update of the calculation of metabolizable energy requirements … · 2011-09-12 · h.-d. haenel,...

H.-D. Haenel, U. Dämmgen, P. Laubach, C. Rösemann / Landbauforschung - vTI Agriculture and Forestry Research 3 2011 (61)217-228 217

Update of the calculation of metabolizable energy requirements for pigs in the German agricultural emission inventory

Hans-DieterHaenel*,1 UlrichDämmgen*,PetraLaubach**,2andClausRösemann*

* JohannHeinrichvonThünenInstitute(vTI),InstituteforAgriculturalClimateResearch,Bundesallee50,38116Braunschweig,Germany

** Association for Technology and Structures in Agriculture (KTBL e.V.), Bartningstr.49,64289Darmstadt,Germany

Abstract

ThecalculationoftheenergyrequirementsofpigsusedintheGermanagriculturalemissioninventoryisupdatedonthebasisoftherecommendationsworkedoutbytheGermanSocietyofNutritionPhysiology(GfE).Atthesametime thenumeric solutions hitherto used in the calcula-tions of energy requirements of weaners and fatteningpigsintheemissioninventoriesarereplacedbyanalyticalsolutions.This results insimplifications in thecalculationprocedures.In the inventory this leads to reduced energy require-

ments for fattening pigs. However, the energy require-mentsforsows,weanersandboarsincrease.

Keywords: pigs, energy requirements, model, emission in-ventory

Zusammenfassung

Aktualisierung der Berechnung des Bedarfs an um-setzbarer Energie von Schweinen im deutschen land-wirtschaftlichen Emissionsinventar

DieBerechnungdesBedarfsanumsetzbarerEnergiefürSchweineimdeutschenlandwirtschaftlichenEmissionsin-ventarwirdaktualisiert.GrundlagesinddievomAusschussfürBedarfsnormenderGesellschaftfürErnährungsphysi-ologie(GfE)erarbeitetenRichtwerte.Gleichzeitigwerdendie bisher im Emissionsinventar üblichen numerischenLösungenderBerechnungendesEnergiebedarfsfürAuf-zuchtferkelundMastschweinedurchanalytischeLösungenersetztunddamitdieRechenverfahrenvereinfacht.ImInventarergebensichdarausfürMastschweineeine

VerringerungdesEnergiebedarfs,fürSauen,Aufzuchtfer-kelundZuchteberjedochErhöhungen.

Schlüsselwörter: Schweine, Energiebedarf, Modell, Emis-sionsinventar

218

1 Introduction

Agricultural production involves the emission of tracegaseswhoseeffectsontheatmosphereandtheenviron-mentmaybeadverse.Attemptstoreducetheseemissionspresupposetheirdetailedquantificationinawaythatal-lowsfortheidentificationandevaluationoftherelevantprocesses.Asemissionreductiongoalsarebeingdiscussedininternationalboards,therespectivepartiesusestandardapproaches todescribe andquantify emissions. Inordertoavoiddistortionofthemarkets,internationalguidancedocumentswereestablishedthatallowtheassessmentofemissionsandthedescriptionofemissionexplainingvari-ablesinaconsistentway(greenhousegases:IPCC,2006;airpollutants:EMEP/EEA,2009).Emissionshavetobereportedasconsistenttimeseries

fortheperiodfrom1990onwards.Forkeysources,calcu-lationsandreportinghavetobedetailed.Hencefatteningpigswillbetreatedmoresophisticatedthanboars.Atpresent,anattemptisbeingmadetobetterdescribe

emissions frompigproduction, includingthedescriptionof feed composition (Dämmgen et al., 2011), updatingemission factors (Dämmgenet al., 2010a) and technicalmeasurestoreduceemissionsfromhouses(Dämmgenetal.,2010b).Allemission ratesare related toexcretion rates.These

aredependingon feed intake rateswhicharegovernedbytheenergyandnutrientrequirementsoftherespectiveanimals.

Thisworkdescribesindetailtheassessmentoftheen-ergyrequirementsinpigproduction.Itisrestrictedtothefractionofenergythatcanbemetabolized(metabolizableenergy,ME).Hitherto, the assessment of energy requirements in pig

production in the German agricultural emission inventorywasbasedondataprovidedinGfE(1987).Meanwhile,therespective datawere updated and themethods improved(GfE,2006).Thecomprehensiverevisionofthedescriptionofemissionsfrompigproductionmakesuseofthisnewedition.Toalargeextent,theliteratureusedinGfE(2006)was

publishedduring the time spanunderlying the emissioninventory(theyearsfrom1990onwards).Hence,itisas-sumedthatthedataandmethodscompiledinGfE(2006)are representativeof thepast twodecadesandthat thecalculationproceduresderivedfromGfE(2006)areappli-cabletoalltheyearssince1990.Thisworkappliesandtransformstherelationsprovided

inGfE(2006)sothattheymeettheneedsoftheagricul-turalemissioninventory.

2 Definition of pig subcategories

Theassessmentofenergyrequirementsiscarriedoutforanimalpopulationswithsimilarfeeding.However,officialGermananimalsurveydatarelyonadifferentiationofani-malsaccordingtoweights.Hence,thesurveydatahavetobetransformedtofitintoenergyrequirementcalculationroutines.Table1comparesthecategoriesusedintheoffi-cialGermansurveyandintheGermanemissioninventory(seeHaeneletal.,2010).

Table1:

Pigs,categorizationandcharacterizationofsubcategories

descriptorintheofficialsurvey typea subcategoryintheemissioninventory weight1b weight2b

(inkganimal-1)

piglets ---c suckling-pigs 1.5 8

we weaners 8 variablewfin, we

youngpigslighterthan50kgliveweight

fp fatteningpigs variablewfin, we variablewfin, we

fatteningpigs50to80kg

fatteningpigs80to110kg

fatteningpigsheavierthan110kg

youngsowsgestating

so sows meanweight:220othersowsgestating

youngsowsnotgestating

othersowsnotgestating

boars bo breedingboars meanweight:200

atype:codeusedtodescribetheanimalcategoriesintheGermaninventory.bweight1:weightatthebeginningoftherespectiveperiod,weight2:weightattheendoftherespectiveperiod;wfin:variablefinalweight.csuckling-pigsdonotconstituteaseparateanimalcategory.Theyareaccountedforwithinthecalculationsofenergyandfeedrequirementsofthesows(seeHaeneletal.,2011)

H.-D. Haenel, U. Dämmgen, P. Laubach, C. Rösemann / Landbauforschung - vTI Agriculture and Forestry Research 3 2011 (61)217-228 219

The subcategory “sows” covers all subcategories ofsows for breeding irrespective of their age andweight.Thecalculationofenergyandfeedrequirementsincludesthesuckling-pigsastheydonotconstituteaseparateani-malcategoryintheinventory(seeHaeneletal.,2011).Weanersareyoungpigsbetweenweaningandthebe-

ginningoffattening.Intheemissioninventory,thislifes-panisassumedtobeginatananimalweightofabout8kganimal-1.Itendswithweightsrangingfrom25toapprox.30kganimal-1 (dependingonyearandregion).Dataforwfin, weareavailableforeachyearanddistrict.Fatteningpigsareallpigsinthefinalfatteningstages,

i.e. with weights above about 25 to 30 kg animal-1 tillslaughtering(105to120kganimal-1liveweight).Again,dataforwfin, fpareavailableforeachyearanddistrict.Forsowsameanweightof220kganimal-1isestimated

asdiscussedbelow.Forbreedingboars,ameanliveweightof200kgani-

mal-1isassumed(expertjudgmentE.Schulz).Thecategoriesusedintheinventoryaredescribedinthe

subsequentchapters.ThevariableanimalweightsusedinTable1fortheinventorycategory“weaners”and“fatten-ingpigs”areobtainedfromofficialstatistics.Theweightdataforpigletsarebasedonexpertjudgment,whilethemeanweightsofsowsandboarswillbediscussedintherespectivechapters.

3 Sows

3.1 Total energy requirements during one reproduction cycle

Thetotalmetabolicenergy(ME)requirementsofasowduringoneround, i.e.duringonereproductioncycle, isgiven by Equation (1). It reflects that the reproductioncyclecomprisestwogestationphases,thelactationphaseandthetimespanbetweenweaningandcovering.

wtclact2 gest,1 gest,sow MEMEMEMEME ΣΣΣΣΣ

whereΣME sow totalmetabolizableenergyrequiredforone round(MJanimal-1round-1)ΣMEgest, 1 metabolizableenergyrequiredduringgestation phase1(inMJanimal-1round-1)ΣMEgest, 2 metabolizableenergyrequiredduringgestation phase2(inMJanimal-1round-1)ΣMElact metabolizableenergyrequiredduringlactation (inMJanimal-1round-1)ΣMEwtc metabolizableenergyrequiredbetweenwean- ingandcovering(inMJanimal-1round-1)

Thephase-relatedenergyrequirementswillbediscussedinthesubsequentchapters.

3.1.1 Energy requirements during gestation

The energy requirements for the development of theconception products, the uterus and the compensationofweightlossesduringthepreviousgestationhavetobetakenintoaccountinadditiontotheenergyrequirementsformaintenance(GfE,2006,pg.34f).ThegestationphasecanbesubdividedintotwoseparatephaseswithdifferentmeansofdailyMErequirementsMEgest, 1andMEgest, 2 (withjtheindexofday).GfE(2006),Table4.13,providesMEgest, 1andMEgest, 2data

dependingontheordinalnumberofpregnancyandtheweight loss during lactation. As no official statistics areavailableonthesecriteria, theGfEdatahavebeenaver-agedwithidenticalweightsyieldingMEgest, 1=33.3MJd

-1andMEgest, 2=40.7MJd

-1fortherespectiveperiods.TheMEdatainTable4.13inGfE(2006)representthe

energyrequirementswhenthesowisexpectedtogivebirthto13piglets.Atpresent,thispigletsnumberperlittermarks theupper limit inGermanpigletproduc-tion.Hence,theuseofMEgest, 1andMEgest, 2wouldavoidunderestimationof the energy requirements used fortheconstructionofemissiontimeseries.

3.1.2 Energy requirements during lactation

Duringthelactationperiod,energyisrequiredformain-tenanceandmilkproduction.Equation(2)definestheto-taldailyenergyrequirementsforthesow-pigletssystemasitisappliedintheinventory.

raisedpiglets,milkjsow, m,jlact, nMEME ⋅ η (2)

whereMElact, j dailymetabolizableenergyrequiredondayj duringlactation(inMJanimal-1d-1)j indexofdayMEm, sow, j dailymetabolizableenergyrequiredformain- tenanceondayj(inMJanimal-1d-1,seebelow)ηmilk specificmetabolizableenergyrequiredformilk production(inMJpiglet-1d-1,seebelow)npiglets, raised numberofpigletsraisedpersowandbirth(in piglet,seebelow)

Thetotalenergyrequirementsformaintenanceduringagestationphasearecalculatedfromthedailyrequirementsformaintenancewhicharegiven inGfE (2006),pg.23,Equation7:

j met,sow m,ME,jsow,m, wME ⋅η (3)

(1)

220

whereMEm, sow, j metabolizableenergyrequiredformaintenance fordayj(inMJanimal-1d-1)j indexofdayηME, m, ,sow specificmetabolizableenergyrequiredfor maintenance(ηME, m, ,sow=0.44MJperkgof metabolicweight,seefootnotetoTable4.13 inGfE,2006)wmet, j metabolicweightondayj(inkganimal-1)

The metabolic weight, wmet, j, is a function of animalweight1:

75.0

unit

jsow,unitj met,

⋅ww

ww (4)

wherewmet, j metabolicweightondayj(inkganimal

-1)wsow, j dailymeanofliveweightondayj(inkganimal

-1, seebelow)wunit unitweight(wunit=1kganimal

-1)

Intheinventorythedailymeanofliveweight,wsow, j,isreplacedbythesowweightaveragedovertheentirere-productioncycle,seeChapter3.3.Thespecificmetabolizableenergyrequiredformilkpro-

duction,ηmilk,canbederivedfromthedataprovidedinthefootnotestoTable4.17inGfE(2006),pg.81:productionofmilkperkgpigletweightgain(4.1kgkg-1),energycontentofmilk (5.0MJkg-1),percentageofmetabolizableenergyusedformilkproduction(70%).Thesedataleadtoηmilk=6.8MJpiglet-1d-1,whenbeingcombinedwithanaverageestimate for daily pigletweight gain of 232 g piglet-1 d-1whichisobtainedfrombirthandweaningweightsandthedurationofthelactationphase(seeTable2).Thenumberofpigletsper litter canbededuced from

the number of piglets raised per sow and year and thedurationofaproductioncycle(seeTable2).

α

τ roundyearpiglets,raisedpiglets, ⋅ nn (5)

wherenpiglets, raised numberofpigletsraisedpersowandbirth(in piglet)npiglets, year numberofpigletsraisedpersowandyear birth(inpiglet)τround durationofpigletproductioncycle(indround-1)α timeunitsconversionfactor(α =365da-1)

1 Formally, Equation (4)differs from the respectivedescriptiongiven inGfE(2006), pg. 23, Equation 7, i. e. LM0.75where LM is animalweight. ThetermLM0.75wouldimplyunitsofkg0.75whichisnotallowedintheSIsystem.ThisproblemisavoidedbyEquation(4)whichneverthelessyieldsthesamenumericresultlikeLM0.75.

Note that Equation (2) does not explicitly account forthe possible gains of metabolizable energy by weightlossesduringlactationand/oradditionalpigletfeed(GfE,2006, pg. 38) as there are no official statistical data todescribethesecontributions.However,Equation(2)coversawiderangeofMErequirementsdataprovidedinTable4.17inGfE(2006).Henceitisassumedthat,onaverage,Equation(2)describestheGermansituationadequately.Table2listsresultsofEquation(2)obtainedforarange

ofpigletnumbers.

3.1.3 Energy requirements between weaning and covering

For the period between weaning and covering, GfE(2006), pg. 72, assume the same total daily energy re-quirementsasforadvancedgestation.

2gest,jwtc, MEME (6)

whereMEwtc, j dailymetabolizableenergyrequiredduringthe phase“weaningtocovering”(inMJanimal-1d-1)j indexofdayMEgest, 2 dailymetabolizableenergyrequiredduring advancedgestation(inMJanimal-1d-1),see Chapter3.1.1

3.2 Cumulative energy requirements and comparison with the former approach

Table 2 lists the daily requirements for the differentphases(seeChapters3.1.1to3.1.3)aswellasthedura-tionoftherespectivephases.

Table2:

Sows,energyrequirementsasusedintheinventory.Fordetailsseetext.

phase dura-tionind

numberofpigletspersowperbirth

energyrequire-ments***,revisedap-proachinMJanimal-1d-1

energyrequire-ments,formerapproach*inMJanimal-1d-1

gestationphase1 84* 33.3 25

phase2 30* 40.7 29

lactating 28** 8 79.5 56

9 86.3

10 93.1 67

11 99.9

12 106.7 77

13 113.5

weaningtocovering 27* 40.7 29

*basedonGfE(1987),seealsoDämmgenetal.(2007);

**inconnectionwithaweaningweightof8kgpiglet-1(expertjudgmentE.Schulz);

***basedonGfE(2006)

H.-D. Haenel, U. Dämmgen, P. Laubach, C. Rösemann / Landbauforschung - vTI Agriculture and Forestry Research 3 2011 (61)217-228 221

Table 2 also allows for a comparison with the valueshithertousedwhichwerebasedonGfE(1987)(seeDäm-mgenetal.,2007)andconsiderablyfallbelowthoseob-tainedwiththenewapproach.The cumulative energy requirements, i. e. the total of

energyrequiredduringonereproductioncycle,isprovidedinTable3.

Table3:

Sows,totalofenergyrequiredduringonereproductioncycle(ΣME sow)

numberofpiglets 8 9 10 11 12 13

ΣMEsow(inMJanimal-1round-1)

7166 7331 7496 7661 7826 7992

3.3 Animal weights

3.3.1 Estimation of mean sow weight

Ingeneral,theliveweightofasowisnotaconstantdur-ingthereproductioncycle.Theweightgainduringgesta-tioncompensatestheweightlossduringlactationintheprecedent reproduction cycle and comprises theweightgainoftheconceptionproductsandthemammaryglandaswellastheweightgainofthesowitself.Table4showstypicalweightchangedata(takenfromTable4.13inGfE,2006).Aweightof255kganimal-1isconsideredatypicalfinalliveweight(DLG,2008,pg.13).

Table4:

Sows,animalweights(wsow)andweightchanges(Δwsow)asafunctionofthenumberofgravidity(ngr).Allweightdatainkganimal

-1.(Source:GfE,2006,Table4.13.)

Δwsow duringlactation

ngr 1 2 3 4

0wsowatcovering 140 185 225 255

Δwsowduringgravidity 70 65 55 25

-10wsowatcovering 140 185 225 255

Δwsowduringgravidity 80 75 65 35

-20wsowatcovering 185 225 255

Δwsowduringgravidity 85 75 45

However, theseweight changes cannot be accountedforintheinventoryasthetimespantakenbyonerepro-ductioncycleisshorterthantheinventorytimestepwhichisoneyear.Henceenergyconsiderationsfortheinventoryhavetobebasedonameansowweight.SimplyaveragingtheweightsatcoveringaslistedinTable4yields2.1∙102kganimal-1.Howeverasthisestimatemaybebiasedbyarelativeunder-representationoffullygrown-upsows,theinventoryassumesameansowweightof2.2∙102kgani-

mal-1,whichisthearithmeticmeanoftheweightsatcov-eringforthesecondandthefourthgestation. It ignoresthelowestweightinordertoroughlycompensatefortheunder-representedhighestweight.

3.3.2 Mean piglet weights at birth and weaning

Forpiglets,theinventoryisbasedonabirthweightof1.5kgpiglet-1.Thiscanbederivedfromfeedingrecom-mendations in DLG (2008), Table 4.1, where the pigletweightafterthefirstweekwithadailyweightgainof0.2kgpiglet-1d-1reaches2.9kgpiglet-1.According to expert judgment (E. Schulz) the typical

weaningweightisassumedtobe8kgpiglet-1inconnec-tionwithalactationphasedurationof28days(seeTable2).

4 Weaners

Forweaners, themetabolicenergy requirementscom-prisetherequirementsforbothmaintenanceandgrowth.TheyarecalculatedaccordingtotherecommendationsinGfE(2006).

∑∑

⋅⋅Σfinfin k

1jj we,g,day

k

1jj we,m,daywe MEMEME ττ (7)

whereΣME we totalmetabolizableenergyrequired(MJanimal-1 round-1)j indexofdaykfin numberofthefinaldayoftheweaners’lifespanτday unittimeperiod(τday=1dround

-1)MEm, we, j metabolizableenergyrequiredformainte- nancefordayj(inMJanimal-1d-1)MEg, we, j metabolizableenergyrequiredforgrowthfor dayj(inMJanimal-1d-1)

4.1 Daily energy requirements

Dailyenergyrequirementsformaintenancewithwean-ersaredefinedasfollows(cf.discussionChapter3.1.2).

75.0

unit

jwe,unitwem, ME,jwe,m,

⋅⋅ww

wME η (8)

whereMEm, we, j metabolizableenergyrequiredformaintenance fordayj(inMJanimal-1d-1)j indexofdayηME, m, we specificmetabolizableenergyrequiredfor maintenance(ηME, m, we=1.25∙0.44MJkg

-1d-1, GfE,2006,pg.23)wwe, j meanweanerliveweightondayj(inkganimal-1)wunit unitweight(wunit=1kganimal

-1)

222

The energy requireddaily for growth is calculated ac-cordingto:

j we,jwe,g, ME,j we,g,

∆∆

⋅twME η (9)

whereMEg, we, j metabolizableenergyconsumedfordailygrowth ondayj(inMJanimal-1d-1)j indexofdayηME, g, we, j specificmetabolizableenergyrequiredforgrowth ondayj(inMJkg-1,seebelow)(Δw/Δt)we, jdailyweightgainperanimalanddayj(inkg animal-1d-1)

Thespecificmetabolizableenergyrequiredforgrowthisafunctionofproteinandfatgains,henceafunctionofage:

wepf,

jwe,wef,we wep,j we,g, ME, k

FP ⋅⋅

ααη (10)

whereηME, g, we, j day-dependentspecificmetabolizableenergy requiredforgrowth(inMJkg-1)j indexofdayα energycontentofprotein(α =23.8MJkg-1p, we p, we , seeGfE,2006,pg.32)αf, we energycontentoffat(αf, we=39.7MJkg

-1,see GfE,2006,pg.33)kpf , we partialefficiency(kpf, we=0.7MJMJ

-1,see GfE,2006,pg.33)Pwe constantratioofproteingaintoweightgain (Pwe=0.17kgkg

-1,seeGfE,2006,pg.29)Fwe, j day-dependentratiooffatgaintoweightgain (inkgkg-1,seebelow)

According to GfE (2006), pg. 30, the fat content isabout110gkg-1foraliveweightof10kgand170gkg-1foraliveweightof30kg.Fromthisthefollowinglinearequationisdeduced:

j we,weF,weF,jwe, wbaF ⋅ (11)

whereFwe, j day-dependentratiooffatgaintoweightgain (inkgkg-1)j indexofdayaF, we constant(aF, we=0.08kgkg

-1)b -1

F, we constant(bF, we=0.003kg animal)wwe, j meanweanerliveweightondayj(inkganimal

-1)

4.2 Cumulative energy requirements and animal weights

AccordingtoEquation(7),theenergyrequirementshavetobecalculatedseparatelyforeachsingledaytoobtain

(12)

the cumulative energy requirements. Thiswould requireabout50calculationsteps.However,Equation(7)canbetransformedintoaninte-

gralequationyieldingthecumulativeenergyrequirementsin just one calculation step. This transformationpresup-posestheknowledgeaboutthedevelopmentofthedailyweightgainrate.ThelatterisafunctionofanimalweightasshowninFigure1.

100

200

300

400

500

600

700

800

5 10 15 20 25 30 35

live weight [kg animal ]-1

daily w

eig

ht gain

[g a

nim

al

d]

-1-1

Figure1:

Weaners,weightgainasafunctionofliveweight.Exemplaryvariabledata:squares(LfL,2004);solidline:linearapproximation.

Calculations made for comparison purposes with thetotalenergysummationequationgivenaboveshowthat,withoutarelevanterror,thetotalenergymayalsobecal-culatedbasedontheassumptionofaconstant(i.e.mean)weightgainrate.IntegrationthenleadstoarelationfortheMEamount

required for maintenance and growth between animalweightswwe, 0andwwe, 1(fordetailsseeAppendix):

)(

1.75),(

0we,1we,weg, ME,

75.1

unit

0we,75.1

unit

1we,

2unit

wem,ME,1we,0we,we

wwww

ww

gw

wwME

−⋅

−

⋅⋅

⋅Σ

∗η

η

whereΣMEwe(wwe, 0, wwe, 1) MErequiredforthephasebetween theweightswwe, 0and wwe, 1 (inMJanimal-1round-1)ηME, m, we specificmetabolizableenergyre- quiredformaintenance(inMJkg-1d-1)wunit unitweight(wunit=1kganimal

-1)wwe,0, wwe,1 animalweightslimitingaspecial phasebetweenweaningandfattening, withw -1

we, 0 < wwe, 1(inkganimal )g meandailyweightgainduringthe entireperiodbetweenweaningand fattening(inkganimal-1d-1)

H.-D. Haenel, U. Dämmgen, P. Laubach, C. Rösemann / Landbauforschung - vTI Agriculture and Forestry Research 3 2011 (61)217-228 223

(13)

and

⋅⋅⋅

⋅∗

2

1

1we,0we,weF,weF,wef,wewep,

wepf, weg, ME,

wwbaP

k

αα

η

whereη*ME, g, we effectivespecificmetabolizableenergyrequired forgrowth,tobeusedfortheentireperiod betweenweaningandfattening(inMJkg-1)αp, we energycontentofprotein(αp, we=23.8MJkg

-1, seeGfE,2006,pg.32)αf, we energycontentoffat(αf, we=39.7MJkg

-1,see GfE,2006,pg.33)kpf , we partialefficiency(kp, we=0.7MJMJ

-1,see GfE,2006,pg.33)Pwe constantratioofproteingaintoweightgain (Pwe=0.17kgkg

-1,seeGfE,2006,pg.29)aF, we constant(a -

F, we=0.08kgkg1,seeEquation(11))

bF, we constant(bF, we=0.003kg-1animal,

seeEquation(11))wwe,0, wwe,1 animalweightslimitingaspecialfattening phase,withwwe, 0< wwe, 1(inkganimal

-1)

Theresultsobtainedwiththisone-stepcalculationpro-cedurearealmostidenticalwiththemulti-stepapproachusingEquation(7).Thedifferenceisintherangeof0.0002%.Equation (12) canbeused to calculate theenergy re-

quirements of single feeding phases. It requires theknowledgeofweightsratherthandaysasisthecasewithEquation(7).Thisisinlinewiththefactthatinformationregardingphase feedingofweaners is basedon animalweights.Theinitialweanerweightisidenticaltotheweightofa

suckling-pigattheendofthelactationperiod.Inthein-ventory,itisassumedtobe8kganimal-1.Thefinalweightoftheweaners’productionphaseequalsthestartweightofthefatteningprocess.Itisintherangeofabout25kganimal-1to33kganimal-1.Atypicalmeanvalueofthedailygrowthrateis420ganimal-1d-1(KTBL,2008,pg.636).Exemplarytotalenergyrequirementsforastartweight

of8.5kganimal-1,anaveragefinalweightof29kgani-mal-1 andameanweightgainof420ganimal-1d-1 are516.4MJanimal-1.

4.3 Comparison with the former approach

Figure2displaysdailyMErequirementsdataprovidedinGfE(1987),pg.54,comparedtorespectivedataascalcu-latedwithEquation(12)basedonGfE(2006).

2.5

5.0

7.5

10.0

12.5

15.0

17.5

2.5 5.0 7.5 10.0 12.5 15.0 17.5

weaners

,daily M

E, G

fE 1

987 [M

J a

nim

al

d]

-1-1

weaners,daily ME, GfE 2006 [MJ animal d ]-1 -1

Figure2:

Weaners,dailyMErequirements,GfE(1987)datacomparedtocalcu-lationsaccordingtoEquation(12)basedonGfE(2006).Dottedline:1to1line;solidline:regression(intercept:0,slope:0.9952,R2=0.953).

FromFigure2westatethatfortherangeofMErequire-mentstypical fortheearly1990iesthere isnosubstantialdifferencebetweentheMErecommendationsgiveninGfE(1987)undGfE(2006).Thus,the inventorymakesuseoftheGfE(2006)calculationmethodfortheentiretimeseriesfrom1990onwards.

5 Fattening pigs

Forfatteningpigs,themetabolicenergy(ME)requirementscomprisetherequirementsforbothmaintenanceandgrowth.ThetotalMErequiredforafatteningperiodisgivenby

∑∑

⋅⋅Σfinfin k

1jjfp, g,day

k

1jjfp, m,dayfp MEMEME ττ (14)

whereΣME fp totalmetabolizableenergyrequired (inMJanimal-1round-1)kfin numberofthefinaldayofthefatteningperiodτday unittimeperiod(τday=1dround

-1)j indexofdayMEm, fp, j metabolizableenergyrequiredformaintenance fordayj(inMJanimal-1d-1)MEg, fp, j metabolizableenergyrequiredforgrowthfor dayj(inMJanimal-1d-1)

5.1 Daily energy requirements

Thedailyenergyrequirementformaintenanceisdefinedby(cf.discussionChapter3.1.2):

224

75.0

unit

jfp,unitfp m, ME,jfp, m,

⋅⋅ww

wME η (15)

whereMEm, fp, j metabolizableenergyrequiredformaintenance fordayj(inMJanimal-1d-1)ηME, m, fp specificmetabolizableenergyrequiredformainte- nance(inMJkg-1d-1,seebelow)wfp, j liveweightondayj(inkganimal-1)wunit unitweight(wunit=1kganimal

-1)

AccordingtoGfE(2006),pg.23,thespecificenergyformaintenancecanbedescribedby

−−

⋅−⋅BA

Bjfp,mmnfp, m, ME,fpm, ME, ww

wwbaηη (16)

whereηME, m, fp specificmetabolizableenergyrequiredformainte- nance(inMJkg-1d-1)ηME, m, fp, n referencevalueofspecificmetabolizableenergy formaintenance(η -1

ME, m, fp, n=0.44MJkgd-1,

GfE,2006,pg.23)am constant(am=1.25MJMJ

-1)b constant(b =0.25MJMJ-1m m )wfp, j liveweightondayj(inkganimal-1)wA, wB thresholdsanimalweights(inkganimal-1,see below)

GfE(2006)usesw =30kganimal-1A andwB=100kgani-mal-1.GfE(2006)appliesEquation(16)alsotoanimalweightsfallingbelowwAandexceedingwB.Then,incaseofanimalweightssmallerthanwA,theterminbracketsissetequaltoam,whileforweightslargerthanwBitequalsam – bm.Theenergyrequiredforgrowthiscalculatedaccordingto:

jfp,jfp,g, ME,jfp, g,

∆∆

⋅twME η (17)

whereMEg, fp, j metabolizableenergyrequiredfordailygrowth ondayj(inMJanimal-1d-1)j indexofdayηME, g, fp, j specificmetabolizableenergyrequiredfor growthondayj(inMJkg-1,seebelow)(Δw/Δt)fp, j dailyweightgainperanimalanddayj(inkg animal-1d-1)

Thespecificenergyrequirementsforgrowth,ηME, g, fp, j,isafunctionofproteinandfatgains,whichmeans,itisalsoafunctionoflifetime:

j

f

fj

p

pj fp, g, ME, F

kP

k⋅⋅

ααη (18)

whereηME, g, fp, j specificmetabolizableenergyrequiredfor growthondayj(inMJkg-1)j indexofdayαp energycontentofprotein(αp=23.8MJkg

-1, seeGfE,2006,pg.32)αf energycontentoffat(αf=39.7MJkg

-1,see GfE,2006,pg.33)kp partialefficiency(kp=0.56MJMJ

-1,seeGfE, 2006,pg.33)kf partialefficiency(k -1

f=0.74MJMJ ,seeGfE, 2006,pg.33)Pj day-dependentratioofproteingaintoweight gain(inkgkg-1,seebelow)Fj day-dependentratiooffatgaintoweightgain (inkgkg-1,seebelow)

TherelativeproteingainP isobtainedfromtheEqua-tion(8)inGfE(2006)differentiatedwithrespecttoanimalweight.

j fp,PPj wbaP ⋅− (19)

wherePj day-dependentratioofproteingaintoweight gain(inkgkg-1,seebelow)j indexofdayaP constant(aP=0.168kgkg

-1)b -1

P constant(bP=0.0001828kg animal)wfp, j liveweightondayj(inkganimal-1)

DifferentiationofEquation(9)inGfE(2006)withrespecttoanimalweightyieldstherelativefatgainF.Acorrectionfactorof0.94kgkg-1hastobetakenintoaccount(GfE,2006,pp.28and31).

)( j fp,FFFj wcbaF ⋅⋅ (20)

whereFj day-dependentratiooffatgaintoweightgain (inkgkg-1)j indexofdayaF constant(a -1

F=0.94kgkg )bF constant(bF=0.1162kgkg

-1)cF constant(cF=0.002778kg

-1animal)wfp, j liveweightondayj(inkganimal-1)

5.2 Cumulative energy requirements and animal weights

By analogy to the procedure used for weaners (seeChapter4.2)thesummationformula(14)istransformedintoanequation thatallows tocalculate thecumulativemetabolizableenergybyonesinglecalculationsteprather

H.-D. Haenel, U. Dämmgen, P. Laubach, C. Rösemann / Landbauforschung - vTI Agriculture and Forestry Research 3 2011 (61)217-228 225

than summing up daily energy requirementswithmorethanahundredsinglesteps(fordetailsofthetransforma-tionprocessseeAppendix).Inordertoaccountforthefactthatthespecificmetab-

olizableenergyηME, m isdefined separately for theanimalweightintervals“fallingbelow30kganimal-1“,“30to100kganimal-1“and“exceeding100kganimal-1“,thetransfor-mationhastobeperformedseparatelyfortheseintervals.

As for weaners, the transformation is performed un-dertheassumptionofaconstant(i.e.mean)weightgainrate (cf. also Dämmgen et al., 2009, pg. 178). Integra-tionthenleadstoanequationfortheamountofMEre-quired for the growth between animal weightsw0 andw1,wherew0andw1representwfp, 0andwfp, 1,respectively:

(21)

(22)

)(),,(),,,(),,(),( 01g ME,

B103BA102A101nm,ME,10fp ww

gwwwwwwwwwwwwME −⋅

⋅Σ ∗ηϕϕϕη

whereMEfp(w0, w1) MErequiredforthefatteningphasebetweentheweightsw -1

0and w1(inMJanimal ME)ηME, m, n referencevalueofspecificmetabolizableenergyformaintenance(ηME, m, n=0.44MJkg

-1d-1,GfE,2006,pg.23)w0, w1 animalweightslimitingaspecialfatteningphase,withw0< w1(inkganimal

-1ME)wA, wB thresholdsofanimalweight(inkganimal-1,seeChapter5.1)g meandailyweightgainduringtheentirefatteningperiod(inkganimal-1d-1)

and

−

⋅

⋅

75.1

unit

A075.1

unit

A12unitm

1),min(,min(

1.75 www

wwwwa

ϕ

−

⋅

−⋅

⋅

−

−

⋅

−

⋅⋅

75.2

unit

A0B75.2

unit

B1A

AB

3unitm

75.1

unit

A0B75.1

unit

B1A

AB

Amm

2unit

2

)),max(,min()),min(,max(

)(2.75

)),max(,min()),min((,max(1.75

wwww

wwww

ww

wb

wwww

wwww

ww

wba

wϕ

−

⋅

75.1

unit

B075.1

unit

B12unit

3),max(),max(

1.75 www

wwww

ϕ

⋅⋅⋅

⋅−⋅∗

2210

FFFf

f10PP

p

pg ME,

wwcbak

wwba

kαα

η

whereφ φ φ functionsofw , w w ,andw (inkg2animal-21, 2, 3 0 1, A B )w0, w1 animalweightslimitingaspecialfatteningphase,withw0< w1(inkganimal

-1)wA, wB animalweightthresholds(inkganimal-1,seeChapter5.1)wunit unitweight(wunit=1kganimal

-1)am constant(am=1.25MJMJ

-1,GfE,2006,pg.23)bm constant(bm=0.25MJMJ

-1,GfE,2006,pg.23)η*ME, g meanspecificmetabolizableenergyrequiredforgrowth,seeabove(inMJkg-1)αp coefficient(αp =23.8MJkg

-1,seeGfE,2006,pg.32)kp coefficient(kp=0.56MJMJ

-1,seeGfE,2006,pg.33)aP constant(aP=0.168kgkg

-1,seeabove)

(23)

(24)

(25)

226

bP constant(bP=0.0001828kg-1animal,seeabove)

αf coefficient(αf=39.7MJkg-1,seeGfE,2006,pg.33)

kf coefficient(kf=0.74MJMJ-1,seeGfE,2006,pg.33)

aF constant(aF=0.94kgkg-1,seeabove)

bF constant(bF=0.1162kgkg-1,seeabove)

cF constant(cF=0.002778kg-1animal,seeabove)

Again,exemplarycomparisonsbetweentheresultsob-tainedwiththeapplicationofEquations(14)and(21)ffshowsaperfectagreement(relativedeviation0.0001%).According to the data compilation in Haenel et al.

(2010), Chapter 5.5.1.2, the initial weight of fatteningpigsisintherangeofabout25kganimal-1to33kgani-mal-1while thefinalweight is between105kganimal-1

and120kganimal-1;averagingthedailygrowthrateoverthetwodecadesfrom1990onandoverallfederalstatesyieldsabout680ganimal-1d-1.Exemplary total energy requirements for amean start

weightof29kganimal-1,ameanfinalweightof113kganimal-1andameandailyweightgainof680ganimal-1d-1(witharesultingfatteningperioddurationof124days)are3,3GJanimal-1.

5.3 Comparison with the former approach

Figure3displaysdailyMErequirementsdataprovidedinGfE(1987),pg.35,comparedtorespectivedataascalcu-latedwithEquation(21)accordingtoGfE(2006).

10

15

20

25

30

35

40

10 15 20 25 30 35 40

fatteners, daily ME, GfE 2006 [MJ animals d ]-1 -1

fatteners

, daily M

E, G

fE 1

987

[MJ a

nim

al

d]

-1-1

Figure3:

Fatteners,dailyMErequirements,GfE(1987)datacomparedtocal-culationsaccordingtoEquation(21)basedonGfE(2006)(squares).Dottedline:1to1line.

TheMErequirementsascalculatedusingtheGfE(1987)approachexceedthoseobtainedwithEquation(21)basedonGfE(2006)byupto12%.GfE(2006),pg.27ff,ex-plain thiswith thedifferentexperimentaldataavailable.However,the2006GfEeditionisbasedondatapublished

since1980whichleadstotheassumptionthattheenergyrequirementsrecommendations inthiseditionshouldbeappropriatetodescribethesituationintheyearscoveredbytheinventory,i.e.thepasttwodecades.

6 Breeding boars

Forbreedingboars,themetabolicenergyrequirementscomprise the requirements for both maintenance andgrowth.However,asthecontributionofboarstotheover-allemissionsfrompighusbandryisalmostnegligible,theinventorysimplyassumesallboarscountedbytheofficialsurveytobebreedingboarswhoseweightgainisrestrict-ed(GfE,2006,pg.84).Duetothebreedingboars’limitedimportanceandthe

scarcityofdata(GfE,2006,pg.84)theinventorydoesnotattempttomodelenergyrequirementsofboars.WhileGfE(1987),pg.68,suggestedmeanMErequirementsof30MJanimal-1d-1,GfE(2006),pg.84,recommendsarangeof30to35MJanimal-1d-1.Aroughestimatebasedonthedataprovided inGfE(2006),pg.83,andtheuseofMEcalculationapproachforfatteningpigsindicatesthatthevalueof35MJanimal-1d-1matchesameanboarweightofabout200kganimal-1(expertjudgmentE.Schulz)betterthan30MJanimal-1d-1.HencetheinventoryassumesdailyMErequirementsof35MJanimal-1d-1leadingtocumula-tiveannualrequirementsof12775MJanimal-1a-1.

7 Conclusions

Itisgoodpracticetousethebestdataavailabletocon-struct emission inventories. For pigs, the national situa-tionhadformerlybeenreflected inadatasetpublishedinGfE (1987)withbackground informationdating fromthe1970sandearly1980s.TheupdatedmethodologiesanddatapublishedinGfE(2006)werearemarkablestepforwardwithrespecttothereliabilityandaccuracyoftheGermanagriculturalemissioninventory.Theuseofequa-tionsratherthantablesallowsforasimplertreatmentofvariableenergyrequirementcalculations.Forthemostimportantsubcategory,i.e.fatteningpigs,

theapplicationof theupdatedGfE (2006)methodologyresultsinreducedenergyrequirements,henceinreducedexcretionratesforfaecesandurineundsubsequentlyre-ducedemissions.Theoppositeisthecaseforsows,wean-

H.-D. Haenel, U. Dämmgen, P. Laubach, C. Rösemann / Landbauforschung - vTI Agriculture and Forestry Research 3 2011 (61)217-228 227

ers andboars, but this is outweighedby the reductionsachievedforfatteningpigs.

Acknowledgement

The authors express their thanks to Dr Edgar Schulz,co-authorofGfE(2006)forhisdetailedandconstructivereview.

Appendix: Derivation of a closed mathematical descrip-tion of the cumulative ME requirements of weaners

Cumulative energy requirements can be calculated byaddingupdailyrequirementsoverthetimespanconsidered:

∑

⋅Σfink

1jjwe,daywe MEME τ (A1)

whereΣMEwe totalmetabolizableenergyrequiredbetween weaningandfattening(inMJanimal-1round-1ME)τday unittimeperiod(τday=1dround

-1)j indexofdaykfin numberofthefinaldayoftheweaners’lifespanMEwe, j metabolizableenergyrequiredformaintenance andgrowthondayj(inMJanimal-1d-1ME)

In the German agricultural inventory, equations hadbeenderivedusingdata inGfE (1987) that expressed asumlikeEquation(A1)inasingleequationusingafittedpower series (Dämmgenet al., 2007). The latterhad tobe replacedwith theuseofnewdataaccording toGfE(2006). Itwas decided to base the derivation of a newsingleequationonmathematicalintegrationinsteadoffit-tingpowerseries.Asapreparation for themathematical solution,Equa-

tion(A1)hastoberewrittenasdifferencequotient:

)()(

jwe,jwe,jwe wMEMEME

∆

Σ∆τ

(A2)

whereΔ(ΣMEwe) incrementoftotalmetabolizableenergyrequired betweenweaningandfattening(inMJanimal-1 round-1ME)Δτ timeincrement(Δτ = τday =1dround

-1)j indexofdayMEwe, j metabolizableenergyrequiredformaintenance andgrowthondayj(inMJanimal-1d-1ME)wwe, j meanweanerliveweightondayj(inkganimal-1)

Itisplausiblethatthisprocedureisvalidnotonlyfordai-ly timestepsbutalso for infinitesimally small timesteps.Hencethedifferencequotientcanbetransformedinadif-

ferentialquotientforeachtimeτ’k.Here,τ’isacompart-mentalizedtimescale(insround-1)thatisconnectedtothetimescaleτ(indround-1)byatimeunitsconversionfactor.

)())(('d

)(d ''kwe

1we'k

ττγτ τ fwMEME

⋅Σ − (A3)

where(ΣMEwe) incrementoftotalmetabolizableenergyrequired betweenweaningandfattening(inMJanimal-1 round-1ME)τ’ time(insround-1)τ’ -1

k specifictime(insround )γ timeunitsconversionfactor(γ=86400sd-1)wwe(τ’k) meanweanerliveweightattimeτ’k(inkg animal-1)

and

gewdcwaf ⋅⋅⋅⋅ −we

bwe

1' )()( γτ (A4)

wheref(τ’) metabolizableenergyrequiredperanimal andsecond(inMJanimal-1s-1ME)γ timeunitsconversionfactor(γ =86400sd-1)a, b, c, d, e, g seetextbelowwwe = wwe(τ’) timedependentmeanweanerliveweight (inkganimal-1)

Theentitiesa, b, c, d, eandgoriginatefromthecompari-sonoftheequationsdescribingtheenergyrequirementsformaintenanceandgrowth(Chapter4.1).Inparticular,g denotesaconstantgrowthrate.Integration of f(τ’) leads to the cumulative energy re-

quirements:

∫Σ

'1

0

''wewe d))((

τ

ττwfME (A5)

whereΣMEwe totalmetabolizableenergyrequiredbetween weaningandfattening(inMJanimal-1round-1ME)τ’ time(insround-1)f(wwe(τ’)) metabolizableenergyrequiredperanimaland second(inMJanimal-1s-1ME)wwe(τ’) timedependentmeanweanerliveweight(in kganimal-1)

and

dayfin'1 k τγτ ⋅⋅ (A6)

whereτ’1 timeoftheendoftheweaners’lifespan(in sround-1)

228

γ timeunitsconversionfactor(γ =86400sd-1)kfin numberofthefinaldayoftheweaners’lifespanτday unittimeperiod(τday=1dround

-1)

TheentitygcanbeusedinEquation(A5)tosubstitutetheindependentvariabletimebyweight

∫⋅Σ1we,

0we,

wewewe d)(w

w

wwfg

ME γ (A7)

whereΣMEwe totalmetabolizableenergyrequiredbetween weaningandfattening-period(inMJanimal-1 round-1ME)γ timeunitsconversionfactor(γ =86400sd-1)g animalweightgainperunittime(in kganimal-1d-1)f(wwe) metabolizableenergyrequiredperanimaland second(inMJanimal-1s-1ME)wwe meanweanerliveweight(inkganimal-1)wwe, 0 meanweanerliveweightatweaning(inkg animal-1)wwe, 1 meanweanerlivebeginattheendofthe fatteningperiod(inkganimal-1)

Executionoftheintegralandsubsequentre-substitutionoftheentitiesa, b, c, d, e and ginf(wwe)resultsinEquation(12)inChapter4.2.

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