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- Review of previous modelling approaches of the Nile basin
Different studies have been conducted in order to assess and evaluate the water resources management and development plans across the basin. These studies are varied according to the study area, temporal resolution, and the model type (hydrologic models, economic models, hydro-economic model, etc.). The review is organised based on the level of the area of study i.e. (Regional level or sub-basin level), while another classification based on the modelling approach (simulation, optimization and combined simulation and optimization) can be found here .
1.1. Hydro-economic models developed for the Nile basin
Whittington et al.  studied the economic value of cooperation across the Nile basin, by applying a non-linear optimization model for an average year inflows. They concluded that the total annual direct economic benefits from irrigation and hydropower are about (7-11) billion USD without considering the capital cost of the infrastructures. However, this model assumes that the managers know and confident with the inflow data across the whole basin for the next year, which is a deterministic model. The model did not address the over year storage as it is an annual model. The model maximizes the total economic benefits from irrigation and hydropower generation for each year however it did not address the socio-economic impacts on the water system and the water, energy, and food interlinkages.
The filling stages and long-term periods of the proposed 4 main dams on the main stem of the Blue Nile were analysed under different economic, flow policies, climatic conditions and the downstream implications, Paul . A standalone optimisation model called Investment Model for Planning Ethiopian Nile Development (IMPEND) was used. Two flow policies were tested for filling the reservoirs (5% of average annual inflow or 50% of flow above annual average flow at Roseires dam, with no clear methodology). It was concluded that the benefit-cost ratio (b/c) for the transient period was less than for no transient period of about (0.2-0.8) or (1-6) $ billion. The same model was used to assess the economic valuation of the 4 main dams while ignoring the filling periods of the reservoirs, and the dams construction sequences . It was found that ignoring the reservoir impoundment stages and the construction stagger of the dams would overestimate the benefits by 6.40 billion USD and the downstream flows by 170%. This model is like other models which assume that Egypt, Ethiopia, Sudan agreed to fill and operate the dams cooperatively. The model is a benefit model only that weighs the trade-off value of hydropower and water for irrigation. However, it failed to address the socio-economic impacts on the water, energy, and food and their interdependency.
Arjoon, et al. , examined the hydrologic and economic risks of the Grand Ethiopian Renaissance Dam (GERD) on the downstream countries. A Stochastic Hydro-economic optimisation model, with monthly time step was used with a time horizon of 10 years. Full and intermediate cooperation levels across the Eastern Nile river basin were considered for the examined scenarios. The model did not consider the inter-annual variability and assumes that all riparian countries cooperate for operating their infrastructures. The model can be used to assess the effects of new infrastructure on regional water systems it did not address the water, energy, and food interlinkages and the socio-economic impacts on the water system.
Blackmore and Whittington  evaluated the water resources developments and the cooperation opportunities in the eastern Nile countries (Egypt, Ethiopia, and Sudan) using a modified DST version. In their model, the analysts decide which projects would be included which might be misleading especially if a poor economic project is included in the model. The model is not able to optimize the new projects (e.g. dams), as it is a simulation model. The model did not address the socio-economic impacts of the large developments on the water, energy, and food in the eastern Nile countries or their interlinkages. Goor, et al.  assessed the costs and benefits associated with the storage plans in Ethiopia, and the re-operation of these infrastructures and the AHD, using a stochastic hydro-economic model. The infrastructure’s operations were assumed to be coordinated as well as they are in the steady state conditions similar to many previous models i.e. (infrastructure costs and filling periods were neglected). They found that, under the full development scenarios, the loss in hydropower power generation would be at 9%, while the irrigation target will not be affected in Egypt.
1.2. The DST for the Nile basin
The Decision Support Tool (DST) has been developed by Georgakakos  for planning and managing the water resources in the Nile basin. It was developed under the auspicious of the FAO and the Italian government. It has a river simulation and management and agricultural planning modules, hydrologic and remote sensing modelling components which are provided to facilitate regional assessment. However, it is difficult to make changes to the model. The tool enables “cost/benefit assessments for new agricultural and hydropower projects, environmental assessments, public health warning and intervention systems for water and vector-borne diseases, and socio-economic assessments” , however, it did not provide an integrated framework for considering the water, energy, and food interdependency and socio-economic dynamics and their interlinkage with the natural resources.
Guariso and Whittington  evaluated the implications on Egypt and Sudan due to long-term water development in Ethiopia. A classical multi-objective linear programming model was used to maximise the hydropower generation in Ethiopia while maximising water supply for irrigation in Egypt and Sudan. The model suggested that there is no conflict between the Ethiopian hydropower and Sudanese and Egyptian agriculture water use.
It is obvious that the hydro-economic models used in the literature provide a framework to integrate the hydrology, economy, and policies for infrastructure operation (e.g. dams) . These models focus on optimizing the profits and minimizing the cost and impacts of the potential developments, however, they did not consider the socio-economic dynamics and interlinkages among water, energy, and food and the interlinks between the socio-economic and the WFE nexus.
1.3. The NBDSS framework for the Nile basin
The Nile Basin Decision Support System (NBDSS) is an analytical tool developed by the Nile Basin Initiative, . It includes three main components; database, analytical tools include simulation and optimization tools, and multi-criteria analysis. The NB-DSS can be used to support water resources planning and investment decisions. It can be used to evaluate different water management and development options. A pilot application of the Nile Basin Decision Support System (NB-DSS) was conducted to assess the potential impacts of development and management plans for the whole basin . The average annual inflows into AHD would be reduced by 11% under the full development scenario and the total GDP across the basin will increase by 6.70 billion USD. The Water, Food and Energy (WFE) interdependency and the socio-economic dynamics and their interlinkage with the Nexus are not fully considered in the NB DSS.
Levy and Baecher,  have developed NileSim model for the entire Nile basin. The model was established as an educational tool to assist technical and non-technical people, who are involved in decision-making, policy analysis, and negotiations, in understanding the complexity of the river hydrology and management. The model is a real-time simulator based on the physical hydrology of the river and uses the historical records in the analysis. Although the model is considered an assistance tool for non-technical people, it did not address the inter-relationships among socioeconomic and the WFE Nexus in the basin.
1.4. WEAP applications in the Nile basin
The Water Evaluation and Planning (WEAP) is a user-friendly tool that provides an integrated framework for water resources planning, . It provides a platform for calculating water demands, supply, runoff, infiltration, crop requirements, flows, storage, and water quality. Policy scenarios and water management options can be investigated and evaluated. It has been applied for a wide range of applications across the Nile basin. Seleshi, et al.  simulated the current and future demands and supplies for the entire Nile basin using WEAP model. They found the water availability in the short and long term would not be sufficient for irrigation demands compared to current situation. McCartney, et al.  analyzed the current and full development plans (irrigation and hydropower) in the Blue Nile basin using a WEAP model. It optimizes the water uses (hydropower and irrigation) in the basin using a linear programming algorithm. The model was run as a single system and the filling stages of the reservoirs are not included in the model.
Omar and Moussa,  examined the future water shortage in Egypt by the year 2025 using WEAP model. They tested the future water demands under the continuation of current policies considering the agricultural expansion, population growth. A number of measures in agriculture, domestic, and industrial water sectors were tested. The future water deficit estimated at 26.0 BCM/yr. under the continuation of current policy. While applying the proposed measures will lead to annual water shortage 5.20 BCM and this deficit will be compensated by deep groundwater. It is obvious that WEAP provides an integrated framework for evaluating the different development plans and management scenarios in a water system, however, the interrelationships among the water, food and energy in such a basin are not fully considered and their interaction with the socio-economic dynamics. Moreover, the socio-economic impacts if considered in such an analysis, it can be considered as an external to the water system (i.e. their dynamics and interaction with the biophysical system are not fully addressed).
1.5. Previous models for assessing the impacts GERD filling
Abdelhaleem and Helal,  studied the potential impacts of the reduction in AHD releases due to GERD construction, on different water uses in Upper Egypt (agriculture lands, irrigation pump stations, hydropower generation, navigation, and domestic and industrial water supply). The study area included the reach from Lake Nasser to Assiut barrage. A hydrodynamic 1-D SOBEK model was developed with a daily time step for a one-year horizon. They concluded that the intakes of domestic, irrigation and industrial pump stations and the safe navigation draft would be troubled if the annual reduction in Egypt water share is more than 15%, 10%, and 5% respectively. Wheeler et al.  tested a number of different potential strategies for filling the GERD in a cooperative way with downstream infrastructure using RiverWare platform, . They found that coordination of reservoir operation across the eastern Nile countries would reduce the water supplies and energy production risks in downstream countries. These applications are useful for evaluating and testing reservoir operation policies, river basin simulation, and optimization and could include the socio-economic related water activities. However, the interrelationships among the socio-economic dynamics and WFE interlinkages are not considered.
The aforementioned models provide various frameworks to evaluate the water resources plans and the different management options, some of them could include the socio-economic drivers to the water system and provides an integrated framework to evaluate their impacts on the water system. They could be used for optimizing the competing water demands to maximize the profit and minimize the impacts. However, these models could not capture the socio-economic dynamics and the interlinkages among the water, food and energy in such a river basin like the Nile. Moreover, the interactions among the socio-economic and the WFE Nexus are not effectively considered in these models. In other words, they did not provide an effective assistance for multi-sector management or a holistic framework to consider the different dimensions of the human-environmental system. An integrated model that; (a) combines the socio-economic dynamics, and biophysical process, (b) captures the interdependency and the feedback process between the socio-economic and the natural resources, (c) enables evaluating different policy and management options in the different sectors is required. System Dynamics Modelling (SDM) approach is considered a suitable paradigm for meeting these objectives. The next paragraph describes the modelling approach along with a review of different applications developed by this approach.
- The Water-Food-Energy Nexus
The Water, Food and Energy are essentials human needs and for economic development. The WFE Nexus emphasizes the interdependencies among the water, food and energy. It focuses on the system efficiency rather than the productivity of individual sectors, and provides a transparent framework for managing the resources in a sustainable way. It points to the opportunities and synergies for increasing the overall resource efficiency [21, 22]. The linkages between water, food, and energy seem clear in many ways. From food production perspective, the water and energy are inputs, from an energy perspective, water and biomass (e.g. biofuels) are resources requirements. It is clear that the Nexus resources are interdependent in many ways and the action in one sector would not only affect that sector but can have significant impacts on the other sectors.
The Nexus approach is considered a useful concept to address the interrelated human activities and the natural resources e.g. river basins. The WFE Nexus is challenging in transboundary rivers. Due to rapid population and economic growth in riparian countries, each riparian country continues to utilize its own natural resources to meet the growing demand for water, food and energy. This might lead to either more potential conflict or increased cooperation among riparian countries . That makes a nexus approach is an appropriate approach for addressing the water management over a transboundary river as it can reveal the potential for a win-win situation and ease the conflict by mobilizing other resource potentials to meet the growing resource needs. The Nile basin is a transboundary river, in which there is a strong dependency on water for food production and energy generation.
Recently a few number of studies considered the WFE Nexus in the Nile basin. Tan et al.  studied the water, food and energy in the Blue Nile basin in the context of different operating policies for the Grand Renaissance Dam. An optimization model was linked to a System Dynamics model to investigate the different operating policies of GERD. However, the food production were not considered in their research. Al-Riffai et al., employed a framework for the WFE nexus and its impacts on the economies of the Eastern Nile countries (Egypt, Ethiopia, and Sudan). Basheer et al.  studied the cooperation and the economic gains in the Blue Nile basin in the context of water, food and energy. Elgafy et al. developed a system dynamics model for the water, food, and energy model (SD-WFEN) and applied it for Egypt and focused on the crop production and consumption. However, the causal feedbacks, the interactions among the WFE, and the socio-economic dynamics were not considered in most of these studies. To address the interactions among the WFE there is a need to address them equally and recognize their interdependency in an integrated analysis, [26, 27].
- System Dynamics Modelling Approach
System Dynamics Modelling (SDM) is a rigorous method that is based on nonlinear dynamics theory and feedback control theory . It was originally developed to understand the dynamics and the underlying structure of the industrial processes by Forrester and his colleagues. However, it is a general method and can be applied to any dynamic system with any temporal and spatial scale . It has been widely applied to various problems in (economics, ecology, engineering, public health, etc.) to understand the underlying structure and the feedback process among the system components [28, 29]. SDM starts with a qualitative conceptual model (dynamic hypothesis) in which the main interactions among the system variables are defined qualitatively in form of a Causal Loop Diagrams (CLDs),[28, 30]. CLDs are composed of variables connected by arrows and positive/negative signs, which represents the causal relationships between the system variables. Positive causal relationship (reinforcing) means that a decrease/increase in variable (A) would result in a decrease/increase in variable (B) i.e. the change in the same direction. While negative causal relationship (balancing) means that a decrease/increase in variable (A) would lead to an increase/decrease in variable (B) i.e. the change is in the opposite direction. The combination of positive and negative relationships might form feedback loops, .
There are two types of feedback loops; (a) reinforcing feedback loop, and (b) balancing feedback loop. A reinforcing feedback loop is characterized by the continuation of growth or decline within the system state, while a balancing loop tries to reduce the difference between the current system state and the desired state. CLDs represents the system through causal relationships, feedback loops, loop dominance, and time delays, . It can be used to determine the dynamic behavior of some variables even before conducting the quantitative modelling, .The population can be used as an example to illustrate the CLDs, Figure 1. The number of births loop is a reinforcing loop (R) in which the increase in the number of births increases the population, and while the population increase with the birth rate results in incremental of the births number. While the number of deaths loop is a balancing loop (B), in which the increase in the number of deaths decreases the population, and while the population increase along with the death rate leads to increase in the number of death.
The CLDs are then quantified through the Stock and Flow Diagrams (SFDs). CLDs and SFDs are the core concepts of System Dynamics (SD). It could be considered that CLDs emphasize the feedback of the system while the SFDs emphasizes the underlying mathematical relationships), . An SD components are: (a) Stocks, which represent anything that accumulates (e.g., reservoir), (b) Flows, which are activities that fill or deplete stocks (e.g., inflow and outflow), (c) Connectors, which link model elements and transfer information among model elements, and (d) Convertors, which include arithmetic operations that can be performed on flows and logical functions that operate the system (e.g., operating rules for a reservoir). An SFDs for the above described CLDs for the population is shown in Figure 2.
3. Block, P.J., Integrated management of the Blue Nile Basin in Ethiopia: Precipitation forecast, hydropower, and irrigation modeling, in Department of Civil, Environmental and Architectural Engineering. 2006, University of Colorado: Available from ProQuest Dissertations & Theses Global.
4. Block, P. and K. Strzepek, Economic analysis of large-scale upstream river basin development on the Blue Nile in Ethiopia considering transient conditions, climate variability, and climate change. Journal of Water Resources Planning and Management, 2010. 136(2): p. 156-166.
6. Blackmore, D. and D. Whittington, Opportunities for cooperative water resources development on the Eastern Nile: risks and rewards. Report to the Eastern Nile Council of Ministers, Nile Basin Initiative, Entebbe, 2008.
14. SEI. WEAP (Water Evaluation And Planning system). 2017; Available from: http://www.weap21.org/index.asp?gclid=CjwKCAiA9rjRBRAeEiwA2SV4Zda-1atN_8DqrsoKcHqhaN5uD2jYiELWnLkqhnx64mP0OP0nEktxrBoCKHkQAvD_BwE&NewLang=EN.
16. McCartney, M., et al., Simulating current and future water resources development in the Blue Nile River Basin. The Nile River Basin: water, agriculture, governance and livelihoods. Routledge-Earthscan, Abingdon, 2012: p. 269-291.
25. Basheer, M., et al., Quantifying and evaluating the impacts of cooperation in transboundary river basins on the Water-Energy-Food nexus: The Blue Nile Basin. Science of the Total Environment, 2018. 630: p. 1309-1323.
30. Kotir, J.H., et al., A system dynamics simulation model for sustainable water resources management and agricultural development in the Volta River Basin, Ghana. Science of the Total Environment, 2016. 573: p. 444-457.
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