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--- input_allocation [2020/02/24 11:58] – [Input allocation for feed] matsz
+++ input_allocation [2022/11/07 10:23] (current) – external edit 127.0.0.1
@@ Line 43: / Line 43: @@
 **Figure 5: The cattle chain**
-{{:figure_5.png?600|}}
+{{:figure_5.png?600|}} \\ Source: CAPRI Modelling System
 Accordingly, each raising and fattening process takes exactly one young animal on the input side. The raising processes produce exactly one animal on the output side which is one year older. The output of calves per cow, piglets per sow, lambs per mother sheep or mother goat is derived ex post, e.g. simultaneously from the number of cows in t-1, the number of slaughtered bulls and heifers and replaced in t+1 which determine the level of the raising processes in t and number of slaughtered calves in t. The herd flow models for pig, sheep and goat and poultry are similar, but less complex, as all interactions happen in the same year, and no specific raising processes are introduced.
@@ Line 105: / Line 105: @@
 |GROFYCOW|	Numer of heifers raised to young cows|	235,45	|227,16	|229,4|
 |HEIRLEVL|	Activity level of the heifers raising process	|235,45	|227,16	|229,4|
+ \\ Source: CAPRI Modelling System
@@ Line 115: / Line 116: @@
 |Bull fattening (BULF)	|BULL: 20% lower meat output, variable inputs besides feed an young animals at 80% of average	|BULH: 20% higher meat output, variable inputs besides feed an young animals at 120% of average|
 |Heifers fattening (HEIF)|	HEIL: 20% lower meat output, variable inputs besides feed an young animals at 80% of average	|HEIH: 20% higher meat output, variable inputs besides feed an young animals at 120% of average|
+ \\ Source: CAPRI Modelling System
 ====Input allocation for feed====
@@ Line 146: / Line 148: @@
 Wide supports for the Gross Value Added of the fodder activities mirror the problem of finding good internal prices but also the dubious data quality both of fodder output as reported in statistics and the value attached to it in the EAA. The wide supports allow for negative Gross Value Added, which may certainly occur in certain years depending on realised yields. In order to exclude such estimation outcomes as far as possible an additional constraint is introduced:
-FIXME
 \begin{equation}
@@ Line 190: / Line 190: @@
 | |FEDAGGR_ |aggregate to roughage, concentarte feed, etc|Defines feed aggregates from single bulks FEED|
 | |FeedAggrShare_ |Calculate share of feed aggregates (roughage, concentrates, other)|shares of roughage and concentrate feed enter objective|
-| |MeanFeedTotal_ |Calculates total feed intake in DM per animal|Part of revised objective function|
+| |MeanFeedTotal_ |Calculates total feed intake in DM per animal|Part of revised objective function| \\ Source: own compilation
 The four additional equations developed in the new feed allocation procedure are described in more detail in the following.
@@ Line 211: / Line 211: @@
 ^FeedCons| | | | | | | |  X  |  X  |  X  |  X  | |
 ^FeedOth| | | | |  X  |  X  |  X  | | | | |  X  |
-^FeedTotal|  X  |  X  |  X  |  X  |  X  |  X  |  X  |  X  |  X  |  X  |  X  |  X  |
+^FeedTotal|  X  |  X  |  X  |  X  |  X  |  X  |  X  |  X  |  X  |  X  |  X  |  X  | \\ Source: own compilation
 __ FeedAggrShare_ __
@@ Line 235: / Line 235: @@
 {{:code_p_73.png?600|}}
-This part of the objective functions tries to minimize the difference between the requirements calculated from the feed input coefficients (v_animReq) and the expected (mean) requirements (p_animReq) coming from literature. Due to the weighting with number of animals (v_actLevl) and expected requirements (p_animReq) the optimal solution tends to distribute over or under supply of nutrients relatively even over all activities and regions. It has been decided to attach an exponent smaller one to these weights which strongly pulls them towards unity (see: [...] FIXME (doppelstern) .1). This tends to give more weight to “less important” animal types compared with untransformed weights.
+This part of the objective functions tries to minimize the difference between the requirements calculated from the feed input coefficients (v_animReq) and the expected (mean) requirements (p_animReq) coming from literature. Due to the weighting with number of animals (v_actLevl) and expected requirements (p_animReq) the optimal solution tends to distribute over or under supply of nutrients relatively even over all activities and regions. It has been decided to attach an exponent smaller one to these weights which strongly pulls them towards unity (see: [...] FIXME (section? .1). This tends to give more weight to “less important” animal types compared with untransformed weights.
 __Deviation of sub regional total feed intake from regional average__
@@ Line 273: / Line 273: @@
 ^  SHGF  |  6.3	  |  5.8	  |  7	  |  0.155  |  	0.14  |  	0.17  |
 ^  HENS  |  8  |  	7.8	  |  8.2	  |  0.18  |  	0.14	  |  0.2  |
-^  POUF  |  8  |  	7.8	  |  8.2	  |  0.18  |  	0.14  |  	0.2  |
+^  POUF  |  8  |  	7.8	  |  8.2	  |  0.18  |  	0.14  |  	0.2  | \\
 __Shares of feed aggregates in total feed intake in DRMA __
@@ Line 301: / Line 301: @@
 ^  SHGF	 | |  0.3  | | 	0.05  |
 ^  HENS	 | | | |  0.99  |
-^  POUF	 | | | |  0.99  |
+^  POUF	 | | | |  0.99  |  \\ Source: own compilation
 For „other feed“ there are no lower bounds but rather low upper bounds: 10% for adult cattle, 5% for calves and sheep, 1% for pigs and 1E-6 (so near zero) for poultry.
@@ Line 376: / Line 376: @@
 | | | |Nitrogen in ammonia, NOx, N2O and runoff losses from mineral fertiliser|  l  |  2.89  |
 |  **TOTAL INPUT**  |  **e=a+b+c+d**  |  **162.768**  |  **TOTAL OUTPUT**  |  **n=f+k+l+m**  |  **103.92**  |
-| | | |  **Nutrient losses at soil level (SURPLUS)**  |  **m=e-f-k-l**  |  **58.85**  |
+| | | |  **Nutrient losses at soil level (SURPLUS)**  |  **m=e-f-k-l**  |  **58.85**  | \\ Source: CAPRI modelling system
 The difference between nutrient inputs and outputs corresponds to the soil surplus. For nitrates the leaching is calculated as a fraction of the soil surplus, which is based on estimates from the MITERRA project, and depends on the soil type, the land use (grassland or cropland), the precipitation surplus, the average temperature and the carbon content in soils. For details see Velthof et al. 2007 “Development and application of the integrated nitrogen model MITERRA-EUROPE”. Alternatively, a version was developed which uses the leaching fractions from the official Greenhouse gas inventories of the member states. For phosphate, currently emissions (mainly superficial runoff) are not quantified.
@@ Line 389: / Line 389: @@
 |**Cattle**|  2.0  |  5.5  |
 |**Swine**|  3.3  |  3.3  |
-|**Poultry**|  6.3  |  5.1  |
+|**Poultry**|  6.3  |  5.1  | \\ Source: Lufa von Weser-Ems, Stand April 1990, Naehrstoffanfall.
-Source:Lufa von Weser-Ems, Stand April 1990, Naehrstoffanfall.
 These data are converted into typical pure nutrient emission at tail per day and kg live weight in order to apply them for the different type of animals. For cattle, it is assumed that one live stock unit (=500 kg) produces 18 m³ manure per year, so that the numbers in the table above are multiplied with 18 m³ and divided by (500 kg *365 days).
@@ Line 409: / Line 408: @@
 |N|0.0084|
 |P|0.004|
-|K|0.0047|
+|K|0.0047| \\ Source: RAUMIS Model [[http://www.agp.uni-bonn.de/agpo/rsrch/raumis_e.htm]].
-Source: RAUMIS Model [[http://www.agp.uni-bonn.de/agpo/rsrch/raumis_e.htm]].
+ FIXME
 The factors shown above for pigs are converted into a per day and live weight factor for sows by assuming a production of 5 m³ of manure per sow (200 kg sow) and 15 piglets at 10 kg over a period of 42 days. Consequently, the manure output of sows varies in the model with the number of piglets produced.
@@ Line 493: / Line 492: @@
 **Figure 6. Ex-post calibration of NPK balances and the ammonia module**
-{{::figure_6.png?600|}}
+{{::figure_6.png?600|}} \\ Source: CAPRI modelling system
 The following equations comprise together the cross-entropy estimator for the NPK (Fnut=N, P or K) balancing problem. Firstly, the purchases (NETTRD) of anorganic fertiliser for the regions must add up to the given inorganic fertiliser purchases at Member State level:
 \begin{equation}
-Nettrd_{MS}^{Fnut}=\sum_r Nettrd_r^{Fnut}
+\overline{Nettrd}_{MS}^{Fnut}=\sum_r Nettrd_r^{Fnut}
 \end{equation}
+The crop need –minus biological fixation for pulses– multiplied with a factor describing fertilisation beyond exports must be covered by:
+  - inorganic fertiliser, corrected by ammonia losses during application in case of N,
+  - atmospheric deposition, taking into account a crop specific loss factor in form of ammonia, and
+  - nutrient content in manure, corrected by ammonia losses in case of N, and a specific availability factor.
+FIXME
+\begin{align}
+\begin{split}
+&\sum_{cact} Levl_{r,cact}Fnut_{r,cact}(1-NFact_{Fnut,cact}^{biofix})\\
+&NutFac_{r,fnut}(1+NutFacG_{r,fnut}\wedge cact \in ofar,grae,grai)\\
+&=NETTRD_r^{Fnut}(1-NH3Loss_{Fnut,r}^{Anorg})\\
+&+NBal_r^{AtmDep}NFact_{Cact}^{AtmDep}\\
+&\sum_{aact}Levl_{r,aact}Fnut_{r,aact}(1-NH3Loss_{Fnut,r}^{Manure})(1-NavFac_{r,fnut})
+\end{split}
+\end{align}
+The factor for biological fixation ( $NFact^{biofix}$ ) is defined relative to nutrient export, assuming deliveries of 75 % for pulses (//PULS//), 10 % for other fodder from arable land (//OFAR//) and 5 % for grassland (//GRAE, GRAI//).
+The factor describing ‘luxury’ consumption of fertiliser (//NutFac//) and the availability factors for nutrient in manure (//NavFac//) are estimated based on the HPD Estimator:
+\begin{align}
+\begin{split}
+min \; HDP &-\sum_{r,fnut} \left(\ \frac{NutFac_{r,fnut}-\mu_{r,fnut}^{NutFac}}{\sigma_{r,fnut}^{NutFac}}\right)^2\ \\
+&-\sum_{r,fnut} \left(\ \frac{NavFac_{r,fnut}-\mu_{r,fnut}^{NavFac}}{\sigma_{r,fnut}^{NavFac}}\right)^2\ \\
+&-\sum_{r,fnut} \left(\ \frac{NutFacG_{r,fnut}-\mu_{r,fnut}^{NutFacG}}{\sigma_{r,fnut}^{NutFac}}\right)^2\ \\
+&-\sum_{r,ngrp} \left(\ \frac{Nitm{r,ngrp}-\mu_{r,ngrp}^{Nitm}}{\sigma_{r,fnut}^{NavFac}}\right)^2\ \frac{\overline {LEVL}_{r,UAAR}}{\overline {LEVL}_{r,ngrp}} \\
+\end{split}
+\end{align}
+The expected means  $\gamma$  for the availability for P and K in manure (//Navfac//) are centred around 50 %, for N at 50 %*40 %+25 %*86%, since 50 % are assumed to be released immediately, of which 60 % are lost as ammonia and 25 % are released slowly, with a crop availability of 86 %. These expected means at national level are multiplied with the regional output of the nutrient per hectare divided by the national output of nutrient per hectare so that the a priori expectation are higher losses with higher stocking densities. The lower limits are almost at zero and the upper limits consequently at the unity. The standard deviation  $\sigma$  is calculated assuming a probability of 1% for a zero availability and 1% for an availability of 100%.
+The expected mean  $\gamma$  for the factor describing over fertilisation practices (//Nutfac//) is centred around 120 %, with a 1% probability for 160 % and a 1 % probability for 80 % (support points) with define the standard deviation  $\sigma$ . Upper and lower limits are at 500% and 5%, respectively. A second factor (//Nutfacg//) is only applied for grassland and other fodder from arable land and centred around zero, with expected mean of +10% and a  10% with probabilities of 1%. Bounds for the factor //Nutfacg// are at  0.5 and 2.5.
+The last term relates to the distribution of organic N to the different group of crops. The distribution is needed for simulation runs with the biophysical model DNDC (Joint Research Center, Ispra, Italy) linked to CAPRI results in the context of the CAPRI-Dynaspat project.
+It is important to note that the CAPRI approach leads to nutrient output coefficient at tail taking into account regional specifics of the production systems as final weight and even daily weight increase as well as stocking densities. Further on, an important difference compared to many detailed farm models is the fact that the nutrient input coefficients of the crops are at national level consistent with observed mineral fertiliser use.
+The nutrient balances are constraints in the regional optimisation models, where all the manure must be spread, but mineral fertiliser can be bought at fixed prices in unlimited quantities. Losses can exceed the magnitude of the base year but are not allowed to fall below the base year value. The latter assumption could be replaced by a positive correlation between costs and nutrient availability of the manure spread. There is hence an endogenous cross effect between crops and animals via the nutrient balances.
+The factors above together with the regional distribution of the national given inorganic fertiliser use are estimated over a time series. Trend lines are regressed though the resulting time series of manure availability factors of NPK and crop nutrient factors for NPK, and the resulting yearly rates of change are used in simulation to capture technical progress in fertiliser application. The following table shows a summary by highlighting which elements of the NPK are endogenous and exogenous during the allocation mechanism and during model simulations:
+**Table 18: Elements entering the of NPK balance ex-post and ex-ante**
+|  **Ex-post**  |  **Ex-ante**  |
+|**Given:**\\ -Herd sizes\\  => Manure output\\ -Crop areas and yields\\  => Export with harvest\\ -National anorganic application\\ **Estimated:**\\ -Regional anorganic application\\ -Factor for Fertilization beyond N export\\ -Manure availability |**Model result:**\\ -Herd sizes\\  => manure output\\ -Crop areas and yields\\ => Export with harvest\\ -National and Regional anorganic application\\ **Given:** \\ -Factor for Fertilization beyond export (trended)\\ -Manure availability (trended)|
+A good overview on how the Nitrogen balances are constructed and can be used for analysis can be found in: Leip A., Britz W., de Vries W. and Weiss F. (2011): Farm, land, and soil nitrogen budgets for agriculture in Europe calculated with CAPRI, Environmental Pollution 159(11), 3243-3253 and Leip, A., Weiss, F. and Britz, W. (2011): Agri-Environmental Nitrogen Indicators for EU27, in: Flichman G. (ed.), Bio-Economic Models applied to Agricultural Systems, p. 109-124, Springer, Netherlands.
+==Update note==
+The overall N Balance calibration problem has been revised several times. For example, since 2007 it delivers estimates of the shares of different sources of N (mineral fertiliser, excretions, crop residues) distinguished by crop groups. As of Stable Release 2.1, the calibration problem is augmented by an explicit maximization of the probability density functions described in the section on fertilization in the supply model chapter of this documentation ((A rather self contained presentation with a focus on the fertiliser calibration methodology (rather than environmental indicators or data sources) is given in Deliverable 4a: "Revision of the fertilizer module in CAPRI" in the context of specific contract 154208.X39 “IMPROVEMENT OF THE STABLE RELEASE OF THE CAPRI MODEL: FERTILIZER AND FEED ALLOCATION ROUTINES” (Star2). )).
+===The ammonia module ===
+The ammonia (NH3) and nitrous oxide (NOx) output module takes the nitrogen output per animal from the existing CAPRI module and replaces the current fixed coefficient approach with uniform European factors per animal type by Member State specific ones, taking into account differences in application, storage and housing systems between the Member States. The general approach follows the work at IIASA and has been updated under the Ammonia project in 2006/07. The following diagram shows the NH3 sinks taken into account by coefficients.
+**Figure 7: Ammonia sinks in the Ammonia emission module**
+{{::figure_7.png?600|}} \\ Source: CAPRI modelling system
+In the figure above, white arrows represent ammonia losses and are based on uniform or Member State specific coefficients. A first Member State specific coefficient characterises for each animal type the share of time spent on grassland and spent in the stable. For dairy cows, for example, the factors are between 41 % spent in the stable in Ireland and 93 % in Switzerland. During grazing about 8% of the excreted N is assumed lost as ammonia.
+The time spent in the stable is then split up in liquid and solid housing systems. To give an example, 100 % of the Dutch cows are assumed to use liquid manure systems, whereas in Finland 55 % of the cows are in solid systems. Ammonia losses in both systems are assumed to be identical per animal types but differ between animals. 10 % ammonia losses are assumed for sheep and goat, 12 % for cattle, 17 % for pigs and 20 % for poultry, if no abatement measures are taken.
+The remaining nitrate is then either put into storage or directly applied to the ground. No storage is assumed for sheep and goats and in all remaining cases not-covered systems are assumed with loss factors of 4-20 % of the N brought initially into storage.
+After storage, the remaining N is applied to the soil, either spread to the surface –losses at 8 40%% or using application techniques with lower (20-40% saving) or high (80% saving) emission reductions. According to IIASA data most farmers work still with the standard techniques.
+The update of this calculation during the Ammonia project in 2006/07 has included new coefficients from IIASA through the project partner Alterra. Furthermore, it has been acknowledged that in addition to NH3 there are losses of N as N2O, NOx and N2. The loss factors depend on the application of abatement techniques the penetration of which may be varied in scenarios. Technically, the underlying calculations are embedded as GAMS code in an own module both called during updates of the data base and model runs. This module in turn includes GAMS code borrowed from the MITERRA-Europe model of our former partner.
+Recently ammonia mitigation technologies have been implemented as endogenous farm practices (see section on greenhouse gases) and environmental constraints related to important environmental directives like the Nitrates Directive (ND), the National Emisssions Ceiling (NEC), and the Industrial Emissions Directice (IED) have been implemented directly to the supply model. For the ND we consider upper limits for the application of manure and total nitrogen, for the NEC the upper limits member states committed to until 2030, and for the IED minimum reqirements for the implementation of manure storage measures.
+===Carbon balance ===
+The carbon cycle model quantifies relevant carbon flows in the agricultural production process related to both livestock and crop production (see Figure 6). Carbon flows and CO2 emissions from land use changes (LUC) are not considered meaning that the quantified balance applies to cropland remaining cropland and pasture/meadow land remaining in use. Default IPCC coefficients are used to quantify the carbon effects of LUC.
+In CAPRI, so far the following carbon flows are taken into account, starting with animal production and ending with crop production (Weiss and Leip, 2016):
+  * Feed intake in livestock production (C)
+  * Carbon retention in livestock and animal products (C)
+  * Methane emissions from enteric fermentation in livestock production (CH4)
+  * Animal respiration in livestock production (CO2)
+  * Carbon excretion by livestock (C)
+  * Manure imports and exports to the region (C)
+  * Methane emissions from manure management in livestock production (CH4)
+  * Carbon dioxide emissions from manure management in livestock production (CO2)
+  * Runoff from housing and storage in livestock production (C)
+  * Manure input to soils from grazing animals and manure application (C)
+  * Carbon input from crop residues (C)
+  * Carbon export by crop products (C)
+  * Carbon dioxide emissions from the cultivation of organic soils (CO2)
+  * Carbon dioxide emissions from liming (CO2)
+  * Runoff from soils (C)
+  * Methane emissions from rice production (CH4)
+  * Carbon sequestration in soils (C)
+  * Carbon losses from soil erosion (C)
+  * Carbon dioxide emissions from soil and root respiration (CO2)
+Accordingly, CAPRI does not consider the following carbon flows:
+  * Volatile organic carbon (VOC) losses from manure management (C)
+  * Carbon losses from leaching (C)
+  * Carbon dioxide emissions from urea application (CO2)
+The VOC losses (non-CH4) from manure management are small and can be neglected. Carbon losses from leaching can be a substantial part of carbon losses from agricultural soils (see e.g. Kindler et al. 2011). Although they are not yet specifically quantified in the CAPRI approach, they are not neglected but put together with soil respiration in one residual value in the CAPRI carbon balance. CO2 emissions from urea application account for about 1% of total GHG emissions in the agriculture sector, but are not yet included in the CAPRI carbon cycle model.
+**Figure 8: Carbon flows in the agricultural production process**
+{{:figure_8.png?600|}} \\ Source: Weiss and Leip (2016)
+In the following, we briefly describe the general methodology for the quantification of the carbon flows that are taken into account in the CAPRI approach.
+Subsequently, some details on the quantification of carbon flows (emissions and removals) are presented:
+//Feed intake in livestock production// \\
+Feed intake is determined endogenously in CAPRI based on nutrient and energy needs of livestock. The carbon content of feedstuff is derived from the combined information on carbon contents of amino acids and fatty acids, the shares of amino acids and fatty acids in crude protein and fats of different feedstuffs, and the respective shares of crude protein, fats and carbohydrates. For carbohydrates we assume a carbon content of 44%. Data was taken from Sauvant et al. (2004) and from NRC (2001).
+//Carbon retention in livestock and animal products// \\
+Similar to feed intake, we can quantify the carbon stored in living animals using the above mentioned data for animal products. At the end the values from meat are multiplied with the animal specific relation of live weight to carcass. For simplification, the fact that bones or skins etc. may have different carbon contents than meat is ignored.
+//Methane emissions from enteric fermentation// \\
+Methane emissions from enteric fermentation are calculated endogenously in CAPRI based on a Tier2 approach following the IPCC guidelines.
+//Animal respiration in livestock production// \\
+Intake of carbon is a source of energy for the animals. CAPRI calculates the gross energy intake on the basis of feed intake as described above. However, not all carbon is ‘digestible’ and hence can be transformed into biomass or respired. Digestibility of feed (for cattle activities) is calculated on the basis of the NRC (2001) methodology. Non-digestible energy (or carbon) is excreted in manure (see next point 5), while the ‘net energy intake’ refers to the equivalent to the energy stored in body tissue and products plus losses through respiration and methane.
+According to Madsen et al. (2010) the heat production per litre of CO2 is 28 kJ for fat, 24 kJ for protein and 21 kJ for carbohydrates. Using a factor of 1.98 kg/m3 for CO2 (under normal pressure) or 505.82 l/kg we get 14.16 MJ/kg CO2 for fat, 12.14 MJ/kg CO2 for protein and 10.62 MJ/kg CO2 for carbohydrates, which translates into 0.071, 0.082 and 0.094 kg CO2 per MJ, respectively. These values are used to get the carbon directly from net energy intake (for each feedstuff), which is an endogenous variable in CAPRI depending on the feed intake. From this we subtract the carbon retained in living animals and in animal products and the methane emissions from enteric fermentation in order to compute the carbon respiration from livestock.
+//Carbon excretion by livestock// \\
+Carbon excretion is defined as the difference between the carbon intake via feed, the retention in livestock and the emissions as carbon dioxide (respiration) and methane (enteric fermentation):
+\begin{equation}
+Excretion = Feed \; intake – retention – emissions (CO_2, CH_4)
+\end{equation}
+Carbon excretion can, therefore, be determined as the balance between the positions 1-4. As Carbon retention plus emissions by default gives the net energy intake (see 4), this is equivalent to
+\begin{equation}
+Excretion = C \; from \; gross \; energy \; intake – C \; in \; net \; energy  \; intake
+\end{equation}
+//Manure imports and exports to the region//  \\
+Manure available in a region may not just come from animal’s excretion in the region but could also be imported from other regions, while, conversely, manure excreted may be exported to another region. CAPRI calculates the net manure trade within regions of the same EU member state, and this has to be accounted in the carbon balance as a separate position. For simplification, the model assigns the emissions of all manure excreted to the exporting region, while the carbon and nutrients are assigned to the importing region.
+//Methane emissions from manure management in livestock production// \\
+Once the carbon is excreted in form of manure (faeces or urine), it will either end up in a storage system or it is directly deposited on soils by grazing animals. Depending on temperature and the type of storage, part of the carbon is emitted as methane. These emissions are quantified in CAPRI following a Tier 2 approach, using shares of grazing and storage systems from the GAINS database (for more explanation see also Leip et al. 2010).
+//Carbon dioxide emissions from manure management in livestock production// \\
+During storage or grazing, carbon is not only emitted in form of methane, but part of the organic material is mineralized and carbon released as carbon dioxide. Following the FarmAC model((The FarmAC model simulates the flows of carbon and nitrogen on arable and livestock farms, enabling the quantification of GHG emissions, soil C sequestration and N losses to the environment (for more information see: [[http://farmac.dk]]). )), we assume a constant relation between carbon emitted as methane and total carbon emissions (methane plus carbon dioxide) of 63%. Therefore, the carbon loss through carbon dioxide emissions can be quantified as:
+\begin{equation}
+C (CO_2) = C(CH_4) * 0.37/0.63
+\end{equation}
+//Runoff from housing and storage in livestock production// \\
+Part of the carbon excreted by animals is lost via runoff during the phase of housing and storage. We assume the share to be equivalent to the share of nitrogen lost via runoff. In CAPRI we use the shares from the Miterra-Europe project, which are differentiated by NUTS 2 regions (for more information see Leip et al. 2010).
+//Manure input to soils from grazing animals and manure application// \\
+Carbon from manure excretion minus the emissions from manure management and runoff during housing and storage, corrected by the net import of manure to the region, is applied to soils or deposited by grazing animals. Other uses related to manure (e.g. trading, burning, etc.) are so far not considered in CAPRI. Moreover, we add here the carbon from straw from cereal production not fed to animals, assuming that all harvested straw (endogenous in CAPRI) not used as feedstuff is used for bedding in housing systems. The carbon content from straw is quantified in the same way as for feedstuff (see position 1). By contrast, other cop residues are treated under the position “carbon inputs from crop residues”. Bedding materials coming from other sectors are currently ignored.
+//Carbon input from crop residues// \\
+The dry matter from crop residues is quantified endogenously in CAPRI following the IPCC 2006 guidelines (crop specific factors for above and below ground residues related to the crop yield). For the carbon content, a unique factor of 40% is applied as the information used in position 1 (feed input) is generally only available for the commercially used part of the plants, but not specified for crop residues.
+//Carbon export by crop products// \\
+Carbon exports by crop products are calculated as described under position 1, using the composition of fat and proteins by fatty and amino acids and the respective shares of these basic nutrients in the dry matter of crops.
+//Carbon fixation via photosynthesis of plants// \\
+Photosynthesis is the major source of carbon for a farm. Carbon is incorporated in plant biomass as sugar and derived molecules to store solar energy. Some of these molecules are ‘exudated’ by the roots into the soil. They provide an energy source for the soil microorganism – in exchange to nutrients. In the current version of CARPI, we assume that 100% of the photosynthetic carbon not stored in harvested plant material or crop residues, returns ‘immediately’ to the atmosphere as CO2 (root respiration) and has therefore no climate relevance. Accordingly, the effective fixation of carbon via photosynthesis is assumed to equal the exported carbon with crop products plus the carbon from crop residues. It is, therefore, not calculated as an explicit term.
+//Carbon dioxide emissions from the cultivation of organic soils// \\
+Carbon dioxide emissions from the cultivation of organic soils are calculated by using shares of organic soils derived from agricultural land use maps for the year 2000. For details see Leip et al. (2010).
+//Carbon inputs from liming// \\
+Agricultural lime is a soil additive made from pulverised limestone or chalk, and it is applied on soils mainly to ameliorate soil acidity. Total liming application on agricultural land as well as the related emission factor is taken from past UNFCCC notifications. A coefficient per ha is computed dividing the UNFCCC total amount by the UAA in the CAPRI database. For projection purposes this coefficient per ha, computed from the most recent data, is maintained in simulations. In the context of the carbon balance the CO2 emissions are converted into C and become carbon input into the system.
+//Carbon runoff from soils// \\
+Similar to position 9 (runoff from housing and storage in livestock production) we assume that the share of carbon lost via runoff from soils is equivalent to the respective share of nitrogen lost. The respective shares are provided by the Miterra-Europe project (see Leip et al. 2010).
+//Methane emissions from rice production//  \\
+Methane emissions from rice production are relevant only in a few European regions and they are quantified in CAPRI via a Tier 1 approach following IPCC 2006 guidelines.
+//Carbon sequestration in soils// \\
+Finally, we quantify the sequestered material after 20 years. The carbon change is based on simulations with the CENTURY agroecosystem model (Lugato et al. 2014) (aggregated from 1 km2 to NUTS2 level), and calculated from the difference in the manure and crop residue input to soils between the simulation year and the base year. This is done because carbon sequestration is only achieved from an increased carbon input, assuming that the carbon balance in the base year is already in equilibrium. The total cumulative carbon increase is divided by 20, in order to spread the effect over a standardised number of years (consistent with the 2006 IPCC guidelines).((The simulations with the CENTURY model were carried out by Emanuele Lugato from JRC.D3 in Ispra (for more details see Lugato et al. 2014).))
+//Carbon losses from soil erosion// \\
+Carbon losses from soil erosion are calculated on the basis of the RUSLE equation (see the setion on soil erosion). In order to get the carbon loss we have to multiply with the carbon content of the soil. As approximation we assume a 3% humus share for arable land and a 6% humus share for grassland. The carbon share in humus is around 2/3.
+//Carbon dioxide emissions from respiration of carbon inputs to soils// \\
+Carbon losses from soil are quantified as the residual between all carbon inputs to soils, the emissions and the carbon sequestered in the soils:
+\begin{align}
+\begin{split}
+&Carbon \; losses\; via\; soil\; and\; root\; respiration = \\
+&Manure\; input\; from\; grazing\; and\; manure\; application \\
+&+ input\; from\; crop\; residues \\
+&- carbon \;losses \;(CH4)\; from \;rice\; production \\
+&- carbon \;losses \;(CO2) \;from \;the \;cultivation\; of \;organic\; soils \\
+&- carbon \;losses \;from \;runoff \;from \;soils \\
+&- carbon \;losses\; from \;soil \;erosion \\
+&- carbon \;sequestration \;in \;soils \\
+\end{split}
+\end{align}
+Carbon losses from leaching should also be subtracted, but they are not specifically quantified in the CAPRI carbon cycle model so far. Therefore, the share of soil respiration is currently overestimated by the model.
+===Greenhouse Gases===
+For the purpose of modelling GHG emissions from agriculture, a //multi strategy approach// is followed. It is important to take into account that agriculture is an important emitter of several climate relevant gases other than carbon dioxide. Therefore, three types of pollutants are modelled: methane (CH4) ,nitrous oxide (N2O), and carbon dioxide (CO2) emissions. The sources considered are: //CH4 emissions from animal production, manure management and rice cultivation, N2O from agricultural soils and manure management, and CO2 emissions from agricultural soils//. Moreover, carbon removals and emissions from land use change are quantified, and translated into CO2.
+In CAPRI consistent GHG emission inventories for the European agricultural sector are constructed. As already mentioned, //land use// and //nitrogen flows// are estimated at a regional level. This is the main information needed to calculate the parameters included in the IPCC Good Practice Guidance (IPCC, 2006). The following table lists the emission sources modelled:
+**Table 19: Agricultural greenhouse gas emission sources included in the model**
+|  **Greenhouse Gas**  |  **Emission source**  |  **Code**  |
+|**Methane**|Enteric fermentation|CH4Ent|
+|:::	|Manure management|CH4Man|
+|:::	|Rice production|CH4Ric|
+|:::	|Land use change emissions from\\ biomass burning|CH4bur|
+|**Nitrous Oxide**|Manure management|N2OMan|
+|:::	|Manure excretion on grazings|N2OGra|
+|:::	|Application of synthetic fertiliser|N2OSyn|
+|:::	|Application of manure|N2OApp|
+|:::	|Crop residues|N2OCro|
+|:::	|Indirect emissions from ammonia \\ losses|N2OAmm|
+|:::	|Indirect emissions from leaching \\ and runoff|N2OLea|
+|:::	|Cultivation of histosols|N2Ohis|
+|:::	|Land use change emissions from the \\ burning of biomass|N2Obur|
+|**Carbon dioxide**|Cultivation of histosols|CO2his|
+|:::	|Applicaton of ureum|CO2urea|
+|:::	|Liming|CO2lim|
+|:::	|Land use change emissions from above \\ and below ground biomass|CO2bio|
+|:::	|Land use change emissions from soil \\ carbon changes|CO2soi| \\ Source: CAPRI Modelling System
+For a detailed analysis of these single emission sources refer to Pérez 2006: Greenhouse Gases: Inventories, Abatement Costs and Markets for Emission Permits in European Agriculture -A Modelling Approach and Leip et al 2010: Evaluation of livestock sector’s contribution to the RU greenhouse gas emissions (GGELS).
+The model code also comprises a life-cycle assessment for GHGs (first approach explained in Leip et al, 2010, but newer approach not yet documented in an official publication), and a module to estimate emission leakage in Non-European world regions (for details see e.g. Jansson et al.,2010: Estimation of Greenhouse Gas coefficients per commodity and world region to capture emission leakage in European Agriculture; Pérez Dominguez et al., 2012: Agricultural GHG emissions in the EU: An Exploratory Economic Assessment of Mitigation Policy Options., Van Doorslaer et al, 2015: An economic assessment of greenhouse gas mitigation options for EU agriculture). Moreover, in recent projects (Ecampa1-3) mitigation technologies and farm practices have been introduced to the supply model, which directly impact on the emissions. Currently, the following mitigation technologies can be activated:
+  * Anaerobic digestion
+  * Feed additives to reduce methane emissions from ruminants (lineseed, nitrate)
+  * Precision farming
+  * Variable Rate Technology
+  * Nitrification Inhibitors
+  * Better timing of fertilizer application
+  * Winter cover crops
+  * No Tillage
+  * Conservation Tillage
+  * Buffer strips
+  * Fallowing of histosols
+  * Measures to reduce methane emissions in rice production
+  * Increased legume share on temporary grassland
+  * Genetic measures to increase milk yields and feed efficiency
+  * Urea Substitution
+  * Manure application measures to reduce ammonia emissions (high and low efficiency)
+  * Manure storage measures to reduce ammonia emissions (high and low efficiency)
+  * Stable design measures to reduce ammonia emissions
+  * Low Nitrogen Feed
+  * Manure storage basins in concrete to reduce nitrate leaching
+  * Flexible limits for nitrogen application to soils
+  * Flexible limits for livestock density
+  * Vaccination against methanogenic bacteria
+For details see Van Doorslaer et al. 2015, and Perez et.al 2016 (Most recent developments not yet published).
+===Soil erosion===
+Soil erosion is calculated on the basis of the RUSLE equation. The equation has the following form:
+\begin{equation}
+A = R \cdot K \cdot L \cdot S \cdot C \cdot P
+\end{equation}
+where \\
+A = soil loss in ton per ha/acre per year \\
+ R = rainfall-runoff erosivity factor \\
+ K = soil erodibility factor \\
+ L = slope length factor \\
+ S = slope steepness factor \\
+ C = cover management factor \\
+ P = support practice factor \\
+For more details on the factors used see Panagos et al. (2015).
+==== Input allocation for labour ====
+Labour (and other inputs) in CAPRI are estimated from a Farm Accounting Data Network (FADN) sample ((More details on the FADN estimation were reported older versions of this section (originally drafted by Markus Kempen and Eoghan Garvey) the CAPRI documentation, accessible in the \doc folder of any stable release of the CAPRI system up to star 2.4 from [[https://www.capri-model.org/dokuwiki/doku.php?id=capri:get-capri.]])) and then these estimation results are combined with total labour requirements within a region (or aggregate national input demand reported in the EAA), using a Highest Posterior Density (HPD) estimation framework.
+===Labour Input Allocation===
+Input coefficients (family labour and paid labour, both in hours, as well as wage regressions for paid labour) were estimated using standard econometrics from single farm records as found in FADN. While many of results from this process are plausible a number of CAPRI estimates of labour input are inaccurate and untrustworthy, not least when fitted values for labour using the econometric coefficients are compared with total regional labour inputs recoverable from FADN data survey weights. To remedy this, a reconciliation process is undertaken to correct figures for labour input by adjusting the labour input coefficients for both total labour and family labour, handled in file gams\inputs\labour_calc.gms.
+The reconciliation process has two components. The first component is to fix on a set of plausible estimates for the labour input coefficients (based on the econometric results) while the second involves a final reconciliation, where further adjustments are made to bring the estimates into line with the FADN values for labour inputs. Implementing these two steps involves the following procedures.
+Step one involves preparing the econometric estimates in order to remove unreliable entries. This process removes specific unsuitable estimates for particular regions and crop types. In addition, this process also involves adjusting certain agricultural activities labour input coefficients (such as the estimates for triticale) so as to bring them into line with similar activities (such as for soft wheat). Furthermore, a Bayesian probability density function is used where EU averages are used as priors, and a number of bounds are added, in order to generate realistic labour input coefficients.
+While the procedure described above help to ensure plausible estimates, the labour input values generated will still not be such as to reconcile total fitted labour with total actual labour at a regional or national level (as estimated by FADN). Step 2 in this process is to implement a final reconciliation, where the labour input coefficients are adjusted in order to bring estimates of labour input closer to the total labour used in the region/country. However, this adjustment process has to be balanced with a recognition that many of the labour input coefficient estimates are relatively reliable and that we don’t need or want to radically adjust all of them. Therefore the final reconciliation has to specify which input coefficients have to be adjusted most.  The main way in which this is achieved is through the consideration of the coefficients’ standard errors in a second Bayesian posterior density function.
+As well as the reconciliation process, two other procedures have to be carried out. The first results from the fact that a number of activities don’t have labour input coefficient estimates. In order to estimate them, the revenue shares for the relevant activities are used as a proxy for the amount of labour they require.  Labour input for the different activities is then calculated based on these shares. The second procedure is due to the presence of infeasibilities in this model. In order to try and eliminate them, a number of courses of action can be followed from excluding outlying estimates to dropping regional estimates.
+It should be noted that the reconciliation process has to be divided into these two steps because it is highly computationally burdensome. For the model to run properly (or even at all), it is necessary to divide it into two parts, with the one part obtaining plausible elements and the other implementing the final reconciliation.
+**Table 20: Total labour input coefficients from different econometric estimations and steps in reconciliation procedure (selected regions and crops)**
+|  Region  |  crop or aggregate  |  Econometric estimation  |||  HPD solution including  |||
+|:::| |  regional  |  national- \\ including yield  |  national - \\ without yield  |  regional, \\ national, crop \\ aggregates  |  + expert assumption  |  + regional \\ labour supply  |
+|Belgium (BL24)|Soft wheat|	31.49|	31.26|	31.49|	24.99|	32.73|	53.88|
+|:::|Sugar beet	|  76.25|	77.39|	76.25|	62.19|	48.27|	68.36|
+|:::|Cereals	|  28.23|	32.89|	28.23|	32.78|	28.16|	32.66|
+|:::|Root crops	|  58.75|	65.43|	58.75|	58.8|	64.52|	105.89|
+|Germany (DEA1)|Soft wheat|	36.78|	35.32|	36.78|	36.98|	38.62|	34.46|
+|:::|Sugar beet	|  82.01|	58.99|	82.01|	55.06|	39.61|	43.58|
+|:::|Cereals	|  40.13|	32.63|	40.13|	39.94|	41.65|	35.12|
+|:::|Root crops	|  28.83|	14.23|	28.83|	38.32|	41.26|	0.01|
+|France (FR24)	|Soft wheat|	14.65|	23.3|	23.68|	14.71|	16.5|	13.22|
+|:::|Sugar beet	|  -7.42|	2.24|	-1.68|	11.08|	19.72|	18.5|
+|:::|Cereals	|  10.48|	35.9|	22.7|	15.61|	15.43|	12.7|
+|:::|Root crops	|  11.68|	29.78|	19.42|	17.05|	24.64|	18.43| \\ Source: CAPRI Modelling System
+The Table visualizes the adjustments regarding an implausible labour input coefficient for sugar beet in a French region. The econometric estimation come up with very low or negative values. The HPD solution combining crop specific estimates with corresponding averages of crop aggregates corrects this untrustworthy value to 11.08 h/ha. This value is in an acceptable range but it strikes that in opposite to many other regions the labour input for sugar beet is still less than for soft wheat. After adding equations in the reconciliation procedure that ensure that the relation of labour input coefficients among crops follows an similar “European” pattern the labour input is supposed to be 19.72 h/ha. There is up to now no theoretical or empirical evidence for this similar pattern regarding relation of input coefficients but the results seem to be more plausible when checked with expert knowledge. In the last column bounds on regional labour supply derived from FADN are added which “scales” the regional value. This final result is and is now part of the CAPRI model.
+===Projecting Labour Use===
+For typical applications of CAPRI, regional projections of labour use are needed. Such projections have been prepared as well in the CAPSTRAT project, using a cohort analysis to separate 2 components of changes over time: (1) an autonomous component, which comprises structural changes due to demographic factors such as ageing, death, disability and early retirement, and (2) a non-autonomous component, which incorporates all other factors that influence changes in farm structure and has been analysed econometrically.
+The results of this analysis are loaded in the context of CAPRI task “Generate trend projection” in file baseline\labour_ageline.gms, but only to serve as one type of bounds for labour use in the contrained trends for European regions. Other bounds are derived from engineering knowledge (or assumptions) on plausible labur use per activity which is based on the initial estimation of labour allocation by activity.