1 Introduction

The interactions among water, energy, and food are numerous and decisions about any of the sectors without considering their interconnections may lead to acute negative consequences (Bizikova et al. 2013; Hoff 2011; Bonn 2011; FAO 2014a). Recognizing their interdependence is critical because global agricultural projections indicate that the need for water, energy, and food will increase significantly over the next decades due to the pressure of drivers such as population growth, economic development, cultural and technological changes, and climate change. Irrigated agriculture accounts for 70% of total global freshwater withdrawals, and the food production and supply sequence uses about 30% of total energy consumed globally (FAO 2012, 2014b). With water and energy scarcity, one of the principal concerns is the optimum usage of available resources to provide food security and progress toward Sustainable Development Goals (SDGSs).

Responsibility to attain optimal use of available resources falls mainly into national water resources and agricultural policy arenas. The present water policy in many countries aims at increasing available water resources through irrigation improvement and changing cropping patterns. This leads to enhancement of water supply management while maximizing economic, social, and environmental returns.

The research reported here focuses on comparisons between nexus and non-nexus approaches for cropping pattern adjustments to support the optimal use of water and energy. The study shows how the nexus approach can be used effectively to consider economics and environmental issues along with food and energy. Data from cropping patterns in Egypt are used to assess and validate the proposed method.

The background of the research indicates that adjustments of cropping patterns for optimal use of water resources show high levels of global research interest. Most studies focus on optimal use issues taking into account the economic return of the cropping pattern (Kaushal et al. 1985, Mayya and Prasad 1989, Paudyal and Gupta 1990, Shahata 1993, Abu-Zeid 1998, Keith et al. 1998, Sethi et al. 2002, Salah 2002, Nimah 2004, Negm et al. 2006, Shahata and Raghab 2008, Fawzy 2009, Kaur et al. 2010, PS 2012, MWRI 2012 , El-Gafy et al. 2013, El-Gafy 2013). A number of other studies consider a multi-objective optimization approach with optimal use of water while considering the environment and land use as well (Xevi and Khan 2012, El-Gafy 2013). The objective function applied in the previous studies focus only on minimizing water use and maximizing net return and the studies address the optimal cropping pattern issue without considering the water-energy–food nexus.

Results of this study can be applied in countries with different approaches to farm policy. The study region of Egypt uses a national planning approach, which can use the methodology directly. A large country such as the United States can use the methodology to evaluate national cropping patterns in diverse regions, leading to reforms in farm policies.

2 Methodology

2.1 Non-Nexus and Nexus Approaches

To compare non-nexus and nexus approaches, summer optimal cropping patterns for Egypt are proposed under five scenarios, as illustrated in Fig. 1. Four of the scenarios represent the non-nexus approach. Under Scenario 1 (Sc 1 ), the cropping pattern is the same as it is currently. Under Scenario 2 (Sc 2 ), Scenario 3 (Sc 3 ), and Scenario 4 (Sc 4 )the proposed cropping patterns are to minimize water use, minimize energy use, and maximize agricultural net return respectively.

Fig. 1
figure 1

Methodology frame work

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The fifth scenario, Scenario 5 (Sc 5 ), represents the nexus approach through maximizing the Water-Food-Energy Nexus Index (WFENI). WFENI is an index that illustrates the performance of water-food-energy management by integrating major variables of the nexus. Its significance is integrating a number of aspects that reflect major concerns in the water-food-energy nexus into a single number to assess and compare strategies (El-Gafy et al. 2017, El-Gafy 2017).

2.2 Optimization Models

Comparison of the scenarios is achieved by applying four linear optimization models to simulate the non-nexus and nexus approaches. The non-nexus approach is assessed by utilizing the objective functions within linear programmingoptimization models to minimize water use (Sc 2 ), minimize energy use (Sc 3 ), and maximize agricultural net return (Sc 4 ), as shown in Eqs. 1 to 3:

$$ \mathit{\operatorname{Min}}.W=\sum_{i=1}^r{w}_i\times {A}_i $$
(1)
$$ \mathit{\operatorname{Min}}.E=\sum_{i=1}^r{e}_i\times {A}_i $$
(2)
$$ \mathit{\operatorname{Max}}.N=\sum_{i=1}^r{N}_i\times {A}_i $$
(3)

Where: w i (m3/ha) is the water required per ha for crop (i), e i (J/ha) is the energy input per ha from crop (i), N i ($/ha) is the net return per ha from crop (i), A i (ha) (decision variable) is the cultivated area of crop (i), r is the number of crops of the study.

The fourth model was developed to demonstrate the nexus approach. Its objective function is to maximize WFENI, as shown in Eq. 4.

$$ \mathit{\operatorname{Max}}.z=\sum_{i=1}^r{WFENI}_i\times {A}_i $$
(4)

Where: WFENI i is the water-food-energy nexus index of crop (i) , A i is the cultivated area of crop (i), and r is the number of crops of the study. WFENI is a composite of indicators that represents the interrelation between water-food-energy, as shown in Fig. 2, which also indicates where interventions would take place to improve the nexus. The interrelation between water and food is addressed through water consumption, water mass productivity, and water economic productivity indicators. The interrelation between energy and food is measured by energy consumption, energy mass productivity and energy economic productivity indicators. Finally, the interrelation between energy and water is represented through energy consumption for irrigation. The components of WFENI (j) are combined utilizing Eq. 5 (EL-Gafy et al. 2017, EL-Gafy 2017):

Fig. 2
figure 2

Interrelation between water-food-energy within WFENI

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$$ \raisebox{1ex}{$\boldsymbol{WEFNI}={\sum}_{\boldsymbol{i}=1}^{\boldsymbol{j}}{\boldsymbol{w}}_{\boldsymbol{i}}{\boldsymbol{X}}_{\boldsymbol{i}}\ $}\!\left/ \!\raisebox{-1ex}{${\sum}_{\boldsymbol{i}=1}^{\boldsymbol{j}}{\boldsymbol{w}}_{\boldsymbol{i}}$}\right. $$
(5)

Where: X i refers to WFENI’s normalized indicator i, w i is the weight applied to each component and (j) is the number of WFENI variables. The highest value 1 is taken to be the best situation while 0 is the worst. According to the weights, equal values are given in this study for the different crops.

The indicators of WFENI are normalized in order to exclude the influence of different dimensions by applying the Min-Max normalization technique as in Eqs. 6 and 7. Equation 6 is used when the Min(x i ) of the indicator is the least preferred value and Max (x i ) is the most preferred value, where Eq. 7 is used for the opposite situation.

$$ {X}_i=\frac{{\boldsymbol{x}}_{\boldsymbol{i}\boldsymbol{a}}-\boldsymbol{\operatorname{Min}}\left({\boldsymbol{x}}_{\boldsymbol{i}}\right)}{\boldsymbol{\operatorname{Max}}\ \left({\boldsymbol{x}}_{\boldsymbol{i}}\right)-\boldsymbol{\operatorname{Min}}\left({\boldsymbol{x}}_{\boldsymbol{i}}\right)} $$
(6)
$$ {X}_i==1-\frac{{\boldsymbol{x}}_{\boldsymbol{i}\boldsymbol{a}}-\boldsymbol{\operatorname{Min}}\left({\boldsymbol{x}}_{\boldsymbol{i}}\right)}{\boldsymbol{\operatorname{Max}}\ \left({\boldsymbol{x}}_{\boldsymbol{i}}\right)-\boldsymbol{\operatorname{Min}}\left({\boldsymbol{x}}_{\boldsymbol{i}}\right)} $$
(7)

Where: x ia is the actual value of WFENI’s indicator i.

2.3 Constraints

The objective functions in the four models are subjected to constraints for area, water, and energy as presented by Eqs. 8, 9, and 10 respectively.

  • Area constraint:

$$ \sum_{i=1}^r{A}_i\le {A}_a $$
(8)

Where: A is the cultivated area by crop (i) at season s, A is the total area cultivated at in season (s), r is the number of cultivated crops and s is the season.

  • Water constraint:

$$ \sum_{i=1}^r{w}_i\times {A}_i\le {W}_a $$
(9)

Where: W a is the available water for irrigation.

  • Energy constraint:

$$ \sum_{i=1}^r{e}_i\times {A}_i\le {E}_a $$
(10)

Where: E a is the available energy for agricultural. Energy requirements includes energy of human labor, machinery, diesel oil, electricity, fertilizer, pesticides, seeds, and irrigated water inputs for crop (i) production.

2.4 Evaluation Index

The Evaluation index (EVI) is applied to determine the best scenario. This index is the average summation of three evaluating indicators for water consumption (W), energy consumption (E), and agricultural net return (N). The four indicators are combined utilizing Eq. 11. The indicators of EVI are normalized in order to exclude the influence of different dimensions applying the Min-Max normalization technique. The highest value of EVI is taken to the best scenario.

$$ \raisebox{1ex}{$\boldsymbol{E}\boldsymbol{V}\boldsymbol{I}=\left(\mathbf{W}+\mathbf{E}+\mathbf{N}\right)$}\!\left/ \!\raisebox{-1ex}{$3$}\right. $$
(11)

3 Results and Discussion of Egyptian Data

3.1 Determination of WFENI

The indicators of WFENI were determined for 19 summer Egyptian crops, Table 1. These indicators were normalized using Eqs. 6 and 7 and the final WFENI was determined applying Eq. 5. The normalized indicators and the final WFENI are shown in Table 2. Onion had the highest WFENI with value 0.79 and rice the lowest value among the 19 crops with value 0.21. Onion has four indicators (water and energy economic productivity, water and energy consumption, and water mass productivity) with high scores that lie between 1.0 and 0.6, Table 2. Rice has comparative lower indices between 0.02 and 0.55, Table 2.

Table 1 Food-Water-Energy nexus index indicators
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Table 2 Food-Water-Energy nexus index and its normalized indicators
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3.2 Evaluating Non-Nexus and Nexus Approaches

The change in water-food-energy nexus due to the proposed cropping pattern under different scenarios is illustrated in Table 3. The total cultivated area under the different scenarios will be same as it is currently. The water, energy, and net return will be different according to the objective of each scenario. Sc 1 has EVI with scores 0 for water and energy use. Sc 1 is the worst scenario for reducing the water and energy use. Sc 5 (the nexus approach) is the best scenario as it has the highest EVI with value 0.82. Sc 5 is followed by Sc 4 , Sc 2 , Sc 3 , and Sc 1 respectively, as shown in Table 4.

Table 3 Water-food-energy nexus change due to the proposed cropping pattern under different scenarios
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Table 4 Evaluation index (EVI) of Water-food-energy nexus under different scenarios
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4 Conclusion

The research reported here focuses on comparing nexus and non-nexus approaches to develop strategies for cropping patterns adjustments to lead to optimal use of water and energy. The results illustrate that the proposed cropping pattern applying the nexus concept is the best approach. This result is achieved by utilizing the objective function in an optimization model to maximizethe water-food-energy nexus index.

Compared to the current cropping pattern, the nexus approach saves water andenergy and increases agricultural net return more than the non-nexus approch. The annual water and energy saving might approach 1.9 BCM and 1006 TJ respectively. About $86 million per year in economic return could be gained if the nexus approach is applied to propose optimal cropping pattern.

The result of the study shows that attention to inter-linkages of the water, energy, and food nexus, along with implications for sustainable development and adaptation, must be considered when developing national polices and strategies.