Spec­i­fi­ca­tions of the Indus­try Foot­print Calculator

The over­all con­cept and devel­op­ment of the Indus­try Foot­print Cal­cu­la­tor is based on the work out­lined in the paper by Müller, M. (2021).

(1) Abun­dances

Abun­dances are reg­u­lar­ly mea­sured atmos­pher­ic con­cen­tra­tions of green­house gas­es. The three most impor­tant anthro­pogenic green­house gas­es (GHG) are con­sid­ered here. The gas con­cen­tra­tions deter­mine the radia­tive forc­ings (RF), how­ev­er not lin­ear­ly, but as a func­tion of the sat­u­ra­tion lev­els and in mutu­al depen­dence on each oth­er. There­fore, their con­tent can deter­mine the glob­al warm­ing poten­tials (GWP) of CH4 and N2O and thus influ­ence the indus­try’s con­tri­bu­tions to glob­al warming.

Most cur­rent data can be accessed from the Glob­al Mon­i­tor­ing Lab­o­ra­to­ry (GML) of the Nation­al Ocean­ic and Atmos­pher­ic Admin­is­tra­tion (USA): https://www.esrl.noaa.gov/gmd/ccgg/trends or from the The World Data Cen­tre for Green­house Gas­es (Japan): https://gaw.kishou.go.jp.

The fields are pre-filled with data from Novem­ber 2020 to March 2021.

(2) CH4 Indi­rect Forcings

The con­cen­tra­tion of CH4 has a cer­tain RF. How­ev­er, since methane has indi­rect effects on oth­er GHGs, the actu­al forc­ing of CH4 is approx­i­mate­ly twice as high or even higher.

  1. Through sev­er­al chem­i­cal inter­ac­tions, CH4 leads to an increase in tro­pos­pher­ic and stratos­pher­ic ozone which is esti­mat­ed to be addi­tion­al 50% to the direct effect (here denot­ed as iF1).
  2. CH4 decom­pos­es to stratos­pher­ic H2O being about 15% of the direct effect (here denot­ed as iF2).
  3. CH4 inter­acts with sul­phate and degrades this cool­ing aerosol, which accounts for a fur­ther 30% forc­ing above the direct effect (here denot­ed as iF3).
  4. Exper­i­ments showed that increas­es in glob­al methane emis­sions cause sig­nif­i­cant decrease in hydrox­yl, lead­ing to a neg­a­tive feed­back loop for CH4 decom­po­si­tion and thus increas­ing CH4 poten­cy (here denot­ed as iF4).
  5. CH4 final­ly decom­pos­es to CO2. Since the amounts are small, the forc­ing effects (< 1%) are not specif­i­cal­ly inte­grat­ed in the models.

The IPCC and almost all oth­er stud­ies and reports only con­sid­er indi­rect effects 1 & 2 to cal­cu­late the Glob­al Warm­ing Poten­tials of CH4 and N2O. Effects 1 & 2 are pre-pop­u­lat­ed with esti­mates from Myhre et al. (2013), effects 3 & 4 are described by Shin­dell et al. (2009), although only effect 3 is pre-pop­u­lat­ed here due to uncer­tain­ties about the mag­ni­tude of effect 4. 

(3) Radia­tive Forcings

RF is the addi­tion­al ener­gy per sec­ond trapped in the atmos­phere by cur­rent GHGs and aerosols that have been emit­ted due to human activ­i­ties since the begin­ning of the indus­tri­al era (year 1750). The RFs of the dif­fer­ent green­house gas­es can be cal­cu­lat­ed using radia­tive trans­fer mod­els, devel­oped by Myhre et al. (1998) and fur­ther spec­i­fied by Myhre et al. (2013) for the IPPC report AR5. The mod­els used here have uncer­tain­ties of only about 10%.

Cal­cu­la­tion of RFCO2

$$RF_{CO2} = αln \left (\frac {C}{C_0} \right )$$

where α=5.35, C0=278ppm and C is the entered cur­rent glob­al mean atmos­pher­ic con­cen­tra­tion of CO2.

Cal­cu­la­tions of RFCH4 and RFN2O

$$RF_{CH4} = (1+iF_1+iF_2+iF_3+iF_4) × (β(\sqrt{M}-\sqrt{M_0})-(f(M,N_0)-f(M_0,N_0)))$$

$$RF_{N2O} = ε (\sqrt{N}-\sqrt{N_0})-(f(M_0,N)-f(M_0,N_0)) $$

where iFx are the indi­rect CH4 forc­ing effects as entered in (2), β=0.036, ε=0.12, Mo=722ppb, N0=270ppb, and M, N are the entered cur­rent glob­al mean atmos­pher­ic con­cen­tra­tions of CH4 and N2O respec­tive­ly and $$f(M,N)=0.47 ln \left (1+2.01× 10^{-5} × (MN)^{0.75} + 5.31 × 10^{-15} × M(MN)^{1.52} \right )$$

(4) Glob­al Warm­ing Potential

GWPs express how much more ener­gy a one-time pulse of a giv­en mass of gas traps in the atmos­phere com­pared to a one-time pulse of an equal mass of CO2 over a defined peri­od of time. The cal­cu­la­tions of GWPs are defined by Myhre et al. (2013) in the IPCC report AR5.

$$GWP_g (H) = \frac {\int_0^H RF_g(t)~dt}{\int_0^H RF_{CO2}(t)~dt} = \frac {AGWP_g(H)}{AGWP_{CO2}(H)}$$

where H is the time hori­zon and AGWP the absolute (time inte­grat­ed) GWP of gas g or CO2. RFg is the radia­tive forc­ing due to a pulse emis­sion of a gas g giv­en by RFg = AgRg where Ag is the RFg per unit mass increase in atmos­pher­ic abun­dance of species g (radia­tive effi­cien­cy (RE) per unit mass), and Rg is the frac­tion of species g remain­ing in the atmos­phere after the pulse emis­sions. RFCO2 is the radia­tive forc­ing of CO2.

Cal­cu­la­tion of AGWPCO2

$$AGWP_{CO2} (H) = A_{CO2} \left (a_0H + \sum\limits_{i = 1}^3 {a_i 𝜏_i} \left (1 ‑exp \left (- \frac {H}{𝜏_i} \right ) \right ) \right )$$

where H is the time hori­zon, ai are frac­tions of abun­dances, 𝜏i are timescales. Accord­ing to mod­els by Joos et al. (2013), a0 = 0.2173, a1 = 0.2240, a2 = 0.2824, a3 = 0.2763, 𝜏1 = 394.4, 𝜏2 = 36.54, 𝜏3 = 4.304 and 

$$A_{CO2} = RE_{CO2} × M_{CO2}^{-1} = \left ((RF_{CY} — RF_{2010}) ×(C_{CY} — C_{2010})^{-1} \right ) × M_{CO2}^{-1} $$

where RFCY is the Radia­tive Forc­ing at the entered CO2 lev­els of the cur­rent year based on cal­cu­la­tions in (3), RF2010 is the Radia­tive Forc­ing in 2010, CCY is the atmos­pher­ic con­cen­tra­tion of CO2 at the year entered, C2010 is the atmos­pher­ic con­cen­tra­tion of CO2 in 2010 and MCO2 is the molar mass of CO2.

Cal­cu­la­tion of AGWPCH4

$$AGWP_{CH4} (H) = A_{CH4} × 𝜏 × \left (1 ‑exp \left (- \frac {H}{𝜏} \right ) \right )$$

where H is the time hori­zon, 𝜏 the per­tu­ba­tion life­time of CH4 of 12.4 years and 

$$A_{CH4} = RE_{CH4} × M_{CH4}^{-1} = \left ((RF_{CY} — RF_{2010}) ×(M_{CY} — M_{2010})^{-1} \right ) × M_{CH4}^{-1} $$

where RFCY is the Radia­tive Forc­ing at the entered CH4 lev­els of the cur­rent year includ­ing indi­rect CH4 forc­ings based on cal­cu­la­tions in (2) and (3), RF2010 is the Radia­tive Forc­ing in 2010, MCY is the atmos­pher­ic con­cen­tra­tion of CH4 at the year entered, M2010 is the atmos­pher­ic con­cen­tra­tion of CH4 in 2010 and MCH4 is the molar mass of CH4.

Cal­cu­la­tion of AGWPN2O

$$AGWP_{N2O} (H) = A_{N2O} \left (1–0.36 \left (\frac{RE_{CH4}}{RE_{N2O}} \right ) \right )× 𝜏 × \left ( 1 ‑exp \left (- \frac {H}{𝜏} \right ) \right )$$

where H is the time hori­zon, 𝜏 the per­tu­ba­tion life­time of N2O of 121 years and

$$A_{N2O} = RE_{N2O} × M_{N2O}^{-1} = \left ((RF_{CY} — RF_{2010}) ×(N_{CY} — N_{2010})^{-1} \right ) × M_{N2O}^{-1} $$

where RFCY is the Radia­tive Forc­ing at the entered N2O lev­els of the cur­rent year based on cal­cu­la­tions in (3), RF2010 is the Radia­tive Forc­ing in 2010, NCY is the atmos­pher­ic con­cen­tra­tion of N2O at the year entered and N2010 is the atmos­pher­ic con­cen­tra­tion of N2O in 2010 and MN2O is the molar mass of N2O.

Time hori­zon H is pre­set to 0 years, which cal­cu­lates instan­ta­neous glob­al warm­ing poten­tials (GWPins).

(5) Emis­sions & Car­bon Oppor­tu­ni­ty Costs

Direct emis­sions of CH4, CO2, N2O, and Car­bon Oppor­tu­ni­ty Costs (COC) are the main dri­vers of cur­rent con­tri­bu­tions to anthro­pogenic glob­al warm­ing. Car­bon Oppor­tu­ni­ty Costs are defined as unused car­bon sinks, mea­sured in Gt CO2, lost by a food sys­tem with ani­mal agri­cul­ture ver­sus a pure­ly plant-based food system.

Direct emis­sions are pre-filled with val­ues from the 2019 IPCC spe­cial report on cli­mate change, deser­ti­fi­ca­tion, land degra­da­tion, sus­tain­able land man­age­ment, food secu­ri­ty, and green­house gas flux­es in ter­res­tri­al ecosys­tems (p. 10).

Car­bon Oppor­tu­ni­ty Costs are pre-filled with cal­cu­la­tions by Müller, M. (2021).

(6) Emis­sions per industry

The emis­sions of green­house gas­es by indus­tries are pre-filled with results from cal­cu­la­tions by Müller, M. (2021), based on data by FAOSTAT of the UN Food and Agri­cul­ture Orga­ni­za­tion (2020), the Glob­al Change Data Lab (2020), the Inter­na­tion­al Ener­gy Agency (2020), the FAO report Livestock’s Long Shad­ow (2006) and the World Resource Insti­tute (2020).

(7) Indus­try Con­tri­bu­tions to Glob­al Warming

The con­tri­bu­tion of ani­mal agri­cul­ture to glob­al warm­ing (CGWAA) is

$$ CGW_{AA} = \frac {E_{CH4}P_{CH4[AA]}GWP_{CH4}+E_{CO2}P_{CO2[AA]}+E_{N2O}P_{N2O[AA]}GWP_{N2O}+COC}{E_{CH4}GWP_{CH4}+E_{CO2}+E_{N2O}GWP_{N2O}+COC} × 100 \% $$

and the con­tri­bu­tions of all oth­er indus­tries (CGWI) are

$$ CGW_{I} = \frac {E_{CH4}P_{CH4[I]}GWP_{CH4}+E_{CO2}P_{CO2[I]}+E_{N2O}P_{N2O[I]}GWP_{N2O}}{E_{CH4}GWP_{CH4}+E_{CO2}+E_{N2O}GWP_{N2O}+COC} × 100 \% $$

where E are glob­al emis­sions of CH4, CO2 and N2O, P the por­tions of dif­fer­ent indus­tries I per species, GWP the glob­al warm­ing poten­tials of CH4 and N2O as cal­cu­lat­ed in (4) and COC the car­bon oppor­tu­ni­ty costs of ani­mal agriculture.


Glob­al Change Data Lab: Our World in Data, 2020, data based on FAOSTAT (FAO, 2016) for Agri­cul­ture total, Land Use sources and For­est and on the EDGAR Data­base (JRC/PBL, 2016) for the oth­er sec­tors. Avail­able at https://ourworldindata.org. Accessed June 21, 2020

Inter­na­tion­al Ener­gy Agency, Data and sta­tis­tics, 2020, Avail­able at https://www.iea.org. Accessed June 21, 2020

Joos, F. et al., 2013: Car­bon diox­ide and cli­mate impulse response func­tions for the com­pu­ta­tion of green­house gas met­rics — a mul­ti-mod­el analy­sis. Atmos. Chem. Phys., 13, 2793–2825, 2013. Avail­able at https://doi.org/10.5194/acp-13–2793-2013. Accessed April 12, 2021

Müller, M. (2021): The con­tri­bu­tions of ani­mal agri­cul­ture and major fos­sil-fuel-based indus­tries to glob­al warm­ing. Avail­able at https://doi.org/10.13140/RG.2.2.22613.35040/1. Accessed April 12. 2021

Myhre, G., et al., 1998: New esti­mates of radia­tive forc­ing due to well mixed green­house gas­es. Geo­phys. Res. Lett., 25, Pp. 2715–2718. Avail­able at https://doi.org/10.1029/98GL01908. Accessed April 12, 2021

Myhre, G., et al., 2013: Anthro­pogenic and Nat­ur­al Radia­tive Forc­ing Sup­ple­men­tary Mate­r­i­al. In: Cli­mate Change 2013: The Phys­i­cal Sci­ence Basis. Avail­able at www.climatechange2013.org and www.ipcc.ch. Accessed April 12, 2021

Shin­dell, D.T., et al., 2009: Improved attri­bu­tion of cli­mate forc­ing to emis­sions. In: Sci­ence, 326, 716–718. Avail­able at https://doi.org/10.1126/science.1174760. Accessed April 12, 2021

Unit­ed Nations Food and Agri­cul­ture Orga­ni­za­tion, FAOSTAT, 2020, Avail­able at www.fao.org/faostat. Accessed June, 21, 2020

Unit­ed Nations Food and Agri­cul­tur­al Orga­ni­za­tion, 2006: Livestock’s Long Shad­ow, Envi­ron­men­tal Issues and Options. Chief, Elec­tron­ic Pub­lish­ing Pol­i­cy and Sup­port Branch, Com­mu­ni­ca­tion Divi­sion – FAO, Viale delle Terme di Cara­calla, 00153 Rome, Italy. Avail­able at http://www.fao.org/3/a0701e/a0701e00.htm. Accessed June, 21, 2020

World Resources Insti­tute, CAIT Cli­mate Data Explor­er, 2020, Avail­able at https://www.climatewatchdata.org. Accessed June, 21, 2020