*2.1. IFEW System Model Interdependencies*

The IFEW system model has five distinct macro-level domains, namely, weather, water, agriculture, animal agriculture, and energy (Figure 1). The weather discipline provides environmental factors, such as vapor pressure, temperature, rainfall, and solar radiation. Rainfall and snowfall supply surface water and groundwater components for the water discipline. The amount of crop production in the agriculture discipline is strongly related to precipitation and temperature [11]. The water discipline supplies water for drinking and service usage for the animal agriculture discipline, and the production and ethanol and fertilizer for the energy system. Dry distillers' grain soluble (DDGS) that is produced during the ethanol production process and commercial fertilizers provide protein to animals and fertility to soil in the animal agriculture and agricultural domains, respectively. Demand for food protein by society is satisfied by the animal agriculture discipline. Corn yield in the agricultural discipline is used for ethanol production in the energy discipline and the satisfaction of socioeconomic demand. Other socioeconomic demands are satisfied by the corresponding domains except the weather discipline. The excess nitrogen from animal lands and crop fields is carried by water flow in the form of nitrates draining into the Mississippi River basin and further into the Gulf of Mexico.

**Figure 1.** A model of the interdependencies of the Iowa food-energy-water (IFEW) system. **Figure 1.** A model of the interdependencies of the Iowa food-energy-water (IFEW) system.

#### *2.2. IFEW Macro-Level Simulation Model 2.2. IFEW Macro-Level Simulation Model*

In this work, an extended simulation-based model of the IFEW system introduced in [10] is proposed to calculate the surplus nitrogen (*Ns*) considering only the weather, agriculture, and animal agriculture domains in Figure 1. Figure 2 shows the flow of components and the process of calculation via an extended design structure matrix (XDSM) diagram [14]. The input parameters are the weather model parameters (*w*1–5), May crop planting progress (*cw*1), rate of commercial nitrogen for corn (*x*3), rate of commercial nitrogen for soybean (*x*4), the total hog/pig population (*x*5), number of beef cows (*x*6), number of milk cows (*x*7), and number of other cattle (*x*8) including the population of steers, heifers, and slaughter cattle. Other intermediate response parameters are corn yield (*x*1), soybean yield (*x*2), the application of commercial nitrogen (*CN*), nitrogen generated from manure (*MN*), nitrogen fixed by soybean crop (*FN*), and the nitrogen present in harvested grain (*GN*). The model estimates the nitrogen surplus (*Ns*) based on output quantities yielded by each discipline. In this work, an extended simulation-based model of the IFEW system introduced in [10] is proposed to calculate the surplus nitrogen (*Ns*) considering only the weather, agriculture, and animal agriculture domains in Figure 1. Figure 2 shows the flow of components and the process of calculation via an extended design structure matrix (XDSM) diagram [14]. The input parameters are the weather model parameters (*w*1–5), May crop planting progress (*cw*1), rate of commercial nitrogen for corn (*x*3), rate of commercial nitrogen for soybean (*x*4), the total hog/pig population (*x*5), number of beef cows (*x*6), number of milk cows (*x*7), and number of other cattle (*x*8) including the population of steers, heifers, and slaughter cattle. Other intermediate response parameters are corn yield (*x*1), soybean yield (*x*2), the application of commercial nitrogen (*CN*), nitrogen generated from manure (*MN*), nitrogen fixed by soybean crop (*FN*), and the nitrogen present in harvested grain (*GN*). The model estimates the nitrogen surplus (*Ns*) based on output quantities yielded by each discipline.

This simulation model is an extension from the authors' previous work with the addition of the crop-weather model [10]. Westcott and Jewison [11] discovered that the amount of corn yield is linear to mid-May planting progress, July temperature, and June precipitation short fall, but is nonlinear to July precipitation. Meanwhile, the productivity of soybean is linear to the average value of July and August temperatures, and June precipitation short fall, but is nonlinear to the average value of July and August precipitations. The crop-weather model of the work is developed based on [11] given a set of temperature and precipitation data of certain months over a 10-year period (2009–2019) from [15]: July temperature (*w*1), July precipitation (*w*2), June precipitation (*w*3), July-August average temperature (*w*4), and July-August average precipitation (*w*5). The corn yield (*x*1) is estimated by a regression model with May planting progress (*cw*1), July temperature (*w*1), July precipitation (*w*2), and June precipitation (*w*3). Similar to the corn model, the model This simulation model is an extension from the authors' previous work with the addition of the crop-weather model [10]. Westcott and Jewison [11] discovered that the amount of corn yield is linear to mid-May planting progress, July temperature, and June precipitation short fall, but is nonlinear to July precipitation. Meanwhile, the productivity of soybean is linear to the average value of July and August temperatures, and June precipitation short fall, but is nonlinear to the average value of July and August precipitations. The crop-weather model of the work is developed based on [11] given a set of temperature and precipitation data of certain months over a 10-year period (2009–2019) from [15]: July temperature (*w*1), July precipitation (*w*2), June precipitation (*w*3), July-August average temperature (*w*4), and July-August average precipitation (*w*5). The corn yield (*x*1) is estimated by a regression model with May planting progress (*cw*1), July temperature (*w*1), July precipitation (*w*2), and June precipitation (*w*3). Similar to the corn model, the model for soybean yield (*x*2) is created using June precipitation (*w*3), July-August average temperature (*w*4),

and July-August average precipitation (*w*5). For simplicity, July and August average values are represented by July values in this work. perature (*w*4), and July-August average precipitation (*w*5). For simplicity, July and August average values are represented by July values in this work.

for soybean yield (*x*2) is created using June precipitation (*w*3), July-August average tem-

*Sustainability* **2022**, *14*, x FOR PEER REVIEW 4 of 11

**Figure 2.** An extended design structure matrix diagram of the proposed Iowa nitrogen export model.

**Figure 2.** An extended design structure matrix diagram of the proposed Iowa nitrogen export model. The nitrogen present in harvested grain (*GN*) is calculated using two input parameters, namely, the corn yield (*x*1) and soybean yield (*x*2) as

$$GN = \left(\mathbf{x}\_1 \left(\frac{1.18}{100}\right) A\_{corr} + \mathbf{x}\_2 \left(\frac{6.4}{100}\right) A\_{soy}\right) / A\_\prime \tag{1}$$

 = ቀଵ ቀ ଵቁ + ଶ <sup>ቀ</sup> .ସ ଵቁ ௦௬ቁ /, (1) where *Acorn* and *Asoy* represent the Iowa corn and the soybean acreage, whereas *A* represents the total area under corn and soybean crop. It is assumed that 6.4% and 1.18% of nitrogen are in the soybean seed and the corn seed while harvesting, respectively [16]. The where *Acorn* and *Asoy* represent the Iowa corn and the soybean acreage, whereas *A* represents the total area under corn and soybean crop. It is assumed that 6.4% and 1.18% of nitrogen are in the soybean seed and the corn seed while harvesting, respectively [16]. The biological nitrogen fixation from the soybean crop (*FN*) is estimated as [17].

$$FN = (81.1x\_2 - 98.5)A\_{sy} / A. \tag{2}$$

The commercial nitrogen (*CN*) is estimated using the rate of commercial nitrogen for corn (*x*3) and the rate of commercial nitrogen for soybean (*x*4) as The commercial nitrogen (*CN*) is estimated using the rate of commercial nitrogen for corn (*x*3) and the rate of commercial nitrogen for soybean (*x*4) as

$$\text{CN} = \left(\mathfrak{x}\_{\text{3}} A\_{\text{corr}} + \mathfrak{x}\_{\text{4}} A\_{\text{say}}\right) / A. \tag{3}$$

The values of the corn and soybean acreages are obtained from the USDA [18]. The annual manure nitrogen contribution of each animal type is estimated [19] The values of the corn and soybean acreages are obtained from the USDA [18]. The annual manure nitrogen contribution of each animal type is estimated [19]

$$\text{MN}\_{\text{axial}} = \text{P } \text{A}\_{\text{MN}} \text{ LF}\_{\text{\textdegree}} \tag{4}$$

where *P*, *AMN*, and *LF* are the livestock group population, nitrogen in animal manure, and life cycle of animal, respectively. *P* is substituted by the corresponding parameters with respect to different animal alternatives: the total hog/pig population (*x*5), number of beef cows (*x*6), number of milk cows (*x*7), and number of other cattle (*x*8). The total nitrogen generated from manure (*MN*) can be determined by the normalized sum of *MN* for each livestock group with total area *A* as where *P*, *AMN*, and *LF* are the livestock group population, nitrogen in animal manure, and life cycle of animal, respectively. *P* is substituted by the corresponding parameters with respect to different animal alternatives: the total hog/pig population (*x*5), number of beef cows (*x*6), number of milk cows (*x*7), and number of other cattle (*x*8). The total nitrogen generated from manure (*MN*) can be determined by the normalized sum of *MN* for each livestock group with total area *A* as

in (5). Lastly, the rough agronomic annual nitrogen budget of Iowa [16,20] provides the

$$\text{MN} = \left( \text{MN}\_{\text{Hog}/\text{pigs}} + \text{MN}\_{\text{Beff}-\text{cattle}} + \text{MN}\_{\text{Milk}-\text{cow}} + \text{MN}\_{\text{other}-\text{cattle}} \right) / A. \tag{5}$$

function calculated for the nitrogen surplus (*Ns*) given as

Table 1 gives the nitrogen content in manure and life cycle for livestock groups used in (5). Lastly, the rough agronomic annual nitrogen budget of Iowa [16,20] provides the function calculated for the nitrogen surplus (*Ns*) given as

$$N\_{\rm s} = \text{CN} + \text{MN} + \text{FN} - \text{GN}.\tag{6}$$

**Table 1.** Nitrogen content in manure and life cycle for livestock groups used in manure N calculation [19].

