Here, we use the control simulations presented in Sand et al. (2023) for five models – OsloCTM3, UCI CTM, UKCA, LMDZ-INCA and GFDL-AM4.1. For WACCM6, we use a more recent simulation that is set up as the CTRL simulation described in Sand et al. (2023), except that it is run using CESM v. 2.1.2 and with 70 vertical levels (instead of 88 in Sand et al., 2023). All simulations use present-day (2010) atmospheric compositions and fixed hydrogen and methane surface concentrations. Further details on the models are provided in Table 1 and Sand et al. (2023).

To evaluate model chemistry, we compare selected species that are critical to atmospheric production and loss of H₂, namely monthly model output for HCHO, OH, CO, NO₂ and NO. A qualitative comparison for these species is also made between the model results and satellite retrievals. Monthly-averaged satellite data for 2010 are downloaded for TROPOMI (Veefkind et al., 2012) for the time period between July 2018–June 2019 – to compare against the model simulations for the year 2010. The TROPOMI satellite has global daily coverage and retrieves multiple atmospheric trace gas components O₃, NO₂, and HCHO with a spatial resolution of 5.5 km × 3.5 km and an equator crossing time at about 13:30 local time. Column-averaged tropospheric values are post-processed to calculate annual averaged values for HCHO, NO₂, and CO (no averaging kernels are applied to the retrievals; vertical profiles are shown in Figs. A6, A7). Similarly, MOPITT data for CO (Deeter et al., 2003) for 2018 are compared to model results. This analysis is limited by the mismatch that arises due to the comparison of the monthly mean model outputs with satellite retrievals taken at a specific overpass time. To test how much this discrepancy can affect our comparison, we run an additional OsloCTM3 simulation for a year where the three hourly outputs are used.

Running the 3-D ACM takes substantial computing resources, limiting its applicability in evaluating the relationship between the different budget terms and the atmospheric concentration of hydrogen. We use a box model that calculates the change in global atmospheric H₂ based on production and loss at every timestep (one month; Eq. 1) 1dCdt=Production-Loss=E+Patmβ-C1τ where C is concentration in ppb; dCdt is change in concentration at every timestep; E corresponds to Emissions; Patm is the atmospheric production of H₂; β is a factor used to convert from Tg to ppb; and 1τ represents the loss terms as a lifetime calculated by 1τ=1τOH+1τSoil where τOH and τSoil represent the lifetimes due to the OH radical and the soil-sink, respectively.

Emissions include time-varying emissions of H₂ from anthropogenic sources and biomass burning, and a constant natural source. Atmospheric production is calculated using time-varying methane concentrations and emissions of anthropogenic VOCs (including constant natural emissions). The two loss terms for atmospheric H₂ are represented by the soil-sink lifetime and the atmospheric lifetime.

A key aspect of this simple model is its flexibility, i.e. the model can be adapted to each atmospheric chemistry model. Atmospheric production, β-value (used to convert mass-values to concentration), and the loss terms vary between the 3-D models and are tied to one another. The anthropogenic and biomass burning emissions for H₂ are adapted for each model. The sinks are determined by setting the atmospheric and soil uptake lifetimes.

We include a function in the box model to calculate the isotopic composition of atmospheric H₂. The different sources and sinks of hydrogen have distinct isotopic signatures. Combining the burden and the isotopic values, we use a mass-balance approach to calculate the isotopic values of tropospheric H₂ at every time step. This is compared with modern-day observation and acts as a two-pronged check on the total budget. Unless otherwise stated, we use isotopic compositions for sources and sinks from Price et al. (2007) which are as follows: Anthropogenic emissions: -196 ‰; biomass burning: -290 ‰; atmospheric production (from CH₄ and NMVOCs): 162 ‰; Nitrogen fixation: -628 ‰ (Table 2). Fractionation factors of 0.943 and 0.58 are used for the soil-sink and OH loss, respectively. The box model does not account for the tropospheric-stratospheric H₂-cycling and the resulting tropospheric H₂-enrichment (Price et al., 2007; Pieterse et al., 2011). The stratospheric-tropospheric H₂ flux is not diagnostic output in the models considered in this study and this omission can result in a 29 ‰–37 ‰ offset in δD (Price et al., 2007; Pieterse et al., 2011, 2013).

Table 2 shows the different budget terms from the ACMs and previous literature studies. Atmospheric production values for the ACMs range from 34 Tgyr-1 (WACCM6) to 56 Tgyr-1 (OsloCTM3) for the models. The lower model values overlap the lower limit of the 38.4±6.1 Tgyr-1 estimate from Ouyang et al. (2025), with the higher model values exceeding it. The model spread is smaller than the range reported in published studies. Since the photolysis of HCHO is an important source of H₂, correctly capturing the background HCHO concentration is essential for constraining atmospheric H₂ production.

All models show broadly similar annual mean HCHO spatial patterns, with some regional differences (Fig. 1). GFDL-AM4.1, LMDZ-INCA, and UCI have higher HCHO concentrations over South America, Africa, and parts of East Asia. OsloCTM3 and UKCA exhibit lower concentrations over land, but higher over the oceans (Fig. A1). WACCM6 produces lower HCHO concentrations over land compared to the other models.

When compared with TROPOMI satellite retrievals, all models except WACCM6 produce reasonable HCHO concentrations, within 6.5 % of the TROPOMI retrieval; Figs. 1, A1). The multi-model mean for HCHO matches well with the TROPOMI global mean, albeit affected by the lower values from WACCM6. Broadly similar values between HCHO in the models and TROPOMI retrievals suggest that the 3-D models represent the production of atmospheric H₂ fairly well, however there are several uncertainties that can affect model simulations that have not been explored in this study, such as the uncertainty in the photodissociation of HCHO, and biogenic NMVOC emissions. Furthermore, all models show a large bias in the Southern Ocean compared to the TROPOMI retrieval (Fig. A4). Reasons for these differences between the models and the satellite retrievals will be explored in future work.

Additionally, we also compared model results against ATom measurement campaigns for nine different regions and four seasons (Figs. A6–A7). All models have comparably similar vertical profiles. They generally also match the ATom measurements other than in the West Atlantic (A3) in the summer and autumn; and North Pacific (P1) in the summer, and winter.

Atmospheric loss in the ACMs ranges from 21 Tgyr-1 (GFDL-AM4.1) to 28 Tgyr-1 (OsloCTM3). This spread is larger than 18.4±2.2 Tgyr-1 for 2010–2020 estimated in Ouyang et al. (2025) and other published studies (Table 2). The atmospheric loss of H₂ is primarily driven by its reaction with OH, a key oxidant in the atmosphere. Due to the short lifetime of OH (<1 s), direct retrievals of OH concentrations are not possible, therefore limiting a model-data comparison for OH. Indirect approaches, such as the use of a combination of CO and NO_x concentrations have been used to estimate OH levels for urban plumes and specific emission sources (Dalsøren et al., 2016; Lama et al., 2022). Although OH chemistry is influenced by several factors – such as photolysis reactions, temperature, tropospheric ozone, humidity, methane and NMVOCs – NO_x generally acts to increase OH concentrations and CO reduce the OH concentrations.

In Fig. A2, we show model outputs for CO, OH, and NO₂ along with satellite retrievals for CO from TROPOMI and MOPITT, and NO₂ from TROPOMI. All models show broadly similar spatial patterns albeit with some regional differences in magnitude. Compared with satellite retrieval, all models simulate larger values for NO₂, with the global means at least twice that of retrievals (Fig. A4). These differences are seen both over land and oceans (Figs. A2a and A4). This overestimation may result from comparing monthly mean outputs with satellite retrievals, which are restricted to specific overpass times and air mass factors. As the simulation and the satellite reanalysis datasets are for two different time-periods, we cannot replicate the specific air mass factors in OsloCTM3, limiting this comparison. But if we restricted mean calculations to specific satellite overpass times with the 3-hourly OsloCTM3 simulation, OsloCTM3 results show much lower values, bringing the model means closer to TROPOMI values, with an underestimation (Fig. A4a). The effect of using the ratio of NO₂ during overpass to the monthly mean for OsloCTM3 for the other models is shown in Fig. A8 where there is a decrease in model NO₂ for all models, more in line with the satellite retrieval. Thus, comparing the monthly mean model output with satellite-overpass times only allows for a broad qualitative analysis. Future simulations should save the 3-hourly output so that such comparisons can be made.

For CO, the models are broadly consistent with one other, with a multi-model standard deviation of 0.002 molCOm-2. The inter-model spread is larger over land (0.003 molCOm-2) than over oceans (0.001 molCOm-2). These results can be compared against TROPOMI and MOPPITT, which are broadly consistent with each other (Fig. A2b), with a global mean difference of 0.002 molCOm-2. Over the oceans, the difference between the two satellite retrievals is 0.003 molCOm-2, while over land it is 0.001 molCOm-2. All models underestimate CO relative to the satellite retrievals, with large differences (10 %–20 %) over the Northern Hemisphere mid- and high latitudes. WACCM6 and OsloCTM3 have lower CO values compared to GFDL-AM4.1 and LMDZ-INCA models. Although the global mean differences between MOPITT and TROPOMI are similar to the multi-model standard deviation, the models have lower CO over land, compared to the satellite retrievals. All models also do a reasonable job of matching the vertical profiles of CO observed during the ATom campaign (Figs. A1 and A2). GFDL-AM4.1 and INCA have lower NO2/CO ratio values compared to OsloCTM3, consistent with the elevated OH concentration in OsloCTM3 (Fig. A2c, d). Our results suggest that OH differences between models could be related to the local chemical environment (NOx/CO differences) with models showing a larger NO2/CO ratio having larger OH values or vice versa. This could explain some of the diversity in atmospheric loss of H₂ in the models.

Here, we use the box model for two applications: (1) to model the sensitivity of modelled H₂ concentrations from pre-industrial to 2015, to two input parameters that impact atmospheric production and loss, and (2) evaluate the feasibility of the different sources and sinks using isotopic values.

Although 3-D model simulations have been conducted for the modern-day time slices, simulating the temporal evolution of tropospheric H₂ from the pre-industrial period to 2015 using 3-D models is computationally very intensive and often prohibitive, making box models an attractive alternative (Fig. 2). The box model is initialized using an inferred pre-industrial H₂ concentration of 330 ppb (Patterson et al., 2020, 2021) and model parameters are chosen based on existing datasets (Table A1). While these choices are not unique, the goal here is to present the model sensitivity to two specific parameter choices – split of atmospheric H₂ production between CH₄ and VOCs, and the atmospheric H₂ loss mediated by the lifetime of OH. All parameters are adjusted so that they match the model results for the present-day OsloCTM3 simulations panel (a) shows the evolution of the different emission and production terms of the budget in the box model, with anthropogenic emissions of H₂ scaled to CO emissions and atmospheric production following CH₄ concentrations showing a rise after the 1970s. Atmospheric H₂ production from NMVOCs also increases slowly post-1970s from ∼20 to ∼25 Tgyr-1. Nitrogen fixation is set constant at 8 Tgyr-1 through the simulation and biomass burning emissions are set at 8 Tgyr-1 till the 1990s, following which emissions are allowed to vary. Figure 2b shows the split between total emissions and atmospheric production and Fig. 2c shows the resulting evolution of global mean tropospheric concentration of H₂. Crosses in Fig. 2b and c indicate H₂ concentrations from pre-industrial and present-day OsloCTM3 simulations.

While the box model allows exploration of various uncertainties in H₂ evolution, such as the impacts of natural vs. anthropogenic emissions, different emission inventories, and the use of variable versus fixed soil-sinks - this study focuses on two specific issues related to atmospheric production and losses. A key question regarding atmospheric production is the significance of the relative contributions of H₂ production from CH₄ or NMVOCs. Total production is the sum of production from CH₄ and NMVOCs (not diagnosed in the ACMs), with the increase in production from CH₄ showing a larger increase over time. The box model can be used to test the impacts of modifying this split (Fig. 3). We run two cases – in the first case (solid lines in Fig. 3), production from NMVOCs accounts for 44 % of the total production consistent with the estimate of Ehhalt and Rohrer (2009), while in the second case (dashed lines in Fig. 3), this production from NMVOCs is reduced to 39 % following Paulot et al. (2024). For the first case, the crossover when production from CH₄ surpasses production by NMVOCs occurs in the 1950s (solid pink and blue lines in Fig. 3a), while in the second case, this crossover occurs in the 1910s (dashed pink and blue lines in Fig. 3a). In the first case, the pre-industrial H₂ production from NMVOCs decreases from ∼20 to ∼13 Tgyr-1, while production from CH₄ increases from ∼14 to ∼18 Tgyr-1 (Fig. 3a). Total production in 1850 is reduced by ∼4 Tgyr-1 with the gap narrowing over time until the 1980s, when both cases converge. The maximum difference in H₂ concentration between the two cases does not exceed ∼15 ppb.

In the box model, atmospheric losses are defined by their lifetime, which depend on OH concentrations. We assess the effect of different temporal evolution of lifetimes due to OH concentrations on tropospheric H₂, by running the model with three different atmospheric lifetimes that correspond to: (1) constant OH concentrations from pre-industrial to today; (2) pre-calculated OH concentrations by combining historical trends from Stevenson et al. (2020) and Skeie et al. (2023a); and (3) using a scheme from the Third Assessment Report (TAR) where the OH-sink lifetime is adjusted following Ehhalt et al. (2001; Table 4.11, footnote b) based on CH₄ concentrations, and emissions of CO, NO_x, and VOCs (Fig. 4). The impact of the different OH concentrations on the OH-sink lifetime is shown in Fig. A11. Note that the OH concentrations here only affect the losses/sink term and not atmospheric production. These results indicate that using constant versus pre-determined OH-sink lifetimes produce similar H₂ concentrations (within 10 ppb) through time. In contrast, applying the TAR scheme leads to higher H₂ concentrations, ∼40 ppb greater than the other cases until the early 1970s – a couple of decades after the increase in anthropogenic emissions and a few years after the crossover point when atmospheric production from CH₄ dominates over production from NMVOCs. This indicates a higher atmospheric lifetime early in the box model simulation (pre-1940s) as calculated by CH₄ concentrations, and emissions of CO, NO_x, and VOCs. Notably, all these terms have a large uncertainties. After the 1970s, the H₂ concentration from the three atmospheric lifetime cases broadly match each other.

Results indicate that the various assumptions in the box model for the split between H₂ production from NMVOCs and CH₄ and for the time evolution of the atmospheric lifetime, which are not provided by the ACMs, have only a small effect on the H₂ concentration over recent decades.

In addition to H₂ concentrations, isotopic values of atmospheric H₂ are calculated in the box model at every time step, depending on the relative contributions from the different sources and sinks. Figure 5 shows the hydrogen atmospheric concentration vs. isotopic composition for the different box model simulations fit to match the ACMs (using model parameters as inputs for steady-state 2010 conditions) and from published literature. All the models' box model simulation results show a narrow range of atmospheric H₂ concentrations (520–540 ppb; by design) and a wider range for isotopic values (20 ‰–210 ‰), with WACCM6 at the lower-end and UKCA at the higher-end. The enriched isotopic value in WACCM6 is due to the combination of high emissions (anthropogenic and biomass burning sources), low atmospheric H₂ production and high soil sink. The more negative value for isotopic composition in UKCA is due to low emissions and low soil sink in UKCA. OsloCTM3 has higher atmospheric production, but this is isotopically balanced out by higher soil sink. Published studies have ranges for both predicted H₂ and isotopic values of 365–550 ppb and 0 ‰–150 ‰ respectively. That the isotopic range is large is not surprising as most of these studies look at the concentration budget and not the isotopic budget. For example, Fig. A9 shows the resulting budgets if isotopic values and fractionation factors for the different sources and sinks are taken from Pieterse et al. (2011) rather than Price et al. (2007) without and with stratospheric enrichment of 29 ‰. The mean changes for the models and literature values are 7.8 ‰ and 24.56 ‰ without stratospheric enrichment and 20.61 ‰ and 49.61 ‰ with the stratospheric enrichment respectively. This difference is driven by the Pieterse et al. (2011) having isotopic compositions of -260 ‰ and 116 ‰ for biomass burning and atmospheric production of CH₄ instead of -290 ‰ and 162 ‰ in Price et al. (2007). We present this spread here, not to evaluate them against models, but to reiterate the benefit of combining H₂ concentrations with δD to constrain the different budget terms.

We present five cases where the sources and sinks are modified to demonstrate this approach (Fig. 6): (1) a base case using modern-day values; (2) high atmospheric production where atmospheric production values from a top-down estimate (Rhee et al., 2006) are used; (3) low atmospheric production; (4) additional geological source of 23 Tgyr-1 as suggested by Zgonnik (2020) and (5) the additional geological source of 23 Tgyr-1 along with a high OH sink. To balance the budget for H₂-concentrations, we adjusted the soil sink (Table 3). These cases are chosen to constrain the range of atmospheric production estimates and potential geological inputs by evaluating the feasibility to fall within observed concentration and isotopic ranges. It should be noted that geological sources can span a wide range of isotopic values from 0 ‰ to -1000 ‰. We choose a value of -385 ‰ which is the mean of the white hydrogen values suggested in Gibson et al. (2024). The effect of using a different isotopic value for a geological source is shown in Fig. A10.

Figure 6a shows the magnitude of the different sources and sinks for hydrogen in the five cases and Fig. 6b shows the isotopic values for the sources used in the box model. The resulting hydrogen concentrations for the four cases are shown in Fig. 6c. By design all five cases produce atmospheric concentrations that are broadly near the observed concentration range (530–560 ppb, dashed lines). However, the corresponding isotopic compositions are much more sensitive compared to H₂ concentration and fall far outside the observed ranges (130 ‰–160 ‰) for the three perturbed cases. This clearly indicates that low and high atmospheric production values do not agree with the observed H₂-isotopic values. Further, a geological source (with a corresponding increase in soil uptake) shows an even bigger shift in δD – not observed today.

Uncertainty ranges for the isotopic signatures of each source were used to calculate the maximum possible uncertainty. The most depleted and enriched source combinations were applied to calculate the minimum and maximum ranges shown in Fig. 6d. These results indicate that while high atmospheric production can be accommodated within the budget if extremely depleted isotopic values are used for the other sources, scenarios with lower atmospheric production and high geological sources do not fit the budget.

We also performed an uncertainty analysis to evaluate the joint uncertainties using the distributions of all the sources and sinks and their isotopic values (ranging from the most negative and most positive values in literature; Fig. 7). Additionally, we also check the impact of the stratospheric contribution to the analysis, by assuming the enrichment of the final atmospheric δD composition by randomly picking a value between 29 ‰–37 ‰. We use a Monte-Carlo approach by randomly picking 100 000 different combinations of sources and sinks to run the box model and check whether the resulting atmospheric concentration and the isotopic composition of atmospheric H₂ is within the ranges of 530–560 ppb (to account for the increasing trend till 2021) and 130 ‰–160 ‰, respectively. Applying the joint certainly analysis, the 97.5th percentile upper bound on the geological sources decreases from 9.4 Tgyr-1 in the initial distribution to 6.3 and 7.7 Tgyr-1 without and with a stratospheric contribution, respectively. Relative to the initial distribution, only 88 % and 91 % of the geological flux distribution overlap with the 95 % constrained intervals without and with a stratospheric contribution, ruling out 12 % and 9 % of the distribution, respectively.

The influence of the individual sources and sinks on the final tropospheric mole fraction and isotopic composition of tropospheric H₂ is shown in Fig. 8 as the effect of a 2 % change in the source or sink strength. Among the sources, atmospheric production has the largest effect on both the tropospheric H₂ and isotopic compositions, with each of the other sources having less than 1/3rd of the impact. The two sinks also play a huge role with the soil sink making the isotopic values more negative, while the OH sink shifting them to more positive values.

We extend this analysis by evaluating what adjustments to individual sources would be required to accommodate geological sources. While multiple source-sink combinations exist that fit within the concentration and isotopic constraints, we restrict this sensitivity analysis to emissions from anthropogenic sources, biomass burning, and nitrogen fixation. Based on model evaluations and box model constraints the atmospheric production and soil sink are allowed to vary between 37–60 and 49–77 Tgyr-1 respectively. The range for soil sink is derived by running the box model across the specified range of atmospheric production values to identify feasible soil sink estimates that satisfy the observed concentration and isotopic constraints for tropospheric H₂.

Table 4 shows the maximum geological source consistent with low, mid, and high estimates of the three sources. The results indicate that the maximum plausible geological source given the constraints is 9 Tgyr-1. Thus an estimate of 23 Tgyr-1 as suggested by Zgonnik (2020) is not possible with our assumed isotopic composition of the geological input. However, greater contributions from isotopically enriched volcanic sources can affect this upper bound.