The 3D global chemical and transport model, STOchastic CHEMistry – Common Representative Intermediates (STOCHEM-CRI), was used to simulate the emissions, transport and chemical reactions of the various species under investigation. STOCHEM-CRI, and its preceding versions, has been used previously to model atmospheric trace gas species , including the fluorinated species HFO-1234yf and perfluorooctanoic acid . The model transport is driven by archived meteorological data from the UK Meteorological Office, and adopts a Langrangian approach to advect air parcels in the troposphere. Further details of the transport and meteorology can be found in and . In this study, we simulated a full year (2023) of HFC-23 in-atmosphere production following an initial spin-up simulation, which was used to initialise the atmospheric conditions and then discarded.

The model chemistry uses a reduced chemical Common Representative Intermediates (CRI) mechanism to which the chemical reactions, physical loss processes and emissions of the fluorinated source gases are added (see Sect. ). OH and O3 concentrations are calculated for each grid cell in the model based on emissions, kinetics and photolysis. Abundances of all species are calculated at three-hourly time steps. For non-fluorinated species (e.g., other selected VOCs, CO and NOx), emissions were taken from the Precursor of Ozone and their Effects in the Troposphere (POET) inventory and physical removal processes such as wet and dry deposition were parametrized as in .

Several saturated fluorinated gases contain the CF3CH2- moeity required to produce CF3CHO upon reaction with the OH radical . Of these, HFC-143a (CF3CH3, tropospheric lifetime τtrop = 57.2 years), HFC-236fa (CF3CH2CF3, τtrop = 253 years), HFC-245fa (CF3CH2CHF2, τtrop = 8.1 years) and HFC-365mfc (CF3CH2CF2CH3, τtrop = 9.3 years) have been measured in the global atmosphere . HCFC-133a (CF3CH2Cl) is another species containing the relevant CF3CH2- moeity , but there is limited evidence to support the formation of CF3CHO in a quantifiable yield from the reaction of this species and so it is excluded from the present study. The rate coefficients and yields of the reactions of these HFCs with OH are taken from the NASA/JPL recommended values . In addition, three unsaturated fluorinated gases with measured atmospheric abundances have also been shown to react with OH to produce CF3CHO . These species are HFO-1234ze(E) (trans-CF3CH=CHF, τtrop = 19 d), HFO-1336mzz(Z) (cis-CF3CH=CHCF3, τtrop = 27 d) and HCFO-1233zd(E) (trans-CF3CH=CHCl, τtrop = 41.9 d). These three species also react with O3 to produce HFC-23 directly. All rate coefficients and yields for included reactions are shown in Table .

For the four long-lived source gases (HFC-143a, HFC-236fa, HFC-245fa and HFC-365mfc), baseline mole fractions are taken from the Advanced Global Atmospheric Gases Experiment (AGAGE) network . In the model runs, we initialise hemispheric average mole fractions for 2023 and prescribe global emissions for that same year from , as shown in Table . The emissions for each of the HFCs are spatially distributed over the 5° × 5° surface grid used in STOCHEM according to the EDGAR v8.0 inventory . While these emissions estimates have uncertainties of up to 30 % (1σ), the reaction to form CF3CHO (and subsequently HFC-23) is predominantly driven not by emissions but by the background mole fraction, which is better-constrained (typically on the order of a few percent; see ). We therefore do not consider the uncertainties in HFC emissions in this analysis.

The shorter lifetimes of the HFOs make them unsuitable for top-down emissions estimation with a global box model e.g., and no global 3D top-down inversion or bottom-up inventory of emissions is available, either. Therefore, we make several approximations in estimating the magnitude and spatial distribution of HFO emissions and carry out a wide range of tests (detailed in Sect. ) to explore the sensitivity of our results to these assumptions. Firstly, we assume that the adoption and emission of HFOs is correlated with national Gross Domestic Product (GDP) globally. Although it ignores the differing rates of transition from HFCs to HFOs in different regions, we use GDP as a proxy for emissions as it has been used previously to estimate demand for HFCs globally . Previous work suggests this correlation is unlikely to hold globally, since phase-out of HFCs in favour of HFOs seems to be slower in areas such as East Asia than in Europe, where regulation of fluorinated species has accelerated this transition. However, in the absence of other suitable proxies, we take published HFO emissions for Europe and scale them up using national GDP totals to give global estimates. Emissions of HFO-1234ze(E) and HCFO-1233zd(E) were 0.96 and 1.0 Ggyr-1, respectively, in 2023 for Northwest Europe, a region defined as Ireland, the United Kingdom, France, Germany, Luxembourg, the Netherlands and Belgium. These countries accounted for approximately 12.5 % of the global GDP for that year . Therefore, we scale these emissions up by a factor of 8 and use global emissions of 7.7 and 8.0 Ggyr-1 for these two species, respectively, in the STOCHEM-CRI model. Despite concerns about overestimating emissions via this method, our estimates are approximately 50 % lower than those made by , who estimated global HFO-1234ze(E) emissions at 15 Ggyr-1.

For HFO-1336mzz(Z), no recent emissions estimates are available. However, estimated Swiss emissions of HFO-1336mzz(Z) at 5 Mgyr-1 in 2019–2020. Swiss emissions of the other two HFOs considered in this model were also estimated for 2019–2020 at 34 Mgyr-1 (HFO-1234ze(E)) and 7.3 Mgyr-1 (HCFO-1233zd(E)) . Using a tracer ratio method and scaling up to global emissions, this suggests that HFO-1336mzz(Z) emissions are between 1.2 and 5.4 Ggyr-1, depending on which HFO is used as a tracer. Here, we take a mean of these values and estimate global HFO-1336mzz(Z) emissions at 3.3 Ggyr-1. We note that the use of the other HFOs as tracers for HFO-1336mzz(Z) emissions may not be reasonable, as evidenced by the large disparity in emissions when selecting alternative tracers. Nonetheless, in the absence of complete emission inventories derived from atmospheric measurements, we believe the wide range of sensitivity tests conducted here (see Sect. ) produce a sound order-of-magnitude estimate for global HFO emissions, sufficient to estimate the in-atmosphere production of HFC-23. We also note that the amount of HFC-23 produced by the in-atmosphere breakdown of HFOs is likely to be linearly dependent on the global emissions of each species, so if improved emission estimates were to become available, our totals could be scaled. We explore the extent to which this is true, as well as the effect of varying emissions totals, in the sensitivity analysis.

The spatial distribution of the HFO emissions is also poorly constrained. In the absence of gridded emissions estimates, the emissions are distributed according to the method used by and . This takes the spatial distribution for HFC-134a emissions in the EDGAR database and replaces the emissions inventory from China using gridded estimates from . The impact of changing these spatial distributions and therefore releasing the HFOs into regions of varying O3 and OH concentrations, is investigated through a set of sensitivity tests outlined in Sect. . These tests also probe the validity of scaling up emissions by GDP.

A “base” run was established for the sensitivity analysis, with the photolysis scheme set out as above (see Sect. ) and total HFO emissions of 19.0 Ggyr-1 (7.7 Ggyr-1 HFO-1234ze(E), 8.0 Ggyr-1 HCFO-1233zd(E) and 3.3 Ggyr-1 HFO-1336mzz(Z) as derived in Sect. ). Dry deposition velocities over both land and sea were set to 0.01 cms-1, and dynamic and convective scavenging coefficients to 3.0 cm-1.

Starting from this “base” scenario, nineteen further runs were performed, to explore the loss processes that are poorly constrained by experimental data. Firstly, the effect of changing photolysis setup between the three scenarios “base”, “Phot_Low” and “Phot_Hi” was assessed, as well as a pair of runs (“AXS_Hi” and “AXS_Low”) assessing the impact of increasing or decreasing the absorption cross-section of CF3CHO. Secondly, we varied the emissions of the three HFOs considered in this model, increasing and decreasing emissions by a factor of three relative to the values outlined above to give “Em_Low” and “Em_Hi” runs. We also performed runs in which we varied the spatial distribution of HFO emissions, while keeping the magnitude constant. These explored the impact of distributing global emissions uniformly across the land and sea (“Dist_flatlandsea”), uniformly across the land only (“Dist_flatland”), in a zonal band at the equator (between 30° N and 30° S, run “Dist_equator”), and in two bands at the poles (latitudes greater than 60° N/S, run “Dist_polar”). This was done to explore how releasing the fluorinated source gases into regions of high and low OH or O3 concentrations would impact their breakdown, and these are not presented as plausible emissions distributions. Thirdly, a set of runs was carried out to assess the impact of changing the dry deposition velocity of CF3CHO. In addition to the base run with a dry deposition velocity of 0.01 cms-1, further runs were performed with dry deposition velocities of 0.001 cms-1 (“Dep_0.001”), 0.1 cms-1 (“Dep_0.1”), 1.0 cms-1 (“Dep_1”) and 10.0 cms-1 (“Dep_10”). The higher dry deposition scenarios enable the exploration of deposition rates in the range of values proposed by The impact of changing the convective and dynamic scavenging coefficients, which parametrise wet deposition in the model, was also investigated. While the base runs set this parameter at 3.0 cm-1, we also ran further simulations with the coefficients set to 1.0 cm-1 (“Scav_1”), 5.0 cm-1 (“Scav_5”), 7.0 cm-1 (“Scav_7”) and 10.0 cm-1 (“Scav_10”). These values span the full range of scavenging coefficients tabulated for common species in (1.0 to 5.0 cm-1) and extend to higher scavenging coefficients to fully explore the impacts of even higher rates of wet deposition. Finally, a single run (“HO2”) was performed to explore the impact of including the reversible reaction between CF3CHO and the HO2 radical, which has been suggested as a potential additional sink for CF3CHO in the atmosphere. This model run incorporates the forward (2.48 × 10⁻¹³ molec.cm-3s-1) and reverse (1.73 × 10³ s-1) rate constants derived from theoretical calculations taken from . This run was compared to the “base” scenario, to assess the impact of this reaction of HFC-23 production.

Full details of all sensitivity analysis runs can be found in Table .

Global Warming Potentials (GWPs) quantify the climate impact of a greenhouse gas species, by comparing the time-integrated radiative forcing of a single pulse of emissions to that of carbon dioxide, over a given time horizon (typically 20, 100 and 500 years). The lifetime of the species relative to the time horizon is an important factor in determining the GWP. For example, short-lived species such as HFOs typically have very small GWPs, since their breakdown on timescales far shorter than the time horizon means that their time-integrated radiative impact is much smaller than species with longer lifetimes .

Generally, only the radiative impact of the single species is considered in such calculations, and not the impact of any breakdown products. However, for gases that breakdown to form long-lived, radiatively active species such as HFC-23, the indirect GWP may need to be considered, incorporating both the source gas's radiative impact and that of its breakdown products. This has been done previously for various HFOs , considering only their ozonolysis, and for some of the HFOs that break down to CF3CHO . A similar approach has been taken for chlorofluorocarbons (CFCs) as well, due to the negative radiative forcing resulting from their ability to deplete stratospheric ozone .

We calculated indirect GWPs for each of the eight source gases considered here. These were derived by assimilating the rates and yields of reactions contributing to the in-atmosphere HFC-23 production into a simple one-box model of the atmosphere. This model tracks the abundances of the relevant gas species over time according to a simple kinetic scheme, but is otherwise static with respect to atmospheric conditions. The reactions of each source gas with OH were simulated, using the same rate constants as in the STOCHEM-CRI model (see Table ). A uniform temperature in the box model of 265 K was chosen to most accurately simulate the tropospheric lifetimes of the source gases. The concentration of OH radicals in the box model was set at 0.04 ppt. For the HFOs, the loss via reaction with O3 was also simulated, with the same (temperature-independent) rate constants as in the 3D model and a uniform O3 concentration of 50 ppb. From each member of the STOCHEM-CRI ensemble of runs, the CF3CHO lifetime and the fraction of the loss that yielded HFC-23 was extracted. Although the loss of HFC-23 in the STOCHEM-CRI model is negligible due to its long lifetime relative to the one-year simulations, the reaction with OH was also incorporated into the kinetic scheme here, tuned such that HFC-23 had a tropospheric lifetime of 243 years (ignoring stratospheric loss) .

To determine the indirect GWPs, a 1 kg pulse of emissions was emitted at t = 0 for each source gas species independently. The evolution of HFC-23 over time was tracked over time periods of 20, 100 or 500 years. This was integrated with respect to time and multiplied by the radiative forcing. To give an indirect global warming potential for each source gas due to the production of HFC-23, this was divided by the equivalent time-integrated radiative forcing for an equivalent pulse of CO2, taken from .

Across the twenty model scenarios, total HFC-23 production ranged from 0.013 to 0.035 Ggyr-1, with all but two of the runs yielding HFC-23 production rates between 0.016 and 0.022 Ggyr-1. The factors influencing HFC-23 production are discussed below. Figure a illustrates that the main source of HFC-23 in these model runs comes from the photolysis of CF3CHO, with the remaining production (< 17 % in all cases) coming from ozonolysis reactions. The absolute contribution from ozonolysis is similar for most runs, since most of the parameters investigated do not significantly impact that reaction pathway. However, differences in HFC-23 produced from ozonolysis are seen when the spatial distribution of HFO emissions is changed, and this is discussed below. Previous work by put the contribution of ozonolysis reactions at 4 % of the total production, with photolysis of CF3CHO yielding the remaining 96 %. Our results suggest a slightly larger relative contribution, with ozonolysis contributing between 5 % and 17 % of the total HFC-23 production and a mean contribution of 11 % across the twenty runs.

These results are an order of magnitude lower than than the previous estimate of in-atmosphere HFC-23 production by , who estimated global emissions of 0.215 Ggyr-1 from photochemical sources for 2022. That value, however, was calculated as an conservative upper bound and so is consistent with the results presented here. These results confirm that in-atmosphere HFC-23 production is likely negligible compared to the global emissions derived from atmospheric measurements. Modelled in-atmosphere production in this study was between 0.1 % and 0.25 % of the global emissions of 14.0 Ggyr-1 published for 2023 . While some parameters influencing HFC-23 production (such as deposition and in-cloud hydrolysis of CF3CHO) are poorly constrained by experimental data, these model runs were designed to capture a wide range of plausible values for the production of HFC-23. As a result, it is likely that the true contribution of in-atmosphere production to the global HFC-23 burden lies within this range.

These emissions lead to an increase in the global mean mole fraction of HFC-23 of roughly 0.001 pptyr-1 in the model, in reasonable agreement with the value estimated by . Not only is this value three orders of magnitude lower than the measured increase in global mean mole fraction (on the order 1 pptyr-1), it is substantially lower than the precision of current measurement techniques . This means that even in the absence of industrial emissions, the production of HFC-23 in the atmosphere would be undetectable at present.

Given the importance of atmospheric CF3CHO to the in-atmosphere production of HFC-23, the fate of this compound was investigated. The sinks considered in the model were photolysis via two different pathways, reaction with the OH radical, and wet and dry deposition. As illustrated in Fig. b, photolysis pathway (a), generating non-HFC-23 products was the dominant loss process in every model run, except for “Scav_7” and “Scav_10” in which it was surpassed by wet deposition. Photolysis removed between 43 % and 71 % of the atmospheric CF3CHO across the twenty runs, while wet deposition (23 %–48 %) and reaction with OH (6 %–12 %) made up most of the remaining CF3CHO loss. Dry deposition contributed 11 % of CF3CHO loss in the “Dep_10” run and 2.4 % in the “Dep_1” run, but < 0.3 % in all other runs. Pathway (b) photolysis, which produces HFC-23, contributed < 0.1 % in all runs. In the “HO2” run, in which loss of CF3CHO via the reversible reaction with HO2 was included in the chemistry scheme, the relative contribution of the major loss processes was unchanged from the “base” run.

Again, the relative contribution of CF3CHO sinks can be compared with previous estimates in the literature. modelled the photolysis pathway (a) as contributing between 46 % and 74 % of the total CF3CHO loss, which agrees well with the range of values from this study. The contribution of deposition processes (wet and dry) in this study was also similar to that in (23 %–48 % compared to 7 %–41 % in that work). However, the contribution of the photolysis pathway (b) (i.e., that which produces HFC-23) in this study is far lower, because assumed a HFC-23 quantum yield much greater than measured experimentally in and .

also modelled the various sinks of CF3CHO, using the GEOS-Chem atmospheric chemistry and transport model. They found a broadly similar distribution of loss processes, although with deposition much more evenly split between wet and dry compared to this study, in which wet deposition dominated in all runs.

The globally averaged lifetimes of the HFOs considered here can be calculated and compared to the literature, to assess the model's simulation of their breakdown. For all three HFOs, the lifetime was the same through all the model runs except for those that varied the spatial distribution of emissions. In these, a large variation in lifetimes was seen, which can be attributed to the latitudinal distribution of the OH radicals that represent the main sink of HFOs. While some of these spatial distributions are unrealistic, they demonstrate that changing the spatial emission profile would make a minimal difference to HFC-23 production. The lifetimes quoted here are from the “base” scenario.

For HFO-1234ze(E), the modelled lifetime was 19.0 d, in excellent agreement with the literature value of 19 d reported in the WMO Ozone Assessment 2022 . The other species also showed good agreement with the literature values (24.5/27 and 36.0/41.9 d for the modelled/literature lifetimes for the HFO-1336mzz(Z) and HCFO-1233zd(E), respectively ). While the model tended to slightly underestimate the lifetimes, all three species agree to within 12 % of the literature value. This suggests a reasonable simulation of the sinks of these species, especially given the large variation in their lifetimes with latitude.

For the eight source gases investigated here, their indirect global warming potential due to their breakdown to HFC-23 is calculated over 20-, 100- and 500-year time horizons using the box model described in Sect. . The 100-year indirect GWPs are presented in Table , while the 20- and 500-year values can be found in the supplement. The GWP values are dependent on the fractional yield of HFC-23 from CF3CHO loss, which varied across the twenty model runs from 0.05 % to 0.07 %. Here, we present the mean and standard deviation in the GWP100 values obtained from the STOCHEM-CRI simulations, alongside their published direct GWPs .

From Table , we see that the indirect GWPs for the long-lived source gases are negligible compared to their direct GWPs. The indirect GWPs of the HFOs, however, are larger than their very low direct GWPs. The value for HFO-1234ze(E) falls within the range of uncertainty published by , who estimated an indirect GWP between 8.2 and 11.6. It is also in reasonable agreement with the OH-only and O3-only indirect GWPs from and , respectively, which summed to give a total of ∼ 9.3.