=====Downscaling of Livestock numbers=====

Files: \\
  %curdir%/capdis/dislivestock.gms
  %datdir%/capdishsu/corine2018classes.gms
  %datdir%/capdishsu/s_fracGraz.gms
  %datdir%/capdishsu/p_fracGraz.csv
  %datdir%/capdishsu/p_grazsharesCorine.gms
  %datdir%/capdishsu/p_fsuCorineArea.gdx
  
A different approach is used for the distribution of FSS livestock numbers and for the distribution of CAPRI regional data. This is because livestock require some investment/infrastructure that is not easily given up. Also, if feed is more difficult to grow due to a dry or heat spell (e.g. as observed in 2018 in several countries), feed will be purchased from the market or animal numbers.
 
For livestock there will also apply the principle of the ‘Primacy of stability’ already described for the distribution of crop areas.

Animal types are distributed proportionally to their shares in different animal classes:
  * Grazing cattle
  * Grazing sheep and goats
  * Non-grazing ruminants (cattle, sheep and goats)
  * Non-grazing monogastric animals (pig and poultry)

====Distribution of FSS livestock numbers====

We use shares of grazing animals from the national submissions of greenhouse gas inventories to the UNFCCC. These shares are calculated from the quantity of manure N managed in various manure management systems, and the quantity of manure N deposited on ‘pasture, range and paddock’ (Table 3.B(b) of the UNFCCC-Common Reporting Format, CRF, tables).

The distribution of grazing livestock from the FSS grid cells to the FSU is done using areas of various Corine classes as a proxy. This is because grazing can occur also on non-grassland, such as on commune land (outside of the CAPRI UAAR) and mixed land cover classes (agro-forestry, non-agriculural land (shrubland, etc.). 

Based on expert information obtained from the EEA (Jan-Erik Petersen, personal communication), the sum of the following Corine class shares is calculated: 

  # Corine classes to be used to calculate grazing shares and areas 
  #
  # Source: EEA (Jan-Erik Petersen) in email from 19/07/2019. 
  # See kipinca-CLC classes + grazing_draft_+JRC questions_rev 23-07-19.docx
  # Animal types distinguished: DairyCattle, NonDairyCattle, SheepGoats
  parameter p_CorineShares(*, *, *) 'Shares of CLC area used to distribute grazing animals';
  table p_CorineShares
         DairyCattle  NonDairyCattle SheepGoats
  all.211           25             25          10
  all.223            0              0          25
  all.231          100            100         100
  all.242           25             25          25
  all.243           50             50          50
  all.244           50             50          50
  all.321          100            100         100
  all.322           25             25          50
  all.323           25             25          50
  all.324            0              0           0
  all.333           25             25          25
  all.411           50             50          50
  all.412            0              0          25
  all.421           50             50          50
  ;

For classes 322 ('Moors_and_heathland') and 324 ('Transitional_woodland-shrub') a differentiation by countries is done.

We assume that for grazing animals, the density of \(v_{lgr}\) [LU ha<sup>-1</sup>] is constant within each FSS-admin grid cell and the number of livestock depends on the relevant Corine area.

\begin{equation}
ν_{lgr,h}= N_{l,r} \cdot χ_{graz,lgr,r}\cdot A_{lcl,lgr,r}
\end{equation}

\begin{equation}
n_{lgr,h}= ν_{lgr,h} \cdot a_{lcl,lgr,h}
\end{equation}

\(ν_{lgr,h}\)	= Livestock density [parameter, LU ha<sup>-1</sup>] for animals in livestock group //lgr// in spatial unit //h// \\
\(N_{l,r}\)	= Number of livestock [parameter, LU] of animal type //l// in region //r// \\
\(n_{lgr,h}\)	= Number of livestock [parameter, LU] of animals in livestock group //lgr// in region //r// \\
\(χ_{graz,lgr,r}\)	= Share of grazing animals [parameter, dimensionless] of animals in livestock group //lrg// in region //r// \\
\(A_{lcl,lgr,r}, a_{lcl,lgr,h}\)	= Area [parameter, 1000 ha] of Corine Land Cover Classes //lcl// that are assumed to be available for grazing animals in livestock group //lgr// in spatial unit //h//. 

====Distribution of CAPRI livestock numbers====

If livestock numbers change at the regional level if compared to the prior data, we assume that this has no influence on the spatial distribution of the animals. Instead, the livestock number in each spatial unit is multiplied with the regional relative change.

\begin{equation}
n_{l,h}= \hat{n}_{lgr,h} \cdot \frac {N_{l,r}}{\hat{N}_{l,r}}
\end{equation}

\(n_{l,h}\)	Number of livestock [parameter, LU] of animal type //l// in spatial unit //h//.  \\
\(\hat{n}_{l,h}\)	Number of livestock [parameter, LU] of animal type //l// in spatial unit //h// in the prior data set \\
\(N_{l,r}\)	Number of livestock [parameter, LU] of animal type //l// in region //r// \\
\(\hat{N}_{lhr}\)	Number of livestock [parameter, LU] of animal type //l// in spatial unit //h// in the prior data set \\