Effect of Grand Ethiopian Renaissance Dam on the Water Footprint 1 of Aswan High Dam Hydropower

9 Construction of the Ethiopian Grand Renaissance dam (GRD) has many impacts and 10 implication on the water share and future use in Egypt. Especially the period of the reservoir filling 11 will have a great effect on the Nile River and its water in Egypt. Many of these effects of the GRD 12 on Egypt has been studied before, but no study was done on the effect of its existence on the 13 hydropower water footprint of the High Aswan dam. This research is concerned by simulating the 14 effect of the different GRD reservoir filling scenarios on the water footprint of the hydropower 15 generated from the High Aswan dam. Also, the effect on the hydropower of the Aswan dam itself 16 is also simulated and assessed. Mathematical modeling is used to reach those goals. Three filling 17 scenarios of the GRD were investigated: namely 3 years, 5 years, and 6 years. It was found that as 18 the filling duration of the GRD decreases the negative effect on the hydropower water footprint 19 increases. 20

Introduction 24 "Egypt is the gift of the Nile"; that is how the Greek historian Herodotus described the 25 relation between Egypt and the Nile River. Egypt is an arid dry area. In summer, the temperature 26 usually exceeds 38°C in some parts of the country and the average annual rainfall amounts are 27 very low all year long (1). With these nature and limited water resources, Egypt relies on the Nile 28 River to fulfill 97% of the water needs of the Egyptian population that reached more than 100 29 million capita nowadays. However, the seasonal flow of the Nile River cannot fully satisfy these 30 needs during the drought season; whereas, it overflows and causes disaster during excess flooding 31 season. Due to these conditions, the Egyptian government had decided to build Aswan high dam 32 which completed in 1968 and fully operated in 1972. 33 Aswan High Dam (AHD) is a rockfill hydraulic structure that is located 7 km south Aswan 34 City (2). The dame is 3600 m in length, 111 m in height above the riverbed and 980 in top width 35 (3). AHD is very important for the development of the country as it controls the flood of the Nile 36 to protect the Nile valley and Delta areas from high floods and drought hazards. Its existence also 37 led to agriculture developments and expansion and reclamation plans. It also improves the 38 navigation in the Nile. In addition, the dam is supplied by a hydropower station with installed 39 capacity of 2.1 million MW and it generates up to 10,000 Gwh. Upon building the dam, the 40 hydropower generated from AHD was responsible for providing electricity for 4500 villages, many 41 factories and pumping stations for irrigation and drainage which helped in raising the 42 industrialization and standard of living in Egypt (1,3). On the other hand, the AHD reservoir is the 43 evaluate the environmental effect of the hydropower stations on Yalong River Basin. In this study, 90 the evaporated water footprint, the blue water footprint, and the blue water scarcity footprint were 91 calculated as an environmental assessment for 19 hydropower stations; the results indicated that 92 the stations will not affect the local environmental flow requirements (17). On the other hand, a 93 global study was conducted on around 1500 hydropower stations, that generate around 43% of the 94 global annual hydroelectricity generation, using a new approach in calculating the water scarcity 95 footprint. This approach is taking into consideration the evapotranspiration before the dam 96 construction, the seasonal dynamic storage of water, and the allocation of impacts among all 97 purposes of multipurpose dams (18). All these studies spot the light on the importance of water 98 footprint terms in evaluating the environmental effect of the hydropower stations and electric 99 dams. However, this research paper is aiming to study the use of the water footprint concept in 100 simulating and predicting the effect of the different scenarios of filling the GRED on the water 101 security for the AHD electricity production. 102 The aim of this study is to calculate the water footprint of the hydropower generated from 103 the AHD and then to use this estimated water footprint as an indicator of the negative effects of 104 GERD on the hydropower generation from AHD. The water footprint will be calculated 105 considering 3 scenarios of GERD filling period and the results will be analyzed to understand the 106 effects of these scenarios on the hydropower generation from AHD. 107

Methodology and Data 108
The water footprint of electricity generated from the AHD hydropower plant was 109 calculated first considering the case before filling the GRED. Then, three scenarios for the filling 110 period of the GERD were assumed, and the water footprint of electricity generated from the AHD 111 hydropower plant was recalculated for each scenario. The first scenario is assuming the filling 112 period to be 3 years, the second is assuming it to be 5 years and the third is assuming it to be 6 113 years. The calculations were conducted over two periods. The first period is at the highest 114 discharge in Egypt and hence highest water level of the Nile River which takes place during months 115 of June, July and August. The second period is the lowest discharge period of the river in Egypt, 116 namely the drought period. At this time, the water level of the Nile River is at its minimum value. 117 This happens during months of December, January and February. 118 To carry out the study a mathematical model was developed using Excel spreadsheets. The 119 model uses the equations stated in the following paragraphs. Based on the previously discussed 120 definition, the water footprint of electricity generated from the AHD hydropower plant was 121 calculated according to the following equation (16): 122 WF = (eq. 1) 123 Where WF is the water footprint of electricity generated (m3GJ−1), WE is the total volume of 124 water evaporated (m3yr-1), EG is the amount of energy generated (GJ yr-1). 125

a. The total volume of water evaporated Calculations 126
The total volume of water evaporated from Lake Nasser, which is the reservoir of AHD, 127 was calculated according to the following equation: 128 Where E is the daily evaporation rate (mm-1day-1) according to Aswan weather. A is the area of 130 the reservoir (ha) which is 600,000 ha for Lake Nasser. The daily evaporation rate, E, was 131 calculated according to Penman-Monteith: 132 Where E is the daily evaporation rate (mm-1day-1), λ the latent heat of vaporization (MJ/kg), Δw 134 the slope of the temperature saturation water vapor curve at water temperature (kPa/oC); Rn net 135 radiation (MJ m2day-1); G the change in heat storage in the water body (MJ/m2/day); f(u) the wind 136 function (MJ/m2/day/kPa); ew the saturated vapor pressure at water temperature (kPa); ea the vapor 137 pressure at air temperature (kPa); and γ the psychometric constant (kPa/oC). (eq. 6) 147 Where A is the surface area of Lake Nasser (m2) and 2 is the wind speed at 2 m above the water 148 surface (m2/s). 149 On the other hand, net radiation (Rn) (MJ m2day-1) is the difference between the net 150 incoming short-wave radiation (Rns) (MJ m-2 d-1) and the net outgoing long-wave radiation (Rnl) 151 (MJ/m2/day) (Allen et al., 1998): 152 In which the net incoming short-wave radiation (Rns) (MJ m-2 d-1), which is resulting from 154 the balance between incoming and reflected solar radiation, is calculated as (Allen et al., 1998): 155 Where α is the albedo coefficient for open water, which is equal to 0.07 according to (Lenters et 157 al., 2005), and Rs is the incoming solar radiation (MJ/m2/day) which is calculated according to 158 Angstrom formula as follows: 159 Where is the relative sunshine duration (dimensionless), ( + ) is the fraction of 161 extraterrestrial radiation reaching the earth on clear days (when n = N), and Ra is the extraterrestrial 162 radiation (MJ/m2 /day). The net outgoing long-wave radiation (Rnl, MJ/m2/day) is calculated as 163 the difference between the outgoing long-wave radiation (Rl↑, MJ/m2/day) and the incoming long-164 wave radiation (Rl↓, MJ m-2 d-1) ( Where εa is the emissivity of air (dimensionless); σ the Stefan-Boltzmann constant that equals 169 4.903x10-9 MJ/K4/m2/day; Cf the fractional cloud cover (dimensionless); and rlw the total 170 reflectivity of the water surface for long wave radiation was taken as 0.03 , is the emissivity of 171 water which is equal to 0.97, and Tw the water surface temperature (oC) which was calculated as 172 (eq. 15) 180 Where vapor pressure ea (kpa), which was used also in eq.3, was calculated as (16) (eq. 17) 185 The net radiation at wet-bulb temperature Rn* (MJ/m2/day) was calculated using the albedo 186 coefficient as follows (16) Where P (kW) is the generated electric power output of each turbine, is station efficiency, is 220 the specific weight of water (N/m3) and H is the head of turbine (m). The amount of energy 221 generated annually EG (GJ/yr) was calculated as: 222 For the 3 scenarios for the filling GRED, the reduction in AHD generated electricity was 224 calculated based on the expectations that implied that for each billion m3 deducted from the 225 Egypt`s share of Nile River water, the hydropower generated from AHD will be reduced by 2%. 226 The maximum and minimum discharge flow through the turbines were assumed to be reduced by 227 the same percentage of reduction of the Egypt`s share of the Nile. So, the maximum and minimum 228 head of turbines were calculated using eq. 24, the amount of energy generated annually EG was 229 calculated using eq. 25. 230 Calibration 231 The mathematical model used for calculating the water footprint of the hydropower 232 generation was calibrated using data for the Three Gorges hydropower plant in China (Zhao & Liu,

237
It could be seen that the percentage errors are zero so it could be concluded that the model 238 is a reliable mean to predict the hydro power water footprint of the High Aswan Dam. 239

Results 240
All calculations were conducted in an excel sheet and the results were summarized in the 241 following sections. 242

a. The total volume of water evaporated 243
The daily evaporation rate of AHD reservoir (Lake Nasser) was calculated using Penman-244 Monteith equation for the period from December to February (drought period) and June to August 245 (flooding period). Then the total volume of the evaporated water was calculated using eq.2 as 246 shown in table 1. 247 248  The generated electrical power output (P) and the energy generated annually (EG) from 252 AHD, before filling the GRED, were calculated using the data collected from the annual report 253 issued by Egyptian Electricity Holding Company, as explained before and the results are 254 summarized in table 2. The number of turbines that operates in the summer is 12 turbines; however, 255 in the drought period, which is during December to February, only 6 turbines are operated. The 256 discharge values in table.2 were calculated using eq. 24. 257

259
For the filling scenarios, the generated electrical power output (P) and the energy generated 260 annually (EG) from AHD were calculated according to the expected reduction in the discharge 261 and the head of the turbines for each scenario; the results of these calculations were summarized 262 in tables 3, 4 and 5. The discharge values are reduced by the same percentage of deduction of 263 Egypt`s share of the Nile for each filling scenario of the Ethiopian dam. However, the turbine head 264 values were calculated using eq. 24. 265    The impact of three filling scenarios; namely 3 years, 5 years and 6 years, were modeled 299 and the water footprint was calculated. The results of the simulation indicated that as the filling 300 period of the Ethiopian Dam's reservoir decreases, the hydropower footprint of the Aswan High 301 Dam increases. Also, as the filling period decreases the generated hydropower decreases. 302 From the previous paragraph, it could be concluded that the negative impact of the Grand 303 Ethiopian Renaissance Dam on the hydropower and its water footprint in Egypt will be greater as 304 the period of time of the filling is shorter. So, to reduce this negative impact, it is recommended to 305 fill the Ethiopian Dam's reservoir on an extended period of time. 306

Declarations 307
Availability of data and materials 308 All data analyzed during this study are cited and the references are mentioned in the 309 references section. 310