, 2.2. Overview of the data and their sources

, LEGUME PRODUCTION AND USE IN FEED: ANALYSIS OF LEVERS TO IMPROVE PROTEIN SELF-SUFFICIENCY FROM FORESIGHT

, 133 Definition of study boundaries and representation of the system

. .. , Definition of final states and hypothesis through a participatory approach, p.135

. .. Design-of-scenarios,

, Overview of the SYNERGY model used

S. .. Coupling,

, From scenarios to levers: modeling choices

, Results of the modeling framework

). .. Le_su, Coupled support for legumes

). .. Le_gmo, Increased demand for GMO-free animal products, p.142

. .. Appendices,

A. Appendix, The role of agriculture in the status of the nine planetary boundaries

B. Appendix, Livestock density in EU and modelling of agriculture N emissions to freshwater, p.173

C. Appendix, Evolution of harvested grain legume areas (i.e., pulses) in the EU

D. Appendix, PMP: from the standard approach to the Röhm and Dabbert

E. Appendix, Description of agricultural productions in western France

F. Appendix, Extracts from SYNERGY program coded under

G. Appendix, Description of technical coefficients and data sources of the SYNERGY model, p.189

H. Appendix, Executive summary of the TERUnic foresight

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M. Torralba, N. Fagerholm, and P. J. Burgess, Do European agroforestry systems enhance biodiversity and ecosystem services? A meta-analysis. Agriculture, Ecosystems & Environment, vol.230, pp.150-161, 2016.

J. Van-den-bergh, A third option for climate policy within potential limits to growth, Nature Climate Change, vol.7, pp.107-112, 2017.

M. K. Van-ittersum, F. Ewert, and T. Heckelei, Integrated assessment of agricultural systems -A component-based framework for the European Union (SEAMLESS), 2008.

, Agricultural Systems, vol.96, pp.150-165

, Union that strives for more: my agenda for Europe. Political guidelines for the next European Commission, European Commission, 2019.

F. Weiss and A. Leip, Greenhouse gas emissions from the EU livestock sector: A life cycle assessment carried out with the CAPRI model, Ecosystems & Environment, vol.149, pp.124-134, 2012.

A. Wilfart, S. Espagnol, and S. Dauguet, ECOALIM: a dataset of environmental impacts of feed ingredients used in French animal production, PLOS ONE, vol.11, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01595321

W. Willett, J. Rockström, and B. Loken, Food in the Anthropocene: the EAT-Lancet Commission on healthy diets from sustainable food systems, The Lancet, vol.393, pp.447-492, 2019.

. Where, are, respectively, the vectors of slope of the cost function of each crop, and of each crop activity (i.e., variant of the same crop), represents the vectors of intercepts of the cost functions for crop activities, vol.1

. France, Gallus species) and 36% of dairy cows (French Ministry of Agriculture, 2018.

, Regarding dairy production, milk deliveries have increased by 14% since 2000, to reach 91.4 million hectoliters in 2018. The dairy production is mainly located in Brittany that is the first dairy region in France. It has been substantially concentrated, with less farms producing more milk (e.g., -44% of milk-oriented farms in Brittany since 2000, but +14% of milk production) western France, 2018.

, Regarding pig production, the herd of pig has increased by 4% since 2000, mainly due to the increase in Brittany. Brittany is the first pig-production region in France, far ahead Pays de la Loire that ranks second

. Overall, western France

, This share has increased by 4 percentages points since 2000. However, crop production is mainly oriented to feed livestock: annual forage (mainly corn) represented in 2018 41% of the UAA, temporary pasture represent 25% of UAA, and permanent pasture 16%. Legume production remains low, 2018.

). , L. , ). , and M. , maizeG.(maG_maG, fa_ba_maG, fa_maG_maG, fa_wh_maG, fa_wh_ra_maG, lu_maG_wh, lu_wh_maG, maG_ba, maG_wh, maG_wh_ba, maG_wh_sun, pea_maG_maG, pea_wh_lu_maG, pea_wh_maG, pt_maG_ba, pt_maG, pt_maG_wh, pea_maG_wh_ra_wh, ra_wh_maG_wh, ra_maG_wh), pastureP.(pp_pp), pastureT.(pt_pt, pt_maF, pt_maG, pt_maF_ba, pt_maG_ba, pt_maF_wh, pt_maG_wh), pea.(pea_ba_ba, pea_wh_ba, pea_wh_wh, pea_maF_wh_ra_wh, pea_maG_maG, pea_maG_wh_ra_wh, pea_wh_maF, pea_wh_maG), rapeseed.(ra_ra, fa_wh_ra_maF, fa_wh_ra_maG, pea_maF_wh_ra_wh, pea_maG_wh_ra_wh, ra_wh_ba, ra_wh_maF_wh, ra_wh_maG_wh, ra_wh_wh), sunflower.(maF_wh_sun, maG_wh_sun, wh_sun) wheat.(wh_wh, fa_wh_ba, fa_wh_wh, lu_wh_wh, fa_wh_maF, fa_wh_maG, fa_wh_ra_maF, fa_wh_ra_maG, lu_maF_wh, lu_maG_wh, lu_wh_maF, lu_wh_maG, maG_wh, maF_wh_ba, maG_wh_ba, maF_wh_sun, maG_wh_sun, pea_wh, pea_maF_wh_ra_wh, pea_maG_wh_ra_wh, pea_wh_lu_maF, pea_wh_lu_maG, pea_wh_maF, pea_wh_maG, pea_wh_ba

, U=e=sum((i,s), GM_total(i,s))

, profit_total(i,s)

, mean'))-(BW_C(cc,t,i,s)*pwb_c(cc,t,'mean'))) +sum((c,t), (SL_C(c,t,i,s)*pws_c(c,t,'mean'))-(BL_C(c,t,i,s)*pwb_c(c,t,'mean')*0.9)) -sum((c,r,t)$rc(c,r),X(c,r,t,i,s)*chop_c(c,r,t,s)) -sum(ma,SL_FE(ma,i,s)*tc)-sum, GM_total(i,s)=e= sum((cc,t), (SW_C(cc,t,i,s)*pws_c(cc,t

, SW_A(a,ra,i,s)*weight_a(a)*pws_a(a,ra,'mean'))+ sum(ra,SW_milk(ra,i,s)*pws_milk(ra,'mean')) -sum(co,BW_CO(co,i,s)*pwb_co(co,'mean'))-sum((a,ra)$ai(i,s,a,ra)

*. Rc,

, X(c,r,t,i,s)=e= nb_cr(c,r)*Xrot(r,t,i,s)*nb_rot(r)

, Landtot1(s).. sum((r,t,i), Xrot(r,t,i,s))=l=Dlandtot(s)

, Landtot2(s).. sum((c,r,t,i)$rc(c,r), X(c,r,t,i,s))=l=Dlandtot(s)

(. Production_cc and ). , sum(r$rc(cc,r), X(cc,r,t,i,s)*y_c(cc,t,s))=e= SW_C(cc,t,i,s)+SL_C(cc,t,i,s)+ K_C

(. Production_foc and ). , sum(r$rc(foc,r), X(foc,r,t,i,s)*y_c(foc,t,s))=e= SL_C(foc,t,i,s)+ K_C

&. X('pasturet and . Rc, pastureT',r)*y_c('pastureT',t,s))=e=K_GR('grassT',i,s)+K_GR('hayT',i,s)+K_GR('silageT

&. X('pasturetleg and . Rc, pastureTleg',r)*y_c('pastureTleg',t,s))=e=K_GR('grassTleg',i,s)+K_GR('hayTleg',i,s)+K_GR('silageTleg

, Production_GrP(gr,i,s).. sum((r,t), X('pastureP',r,t,i,s)$rc('pastureP',r)*y_c('pastureP',t,s))=e=K_GR('grassP',i,s)+K_GR('hayP

. Legume1, sum((leg,r,t,i,s)$rc(leg,r),X(leg,r,t,i,s))=g=sum(s,Dlandtot(s)*0

, X('pastureP',r,t,i,s)$rc('pastureP',r))=l=x_culture_tot('pastureP',i,s)*1, p.1

, X('pastureP',r,t,i,s)$rc('pastureP',r))=g=x_culture_tot('pastureP',i,s)*0, p.99

. N_a, calve",ra,i,s)$ai(i,s,"calve",ra) =e= N_a("cow",ra,i,s)$ai(i,s,"cow",ra)*rate_prolif("cow

). N_a, heifer",ra,i,s)$ai(i,s,"heifer",ra) =e= N_a("cow",ra,i,s)$ai(i,s,"cow

). N_a, pig",ra,i,s)$ai(i,s,"pig",ra)=e= rate_prolif("sow",ra)*N_a("sow",ra,i,s)$ai(i,s,"sow

). .. Bw_a, sow",ra,i,s)$ai(i,s,"sow",ra)=e= rate_purchase("sow")*N_a("sow",ra,i,s)$ai(i,s,"sow

, Production_a(a,ra,i,s)

, SW_A(a,ra,i,s)$ai(i,s,a,ra) =e= N_a(a,ra,i,s)$ai(i,s,a,ra)*rate_sale(a)

, Production_milk(ra,i,s)

, SW_milk(ra,i,s) =e= sum(a$ai(i,s,a,ra), N_a(a,ra,i,s)$ai(i,s,a,ra)*y_milk(a,ra

, Numerous1(a,ra,cr,s)

, N_a(a,ra,cr,s)$ai(cr,s,a,ra)=e=0

, alim_cc(cc,i,s).. sum((a,ra)$ai(i,s,a,ra),(need_c(a,ra,cc)/1000)*N_a(a,ra,i,s)) =l= sum(t, BL_C(cc,t,i,s)+BW_C(cc,t,i,s)+ K_C

, alim_foc(foc,i,s).. sum((a,ra)$ai(i,s,a,ra),(need_c(a,ra,foc)/1000)*N_a(a,ra,i,s))=l= sum

). Co, sum((a,ra)$ai(i,s,a,ra),(need_co(a,ra,co)/1000)*N_a(a,ra,i,s))=l= BW_CO(co,i,s)

, alim_grass(i,s).. sum((a,ra)$ai(i,s,a,ra),need_gra(a,ra,'grass')*N_a(a,ra,i,s))=l=K_GR('grassT',i,s)+ K_GR('grassP

, alim_silage(i,s)..sum((a,ra)$ai(i,s,a,ra),need_gra(a,ra,'silage')*N_a(a,ra,i,s))=l=K_GR('silageT

, alim_hay(i,s)..sum((a,ra)$ai(i,s,a,ra),need_gra(a,ra,'hay')*N_a(a,ra,i,s))=l=K_GR('hayT',i,s)+ K_GR('hayP

, Fertilisation1(ma,i,s)

, Q_MA(ma,i,s)=e=K_FE(ma,i,s)+BL_FE(ma,i,s)

, Fertilisation1bis(ma,i,s)..sum((c,r)$rc(c,r),Q_MA_C(c,r,ma,i,s))=e=Q_MA(ma,i,s)

, Fertilisation2(ch,i,s)

, Q_FE(ch,i,s)=e=BW_FE(ch,i,s)*rate_n_fe(ch)

, Fertilisation2bis(ch,i,s).. sum((c,r)$rc(c,r),Q_FE_C(c,r,ch,i,s))=e= Q_FE(ch,i,s)

, fertilisation3(c,r,i,s)

, NEED_N(c,r,i,s)$rc(c,r)=e=sum(ma, Q_MA_C(c,r,ma,i,s)$rc(c,r)*Keq_ma(c,r,ma))+ sum(ch,Q_FE_C(c,r,ch,i,s)$rc

, fertilisation4(i,s)..sum(ma,K_FE(ma,i,s)+BL_FE(ma,i,s))=l=170*sum((c,r,t)$rc(c,r)

, fertilisation5(nfod,r,i,s)

, Q_MA_C(nfod,r,'dropping_dairy',i,s)$rc(nfod,r)=e=0

). , , p.6

, Q_MA_C(nspc,r,ma,i,s)$rc(nspc,r)=e=0

, fertilisation7(ma,s)

. Bl_fe(ma, PO',s)=e=0

). , .sum(ma,Q_MA_C(c,r,ma,i,s)$rc(c,r))=l=max_ma(c)*(sum(ma, Q_MA_C(c,r,ma,i,s)$rc(c,r))+ sum(ch,Q_FE_C(c,r,ch,i,s)$rc

). Production_ma(ma, .sum((a,ra)$ai(i,s,a,ra), N_a(a,ra,i,s)*y_N(a,ra,ma))=e= SL_FE(ma,i,s)+ K_FE

, need_n_culture(c,r,i,s)

, NEED_N(c,r,i,s)$rc(c,r) =e= sum(t, X(c,r,t,i,s)$rc(c,r)*Xxa(c,r,i,s))

, Exchange_C1(c,t).. sum ((i,s),SL_C(C,t,i,s))=e= sum((i,s)

, Exchange_C2(c,t).. sum ((i,s),SL_C(C,t,i,s))=e= sum ((i,s),SL_C(C,t,i,s)*1)

, Exchange_C3(c,t).. sum ((i,s),SL_C(C,t,i,s))=l= 0.001

, Exchange_FE1(ma,s).. sum (i,SL_FE(ma,i,s))=e= sum(i,BL_FE(ma,i,s))

, Exchange_FE2(ma,i,s)

, SL_FE(ma,i,s)=e=SL_FE(ma,i,s)*1

, s,a_c,ra),N_a(a_c,ra,i,s))=l= x_animal_tot(a_c,i,s)*(1+epsilon1)

, calib_a1bis(a_c,i,s).. sum(ra$ai(i,s,a_c,ra),N_a(a_c,ra,i,s))=g= x_animal_tot(a_c,i,s)*(1-epsilon1)

, calib_a2(a_c,ra,i,s)

, N_a(a_c,ra,i,s)=l= x_animal(a_c,ra,i,s)*(1+epsilon2*100)

, calib_c1(c,i,s)

, X(c,r,t,i,s))=l= x_culture_tot(c,i,s)*(1+epsilon1), r,t)$rc(c,r)

, calib_c1bis(fo,i,s).. sum((r,t)$rc(fo,r),X(fo,r,t,i,s))=g= x_culture_tot(fo,i,s)*(1-epsilon1)

. ********************first-step-of-pmp********************, , vol.2, p.2

, mean'))-(BL_C(c,t,i,s)*pwb_c(c,t,'mean'))) -sum((c,r,t)$rc(c,r),X(c,r,t,i,s)*chop_c(c,r,t,s)) -sum((c,r,t)$rc(c,r),alpha_c(c,r,t,i,s)*X(c,r,t,i,s)+ 0.5*beta_c(c,r,t,i,s)*sqr(X(c,r,t,i,s))) -sum(ma,SL_FE(ma,i,s)*tc)-sum

, SW_A(a,ra,i,s)*weight_a(a)*pws_a(a,ra, a,ra)$ai(i,s,a,ra)

, BW_A(a,ra,i,s)*pwb_a(a,'mean')) -sum((a_c),alpha_a1(a_c,i,s)*sum(ra$ai(i,s,a_c,ra), +sum(ra,SW_milk(ra,i,s)*pws_milk(ra

, N_A(a_c,ra,i,s)))) -sum((a,ra)$ai(i,s,a,ra),N_A(a,ra,i,s)*chop_a, *beta_a1(a_c,i,s)*sqr(sum(ra$ai(i,s,a_c,ra)

, r,t)$rc(c,r),su_c(c)*X(c,r,t,i,s))

, INPUT_atm(i,s,sc)=sum((c,r,t), X.l(c,r,t,i,s)*deposition)

, INPUT_NfIX(i,s,sc)=sum((c,r,t), X.l(c,r,t,i,s)*no_symb_Nfix)

, INPUT_BIO(i,s,sc)=sum((c,r,t), X.l(c,r,t,i,s)*y_c(c,t,s)*content_dryM_c(c)*prop_leg(c,s)*symb_Nfix(c))

, INPUT_EN_DIR(i,s,sc)=sum((c,r,t),X.l(c,r,t,i,s)*fuel_conso*fuel_dir_emission/1000)

, INPUT_EN_INDIR(i,s,sc)=sum((c,r,t),X.l(c,r,t,i,s)*fuel_conso*fuel_indLoss/1000)

, INPUT_SEED_DIR(i,s,sc)=sum((c,r,t), X.l(c,r,t,i,s)/time_c(c)*density_seed(c,t)*rate_N_seed(c)/1000*content_dryM_seed(c))

, INPUT_SEED_INDIR(i,s,sc)=sum((c,r,t),X.l(c,r,t,i,s)/time_c(c)*density_seed(c,t)*indloss_N_seed(c)/1000*content_dryM_seed(c))

, INPUT_INORG_FE_DIR(i,s,sc)=sum(ch, BW_FE.l(ch,i,s)*rate_N_fe(ch))

, INPUT_INORG_FE_INDIR(i,s,sc)=sum(ch, BW_FE.l(ch,i,s)*inorgfe_indloss)

, INPUT_MANURE(i,s,sc)=sum(ma,BL_FE.l(ma,i,s)-SL_FE.l(ma,i,s))

, FEED_LEG_DIR(i,s,sc)=(sum

, s))*rate_N_c(hp)*content_dryM_c(hp))+sum(co,BW_CO.l(co,i,s)*rate_N_co(co)*content_dryM_co(co)))

, CULTURE_LEG(i,s,sc)=(sum((hp,t),(SW_C.l(hp,t,i,s)+SL_C.l(hp,t,i,s))*rate_N_c(hp)*content_dryM_c(hp)))

, FEED_LEG_INDIR(i,s,sc)=(sum

, s))*indloss_N_c(hp)*content_dryM_c(hp))+sum(co,BW_CO.l(co,i,s)*indloss_N_co(co)*content_dryM_co(co)))

, FLOW_HP(i,s,sc)= FEED_LEG_DIR(i,s,sc)-CULTURE_LEG(i,s,sc)

, OUTPUT_HP_DIR(i,s,sc)= abs(FLOW_HP(i,s,sc))$(FLOW_HP(i,s,sc)<0)

, INPUT_HP_DIR(i,s,sc)= abs(FLOW_HP(i,s,sc))$(FLOW_HP(i,s,sc)>0)

, INPUT_HP_INDIR(i,s,sc)= (FLOW_HP(i,s,sc)*FEED_LEG_INDIR(i,s,sc)/FEED_LEG_DIR(i,s,sc))$((FLOW_HP(i,s,sc)>0) and (FEED_LEG_DIR(i,s,sc)<>0))

, FEED_NLEG_DIR(i,s,sc)=(sum((lp,t),(BW_C.l(lp,t,i,s)+ BL_C.l(lp,t,i,s))*rate_N_c(lp)*content_dryM_c(lp)))

, CULTURE_NLEG(i,s,sc)=(sum((lp,t),(SW_C.l(lp,t,i,s)+SL_C.l(lp,t,i,s))*rate_N_c(lp)*content_dryM_c(lp)))

, FEED_NlEG_INDIR(i,s,sc)=(sum((lp,t),(BW_C.l(lp,t,i,s)+ BL_C.l(lp,t,i,s))*indloss_N_c(lp)*content_dryM_c(lp)))

, FLOW_LP(i,s,sc)= FEED_NLEG_DIR(i,s,sc)-CULTURE_NLEG(i,s,sc)

, OUTPUT_LP_DIR(i,s,sc)= abs(FLOW_LP(i,s,sc))$(FLOW_LP(i,s,sc)<0)

, INPUT_LP_DIR(i,s,sc)= abs(FLOW_LP(i,s,sc))$(FLOW_LP(i,s,sc)>0)

, INPUT_LP_INDIR(i,s,sc)= (FLOW_LP(i,s,sc)*FEED_NlEG_INDIR(i,s,sc)/FEED_NLEG_DIR(i,s,sc))$((FLOW_LP(i,s,sc)>0) and (FEED_NLEG_DIR(i,s,sc)<>0))

, OUTPUT_milk(i,s,sc)=sum(ra,(SW_milk.l(ra,i,s)*milk_density*(0.337+(0.116*tb_milk(ra)/10)+(0.06*tp_milk(ra)/10))*(milk_protei n/1000)/milk_convprot))

, ANIMAL_BUY_DIR(i,s,sc) = sum(ra,BW_A.l('sow',ra,i,s)*113*rate_n_a, vol.1000

, ANIMAL_BUY_INDIR(i,s,sc)=sum(ra,BW_A.l('sow',ra,i,s)*113*indloss_N_a, vol.1000

, ANIMAL_SELL(i,s,sc) = sum((a,ra),SW_A.l(a,ra,i,s)*weight_a(a)*rate_n_a(a)/1000)

, FLOW_ANIMAL(i,s,sc) = ANIMAL_BUY_DIR(i,s,sc)-ANIMAL_SELL(i,s,sc)

, OUTPUT_ANIMAL(i,s,sc)= abs(FLOW_ANIMAL(i,s,sc))$(FLOW_ANIMAL(i,s,sc)<0)

, INPUT_ANIMAL_DIR(i,s,sc)= abs(FLOW_ANIMAL(i,s,sc))$(FLOW_ANIMAL(i,s,sc)>0)

, INPUT_ANIMAL_INDIR(i,s,sc)=(FLOW_ANIMAL(i,s,sc)*ANIMAL_BUY_INDIR(i,s,sc)/ANIMAL_BUY_DIR(i,s,sc))$((FLOW_ANIMAL(i,s, sc)>0) and (ANIMAL_BUY_DIR(i,s,sc)<>0))

, CARBONE_A_FARM(i,s,sc)=(sum((a,ra,ma), N_a.l(a,ra,i,s)*y_N(a,ra,ma)*rate_cn_fe(ma)))

, CARBONE_A_EXCHANGE(i,s,sc)=(sum(ma,(BL_FE.l(ma,i,s)-SL_FE.l(ma,i,s))*rate_cn_fe(ma)))

, BIOMASS_C_AIR(i,s,sc)=sum((spois,r,t

X. Y_c,

, BIOMASS_C_ROOT(i,s,sc)=(sum((rootC,r,t

X. Y_c, t,s)*content_dryM_c(rootC)*coeff_biomass_root(rootC))+sum((pois,r,t),X.l(pois,r,t,i,s)*2) +sum((t,r),X.l("pastureP

, Carbone_A_TOTAL(i,s,sc)=(CARBONE_A_FARM(i,s,sc)+CARBONE_A_EXCHANGE(i,s,sc))/1000

, Carbone_C_TOTAL(i,s,sc)= (BIOMASS_C_AIR(i,s,sc)+ BIOMASS_C_ROOT(i,s,sc))*40

. Carbone_actif, , p.0

, F1(i,s,sc)=20/(1+(20-1)*exp(-0.120*(Tmoy(i,s)-15)))

, F2(i,s,sc)=exp(-2.440*rate_clay(i,s)/1000)

, F3(i,s,sc)=1+0.19*rate_clay(i,s)/1000

, h(i,s,sc)=0.166*F3(i,s,sc)

, coeff_min(i,s,sc)=0.048*f1(i,s,sc)*F2(i,s,sc)

, kca(i,s,sc)=Carbone_actif(i,s,sc)*coeff_min(i,s,sc)*sum

, hm(i,s,sc)=(h(i,s,sc)*Carbone_C_TOTAL(i,s,sc)*10)+(Carbone_A_TOTAL(i,s,sc)*1000*0, vol.4

, stock_n_soil(i,s,sc)=((hm(i,s,sc)-kca(i,s,sc))/10)

, TOTAL_INPUT_DIR(i,s,sc)=INPUT_atm(i,s,sc)+INPUT_NfIX(i,s,sc)+INPUT_BIO(i,s,sc)+INPUT_EN_DIR(i,s,sc)+INPUT_SEED_DIR(i,s,sc) +INPUT_INORG_FE_DIR(i,s,sc) +INPUT_MANURE(i,s,sc)+ INPUT_LP_DIR(i,s,sc)+ INPUT_HP_DIR(i,s,sc)+INPUT_ANIMAL_DIR

, TOTAL_INPUT_INDIR(i,s,sc)= INPUT_EN_INDIR(i,s,sc)+

, INPUT_SEED_INDIR(i,s,sc)+INPUT_INORG_FE_INDIR(i,s,sc)+INPUT_HP_INDIR(i,s,sc)+INPUT_LP_INDIR(i,s,sc)+INPUT_ANIMAL_IND IR(i,s,sc)

, TOTAL_OUTPUT(i,s,sc)= OUTPUT_LP_DIR(i,s,sc)+ OUTPUT_HP_DIR(i,s,sc)+ OUTPUT_milk(i,s,sc)+ OUTPUT_ANIMAL

, SYNE(i,s,sc)= (TOTAL_OUTPUT(i,s,sc))/(TOTAL_INPUT_DIR(i,s,sc)+TOTAL_INPUT_INDIR(i,s,sc)-(stock_n_soil(i,s,sc)))

, s,sc)+TOTAL_INPUT_INDIR(i,s,sc)-(TOTAL_OUTPUT(i,s,sc))-(stock_n_soil(i,s,sc)))/sum