An observation-based, reduced-form model for oxidation in the remote marine troposphere

Significance

The hydroxyl radical (OH) controls tropospheric methane loss rates. Global or hemispheric annual mean methane loss rates are currently inferred from observations of well-mixed gases, such as methyl chloroform. The short OH lifetime (1 to 2 s) and associated sharp spatiotemporal variations limit constraints on global models and understanding of “why” globally integrated OH fluctuates. From airborne measurements and steady-state chemistry, we develop a proxy to infer OH spatial variations and their sensitivity to individual photochemical drivers over 30 different regions in the remote marine troposphere. Two terms, water vapor and nitric oxide, contribute most of the within-region proxy variations, implying that a limited set of observations could serve as bellwethers of changing atmospheric oxidation patterns.

Abstract

The hydroxyl radical (OH) fuels atmospheric chemical cycling as the main sink for methane and a driver of the formation and loss of many air pollutants, but direct OH observations are sparse. We develop and evaluate an observation-based proxy for short-term, spatial variations in OH (Proxy_OH) in the remote marine troposphere using comprehensive measurements from the NASA Atmospheric Tomography (ATom) airborne campaign. Proxy_OH is a reduced form of the OH steady-state equation representing the dominant OH production and loss pathways in the remote marine troposphere, according to box model simulations of OH constrained with ATom observations. Proxy_OH comprises only eight variables that are generally observed by routine ground- or satellite-based instruments. Proxy_OH scales linearly with in situ [OH] spatial variations along the ATom flight tracks (median r² = 0.90, interquartile range = 0.80 to 0.94 across 2-km altitude by 20° latitudinal regions). We deconstruct spatial variations in Proxy_OH as a first-order approximation of the sensitivity of OH variations to individual terms. Two terms modulate within-region Proxy_OH variations—water vapor (H₂O) and, to a lesser extent, nitric oxide (NO). This implies that a limited set of observations could offer an avenue for observation-based mapping of OH spatial variations over much of the remote marine troposphere. Both H₂O and NO are expected to change with climate, while NO also varies strongly with human activities. We also illustrate the utility of Proxy_OH as a process-based approach for evaluating intermodel differences in remote marine tropospheric OH.

As the primary sink for methane, a strong greenhouse gas and air pollutant precursor, the hydroxyl radical (OH) is an influential yet poorly quantified lever on methane variations. Uncertainty in OH interannual variations is sufficiently high that it can hinder attribution of annual methane fluctuations. For example, inverse modeling analyses suggested several—sometimes conflicting—source sectors could explain the observed stabilization in methane levels from 2000 to 2005 (1–5), while uncertainty in the OH sink hinders effective trend attribution (6–8). Declining OH due to COVID-19 lockdowns has been invoked as a cause of the record-breaking increase in methane concentration observed since 2020 (9). The lack of constraints on OH also affects its representation in models that are applied to project future atmospheric composition and climate. Even when using the same emission inventories, chemistry-climate models simulate different methane lifetimes (10, 11), global mean OH (12, 13), and OH sensitivity to its drivers (13–15). Here, we develop and evaluate a proxy (Proxy_OH) built from OH steady-state chemistry over the remote marine troposphere. Proxy_OH maps spatial variations in OH and can also be deconstructed to infer the processes contributing to OH fluctuations, information that extends beyond the capacity of existing proxies.

Sharp spatiotemporal variations in OH confound the development of a representative measurement network. Interannual variability in global (16–19) or hemispheric (20) mean OH is typically inferred using the loss rate of relatively long-lived, well-mixed chemicals that react principally with OH, such as methyl chloroform (21–23). Formaldehyde, an intermediate product of methane oxidation with a lifetime of several hours, shows promise for reflecting daily OH fluctuations at the relatively small scale of a tropospheric column (24, 25). Although they offer much-needed information on OH variability, none of the existing proxies provides insight into the individual photochemical processes controlling OH.

We use an unprecedented set of observations from the NASA Atmospheric Tomography (ATom) airborne campaign (26). This dataset, comprising 146,494 10-s average air parcels (27), offers the most spatially comprehensive set of in situ profile measurements of OH and its chemical and radiative drivers to date (28). In general, we subset the relatively unpolluted, remote marine tropospheric data into regional bins to account for large-scale vertical and latitudinal variations in OH. We first consider potential formulations of Proxy_OH using a chemical box model (the Framework for 0-D Atmospheric Modeling, F0AM) constrained to the ATom observations (24, 29). Then we calculate Proxy_OH directly from the observations and evaluate it against ATom [OH]. While there is a rich history of using box models constrained by airborne data to examine OH and its sensitivities to individual photochemical drivers (e.g., refs. 30–34), we instead calculate the proxy directly from observations and laboratory-measured kinetic rate coefficients (35) using only eight variables (Section 2.1.1). This differs from other analyses that, for example, calculate daily average methane loss rates in models constrained by ATom observations (36).

Proxy_OH serves as a reduced-form model that offers a first-order estimate of the sensitivity of OH spatial variations to individual reaction rates or variables over the remote marine troposphere. We show below that Proxy_OH suggests that two key drivers, water vapor (H₂O) and nitric oxide (NO), contribute most to regional variations in OH observed during the ATom campaign. We also apply Proxy_OH to evaluate the simulated abundance and sensitivity of OH spatial variations in a global model used to project future composition and climate.

1. Results

1.1. Proxy Formulation over the Remote Marine Troposphere.

We define variations in OH as the spread in concentration at a specified spatiotemporal scale. Our goal is to distill the representation of OH to terms (e.g., photolysis rates or chemical species) that individually shape local OH distributions and, when combined, collectively capture measured OH variations. We use the F0AM photochemical box model constrained with ATom observations to test potential formulations of a proxy for OH spatial variations (Section 2.1.2).

Relatively few processes dominate OH variations over long timeframes or large spatial scales (37–39). Five years of OH measurements from a site in southern Germany suggest that insolation largely controls its temporal variations (40). Modeled global annual mean OH scales as a simple function of the ratio of reactive nitrogen and carbon emissions from preindustrial times to present-day (41). When combined with atmospheric humidity and overhead ozone columns, a proxy constructed from these four variables alone can capture global mean OH changes on glacial-interglacial (42) and decadal (13) timescales. Column-based satellite retrievals of species serving as OH sources and sinks reflect interannual modeled OH variations across U.S. cities from 2005 to 2014 (43) and to within 20 to 30% over the oceanic mid-troposphere from 2008 to 2017 (44). Here, we build on these previously identified sets of OH drivers to develop a proxy from observable quantities that reflect OH variations over smaller regional scales. We seek the simplest possible formulation that correlates strongly with ATom-measured [OH], so that Proxy_OH may also serve as a reduced-form model. The advantage of a reduced-form model is that it can infer the relative importance of specific chemical species or reactions in contributing to variations in observed or simulated OH.

Locally, [OH] should be at steady state (OH production rate = OH loss rate) on timescales that exceed the OH lifetime of ~1 to 2 s (37). Over much of the troposphere, OH production is dominated by the reactions between singlet D atomic oxygen (produced from ozone photolysis) and water vapor (O(¹D) + H₂O) and the hydroperoxyl radical with nitric oxide (HO₂ + NO), while losses are dominated by carbon monoxide (CO) and, secondarily, methane (38). We confirm that these two dominant production pathways capture spatial variations in OH production with the F0AM box model. In F0AM, the sum of the O(¹D) + H₂O and HO₂ + NO production rates strongly covary across the full ATom dataset with the total OH production rate (∑P_OH; r² = 0.98) and account for 60% of ∑P_OH (related to the slope of the regression between the proxy production rates and ∑P_OH regression slope; m = 0.75). The tight fit between OH and the sum of the two largest production terms, even though these terms cumulatively comprise only 60% of ∑P_OH, implies that O(¹D) + H₂O and HO₂ + NO covary with other terms that contribute to ∑P_OH. We show example correlated reactions included in F0AM in SI Appendix, Table S1. The O(¹D) + H₂O and HO₂ + NO pathways, plus the HO₂ + O₃ reaction and the photolysis of hydrogen peroxide (H₂O₂) and methyl hydroperoxide (CH₃OOH) cumulatively represent 98% of ∑P_OH (m increases to 0.98), with all other processes contributing <1% to ∑P_OH individually. While including additional OH production processes beyond the two dominant pathways increases the slope to approach 1, it has little influence on the fit between the simplified representation of production and ∑P_OH (Δr² < 0.01). This general pattern holds on smaller scales; the correlation coefficient between the sum of the O(¹D) + H₂O and HO₂ + NO with ∑P_OH is r² = {0.97, 0.98} over the Pacific or Atlantic, respectively, and the median ( $r_{\mathit{Mdn}}^2$ ) is 0.98 across smaller regional domains of 2 km by 20° latitudinal bins (Section 2.1.3). The composition of ∑P_OH also generally holds over smaller scales (SI Appendix, Fig. S1). Thus, we adopt a simplified proxy representation of OH production that includes only the O(¹D) + H₂O and HO₂ + NO reactions (Eq. 1). Note that this formulation does not rely on the relatively uncertain NO₂ measurement (36).

$$\begin{array}{c}{\mathrm{P}}_{OH} = \frac{{2J}_{\mathrm{O}{(}^1\mathrm{D})}{k}_{\mathrm{O}{(}^1\mathrm{D}) + {\mathrm{H}}_2\mathrm{O}}\left[{\mathrm{O}}_3\right]\left[{\mathrm{H}}_2\mathrm{O}\right]}{k_{\mathrm{O}{(}^1\mathrm{D}) + M}\left[M\right] + k_{\mathrm{O}{(}^1\mathrm{D}) + {\mathrm{H}}_2\mathrm{O}}\left[{\mathrm{H}}_2\mathrm{O}\right]}\hfill \\ +k_{{\mathrm{HO}}_2 + \mathrm{NO}}\left[\mathrm{H}{\mathrm{O}}_2\right]\left[\mathrm{N}\mathrm{O}\right].\hfill \end{array}$$ [1]

The OH sink terms also range in integration timescales. Within a parcel, OH loss to more reactive chemical species can fluctuate rapidly, on the order of minutes (e.g., OH + HO₂) to hours (e.g., OH + isoprene). CO or methane, the dominant OH sinks over the remote troposphere, may not vary within a parcel because their lifetimes range from months to years, though transport can produce sharp gradients across neighboring air parcels. The most appropriate terms to represent OH loss will thus vary with the local chemical regime and spatiotemporal scale under consideration.

To determine which loss pathways to include in the proxy, we consider the component of OH loss that is independent of its concentration, the “OH reactivity,” denoted k′_OH.. We focus on the 2-km altitude by 20° latitudinal regional bins before considering oceanic scales or all ATom observations together. Within the regional bins, F0AM indicates that CO is the largest contributor to the magnitude of ∑k′_OH in each bin (22 to 53%), followed by CH₄ (9 to 22%). This holds everywhere except the southern tropical lower troposphere, where CH₃OOH reactivity is maximum at 20% (SI Appendix, Fig. S2). CO reactivity spatially covaries with ∑k’_OH ( $r_{\mathit{Mdn}}^2$ = 0.45) within the 2-km altitude by 20° latitudinal bins more than does methane reactivity ( $r_{\mathit{Mdn}}^2$ = 0.22). The reactivities of HO₂, H₂O₂, and small, shorter-lived VOCs like formaldehyde (HCHO), CH₃OOH, or methanol (CH₃OH) frequently correlate most strongly with ∑k’_OH over this regional scale (SI Appendix, Fig. S3). However, they also moderately correlate with CO in any given regional bin (r² of approximately 0.3 to 0.5; SI Appendix, Fig. S4). Thus, the regional analysis suggests that, among all OH sink terms, CO contributes most to both the magnitude and spatial variations of ∑k′_OH across the remote marine troposphere, as it often covaries with other OH sinks.

When considering all ATom observations together or when subsetting for the Pacific, methane reactivity emerges as a better predictor of ∑k′_OH variations than other sinks, including CO (SI Appendix, Fig. S5). The methane and CO reactivities correlate across the full ATom dataset (r² = 0.58). Although using both CO and methane reactivity slightly improves the slope of the regression with ∑k′_OH (with CO reactivity alone, m = 0.24; when summing CO and methane reactivities, m = 0.37), it does not substantially improve the correlation either over the full dataset or within a given oceanic basin (Δr² ≤ 0.05). We therefore opt for simplicity and represent the OH sink term using only the CO reactivity, or equivalently, the lifetime of OH against its reaction with CO (denoted τ_OH,CO, Eq. 2).

$${\tau }_{OH,CO}=\frac{\left[\mathit{OH}\right]}{k_{co+OH}\left[\mathit{CO}\right]\left[\mathit{OH}\right]}={\left(k_{co+OH}\left[\mathrm{CO}\right]\right)}^{-1}.$$ [2]

As a simplified version of OH steady-state chemistry in the remote marine troposphere, Proxy_OH is a reduced-form model for OH comprising the sum of the O(¹D) + H₂O and HO₂ + NO reactions scaled by τ_OH,CO (Eq. 3).

$${\mathrm{Proxy}}_{\mathit{OH}}={\mathrm{P}}_{\mathit{OH}}{\tau }_{OH,CO}.$$ [3]

Combining the ATom observations directly with reaction rate coefficients (35), we demonstrate that alternative proxy formulations do not improve upon the Proxy_OH fit with measured OH spatial variations (Section 1.2), though some formulations provide more comprehensive insight into the observed OH magnitude (Section 1.3). The remainder of this manuscript uses the ATom measurements directly (in other words, the F0AM box model is not used).

1.2. Proxy_OH Captures Much of the ATom-Observed Variations in OH.

We assess the skill of Proxy_OH, calculated directly from the ATom observations, in predicting measured OH variations within each bin of our regional domain (Fig. 1 and Sections 2.1.1 and 2.1.3). We fit the Proxy_OH-[OH] regression slope and intercept within each bin using a Bayesian mixed-effects model implemented with Markov Chain Monte Carlo (MCMC) simulations (Section 2.2). The altitude and latitude are random effects in this mixed-effects model. The Bayesian approach offers an advantage over a frequentist method (e.g., ordinary least square regression, among other maximum likelihood approaches) because it evaluates distributions of Proxy_OH and [OH] that account for the instruments’ uncertainties. “True” values for OH and the proxy terms (i.e., $J_{O{(}^{1}D)}$ and the concentrations of H₂O, HO₂, NO, etc.) are drawn from normal distributions with mean and variance defined by the measured concentration and error, respectively. The posterior distributions, Proxy_OH,true and [OH]_true), are used to assess the Proxy_OH predictive skill quantified by the coefficient of determination and slope and intercept regression parameters. For comparison, SI Appendix, Fig. S6 shows these parameters when derived by an ordinary least squares regression, without accounting for measurement uncertainty, and the sample size and Proxy_OH and [OH] value ranges within each spatial bin (the subplot axes in SI Appendix, Fig. S6 are the same as in Fig. 1). A comparison of the coefficient of determination (subplot background colors) SI Appendix, Fig. S6 demonstrates that the Bayesian mixed-effect approach (Fig. 1A) places less emphasis than ordinary least square regressions (SI Appendix, Fig. S6A) on few points distant from the data’s primary mode of variation (for example, in subplots over the Pacific between −60° and −40°N and above 2 km).

Fig. 1.

The steady-state proxy for OH (Proxy_OH) captures much of the in situ measured and modeled [OH] variations along the ATom flight tracks. Shown is the spatial distribution over the (A) Pacific and (B) Atlantic oceans of the ATom-observed (blue dots) or AM3 modeled (orange dots) regression between Proxy_OH and [OH] (both in ppt). The background color and number in the upper left corner of each subplot indicates the mean r-squared coefficient of determination (r²) of the ATom Proxy_OH-[OH] posterior distributions, and the light blue shading illustrates the 95% Bayesian credible interval (Section 2.2). The model correlation is not shown but is slightly higher than observed (see text). The orange line is the AM3 Proxy_OH-[OH] ordinary least square regression. See SI Appendix, Fig. S6 for axes’ descriptions.

The Proxy_OH-[OH] within-bin covariation is generally robust, with a median coefficient of determination ( $r_{\mathit{Mdn}}^2$ ) across all spatial bins of 0.90 (IQR = 0.80 to 0.94). It is highest between 2- to 8-km altitude ( $r_{\mathit{Mdn}}^2$ = 0.93, IQR = 0.87 to 0.95) and over the Northern Hemisphere ( $r_{\mathit{Mdn}}^2$ = 0.93, IQR = 0.88 to 0.95). The proxy skill is expected to degrade where processes that are not included in its formulation affect OH variations. For example, convection may affect OH variations, potentially due to lofted peroxides (45), in some midlatitude plumes above 4 km (SI Appendix, Fig. S7). The comparably weaker fit in the lower troposphere may stem from marine-emitted halogens affecting the oxidation regime (46–48). However, the residuals of the Proxy_OH-[OH] regression do not show a systematic relationship (spatial median r² ≤ 0.03) with other variables that affect oxidation (e.g., particle number concentration, halogens, convection; SI Appendix, Table S2). Overall, the aircraft observations suggest that Proxy_OH reflects observed OH spatial variations on smaller scales than has previously been possible to discern using existing, globally well-mixed proxies.

In Section 1.1, the F0AM simulations indicated that alternate forms of a steady-state proxy over the 2-km altitude by 20° latitude bins could employ the OH lifetime against small oxidized carbon compounds (e.g., HCHO and CH₃OOH, which are included in the 10-s ATom observations; SI Appendix, Figs. S2 and S3) in place of, or in combination with, τ_OH,CO. However, using the ATom observations directly to assess alternative proxy formulations that use these variables indicates that the simplest proxy formulation, using only CO as in Fig. 1, best reflects OH variations over the regional domain (SI Appendix, Table S3).

On larger scales, Proxy_OH demonstrates similar predictive skill in reflecting OH variations when all observations in the domain are considered together (ordinary least squares r² = 0.52) as when subsetting for the Pacific or Atlantic (r² = 0.49 or 0.60, respectively). Replacing τ_OH,CO in Eq. 3 with the OH lifetime against methane [= ( $k_{C{H}_4+OH}$ [CH₄])⁻¹] does not improve the correlation across all flight tracks (r² = 0.44), even when representing the OH sink in the proxy denominator as the sum of both rates (r² = 0.51). Despite the role of methane in modulating the global OH abundance, including it in Proxy_OH does not improve the fit with observed OH because methane reactivity does not spatially covary with the total OH sink.

1.3. Inferring the ATom-Observed OH Abundance.

While the coefficient of determination describes the extent to which the proxy fits the observed variations in ATom [OH], the intercept and slope infer the magnitude of the proxy in comparison with [OH]. When considering all data together, the Proxy_OH-[OH] intercept overlaps zero, averaging 0.05 ± 0.05 ppt (μ ± 95% CI), though the intercept is generally positive within a given bin (Fig. 2 A and B). A positive intercept indicates a small missing background source or underestimated sink, though the within-bin MCMC mean intercept does not correlate with the mean of the processes considered for the residual analysis (across bins, r² ≤ 0.14; SI Appendix, Table S2). The strongest residual relationship is shown with CH₃OOH, the probability of convective influence, and solar zenith angle. This suggests that Proxy_OH could potentially be refined to reduce the regression intercept by accounting for the lofting and photolysis of CH₃OOH.

Fig. 2.

The Proxy_OH-[OH] regression slope and intercept reflect the relationship between OH sources and sinks. The distinct spatial patterns in the regression parameters indicate that using the Proxy_OH to infer the local OH concentration requires accounting for vertical and latitudinal distributions. Spatial distribution of the intercept (Top; A and B) and slope (Bottom; C and D) posteriors from the Bayesian linear regression between Proxy_OH and observed [OH] are shown. Boxes span six 20° latitudinal bins (x axis and gradient in gray background color) and five 2-km altitude bins (color), separated by ocean basin (Left or A and C: Pacific; Right or B and D: Atlantic). For a given bin, the posterior is drawn as the final 1,000 iterations across three chains from Markov Chain Monte Carlo simulations used to implement the Bayesian fit (Section 2.2). Vertical colored lines indicate the 95% credible interval of the intercept and slope for that spatial bin.

The Proxy_OH-[OH] slope overall averages to 0.39 ± 0.25. It generally maximizes below 4 km and at higher latitudes, particularly in the northern hemisphere, and minimizes in the upper troposphere (Fig. 2 C and D and SI Appendix, Fig. S9). The slope reflects the relative contribution of Proxy_OH terms to total OH production and loss (SI Appendix, Fig. S8). For example, a larger slope could indicate that the Proxy_OH production terms encompass more of the total OH production; alternatively, but not exclusively, it could suggest that the Proxy_OH loss terms encompass less of the total OH loss (refer to Section 1.1 and SI Appendix, Figs. S1 and S2). While the Proxy_OH representation of the magnitude of both OH production and loss influence the regression slope, the slope is more tightly coupled with the contribution of CO to the total OH loss (compare SI Appendix, Fig. S8 B and C), stemming from a larger underestimate in the OH sink than in its source as part of the Proxy_OH formulation (compare F0AM-simulated percent contributions in SI Appendix, Fig. S1 with SI Appendix, Fig. S2).

Including additional sink terms in the proxy formulation increases the slope (SI Appendix, Table S3 and Fig. S9), but as described in Section 1.2, it does not improve the [OH] fit (little change in r²). Proxy_OH only uses the OH lifetime against CO. Expanding to include the OH lifetime against HCHO (k_HCHO+OH[HCHO]) and/or CH₃OOH (k_CH3OOH+OH[CH₃OOH]) in the proxy sink term reduces the spatial gradients in the MCMC-simulated slopes (compare stars and squares to circles in SI Appendix, Fig. S9). The slope spatial gradients are smallest when including the OH lifetime against CH₃OOH (squares in SI Appendix, Fig. S9), although the spread (vertical bars) increases due to larger CH₃OOH measurement uncertainty. For all proxy formulations, the slope is generally smallest between 8- and 10-km altitude. In this vertical layer, SI Appendix, Fig. S1 indicates that H₂O₂ photolysis and the reaction of HO₂ + O₃ are often larger contributors to P_OH than O(¹D) + H₂O. Overall, this analysis suggests that changes in the composition of k’_OH generally drive the spatial variations in the slope, while missing sources may contribute most in the upper troposphere.

The Proxy_OH underestimate of the total magnitude of the OH source and sink terms stems from its intended simplicity, such that one limitation of Proxy_OH is that it does not represent the exact ratio of OH production to loss. However, the tight fit of the regression between Proxy_OH and measured [OH] implies that the spatial distribution of slopes and intercepts derived here can be used to infer the total magnitude of [OH] over the remote marine troposphere (further discussion of the spatial variations in regression parameters is available in SI Appendix, Text S1).

1.4. Decomposing the Observation-Based Proxy to Evaluate the Sensitivity of OH Variations.

We decompose Proxy_OH across all ATom observations, by oceanic basin and within each altitude–latitude bin as a first-order estimate of the chemical sensitivity of OH variations to individual species and chemical production or loss pathways. This decomposition is a major advantage relative to existing OH proxies because it enables inference of the relative importance of different processes in contributing to spatial OH variations. Specifically, we construct sensitivity versions of the proxy in which we hold a single reaction rate (e.g., O(¹D) + H₂O) or term (e.g., NO or temperature, T) constant at its mean value per 2 km by 20° zonal bin, and then calculate the coefficient of determination (r²) between Proxy_OH and each sensitivity version to assess the change in fit (1 – r²). This simple approach assumes a linear relationship between each term or rate and Proxy_OH. Because it neglects higher order chemical processes that may lead to nonlinear responses, the contributions summed across variables may not add to 100%. In addition, some of the drivers (e.g., NO and ozone) may be correlated. Below we display the influence of rates or terms as their contribution to the total proxy fit (1 – r²), such that 1 – r² approaching 1 indicates a rate or term with a strong influence on [OH] variations.

We first evaluate the role of individual terms composing Proxy_OH in each of the 2-km altitude by 20° latitude subsets of the ATom observations. We find that H₂O dominates most of the ATom-observed Proxy_OH variations (Fig. 3A), especially in the midtroposphere. This result is also robust when considering all ATom observations together or when subsetting by oceanic basin (SI Appendix, Table S4). Controls on proxy variations over either oceanic basin are shown in SI Appendix, Fig. S10. Our observation-based analysis affirms that, consistent with previous model-based analyses of the remote troposphere (37, 38), O(¹D) + H₂O is most influential throughout much of the free troposphere, while HO₂ + NO dominates in the upper troposphere and sometimes in the more polluted lower troposphere. In addition, our results are consistent with earlier work showing that several models constrained with ATom chemical observations attribute much of the difference in intermodel OH distributions to H₂O discrepancies (27). Further, climate model intercomparisons demonstrate biases in H₂O of ± 10% in the lower troposphere that increase to as much as ± 100% in the upper troposphere (49, 50). Convection and cloud microphysics have long challenged accurate simulations of water vapor vertical profiles (e.g., refs. 51–55). Our results reinforce that variations in OH are heavily tied to water vapor. Improving the accuracy of atmospheric hydrologic processes in chemistry-climate models should thus improve OH trend simulations, as well as those for methane, CO, and other trace gases whose primary sink is reaction with OH.

Fig. 3.

Few terms—water vapor (H₂O), nitric oxide (NO), the hydroperoxy radical (HO₂), ozone (O₃) and the rate of O₃ photolysis to O(¹D) ( $J_{O{(}^{1}D)}$)—dominate the sensitivity of Proxy_OH variations over the remote troposphere. Spatial distribution of the difference in the Proxy_OH-[OH] fit (1 - r²) attributed to each of the physical or chemical terms that comprise Proxy_OH H₂O, NO, HO₂, $J_{O{(}^{1}D)}$ , O₃, temperature (T), CO or the pressure dependence of the CO reaction rate ( $M_{k_{\mathit{CO}}}$ ) are individually held constant, for (A) ATom observations and (B) AM3 fields sampled along the ATom flight tracks. The colors indicate which of the terms is the largest contributor to proxy variance in that cell, with bold text and an asterisk indicating that the colored term contributes 0.20 more (r² units) than the next-most influential term.

The water vapor feedback due to anthropogenic climate change could increase methane destruction by accelerating its loss through reaction with tropospheric OH (39). Global average OH has historically been well buffered (18) because its variability was dominated by anthropogenic combustion (41), which affects both its production (via NO and O₃) and loss (via CO and other forms of reactive carbon). However, rising atmospheric [H₂O] only directly affects OH production, in the absence of a compensating increase in the OH sink. A coupled chemical model would be necessary to account for the full effect of climate change on atmospheric oxidation, for example, due to offsetting feedbacks, like an increase in H₂O₂ production followed by deposition or weather-sensitive emissions such as methane from wetlands. Proxy_OH instead offers a simple, first-order projection of how OH might respond to the expected rise in atmospheric water vapor abundances with future climate change. Applying the mean increase in water vapor between 2,010 and 2,100 from RCP 8.5 (56), used by Holmes et al. (39), we infer from Proxy_OH that the projected magnitude of change in [H₂O] (42.3%) along the ATom flight tracks where H₂O dominates the OH sensitivity (between 2- and 8-km altitude) could increase regional average [OH] by 19%. This estimate indicates the potential for a large, negative feedback to climate change by increasing the methane sink. However, this sensitivity was derived from short-term, regional observations, and needs further study into the connection to long-term global trends. This approach also neglects nonlinear chemical feedbacks and potential simultaneous offsetting processes (e.g., an increase in methane). While additional work employing a more complex model is needed, this first-order estimate suggests that higher water vapor associated with anthropogenic climate change could cause a departure from the recent era, in which OH derived from globally well-mixed proxies has not shown a substantial trend since the start of the methyl chloroform record (18, 19, 57).

NO is the second-largest driver of within-bin Proxy_OH spatial variations based on our analysis of the ATom observations over the remote marine troposphere (Fig. 3A and SI Appendix, Fig. S10). $J_{{O(}^{1}D)}$ sometimes dominates over midlatitude, lower tropospheric regions in the Southern Hemisphere. HO₂ emerges as influential in some regions, in particular when separating the data by oceanic basin (SI Appendix, Fig. S10 A and C). Ozone also affects the Proxy_OH spatial variations in several bins, though not substantially more (Δr² < 0.2) than the next-most influential term (Fig. 3A). On larger scales, ozone is generally a stronger driver of Proxy_OH spatial variations than NO, $J_{{O(}^{1}D)}$ or HO₂, while H₂O still dominates (SI Appendix, Table S4). The OH lifetime against CO does not dominate in any of the 2 km by 20° latitudinal bins or over larger spatial scales (SI Appendix, Table S4) likely due to the relatively long lifetime of CO. However, trends in CO sources may affect the OH sensitivity over longer timescales, for example, due to climate-driven changes in biomass burning emissions (58).

We compare a parallel decomposition of a more comprehensive proxy version with the terms that covary most strongly with Proxy_OH (compare Fig. 3 and SI Appendix, Fig. S11). The expanded proxy includes additional terms affecting [OH] that were identified in previous sections as important for reconstructing the total OH abundance based on their contribution to the total OH source or sink (SI Appendix, Figs. S1 and S2 and Table S1) or an increased slope of the proxy-[OH] fit (SI Appendix, Fig. S9 and Table S3). Additional OH production terms are H₂O₂ photolysis and the reaction of HO₂ with O₃; OH sink terms are its reaction with methane, formaldehyde, and methyl hydroperoxide. Conducting the same sensitivity analysis, as in Fig. 3A, the same terms dominate the base and expanded proxy sensitivity analysis (SI Appendix, Fig. S11). We conclude that the base Proxy_OH captures key terms for inferring within-bin OH spatial variations (compare bins with asterisks in Fig. 3 and SI Appendix, Fig. S11). This sensitivity analysis indicates that, even though some of the expanded proxy terms affect the magnitude of OH (e.g., CH₃OOH; see SI Appendix, Fig. S9), they are not as influential over OH spatial variations on these scales.

1.5. Evaluating a Chemistry-Climate Model Using Proxy_OH.

We illustrate how Proxy_OH can be used to evaluate the processes that control spatial OH variations in a chemistry-climate model. Paralleling our observation-based analysis, we construct Proxy_OH from hourly fields archived from the GFDL AM3 chemistry-climate model for comparison with AM3-simulated OH (Section 2.1.4). Proxy_OH-[OH] correlations in the global AM3 model sampled along the ATom flight tracks (orange points and line in Fig. 1) have a spatial median $r_{\mathit{Mdn}}^2$ = 0.95, just above the interquartile range of the observationally derived $r_{\mathit{Mdn}}^2$ (0.90, IQR = 0.80 to 0.94). The slightly tighter modeled relationship may reflect the different spatiotemporal coverage of the two datasets, or it could indicate a model underestimate in OH sink variations (59, 60). On larger spatial scales (here, considering the full ATom dataset), AM3 indicates the strength of relationship would be similar if the OH sink were represented through methane (r² = 0.67 for all ATom; r² = 0.63 or 0.71 over the Pacific or Atlantic, respectively) instead of CO (r² = 0.65, 63, or 0.75, respectively). Overall, we conclude that the link between OH production and [OH] is tighter in AM3, and in F0AM (refer to SI Appendix, Fig. S5), than in the observations due to an underestimate in the variability of OH reactivity, potentially due to missing OH loss processes (SI Appendix, Fig. S12).

Decomposing the modeled Proxy_OH variations by individual terms, we find similar spatial patterns for within-bin relationships as in the observations, with some exceptions (Fig. 3B versus Fig. 3A). In both analyses, H₂O emerges as the most influential term in most of the 2 km by 20° latitude bins, especially in the mid-troposphere. NO dominates the within-bin Proxy_OH variations in the upper troposphere, though the model simulates NO influence on Proxy_OH variations over a larger swath of the upper troposphere (>6 km) than indicated by the measurements (>8 km). This overestimate is generally associated with a high normalized mean bias in NO (in other words, modeled NO is higher than observed; Section 2.1.4 and SI Appendix, Fig. S13), possibly indicating an error in low-temperature kinetic data for NO_x-O₃ photochemical cycling (61). Conversely, AM3 underestimates the extent of HO₂ influence over Proxy_OH spatial variations in the upper troposphere, colocated with a low normalized mean bias in modeled HO₂ (SI Appendix, Fig. S14). AM3 also has a low bias in H₂O in this region (SI Appendix, Fig. S15).

The model also fails to capture the observed variability in the drivers of Proxy_OH spatial variations in the lower troposphere. AM3 suggests that only $J_{O{(}^{1}D)}$ is influential across the Southern Hemisphere, while H₂O modulates modeled Proxy_OH spatial variations throughout the Northern Hemisphere in this vertical layer. The observations, in contrast, limit the $J_{O{(}^{1}D)}$ influence to a smaller horizontal extent, and indicate that H₂O does not dominate spatial variations in any lower tropospheric region (Fig. 3A). When considering individual oceanic basins, H₂O emerges as a primary driver of Proxy_OH variations over two lower tropospheric bins in the Atlantic (SI Appendix, Fig. S10). The model underestimates the sensitivity of Proxy_OH spatial variations to NO in the lower troposphere, but the model NO bias differs in sign by hemisphere. We infer that, in the lower troposphere, modeled NO may be too low to drive Proxy_OH variations in the Southern Hemisphere but is excessively high in the Northern Hemisphere, where Proxy_OH variations may no longer be sensitive to NO.

The analysis above illustrates how Proxy_OH can be used as a tool for rapid assessment of the relative importance of chemical processes that control tropospheric oxidation variations. This information can be applied to model evaluation, or to inform areas for exploration using more comprehensive, but more expensive, global chemistry-climate models. Overall, the modeled sensitivity of Proxy_OH variations is consistent with the observations in demonstrating that few terms, mainly H₂O and NO, dominate the sensitivity of regional oxidation variations over the remote marine troposphere.

1.6. Discussion: Advancing Understanding of the Methane Lifetime Using Proxy_OH.

Improved confidence in methane trend attribution relies on a better understanding of OH variations (62), but OH variations have been difficult to constrain, in part, because of nonlinear relationships between OH and its numerous underlying drivers. We develop and evaluate an observation-based proxy for subhemispheric spatial variations in OH (Proxy_OH) over the remote marine troposphere. Proxy_OH is based on a simplified version of steady-state OH chemistry (two production and one loss pathway) that accounts for the contribution from key drivers to regional spatial variations in OH. By enabling a first-order approximation of the influence of individual variables on OH spatial variations, Proxy_OH serves as a reduced-form model that can provide process-based insight into OH fluctuations.

Decomposing the ATom-observed Proxy_OH, calculated directly from the aircraft observations, suggests that few terms—H₂O and, to a lesser extent, NO—modulate almost all of the inferred OH variations over the remote marine troposphere on regional scales (i.e., 2-km altitude by 20° latitude bins). Thus production processes control the sensitivity of OH variations within a regional bin. On larger scales (i.e., across bins), the composition of OH reactivity modulates the regression slope, relevant for inferring the OH magnitude.

ATom, by design, flew over atmospheric swaths where chemistry is relatively pristine and homogeneous. Additional development of Proxy_OH is needed over more polluted terrestrial regions, where higher NO_x levels and more complex reactive carbon compounds should likely be included among the processes comprising Proxy_OH (e.g., HONO as a source or OH + NO₂ as a sink). Retrieving key Proxy_OH variables from satellites should also advance understanding of OH, at least on a column basis. For example, H₂O is currently measured directly (63) while NO or $J_{O{(}^{1}D)}$ may be inferred (64–67) using space-based instrumentation. In a similar vein, machine learning (ML) has already been applied to approximate long-term trends in OH using chemical transport model simulations and satellite retrievals in urban environments over North America (43). This analysis found that a similar set of variables to those included in Proxy_OH contribute most of the variation in temporal trends in model OH over several North American cities (noting that HCHO was more influential than the CO included in Proxy_OH in these relatively polluted terrestrial environments). While this ML approximation is yet to be evaluated against OH observations, these results indicate promise for the rapid development of alternative possible formulations for Proxy_OH over a range of conditions. At the same time, our method could be applied to evaluate ML approximations, potentially by mining previous airborne observations of OH for in situ constraints on environment-specific formulations of Proxy_OH (a comprehensive compilation of ATHOS OH measurements is available in ref. 34).

Our analysis using in situ observations suggests that future column-based applications of Proxy_OH should account for the vertical and latitudinal distribution of the relationship between this proxy and OH, for which we estimated initial slope and intercept values over the remote marine troposphere. A column-based proxy should also consider the distribution of temperature and pressure in the representation of reaction rate constants. A satellite-observed form of Proxy_OH, especially in combination with HCHO retrievals that map column OH variations (24, 25), could offer a spatially expansive dataset for inference of not only the OH abundance but also its sensitivity to key drivers of atmospheric oxidation. By placing much-needed constraints on the methane sink via reaction with tropospheric OH, this knowledge will improve confidence in the interpretation of observed methane trends as well as future projections under global change.

By offering insight into the sensitivity of OH spatial variations to individual OH source and sink terms, Proxy_OH serves as a process-based, simple model that bridges point measurements and global atmospheric chemistry model simulations. Across global models, the decadal mean OH concentration shows a linear relationship with a combination of $J_{O{(}^{1}D)}$ , specific humidity and the source of nitrogen and carbon (13). Here, we demonstrate that an observation-based version of this combination of variables, Proxy_OH, maintains a linear relationship with measured OH concentrations over regional scales in the remote marine troposphere. Our observation-based results suggest that future evaluation of modeled tropospheric oxidation over global background regions, in particular over timescales shorter than the methane lifetime (12, 68), should target an accurate model representation of variations in H₂O and NO and their relationships with OH. As a test case of the steady-state proxy’s potential to evaluate and interpret global models, we evaluate GFDL AM3 chemistry-climate model simulations sampled along the ATom flight tracks. The proxy decomposition identified a model mismatch in processes modulating OH in the upper-troposphere to midtroposphere and points to an underestimate in H₂O. Provided that diagnostics on the same spatiotemporal scales are available, our AM3 evaluation could be extended to additional models, so that Proxy_OH may be applied to evaluate the representation of remote marine tropospheric OH and the species controlling its production and loss. A separate model analysis using the ATom data also concluded that intermodel differences in H₂O distributions lead to large differences in simulated methane loss rates along the ATom flight tracks (27). This shortcoming could undermine simulated relationships, for example between lightning and the NO_x lifetime, which is a crucial component of accurate process-based representations of OH (13, 69–71). Probing Proxy_OH thus provides insight into the sensitivity of OH variations to H₂O and NO, which would not have been apparent from conventional comparisons of measured and modeled H₂O or NO distributions.

We identify both H₂O and NO as key drivers of [OH] variations in the remote troposphere. Nevertheless, these two parameters do not fully explain the OH variability, and further investigation is recommended over a range of pollution regimes and environmental conditions. Both H₂O and NO are expected to respond to climate change and variability, while human activities like fossil fuel combustion also affect NO distributions. Climate studies have emphasized the need for additional constraints on H₂O vertical profiles because it is a critical feedback on the global energy budget in response to anthropogenic climate change (52–55). Here, we identify another rationale relevant for both climate and air quality: improved representation of the H₂O spatial distribution would facilitate a better understanding of the OH influence on the methane lifetime. Therefore, accurate characterization of regional H₂O and NO spatiotemporal distributions could advance our understanding of the effect of global change on atmospheric oxidation.

2. Materials and Methods

2.1. Observations and Model Simulations.

2.1.1. Aircraft Measurements.

ATom deployed the NASA DC-8 aircraft to measure OH concentrations as well as several key drivers of OH production and loss rates: water vapor, actinic fluxes, and reactive carbon and nitrogen. ATom flew south along the center of the Pacific basin, following 180°W within ~15° longitude, and north along the center of the Atlantic basin, generally between 15° and 30°W (SI Appendix, Fig. S16). SI Appendix, Table S5 describes the measurements used in our analysis (72–88), which spans ATom-1, 2, 3, and 4, corresponding to Northern Hemisphere summer (28 July to 22 August, 2016), winter (26 January to 22 February, 2017), fall (28 September to 26 October, 2017), and spring (24 April to 21 May, 2018).

2.1.2. Box Model Simulations.

To provide further support for our observation-based proxy, we draw on 60-s average OH simulations along the ATom flight tracks from the Framework for 0-D Atmospheric Modeling (F0AM v.4, available at https://github.com/AirChem/F0AM/; ref. 29 with the Master Chemical Mechanism (MCM) version 3.3.1; ref. 89). A subset of MCM v3.3.1 is implemented within F0AM. The box model is constrained with the ATom data, including meteorological, radiative, and chemical variables following (30). Box model simulations of HO_x (OH plus hydroperoxyl, HO₂) forced by measurements (excluding HO_x) along the ATom-1 and 2 flight tracks show consistency with ATom-1 and 2 observed HO_x (24).

Data at 1 Hz time resolution are averaged to 1-min frequency and gap-filled via linear interpolation for gaps less than 5 min by correlating with CO for species with a correlation coefficient (r ≥ 0.7) for all data within 500 m of aircraft altitude, and substituting data below an instrument’s limit of detection (LOD) with 20% of the LOD concentration, as in previous box model applications (90). The following reactions are added to the F0AM chemical mechanism (MCM v3.3.1): CH₄+O(¹D), photolysis of HO₂NO₂, and CH₃O₂+OH (91). Box model simulations are performed for all data points where the CO and O₃ values are valid (following gap-filling) and where either or both NO and NO₂ are greater than zero. All flights from all four ATom deployments are simulated with the following exceptions: ATom-3 flight 20170928 (for which NO₂ measurements are missing), ATom-3 flights 20171014, 20171025, and 20171027 (for which photolysis measurements are missing), and ATom-4 flight 20180518 (a transit flight during which VOC measurements were not made).

The F0AM simulations are integrated with a 10-min time step to diurnal steady state, which occurs when the fractional change in short-lived species through a simulated solar cycle falls below 0.1%. Photolysis frequencies vary diurnally and are scaled to match the measured J-values at the local time of observation. All other constraints are held fixed throughout the simulation. A family constraint is imposed for NO_x, such that NO and NO₂ concentrations are allowed to fluctuate diurnally, while their sum remains fixed to that measured. A second simulation then adjusts the total NO_x abundance, such that the resulting simulated NO concentration matches the observed NO, which is less susceptible to measurement artifacts than NO₂. This approach thus imposes an NO constraint while allowing NO and NO₂ to undergo diurnal variation during the simulation in a realistic manner.

2.1.3. Data Preparation.

For much of our analysis, we spatially subset the ATom data, F0AM (Section 2.1.2) and AM3 simulations (Section 2.1.4) into a 2-km altitude by 20° latitudinal (~2,000 km) grid that spans 0 to 10 km and −60° to 60°N, including both ocean basins. We refer to the 0 to 2, 2 to 8, or 8 to 10-km altitude ranges as the lower, mid-, or upper troposphere and to the 0° to 20°, 20° to 40°, or 40° to 60° zonal ranges in either hemisphere as tropical, extratropical, or midlatitude, respectively. Referencing the previously calculated 0.25-km vertical by 6-km horizontal coverage per 30 s of ATom sampling (36), our spatial bins integrate approximately 4 min of vertical and 2 h of horizontal measurement, in comparison with the hourly timestep of our global model. For consistency, we use ATom data between 60°S and 60°N and below 10 km when considering larger spatial scales.

Within our domain, we filter the ATom data to exclude air masses with strong influence from biomass burning (CO concentration over 150 ppb, 2.2% of valid observed points), the stratosphere [water vapor (H₂O) mixing ratio below 10 ppm, 0.7% of valid data], low incident sun (solar zenith angle >80°, 7.0% of valid data) or anthropogenic pollution (high concentration outliers in NO, defined as above the 75th percentile plus three times the interquartile range in the log-transformed distribution for the spatial domain under consideration; 1.2% of valid observations together or 0 to 10% of each 2 km by 20° latitude bins). We also filter the F0AM and AM3 simulations using the same screening criteria applied to their respective model diagnostics. Because we are interested in the OH drivers and variations, we remove observations with a low signal-to-noise ratio, specifically with [OH] below the ATHOS limit-of-detection of 0.018 ppt (9.2% of observed or 9.0% of modeled points) and in which [NO] is less than its corresponding 2-sigma uncertainty (14% of observed points). To avoid interpreting noise as part of the observed Proxy_OH-[OH] relationship, we do not draw conclusions in air masses with very low [OH] or [NO]. Overall, we retain 74.7 to 74.9% of valid observations within our domain, depending on the spatial scale considered.

2.1.4. GFDL AM3 global chemistry-climate model simulations.

We evaluate hourly fields for the variables that comprise Proxy_OH (H₂O, NO, HO₂, etc.) from the National Oceanic and Atmospheric Administration (NOAA) Geophysical Fluid Dynamics Laboratory AM3 chemistry-climate model (14, 92, 93). AM3 has 48 vertical levels on a cubed sphere grid with approximately 2° by 2° horizontal resolution (14). Our base configuration, described previously (94–96), nudges the horizontal wind fields to the National Centers for Environmental Prediction Global Forecast System with a nudging strength that falls off with pressure (97). Global NO emissions total 44.7, 44.9 and 45.2 Tg N yr⁻¹, and CO emissions total 1221, 1223 and 1226 Tg yr⁻¹ for the ATom years 2016, 2017, and 2018, respectively. MEGAN-simulated isoprene emissions are included in AM3, totaling 418, 395 and 394 (98, 99) Tg C yr⁻¹ globally for 2016, 2017, and 2018, respectively. The anthropogenic and biomass burning emissions are drawn from the Representative Concentration Pathway 8.5 scenario (RCP 8.5; ref. 56) for the years spanning the ATom campaign (2016 to 2018) by interpolating between 2010 and 2020 values following (14). The global biomass burning emissions total 5.2 to 5.3 Tg N yr⁻¹ for NO and 437 to 438 Tg CO yr⁻¹ for each year overlapping with ATom.

We compare the model with ATom by sampling the grid cells containing the corresponding observed latitude, longitude, altitude, and time for each observed data point and evaluate AM3 using the normalized mean bias (Eq. 4), in which i,obs and i,mod represent a 10-s average observation from ATom and the colocated hourly average model diagnostic from AM3, respectively. The AM3 $J_{O{(}^{1}D)}$ photolysis rates were previously shown to be consistent with CAFS observations over the tropical and northern Pacific ATom-1 flight tracks (100).

$$\begin{array}{c}\mathrm{Normalized}\mathrm{mean}\mathrm{bias}\left(\%\right)=\frac{\sum \left(x_{i,mod}-x_{i,obs}\right)}{\sum \left(x_{i,obs}\right)}.\hfill \end{array}$$ [4]

2.2. Bayesian Mixed-Effects Model.

Mixed-effects models are an extension of linear regression. For predictor variables, they combine a fixed effect (i.e., Proxy_OH) and random effect (a grouping variable or source of nonindependence; here, the arbitrary spatial bin selection). Previous atmospheric chemistry research has applied some form of mixed-effect model for applications such as mapping high-resolution urban pollution (101) or for cluster analysis of surface ozone episodes (102). For our project, it would be challenging to incorporate observational uncertainty using a frequentist (e.g., maximum likelihood) approach. Instead, we fit the mixed-effects model using a Bayesian regression, which incorporates measurement uncertainty while assessing the predictive strength and significance of fit. The model fits distributions of Proxy_OH and [OH] that are sampled from the ATom observations combined with information regarding the instruments’ uncertainty distributions. The true gas concentrations, and the Proxy_OH derived from them, are considered to be unobserved but implicit (“latent”) variables and are designated using the subscript true. Each true concentration is drawn from a normal distribution with mean and SD corresponding to the measured concentration and uncertainty (i.e., P([X]_true|[X]_Obs, σ_x); uncertainties listed in SI Appendix, Table S6). SI Appendix, Fig. S17 illustrates the parameter relationships for the Bayesian mixed-effects model through a directed acyclic graph.

This approach was implemented in R using MCMC with the Just Another Gibbs Sampler (JAGS) packages rjags (103, 104) and runjags (105). We used three parallel chains of MCMC samplers, discarding the first 1,000 iterations as a burn-in and another 500 iterations to adapt before retaining the final 1,000 iterations to be analyzed for the posterior distribution. The model begins by using uninformative prior values (SI Appendix, Table S7), noting that the choice of prior does not affect the ultimate posterior distributions. We performed posterior predictive checks for the fit, mean, and SD to assess that the model choice and likelihood distribution are appropriate, finding that each fall within ±0.01 of 0.5 for Proxy_OH (with ideal values falling as close as possible to 0.5; ref. 106). The MCMC chains for the Proxy_OH-[OH] slope and intercept parameters converge, as indicated by a Gelman–Rubin diagnostic between 1.000 and 1.005 for each spatial bin (a Gelman–Rubin diagnostic below 1.1 indicates convergence; ref. 107). We combine the posterior distributions across the three chains for 3,000 total values, per aircraft observation, to develop 95% credible intervals for the slope and intercept of the linear fit between the proxy and [OH].

Supplementary Material

Appendix 01 (PDF)

Data, Materials, and Software Availability

Model simulations and analysis code have been deposited in Zenodo (https://zenodo.org/record/7512701) (108). All other study data are included in the article and/or supporting information.