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--- input_allocation [2020/02/24 10:22] – [Input allocation for fertilisers and nutrient balances] matsz
+++ input_allocation [2020/02/25 08:50] – [Input allocation for fertilisers and nutrient balances] matsz
@@ Line 150: / Line 150: @@
 \begin{equation}
-GVAM_{r,fint} \ge \overline{TOIN}_{r,fint}\overline {gvafac} \text PLATZHALTER EQUATION 37
+GVAM_{r,fint} \ge \overline{TOIN}_{r,fint}\overline {gvafac}
 \end{equation}
@@ Line 367: / Line 367: @@
 **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.