Towards the optimization of sustainable food-energy-water systems: A stochastic approach

Accepted Manuscript Towards the optimization of sustainable food-energy-water systems: a stochastic approach

Ebrahim Karan, Somayeh Asadi, Rabi Mohtar, Mahad Baawain PII:

S0959-6526(17)32343-0

DOI:

10.1016/j.jclepro.2017.10.051

Reference:

JCLP 10843

To appear in:

Journal of Cleaner Production

Received Date:

18 July 2017

Revised Date:

04 October 2017

Accepted Date:

06 October 2017

Please cite this article as: Ebrahim Karan, Somayeh Asadi, Rabi Mohtar, Mahad Baawain, Towards the optimization of sustainable food-energy-water systems: a stochastic approach, Journal of Cleaner Production (2017), doi: 10.1016/j.jclepro.2017.10.051

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Interactions among the nexus are explored through the design of small scale systems The greenhouse is the smallest scale of sustainable food-energy-water (FEW) systems A quantitative modeling is used to estimate the cost of sustainable FEW systems The energy component is the most critical element of a sustainable FEW system

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Towards the optimization of sustainable food-energy-water systems: a stochastic approach Ebrahim Karana*, Somayeh Asadib, Rabi Mohtarc, and Mahad Baawaind Department of Applied Engineering, Safety, and Technology, Millersville University, Osburn Hall, PO Box 1002, 40 East Frederick Street, Millersville, PA 17551, USA a

Department of Architectural Engineering, Pennsylvania State University, 104 Engineering Unit A, University Park, PA 16802, USA b

Biological and Agricultural Engineering Department and Civil Engineering Department, Texas A&M University, Scoates Hall, Suite 201, 2117 TAMU, 333 Spence St, College Station, TX 77843, United States c

d Department

of Civil and Architectural Engineering, Sultan Qaboos University, P.O. Box 33, Al‐Khodh, P.C. 123, Muscat, Oman

Abstract The interlinkage between the food, energy and water (FEW) supply systems, known as the nexus, has received considerable attention in recent years. Despite this intense interest, there is little work focusing on how to design a sustainable FEW system that can consistently meet its food, energy, and water demands. In an effort to better understand the dynamics among the nexus, the scope of the study is limited to a smallscale FEW system that can consistently yield food for a family of four (two adults and two children) and collect or recycle its own water and supply its own energy needs through solar panels (electricity demand). In order to determine the influence of each component (i.e. food, water, or energy) on the system’s output and identify the weakest link of the system (e.g. water scarcity, energy shortage, inconsistent supply of food, etc.), a quantitative modeling is used to calculate the total cost of sustainable FEW systems. The impact of each design decision variable (e.g. size of the system, water recycling capacity, solar system) on the system’s output is formulated and then optimized. The model is analyzed for two different climate scenarios; a cloudy and humid scenario and sunny and arid scenario. In both scenarios, the energy component represents a large portion of the system’s total cost (around 86% in the humid climate and 73% in the arid climate). This shows that innovative energy production technologies are needed to improve the sustainability of FEW systems at a reasonable cost. Keywords: food; energy; water; sustainability; quantitative modeling; greenhouse 1. Introduction Population growth and demographic transition—an increasing middle class with varying lifestyles and diets— and the crucial need to improve food, energy, and water security place emergent pressure on limited resources. In terms of literature, many researchers emphasize that the world’s food, energy, and water resources are already experiencing significant stress and shortfalls, and yet we predict rapidly increasing demands for these resources in the coming years (Bizikova et al., 2013; Hellegers et al., 2008; McCornick et al., 2008). By 2050, the demand for energy will nearly double globally, with water and food demand predicted to rise by over 50%. This means that the existing food, energy, and water sectors will not be able to meet this growing demand. Besides, many studies such as Van Vuurel et al. (2012) have shown that the Page 1 of 25

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challenges in balancing elements of the relationship between food, energy, and water are amplified because of climate change and its impacts on the availability of drinking water, food production and ecosystems, as well as changes in energy consumption pattern. To address these issues and also improve well-being of the poorest and vulnerable populations by providing access to food, energy, and water (FEW), the interlinkage between these sectors, known as the nexus, should be investigated (Scott et al., 2015). The FEW nexus is where these systems intersect and considers the amount of energy required to treat wastewater and transport clean water, water needed to generate electricity and produce transportation fuels, and the amount of water and energy required to grow food. If a FEW system is designed properly, then the nexus (not isolated) view determines to what degree food, energy, and water security objectives can be simultaneously accomplished. With the increasing interdependencies between FEW sectors, the adoption of a nexus approach is becoming crucial for enabling sustainable development and mitigating the adverse effects of climate change. All of these challenges impel researchers to focus on the trade-offs and synergies of the FEW nexus as a potential strategy for integrated and efficient resource management. Recently, attention has been directed towards the study of the interdependencies across the FEW sectors. Among such studies, Kılkış and Kılkış (2017), Carrasquer et al. (2017), and Karabulut et al. (2017) addressed aspects of a FEW nexus in the food sector and Hang et al. (2016) designed a local food, energy and water production system based on the nexus concept. Mohtar and Daher (2016) developed an integrated FEW nexus framework to compare resource allocation strategy choices. This framework is evolved into a more advanced trade-offs and decision support tool for FEW nexus oriented management (Dahet et al., 2017). The research on the FEW nexus is still in its early stages and there is much to do to fully understand the complex interconnections and interdependencies associated with the FEW nexus. Thus, it is perhaps not surprising that most studies to date have focused on only macro level and their practical features are lacking in areas such as quantitative and computational modeling; decision-making under uncertainty; and cost evaluation. To pinpoint these deficiencies, this study aims at improving our understanding of the FEW system through quantitative, stochastic modeling of small-scale interactions between the FEW components. The objective is to investigate how food, energy, and water resources are interlinked and which resource is under pressure. A key part of the proposed quantitative analysis is to define measurable sustainability metrics, for which data on both supply and demand sides are needed. The results of this study contribute to the complex challenges at the FEW nexus by (1) identifying characteristics (e.g. deterministic or stochastic) and processes to design and prototype sustainable FEW systems, (2) exploring and quantifying the influence of driving factors (e.g. weather conditions) on FEW systems operation, and (3) estimating the energy intensity of water and food supplies and water intensity of different types of energy and food production systems. There is no doubt that with today’s large-scale FEW supply systems, a macro-level analysis of FEW consumption patterns is needed to understand the synergy among these systems in the context of sustainability, but it should ultimately be based on the collection of micro-level data. Thus, this study focuses on designing a small-scale FEW system that can consistently meet its food, energy, and water demands from sustainable sources. This paper presents a stochastic mathematical model for predicting the FEW demand and production with the objective of addressing system stress and ensuring its sustainability. Through an in-depth analysis of the costs of alternative designs for the sustainable FEW systems, the results Page 2 of 25

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of this study have important practical implications. Furthermore, an optimization process is used for finding an alternative with the most cost effective or highest achievable sustainability under the given constraints. 2. State of the art of food-energy-water nexus A number of recent studies investigated the relationship between FEW sectors, many of them examined the challenges in each area individually. Some of these studies focused on the lack of access to clean water, globally and locally, especially in rapidly growing areas, the lack of food security and resultant hunger, and the lack of access to safe energy supply for cooking and electricity. Loy et al. (2017) evaluated the state of knowledge regarding water for food within the nexus framework and identified opportunities to increase water use efficiency and/or decrease water usage throughout the food supply chain. Increasing yields because of improved irrigation water use efficiency is predictable, but its impact on the performance of the FEW system remains poorly understood. To optimize water use efficiency in the food sector, various sensors can be utilized to determine the quality of soil (e.g. pH, salinity), soil moisture level, nutrient levels (phosphorus, nitrogen and potassium), weather patterns, and crop yield (Kim et al., 2013). Besides advances in precision agriculture, it should be a part of future work to provide more information about the role of irrigation productivity in FEW systems. For example, a sustainable FEW system requires nearly three times more water for livestock (protein and dairy) than irrigation. Current status indicates that investing for the livestock water use is given a higher priority than investing for irrigation water use. In response to strong growth in energy intensive wastewater treatment, Longo et al. (2016) reviewed wastewater treatment plant energy performance and the state of the art methods for energy benchmarking. They concluded that overall energy savings result from operational optimization and technology improvements of between 5 and 30% seem reasonable. While methods for the control and treatment of wastewater have matured, the water desalination processes remains undeveloped in the water sector. The famous ways of desalination are multistage flash, multi-effect desalination, solar distillation, reverse osmosis and the electro-dialysis (Karagiannis and Soldatos, 2008; Virgili and Pankratz, 2016). All these methods suffer from desalination shortcomings with the difficulties of maintenance, relatively high energy consumption and also high cost (Alsaman et al., 2016). To address the need for low energy consumption desalination system, both water supply (producing fresh water from seawater) and demand (uses for water) sides must be considered. For example, seawater desalination for sustaining agricultural production could address some of the trade-offs between water and food sectors. However, the existing desalination technologies, such as membrane and thermal, are energy intensive and contribute significantly to climate change. Therefore, any approach that concentrates only on one part of the FEW nexus without considering its interconnections can result in serious unintended consequences. The energy resilience can be described as the ability to adjust to interruptions in the supply of energy. Given the global market of energy, the idea of complete energy independence is unfeasible and unrealistic. The true weakness is rooted in the interdependency and vulnerability of energy production systems. Total water withdrawals for thermoelectric power for 2010 in the U.S. accounted for 45% of total water withdrawals, and 38%of total freshwater withdrawals (USGS, 2010). Energy generation and distribution infrastructures are centralized and vulnerable to disruptions. In addition to environmental benefits of renewable energies, they are decentralized and more efficient. For example, solar power can significantly reduce the amount of water needed to produce electricity and thus improve water scarcity. Although there are many alternative energy technologies already studied in the literature, these technologies are currently at different levels of technological maturity with a few already analyzed in a nexus framework. The realization of Page 3 of 25

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interdependencies among FEW systems should guide our investments in food, water, and energy innovations. Despite the improvements made in the performance of each of these systems individually, the interaction between the FEW sectors should also be examined. Examples of these interactions include, but not limited to the significant amounts of water used in food production for irrigation (Chaves and Oliveira, 2004; Gerbens-Leenes et al., 2009) and for industrial meat production (Emmerson, 2011); energy used in food production in post-harvest stages (Canning et al., 2010); and negative environmental impacts of deforestation, overgrazing, and often low-productivity agricultural methods as a consequence of ensuring energy and food (Bazilian et al., 2011). 3. Scope and assumptions A sustainable FEW system is defined as a system that can consistently meet its food, energy, and water demands with sustainable inputs rather than using non-renewable sources. The interactions between the FEW components can be better understood through the design and analysis of a small scale system. Regardless of the scale, design decisions and analysis of the interactions can easily be applied to a larger scale such as a town, a city, and even a country. The greenhouse is the smallest scale of a FEW system than can consistently yield food and collect or recycle its own water and supply its own energy (electricity demand). The manipulation and control of temperature, light, and water make the greenhouse an ideal option for consistent year-round growing, regardless of prevailing weather conditions on the outside. The size of the population determines the demand for food and food production determines water and energy demands. The greenhouse is design and analyzed for a typical family of four (two adults and two children). The renewable sources of energy include the generation of the power with the help of solar, wind, biogas, geothermal and ocean. Since solar energy is the only small-scale source of renewable energy, the smallscale sustainable FEW system is designed as a greenhouse powered with a solar system. Wastewater, rainwater, and seawater are sustainable sources of water. Because the desalination of seawater is more expansive than water treatment from wastewater for irrigation purposes, only reclaimed wastewater and harvested rainwater are considered in the analysis. To treat the wastewater, different technologies including simple (coarse filtration and disinfection), chemical (photocatalysis, electro-coagulation and coagulation), physical (sand filter, adsorption and membrane), biological (biological aerated filter, rotating biological contactor and membrane bioreactor), and extensive (constructed wetlands) are used. Each of these systems has advantages and disadvantages which interested readers can refer to (Al-Jayyousi, 2003; Fryer, 2012; Jefferson et al., 2000) for a full review of them. Although the amount and quality of wastewater generated within a house depends on several factors such as the habits and life style of occupants, a constant value of 1500 L/d is assumed in the present study. It is also assumed that land availability is not limited and human resources for building and operating the system are either available or not required. There are two approaches to ensure sustainability of FEW systems. In a within system approach, all changes are happening within a system and without using external resources. This can be achieved by converting one resource to another (e.g. producing energy and increase food production) or storing a resource (e.g. water) and use it later when the resource is scarcer. The within system solutions include but not limited to energy generation from sustainable resources (e.g. wind turbine, solar system, biogas), water recycling and desalination, greenhouse and aqua farming. In a between system approach, a system is integrated with one or more systems to compensate its weakness (e.g. importing energy from a country with oversupply energy). In both approaches, the focus is on adopting appropriate solutions or technologies that enable the

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FEW system to meet its food, energy, and water demands while achieving minimum cost (model optimization process). A quantitative modeling is used to determine the influence of each resource (i.e. food, water, or energy) on the greenhouse’s output. Not only this approach advances our understanding of FEW systems, but also shows us the weakest link of the systems (e.g. water scarcity, energy shortage, inconsistent supply of food, etc.). A within system approach is proposed to strengthen the weakest link, optimize the FEW system such as characteristics of solar system for energy generation, water collection and recycling system, and supplyand demand-side of light source for plants, and achieve the minimum cost. The household food consumption in this study is calculated based on the dietary information provided by the Food and Agriculture Organization (FAO) of the United Nations (UN) (Kennedy et al., 2011).The amounts of calories needed for a household consists of one male and one female adult, 36 to 45 years old, and two children, 2 to 10 years old, is estimated to be 54,600 cal/wk (or 7,800 cal/day). For adults, the reference man is 178 cm tall and weighs 70 kg and the reference woman is 162 cm tall and weighs 57 kg. The level of activity for the study household is considered as moderately active means a lifestyle that includes physical activity equivalent to walking about 2.4 to 4.8 km/d at 4.8 to 6.4 km/hr, in addition to the light physical activity associated with typical day-to-day life. Table 1 shows the vegan adoption of the United States Departments of Agriculture (USDA) and Health and Human Services (HHS) food pattern for this family of four people (USDA, 2010). Table 1: Recommended average daily intake amounts for a family of two adults and two children Food Type

grams/day

Fruits

1,656

Vegetables

2,366

Dark-green vegetables

237

Red and orange vegetables

693

Beans and peas (legumes)

203

Starchy vegetables

676

Other vegetables

558

Grains

652

Whole grains

326

Refined grains

326

Protein Food

620

Eggs

215

Beans and peas

158

Soy products

247

Nuts and seeds

1.57

The proposed model is not limited to a family with two children and can be applied to other types of households and demographic variables. To demonstrate the effectiveness of the proposed methodology, the optimal values of decision variables are calculated for different households varying in size and composition. Additionally, the model is analyzed for two different climates; one is relatively cloudy (with an average solar radiation of 3.6 kWh/m2/d) and humid (with an average rainfall of 1,000 mm/yr) and the other is sunny Page 5 of 25

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(with an average solar radiation of 5.6 kWh/m2/d) and arid (with an average rainfall of 100 mm/yr). Figure 1 shows the main factors affecting the output of the small-scale FEW system as well as design decisions.

Figure 1: Decision variables and factors affecting the sustainable design 4. Design process The steps taken to design a sustainable FEW system are shown in Figure 2. In order to design a sustainable FEW system, one has to make the decision on what to grow to provide the recommended types and amounts of food for a household (design step 1). This decision will affect other aspects of the plants’ growth, including the amount of water, the color and intensity of light, and the temperature and humidity requirements. To calculate the size of the system (e.g. greenhouse space, fish farm pond size, farm area), first the intake calories per week based on the gender, age and activity level is determined for the study household. Once the total growing space for each crop is calculated based on the needed intake calories for this household, the size of the FEW system (e.g. required greenhouse space) can be determined (design step 2).

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Figure 2: Proposed procedure to design a sustainable FEW greenhouse system The average daily intake amounts identified in Table 1 are used to select the right kind of fruits and vegetables. The climate zone and estimated water and light requirements govern the selection of plants and crops for the FEW system. Although the proposed model is analyzed for two different climates, similar kinds of plants are considered in this study. Data availability and nutrition values are other factors that influenced the selection of food type. Examples of the selected fruits and vegetables with their required space, water, and temperature are listed in Table 2 (FAO, 2015). Table 2: List of crops and plants to meet the recommended average daily intake amounts Name

Food type (Table 1)

Watermelon Lettuce

Fruits Dark-Green vegetables Red and orange vegetables

Tomato Lima Beans Potato

Beans and peas (legumes) Starchy vegetables

Spinach Other vegetables Zea Corn Whole grains Wheat Refined grains Peas Beans and peas Soybean Soy products Peanuts Nuts and seeds Note: error margin of 15%

Yield period (days) 95 45

Average yield (g/wk) 683 423

Space (m2/seed) 0.27 0.14

Temp. (°C) 18-35 4-24

Water (Lkg/mo) 4.4 2.9

105

756

0.02

18-25

0.1

90

316

0.16

10-27

5.4

135

256

0.40

2-24

10.9

40 80 115 85 75 130

655 172 328 460 277 78

0.15 0.16 0.05 0.02 0.08 0.06

10-24 20-30 18-26 10-23 20-30 10-20

0.1 0.2 1.3 0.27 6.62 0.23

The primary sustainable source of water for plant growth is precipitation. Rainwater can be collected from roofs and the water collected is redirected to a reservoir. Based on the rainfall forecast and upon consideration of water requirements for plants, which are obtained in design step 1, the surface area of the roof is calculated (design step 3). When rainfall is insufficient, the system should be able to recycle enough greywater to meet crop needs (design step 4). Greywater is defined as the domestic wastewater without the contribution of blackwater from the toilets, i.e., corresponds to the wastewater from baths, washbasins, bidets, washing machines and dishwashers and kitchen sink. The key difference between greywater and sewage (or blackwater) is the concentration of organic materials. Because sewage has a high concentration of organic in comparison with greywater, a greywater recycling system captures this water before it reaches the sewer. Sunlight is the primary light source for plants and artificial lightings can be used as a secondary or supplementary light source for greenhouse growing. The light requirements of plants, obtained from the first design step, determine the transparent area of the roof (for natural light) or the amount of artificial light (design steps 5 and 6). Most plants and vegetables need about 12 to 18 hours of 36,000 lux (limens per m2) of light/d in order to grow. Since direct sunlight provides about 100,000 lux or 790 W/m2 to earth’s surface, it is important to make sure that plants and vegetables receive around six hours of direct sunlight per day (4740 Wh/m2/d). Research conducted at Michigan State University indicated that maintaining a minimum Page 7 of 25

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daily light integral (DLI) between 4 to 12 mol/m2/d is necessary for growth and development (Morrow, 2008). This is equal to 1.5 to 4.4 hours of light emitting from a 400-watt high pressure sodium (HPS) lamp placed at a distance of 25 cm or 650 to 2150 Wh/m2/d direct sunlight. DLI is the amount of photosynthetically active radiation received each day as a function of light intensity and duration and expressed as moles of light (mol)/m2/d (Randall and Lopez, 2014). Artificial light is commonly used to provide high intensity light when the natural sunlight is not adequate for optimal plant growth. In general, there are four basic types of lighting available for greenhouse use: incandescent, high intensity discharge (HID) fluorescent, high intensity fluorescent and light emitting diode (LED) lights. Among them, HID lamps have high wattage and generate light in the red and blue spectrums that are valuable to different stages of plant growth. They are also considered by many growers to be the best lights available for providing supplemental greenhouse light. According to the literature, a general guideline for greenhouse lighting is 170-270 W/m2 of garden space if the artificial light is used as a primary light source. Less is required if artificial lights are used to supplement natural sunlight or if the plants do not need as much light for their growth. An efficient heating, ventilating, and air conditioning (HVAC) system is used to control the temperature and humidity inside the greenhouse. The solar system should be designed to generate all the electricity required for artificial lighting, water recycling, heating, cooling, and air conditioning of the greenhouse (design step 7). The ultimate step in the design process is to optimize energy and water systems based on the demand, expected FEW productions, and ensuring sustainability while minimizing the cost of the system (design step 8). As seen in Figure 2, the decision variables can take many different forms. To deal with this inconsistency and to ensure the ultimate goal of system sustainability, an index is defined to compare the impact of each decision variable on the system’s output. A sustainability index (SI) is defined as the probability that a system (e.g. greenhouse) will be able to meet its consumption needs without using external resources. For example, there is 85% chance that a system with a SIwater = 85% meets its water consumption demand (e.g. water needed for irrigation). Due to the scale of the proposed system, obviously this index cannot be the case for all FEW demands at its present form. The sustainability index is defined as: SIi = P (Si ≥ Di), i = food, water, energy

(1)

Where, Si is the expected supply and Di is the expected demand for component i during the analysis period (one year in this study). The food demand depends on the study household (e.g. table 1) and demand for energy and water is derived from the demand for the household food pattern. The sustainability index can exceed 100% if the system supplies more than 100% of its consumption needs. In this case, the sustainability index represents the certain extra production of food, water, or energy. For example, a system with a SIwater = 130% can certainly supply 30% water more than its expected demand. In the next section, the SI is calculated for each decision variable. 5. Calculation of the small-scale FEW system The average yields and the number of plants to grow for each person are considered in the system size calculation. Table 3 shows the required area (m2) and average yields (g/wk) of the selected plants (design step 1). To determine the size of the FEW system, containers are assumed to be spaced at certain distances to obtain required yield per m2of production area. There is a tradeoff between container spacing and plant Page 8 of 25

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quality: closer spacing tends to reduce plant quality but results in a greater number of containers per area of production, whereas greater spacing increases plant quality but yields fewer containers per m2. Therefore, optimum spacing would allow the leaves of one container to slightly overlap the leaves of adjacent containers. Table 3: The required space and average amounts of yield of crops and plants to meet the food consumption of a family of two adults and two children Food type and name Fruits Vegetables Dark-green vegetables Red and orange vegetables Beans and peas (legumes) Starchy vegetables Other vegetables Grains Whole grains Refined grains Beans and peas Protein food Soy products Nuts and seeds

Area (m2) 4.58

Yield (g/wk) 11,593

0.15 0.02 0.83 7.69 0.44

1,538 4,968 1,420 4,850 3,785

2.48 1.32 0.03

2,480 2,480 1,446

0.66 0.15

1,049 1,644

The weekly caloric intake of 7,800 and the average yield per m2for each crop are assumed to be deterministic values in calculating the size of the FEW system. This means that they defined as constant input parameters during the calculation. The sustainable FEW system is designed for a family with two children; however, the proposed model can be applied to other types of households and demographic variables. The size of the FEW system and the water requirements for different types of households are calculated and shown in Figure 3. The required size of the system and water supply for the study household with 7,800 cal/day are 17 m2 and 554 L/mo, respectively (design step 2).

Figure 3: The required amounts of space and water to meet different food consumptions Once a list of potential crops and plants is complied, the quantity of water required by a crop in a given period of time for normal growth can be determined. Although the water demand of the system is calculated under greenhouse conditions, but it can also be applied to outdoor growing with large plants. The water requirements serve as the basis for the design of the rainfall harvesting system. Precipitation or rainwater Page 9 of 25

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runoff, as the primary source of sustainable water, is collected from roof surfaces and transferred down into a reservoir using gutters and down pipes that are usually installed at the edge of a roof. To prevent overflow, the number and dimensions of the gutters and rainwater downpipes are determined based on the maximum rainfall intensity. However, the optimum effective roof surface (i.e. horizontal projection of the greenhouse roof) must be determined based on the expected rainfall amounts. A stochastic process is used in this paper for rainfall prediction. The probability estimation of rainfall states from the weather records over the last 16 years (1998 to 2014) is used to obtain predictions for rainfall statistical parameters such as the averages and standard deviations. A comprehensive discussion regarding this stochastic process can be found in Karan et al. (2016). Next, the effective roof surface is calculated using the probability distribution of monthly precipitation in State College, PA (as the humid climate) and Las Vegas, NV (as the arid climate). The results of the selected cities can be generalized to other regions with similar climates, for instance Qatar, Oman, and other countries which border the Persian Gulf have similar climates to Las Vegas, NV. Figure 4 shows the probability distributions of precipitation as well as the probability distributions of water collection for 1 m2roof surface during a one-month time period (January). In the example shown in Figure 4, there is 26% chance that precipitation will exceed 78 mm and will be below 80 mm in State College, PA and there is 15% chance that precipitation will exceed 13 mm and will be below 14 mm in Las Vegas, NV during January. Also, there is 24% chance that 1 m2roof surface collects 80 L or less water in State College, PA and there is 23% chance that 1 m2roof surface collects 16 L or less water in Las Vegas, NV during January.

(a)

(c)

(b)

(d)

Figure 4: Examples of probability distributions for (a) precipitation in State College, PA, (b) precipitation in Las Vegas, NV, (c) water collection for 1 m2roof surface in State College, PA, and (d) water collection for 1 m2roof surface in Las Vegas, NV (time horizon of prediction: January) Page 10 of 25

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The decision variable of roof surface area is formulated and solved by the SIwater. As explained in Eq. 1, the SI represents the probability of being able to meet systems demands. While Dwater is determined in the previous step, the expected water supply (Swater) can be obtained using Eq. (2): 𝑆𝑤𝑎𝑡𝑒𝑟 = ∑

12

𝐸𝑅𝑆 × (𝐹𝑤𝑎𝑡𝑒𝑟(𝑥))𝑛

𝑛=1

(2)

where, ERS is the effective roof surface, Fwater(x) is the cumulative probability of precipitation and refers to the probability that the monthly precipitation is less than or equal to x (as a specified value), and n is the number of the month. The annual water demand of the crops that meet the food consumption of the study household is found to be 11,766 L (6,642 L for irrigation and 5,124 L for evaporation loss). Figure 5 shows the sustainability indices for different effective roof surfaces in State College, PA and Las Vegas, NV (design step 3). For the humid climate (i.e. State College, PA), a system with an effective roof surface of 20.4 m2 has the minimum surface area with a SIwater = 100%. A surface area smaller than 20.4 m2 will not be able to meets the water consumption demand from sustainable sources, but, a surface area greater than that will not only meet water consumption needs, but also certainly will collect extra water. A system with an effective roof surface of 17 m2 in State College, PA can certainly collect 10,092 L water/yr (SIwater = 88%). However, we need a system with an effective roof surface of 255.8 m2 in Las Vegas, NV (arid climate) to achieve SIwater = 100%. There is 0% chance that a system in Las Vegas, NV with a surface area smaller than 122.6 m2 meets its water consumption demand (SIwater = 0%), although it can certainly collect 6,496 L water/year. There is 73% chance that a system in Las Vegas, NV with a surface area of 196.1 m2 can meet its water consumption demand (SIwater = 73%), but it can certainly collect 10,394 L water/yr. A system with an effective roof surface of 17 m2 in Las Vegas, NV can certainly collect 748 L water/yr.

(a)

(b)

Figure 5: sustainability indices and certain collection amounts of water for different roof areas (a) State College, PA and (b) Las Vegas, NV. When precipitation is not sufficient to meet water consumption (e.g. a system in Las Vegas, NV with a surface area smaller than 255.8 m2), greywater recycling is taken into consideration to guarantee a 100% SIwater. For a typical household, approximately 27% of water is used for toilets, and greywater accounts for 68% mainly composed of clothes washer (22%), shower (17%), kitchen (10%), and hand wash (7%). Several measurements, such as electric conductivity of water, sodium adsorption ratio, and total dissolved solids, are used to assess the suitability of greywater supply for uses such as toilet flushing and irrigation. Table 4 shows the classification of greywater for various sources, recommended treatment method, and estimated cost of recycling. Page 11 of 25

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Table 4: greywater quality measurements and recommended treatment methods (EPA, 1999; Matos et al., 2014; Selecky et al., 2003) Source Bath/shower Hand wash Washing machine Dishwasher

Daily consumption (lit) 255 105 330 70

Average total solids (mg/L) 605 696 1,047 1,464

Recommended treatment method Sand filtration Sand filtration Chemical Biological contactor

150

2,125

Extensive

Kitchen sink

Estimated Cost ($) 4,140 + 6.5×L 4,140 + 7.5×L 4,480 + 8.4×L 7,890 + 10.5×L 8,850 + 13×L

Note: L = liter of recycled water At times of low water demand (e.g. less than 360 L/d), sand filtration system is used because it is not only the cheapest and simplest system but also it is characterized by a high reliability and rather low lifecycle costs. However, it is needed to use more expensive treatment methods (e.g. chemical or biological) to meet higher demands. Using the cost estimates for treatment methods in Table 4, the average cost of recycled greywater (RW) is calculated using Eq. 3.

{

4,140 + 6.5 × 𝐷𝑤 3,885 + 7.5 × 𝐷𝑤 𝐶𝑜𝑠𝑡 𝑅𝑊($) = 3,901 + 8.4 × 𝐷𝑤 5,862 + 10.5 × 𝐷𝑤 4,922 + 13 × 𝐷𝑤

𝑖𝑓 𝑖𝑓 𝑖𝑓 𝑖𝑓

𝑖𝑓 𝐷𝑤 ≤ 255 𝑙𝑖𝑡/𝑑𝑎𝑦 255 < 𝐷𝑤 ≤ 360 𝑙𝑖𝑡/𝑑𝑎𝑦 360 < 𝐷𝑤 ≤ 690 𝑙𝑖𝑡/𝑑𝑎𝑦 690 < 𝐷𝑤 ≤ 760 𝑙𝑖𝑡/𝑑𝑎𝑦 760 < 𝐷𝑤 ≤ 910 𝑙𝑖𝑡/𝑑𝑎𝑦

(3)

where, DW is the water demand per day. For example, the average cost of a greywater recycling system to meet the required water supply of 18 L/d for the study household will be 4,140 + 6.5 × 18 = $4,258 (design step 4). After formulating the SIwater, we will measure how sustainable the energy component is (SIenergy). While the energy is supplied by the solar system, the energy demand includes all the energy required for water recycling, artificial light, heating, cooling, and air conditioning of the greenhouse. First of all, in order to figure out energy required for artificial light, the available amount of sunlight should be calculated. If the FEW system is designed for outdoor plants, this amount only depends on sunlight irradiance in the system location. However, for a greenhouse system, it also depends on the transparent area (TA) of the greenhouse structure. Light from the sun passes through the transparent (or glass) roof and walls of the greenhouse to power the growth of plants. The TA of the roof is calculated using Eq. 4. 𝑇𝐴 =

[

(𝑅𝐼 ‒ 𝑆𝐿𝑤) 𝑆𝐿𝑟

] × 100%

(4)

Where, RI is the required irradiance (W/m2/d), SLw is the sunlight irradiance passing through walls and SLr is the sunlight irradiance passing through the roof. The amount of sunlight passing through the transparent roof and walls can be calculated using Eq. 5. 𝑗 = 24

𝑆𝐿𝑤 = ∑𝑖 = 1 𝐷𝐿𝑖 𝑗 = 24 𝑆𝐿𝑟 = ∑𝑖 = 1 𝐷𝐿𝑖

𝑖𝑓 𝑎𝑙𝑡𝑖𝑡𝑢𝑑𝑒 𝑎𝑛𝑔𝑙𝑒 ≤ 𝐻𝑊𝑃 𝑖𝑓 𝑎𝑙𝑡𝑖𝑡𝑢𝑑𝑒 𝑎𝑛𝑔𝑙𝑒 ≥ 𝐻𝑊𝑃

(5)

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where, DL is the hourly direct irradiance (amount of solar radiation received per unit area), and HWP is the height to width proportion and is measured by the inverse tangent function of height/width. The altitude angle describes how high the sun appears in the sky and is measured between an imaginary line between the center of the greenhouse and the sun and the horizon (see Figure 6).

(a)

(b)

Figure 6: sunlight irradiance passing through the (a) roof, and (b) walls In order to reduce the need for artificial lighting during daylight hours, the transparent area of the roof must be calculated for either the shortest daylight period of the year (i.e. winter solstice) or the period of time when the need for the transparent roof is highest (i.e. the least amount of light passes the walls). Using the solar irradiance and altitude angle data for the study household, the transparent area of the roof would result in a minimum of 100% for the State College, PA and 46% for the Las Vegas, NV. The need for the transparent roof is highest in March 20, when only about 3,360 W/m2/d of solar radiation (70% of required solar radiation) passes through the walls in Las Vegas, NV. Therefore, 100% of the greenhouse roof in State College, PA and 46% of the greenhouse roof in Las Vegas, NV must be transparent to meet the required sunlight supply for the study household (design step 5). Under light-limiting conditions (such as during the winter), greenhouse plants and vegetables can benefit from artificial lighting (AL). The amount of AL (measured in watts-hour) can be calculated using Eq. 6.

0  AL   DLI min  DLi   h AL  Wm 2  GS  DLI min

if DLi  DLI min if DLi  DLI min

(6)

where, DLImin is the minimum daily light integral (i.e. 650 to 2,150 Wh/m2/d direct sunlight), DLi is the daily direct sunlight irradiance, hAL is the hour of necessary artificial lighting for growth and development (e.g. 1.5 to 4.4 hours of light emitting from a 400 watt HPS lamp placed at a distance of 25 cm), GS is the greenhouse space (e.g. 17 m2 for the study household), and Wm2 is the watts per m2of greenhouse lighting (170-270 W/m2 based on literature). On low sunlight irradiance days, the system required the highest artificial light demand (e.g. December 21 in State College, PA with an average of 1704 Wh/m2/d sunlight irradiance or December 17 in Las Vegas, NV with an average of 4,055 Wh/m2/d sunlight irradiance). Figure 7 shows the probability distributions of required artificial lighting for a greenhouse in State College, PA and Las Vegas, NV during their low sunlight irradiance days. In the example shown in Figure 7, there is 5% chance that between 5,122 to 7,093 Wh of artificial lighting is needed in State College, PA during December 21 while only 2% of the time we need to use the same amount of artificial lighting in Las Vegas, NV during December 17 (design step 6). Page 13 of 25

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(a)

(b)

Figure 7: Examples of probability distributions of artificial lighting for (a) December 21 in State College, PA, and (b) December 17 in Las Vegas, NV There are four basic considerations when calculating energy flow (heat gain or loss) through a greenhouse. Conduction and convection are major considerations of heat losses while the energy gained by solar radiation and emitted by artificial lightings can increase internal heat gains. The transfer of heat, or total heat loss (HL), can be calculated using Eq. 7. 𝑇𝑜𝑡𝑎𝑙 𝐻𝐿 = 𝐻𝐿𝑐𝑜𝑛𝑑𝑢𝑐𝑡𝑖𝑜𝑛 + 𝐻𝐿𝑐𝑜𝑛𝑣𝑒𝑐𝑡𝑖𝑜𝑛 ‒ 𝐻𝐺𝑠𝑜𝑙𝑎𝑟 ‒ 𝐻𝐺𝑙𝑖𝑔ℎ𝑡𝑖𝑛𝑔

(7)

Where, HLconduction is the transfer of heat through the structure (Wh/d), HLconvection is the transfer of heat as a result of movement of the masses of air (Wh/d), HGsolar is the total heat gained by solar radiation and is estimated to be one-third of the sunlight’s energy hitting the ground space of the greenhouse, equal to the expected solar radiation multiplied by the transparent area of the roof as well as by a solar-heat-gain coefficient of the envelope material, and HGlighting is the total heat emitted by artificial lighting and can be calculated using Eq. 8. 𝐻𝐺𝑙𝑖𝑔ℎ𝑡𝑖𝑛𝑔 = 𝑊𝑙𝑖𝑔ℎ𝑡 ‒

𝑙𝑢𝑚𝑒𝑛𝑠 683

(8)

Where, Wlight is the watts and lumens is the lumen output of the artificial light. For instance, a 400 W HPS lamp with 50,000 lumens would produce 400 – 50,000/683 = 327 Wh heat per hour. To calculate the total energy consumption of the greenhouse, its geometry was created in Design Builder software. The Design Builder combines the energy simulation capabilities of the EnergyPlus with advanced building modeling technologies. EnergyPlus is a whole building dynamic energy simulation software which model heating, cooling, lighting, and ventilation. Using EnergyPlus avoids imprecisions introduced by simplifying algorithms, and since it is coupled with Design Builder software which is a configurable tool, it can be utilized for detailed design. In this study, one thermal zone was defined and the indoor design temperature was 18°C for space heating and 23°C for space cooling. A stochastic process is used for energy flow calculation. The indoor temperature is set for the plants (see Table 2) and the probability estimation of outdoor temperature obtained from the weather records over the last 16 years. Figure 8 shows the probability distributions of energy demand for a greenhouse in State College, PA and Las Vegas, NV during their coldest and hottest dates. In the example shown in Figure 8, there is 15% chance that 55 kWh energy for heating is needed in State College, PA and there is 14% chance that 24 kWh energy for heating is needed in Las Vegas, NV during their coldest dates. Also, there is 23% Page 14 of 25

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chance that 60 kWh energy for cooling is needed in State College, PA (the expected energy consumption is 44.9 kWh) and there is 20% chance that 65 kWh energy for cooling is needed in Las Vegas, NV during their hottest dates (the expected energy consumption is 74.3 kWh).

(a)

(b)

(c)

(d)

Figure 8: Examples of probability distributions of (a) energy loss in coldest date of State College, PA, (b) energy gain in hottest date of State College, PA, (c) energy loss in coldest date of Las Vegas, NV, and (d) energy gain in hottest date of Las Vegas, NV Since solar energy is the only source of renewable energy that can be applied at a small scale (e.g. directly to the roof decking or solar window), it is used as the primary source of sustainable energy in this study. The electricity generated by solar system is calculated using Eq. 9.





PSolar  E cell  G  Acell  1  TkP  T  25

0

C



(9)

where, PSolar is the electricity generated by solar system and measured in W, Ecell is the solar cell efficiency (i.e. portion of sunlight energy that can be converted via solar panels into electricity) (%) under standard test conditions (temperature of 25 oC, irradiance of 1000 W/m2, air mass 1.5 spectrum), G is the irradiance of input light and measured in kW/m2, Acell is the surface area of the solar panels and measured in m2, and TkP is the temperature coefficient of solar panel (%/oC). Among these factors, Ecell and TkP are deterministic variables that are determined based on average values derived from a database of 46 solar panels from 15 manufacturers. On average, a single solar module is 1.7 m2 and works at 15.86% efficiency and temperature coefficient of -0.44 %/oC. The maximum DC input voltage and the start voltage of the inverter are two important values that determine the maximum and minimum number of solar modules in series. Although it is possible to increase the number of series to generate more electricity, at least 7 solar modules are needed to meet the DC start Page 15 of 25

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voltage of 120-140 volts. Using a battery backup will enable us to power the greenhouse even when the solar system is not producing enough energy, for example during cloudy weather or night. Thus, a solar system of 7 modules of solar panels with 1 kWh storage capacity is used as the baseline for the greenhouse. As explained in Eq. (1), The SIenergy is defined as the probability that a system will be able to meet its energy consumption needs without using external resources. This index can also be expressed as Eq. 10: 365

SI energy 

S i 1 365

i

(10)

D i 1

i

Where, Si is the expected daily supply of electricity generated by the solar system and is calculated using Eq. 11 and can meet at most the greenhouse's demand, and Di is the expected daily consumption of electricity by artificial lighting, heating and cooling systems and can be calculated using Eq. 6 and Eq. 7.

D Si   i  Psolar  No. of panels  SoCi

if S i  Di if S i  Di

(11)

Where, SoCi is the solar battery's state of charge on day i and can be calculated using Eq. 12.

 min S i  Di  SoCi 1 , Cbattery  SoCi   maxS i  Di  SoCi 1 ,0 

if S i  Di , SoC 0  0 if S i  Di

(12)

Where Cbattery is the solar system storage capacity. Figure 9 shows the monthly expected energy supply and demand, as well as the SIenergy for a greenhouse with 7 modules of solar panels and 1 kWh storage capacity in State College, PA and Las Vegas, NV. The SIenergy for this greenhouse is found to be 22% in State College, PA and 29% in Las Vegas, NV. Thus, there is 22% chance that a system with 7 modules of solar panels and 1 kWh storage capacity in State College, PA meets its energy consumption demand. Also, the SIenergy of such a system in Las Vegas, NV is found to be 100% for 97 days (from early January to mid-March), which means that a system with 7 modules of solar panels and 1 kWh storage capacity in Las Vegas, NA can certainly meet its energy consumption demand during this period (design step 7).

(a)

(b)

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Figure 9: Sustainability index and expected energy demand and supply values for a greenhouse with 7 modules of solar panels and 1 kWh storage capacity in (a) State College, PA, and (b) Las Vegas, NV 6. Optimum sustainable FEW system There is no doubt that a sustainable FEW system can be easily designed when there are unlimited financial resources available. It is important that the optimal system, which guarantees minimum costs, is designed. On one hand, the system should be able to meet its food, water and energy consumption needs without using external resources (i.e. SIi ≥ 100%, i = food, water, energy ). This would cause a tendency to overdesign the system (e.g. too many solar panels and high volume recycling system). On the other hand, the excess food, water, and energy produced by the over-designed system are wasted because they can meet at most the system’s demands. Designing an optimal sustainable system involves a trade-off between supply-side and demand-side management for food, energy, and water components. Among these components, the decision on what to grow to meet the food demand determines the water and energy demands of the system. Furthermore, the system size is the only decision variable that can be controlled to guarantee a 100% sustainability index for food. When sunlight or precipitation are not sufficient to meet energy and water demands (i.e. SIwater or energy < 100%), artificial lightings and greywater recycling are other decision variables that can be controlled to guarantee a 100% sustainability index for water and energy. Based on the total cost of the greenhouse, an objective function is developed to find the optimal number of solar panels, the optimal solar system storage capacity, the optimal area of the roof, and the optimal capacity of the water recycling system. The cost of the system can be calculated and minimized using the objective function shown in Eq. 13. Optimal system = minimize cost of system | SIi ≥100%, i = food, water, energy

(13)

In the present study, the total cost of a sustainable greenhouse includes the costs of the wall and roof structure (material: polycarbonate), heating and cooling systems, artificial lighting, greywater recycling system, solar panels, battery, and energy usage. Note that the value of land and ecosystem, and cost recovery of water are not included in the proposed business model. Table 5 shows cost estimates for these components. The cost estimation in this study shows only snapshots of cost data at a certain point in time and they may vary significantly depending on location and source of the data. Table 5: estimates of greenhouse system capital and operating costs Component Roof structure Wall structure HVAC system Artificial lighting Greywater Solar panel Mounting structure Battery Energy usage

Estimated Cost ($) 73.6 × GS + 93 59.4 × (W+L) × Hwall + 93 9.2 × GS + 950 8 × GS Eq. 3 340 × Nsolar + 2,112 138 × Nsolar + 177 212 × Cbattery Erate × De

Parameters GS = greenhouse space (m2) Hwall = height of wall (m) W = width of greenhouse (m) L = length of greenhouse (m) DW = the water demand (L/d) Nsolar = number of solar panels Cbattery = system storage capacity (kWh) Erate = electricity rate ($/kWh) De = energy demand (kWh)

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A baseline system is defined as a greenhouse with 7 modules of solar panels and 1 kWh storage capacity but without greywater recycling capability. A baseline system with 17 m2 area (e.g. W = 4 m, L = 4.25 m, Hwall=3.65 m) would cost around $11,146 in State College, PA (with electricity rate of $0.0746/kWh) and $10,696 in Las Vegas, NV (with electricity rate of $0.1215/kWh). Although the average electricity rate in Las Vegas is greater than the State College, PA, mounting solar panels to the roof could provide a way to save cost (only 46% of the roof must be transparent for the greenhouse located in Las Vegas, NV). However, this system is not sustainable, as it does not meet its water and energy consumption needs without using external resources. Since many of the factors that affect the output of the system (e.g. sunlight, rainfall, and temperature) are unknown at the time the system should be designed, it is difficult to find the optimal quantities of the system’s components (e.g. number of solar panels, storage capacity of the solar system, capacity of the water recycling system, roof area, and greenhouse space) and achieve the minimum cost. Instead, this paper proposes a stochastic model to designing the optimal sustainable system and its corresponding system components. In order to guarantee a 100% sustainability index for water, it is needed to either increase the roof area or recycle greywater, or both. The results of the analysis for a greenhouse with 100% SIwater is shown in Figure 10. The optimal decision is the one that meets the water demand and achieves the minimum cost. First, the certain water collection was estimated for different roof areas. The demand for recycled greywater was also calculated when the roof surface was not large enough to collect sufficient rainfall. Second, the total cost of the water component is calculated between all pairwise combinations of roof areas and recycling capacities. Ultimately, the optimal roof area and/or recycling capacity of the greenhouse in State College, PA is found to be 20.35 m2 (addition of 3.35 m2 roof surface) without the greywater recycling system that costs $288. The optimal greenhouse in Las Vegas, NV is found to be 17 m2 (no addition roof surface) with a 32.2 L/d greywater recycling system that costs $4,349.

(a)

(b)

Figure 10: Optimal roof area and recycling capacity in (a) State College, PA, and (b) Las Vegas, NV A solar system must be used to generate all the electricity required for artificial lighting, water recycling, and HVAC system of the greenhouse (SIenergy=100%). Besides the electricity generated by solar panels, the solar system storage capacity is an important factor affecting the amount of energy supply for the greenhouse. Figure 11 shows the results of the analysis for a greenhouse with 100% SIenergy. First, the electricity generated by one module of solar panel is estimated using Eq. (9). Second, he expected daily Page 18 of 25

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supply of electricity generated by the solar system is calculated for all pairwise combinations of solar modules and storage capacity using Eq. 11. The total cost was then calculated for the combinations with SIenergy=100%. The optimal solar systems are found to be a system of 40 modules of solar panels with 41 kWh storage capacity in State College, PA that costs $29,949 and a system of 45 modules of solar panels with 1 kWh storage capacity in Las Vegas, NV that costs $22,475. Once the solar batteries are fully charged, the extra energy produced by solar panels can be sent to the electrical grid (selling back to utility) and reduce the energy usage cost. Utility companies buy the extra energy at the actual rate as they produce it themselves, which is approximately $0.027/kWh in State College, PA and $0.044/kWh in las Vegas, NV (design step 8).

(a)

(b)

Figure 11: Optimal solar systems for a greenhouse in (a) State College, PA, and (b) Las Vegas, NV The main contribution of this optimization is in formulating decision variables in the FEW design problem that also enables us to indicate the amount of sustainability improved per dollar spent. This step intends to discover whether new materials and technologies can improve the sustainability of FEW systems at a reasonable cost. A practical example of this contribution would be identifying new targets for further development of water treatment technologies. Based on two reports released by the Water Science and Technology Board of the National Research Council (NRC), the SIwater in the U.S. is estimated to be less than 12% (NRC, 2012, 2016). Innovative treatment technologies are needed to improve the current SIwater without a decrease in the SIenergy and SIfood. In such a case, the proposed method will enable us to analyze the impact of these new technologies on the SI and compare that with the baseline system to determine whether the proposed technology is able to improve the sustainability. Figure 12 shows the relationship between the cost and sustainability indices of water and energy (SIwater and SIenergy) for the optimal FEW system. In both climates, energy component makes up a larger portion of the total cost of an optimal FEW system (86% in the humid climate and 73% in the arid climate). While the water component accounts for 14% of the total cost in the arid climate, the food component is the second most component in the humid climate (with 10% of the total cost).

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(a)

(b)

Figure 12: Cost of improvement for (a) SIwater and (b) SIenergy Table 6 compares the estimated cost of the baseline system consists of 17 m2 effective roof area, 7 modules of solar panels, 1 kWh storage capacity and no greywater recycling capability with the optimal system consists of 20.35 m2 effective roof area, 40 modules of solar panels, 41 kWh storage capacity and no greywater recycling capability in State College, PA and the optimal system with 17 m2 effective roof area, 45 modules of solar panels, 1 kWh storage capacity and a 32.2 L/d greywater recycling capability in Las Vegas, NV. Table 6: Comparison of the baseline and optimal greenhouse systems

Roof and wall structure Electrical & mechanical systems Greywater Solar system Energy usage SIfood SIwater SIenergy Total cost (10 yr)

Baseline System State College, PA Las Vegas, NV $3,226 $3,226 $1,242 $1,242 $0 $0 $5,847 $5,108 $831/yr $1,120/yr 100% 100% 88% 0% 22% 29% $18,626 $20,781

Optimal System State College, PA Las Vegas, NV $3,472 $3,226 $1,242 $1,242 $0 $4,349 $29,949 $22,475 $0 $0 100% 100% 100% 100% 100% 100% $34,664 $30,553

For the purpose of determining the effectiveness with which solar panel and water collection or recycling systems have been used to achieve a more sustainable greenhouse, a comparison is made between the expected outcomes, energy and water needs of the proposed systems and the hydroponic and conventional agricultural methods. Yields of lettuce per optimum greenhouse unit of 103 ± 15 kg/yr have water demand of around 415 L/yr and energy usage of around $8.3/yr. In comparison, conventional production yields 26 ± 1.4 kg/yr of produce, with water and energy demands of 6500 (±10%) L/yr and $0.22/yr, respectively (Barbosa et al., 2015). Higher energy demand is needed for consistent year-round food supply. Hydroponics offered 11 ± 1.7 times higher yields compared to conventionally produced lettuce and 2.8 times higher compared to the greenhouse food produced. In contrast, hydroponic agriculture methods require 2.2 times more energy compared to the optimum sustainable FEW system. 7. Discussion The FEW nexus approach provides more flexibility to cope with complex challenges like natural resource depletion and climate change. While nexus is being investigated theoretically, there is much less emerging to implement it in a way to optimize the three critical needs in a coherent or balanced manner. In addition, implementing the nexus approach in a large-scale, system-wide manner may be challenging because we have a limited knowledge of how food, energy and water systems function and interact. One of the potential solutions to tackle this problem is designing a sustainable system that has the ability to meet its food, energy, and water consumption needs without using external resources. Since dollars are the only measure common to food, energy, and water components, the changes in the sustainability are formulated in terms of dollars. The results obtained from this study can guide future decision making across the FEW nexus. One of the Page 20 of 25

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major challenges impeding nexus analysis is the lack of micro-level data. The present study adopted a bottom-up approach for data acquisition to explore the flow of resources in a sustainable FEW system. This helps decision and policy making for transition to more sustainable FEW systems by identifying relevant resource saving opportunities. Also, analyzing the impact of each decision variable and driving factor on the system’s outcome provides useful information for the policy makers about the functional dynamics of FEW systems. Policy makers usually ignore the interdependencies among FEW systems for potential FEW solutions (e.g., abundant energy for sustainable water strategies), but with the results of the study, they will be better able to circumvent such fragmented governances. While it is not even possible (or economically feasible) to be self-sufficient FEW system even for a largescale system, designing a small-scale FEW using mathematical models demonstrate how to reduce the dependencies on these resources or how to improve the productivity (e.g. food yield) and thus increase resilience. Next, the system can be expanded to a larger scale and integrated with one or more systems to compensate its weakness (e.g. importing energy from a country with oversupply energy). The calculations of the study are performed for a sustainable FEW system that can consistently yield food for a family of four (two adults and two children). The food, energy, and water consumption patterns at the household level increase the degree to which our results would generalize to FEW systems with different scales. As defined in this study, the integrated FEW system is comprised of three main components; food, energy and water and each component consists of different sub-components (e.g. fruit, vegetable or grain for the food component). By including all sub-components within a large-scale system (e.g. industrial or thermoelectric power for the water component), the results of the study can be applied and expanded to FEW systems as large as a city or a country. Another improvement could be to add ecosystem cost and full cost recovery of water and then consider social, economic and environmental impacts on the FEW system performance.

8. Conclusions five decision variables and their characteristics have been identified for designing and prototyping smallscale sustainable FEW systems: size of the FEW system, size of the rainwater harvesting system, water recycling capacity, natural sunlight for optimal operation of the FEW system, and solar system characteristics. Next, the influence of each decision variable along with other driving factors (e.g. weather conditions) on FEW systems operation was explored and quantified by designing a sustainable FEW system in two different climate scenarios; a cloudy and humid scenario and sunny and arid scenario. In order to determine the influence of each component (i.e. food, water, or energy) on the system’s output, first we had to design the FEW system and then optimize the design to achieve the minimum cost of a sustainable system. Thus, a small-scale FEW system is designed in this study to satisfy the needs of a household of four people for two different climates and the estimated the cost of each system. In both climates, energy component makes up a larger portion of the total cost of an optimal FEW system (86% in the humid climate and 73% in the arid climate). Because the arid climate was capable of providing a great amount of solar power and ultimately more energy for a given number of solar panels, a sustainable FEW system is less expensive in this area than the humid climate. After the energy component, the water component was the second most expensive part of the sustainable FEW system in the arid climate (with 14% of the total cost), however, the water component accounts for only 4% of the total cost in the humid climate. This shows that future discoveries should focus on energy production technologies to improve the Page 21 of 25

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sustainability of FEW systems at a reasonable cost. Regulated prices, which are set by governments, or providing subsidies or tax incentives by government agencies can stimulate private investment in renewable energy technologies. Note that this conclusion depends on the scale and assumptions used in the present model and although it may also hold for other FEW systems, but further business models would be needed to address system stress and ensure sustainability. The greenhouse system is designed to support decision makers in their search for practical sustainability that provide various tradeoffs among three interconnected components. Although the problems and data may appear to be quite different with respect to scale of FEW systems, but the influence of driving factors (e.g. what to plant, size of solar system, decisions regarding water treatment method) on the sustainability of the FEW system can be measured and compared by the cost of achieving sustainability across the FEW system. This approach is used in the present study for a micro-scale system and determined the relative contribution of each resource to the sustainability of the FEW system. By generating and evaluating optimal trade-offs between the contributions among the nexus, this approach has the potential to be scaled up for FEW systems at macro levels. A within system approach is proposed in this paper to strengthen the weakest link and optimize the FEW system such as characteristics of solar system for energy generation, water collection and recycling system, and supply- and demand-side of light source for plants. Another possibility is a between system approach, in which a system is integrated with one or more systems to compensate its weakness (e.g. importing energy from a country with oversupply energy). The integrated systems (or network of systems) would minimize or eliminate periods of resource shortage. 9. Notations The following symbols are used in this paper:  Acell is the surface area of the solar panels  AL = artificial lighting  Cbattery = solar system storage capacity  DL = hourly direct irradiance  DLi = daily direct sunlight irradiance  DLImin = minimum daily light integral  Dwater = water demand  Ecell is the solar cell efficiency  Erate = electricity rate  ERS = effective roof surface  Fwater(x) = cumulative probability of precipitation  G is the irradiance of input light  GS = greenhouse space  hAL = hour of necessary artificial lighting for growth and development  HL = heat loss  HLconduction = transfer of heat through the structure  HLconvection = transfer of heat as a result of movement of the masses of air  HGlighting = total heat emitted by artificial lighting  HGsolar = total heat gained by solar radiation  Hwall = height of wall Page 22 of 25

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             

HWP = height to width proportion Nsolar = number of solar panels PSolar = electricity generated by solar system RI = required irradiance (W/m2/d),. RW = recycled greywater SI = sustainability Index SLr = sunlight irradiance passing through the roof SLw = sunlight irradiance passing through walls SoCi = solar battery's state of charge Swater= water supply TkP is the temperature coefficient of solar panel TA = transparent area of the roof Wlight = watts output of the artificial light Wm2 = watts per square meter of greenhouse lighting

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Emmerson, C., 2011. Global Risks: An initiative of the Risk Response Network, 6th ed. World Economic Forum, p. 56. EPA, 1999. Wastewater Technology Fact Sheet: Intermittent Sand Filters, September 1999 ed. Office of Water, United States Environmental Protection Agency, p. 7. FAO, 2015. Climate Change and Food Systems, in: Elbehri, A. (Ed.). Food and Agriculture Organization, p. 336. Fryer, J., 2012. The Complete Guide to Water Storage: How to Use Gray Water and Rainwater Systems, Rain Barrels, Tanks, and Other Water Storage Techniques for Household and Emergency Use. Atlantic Publishing Company. Gerbens-Leenes, W., Hoekstra, A.Y., van der Meer, T.H., 2009. The water footprint of bioenergy. Proceedings of the National Academy of Sciences 106, 10219-10223. Hellegers, P., Zilberman, D., Steduto, P., McCornick, P., 2008. Interactions between water, energy, food and environment: evolving perspectives and policy issues. Water Policy 10, 1-10. Jefferson, B., Laine, A., Parsons, S., Stephenson, T., Judd, S., 2000. Technologies for domestic wastewater recycling. Urban water 1, 285-292. Karabulut, A.A., Crenna, E., Sala, S., Udias, A., 2017. A proposal for integration of the ecosystem-waterfood-land-energy (EWFLE) nexus concept into life cycle assessment: A synthesis matrix system for food security. Journal of Cleaner Production. Karagiannis, I.C., Soldatos, P.G., 2008. Water desalination cost literature: review and assessment. Desalination 223, 448-456. Karan, E., Asadi, S., & Ntaimo, L. 2016. A stochastic optimization approach to reduce greenhouse gas emissions from buildings and transportation. Energy, 106, 367-377. Kennedy, G., Ballard, T., Dop, M.C., 2011. Guidelines for measuring household and individual dietary diversity. Food and Agriculture Organization (FAO) of the United Nations. Kılkış, Ş., Kılkış, B., 2017. Integrated circular economy and education model to address aspects of an energy-water-food nexus in a dairy facility and local contexts. Journal of Cleaner Production. Kim, H., Sudduth, K., Hummel, J.W., Drummond, S., 2013. Validation testing of a soil macronutrient sensing system. Transactions of the ASABE 56, 23-31. Longo, S., d’Antoni, B.M., Bongards, M., Chaparro, A., Cronrath, A., Fatone, F., Lema, J.M., MauricioIglesias, M., Soares, A., Hospido, A., 2016. Monitoring and diagnosis of energy consumption in wastewater treatment plants. A state of the art and proposals for improvement. Applied Energy 179, 1251-1268. Loy, S., Tahtouh, J., Munster, C., Wagner, K., Fares, A., Ale, S., Vierling, R., Jaber, F., Jantrania, A., 2017. State of the Art of Water for Food Within the Nexus Framework. Current Sustainable/Renewable Energy Reports, 1-7.

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