System Dynamics-based Carbon Footprint Assessment of Industrial Water and Energy Use

Investigating links between water, energy, and carbon emissions requires more attention on the path toward economic prosperity. This study aims to develop a framework for modeling water-energy-carbon interdependencies by considering the nonlinear relationships in their dynamic feedback processes. The main contribution of this research is the quantification of the carbon footprint of industrial water use through the development of an Industrial Water-Energy-Carbon (I-WEC) nexus model. It is a system dynamics model that is developed with a scenario-driven framework. The GDP as a representative of economic growth is assessed. The proposed methodology is tested on the Netherlands' industrial sector as a pilot due to the relatively good data structure. Based on policy-based complementary scenarios, the results show a 3% increase in total water use by 2030. Energy use and carbon emissions will fall as much as 10% and 25% that year, respectively. It is concluded that the industrial GDP share could be maintained with a 0.76% loss, which is close to the 0.5% loss projected by authorities. This study presents a unique approach that can be used in other regions.


Introduction
The increase in population and economic activities has amplified water and energy demands. Energy and water come from natural resources and are vital, closely interrelated resources that play essential roles in national and regional economies and security. A comprehensive understanding of the water-energy relationship is crucial for sustainable resource management (Razmjoo et al. 2020).
The interconnection between water and energy, i.e., the energy-water nexus (EWN), has lately received growing attention due to water use and energy production in the industrial sector. Simultaneously, a significant amount of energy is used at different stages in the water supply. The relationship between water, energy, and carbon is complicated. Each component is directly linked with the other, where any minor change in one may alter the others. The industry has a higher complexity level than other water use sectors for agriculture and domestic needs. According to its purpose and function, industrial water use can be classified as cleaning and air conditioning, manufacturing, cooling and thermal, and miscellaneous water use (Agana et al. 2013;Endo et al. 2017). Within the European Union, industry corresponds to about 40% of the total share of water use (Förster 2014) and about 25% of the final energy end-use (Eurostat 2017).
Moreover, industrial water use is more easily affected by changes in the external environment, such as production level upgrading and industrial development, environmental protection requirements, and climate change (Van Vliet et al. 2016;Wang et al. 2019). Raihan et al. (2022) explored the Environment-growth nexus in Argentina.The econometric methods have been used to confirm the accuracy of the results and provided recommendations for environmental sustainability. Raihan et al. (2023) investigated the nexus between environmental factors and carbon emissions. They showed the extent of renewable energy, agriculture, and forests in emission reduction potential and recommended certain emission reduction policies.The water and energy nexus in the industrial sector requires a two-way discussion, that is, the process of water to energy and energy to water. From the perspective of the water-to-energy process, water supplies are often essential to generating and supplying energy. It is widely known that thermoelectric power plants demand a considerable volume of water for cooling and hydro-energy production (Cai et al. 2018). Due to excessive water use and temperature restrictions, many power plants or stations must modify operations in response to waterrelated emergencies such as droughts and heat waves (Cook et al. 2015). From the perspective of the energy-to-water process, energy is necessary for the production, distribution, and use of water. However, the withdrawal and discharge of water during energy production can adversely affect water quantity and quality, especially for surrounding ecosystems.
Additionally, the timing of the demand for hydropower and other water demands, such as irrigation, can result in a conflict between the benefits (Cai et al. 2018), as Zeng et al. (2017) shown to be the case for more than half of the hydropower installed globally. As for the process of energy to water, the energy used for water plumage and transfer to supply water for industrial use should be considered in the assessment of energy to water and then water to energy.
Industrial energy use is also a critical issue. It uses nearly one-third of the global primary energy supply and 36% of energy-related CO 2 emissions. The industry's final energy use grew by 65% from 1971 to 2005 (IEA 2020), which is an alarm for energy security issues. It increases greenhouse gas (GHG) emissions, exacerbating the climate change impacts (Mi et al. 2018). The industrial sector accounts for 21% of the total GHG worldwide, mainly from fossil fuel burning, which is responsible for about 72% of energy-related CO 2 emissions (IPCC 2014). Kashem and Rahman (2019 investigated the dynamic linkages between CO2 emissions and development indicators (per capita Gross Domestic Product (GDP), population density, and urbanisation) of Bangladesh. They concluded that policy makers should take extreme care in designing and implementing the environmental protection policies to curb CO2 emissions with a desired level of economic growth and urbanization.
Based on the current situation of China's industrial ecological development, Mingran et al. (2018) constructed the system of industrial "energy-SO2-economy" and utilized the vector autoregressive model, impulse response function and variance decomposition to analyse the coordination and dynamic relationship between the three factors. They concluded that the government should vigorously promote the coordinated effortsdevelopment of the economy and ecosystem in the process of industrial growth, as well as take the road of sustainable development with low energy and other resources consumption, less pollution towards high ecological security.
Water, energy, and carbon interactions are not linear. A System Dynamics (SD) methodology can be a flexible and versatile way of modeling complex interrelationships and feedback. SD has been used in different contexts. Among the numerous studies of SD application in water resources planning and management, we can mention Mirchi et al. (2012), , and Ebrahimi and Karamouz (2022) applied SD to identify effective and sound water resources plans and policies.  studied the impact of subsidy policies on industry sector in China with the focus on recycling and remanufacturing. Ebrahimi and Zarghami (2019) developed a system dynamics model for assessing the effect of different management measures, emphasizing the water resources restoration policies under climate change scenarios. As nations worldwide are now forced to promote less energy use to reduce greenhouse gas emissions (Si et al. 2019), climate change has brought complexity to water resources management. However, due to the importance of climate change mitigation and the close relationship between energy, water, and CO 2 emissions, many investigations are devoted to developing WEC nexus approaches to ensure sustainable development goals (Yang et al. 2018).
De Stercke et al. (2018) developed an SD modeling encompassing water resources planning and an endogenous carbon tax for developing a nexus model utilizing system dynamics. They modeled the energy-water interactions at the residential end-use and their influence on the City of London's demands. Li et al. (2020) reviewed WEC nexus studies regarding research questions, nexus mechanisms, and methodologies. Accordingly, it offers suggestions for future research directions in this field. Their study showed that future WEC nexus research could focus on an economy-wide system's boundary conditions and feedback mechanisms.
Regarding the I-WEC model, quantifying the interactions in a mathematical form is usually recommended to understand the system's complexity. In this context, Kaya Identity is a powerful model widely used for quantitative analysis of CO2 emissions (Masters and Ela 2008;Mavromatidis et al. 2016). The IPCC used this index to build the greenhouse gas emissions scenarios defined in the Special Report on Emissions Scenarios (Nakicenovic and Swart 2000). Wang et al. (2017) evaluated the factors influencing China's carbon emissions in 1990-2004 using a Kaya identity method. Their results showed that economic and population growth had the most significant effect on increasing emissions.
The Water, Energy, and Carbon nexus have drawn many investigators' attention, and their interactions have been studied. However, it has been focused only on the water-energy and lately on Energy-Carbon, but the interaction among them has not been widely investigated. Especially less attention has been given to Water-Carbon interactions. In particular, the nexus in the industrial sector, perhaps due to the lack of information, is quite rare in the literature. These shortcomings are addressed in this study. Attempts have been made to develop a framework to estimate the carbon emission, water, and energy use in industry in a dynamic feedback-based system. The main contribution of this study is in quantifying industrial water use carbon footprint through the development of an industrial waterenergy-carbon (I-WEC) nexus model. Being able to quantify how the carbon reduction policy affects economic gains is also a stand-out outcome of this paper. Scenario assessment analysis is carried out, besides the carbon emission and resource use, in the economic growth change estimations. A rough projection of carbon emission on the industrial portion of GDP is made to test the drawback of I-WEC outputs in terms of economic growth slowdown that has been a political concern and an excuse for not complying in many developed or developing regions. The proposed methodology deals with water and energy, including water use for energy supply/production, energy use, and energy use for energyrelated industrial operations, including thermal and cooling processes.
The remainder of this study is presented as follows. Methodology with emphasis on the system dynamics method and Kaya identity application is considered the core of described, followed by the study area. Then, the results are presented as well as a discussion. Finally, a summary and conclusion are given.

Methods
An important aspect of this research is the integration of its combined qualitative and quantitative methods. Qualitative modeling includes the key variable identification, their interaction, and patterns. In this study, the interdependencies and connections between water, energy, and carbon are elaborated. A system dynamics model is developed for the Water-Energy-Carbon (WEC) nexus. Figure 1 shows a framework for estimating the carbon footprint of water use in the industrial sector. System dynamics Fig. 1 The framework for estimating the carbon footprint of water use in industry modeling of the Kaya identity-based industrial WEC nexus estimates the macro-scale anthropogenic carbon dioxide emissions. The Vensim® software, as a high-level visualoriented programming and simulation language, has been widely utilized for simulation applications. It provides a user-friendly interface, making it possible to visualize how complex dynamic systems work (Wen et al. 2016). The I-WEC model uses statistical datasets to quantify the interlinkages among components. As data for a specific industry is hard to obtain, a pilot model is developed for the Netherlands' national-scale industries. The proposed dynamic model can be applied to the other region if there is comparable information for the industrial sector.

System Dynamics Modeling
System dynamics (SD) modeling, initially founded by Forrester, was applied to industrial and business system management and later expanded to diverse problems. The SD method is well suited for dealing with highly nonlinear problems with multiple feedbacks. It can be applied to predict water, energy, and carbon interdependencies. SD modeling facilitates understanding interactions in a complex system by taking time delays and feedback loops into account.
Causal loop diagrams (CLDs) and stock-flow diagrams (SFDs) are the two essential model formulation tools for identifying causal relationships forming feedback loops within systems (Mirchi et al. 2012). Nexus denotes a link of interdependent elements that cannot be considered individually due to their dynamic dependence on one another (Giampietro et al. 2014). By using CLDs, the connections between nexus elements can become more tangible.

Causal Loop Diagrams (CLDs)
One of the most commonly used visual tools in SD is the causal loop diagram (CLD). CLDs qualitatively capture hypothesized causal relations between variables in a problem space. Martin et al. (2020) communicate the main feedback loops in a more detailed computer simulation model. The primary purpose of the CLD is to show the feedback processes in a system. Developing CLDs is essential for sharing knowledge to build a shared understanding of the problem's emergence. CLD, as a qualitative SD technique, can be utilized for mapping the problem structure (i.e., variables, relationships, and feedback loops).
A CLD consists of variables connected by arrows and signs, indicating the variables' causal relationships. CLDs consist of variables connected by arrows and headed by positive/ negative signs to represent the causal relationship between the system variables. A positive sign represents that cause and effect changes occur in the same direction. The combination of positive and negative relationships might form feedback loops. There are two types of feedback loops: (1) reinforcing feedback loop (R) and (2) balancing feedback loop (B). A reinforcing loop is a cycle in which the effect of any variable's variation reinforces the other variable. While in a balancing loop, the vice versa is correct (Inam et al. 2015).

Stock Flow Diagrams (SFDs)
Based on CLDs, the stock and flow diagrams (SFDs) are developed to quantify the system's elements. A CLD emphasizes the feedback structure, while an SFD emphasizes the underlying mathematical relationships. SFDs consist of (1) stocks, which represent anything that accumulates, (2) flows, which are activities that fill or deplete the stocks, (3) connectors, which link model elements and transfer information among the elements of the system; and (4) converters, which include arithmetic operations performed on flows and logical functions that operate the system. Information between state variables and flows is integrated with the auxiliary variables.
In the industry sector, water-energy interactions manifest themselves in two significant ways. First, the water-energy relation works in either direction; this means that as energy use and water use amplify each other, in the same way, savings should amplify each other (Varbanov 2014). For instance, energy generation and use impose significant water demands; and water delivery, use, and treatment carry significant energy demands. Hence, reducing water demand should result in a reduction in energy demand. Second, energy use would cause carbon emissions. Such complex relations lead to the second manifestation in the methodologies for addressing ever-increasing energy and water needs dynamics. The WEC model entailing interacting problems can be developed using SD. The SD model consists of various sub-models. Submodels considered in this study include water, energy, and carbon, which are explained as follows.
-The water submodel The water sub-model represents the flow, supply, availability, and use of water in the industrial sector and the water use of energy supply in this sector. The total water demand of industries is modeled by including all their water use activities over time (Eq. (1)).
where (W Total ) Ind , W Ind , and W E are total water use in the industrial sector (MCM), industrial processes (MCM), industrial-related energy production (MCM).

-The energy submodel
The energy sub-model covers the energy use in industrial activities and the energy footprint of the water supply. The total energy use is estimated by using Eq. (2).
where (E Total ) Ind , E Ind , and E W are total energy use in the industrial sector (Petajoules (PJ) equal to 10 15 J), energy use in industrial processes (PJ), energy use for water supply (PJ), respectively.
-The carbon submodel The amount of carbon emissions in this subsystem is modeled based on Kaya identity. According to this equation, carbon emissions depend on population, per capita gross domestic product, energy, and carbon intensity.
On the other hand, most countries have goals to reduce carbon emissions to achieve the desired emissions. Allocating taxes on excess carbon emissions to the desired level may guarantee emissions reduction. The carbon sub-model represents the existing CO 2 emissions of energy use and carbon capture.
where CE ind , CE Kaya based , and CC are the final carbon emissions of industry, Kaya-based total carbon emissions, and carbon capture (10 3 tons of carbon) in the industrial sector, respectively.
Generally speaking, carbon emissions increase with economic growth (Menyah and Wolde-Rufael 2010), as could be seen in countries with a growing economy, such as China and US. The negative impact of economic growth due to higher carbon emissions has been a stumbling block for joining the carbon reduction treaties such as the Paris Agreement (2015) by certain governments or by their internal planning to meet the targeted emission goals. Looking for all means to change that notion of growth in societies by improving energy use efficiency (in the policy definition utilized in this study) is a fundamental challenge for the developed and developing nations (Aşıcı, 2013). This is in line with the important objective of greening businesses/industries.
In this study, we are trying to estimate roughly how much economic growth resulted in applying different scenarios. As the available reports do not directly address the economic growth and carbon emission correlation for the Netherlands, and a thorough investigation of that is not in the scope of this study, we have applied the logic used by Acheampong (2018).
It was stated in that study that carbon emissions are proportionally increased with economic growth. It is reported that when carbon emissions increase by 1% as a result of global economic growth increase by 1.63%. Also, see a similar approach by Osobajo et al. (2020). However, for the Netherlands, this ratio is different; we can use the stated logic for estimating the GDP and carbon emission relationship. The ratio of GDP (as a representative of economic growth) and carbon emission is calculated based on the historical data of GDP and applicable carbon emission in the Netherlands (World Bank 2021a; Statista (2021); ; . Considering the related data variations from 2000 to 2018, the ratio is estimated as 2.11% for the Netherlands compared with the global figure of 1.63%. The economic growth is proportionally estimated in the scenarios of this study for 2030 based on the GDP portion of the industries in 2018.
Notably, the industrial sector's share in the Netherlands' total GDP was 17.8% in 2018 and about 20% on average from 2000-2018 (World Bank 2021b). Therefore, the effect of economic growth is roughly estimated in different scenarios using the assumption of GDP change as the economic growth when carbon emissions are increased by 1%. Using this ratio and the I-WEC output data, economic growth for each scenario is estimated as follows: where GDP Sc. x is the GDP of the industrial sector in a given year x as a result of implementing a scenario (Sc.), GDP ind, 2018 is the GDP of the industrial sector in 2018, and Change% is the changes estimated based on the GDP to carbon ratio based on the I-WEC model outputs of carbon emission. The GDP is expressed in billion USD. (3)

Kaya Identity
"Kaya Identity" is a conceptual framework that models the factors affecting anthropogenic carbon emissions (Kaya 1989). This model creates a simple mathematical equation for estimating global CO 2 emissions from human activities calculated by various economic, demographic, and environmental factors. The equation is as follows: where C, E, GDP, CI, EI, and P present CO 2 emissions (tons of CO 2 ), energy use (MJ), GDP (USD), carbon intensity (tons of CO 2 per MJ), energy intensity (MJ per USD), and population (person), respectively.
Population growth is one of the critical factors leading to carbon emissions, especially in developing countries. GDP per capita is a portion of a country's total economic productivity divided by its population. It provides a general indicator of living standards and wealth. Energy intensity is an indicator of energy efficiency in the economy. Some factors, such as industrial development, the combination of services and construction in the economic structure, and attention to energy efficiency, may change this index's rate. Carbon intensity is the amount of carbon emitted per unit of energy (or fuel) used. This index measures the region's energy use efficiency of resources. Therefore, the following equation expression for Kaya can represent carbon emission for the industrial sector as follows: where CE Ind is Carbon emission (10 3 tons of CO 2 ), EI Ind is energy intensity in the industry sector PJ 10 9 USD , CI Ind is Carbon intensity in the industry sector 10 3 tonnes CO2 PJ , GDP Capita is gross domestic product per capita 10 9 USD Person , and P is population (dimensionless). In this equation, it is assumed that the proportion of total GDP divided by the total population is the same as the proportion of GDP associated with industrial activities to the population affected by or engaged in industrial production/activities.

Scenario Implementation
Scenarios are defined to evaluate possible future trends and are called: Current trend (business as usual); an allowance-based increase in Water-Energy use; an incentive-based decrease in Water-Energy use; and all 3 with a policy-based complementary carbon emission restriction A. In the carbon emission limit scenario, it is assumed that about 60% of the tax levied per ton of excess carbon is spent on preventing carbon emissions, and the remaining 40% on increasing energy efficiency. Increasing energy efficiency will reduce energy use and thereby reduce water use, which will also reduce carbon emissions. Following the Dutch national policy to limit carbon emissions to control and reduce emissions by 49% by 2030 compared to 1990, starting in 2021, industries are required to pay taxes for every ton of carbon emitted above the allowed amount. The carbon reduction policy is based on managing carbon emissions (installation of filters and absorbers), energy efficiency (reducing energy intensity and use per unit of GDP), carbon emission efficiency (reducing carbon emissions per unit of energy use), and transferring energy resources to cleaner energies. These will then allow using the tax breaks to achieve the policy goals.
With this background, the scenarios are as follows:

Scenario 1 & 1-A: Current Trend without and with Carbon Emission Restriction A Sce-
nario 1 is defined without directly impacting the influential variables and only projects continuing the historical trend of water-energy use and carbon emissions in 2030. As for Scenario 1-A, additional taxes should be paid after 2021 for any excess carbon emissions.

Scenario 2 & 2-A: Allowance-based Increase in Water-energy Use without and with
Carbon Emission Restriction A In scenario 2, to achieve the goal of 20% GDP growth by 2030 compared to 2018, considering the direct relationship between GDP growth and water and energy use, 20% more water and energy resources can be used. For Scenario 2-A, the same provision as 1-A stands.

Scenario 3 & 3-A: Incentive-based Decrease in Water-energy Use without and with Carbon Emission Restriction A A 20% reduction in water and energy resources is applied
based on environmental protection policies and factors that improve the situation (such as technological advances in energy use and carbon filtration). For Scenario 3-A, the same provision as 1-A is holding. As mentioned above, three of the six scenarios include complimentary scenario (A), which represents the policy-based carbon emission restriction which implies 60% of the excess emitted carbon tax should be spent only to prevent carbon emissions (including the use of cleaner fuels). In addition, 40% of the excess carbon tax will be allocated to increase energy efficiency (energy use reduction).

Case Study
The proposed research method for the industry sector can be applied in different regions, but due to the dynamic modeling in this investigation, the Netherlands has been chosen as a case study to test the applicability of the model. In this case study ample economic, social, energy, and water resources data are available. As one of the founding countries of the International Energy Agency, it regularly releases comprehensive energy reports, broken done with statistics of the affected industries by fuel types. Also, information related to industrial water use is available since 2003. Confirming that industry has the largest share of water use in the Netherlands. In addition, the policies of the Dutch government to reduce carbon emissions are followed seriously. This case study could be a model for many developing regions that used this type of analysis strengthening by their data base structure.
The Netherlands is located in Western Europe with territories in the Caribbean; Belgium and Germany border it (Fig. 2). The Netherlands is primarily low-lying, located at three major European rivers (Rhine, Meuse, and Schelde). The Netherlands has experienced steady population growth for several decades (IEA 2020). Industry plays a crucial role in the economy of this region, and its focus is on energy-intensive activities, including oil refining and the production of chemicals and steel. Energy demand is driven by the industry sector's demand, which varies with economic activity and accounts for 44-47% of the total final use in 2008-2018. Fossil fuels dominate Dutch energy demand. The water-energy and Carbon related data in the study area are collected from CBS (2021), the World Bank (2021a), and Eurostat (2021), as presented in Table 1. The energy use is reported in Petajoules (PJ), which is 1.0E + 15 J, and water use is measured in million cubic meters (MCM), which is 1.0E + 6 cubic meters. GDP is reported in US dollars (USD).
The Dutch National Energy and Climate Plan (NECP) determines 2030 targets for GHG emissions reductions, renewable energy, and energy efficiency set under the EU Clean Energy Package. The measures in the NECP are based primarily on the 2019 Climate Agreement. The Climate Act targets reducing GHG emissions by 49% in 2030 and 95% in 2050 (compared to 1990). A carbon levy has been introduced to encourage industrial emissions reductions starting in 2021. A targeted carbon levy, starting at €30 per ton in 2021 and rising to €125-150 per ton in 2030 on every ton emitted exceeding the levels of a fixed reduction path. To allow the industrial sector to stay competitive while strongly reducing emissions, the government has aimed to balance the cost of the levy. For this purpose, financial support from the sustainable energy transition subsidy scheme and CO 2 -reducing options in the industry are considered, especially for carbon capture and storage, which is expected to deliver the majority of emissions reductions (IEA 2020).

Results and Discussion
Understanding the relations between water, energy, and carbon systems has two significant benefits: 1) Helping decision-makers to understand how changing a part of these systems would affect the entire system; 2) Quantifying water-energy-carbon interactions.
As mentioned in the methodology section, identifying the interdependencies and feedback are considered the qualitative model. Causal Loop Diagrams (CLDs) of Water, energy, and carbon are shown in Fig. 3. Water is displayed on the left, energy is in the Fig. 2 The location of the study area: the Netherlands Table 1 The water-energy and Carbon related data in the study area of the Netherlands * Estimated data center, and carbon on the right is the nuclei of causal effects. The driving forces are positive water use for industrial purposes on the left side and negative carbon emission goals on the right-side end, which are counterplay. The response is energy use for industrial purposes. These are the essence of the rest of the processes in this causal loop structure and the formation of the SD model. There is an inner loop within each of the three WEC elements, and there are outer loops between elements. Given the importance of global warming and climate change, the Netherlands has set carbon emissions controlling goals. The higher the gap between current and desired emissions, the higher the tax for excessive carbon emissions. As the tax for excessive carbon emissions increases, the application of new technologies for energy use enhancement increases. These improvements develop an outer balancing loop by reducing the total energy use and carbon intensity (B1 in Fig. 3). However, tax for excessive carbon emissions increases the tendency to use carbon-capturing technologies such as filters, resulting in lower emissions (B2).
Furthermore, the total energy use and availability shape the third inner balancing loop (B3), based on the total energy resources. Similarly, an inner balancing loop is shown for water resources affected by water use (B4). Following the events, increasing water use comes with growing energy demand (Karamouz and Zare 2021). On the other hand, producing energy by itself (mostly from fossil fuels and hydropower resources) necessitates a significant amount of water. The reinforcing loop (R) is developed based on increasing water demand and supply and increase of energy use consequently.
Similarly, energy is used for using water. Every energy use would result in carbon emissions depending on the energy type. In developing the CLDs, first, the interaction between the water and energy sub-models has been taken into account. Then the relation between energy and carbon sub-models has been included to shape the water-energy-carbon nexus.
As displayed in this Fig. 3, the reinforcing loop (R) will show a growth pattern assuming that water resources have no limitation. As the water supply increases due to the increased demand, it requires more energy and increases the total energy demand. The increase in energy demand increases the energy supply. As a result of the increased energy supply, water demand for energy production is also increased. Hence, the water supply is increased in response to the increased demand. This process makes a reinforcing loop. However, as water resources are limited, and more water supply may result in a water shortage after industrial growth and an increase in water demand, the balancing loop (B4) of the water resources affects the reinforcing loop by restricting growth. After developing the CLDs as an analytical tool for system identification, stock and flow diagrams (SFD) promote the system's dynamics in detail, which may not be supported in the CLDs. By defining stocks, the key variables are figured out, specified, and measured has been specified. SFDs are implemented into a quantitative SD model using simulation software to explore and visualize the effects of assigned scenarios. Modeling the industrial water-energy-carbon nexus in a system dynamics framework leads to understanding how these complex systems behave. Figure 4 shows the stock and flow diagram of an industrial setting for the case study.
There are three stocks displayed as boxes in the system dynamics I-WEC model figure: water resources, energy resources, and total carbon emission from the industrial sector. The population portion of industrial dependencies that forms GDP per capita in Kaya identity carbon emission assessment is also a side stock. The energy resources stock links the water resources and carbon emission stocks. The "carbon limit" variable limits the carbon emission stock, which estimates excess carbon emissions and the corresponding tax. Furthermore, the carbon footprint of water use (carbon/water ratio) as a metric in the industrial sector is estimated based on total water use and total carbon emission. Population dynamics and GDP-related variables are considered in the socio-economic portion of the model. GDP and population as the components of the Kaya identity are linked with energy intensity, carbon intensity, and emissions, respectively. The functional relationships and mathematical equations applied in the I-WEC model are listed in Table 2.
As shown in Table 2 and Fig. 4, the demographic part of the I-WEC model is general. Per capita GDP is calculated by dividing the total GDP of the study area by population, which is utilized to estimate industrial carbon emission and energy intensity. In the context of water use, total industrial water use is represented by E Total which is the summation of industrial water use and water use in the energy sector. As for estimating the carbon subsystem, carbon emission is a consequence of industrial carbon emission, carbon intensity, energy intensity, population, and per capita gross domestic production. Then carbon emission restriction is implemented based on excessive carbon emission and tax. All these lead to energy use reduction based on carbon restriction. E w : Energy use in water sector (PJ), W Total : Total industrial water use (MCM), E coef . ∶ The coefficient of water to energy use (PJ/MCM) EI Ind = E Total ∕ GDP EI Ind : Energy intensity (PJ/10 9 USD), E Total : Total industrial energy use (PJ), GDP ∶ Gross domestic production (10 9 USD) CE Kayabased = CI Ind × EI Ind × GDP Capita × P CE Kayabased : Kaya based industrial Carbon emission (10 3 tons of carbon), CI Ind ∶ Carbon intensity (10 3 tons of carbon/PJ), EI Ind : Energy intensity (PJ/10 9 USD), GDP capita : Per capita gross domestic production (10 9 USD/ person), P: Population (person) CC = 0.6 × CR Total CC : Carbon emission restriction (10 3 tons of carbon), CR Total ∶ Total Carbon emission restriction (10 3 tons of carbon) CE Excessive = CE Total − CE Limit CE Excessive : Excessive Carbon emission (10 3 tons of carbon), CE Total ∶ Total Carbon emission (10 3 tons of carbon), CE Limit : Carbon emission limit (10 3 tons of carbon) CT Ind = CE Excessive × C Tax CT Ind : Excessive Carbon emission tax (10 9 USD), CE Excessive : Excessive Carbon emission (10 3 tons of carbon), C Tax ∶ Emission tax per excessive ton of carbon (10 9 USD/10 3 tons of carbon) CR Total = CT Ind ∕ CR COST CR Total : Carbon reduction (10 3 tons of carbon), CT Ind : Excessive Carbon emission tax (10 9 USD), CR Cost ∶ the average cost of carbon restriction (10 3 tons of carbon/10 9 USD) E CL = 0.4 × CR Total ∕ CI Ind E CL : Energy use reduction based on Carbon restriction (PJ), CR Total : Carbon reduction (10 3 tons of carbon), CI Ind : Carbon intensity (10 3 tons of carbon/PJ) C ∕ W = CE Total ∕ W Total C ∕W : Carbon emission to water use (10 3 tons of Carbon/ MCM), CE Total ∶ Total Carbon emission (10 3 tons of carbon), W Total ∶ Total industrial water use (MCM) After developing the I-WEC model, the model's performance is evaluated by the coefficient of determination (R 2 ) and root-mean-square error (RMSE). R 2 for the total energy use is 0.98, and RMSE is 9.97 PJ (less than 1% of the average energy use in the industrial sector (1758 PJ)). As for water use, R 2 is 0.92, and RMSE is 163 MCM (about 1% of the average water use, 15204 MCM). As for the carbon emission variations in the industrial sector, R 2 and RMSE are 0.79 and 2794 × 10 3 tons of carbon (less than 2% of the average carbon emission of 0.17 × 10 9 tons from 1900 to 2018), respectively. As shown in Fig. 5, the estimated values of WEC in the I-WEC model closely match the observed values. It should be noted that the water use data is available after 2003, whereas others are from 1990. The results are analyzed by applying the scenarios described in Section 2.3 to the I-WEC model. The projected estimates for the 2030-time horizon are compared with that of 2018. The total water use for different scenarios is shown in Fig. 6.
Considering the changes to 2018, according to the results (as shown in Fig. 6), in 2030, the total water use will reach 14447 MCM figures. Nevertheless, with the application of scenario 1-A, the water use amount will be 12691 MCM. In scenario 2, with a 20% rise in water use, the highest water use is shown. According to the results, in 2030, about 17274 MCM water will be used. Considering scenario 2-A, this amount will be reduced to 14877 MCM. In scenario 3, by applying resource constraints, water use will decrease up to 11647 MCM. Applying scenario 3-A, the water use will reach 10601 MCM. The results of energy use derived from I-WEC are shown in Fig. 7.
In scenario 1, energy use in 2030 will be 1760 Petajoules (PJ); as for scenario 1-A, this amount will be 1504.7 PJ. In scenario 2, with the increase in water-energy use, the amount of energy use reaches the highest value because the industries use the resources provided by the government with up to 20% energy use growth compared to 2018. The energy use in 2030 will reach 2131 PJ. If scenario 2-A is applied, this value is reduced to 1585 PJ. Scenario 2-A shows using the resources will continue until 2021. However, energy use will decrease with the imposed tax policy and investment in improved energy efficiency. In scenario 3, the energy use will reach 1395 PJ in 2030. Applying scenario 3-A will also reduce this amount to 1308 PJ, which is the lowest energy use in 2030. The results of Carbon emission are obtained from the I-WEC.
In the context of the carbon subsystem, under Scenario 1, carbon emissions are estimated at 159830 × 10 3 tons of carbon (as shown in Fig. 8) in 2030. Applying Scenario 1-A will decrease carbon emissions to 105711 × 10 3 tons by 2030. By applying scenario 2, the total emissions in 2030 will reach 0.19 × 10 9 tons of carbon; this is the highest value among other scenarios. As for scenario 2-A, by improving the energy use efficiency, in 2030, the emissions will reach 0.12 × 10 9 tons of carbon. As for scenario 3, the total carbon emissions will be 0.13 × 109 tons in 2030. With the implementation of scenario 3-A, the lowest carbon emissions will be experienced (0.09 × 10 9 tons of carbon). Given the stated goal of reducing carbon emissions by 49% compared to 1990 by the Dutch authorities, scenario 3-A, with a 43% reduction in carbon emissions (compared to 1990), is the scenario meeting the closest results to the carbon reduction targets. The amount of emitted carbon corresponding to 1 MCM of water use (carbon footprint of water use) is shown in Fig. 9.
According to the results, the C/W ratio (carbon footprint of water use) under scenarios 1, 2, and 3, at the end of the forecast period, will be 11.06, 11.11, and 11.03 × 10 3 tons/MCM, respectively. The ratio will not change significantly without changing the resource use efficiency and carbon emissions. Applying scenarios 1-A to 3-A, the effect In the best scenario evaluation context, by applying Scenario 2-A, in line with the allowance-based increase in water-energy use, energy use will rise until 2022. Then it will be reduced due to the implemented restrictive imposed tax policies. Generally, during scenario 2-A, the upward trend will be offset by concerns about tax levies. Also, carbon emissions targets will still be lower than the current emissions rate. The amount of water use in 2030 compared to 2018 will increase by only about 2.5%, which is 17.5% less than scenario 2 in the absence of applying policy A. However, the most significant reduction in Fig. 9 The industrial carbon footprint of water use under different scenarios  Table 3. It should be noted again that the carbon footprint of water use is defined as the carbon emission to water use ratio (C/W). Interpretation of this ratio could be biased. If the carbon emission remains constant, by increasing water use, C/W will be decreased. However, constant carbon emission and increased water use and, as a result, lower C/W may have been stated as the increased efficiency of carbon emission, which is not quite right. If water use increases while increasing carbon emission, C/W should be evaluated based on the significance of the changes in carbon and/or water. Generally, the lower ratio should be accompanied by less overall carbon emission to prevent misleading conclusions. The carbon reduction goals include specifically successful carbon capture and storage figures, which are expected to deliver the majority of emissions reductions (IEA 2020).
As explained in the methodology section, based on the logic used by Acheampong (2018), the economic growth is proportionally estimated in the scenarios for 2030 based on the GDP value in 2018 as the economic growth indicator, which was also used by Osobajo et al. (2020). Therefore, besides the water and energy resources availability and carbon emission, the effect of economic growth is roughly estimated in different scenarios using the assumption of economic growth (applying to GDP) of 2.11 ratio when carbon emission is increased by 1%.
The effect of economic growth, water and energy use and availability, and carbon emission are reflected in different scenarios. The effect of economic growth is roughly estimated, as discussed earlier, using the stated ratio, which is estimated based on the historical data of GDP and applicable carbon emission in the Netherlands (World Bank 2021a; Statista 2021). Three scenarios are chosen to be discussed more preciously compared to the current trend as the base scenario. The results of scenario 2 (highest rate of water and energy resources availability), 2-A (lowest carbon footprint of water use), and 3-A (lowest carbon emissions) are shown in Fig. 10 and compared in the 2018-2030 time horizon.
In Scenario 1, the current condition will continue until 2030. As for Scenario 2, more use of resources would occur due to the availability of water and energy resources and result in a 13% increase in carbon emissions compared to 2018. In Scenario 2-A, resources are provided, and simultaneously, industries move towards emission reduction goals by imposing restrictions. In this scenario, the reduction in energy use is due to improved energy efficiency. This scenario has the lowest carbon footprint of water use. In Scenario 3-A, for achieving the goals of carbon emission reduction, the highest rate of carbon emission reduction (about 43% compared to 1990 and 46% compared to 2018) occurs due to the increased energy use efficiency. Therefore, scenario 3-A aligns with carbon emission reduction goals and can be selected as the better scenario.
Furthermore, scenarios 2-A and 3-A are compared, responding to the carbon emission reduction goals and taking the economic growth rough estimates into account. Scenario 3-A has about 41% (the difference of 46% in 3-A and -5% in scenario 1) reduction in carbon emission compared to the current trend. This value for scenario 2-A is 22% (the difference of 27% in 2-A and -5% in 1). See the details in Table 3. Linderhof et al. (2020) stated that the total GDP growth for the Netherlands was 10% in 2030, which could be applied to the 162.77 × 10 9 USD figure, which is the GDP share of industries in 2018. However, we have estimated, using scenario 2, without implementing any carbon reduction, a projected growth change of only 2.82% in GDP in 2030 compared to 2018, yielding to 167.37 × 10 9 USD figure. As for scenario 2-A, the increased energy use efficiency only partly balances the policy-based GDP reduction, yielding a GDP of 153.44 × 10 9 USD (9% less). Not as much for scenario 3-A, the economic gain is reduced by 13.8% (4.8% less than implementing scenario 2-A), yielding a GDP of 146.99 × 10 9 USD. All of these are based on a rough correlation of carbon emission and economic growth and assuming that other factors affecting GDP stay intact and there will not be another financial crisis by 2030.
Considering the industrial GDP value of 161.09 × 10 9 USD in scenario 1, which has a modest carbon emission reduction of 4.9% (due to better energy production and use of technology), the economic growth reduction in Scenario 3-A compared to scenario 1 is about 7% of the industrial share of GDP. As the projected Netherlands GDP is 1003.69 × 10 9 USD, the economic growth reduction corresponds to 1.4% of that total in 2030. These figures are 3.8% and 0.76% for Scenario 2-A in that year, respectively. As for the ff between scenarios 3-A with 2and Among the assessed six scenarios, it is expected that the economic loss in scenario 2-A will be about 0.76% of the total GDP, which should be acceptable to the environmentalists considering carbon emission reduction benefits, but perhaps economists see it differently. These findings align with the Climate Agreement report (2019), which states that additional annual costs for the Netherlands associated with the Climate Agreement are less than 0.50% of GDP in 2030.

Fig. 10
Variations of total water, energy, and carbon used/production and carbon footprint of water use for four selected scenarios in the study area (2018)(2019)(2020)(2021)(2022)(2023)(2024)(2025)(2026)(2027)(2028)(2029)(2030) It should be noted that this study's results The report stated that reducing greenhouse gas emissions and materials used for production resulted in an economic growth slowdown. The future carbon target for a low-carbon economy will not meet as the implementation of technological mitigation options is too slow (Linderhof et al. 2020). With this perspective, perhaps one can imply that even though scenario 3-A is theoretically the best scenario, considering the potential economic growth slowdown could make scenario 2-A a good competitive alternative. The result of this study shows the significant value of utilizing a water-use carbon footprint in investigating the practical application of the waterenergy-carbon nexus in the industrial sector. The proposed methodology presents a unique approach that can be used in different socio-economic industrial settings for other regions.

Summary and Conclusion
Industrialization and water dependencies have led to a remarkable increase in water demand. Water use for industrial and cooling processes is directly related to energy production. The by-product is carbon dioxide emissions, which need to be curbed to maintain sustainability. Besides the environmental impacts of carbon emissions, and effective water supply, and demand management are crucial challenges in planning sustainable societies. Energy and water have complex interactions and are inseparable.
This paper explains the interdependencies among water, energy, and carbon using qualitative and quantitative methods. A system dynamics model in the industrial Water-energy-Carbon nexus (I-WEC) is developed. This model is utilized for the macro-scale anthropogenic carbon dioxide evaluation and estimating the carbon footprint of water use. The model is tested on a general national scale for industries in the Netherlands.
Three scenarios are defined to project possible future trends in three aspects of waterenergy use, and then a complementary policy-based variant for each is assigned. Variants are policy-based complementary carbon emission restrictions (with the letter A identifier) based on tax breaks/use for carbon emissions reduction and increased energy efficiency.
Then, four different scenarios were selected for further observations and analysis. In Scenario 1, the current condition is continued until 2030 with a no carbon emissions reduction. It is used as a basis for selecting better scenarios. As for Scenario 2, the highest economic growth is projected due to the availability of resources, and industry utilizes a portion of the allowance for water and energy use increase. In Scenario 3-A, by implementing a carbon emission reduction policy, carbon emissions will be reduced in 2030 by about 43% and 46% compared to 1990 and 2018, respectively, while energy use and water use will be decreased by 27% and 26%, respectively. This is remarkable. However, the GDP-based economic growth in 3-A is 6.5 billion USD (4%) less compared to scenario 2-A. In Scenario 2-A, with the provided resources (3% more water use) and imposing carbon emission reduction restrictions, the lowest carbon footprint of water use can also be reached, qualifying it as a good alternative scenario.
This research's main contribution is quantifying industrial water use carbon footprint through the development of an industrial water-energy-carbon (I-WEC) nexus model. The resources used, carbon emission (outputs of I-WEC), and the rough economic growth change are regarded in the scenario assessment. Besides, a framework for the carbon footprint of water use has been developed to be used as a metric in decision-making. The results show the proposed methodology's significant value in assessing the water-carbonenergy nexus model, developing and predicting the possible scenarios and policy's effect