CAPRI Online Manual (update)

Files:

%curdir%/capdis/disyield.gms 
%curdir%/capdis/disyield_sets.gms 
%curdir%/capdis/m_hpdCropSpat.gms 
%datdir%/capdishsu/pesetagrid_fractionfsu.gdx 
%datdir%/capdishsu/irriShare2000fsu.gdx 

The principle of the distribution of crop areas is based on few constraints only: full exhaustion of available ares for each spatial unit, vertical consistency, and primacy of land stability.

Vertical consistency means that the sum of each land use type over all spatial units recovers available land use at the higher spatial level. As available information are not (necessarily) geo-referenced, the allocation of a given statistical information to a spatial unit is associated with uncertainty. For example, a farmer with the residence in region A can have land also in regions B and C, but will declare them together, and they will be allocated to her residence (region A). Accordingly, there is some blurring in particular at boundaries and this is accounted for in the methodology: also at the high disaggregation level, the land uses are principally to be interpreted as ‘Land owned by a farmer with residence in this spatial unit’.

Primacy of land stability means that if there is no indication (i. e. new observation, policy restricting previous land distributions, …) it is more likely that the spatial pattern remains similar to the previous (prior) pattern. Therefore, once a likely distribution of land and livestock has been determined on the basis of high-resolution FSS statistics, the model tries to stay as close as possible to this distribution. This is achieved with penalty factors that are activated as soon as the estimated land use area deviated from the prior values, assigning a higher penalty for deviations of permanent crops and forests, and very high penalties of a land use is estimated in a spatial unit where it didn’t exist in the prior’s data base.

The disaggregation model m_hpdCropSpat is described in Section 7.4.1. Section 7.4.2 describes the required input data, and Section 7.4.3 describes the preparation of the input data for their use in hpdCropSpat.

     The levels assigend to the FSUs must recover the given NUTS II area
     both NUTS2 level and FSU level in 1000 ha
     rur = grid cell in mode LAPM, rur = NUTS2 in all other modes
RULEVL_(rur,curact) ..
SUM(regmap(rur,cur%spatunit%),v_levlCon(rur,cur%spatunit%,curact))
=E= p_nutsLevl(rur,curact);

\begin{equation} A_{c^*,r}=\sum_h\{a_{c^*,h}\} \end{equation}

\(a_{c^*,h}\) = Area [parameter, km2] cultivated with crop c or covered by ‘other land’ use excluding forest in spatial unit h
\(A_{c^*,h}\) = Area [parameter, km2] cultivated with crop c or covered by ‘other land’ use excluding forest in region r

Due to several reasons it could be impossible to distribute all agricultural area under the given constraints of total available area in the spatial units (net of the area of ‘nogo’ units and forest area). In order to enable a feasible solution, an error term is introduced that allows the units to slightly shrink or grow. The reason:

• Statistical data are not (necessarily) geo-referenced; i.e. an area of crops (or a livestock) might be assigned to one unit/grid cell because this is where the farm is registered rather than the physical location of crop/livestock
• Uncertainties in the data
• Inconsistencies of data sources (i.e. FSS agricultural statistics, Corine Land Cover data, CAPRI regional statistics)

1. – The FSU area must be exhausted, but the variable v_%spatunit%SizeChg

allows some flexibility if needed.

ADDUPGRID_(rur,cur%spatunit%) $ p_levlunit(rur,cur%spatunit%,"area") .. 
SUM(curact,v_levlCon(rur,cur%spatunit%,curact)) 
=E=  
v_%spatunit%SizeChg(rur,cur%spatunit%)*p_levlunit(rur,cur%spatunit%,"area"); 

\begin{equation} a_h⋅\epsilon_{a,h}=\sum_{c^*}\{a_{c^*,h}\} \end{equation}

\(a_h\) = Area [parameter, km2] of spatial unit h \(a_{c^*,h}\) =Area [parameter, km2] cultivated with crop c or covered by ‘other land’ use excluding forest in spatial unit h \(\epsilon_{a,h}\) = Error term, allowing a spatial unit to shrink or grow slightly in order to enable a feasible disaggregation of statistical data.

The most likely solution is obtained with the ‘Highest Posterior Density’ method. A penalty function calculates deviations from prior information, applying uncertainties

• A random re-allocation of crops should be avoided. Therefore, a penalty is given with increasing deviation from the prior distribution to ensure stability in the time series
• In particular the ‘appearance’ of crops in spatial units where they have not been observed in the prior data should be restricted (disagg(“penelizenewcrops”))
• The error term for the area of the spatial units should be kept at a minimum (disagg(“penalizesizechange”))

PDF_ .. 
# Scale density value a good couple of magnitudes for numerical reasons. 
v_hpd 
*[SUM((curact,regmap(rur,cur%spatunit%)) $ p_levlStde(cur%spatunit%,curact),  
p_levlunit(rur,cur%spatunit%,"area")) 
 +SUM(regmap(rur,cur%spatunit%) $(v_%spatunit%SizeChg.LO(rur,cur%spatunit%) NE 
v_%spatunit%SizeChg.UP(rur,cur%spatunit%)), 
    p_levlunit(rur,cur%spatunit%,"area")) 
 ] 
=E= 
# hsu area-weighted mean square of the deviation from prior mean area, scaled by its stdev 
(SUM((regmap(rur,cur%spatunit%),curact),p_levlunit(rur,cur%spatunit%,"area") 
       * SQR( (v_levlCon(rur,cur%spatunit%,curact)-p_levlunit(rur,cur%spatunit%,curact)) 
               *(                  1 $      p_levlunit(rur,cur%spatunit%,curact)  
                  + disagg("penalizenewcrops") $ (not p_levlunit(rur,cur%spatunit%,curact))) 
               /max(1e-3,  
                         $$ifi     %MODE%==LAPM p_levlStde(cur%spatunit%,curact) 
                         $$ifi NOT %MODE%==LAPM 1 
                   ) 
             ) \\
    )/SUM((regmap(rur,cur%spatunit%),curact)  \\
$p_levlStde(cur%spatunit%,curact),p_levlunit(rur,cur%spatunit%,"area")) \\
)$sum((regmap(rur,cur%spatunit%),curact),p_levlStde(cur%spatunit%,curact)) \\
# penalty for deviation from hsu area \\
+(SUM(regmap(rur,cur%spatunit%),  \\
disagg("penalizesizechange")*p_levlunit(rur,cur%spatunit%,"area")*SQR((v_%spatunit%SizeChg(rur,cur%spatunit%)-1))) \\
 /SUM(regmap(rur,cur%spatunit%), p_levlunit(rur,cur%spatunit%,"area")) \\
 )$SUM(regmap(rur,cur%spatunit%),p_levlunit(rur,cur%spatunit%,"area")) \\
; \\