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.

In this chapter, the terms of both N application rate (kg N ha–1) and the amount of N (kg N) are used. To avoid confusion, and for consistency, N amounts are represented with a tilde (~) over the letter N (Ñ).

Note that this convention applies to only this chapter.

7.1. Distribution of grazing excretions

Animal excretions during grazing are distributed to permanent grasslands, temporary grasslands and rough grazing (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:

is the total N (from both solid and liquid manure) deposited from excretions during the grazing period for each grassland type (kg N ha–1). The subscripts perm, temp, and nat represent permanent, temporary, and natural grasslands, respectively.

is the total N in solid or liquid excretions during the grazing period (kg N). See 3.3. N content in livestock excretion and Equation 3.1.

is the area of respective grassland type (ha).

7.2. Distribution of animal manure

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

The total amount of manure N available for distribution after the storage period is described in 4. N Emissions from Manure Management, as Nex_storage in Equation 4.11.

Table 7.1: Distribution of animal manure to crops.
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 pig manure N (Ñpig_manure, kg N); distributed as follows:

  1. Let to be the total area (ha) of non-fodder crop group I to III.

  2. The base application rate (kg N ha–1) for all 3 groups is calculated as:

  3. Application rate for Group II crops .

  4. Application rate for Group III crops .

  5. 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 derogation 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.

These indices are used consistently in the following equations of this section:

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, and the provisionally applied manure N are calculated for each crop in each region of the country:

Equation 7.2

where:

is the maximum amount of manure N (kg N) allowed for crop c in region r.

is the amount of manure N (kg N) provisionally applied for crop c in region r, disregarding EU and local regulations. The prime symbol ( ) is used to indicate that this amount is subject to adjustement by EU regulations or local derogations.

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 Table 7.1.

is the area of crop c in region r (ha).

To disaggregate Ñ'app[r, c] among each manure type later, the fraction of N in each manure type over the total manure N applied in the region is calculated.

Equation 7.3

where:

is the ratio of N in manure type m relative to the total manure N applied in region r (unitless).

is the N application rate (kg N ha–1) of manure type m for crop c in region r, as estimated in Table 7.1.

is the area of crop c in region r (ha).

is the amount of manure N (kg N) provisionally applied for crop c in region r. See Equation 7.2.

Step 2

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

Equation 7.4

where:

is the amount of manure N (kg N) that exceeds the maximum manure N allowed for crop c in region r.

is the amount of manure N (kg N) that is below the maximum manure N allowed for crop c in region r.

is the maximum amount of manure N (kg N) allowed for crop c in region r. See Equation 7.2.

is the amount of manure N (kg N) provisionally applied for crop c in region r. See Equation 7.2.

Step 3

The manure N surplus is calculated for the country:

Equation 7.5

where:

is the amount of manure N surplus (kg N) in the country by summing up the surplus for each crop and each region.

is the amount of manure N gap (kg N) in the country by summing up the gap for each crop and each region.

is the amount of manure N (kg N) that exceeds the maximum manure N allowed for crop c in region r. See Equation 7.4.

is the amount of manure N (kg N) that is below the maximum manure N allowed for crop c in region r. See Equation 7.4.

Step 4

Derogation or redistribution takes place depending on whether there is surplus or gap in the country.

Scenario 1

Ñsurplus, country = 0
There is no surplus in the country (i.e., every crop in every region received no more manure N than what’s permitted by regulation). No derogation or redistribution is available. In this case, the final amount of manure N applied for each crop in each region is the same as the provisionally applied manure N.

Equation 7.6

where:

is the final amount of manure N (kg N) applied for crop c in region r.

is the amount of manure N (kg N) provisionally applied for crop c in region r. See Equation 7.2.
Scenario 2

Ñsurplus, country > 0
There is a surplus in the country, which may be redistributed to crops with a gap in the country. We consider 2 sub-scenarios:

Scenario 2.1

Ñsurplus, country ≥ Ñgap, country
There is enough surplus in the country to cover the gap in all regions of all crops.

Equation 7.7

where:

is the final amount of manure N (kg N) applied for crop c in region r.

is the maximum amount of manure N (kg N) allowed for crop c in region r. See Equation 7.2.
Scenario 2.2

Ñsurplus_country < Ñgap_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 7.8

If :

Else:

where:

is the final amount of manure N (kg N) applied for crop c in region r.

is the amount of manure N (kg N) provisionally applied for crop c in region r. See Equation 7.2.

is the maximum amount of manure N (kg N) allowed for crop c in region r. See Equation 7.2.

is the amount of manure N (kg N) that is below the maximum manure N allowed for crop c in region r. See Equation 7.4.

is the amount of manure N surplus (kg N) in the country. See Equation 7.5.

is the amount of manure N gap (kg N) in the country. See Equation 7.5.
Since Ñsurplus, country < Ñgap, country, the right-hand side will never exceed Ñmax.

Step 5

Disaggregate Ñapp[r, c] among each manure type and distribute over each crop:

Equation 7.9

where:

is the final application rate of manure N (kg N ha–1) in manure type m applied for crop c in region r.

is the final amount of manure N (kg N) applied for crop c in region r.

is the ratio of N in manure type m relative to the total manure N applied in region r (unitless). See Equation 7.3.

is the area of crop c in region r (ha).

Manure export

The amount of manure N transported out of the country is calculated by comparing the total amount applied before and after derogation/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 7.10

where:

is the amount of manure N (kg N) exported out of the country.

is the amount of manure N (kg N) provisionally applied for crop c in region r before derogation/re-distribution. See Equation 7.2.

is the final amount of manure N (kg N) applied for crop c in region r after derogation/re-distribution. See Step 4 above.

7.3. Crop available N

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

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

Crop available N from mineral N

Equation 7.11

where:

is the crop available N from all mineral sources (kg N ha–1).

is the total mineral N from applied manure (kg N ha–1) for each crop in each region.

where:

is the final amount of manure N (kg N) in manure type m applied for crop c in region r. See Equation 7.9 and 7.2. Distribution of animal manure.

is the fraction of mineral N in total manure N (unitless) for manure type m. 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 area of crop c in region r (ha).

is the total mineral N from grazing excretions (kg N ha–1) for each grassland type in each region. See 7.1. 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 application (kg N ha–1). See 8.2. Nutrient content in compost. It is assumed that 51% of the compost is applied in agriculture, distributed to all crops in equal amount per hectare.

is the total N from sludge application (kg N ha–1). See 8.3. Nutrient content in sludge. The total amount of sludge used in agriculture is provided as an input in Miterra, distributed to all crops in equal amount per hectare.

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

is the coefficient for plant available N for the respective N source (unitless).

N Source ρ Remarks

Applied
manure

Nemissions, manure/grazing is the combined emissions of NH3, N2O & NOx from manure application or grazing excretions ( 10. N Losses from Soil).

Lrunoff is the surface runoff fraction ( 5.2. Surface runoff).

Nmanure/grazing is the total N of applied manure ( 7.2. Distribution of animal manure) or grazing excretions ( 7.1. Distribution of grazing excretions).

Grazing
excretion

Deposition

0.75

Compost

0.1

Sludge

0.5
For compost and sludge, the total N is used instaed of mineral N.

Crop available N from organic N mineralization

Equation 7.12

where:

is the crop available N from mineralization of organic N (kg N ha–1).

is the amount of N in crop residues incorporated into soil (kg N ha–1). See 6.4. Residue removal & incorporation.

is the amount N uptake by cover crops following the main crop (kg N ha–1). See Cover crop C and N production.

is the area fraction of cover crops following the main crop (unitless). See Equation 6.6.

is the total organic N from manure application or grazing excretions (kg N ha–1). See 7.1. Distribution of grazing excretions and 7.2. Distribution of animal manure. The organic part of manure and grazing excretions can be calculated by subtracting the mineral fractions ( Equation 7.11) from the total amount.

is the fraction of mineralized N that is available to crops (unitless), 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 7.13

where:

is the combined crop available N from manure application, grazing excretions, compost/sludge application, residue incorporation, and atmospheric depositions (kg N ha–1).

is the crop available N from all mineral sources (kg N ha–1). See Equation 7.11.

is the crop available N from mineralization of organic N (kg N ha–1). See Equation 7.12.

7.4. Distribution of mineral N fertilisers

First, the requirement of mineral N fertilisers by each crop (Nreq) 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 7.14

where:

is the requirement of mineral N fertilization by the crop (kg N ha–1).

is the N demand by the crop (kg N ha–1). See Equation 6.23.

is the soil available N to the crop (kg N ha–1). See Equation 7.13.

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 7.15

For each region, calculate:

where:

is the weighing factor for crop c (unitless).

is the requirement of mineral N fertilization by crop c (kg N ha–1).

is the total area of crop c in the region (ha).

is the application rate of mineral N fertilisers for crop c (kg N ha–1).

is the sum of the amount of all mineral N fertilisers applied in the region (kg N).