Integrated model for Food-Energy-Water (FEW) nexus to study global sustainability: The water compartments and water stress analysis

Analysis of global sustainability is incomplete without an examination of the FEW nexus. Here, we modify the Generalized Global Sustainability Model (GGSM) to incorporate the global water system and project water stress on the global and regional levels. Five key water-consuming sectors considered here are agricultural, municipal, energy, industry, and livestock. The regions are created based on the continents, namely, Africa, Asia, Europe, North America, Oceania, and South America. The sectoral water use intensities and geographical distribution of the water demand were parameterized using historical data. A more realistic and novel indicator is proposed to assess the water situation: net water stress. It considers the water whose utility can be harvested, within economic and technological considerations, rather than the total renewable water resources. Simulation results indicate that overall global water availability is adequate to support the rising water demand in the next century. However, regional heterogeneity of water availability leads to high water stress in Africa. Africa’s maximum net water stress is 140%, so the water demand is expected to be more than total exploitable water resources. Africa might soon cross the 100% threshold/breakeven in 2022. For a population explosion scenario, the intensity of the water crisis for Africa and Asia is expected to rise further, and the maximum net water stress would reach 149% and 97%, respectively. The water use efficiency improvement for the agricultural sector, which reduces the water demand by 30%, could help to delay this crisis significantly.

ences to some of the statements in the introduction and check the grammar.But otherwise this is a very good study.Response: Thank you for your valuable review comment.To address the concerns, we have altered the introduction to incorporate missing references and have carried out another grammar check.Relevant text is reproduced here:Energy is an important contributor to human development and well-being, and it is also a key input to

gri
ulture[1].line 12Additionally, excessive water withdrawal due to cheap energy may further deplete groundwater resources[2].line 48Currently, prima facie, the available water is adequate to match human consumption on an aggregate level[3].line 64Lastly, the SDG 6 measures are expected to improve the overall water management[4].Other significant changesTo address comments of Reviewer 3, model description equations have been revised and tables summarizing parameter values and variable description are included.

taking into consideration factors such as: the economic and environmental taking into consideration factors such as: the economic and environmental feasibility of storing floodwater behind dams, extracting groundwater, the physical possibility of storing water that naturally flows out to the sea, and minimum flow requirements (navigation, environmental services, aquatic life, etc).Methods to assess exploitable water resources vary from country to country."

asi
ility of storing floodwater behind dams, extracting groundwater, the physical possibility of storing water that naturally flows out to the sea, and minimum flow requirements (navigation, environmental services, aquatic life, etc).Methods to assess exploitable water resources vary from country to country."

Comment: How is water demand of the different sector satisfied?

Response: The water demand by different sectors i Comment: How is water demand of the different sector satisfied?
Response: The water demand by different sectors is satisfied by allocating available water to these sectors.The focus of the current work is modeling global water system, its linkages with GGSM, modelling demand and computing stress.The specific sequence of calculations is as follows.

sat
sfied by allocating available water to these sectors.The focus of the current work is modeling global water system,

ts
inkages with GGSM, modelling demand and computing stress.The specific sequence of calculations is as follows.

In order to elucidate the workings of the water system, a schematic diagram is incorporated (main manuscript line 182).The diagram and associated description are reproduced here:

A schematic representation of the working of the water model of the GGSM is shown in Figure 1.On a global level, state variables are used with the sectoral intensities to obtain the total global sectoral demands.

Geographical distributions for each of the sectors is used to disaggregate the total sectoral water demand into regional sectoral water dem In order to elucidate the workings of the water system, a schematic diagram is incorporated (main manuscript line 182).The diagram and associated description are reproduced here: A schematic representation of the working of the water model of the GGSM is shown in Figure 1.On a global level, state variables are used with the sectoral intensities to obtain the total global sectoral demands.
Geographical distributions for each of the sectors is used to disaggregate the total sectoral water demand into regional sectoral water demand.At this stage water demands for all the sectors and regions are available.Now, for each region all the sectoral demands are aggregated to get total regional water demand.Then, using the water availability for that region, regional water stress can be computed.For the industrial sector, industrial production would be used to obtain the global industrial water demand.Using geographical distribution, regional IS demand is obtained.For a region, for example, Africa, total regional demand is computed from regional demands for agriculture, energy, municipal and industrial demands.This total regional demand is used to compute the water stress for Africa.In the context of supplying these demands, the water reservoirs which represent the stock of exploitable water are utilized.Here, specific modes of demand-supply are not considered, and the competition between sectors is ignored.A simple water balance based on material flow analysis is employed.The water stress is computed for all regions and sectors.If the water stress is > 100%, it represents a situation where non-renewable water would be used.
emands for all the sectors and regions are available.Now, for each region all the sectoral demands re aggregated to get t tal regional water demand.Then, using the water availability for tha region, regional water stress can be computed.For the industrial sector, industrial production would be used to obtain he d.Using geographical distribution, regional IS demand is obtained.For a region, for example, Africa, total regional demand is computed from regional demands for agriculture, energy, municipal and industrial demands.This total regional demand is used to compute the water stress for Africa.In the context of supplying these demands, the water reservoirs which represent the stock of exploitable water are utilized.Here, specific modes of demand

upp
y are not considered, and the competition between sectors is ignored.A simple water balance based on material flow analysis is employed.The water stress is computed for all regions and sectors.If the water stress is > 100%, it represents a situation where non-renewable water would be used.

Comment: How was the model validated (Figs. 2 and 3 are not clear at all)? January 11, 2022 5/18

R Comment: How was the model validated (Figs. 2 and 3 are not clear at all)? January 11, 2022 5/18 Response: We would like to respond to this comment by first explaining how the water demand is determined and then providing details regarding validation.

pon
e: We would like to respond to this comment by first explaining how the water demand is determin

d and then p
Sectoral intensity trends represent the transformation functions to obtain the water demand for a particular sector from corresponding state variables.The data source and the computation method along with the example of use of these trends is incorporated in the Model Parameterization and Validation section (line 211) and reproduced below: The sectoral intensity trends are used to compute the water demand for a sector using GGSM variable values.In other words, they represent the transformation functions to obtain the water demand for a particular sector from corresponding state variables.The historical sector-wise water demand data is obtained from the AQUASTAT database [8].This country-level data is then aggregated continent-wise and mapped against state variable data (Y i ) for the same period to obtain the sectoral intensity plots (Ψ). 1. Seawater is ignored.

t the tr
2. Only exploitable water, that is, the total surface water and regular renewable groundwater, is considered.
3. Fossil groundwater, desalinated water, environmental water requirements, and flows are not considered.
4. Effect of climate change and extreme weather events are not modeled in the present effort, but they could be addressed using this paradigm in future work.

d be addressed using this paradigm in
5. Economics of water supply-demand is not considered.
6. Historical sectoral water intensity trends are assumed to be valid in future and the possibility of a disruptive technology becoming available is ignored.

Limitations
This work was subject to several assumptions and simplifications, which also form a basis for potential avenues for future research.These are as follows: 1.This work focuses only on the demand side.It does not delve into detailed modeling of the recycling of water which is a critical factor in the context of high water stress region.Moreover, often the water use efficiency improvement is at the expense of energy resources.Hence, the dynamics between water recycling in water-stressed regions and energy requirements can shed light on a trade-off between efficiency improvement and water recycling.
2. Secondly, the economics of water is not considered.This is a crucial limitation.Incorporation of water pricing will permit modeling the impact of stress on water demand, thereby providing greater insights.4. Lastly, as a simplification, the regional aggregation of countries is carried out based on the continent in which that they are part of.
However, a better approach would be grouping the countries based on the river basins they are sharing.Another simplification is aggregate modeling of the agricultural water demand.Incorporation of different crops and their water demand could make the model outcomes more realistic.
These are included in the Modelling global water system section (line 86) and conclusion section on (line 466).
Comment: Are the two-way interactions between food, water and energy taken into account?And if yes, how?I am sorry for the short review, but without these details, I am unable to provide any additional feedback on the results.At this stage, I thus recommend its rejection.
Response: Thank you for your valuable review comment.Two way interactions between different sectors mentioned by the reviewer are not taken into account in the present work.We are currently working on capturing these feedback effects and two way interactions.The scope of this work is limited to • Modelling and integrating global water system with GGSM • Capturing sectoral and regional demand dynamics • Analysing the regional stress

Other significant changes
To address comments of Reviewer 3, model description equations have been revised and tables summarizing parameter values and variable description are included.

Reviewer 3
Comment: The authors present an interesting approach to model the water stress on the continents.However, there are still some parts that make it very hard to understand and therefore unsuitable for publication in its present form.The section Modeling global water system would improve a lot from a more detailed presentation of the equations and variables.Some problems currently are Equation ( 1) uses Q i W R,s which is not introduced at that point and uses indices i and s that are also not introduced.

e also n
Response: Thank you for your valuable review comment.Relevant indices are included (revised model description is included in response to next comment).

Comment:
In equation ( 2) . This is not recommended because it uses the same variable for two different flows.

Response:
The variable description has been updated as per the reviewer's suggestion; and , s, r are revised as T r i r , T s i s , and Rs i s, r , respectively.
Additionally, equations for regional water availability and water stress computation are included for clarity.Relevant text and equations (line 132) are reproduced below: Equation 1 shows the utility of sectoral water intensity Ψ to obtain the total sectoral water demand T s for sector s at timestep i from GGSM variables Y .
Equation 2 is used to compute the regional sectoral water demand Rs for region r and sector s.
January 11, 2022 9/18 Total regional water demand T r can be computed by aggregating the regional sectoral water demand Rs for all sectors for a particular region as shown in Equation 3.
To compute the regional water stress, regional water availability A is required.It can be computed using Equation 4.
where, M i W R represents global water availability at timestep i and Ga r represents geographical distribution factor for availability for region r at timestep i Now, using outcomes of Equations 3 and 4, regional water stress W s can be computed using Equation 5. Comment: Line 143: The meaning of variable X needs far more explanation.What is it representing?The same holds for X r and X rc .I also recommend to always write into the sum over which indexes the sum is taken.
Response: Thank you for your comment.A more detailed description regarding variable X has been included in the revised manuscript.Further, the section describing January 11, 2022 10/18 model has been modified to include an explicit and more readable (bulleted) description of the terms used in the equations.

del
The variable over which sum is taken are mentioned in the equations.However, since these variables are summed over a list of entities (for example, countries or sectors), instead of including an index, the set of all the corresponding entities is incorporated in the description of the equation.
Relevant text and equations (line 155) are reproduced below:

t text and eq
The total value of the representative variable v for region r represented by X can be obtained using Equation 6a.Its distribution, that is, contribution of region r to the global value of sector s is represented by G. Here, v is a representative variable in Agricultural area, GDP, Meat production, or Population; c is a country in the list of countries in the world; and r is a region in Africa, Asia, Europe, North America, Oceania or South America.
Equation 6b shows computation of G.
Comment: In equations (4) new variables X i r appear that are also not introduced.
Response: To address the comment, new variables appearing in the equations have been introduced.A detailed description of modified equations involving X has been included in the response of the earlier comment.

Comment:
The readability would also improve significantly with the addition of a variable description table.
Response: We thank the reviewer for the valuable review comment.A variable description table is included and the same is reproduced here (

Fig 1 .
Fig 1.Schematic representation of water system modelling: Green colored boxes represent historical/literature based data, blue boxes represent interim variables, yellow box represents model outcomes based data and orange box shows the final outcome.

3 .
The influence of climate change is another factor that is beyond the scope of the current work.Regional as well as global precipitation patterns can change because of climate change.Climate change may also influence the crop patterns, thus, altering the water intensity of the agricultural sector.Hence, one of the potential future research January 11, 2022 7/18 avenues could be the modeling the climate change influences on water demand and availability.

Comment:
The variables in the text have a different font then in the equations (for example compare equation (3) with line 130 and 131) Response: The model description is modified to ensure that variable text have same font in the equation and text.The same can be seen in the response of earlier comment.

Table 1 .
Variable description