**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 CH_{4} and N_{2}O 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) CH _{4} Indirect Forcings**

The concentration of CH_{4} has a certain RF. However, since methane has indirect effects on other GHGs, the actual forcing of CH_{4} is approximately twice as high or even higher.

- Through several chemical interactions, CH
_{4}leads to an increase in tropospheric and stratospheric ozone which is estimated to be additional 50% to the direct effect (here denoted as iF_{1}). - CH
_{4}decomposes to stratospheric H_{2}O being about 15% of the direct effect (here denoted as iF_{2}). - CH
_{4}interacts with sulphate and degrades this cooling aerosol, which accounts for a further 30% forcing above the direct effect (here denoted as iF_{3}). - Experiments showed that increases in global methane emissions cause significant decrease in hydroxyl, leading to a negative feedback loop for CH
_{4}decomposition and thus increasing CH_{4}potency (here denoted as iF_{4}). - CH
_{4}finally decomposes to CO_{2}. 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 CH_{4} and N_{2}O. 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 RF _{CO2}**

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

where α=5.35, C_{0}=278ppm and C is the entered current global mean atmospheric concentration of CO_{2}.

**Calculations of RF _{CH4} and RF_{N2O}**

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

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

where iF_{x} are the indirect CH_{4} forcing effects as entered in (2), β=0.036, ε=0.12, M_{o}=722ppb, N_{0}=270ppb, and M, N are the entered current global mean atmospheric concentrations of CH_{4} and N_{2}O 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 CO_{2}. RF_{g} is the radiative forcing due to a pulse emission of a gas g given by RF_{g} = A_{g}R_{g} where A_{g} is the RF_{g} per unit mass increase in atmospheric abundance of species g (radiative efficiency (RE) per unit mass), and R_{g} is the fraction of species g remaining in the atmosphere after the pulse emissions. RF_{CO2} is the radiative forcing of CO_{2}.

**Calculation of AGWP _{CO2}**

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

where H is the time horizon, a_{i} are fractions of abundances, ?_{i} are timescales. According to models by Joos et al. (2013), a_{0} = 0.2173, a_{1} = 0.2240, a_{2} = 0.2824, a_{3} = 0.2763, ?_{1} = 394.4, ?_{2} = 36.54, ?_{3} = 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 RF_{CY} is the Radiative Forcing at the entered CO_{2} levels of the current year based on calculations in (3), RF_{2010} is the Radiative Forcing in 2010, C_{CY} is the atmospheric concentration of CO_{2} at the year entered, C_{2010} is the atmospheric concentration of CO_{2} in 2010 and M_{CO2} is the molar mass of CO_{2}.

**Calculation of AGWP _{CH4}**

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

where H is the time horizon, ? the pertubation lifetime of CH_{4} 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 RF_{CY} is the Radiative Forcing at the entered CH_{4} levels of the current year including indirect CH_{4} forcings based on calculations in (2) and (3), RF_{2010} is the Radiative Forcing in 2010, M_{CY} is the atmospheric concentration of CH_{4} at the year entered, M_{2010} is the atmospheric concentration of CH_{4} in 2010 and M_{CH4} is the molar mass of CH_{4}.

**Calculation of AGWP _{N2O}**

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

where H is the time horizon, ? the pertubation lifetime of N_{2}O 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 RF_{CY} is the Radiative Forcing at the entered N_{2}O levels of the current year based on calculations in (3), RF_{2010} is the Radiative Forcing in 2010, N_{CY} is the atmospheric concentration of N_{2}O at the year entered and N_{2010} is the atmospheric concentration of N_{2}O in 2010 and M_{N2O} is the molar mass of N_{2}O.

Time horizon H is preset to 0 years, which calculates instantaneous global warming potentials (GWP_{ins}).

**(5) Emissions & Carbon Opportunity Costs**

Direct emissions of CH_{4}, CO_{2}, N_{2}O, 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 CO_{2}, 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 (CGW_{AA}) 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 (CGW_{I}) 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 CH_{4}, CO_{2} and N_{2}O, P the portions of different industries I per species, GWP the global warming potentials of CH_{4} and N_{2}O as calculated in (4) and COC the carbon opportunity costs of animal agriculture.

*References*

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