### Climate metrics calculations

We use analytical Impulse Response Functions (IRFs) to calculate the hydrogen GWP and GTP^{52}. The mass of a species *S* evolves in time in the atmosphere according to:

$${Delta {{{{{rm{M}}}}}}}_{S}left({{mbox{t}}}right){{mbox{=}}}{int }_{{{{mbox{t}}}}_{0}}^{{{mbox{t}}}}{{{mbox{E}}}}_{{{mbox{S}}}}left(t^{prime} right){{{mbox{IRF}}}}_{{{mbox{S}}}}left(t-t^{prime} right),{{mbox{dt}}}^{prime}$$

(1)

where M_{S}(t) is the species atmosphere mass (kg) at time t, ({{{{{{rm{E}}}}}}}_{S}({{{{{rm{t}}}}}})) the emission of the species (kg/year), and t_{0} is the initial year of integration (we assume t_{0} = 0). The atmospheric mass M_{S} is converted to mixing ratio *q*_{S} (ppbv) with ({q}_{S}) = 5.625 × 10^{−9} ({{{{{{rm{M}}}}}}}_{S})/m_{S}, where m_{S} is the molecular mass.

The H_{2} IRF is a simple exponential decay function with a characteristic atmospheric global lifetime ({tau }_{{{{{{{rm{H}}}}}}}_{2}}) of 2.5 years (corresponding to a global tropospheric lifetime of 2.1 years)^{15}:

$${{{{{{rm{IRF}}}}}}}_{{{{{{{rm{H}}}}}}}_{2}}(x)={{exp }}left(-frac{x}{{tau }_{{{{{{{rm{H}}}}}}}_{2}}}right)$$

(2)

A similar IRF is used for methane with a perturbation lifetime ({tau }_{{{{{{{rm{CH}}}}}}}_{4}}) of 12.4 years^{43}. The IRF for CO_{2} is calculated with refs. 52, 60:

$${{{{{{rm{IRF}}}}}}}_{{{{{{{rm{CO}}}}}}}_{2}}left(xright)={a}_{0}+mathop{sum }limits_{i=1}^{3}{a}_{i},{{exp }}left(-frac{x}{{b}_{i}}right)$$

(3)

with *a*_{0} = 0.217, *a*_{1} = 0.259, *a*_{2} = 0.338, *a*_{3} = 0.186, *b*_{1} = 172.9 year, *b*_{2} = 18.51 year, and *b*_{3} = 1.186 year. These parameters used in the IRF were determined from a 400 GtC impulse emission in the Bern carbon cycle model^{52,60}.

The CO_{2} radiative forcing (RF, or ERF) is then calculated based on the calculated (triangle {q}_{{{{{{rm{CO}}}}}}2})(t) and the radiative forcing efficiency^{41} of 1.33 × 10^{−5} W m^{−2} ppbv^{−1}. For H_{2} indirect forcings, a similar procedure is used based on the GFDL-AM4.1 radiative forcings efficiencies^{15}. The H_{2} forcing is further decomposed into its various components corresponding to the stratospheric H_{2}O, tropospheric and stratospheric ozone components and for these forcings the H_{2} lifetime is used.

A special treatment is used for the methane perturbation associated with the change in OH resulting from H_{2} emissions in order to account for the different lifetime of the perturbation. The methane lifetime associated with OH oxidation 9.7 years in the GFDL-AM4 model^{40} is ajusted to account for the stratospheric loss of methane with a lifetime of 120 years, and for the methane soil uptake with a lifetime of 160 years. Based on the change in OH of +8% for a 200 Tg H_{2} emission increase^{15}, the steady state methane concentration due to the H_{2} perturbation is calculated with^{61,62};

$$triangle {q}_{{{{{{rm{CH}}}}}}4}^{{SS}}=f,{q}_{{{{{{rm{CH}}}}}}4}^{{ref}}triangle {{{{{{rm{tau }}}}}}}_{{{{{{rm{CH}}}}}}4}$$

(4)

where (Delta {q}_{{{{{{rm{CH}}}}}}4}^{{SS}}) is the steady-state change in methane mixing ratio due to H_{2} increase in the atmosphere per TgH_{2}, ({q}_{{{{{{rm{CH}}}}}}4}^{{ref}}) (1808 ppbv) is the reference methane mixing ratio, *f* = 1.3^{15} denotes the methane feedback on its own lifetime and Δτ_{CH4} (%/TgH_{2}) is the change in methane lifetime per TgH_{2}. We approximate the change in methane due to the H_{2} impact on OH with^{63}:

$${Delta {{{{{rm{M}}}}}}}_{{{{{{rm{CH}}}}}}4}left({{{{{rm{t}}}}}}right),=, Delta {q}_{{{{{{rm{CH}}}}}}4}^{{SS}},{int }_{{t}_{0}}^{t}{triangle {{{{{rm{M}}}}}}}_{{{{{{rm{H}}}}}}2}left({t}^{{prime} }right),left[(1-{e}^{-frac{1}{{{{{{{rm{tau }}}}}}}_{{{{{{rm{CH}}}}}}4}}})delta left({t}^{{prime} }-{t}_{0}right)right.\ +left.(1-{e}^{-frac{1}{{{{{{{rm{tau }}}}}}}_{{{{{{rm{CH}}}}}}4}}}){e}^{-frac{(t-{t}^{{prime} })}{{{{{{{rm{tau }}}}}}}_{{{{{{rm{CH}}}}}}4}}}(1-delta left({t}^{{prime} }-{t}_{0}right))right]{dt}^{prime}$$

(5)

where (delta)(x) is the Dirac function. Each year following the hydrogen pulse emission, due to the change in H_{2}, CH_{4} increases towards the steady-state perturbation (first term of equation) and decreases exponentially from this value the following years (second term). Supplementary Fig. S8a shows the response of the atmospheric mass of H_{2}, CH_{4}, and CO_{2} after a pulse emission of H_{2} (and CO_{2}) of 1 Tg. H_{2} decreases exponentially after emission with a characteristic lifetime ({tau }_{{{{{{{rm{H}}}}}}}_{2}})and CO_{2} decreases with a much longer lifetime ({tau }_{{{{{{{rm{CO}}}}}}}_{2}}.) Methane resulting from the H_{2} increase in the atmosphere and the subsequent perturbation in OH, increases from 0 to a peak of 60 pptv 4 years after the initial 1 TgH_{2} emission. This value is in agreement with the 80 pptv calculated with the STOCHEM three-dimensional model^{28} for 1.67 TgH_{2} (*i.e*. 48 pptv/TgH_{2}). The peak CH_{4} increase is however larger in our estimate, essentially due a shorter H_{2} tropospheric lifetime in STOCHEM (1.6 year) compared to GFDL-AM4.1 (2.1 year). Based on the calculated change in methane mixing ratio, the radiative forcing efficiency of 44.3 × 10^{−5} W m^{−2} ppbv^{−1} is used^{45} to derive the associated radiative forcing. The direct methane forcing is increased to account for the indirect tropospheric ozone (0.116 × 10^{−3} W m^{−2} ppbv^{−1}) and stratospheric H_{2}O (0.027 × 10^{−3} W m^{−2} ppbv^{−1}) forcings^{64}. The indirect CO_{2} produced from CH_{4} oxidation^{64,65} is not accounted for in this work. The tropospheric ozone and stratospheric water vapour forcings reported with GFDL-AM4.1 are associated with both H_{2} and CH_{4} changes. In our calculations, the methane forcing also accounts for the indirect tropospheric O_{3} and stratospheric H_{2}O indirect contributions. In order to avoid double counting, we calculate the methane forcing at steady-state for a 1 Tg H_{2} perturbation. This forcing is higher that the methane forcing calculated with GFDL-AM4.1 due to these indirect ozone and stratropheric H_{2}O contributions included. The tropospheric ozone and stratospheric H_{2}O radiative forcing efficiencies from GFDL-AM4.1 are then rescaled in order to account for this difference and hence separate the H_{2} and CH_{4} impact on these forcings.

The climate response, in terms of global surface temperature change, is also estimated based on an IRF^{52}:

$$Delta Tleft({{{{{rm{t}}}}}}right)={int }_{{t}_{0}}^{t}{{{{{rm{RF}}}}}}left({{{{{rm{t}}}}}}^{prime} right),{{{{{{rm{IRF}}}}}}}_{{{{{{rm{T}}}}}}}left(t-t^{prime} right),{dt}^{prime}$$

(6)

The climate response IRF_{T} is provided by:

$${{{{{{rm{IRF}}}}}}}_{{{{{{rm{T}}}}}}}left(xright)=frac{1}{lambda }mathop{sum}limits_{i={s,f}}frac{{c}_{i}}{{d}_{i}}{{exp }}left(-frac{x}{{d}_{i}}right)$$

(7)

where (lambda) is the climate sensitivity parameter, and subscripts *f* and *s* refer to the fast and slow climate responses, respectively. The updated coefficients^{66,67} of IRF_{T} are: *c*_{f} = 0.587, *c*_{s} *=* 0.413, *d*_{f} = 4.1 year, and *d*_{s} = 249 year. The sum of the *c*_{s} and c_{f} coefficients is normalized and the climate sensitivity parameter, (lambda) = 1.04 W/m^{2}/K, is introduced in the IRF, assuming a 3.78 K warming for a CO_{2} doubling radiative forcing (3.93 Wm^{−2})^{41}. Supplementary Fig. S8b, c show the resulting radiative forcing and temperature change after a 1Tg pulse emission of H_{2} (or CO_{2}). The additional carbon cycle responses to temperature are excluded in our calculations^{68}.

The Absolute GWP (AGWP) of H_{2} is calculated based on:

$${{{{{{rm{AGWP}}}}}}}_{{{{{{{rm{H}}}}}}}_{2}}left({t}_{h}right)={int }_{{t}_{0}}^{{t}_{h}}{{{{{{rm{RF}}}}}}}_{{{{{{{rm{H}}}}}}}_{2}}left(tright),{dt}$$

(8)

The GWP of H_{2} is then calculated by definition as the ratio between the AGWP of H_{2} (or individual components) relative to the AGWP for CO_{2}:

$${{{{{{rm{GWP}}}}}}}_{{{{{{rm{H}}}}}}2}left({t}_{h}right)=frac{{{{{{{rm{AGWP}}}}}}}_{{{{{{rm{H}}}}}}2}left({t}_{h}right)}{{{{{{{rm{AGWP}}}}}}}_{{{{{{rm{CO}}}}}}2}left({t}_{h}right)}$$

(9)

This methodology is repeated in order to decompose GWP_{H2} into its various individual components (i.e., GWP_{CH4}, GWP_{H2O}, GWP_{O3t}, GWP_{O3s}), substituting ({{{{{{rm{RF}}}}}}}_{{{{{{{rm{H}}}}}}}_{2}})by the individual radiative forcings of methane, stratospheric water vapour, tropospheric ozone, and stratospheric ozone.

The Absolute GTP (AGTP) of H_{2} is calculated based on:

$${{{{{{rm{AGTP}}}}}}}_{{{{{{{rm{H}}}}}}}_{2}}left({t}_{h}right)={int }_{{t}_{0}}^{{t}_{h}}{{{{{{rm{RF}}}}}}}_{{{{{{{rm{H}}}}}}}_{2}}left(tright),{{{{{{rm{IRF}}}}}}}_{{{{{{rm{T}}}}}}}left({t}_{h}-tright),{dt}=,Delta {T}_{{{{{{{rm{H}}}}}}}_{2}}left({t}_{h}right)$$

(10)

The GTP is calculated by definition as the ratio between the AGTP of H_{2} (or of its individual componenets) and the AGTP for CO_{2}:

$${{{{{{rm{GTP}}}}}}}_{{{{{{rm{H}}}}}}{2}}left({t}_{h}right)=frac{{{{{{{rm{AGTP}}}}}}}_{{{{{{rm{H}}}}}}2}left({t}_{h}right)}{{{{{{{rm{AGTP}}}}}}}_{{{{{{rm{CO}}}}}}2}left({t}_{h}right)}$$

(11)

The emission profile ({{{{{{rm{E}}}}}}}_{{{{{{{rm{H}}}}}}}_{2}}({{{{{rm{t}}}}}})) (or ({{{{{{rm{E}}}}}}}_{{{{{{{rm{CO}}}}}}}_{2}})) is taken to be a pulse emission of 1 Tg for the calculation of the pulse metrics GWP_{p} and GTP_{p} or a step sustained emission of 1 Tg for the sustained metrics GWP_{s} and GTP_{s}. It should be noted, that the exact definition of the GWP refers to an instantaneous pulse emission. In our calculations, a time-step of 1 year is considered, implying a 1-year pulse emission even for GWP_{p}. This limitation induces a 10% difference in the GWP_{p,100} calculation^{3}.

In order to derive the combined metrics^{44}, we first define the Absolute Global Forcing Potential (GFP):

$${{{{{{rm{AGFP}}}}}}}_{{{{{{{rm{H}}}}}}}_{2}}left({t}_{h}right)={int }_{{t}_{0}}^{{t}_{h}}{{{{{{rm{RF}}}}}}}_{{{{{{{rm{H}}}}}}}_{2}}left({t}_{h}-tright)delta left(t-{t}_{0}right),{dt}={{{{{{rm{RF}}}}}}}_{{{{{{{rm{H}}}}}}}_{2}}left({t}_{h}right)$$

(12)

Similar to the AGTP which provides the temperature at a considered time-horizon, the AGFP is an end-point metric providing the radiative forcing at a considered time-horizon. The H_{2} Combined GWP (CGWP) is then calculated with:

$${{{{{{rm{CGWP}}}}}}}_{{{{{{rm{H}}}}}}2}left({t}_{h}right)=frac{{{{{{{rm{AGFP}}}}}}}_{{{{{{rm{H}}}}}}2,{{{{{rm{s}}}}}}}left({t}_{h}right)}{{{{{{{rm{AGFP}}}}}}}_{{{{{{rm{CO}}}}}}2}left({t}_{h}right)}$$

(13)

and the H_{2} Combined GTP (CGTP) is calculated with:

$${{{{{{rm{CGTP}}}}}}}_{{{{{{rm{H}}}}}}2}left({t}_{h}right)=frac{{{{{{{rm{AGTP}}}}}}}_{{{{{{rm{H}}}}}}2,{{{{{rm{s}}}}}}}left({t}_{h}right)}{{{{{{{rm{AGTP}}}}}}}_{{{{{{rm{CO}}}}}}2}left({t}_{h}right)}$$

(14)

where the subscript ‘s’ refers to the sustained emission metrics.

The uncertainties in the H_{2} and CH_{4} metrics are estimated following the exact same methodology as developed and presented by IPCC^{41}. Since a large fraction of the H_{2} indirect climate impact is associated with methane, several uncertainties are similar for these two species. Supplementary Tables S1 and S2 provide, for respectively CH_{4} and H_{2}, the total uncertainty calculated in various metrics, as a percentage of the best estimate and expressed as 90% confidence interval. The uncertainties are also provided by component of the total emission metric calculation (radiative efficiency, chemical response and feedbacks, atmospheric lifetime, CO_{2} combined uncertainty in radiative efficiency and CO_{2} impulse response function, carbon cycle response, fate of oxidized fossil methane, and impulse-response function for temperature increase). The uncertainties in individual terms are taken from Section 7.6 of IPCC AR6 report^{41}, except for the CO_{2} impulse response which comes from Joos and Bruno^{60}. The uncertainties are however modified for H_{2} when needed, in particular the lifetime uncertainty is estimated assuming a H_{2} atmospheric lifetime uncertainty of 0.5 year around our best estimate of 2.5 year. The uncertainties on the temperature impulse-response function were recalculated by taking 1.645 x standard deviation of the GTPs generated from 600 ensemble members of the impulse response derived from two climate emulators (see Forster et al.^{41} for more details). The resulting estimated total uncertainty in the H_{2} GWP is 31–36%. A value in agreement with previous estimates^{35}. The uncertainty on the H_{2} GTP ranges from 131 to 64% and is largely dominated by the climate response function uncertainty. The uncertainty on the GTP is in the range 47–73%. These uncertainties on the metrics directly translate into similar uncertainties on the calculated CO_{2} equivalent emissions.

### Future hydrogen emission scenarios

The estimated hydrogen production in 2020 is 87^{53}–90^{54} Mt H_{2}/year. It is beyond the scope of this study to propose future hydrogen energy supply scenarios. Instead, we base our analysis on the scenarios developed by the Hydrogen Council for the worldwide hydrogen energy transition and on the European Union (EU) roadmap for a future hydrogen economy in Europe. These scenarios are succinctly summarized below and we refer the reader to the full reports for a more in-depth overview of the underlying economic and energy assumptions. The worldwide energy transition scenario used in this study is based on the scenario developed by the Hydrogen Council as a roadmap for long-term hydrogen deployment^{50}. This scenario (referred to as HC2017) analyses the possible deployment of hydrogen in the various sectors: transportation, industrial energy, building heating and power, industry feedstock and power generation, and assumes an almost eight-fold increase in hydrogen demand between 2020 and 2050. According to this scenario the global energy supply of hydrogen was 10 EJ (2778 TWh) in 2020, and is projected to increase to 14 EJ (3889 TWh) in 2030; 28 EJ (7778 TWh) in 2040, and 78 EJ (21,667 TWh) in 2050. In this study, we use a hydrogen energy density of 142 MJ/kg as used in previous work^{3,4,11,50}. This value is the Higher Heating Value (HHV) of the hydrogen fuel defined as the amount of heat released once it is combusted and the products have returned to a temperature of 25 °C, considering the latent heat of vaporization of water in the combustion products. Currently, the hydrogen technologies do not condense the water to use the full heating value of hydrogen. The hydrogen Lower Heating Value (LHV) of 120 MJ/kg, defined as the amount of heat released by combusting hydrogen and returning the temperature of the combustion products to 150 °C, and hence assuming that the latent heat of vaporization of water in the reaction products is not recovered, should be used. For consistency with previous work but also assuming an improvement of the hydrogen technologies over the next 30 years, we apply the HHV in our analysis. Based on this value we derive a production of 98 Mt H_{2}/year in 2030, 197 Mt H_{2}/year in 2040 and 549 Mt H_{2}/year in 2050. Using the LHV instead of the HHV would increase the hydrogen production for a given energy demand by 18% and provide 650 Mt H_{2}/year in 2050. The sensitivity of the results to the use of the LHV instead of the HHV will be illustrated. Please note that using the LHV (more consistent with current hydrogen technologies), we derive a hydrogen production in 2020 (estimated in 2017^{50}) of 83 Mt H_{2}/year, a value lower by 4–8% compared to the actual production reported for 2020^{53,54}. In addition to this total energy supply, this scenario further assumes a phase-out of grey hydrogen by 2040 and an increased supply of blue and green hydrogen to about 33% grey, 33% blue, and 33% green in 2030; 50% blue in 2030, and 30% blue in 2050^{51}. For the year 2050, the HC2017 scenario results in an annual 6 GtCO_{2}/year abatement. We assume the 2050 values over the period 2050–2100. Over the entire 2030–2100 period, the HC2017 scenario results in a cumulative CO_{2} emission abatement of 331 GtCO_{2}.

There is a continued acceleration in hydrogen deployment and a strong momentum for future transition to an hydrogen economy. A more ambitious hydrogen scenario with hydrogen reaching 22% of the global energy demand in 2050 has been developed by the Hydrogen Council and McKinsey & Company^{54}. According to this scenario (referred to as HCMK2021), the hydrogen worldwide end-use demand increases from 20 EJ (5555 TWh) in 2030; 55 EJ (15,278 TWh) in 2040; to 94 EJ (26,111 TWh) in 2050. This corresponds to 140, 385, and 660 Mt H_{2}/year in 2030, 2040 and 2050, respectively. This scenario further assumes 50%, 30 and 20% of grey, blue, and green hydrogen, respectively, in 2030; 5%, 40%, and 55%, respectively in 2040; and 100% green hydrogen in 2050. The HCMK2021 scenario results in an annual CO_{2} emission abatement of 7 GtCO_{2}/year in 2050. If we further assume the 2050 values constant for the following decades, over the entire 2030–2100 period, the HCMK2021 scenario results in a cumulative CO_{2} emission abatement of 417 GtCO_{2}. Other scenarios for future hydrogen production have been developed. In particular, in its “Net Zero by 2050” roadmap, the International Energy Agency (referred to as IEA2021) assumes a future hydrogen supply of 212 Mt H_{2}/year in 2030, 390 Mt H_{2}/year in 2040, and 528 Mt H_{2}/year in 2050^{53}. This scenario further assumes 30%, 32 and 38% of grey, blue, and green hydrogen, respectively, in 2030, and 9%, 38%, and 53%, respectively in 2040. In 2050, this scenario still assumes a significant fraction of blue hydrogen with 1% of grey, 37% of blue, and 62% of green hydrogen. The IEA2021 scenario results in an annual CO_{2} emission abatement of 5.7 GtCO_{2}/year in 2050. If we further assume the 2050 values constant for the following decades, over the entire 2030–2100 period, the IEA2021 scenario results in a cumulative CO_{2} emission abatement of 353 GtCO_{2}. Another set of three future scenarios for global scale transition to an hydrogen economy has also been proposed by Bloomberg NEF^{69}. These scenarios estimate a total energy demand for hydrogen in 2050 of 27 EJ (190 Mt H_{2}/year), 99 EJ (697 Mt H_{2}/year), and 195 EJ (1373 Mt H_{2}/year) for the “Weak Policy”, “Strong Policy” and “Theoretical Max” scenarios, respectively. We note that the “Strong Policy” scenario is close to the HCMK2021 scenario. In addition, the “Theoretical Max” scenario, which assumes that all unlikely-to-electrify sectors in the economy use hydrogen, suggests that there is an enormous potential for hydrogen use in the economy, resulting in a yearly CO_{2} abatement of almost 15 GtCO_{2}/year in 2050. In this study we focus on the HC2017 and further illustrate the HCMK2021 and IEA2021 scenarios which cover a reasonable range allowing to assess the sensitivity of the results to the development of a future hydrogen economy, but we note that other scenarios are also available.

The European Union (EU) has issued an hydrogen roadmap aiming at generating 8.1 EJ (2250 TWh) of hydrogen in 2050, representing roughly a quarter of the EU’s total energy demand^{53}. Achieving this objective would reduce EU annual CO_{2} emissions by about 560 Mt CO_{2} in 2050. Instead of using this scenario, we rather use a more recent and slightly more ambitious scenario developed for European future energy transition by the European Network of Transmission System Operators for Gas and Electricity (ENTSOG/ENTSO-E)^{55}. The “Global Ambition” scenario^{55} (referred to here as TYNDP2022) pictures a EU pathway to achieving carbon neutrality by 2050 with a hydrogen demand developing as of 2030 and becoming the main gas energy carrier in 2050. According to this scenario 1.7 EJ (466 TWh) are produced from hydrogen in 2030; 5.7 EJ (1575 TWh) in 2040; and 9.0 EJ (2496 TWh) in 2050; corresponding to a supply of 12 Mt H_{2}/year in 2030, 40 Mt H_{2}/year in 2040 and 63 Mt H_{2}/year in 2050. The TYNDP2022 scenario further assumes a phase-out grey hydrogen before 2030, and 51%, 13.5 and 6% of blue hydrogen in 2030, 2040, and 2050, respectively. This scenario reduces the annual CO_{2} emissions by 620 MtCO_{2}/year in 2050. Assuming 2050 values for the following decades, the TYNDP2022 scenario leads to a mitigation of cumulative CO_{2} emissions of 36 GtCO_{2} over the full period 2030–2100.

### Carbon dioxide and methane emissions from blue and grey hydrogen

At present, 95% of the hydrogen is produced via the Steam Methane Reforming (SMR) process using fossil natural gas as a feedstock^{70}. The CO_{2} emissions from grey hydrogen production were recently calculated^{4} considering both the CO_{2} emissions during the SMR process itself (38.5 gCO_{2}/MJ), during the heat and electricity generation needed to drive the SMR process (31.8 gCO_{2}/MJ), and the upstream emission from the energy used to produce, process and transport natural gas and hydrogen (5.3 gCO_{2}/MJ). The sum of these three terms (75.6 gCO_{2}/MJ), combined with the energy content of gaseous hydrogen (7 gH_{2}/MJ) provides an emission of 10.8 kgCO_{2}/kgH_{2}. We also account for the methane needed to produce hydrogen^{4}. The methane needed for the SMR process itself (14.04 gCH_{4}/MJ) plus the amount burned to generate the heat and pressure needed for SMR (11.6 gCH4/MJ) provides a total of 25.6 gCH4/MJ, or 3.65 kgCH_{4}/kgH_{2}. Based on this total methane amount, we account for the leakage during production and use of unburned methane to the atmosphere with a leakage fraction *fl*_{CH4} (see below). The total methane amount needed is slighly larger than the previous estimates of 3.0 kgCH_{4}/kgH_{2}^{71} and 3.2 kgCH_{4}/kgH_{2}^{5}.

Blue hydrogen differs from grey hydrogen because some of the carbon dioxide released by the SMR process or/and heat and pressure generation is captured. We use capture rates^{4} of 85% efficiency for SMR and 65% efficiency for driving the SMR. The total CO_{2} emissions remaining, assuming CO_{2} capture for both processes, is therefore 15% × 38.5 gCO_{2}/MJ + 35% × 31.8 gCO_{2}/MJ = 16.9 gCO_{2}/MJ. In addition, we consider the energy required to capture carbon dioxide^{4}. The CO_{2} emissions associated with carbon sequestration during both SMR and energy production to drive SMR is 16.3 gCO_{2}/MJ^{4}. An additional emission of 6.5 gCO_{2}/MJ is added for indirect upstream emissions, providing a total CO_{2} emission from blue hydrogen production and transport of 39.7 gCO_{2}/MJ, or 5.7 kgCO_{2}/kgH_{2}. This value, which accounts in particular for the energy needed to ensure the carbon sequestration, is significantly higher than previous estimate^{51} of 1.5 kgCO_{2}/kgH_{2}.The methane amount needed for blue hydrogen is similar to grey hydrogen except for the amount associated with the increased energy needed to drive the carbon sequestration process^{4}. This amount is estimated at 6.0 gCH_{4}/MJ, providing a total ammout of CH_{4} of 31.6 gCH_{4}/MJ, or 4.5 kgCH_{4}/kgH_{2.} Based on this total methane amount, we apply a leakage fraction *fl*_{CH4} (see below) to account for unburned methane emission to the atmosphere. The equivalent CO_{2} emissions, at a given time-horizon, from methane leakage during the grey and blue hydrogen production are calculated by multiplying the methane fugitive emissions by the corresponding recalculated methane climate metric (see Supplementary Table S3).

The hydrogen leakage rate *fl*_{H2} is varied in our calculations from 0.1 to 15% in order to calculate the hydrogen climate footprint. The overall methane leakage rate *fl*_{CH4} was recently estimated at 3.5%^{4}. In this study, we derive *fl*_{CH4} based on the considered *fl*_{H2}. Due to its lower volumetric density compared to natural gas, it is estimated that H_{2} will be transported at three times the pressure of natural gas^{5}. At these higher pressures and since the gas viscosity of H_{2} is lower than CH_{4}, the leakage rate of H_{2} is calculated 3.7–4.5 times higher than CH_{4} (assuming that most of the flow is laminar). Based on these values, we assume a volumetric leakage ratio between *fl*_{H2} and *fl*_{CH4} of 4. For emissions, we are interested by the mass of leakage and this ratio needs to be divided by the density ratio of CH_{4} to H_{2} (0.72 kg m^{−3}/0.09 kg m^{−3} = 8), providing *fl*_{H2} / *fl*_{CH4} = 0.5^{5}. The methane fugitive emission needs to be corrected in order to account for the fact that hydrogen is deployed in order to replace natural gas use^{29}. A fraction of the CH_{4} fugitive emissions would hence also be released to the atmosphere under the use of fossil fuel natural gas use. We have assumed a methane amount of 25.6 gCH_{4}/MJ needed for hydrogen production^{4}. For methane (natural gas), we assume an energy content of 53.6 MJ/kg^{72} or 18.6 gCH_{4}/MJ. The difference (25.6–18.6) 7.0 gCH_{4}/MJ is the additional methane amount needed for hydrogen production. The calculated fugitive methane emission is hence corrected and multiplied by a 0.27 ratio (7.0/25.6). In the case of blue hydrogen, accounting for the additional methane needed for carbon sequestration provides a difference between hydrogen production and natural gas use of (31.6–18.6) 13.0 gCH_{4}/MJ, and a correction factor of 0.41 (13.0/31.6). The methane leakage rate *fl*_{CH4} is then equal to 0.54 *fl*_{H2} in the case of grey hydrogen and 0.82 *fl*_{H2} for blue hydrogen.