The data assimilation system is constructed based on a global CTM MIROC-Chem (Watanabe et al., 2011) and an EnKF described in Miyazaki et al. (2017), which can be consulted for more detailed information. We use the 2-hourly global chemical reanalysis data for the period 2005–2009 when tropospheric ozone fields are strongly constrained by TES tropospheric ozone measurements. The availability of TES measurements is strongly reduced after 2010, which led to a degradation of the reanalysis performance, as demonstrated by Miyazaki et al. (2015).

A major update from the system used in Miyazaki et al. (2015) to the system used in this study is the replacement of forecast model from CHASER (Sudo et al., 2002) to MIROC-Chem (Watanabe et al., 2011), which caused substantial changes in the a priori field and thus the data assimilation results of various species. Microwave Limb Sounder (MLS) retrievals have been updated from v3.3 in Miyazaki et al. (2015) to v4.2 in this study. In addition, we attempt to optimize the surface NOx emission diurnal variability using data assimilation of multiple NO2 satellite retrievals obtained at different overpass times in the updated system (Miyazaki et al., 2017).

The Atmospheric Chemistry Climate Model Intercomparison Project (ACCMIP) focuses on chemistry–climate interactions needed to compute the proper climate forcing for the Climate Model Intercomparison Project Phase 5 (CMIP5) climate simulations (Taylor et al., 2012) as well as the impact of climate change on chemical species. The ACCMIP consists of a series of time-slice experiments for the long-term changes in atmospheric composition between 1850 and 2100, as described by Lamarque et al. (2013). The experimental design was based on decadal time-slice experiments driven by decadal mean sea surface temperatures (SSTs). This study uses the 2000 decade simulation results from 15 models (1. CESM-CAM, 2. CICERO-OsloCTM2, 3. CMAM, 4. EMAC, 5. GEOSCCM, 6. GFDL-AM3, 7. GISS-E2-R, 8. GISS-E2-TOMAS, 9. HadGEM2, 10. LMDzORINCA, 11. MIROC-CHEM, 12. MOCAGE, 13. NCAR-CAM3.5, 14. STOC-HadAM3, 15. UM-CAM). The number of years that the ACCMIP models simulated for the 2000 decadal simulation mostly varied between 4 and 12 years for each model. Each model simulation was averaged over the simulated years.

Meteorological fields were obtained from analyses in CICERO-OsloCTM2 and from climate model fields in MOCAGE. UM-CAM and STOC-HadAM3 simulated meteorological and chemical fields, but chemistry did not affect climate. In all other models, simulated chemical fields were used in the radiation calculations and hence provide a forcing effect on the general circulation of the atmosphere. Lamarque et al. (2013) indicated that most models overestimate global annual precipitation and have a cold bias in the lower troposphere.

Different models vary greatly in complexity. The calculated chemical species vary from 16 to 120 species. Photolysis rates are computed with offline or online methods, depending on the model. Many models include a full representation of stratospheric ozone chemistry and the heterogeneous chemistry of polar stratospheric clouds, but several models specify stratospheric ozone. Methane concentration is prescribed for the surface or over the whole atmosphere in many models. Ozone precursor emissions from anthropogenic and biomass burning sources were taken from those compiled by Lamarque et al. (2010). Natural emission sources such as isoprene emissions and lightning and soil NOx sources were not specified and were accounted for differently between models. There is a large range in soil NOx emissions from 2.7 to 9.3 TgNyr-1 and in LNOx sources from 1.2 to 9.7 TgNyr-1 for the 2000 conditions. The range of natural emissions is a significant source of model-to-model ozone differences (Young et al., 2013). A complete description of the models along with the experiment design can be found in Lamarque et al. (2013).

Both the ACCMIP models and chemical reanalysis are interpolated to a 2∘ × 2.5∘ spatial resolution and 67 levels, following Bowman et al. (2013), and then compared with each other. Spatial correlations are computed with consideration of weighting for the latitude.

Ozonesonde observations were taken from the World Ozone and Ultraviolet Radiation Data Center (WOUDC) database (available at http://www.woudc.org/home.php). All available data from the WOUDC database are used for the evaluation of reanalysis data (Sect. 3), as listed in Table 2. For the evaluation of ACCMIP models and ozonesonde sampling biases (Sects. 4 and 5), we use the ozonesonde sampling based on the compilation by Tilmes et al. (2012), which is shown in bold in Table 2. Because there is no observation after 2003 in Scoresby Sund, this location has been removed from the compilation in this study. The accuracy of the ozonesonde measurement is about ±5 % in the troposphere (Smit and Kley, 1998).

To compare ozonesonde measurements with the data assimilation and ACCMIP models, all ozonesonde profiles have been interpolated to a common vertical pressure grid, with a bin of 25 hPa. The 2-hourly reanalysis and forecast model (i.e., control run) fields were linearly interpolated to the time and location of each measurement, with a bin of 25 hPa, and then compared with the measurements. For the ACCMIP models, the monthly model outputs were compared with the measurements at the location of each measurement. The averaged profile is computed globally and for four latitudinal bands, SH extratropics (90–30∘ S), SH tropics (30∘ S–Equator), NH tropics (Equator–30∘ N), and NH extratropics (30–90∘ N).

The current ozonesonde network does not cover the entire globe and is not homogeneously distributed between the hemispheres, ocean and land, and urban and rural areas. Additionally, the sampling interval of ozonesonde observations is typically a week or longer, which does not reflect the influence of diurnal and day-to-day variations. Model errors are also expected to vary greatly in time and space at various scales. Therefore, the implications of model differences at ozonesonde locations to regional and seasonal processes is uncertain. Thus, we evaluate how changes in evaluated model performance could be obtained by using the complete sampling chemical reanalysis fields instead of the existing ozonesonde network on simulated regional ozone fields.

Sampling bias is an error in a computed quantity that arises due to unrepresentative (i.e., insufficient or inhomogeneous) sampling, which induces spurious features in the average estimates (e.g., Aghedo et al., 2011; Foelsche et al., 2011; Toohey et al., 2013; Sofieva et al., 2014) and long-term trends (Lin et al., 2015). Sampling bias may occur when the atmospheric state within the time–space domain over which the average is calculated is not uniformly sampled. In regions where variability is dominated by short-term variations, limited sampling may lead to a random sampling error. The primary technique for sampling bias estimation is to subsample model or reanalysis fields based on the sampling patterns of the measurements and then to quantify differences between the mean fields based on the measurement sampling and those derived from the complete fields. Sampling bias cannot be negligible, even for satellite measurements (Aghedo et al., 2011; Toohey et al., 2013; Sofieva et al., 2014).

To estimate sampling biases of the ozonesonde network in the ACCMIP model evaluation, two evaluation results of mean model bias are compared using the chemical reanalysis. The first evaluation was conducted based on the complete sampling; the second evaluation used the ozonesonde sampling (in both space and time) that is based on the compilation by Tilmes et al. (2012). By using the 2-hourly reanalysis fields, we can address possible biases due to the limited model sampling (i.e., monthly ACCMIP model outputs were used). Note that the relatively coarse horizontal resolution of the reanalysis may lead to an underestimation of the sampling bias in the model evaluation, because the variability of a sampled field depends on the resolution of the measurement. Tilmes et al. (2012) stated that regional aggregates of individual ozonesonde measurements with similar characteristics are more representative for larger regions; however, this may not mean that evaluation results using the compiled data generate model errors that are representative of actual monthly mean for a surrounding area.

We use the global chemical reanalysis to evaluate the global ozone profiles in ACCMIP simulations. Figure 3 compares the global distribution of the annual mean ozone concentration between the 5-year mean reanalysis and the ensemble mean of the ACCMIP models. The average over the multiple models can be expected to improve the robustness of the model simulation results, because some parts of the model errors may cancel each other out. As summarized in Table 4, the global spatial distributions are similar between the 5-year mean reanalysis field and the ensemble mean when estimated at 2∘ × 2.5∘ spatial resolution, with a spatial correlation (r) greater than 0.94 from the lower troposphere to the lower stratosphere, except for the NH extratropical middle troposphere (r=0.57). The reanalysis and multi-model mean commonly reveal distinct inter-hemispheric differences associated with a stronger downwelling across the tropopause and stronger emission sources of ozone precursors in the NH. The wave-1 pattern in the zonal ozone distribution in the tropics, with a minimum over the Pacific Ocean and maximum over the Atlantic (Thompson et al., 2003; Bowman et al., 2009; Ziemke et al., 2011), can also be commonly found in the reanalysis and the multi-model mean and was also suggested by Young et al. (2013).

Large errors between the reanalysis and the multi-model mean in the troposphere are found in the NH extratropics and SH tropics (right panel in Fig. 3). The multi-model mean overestimates the zonal and annual mean concentrations by 6–11 ppb at 800 hPa and by 2–9 ppb at 500 hPa in the NH extratropics. The overestimation is larger over the oceans than over land at the NH mid-latitudes at 800 hPa. Both the mean RMSE and bias are larger at 800 hPa than at 500 hPa in the NH extratropics, whereas they are larger at 500 hPa in the NH tropics (Table 4). In the SH tropics, the multi-model mean underestimates the concentration over the eastern Pacific by up to 9 ppb, over the Atlantic by up to 18 ppb, and over the Indian Ocean by up to 8 ppb at 500 hPa. These negative biases are larger in the middle troposphere than in the lower troposphere for most places and also for the zonal means in the SH tropics (-15 % in the middle troposphere and -10 % in the lower troposphere; Table 4). Young et al. (2013) consistently revealed the positive bias in the NH and negative bias in the SH using OMI–MLS tropospheric ozone column measurements. At 200 hPa, the multi-model mean underestimates the zonal mean concentration by 20–30 ppb at high latitudes in both hemispheres, with a larger error in the SH than in the NH (Table 4).

Figure 4 shows the Taylor diagram of the ACCMIP models against the reanalysis for three latitudinal bands for three levels. The relevant statistics at 500 hPa are summarized in Table 5, for which the tropics are separated into two hemispheres. In the NH extratropics at 800 hPa, most models reproduced the spatial distribution (r=0.8–0.95), while underestimating the spatial standard deviation (SD) by up to 50 %. Three exceptional models (1, 7, 8) show relatively poor agreements (r=0.45–0.6 and SD underestimations by 50–60 %). At 500 hPa, there is a large diversity in the agreement. Only a few models (2, 4, 9, 11) show close agreement with the reanalysis (r>0.8, SD error < 20 %). Notably, two models (12, 15) reveal too-large spatial variabilities (SD error > 80 %), and five models (1, 6, 7, 8, 12) reveal small spatial correlation (r<0.15). The regional mean bias is largely positive (> 10 ppb) in several models (7, 8, 12; Table 5). In the NH extratropics in the lower and middle troposphere, ozone distributions are modified by various processes, including vertical transport by convection and along conveyor belts, inflow from the stratosphere, long-range transports, and photochemical production (e.g, Lelieveld and Dentener, 2000; Oltmants et al., 2006; Sudo and Akimoto, 2007; Jonson et al., 2010). The evaluation results indicate that these processes occur differently among models. At 200 hPa, all the models simulate well the spatial distribution (r>0.95), whereas the spatial variability differs between the models (SD error ranges from -50 to +30 %). There is relatively large variation in the stratospheric concentration, which results in the diversity in the UTLS, as also discussed by Young et al. (2013).

In the tropics, the spatial correlation is greater than 0.8 at all levels for most models (except for 12, 15), as they capture the wave-1 structure. When dividing the tropics into two hemispheres (Table 5), only a few models (4, 12) reveal low spatial correlation (r<0.8) for the SH tropics (30∘ S–EQ) at 500 hPa. The spatial correlation in the tropics is lower at 500 hPa than at 800 hPa for most models. The SD error is less than 40 % for all the models at 800 and 500 hPa, while mostly overestimating the spatial variability at 800 hPa by up to 30 %. The mean bias is negative for most models at 500 hPa in the tropics in both hemispheres, with larger negative biases in the SH tropics (Table 5). Young et al. (2013) noted that correlations between the biases for the NH and SH tropical tropospheric columns are strong. Similarly, our analysis using the reanalysis reveals a high correlation (0.91) between the NH and SH tropical biases at 500 hPa, suggesting that similar processes are producing the model biases in the tropical middle troposphere between the hemispheres. For instance, biomass burning emissions are handled differently across the models, which may lead to differences in ozone simulations in the tropics (Anderson et al., 2016). At 200 hPa in the tropics, the SD error differs among models, which could primarily be associated with the different representations of convective transports and ozone production by LNOx sources (e.g., Lelieveld and Crutzen, 2007; Wu et al., 2007).

In the SH extratropics at 800 hPa, most models reproduce the spatial distribution (r>0.9), while underestimating the SD by 15–70 %, except for model 15. The model performance is similar between 800 and 500 hPa, with a smaller SD error at 500 hPa for most models. These high spatial correlations may be related to a lack of local precursor emissions in the SH. At 500 hPa, a majority of the models underestimate the mean concentration (Table 5), with large negative biases (< -8 ppb) in several models (1, 2, 12, 14). At 200 hPa, the SD error varies from -80 to +65 %. The large diversity at 200 hPa may be related to the different representation of the tropopause and stratosphere–troposphere exchange (STE) among models.

Figure 5 compares the seasonal variation of zonal mean ozone concentration between the ACCMIP models, the reanalysis, and ozonesonde observations. The comparison between the reanalysis concentrations sampled at ozonesonde sites/time (black dashed line) and the ozonesonde observations (blue solid line) shows that the reanalysis is in close agreement with the ozonesonde observations over the globe, as described in Sect. 3. However, in the NH extratropics at 800 hPa, the reanalysis concentration is too low from boreal spring to summer by up to 4 ppb, which leads to an underestimation of the seasonal amplitude (as estimated from the difference between maximum and minimum monthly mean concentrations). In the NH tropics at 500 hPa, the reanalysis overestimates the concentration, except in April. In the SH tropics at 500 and 800 hPa, the reanalysis slightly overestimates the concentrations throughout the year by up to 5 ppb. In the SH extratropics at 800 hPa, the reanalysis concentration is too low by up to 5 ppb from austral autumn to winter. The reanalysis concentration and seasonal variation differs largely between the complete sampling (black bold line, where the concentrations were averaged over all grid points) and the ozonesonde sampling (black dashed line) for the globe. The impact of using the reanalysis instead of the ozonesonde network in characterizing the ozone seasonal variation is discussed in Sect. 5.

The global ozone concentrations averaged over all grid points with area weights are compared between the ACCMIP models and the reanalysis (black solid line vs. red solid line for the multi-model mean and thin colored lines for individual models). There is considerable interannual variability in both the reanalysis and the ACCMIP models. We confirmed that the ACCMIP ensemble mean is mostly within the standard deviation (i.e., year-to-year variation) of the reanalysis (not shown). In the NH extratropics, the multi-model mean overestimates the monthly mean concentrations by 6–9 ppb at 800 hPa and by 3–6.5 ppb at 500 hPa. The multi-model mean reproduces the seasonal variation, whereas there is large diversity among the models. The increase from winter to spring differs among models at 500 hPa, which is probably associated with different representations of downwelling from the stratosphere. Figure 6 compares the seasonal amplitude. Most models overestimate the seasonal amplitude in the NH lower and middle troposphere, with a mean overestimation of 50–70 % at 800 hPa and 25–40 % at 500 hPa at NH high latitudes. At 200 hPa, the multi-model annual mean concentration is in good agreement with that of the reanalysis, whereas the seasonal amplitude is underestimated by most models at NH high latitudes, with a mean underestimation of 15–25 %.

In the NH tropics at 500 hPa, the multi-model mean underestimates the concentration by 1–4 ppb throughout the year, which can be attributed to the anomalously low concentrations in several models. There is a large diversity among the models in this region. In the SH subtropics, the multi-model mean is lower by up to 5 ppb at 800 hPa and by up to 11 ppb at 500 hPa, with the largest errors occurring in austral spring. A majority of models overestimate the seasonal amplitude in the NH subtropics at 800 hPa (by about 10–40 %), whereas they mostly underestimate the amplitude in the SH tropics at 800 and 500 hPa. In the tropical upper troposphere in both hemispheres, a few models reveal anomalously high or low concentrations. Both the ozonesondes and reanalysis reveal a sharp increase in ozone between March and April in the NH subtropics, which is not captured in the multi-model mean, as suggested by Young et al. (2013).

In the SH extratropics, the multi-model mean and the reanalysis are in good agreement at 800 hPa, whereas it largely underestimates the peak concentration in austral winter–spring at 500 hPa (by up to 7 ppb) and 200 hPa (by up to 35 ppb). The large diversity among the models and the large underestimation in the multi-model mean at 500 hPa in spring could be attributed to the differing influence of stratospheric air. The seasonal amplitude is overestimated at 800 and 200 hPa by most models at SH high latitudes.

Figure 7 compares the inter-hemispheric gradient (NH / SH ratio) of the annual mean ozone concentration. We calculated the gradient of area-weighted ozone concentrations across the Equator; however, we recognize a more careful definition of the boundary between the two hemispheres would be required to isolate air masses originated from each hemisphere (e.g., Hamilton et al., 2008). For the estimation of the gradient using the ozonesonde observations, we made a gridded dataset from the ozonesonde observations based on the completion by Tilmes et al. (2012) at 2∘ × 2.5∘ spatial resolution and then calculated area-weighted hemispheric mean concentrations using the gridded dataset. The gradient is similar between the ozonesonde observations (blue solid line) and the reanalysis concentration from the ozonesonde sampling (black dashed line) throughout the troposphere. In these estimates, the NH mean concentration is higher than the SH mean by 60–70 % in the lower troposphere, by 30–40 % in the middle troposphere, and by 55–60 % around 200 hPa. Near the surface, the reanalysis slightly overestimates the NH / SH ratio, mainly because of overestimated concentrations at the NH mid-latitudes.

By taking a complete sampling in the reanalysis (i.e., averaging over all model grid points for each hemisphere; black solid line), the NH / SH ratio becomes smaller by about 25–30, 7–10, and 15–25 % in the lower troposphere, the middle troposphere, and around 200 hPa, respectively, compared to the average at the ozonesonde sampling sites (black dashed line). The difference is a consequence of ozonesonde stations located near large cities at NH mid-latitudes, and they therefore tend to observe higher ozone concentration than the hemispheric average. At around 200 hPa, the difference could also be attributed to the presence of atmospheric stationary waves and Asian monsoon circulation in the NH, which result in substantial spatial ozone variations in the UTLS (e.g., Wirth, 1993; Park et al., 2008; cf. Fig. 3). The annual mean NH / SH ratios based on the global reanalysis field estimated at the surface, 800, 500, and 200 hPa are 1.36, 1.42, 1.30, and 1.35, respectively.

Most models overestimate the NH / SH ratio compared with the reanalysis, with a mean overestimation (black solid line vs. red solid line) of 34 % at the surface and 22–30 % in the free troposphere, attributing to both too-high concentrations in the NH extratropics and too-low concentrations in the SH subtropics in most models (cf. Figs. 3 and 5). The multi-model mean reveals annual mean NH / SH ratios of 1.71, 1.73, 1.54, and 1.49 at the surface, 800, 500, and 200 hPa, respectively. The large systematic error in the NH / SH ratio suggests that, for instance, the inter-hemispheric distribution of radiative heating due to tropospheric ozone in chemistry–climate simulations are largely uncertain in most models, and such comprehensive information for different altitudes in the troposphere cannot be obtained using any individual measurements, as is further discussed in Sect. 6.3.

The model evaluation results differ greatly for many regions between the complete sampling and the ozonesonde sampling, as shown by Fig. 9 and summarized in Table 8. The sampling bias is evaluated using the median of the multiple models to provide robust estimates of the model performance. For the NH polar regions, Tilmes et al. (2012) stated that separating the regions into eastern and western sectors reduces the variability in ozone within each region because long-range transports of pollution from low and mid-latitudes into high latitudes shows longitudinal variations in the NH (e.g., Stohl, 2006). Comparisons further suggest that, except for the UTLS in winter (December–February, DJF), the evaluated model performance using the ozonesonde measurements is representative of the surrounding regional and seasonal mean model performance. For the two NH polar regions at 200 hPa in DJF, the validation based on the ozonesonde sampling reveals a large negative sampling bias in the model bias as compared with regional and monthly means. Large negative model biases against the ozonesonde observations have been reported by Young et al. (2013) for 250 hPa (by about -13 % for the NH polar west and -18 % for the NH polar east for the annual mean concentration), whereas results from this study suggest that these errors based on the ozonesonde sampling (by -14 % for the NH polar west and -18 % for the NH polar east in DJF in our estimates) are larger than those from regional and seasonally representative model bias (by -3 and +5 %, respectively). At 500 hPa, the ozonesonde network reveals a negative sampling bias for the NH polar east in DJF. Thus, the positive bias reported in Young et al. (2013) for the NH polar east at 500 hPa may be lower than regional and seasonally representative model biases. Our analysis using monthly reanalysis fields sampled at the ozonesonde locations (brackets in Table 8) suggests a greater impact of the spatial sampling bias than the temporal sampling bias for the NH polar east in DJF. The large discrepancy between the two estimates in the UTLS model performance can be attributed to the large variability of ozone distribution and associated model errors on a regional and seasonal scale.

For Canada, large differences (> 30 %) exist in the two evaluations in the lower troposphere and for the UTLS in DJF and for the middle troposphere in March–May (MAM). The ozonesonde measurements reveal a large negative sampling bias in the model evaluation in DJF at 200 hPa (-4 % in the complete sampling and -25 % in the ozonesonde sampling), while they reveal a negative sampling bias (by about 50 %) at 500 hPa in MAM. At 500 hPa over Canada, the relative importance of the spatial and temporal sampling biases varies with season: the spatial (temporal) sampling bias is dominant in DJF (JJA), whereas both of them are important in MAM. Similar differences between the two evaluations are found for western Europe at 500 and at 200 hPa in DJF. These results suggest that, for instance, the positive bias for western Europe estimated by Young et al. (2013) may be lower than regional and seasonally representative model bias, even for such a small area. The smaller discrepancy between the two estimates for western Europe as compared with Canada for most cases could be associated with the better coverage of the ozonesonde measurements for western Europe. Even for the small area of the eastern United States, the two validations differ largely in the UTLS (e.g., -9 % in the ozonesonde sampling and +6 % in the complete sampling at 200 hPa in MAM) and at 500 hPa in MAM, JJA, and September–November (SON). In the NH subtropics, the two evaluations disagree largely in the middle and upper troposphere in JJA and SON.

The tropical stations were separated into the three sub-regions: western Pacific and east Indian Ocean, equatorial America, and the Atlantic Ocean and Africa. These regions reflect the different dominant tropical processes including biomass burning and lightning over the Atlantic and Africa. The large variability of tropical ozone and its associated model error, together with the sparse ozonesonde network in these regions, results in large discrepancies between the two evaluations in the tropical regions. At 500 hPa, the ozonesonde measurements reveal a large (by 40–50 %) negative sampling bias in MAM and a positive sampling bias in DJF over the western Pacific and east Indian Ocean, whereas it shows a large negative sampling bias (by 110 %) in MAM over the equatorial Americas. Over the western Pacific and east Indian Ocean, the sampling bias is not reduced by using monthly mean reanalysis fields (sampled at the ozonesonde locations) in DJF and JJA. This suggests that ozone varies with time and space in a complex manner, and a dense (in both space and time) network would be required to capture the regional and seasonally representative model biases in this region. The probability distribution function (PDF) estimated using monthly mean reanalysis and model fields also differs largely between the two samplings (Fig. 10). Over the western Pacific and east Indian Ocean in SON at 500 hPa, the multi-model mean shows a sharp peak around 54–58 ppb, in contrast to the broad distribution seen in the reanalysis with two peaks around 65 and 35–45 ppb for the complete sampling (left bottom panel in Fig. 10). This information is useful to characterize model errors and for process-oriented model validation. On the other hand, the validation based on the ozonesonde sampling (left top panel) does not show any clear pattern and does not support model evaluation. Note that the influence of interannual variability was not considered in the analysis because the monthly climatological data were used by averaging over 10 years for the models and 5 years for the reanalysis.

Although the variability of ozone is generally smaller in the SH than in the NH because of smaller local precursor emissions, large sampling biases exist even at SH mid- and high latitudes due to the sparse ozonesonde network. In the SH mid-latitudes, for example, the sign of the evaluated bias is opposite between the two cases at 200 hPa in DJF (-2.8 ppb in the complete sampling and +25.1 ppb in the ozonesonde sampling). In the SH high latitudes, evaluation results differ largely throughout the year in the middle troposphere. The temporal sampling bias mostly dominates the difference in the SH high latitudes in MAM and JJA, whereas the spatial sampling bias is also important in the SH mid-latitudes in DJF and MAM. Based on the complete sampling, the ozone PDF is broadly distributed with a peak around 38 ppb at 500 hPa in SON at the SH high latitudes (right bottom panel in Fig. 10), while the multi-model mean underestimates high concentrations (> 47 ppb) and shows a sharp peak of about 35 ppb. The PDF generated by the ozonesonde sampling does not provide a strong information on the distribution of the ozone (right top panel). These results highlight the advantage of using the reanalysis data for evaluating regional and seasonally representative model performance and for characterizing these distributions.

Table 8 also shows the model evaluation results for four latitudinal bands at 500 hPa. The observations used are shown in bold in Table 2. The differences between the two evaluations are small in the NH extratropics (30–90∘ N) in all seasons, because of the relatively large number of observations. There are large differences in the tropics of both hemispheres: the ozonesonde network reveals a large negative sampling bias in the model evaluation in the NH tropics (Eq–30∘ N) in SON (-9 % in the complete sampling and -16 % in the ozonesonde sampling) and in the SH tropics (30∘ S–Eq) in MAM (-14 and -21 %) and a large positive sampling bias in the NH tropics in JJA (-7 and -3 %). Large sampling biases (> 60 %) also exist in the SH extratropics (90–30∘ S) in DJF and MAM due to the sparse ozonesonde network.

Further, ozonesonde sampling bias is evaluated for the control run and reanalysis comparisons. As summarized in Table 9, at 500 hPa, there are large differences (> 30 %) between the two evaluations in many regions, especially in the NH mid-latitude regions in winter and in the tropics throughout the year, as also found in the ACCMIP models and reanalysis comparisons (Table 8). The analysis increments introduced by data assimilation vary with space and time, reflecting the changes in coverage and uncertainty of assimilated measurements as well as in model errors. Nevertheless, observational information was propagated globally and integrated with time through forecast steps during the data assimilation cycles. This is true for ozone because of its relatively long lifetime in the free troposphere. Therefore, the spatial distribution is well constrained by data assimilation, and we do not expect large variations in the reanalysis quality within each analysis region.

The seasonal cycle of tropospheric ozone is determined by various factors such as local photochemical production and atmospheric transport (e.g., Monks, 2000). Carslaw (2005), Bloomer et al. (2010), and Parrish et al. (2013) found multi-decadal changes in the amplitude and phase of the seasonal cycle at NH mid-latitudes. It was suggested that these changes can be attributed to changes in atmospheric transport patterns combined with spatial and temporal changes in emissions. CTMs have been used to explore the causal mechanisms; however, they failed to simulate several important features of the observed seasonal cycles (e.g., Ziemke et al., 2006; Stevenson et al., 2006; Parrish et al., 2014; Young et al., 2013). Accurate validation of the seasonal cycle is thus important for evaluating general model performance.

Table 10 compares the relative error in the seasonal amplitude obtained from the multi-mean model with that of the reanalysis for the complete and ozonesonde samplings. The evaluation based on the ozonesonde sampling results in a larger overestimation of the seasonal amplitude in the NH lower troposphere for most regions (+13.4–+63.4 % in the sonde sampling and -19.0–+40.2 % in the complete sampling). The large discrepancies can be attributed to large spatial variability in the seasonal variations of ozone and its model errors within each defined region and also to the existence of short-term variability that is not completely captured by the ozonesonde sampling. For the eastern US and western Europe at 800 hPa, the sign of the bias is opposite between the two estimates. In contrast, at 200 hPa in the NH, results between the two evaluations are similar, suggesting spatial homogeneity in the seasonal cycle and its model errors within each region in the NH. Because the seasonal variations differ among different regions, the seasonal amplitude estimated for the entire NH extratropics (30–90∘ N) is largely different between the two estimates throughout the troposphere.

In the tropics, the estimated errors of the seasonal amplitude largely differ between the two samplings throughout the troposphere, suggesting that information obtained from the sparse ozonesonde network cannot be applied to characterize regional model errors in the seasonal cycle, even within the small defined area. The sampling bias in the seasonal amplitude estimated for the entire tropics is larger than 60 % throughout the troposphere both in the NH (Eq–30∘ N) and SH (30∘ S–Eq). Because of the large spatial variability, detailed validations using the chemical reanalysis (e.g., for each grid point) would be helpful. Additionally, in the SH high latitudes, large disagreements in the seasonal amplitude exist at 800 and 200 hPa.

Although the reanalysis dataset provides comprehensive information for global model evaluations, its performance still needs to be improved, especially for the lower troposphere, as also discussed by Miyazaki et al. (2015). Performance can be improved by ingesting more datasets including meteorological sounders such as IASI (Clerbaux et al., 2009), AIRS (Chahine et al., 2006), and CrIS (Glumb et al., 2002). Application of a bias correction procedure for multiple measurements, which is common in numerical weather prediction (e.g., Dee, 2005), is needed to improve reanalysis accuracy. Recently developed retrievals with high sensitivity to the lower troposphere (e.g., Deeter et al., 2013; Fu et al., 2016) and the optimization of additional precursor emissions would be helpful to improve analysis of the lower troposphere. The relatively coarse resolution of the model could cause large differences between the simulated and observed concentrations at urban sites and may degrade the reanalysis.

The statistical information obtained from the reanalysis and the multi-model simulations can be used to suggest further developments for the models and observations. The analysis ensemble spread from EnKF can be regarded as uncertainty information about the analysis mean fields, indicating requirements for additional observational constraints. As shown in Fig. 11 (left panels), the relative reanalysis uncertainty is large over the tropical areas of the oceans at 800 hPa (> 20 %), over the Southern Ocean at 500 hPa (10–20 %), and over the tropics of the Pacific Ocean and the Antarctic at 200 hPa (> 16 %). Conversely, the reanalysis uncertainty is small from the tropics to mid-latitudes in both hemispheres at 500 hPa (< 11 %). Miyazaki et al. (2015) investigated that the analysis spread is caused by errors in the model input data, model processes, and assimilated measurements, and it is reduced if the analysis converges to a true state. The analysis spread is smaller in the extratropical lower stratosphere than in the tropical upper troposphere at 200 hPa, because of the high accuracy of the MLS measurements. In contrast, in the middle troposphere, the analysis spread is generally smaller in the tropics than the extratropics because of the higher sensitivities in the TES retrievals. Note that the data assimilation setting influences the analysis uncertainty estimation in the reanalysis. In particular, the analysis spread was found to be sensitive to the choice of ensemble size (Miyazaki et al., 2012b). A large ensemble size is essential to capture the proper background error covariance structure (i.e., analysis uncertainty).

The 5-year reanalysis (2005–2009) may cause biases in the estimated model errors in the evaluation of the 2000 decade ACCMIP simulations that used decadal-averaged SST boundary conditions and biomass burning emissions averaged over 1997–2006 (Lamarque et al., 2010). It may neglect the influences of interannual and decadal changes in both anthropogenic and biomass emissions and meteorology. Longer-term reanalysis and time-consistent validation are required to obtain more robust error estimations.

The variability across the ensemble models (i.e., ensemble spread) identifies where the models are most consistent or uncertain (center panels in Fig. 11). As discussed by Young et al. (2013), the relative spread among the ACCMIP models is large over the tropical areas of the oceans in the lower and middle troposphere, which is a reflection of the important differences among the models in various processes such as convective processes, lightning sources, and biogenic emission sources with related chemistry. The large relative spread (> 20 %) at the NH mid-latitudes and in the SH at 200 hPa may be associated with the different representations of the tropopause and STE among models. In contrast, the relative spread is small around 20–40∘ N at 500 hPa (< 10 %).

The simultaneous enhancement of the analysis uncertainty (cf. Sect. 6.1), together with the model spread, indicates low robustness of the validation results for some tropical regions over the oceans in the lower troposphere and over the tropics in the Pacific Ocean as well as the Antarctic at 200 hPa. Meanwhile, the magnitudes of the model spread and analysis uncertainty differ considerably for some regions. At 200 hPa and higher in the extratropics, the analysis uncertainty is smaller than the model spread, where the reanalysis fields are strongly constrained by MLS measurements. These results suggest that further improvements, for instance, on the representation of the tropopause and STE are required for some of the models, in order for the reanalysis and ensemble models to have similar levels of uncertainty. In the lower troposphere, in contrast, the larger analysis uncertainty than the ensemble spread suggests that further observational constraints are required for the reanalysis for a fair comparison.

The ACCMIP model standard deviation with respect to the reanalysis could be used to identify the averaged uncertainty of ACCMIP models (right panels in Fig. 11). The standard deviation is large at NH high latitudes and over the tropical ocean areas at 800 hPa, over the SH tropics at 500 hPa, and in the SH extratropics at 200 hPa (> 25 %).

Numerous studies have identified decadal-scale changes in global tropospheric ozone using observations, such as the shift in the seasonal cycle at NH mid-latitudes and trends observed over many regions (e.g., Parrish et al., 2014; Cooper et al., 2014). A long record of the reanalysis will allow detailed structures in simulated interannual and long-term variations to be evaluated in association with changes in human activities and natural processes. However, any discontinuities in the availability and coverage of the assimilated measurement will affect the quality of the reanalysis and estimated interannual variability, which limit the usability of a long-term reanalysis for model evaluation, as discussed in Miyazaki et al. (2015) for chemical reanalyses and in Thorne and Vose (2010) for climate reanalyses. This also requires a bias-correction procedure for each assimilated measurement, in order to improve the reanalysis quality (Inness et al., 2013). It is noted that the influence of ENSO was not considered in ACCMIP due to a decadal-averaged SST boundary condition, which limits the evaluation of interannual variations and could lead to bias in the ACCMIP models and reanalysis comparisons.

Process-oriented validations using the reanalysis would be useful for understanding the uncertainty in simulated ozone fields and associated mechanisms. The ACCMIP models reveal large variations in short-lived species such as OH and ozone precursors (Naik et al., 2013; Voulgarakis et al., 2013), whereas information obtained from direct in situ measurements cannot be applied for investigating global distributions because of the limited coverage of the measurements and the large spatial variability of concentrations. Miyazaki et al. (2012b, 2015) demonstrated that the multiple-species assimilation results in a strong influence on both assimilated and non-assimilated species. Validation of various species using the chemical reanalysis product can be used to identify potential sources of error in the simulated ozone fields. Meanwhile, the global monthly products of precursor emissions from the chemical reanalysis calculations (Miyazaki et al., 2012a, 2014, 2017) can be used to validate emission inventories and LNOx source parameterizations used in model simulations. As changes in tropospheric ozone burden associated with different future scenarios show a broadly linear relation to changes in NOx emissions (Stevenson et al., 2006), evaluations using up-to-date estimated emissions (Miyazaki et al., 2017) may prove useful to partly validate emissions for each scenario.

The performance of the simulated radiative forcing is largely influenced by representation of ozone in model simulations (Bowman et al., 2013; Shindell et al., 2013; Stevenson et al., 2013). Bowman et al. (2013) suggested that overestimation of the outgoing longwave radiation in the tropical seas of the east Atlantic Ocean and over southern Africa is associated with model ozone errors, a persistent feature in all ACCMIP models, which was also found in this study using the reanalysis. Validation of short-lived species is also important for evaluating the radiative forcing because simulated OH fields influence simulated climates through, for instance, their influences on methane (Voulgarakis et al., 2013). Thus, detailed information on model errors in ozone and other short-lived species could be used to improve estimates of radiative forcing in climate studies. Meanwhile, model biases for present-day ozone may be correlated with biases in other time periods. Young et al. (2013) showed that ACCMIP models with high, present-day ozone burdens also had high burdens for the other periods of time, including the preindustrial period. Thus, the validation of present-day ozone fields using the reanalysis has the potential to evaluate preindustrial to present-day ozone radiative forcing.