The increase in abundance of atmospheric H2 in a future hydrogen economy is not well constrained due to uncertainties in fugitive emissions, which will depend on the ultimate size of the hydrogen economy, H2 leakage rates and uncertainties in the amount of H2 undergoing uptake by soils. To guide our model scenarios, we estimate how emissions of H2 and other species may change in response to a switch from fossil fuel to hydrogen technologies in an illustrative hydrogen economy scenario. In this scenario, approximately 23 % of global energy consumption (about 133 EJ) is supplied by hydrogen (BP, 2020). We, here, assume that in the buildings sector, the transport sector and the power generation sector, 100 %, 50 % and 10 % respectively of the final consumption of fossil fuels switches to hydrogen. The lower percentages for the transport sector and the power generation sector reflect the smaller role hydrogen is assumed to play in these energy sectors due to the existence of low-carbon alternatives such as electric vehicles, wind power and solar power, as well as alternative storage options such as pumped hydro, batteries and compressed air (e.g. Staffell et al., 2019). New hydrogen technologies are assumed to have the same energy efficiency as the fossil fuel technology they are replacing (Staffell et al., 2019), except for in the transport sector, where we assume diesel vehicles and petrol vehicles with an average tank-to-wheel energy efficiency of 30 % will be replaced by vehicles using hydrogen fuel cells with an average efficiency of 50 %. Using a net calorific value of 1 kg H2 = 33.3 kWh, approximately 860 Tg H2 yr-1 would be required to provide the energy consumption outlined above.

H2 leakage rates of the infrastructure associated with a hydrogen economy are uncertain and will depend on many factors (e.g. E4tech, Ltd, 2019). However, all else being equal, H2 leakage rates of the infrastructure associated with a hydrogen economy are likely to be higher than the leakage rates of natural gas, owing to the small molecule size of hydrogen. A recent study, looking at the US natural gas supply chain, indicated natural gas leaks of around 2.3 % of gross gas production, which is ∼ 60 % higher than the US EPA inventory estimate (Alvarez et al., 2018). H2 leakage rates of 1 % and 10 % (which represent the range of values used in previous studies e.g. Shultz et al., 2003; Warwick et al., 2004) would lead to additional H2 emissions of 9 and 96 Tg H2 yr-1 respectively based on a hydrogen economy supplying 23 % of total present-day energy consumption.

We bypass some of the uncertainties in H2 leakage rates, the ultimate size of the hydrogen economy and soil uptake rates, by performing a range of hydrogen economy scenarios with fixed H2 lower boundary mixing ratios. We consider scenarios with H2 lower boundary conditions ranging from 500 to 2000 ppb (i.e. increases relative to present-day mixing ratios of 0 to 1500 ppb), which we believe span many of these uncertainties (see Table 1). For example, based on the size of a hydrogen economy under the conditions outlined above, and assuming the magnitude of the soil sink increases in line with the increase in H2 mixing ratios (i.e. a constant deposition velocity), box model simulations indicate H2 lower boundary conditions of 750, 1000 and 1500 ppb represent H2 leakage rates of about 3 %, 7 % and 13 % respectively (see Sect. 2.2 for further details on the box modelling). However, these H2 lower boundary conditions would also be consistent with other fractions of total energy supplied by H2, alternative soil sink responses and H2 leakage rates. Use of this range of H2 lower boundary conditions provides a clear signal in the atmospheric response to increased H2 mixing ratios relative to interannual variability and allows us to explore the linearity of the atmospheric response to increasing H2. Note that our 2000 ppb H2 scenario should be considered an extreme end member designed to assess the linearity of the atmospheric response to increasing atmospheric H2, rather than a projection of potential future atmospheric H2 levels in a hydrogen economy.

To determine the associated changes in CH4, CO, NOx and VOC emissions, further assumptions are required about the new technology employed, in addition to the percentage of different energy sectors switching to H2. In the building sector, we assume that H2 will be combusted and NOx emissions will be limited such that they remain unaltered (despite the potential for higher NOx emissions from the increased flame temperature), whilst emissions of CH4, CO and VOCs are eliminated. In the transport sector, we assume a 50 % reduction in emissions of CH4, CO, NOx and VOCs based on 50 % of oil-based transport being replaced by hydrogen fuel cells. In the power sector, we assume that stored hydrogen will be used to generate 30 % of the electricity that is currently generated using natural gas via combustion and that NOx will remain unaltered, whilst emissions of CH4, CO and VOCs are scaled appropriately. CH4 emissions associated with energy production are also scaled according to the decreased use of CH4 where it has been replaced by H2. The assumptions above lead to reductions in CH4, CO and NO2 emissions of 43, 259 and 19 Tg yr-1 (see Warwick et al., 2022, for further details).

Emission reductions for CO, NOx and VOCs are determined by applying a uniform global-scaling factor to emissions from the specific energy sectors mentioned by Gidden et al. (2019) where hydrogen is assumed to play a role. The emission reductions determined for CH4 are converted to a change in the CH4 lower boundary condition for UKESM1 using the box model (see Sect. 2.2). To separate the atmospheric impacts of increasing hydrogen mixing ratios, the feedback on the CH4 abundance and changes in the emissions of other species emitted by the consumption of fossil fuels, four different sets of hydrogen economy model simulations are performed as described in Table 1.

For the BASE simulation, all boundary conditions are taken from the recently developed Coupled Model Intercomparison Project, Phase 6 (CMIP6), data set and we assume an H2 LBC of 500 ppb. Climatological boundary conditions for sea-surface temperatures, sea-ice extent and anthropogenic and natural emissions are averaged over the years 2000–2014. In the first set of hydrogen economy scenarios, we consider changes in the atmospheric H2 abundance only. In these simulations, the methane abundance is fixed at 1835 ppb (the 2014 year level) and does not respond to changes in the methane lifetime. In the second set of hydrogen economy scenarios, we include the methane response to changes in atmospheric H2 via the impact of H2 on OH and the methane lifetime. The methane LBCs in these simulations are determined via a series of box model simulations where H2 is varied (see Sect. 2.2). In the third set of hydrogen economy scenarios, we consider reductions in emissions of the ozone precursors, CO, NOx and VOCs, from reduced fossil fuel use, whilst the methane abundance is fixed at 1835 ppb. The fourth set of hydrogen economy scenarios includes decreases in the emissions of CH4, CO, NOx and VOCs from reduced fossil fuel use, in addition to the feedback of changes in the methane lifetime on the methane abundance. In these scenarios, we assume that all hydrogen will be green hydrogen with no emissions of other species associated with the H2 production method. In the case that blue or grey hydrogen is used, it is possible methane emissions may increase due to emissions occurring during hydrogen production (e.g. Bertagni et al., 2022). Each simulation was run for 40 years using annually repeating conditions with the final 25 years of each simulation used for analysis and the initial 15 years treated as a spin-up period.

For our GWP calculation, we derive a more universal version of the approach presented by Fuglestvedt et al. (2010) for calculating GWPs for species whose emissions result in indirect radiative forcings, which was also implicitly adopted for global temperature change potentials in the IPCC Sixth Assessment Report (Forster et al., 2021). The method of Fuglestvedt et al. (2010) assumes that the time evolution of the radiative forcing depends only on the lifetime of the species causing the forcing and not the lifetime of the species being emitted. In their method, the time evolution of the radiative forcing during a 1-year constant emission is described by an approach to a steady state with a time constant according to the lifetime of the species causing the forcing. The peak forcing is assumed to occur directly at the end of the 1-year emission and to subsequently decay with the same lifetime as in the growth phase. Although this assumption may be a good approximation for short-lived emission species such as NOx, it may not be for species with longer lifetimes such as H2. Our extension of their method (see Warwick et al., 2022) accounts for both the lifetime of the emitted species and the lifetime of the species causing the forcing, as well as allowing the time period of the constant emission to be varied. The use of a 1-year constant emission rather than an emission pulse has the benefit of removing the time-of-year dependence for when the emission pulse occurs.

In our method for deriving indirect GWPs from steady-state simulations, we include the indirect forcing due to perturbations in radiatively active species arising (a) during the constant emission (AGWP1, Eq. 1), (b) from the decay of the perturbation subsequent to the end of the constant emission (AGWP2, Eq. 2) and (c) from perturbations arising from the emission species remaining in the atmosphere after the end of the constant emission (AGWP, Eq. 3). Derivations for Eqs. (1) to (3) are presented in the Supplement. 1AGWP1=RaMαMαHCtptp-αM1-exp⁡-tpαM-αHαH-αMαH1-exp⁡-tpαH-αM1-exp⁡-tpαM,2AGWP2=RaMαH2αMC1-exp⁡-tpαHtpαH-αMαH1-exp⁡-Hz-tpαH-αM1-exp⁡-Hz-tpαM,3AGWP3=RaMαM2αHCtp1-exp⁡-tpαM-αHαH-αMexp⁡-tpαH-exp⁡-tpαM1-exp⁡-Hz-tpαM, where AGWP is the absolute global warming potential (W m-2 kg-1 yr); M is the species resulting in the indirect radiative forcing, CH4, O3 and H2O (ppb or DU for tropospheric O3); RM is the radiative forcing efficiency for M (W m-2 ppb-1 or W m-2 DU-1 for tropospheric O3); aM is the production rate of M (ppb yr-1) per ppb H2 change at the steady state (yr-1); αM is the atmospheric lifetime of M (years); αH is the atmospheric H2 lifetime (combined chemical and deposition lifetime) (years); Hz is the time horizon considered (years); C is the conversion factor for converting H2 mixing ratio (ppb) into H2 mass (kg) and tp is the length of step emission (years).

Equations (1) to (3) are applied separately to methane, non-methane-induced ozone and stratospheric water vapour to calculate a net GWP for H2. The associated indirect GWPs for each radiative species perturbed by hydrogen are then given by 4GWPH2=AGWPH2AGWPCO2. A comparison of the time evolution of the methane perturbation resulting from a change in H2 mixing ratio based on the standard (Fuglestvedt et al. 2010) equations and Fig. 5 shows our updated equations. Accounting for the atmospheric lifetime of hydrogen in the updated equations results in a slower predicted rate of increase in methane during the 1-year constant emission relative to the standard (Fuglestvedt et al. 2010) equations, a delayed methane peak (peaking at 5 years rather than 1 year, using the parameters specified in the caption) and a slower rate of methane decrease subsequent to that peak, as methane is still being impacted by the remaining H2. This difference occurs because the equations of Fuglestvedt et al. (2010) assume that the emitted species instantaneously reaches a new steady-state atmospheric concentration at the start of the 1-year constant emission. In addition, their assumption that the decay following the peak forcing is controlled only by the lifetime of the radiatively active species neglects any subsequent perturbations to atmospheric chemistry as a result of the emitted species still present in the atmosphere after the end of the 1-year constant emission. A comparison of the transient methane growth due to a H2 perturbation, as determined by Eqs. (1) to (3) in Fig. 5 (grey line), with model studies where methane has been free to respond to a H2 perturbation (including the box model described in Sect. 2.2 and the model studies of Derwent et al., 2020, and Bertagni et al., 2022) shows that the response represented by Eqs. (1) to (3) is similar to that found in transient model simulations following a H2 pulse emission.

Equations (1) to (3) are obtained using a framework assuming a 1-year constant emission rather than an emission pulse. This has the benefit of removing the time-of-year dependence of the atmospheric perturbations arising from the emission pulse. However, once obtained, the chemical parameters from our UKESM1 simulations can also be applied to the pure pulse approach with little error. Equations (1) to (3) can be simplified by using the tp→0 limit of Eq. (2), which is given in Eq. (5). Based on our obtained parameters, using Eq. (5) rather than Eqs. (1) to (3) leads to a difference of 0.1 % for our hydrogen GWP(100) and 1.5 % for our hydrogen GWP(20). In contrast, using the original method of Fuglestvedt et al. (2010) leads to a 0.1 % difference in our hydrogen GWP(100) but a 5 % difference in our hydrogen GWP(20) relative to Eqs. (1) to (3). 5AGWP=RaMαHαMCαH-αMαH1-exp⁡-HzαH-αM1-exp⁡-HzαM

In our calculations, AGWPCO2(100) and AGWPCO2(20) are taken to be 9.17 × 10-14 (± 26 %) and 2.49 × 10-14 (± 18 %) W m-2 kg-1 yr (Myhre et al., 2013) respectively. AGWPH2 is taken as the sum of AGWP1–3. The values for AGWPCO2(100) and AGWPCO2(20) change slightly to 8.95 × 10-14 (± 26 %) and 2.43 × 10-14 (± 18 %) W m-2 kg-1 yr respectively in Forster et al. (2021). Table 3 shows the impact of this on our H2 GWP calculation, along with other IPCC AR6 (Forster et al., 2021) updates. The length of the step emission, tp, is 1 year, Hz is taken to be 20 or 100 years, and aH is 1.96 years (with an uncertainty range from 1.4 to 2.2 years). The conversion factor, C, for converting H2 mixing ratio into H2 mass based on the UKESM1 data is 3.52 × 10-9 ppb kg-1. Values for RM, aM and αM are dependent on the species causing the indirect forcing (methane, ozone and stratospheric water vapour).

For methane, RCH4 is taken to be 0.000363 (± 10 %) W m-2 (ppb CH4)-1 (Myhre et al., 2013) or 0.000389 W m-2 (ppb CH4)-1 (Forster et al., 2021). The methane perturbation lifetime, αCH4, in UKESM1 is determined to be 11.8 years in this study, which falls within the range given by IPCC AR5 (12.4 ± 1.4 years, Myhre et al., 2013). The value for aCH4, an additional methane production rate term per unit increase in H2, represents the positive CH4 tendency resulting from an increase in H2 and corresponding decrease in OH and is defined as 6aCH4=CH4kCH4+OHdOHdH2, where CH4 is the methane lower boundary condition (1835 ppb in UKCA), kCH4+OH is the global mean air-mass-weighted rate constant for the reaction of CH4 with OH and dOH/dH2 is the rate of change in air-mass-weighted tropospheric mean OH with respect to H2. Values for these parameters derived from UKESM1 simulations are as follows: k(CH4+OH) = 2.8 × 10-15 cm3 molec.-1 s-1 and dOH/dH2 = 3.68 × 10-9 (dimensionless). k(CH4+OH) is determined from the gradient of methane lifetime against 1 / (global air-mass-weighted mean OH) and dOH/dH2 from the gradient of the mass-weighted tropospheric mean OH concentration against H2 surface mixing ratio for the UKESM1 simulations including the feedback on the methane lifetime via an adjusted CH4 lower boundary condition determined by the box model (see Fig. 1a). Note that if we weight OH by reaction with CH4 instead of air mass, the value determined for k(CH4+OH) halves (1.4 × 10-15 cm3 molec.-1 s-1), the value for dOH/dH2 doubles (7.36 × 10-9 (dimensionless)) and our value for aCH4 remains unaltered. It is also possible to derive dOH/dH2 using the gradient of the mass-weighted tropospheric mean OH concentration against H2 surface mixing ratio from the UKESM1 simulations where only the H2 LBC is varied (whilst the CH4 LBC is held constant), in combination with the equation below from Stevenson et al. (2013), and the methane feedback factor of 1.39 derived for UKESM1, 7CH4new=CH4baseτnewτbasef, where f is the methane feedback factor, CH4base and τbase are the lower boundary condition and methane lifetime in the base scenario, and CH4new and τnew are the lower boundary condition and methane lifetime in the perturbed H2 scenario. The difference between the dOH/dH2 values obtained using the two methods above is approximately 3 %. This, in turn, leads to a 3 % difference in the methane-induced hydrogen GWP terms and a difference of less than 1 % in the total hydrogen GWP when accounting for all forcings. This difference is negligible in comparison to other uncertainties (see Table 3); therefore our GWP calculation remains independent of the box model results.

The indirect forcing from methane-induced changes in tropospheric ozone and stratospheric water vapour are determined by multiplying the calculated direct methane forcing (RCH4) by scaling factors of 0.5 ± 55 % and 0.15 ± 70 % respectively (Myhre et al., 2013). Equivalent scaling factors, from Forster et al. (2021), are 0.37 ± 50 % and 0.106 ± 100 %.

In addition to the methane-induced indirect radiative forcing from ozone and water vapour outlined above, we also consider non-methane-induced radiative forcing from H2 as a source of tropospheric ozone and stratospheric water vapour. For stratospheric water vapour, the e-folding lifetime of the water vapour perturbation following a change in H2, αH2O, is derived from model spin-up data following a change in the H2 lower boundary condition and is determined to be 8 years in the lower stratosphere. Values for both RH2O and aH2O are determined by the steady-state change in the stratospheric water profile between our UKESM1 BASE simulation and the simulation where the H2 lower boundary condition is increased from 500 to 2000 ppb. A comparison of the vertical profile of stratospheric water vapour changes resulting from H2 changes in our study (Fig. 1d), with that resulting from methane changes between 1950 and 2000 in Fig. 2b of Myhre et al. (2007), shows very similar H2O changes at all altitudes. We therefore adopt the radiative forcing determined by Myhre et al. (2007) of 0.05 W m-2 with an estimated uncertainty of ±20 % for stratospheric water vapour changes relative to base in our 2000H2 UKESM1 scenario. This water vapour forcing is associated with a change of ∼ 500 ppb in stratospheric water vapour at 30 km altitude, giving a value for RH2O of 1 × 10-4 W m-2 (ppb H2O)-1 when considering changes at 30 km. We assume that the entire stratospheric H2O profile will scale proportionally with the H2 lower boundary condition (following results from our UKESM1 simulations using H2 LBCs of 750, 1000, 1500 and 2000 ppb H2), so the choice of 30 km for determining RH2O is arbitrary. The production rate of water vapour per ppb change in H2, aH2O, can then be defined as the change in steady-state H2O at 30 km (500 ppb) divided by the lifetime of 8 years and the change in H2 mixing ratio of 1500 ppb.

For changes in the global mean tropospheric ozone column, the value for RO3 is 0.042 (0.037 to 0.047) W m-2 DU-1 and is taken directly from Myhre et al. (2013). No updated value for RO3 was presented by Forster et al. (2021), although a similar value of 0.039 W m-2 DU-1 can be obtained based on the estimated change in tropospheric ozone of 109 ± 25 Tg between 1850 and 2005 and a stratospheric-temperature-adjusted radiative forcing due to tropospheric ozone of 0.39 ± 0.07 W m-2 between 1850 and 2010. The e-folding lifetime associated with the ozone perturbation, αO3, is taken to be 0.07 years, calculated as the tropospheric O3 burden divided by the loss in our UKESM1 base simulation. This is shorter than the lifetime used for the short-lived ozone perturbation by Fuglestvedt et al. (2010) of 0.267 years. However, our results are insensitive to the difference between these values and small variations around them. The value for aO3 is calculated as the change in the steady-state global mean tropospheric ozone column in our 2000H2 simulation relative to base (0.59 DU) divided by the lifetime of 0.07 years and the change in H2 mixing ratio of 1500 ppb. A list of all the input parameters, with the values used in our AGWP calculations, is presented in Table S1. Changes in the H2 mixing ratio can also influence stratospheric ozone. In our UKESM1 simulations, the change in global mean stratospheric ozone column between our base and 2000H2_CH4f (increased H2, including the chemical feedback on the methane lifetime) scenarios was negligible at +0.10 DU, relative to a base value of 283.78 DU and interannual variations of up to several DU. Based on a value of R for stratospheric ozone of 0.0054 W m-2 DU-1 (Schwarzkopf and Ramaswamy, 1993) and a range of e-folding lifetimes for the stratospheric ozone perturbation of between 1 and 10 years, the results obtained are a GWP(100) of less than 0.03 using Eqs. (1) to (4). We consider this to be below the uncertainty involved in the calculation and conclude that changes in stratospheric ozone for our range of scenarios do not significantly contribute to the hydrogen GWP.

For a 100-year time horizon we determine a H2 GWP of 12 ± 6 (see Table 3). This value is larger than previously published studies, which do not account for changes in stratospheric composition (Derwent et al., 2020, 5 ± 1, and Field and Derwent, 2021, 3.3 ± 1.4), but similar to the values of Hauglustaine et al. (2022) (12.8 ± 5.2) and the multimodel study of Sand et al. (2023) (11.6 ± 2.8, 1 standard deviation), which include a tropospheric and stratospheric response. Approximately two-thirds of our GWP arise from the influence of H2 on methane and ozone distributions in the troposphere, and one-third arises from the influence of H2 on stratospheric water vapour. Results from our study can also be compared with that of Paulot et al. (2021), who estimated the indirect radiative forcing at a steady state due to an increase in H2. Their study accounted for changes in methane, tropospheric ozone and stratospheric water vapour and found an indirect radiative forcing arising from a H2 of 0.13 mW m-2 (ppb H2)-1. Using the radiative forcing scaling factors, we obtain a larger value of 0.18 ± 0.03 mW m-2 (ppb H2)-1 (the same value is obtained using both the Myhre et al., 2013, and Forster et al., 2021, radiative efficiency scaling factors), which may partly be explained by the larger methane feedback factor in UKESM1 (1.39) relative to the chemistry–climate model used in (Paulot et al., 2021).

Uncertainties in our calculation are based on uncertainties in the hydrogen lifetime with respect to soil uptake, uncertainties in radiative forcing scaling factors and the AGWP for CO2. We do not account for uncertainties in chemical lifetimes and other UKESM1-derived quantities which are likely to vary when using different atmospheric models with different chemistry schemes. In addition, we also note that the sensitivity of ERF in UKESM1 to changes in methane is approximately 65 % larger than that indicated by the radiative scaling factors used in the empirical relationships applied in the GWP calculation (O'Connor et al., 2022). This suggests a further source of uncertainty than accounted for by the radiative forcing scaling factor uncertainties outlined by Myhre et al. (2013) and Forster et al. (2021), associated with the response of aerosols, clouds, ozone and water vapour to changing methane levels.