduce or reverse channel bed erosion in the upstream part of the modeled reach and to increase the volume of sand annually delivered to the delta and the Egyptian coast.

The zeroed model was used to estimate the average volume of sand that is required to control channel bed erosion in the upstream part of the modeled reach with reasonable channel bed aggradation in the downstream part of the Nile River for the two restoration scenarios of Figures 3.6 and 3.7.

To investigate the feasibility of the proposed restoration project the model results have been compared against 1) the minimum water depth to ensure navigation (2.3 m) during the touristic season (February - September) (Hamza, 1990; Attia et al., 2005;

Sadek, 2013; El Sersawy et al., 2016), and 2) the maximum water elevation at high flow to prevent flooding in urban areas.

3.5.1 Effects of the Proposed Restoration Project on the Longitudinal Profile of the Nile River

The initial condition for the model simulations is the Nile River longitudinal profile predicted with the zeroed model 60 years after the closure of the High Aswan Dam. The barrages are explicitly modeled as localized water and sediment diversions, as discussed in the post-dam model zeroing. The prediction of the equilibrium condition (no net erosion or deposition on the channel bed) for the Nile River under the proposed restoration scenarios was performed with a specified downstream water surface base level that is controlled with the operation of the Delta Barrage for each generic discharge in the hydrograph.

The long-term evolution of the river profile is presented in Figure 3.8 in terms of channel bed elevation with the thin black line representing the model initial condition, the grey line the channel bed elevation 300 years in the future and the dotted line the

equilibrium longitudinal profile. The continuous thick and dashed black lines represent the minimum and maximum water surface elevation at mobile bed equilibrium. The black dots indicate the maximum allowed water surface elevation to prevent flooding of the urban areas (e.g., Abdelabary, 1992 a,b; El-Nefary, 2010).

Figure 3.8a shows the response of the Nile River longitudinal profile to the controlled flow releases of scenario I (Figure 3.6a) with a sand augmentation rate of 3

Mt/yr. Figure 3.8b shows the predicted longitudinal profile evolution to the controlled flow releases of scenario II (Figure 3.6b) with a sand augmentation rate of 3.75 Mt/yr.

The comparison between the longitudinal profiles at equilibrium (dotted black line) and

300 years after the beginning of the restoration project (grey line) reveals that after 300 years the system is not far from equilibrium. The model results for the scenario I show that for this combination of flow releases and sand augmentation rate the river bed erosion in the upstream part of the modeled reach is controlled (compare Figure 3.8a with

Figure 3.4) and limited deposition occurs in the downstream part of the modeled reach.

For the restoration scenario II, a similar evolution of the Nile River profile is observed.

Problems associated with river flooding and navigation safety should not represent a major concern for scenario I and scenario II.

The quantification of the changes in bed elevation over time associated with the proposed restoration project is presented in Figure 3.9 for the two proposed restoration scenarios with sand augmentation rates of 3 Mt/yr for the flow releases of Scenario I

(Figure 3.9a), and 3.75 Mt/yr for the flow releases of Scenario II (Figure 3.9b). The net changes in bed elevation are denoted as ηc-ηo, where ηo represents the initial bed profile

(thin black line of Figure 3.8), and ηc the post-restoration bed profile 50, 100, 200, and

300 years after the beginning of the restoration project. The black dash lines represent model results after 50 years, the continue grey lines after 100 years, the dash grey lines after 200 years, and the continues black lines after 300 years of the restoration project.

The black triangles on the horizontal axis represent the locations of the main barrages, starting from upstream are Isna Barrage, Nag Hammadi Barrage, Asyut Barrage, and

Delta Barrage.

The model simulations show that the maximum in-channel deposition is ~3.4 m in

Scenario I and ~2.5 m in Scenario II at the Delta Barrage after 300 years of simulated time. It is important to note here, however, that this high deposition is associated with the migration of the wave of alluviation associated with the pre-dam initial condition (see

Figures 3.8 and 3.4). This wave of aggradation that was located ~750 km downstream of the Old Aswan Dam in the pre-dam model zeroing reached the downstream part of the domain (~950 km downstream of the Aswan Dam) at the end of the post-dam zeroing.

Downstream of the Asyut Barrage, where the effects of the wave of alluviation are not felt, the in-channel sediment deposition varies between ~0.5 m and ~1.8 m respectively 50 years and 300 years after the beginning of the restoration project.

Minimum changes in channel bed elevation are predicted in the central part of the modeled reach between the Nag Hammadi Barrage and the Asyut Barrage, while up to

1.3 m of channel bed erosion are predicted downstream of the Isna Barrage after 300 years of simulated time from the beginning of the restoration project. If needed, the deposition in the downstream part of the modeled reach, i.e., between the Asyut Barrage and the Delta Barrage, can be controlled with a specifically designed dredging program,

while the erosion in the upstream part of the modeled reach can be controlled with engineered structures.

3.5.2 Sediment Load to the Delta

Figure 3.10 summarizes the temporal changes in the mean annual sand load at the Delta

Barrage, and thus supplied to the Nile River delta, for the proposed scenarios up to ~300 years after the beginning of the restoration project. The grey line represents the present situation, i.e., no restoration, the dashed black line represents the sand load in the case of restoration scenario I and 3 Mt/yr of sand augmentation rate, and the black line summarizes the results of scenario II with 3.75 Mt/yr of sand annually supplied at Aswan.

The model results of Figure 3.10 clearly illustrate that in the proposed restoration project the sand load to the delta is larger than present with the largest sediment load obtained in the case of a single month of flood flow (Scenario II). Further, the sand supplied to the Nile River delta increases in time for both the restoration scenarios due to the adjustment of the Nile River longitudinal profile to the new hydrograph and sand supply. After 300 years of the simulated time the sand load to the Nile River delta is equal to ~2.65 and ~3.65 Mt/yr for scenarios I and II respectively.

The shape of the imposed hydrograph strongly influences the sediment load supplied to the delta with Scenario II supplying about 40% more sand than Scenario I, when the imposed flood season spans from August to October (Figure 3.7). The impacts of the controlled flow and sediment releases on the Nile Delta will be quantified in future work of the second part of the restoration project.

3.5.3 Estimate the Impact of Predicted Mean Sea Level Rise on the Restoration of the Nile River

In our model simulations, the downstream boundary condition of the modeled reach is fixed with known water surface elevation at the Delta Barrage. This structure controls the water surface elevation at the downstream, and thus it is reasonable to ignore the impact of the mean sea level rise on the modeled reach. This notwithstanding, a comparison between the model predictions presented in the previous sections and model predictions obtained with an imposed rate of base level rise ζ of 5 mm/yr at the Delta Barrage has been performed.

The comparison between numerical results obtained with and without an imposed rate of base level rise does not show an appreciable change of the model results. In particular, the model results indicate that the impact of an imposed rate of base level rise is not significant on the morphodynamic evolution of the upstream ~780 km of the modeled reach, while differences are observed in the downstream most part of the model reach. With an imposed rate of base level rise of 5 mm/yr, the in-channel deposition is ~

4.3 m in Scenario I and ~3.3 m in Scenario II at the Delta Barrage after 300 years of simulated time versus the ~3.4 m and ~2.5 m predicted in the case of the constant base level. Downstream of the Asyut Barrage, the in-channel sediment deposition varies between ~0.5 m and ~2.3 m respectively 50 years and 300 years after the implementation time of the restoration project, the deposition in the case of the constant base level is 0.5 m and 1.8 m at 50 years and 300 years respectively. Finally, when the base level rise is accounted for in the numerical simulations, the model predicts a slight reduction in the sand load delivered to the delta. In particular, after 300 years of simulated time, the sand

load supplied to the Nile River delta is equal to ~2.0 Mt/yr and ~3.0 Mt/yr for scenarios I and II respectively.

3.6 CONCLUSIONS

This paper presents results of modeling study for the restoration of the Egyptian Nile

River-delta complex with controlled flow releases at Aswan to restore a semi-natural hydrograph and sediment augmentations downstream of the Aswan Dams to control the ongoing channel bed degradation, improve the water quality in the Nile River delta, and increase the sand supplied to the Nile Delta shoreline.

Two restoration scenarios characterized by monthly hydrographs with a three month-long (Scenario I) and one month-long (Scenario II) flood seasons were considered.

These hydrographs do not imply changes in the operation of the High Aswan Dam and respect the Egyptian share of Nile River water set by international treaties at 55.5 billion cubic meters per year.

Previous studies have shown that ~10 billion cubic meters of water can be saved each year with the improvement of the irrigation methods, and this volume was used herein to design the restoration hydrographs.

The proposed controlled flow releases are associated with sand augmentations of

3.0 Mt/yr (Scenario I) and 3.75 Mt/yr (Scenario II). These sand volumes correspond to the minimum sand supply rate to control the erosion in the upstream part of the modeled reach with limited deposition in the downstream part.

Under the proposed restoration scenarios navigation safety and flood control are guaranteed on the Egyptian reach of the Nile River. Flow rates higher than present are

delivered to the Nile River delta, and these flow rates are associated with sand loads that are higher than the current sand loads. Numerical simulations show that the sand load delivered to the delta will increase during the restoration project as the Nile River responds to the imposed hydrograph and sand supply.

The comparison between the two restoration scenarios considered herein suggests that the imposed one month long semi-natural flood season of scenario II results in sand loads delivered to the delta are 40% larger than the sand loads delivered to the delta in the case of the three-month long flood season of scenario I. Quantifying the impacts of the proposed restoration scenarios on the Nile River delta in terms of shoreline migration rate and changes in the elevation of the channelized and not-channelized portion of the delta top is the future development of the present research work.

Acknowledgments

The authors wish to acknowledge the Ministry of Higher Education and Scientific

Research (MoHESR), Iraq, for the support and fund for this study. The authors thank the

Nile Research Institute (NRI), Egypt, for providing the field data of the study.

Parameter Definition Value (s) unit

Pre-dam Post-dam

Qtf Bed material load 37.2 2.5 Mt/yr

S Average channel bed slope 0.07 --- m/km

B1 Average channel width of Subreach 1 870 635 m

B2 Average channel width of Subreach 2 800 570 m

B3 Average channel width of Subreach 3 920 590 m

B4 Average channel width of Subreach 4 1000 540 m

D50 Mean grain size diameter 0.25 0.25 mm

D90 Grain size at which 90% is finer 0.70 0.70 mm

ξd Downstream water surface elevation 15 -- m

ζ Mean sea (or base) level rise rate -- 5 mm/yr

Difference ∆ (m) Barrage Site 20 120 Final (years) (years) equilibrium

Upstream 0.1 0.15 0.1 Isna Downstream 0.2 0.4 1.0

Upstream 0 0 0.05 Nag Hammadi Downstream 0.2 0.05 0.4

Upstream 0.1 0.1 0.1 Asyut Downstream 0.2 0.1 2.3

Delta Upstream 0.1 0.3 0.2

Nile Delta

N 30o Delta Barrage Cairo ³ (Rkm 954)

Egypt SUBREACH 4 Nile River

Asyut Barrage (Rkm 545)

SUBREACH 3 Nag Hammadi Barrage (Rkm 359) SUBREACH 2 Isna Barrage

N 25o SUBREACH 1 (Rkm 167)

Bedrock Reach (Not Modeled) Old Aswan Dam Study (Rkm 0) High Aswan Dam Area (Rkm -7) Lake Nasser E 30o E 35o

Figure 3.1. Map of the Nile River with location of the infrastructures relevant for this study, Egypt. The Image of the African continent is from Google Earth.

Figure 3.2. The mean monthly hydrographs of pre- and post-High Aswan Dam at Aswan, upstream end of the study reach (Nile Research Institute database). The hydrograph with grey columns and thick borders represent the post-dam flow regime. The dashed columns represent the pre-dam flow regime.

A) 45

yr 40

Suspended discharge sediment (Sand)Mt/ 0 0 100 200 300 400 500 600 700 800 900 1000 River distance from the Old Aswan Dam (km)

B) 100

90 Isna Barrage 80 Nag Hammadi Barrage 70 Asyut Barrage 60

40 Elevation(m) 30 Delta Barrage

0 0 100 200 300 400 500 600 700 800 900 1000 Downchannel distance from the Old Aswan Dam (km)

Figure 3.3. Figure A represents a comparison between pre-dam mean annual suspended sand load in the study reach. The black line represents model results, and the black diamonds are measurement data from Nile Research Institute. Error bars denote ± 5% of the measured value. The grey circle identifies the aggradation wave. Figure B represents the predicted pre-dam longitudinal profile of the Nile River, and black triangles represent the elevations at the barrages.

6 Isna Barrage Nag Hammadi Asyut Barrage Delta Barrage 4 Barrage 2 Deposition 1984 0 -2 Erosion 2084 -4 -6 Post-dam equilibrium -8

(m) -10 o

η -12 -

c -14 η -16 -18 ` -20 -22 -24 -26 -28 -30 0 100 200 300 400 500 600 700 800 900 1000 Downchannel distance from the Old Aswan Dam (km)

Figure 3.4. Post-dam changes in longitudinal profiles in the study reach. ηc denotes the channel bed elevation at the generic time t and ηo is the pre-dam channel bed elevation. The black triangles represent the location of the main barrages. The black dotted line indicates a condition of no net erosion (or no net deposition). The continuous black and grey lines are respectively model results in 1984 and 2084, i.e., 20 and 120 years after the closure of the High Aswan Dam. The dashed black line represents the net change in bed elevation at post-dam mobile bed equilibrium. The black points are the available field data.

3 a) Rkm 162 – Rkm 180 2.5

1.5

0.5 Suspended sediment (Mt/yr) Suspended sediment

0 0 500 1000 1500 2000 2500 3000 Discharge (m3/s)

8 b) Rkm 340 – Rkm 356

7 )

yr 6

2 Suspended sediment (Mt/ sediment Suspended 1

0 0 500 1000 1500 2000 2500 3000 Discharge (m3/s)

6 c) Rkm 520 – Rkm 552

) 5 yr

1 Suspended sediment (Mt/Suspended sediment

0 0 500 1000 1500 2000 2500 3000 Discharge (m3/s)

Figure 3.5. Comparison between measured (grey circles) and predicted (black triangles) suspended sand loads in time period range between 2008 and 2015, i.e., ~47 years after the closure of the High Aswan Dam, a) at Rkm 162 to Rkm 180, b) at Rkm 340 to 356, and c) at Rkm 520 to 552. Error bars denote ±10% of the measured value.

6000 a) Scenario I 5500 5000 4500

4000

/s) 3 3500 3000 2500

2000 Discharge Discharge (m 1500 1000 500 0 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

6000 b) Scenario II 5500 5000 4500

4000 /s) 3 3500 3000 2500

2000 Discharge (mDischarge 1500 1000 500 0 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

Figure 3.6. Imposed flow hydrographs for the restoration project at Aswan; a) Scenario I; and b) for scenario II. The grey bars indicate the current mean monthly flow releases at Aswan, and the black bars are the proposed mean monthly flows released at Aswan during the restoration project.

6000 a) Pre-restoration

5000 /s)

3 4000

3000

2000 Discharge (mDischarge 1000

0 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

6000 b) Restoration: Scenario I

5000 /s)

3 4000

3000

2000 Discharge (mDischarge 1000

0 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

6000 c) Restoration: Scenario II

5000 /s)

3 4000

3000

2000 Discharge (mDischarge 1000

0 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

Figure 3.7. Water discharge at Aswan and at the Delta Barrage for a) the pre-restoration, and b) and c) for the river restoration scenarios I and II respectively. Grey columns represent the discharges at Aswan, and black ones are at the Delta Barrage.

a) Scenario I 100

90 Isna Barrage Nag Hammadi 80 Barrage

70 Asyut Barrage 60

40 Elevation Elevation (m) 30 Delta Barrage

0 0 100 200 300 400 500 600 700 800 900 1000 Distance from the Old Aswan Dam (km)

b) Scenario II 100 Isna Barrage 90 Nag Hammadi Barrage 80

70 Asyut Barrage 60

40 Elevation Elevation (m) Delta Barrage 30

0 0 100 200 300 400 500 600 700 800 900 1000 Distance from the Old Aswan Dam (km)

Figure 3.8. The longitudinal profiles of the channel bed of the river restoration project where (a) is for the scenario I, and (b) is for scenario II. The thin black line represents the initial condition of the bed elevation, the grey line represents the bed elevation at 300 years after the beginning of the restoration project, the dotted line represents the bed elevation at mobile bed equilibrium, the thick black line is the maximum water surface elevation, the dashed black line is the minimum water surface elevation, and the black points are the allowable water surface elevation from field measurements.

a) Scenario I

4 Isna Barrage Nag Hammadi Asyut Barrage Delta Barrage Barrage

(m) o

η 1

– c

η Deposition 0 Erosion

-1

-2 0 100 200 300 400 500 600 700 800 900 1000 Distance from the Old Aswan Dam (km)

b) Scenario II

4 Isna Barrage Nag Hammadi Asyut Barrage Delta Barrage Barrage

(m) o

η 1 –

c Deposition η 0 Erosion

-1

-2 0 100 200 300 400 500 600 700 800 900 1000 Distance from the Old Aswan Dam (km)

Figure 3.9. The net change in channel bed elevation of the river restoration scenarios. a) is restoration scenario I, and b) is the scenario II. The black dash line represents model results at 50 years, the continues grey line represents model results at 100 years, the dash grey line represents the result at 200 years, and the continues black line is the result at 300 years of the restoration project.

3.5

2.5

1.5

Sand load atSand Delta (Mt/yr) Barrage 0.5

0 0 50 100 150 200 250 300 350 Time (yr)

Figure 3.10. Mean annual sand load at the delta of the river restoration scenarios and without restoration. Grey line represents the post-dam scheme, dashed black is for the scenario I, and the black line one on the top is for the scenario II.

CHAPTER 4

CONCURRENT MODELING OF DELTA GROWTH AND CHANNEL

GEOMETRY IN THE HIGH ASWAN DAM RESERVOIR, SUDAN-

EGYPT1

4.1 INTRODUCTION

The High Aswan Dam was built in 1960s close to the Egypt-Sudan border to provide

Egypt with electricity and water for irrigation, protect Egypt from floods and droughts and improve navigation on the Nile River. The closure of the High Aswan Dam resulted in the impoundment of the second largest man-made reservoir in the world, which is the

High Aswan Dam Reservoir (Kim and Sultan, 2002; Moussa, 2013; Elsaeed et al., 2016).

With the closure of the High Aswan Dam (HAD), most of the sediment transported by the Nile River has deposited in the upstream part of the reservoir forming a prograding delta called herein the HAD delta. Sediment deposition in the HAD reservoir is gradually reducing the useful storage capacity and altering the Nile River morphology in Sudan. As discussed in the previous chapters of this dissertation, the changes in hydrology and sediment supply to the Egyptian reach of the Nile River

1 Basim M. Al-Zaidi, Ahmed Moussa, Zeyad A. Sulaiman, and E. Viparelli. To be submitted to Earth Surface Dynamic (ESurf).

associated with the closure of the HAD have resulted in river degradation, navigation impairment, shoreline retreat and deterioration of the water quality and of the wetlands in the Nile delta (Simaika, 1970; Hammad, 1972; Shalash, 1980; Galay et al., 1990;

Abdelbary, 1992a; Abu Zeid et al.,1997; Stanely and Warne, 1998, Abdel-Shafy, 2002;

El Banna and Frihy, 2009).

In this chapter, a model of delta morphodynamic that concurrently predicts delta progradation and the geometry of the channelized portion of the delta top is presented.

The geometry of the channelized portion of the delta top is computed based on the work of Li et al. (2015) who derived an empirical relation linking the bankfull Shields number to the bed material size and the channel slope. This relation is called channel formative closure. The channel formative closure estimates the bankfull Shields number as a function of the flow and sediment properties and is based on the analysis of 230 river data with bed material ranging from silt to cobbles, bankfull discharges varying between 0.34 m3/s and 216,340 m3/s, channel widths varying between 2.3 m and 3400 m, water depths varying between 0.22 m and 48.1 m, and channel slopes varying between 8.8×10-6 m/m and 5.2×10-2 m/m. One of the main results of these analysis is that the bankfull Shields number is an increasing function of bed slope over a range of characteristic bed material sizes.

The model presented in this chapter can be of aid in predicting of the effects that the restoration project of the Nile River-delta complex characterized by controlled flow releases and sediment augmentations presented in the previous chapters has long term evolution of the Nile Delta. Model verification at field scale was performed on the HAD delta, where detailed field data are periodically collected by the Nile Research Institute.

A parametric study was then performed to explore the effects of sea level rise, subsidence, and wave action, which play a prime control on delta growth in large deltas such as the Nile delta (Bharracharya and Giosan, 2003; Parker, 2004; Swenson et al.,

2005), and to investigate the impact of these controls on the geometry of the channelized portion of the delta top. The application to the Nile delta is the future step of this work.

4.2 THE HAD RESERVOIR AND ITS DELTA

4.2.1 Site Description

The HAD Reservoir is an international, artificial water body at the Egypt-Sudan border.

The downstream part of the reservoir extends for about 350 km in the Southern part of

Egypt (Lake Nasser) and for ~150 km in Sudan (Lake Nubia), as shown in Figure 4.1 (El-

Shabrawy, 2009; Elsaeed et al., 2016; El‐Manadely et al., 2017). In Figure 4.1, the HAD

Reservoir and the location of its delta are indicated, with the 20 cross sections that the

Nile Research Institute (NRI) periodically surveys.

The inlet of the reservoir is located 500 km upstream of the dam, and Cross

Section 23 (El Daka), the upstream most surveyed cross section 478.5 km upstream of the

High Aswan Dam. Streamwise distances in this chapter are measured in river kilometers

(Rkm) downstream of Cross section 23. In this reference system, Cross Section 23 represents Rkm 0, while the downstream most surveyed cross section, which is Cross

Section 22 (Debrosa), is located at 357 km upstream of the dam, i.e., Rkm 150 (see

Figure 4.1).

The HAD reservoir is a multi-year storage lake with a total capacity of about 162 billion m3. The total surface area of the reservoir covers about 6500 km2, with an average width ~12 km and total length 500 km (Said, 1993; Kim and Sultan, 2002; Elsaeed et al.,

2016). The dead storage is of 31.5 billion m3 with maximum level at 147 m above mean sea level (Shalash, 1980; Said, 1993; Moussa, 2013; Elsaeed et al., 2016). The live storage capacity is about 90 billion m3, and lies between levels of 147 m and 175 m above mean sea level. The flood control capacity is about 41 billion m3 between levels of

175 m and 182 m above mean sea level (Moussa et al., 2001; Moussa, 2013). The maximum water level in the reservoir is 182 m above mean sea level. The life span of the reservoir is estimated to be ~360 years (Shalash, 1980; Smith, 1990).

4.2.2 Hydrology of the HAD Reservoir

The Nile Research Institute has monitored the discharge entering the HAD reservoir since

1964. Data are collected at the Dongola station, Sudan, located at 780 kilometers upstream of the HAD reservoir. There are no gaging stations with continuous records between Dongola and the Aswan Dam.

The HAD reservoir provides an annual volume of 55.5 billion m3 for Egypt

(Mohie El-Din and Moussa, 2016). The annual average flood discharge from August through October at Dongola during the flood season is about 7000-8000 m3/s. The average peak discharges during flood is ~7700 m3/sec, and the annual volume of flood flow ranges from a minimum of 43 billion cubic meters per year to maximum of 150 billion cubic meters per year (Moussa et al., 2001).

The suspended sediment concentrations are high during the flood season, with more than 95% of the annual sediment load transported between August and October.

The flood intermittency, i.e., the average fraction of the year in which the river is morphologically active, is thus estimated to be equal to 0.25.

The monthly average water levels upstream of the High Aswan Dam from 1964 to

2014 are presented in Figure 4.2, where the red line represents the simplified water levels used in the simulations presented continuing of this chapter, and the yellow circle indicates a drought period that started in 1980 and ended in 1989. The data show that the water levels increased during the period 1964-1976, when the reservoir was filled. Due to a long, severe drought, the water levels in the HAD reservoir decreased from 1978 and reached a minimum of 150 m above mean sea level, just three meters above the dead storage, in 1988. Water levels gradually increased between 1988 and 1998 and reached the maximum level of 181 m at the end of flood season in 1999-2000.

The short-term fluctuations in the average water levels of Figure 4.2 is due to the operation rules of the HAD that include water releases when normal floods are expected to occur. Based on the reservoir operation policy, on the first of August, the water level in the HAD reservoir must be at 175 m above mean sea level (normal pool level). This level is controlled with three spillways, one emergency spillway and the Toshka Spillways

(Elsaeed et al., 2016).

4.2.3 Geometry and Longitudinal Profile of HAD Delta

The longitudinal profiles of the lowest bed elevation of the channelized portion of HAD delta top and of the HAD reservoir from 1964 to 2012 are presented in the Figure (4.3).

Figure 4.3 clearly shows that after the closure of dam a delta formed and prograde into the lake.

The width of the HAD delta top varies with the distance and ranges between 1000 m at the inlet of the reservoir from Cross section 23 to Cross Section 6, and reaches ~

7500 m at the lake from Cross Section 27 to Cross Section 22 as shown in Figure (4.4), where the red points are data provided by the Nile Research Institute and the blue points are Google Earth based estimates. The dashed line in Figure 4.4 represents the width of the delta top used in the numerical simulation presented in the continuing of this chapter.

Figure 4.5 Shows the interpretation of the field measurements to determine the channel width and depth for the cross sections 23, and 3 in different years, where the blue line represents the water surface elevation during the measured time.

4.2.4 High Aswan Dam Reservoir Sedimentation

The average annual sediment load deposited in the HAD reservoir is estimated to be ~124 million tons (Shalash, 1980). More than 60 m thickness of sediment deposition occurred at the entrance of the reservoir close to Egypt-Sudan border since the dam construction in the 1960s (Moussa, 2013).

The grain size distribution of the Nile River sediment delivered to the HAD reservoir consists of 30% sand, 40% silt, 30% clay (Coleman, 1981). The average median grain size, D50, of the sand is 0.25 mm (El Din, 1974). Figure 4.6 shows variation in the streamwise direction of the D50 on the HAD delta top in 2006. The sediment samples were collected at the 20 cross sections shown in Figure 4.1. Figure 4.6 clearly shows that the sediment at the HAD delta top becomes finer in the streamwise direction. The D50 of

collected samples is equal to 0.5 mm at Cross Section 23 and declines to about 0.015 mm at Cross Section 22 which is located in the delta front (El‐Manadely, 2017).

4.3 MODEL DESCRIPTION

Model governing equations are the shallow water equations of open channel flow and the equation of conservation of channel bed material, i.e., the Exner equation. A channel formative closure (Li et al., 2015) is used to predict the geometry of the channelized portion of the delta top, as illustrated in the continuing of this section. Delta migration is modeled by imposing that all the bed material reaching the shoreline is trapped on the delta front ( Swenson et al., 2000; Kostic and Parker, 2003).

For the model application on the ~130 km long HAD delta, the following assumptions and approximations were made:

1) The quasi-steady approximation holds, i.e., the volumetric bed material load

is assumed to be orders of magnitude smaller than the flow discharge so that

the time dependence in the flow equations can be dropped and the flow is

assumed to be steady (De Vries, 1965);

2) The flow is assumed to be Froude subcritical, with the water depth at bankfull

flow, Hbf, equal to the depth of the cross section;

3) The bed sediment is modeled as uniform sand with a single grain size D50

equal to 0.25 mm (e.g., Viparelli et al., 2015);

4) The flow is assumed to be at bankfull condition, and the bankfull flow is

considered to be responsible for shaping the channel geometry (Leopold et al.,

2012);

5) To predict the geometry of the channelized portion of the delta top, the delta

top is divided in two regions, the channelized portion which conveys the

bankfull flow and the bed material load, and the non-channelized portion,

which is submerged when the flow is above bankfull and where the wash load

is deposited. The schematic representation of the cross section of the delta top

is presented in Figure 4.7, where c denotes elevation of the channelized

portion of the delta top, f is the elevation of the non-channelized portion of

the delta top, and avg is the average elevation of the delta top. The cross

sections of the channelized and non-channelized portions of the delta top and

of the delta top are approximated as rectangular with widths equal to Bbf and

Bf, where the subscript bf denotes bankfull conditions for the channelized

portion of the delta top and f indicates the non-channelized portion of the delta

top, i.e., the floodplain; the depth of the channelized portion of the delta top is

Hbf , equal to the flow depth of the bankfull flow.

The presentation of the model governing equations is divided in three parts, flow equations; channel formative closure, i.e., the empirical equations used to estimate width and depth of the channelized portion of the delta top (Li et al., 2015); and sediment equations.

4.3.1 Flow Equations

The model governing equations for the flow express are the conservation of water mass and streamwise momentum as follows (Chaudhry, 2008)

휕퐵 퐻 휕푄 푏푓 푏푓 + 푤푏푓 = 0 (4.1) 휕푡 휕푥

휕푄 휕푄 푈 휕퐻 푤푏푓 + 푤푏푓 푏푓 = −푔퐻 퐵 푏푓 + 푔퐻 퐵 (푆 − 푆 ) (4.2) 휕푡 휕푥 푏푓 푏푓 휕푥 푏푓 푏푓 푓푏푓

where 푄푤푏푓 denotes the bankfull flow discharge, 퐻푏푓 the bankfull water depth, 퐵푏푓 is the bankfull channel width, 푈푏푓 the flow velocity at bankfull flow, g the acceleration of gravity, S the bed slope defined as 푆 = −휕휂푐/휕푥, t and x are a temporal and a downchannel coordinate respectively. Sfbf is the bankfull friction slope and equal to

2 2 Cf 퐹푟푏푓, where Cf is non-dimensional friction coefficient, and 퐹푟푏푓 being the Froude number squared

2 2 푄푤푏푓 퐹푟푏푓 = 3 2 (4.3) 푔퐻푏푓퐵푏푓

Equations (4.1) and (4.2) are simplified with the quasi-steady approximation, i.e., the time dependence terms are dropped, and the equation of mass conservation reduces to

푄푤푏푓 = 푈푏푓퐻푏푓 퐵푏푓. The momentum equation (4.2) can be reduced to the following

2 휕퐻푏푓 2 퐻푏푓 휕퐵푏푓 2 (1 − 퐹푟푏푓) − 퐹푟푏푓 = 푆 − 퐶푓 퐹푟푏푓 (4.4) 휕푥 퐵푏푓 휕푥

The unknowns in the equation (4.4) are the water depth 퐻푏푓, channel width 퐵푏푓, and the friction coefficient Cf.

4.3.2 Channel Formative Closure

To predict the geometry of channelized portion of the delta top, the Li et al. (2015) empirical relations are used to compute the dimensionless Chezy friction coefficient and the formative (bankfull) Shields number. The non-dimensional Chezy coefficient at bankfull flow is computed as (Li et al., 2015)

−푛푅 퐶푧푏푓 = 훼푅푆 (4.5)

where 훼푅 and 푛푅 are the model constants respectively equal to 2.53 and 0.19. Recalling

-2 that Cf = Czbf and substitute the channel slope S with friction slope Sfbf, the non- dimensional friction coefficient is determined as following

−2 2푛푅 퐶푓 = 훼푅 푆푓푏푓 (4.6)

The Shields number at bankfull flow, which is a non-dimensional parameter defined as the ratio of the bed shear stress and ρRgD, with ρ is water density, R being the submerged specific gravity of the sediment and D the characteristic bed material size, is computed as (Li et al., 2015)

∗ ∗ 푛 푚 휏푏푓 = 훽(퐷 ) 푆푓푏푓 (4.7) where  = 1220, n = -1.0, and m = 0.53 are empirical constants, and 퐷∗ is the non- dimensional grain size of the bed material defined as

1 (푅푔) ⁄3 ∗ (4.8) 퐷 = 2 퐷 휈 ⁄3 where ν denoting the kinematic viscosity of the water.

For the schematic cross section considered here (see Figure 4.7), the elevation of the non-channelized portion of the delta is computed as

휂푓 = 휂푐 + 퐻푏푓 (4.9)

The average elevation of the delta top is the average between 휂푐 and 휂푓, and it is computed as

퐵푓휂푎푣 = 퐵푏푓휂푐 + (퐵푓 − 퐵푏푓)휂푓 (4.10)

Substituting equation (4.9) into equation (4.10) the channel bed elevation can be obtained as a function of the bankfull channel depth and channel width

퐵푏푓 휂푐 = 휂푎푣 − 퐻푏푓 (1 − ) (4.11) 퐵푓

Thus, equation (4.6) and (4.7) represent the additional relations used to solve equation

(4.4). Equation (4.11) is used to determine the 휂푐 in each computational node. The boundary conditions to solve equation (4.11) are the bankfull flow at upstream end of the domain and the water level in the reservoir 휉푑. Recalling that the model simulation is performed at bankfull flow. The water surface elevation (base level) at the downstream is given as

휉 (푡) = 휂 | = 휂 | + 퐻 | 푑 푓 푑 푐 푑 푏푓 푑 (4.12)

Where the subscript d denoted the downstream end of the modeled reach, i.e., the delta top. In the present analysis 휉푑 is allowed to vary in time as shown in Figure 4.2. With the aid of of equation (4.11) equation (4.12) can be rewritten as

퐵푏푓 휉 = 휂 + 퐻 ( ) (4.13) 푑 푎푣,푑 푏푓,푑 퐵 푓 푑

4.3.3 Sediment Relations

The sediment transport rate is computed from the calibrated form of the Engeluand-

Hansen relation of the total bed material for the Nile River is given by

0.05 ∗ 5/2 푄푡푏푓 = 훽푐 √푅푔퐷 퐷 Bbf (휏푏푓) (4.14) 퐶푓

where Qtbf here is the volumetric bed material load (sand), c is a calibrated factor equal to 5.2 (Al-Zaidi et al., 2016).

4.3.3.1 Sediment Conservation

The time rate of change of the average elevation of the delta top is computed with the equation of sediment conservation, i.e., the Exner equation in the following form (Parker,

2004)

휕av Ω(1 + 훬) 휕푄푡푏푓 (1 − 휆푝) ( ) = −퐼푓 (4.15) 휕푡 Bf 휕푥

The Euler method is used to integrate the equation (4.15) in time. The initial condition is a specified average elevation of the delta top.  is the fraction of wash load deposited per unit of sand deposited in the channel, Ω is the channel sinuosity. For the channelized portion of the HAD delta, the channel sinuosity ranges between 1.0 and 1.25.

Sediment load is transported in the channelized portion of the delta top Bbf, can be

deposited over the floodplain width Bf. The boundary condition is a specified input of sand 푞푡푓 at the upstream end of the modeled domain equal to the mean annual sand load of the Nile River 37.2 Mt/yr.

This form of the Exner equation of conservation of bed material was implemented because it allows us to account for a variable geometry of the channelized portion of the delta top. If the standard 1D form of the Exner equation was implemented, i.e., the equation expressing conservation of channel bed material only, the changes in the elevation of the non-channelized portion of the delta top would not have been computed, and the elevation of the channel geometry could not have been predicted.

4.3.3.2 Shoreline Migration Model

Shoreline migration is computed with a shock condition expressing sediment conservation at the delta front (Swenson et al., 2000; Parker, 2004). This shock condition is obtained by integrating the Exner equation over the delta front. The schematic delta longitudinal profile of the relevant model variables are presented in Figure 4.7 (Parker,

2004). The form of the shock condition used herein is (Parker, 2004)

1 퐼푓(1 + 훬)Ω푄푡푠푏푓 휕휂푎푣 푆푠̇ = [ − | ] (4.16) (푆푎 − 푆푠) (1 − 휆푝)(푥푏 − 푥푠)퐵푓 휕푡 푥s

where 푆푠̇ denotes shoreline migration rate, Ss denotes the bed slope of the fluvial region at the shoreline and is defined as

휕휂푎푣 푆푠 = − | (4.17) 휕푥 xs

where xb and xs represent the coordinates of the shoreline and delta toe respectively (see

Figure 4.7), and λp is the bulk bed porosity. Qtsbf here is the volumetric bed material load that delivered to the brink of the foreset. Sa is the slope of delta front assumed to have a constant angle, and the slower slope depends on the fine-grained material.

The continuity condition at foreset-bottomset break is used to express the continuing of elevation at the delta toe, which is the downstream most point of the delta front and the upstream most point of the basement. The following form of the continuity condition was used to compute the migration rate of the delta toe 푆푠̇

휕휂푎푣 (푆 − 푆 )푆̇ = (푆 − 푆 )푆̇ + | (4.18) 푎 푏 푏 푎 푠 푠 휕푡 푥s

The changes in bed elevation associated with transport of wash load are not modeled

(Kostic and Parker, 2003).

4.4 MODEL VALIDATION

Model results are compared with field data collected on the HAD in terms of longitudinal profiles of channel bed elevation, shoreline migration rate, widths and depths of the channelized portion of the delta top. Model input parameters are summarized in Table

4.1.

4.4.1 Longitudinal Profile

The comparison between numerical predictions of channel bed elevation and an average elevation of the delta top is presented in Figure 4.8 where the elevations are represented

in meters above mean sea level. The red dots represent measurements of channel bed elevation, and the blue lines are numerical predictions, the black lines represent the average elevation of the delta top. The initial condition is the average channel-floodplain elevation of the longitudinal profile in 1977, when the delta started prograding in the

HAD reservoir.

Figure 4.8 shows that the predicted longitudinal profiles are in reasonably good agreement with the measured data in terms of channel bed aggradation and progradation.

The longitudinal profiles shown in Figure 4.8 show that the average elevation of the delta top is highest in the downstream part of the delta where the width of the delta top increase from 1000 m to 7500 m. This is likely a consequence of the values of  used in the simulations,  = 2 where Bf = 1000 m, and  = 5 where Bf = 7500 m.

4.4.2 Shoreline Progradation

The comparison between numerical predictions and field based estimates of shoreline position is presented in Figure 4.9, where the blue line represents the model prediction of shoreline position, and the red line is the shoreline migration rate, the black triangles are the filed measurement of the shoreline positions. The comparison between the predicted location of the shoreline and the field data shows that the model can reasonably capture delta progradation in HAD reservoir with an error not larger than  15%.

In the initial part of the simulations (1977-1990), the shoreline migration rate (red line) was larger than the post-1990 period due to the model adjustment to the initial conditions and the drought (1981-1987). During the drought, the water level in the HAD

reservoir dropped with a consequence erosion of the delta top and high sediment loads delivered to the shoreline.

4.4.3 Channel Geometry

Further validation of the model is done in terms of widths and depths of the channelized portion of the delta top. The widths and the depths of the channelized portion of the delta top were extracted from Nile Research Institute (NRI) surveys of the cross sections in

1999, and 2008, where the interpretation of the field measurements to determine the widths and depths for cross section 23 and 3 in different years is presented in Figure 4.5.

Figure 4.10 shows the comparison between numerical and interpreted channel geometry at different cross sections. The model is able to reasonably capture the channel geometry of the HAD delta in the upstream part of the delta, i.e., from the inlet zone

(reservoir headwater region) until Rkm 368 upstream the dam. However, model predictions in the downstream most part of the delta, can not reproduce the observed increase in channel width. This probably due to the channel formative closure used herein, which was derived from data predicting to well-formed channels and not Jubenile channels such as those that form on the delta.

4.5 MODEL MODIFICATION

The model presented in the previous sections of this chapter was modified to study the effects of subsidence, sea level rise, and wave action, i.e., prime controls on the delta morphodynamics, and on the geometry of the channelized portion of the delta top.

4.5.1 Subsidence and Sea Level Rise

When subsidence is accounted for in the calculations, the Exner equation takes the form

휕av Ω(1 + 훬) 휕푄푡푏푓 (1 − 휆푝) ( + 휎) = −퐼푓 (4.19) 휕푡 Bf 휕푥 where 휎 is the subsidence rate. Consequently, the shock and continuity conditions become

1 퐼푓(1 + 훬)Ω푄푡푠푏푓 휕휂푎푣 푆푠̇ = [ − | − 휎] (4.20) (푆푎 − 푆푠) (1 − 휆푝)(푥푏 − 푥푠)Bf 휕푡 푥s

휕휂푎푣 (푆푎 − 푆푏)푆푏̇ = (푆푎 − 푆푠)푆푠̇ + | + 휎 (4.21) 휕푡 푥s

In the model simulation, the boundary condition of equation (4.13), i.e., water surface elevation at the downstream end, is allowed to vary with the time. To account for the sea level rise, the water surface elevation at the shoreline is expressed as

휉 (푡) = 휂 | = 휂 | + 퐻 | + 휁∆푡 푑 푓 푑 푐 푑 푏푓 푑 (4.22) where ζ is the rate of sea level rise. Equation (4.22) is used as downstream boundary condition for the equation (4.13).

4.5.2 Wave Action

The shape and the growth of the delta lobes are affected and controlled by surf zone dynamics and shallow marine morphodynamics (Bharracharya and Giosan, 2003;

Swenson et al., 2005). In our delta model, to account for the wave effect on delta

morphodynamics, we used the formulation presented by Swenson et al. (2005), in which the fluvial input interacts with wave/current due to coastal storms, which control the sediment partition between the subaerial delta considered herein and the subaqueous delta

(Swenson et al., 2005).

In the Swenson et al. model, the boundary between the fluvial zone and the shallow marine zone is the surf or breaker zone, in which fluvial and shallow marine sediment dynamics are combined. This interaction between fluvial and shallow marine transport processes is accounted for in the shoreline migration model with the following form of the shock condition

1 퐼푓(1 + 훬)Ω(푄푡푠푏푓 − 푞푠) 휕휂푎푣 푆푠̇ = [ − | − 휎] (4.23) (푆푎 − 푆푠) (1 − 휆푝)(푥푏 − 푥푠)Bf 휕푡 푥s

where qs is the seaward directed sediment flux and computed from the following equation

(Coco, 1999; Swenson et al., 2005).

2 2 16 휌 퐶푓ℇ푠푠 푈표푚 푈표푚 휕ℎ 푞푠 = 퐼푠 [푣표 + ] (4.24) 3휋 휌푠 − 휌 푔 푊푠 5푊푠 휕푥

where ρ denotes the water density, ρs is the density of sediment, Cf is the drag coefficient,

ss efficiency of suspended sediment transport, g is acceleration of gravity, Is storm intermittency, Ws sediment fall velocity, vo is downwelling current-response to tilting of the sea surface, Uom is the nearbed velocity of the shoaling waves and computed as follows

3 − 훾푏 ℎ 4 (4.25) 푈표푚(ℎ) = √푔ℎ푏 ( ) 2 ℎ푏

Where h is water depth, hb is the breaker depth, b is breaker index which represents the ratio between the height of breaking waves Hb and the breaker depth hb, i.e., b = Hb/hb.

The breaker index ranges between 0.4 and 0.8. In the model, we take Is equal to 0.5

(Stanley and Warne, 1998); and b as 0.6.

4.5.3 Model Results under the Effect of Sea Level Rise, Subsidence, and Wave Action

We used the modified model to investigate the effects of the wave action, sea level rise, and subsidence on the delta growth and channel geometry. Two different cases are considered, one with a constant width of the delta plain equal to 1000 m, and the other with the variable delta plain width shown in Figure 4.4. Figures (4.11- 4.16) present the model results in terms of delta profile when sea level rise, subsidence, and wave action are accounted for. Figures (4.11- 4.13) show the model results for the case of constant delta plain width, while Figures (4.14 - 4.16) show the model results of the case of variable delta plain width.

Figure 4.11 shows the change in the longitudinal profile of the delta in terms of average channel floodplain and channel bed at simulation time of 320 years. The black line represents the base case, i.e., without accounting the sea level rise, subsidence, and/or the wave action, the dashed black line represents the model results with sea level rise effects. The grey line represents the model results of subsidence; the dashed grey line represents the model results of wave action. We assume that the rate in base level rise of

5 mm/yr, and the subsidence rate is 5 mm/yr. As a comparison with the base case, i.e., the black line, it seems there is no significant change in the longitudinal profile for the results

of sea level rise, subsidence with rates of 5 mm/yr during the simulation time (i.e., 320 years). From the results, it is clear that the wave action has more effect on the position of the delta shoreline in the simulated time in both scenarios.

Figure 4.11b shows the change in the channel bed elevation in the streamwise direction. The lowest channel bed elevation is predicted in the case of significant wave effects, and a slight change in the longitudinal profile is observed in the case of subsidence. In the run with rising sea level, the results show a slight deposition in the upstream part due increase in the water depth, with a slight reduction in the delta progradation. The sea level rise elevated the base level so that channels became shallow and with relatively mild slopes in the upstream part.

Figure 4.12 shows that the bankfull water depth is highest in the case of wave action, and smallest in the case of sea level rise due to the sediment deposition in the upstream part of the domain. The results also show a wider bankfull channel width in the case of sea level rise than in the case of wave action.

Changes in the shoreline position and delta migration rate are presented in Figure

4.13. These changes were forced by increase in the rate of relative sea-level rise, wave action, and subsidence under the same rate of sediment supply and flow discharge. In another words, the migration of the shoreline depends upon the balance between the quantity of sediment supplied to the coast and that carried away by hydrodynamic factors.

The results show that the minimum shoreline position and delta migration rate is indicated in the case of accounting for wave action.

Figures (4.14-4.16) are model results with variable delta plain width, the longitudinal profile of the delta in term of the average channel-floodplain and channel

bed is presented in Figure 4.14. As a comparison with the base case, i.e., the black line, it seems the reduction in delta progradation is still present in the case of wave effect, with lowest delta progradation rates than those in the case of constant width of the delta plain.

For the channel geometry, we have similar results as that shown in the first case of constant floodplain width. Figure 4.16 shows delta progradation and delta migration rates for the case of variable width of the delta plain. The comparison between the model results in the cases of the constant and variable width of the delta plain shows that subsidence, sea level rise, and wave action have less effect on the model results than the width of the delta plain and associated with mud trapping efficiency.

4.6 CONCLUSIONS

In this chapter, a model of delta morphodynamic is presented, the model is able to account for delta growth and changes in channel geometry. The model is validated against field data of in HAD reservoir. A reasonable agreement between the numerical results and the measured data was obtained during the model verification. The model was then modified to account for wave action, subsidence, and sea level rise. Two types of simulations were performed, one with constant width the delta plain and the other with a variable delta plain width.

The results show that the wave action has the most influence on the model results in terms of delta progradation, and channel geometry for the same sediment supply and flow discharge, with highest delta progradation rates in the case of constant width of the delta plain.

Furthermore, the hydrodynamic factors have a slight effect on the channel geometry close to the shoreline. The cross section becomes deeper and narrower with the effect of wave, subsidence, and sea level rise, in the most downstream. The bankfull water depth is highest, and the channel width is narrowest in the case of significant wave effect, while the bankfull depths are smallest and the channel width is widest in the case of the base level rise modeling. The subsidence effects are intermediate between the wave action and sea level rise simulations.

Table 4.1 Summary of input parameters for the delta model during the model validation, data are from Nile Research Institute (NRI) database.

Parameter Definition Value(s) unit

3 Qwbf Bankfull water discharge 7700 m /s

Qtf Bed material load 129 Mt/yr

If Flood intermittency 0.25 ---

D50 Mean grain size diameter 0.25 mm

Ω Channel sinuosity 1.25 ---

 Fraction of mud deposition 2 and 5 ---

Sa Foreset slope of the delta 0.0012 m/m

Sb Bed slope of the delta 0.073 m/km

Sf Fluvial bed slope of the delta 0.00035 m/m

Study area 5 ³ Nile River

Sudan New Nile Delta

0 km 530 Dongola

0 km 53

Figure 4.1. The location map of the HAD Reservoir showing the cross sections of the field data of the new Nile delta upstream High Aswan Dam. Images are from Google Earth.

190

180

170

160 Drought

150

140

130

Water Level(m) Water 120

110

100 Mar-60 Sep-65 Mar-71 Aug-76 Feb-82 Aug-87 Jan-93 Jul-98 Jan-04 Jul-09 Dec-14 Time

Figure 4.2. The monthly average water levels upstream of the HAD from 1964 to 2014 above mean sea level, the red line represents the simplified water level used in the simulations, the data from Nile Research Institute (NRI). The yellow circle indicates the drought period.

1990

1997

HAD

Figure 4.3. Longitudinal profiles of the new Nile delta in the High Aswan Dam reservoir (HAD delta), all elevations are above mean sea level (M.S.L). HAD delta profiles are courtesy of the Nile Research Institute (NRI).

100000 180

Bf ~ 7500 m 160

10000 140

(m) Bf ~ 1000 m

f 120 B 1000 100

100 Elevation (m) Elevation

Field data 60 Google Earth Delta plain width Delta plain Flow Channel bed – 2006 40 10 6 27 23 22 20

1 0 0 20 40 60 80 100 120 140 160 180 200 Distance (km)

Figure 4.4. Streamwise variation of floodplain width along the modeled reach, Cross Section 23 is at 0Rkm (i.e., the upstream end of the modeled reach). The red points represent the field data, where the blue points represent the predicted data using the Google Erath during the study time. The black line with circle marks represents the bed elevation at 2006.

100

CS 23 - 1977 CS 23-1999 CS 23-2008 210 210 210

200 200 200

190 190 190 Bbf Bbf 180 180 Bbf 180 H 170 170 Hbf 170 bf Hbf

160 160 160

Elevation above M.S.L (m) M.S.L aboveElevation

Elevation above M.S.L (m) M.S.L above Elevation Elevation above M.S.L (m) M.S.L aboveElevation 150 150 150 0 200 400 600 800 0 200 400 600 800 0 200 400 600 800 Distance from left bank (m) Distance from left bank (m) Distance from left bank (m)

CS 3 - 1977 CS 3 - 1999 CS 3 - 2008 200 200 200

190 190 190 Bbf 180 180 Bbf 180 Bbf 170 170 Hbf 170 Hbf 160 160 160 Hbf

150 150 150

Elevation above M.S.L (m) M.S.L aboveElevation Elevation above M.S.L (m) M.S.L aboveElevation Elevation above M.S.L (m) M.S.L aboveElevation 140 140 140 0 200 400 600 800 1000 1200 0 200 400 600 800 1000 1200 0 200 400 600 800 1000 1200 Distance from left bank (m) Distance from left bank (m) Distance from left bank (m)

Figure 4.5. Interpretation of the cross-section measurements to determine bankfull geometry, the comparison between cross sections 23 and 3 in different years.

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23 19 13 6 28 16 10 1000 180

160

140 100 22 120

100 10

80 Elevation (m) Elevation Sediment size size (µm)Sediment 60 1 40

Flow 20

0.1 0 0 20 40 60 80 100 120 140 160 180 200 Distance (km)

Figure 4.6. Downstream fining on the delta top. The data were collected in 2006 by the Nile Research Institute (NRI). The red dots represent the median diameter D50 of the sediment samples. The black line with circle marks represents the bed elevation at 2006.

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Delta front Bf Qw Bbf Qtf Wave ζ σ S s Hbf η Sa ηavg ξd Sb ηf xs ηs xb Delta toe η b Datum Datum

Figure 4.7. Geometry of channel-floodplain cross-section of the model, and schematic of delta progradation profile with the relevant model parameters.

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A) 1990 200 B > 1000 m 180 f 160 140 120 100 80 Channel bed - Model

Elevation (m) 60 Average channel-floodplain - Model 40 20 Channel bed - Data 0 0 50 100 150 200 Streamwise distance from CS 23 (km)

B) 1997 200 B > 1000 m 180 f 160 140 120 100 80 Channel bed -Model

Elevation (m) 60 40 Average channel-floodplain - Model 20 Channel bed - Data 0 0 50 100 150 200 Streamwise distance from CS 23 (km)

C) 2012 200 Bf > 1000 m 180 160 140 120 100 80

Elevation (m) 60 Channel bed - Model 40 Average channel-floodplain - Model 20 Channel bed - Data 0 0 50 100 150 200 250 Streamwise distance from CS 23 (km)

Figure 4.8. Comparison between numerical predictions of channel bed elevation (blue lines) and average elevation of the delta top (black line) and measured data. The red dots represent measurements of channel bed elevation. Cross section 23 is at 0Rkm (i.e., the upstream end of the modeled reach).

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200 5

180 4.5

160 4

140 3.5

120 3

100 Drought 2.5

80 2

60 1.5 Shoreline Postion (km) Shoreline

40 Model adjustment 1 (km/yr) rate Delta migration

20 0.5

0 0 1970 1975 1980 1985 1990 1995 2000 2005 2010 2015 2020 Time

Figure 4.9. Comparison between the predicted location of the shoreline (blue line) and the field data (black triangles), the model captures delta progradation in HAD Reservoir (error bars 15%). Data source is the Nile Research Institute (NRI). The red circle represents the drought period, and the yellow circle in the initial part represents the model adjustment to the initial conditions.

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1999 1999 40 6000 Data Data 35 5000

Model Model (m)

30 (m) bf

bf 4000 B H 25 Bf ~1km Bf ~7.5km 20 3000

15 2000

Water depth Water 10

B ~1km B ~7.5km Channelwidth 1000 5 f f

0 0 0 20 40 60 80 100 120 140 160 0 20 40 60 80 100 120 140 160 Distance (km) Distance (km)

2008 2008

40 6000 Data 35 Data 5000 Model (m) (m) Model

30 bf Bf ~1km B ~7.5km

bf f B

H 4000 25

20 3000

15 2000

10 Water depth Water B ~1km B ~7.5km Channelwidth 1000 5 f f

0 0 0 20 40 60 80 100 120 140 160 0 20 40 60 80 100 120 140 160 Distance (km) Distance (km)

Figure 4.10. Comparison of bankfull channel geometry between the predicted and interpreted field data along the modeled reach for different time periods.

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A) 180 170 160 150 140 130

120 Base case

Elevation (m)Elevation 110 Sea level rise Subsidence 100 Wave action 90 80 0 100 200 300 400 500 Distance (km)

B) 165

160

155

150 Base case

Elevation (m)Elevation Sea level rise Subsidence 145 Wave action

140 0 50 100 150 200 250 300 350 400 Distance (km)

Figure 4.11. The longitudinal profiles of the delta with a constant floodplain width scenario at 320 years under the effect of sea rise, subsidence, and wave action, where A) represents the average channel floodplain elevation, and B) is the channel bed elevation. The black line represents the base case where no effect, the dashed black line is the sea level rise, the grey line is the subsidence, and the dashed grey line is for the wave effect.

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A) 45 40 35

30 (m)

bf 25 H 20

15 Base case Sea level rise 10 Subsidence Water depth Water 5 Wave action 0 0 50 100 150 200 250 300 350 400 Distance (km)

B) 500 450 400

(m) 350 bf B 300 250 200 150 Base case Sea level rise Channelwidth 100 Subsidence 50 Wave action 0 0 50 100 150 200 250 300 350 400 Distance (km)

Figure 4.12. The effect of the sea level rise, subsidence, and wave action on channel geometry at 320 years in the case of the constant floodplain width scenario, where A) is the bankfull water depth, and B) the bankfull channel width.

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A) 450

400

350

300

250

200 Base case 150 Sea level rise

100 Subsidence Shoreline postion (km) Shoreline Wave action 50

0 0 50 100 150 200 250 300 350 Time (year)

B) 2.5 Base case 2 Sea level rise Subsidence Wave action 1.5

0.5 Delta migration rate (km/yr) rate Deltamigration

0 0 50 100 150 200 250 300 350 Time (year)

Figure 4.13. Change in delta progradation at 320 years in the case of the constant floodplain width under the effect of sea rise, subsidence, and the wave action, where A) is in terms of the shoreline position, (B) is the delta migration rate. The black line represents the base case, the dashed black line represents the sea level rise, the grey line is for the subsidence, and the dashed grey line is the wave action.

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A) 190 180 170 160 150 140

Elevation(m) 130 Base case 120 Sea level rise Subsidence 110 Wave action 100 0 50 100 150 200 250 300 Distance (km)

B) 165

160

155

150

Elevation(m) 145 Base case Sea level rise 140 Subsidence Wave action 135 0 50 100 150 200 250 Distance (km)

Figure 4.14. The longitudinal profiles of delta with a variable floodplain width scenario at 320 years under the effect of sea rise, subsidence, and wave action, where A) represents the average channel floodplain elevation, and B) is the channel bed elevation. The black line represents the base case where no effect, the dashed black line is the sea level rise, the grey line is the subsidence, and the dashed grey line is for the wave effect.

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A) 45 40 35

(m) 30

bf H 25 20 Base case 15 Sea level rise

Water depth Water 10 Subsidence Wave action 5 0 0 50 100 150 200 250 Distance (km)

B) 500 450 400

(m) 350

bf B 300 250 200 Base case 150 Sea level rise Channelwidth 100 Subsidence 50 Wave action 0 0 50 100 150 200 250 Distance (km)

Figure 4.15. The effect of the sea level rise, subsidence, and wave action on channel geometry at 320 years in the case of the variable floodplain width, where A) is the bankfull water depth, and B) the bankfull channel width.

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A) 250

200

150

100 Base case Sea level rise

Shoreline postion (km) Shoreline 50 Subsidence Wave action 0 0 50 100 150 200 250 300 350 Time (year)

B) 2 Base case 1.8 Sea level rise 1.6 Subsidence Wave action 1.4 1.2 1 0.8 0.6 0.4

Delta migrationrate(km/yr) 0.2 0 0 50 100 150 200 250 300 350 Time (year)

Figure 4.16. Change in delta progradation at 320 years in the case of the variable floodplain width under the effect of sea rise, subsidence, and the wave action, where A) is in terms of the shoreline position, (B) is the delta migration rate. The black line represents the base case, the dashed black line represents the sea level, the grey line is for the subsidence, and the dashed grey line is the wave action.

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CHAPTER 5

SUMMARY AND CONCLUSIONS

5.1 SUMMARY AND CONCLUSIONS

The research presented in this dissertation focuses on the study of a large restoration project for the densely populated Nile River-Delta system, Egypt. This system entered a phase of deterioration due to water resources management in the river basin. The problem accelerated after the construction of the High Aswan Dam during the 1960s close to the

Egypt-Sudan border.

Today virtually no water is delivered to the Mediterranean Sea. Consequently, the sediment load delivered to the Mediterranean Sea is also negligible compared to pre-dam conditions. The net results of this change in Nile River hydrology are delta wide wetland loss and shoreline retreat, widespread delta pollution, reduction of soil quality, salination of cultivated land and saltwater intrusion in the groundwater. The considered solution to the problem is a restoration project characterized by sediment augmentations associated with controlled flow releases at the Aswan.

Previous studies showed that ~10 billion m3 of water can be saved annually by improving the Egyptian irrigation system. Here we propose to use the water that can be saved with a change of the irrigation system to increase the water discharge to the Nile

River and Delta. We modulate the river flow by storing the saved water during the

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agriculture season upstream of the High Aswan Dam (Lake Nasser) and releasing it in the months coinciding with the natural flood season, i.e., August - October.

The sand for the sediment augmentations will be mined from High Aswan Dam

Reservoir delta, i.e., the delta that is naturally forming upstream of the High Aswan Dam, and the mined sediment will be conveyed downstream of the Old Aswan Dam with slurry pipelines. The controlled flow releases will transport the augmented sediment through the

Nile River under semi-natural conditions. This project will be sustainable because the

High Aswan Dam Reservoir delta continues to grow due to the input of sand from the

Nile River, and the restoration project will not affect navigation and flood control.

The research work has been divided into three connected studies:

• the first study explores the ability of 1D morphodynamic models to capture the

changes in channel bed elevation on the Nile River under the impacts of the High

Aswan Dam and the barrages, which is considered a first and necessary step for

the restoration project of the Nile River-Delta system;

• the second study focuses on the quantification of the impacts of the proposed

restoration project on the Nile River and to estimate the sand loads delivered to

the delta of the Nile River;

• the third study consists of the development and validation of a delta model that is

able to account for delta growth and the changes in channel geometry. The model

is then modified to account for factors controlling the evolution of large deltas

such as wave action, sea level changes, and subsidence. This study represents the

first and necessary step for the delta restoration project, i.e., the second part of the

Nile River-Delta restoration project.

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The main findings of this study are listed below:

• The upstream channel bed degradation of the Nile River can be controlled with

the proposed sediment augmentations and controlled flow releases. The model

simulations show sedimentation control in the downstream part of the study reach.

Minimum changes in channel bed elevation are predicted in the central part of the

modeled reach after 300 years of simulated time from the beginning of the

restoration project by achieving sediment transport capacity;

• The proposed restoration project results in an increase in the volume of water and

sand delivered to the delta. Changes in the sand supply to the delta are associated

with the shape of the hydrograph released at Aswan. Sediment load will increase,

in a relative sense, in response to an increase in peak flow;

• the restoration project ensures safe navigation and does not increase the flood

hazards along the river;

• the model of the Nile River predicts a significant reduction in the sand load to the

delta when the base level rise is accounted for at a rate of 5 mm/yr;

• a model of delta morphodynamic is presented and validated against field data

collected on the HAD delta;

• the delta model is able to account for the change in shoreline position, delta

migration and channel geometry;

• the delta model is modified to account for the effect of wave action, subsidence,

and sea level rise.

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5.2 FUTURE WORK

Future work consists in computing the study of the impacts of the restoration project on the Nile delta. A model of delta morphodynamics that concurrently predicts delta progradation and channel geometry has been developed. The model is validated against field data collected by the Nile Research Insitute on the HAD Reservoir delta, i.e., a delta that is naturally forming upstream of the High Aswan Dam. The model is modified to account for the effect of waves, subsidence, and sea level rise and will be applied to study the impacts of the proposed restoration project on the Nile delta in the Mediterranean Sea when the data become available.

Our hypothesis is that coastal erosion and ecosystem deterioration on the Nile delta can be reduced, if not reversed, by means of controlled flow and sediment releases from the two Aswan dams. In particular, the restoration of a semi-natural flow hydrograph combined with the sediment releases will re-establish a) sediment deposition on the delta plain to mitigate relative sea level rise, subsidence, and wave action; b) sediment transport to the Mediterranean Sea to reduce coastal erosion; c) sufficient influx of water to the delta to reduce the high level of salt and pollutants throughout the system, prevent and reverse canal siltation by effectively transporting fine sediment to the Mediterranean

Sea; and d) a healthy deltaic ecosystem that may keep up with the predicted rates of relative sea level rise. It is important to mention that the sustainability of this project, however, strongly depends on the present and future water needs in the Nile River basin.

Further, the following future investigations are recommended for additional studies related to the topic:

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• determine the effects of vegetation on time sediment trapping rate in the system,

i.e., in both channel and the delta;

• develop two- or three- dimensional computational models to estimate the local

impacts of all type of barrage structures on the Nile River;

• account for the additional storage volumes of water that are available upstream of

the major barrages along the modeled reach beside water that can clawed back

from other users as additional water supplies, these volumes can also be used with

an sufficient management during the proposed restoration project because of one

of the main objectives of the barrages is to conserve water;

• modify the delta model into a fan delta model, because of the Nile delta is fan

shaped delta;

• modify the delta model to account for the hydrograph to apply for the restoration

project of the delta restoration;

• the study provides a blueprint for addressing similar problems in other dammed

rivers within the region, such as the Tigris-Euphrates Rivers-Delta in Iraq since

the lower of Tigris-Euphrates valley has lost millions of acres of wetland areas in

the delta region and converted into saltpans and sabkhas due to the deficit in

sediment and fresh water and that resulted in increased salinity in the wetland

areas. The Tigris-Euphrates Rivers-Delta system is also controlled by other

external forces such as tides and wind; thus, in order to apply our model to this

system, the model has to be modified account for other external forcings such as

tides and wind. Moreover, this system is significantly controlled by several

structures such as dams, barrages, and small dams. Therefore, the approach used

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in this dissertation can be seen, further, as a tool to assess the sustainability of large-scale regulated rivers management practices, and restoration projects for

Marshes and Tigris-Euphrates Rivers Delta (Shatt al Arab Delta) in Iraq.

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APPENDIX A

PERMISSION TO REPRINT

The appendix explores permission to reprint the manuscript presented in Chapter 2 of this dissertation.

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