Structure of the modeling framework
The coevolutionary macroeconomy and river system simulation framework introduced in this study consists of two modeling components: (a) the Egyptian economy and (b) the Nile river system. The modeling framework accounts for the coevolutionary dynamics of river and economic systems using an iterative process. This multi-sector framework is designed for river systems with multiyear storage dams and a mix of hydro and non-hydro electricity generation. The two modeling components are described separately below, followed by a description of their interaction, which characterizes two-way hydro-economic feedbacks. The application of the coevolutionary framework to the Nile is then discussed.
Economy-wide modeling component
The Egyptian economy-wide modeling component is based on the IFPRI (International Food Policy Research Institute) standard open-source CGE model43. The model was modified to include water, energy, and land components and run dynamically (i.e., for a multiyear period). In previous studies, water, energy, and land resources have been included in the productive activities of CGE models in a variety of ways. A recent review of the literature distinguished between CGE models that treat water as an explicit factor of production, those that include water as an implicit factor of production (i.e., embedded in land productivity), and those that treat water as a commodity (i.e., an intermediate input)58. Energy-oriented CGE models typically combine energy with capital in the production structure of goods and services59,60. The inclusion of energy in CGE models is straightforward compared to water because energy is a marketed commodity that can be easily reallocated to different sectors. The reallocation of water supplies across space and time requires storage and network infrastructure and is often constrained by unpredictable supplies (stochastic hydrology). Moreover, raw water supplies are typically unpriced61,62,63,64; thus, the economic value of water is not included in economic data (e.g., social accounting matrices and input–output tables).
In this study, we modified IFPRI’s standard CGE model such that economic activities produce commodities using a three-level process (Supplementary Fig. 5). At the top level, composite intermediate inputs and the value-added-energy bundle are combined to produce commodities using a Leontief Function65. The function maintains fixed proportions of inputs (composite intermediate inputs and value-added energy in this case) for each unit of output (commodity). At the second level, energy and value-added are aggregated using a Constant Elasticity of Substitution function (CES)66, such that the optimal input quantities of value-added and energy for each activity are determined based on relative prices subject to substitution elasticity similar to energy-oriented CGE models59. At the third level, substitution is allowed between the electricity commodity and other energy commodities using a CES function. A CES function is also used to combine labor, capital, and land into value-added.
The model is customized to allow each household group to allocate its consumption budget to the purchase of commodities based on a nested linear expenditure system (LES)67 and CES (Supplementary Fig. 5). At the top level, a LES function is used to divide the consumption budget between essential and nonessential demands68. The nonessential consumption budget is divided between five commodity categories using fixed shares. Each category includes different commodities that can substitute each other based on CES functions.
We modified the IFPRI CGE model to include four types of capital: (a) hydro capital used by a hydropower activity to produce electricity, (b) non-hydro capital used by a non-hydro activity to produce electricity, (c) water capital used by a municipal water activity to produce municipal water, and (d) general capital used by other activities. The use of land and water capital varies endogenously based on their rents. Logistic functions are used to simulate the response of the use of land and water capital to their rents. General and non-hydro capital grow based on past investments. Investment is allocated between these two capital types according to their relative rates of return. Given the increase in electricity demand resulting from economic growth, this specification of investment behavior allows for an incremental expansion of non-hydro electricity generation capacity; hydropower capacity does not grow endogenously with the year-to-year investment allocation. It is assumed that no new hydropower investments are made over the 30-year simulation period. To connect the economy-wide model with the river system model, dynamic exogenous shocks on land, water capital, hydro capital, and non-hydro capital are introduced to the economic model based on the river system modeling component, which simulates water and electricity availability, as explained below.
River system modeling component
Pywr, a generic open-source Python library for simulating resource system networks42, is used to model the water system, including hydropower generation, in addition to an aggregated representation of non-hydro electricity generation. Pywr allows building resource system elements using input (e.g., catchments), output (e.g., water abstraction), and storage nodes (e.g., reservoirs). Nodes are linked in a network fashion to enable the flow and allocation of resources such as water and electricity. Pywr uses a time-stepping linear programming approach to drive resource allocation using priorities and system operating rules. Any time step resolution can be selected for Pywr simulations (e.g., hourly, daily, weekly, and monthly). Pywr’s multi-scenario simulation allows consideration of uncertainty in resource systems, e.g., hydrologic stochasticity.
The simulation results of Pywr can be processed, observed, and/or saved through “recorders.” We extended Pywr “recorders” to enable annual aggregation of the water and electricity metrics required for integration with the economy-wide modeling component. These metrics include annual irrigation and municipal water supply fractions, annual electricity generation from hydropower dams, and annual electricity generation from non-hydro energy generators.
Coevolutionary macroeconomy and river system simulation
Supplementary Fig. 6 shows a flowchart of the novel coevolutionary macroeconomy and river system generalized hydro-economic69 modeling framework. The figure shows the interaction between the economy-wide modeling component (with an annual time step) and the river system modeling component (with a monthly time step) within each annual time step. Dynamic-recursive multiyear simulations are performed by repeating the procedure in Supplementary Fig. 6 multiple times.
The dynamic behavior of CGE models is typically driven by external drivers, such as capital growth (determined as a function of previous investment levels), labor growth, and productivity trends. In the first iteration, the CGE model solves based on its external drivers and determines changes to annual water and electricity demands and non-hydro electricity generation capacity relative to the economy’s initial year. Changes produced by the CGE model in relation to the irrigated area, the water capital, the demand for the electricity commodity, and the non-hydro capital are used as an estimate in the river system model for changes in irrigation water demand, municipal water demand, electricity demand, and non-hydro electricity generation capacity, respectively. The first CGE iteration assumes no irrigation deficit and electricity generation equal to that of the base year. The CGE and the river system models iteratively correct the initial assumptions of water curtailments and electricity generation, as explained in more detail below.
CGE models typically have an annual time step, but river system models run at smaller time intervals (e.g., monthly, weekly, daily, hourly). River system models have finer temporal resolutions to enable simulation of the spatial and temporal constraints of river basin resource systems, i.e., to better capture the consequences of stochastic hydrology and infrastructure constraints (e.g., reservoir storage). Although the iterative framework presented in Supplementary Fig. 6 is based on a monthly river system model, models with smaller time steps could also be used. The river system model uses the changes in irrigation water demand, municipal water demand, electricity demand, and non-hydro electricity generation capacity, computed by the economy-wide modeling component, to scale the corresponding water and electricity parameters. The river system model then performs a monthly simulation over a 12-month period based on monthly river flow data and the modified water and electricity demands and non-hydro capacity. The river system model then computes the fractions of annual irrigation and municipal water demands that can be met in addition to the annual hydro and non-hydro electricity generation. Water supply and electricity generation depend on the spatial and temporal availability of natural resources (e.g., river flow), infrastructure capacities (e.g., non-hydro and hydro capacities), and infrastructure operating rules.
After the river system modeling component determines water supply fractions and electricity generation, two tests are performed to determine (a) whether the models have converged and (b) when to stop iterating. These tests indicate whether to proceed to the next iteration or accept the current state of the CGE and the river system models as a solution for the annual time step. Passing either of the two tests terminates the iterative convergence process. The CGE and the river system models pass the convergence test when the difference between the current and the previous iteration’s values of an annual economy, water, or energy metric falls below a certain convergence threshold. The value of the threshold depends on the desired level of accuracy and available computational capacity. The stopping test imposes a maximum number of iterations at which the current state of the CGE and the river system models is considered a solution for the annual time step. The stopping test acts as a safeguard to prevent excessively long iteration over one annual time step. The convergence test is performed starting from the second iteration. Thus, at least two iterations are performed within each annual time step to ensure convergence.
Failure in the convergence and stopping tests results in proceeding to the next iteration. In the next iteration, annual water supply fractions and electricity generation of the previous iteration are applied to the CGE model to compute new changes to annual water and electricity demands and non-hydro electricity generation capacity relative to the initial year of the economy (i.e., the base year). The irrigation and municipal water supply fractions, computed by the river system modeling component, are introduced to the CGE model as shocks to the land and water capital, respectively. The ratio between current electricity generation and electricity generation in the initial year of the economy is calculated for each of the two electricity generation technology groups (i.e., hydro and non-hydro) and introduced as shocks to the hydro and non-hydro capitals.
Implementation of the coevolutionary framework
The open-source Python Network Simulation (Pynsim) framework44 was extended and used to integrate the economy-wide and river system modeling components and to manage their iteration, sequencing, and time stepping. Each of the two components was specified as a Pynsim “engine”44. Although the IFPRI CGE model is written in the General Algebraic Modeling System (GAMS)70, it was linked to Pynsim through the GAMS Python Application Programming Interface. Eight Pynsim integration nodes were created for data exchange between the economy-wide and river system modeling components. Four of the integration nodes transfer changes in annual water (irrigation and municipal) and electricity demands and non-hydro electricity generation capacity from the economy-wide to the river system modeling components. The other four integration nodes transfer the annual water (irrigation and municipal) supply fractions and hydro and non-hydro electricity generation from the river system to the economy-wide modeling components.
Eastern Nile River system model
Supplementary Fig. 7 shows a schematic of the monthly river system model of the Eastern Nile Basin. The model uses naturalized inflow data for the period 1901–2002, obtained from the Eastern Nile Technical Regional Office54. The Eastern Nile River System model contains all major dams and water consumers in the basin, including the GERD and the HAD. The baseline water withdrawal targets are shown in Supplementary Fig. 8. Supplementary Table 1 reports the main characteristics of the dams included in the Nile River System model. The model was calibrated and validated at eight locations across the basin based on historically observed river flows and reservoir water levels over 1970–2002. This period was chosen based on the availability of observed data. Supplementary Fig. 9 and Supplementary Table 2 show the performance of the Eastern Nile River system at eight locations. In the model, non-hydro electricity generation is used to fill the gap between hydropower generation and electricity demand, subject to generation capacity. This assumption is valid since hydropower in Egypt is a by-product of other activities. Furthermore, the historical evolution of the Egyptian electricity mix shows relatively regular annual hydropower generation with a steady increase in electricity generation from other technologies to fill the supply-demand gap8.
Initial filling assumptions of the Washington draft proposal
Supplementary Table 3 describes the 5-year plan for the initial filling of the GERD in the Washington draft proposal assuming normal or above-average hydrological conditions. We assumed that after achieving the water retention target of the first year (4.9 bcm), two 375 MW turbines become operational. The rest of the turbines become operational after achieving the second year’s water retention target (18.4 bcm). We assumed that once the filling targets of year-1 or year-2 are achieved, reservoir storage is always maintained above these targets in order to keep the turbines operational. In the Washington draft proposal, water retention is limited to July and August, with a minimum environmental release of 43 Mm3/day. During the initial filling period, from September to June, releases from the GERD equal the inflow to the reservoir. However, if a drought occurs during the 5-year initial filling plan specified in Table S3, the Washington draft proposal has provisions for implementing delays in filling the GERD (our assumptions for these provisions are described in a later section).
Long-term operation assumptions of the Washington draft proposal
The Washington draft proposal’s operating rules for the long-term operation of the GERD begins when reservoir storage reaches 49.3 bcm. We assumed that when reservoir storage is at or above 49.3 bcm, water is released through the GERD’s turbines to maintain a constant monthly energy production of 1170 GWh to maximize the 90% power generation reliability71. If reservoir storage drops below 49.3 bcm, the target monthly energy production is reduced to 585 GWh. The purpose of reducing the energy generation target is to enable the GERD storage to recover above 49.3 bcm. Water releases designed to maintain a regular power rate depend on the reservoir water level at the beginning of the time step (the higher the water level, the lower the releases required). A minimum environmental release of 43 Mm3/day is maintained throughout the year when possible. Additional water releases may be made following drought mitigation mechanisms that resemble those of the Washington draft proposal, as described below.
Drought mitigation assumptions of the Washington draft proposal
The Washington plan includes three mechanisms to mitigate the adverse effects of droughts, prolonged droughts, and prolonged periods of dry years on the downstream riparians46. The mechanism for mitigating droughts is triggered when the GERD’s annual inflow is forecast to be ≤37 bcm. This first mechanism requires Ethiopia to release a minimum annual water volume, depending on the forecast annual inflow and GERD storage at the beginning of the hydrologic year (see Exhibit A in Egypt’s letter to the United Nations Security Council dated 19 June 202046).
The effectiveness of the mechanism for mitigating droughts depends on the accuracy of the forecast of the annual inflow for the upcoming hydrological year. To implement the Washington plan in this study’s river simulation model, we do not forecast annual flows for the next hydrological year. Instead, drought mitigation conditions are checked in March of every hydrologic year, by which time, on average, about 96% of the river’s annual flow is already known because it occurs from June to February. If necessary, water releases during the remaining 3 months of the hydrological year (March–May) are increased to achieve the minimum annual releases specified in the mechanism for mitigating droughts. These increased releases during March–May effectively offset any deviations from water releases specified by the drought mitigation mechanism given the dam inflows and releases in the previous 9 months of the current hydrologic year.
The mechanism for mitigating prolonged droughts requires that the average annual release over every 4-year period equal at least 39 bcm (37 bcm during the initial filling). In the implementation of this prolonged drought mitigation mechanism of the Washington draft proposal in our river simulation model, we check in March of every hydrological year to ensure that this annual average release over the previous 4-year period is achieved. Although this mechanism does not depend on reservoir inflow, it is also checked for in March to provide flexibility to GERD operation during the rest of the year.
The mechanism for mitigating prolonged periods of dry years is similar to the prolonged drought mitigation mechanism, except the period over which annual releases are averaged is longer (5 years) and the average annual release is higher (40 bcm). We implement this mechanism in our river simulation model in the same way, checking in March of every hydrological year to ensure that the annual average release over the previous 5-year period is achieved. Supplementary Fig. 10 shows the exceedance probability of the annual, 4-year average annual, and 5-year average annual flow of Blue Nile at the location of the GERD over the period 1901–2002. The drought mitigation thresholds of the Washington draft proposal are marked in the figure to show their probability of occurrence in the river flow data.
If a deficit from the minimum releases of any of the three mechanisms is identified at the beginning of March, water releases over March–May are increased equally in each month to offset the deficit.
Initial filling assumptions of the coordinated operation
The coordinated operating strategy for the initial filling of the GERD is similar to the Washington plan, except for the retention of inflows to meet the targets in Table S3 is not constrained to July and August. The coordinated operation requires that a minimum environmental release of 43 Mm3/day be maintained throughout the year when possible. If physically possible, releases from the GERD are also greater than or equal to (1) Sudan’s monthly water withdrawal targets along the Blue and Main Nile, plus (2) Egypt’s monthly water release target from the HAD if HAD storage is below 50 bcm (156 m a.s.l.). This operating strategy enables Ethiopia to avoid delays in filling the GERD as long as HAD storage is at or above 50 bcm. In simulating coordinated operation, the operations of the Roseires, Sennar, and Merowe dams have been adapted to pass GERD releases intended to benefit Egypt. It was assumed that two of the GERD turbines become operational after achieving the first year’s water retention target, and the rest of the turbines become operational once the second year’s filling target is achieved. After achieving the filling targets of year-1 or year-2, reservoir storage is always maintained above these targets (i.e., 4.9 or 18.4 bcm) to keep the turbines operational.
Long-term operation assumptions of the coordinated operation
As with the Washington draft proposal, the long-term operation of the GERD begins as soon as reservoir storage reaches 49.3 bcm. Also the same as the Washington plan, it was assumed that when reservoir storage is at or above 49.3 bcm, water is released through the GERD’s turbines to maintain a constant monthly energy production of 1170 GWh to maximize the 90% power generation reliability71. If reservoir storage drops below 49.3 bcm, the target monthly energy generation is reduced to 585 GWh. A minimum environmental release of 43 Mm3/day is maintained throughout the year when physically possible. The key difference between the Washington draft proposal and coordinated operation is that when physically possible, the coordinated operation ensures that the GERD releases are greater than or equal to Sudan’s water withdrawal targets on the Blue and Main Nile plus Egypt’s target releases from the HAD if HAD storage is below 50 bcm (156 m asl). This provides Ethiopia more flexibility in the operation of the GERD as long as HAD storage is at or above 50 bcm.
Drought mitigation assumptions of the coordinated operation
The coordinated operation strategy does not include drought mitigation measures that are based on minimum annual water releases. Instead, a dynamic mechanism is used to help reduce downstream water deficits during periods of water scarcity, as explained in previous sections. Such an approach provides flexibility to Ethiopia in GERD operation and increases the basin-wide and national water, electricity, and economic gains.
Economy-wide model of Egypt
The CGE model of Egypt represents a dynamic-recursive, single-country, open-economy, including four agent types: households, enterprises, the government, and the rest of the world. Households are classified into ten groups based on location (urban or rural) and income (five quintiles). The model includes 11 production activities: agriculture, light industry, heavy industry, construction, transport, hydropower, non-hydro, other energy, municipal water supply, public services, and other services. Each of the 11 activities produces a distinct commodity except hydropower and non-hydro, which produce a similar commodity (i.e., electricity). Production activities use six factors of production to produce commodities: labor, land, general capital, water capital, hydro capital, and non-hydro capital. Labor and general capital are assumed to be mobile across production activities, whereas land, water capital, hydro capital, and non-hydro capital are specific to agriculture, municipal water supply, hydropower, and non-hydro, respectively. Labor is updated exogenously to follow the projected changes in the 16–64 age group of the shared socioeconomic pathways (SSPs) “middle of the road” scenario72. Total factor productivity is also updated exogenously to follow economic performance under the “middle of the road” scenario.
The CGE model of Egypt assumes fixed price of commodities on the international market following the small open-economy assumption, i.e., that the economy participates in international trade but does not affect world prices73. Government spending is simulated as a fixed share of total absorption (total demand for marketed goods and services). The model follows the saving-investment identity (savings are equal to investment) assuming fixed saving propensities. Foreign savings are assumed fixed, and the exchange rate is flexible.
The baseline model was calibrated to a 2019 Social Accounting Matrix (SAM) of Egypt. The 2019 SAM was generated based on a 2011 SAM using an expansion factor equal to the ratio between the Egyptian GDP in the 2 years. We compared the generated SAM with the structure of Egypt’s economy based on the most recent data in the World Bank Database; no significant differences were found in the economy’s structure. Supplementary Fig. 11 shows this comparison.
Nile River system–Egypt’s economic integration
The Eastern Nile River system model and the CGE model of Egypt run dynamically over a 30-year simulation period (2020–2049) and multiple scenarios. For each 30-year simulation, the CGE model executes 30 annual time steps, and the river system model executes 360 monthly time steps (30 years × 12 months). The CGE and river system models are integrated through the water and electricity sectors, as described earlier. The convergence test is performed using the GDP at market prices with an assumed convergence threshold of US$ 5 million. A maximum of 50 iterations is specified for each annual time step. All simulated time steps converged in <50 iterations.
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