**2. Materials and Methods**

In this multidisciplinary study, we investigate the environmental and economic impact of the GERD. In particular, we examine the effects of GERD on downstream water flows along the NRB, focusing on Egypt. We also assess the impact of the project on available agricultural land, agricultural production, and overall economic activity in Egypt. In carrying out this exercise, we first quantify the volume of projected losses in Egypt's annual water allocation from the Blue Nile while taking into account specific reservoir filling periods that are currently under consideration. We then estimate the resultant losses in Egypt's agricultural land and the corresponding impact on macroeconomic variables such as food production, food import and export, employment, the cost of living, real GDP per capita, and welfare. In order to provide a clearer presentation, we confine our study to three of the reservoir filling scenarios under consideration. Specifically, we examine losses under the 3, 7, and 10-year filling scenarios. Figure 2 presents a flow diagram illustrating the sequence of events from water losses through economic losses.

**Figure 2.** Egypt's water and economic losses due to GERD construction.

#### *2.1. Nile River Water Losses*

The current Egypt annual Nile water allocation is estimated at 55 km3. This volume will be significantly affected by the construction of the GERD reservoir, particularly by the reservoir volume and filling period. Media reports suggest different GERD reservoir volumes to be filled in different time periods, for example, filling 16, 63, 67, 70, and 74 km<sup>3</sup> in 3, 5, 7, 10, and 15 years. In this study, we simulate the Nile water losses attributed to filling the GERD reservoir volume of 74 km<sup>3</sup> over 3, 7, and 10 years. We calculate the volume by summing up the impoundment (filling) volume, infiltration losses, evapotranspiration losses, and climate change-related losses. Errors in the average annual water losses were calculated as the standard deviation of water losses in individual years. Figure 3 and Table 1 show the average annual losses in Egypt's Nile water allocation as a function of the GERD filling scenarios.

**Figure 3.** Average annual water loss from Egypt's Nile water allocation (in km<sup>3</sup> and %) as a function of filling scenarios (in years).

**Table 1.** Average annual losses in Egypt's Nile water allocation and the associated losses in agricultural land relative to the baseline (no GERD) scenario.


**Impoundment Volume:** The annual impoundment volume was calculated by dividing the GERD reservoir volume (74 km3) by the number of years in each filling scenario. We assumed a constant yearly filling volume for each filling scenario.

**Infiltration Losses:** Given the lack of infiltration information at the GERD site, we used the infiltration rate of the High Aswan Dam reservoir (e.g., Lake Nasser; Figure 1a). The Lake Nasser infiltration rate was estimated at 2% of the lake volume [12].

**Evapotranspiration Rate:** The evapotranspiration rate at the Roseries reservoir (90 km downstream from GERD) was used in this study. This rate was estimated at 2000 mm/yr [13]. We also accounted for an 8.3% increase in evapotranspiration rates, predicted in different climatic models [14]. The final evapotranspiration rate used in this study is 2166 mm/yr. The evapotranspiration volume was calculated by multiplying the rate by the area of the GERD reservoir (1770 km2). The GERD reservoir area was calculated using a 30 m digital elevation model (DEM) extracted from the Shuttle Radar Topography Mission (SRTM) for the UBN sub-basin (Figure 1b) [4]. Knowing the GERD reservoir volume (74 km3), the water height could be estimated using ArcGIS tools, yielding a raster with the shape of the final reservoir. This raster was then used to calculate the reservoir area at each filling stage.

**Climate Change Losses:** We use the average annual rainfall rates over the UBN subbasin to calculate the rainfall/discharge ratio. This ratio was then used to calculate the loss in discharge rates as a result of climate changes. The Global Precipitation Climatology Project (GPCP) rainfall data was used to calculate the average annual rainfall for the UBN sub-basin during the period from 1979 to 2020. An annual discharge rate of 48.9 km3 was reported at El Diem station (located right above the GERD location). Using this rate, the discharge to rainfall ratio was calculated at 28%. We accounted for a 5.5% decrease in rainfall rates, predicted from different climatic models [14]. The corrected average annual discharge rate was estimated at 46.21 km3.

#### *2.2. Losses in Agricultural Land*

The loss in downstream water flows constitutes a significant shock to Egypt's agricultural land by rendering a significant part of an otherwise fertile land less suitable for farming and other agricultural activities. We estimate the losses in agricultural land by using the conversion rates published by Abdelhaleem and Helal [15]. In their work, they calculate the average loss in agricultural land for Upper Egypt as follows:

$$\text{Agricultual Land Loss} = -0.0173 \times \text{Nile water loss} + 1.0376 \tag{1}$$

For middle Egypt and Nile Delta, they use the following formula:

$$\text{Agriculturul Land Loss} = -0.0164 \times \text{Nile water loss} + 0.9369 \tag{2}$$

We averaged estimates from Equations (1) and (2) in order to calibrate the losses in agricultural land for all of Egypt that are attributable to GERD. Errors in the average annual losses in agricultural lands were calculated as the standard deviation of land losses in individual years. Figure 4 and Table 1 present projected annual losses in Egypt's agricultural land as a function of the filling period (in years).

**Figure 4.** Impact of the GERD on Egypt's agriculture land (in km<sup>2</sup> and %) as function of filling scenario (in years).

#### *2.3. Impact on Egypt's Economy*

Having estimated the losses in Egypt's water allocation under the alternative filling scenarios (e.g., 3, 7, and 10-year filling scenarios) and the corresponding losses in agricultural land, we then look at mechanisms through which this affects Egypt's economy. In particular, we analyze the effects of GERD on Egypt's agricultural sector output, employment in the agricultural sector, food import, and food export. We also look at the impact of this project on Egypt's real GDP and cost-of-living. In order to carry out this analysis, we first build an empirical framework to forecast trends in the selected economic variables (baseline model). We then examine deviations from these trends caused by the shocks from GERD under the alternative filling scenarios.

#### 2.3.1. Baseline Model Structure

The quantitative framework for trend analysis builds on a Vector Auto Regressive (VAR) model, presented in the general form as follows:

$$Y\_t = \beta Y\_{t-1} + \epsilon\_t \tag{3}$$

where *Yt* is an *LX*1 vector of endogenous variables, *β* is an *LXLp* matrix of coefficients, and  *<sup>t</sup>* is an *LX*1 vector of white noise. Given the number of lags *p*, the companion matrix *β* is given as follows:

$$
\beta = \begin{pmatrix}
\beta\_1 & \beta\_2 & \dots & \beta\_{p-1} & \beta\_p \\
1 & 0 & \dots & 0 & 0 \\
0 & 1 & \dots & 0 & 0 \\
\vdots & \vdots & \ddots & \vdots & \vdots \\
0 & 0 & \dots & 1 & 0
\end{pmatrix} \tag{4}
$$

In order to determine the appropriate number of lags, we carry out fitness tests based on the Akaike's Information Criterion (AIC) [16], Schwarz's Bayesian Information Criterion (SBIC) [17], and the Hannan and Quinn Information Criterion (HQIC) [18]. We then set *p* based on the selection order criteria for the system (Appendix A). We also test for stationarity by examining the eigenvalue stability conditions of the companion matrix, thereby ensuring that all the eigenvalues lie within the unit circle [17]. Moreover, we follow-up with a Johansen test for cointegration to gauge if there is a long-run relationship between the series [19]. We then employ vector error correction procedures [19] where appropriate (Appendix A).

Given this multivariate VAR framework, we then map out expected values of the system *n* periods ahead recursively [20]. Based on the availability of data up to period *t*, we can forecast for periods (*t* + 1), (*t* + 2), and (*t* + *n*) as follows, respectively:

$$E(\mathbf{Y}\_{t+1}) = \mathcal{B}\mathbf{Y}\_t + E(\epsilon\_{t+1}) \tag{5}$$

$$E(\mathbf{Y}\_{t+2}) = \beta E(\mathbf{Y}\_{t+1}) + E(\mathbf{e}\_{t+2}) \tag{6}$$

$$E(\mathcal{Y}\_{t+n}) = \beta E(\mathcal{Y}\_{t+n-1}) + E(\mathfrak{e}\_{t+n}) \tag{7}$$
