Optimization-Based Proposed Solution for Water Shortage Problems: A Case Study in the Ismailia Canal, East Nile Delta, Egypt

: Water conﬂicts in transboundary watersheds are signiﬁcantly exacerbated by insufﬁcient freshwater sources and high water demands. Due to its increasing population and various development projects, as well as current and potential water shortages, Egypt is one of the most populated and impacted countries in Africa and the Middle East in terms of water scarcity. With good future planning, modeling will help to solve water scarcity problems in the Ismailia canal, which is one of the most signiﬁcant branches of the Nile River. Many previous studies of the Nile river basin depended on quality modeling and hydro-economic models which had policy or system control constraints. To overcome this deﬁcit position and number, the East Nile Delta area was investigated using LINDO (linear interactive, and discrete optimizer) software; a mathematical model with physical constraints (mass balances); and ArcGIS software for canals and water demands from the agriculture sector, which is expected to face a water shortage. Using the total capital (Ismailia canal, groundwater, and water reuse) and total demand for water from different industries, the software measures the shortage area and redistributes the water according to demand node preferences (irrigation, domestic, and industrial water demands). At the irrigation network’s end, a water deﬁcit of 789.81 MCM/year was estimated at Al-Salhiya, Ismailia, El Qantara West, Fayed, and Port Said. The model was then run through three scenarios: (1) the Ismailia Canal Lining’s effect, (2) surface water’s impact, and (3) groundwater’s impact. Water scarcity was proportional to lining four sections at a length of 61.0 km, which is considered to be optimal—based on the simulation which predicts that the Ismailia canal head ﬂow will rise by 15%, according to scenarios—and the most effective way to reduce water scarcity in the face of climate change and limited resources as a result of the increasing population and built-in industrial projects in Egypt.


Introduction
In many countries around the world, water shortage is one of the most serious issues. About 1.2 billion people, or nearly one-fifth of the world's population, live in waterscarce regions, and 500 million more people are living in regions that are on the verge of becoming water-scarce [1,2]. Water shortage problems, negative effects of climate change, and growing populations lead to conflicts around transboundary surface and groundwater resources between two or more countries, such as in the Euphrates-Tigris (ET) basin [3][4][5].
Egypt is one of the countries facing significant challenges as a result of its restricted water supplies, which are primarily a result of its fixed share of Nile River water, its general aridity [6], and its dependence on agriculture, which provides a living for 55 percent of quality indexes for agriculture, manufacturing, drinking water, and aquatic life [27], was all of which contributed to a mathematical model for integrating complex data to produce a score that informs the public and the policymakers about the state of water quality. Water quality index (WQI) can also be used to compare the quality of different water sources and to monitor improvements in water quality over time [28]. The mathematical optimization model was used to increase the yearly return in Egypt from three regions by selecting the best land locations for various crops and imposing various constraints on the model, such as land availability in various seasons, water availability, crop effective areas, and sufficiency ratios. From 2008 to 2012, researchers collected data on 28 crops and built a model that included irrigation water requirements, spatial crop variations, crop yields, and food requirements. The findings revealed that by increasing tomato production, the annual return from crops could increase. Furthermore, by restricting non-strategic crop areas while preserving strategic crop areas, the principles of self-sufficiency could be met [29].
We focused in this study on offering a feasible solution to the water scarcity/shortage issue in the area of the Ismailia canal. This could be done efficiently by applying a mathematical optimization model which is capable of analyzing various organizational guidelines. The selected optimization model is uses LINDO (linear interactive, and discrete optimizer) software which is a convenient and powerful tool for solving linear, integer, and quadratic programming problems. These problems occur in the areas of business, industry, research, and government. Specific application areas in which LINDO has proven to be of great use includes water distribution and inventory management. The model optimizes the physical system and desired operation rules as a collection of the constraints embedded in the model, resulting in the best feasible solution for water delivery with a low deficit in order to achieve the best solution to the water scarcity problem [30].

Physical Conditions for the Study Area
The study area is the East Delta zone, which is bounded and dissected by several canals, drains, and lakes and contains four major governorates (Al-Qalubia, Al-Sharkia, Ismailia, and Port Said). Figure 1 depicts the Irrigation canals in the East Delta, including the Ismailia Canal. Such fresh surface water bodies as the Ismailia Canal and its branches, as well as the Suez Canal, will be studied for simplicity, as will the regions that stretch along the length of Ismailia Canal and benefit from its fresh surface water. As shown in Figure 2, the canal covers a latitude range of 30 • 15 0" to 31 • 0 0" N and a longitudinal range of 31 • 15 0" to 32 • 15 0" E. Ismailia Canal is one of Egypt's most significant branches of the Nile River, providing surface water for four governorates in the East Nile delta. Its length is 128 km, with a depth of 1-3 m and a width of 30-70 m [31]. The area irrigated by the Ismailia Canal has a population of 4,869,573 people [32]. The canal irrigates approximately 778,656 feddan in the current case, or about 9% of Egypt's agricultural land [33][34][35][36].   Figure 3 shows the flow chart of the optimization model applied in this research, where a mathematical model with physical constraints (mass balance) was developed using LINDO (linear interactive and discrete optimizer) for studying the East Nile Delta area. The ArcGIS 10.3 software and Google Earth were used for digitizing and locating the canals and water demands from the agriculture sector. The optimization model was then run, and the results compared the current case with local demands.   Figure 3 shows the flow chart of the optimization model applied in this research, where a mathematical model with physical constraints (mass balance) was developed using LINDO (linear interactive and discrete optimizer) for studying the East Nile Delta area. The ArcGIS 10.3 software and Google Earth were used for digitizing and locating the canals and water demands from the agriculture sector. The optimization model was then run, and the results compared the current case with local demands.  Figure 3 shows the flow chart of the optimization model applied in this research, where a mathematical model with physical constraints (mass balance) was developed using LINDO (linear interactive and discrete optimizer) for studying the East Nile Delta area. The ArcGIS 10.3 software and Google Earth were used for digitizing and locating the canals and water demands from the agriculture sector. The optimization model was then run, and the results compared the current case with local demands.  If the gap between water supply and demands in all DEMs is minimized and local food requirements are met while water quality is affected positively, the model would be feasible. Finally, some scenarios are recommended to avoid future water deficits.

Materials and Methods
However, if the model did not minimize the water shortage, the model would not be considered to be feasible. In this case, the objective function and constraints must be changed in order to satisfy all DEMs and booster demands by redistributing the water across the total networks which are applicable according to all relevant authorities with water distribution and water irrigation under the Ministry of Water Resources and Irrigation (MWRI).

Model Setup
In this section, we will clarify the proposed mathematical model which includes objective functions, data sets, variables, and model constraints:

Sets and Indices
The water allocation model equations include several indices and sets. The basic elements of the model, such as periods and agricultural demands, are described here: t: Time step (month) dem: Agricultural demands, sr: Surface water sources, booster: Domestic demands, If the gap between water supply and demands in all DEMs is minimized and local food requirements are met while water quality is affected positively, the model would be feasible. Finally, some scenarios are recommended to avoid future water deficits.
However, if the model did not minimize the water shortage, the model would not be considered to be feasible. In this case, the objective function and constraints must be changed in order to satisfy all DEMs and booster demands by redistributing the water across the total networks which are applicable according to all relevant authorities with water distribution and water irrigation under the Ministry of Water Resources and Irrigation (MWRI).

Model Setup
In this section, we will clarify the proposed mathematical model which includes objective functions, data sets, variables, and model constraints: Several system variables are necessary to define the characteristics of the system, such as discharge from the canal node. R (sr,dem,t) : Discharge from the canal to agricultural demand area "dem" in time step "t" R (sr, booster,t) : Discharge from the canal to domestic demand site "booster" in time step "t" G (dem,t) : Groundwater pumped to agricultural demand area "dem" in time step "t" G (booster,t) : Groundwater pumped to domestic demand site "booster" in time step "t" RU (dem,t) : Reuse water pumped to agricultural demand area "dem" in time step "t" RS (booster,t) : The ratio of water supply to domestic demand site "booster" in time step "t" Sh (dem,t) : Water shortage between water supply and demands at agricultural demand area "dem" in time step "t".

Objective Functions
The optimization model was used to optimize a common basin's benefit from the water allocated to the rural, urban, and industrial sectors [38,39]. There is a strong public expectation in upstream areas to reduce the environmental water scarcity in the entire basin in order to optimize the water allocated to the downstream region.
In addition, the optimization model reflects the situation in which the transfer of water from the upstream area to the downstream region, which is typically underdeveloped, is minimized. This is because the generated surface water supplies are often used in upstream areas instead of being released downstream, reflecting the selfish actions of stakeholders who choose to use the limited water supplies to satisfy their own water needs rather than opening them to downstream stakeholders by choosing to maximize the minimum amount of water available to stakeholders at all times [40].
The main goal of the optimization model in this study is to reduce water deficits between supply and demand at all agricultural and domestic sites over all periods and demand sites.

Model Constraints
The model constraints are presented as follows: 1.
Water balance at agricultural demand area "dem" in time step "t".

2.
Water balance at domestic demand site "booster" in time step "t".
3. Surface water source limit in time step "t".

LINDO Software
The best software for solving problems with tens of thousands of constraints and hundreds of thousands of variables is LINDO, which is used all over the world. In Indonesia, LINDO was used to solve a model with hydrological constraints for optimal surface and groundwater activity for various crops [41]. In Andhra Pradesh, India, LINDO was used to solve an optimization model for determining the best groundwater and surface water allocation scheme. The results showed that the proposed canal command model was advantageous and practical, with surface water saved for 43,189 ha [42], In India, LINDO was also used to solve a model of hybrid energy systems to optimize costs and various types of resources [43].

Model Development
A mathematical optimization model is developed to optimize real data with theoretical data to solve the water deficit problem and prevent potential water shortages. To address any anticipated water shortage at any point in the study region, a water balance between water supplies Tables 1 and 2 and demands Tables 3-5 are established.    As shown in Figure 4, the East Nile Delta area includes main canals as resources and nodes as demands and can be explained as the availability of water and the demand for water as the following:

•
Water resources: Ismailia Canal with a total water discharge is about 5772.55 BMC/ year [44], groundwater is about 0.25 mm 3 /day, reuse drainage water about 34.44 m 3 /s in Al-Sharkia and about 1.54 m 3 /s in Ismailia governorate [45] and rainfall is between  mm/year [37]. • Water demands: agriculture land (15 demand nodes) and Al-Salhiya is the largest agricultural region in the study area, with 118,371 Feddan, so the area was divided into three demand nodes at the end of the Salhia canal network (D5, D6, D7), drinking purifications (13 boosters) and seepage is about 21.06% of the total discharge [50].
Water 2021, 13, x FOR PEER REVIEW 10 of 27 As shown in Figure 4, the East Nile Delta area includes main canals as resources and nodes as demands and can be explained as the availability of water and the demand for water as the following:

•
Water demands: agriculture land (15 demand nodes) and Al-Salhiya is the largest agricultural region in the study area, with 118,371 Feddan, so the area was divided into three demand nodes at the end of the Salhia canal network (D5, D6, D7), drinking purifications (13 boosters) and seepage is about 21.06% of the total discharge [50].  Table 6 shows that the total water shortage in the study region is 1997.86 Mm 3 /year, which is dispersed over all months with varying values, implying that more than 43.84 percent ( . . ×100) of the study region's water resources are in a deficit because groundwater, drainage, and wastewater reuse are not used. However, in the optimization model, we consider groundwater and drainage reuse, which results in differing water deficit values.   Table 6 shows that the total water shortage in the study region is 1997.86 Mm 3 /year, which is dispersed over all months with varying values, implying that more than 43.84 percent ( 1997.86 4556.5 ×100) of the study region's water resources are in a deficit because groundwater, drainage, and wastewater reuse are not used. However, in the optimization model, we consider groundwater and drainage reuse, which results in differing water deficit values.

Results and Discussion
The model analysis was first run with a focus on the Ismailia Canal Lining's effect, surface water's impact, and groundwater's impact.

Base Case
In this study, a mathematical optimization model was used in the East Delta to close the gap between water supply and demand by feeding the model surface water and groundwater and reusing the irrigation water distributed on 15 demand nodes and 13 boosters. The importance of prioritizing water boosters comes first, followed by prioritizing other demand nodes. The initial condition showed that there is a shortage in the demand nodes (D5, D6, D7, D12, D13, D14, D15) which are located in Al-Salhiya, Ismailia, El Qantara West, Fayed, and Port Said, as in Figure 5, Table 7 and Figure 6 the locations of deficit agricultural areas are shown. The unmet demand in the study region is approximately 789.81 Mm 3 /year, or about 12.05 percent of the agricultural demand for water. Figure 5 depicts the greatest water shortage in Al-Salhiya as a result of illegal farming practices that have resulted in a water shortage in the northern Al Sharkia area. This water shortage is addressed by mixing water in drains with canals, increasing drainage and wastewater reuse after treatment in order to mitigate runoff, and increasing the amount of water delivered to the study area from the Nile River.

Results and Discussion
The model analysis was first run with a focus on the Ismailia Canal Lining's effect, surface water's impact, and groundwater's impact.

Base Case
In this study, a mathematical optimization model was used in the East Delta to close the gap between water supply and demand by feeding the model surface water and groundwater and reusing the irrigation water distributed on 15 demand nodes and 13 boosters. The importance of prioritizing water boosters comes first, followed by prioritizing other demand nodes. The initial condition showed that there is a shortage in the demand nodes (D5, D6, D7, D12, D13, D14, D15) which are located in Al-Salhiya, Ismailia, El Qantara West, Fayed, and Port Said, as in Figure 5, Table 7 and Figure 6 the locations of deficit agricultural areas are shown. The unmet demand in the study region is approximately 789.81 Mm 3 /year, or about 12.05 percent of the agricultural demand for water. Figure 5 depicts the greatest water shortage in Al-Salhiya as a result of illegal farming practices that have resulted in a water shortage in the northern Al Sharkia area. This water shortage is addressed by mixing water in drains with canals, increasing drainage and wastewater reuse after treatment in order to mitigate runoff, and increasing the amount of water delivered to the study area from the Nile River.  The total surface water delivered to the study area is 4577.26 Mm 3 /year only, or about 78.3% of the total discharge, as shown in Table 8. This is due to seepage from the Ismailia Canal, which accounts for about 21.06% of the total discharge, or approximately 1195.29 Mm 3 /year [50]. The lowest water was supplied in the month of February due to winter closures, as can be seen in Figure 7.
The lowest amounts of surface water delivered to the study area occurred at D5, D6, and D7 (located in Al-Salhiya at the end of the irrigation network of the Al-Salhiya Canal), and D15 (located in Port Said at the end of Port Said Sweet Water Canal-two branches of Ismailia canal). The percentage of water demands are shown in Table 8. The reasons for the low level of water supplied at the end of Al-Salhiya Canal and Port Said Sweet Water Canal are due to the bad behavior of some farmers who engage in detrimental activities, such as allowing rubbish to fall on canals, dumping waste, indiscriminating water withdrawal, and discharging sewage into the irrigation network.   The total surface water delivered to the study area is 4577.26 Mm 3 /year only, or about 78.3% of the total discharge, as shown in Table 8. This is due to seepage from the Ismailia Canal, which accounts for about 21.06% of the total discharge, or approximately 1195.29 Mm 3 /year [50]. The lowest water was supplied in the month of February due to winter closures, as can be seen in Figure 7.    The study regions of the Al-Qalyoubia governorate rely on groundwater as a source of drinking water and for irrigation water and daily use, but the study regions of the Al-Sharkia and Ismailia governorates rely on groundwater as irrigation water only, as shown in Table 3. Figure 8 shows the contour map of the Quaternary aquifers at the Nile Delta. It represents the water table in shallow and deep wells and hydrogeological parameters (hydraulic conductivity, storativity, transmissivity, and specific yield). of drinking water and for irrigation water and daily use, but the study regions of the Al-Sharkia and Ismailia governorates rely on groundwater as irrigation water only, as shown in Table 3. Figure 8 shows the contour map of the Quaternary aquifers at the Nile Delta. It represents the water table in shallow and deep wells and hydrogeological parameters (hydraulic conductivity, storativity, transmissivity, and specific yield). Running the model revealed that the amount of groundwater pumped to the study area is approximately 92.05 Mm 3 /year, as shown in Table 9. Figures 9 and 10 show that the direction of groundwater flow is to the north, heading towards the cities of Shubra Al Khaymah, Al Khusus, Al Khankah, Bilbies, Abu Hammad, and Al Salhiya and to the east towards the cities of Tell El Kebir, El Kasasin, Abou Sweir, Ismailia, West-El Qantara and Fayed. The largest quantity groundwater was pumped to the area in the month of February (during the time of the winter closure). Abu Hammad is the center which benefits the most from groundwater in Al-Sharkia governorate, because it contains about 34 wells [40] and most of the groundwater is pumped to the Ismailia governorate, which contains about 1278 wells and 29553 feddan benefit from [34] (see Figure 9). Running the model revealed that the amount of groundwater pumped to the study area is approximately 92.05 Mm 3 /year, as shown in Table 9. Figures 9 and 10 show that the direction of groundwater flow is to the north, heading towards the cities of Shubra Al Khaymah, Al Khusus, Al Khankah, Bilbies, Abu Hammad, and Al Salhiya and to the east towards the cities of Tell El Kebir, El Kasasin, Abou Sweir, Ismailia, West-El Qantara and Fayed. The largest quantity groundwater was pumped to the area in the month of February (during the time of the winter closure). Abu Hammad is the center which benefits the most from groundwater in Al-Sharkia governorate, because it contains about 34 wells [40] and most of the groundwater is pumped to the Ismailia governorate, which contains about 1278 wells and 29553 feddan benefit from [34] (see Figure 9).   Figure 9. Groundwater pumped to study area (MCM).  Drainage water reuse is considered to be the most unconventional water resource in study regions of Ismailia and Al-Sharkia. The reuse of agricultural drainage water is the second most used water resource of the Ismailia and Sharkia governorates, with 93 water mixing stations available in the Sharkia governorate with 1.4 BCM, and serving approximately 140,700 feddan [33]. The length of the covered drains in the Ismailia governorate reached 120 km in 2017, and was comprised of 21 drains serving of approximately 47,000 Drainage water reuse is considered to be the most unconventional water resource in study regions of Ismailia and Al-Sharkia. The reuse of agricultural drainage water is the second most used water resource of the Ismailia and Sharkia governorates, with  [34].
Running the model showed that, in the study area, the amount of reused drainage water that arrived at the agricultural area was approximately 1095.37 Mm 3 /year, as shown in Table 10. The center which benefited the most from the reused drainage water was Al Salhiya, which is situated at the end of the Al Salhiya Canal (a branch of the Ismailia Canal), as shown in Figure 11.   Figure 12 shows the location of the DEMs which benefit from reused drainage water, as drain water is pumping into the Ismailia Canal, resulting in mixed water.  Figure 12 shows the location of the DEMs which benefit from reused drainage water, as drain water is pumping into the Ismailia Canal, resulting in mixed water. Figure 11. Reused drainage water in agriculture area (MCM). Figure 12 shows the location of the DEMs which benefit from reused drainage water, as drain water is pumping into the Ismailia Canal, resulting in mixed water.

The Impact of Lining the Ismailia Canal
A length of 56 km of the Ismailia Canal was found to be responsible for 21.06% of the total discharge of water losses. Therefore, the Ismailia Canal was considered to be the worst case in terms of seepage problems and erosion. The Ministry of Water Resources

The Impact of Lining the Ismailia Canal
A length of 56 km of the Ismailia Canal was found to be responsible for 21.06% of the total discharge of water losses. Therefore, the Ismailia Canal was considered to be the worst case in terms of seepage problems and erosion. The Ministry of Water Resources and Irrigation (MWRI) implemented preliminary technical studies in order to locate the most critical sections along the Ismailia Canal which have the maximum seepage losses [50].
Geosynthetic polymeric materials were used for geotechnical problems in canals, such as seepage losses, with cost-effectiveness, low environmental impact, and quantifiable performance. Lining samples (100 m 2 in area) by standard income were executed in 2016, whereby four sections of lining with a total length of 61 km were defined [50], as shown in Figure 13. most critical sections along the Ismailia Canal which have the maximum seepage losses [50].
Geosynthetic polymeric materials were used for geotechnical problems in canals, such as seepage losses, with cost-effectiveness, low environmental impact, and quantifiable performance. Lining samples (100 m 2 in area) by standard income were executed in 2016, whereby four sections of lining with a total length of 61 km were defined [50], as shown in Figure 13. The lining project had been implemented in three stages [23,35]. In the first stage, the German Hochster company used impermeable geotextile techniques in December 2014. In the second stage, the Italian Carpi company used impermeable geomembrane techniques with concrete fill to fix the membrane in February 2016. The third stage was implemented by the German Knawe company using Geotextile by stone in March 2016. After lining four sections of the Ismailia Canal, seepage decreased from 21.06% to 7.5% [50,[53][54][55] Recently, Eltarabily et al. [50] used a simulation model for lining the optimum three sections, comprising a length of 57 km, which decreased the seepage from 21.06% to 10.16%. We adopted these two cases (lining three reaches with a total length of 57 km and lining four reaches with a total length of 61 km) to run scenarios for the current case study area, as follows:

Lining Three Reaches with a Total Length of 57 km
Both the assumptions and data in this scenario are the same as in the base case, but the seepage rate is reduced from 21.06 percent to 10.16 percent of the total Ismailia Canal discharge [50]. As shown in Table 11, Figure 14, the unmet demand is 291.99 MCM/year at D5, D6, D7, D13, D14, and D15, which reflect Al-Salhiya, El Qantara West, Fayed, and Port Said. The lining project had been implemented in three stages [23,35]. In the first stage, the German Hochster company used impermeable geotextile techniques in December 2014. In the second stage, the Italian Carpi company used impermeable geomembrane techniques with concrete fill to fix the membrane in February 2016. The third stage was implemented by the German Knawe company using Geotextile by stone in March 2016. After lining four sections of the Ismailia Canal, seepage decreased from 21.06% to 7.5% [50,[53][54][55] Recently, Eltarabily et al. [50] used a simulation model for lining the optimum three sections, comprising a length of 57 km, which decreased the seepage from 21.06% to 10.16%. We adopted these two cases (lining three reaches with a total length of 57 km and lining four reaches with a total length of 61 km) to run scenarios for the current case study area, as follows:

Lining Three Reaches with a Total Length of 57 km
Both the assumptions and data in this scenario are the same as in the base case, but the seepage rate is reduced from 21.06 percent to 10.16 percent of the total Ismailia Canal discharge [50]. As shown in Table 11, Figure 14, the unmet demand is 291.99 MCM/year at D5, D6, D7, D13, D14, and D15, which reflect Al-Salhiya, El Qantara West, Fayed, and Port Said.

Lining Four Reaches with a Total Length of 61 Km
In this scenario, all assumptions and data in the base case are the same, but the seepage rate is decreased from 21.06% to 7.5% [50,[53][54][55]. Note that unmet demand is 173.9 MCM/year at D7, D13, D14, and D15, which represent Al-Salhiya, El Qantara West, Fayed, and Port Said, as shown in Table 12, Figure 15. This represents the largest cultivated area at the end of the network.
It means that reducing seepage is one of the most effective ways to minimize the study area's water shortage.

The Impact of Surface Water
Both the base case's data and assumptions are the same in this case, however, the surface water from the Ismailia Canal is changed and the impact on the water scarcity value is studied, as follows:

Lining Four Reaches with a Total Length of 61 Km
In this scenario, all assumptions and data in the base case are the same, but the seepage rate is decreased from 21.06% to 7.5% [50,[53][54][55]. Note that unmet demand is 173.9 MCM/year at D7, D13, D14, and D15, which represent Al-Salhiya, El Qantara West, Fayed, and Port Said, as shown in Table 12, Figure 15. This represents the largest cultivated area at the end of the network.   Both the base case's data and assumptions are the same in this case. However, due to increased surface water from the neighboring governorate; decreased seepage achieved by lining the Ismailia Canal; water quality considerations; and, forcing farmers to grow crops which consume less water and providing alternative crops with a good gross revenue return to farmers, the surface water for the study area of the Ismailia Canal is increased by 15%. The results of this case are represented in Figure 16 and Table 13. The unmet demand fell from 789.81 to 159.8 MCM/year and the water deficits were distributed on D5, D6, D7, D13, D14, and D15, which represent Al-Salhiya, El Qantara West, Fayed, and Port Said. It means that reducing seepage is one of the most effective ways to minimize the study area's water shortage.

The Impact of Surface Water
Both the base case's data and assumptions are the same in this case, however, the surface water from the Ismailia Canal is changed and the impact on the water scarcity value is studied, as follows:

Increased Water Surface of the Ismailia Canal by 15%
Both the base case's data and assumptions are the same in this case. However, due to increased surface water from the neighboring governorate; decreased seepage achieved by lining the Ismailia Canal; water quality considerations; and, forcing farmers to grow crops which consume less water and providing alternative crops with a good gross revenue return to farmers, the surface water for the study area of the Ismailia Canal is increased by 15%. The results of this case are represented in Figure 16 and Table 13. The unmet demand fell from 789.81 to 159.8 MCM/year and the water deficits were distributed on D5, D6, D7, D13, D14, and D15, which represent Al-Salhiya, El Qantara West, Fayed, and Port Said.   It means that reducing seepage is one of the most effective ways to minimize the study area's water shortage.

The Impact of Surface Water
Both the base case's data and assumptions are the same in this case, however, the surface water from the Ismailia Canal is changed and the impact on the water scarcity value is studied, as follows:

Increased Water Surface of the Ismailia Canal by 15%
Both the base case's data and assumptions are the same in this case. However, due to increased surface water from the neighboring governorate; decreased seepage achieved by lining the Ismailia Canal; water quality considerations; and, forcing farmers to grow crops which consume less water and providing alternative crops with a good gross revenue return to farmers, the surface water for the study area of the Ismailia Canal is increased by 15%. The results of this case are represented in Figure 16 and Table 13. The unmet demand fell from 789.81 to 159.8 MCM/year and the water deficits were distributed on D5, D6, D7, D13, D14, and D15, which represent Al-Salhiya, El Qantara West, Fayed, and Port Said.

Decrease in Ismailia Canal Head Flow by 10%
All of the assumptions and data in the base case are the same in this operation scenario, but due to hydrological and political alterations, the Ismailia Canal head flow is reduced by 10%.
The outcomes of this case are shown in Figure 17 and Table 14. The unmet demand rises from 789.81 MCM/year to 1199. 16 MCM/year, and the water deficits are distributed across eight demand nodes (D5, D6, D7, D11, D12, D13, D14, and D15), which perform in Al-Salhiya, Abou Sweir, Ismailia, El Qantara West, Fayed, and Port Said.    In this scenario, soil salinity will be increased which reduces productivity and crop quality in the agricultural land surrounding the Ismailia canal. As such, any new strategy of water resource management or any political changes, like constructing the Grand Ethiopian Renaissance Dam (GERD), may harm water resources across the whole country in general, and particularly in the Delta.

Use Surface-Water Only from the Ismailia Canal
All of the assumptions and data in this scenario are based on only using surface water from the Ismailia Canal, with no use of groundwater or reuse of drainage water. The results of this case are represented in Figure 18 and

The Impact of Groundwater
The total groundwater pump to the study area decreased at a rate of 34.2% from 2016 to 2017, being at an amount of approximately 92.05 mm 3 /year in 2017 [45]. This represents about 1.3% of the total water delivered to the study area, and, thus, the groundwater has a small effect in the study area. In these scenarios, all of the assumptions and data in the current case are the same data, but there are changes in terms of the groundwater, and the deficit areas are D5, D6, D7, D12, D13, D14, and D15, which represent Al-Salhiya, Ismailia, El Qantara West, Fayed, and Port Said. These cases are described in the following: The effect of groundwater in the case study is shown in Figure 19 and Table 16.   Figure 20 show the comparison between the base case and different cases.   Table 17 and Figure 20 show the comparison between the base case and different cases.

Conclusions
A mathematical model has been applied for the Ismailia Canal which displays the best approach to water resource management in the East Nile Delta. The model shows the amount of water which is distributed from the Ismailia Canal at an amount of 5772.55 Mm 3 /year, approximately (representing approximately 9% of Egypt's water resources), and shows an active method for providing surface water and using groundwater and drainage reuse water effectively, leading to a significant impact on water management practices in Egypt once implemented.
According to the optimization model and scenarios, the area served by the Ismailia Canal will face a water shortage issue which will worsen over time, as agricultural and municipal demands develop. The value of water shortage is 789.81MCM/year at the ends of the irrigation network at DEMs (D5, D6, D7, D13, D14, D15), which are located in Al-Salhiya, El Qantara West, Fayed, and Port Said. This is a result of farmers' unlawful actions. The impacts of water shortage can be reduced by lining the Ismailia Canal and minimizing emissions by treating drain water and mixing it with canal water.
The operational scenarios get the following results :

Conclusions
A mathematical model has been applied for the Ismailia Canal which displays the best approach to water resource management in the East Nile Delta. The model shows the amount of water which is distributed from the Ismailia Canal at an amount of 5772.55 Mm 3 /year, approximately (representing approximately 9% of Egypt's water resources), and shows an active method for providing surface water and using groundwater and drainage reuse water effectively, leading to a significant impact on water management practices in Egypt once implemented.
According to the optimization model and scenarios, the area served by the Ismailia Canal will face a water shortage issue which will worsen over time, as agricultural and municipal demands develop. The value of water shortage is 789.81MCM/year at the ends of the irrigation network at DEMs (D5, D6, D7, D13, D14, D15), which are located in Al-Salhiya, El Qantara West, Fayed, and Port Said. This is a result of farmers' unlawful actions. The impacts of water shortage can be reduced by lining the Ismailia Canal and minimizing emissions by treating drain water and mixing it with canal water.
The operational scenarios get the following results: 1.
Lining the Ismailia Canal results in an inverse proportion with the water scarcity value, reduced seepage from 21.06 percent to 10.16 percent, and a lowered water shortage, from 789.81 MCM to 291.99 MCM. Lining three sections of the canal reduced seepage from 21.06 percent to 7.51 percent, and lowered the water shortage from 789.81 MCM to 173.9 MCM; 2.
When the surface water of the Ismailia Canal is increased by 15%, water shortage decreases to 159.8 MCM/year, but when the surface water of the Ismailia Canal is decreased by 10%, water shortage increases to 1199.16 MCM/year. When relying on surface water without groundwater and reusing water, the shortage increases to 159.8 MCM/year; and, 3.
The value of a water shortage is inversely proportional to the amount of groundwater available. For example, increasing the groundwater by 20% reduces the water shortage to 718.7 MCM/year. However, if groundwater is reduced by 10%, the water deficit rises to 829.40 MCM/year. When relying on surface water and reusing it instead of groundwater, the annual shortage rises to 883.48 MCM.

Recommendations
It is suggested, based on the above inference and previous studies, to evolve the following points of research: