Overview

Much of the dynamics Fields of Fuel are reliant on the underlying nitrogen cycle model that occurs on each of the individual fields in the game. The availability and cycling of various forms of nitrogen determine the fertility of each field, which directly influences the yield of different crops, the impact to water quality, and the amount of CO₂ gases emitted. These impacts then have carry-on effect to all three of the subscores used to evaluate success in the game (economic, energy, and environmental).

The model works on the (simplified) premise that crop growth is almost entirely limited by the availability of nitrogen. Crop yields are also influenced by tillage and pests, but those impacts are relatively small and are covered elsewhere. Nitrogen in this system is represented in two main forms: organic nitrogen and inorganic nitrogen. These two forms are represented in the blue boxes of the nitrogen cycle diagram shown below (Figure 1).

In the game, each field begins with a certain amount of organic nitrogen present on each of the fields. Most nitrogen found in soil is of this form, as it is more stable and resistant to being washed away. However, this nitrogen has been assimilated into some sort of organic material (such as plants or animals) and is locked away in a chemical structure which is not directly accessible to the growing crops. Before the plants can access this Nitrogen, it must go through a process called mineralization, during which microbes in the soil decompose the material, releasing the nitrogen from the organic structure into an 'mineralized' form that the plants can utilize, which we refer to as inorganic nitrogen.

The process of mineralization occurs at a set rate; that is, a set proportion of the existing organic nitrogen is converted into inorganic nitrogen each year. In the game, the base mineralization rate is 1%; this can be increased to 3% through tillage, which increases the microbial activity in the soil.

 

 

Detailed Models

Initialization

Nitrogen modeling occurs at the level of the individual field. At the onset of the game, each field is assigned a base amount of organic nitrogen. By default, fields start with 1400 kg/ac, but this value can be adjusted by enabling the variable initial soil health option at the beginning of the game creation. Enabling this feature forces the initial organic nitrogen content of each field to be assigned as a fraction of 2200 kg/ac, with the fraction being a sequentially increasing function of the number of fields present on each farm. As an example, a farm with four fields would calculate the initial organic nitrogen values as:


nFields = 4
for i in (1:nFields){
field(i) = 2200 * (i/nFields)
}


This method ensures that the base starting condition for each field on a farm is evenly distributed between 0 and 2200 as a function of the number of fields, and is flexible to accommodate any number of fields on each farm that is set by the moderator.

 

Inorganic Nitrogen

Crop yield is in most cases a function of the amount of inorganic nitrogen present (alfalfa, a legume that can extract nitrogen from the air, is slightly different; see the energy model section for a detailed description of the yield models). The quantity of inorganic nitrogen (N_i) available to the crops come from two sources; nitrogen applied as fertilizer (N_fert), and a fraction of the organic nitrogen (N_org) that is mineralized and transformed to a plant-accessible through microbial decomposition (N_mineralized). The mineralization of organic nitrogen to inorganic nitrogen happens a at rate (λ_min) Microbial activity is often increased by tillage; as such, the mineralization rate is dependent on whether the field is tilled or not (tilling results in a value of λ_min = 0.03, where no-till practices result in λ_min = 0.01). The amount of mineralized nitrogen can be calculated as:

N_mineralized = N_i * λ_min

N_fert is a function of what the player decides to plant, and whether they implement a high or low fertilizer regime:

Applied fertilizer is also subject to volatilization after it is applied, which is assumed to occur at a rate of 3% (λ_{volatilization}). The total amount of inorganic nitrogen available in the soil is then just the sum of the mineralized nitrogen and the portion of nitrogen from fertilizer that is not volatilized:

N_i = N_fert * (1 - λ_{volatilization}) + N_mineralized

This remaining quantity of inorganic nitrogen in the soil (N_i) either ends up being leached into the groundwater (N_leached) or assimilated into the plant (N_absorbed). The proportion of nitrogen that ends up in either place is determined by the nitrogen use efficiency (NUE):

N_leached = N_i * (1 - NUE)

N_absorbed = N_i * NUE

The nitrogen use efficiency (NUE) is calculated as a negative exponential function in which the use efficiency decreases with increasing availability of inorganic nitrogen in the soil. This implementation means that at some point the plants become saturated and reach the limit of how much nitrogen they are able to take up. These functions are implemented by specifying an initial use efficiency (NUE_init) that specifies the y-intercept, and a decay point (NUE_decay) that describes... , and rate parameter (NUE_rate) that describes...

NUE_modifier = 1 / (1 + ((1/NUE_init)-1)*Math.exp(NUE_rate * (available_N - NUE_decay)))

NUE = NUE_init * NUE_modifier

Once the amount of nitrogen taken up by the plant is calculated, the next step is to determine what proportion of the nitrogen in the plant tissues is removed from the system during harvest (N_removed), and what proportion remains in the field as either living (N_{organic,living}) or dead (N_organic,dead) plant material.

Any dead plant (N_organic,dead) material is immediately returned to the organic nitrogen pool and is available for mineralization the following year. Perennial plants (such as alfalfa and switchgrass), however, retain a portion of their root biomass from year to year, which keeps some of the nitrogen locked up in a living structure (N_organic,live).

where does the inorganic nitrogen go??? (NUE, leaching, crop removal)

Organic Nitrogen

Organic nitrogen in the soil is assumed to be permanently stable until mineralized, and is only replaced by residual biomass from the crop in the form of either roots or any aboveground biomass which is left on the field (corn stover).

 

Nitrogen Leaching