16. The ALFAM2 Model

16.1. General Description

The ALFAM2 model was first described by Hafner et al. (2019), and an updated version with a new parameter set was presented by Hafner et al. (2025). Miterra adopts the 2025 version of the ALFAM2 model.

Model structure

Figure 16.1: Schematic diagram of the ALFAM2 model showing flow directions and associated primary parameters that determine the flow dynamics. (Reproduced from Hafner et al., 2025)

The flow dynamics in the ALFAM2 model are determined by six primary parameters:

Parameter	Description
	Partition fraction of applied TAN to fast pool. The rest (1 – f₀) goes to the slow pool.
	First-order rate constant for NH₃-N emissions from the fast pool.
	First-order rate constant for transfer from the fast pool to the slow pool.
	First-order rate constant for NH₃-N emissions from the slow pool.
	Fraction of the fast pool that remains following slurry incorporation, while 1 – f₄ is transferred to the slow pool.
	First-order rate constant for loss from the slow pool to a sink that no longer makes any contribution to emission.

Parameter

Description

Partition fraction of applied TAN to fast pool. The rest (1 – f₀) goes to the slow pool.

First-order rate constant for NH₃-N emissions from the fast pool.

First-order rate constant for transfer from the fast pool to the slow pool.

First-order rate constant for NH₃-N emissions from the slow pool.

Fraction of the fast pool that remains following slurry incorporation, while 1 – f₄ is transferred to the slow pool.

First-order rate constant for loss from the slow pool to a sink that no longer makes any contribution to emission.

Basic input data requirement

Climate data
- Hourly precipitation (mm h^–1).
- Hourly air temperature (°C).
- Hourly wind speed at 2 m from surface (m s^–1).
Management data
- Slurry application method: broadcast, trailing shoe/hose, open slot injection, or closed slot injection.
- Slurry incorporation method: no incorporation, shallow incorporation, or deep incorporation.
- Time of slurry incorporation after application (h).
- Slurry type: whether the slurry is a pig slurry or not.

16.2. Algorithms

Time points

A simulation by ALFAM2 should include at least 2 time points: the time when slurry is applied to the soil (t_app), and the time when the cumulative emissions are counted (t_end, end of simulation).

If the slurry is incorporated into soil, a third point t_inc at the time of incorporation should be added (t_app < t_inc < t_end).

If the dynamics of NH₃ emissions is of interest, any number of additional time points may be added between t_app and t_end to estimate the instantaneous NH₃ emissions at particular time points after slurry application.

Determination of primary parameters

The value of each primary parameter (p) is determined by a set of predictor variables and associated secondary parameters, and transformed with a logistic (for f parameters) or antilog function (for r parameters):

Equation 16.1

where:

is a standard value of 1 h^–1 for all r parameters or 1 (dimensionless) for all f parameters, which is included for unit consistency.

is a transformation function for the specific primary parameter.

is the secondary parameter corresponding to χ_i.

is the i-th predictor variable associated with the primary parameter.

The values of all numeric predictor variables are first transformed by centering (subtracting the center means from their original values). The center means are given below:

Predictor Variable	Center Mean
Slurry dry matter (%)	6.0
Slurry pH	7.5
Air temperature (°C)	13.0

Rainfall rate (mm h^–1) ^[1]	0

[1] The center mean of rainfall rate is not specifically given in the original ALFAM2 paper. Examination of the model source code indicates that its value is implicitly assumed to be 0.

The table below lists all available predictor variables and associated secondary parameters for each primary parameter:

A predictor should be removed from the list if there is no data available for it. For example, if slurry pH is unknown, then it should not be included in the equation to determine the values of primary parameters r₁ and r₃.

Primary Parameter

Predictor Variable (χ)

Predictor
Data Type

Secondary
Parameter (β)

Intercept

Constant

0.453

Open slot injection

Binary

-2.897

Closed slot injection

Binary

-7.096

Pig slurry

Binary

-0.952

Slurry dry matter (%)

Numeric

0.500

Intercept

Constant

-1.451

Broadcast application

Binary

0.737

Trailing shoe/hose application

Binary

-0.074

Slurry dry matter (%)

Numeric

-0.033

Slurry pH

Numeric

0.421

Air temperature (°C)

Numeric

0.033

Numeric

0.461

Intercept

Constant

-1.170

Rainfall rate (mm h^–1)

Numeric

0.602

Intercept

Constant

-2.688

Closed slot injection

Binary

-0.384

Deep incorporation

Binary

-5.351

Slurry pH

Numeric

0.118

Shallow incorporation

Binary

-1.418

Deep incorporation

Binary

-2.950

Intercept

Constant

-1.80

Rainfall rate (mm h^–1)

Numeric

0.484

Important note on the f₄ parameter
The f₄ parameter is only relevant when incorporation takes place. The value of f₄ is determined for each time point in the simulation. The value is set to 1 when there is no incorporation, or before incorporation takes place. At the time of and after incorporation, the value of f₄ is calculated according to Equation 16.1.

Dynamics of the system

At the beginning of the simulation, applied slurry TAN is partitioned into a fast-emitting pool (F) and a slow-emitting pool (S).

Equation 16.2

For any given time interval Δt, let subscript t₀ denotes the start point of the interval, subscript t denotes the end point of the interval, and subscript t–1 denotes the end point of the previous time interval. Then, the initial sizes of the F and S pools at the beginning of the interval are determined as follows:

Equation 16.3

The sizes of the F and S pools at the end of interval Δt are:

Equation 16.4

where:

As a safety check, ϑ should not exceed 1E200.

The NH₃ emissions from the F and S pools during interval Δt are:

Equation 16.5

Cumulative emission from both pools by the end of the interval may be calculated as:

Equation 16.6

16.3. Integration with Miterra

In Miterra, ALFAM2 is used to estimate NH₃ emissions from two sources: field application of liquid slurry, and deposition of liquid slurry (urine) during grazing.

Input data from Miterra

For field application of liquid slurry, the slurry TAN content is calculated by Equation 4.10. All slurries are assumed to be applied in April.
For liquid slurry deposition during grazing, the TAN content is calculated by Equation 4.1. It is assumed that the total TAN is spread over the grazing months evenly. The grazing months are months with an average temperature over 10°C.

Monthly total precipitation is converted to hourly precipitation by dividing [30 (days) × 24 (hours) × rainfall intensity].

Rainfall intensity refers to the time fraction of a day when rainfall takes place (e.g., if in a day it rains for 1 hour, the rainfall intensity is 1/24). Ammonia volatilization is sensitive to rainfall. Evenly distributing monthly rainfall to hours may underestimate hourly rainfall during the simulation period, as rainfall is likely to occur as showers concentrated in several hours. Miterra currently uses a default value of 0.5, which is purely arbitrary.

Monthly average temperature is used as hourly temperature.

Wind speed at 10 m from surface is converted to wind speed at 2 m using the following equation:

Equation 16.7

where:

	is the wind speed measured at 10 m from surface (m s^–1); and
	is a surface roughness parameter, which equals 1/10 of the crop height when crop height is available; otherwise, it is set to 0.01 (m).

Physics of the Environment and Climate, Guyot, 1998, p106.

Application methods

Miterra uses “Utilised agricultural area fertilised by manure application technique, farm type and NUTS 2 region” from Eurostat to derive the area fractions of each manure application method. Eurostat application techniques are mapped to application methods defined in ALFAM2. Eurostat data indicated whether incorporation takes place, but did not specify incorporation method (harrowing, ploughing, etc.), which is required by ALFAM2. Therefore, any application technique followed by incorporation is further broken down to shallow and deep incorporation as specified in ALFAM2. Incorporation time is assumed to be 4 hours after application, except for technique “manure broadcast incorporation after 4 hours”, where incorporation time is assumed to be 24 hours after application. Slurry injection is considered as a form of immediate slurry incorporation.

Table 16.1: Mapping of Eurostat application techniques to ALFAM2 application and incorporation methods.
Eurostat Application Technique	ALFAM2 Application Method	ALFAM2 Incorporation Method	Incorporation Time
Manure broadcast, no incorporation	Broadcast	No incorporation	/
Manure broadcast, incorporation within 4 hours	Broadcast	Shallow incorporation	4 hours
Manure broadcast, incorporation within 4 hours	Broadcast	Deep incorporation	4 hours
Manure broadcast, incorporation after 4 hours	Broadcast	Shallow incorporation	24 hours
Manure broadcast, incorporation after 4 hours	Broadcast	Deep incorporation	24 hours
Manure band spread, trailing hose incorporation	Trailing hose	Shallow incorporation	4 hours
Manure band spread, trailing hose incorporation	Trailing hose	Deep incorporation	4 hours
Manure band spread, trailing shoe incorporation	Trailing shoe	Shallow incorporation	4 hours
Manure band spread, trailing shoe incorporation	Trailing shoe	Deep incorporation	4 hours
Manure injection, shallow/open slit	Open slot injection	Shallow incorporation	0 hour (immediately)
Manure injection, deep/closed slit	Closed slot injection	Deep incorporation	0 hour (immediately)

Additionally, the following assumptions are made:

For grassland and perennial crops, slurry is not incorporated, as incorporation techniques would destroy these crops.
For winter wheat/barley, slurry is not incorporated, as slurry is assumed to be applied in the spring, and incorporation techniques would destroy winter crops.
For application methods that are artificially broken down to shallow and deep incorporation, it is assumed that shallow incorporation accounts for 90% of the area, and deep incorporation 10%. This is a rough estimation based on the fraction of occurrences of each incorporation method in the ALFAM2 database (due to missing data, area-weighted estimation was not possible).