We use the ensemble mean of three free-running SOCOLv3.0 simulations of the recent past to compare with observations . These simulations were performed for CCMI, and conform to REF-C1 specifications . The simulations cover the period 1960–2010, following a 10-year spin-up period. Greenhouse gas concentrations (CH4, CO2 and N2O) follow observations until 2005, then Representative Concentration Pathway (RCP) 8.5 . Ozone precursor emissions (including NOx, CO and NMVOCs) follow a historical emissions inventory until 2000 , then RCP 6.0 . Sea surface temperatures (SSTs) and sea ice concentrations were prescribed following HadISST observations . Concentrations of ozone-depleting substances followed the World Meteorological Organization's A1 scenario , and stratospheric aerosol surface area densities and optical parameters were prescribed from the SAGE-4λ data set .

We also examine annual-mean tropospheric ozone in REF-C1 simulations performed by models participating in CCMI, described by and references therein. Using the simulated ozone volume mixing ratio and WMO-defined tropopause height from each model, tropospheric ozone columns were calculated for the year 2005 by integrating ozone between the surface and WMO-defined tropopause. The WMO definition of the tropopause was selected to be consistent with the OMI/MLS tropospheric ozone product . Between 2010 and 2014, the average tropospheric ozone burden derived from OMI/MLS was 300 Tg, which is very close to the multi-instrument mean of five satellite products over the same period, of 301 Tg .

Where multiple ensemble members (“realizations”) of the REF-C1 simulation were submitted to the CCMI archive, the ensemble mean is shown. The exception is NIWA-UKCA, which submitted three realizations of the REF-C1 simulation; however only the first realization is shown as ozone precursor emissions were erroneously fixed at 1960 levels for the other two realizations . The EMAC simulations used road traffic emissions which were updated every year rather than every month. Therefore when we examine year 2005 tropospheric column ozone in Sect. , the EMAC simulations used road traffic emissions for August 1954. show that this error results in tropospheric ozone columns that are ∼2 DU lower than if the correct emissions had been used. The UMUKCA-UCAM simulations used CCMVal-2 REF-B2 emissions for NOx aircraft emissions and NOx, CO and HCHO surface emissions.

The SOCOL CCM was developed in Switzerland at ETH Zurich and PMOD/WRC (the Physical Meteorological Observatory Davos/World Radiation Center). Version 3.0 of SOCOL consists of the middle atmosphere version of the ECHAM5 (European Centre Hamburg Model) atmosphere-only general circulation model coupled to the MEZON (Model for Ozone Trends) chemistry transport model . The chemical solver takes into account 41 chemical species, 140 gas-phase reactions, 46 photolysis reactions and 16 heterogeneous reactions. The oxidation of isoprene, an important NMVOC for the tropospheric ozone budget, is accounted for with the Mainz Isoprene Mechanism (MIM-1), which comprises 16 organic degradation products of isoprene and a further 44 chemical reactions . Global isoprene emissions are estimated to range from 440 to 660 Tg(C) yr-1, which is comparable to the annual amount of CH4 emissions . About two-thirds of the annual global emissions of volatile organic compounds (VOCs) are accounted for in SOCOLv3.0 by isoprene and methane. Apart from isoprene and formaldehyde, other NMVOCs are not included explicitly in the model but their contribution to CO is accounted for via the addition of a certain fraction of NMVOC emissions to CO. For anthropogenic, biomass burning and biogenic NMVOC emissions the conversion factors to CO are 1.0, 0.31 and 0.83, respectively .

Clear-sky photolysis rates are calculated using a lookup-table (LUT) approach, which provides photolysis rates as a function of overhead ozone and oxygen columns . Variability of solar irradiance is included in the LUTs. Cloud impacts on photolysis are accounted for in the troposphere by the inclusion of a cloud modification factor following the parametrization described by . From a recent intercomparison of photolysis rates simulated by different CCMI models we learned that SOCOLv3.0 overestimates tropospheric NO2 photolysis by roughly a factor of 2 compared to other models . This overestimation is likely related to the treatment of backscattering from clouds in the calculations of the photolysis LUTs and the missing impact of aerosols. Both effects cannot be easily corrected by the implemented cloud modification factor, and so an online photolysis scheme is planned for future model versions.

Dry deposition velocities of O3, CO, NO, NO2, HNO3 and H2O2 are based on . This simplified approach assumes constant dry deposition velocities over land and ocean, without accounting for seasonal or geographical variability. The tropospheric washout of HNO3 and H2O2 is calculated by using a constant removal rate of 4×10-6 s-1, irrespective of precipitation occurrence. At every chemical time step, i.e. every 2 h, 2.8 % of tropospheric HNO3 and H2O2 below 160 hPa are removed. Boundary conditions for the ozone precursor gases NOx, CO and NMVOCs are implemented as surface emission fluxes. Methane's global average surface mixing ratio is prescribed on the six lowermost model levels. For this study, both SOCOL configurations were run with 39 vertical levels between the Earth's surface and 0.01 hPa (∼80 km) and T42 horizontal resolution (grid cells approximately 2.8∘ × 2.8∘).

SOCOLv3.1 was developed to address SOCOLv3.0's representation of processes relevant to tropospheric ozone chemistry, with the aim of improving the model's large tropospheric ozone bias as shown by . First, we implemented heterogeneous hydrolysis of N2O5 on tropospheric aerosol, as this is an important removal process for atmospheric NOx and was not included in SOCOLv3.0. As SOCOLv3.0 does not explicitly simulate tropospheric aerosols, the new scheme makes use of the ECHAM5 internal tropospheric aerosol climatology considering aerosol properties of 11 Global Aerosol Data Set types . The reaction probabilities for the different aerosol types are calculated following the parametrization by .

Second, the simplified treatment of dry deposition was replaced by a more sophisticated scheme in SOCOLv3.1 based on the surface resistance approach for the estimation of dry deposition velocities proposed by . This takes into account actual meteorological conditions, different surface types and trace gas properties like solubility and reactivity. Further details of this scheme are given by .

Third, we adjusted how methane is prescribed in the model. In previous versions of SOCOL, methane was prescribed as a global surface average mixing ratio on the six lowermost model levels (covering approximately 2.5 km). This was changed to only the surface level in SOCOLv3.1. While the amount of methane entering the atmosphere is the same in both configurations, prescribing it on one level instead of six means that methane-induced ozone production in the mid-troposphere–upper troposphere is reduced. Because SOCOLv3 has a high OH bias compared to the ACCMIP models , ozone production from methane oxidation is amplified by the continuous resupply of methane due to the mixing ratio boundary condition when methane is prescribed on six levels instead of one. An interhemispheric gradient and seasonal cycle in methane have also been implemented in SOCOLv3.1; however these were not used in this study and instead methane was prescribed as a global average surface mixing ratio to test the general sensitivity of tropospheric ozone to surface methane concentrations.

Finally, because the LUTs used in SOCOLv3.0 cause tropospheric NO2 photolysis to be overestimated due to the treatment of backscattering from clouds (Sect. ), we recalculated LUTs for SOCOLv3.1. While the SOCOLv3.0 LUTs were calculated assuming 0.5 cloud coverage and a surface albedo of 0.3, the SOCOLv3.1 LUTs were based on clear-sky conditions and also used a surface albedo of 0.3.

Variance-based global sensitivity analysis quantifies the contribution of a single parameter to the variance of a model's output. Because the large number of model simulations required would make one-at-a-time testing computationally too expensive, a type of statistical model called a GP emulator can be used as a surrogate for the input–output relation of a complex model, such as a CCM . For “training” data on which the GP emulator is built, we know that the true value of the emulated output should be the same as the input, so the emulator should return the output with no uncertainty. For inputs that the emulator is not trained at, the outputs should have a probability distribution specified by a mean function and covariance function . Here, we use tropospheric ozone columns from SOCOLv3.1 to train the emulator.

Interacting contributions to the overall uncertainty in tropospheric column ozone can be identified by comparing the main effect variance (the reduction in the ozone variance when a particular model forcing is fixed, e.g. NOx emissions), with the total effect variance (the remaining variance in the tropospheric column ozone when everything except a particular model forcing is fixed). Various software packages are available for GP emulation. We used the Gaussian Emulation Machine for Sensitivity Analysis (GEM-SA), available at http://tonyohagan.co.uk/academic/GEM/index.html (last access: 11 November 2018), to build an emulator for tropospheric column ozone.

Although many factors influence the tropospheric ozone budget, we restricted our analysis to nine model forcings/parametrizations (see Table  for details of the scalings applied). These are listed below, followed by a section rationalizing the inclusion of each variable. We reiterate that this list above does not constitute a comprehensive list of variables controlling tropospheric ozone; however by illustrating the methodology used, we aim to demonstrate its utility.

natural and anthropogenic NOx emissions (denoted in figures as “NOx”).

Variables (1–3) were selected due to their importance as tropospheric ozone precursors. CO and NMVOC emissions were varied simultaneously (3) because the only NMVOCs included explicitly in SOCOL are isoprene and formaldehyde; other NMVOCs are represented via additional CO using a “lumped” approach (Sect. ). For models with a more complex representation of NMVOCs, we recommend testing CO and NMVOC emissions separately when constructing a GP emulator.

The remaining variables were included to investigate the sensitivity of tropospheric ozone to the model improvements implemented in SOCOLv3.1. SOCOLv3.0 and its predecessors prescribed methane on the lowermost six model levels. This was changed to only the surface level in SOCOLv3.1, and variable (5) was included in our analysis to investigate the sensitivity of tropospheric ozone to this implementation. The lowermost level in SOCOL covers approximately 100 m, and the six lowermost levels combined cover approximately 2.5 km. To explore whether other ozone precursors are sensitive to the number of levels they are prescribed on, variable (4) was included, even though it is prescribed only as a surface emissions flux in most, if not all, CCMs. By doing so, we aim to test the exchange of emissions between the boundary layer and free troposphere.

Because ozone production and destruction reactions are mostly photochemical, i.e. they occur in the presence of sunlight, we selected variable (6) to test the sensitivity of the current CMF parametrization, and examine impacts of the updated LUTs on tropospheric ozone in SOCOLv3.1. HNO3 washout is the main sink for NOx, and therefore affects the ozone budget. Future SOCOL versions will include an online wet deposition scheme, and so variable (7) was selected to probe the sensitivity of tropospheric ozone to the rate of HNO3 loss. Heterogeneous N2O5 hydrolysis is similarly important as it leads to HNO3 formation; however it was not included in SOCOLv3.0. Therefore variable (8) was included in our analysis to quantify its relevance for tropospheric ozone abundances. Finally, variable (9) was chosen to test the sensitivity of tropospheric ozone to the newly implemented dry deposition parametrization (Sect. ).

Typically 10n simulations are recommended for training a GP emulator, where n is the number of variables under investigation . Hence we performed 90 SOCOLv3.1 training simulations, and used the resulting annual-mean tropospheric ozone column to construct the GP emulator in several geographical regions (Europe, United States, Asia, the Southern Ocean and the global mean). For each of the 90 training simulations, the nine input variables were scaled simultaneously, with the scaling factors determined using a “maximin” Latin hypercube design, which generates a near-random sample of parameter values from a multidimensional distribution and fills the uncertainty space of the parameters . The Latin hypercube was generated using GEM-SA. For the discrete input parameters (e.g. (4) and (5) in the list above), the scaling factor was rounded to the nearest whole number. Table  summarizes the minimum and maximum scalings applied to each of the nine variables. This is discussed further in Sect. . Figure  shows the experimental design for the 90 training simulations.

SOCOLv3.1 training simulations were performed for the year 2005 (following a common model spin-up period of 10 years, which was discarded from our analysis). The feedback between chemistry and radiation was switched off to keep internal variability as small as possible. Switching off the chemistry–radiation feedback means that all simulations have the same meteorology (given that they started from the same initial conditions and ran with the same dynamical boundary conditions), despite having different chemistry. Therefore, we can be confident that the differences between the simulations are caused by differences in chemistry and not dynamics.

The emulator was constructed using tropospheric ozone columns calculated between the surface and the WMO-defined tropopause. Alongside the global mean, we focus on four regions, namely Europe (37–60∘ N, 0–42∘ E), the United States (32–52∘ N, 67–124∘ W), Asia (6–49∘ N, 70–146∘ E) and the Southern Ocean (45–60∘ S, all longitudes), where different chemical regimes may dominate; see e.g. .

After constructing the GP emulator, the next step is to validate it by comparing emulator-predicted ozone with SOCOL-simulated ozone. This was done by performing a further 27 (i.e. 3n) SOCOLv3.1 “test” simulations. The set-up for these simulations was similar to the training simulations, with a new Latin hypercube generated by GEM-SA to supply the scaling factors.

Figure  compares annual-mean tropospheric column ozone as simulated by SOCOLv3.0 and 3.1 with observations derived from OMI/MLS. Although SOCOLv3.0 captures the spatial distribution of tropospheric ozone fairly well in a qualitative sense, i.e. elevated ozone in the Northern Hemisphere and a minimum over the tropical Western Pacific (Fig. a), it overestimates tropospheric column ozone between 60∘ N and 40∘ S by up to 30 DU – approximately a factor of 2 (Fig. c). The improved treatment of ozone sink processes in SOCOLv3.1 means that tropospheric ozone columns are reduced regionally by up to 8 DU compared with SOCOLv3.0 (Fig. d–e). Individual sensitivity tests (not shown) indicate that this is due mostly to the inclusion of heterogeneous N2O5 hydrolysis on tropospheric aerosol.

Both SOCOLv3.0 and 3.1 show a small negative bias in tropospheric ozone over the Southern Ocean. This was also visible in the SOCOLv3.0 and TES comparison presented by . Recent work by has indicated that the dry deposition scheme overestimates the observed ozone deposition velocity by a factor of 2–4 in the Southern Ocean, where SSTs are low and chemical reactions are slow. Further upgrades to the model's deposition scheme may therefore improve comparisons of simulated and observed tropospheric ozone in cold oceanic regions.

The global-mean tropospheric ozone column in SOCOLv3.1 is 36.4 DU (Fig. d), which is still at the upper end of the range of the CCMI models (Fig. ), but comparable to other models such as ACCESS (36.3 DU), EMAC-L47 (37.3 DU) and MRI-ESMr1 (35.7 DU). Despite the improvements to SOCOLv3.1, a large bias in tropospheric ozone of approximately 20 DU compared with OMI/MLS remains (Fig. f). The bias maximizes over continental regions in the Northern Hemisphere, and over Southeast Asia.

To understand the drivers of the remaining tropospheric ozone bias in SOCOLv3.1, we constructed a GP emulator from the 90 SOCOLv3.1 training simulations (Sect. ). Tropospheric ozone predicted by the emulator is compared with SOCOLv3.1 test simulations in Fig. . In all geographical regions shown, the goodness of fit between emulated and simulated tropospheric ozone is high (R2≥0.85) and the points fall mostly along the 1:1 line, indicating that the emulator performs well in these regions. The point with the largest simulated tropospheric ozone column corresponds to a simulation in which two ozone loss processes, HNO3 washout and ozone dry deposition, were set to zero and large scalings (4.00 and 3.54) were applied to the ozone precursors NOx and CH4, respectively, following the Latin hypercube design (Fig. ). The emulator underestimates tropospheric ozone for this point in all regions examined, indicating that it may not be well constrained at the extreme ends of the parameter uncertainty space.

Figure  displays the sensitivity of global-mean tropospheric ozone to each parameter, obtained by averaging over all other parameters, and indicates whether tropospheric ozone increases or decreases in response to an individual forcing/parametrization. Greater uncertainty is indicated where the lines diverge (appearing as a thicker line – i.e. the emulator is less well constrained). Tropospheric ozone exhibits a strong sensitivity to its precursor gases (Fig. a–c), and while the correlation between CH4 and CO+NMVOCs is approximately linear, for NOx there appears to be a saturation effect for scaling factors greater than 1, likely due to the “NOx titration effect” . In our calculations a uniform sampling distribution was applied when generating the Latin hypercube, which means that in 25 % of our training simulations the NOx (and CH4, CO and NMVOC) scaling factors are less than 1, while in the other 75 % of simulations they are larger than 1.

To test whether the emulator may be biased due to the sampling distribution used, we calculated tropospheric column ozone as a function of NOx and CO+NMVOCs using the gradients in Fig. a and c. Assuming a uniform sampling distribution between 0 and 4, as per the Latin hypercube design used here, the sensitivity indices for NOx and CO+NMVOCs are 0.68 and 0.32, respectively. If we assume a piecewise uniform distribution, so that 50 % of the points are between 0 and 1, and 50 % are between 1 and 4, the sensitivity indices are 0.72 for NOx and 0.28 for CO+NMVOCs. That is, the differences are negligible, implying that the type of sampling distribution used does not bias the result. However, given the NOx saturation effect above 1 (Fig. a), if we assume a uniform distribution between 0 and 2 instead of 0 and 4, the NOx sensitivity index increases to 0.86, while the CO index decreases to 0.14. This shows the importance of selecting an appropriate range for the parameter uncertainty space. However, the conclusions of our emulator analysis – that ozone precursors are the dominant driver of tropospheric ozone variability – remain unchanged.

Figure  shows the percentage of variance that each parameter contributes to in each geographic region, either jointly or alone. In all regions examined, ozone precursors – CH4, NOx, CO and NMVOCs – account for more than 90 % of the variance in tropospheric column ozone. In other words, changing these ozone source input parameters has a far larger impact on tropospheric ozone abundances than changing ozone sink parameters does, and this applies to both polluted regions (Europe, the United States and Asia) and relatively pristine environments (the Southern Ocean). NOx emissions are generally the dominant driver of variability (in the European region they are approximately equal to the contribution from CH4; Fig. a). Over Asia, where CO emissions are larger than over Europe and the United States, the ratio of NOx:CO is also lower than it is over Europe and the United States . NOx emissions therefore become more important as a driver of ozone variability over Asia (Fig. c). In all regions, joint interactions between NOx, CH4 and CO+NMVOCs play a relatively minor role compared with the individual influences of these species.

Although updating SOCOLv3.1 with regards to N2O5 hydrolysis, HNO3 washout, LUTs and ozone dry deposition results in a reduction in tropospheric ozone of up to 8 DU regionally (Fig. e), as drivers of tropospheric ozone variability in SOCOLv3.1 they are insignificant compared with ozone precursors. However, we cannot discount the possibility that it is not the ozone precursor emissions themselves that are responsible for SOCOLv3's tropospheric ozone bias, but rather the way in which the emissions are handled by the model; this is considered further in the Discussion and conclusions.

We now consider SOCOL's tropospheric ozone bias in the context of the CCMI models. Figure  illustrates the diversity in simulated tropospheric ozone amongst the CCMI models. Despite most of the models using ozone precursor emissions following the REF-C1 recommendations (Sect. ), they simulate vastly different representations of tropospheric ozone. A few of the models are closely related, as discussed by ; for example the CESM1 models, WACCM and CAM4-chem, are essentially the same model in terms of tropospheric ozone. They differ only in the height of the model lid, which is 140 km for WACCM and 40 km for CAM4-Chem.

ACCESS and NIWA-UKCA can also be considered the same model for the REF-C1 experiment; although a coupled ocean was used for most of NIWA-UKCA's CCMI simulations, for the REF-C1 experiment they used the same prescribed sea surface conditions (temperature and ice coverage) as ACCESS. Differences between ACCESS and NIWA-UKCA in the REF-C1 simulation, therefore, are likely related to issues with the different compilers used which may induce small differences in stochastic physics and tropospheric age of air .

The EMAC L47 and L90 models are also very similar; both have a model lid at 0.01 hPa (∼80 km), but they differ in the number of model levels between the surface and 0.01 hPa (47 and 90, respectively). They also use different time steps.

Figure  shows the difference in tropospheric ozone between each of the CCMI models and OMI/MLS, and the root-mean-square error (RMSE) for the model–OMI/MLS difference. Alongside Fig. , Fig.  indicates clear outlying models in terms of tropospheric ozone. UMUKCA-UCAM simulates the smallest amount of tropospheric ozone (14.9 DU in the global mean Fig. o); however it only contains one NMVOC (formaldehyde) and does not lump NMVOCs together in the way that many other CCMs do. This means that additional NMVOC source gases are not considered by substituting with represented species, such as in SOCOLv3, whereby additional NMVOCs are included in the form of CO. Of the CCMI models, SOCOLv3.0 simulates the largest global-mean tropospheric ozone column, of 40.2 DU (Fig. a). In ULAQ-CCM, the zonal bands of large ozone abundances at northern and southern mid-latitudes are related to the model's coarse horizontal resolution (5.6∘ × 5.6∘), which affects surface fluxes and tropospheric transport .

Interestingly, EMAC-L90 simulates a better representation of tropospheric column ozone than EMAC-L47, despite the fact that EMAC-L90 has three fewer model levels between the surface and 300 hPa than EMAC-L47 and a longer time step. The difference in tropospheric column ozone between the two models likely results from the increased vertical resolution around the tropopause in EMAC-L90, which has 11 levels between 300 and 100 hPa compared with 7 in EMAC-L47, meaning that EMAC-L90 better simulates stratosphere–troposphere exchange.

Figure  shows multi-model means (MMMs) and standard deviations. The MMM in Fig. a was calculated for all models, while the MMM in Fig. d was calculated only for models with a RMSE less than 10 DU, as indicated in Fig.  – i.e. all models except SOCOLv3.0, ACCESS CCM, EMAC-L47, ULAQ-CCM and UMUKCA-UCAM. The CCMI models simulate a global-mean tropospheric ozone abundance of 31.1 DU (Fig. a) and 30.2 DU (Fig. d), depending on the MMM definition applied. Both global-mean MMMs are close to the OMI/MLS global mean of 28.6 DU (Fig. b); however the MMMs differ markedly from OMI/MLS in terms of the global tropospheric ozone distribution.

Compared to OMI/MLS, the models overestimate tropospheric column ozone almost everywhere between 60∘ N and 60∘ S (the region where OMI/MLS data are available), regardless of the MMM definition. The exception is at southern mid-latitudes, where the models underestimate tropospheric ozone compared to OMI/MLS. When the MMM is calculated for all models, the positive bias is up to 50 %, and the negative bias reaches up to -33 % (Fig. c). When models with an RMSE >10 DU are discarded from the MMM, the negative bias is largely unchanged at -32 %, but the positive bias is reduced, and reaches up to 40 % (Fig. f).

These results broadly agree with models evaluated as part of ACCMIP , and phase 5 of the Coupled Model Intercomparison Project (CMIP5) , which used the same ozone precursor emissions as for CCMI. The ACCMIP models simulated, on average, up to 30 % more tropospheric column ozone compared with OMI/MLS at northern mid-latitudes . The global-annual-mean tropospheric ozone column simulated by these models was 30.8 DU, calculated from 15 models. For the 18 CHEM models participating in CMIP5 (those models with interactive chemistry, i.e. ozone was calculated online and not prescribed from a climatology), the climatological-mean annual-mean MMM averaged over 2000–2005 was 30.5 DU , which is similar to the MMMs calculated here. The CMIP5 and ACCMIP MMMs also show a stronger interhemispheric gradient than OMI/MLS observations do, consistent with our findings.

The standard deviation on the MMM is up to 11.3 DU when calculated for all models (Fig. b), and reduces to a maximum of 9.5 DU when calculated for only the models with RMSE <10 DU (Fig. e). The variability between models is largest at northern mid-latitudes and in the continental outflow region off the west coast of Africa.