Introduction

The OH radical representing most of the atmosphere’s oxidizing capacity is central to atmospheric chemistry due to its reactivity with almost all gaseous pollutants, both industrial and natural1,2,3. In particular, the important greenhouse gas methane is almost wholly removed by reaction with OH. Both its OH sink and consequently its emissions remain poorly constrained4, making OH a key frontier in climate science. Efforts to mitigate methane would benefit from a better understanding of OH.

OH is very short-lived, highly variable, and challenging to measure5,6, and due to insufficient coverage the few existing direct measurements of OH can neither sufficiently quantify its global abundance nor any possible trends5,6 caused by anthropogenic air pollution and climate change. Concentrations of OH have been inferred using industrial trace-gas proxies removed by OH7,8, with methyl chloroform (CH3CCl3, MCF) being the most commonly used9,10. However, emissions of MCF are now very substantially reduced due to the successful implementation of the Montreal Protocol, leading to large relative uncertainties in its budget8. Therefore, atmospheric inversions of OH, based on MCF, are under-constrained11,12, and the trend estimates of OH based on such approaches can disagree with each other11,13,14,15. Emissions of industrial proxies are generally subject to large uncertainties, affecting their suitabilities as OH constraints8,11,12,13,14,16. Global chemistry models simulate OH17,18, but a multitude of competing influences on OH and the lack of observational constraints cause model disagreements in OH abundances and the associated methane lifetime12,16,19,20,21. Recent modelling studies18,22 suggest there was no substantial change in OH throughout the industrial period, but then an increase occurred since the 1980s (which may have been associated with a decrease in CO emissions in recent decades23), whereas OH trends inferred using industrial tracers show no change or a decrease after the mid-2000s10,24.

Here we analyze the longest and most consistent radiocarbon monoxide (14CO) records from two remote Southern-Hemisphere locations, Baring Head (New Zealand) and Arrival Heights (Antarctica), for evidence of trends in the atmospheric oxidizing capacity25,26,27, Supplementary Table 1. 14CO complements industrial proxies as a constraint on OH because it is almost exclusively removed by OH with a well-defined natural source15,25,26,28,29. Most 14CO forms in the nuclear cascade initiated by energetic cosmic-ray particles throughout the stratosphere and troposphere. This cosmogenic 14CO production peaks in the lower stratosphere over both magnetic poles where the geomagnetic shielding of cosmic rays is minimal15,30,31,32. The production of 14CO is much better quantified than emissions of MCF [section “Galactic 14C production and the NIWA-UKCA model”,15]. However, the relatively short global lifetime and inhomogeneous distribution of 14CO mean that 14CO is mainly a constraint on regional OH, whereas MCF imposes a global constraint, with the greatest sensitivity to variations in tropical OH27. Earlier studies have used 14CO to constrain the OH abundance25,26,27. However, the lack of long-term 14CO time series has previously precluded its usage as a constraint on multi-decadal OH trends26.

Results

Normalization of the 14CO data

Two dominant natural influences on these measurements become evident (Fig. 1a,b) once corrected for instrumental artefacts and post-collection production of 14C in the sampling flasks (section “14CO records”): The first is seasonality, with minima during February-March and maxima during August-September. The seasonal cycle is due to OH-induced loss of 14CO and seasonally varying stratosphere-to-troposphere transport. OH production requires sunlight; hence the 14CO loss rate is seasonal, particularly at Arrival Heights, which is in darkness for 5 months of the year. Secondly, with the time series now covering three 11-year solar cycles, the influence of the solar state is obvious. Solar activity influences the interplanetary magnetic field, which modulates the flux of energetic cosmic rays impinging on the atmosphere near both magnetic poles to produce 14C, which rapidly oxidizes to 14CO (section “ Galactic 14C production and the NIWA-UKCA model”). This modulation is often quantified via the solar modulation parameter [SMP32,33,34, Fig. 1c]. The SMP and 14CO anticorrelate at both stations (Fig. 1), and the SMP exhibits a long-term declining trend since 1989 superimposed on the 11-year solar cycle (Fig. 1c).

Fig. 1: The Southern-Hemisphere 14CO measurements and model results and the solar modulation parameter as functions of time.
figure 1

(red) 14CO measurements at (a) Baring Head and (b) Arrival Heights. The red vertical bars reflect the standard measurement errors. (black solid lines) Monthly-mean surface 14CO, interpolated to the locations of Baring Head and Arrival Heights, as simulated by the NIWA-UKCA model (see below and section “ Galactic 14C production and the NIWA-UKCA model”). c Monthly-mean “solar modulation parameter" (SMP, in MeV) since 1989 (https://cosmicrays.oulu.fi/phi/Phi_Table_2017.txt). The blue digits and vertical bars conventionally enumerate and bound, respectively, the solar cycles (https://www.spaceweather.com/en/solar-activity/solar-cycle/historical-solar-cycles.html).

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To reveal long-term trends in 14CO we normalize the measurements. We denote by

$${{14}\atop}\! {{\text{CO}}}_{{{\text{norm}}}}=\frac{ {{14}\atop}\!{{\text{CO}}}} {\langle{{14}\atop}\!{{\text{CO}}}\rangle}$$
(1)

the 14CO data normalized for seasonal and solar influences. 〈14CO〉 is a regression fit to the 14CO measurements (section “Normalization for seasonal and solar influences”). Pertinent long-term trends are apparent in 14COnorm (Fig. 2). At both locations, the data indicate a peak of 14COnorm around 1997 followed by a period of decline. The large negative anomalies in 14COnorm around 1991/1992 and positive anomalies around 1997/1998 are consistent with variations in OH26 that have been attributed to the eruption of Mt Pinatubo in 1991, which strengthened OH35, and the 1997 Indonesian wildfires which produced large amounts of pollutants that suppressed global OH36,37.

Fig. 2: Normalized 14CO measurements and their trends.
figure 2

a, c Normalized measurements 14COnorm as functions of the times of the measurements (section “Normalization for seasonal and solar influences”). The thick black lines mark least-squares piecewise linear regression fits for central nodes in 1997. Colours mark the solar modulation parameter (SMP) at the times of the measurements. Vertical lines denote the standard measurement errors. The numbers are the post-1997 trends and their uncertainties. b, d Post-1997 trends in 14COnorm (% a−1) and their standard errors as functions of the month of the year, using the same piecewise-linear fitting method as used in panels (a) and (c) applied to subsets of the data grouped by month.

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At Baring Head, the post-1997 trend of  −0.50 ± 0.09% a−1, corresponding to a  ~ 12 ± 2% decrease in 14COnorm over the period 1997-2022, is significant throughout most of the year. (The error calculation used here is detailed in section “Uncertainty calculation”. All uncertainties are at 68% confidence.) However there is noteworthy multi-year variability in this period of decline, such as anomalously low values of 14COnorm around 2015 and a partial recovery thereafter.

At Arrival Heights, we find a substantial  ~1.8 ± 1% a−1 decrease during December and January, or  ~ 43 ± 24% over 1997-2021, but the negative trend is significant only from October to January (Fig. 2). This is consistent with the strong seasonality of 14CO removal by OH, which at polar latitudes only exists during spring and summer, and therefore here OH only drives 14CO trends during the polar day.

Potential causes for 14CO trends not involving OH

Multidecadal influences on 14CO include the recovery from the spike of atmospheric 14C caused by atmospheric nuclear bomb explosions, which ceased in 1963, and the Suess effect of dilution of 14C in the climate system by the combustion of 14C-depleted fossil fuels. Both factors are reflected in the Baring Head Δ14CO2 signal, which between 1997 and 2022 decreased from 110‰ to 3‰ [i.e. a  ~10% reduction in 14C/C38, extended data available at https://gaw.kishou.go.jp]. Similar trends are occurring around the globe39. Assuming this decrease is instantly reflected in biological material (via photosynthetic uptake) and in biomass-burning CO, which contributes  ~2 molecules cm−3 to 14CO at both locations15,40, its impact of 0.06 molecules cm−3 decade−1 or 0.2 molecules cm−3 over 1989–2022 is an order of magnitude smaller than the actual 14CO trend at Baring Head. Other 14CO sources, such as the oxidation of 14CH4, also do not explain the 14CO trends15. During much of the post-1989 period of interest here, 14CH4 has been on an increasing trend41,42, ruling out 14CH4 as a contributing factor in the decrease found here of 14COnorm.

The seasonality of the 14COnorm trends at Arrival Heights suggests that changes in transport from the lower stratosphere (where 14CO production and abundance maximize, section “Galactic 14C production and the NIWA-UKCA model”) are not the leading cause of these trends. Downward stratosphere-to-troposphere transport maximizes in austral winter and spring43, but large negative trends in 14COnorm occur in December and January. This detail rules out transport from the stratosphere as the leading cause of the 14CO trends at Arrival Heights.

Modelled 14CO and OH

To link the 14CO observations to OH, we use the NIWA-UKCA atmosphere-only chemistry-climate model, expanded to include a representation of only cosmogenic 14CO production and loss to OH. Unlike some previous approaches44, NIWA-UKCA simulates OH interactively as part of a predictive stratosphere-troposphere chemistry scheme. More details are in section “Galactic 14C production and the NIWA-UKCA model”. NIWA-UKCA is free-running, i.e. simulated weather-related variations of 14CO are not expected to correlate with observed variations.

The model closely reproduces key characteristics of the data, including the seasonal cycle, the solar dependence, and larger 14CO values at Arrival Heights than at Baring Head (Fig. 1). Replacing in Fig. 1 monthly mean with 10-daily instantaneous 14CO makes no major difference.

The model simulates variability in 14COnorm (Fig. 2 and section “Normalization for seasonal and solar influences”) similar to what is seen in the observations, regarding both the annual- and shorter-scale variability as well as multi-year variations such as those highlighted by the piecewise-linear fits (red lines in Fig. 3). In particular, the model simulates a trough of 14COnorm around 1990, a peak around 1998, and another minimum around 2015. We note the good similarity of these variations with the observations, although the model generally simulates smaller amplitudes than those found in the observations. Superimposed on these variations, however, are long-term negative trends of simulated 14COnorm at both locations ( −0.10% a−1 at Baring Head and  −0.15% a−1 at Arrival Heights for the period 1980-2020, amounting to decreases of 14COnorm by 4.1 and 6.1% respectively). It therefore appears that the decreases in observed 14COnorm highlighted for 1997-2020 in Fig. 2 are best understood as episodes of longer-term 14COnorm decreases that have been occurring over several decades18. At both locations these trends are substantially smaller than in the observations. This is discussed in section “Discussion”.

Fig. 3: Normalized 14CO model results and their trends.
figure 3

a, e Zonal- and monthly-mean surface 14COnorm derived from the NIWA-UKCA simulation at the latitudes 42.5°S and 77.5°S (the model latitudes closest to Baring Head and Arrival Heights). Red: Piecewise linear fits with nodes in 1989, 1997, and 2021. Blue: Simple linear fit for the whole simulation period (1980-2020). The trend values are for (red) 1997–2020, and (blue) 1980–2020. b, f 1997–2020 trends in 14CO resolved by month, with their uncertainty ranges at 68% confidence. c,g Annual-mean OH (relative to its mean for 1989–2009) averaged by concentration over the region below 500 hPa. c Mid-latitude average (30°S-60°S). g Polar average (60°S-90°S). Red and blue lines are the trends as for (a) and (e). d, h Monthly trends for 1997-2020 in normalized OH, in % a−1, with the 68% confidence uncertainty ranges. Note the different scales.

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Next we assess simulated OH. Firstly, at both locations the pertinent long-term declines in 14COnorm have coincided with concurrent multidecadal increases in OH. In fact this OH increase, in our model, is nearly global (Fig. 4), as has been found in some previous CMIP6 modelling studies e.g.16,18. (As a caveat, only three CMIP6 models are suitable for this analysis, one of which (UKESM1) has some heritage and largely the chemistry scheme in common with NIWA-UKCA.) Resultant annual trends for mid-latitude OH integrated below 500 hPa (Fig. 3c) are of comparable relative magnitude but opposite in sign to those for surface 14COnorm, for both 1980-2020 and 1997-2020, but these trends are altitude-dependent (see below). As for 14COnorm, the OH trends occur almost year round (Fig. 3d), and relative seasonal trends for OH are mostly similar to those of 14COnorm. This similarity strongly suggests that indeed the OH trends cause the 14COnorm trends.

Fig. 4: Global 14COnorm and OH trends.
figure 4

a Trend (% a−1) in simulated annual- and zonal-mean 14COnorm, relative to its 1989–2010 mean, for the period 1980–2020. Stippling means the trends are insignificant at 68% confidence. b Same but for the annual- and zonal-mean OH concentration, relative to its 1989–2010 mean.

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At 77.5°S, OH is dominated by photochemistry during peak summer (December / January). In these months significant positive trends in OH occur (Fig. 3h), which are similar in magnitude to the 14COnorm trends at 77.5°S but opposite in sign (Fig. 3f). The large relative trends in OH simulated for the winter months have no bearing on 14CO as they occur against near-zero abundances of OH.

To put these findings into perspective, our assessment, based on NIWA-UKCA (Fig. 4) and18, is that trends of 14COnorm derived from our measurements may be representative of downward trends in 14COnorm and upward trends in OH that have occurred throughout most of the Southern Hemisphere. OH trends here largely mirror 14COnorm trends, but are of opposite sign. At southern high latitudes, larger absolute trends occur for OH than for 14COnorm (Fig. 3e,g). Also noteworthy are the substantially larger absolute trends in OH and 14COnorm occurring in the Northern Hemisphere. Positive OH trends have been associated with increasing emissions of NOx that are concentrated in the Northern Hemisphere18. A factor decomposition of the OH trend (Fig. 7) indicates that at Baring Head growing NOx emissions and increasingly also global warming are driving positive OH trends, whereas at Arrival Heights the leading factor is Antarctic ozone depletion. At both locations, methane increases drive decreases in OH18. Gaubert et al.23 find that CO emission decreases in Europe and North America since the 1980s drive OH increases. At the two Southern-Hemisphere locations, such CO decreases do not play a leading role in causing the simulated OH increase but are more important in the Northern Hemisphere (not shown).

An observation-based analysis equivalent to the one performed here for Southern-Hemisphere OH is unfortunately presently not possible for the Northern Hemisphere due to the unavailability of sufficiently long and consistent 14CO measurements from there. Hence while there is model agreement that substantial OH increases have happened there, and NIWA-UKCA simulates substantial Northern-Hemisphere negative trends also for 14COnorm, these findings do remain mere model indications in need of observational validation.

The NIWA-UKCA simulated zonal-mean OH trend patterns are similar to the OH change patterns since 1850 found for three CMIP6 models. Given that trends prior to 1980 were small and these changes have occurred predominantly since 1980, we find that the NIWA-UKCA OH trends are quantitatively similar and consistent with those simulated by the CMIP6 models18.

Discussion

The observed multidecadal decreases in 14COnorm are the first strong evidence for positive multi-decadal OH trends at southern mid- and high latitudes. In chemistry-climate model simulations, global multi-decadal OH increases are mainly caused by increasing ozone precursor emissions (especially NOx), with an offset by increasing methane which suppresses OH12,18,37, and references therein. This explains the much larger OH and 14COnorm trends simulated for the more industrialized Northern Hemisphere, compared to the South (Fig. 4). Industrial ozone precursor emissions are relatively small at southern mid-latitudes, yet even for this remote region the 14CO measurements imply positive trends in OH.

In addition to short-lived pollutants, increases in ozone-depleting substances (ODSs) until the late 1990s have caused an increase in modelled OH at southern high latitudes, due to the effect of changes in the overhead ozone column that impact the OH production through ozone photolysis18. This effect explains a part of the large relative trend in OH over Antarctica evident in our model simulations (Fig. 4). However there is no evidence of a change in the trend of OH after 2000 (when ODSs stabilized, Fig. 3g), so this cannot be the only explanation.

Whilst our model NIWA-UKCA qualitatively corroborates this increase in OH, it simulates only about 1/4 of the observed 14COnorm trends calculated for the two stations. Since NIWA-UKCA OH trends are similar to those simulated by three CMIP6 models, we suggest that this model behaviour might reflect a misrepresentation of Southern-Hemisphere OH trends also by the three CMIP6 models considered by18.

As noted, at least at Baring Head, the discrepancy between the simulated and observed 14CO trend might indicate that NIWA-UKCA does not correctly represent the cancellation of opposing effects there. In particular, it is possible that NIWA-UKCA does not well represent the low NOx abundance in the remote Southern extratropics. NOx in this region is the product of relatively poorly understood processes including long-range transport of odd nitrogen compounds from industrialized regions and lightning. In the more polluted Northern Hemisphere, these processes are relatively less important, meaning that the deficiencies found here for the Southern extratropics may not apply to the Northern Hemisphere. Irrespectively of the precise causes, the near-complete cancellation of the two competing influences of NOx and methane makes the net OH trend at southern midlatitudes highly sensitive to shortcomings in the representation particularly of NOx (section “ Galactic 14C production and the NIWA-UKCA model”).

Plausibly then the observational 14COnorm trends since 1997 discerned here, supported by modelling studies16,18,37, and references therein, suggest multi-decadal global-scale increases of OH that may have started in around 198018. Given various limitations affecting all existing studies of this topic, including our own, we do, however, consider that further research, using both observations and models, would help corroborate this statement. For example, this inference is notwithstanding conclusions based on recent MCF inversions and similar techniques that have found no significant change or a decrease in the global OH burden after the mid-2000s. Naus et al.24 only focus on variations not trends as they adjust inferred MCF emissions to match the observed MCF variations. A study that derives OH from the inversion of multiple industrial proxies45 finds stabilization of OH over a shorter period (2004-2020). This is likely consistent, within statistical uncertainties, with our model results and the 14CO observations, given the multiannual variations of 14COnorm after 2004 alluded to above (Fig. 2a).

A pertinent decades-long strengthening trend in the oxidizing capacity implies a corresponding additional increase in methane emissions required to balance its increasing sink, e.g. 23 Gt a−1 for 1986-201037, relative to a scenario with stable OH such as 46. Such an increase compares to other sizeable sources of methane, e.g. global emissions from rice paddies [30 Gt a−1, out of a total CH4 emission strength of  ~ 576-727 Tg a−1 in 2008-201746].

Maintaining the observations since 1989 has enabled the detection reported here of a multidecadal strengthening of the atmospheric oxidizing capacity in the Southern extratropics. It exemplifies the value of environmental monitoring. In some situations these measurements have to be sustained for decades before a trend analysis can yield valuable insights into environmental change. More 14CO data from the more polluted Northern Hemisphere, where according to modelling studies larger OH trends occur, would be valuable to better constrain global OH trends. In due course a nascent 14CO measurement network, complementing the two stations considered here, may provide this much needed global coverage47.

Methods

14CO records

Air samples are taken only when air arriving at the stations is free of locally produced contamination and representative of clean marine or polar conditions. The 14CO content is determined using accelerator mass spectrometry, preceded by complex sample preparation including removal of CO2, conversion of CO to CO2, dilution with 14C-free CO2 gas, as well as stable isotopic measurement26,48. Measured 14CO values are corrected to account for production of 14CO within the flasks during storage and transport. Longer storage times and larger cosmic-ray fluxes lead to larger corrections and associated uncertainties at Arrival Heights than at Baring Head. More details on the measurement process, post-measurement corrections, and measures taken to ensure the absence of analytical artefacts are in the Supplementary Sections 1 to 5.

Galactic 14C production and the NIWA-UKCA model

While the flux of galactic cosmic rays (GCR) is considered nearly constant in the local galactic environment, it changes significantly in the vicinity of the Earth as a result of the modulation by the solar wind and the embedded heliospheric magnetic field. The modulation process is complex [e.g. 49] but for practical purposes it is often parameterized via a single synthetic solar modulation parameter (SMP) which roughly corresponds to the average rigidity loss of cosmic-ray particles inside the heliosphere in the framework of the force-field approximation33,50. Values of the SMP are typically assessed using data from the global network of ground-based neutron monitors33,51. Here we use the SMP, obtained following the methodology by51, available at https://cosmicrays.oulu.fi/phi/phi.html, as a continuously updated SMP dataset. The reconstructed SMP values may slightly depend on the assumed shape of the unmodulated GCR spectrum. However, since different reconstructions are linearly scalable to each other51,52, the analysis presented here is insensitive to the exact choice of the SMP dataset because the regression fit 〈14CO〉 (equation 1) is invariant under a linear transformation of the SMP (equations 4, 5).

Cosmogenic 14CO production can thus be thought of as a function of magnetic latitude, pressure, and the SMP, where the “magnetic latitude” is the latitude relative to the magnetic, not the geographic, poles. In conventional, geographic latitude-longitude coordinates, this implies an explicit dependence also on longitude. The generation function32 is displayed in Fig. 5.

Fig. 5: The 14CO galactic source function.
figure 5

a, b Zonal-mean (ZM) rate of production of 14CO (molecules cm−3 year−1 STP) at SMPs of 400 and 800 MeV. Thick contour: For illustration, the approximate annual-average tropopause pressure. c 14CO production rate averaged over the Antarctic polar cap (90°S-60°S) as a function of the SMP (section “Normalization of the 14CO data”) and pressure. Contours: Polynomial regression fit to the logarithm of the 14C production rate (equation 2).

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The production maximizes over both poles and is decreasing markedly for an increasing SMP. The contours in Fig. 5c represent least-squares fits of the form

$$E(p,s)=\exp \left[\mathop{\sum }\limits_{i=0}^{2}{U}_{i}(p){s}^{i}\right],$$
(2)

expressing the logarithm of the production function E as a quadratic polynomial in the SMP s with coefficients Ui depending on pressure p. Figure 5 illustrates that 14CO is dominantly produced over both poles, with production rates around two orders of magnitude larger at 100 hPa than at the surface. However, transport times between the lower stratosphere and the surface can be considerable, relative to the global mean lifetime of 14CO, especially during summer when upward motion prevails over much of the polar stratosphere, inhibiting any 14CO reaching the surface. These factors help explain the large seasonality in 14CO evident in Fig. 1.

We have implemented a 14CO tracer including its cosmogenic source in the established NIWA-UKCA chemistry-climate model. In brief, the model comprises an interactive chemistry scheme representing Ox-HOx-NOx-VOC-halogens chemistry suitable for the troposphere and stratosphere, targeting a realistic representation of ozone at global scales53,54,55,56. The model is low-resolution (3.75° × 2. 5° in longitude and latitude, with 60 levels extending to 84 km, ca. 25 of which are in the troposphere). Photolysis rates in the model respond interactively to variations in ozone, but scattering and absorption due to aerosol are ignored. Volcanic aerosol affects stratospheric chemistry via an externally supplied surface area density climatology. The set-up used here is identical to the model used for the Chemistry-Climate Model Initiative (CCMI) 2022 simulations57 but the model chemistry scheme is expanded to simulate cosmogenic 14CO production, its losses to OH and deposition to the Earth’s surface, and transport. The loss rates to OH and to dry deposition are the same as for regular CO. In particular, the reaction rate coefficient r associated with OH + 14CO is represented as58,

$$r=\frac{1.44\cdot 1{0}^{-13}}{1+\nu /4.2\cdot 1{0}^{19}}{\text{cm}}^{3}{\text{molecule}}^{-1}{\text{s}}^{-1},$$
(3)

where ν is the molecular number density in molecules cm−3. The model does not explicitly represent any other sources of 14CO such as biogenic recycling or 14CH4 oxidation. This means also the nuclear bomb signal is not simulated.

Using NIWA-UKCA, we conduct a base simulation covering 1980-2020 (41 years), driving the model with 6th Coupled Model Intercomparison Project (CMIP6) “historical and Shared Socioeconomic Pathway (SSP) 24559 forcings and Hadley Centre Ice and Sea Surface Temperature HadISST.2,60 ocean surface forcings. In postprocessing we adjust the simulated cosmogenic 14CO to account for a 94% quantum yield of 14CO production from 14C produced by cosmic rays40,47,61. Furthermore we account for biogenic recycling by adding 1.27 ⋅ 10−12[CO], using the CO field simulated by the model26. 14C/C = 1.27 ⋅ 10−12 is equivalent to assuming a 1 molecule cm−3 contribution of biogenic recycling for 30 ppbv of ambient CO15. (This correction would be more questionable in the Northern Hemisphere where this rule may not apply, due to more substantial and variable contributions of 14C-depleted fossil-fuel burning to ambient CO.) Both adjustments are practically immaterial after normalization of 14CO (section “Normalization for seasonal and solar influences”).

Figure 6 suggests that the model slightly overestimates 14CO (more at Baring Head than at Arrival Heights) but produces high correlations with the observed 14CO values.

Fig. 6: Comparison of observed and modelled 14CO.
figure 6

Symbols: 14CO measurements versus corrected NIWA-UKCA 14CO. Vertical bars indicate the standard measurement errors. Yellow lines: diagonals. Red lines: Least-squares linear fits. Red labels: Linear fit and Pearson’s correlation coefficients. a Baring Head. b Arrival Heights.

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We furthermore conduct all-minus-one sensitivity simulations in which one forcing agent is held constant at 1980 levels, but all other forcings develop in the same way as in the base simulation. For CO2, apart from holding the atmospheric mixing ratio of CO2 constant, in an effort to also suppress the warming caused by CO2 this also involves prescribing SSTs and sea ice concentrations as annually periodic lower boundary conditions following their 1980 annual cycles.

Essentially, at mid-latitudes the leading influences on tropospheric OH are CH4, increases of which drive a decrease in OH, and NOx emissions, increases of which drive a similarly sized increase in OH (Fig. 7). Other drivers (ODSs, CO2, CO) play smaller roles, although at the end of the simulation, the influence of CO2 and global warming is as large as that of NOx. At Arrival Heights, the leading influence is due to ODSs which drive an overall increase in OH, partially offset by CH4 driving a decrease. Here we find less cancellation of opposing effects, explaining the much larger but seasonal trends in OH and 14CO in the base simulation. Not shown are the influences of VOCs which are small at both locations. These trends are consistent with the OH trends simulated by the three CMIP6 models analyzed by18.

Fig. 7: Modelled sensitivity of OH to anthropogenic pollution.
figure 7

Displayed are changes in annual-mean OH, vertically integrated between the surface and 500 hPa, averaged over middle and high southern latitudes as indicated. All curves are smoothed with a 5-year symmetric boxcar filter and expressed relative to their 1980–1984 means. Black: base, all-forcings simulation. Colours: Differences in integrated OH between the base and the sensitivity simulations, each with one forcing held constant, relative to the base simulation, in percent. a Southern mid-latitude average (35°S-55°S). b Southern polar-cap average (60°S-90°S).

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Normalization for seasonal and solar influences

We use the following regression model to represent the 1989–2009 14CO measurements at Baring Head and Arrival Heights. The later 14CO data are used in an out-of-sample test of the suitability of the regression model, see below:

$$A(s,t)=\mathop{\sum }\limits_{i=0}^{2}s{(t)}^{i}\left\{\mathop{\sum }\limits_{j=0}^{2}{P}_{ij}\cos \left(2\pi jt\right)+\mathop{\sum }\limits_{j=1}^{2}{Q}_{ij}\sin \left(2\pi jt\right)\right\}$$
(4)
$$B(\Delta s,t)=\Delta s(t)\left\{{R}_{10}+{R}_{11}\cos \left(2\pi t\right)+{U}_{11}\sin \left(2\pi t\right)\right\}$$
(5)
$$\left\langle{{}^{14}{\text{CO}}}\right\rangle(s,{{\Delta}} s,t)=A+B$$
(6)

Here t is time, measured in years, and s represents the SMP, nondimensionalized by removing the mean of the monthly-mean SMP values (620 MeV) and then dividing by their standard deviation (182 MeV) for January 1989 to December 2021. \(\Delta s(t)=\overline{s}(t)-\overline{s}(t-1\,\text{a}\,)\), where the overbars indicate smoothing with a 13-months symmetric boxcar filter, and \(\overline{s}(t-1\,\text{a}\,)\) is \(\overline{s}\) evaluated one year before t. Its presence accounts for a slight phase shift between s and 14CO, indicating that measured 14CO is influenced by solar activity occurring before the measurements are taken. The 18 coefficients Pij, Qij, Rij, and Uij in equations (4) and (5) minimize the squared residual \(\sum_k \epsilon_k^{-1}{\left[{}^{14}{{\text{CO}}}_k- \langle{^{14}{{\text{CO}}}}\rangle(s_k,{{\Delta}} s_k,t_k) \right]}^2\), where k enumerates the measurements at either location, and ϵk are the observational measurement uncertainties. The above ansatz amounts to a multilinear regression of the 14CO measurements (in molecules cm−3 STP). Importantly it only allows for seasonal and solar influences on 14CO, and excludes any other influences such as those associated with long-term variations in OH. For both locations, the solutions to the linear regression are listed in Table 1.

Table 1 The regression coefficients defining 〈14CO〉
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The regression fits decompose into sums of a term A(s, t), associated with the regression coefficients Pij and Qij (equation 4), and a further term B(Δs, t), associated with regression coefficients Rij and Uij (equation 5; Fig. 8). A explains most of the variability of 14CO. At both locations 14CO maximizes in spring, and the abundance of 14CO decreases with increasing SMP. B amounts to a correction of the order of about  ± 1 molecule cm−3. Particularly at Arrival Heights, it expresses that 14CO is systematically smaller when Δs < 0, i.e. the SMP is in its decreasing phase, and vice versa when the SMP is increasing. This hysteresis effect (or lag of the 14CO signal versus the solar forcing) is also present at Baring Head but with a smaller amplitude and a different annual cycle.

Fig. 8: Graphical representations of regression fits 〈14CO〉.
figure 8

a, c Component of regression fit A(s, t), where s is the SMP (section “Normalization of the 14CO data”). b,d Component of regression fit B(Δs, t), where Δs is the trend in the smoothed SMP (section “Normalization of the 14CO data”). a, b Baring Head. c,d Arrival Heights.

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The regression fits capture much of the variability of measured 14CO (Fig. 9). Extrapolated to measurements taken during the later period (2010-2021), \(\left\langle{}^{14}{{\rm{CO}}}\right\rangle\) systematically overestimates the actual measurements of 14CO at Baring Head. This effect is not evident at Arrival Heights. At Baring Head, this drift indicates a year-round increase in OH noted above, whereas at Arrival Heights, the seasonality of this effect means that Fig. 9 is not suitable for identifying the trend.

Fig. 9: 14CO measurements versus the regression fits \(\left\langle{{14}\atop}{{\text{CO}}}\right\rangle\).
figure 9

Grey: Measurements taken before 2010. Red: Measurements after 2010. (a) Baring Head. (b) Arrival Heights. The horizontal lines mark the standard measurement errors. The blue lines mark the diagonals.

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Variants of the approach laid out here (we have tested replacing 14CO with its logarithm and with its inverse, and assuming equal weights in the regression) yield essentially the same result for \(\left\langle{}^{14}{{\text{CO}}}\right\rangle\) because it is well constrained by hundreds of observations at both locations. The trend analysis is performed on the normalized measurements 14COnorm = 14CO/\(\left\langle{}^{14}{{\rm{CO}}}\right\rangle\) (equation 1; Fig. 2).

When applying this regression analysis to the gridded model results, a simpler ansatz is pursued whereby individually for the 12 months of the year we form

$$\left\langle{{14}\atop}\!{{\text{CO}}}\right\rangle_m=\sum\limits_{i=0}^2P_{im}s(t_m)^i+R_{1,m}{{\Delta}} s(t_m).$$
(7)

For a given month m of the year, this amounts to fitting by least squares a parabola in s and a term linear in Δs to the monthly-mean 14CO values simulated by the model for this month throughout the data for the period 1989-2009 (21 years). Equation (7) avoids the harmonic expansion in time t (which is unnecessary for the model data, which come as monthly means at regular monthly intervals) and expresses the model-derived \(\left\langle{}^{14}{{\text{CO}}}\right\rangle\) as a function of s, Δs, and month m, thus producing 48 regression coefficients (4 for each month of the year).

Uncertainty calculation

The trend uncertainties in our calculations are made up of two components. One is the statistical uncertainty associated with variability in the climate system. We denote this component as ω. It is quantified as the standard error of the regression coefficients returned by our trend calculation. The other is the instrumental measurement uncertainty (ϵk in section "Normalization for seasonal and solar influences"). We assume that these two errors are independent of each other and that for all measurements the measurement error is normally distributed. To combine these two sources of uncertainty into a single uncertainty estimate, we conduct a Monte-Carlo simulation: We produce 10,000 variant realizations of the measurement timeseries with normally distributed random perturbations added to the measurements. For every measurement, the width of this distribution of random additions equals the standard measurement uncertainty. On these 10,000 variant timeseries we then conduct piecewise linear regression analyses and obtain trend estimates ti and their statistical uncertainties ωi, where the index i enumerates the randomly perturbed realizations. The best-estimate trend T is then given as \(T=\overline{{t}_{i}}\); it is practically identical to the central-estimate trend. The combined uncertainty ϵ is

$$\epsilon=\sqrt{\overline{{\omega }_{i}^{2}}+{\text{std}}^{2}({t}_{i})}$$
(8)

i.e. ϵ is given as the square root of the sum of the average squared statistical uncertainty \(\overline{{\omega }_{i}^{2}}\) (where the ωi turn out to be similar for all realizations) and the squared standard deviation (std) of the trends ti associated with the random perturbations, std2(ti). In all cases, the trend errors are increased by less than 50% if the measurement uncertainty is taken into account versus if only the statistical uncertainty is considered. In Fig. 2(b,d), the stated standard (i.e. 68% confidence) trend error estimates reflect the combined measurement and statistical uncertainties calculated using equation (8).