Introduction

The Nile River has a length of 6670 km, with a watershed drainage area of 3.2 × 106 km2. The White Nile, which joins the Blue Nile (Ethiopian plateau) in Khartoum, Sudan, is drained by tributaries from the Equatorial Lakes plateau in Uganda. Another major tributary of the Nile system is the Atbara River. The Atbara River has headwaters on the Ethiopian plateau and meets the main Nile stream near Atbara in the north of Khartoum. The main Nile then flows through the Sahara desert, with no important tributaries (El Bastawesy et al. 2014). There are many advantages of dams, such as economic development, increased irrigated area, power generation, and flood protection. The Grand Ethiopian Renaissance Dam (GERD) is located about 20 km upstream of the Ethiopia–Sudan border on the Abay/Blue Nile. Many dams, including Roseires, Sennar, Jebel Aulia, Khashm El Girba, Merowe, and the Aswan High Dam (AHD), regulate the Nile River’s flow. These dams provide water storage and flow regulation, as well as hydropower, flood, and drought protection.

The flood caused by the dam break has resulted in a significant loss of human life and property. The quantity of human life and property are lost because a dam failure varies depending on the size of the population at risk, the size of the flood area, and the warning time available. Many forecasts are needed to prepare an emergency and evacuation plan to reduce dam break threats, such as dam break floods, the inundated area, flood wave propagation, flow velocity, flood depth, and flood wave travel time along the zone.

Ramadan et al. (2011, 2013, 2015) applied the river basin modeling and simulation package (MODSIM)) model to quantify the deficit of water in Lake Nasser active storage that is caused by GERD reservoir impoundment. Impounding scenarios of 6, 3, and 2 years were studied under various inflow conditions. They evaluated the impact of three GERD impoundment scenarios on Lake Nasser storage. Their results revealed that GERD impoundment at normal flow from the Blue Nile through 6, 3, and 2 years may reduce the active storage of Lake Nasser by 13.287, 25.413, and 37.263 BCM through each year in the first scenario. Second, impounding GERD at the minimum average flow from the Blue Nile for 6, 3, and 2 years may reduce Lake Nasser active storage by 25.963, 37.814, and 45.105 BCM per year. The third scenario of impounding GERD at the minimum flow case for 6, 3, and 2 years reduces Lake Nasser active storage by 44.398, 54.415, and 55.138 BCM per year. Moreover, they believed that GERD impoundment has a significant detrimental influence on Lake Nasser Storage, particularly if the filling duration is less than 6 years. Abdelhaleem and Helal (2015) analyzed the probable impact of Egypt’s water scarcity on the Nile water, which will limit the flow from AHD owing to the construction of the GERD. They decided that Egypt’s water share should not be reduced by more than 5 to 15%. They reported that a win–win strategy should be followed between Egypt and Ethiopia regarding the GERD reservoir’s capacity, imposition criteria, and operation rules.

Abdelhaleem et al. (2011a) calculated the likelihood of the AHD failing due to overtopping and piping. Using the HR Breach model, they created scenarios to depict minimal, normal, and maximum flood flow owing to AHD breach. They also applied SOBEK 1D–2D models to simulate outflow hydrographs caused by the AHD failure. Abdelhaleem et al. (2011b) described how the flood waves of AHD failure move along the water course from AHD to Delta Barrages in Egypt. They depicted the results including inundation maps, flows, water levels, flood arrival times, and flow speeds. The probability of the Aswan High Dam collapse because of overtopping was numerically presented by Ibrahim et al. (2011). The 1D–2D model was used to apply the results from the dam failure scenario of maximum inflow to typical Lake Nasser water level. In addition, a risk assessment for a dam breach has been completed.

The importance of the GERD and the implications of its construction and filling were addressed by (Chen et al. 2021, Heggy et al. 2021, Kahsay et al. 2015, Kansara et al. 2021, Elsayed et al. 2020, Abtew and Dessu 2019, Basheer et al. 2020, Dandrawy and Omran 2020, Wheeler et al. 2020, and Zhang et al. 2015). Najm et al. (2019) presented an overview of GERD as shown in Fig. 1. Soliman et al. (2019) classified the area between GERD and AHD into six distinct reaches. The GERD break modeling showed that the peak outflow was estimated to be 2,000,000 m3/s (mm3/s) and occurred within the first 5 h of the break. After 3 weeks of GERD pause, the peak inflow to the AHD reservoir was 37,000 m3/s. Within 4 days of the start of the GERD rupture, Khartoum will be submerged by water up to 15 m above ground level. The amount of AHD affected by GERD failure is determined by the water level in its reservoir during the GERD break. The GERD has two powerhouses downstream of the main dams. With a total installed generating capacity of 6000 MW, they will house 10 and 5 Francis Turbine Units, respectively. The annual energy generation averages 15,692 Gwh Sayed et al. (2013). (Idress et al. 2018 and Idress 2022) used a HEC-RAS model to anticipate the outflow hydrograph that could occur if the GERD breaks. Flood hazards were reported by Idress et al. (2021) as a result of GERD breaking. The HEC-RAS model was used to obtain outflow hydrographs owing to GERD break. SOBEK 1D–2D model was also used to simulate the Blue Nile and Nile River downstream of GERD until the AHD.

Fig. 1
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The GERD, (Negm et al. 2019)

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Reviewing the available literature showed that a few studies have reported the impact of GERD break on Sudan and Egypt. Thus, this study was conducted to figure out the outflow when the GERD breaks. The major goal of this research is to assess the flood risk associated with GERD break in the downstream area encompassed by GERD till the AHD. Scenarios for the consequences for the predicted defects that may occur to the upstream dams were designed and severely governed. That is to medium flood ranging from 84 to 150 Billion cubic meter (BCM) yearly to estimate the incoming discharges to the Lake Nasser. These discharges were run in case of Toshka spillway operation and in case of spillway shutdown. A risk assessment of the GERD break is being undertaken, and many scenarios are being offered. The findings of this research can assist decision makers in developing emergency and evacuation strategies to deal with the hazards of dam breakage based on knowledge of the flood’s arrival timing.

Materials and methods

Study area and assembled data

Data were collected for the Blue Nile from the Hydraulics Research Institute (HRI). They were collected for a numerical model conducted by HEC-RAS through the Eastern Nile Technical Regional Office (ENTRO) projects by “Global Science Solutions” expert. These data represent 840 cross section covering 721 km from Ethiopia–Sudan borders to Khartoum. Calibration was performed applying their model, and Manning roughness coefficient was 0.03 s/m1/3 for Nile reach and 0.045 s/m1/3 at reservoirs areas upstream of the dams. Figure 2 depicts a cross-sectional profile located between Roseires and Sennar dams.

Fig. 2
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Cross section located at km 206 at Blue Nile downstream GERD

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The reach from Khartoum to Lake Nasser with a length of 2332 km was simulated by cross sections taken from model conducted and prepared for Nile reach, and these cross sections are allocated every 2 km. Cross sections and maps collected from Nile Research Institute (NRI) were used to generate DEM with high accuracy for Lake Nasser and model was calibrated by confirming the relation between volume stored at Lake Nasser and water levels. Manning roughness coefficients ranged from 0.03 to 0.045 s/m1/3. Fiord with a length of 19 km and Toshka spillway with a length of 21 km were surveyed by High Aswan Dam Authority (HADA). DEM was used to cover an area of 1,000,000 km2 starting from GERD till Lake Nasser covering all rural and urban lands that are bounded to flood. The Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) Global DEM V2 as shown in Figure 3 which is considered highly accurate with accuracy from 10 to 40 m was used to generate 800 grids for the study area.

Fig. 3
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DEM for the study area covering 1,000,000 km2 from GERD to Lake Nasser

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Dams on the study area

There are five important hydraulic structures in the study area starting from GERD to Lake Nasser. These hydraulic structures include GERD, Roseires, Sennar, Merowe, and AHD. Table 1 lists the hydraulics characteristic of each dam.

Table 1 Dams on the study area
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GERD is considered one of the biggest dams located in Africa, on the borders between Ethiopia and Sudan, in the east with a height of 145 m and a volume storage of 74 BCM. Ethiopia initiated dam construction in 2011. The maximum volume storage is 74 BCM, the average volume storage is 49 BCM, and the minimum volume storage is 19 BCM (Madson and Sheng 2020; Siddig et al. 2021). AHD was initiated in 1960 to safeguard Egypt from drought during low flood years and from flood during high flood years. It can also control water releases during the year. AHD is 111 m high and is allocated 2676 km downstream GERD with a volume storage of 162 BCM at water level of 182m + MSL (mean seal (is it seal or sea?) level). The Ministry of Water Resources and Irrigation (MWRI) in Egypt takes a mitigation measure to safe AHD from any excessive water coming from upstream by constructed Toshka Spillway release water to Toshka depression in emergency cases. Toshka spillway was constructed in 1978 to release water above 178 m upstream AHD from Lake Nasser as shown in Fig. 4. The main objective of the Toshka spillway is to keep the upstream water level all the time less than 182 m.

Fig. 4
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Toshka depression’s location according to Nile River

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Numerical model

The Sobek 1D–2D model was applied to explore the water outflow in case of the break of any of the dams located between upstream GERD to Aswan dam. An area of 661 km by 1522 km was to cover the inundated area as follows:

  • Grid with vertical and horizontal lines (828 × 1902) with spacing 800 m × 800 m was generated using bathymetric collected of the study area.

  • Cross sectional and collected data were used as an input to Sobek-1D model. Figures 5 and 6.

Fig. 5
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Part of the grid generated using DEM for the study area at GERD

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Fig. 6
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Plan view for the model of this study describing Nile River, dams and DEM

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Evaporation rate data at Lake Nasser were collected from NRI, and it ranged from 4.52 to 7.56 mm/day. Volume losses reach about 10% of the total volume based on this evaporation rate. Additionally, all spillways for each dam were simulated in the model.

Model assumptions and designed scenarios

Flood was considered to occur on August 1st in 2018, and GERD break would occur at level 640 m + MSL. Failure takes place in about 1 h; this assumption was taken based on concrete dams GERD. Dams in series will fail at water level 2 m higher than their maximum designed levels. 300 MCM will be abstracted to Shiekh Zayed channel in the following day to the failure day. Toshka spillway will be in operation when water level on Lake Nasser starts exceeding 178 m. Assumption was taken to reach the maximum designed water levels upstream Roseires, Sennar and Merowe. Some scenarios considered that all spillways are not under operation. Other assumption considered opening the spillway of Sennar and Merowe and not opening the spillway of Roseires as water reaches after failure in only 3 h. Water reaching Lake Nasser was based on Donkla station recorded data in the last 115 years and was obtained from NRI and Nile Water Sector. The discharges ranged from 84 to 150 BCM as shown in Fig. 7. Assumption of discharges of 19 BCM (min), 73 BCM (Max) and 49 BCM (Dom) was simulated and used in the model input data as shown in Fig. 8.

Fig. 7
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Daily discharges for monthly bases based on the discharges were ranging from 84 to 150 BCM

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Fig. 8
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Daily discharges for monthly bases based on 73 BCM

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Designed scenarios in this research are shown in Table 2. The parameters of concern of these scenarios were water level in Lake Nasser, flow reaching Donkla station, and flow caused by GERD failure. Prior to model simulations, each dam failure was conducted individually to calculate the volume released in case of failure that occurs in 60 min. Figure 9 shows the relation between time and discharge when Roseires dam fail. By calculating the area under curve, the volume storage on the Lake 6.13 BCM will be obtained. Figure 10 shows the relation between time and discharge when Merowe dam fail. When the area under curve is calculated, the volume storage on the Lake 0.8 BCM will be obtained.

Table 2 Designed Scenarios with spillway operation condition at each dam
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Fig. 9
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Time and discharge relationship in case of Roseires dam failure

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Fig. 10
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Time and discharge relationship in case of Merowe dam failure

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GERD break simulations at different time periods

GERD model simulations including 13 scenarios for failure were studied at different time periods for failure starting from 1 to 24 h at upstream water level 640 m as shown in Fig. 11. Discharge of 1,513,700 m3/s in case of dam failure in 1 h and 857,350 m3/s in case of dam failure in 24 h. Figure 12 shows water level at different failure time periods. In this study, the strongest wave which occurs in case of failure in 1 h was considered while investigating the consequences of the dam failure.

Fig. 11
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Time and discharge relationship downstream GERD in case of failure at different time periods

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Fig. 12
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Time and water level relationship at GERD Lake in case of failure at different time periods

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Model calibration

Calibration is the process of adjustments to the input parameters of the model until obtaining results that match the field measurements. Several runs were performed to achieve the best agreement between measured and computed values from the model. This was carried out by adjusting roughness coefficients at various locations along the modeled reaches, for 1D model (the river). Calibration of the SOBEK model from GERD to AHD which shows the computed water level as shown in Fig. 13 is in good agreement with the measured water level. However, regarding 2D model (urban areas), the areas at the river sides of bed level are considered higher than the water level on Lakes. Using satellite images and geological maps in addition to Manning’s values recommended by Chow 1959, the modeled areas were classified to urban, rural, building, and mountains. Manning’s coefficients for river and floodplains were estimated. The roughness of each type was taken according to US ARMY CORPS MANUAL.

Fig. 13
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Calibration of 1D SOBEK model

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The downstream river reaches can be well simulated using a coupled one–two dimensional, (1D–2D) flow model. Hence, a model was schematized based on the numerical SOBEK software package, Delft Hydraulics (2019), which is the 1D analysis along the modeled reaches of the river and the 2D unsteady formulations of the full dynamic equations along overland water flooded flow.

Results and discussion

After confirming the accuracy of the model results to simulate the volume of water storage upstream dams, the model was run with the strongest wave when failure occurs in 1 h, and herein after the simulation results.

Model scenarios simulations results (Scenario 1)

In this scenario, failure occurs at maximum water level upstream GERD and the model was run for six-month period. The model boundaries were as follows: water level upstream GERD 640 m, water level upstream Roseires dam 490 m, water level upstream Sennar dam 421 m, water level upstream Merowe dam 300 m, closed Emergency spillway, upstream water level on Lake Nasser 175 m, daily discharge downstream Aswan High Dam 276 MCM, zero flow coming at Donkla, Shutoff Toshka Spillway.

Figure 14 shows plan view for part of the model upstream GERD and Roseires dam just before the dam failure. Figure 15 shows the wave spread of the wave after 2 h from the failure at the area from GERD till Sennar dam. This figure also shows the significant part of the water spread out of the Nile River. Then, after some time, a part comes back to the Nile after Sennar dam, whereas another part does not come back and stays in lower lands. The wave width around the Nile ranges from 10 to 40 km at the part between GERD and Roseires dam and about 125 km between Roseires and Sennar dams.

Fig. 14
figure 14

Water spreading upstream GERD and Roseires dam just before failure

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Fig. 15
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Water spreading 2 h after failure from GERD till Sennar dam

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Figure 16 shows wave spread after 12 days from failure at the part from Roseires dam and Khartoum city. This is when water inundates large areas in Khartoum and part of water come back toward White Nile for a length of 300 km. Results showed that water spread for spacious areas at the part from Sennar dam to Khartoum city has a width of 150 km. It gradually decreases after Khartoum city as shown in Fig. 17. The figure shows that water spreads after 16 days from the failure at the part from Khartoum and Merowe dam where water spreads for a width of 15 km. Figure 18 shows water spread after 21 days from failure.

Fig. 16
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Water spreading after 12 days from failure in the part from Roseires dam and Khartoum

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Fig. 17
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Water spreading after 16 days from failure in the part from Khartoum and Merowe dam

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Fig. 18
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Water spreading after 21 days from failure in the part downstream Merowe dam

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Wave time arrival and water levels at dams

As mentioned above, 1 h was predicted for the failure of the GERD when levels at all lakes of the dams were at their highest except at AHD was at 175 m. Table 3 describes wave time arrival at different dams of interest of this study as it spent 3 h till Roseires dam and 22 days and 9 h till AHD.

Table 3 Wave time arrival at dams and stations downstream GERD
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Figure 19 shows water levels upstream GERD, Roseires, Sennar, Merowe dams and Khartoum city after failure. Water level upstream GERD decreases from 640 to 522 m in 3 days. Water spent 3 days to travel to Roseires dam and the level increases from 490 to 502 m then failure on Roseires dam starts failing when water level by 2 m above the designed water levels. Next, it takes three and half days till the levels decrease back to the lowest level. After 1 day and 5 h, water reaches Sennar dam and increases from 421 to 424.75 m. The failure begins when levels exceed the designed levels by 2 m and water starts decreasing for 17 days till it reaches the lowest level. After 4 days and 1 h, water arrives in Khartoum city and increases by 18 m, then arrives at Merowe dam after 10 days, and water exceeds from 300 to 303.70 m as shown in Fig. 19.

Fig. 19
figure 19

Water level at GERD, Roseires, Sennar, Merowe dams and Khartoum city after failure

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Discharges downstream dams due to GERD break

Discharges were calculated downstream GERD as shown in Fig. 20. Total discharges reach a value of 72.60 BCM and maximum discharges of 1,513,700 m3/sec. Table 4 shows arrival time which varies from 1 h to 19 days and 1 h for Merowe dam. Discharges significantly decrease after Roseires and Sennar dams due to wave spread at these two dams compared to Merowe dam which has higher discharges flowing in the river. Table 4 shows water volume directly after dams of this study and maximum discharges flowing inside the river. More than half of water volume spread out of the Nile River in the reaches from GERD and Roseires dam and the reach from Roseires and Sennar dams then part comes back to the Nile River and the rest inundate Khartoum city as shown in Fig. 16.

Fig. 20
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Discharges downstream GERD due to its failure

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Table 4 Water volume directly after dams of interest of this study
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Discharges reaching Lake Nasser and their corresponding water levels

Water arrives Lake Nasser after 22 days and 9 h and water levels decrease from 175 to 173.60 m due to water abstraction of 300 MCM daily from power plant and Toshka Spillway. Water level starts raising due to wave arrival till reaching level of 179.18 m and then starts decreasing with respect to time as shown in Fig. 21. Total water volume arrives Lake Nasser is 43.25 BCM due to dams failure. Figure 22 shows relationship between discharges reaching Lake Nasser and time. Figure 23 shows water extended in Lake Nasser 2 months after failure.

Fig. 21
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Water level at Lake Nasser with respect to time due to dam break

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Fig. 22
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Discharges arriving at Lake Nasser with respect to time due to dam break

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Fig. 23
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Inundated area at Lake Nasser 2 months after GERD Break

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Scenario A-1

In this scenario, model boundaries look like scenario 1 except for opening spillway for Sennar and Merowe dams in the next day after the failure as there was enough time to put them in operation. Results are similar to the results of scenario 1 except for water levels upstream the two dams and discharge curve downstream. Whereas, total discharge downstream Sennar dam is identical to scenario 1 as the dam is small and the water level decreases rapidly in the upstream. When flood wave comes, water increases rapidly above the designed water levels by 5 m then the dam collapse as shown in Fig. 24. Merowe spillway has a positive effect of keeping water levels upstream Merowe dam less than the designed water levels which save the dam from collapse. When spillway is open, water levels decrease rapidly from 300 to 286 m as shown in Fig. 25. When wave arrives, water increases again till 296.5 m. Merowe dam under wave flood case could store 3 BCM in its lake which has a positive effect on decreasing water levels in Lake Nasser as well. Figures 26 and 27 show the relation discharge and time downstream each dam. Figure 28 shows the relationship between water levels and time in scenario A-1 compared to scenario 1. Water levels are decreased by 90 cm compared to scenario 1 as water level showed a value of 179.18 m instead of 178.28 m.

Fig. 24
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Water levels at Sennar dam at scenario A-1 compared to scenario 1 after failure

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Fig. 25
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Water levels at Merowe dam at scenario A-1 compared to scenario 1 after failure

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Fig. 26
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Discharge downstream Sennar dam at scenario A-1 compared to scenario 1

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Fig. 27
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Discharge downstream Merowe dam at scenario A-1 compared to scenario 1

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Fig. 28
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Water levels at Lake Nasser dam at scenario A-1 compared to scenario 1

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Scenario 2

In this scenario, model boundaries look like scenario A-1 except for receiving normal flow in Nile as 84 BCM and running Toshka spillway is put in operation at level 176 m and can release 270 MCM daily at level 182 m upstream AHD. Model run for 6 months and water level at Lake Nasser as shown in Fig. 29 was predicted as 181.12 m compared to 178.28 as in scenario A-1. Figure 30 shows discharge of Toshka spillway as 208 MCM that is less than the maximum discharge with 62 MCM. The volume of discharge entered Toshka depression is 19.4 BCM.

Fig. 29
figure 29

Water levels at Lake Nasser at scenario 2 compared to scenario 1 after failure

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Fig. 30
figure 30

Toshka spillway discharge in MCM after GERD break

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Scenario 3

In this scenario model, normal flow in Nile is 128 BCM which is considered high flood occurred at (1964–1965) and Toshka spillway is put into operation at level 176 m at channel beginning. Water level at Lake Nasser was predicted as shown in Fig. 31 as 182.12 m instead of 181.12 m. Figure 32 shows Toshka spillway discharge as maximum flow was 289 MCM instead of 208 MCM in the previous scenario and this was considered 19 MCM higher than spillway discharge. Water level at Lake Nasser was increased by 12 cm above the maximum allowable level of 182 m. Volume of water entered Toshka depressions are 31.9 BCM.

Fig. 31
figure 31

Water level at Lake Nasser after GERD break

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Fig. 32
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Toshka spillway discharge in MCM after GERD break

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Scenario 4

This scenario is different from the previous scenario regarding:

  • High flood coming at Donkla station which is 150 BCM which occurred previously in (1878–1879)

  • Toshka spillway is in operation after expansion works by 750 m to be able to release 700 MCM at level 182 m.

Figure 33 shows the predicted water levels at Lake Nasser and water level reached level of 181.94 m instead of 182.12 m in scenario 3. Figure 34 shows Toshka spillway discharge as the maximum predicted discharge was 706 MCM compared to 289 MCM in scenario 3. Table 5 shows the maximum water level at Lake Nasser after GERD Break, this led to decreasing water level in Lake Nasser near normal water levels. Table 6 shows a comparison between Toshka spillway discharge and time. The maximum discharge reaches 208 MCM in case of average flood and 706 MCM at maximum flood. Total water volume entered Toshka depressions is 64.94 BCM.

Fig. 33
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Water level at Lake Nasser after GERD break

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Fig. 34
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Toshka spillway discharge in MCM after GERD break

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Table 5 Water level at Lake Nasser after GERD break
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Table 6 Discharge of Toshka spillway after GERD break
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Scenario possibility for occurrence

The possibility of occurrence of scenarios for GERD break was studied as shown in Table 7. The possibility of dam break at Level of Lake Nasser of 175 m and a level of 640 m is low possibility as water level at Lake Nasser will decrease less than 175 m after GERD operation can raise back to 175 m in case of arriving consequences flood and storing it in Lake Nasser. Furthermore, possibility of Scenario 1 and 2 is high. Possibility of Scenario 3 is high. Possibility of scenario 4 is low as it is difficult for the level to raise to the maximum and also receive high flood 150 (MCM), usually on average about 40 BCM will be subtracted from 150 BCM, so about 110 BCM will be arriving.

Table 7 Scenario possibility for occurrence
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Conclusions

In this study, assessing the risk of GERD failure was explored. All the dams on the Blue Nile were simulated (GERD, Roseires, Sennar and Merowe). In case of break to any of these dams, significant damages could occur due to the water arriving to Lake Nasser and the corresponding water levels. Discharges releasing from AHD, Toshka spillway, and Shiekh Zayed canal were studied to keep water levels less than 182 m. One overall model was used for the whole study area and water upstream GERD was considered as upstream boundary and discharge released from AHD as downstream boundary. This model cannot be divided into parts due to the existence of intermediate dams where water levels will be calculated as model outputs. Discharges arriving at Dongola station were calculated based on data received 115 years ago. (Low flood is 40 BCM, Intermediate flood is 84 BCM, and High flood is 150 BCM.) The discussion and analysis of the results highlighted the following conclusions:

-In case of GERD break, Roseires and Sennar dams will collapse, while Merowe dam can sustain if emergency spillway is put in operation.

-The whole city of Khartoum will inundate.

-Wave width is on average from 10 to 150 km in Khartoum city.

-Water velocity downstream dams range from 9 to 36 m/s.

-Wave height reaches 100 m downstream GERD and 64 m downstream Roseires dam and 31 m downstream Merowe dam.

This study raises concerns about the stability of the structure on the downstream countries, as a result of the GERD Break. Therefore, Sennar and Merowe Spillways should be opened after the GERD break. Conducting the required protection works for water structures located at Toshka spillway. Conducting expansion works for Toshka spillway by enlarging it by 750 m to be able to release 700 MCM. The scenario was conducted to increase the discharge to 700 MCM daily. Eventually, this expansion showed a good result at flood 150 BCM and water level at Lake Nasser 175 m.