7. Fertilization

This section describes an approach to apply local derogation and distribute N fertilisers to various crops within a country. This distribution is mostly relevant to Miterra-Europe, as information on application rates to different crops is often lacking. For Miterra-Farm, fertiliser application rate to each crop should be provided as an input. However, if such data is not available, the method below may also be used.

Distribution of grazing excretions

Animal excretions during grazing are distributed to permanent grasslands, temporary grasslands and rough grazings (natural grasslands). It is assumed that all permanent grasslands are used for grazing, half of the temporal grasslands are used for grazing (because they are often used for mowing/silage), and the grazing intensity on natural grasslands is 50% lower than on permanent grasslands (equivalent to half of the natural grasslands are grazed). The deposition rate of grazing excretion (kg N ha^–1) is therefore calculated as follows:

Equation 7.1

where:

	represents permanent, temporary, and natural grasslands, respectively.
	is the total N in solid and liquid excretions during grazing in the region (kg N).
	is the area of respective grassland type (ha).

Distribution of animal manure

Animal manure is distributed based on both manure type and crop type, following the approach described by Gerard et al. (2009).

Manure Type	Crop Type	Distribution
Cattle, sheep & goat manure	Fodder crops Grasslands, fodder maize, other fodder crops	Each type of manure is evenly distributed to all fodder crops.
Pig manure	Fodder crops Same as above	25–75% of total manure N remaining after storage, distributed to all fodder crops in equal amount per hectare. 75% for Belgium and the Netherlands; 50% for Germany, Denmark, Spain, France, Italy, Ireland, Poland, Portugal, and UK; 25% for the other EU member states.
Group I crop Potato, sugar beet, other root crops, vegetables, barley, rape, soft wheat	Receives the remaining 75–25% of manure N; distributed as follows: Let to be the total area of non-fodder crop group I to III. The base application rate for all 3 groups are calculated: Application rate for Group II crops . Application rate for Group III crops . All remaining pig manure N goes to Group I crops, distributed in equal amount per hectare:
Group II crop Durum wheat, rye, oat, grain maize, rice, other cereals, sunflower
Group III crop Fruits, citrus, olives, oil crops, grapes, other crops
Poultry manure	Non-fodder crops Group I-III crops above	Distributed among all non-fodder crops in equal amount per hectare.

Manure Type

Crop Type

Distribution

Cattle, sheep & goat manure

Fodder crops
Grasslands, fodder maize, other fodder crops

Each type of manure is evenly distributed to all fodder crops.

Pig manure

Fodder crops
Same as above

25–75% of total manure N remaining after storage, distributed to all fodder crops in equal amount per hectare.

75% for Belgium and the Netherlands;
50% for Germany, Denmark, Spain, France, Italy, Ireland, Poland, Portugal, and UK;
25% for the other EU member states.

Group I crop
Potato, sugar beet, other root crops, vegetables, barley, rape, soft wheat

Receives the remaining 75–25% of manure N; distributed as follows:

Let to be the total area of non-fodder crop group I to III.
The base application rate for all 3 groups are calculated:
Application rate for Group II crops .
Application rate for Group III crops .
All remaining pig manure N goes to Group I crops, distributed in equal amount per hectare:

Group II crop
Durum wheat, rye, oat, grain maize, rice, other cereals, sunflower

Group III crop
Fruits, citrus, olives, oil crops, grapes, other crops

Poultry manure

Non-fodder crops
Group I-III crops above

Distributed among all non-fodder crops in equal amount per hectare.

Derogation & redistribution of manure N

EU Nitrates Derective sets a maximum rate of 170 kg N ha^–1 for manure application, unless local derogations apply. The manure N application rate must not exceed the maximum rate, and if it does, the extra manure may be reallocated to other crops in the region or country.

In the following equations in this section, the following indexes are used:

	denotes the NUTS region in a country;
	denotes the type of crop, e.g., wheat, maize, grassland, etc.; and
	denotes the type of manure, e.g., solid cattle manure, pig slurry, etc.

Step 1

The maximum manure N allowed (N_max), and the provisionally applied manure N (N_app) are calculated for each crop in each region of the country:

Equation 7.2

where:

	is the maximum manure N rate (kg N ha^–1) allowed for crop c in region r by EU Nitrates Directive or local derogation.
	is the N application rate (kg N ha^–1) of manure type m for crop c in region r, as estimated in Distribution of animal manure.
	is the area of crop c in region r (ha).

To disaggregate N_{app[r, c]} among each manure type later, λ_{[r, m]} is the ratio of N in manure type m to the total manure N applied in region r.

Equation 7.3

Step 2

The manure N surplus and gap is determined for each crop in each region:

Equation 7.4

If :

Else:

Step 3

The manure N surplus is calculated for the country:

Equation 7.5

Step 4

4.1: If N_{surplus, country} = 0: There is no surplus in the country (i.e., every crop in every rgion received no more manure N than what’s permitted by regulation). No derogation or redistribution is available in this case.

4.2: If N_{surplus, country} > 0: There is a surplus in the country, which may be redistributed to crops with a gap in the country. We consider 2 scenarios:

4.2.1: If N_{surplus, country} ≥ N_{gap, country}: There is enough surplus in the country to cover the gap in all regions of all crops.

Equation 7.6

4.2.2: If N_{surplus_country} < N_{gap_country}: There is a surplus in the country, but it is not sufficient to cover all the gaps. A proportion of the country surplus is redistributed, which is equal to the relative size of the regional deficit to the country deficit.

Equation 7.7

If :

Else:

Since N_{surplus, country} < N_{gap, country}, the right-hand side will never exceed N_max.

Step 5

Disaggregate N_{app[r, c]} among each manure type:

Equation 7.8

Manure export

The amount of manure N transported out of the country is calculated by comparing the total amount applied before and after derogtion/re-distribution. Any manure that is not field applied is assumed to be exported. No destination for manure export is assumed: manures are not tracked by the Miterra model once they are transported out of the country border.

Equation 7.9

where:

	is the total amount of manure N applied (kg N) for crop c in region r before derogation/re-distribution.
	is the total amount of manure N applied (kg N) for crop c in region r after derogation/re-distribution.

Crop available N

The plant available N (N_avail) is calculated from applied manure, grazing excretion, deposition and crop residues. This value is then be substracted from the crop N demand to give a more realistic mineral fertilizer application per crop.

The plant available N is calculated in two parts: N_{avail, mineral} for mineral N sources, and N_{avail, organic} for N mineralized from crop residues, and organic fractions of manure & grazing excretions. The total N_avail is the sum of the two parts.

Crop available N from mineral N sources

Equation 7.10

where:

is the total mineral N from applied manure (kg N ha^–1. See Distribution of animal manure). If mineral N fraction is unknown, the default value is assumed to be 0.75 for solid manure, and 0.4 for liquid slurry.

is the total mineral N from grazing excretions (kg N ha^–1. See Distribution of grazing excretions). If mineral N fraction is unknown, the default value is assumed to be 0.5.

is the total N from compost (kg N ha^–1. See Nutrient content in compost).

is the total N from sludge (kg N ha^–1. See Nutrient content in sludge).

is the annual N input from atmospheric deposition (kg N ha^–1).

are coefficients for plant available N for the respective N source.

N Source

Remarks

Applied
manure

N_{emissions, manure/grazing} is the combined emissions of NH₃, N₂O & NO_x from manure application or grazing excretions ( 10. N Losses from Soil).

L_runoff is the surface runoff fraction ( Surface runoff).

N_{manure/grazing} is the total N of applied manure ( Distribution of animal manure) or grazing excretions ( Distribution of grazing excretions).

Grazing
excretion

Deposition

0.75

Compost

0.1

Sludge

0.5

Crop available N from organic N sources

Equation 7.11

where:

	is the amount of N in inccorporated crop residues (kg N^–1 ha, see Residue removal & incorporation).
	is the amount N uptake by cover crops following the main crop (kg N^–1 ha, see Cover crop C and N production).
	is the area fraction of cover crops following the main crop (see Equation 6.6).
	is the fraction of mineralized N that is available to crops, with a default value of 0.9 for grasslands, and 0.7 for other crops.

Finally, the total plant available N is determined by combining the two parts above:

Equation 7.12

Distribution of mineral N fertilisers

First, the requirement of mineral N fertilisers by each crop (N_req) is determined from crop N demand and N already available to the crop from other sources. To obtain a more equal fertiliser distribution among crops, we assume that at least 30% of the N demand will come from mineral fertiliser.

Equation 7.13

where:

	is the N demand by the crop (kg N^–1 ha. See Equation 6.24).
	is the soil available N to the crop (kg N^–1 ha).

The mineral N fertilizers are distributed over crops using weighing factors, so that crop with highest N demand receives the highest amount of N fertilizers. The weighing factors are calculated from the crop N uptake and the total area of the crop.

Equation 7.14

For crop i in the region:

where:

	is the weighing factor for the crop.
	is the total area of the crop in the region (ha).
	is the collection of all crops grown in that region, i ∈ n.
	is the application rate of mineral N fertilisers for the crop (kg N ha^–1).
	is the sum of the amount of all types of mineral N fertiliser applied in the region (kg N).