In this study, we analyze the OH fields simulated by five models (CESM1 CAM4-chem, CESM1 WACCM, EMAC-L90MA, GEOSCCM, MRI-ESM1r1), which include detailed tropospheric ozone chemistry and multiple primary VOC emissions. All five models conducted the REF-C1 experiments (free-running simulations driven by state-of-the-art historical forcings including sea surface temperature and sea ice concentrations) for 1960–2010, and four of them (excluding GEOSCCM) conducted the REF-C1SD experiments (similar to REF-C1 but nudged to the reanalysis meteorology data) for 1980–2010. Thus, we have nine OH fields generated by models with different chemistry, physics, and dynamics covering the period 1980–2010. A detailed description of these CCMI models and experiments and of characteristics of the OH fields can be found in Morgenstern et al. (2017) and Zhao et al. (2019).

To eliminate the influence of different magnitudes of global OH burden simulated by those models, we scale all OH fields to the same CH4 loss for the year 2000 based on the reaction with OH used in the TransCom-CH4 intercomparison exercise (Patra et al., 2011). The inferred global mean scaling factors are calculated for the year 2000 and each OH field and then applied to the whole period (1980–2010). The production (O(1D) + H2O, NO + HO2, O3+ HO2) and loss processes (removal of OH by CO, CH4, formaldehyde – CH2O, and isoprene) for each OH field are estimated using the CCMI database (Sect. S1 in the Supplement). For each OH field, we separate trends and year-to-year variations in the global tropospheric mean CH4-reaction-weighted OH concentration ([OH]GM-CH4, weighting factor = reaction rate of OH with CH4× dry air mass; Lawrence et al., 2001) as well as in its production and loss rates.

To evaluate the influences of OH temporal variations on the top-down estimation of CH4 emissions, we have conducted Bayesian atmospheric inversions using (1) a two-box model similar to that described by Turner et al. (2017) and (2) a 4D variational inversion system based on the version LMDz5B of the LMDz atmospheric transport model under the PYVAR-SACS framework (Chevallier et al., 2007; Pison et al., 2009) as described by Locatelli et al. (2015) and Zhao et al. (2020). The two-box model inversions allow us to easily conduct multiple long-term global-scale inversions (1984–2012) with each of the nine OH fields to estimate the global CH4 emission variations caused by various OH fields. The 4D variational inversions allow us to better represent the atmospheric transport, account for the variation in meteorological conditions, and address regional CH4 emission distributions. Thus, we have conducted both two-box model inversions with each of the nine OH fields and variational inversions with the multimodel mean OH field (average of the nine OH fields).

Both the box model and the variational inversions optimize the CH4 emissions and initial mixing ratios by assimilating the observation data from the Earth System Research Laboratory of the US National Oceanic and Atmospheric Administration (Dlugokencky, 2020). The OH concentrations are prescribed and not optimized in both inversion systems. A detailed description of the two-box model, the LMDz atmospheric transport model, and the variational inversion method used here is provided in the Supplement (Sect. S2).

We have designed an ensemble of inversion experiments as listed in Table 1 using the two-box model with each OH field. Here, Inv_OH_std uses the aforementioned scaled OH fields; Inv_OH_cli uses a climatology of each OH field, which is constant over the years and correspond to an average over 1980–2010; Inv_OH_var stands for the inversion using the detrended OH (only keeping the year-to-year variations); Inv_OH_trend uses the OH without the year-to-year variability (retaining only the trend). By comparing Inv_OH_cli with Inv_OH_std, Inv_OH_var, and Inv_OH_trend, it is possible to assess the influence of total OH temporal changes, year-to-year variations, and OH trends, respectively, on the overall CH4 changes. The box model inversions are conducted from 1984 to 2012 (2010 OH fields are used for 2011 and 2012). The first and last 2 years are treated as spin-up and spin-down, and we only analyze the inversion results over 1986–2010.

We have conducted two 4D variational inversions, Inv_OH_std and Inv_OH_cli, using the multimodel mean OH field to test the influence of OH temporal variations on the top-down estimates of global to regional CH4 emissions. The LMDz inversions are conducted for four time periods (1994–1997, 1996–1999, 2000–2004, and 2006–2010; Sect. 3.4). We only spin-up and spin-down the 4D variational inversions for 1 year to save computing time. The four time periods are chosen to represent the transition from La Niña (1995–1996) to El Niño (1997–1998) years and the years of stagnated (2001–2003) and renewed growth (2007–2009) of observed CH4.

All CCMI models simulate positive OH trends from 1980 to 2010 after removing the year-to-year variability (Fig. 1a), consistent with previous analyses of CCMI OH fields (Zhao et al., 2019; Nicely et al., 2020) and model results of the Aerosol Chemistry Model Intercomparison Project (Stevenson et al., 2020). The multimodel mean [OH]GM-CH4 increased by 0.7 ×105 molec cm-3 from 1980 to 2010. The growth rates in [OH]GM-CH4 are estimated as ∼ 0.03 ×105 molec cm-3 yr-1 (0.3 % yr-1) during the early 1980s, ∼ 0.01 ×105 molec cm-3 yr-1 (0.1 % yr-1) between the mid-1980s and the late 1990s, and 0.03–0.05 ×105 molec cm-3 yr-1 (0.3 %–0.5 % yr-1) since the 2000s. This continuous increase in [OH] is different from the results based on the MCF inversions using the two-box model approach (Turner et al., 2017; Rigby et al., 2017), which yield increases in [OH] from the 1990s to the early 2000s and a decrease in OH afterward.

The ensemble of the anomaly of detrended [OH]GM-CH4 (Fig. 1b) shows a strong anticorrelation (r = -0.50) with the bimonthly Multivariate ENSO Index Version 2 (MEI.v2, 2020; Fig. 1c and Sect. S3; Zhang et al., 2019), with higher [OH]GM-CH4 during La Niña and lower [OH]GM-CH4 during El Niño. From 1980 to 2010, the CCMI model simulations show several negative anomalies of [OH]GM-CH4, the three largest reaching as high as -0.4 ± 0.2 ×105 molec cm-3 (-4 ± 2 %) during 1982–1983 and 1991–1992 and -0.5 ± 0.4 ×105 molec cm-3 (-5 ± 4 %) during 1997–1998. The negative [OH]GM-CH4 anomalies during 1982–1983 and 1997–1998 correspond to the two strongest El Niño events (MEI > 2.5). During 1991–1992, the negative [OH]GM-CH4 anomaly corresponds to both the weaker El Niño event (MEI up to 2.0), and the eruption of Mount Pinatubo. During other weak El Niño events (1986–1987, 2002–2003, 2004–2005, and 2006–2007), the multimodel mean [OH]GM-CH4 shows smaller negative anomalies of 1 %–2 %. Only the negative OH anomaly during 2006–2007 (2 ± 1 %) is simulated by all models during the four weak El Niño events. The negative anomalies are consistent with an up to 9 % reduction in [OH] during 1997–1998 simulated by TOMCAT-GLOMAP as shown by Rowlinson et al. (2019), as well as with a 5 % reduction in [OH] over tropical regions during 1991–1993 constrained by MCF observations (Bousquet et al., 2006). During La Niña events, the [OH]GM-CH4 shows ∼ 2 % positive anomalies, resulting in more than a 6 % increase in OH (max–min) during 1983–1985, 1992–1994, and 1998–2000.

The negative [OH]GM-CH4 anomalies during strong El Niño events correspond to the highest growth rates of the CH4 mixing ratio from the surface observations (Dlugokencky, 2020), which are 14 ± 0.6 ppbv yr-1 in 1991 and 12 ± 0.8 ppbv yr-1 in 1998 (Fig. S1). The positive anomalies of [OH]GM-CH4 during La Niña events correspond to a much smaller CH4 growth (e.g., 4 ± 0.6 ppbv yr-1 in 1993 and 2 ± 0.8 ppbv yr-1 in 1999) compared with that during the adjacent El Niño years (Fig. S1).

The changes in tropospheric [OH] are due to changes in the balance of production and loss. Here we assess the drivers of OH year-to-year variations and trend by calculating the OH production and loss processes listed in Table 2 following Murray et al. (2013, 2014) and Lelieveld et al. (2016). The multimodel calculated OH production and loss in the troposphere averaged over 1980–2010 is 209 ± 12 Tmol yr-1, similar to the ∼ 200 Tmol yr-1 reported by Murray et al. (2014). Of the total OH production, 46 % (96 ± 2 Tmol yr-1) is from primary production (O(1D) + H2O). Two main secondary productions of NO + HO2 and O3+ HO2 account for 30 % (63 ± 4 Tmol yr-1) and 13 % (26 ± 2 Tmol yr-1), respectively. For the OH loss, reactions with CO and CH4 account for 39 % (82 ± 4 Tmol yr-1) and 15 % (32 ± 1 Tmol yr-1), respectively. We have also calculated the OH loss by reactions with isoprene (C5H8) and formaldehyde (CH2O), which both remove 6 % of OH, reflecting the influences of NMVOCs from natural and anthropogenic sources, respectively. Besides, there are 12 % of OH production and 33 % of OH loss not analyzed here due to lack of data in the CCMI model outputs (e.g., output of OH loss due to reaction with NMVOCs included in different models).

Figure 2 shows the changes in the trends of OH production and loss processes (year-to-year variations are removed) with respect to the year 1980. The OH primary production (O(1D) + H2O) shows a large increase of 10 ± 1 Tmol yr-1 from 1980 to 2010, as the dominant driver of the positive OH trend. The increase in OH primary production is due to an increase in both tropospheric O3 burden (producing O(1D)) and water vapor (Dentener et al., 2003; Zhao et al., 2019; Nicely et al., 2020). The OH loss from CO increased by 7 ± 0.7 Tmol yr-1 from 1980 to 2001 but then decreased by 4 ± 2 Tmol yr-1 from 2001 to 2010. The negative trend of CO simulated by CCMI models during 2000–2010 is consistent with MOPITT observations over most of the regions (Strode et al., 2016). We find that the decrease in OH loss by CO can explain the accelerated OH increase after 2000, despite a stagnated OH primary production and a slight decrease in the OH secondary production. The OH loss by CH4, which shows a continuous increase of 6 ± 0.5 Tmol yr-1 from 1980 to 2010, buffers the increase in OH production by NO (5 ± 1 Tmol yr-1). The OH production by O3+ HO2 and OH loss by CH2O and isoprene show smaller changes of 2 ± 1, 2 ± 0.3, and 1 ± 0.6 Tmol yr-1, respectively, during 1980–2010. By comparing the magnitude of the production and loss processes, we conclude that an enhanced OH primary production and changes in OH loss by CO are the most important factors leading to the increased OH trend inferred from CCMI models from 1980 to 2010.

Figures 3 and S2 show the year-to-year variations in the global total OH production and loss due to several processes (calculated after trends have been removed). Year-to-year variations in global [OH] are mainly determined by the primary (O(1D) + H2O) and secondary (NO + HO2; O3+ HO2) production and by OH loss due to CO (Fig. 3). Other OH loss processes, including reactions with CH4, CH2O, and isoprene, show much smaller year-to-year variations but larger uncertainties (Fig. S2), revealing a larger model spread for these processes.

As shown in Fig. 3, negative anomalies of [OH] during El Niño events are dominated by increased OH loss through the reaction with CO in response to enhanced biomass burning (Fig. S3), which is similar to the conclusions of Rowlinson et al. (2019) and Nicely et al. (2020). During the strong El Niño events in 1982–1983, 1991–1992, and 1997–1998, the OH loss by CO increased by up to 3 ± 0.4, 5 ± 0.6, and 8 ± 0.5 Tmol yr-1, respectively, compared to the mean value of 1980–2010. The increase in OH loss by CO can be partly offset by an increase in OH production. Indeed, in 1998, the OH primary production (O(1D) + H2O), OH produced by NO + RO2, and O3+ RO2 increased by 3 ± 0.7, 3 ± 0.5, and 2 ± 0.3 Tmol yr-1, respectively, offsetting most of the OH loss increase. The increase in OH primary production is mainly due to an increase in tropospheric water vapor and O3 burden during El Niño events (Figs. S3 and S12 in Nicely et al., 2020), while the increase in OH secondary production is caused by enhanced NOx emissions (Fig. S3) and O3 formation (Nicely et al., 2020) related to biomass burning as well as to more HO2 formation by CO + OH. As a result, the OH year-to-year variations found here are much smaller than those estimated by Nguyen et al. (2020), who mainly considered the response of OH to enhanced CO emissions during the El Niño events. The positive anomaly in OH primary production (0.2 ± 0.5 Tmol yr-1) is not significant during the 1991–1992 El Niño event, maybe due to the absorption of ultraviolet (UV) radiation by volcanic SO2 and scattering of UV radiation by sulfate aerosols as well as to the reduction in tropospheric water vapor after the eruption of Mount Pinatubo (Bândă et al., 2016; Soden et al., 2002). Thus, the negative [OH] anomaly during the weak El Niño event in 1991–1992 is potentially being enhanced by the eruption of Mount Pinatubo. Previous studies have shown that NOx emissions from lightning can contribute to the OH interannual variability (Murray et al., 2013; Turner et al., 2018). In addition, soil NOx emissions depend on temperature and soil humidity (Yienger and Levy, 1995), which vary during the El Niño events. The year-to-year variations in NOx emissions from lightning show large differences among CCMI models (Fig. S4), and only EMAC and GEOSCCM apply interactive soil NOx emissions that vary with meteorology conditions (Morgenstern et al., 2017) based on Yienger and Levy (1995). Thus NOx emissions from lightning and soil mainly contribute to intermodel differences instead of showing a consistent response to El Niño.

Using a machine learning method, Nicely et al. (2020) attributed the positive [OH] trend simulated by the CCMI models mainly to the increase in tropospheric O3, J(O1D), NOx, and H2O, and attributed [OH] interannual variations to CO changes. Overall, the explanations of the drivers of OH year-to-year variations and trends found in our process analysis are broadly consistent with those reported by Nicely et al. (2020), and we emphasize that the decrease in CO emissions and concentrations after 2000 (Zheng et al., 2019) is important for determining the accelerated positive OH trend.

Figure 4a shows the anomaly of global total CH4 emissions estimated by inv_OH_std (nine scaled OH fields; orange line) and inv_OH_cli (nine climatological OH; blue line) using the two-box model during 1986–2010. With the climatological OH fields (blue line), the top-down-estimated CH4 emissions show no clear trend before 2005, with large positive anomalies during strong El Niño years. There are two peaks of positive CH4 emission anomalies during this period: 10 Tg yr-1 in 1991 and 14 Tg yr-1 in 1998. From 2005 to 2008, the CH4 emissions show a large increase of 26 Tg yr-1. The CH4 emissions averaged over 2006–2010 are 20 Tg yr-1 higher than over 2000–2005, consistent with the 17–22 Tg yr-1 estimated by an ensemble of inversions in Kirschke et al. (2013).

The OH temporal variations are found to largely influence the interannual changes in top-down-estimated CH4 emissions (orange line of Fig. 4a), with differences between the two inversions reaching up to more than 15 Tg yr-1 (Fig. 4b). The contributions from the OH year-to-year variations and trends are also shown in Fig. 4. The negative anomalies of OH during El Niño years reduce the unusually high top-down-estimated CH4 emissions in 1991–1992 by 7 ± 3 Tg yr-1 and in 1998 by 10 ± 3 Tg yr-1 (Fig. 4c). As a result, the high-emission peaks to match the observed CH4 mixing-ratio growth in 1991 (14 ppb yr-1) and 1998 (12 ppbv yr-1), as estimated using the climatological OH, are largely reduced.

The identified positive OH trend leads to an additional 23 ± 9 Tg yr-1 increase in CH4 emissions from 1986 to 2010 (Fig. 4d). During 1986–2005, the mean CH4 emissions, as estimated with the scaled OH, show a positive trend of 0.6 ± 0.4 Tg yr-2 (P < 0.05). Increased CH4 emissions offset the increase in the OH sink to match the observations. From 2005 to 2008, in contrast to previous studies, which attribute the increased observed CH4 mixing ratios to decreased OH based on MCF inversions (Turner et al., 2017; Rigby et al., 2017), the increasing OH trend simulated by CCMI models results in an additional 5 ± 2 Tg yr-1 CH4 emission increase in the inversion to match the observations.

We compare the inversion using the two-box model (“×” in Fig. 5) with the results from the variational approach (bars in Fig. 5), using the multimodel mean OH field, to evaluate the performance of the simplified two-box model inversions. Despite the limitations inherent to two-box model inversions, such as treatment of interhemispheric transport, stratospheric loss, and the impact of spatial variability (Naus et al., 2019), the two-box model inversion estimates similar temporal changes in CH4 emissions and losses compared to the variational approach for the four periods, as well as to their response to OH changes (Fig. 5), on a global scale. Such comparisons reinforce the reliability of the conclusions made from the two-box model inversions regarding changes in the global total CH4 budget.

The variational inversions allow us to assess the regional contribution of the drivers to observed atmospheric CH4 mixing-ratio changes. Here, as a synthesis, we focus on four latitude bands (Fig. 5 and Table S2), including the southern extratropical regions (90–30∘ S), the tropical regions (30∘ S–30∘ N), and the northern temperate (30–60∘ N) and boreal (60–90∘ N) regions. On average, OH over the tropical and northern temperate regions removes 74 % and 14 % of global total atmospheric CH4, respectively.

Between the periods 1995–1996 and 1997–1998, if one does not consider the OH temporal variations (Inv_OH_cli), the CH4 loss by OH shows a slight increase of 2 Tg yr-1 due to an increase in atmospheric CH4 mixing ratios. The main driver of observed atmospheric CH4 mixing-ratio changes is the 10 Tg yr-1 increase in CH4 emissions over the tropics and the 7 Tg yr-1 increase over the northern temperate regions (Fig. 5b and Table S2). When the multimodel mean OH temporal variations are included (Inv_OH_std), the negative anomaly of OH in 1997–1998 leads to a 9 Tg yr-1 decrease in CH4 loss in 1997–1998 compared to 1995–1996, of which 7 Tg yr-1 (78 %) is contributed by the tropical regions (Fig. 5a). As a result, the decrease in CH4 loss by OH contributes a bit more to match the observed CH4 mixing-ratio increase during the El Niño periods than the changes in CH4 emissions (a global increase of 8 Tg yr-1). The emission increases from 1995–1996 to 1997–1998 over the tropics, and the northern temperate regions are reduced to 3 and 5 Tg yr-1 (Fig. 5a, Inv_OH_std), respectively, which is similar to the inversion results given by Bousquet et al. (2006).

From the period 2001–2003 to 2007–2009, positive OH trends lead to a 13 Tg yr-1 increase in the CH4 loss, of which 10 Tg yr-1 (76 %) originates from the tropics (Inv_OH_std, Fig. 5a). In response to increased CH4 losses, the increase in optimized emissions over tropical regions (16 Tg yr-1, Inv_OH_std) is more than twice that of the inversion using climatological OH (7 Tg yr-1, Inv_OH_ cli). The emission increases during the two periods over the northern region show a smaller change of 2 Tg yr-1 (12 Tg yr-1 estimated by Inv_OH_std versus 10 Tg yr-1 by Inv_OH_cli, Fig. 5). The variational inversions show that the OH temporal variations are most critical for top-down estimates of CH4 budgets over the tropical regions since OH over tropical regions shows larger interannual variations and trends than middle- to high-latitude regions (Fig. S5) and most of the CH4 (74 %) is removed from the atmosphere by OH over the tropical regions.