Differences

This shows you the differences between two versions of the page.

--- input_allocation [2020/02/13 11:18] – [Input allocation for young animals and the herd flow model] matsz
+++ input_allocation [2020/02/25 08:50] – [Input allocation for fertilisers and nutrient balances] matsz
@@ Line 130: / Line 130: @@
 \begin{equation}
-\sum_{r,fint}\bar{FEDUSE}_{r,fint}PFOD_{r,fint} = \bar{EAAP}_{OFAR,MS}+\bar{EAAP}_{GRAS,MS}
+\sum_{r,fint}\overline{FEDUSE}_{r,fint}PFOD_{r,fint} = \overline{EAAP}_{OFAR,MS}+\overline{EAAP}_{GRAS,MS}
 \end{equation}
+Secondly, the Gross Value Added of the fodder activities is defined as the difference between main revenues (from main fodder yield), other revenues, and total input costs based on the input allocation for crops described above.
+\begin{equation}
+GVAM_{r,fint} = \overline{YIELD}_{r,fint}PFOD_{r,fint}+\overline{OREV}_{r,fint}-\overline{TOIN}_{r,fint}
+\end{equation}
+Other revenues may be from the nutrient value in crop residues. Next, an HDP objective is added which penalises deviations from the a priori mode.
+The a priori mode for the prices of ‘grass’ and ‘other fodder on arable land’ are the EAAP values divided by total production volume which is by definition equal to feed use. The price of straw for feed use is expected to be at 1 % of the grass price.
+Supports for Gross Value Added per activity are centred around 150 % of the value of total inputs as allocated by the rules and algorithm described above, with wide bounds.
+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}
+GVAM_{r,fint} \ge \overline{TOIN}_{r,fint}\overline {gvafac}
+\end{equation}
+The parameter \(gvafac\) is initialised with zero so that first a solution is tried where all activities have positive GVAs. If infeasibilities arise, the factor is stepwise increased until feasibility is achieved, to ensure that estimated fodder prices are giving the minimal number of activities with negative Gross Value Addeds.
+===Calibration of the feed allocation ===
+The allocation of feed to animal activities has been changed several times (like the fertiliser allocation). The most recent version has been developed ((This section draws upon a corresponding Star 2 deliverable and coding which are due in major parts to CAPRI expert Markus Kempen. As Markus was not involved in this documentation, he is released from any responsibility for remaining errors. A more detailed version of this section is offered as [[https://www.capri-model.org/dokuwiki/lib/exe/fetch.php?media=docu_feed_calib.pdf]].)) in the Stable Release 2 (in the following: “Star2”) project which will become also the standard version in the CAPRI trunk at the next opportunity.
+**General concept**
+In the “pre-Star2”((It has to be acknowledged that the specificaiton described in this section is not activated by default in CAPRI task “build regional database” whereas it is active in CAPRI task “Calibrate supply models”. This setting will be changed shortly.))  implementation, based on the CAPRI model procedures, the objective in the data consolidation in tasks “build regional database” (capreg base year) and “baseline calibration supply” (capmod, baseline mode) is to cover the daily needs per animal with the available feed stuff (considering the daily feed intake capacity). In CAPRI most parameters determining the actual requirements of animals can be derived from statistics, e.g. milk yield, final live weight, daily gain, Apart from the uncertainty of statistical data, the calculated requirements can be seen as the “true” requirements in a country or region, as the differences between different animal nutrition literature sources are usually small. Nonetheless uncertainty in the data derived parameters can often lead to an over- or underestimation of the requirements in a range of 5-20% from the computed average need. This uncertainty may be taken into account when specifying the objective function for the required allocation model in a high posterior density (hpd) approach where the uncertainty on feeding requirements is expressed in terms of a standard deviation. This basic approach also underlies the “pre-star2” feed allocation.
+The pre-star2 feed calibration approach also considered two economic indicators that depend on the feed allocation:
+  * Feed costs and
+  * Gross margins, in particular the avoidance of negative gross margins ((Note that this refers to gross margins of animal activties, not to the gross margins of fodder activities which have been addressed in the previous section.))
+These two criteria have been abandoned because technical plausibility was considered more important for the feed allocation than the derived value items. It may be argued that uncertainty in feed prices should not be transferred to the physical coefficients which is a consequence when considering both in the objective. Furthermore, the pmp approach of CAPRI has proven able to cope with negative margins even though it is admitted that they may not be entirely plausible.
+In the pre-star2 CAPRI approach minimum and maximum bounds on specified feeding stuffs are specified to ensure technical plausibility, but to prevent infeasibilities they left considerable degrees of freedom. Additional hard constraints were for lysin and fiber contents of feed. However, a detailed analysis revealed that the purpose of these restrictions to ensure plausible feed ratios, for example regarding the relation of concentrate feed and roughage, was often missed. It has been decided therefore to skip these constraints.
+The revised feed allocation methodology includes several new additional terms in its objective to capture technical plausibility beyond the animal requirements in terms of energy and protein and technical reproducibility of the calibration approach. These will be explained in more detail in the following sections.
+**Equations**
+An overview of the equations used in the old and new feed allocation procedure is given in Table below. The objective function has changed significantly and more details on this will be discussed below. The equations ensuring consistency among production and consumption of feed, as well consistency across regional levels are unchanged.
+**Table 9: Equations used in old and new feed allocation routine**
+^equation^^ ^ ^
+^old^new^description ^comment ^
+|hpdFeed_|hpdFeed_|objective function|changed significantly (see following section)|
+|FEDUSE_|FEDUSE_|Balance for feeding stuff regional| needed to achieve consistency between produced feed and feed input to all animals and among regional layers|
+|FEDUSEA_|FEDUSEA_|Aggregation to regional feed input coefficient to aggregate one |:::|
+|FEDUSES_|FEDUSES_|Fixation for feeding stuff regional in calibration| :::|
+|REQSE_|REQSE_|Requirements of animals written as equality|for energy ENNE and crude protein CRPR |
+|REQSN_| |Requirements of animals written as in-equality |other requirements (lysine, dry matter and fibre)|
+|MINSHR_|		|Maximum feed shares|Constraints on single feed stuff not used as hard bounds in new version |
+|MAXSHR_|		|Minimum feed shares|Constraints on single feed stuff not used as hard bounds in new version |
+|CST_|CST_|Definition of feed cost from feed input coefficients and prices|Feed cost in new version only for monitoring, not in objective or constraints|
+|MEANDEV_|		|Definition of average deviation from requirements for all herds|oversupply by animal type was pulled against the mean oversupply.|
+| |NutContFeed_	|Nutrition content in the feed aggregates supplied to an animal category|nutrient content (per kg dry matter) is part of the objective|
+| |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|
+The four additional equations developed in the new feed allocation procedure are described in more detail in the following.
+__NutContFeed_ __
+{{::code_p_71.png?600|}}
+For nutrient content (energy, crude protein) in the total feed mix or in concentrate feed recommendations are frequently given in the animal nutrition literature. The equation NutContFeed_ calculates this based on the estimated feed input coefficients and the data on nutrient content and dry matter per feeding stuff. A small number is added to the denominator to avoid division by zero (e.g. while gams is searching for a feasible solution)
+__FedAggr_ __
+{{:code_p_72.png?600|}}
+An aggregation of specific feeding stuff to aggregates (roughage, concentrates) is done since prior shares as well as minimum and maximum shares are more often found in the literature for aggregates than for single feedstuffs. The mapping is shown in Table below. It has been specified basically by putting into the “other” category all “special” items. Therefore, straw is a component of this “other” category rather than “roughage”.
+**Table 10: Mapping feeding stuff to feed aggregates**
+^ ^FGRA^FMAI^FOFA^FROO^FCOM^FSGM^FSTR^FCER^FPRO^FENE^FMIL^FOTH^
+^FeedRough|  X  |  X  |  X  |  X  | | | | | | | |
+^FeedCons| | | | | | | |  X  |  X  |  X  |  X  | |
+^FeedOth| | | | |  X  |  X  |  X  | | | | |  X  |
+^FeedTotal|  X  |  X  |  X  |  X  |  X  |  X  |  X  |  X  |  X  |  X  |  X  |  X  |
+__ FeedAggrShare_ __
+{{:code_p_72_2.png?600|}}
+__ MeanFeedTotal_ __
+{{:code_p_72_3.png?600|}}
+One of the aggregates calculated is the total feed intake per animal. It is expected that, inspite of regional differences in fodder supply, this total feed intake is mostly a genetic characteristic of animals and hence should not vary markedly across regions. To influence this distribution in the objective, the average across regions needs to be computed.
+**Objective function**
+The objective function is extensively revised compared to the pre-star2 versions. The criteria to be optimised are now:
+  - coverage of animal requirements with feed
+  - regional variation of certain feed input coefficients
+  - concentration of energy and protein in feed mix
+  - shares of feed aggregates (roughage, concentrates, other) in total feed mix
+  - feed input coefficients of all FEED bulks receive prior expectations
+The parameters in the objective function are partly means and imputed standard deviations AND so-called “soft” upper and lower limits. The “soft” limits increase the penalty significant when the solver picks values close to or even beyond them.
+__ Coverage of animal requirements with feed __
+{{: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.
+__Deviation of sub regional total feed intake from regional average__
+{{:code_p_73_2.png?600|}}
+As argued above, we expect that total feed intake in DRMA is mostly a genetic characteristic of animals and hence should not vary markedly across regions. Deviations of (sub-)regional feed intake from the associated regional average (NUTS1 or MS) are therefore penalised.
+__Deviations of sub regional feed input coefficients of non-ruminants from regional average__
+{{:code_p_73_3.png?600|}}
+As the comment explains, non-ruminants should have a rather standardised diet across regions.
+__Concentration of energy and protein in feed aggregates__
+{{:code_p_73_4.png?600|}}
+This part of the objective functions tries to minimize the difference between the nutrient content of feed aggregates (v_nutContFeed) and the expected nutrient (p_nutContFeed(…”MEAN”)) coming from literature or IFM-CAP. To avoid unreasonably large deviations from MEAN, lower and upper limits are introduced (MIN, MAX), where the penalty in the objective function increases significantly. The extra penalties rely on the GAMS built-in smooth approximation of the min operator (Chen-Mangasarian smoothing function ncpcm). The values for mean and upper and lower limits are presented in the table below.
+**Table 11: Expected nutrient content in total feed per animal category**
+^ ^  Energy  ^^^  Crude protein  ^^^
+^ ^  MEAN  ^  MIN  ^  MAX  ^  MEAN  ^  MIN  ^  MAX  ^
+^  DCOL  |  6.7  |  	6.4	  |  7  |  	0.155  |  	0.14  |  	0.17  |
+^  DCOH  |  6.8  |  	6.6	  |  7.2  |  	0.155  |  	0.14  |  	0.17  |
+^  BULL  |  6.7  |  	6.2	  |  7  |  	0.155  |  	0.14  |  	0.17  |
+^  BULH  |  6.8  |  	6.4	  |  7.2  |  	0.155  |  	0.14  |  	0.17  |
+^  HEIL  |  6.3	  |  5.8	  |  7  |  	0.155  |  	0.14  |  	0.17  |
+^  HEIH  |  6.8	  |  6.2	  |  7.2  |  	0.155  |  	0.14  |  	0.17  |
+^  SCOW	 |  6.4	  |  6  |  	7	  |  0.155  |  	0.14  |  	0.17  |
+^  HEIR  |  6.4	  |  6  |  	7	  |  0.155  |  	0.14  |  	0.17  |
+^  CAMF  |  6.6	  |  6.6	  |  7.2  |  	0.155  |  	0.14  |  	0.17  |
+^  CAFF  |  6.6	  |  6.6	  |  7.2  |  	0.155  |  	0.14	  |  0.17  |
+^  CAMR  |  6.6	  |  6.6	  |  7.2  |  	0.155  |  	0.14	  |  0.17  |
+^  CAFR  |  6.6	  |  6.6	  |  7.2	  |  0.155  |  	0.14	  |  0.17  |
+^  PIGF  |  8	  |  7.8	  |  8.2  |  	0.155  |  	0.14	  |  0.17  |
+^  SOWS  |  8	  |  7.8	  |  8.2	  |  0.155  |  	0.14	  |  0.17  |
+^  SHGM  |  6.3	  |  5.8	  |  7	  |  0.155  |  	0.14  |  	0.17  |
+^  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  |
+__Shares of feed aggregates in total feed intake in DRMA __
+{{::code_p_74.png?600|}}
+The shares of roughage and concentrate feed are only controlled by upper (p_maxFeedShare) and lower (p_minFeedShare) limits. The literature suggests that ruminants can digest at most 40% of concentrate feed (or at least 60% roughage), and perhaps 45% for activity DCOH. The upper and lower limits are partially taken from IFM-CAP, literature and expert knowledge of Markus Kempen (Assumed values in table 12).
+**Table 12: Maximum and minimum shares of feed aggregates**
+^ ^  Maximum shares  ^^  Minimum shares  ^^
+^ ^  FeedRough ^  FeedCons  ^  FeedRough  ^  FeedCons  ^
+^  DCOL  |  	0.85  |  	0.4  |  	0.75  |  	0.1  |
+^  DCOH  |  	0.7  |  	0.45  |  	0.6  |  	0.1  |
+^  BULL  |  	0.8  |  	0.4  |  	0.65  |  	0.1  |
+^  BULH  |  	0.8  |  	0.4  |  	0.65  |  0.1  |
+^  HEIL  |  	0.9  |  0.3	  |  0.65  |  	0.1  |
+^  HEIH  |  	0.9  |  	0.3  |  	0.7	  |  0.1  |
+^  SCOW  |  	0.95  |  	0.3	  |  0.7	  |  0.05  |
+^  HEIR  |  	0.9  |  	0.3	  |  0.7  |  	0.05  |
+^  CAMF	 | |  0.3   | |  	0.15  |
+^  CAFF	 | |  0.3   | |  	0.15  |
+^  CAMR	 | |  0.3   | |  	0.1  |
+^  CAFR	 | |  0.3   | |  	0.1  |
+^  PIGF	 | |  1	  | |  	0.95  |
+^  SOWS	 | |  1	  | |  0.9  |
+^  SHGM	 | |  0.3  | |  0.05  |
+^  SHGF	 | |  0.3  | | 	0.05  |
+^  HENS	 | | | |  0.99  |
+^  POUF	 | | | |  0.99  |
+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.
+__ Feed input coefficients for single feed bulks __
+{{::code_p_75.png?600|}}
+Apart from plausibility of the results a second objective of the revision has been reproducability. The previous specification essentially gave random results within the feasible set because no prior expectations had been specified. This has been revised with penalties for deviations of feed input coefficients from their assumed MEAN (specification to be explained below). However, just like is the case for the nutrient content of feed aggregates or their shares in the total, this prior information has to be considered quite imprecise which is reflected in rather low factors (1E2) attached to these terms. The penalties are increased if the solver tries to approach or exceed “soft” lower or upper limits. As the lower limits also turned out useful to prevent the solver from ending up in infeasible corners a higher factor has been attached to them (1E5).
+It should also be reported that in many cases of infeasible solutions encountered in the extensive testing of this and previous specifications the last iteration result reported from the solver had often all feed input coefficients for some animal type zero or near zero. To avoid these cases the solution attempt starts with hard lower bounds:
+{{:cope_p_76.png?600|}}
+In case of infeasibilities after x trials these are removed:
+{{:code_p_76_2.png?600|}}
+This procedure led to an acceptable or at least considerably improved stability of the feed calibration in tasks “build regional database” as well as “baseline calibration supply models”.
+**Priors for feed input coefficients**
+The priors for feed input coefficients are specified in a new include file capri\gams\feed\fedtrm_prior.gms:
+{{:code_p_76_3.png?600|}}
+The shares of feed aggregates in the diets of animal types may build upon recommendations from the literature (see the previous section). They are adjusted to be in line with the statistical ex post data or the baseline projections, giving the “adjusted” aggregate feed input coefficients shown in the code snippet above.
+However, feed recommendations do snot exist for //single// feedstuffs because these are easily substitutable. Stability of the feed calibration requires however some priors. A simple default assumption made has been therefore: the composition of feed aggregates in terms of their components is the same for all animals (corresponding to the regional average). This is evidently a simplification such that the penalties for deviations from these priors have been set rather low to achieve both the desired stabilization effect while not competing too strongly with other components of the objective.
+**Nutrient contens and requirements**
+For the nutrient contents and requirement functions comparisons with IFM-CAP showed a good consistency such that the pre_star2 specifications were retained.
+**Calibration of PMP terms**
+The calibration of pmp terms for feeding coefficients is unchanged. But the constraints of minimum and maximum shares of feeding stuffs and some contents (fibre, lysin, etc) have been removed. The pmp terms have therefore a considerably increased role in simulations: Whereas the feed mix was so far steered by technical constraints, at least to a significant extent, all of these are gone except the equality constraints on feed energy and protein. The feed mix in simulation is therefore critically determined by the feed related pmp terms. In case of undesirable simulation behaviour it might be considered to include at least bounds for the total feed intake in terms of dry matter where feed recommendations apparently provide some bounds for plausible values.
+==== Input allocation for fertilisers and nutrient balances ====
+In the following section, the existing environmental indicators in CAPRI, planned and already achieved improvements, and possible further extensions are briefly discussed. It should be noted that CAPRI is basically a regionalised agricultural sector model, thus concentrating on the modelling of aggregated reactions of agricultural producers and consumers to changes in long term shifters as technical progress, income changes and CAP programs. Most indicators are rather robust pressure indicators and can be calculated easily based on fixed parameters approaches from the endogenous variables of the regional aggregate supply models. Accordingly, economic (dis)-incentives can be linked to the pressure indicators or further passive indicators can be introduced or the current ones changed easily.
+Currently, CAPRI estimates the following environmental indicators:
+  - Greenhouse gas emissions from enteric fermentation (CH4), manure management (CH4, N2O), manure and mineral fertilizer application to soils (N2O, CO2), grazing animals (N2O), crop residdues (N2O), cultivation of histosols (N2O, CO2), indirect emissions from the volatilization of ammonia (N2O), indirect emissions from leaching and runoff (N2O), land use change emissions from carbon stock changes in above and below ground biomass (CO2), soils carbon stock changes (CO2,N2O), the burning of biomass (CH4,N2O). For details see (Pérez 2005) and Leip et al. (2010).
+  - Ammonia emissions from manure management, manure and mineral fertilizer application (Leip et al (2010).
+  - Nitrate Leaching and Runoff (Leip et.al. (2010)
+  - Soil erosion
+Moreover, CAPRI provides the complete nutrient cycle for nitrogen and carbon, while for phosphate and potassium only the separate nutrient balances for crops and feed are considered. An important limitation of phosphate and potassium balancing is that output at tail is unrelated to feed intake because fixed coefficeints are used.
+===Nutrient balances for NPK and Nitrates Leaching===
+Nutrient balances in CAPRI are built around the following elements:
+  * Export of nutrient by harvested material per crop –depending on regional crop patterns and yields, and livestock products, and crop residues.
+  * Output of manure at tail –depending on animal type, regional animal population and animal yields, as final weights or milk yields (see section on Output at tail).
+  * Manure imports and exports (to the region)
+  * Input of mineral fertiliser –as given from national statistics at sectoral level.
+  * Input of crop residues, biological fixation, atmospheric deposition
+  * Emissions (NH3, NOx, N2, N2O, CO2, CH4, NO3, C from soil erosion) only for nitrogen and carbon, and removals (carbon sequestration) only for carbon
+The numbers in the following table are based on older methodology and coefficients but nonetheless provide a useful illustration of the accounting. Details on the emissions are provided in the respective sections on ammonia and greenhouse gases. Details on the inputs in the sections on NPK output at tail and NPK input distribution.
+**Table 13: Nitrogen balance (EU 15, year 2001)**
+|  **INPUT**  |||  **OUTPUT**  |||
+|Import of nitrogen by anorganic fertiliser|  a  |  68.2  |Export of nitrogen with harvested material  |  f  |  80.95  |
+|Import of nitrogen by organic fertiliser (in manure)|  b  |  77.31  |Nitrogen in ammonia, NOx, N2O and runoff losses from manure fallen on grazings|  g  |  2.08  |
+|Nitrogen from biological fixation*|  c  |  2.89  |Nitrogen in ammonia, NOx and N2O losses from manure in stable|  h  |  7.13  |
+|Nitrogen from atmospheric deposition|  d  |  14.36  |Nitrogen in ammonia, NOx, N2O,N2 and runoff losses from manure storage|  i  |  2.53  |
+| | | |Nitrogen in ammonia, NOx, N2O and runoff losses from manure application on the field|  j  |  8.34  |
+| | | |Nitrogen in ammonia, NOx, N2O and runoff  losses from organic fertiliser|  k=g+h+i+j  |  20.08  |
+| | | |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**  |
+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.
+**NPK output at tail**
+The output of P and K at tail is estimated based on typical nutrient contents of manure:
+**Table 14: Nutrient content in manure in kg pure nutrient/m³**
+| |  **P**  |  **K**  |
+|**Cattle**|  2.0  |  5.5  |
+|**Swine**|  3.3  |  3.3  |
+|**Poultry**|  6.3  |  5.1  |
+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).
+For the different types of cattle activities, it is hence necessary to determine the average live weight and the length of the production process.
+For calves fattening (CAMF, CAFF), the carcass weight is divided by 60 % in order to arrive at final weight and a start weight of 50 kg is assumed. Daily weight increases are between 0.8 kg/day and 1.2 kg/day and depend proportionally on average stocking densities of cattle in relation to the average EU stocking density for which a daily weight increase of 1 kg/day is assumed. Total emissions per animal hence increase with final weights but decrease per kg of meat produced for intensive production systems with high daily weight increases. The same relationship holds for all other animal categories discussed in the following paragraphs.
+For calves raising (CAMR, CAFR), two periods are distinguished. From 50 to 150 kg, a daily increase of 0.8 kg/day is assumed. The remaining period captures the growth from 151 to 335 kg for male and 330 kg for female calves, where the daily increase is between 1 kg/day and 1.4 kg/day, again depending on stocking densities.
+The bull fattening process captures the period from 335 kg live weight to final weight. Daily increases are between 0.8 kg/day up to 1.4 kg/day, depending on final weights and stocking densities. Carcass weights as reported in the data base are re-converted into live weight assuming a factor of 54% for low and 57% for higher final weights.
+The heifers fattening process captures the period from 300 kg live weight to final weight, assuming a daily increase of 0.8 kg/day. Carcass weights, as reported in the data base, are re converted into live weight assuming a factor of 54 % for low and 57 % for higher final weights.
+Suckler cows are assumed to be whole year long in production and weight 550 kg, whereas milk cows are assumed to have a weight of 600 kg and are again for 365 days in production. Additional data relate to the additional NPK output per kg milk produced by cows and are taken from the RAUMIS model:
+**Table 15: Additional emission of NPK per kg of milk produced**
+|N|0.0084|
+|P|0.004|
+|K|0.0047|
+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.
+For pig fattening processes, it is assumed that 1.9 m³ are produced per ‘standard’ pig with a final carcass weight of 90 kg at 78 % meat content, a starting weight of the fattening period of 20 kg (weight of the piglet), a production period of 143 days and 2.3 rounds per year. The actual factors used depend on tables relating the final weight to typical daily weight increases.
+For poultry, it is assumed that 8 m³ of manure are produced by 100 laying hens, which are assumed to weigh 1.9 kg and stay for 365 days in production. For poultry fattening processes, a fattening period of 49 days to reach 1.9 kg is assumed.
+For sheep and goat used for milk production or as mother animals, the cattle factors are applied by assuming a live weight of 57.5 kg and 365 days in production. For fattening processes, a daily increase of 200 kg and a meat content of 60 % of the carcass weight are assumed.
+The nitrogen emission factors from animal activities are coupled to crude protein intake (IPCC 2006), and hence the requirement functions for animal activities according to a //farm gate approach//. According to the literature (Udersander et al. 1993), there is a relation of 1 to 6 between crude protein and N in feeding. By combining this information with N retention rates per animal activity (IPCC 2000, Table 4.15), manure production rates can be estimated (N intake minus N retention). A specific advantage of that approach is the fact that gross nutrient surplus is not longer depending on assumption on fodder yields and manure emissions factors. Changing the fodder yields in the combined farm-gate and soil-balance approach in CAPRI will change both nutrient retention in crops and nutrient deliveries from manure by the same values, leaving the balance unchanged.
+**Table 16: Crude protein intake, manure production and nitrogen retention per head (EU 15, year 2001)**
+| |  Crude protein  |  Nitrogen in manure  |  Nitrogen retention  |
+|BULH|  1.7  |  83.8  |  0.07  |
+|BULL|  1.4  |  31.7  |  0.07  |
+|CAFF|  0.8  |  21.5  |  0.07  |
+|CAFR|  0.9  |  38.4  |  0.07  |
+|CAMF|  0.8  |  20.2  |  0.07  |
+|CAMR|  0.9  |  38.6  |  0.07  |
+|DCOH|  4.3  |  210.1  |  0.20  |
+|DCOL|  2.7  |  129.4  |  0.20  |
+|HEIH|  1.5  |  64.4  |  0.07  |
+|HEIL|  1.2  |  20.6  |  0.07  |
+|HEIR|  1.7  |  95.9  |  0.07  |
+|HENS (1000 units)|  21.2  |  900.9  |  0.30  |
+|PIGF|  0.4  |  7.0  |  0.30  |
+|POUF (1000 units)|  7.6  |  52.9  |  0.30  |
+|SHGM|  0.2  |  13.7  |  0.10  |
+|SHGF|  0.1  |  2.0  |  0.10  |
+|SOWS|  0.9  |  36.4  |  0.30  |
+|SCOW|  1.5  |  87.2  |  0.07  |
+**Calibration of the input allocation of organic and inorganic NPK**
+The input allocation of organic and inorganic fertilizer determines how much NPK organic and inorganic fertiliser is applied per ha of a crop, simultaneously estimating the NPK availability in manure as well as parameters describing the degree of overfertilisation. Firstly, nutrient export by the harvested material is determined, based on the following factors:
+**Table 17: Exports of nutrients in kg per ton of yield or constant Euro revenues**
+| |  **N**  |  **P**  |  **K**  |
+|**Soft wheat**|  20  |  	8  |  	6  |
+|**Durum wheat**|  23  |  8  |  	7  |
+|**Rye**|	15  |  8  |  	6  |
+|**Barley**|	15  |  8	  |  6  |
+|**Oats**|	15.5  |  8  |  	6  |
+|**Grain maize**|	14  |  8  |  	5  |
+|**Other cereals**|	 18  |  	8  |  	6  |
+|**Paddy rice**|  	22  |  	7	  |  24  |
+|**Straw**|	  6  |  	3  |  	18  |
+|**Potatoes**|	  3.5  |  	1.4  |  	6  |
+|**Sugar beet**|  	1.8  |  	1.0  |  	2.5  |
+|**Fodder root crops**|  	1.5  |  	0.09  |  	5.0  |
+|**Pulses**|	  4.1  |  	1.2  |  	1.4  |
+|**Rape seed**|  	33  |  	18  |  	10  |
+|**Sunflower seed**|  	28  |  	16  |  	24  |
+|**Soya**|  	58  |  	16  |  	24  |
+|**Other oil seeds**|  	30  |  	16  |  	16  |
+|**Textile crops**|  	3  |  	8	  |  15  |
+|**Gras**|  	5  |  	1.5  |  	3.5  |
+|**Fodder maize**|  	3.2  |  	2.0  |  	4.4  |
+|**Other fodder from arable land**|  	5.5  |  	1.75	  |  3.75  |
+|**Tomatoes**|	  2.0  |  	0.7  |  	0.6  |
+|**Other vegetables**|	  2.0  |  	0.7	  |  0.6  |
+|**Apples, pear and peaches**|	   1.1  |  	0.3  |  	1.6  |
+|**Citrus fruit**|  	2.0  |  	0.4  |  	1.6  |
+|**Other fruits**|  	2.0  |  	0.4  |  	1.7  |
+|**Nurseries, flowers, other crops, other industrial crops**|  	65  |  	22	  |  20  |
+|**Olive oil**|	  4.5  |  	1.0  |  	0.5  |
+|**Table olives**|  	22.5  |  	5.0  |  	2.5  |
+|**Table grapes**|  	1.9  |  	1.0  |  	3.1  |
+|**Table wine, other wine**|  	1.9/0.65	  |  1.0/0.65	  |  3.1/0.65  |
+|**Tobacco**|  	30.0  |  	4.0  |  45.0  |
+The factors above are applied to the expected yields for the different crops constructed with the Hodrick Prescott filter explained above. Multiplied with crop areas, they provide an estimate of total nutrient export at national and regional level (right hand side of the figure below). The maximum exports per ha allowed are 200 kg of N, 160 kg of P and 140 kg of K per ha.
+Ex post, the amount of nutrients found as input in the national nutrient balance is hence ‘known’ as the sum of the estimated nutrient content in manure plus the amount of inorganic fertiliser applied, which is based on data of the European Fertiliser Manufacturer’s Association as published by FAOSTAT. In order to reduce the effect of yearly changes in fertilizer stocks, three year averages are defined for the NPK quantities demanded by agriculture.
+For the nitrogen balance, losses of NH3, N2O, NOx, N2 are handled as in MITERRA-Europe. The remaining loss to the soil, after acknowledging surface run-off, is disaggregated with leaching fractions into leaching or denitrification in soil. Atmospheric sources of N are taken into account as well (for details see section on nutrient balances).
+Figure below offers a graphical representation of these relationships.
+**Figure 6. Ex-post calibration of NPK balances and the ammonia module**
+{{::figure_6.png?600|}}
+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}
+\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.