Large uncertainties in global hydroxyl projections tied to fate of reactive nitrogen and carbon

Significance

Reaction with the hydroxyl radical (OH) is the dominant loss mechanism for many atmospheric gases of interest for air quality, climate change, and stratospheric ozone. Understanding how and why OH may change in the future is therefore paramount for predicting changes in the societal impacts associated with such changes. Future models’ projections strongly disagree in how OH responds to changing emissions and climate—even in the sign. Here, we demonstrate that intermodel differences in OH are best explained by disparate implementations of chemical and physical processes that affect reactive oxides of nitrogen and organic chemical species. Targeted observations can reduce uncertainty in the chemical budgets of these key species to increase confidence in future projections of composition and its impacts.

Abstract

The hydroxyl radical (OH) sets the oxidative capacity of the atmosphere and, thus, profoundly affects the removal rate of pollutants and reactive greenhouse gases. While observationally derived constraints exist for global annual mean present-day OH abundances and interannual variability, OH estimates for past and future periods rely primarily on global atmospheric chemistry models. These models disagree ± 30% in mean OH and in its changes from the preindustrial to late 21st century, even when forced with identical anthropogenic emissions. A simple steady-state relationship that accounts for ozone photolysis frequencies, water vapor, and the ratio of reactive nitrogen to carbon emissions explains temporal variability within most models, but not intermodel differences. Here, we show that departure from the expected relationship reflects the treatment of reactive oxidized nitrogen species (NO_y) and the fraction of emitted carbon that reacts within each chemical mechanism, which remain poorly known due to a lack of observational data. Our findings imply a need for additional observational constraints on NO_y partitioning and lifetime, especially in the remote free troposphere, as well as the fate of carbon-containing reaction intermediates to test models, thereby reducing uncertainties in projections of OH and, hence, lifetimes of pollutants and greenhouse gases.

The hydroxyl radical (OH) is a keystone chemical species in the atmosphere, determining the removal rate of many trace gases of importance to climate, composition, and human and ecosystem health (1). For example, reaction with OH in the troposphere^* is the dominant sink for methane, a powerful greenhouse gas and precursor for tropospheric ozone, a major surface pollutant and greenhouse gas itself (2). Understanding what drives variability in OH is therefore critical for forecasting future changes in the self-cleansing capability of the atmosphere. The fundamental chemistry of background OH has been well known for decades (3–5). Nevertheless, global atmospheric chemistry models show large disagreement in mean OH and its transient response to specified changes in emissions (6, 7).

Fig. 1 shows global mean OH and its temporal evolution within the ensemble of simulations that participated in the Atmospheric Chemistry-Climate Model Intercomparison Project (ACCMIP) (8). The ACCMIP ensemble is a comprehensive suite of global three-dimensional atmospheric chemistry models driven by identical anthropogenic emission scenarios for the period 1850–2100 (9, 10). Despite applying identical anthropogenic emissions in all ACCMIP models, tropospheric mean abundances of OH range $\pm 30 \%$ relative to the multimodel mean during the last decade of the historical simulation (gray-shaded interval of Fig. 1). The models also disagree as to whether OH increases or decreases across any prescribed emission scenario, except for a small window between 1980 and 2010 (when all increase).

Fig. 1.

Large disagreement in decadal mean tropospheric OH and its transient evolution in global atmospheric chemistry models. The models shown prescribe identical anthropogenic emissions from a historical reconstruction (9) and four possible future RCP scenarios (10). Different colors represent different models. The gray rectangle highlights the period 2000 to 2010 in each scenario. Full model names are shown in the key, with a two-letter abbreviation shown in parentheses used in subsequent figures.

Our best estimates of global mean abundance and interannual variability from OH rely on proxy measurements, particularly methyl chloroform (11), as the high reactivity and short lifetime of OH make direct measurement difficult and impractical for constraining spatial and temporal variability (12). On average, global atmospheric chemistry models cannot reproduce meridional gradients in carbon monoxide (CO) and other long-lived reactants, implying possible errors in simulated OH spatial and seasonal distributions (6, 13). They also overestimate global mean OH with respect to observational constraints from the methane and methyl chloroform lifetimes (6, 7) and underestimate the magnitude of interannual variability in OH inferred from proxy observations [$0.5\pm 0.4 \%$ of year-to-year changes in the ACCMIP ensemble versus $2.3\pm 1.5 \%$ derived from methyl chloroform (11)]. These findings highlight gaps in our understanding of the processes that determine the oxidative capacity of the atmosphere and its variability, thereby hindering our ability to accurately predict its future evolution.

In contrast to the intermodel discrepancies in OH abundances, trends, and variability, the models tend to produce consistent simulations for key tropospheric species that are intimately coupled with OH, such as tropospheric ozone (14). This implies that some—or even all—models are capturing mean abundances and spatial and temporal trends of longer-lived species at least partly for the wrong reasons.

The original analysis of OH in the ACCMIP simulations noted that the change in OH over time in a given model correlated with the ratio of change in its burden of reactive nitrogen oxides (NO${}_x\equiv$ NO + NO₂) to change in its CO burden, but did not provide a mechanistic explanation (6). Here, we reexamine the ACCMIP model ensemble through the lens of fundamental OH chemistry to explain the disparate behavior between the models. The key areas of uncertainty we identify provide a target for future observing strategies to advance most rapidly our understanding, as formalized in the models used to project future atmospheric abundances of pollutants and reactive greenhouse gases.

A Steady-State Relationship for OH

The key reactions controlling OH are highly and nonlinearly coupled to one another (refs. 3–5 and SI Appendix, Fig. S1). In the GEOS-Chem chemistry-transport model (CTM; Materials and Methods), primary production of OH by photolysis or photolysis-initiated chains contributes to ∼60% of total production in the present day, with most of that source resulting from photolysis of ozone in the presence of water vapor. The remaining 40% results from chemical recycling of the HO_x family (HO_x $\equiv$ OH + peroxy radicals) via reaction of peroxy radicals with reactive oxides of nitrogen (NO_x) or ozone. Loss of OH is primarily via reaction with reduced carbon species, such as CO (40%) and methane (15%), with products of methane oxidation, other nonmethane volatile organic compounds (NMVOCs) and their oxidation products, ozone, H₂, HO_x species, and other minor species accounting for the remainder. Here, we refer to the sum of CO, methane and, all NMVOCs as total “reactive carbon.”

The equations that describe the dominant OH photochemistry are simple enough that they yield an analytic solution for OH when one assumes “steady state,” in which the sum of the source terms is balanced by all loss terms (SI Appendix, section 1). At steady state, variations in OH should vary proportional to

$$J_{\text{O}{(}^{1}D)} q \frac{S_N}{S_C^{3/2}},$$ (1)

where $J_{\text{O}{(}^{1}D)}$ is the photolysis frequency of ozone to O(${}^{1}D$) (s^{– 1}), q is the specific humidity (kg H₂O kg air^{– 1}), and S_N and S_C are the emission rates of NO_x (Tmol N y^{– 1}) and reactive carbon (Tmol C y^{– 1}) species, respectively. The first two terms limit the rate of total HO_x production, whereas the emission ratio determines the relative partitioning of HO_x between OH and peroxy radicals (with nitrogen oxides favoring OH and reactive carbon favoring peroxy radicals). The exponent in the denominator accounts for nonlinear feedbacks in the coupled chemistry. Collectively, the relationship describes how the basic OH photochemistry changes in response to changing emissions and climate parameters. Eq. 1 has been used to explain global OH variability within a single CTM across a wide range of climate and emissions scenarios with high skill (15). However, in principle, it should hold across multiple models, as it derives from the analytic solution to the steady-state OH photochemistry.

Large temporal and intermodel variability exists within the decadal mean evolution of each component of Eq. 1 of the ACCMIP ensemble (SI Appendix, Fig. S2). The models employed a variety of methods for determining photolysis rates, ranging from look-up tables to online calculation with column radiation codes (8). Most models agree in their mean photolysis frequencies, although outliers exist in the ensemble. Changes in photolysis frequencies with time are relatively small compared to intermodel variability, although it has been shown that OH is especially sensitive to them (e.g., refs. 15–17). These temporal changes are driven primarily by changes in overhead ozone abundances associated with anthropogenic emissions of stratospheric ozone-depleting substances and greenhouse gases (18), with peak photolysis rates in each model occurring during the height of stratospheric ozone loss circa 1980–2010. The models are in tight agreement in both tropospheric mean water-vapor abundance and its exponential increase over time in response to temperature-driven increases in saturation water-vapor pressure (19). NO_x emissions are dominated by the prescribed anthropogenic sources, and, therefore, temporal variability dominates over intermodel variability. However, slight differences do exist between models and in time due to different parameterizations of climate-sensitive natural sources, such as lightning (20). In contrast, emissions of reactive carbon species vary widely across the models and in time. These variations are dominated by natural sources; the models employed a wide range of biogenic NMVOC implementations with respect to species emitted (including none), chemical mechanism, base emissions, and the response of emissions to changes in meteorology, e.g., the increase in isoprene emission by terrestrial plants at warmer temperatures (21).

Fig. 2 shows decadal mean OH in the ACCMIP simulations as a function of Eq. 1. If differences in the four key parameters in SI Appendix, Fig. S2 were sufficient to explain OH variability within and between the models, then all points would fall on the same line with a positive slope. The OH steady-state predictor is usually sufficient to explain variability within individual models, although not in the models with the highest mean OH abundances. A large mode of residual intermodel variability dominates the ensemble variability. This intermodel variability lies largely orthogonal to that explained by the OH photochemistry and is therefore likely independent.

Fig. 2.

Decadal mean OH as a function of the steady-state photochemical relationship. Variability within many individual models is accurately explained by Eq. 1. However, large intermodel variability is not. Individual models are identified by color and emission scenario by shape. An ordinary linear regression line is shown for each model subpopulation. See SI Appendix, Fig. S3 for individual model detail at annual time scales.

Fig. 3 shows that the residual variability can be best explained by considering two parameters derived from available ACCMIP model diagnostics. First, the large intermodel variability is primarily related to the NMVOC “oxidation efficiency,” ${\mathrm{ϵ}}_{\text{C}}$, which we define as the fraction of carbon atoms emitted in NMVOC compounds oxidized to CO before removal from the atmosphere (units of mol C per mol C). Models that have a higher fraction of their emitted carbon converted to CO tend to have lower OH (Fig. 3A). Second, departure from linearity within a single model is primarily related to shifts in the tropospheric lifetime of NO_x, ${\tau }_{{\text{NO}}_x}$ (units of time; Fig. 3B). Variations in these two parameters act to alter the magnitude of the HO_x partitioning response to changes in emissions of NO_x versus reduced carbon species in Eq. 1.

Fig. 3.

Residual intermodel and intramodel variability of Fig. 2 explained by two parameters. (A) The points of Fig. 2 colored by their decadal mean “oxidative efficiency,” the fraction of emitted NMVOC carbon that is oxidized to CO before atmospheric removal. (B) The points colored by ${\tau }_{{\text{NO}}_x}$, i.e., the NO_x burden ($\equiv \text{NO}+{\text{NO}}_2$) divided by its source. Gray-shaded points indicate insufficient model data archived for calculation.

Factors Driving Model Diversity

The most apparent correlation of intermodel variability in Fig. 3 is with the NMVOC oxidative efficiency (${\mathrm{ϵ}}_{\text{C}}$), with models having higher ${\mathrm{ϵ}}_{\text{C}}$ tending to have lower OH. While the greatest sinks of OH are CO and methane, respectively, these do not vary much between the ACCMIP models by design; methane and anthropogenic CO are prescribed, and nearly all methane is oxidized to CO (22). The large intermodel variability in NMVOC emissions is not correlated with intermodel variability in global mean OH, even though NMVOCs consume OH, because relatively short NMVOC lifetimes restrict their influence to be immediately downwind of sources, which are mostly in the continental boundary layer. Instead, differences in the portion of NMVOCs fully oxidized to CO (i.e., ${\mathrm{ϵ}}_{\text{C}}$), a gas with a sufficiently long lifetime to mix into the free and remote troposphere, best explain intermodel variability in global mean OH.

From the perspective of reactive carbon, the atmosphere is a low-temperature furnace: Reduced organic gases are emitted and subsequently oxidized through a chain of increasingly semioxidized species toward CO and CO₂. However, increased oxidation tends toward lower-volatility species that may condense (23). Other intermediates are soluble and/or prone to surface uptake, and physical processes may siphon these from the atmosphere as well. All in all, physical loss is a greater atmospheric sink of NMVOC carbon than chemical conversion to CO and CO₂ in most models (${\mathrm{ϵ}}_{\text{C}}$ often ¡0.5; Fig. 3A and SI Appendix, Fig. S4; also refs. 24–26).

Atmospheric model developers must make choices that influence an individual model’s oxidative efficiency. We must balance a yet-imperfect scientific understanding of atmospheric oxidation mechanisms (e.g., ref. 27) with desired model capabilities and computational limitations. Near-explicit mechanisms using elementary reactions based on observational constraints for the oxidation of isoprene alone would require thousands of reactions and several hundred species (28), intractable for global atmospheric models. For these reasons, global models typically employ reduced chemical mechanisms with lumped surrogate species and empirically derived stoichiometries in order to best reproduce observations within computational limits.

We highlight two end members of the ACCMIP ensemble by contrasting the hydrocarbon oxidation mechanisms of the Goddard Institute for Space Studies (GISS) and Geophysical Fluid Dynamics Laboratory (GFDL) models. In the GISS model (SI Appendix, Fig. S5), gaseous NMVOCs are emitted as 2 explicit and 3 lumped species, transforming among 18 NMVOC species before conversion to CO. All oxidation pathways lead to CO, except for 7 species (39%) that may be physically removed and a terminal pathway included to enable tuning of relative oxidation rates to observations (29). In contrast, the GFDL model (SI Appendix, Fig. S6) emits NMVOCs as 10 explicit and 2 lumped species and transforms among 44 total NMVOC species, with 28 species (64%) physically removable by wet or dry processes. Furthermore, the GFDL empirical oxidation stoichiometries include partial direct conversion of NMVOCs to CO₂, bypassing CO. Given the greater opportunity for loss of intermediates, only 23% of NMVOC emitted by the GFDL model is oxidized to CO, versus 53% in the GISS model. Consequently, the GISS model has a greater fraction of its emitted reactive carbon reacting with OH and, thereby, lower OH.

Despite large intermodel variability, the oxidative efficiency is relatively invariant in time for a given model (SI Appendix, Fig. S7). This implies that the oxidative efficiency is primarily determined by the specific combination of species, reactions, and sinks implemented in a given model. Nevertheless, minor temporal changes occur, reflecting shifts in the distribution and magnitudes of reactive carbon emissions and precipitation. For example, the methane increase in the “Representative Concentration Pathway” (RCP) 8.5 scenario consumes a larger fraction of OH, slowing the oxidation rate of NMVOCs, allowing more time for intermediate species to be lost via deposition, thereby reducing ${\mathrm{ϵ}}_{\text{C}}$ in some models.

In contrast to ${\mathrm{ϵ}}_{\text{C}}$, variability in ${\tau }_{{\text{NO}}_x}$ contributes to both intermodel and intramodel variability in OH. The rapid cycling of NO_x between NO and NO₂ allows for the catalytic production of relatively large quantities of OH (SI Appendix, Fig. S8); otherwise, all OH would be quickly titrated from the atmosphere. Longer ${\tau }_{{\text{NO}}_x}$ enables relatively more OH production per NO_x molecule. Global mean ${\tau }_{{\text{NO}}_x}$ varies by orders of magnitude across models (Fig. 3B), and some models simulate temporal changes by nearly as much, although others suggest little change (SI Appendix, Fig. S7). Therefore, variations in ${\tau }_{{\text{NO}}_x}$ can influence both intermodel and intramodel changes in global mean OH. SI Appendix, Fig. S9 demonstrates the sensitivity of the steady-state OH abundance to mean ${\tau }_{{\text{NO}}_x}$ in the GFDL model. The factors controlling the lifetime of NO_x are many and can compete in sign. We next demonstrate the sensitivity of global mean OH to three key parameters with known intermodel disparities.

First, the ACCMIP models employ very different vertical and meridional distributions of lightning NO_x (cf. figure 3 of ref. 20). Because ${\tau }_{{\text{NO}}_x}$ increases exponentially with altitude, global mean ${\tau }_{{\text{NO}}_x}$ is highly sensitive to the mean vertical injection height of lightning NO_x. Most models release lightning NO_x into the free troposphere. However, two ACCMIP ensemble members (UM and HG; see Fig. 1 for definitions of abbreviations) release their lightning NO_x primarily into the boundary layer. When we compare a sensitivity simulation using the GEOS-Chem CTM with lightning NO_x released at the surface instead of at altitude, global mean OH decreases by 22% (Fig. 4A), a sizable portion of the difference in OH between GEOS-Chem and the two ACCMIP models releasing all lightning NO_x near the surface (Fig. 4D).

Fig. 4.

Global mean OH is highly sensitive to the treatment of reactive nitrogen. (A–C) Change in zonal mean OH in the GEOS-Chem CTM for the year 1980 for the following scenarios: All lightning NO_x is released into the planetary boundary layer instead of at altitude (A); all heterogeneous reactions are turned off (B); and all nitrogen sequestered in isoprene nitrates is recycled back to NO_x (C). The box reports the percent change in the global OH burden. (D) Decadal mean OH in the ACCMIP models for the 1980s versus that in GEOS-Chem and the three sensitivity simulations shown in A–C. The x axis is arbitrary.

Second, heterogeneous reactions can vary substantially between global models. Uptake of gaseous species on the surface of aerosol particles is a highly efficient means for sequestering NO_y and HO_x from the atmosphere, short-circuiting the OH photochemistry included in Eq. 1. Most models include hydrolysis of N₂O₅ on aerosol particles, often the dominant local sink for NO_y, with a known strong influence on global OH (30, 31). However, models differ in implementation (e.g., some models vary the uptake coefficient γ with aerosol composition), as well as in the inclusion of other heterogeneous losses. When we disable heterogeneous losses within GEOS-Chem [normally N₂O₅ hydrolysis with ${\gamma }_{{\text{N}}_2{\text{O}}_5}\le 0.02$ (32) and HO₂ uptake with ${\gamma }_{{\text{HO}}_2}\le 0.1$ (33)], global mean OH increases by 12% (Fig. 4B), the magnitude of many intermodel differences. We note that the only difference in the gas-phase chemistry of the two variants of the GISS model submitted to the ACCMIP study was that one included heterogeneous uptake of HNO₃ on dust particles (GI; ref. 34) and one did not (GT), resulting in a longer ${\tau }_{{\text{NO}}_x}$ and 20% higher OH in the latter (Fig. 4D).

Lastly, NO_y is often stored in relatively long-lived reservoir species, which prolong and redistribute the influence of NO_x on oxidants. However, these reservoir species may also be lost to deposition, which bypasses the assumption that all NO_x is lost via oxidation to HNO₃ intrinsic to Eq. 1. One particular area of model diversity in NO_y reservoirs regards the fate of isoprene nitrates, products of oxidation of isoprene by NO_x, especially at night. Some chemical mechanisms, including that implemented in our version of GEOS-Chem, assume that this nitrate is immediately lost to deposition, reflecting observational evidence that this can be a major local NO_y sink (e.g., ref. 35). Others allow for part of this nitrate to be recycled back to NO_x. When we perform a sensitivity test in GEOS-Chem, in which we allow all isoprene nitrates to be recycled back to NO_x, global mean OH increases by 7% (Fig. 4C), the magnitude of differences between GEOS-Chem and the GFDL model (GA and GF), which included isoprene nitrate recycling (albeit ¡100%; ref. 36).

Disparate implementations of processes that affect ${\tau }_{{\text{NO}}_x}$ therefore cause the NO_y budget to be a key source of model uncertainty with respect to OH. Fig. 5 shows that despite nearly identical NO_x emission magnitudes, the models show large variability in their absolute burdens and relative partitioning of the dominant NO_y species. This is much greater than seen in the longer-lived species, such as ozone and CO. Furthermore, Fig. 5 is missing other major NO_y species not archived for ACCMIP, e.g., HONO or HO₂NO₂, which likely also vary between models.

Fig. 5.

ACCMIP models show large disagreement in their reactive nitrogen budgets. (Left) The cumulative absolute burdens of the four dominant NO_y species: peroxyacetylnitrate (PAN), HNO₃, NO₂, and NO. Decadal tropospheric mean is shown for the 2000s from 13 global atmospheric chemistry models. (Right) The cumulative fractional burdens per model.

Taken together, the sensitivity of global mean OH to ${\mathrm{ϵ}}_{\text{C}}$ and ${\tau }_{{\text{NO}}_x}$ implies that a key assumption of Eq. 1 does not hold between models or within some models, i.e., the sources of reactive nitrogen and carbon are not balanced by their dominant sinks with respect to OH (oxidation to nitric acid and carbon dioxide, respectively). Various processes siphon emitted reactive nitrogen and carbon from the atmosphere before they may influence OH photochemistry. It is variations in the fraction of total nitrogen and carbon loss pathways that involve OH that ultimately control OH abundance in the models and, therefore, the atmospheric chemistry and physics that occur between emission and loss. Fig. 6 shows that we are better able to capture intermodel and intramodel variability in OH by shifting our focus from the sources of nitrogen and carbon to the sinks (R = 0.5 for n = 221 decadal time slices).

Fig. 6.

Variability in decadal mean OH in the ACCMIP simulations is better captured when considering photochemical sinks of reactive nitrogen and carbon (as in this figure) than sources (as in Fig. 2). Instead of emission, we apply the total loss rate of CO and methane (L_C), which is equivalent to the sum of the sources of CO, methane, and the oxidative efficiency times the NMVOC source. Furthermore, we estimate the loss of NO_x to nitric acid (L_N). See Materials and Methods for details. Gray horizontal lines indicate the error in estimating L_N from archived monthly mean values relative to online calculation with GEOS-Chem (not archived by the ACCMIP experiment).

Conclusions

Atmospheric chemistry model contributions to the ACCMIP experiment strongly disagree in their global mean OH and its transient evolution in response to prescribed changes in anthropogenic emissions (Fig. 1). A steady-state relationship derived from the basic coupled photochemistry of the O_x–HO_x–NO_x–CO system explains OH variability within models if the NO_x lifetime (${\tau }_{{\text{NO}}_x}$) remains relatively constant (Fig. 2). However, model OH is sensitive to intermodel differences in the fraction of nonmethane volatile organic carbon that is completely oxidized through CO (and CO₂), ${\mathrm{ϵ}}_{\text{C}}$, as well as ${\tau }_{{\text{NO}}_x}$ (Fig. 3). The oxidative efficiency is generally fixed for a given model, determined by the kinetics of the reactions and species included in the model. In contrast, the NO_x lifetime is much more variable between models, and even within some models, and is especially sensitive to the altitude of lightning emissions, heterogeneous chemistry, and treatment of reactive nitrogen reservoir species (Fig. 4), although this list is not exhaustive. Variations in global mean OH between and within global models are therefore better characterized by variations in the relative loss pathways of reactive nitrogen and carbon than in their emissions (Fig. 6).

We recommend that future efforts diagnose complete reactive nitrogen budgets in models, especially in the tropical free troposphere. Evaluating these simulated budgets requires comprehensive new measurements that expand beyond the recent NASA Atmospheric Tomography mission, the most extensive global in situ dataset to date (37). Likewise, we recommend that future observational campaigns target quantification of the global source of CO from NMVOC oxidation. Improved observational estimates of ${\tau }_{{\text{NO}}_x}$ and ${\mathrm{ϵ}}_{\text{C}}$ will help to constrain models and improve projections of the future oxidizing power of the atmosphere.

Materials and Methods

Data Analyzed

The ACCMIP consisted of 16 atmospheric chemistry models driven by identical anthropogenic emissions and climate forcers over the 1850–2100 period (8). Most models were run as decadal time-slice experiments for a few core decades (1850s, 1980s, 2000s, 2030s, and 2090s), although the GISS-E2-R model submitted its transient simulations for the Coupled Model Intercomparison Project Phase 5 (CMIP5). The ACCMIP and CMIP5 simulations were performed in support of the Fifth Assessment Report of the Intergovernmental Panel on Climate Change. The diagnostics saved for the ACCMIP study are archived at the British Atmospheric Data Centre (https://archive.ceda.ac.uk/), as downloaded in September 2019. Here, we analyze the historical simulations and the four future RCP scenarios (10). All 3-d and 2-d variables were processed at monthly temporal resolution by integrating tropospheric totals or airmass-weighted mean values, as appropriate. The troposphere is defined with a monthly chemical tropopause of 150 parts per billion by volume ozone, consistent with earlier ACCMIP analyses (6, 7, 14). The monthly values are then averaged to obtain decadal means. We supplement the ACCMIP data with transient runs from the GFDL-CM3 contribution to the CMIP5 study that used the same emissions and forcings (38) and GEOS-Chem (Original Simulation Description).

Ozone photolysis is directly archived (photo1d) or estimated from the archived OH production rate (prodohjo3) using coefficients from the Jet Propulsion Laboratory Handbook (39). Specific humidity is archived as hus. S_N is archived as eminox. S_C is the sum of total emission of CO (emico), NMVOCs (emivoc), and methane, which we assume is equivalent to the total loss rate of methane (lossch4). Emission totals are adjusted to match values self-reported by the modeling groups in Lamarque et al. (8), as outlined in SI Appendix, section S2. By assuming that direct emissions and chemical production of CO from methane and NMVOCs are balanced by its total chemical loss, then the oxidative efficiency can be estimated as ${\mathrm{ϵ}}_{\text{C}}\equiv \frac{P{(\text{CO})}_{\text{NMVOC}}}{E_{\text{NMVOC}}}\approx \frac{L(\text{CO})-E_{\text{CO}}-P{(\text{CO})}_{{\text{CH}}_4}}{E_{\text{NMVOC}}}$. Total chemical loss of CO is archived as lossco, and, again, we use emivoc and emico. We estimate the source of CO from methane oxidation by assuming a 100% conversion of oxidized methane from lossch4 to CO (22). ${\tau }_{{\text{NO}}_x}$ is determined as the total burden of NO (vmrno) and NO₂ (vmrno2) divided by the total source (eminox).

To adjust the steady-state relationship for Fig. 6, we estimate L_C as lossco + lossch4, which neglects carbon lost to intermediates. We estimate L_N as the production rate of HNO₃ from the pressure-dependent NO₂ + OH reaction using monthly archived NO₂, OH, air density, and temperature and rate constants from ref. 39.

Original Simulation Description

We use the default GEOS-Chem global CTM (v9-01-03; available at http://www.geos-chem.org) with its “tropchem” mechanism driven by MERRA reanalysis meteorological fields (40) degraded to 4${}^{°}$ latitude by 5${}^{°}$ longitude by 47 vertical levels (38 in the troposphere), and the same emissions used in the ACCMIP study. Methane is prescribed as a surface boundary condition and allowed to advect and react, consistent with the ACCMIP models. The base simulation is initialized over the year 1979, and then archived for 1980–2010. NO_x sensitivity experiments are then performed by reinitializing over 1979 and archiving year 1980 for the three scenarios described in Factors Driving Model Diversity.

Data Availability

Processed data used in the figures have been deposited in Zenodo (DOI: 10.5281/zenodo.5576887). All other study data are included in the article and/or supporting information.