The photochemical O3 production and destruction depend strongly on solar illumination, which changes systematically for a location during the course of a day, resulting in diurnal variation in O3 vertical profiles , but existing O3 profile climatologies have not included O3 profile dependence on local solar time. Remote sensing O3 measurements are collected at different local solar times, even from the same instrument, such as the DSCOVR EPIC, which observes the Earth from sunrise to sunset simultaneously . Proper accounting for the diurnal variations in O3 vertical distribution would enable more accurate O3 retrieval from remote sensing observations. Therefore we construct a local-solar-time-dependent O3 profile climatology from the MERRA-2 O3 field.

We divide the globe equally into 24×18 rectangle tiles, and each has the size of 15∘ longitude × 10∘ latitude. Monthly mean profiles and their variances are calculated from samples that fall within a tile at the eight UTC times of the MERRA-2 O3 field. Note that data samples are weighted by the cosine of latitude in performing the statistics to ensure equal weighting by area. Since each climatological profile of a tile is compiled from O3 profiles at the same UTC, it represents an hourly mean because a tile's 15∘ longitude range is equivalent to 1 h of local solar time (LST).

Figure 2 shows the sample O3 profiles from the MERRA-2 local-solar-time-dependent climatology, illustrating the diurnal, seasonal, and latitudinal variations in O3 vertical distributions. Each panel in Fig.  contains plots of eight climatological O3 mixing ratio profiles for a tile next to and east of the prime meridian, for eight different 1 h LST periods. The differences among the curves in a panel reveal the diurnal O3 mixing ratio changes, which in general increase significantly with altitude from the upper (Z*≳30 km) stratosphere into the mesosphere (Z*≳50 km). The O3 mixing ratio level in the mesosphere reaches its minimum after sunrise but then increases after sunset, recovering its nighttime value quickly, while in the stratosphere where the peak value of O3 mixing ratio is located (Z* between ∼35 and 40 km), O3 diurnal cycle has its maximum in the afternoon and a lower value close to its minimum in the morning. The diurnal variations, which are mainly driven by photochemistry in the upper atmosphere, exhibit a strong latitudinal (panel rows in Fig. ) and seasonal (panel columns) dependence, as expected from the variations in solar insolation with the latitude and the season. The mean nighttime O3 mixing ratio can be an order of magnitude higher than the daytime value in the mesosphere at Z*=70 km. In general, the magnitude of diurnal difference reduces with the altitude, with a maximum of ∼7 % near the stratospheric O3 mixing ratio peak. In the troposphere, the cycle of diurnal variation changes with season and location, with a peak-to-trough difference usually less than 5 % in the lower troposphere. These significant diurnal O3 mixing ratio variations correspond to typically 0.5 % and a maximum of ∼4 % peak-to-trough differences in diurnal variation in total O3 vertical column. The variability of the tropospheric O3 profile, including the diurnal cycle, is mostly subdued in the MERRA-2 O3 field because the assimilation captures only the average behavior of tropospheric O3 but not its variation realistically, a consequence of the limited tropospheric O3 information contained in the source data (OMI columns and MLS profiles). The results for the mesosphere and stratosphere are in general consistent with previous findings of O3 diurnal variations and references therein. Thus, this local-solar-time-dependent climatology correctly captures diurnal variation in upper-atmospheric O3 vertical distributions.

Tropopause altitude varies with month and latitude systematically  and is usually highest in the tropics and drops toward the poles with steep declines in the midlatitudes but exhibits hemispheric asymmetry (e.g., see Fig. ). This figure also illustrates that the dynamic variability of tropopause altitude is characterized by daily standard deviations of approximately 1–2 km, which agrees well with the characterization by . Since O3 concentration is highest in the lower stratosphere above the tropopause and decreases rapidly in the troposphere, the large short-term fluctuation of tropopause altitude results in high variability in the total O3 column, accounting for ∼60 % of its daily variation . Thus grouping O3 profiles according to the tropopause pressure or altitude generates climatological profiles that reflect the dynamical influences on O3 vertical distributions, as demonstrated by the tropopause-altitude-classified O3 profile climatology (named the TPO3 climatology) created by using ozonesonde and SAGE-II data.

Similarly, we create a tropopause-pressure-classified O3 profile climatology (referred to as M2TPO3 climatology hereafter) using the MERRA-2 O3 record, which provides a large number of data covering a diverse range of conditions, likely including all possible tropopause pressures. These mean profiles and their variances are calculated by statistically analyzing the sets of MERRA-2 O3 profiles at the same UTC time, binned by tropopause pressure in 1 km pressure altitude (Z*) steps, calendar month, and 15∘ × 10∘ longitude–latitude tiles. To compare the M2TPO3 with the TPO3 , we create a daytime zonal mean climatology by combining M2TPO3 tiles with the same latitude zone and LST from 09:00 through 17:00. The resulting daytime climatology contains 2154 mean profiles and standard deviations (shown in Appendix A), spanning the range of tropopause pressure (altitude) from 605 hPa (3.56 km) to 62 hPa (19.3 km), distributed in 12 calendar months and 18 10∘ latitude zones that cover the latitude range from -90 to 90∘.

Figures  and display a subset of daytime M2TPO3 profiles and standard deviations and their comparisons with those of TPO3 . The results in Fig.  show that both M2TPO3 and TPO3 have similar O3 profile shapes for similar tropopause altitudes in each month–latitude class. Especially in the tropics, M2TPO3 and TPO3 show very close profiles that are nearly independent of tropopause altitude and season. For profiles at higher latitudes, Fig.  illustrates that the profile change associated with tropopause altitude variation occurs mostly below the O3 concentration peak, exhibiting increasing UTLS O3 with lower tropopause altitude. The O3 column amounts (displayed in the figure legends) of TPO3 profiles are generally (about 1 % to 4 %) higher than the corresponding M2TPO3 profiles. This comparison indicates that there is likely a slight positive bias in the total columns in the TPO3 climatology since MERRA-2 total O3 columns have a latitude-dependent (up to 2 %) low biases . Comparing with the TPO3, there are more tropopause pressure bins with sufficient samples for reliable statistics, and hence more M2TPO3 profiles corresponding to a broader range of tropopause altitudes in each month–latitude class. Under the O3 hole condition, strong O3 spatial variations sampled differently by ozonesondes likely contribute to significant profile differences between M2TPO3 and TPO3 (see Fig.  lower left panel). Note that TpO3 is binned in 1 km tropopause altitude steps, and the corresponding legend shows the midpoint of the altitude bin. Consequently, the tropopause altitude in the legends of Fig.  changes regularly (in 1 km steps). On the other hand, M2TOP3 is binned in 1 km Z* tropopause pressure altitude steps, and the average tropopause altitude of the binned profiles is displayed in the corresponding legend. This average value does not change regularly from one bin to the next because the distribution of tropopause altitude is not necessarily symmetric with respect to the bin center.

The standard deviations in Fig.  show similar magnitudes and vertical structures between the M2TPO3 and the TPO3 profiles with similar tropopause altitudes, demonstrating that the M2TPO3 climatology represents O3 variability realistically. The main differences occur in the lower troposphere of tropical latitude zones, where TPO3 shows higher variability than the M2TPO3, due to ozonesondes better capturing the influence from tropospheric O3 productions, which are not explicitly included in the MERRA-2 reanalysis. Significant differences are also observed over polar latitude zones (90–80∘ S and 80∘ N–90∘ S), likely due to differences in sampling over highly inhomogeneous spatial distributions in these zones.

Results in Fig.  show that the standard deviations of the high-occurrence profiles are in general smaller than those for the downgraded (monthly zonal mean) profile, indicating that tropopause pressure is a good predictor of O3 profile shape, leading to a more accurate profile specification than simply taking the monthly zonal mean profile.

The comparison in this section shows overall good agreement of the M2TPO3 means and standard deviations versus those of the TPO3, with an expected discrepancy in the O3 variability in the tropical lower troposphere, validating the realism of MERRA-2 O3 record and its suitability for climatology construction.

The tropopause-pressure-dependent O3 profiles contained in the M2TPO3 climatology capture profile changes resulting from short-term meteorological disturbances in the UTLS region. The near-linear relationship between mean total column O3 and tropopause altitude (e.g., see legend tables in Fig. ) quantified for each month–latitude class implies that the total column O3 may serve as a good predictor of O3 profile shape as well. Grouping profiles by total column O3 may actually better capture O3 distribution and variability driven by both dynamical and chemical processes; we therefore create a total-column-classified O3 profile climatology (referred to as the M2TCO3 climatology hereafter) from the long-term MERRA-2 O3 record.

The M2TCO3 climatology is constructed by binning the MERRA-2 O3 field at the same UTC time by total column in 25 DU steps, calendar month, and 15∘ × 10∘ longitude–latitude tiles. To compare the M2TCO3 with the TOMS-V8 , we create a daytime zonal mean climatology by combining M2TCO3 tiles with the same latitude zone and LST from 00:09 through 17:00. The resulting climatology contains 1644 mean profiles and standard deviations (shown in Appendix A), spanning the range of total O3 from 94 to 584 DU, distributed in 12 calendar months and 18 latitude zones that cover the latitude range from -90 to 90∘. Figure  displays a subset of daytime M2TCO3 profiles and the corresponding TOMS-V8 profiles, illustrating the distinct characteristics of O3 vertical distributions, as well as significant differences between the two climatologies. Both M2TCO3 and TOMS-V8 profiles exhibit higher altitudes of O3 peak with lower O3 columns for a month–latitude class, lower peak altitudes with higher latitudes for a total O3 column, narrow dynamical O3 ranges and nearly identical profile shapes for different seasons in the tropics but higher seasonal and dynamical variations in midlatitude and high-latitude regions, and hemispherical asymmetry.

The differences between M2TCO3 and TOMS-V8 (shown in each panel of Fig. ) reflect the improvements in the realism of O3 profile representation with the M2TCO3 climatology. The column-averaged TOMS-V8 profiles are represented by the LLM climatology , which is updated to the (ML) climatology, and are very close to the downgraded M2TCO3 profiles (see comparisons in Figs.  and ). Therefore the differences between M2TCO3 and TOMS-V8 profiles shown in Fig.  are attributed to the profiles deviations applied to the mean derived from the standard column-dependent profiles of TOMS-V8 , which are independent of season, coarse in latitude resolution, and symmetric with respect to the Equator. These deficiencies limit the realism of TOMS-V8 climatological profiles, and are eliminated with the new M2TCO3 climatology, which provides improved O3 profile representation that better captures profile changes associated with column variations and their dependence on season and latitude.

The total O3 range of the TOMS-V8 climatology is the same as the set of TOMS-V8 standard (annual mean) profiles. These preset (latitude-zone-dependent) ranges may be different (narrower or broader) than those of M2TCO3 at some months and latitude zones (see Fig. ), but they are likely inconsistent with actual O3 range due to the imposition of annual O3 range on the monthly variation.

Figure  shows the standard deviations of a subset of M2TCO3 profiles with high (>5 %) occurrence percentage and comparisons with those of M2TPO3. A vast majority of high-occurrence climatological profiles of M2TCO3 and M2TPO3 shown in Fig.  exhibit significantly reduced standard deviations compared to those of monthly zonal mean (i.e., downgraded) profiles, illustrating that both tropopause pressure and total column O3 provide information for more precise specification of O3 profiles. Comparisons between M2TPO3 and M2TCO3 show that column classification usually leads to greater reductions in standard deviations in the upper stratosphere but smaller ones in the UTLS than tropopause pressure classification. Since there is much more O3 in the upper stratosphere than below, an overall more realistic specification of the O3 profile is achieved using the M2TCO3 climatology based on the total column O3 than using the M2TPO3 based on the tropopause pressure. Hence the column-dependent climatology is most appropriate in mapping between the O3 column and vertical profile needed in total O3 column retrieval algorithms. However, with the knowledge of tropopause pressure, the tropopause-dependent climatology usually provides closer matches to actual profiles and stronger constraints in the UTLS; therefore its usage significantly improves the accuracy of O3 profile retrieval  from backscattered UV measurements, which have lower vertical resolutions in the troposphere than in the stratosphere .

Previous O3 climatologies e.g., used in O3 profile retrievals include profile standard deviations but not information about O3 profile covariance because their sources (ozonesonde and satellite measurements) have limited coincident samples to quantify the joint O3 variability between different altitudes throughout the atmosphere. In contrast, the MERRA-2 assimilation provides complete profiles simultaneously, allowing direct statistical computation of profile covariance matrices. We expand the classification analysis to quantify the O3 profile covariance. Specifically, we construct an O3 profile covariance matrix from each bin used for the calculation of an M2TPO3 or M2TCO3 climatological profile. The resulting covariance climatology first provides quantification of O3 vertical distribution variabilities, the correlations among different levels, and their dependence on tropopause pressure or total column O3 for different months and longitude–latitude tiles.

Figure  shows a subset of correlation matrices, which are standardized, i.e, diagonal element normalized to covariance matrices, from the daytime M2TPO3 and daytime M2TCO3 climatologies. These density plots highlight the varying degree of level-to-level correlations and their contrasts with the diagonal-constant matrices typically used in O3 profile retrievals e.g.,, which assume positive layer-to-layer correlation that decreases monotonically and exponentially with distance between layers. Contrary to this typical assumption, Fig.  illustrates that the degree of correlation between two levels fluctuates with the level separation and negative correlations are quite common.

The quantification of O3 profile covariance offers a new way to represent O3 vertical distribution realistically and efficiently. Figure  shows the first three leading empirical orthogonal functions (EOFs), which are the ordered set of eigenvectors for each covariance matrix shown in Fig. . Typically the first three leading EOFs combined explain between 65 % and 85 % of the class variance, and the first 15 leading EOFs account for over 95 % of the class variance. Much like a climatological profile describes the likely O3 vertical distribution, the EOFs describe the most probable patterns of profile deviations from the climatological mean. In general, an O3 profile X can be expressed as 1X=Xm+∑k=1nωkek, where Xm is a climatological mean profile, ek the kth EOF, ωk the kth coefficient, and n the total number of EOFs with its maximum limited to the number of levels used to represent the O3 profile. Since a high fraction of class variance may be explained with just a few leading EOFs, they provide the most efficient adjustments to improve the representation of O3 profile when it deviates from the climatological mean. When interpreted physically, the leading EOFs correspond to processes of O3 accumulation, reduction, or redistribution. For instance, the first three EOFs for an M2TPO3 covariance matrix (see Fig. a) describe (1) column increase or decrease, represented by the EOF-1 (monopole) pattern, (2) up or down shift of a profile, represented by the EOF-2 (dipole) pattern, showing O3 increase at one altitude and decrease at another, and (3) shrink or stretch of a profile, represented by the EOF-3 (tripole) pattern, showing O3 decrease (increase) at one altitude and increase (decrease) at adjacent (above and below) altitudes. The results in Fig. a indicate that the highest or the second highest contribution to the variance of a tropopause class originates from the total column variation. However, the highest contribution to the variance of a total column class comes from O3 profile shift, represented by EOF-1 (dipole) in Fig. b, usually linked with tropopause variation, since the dominant profile change resulting from column variation is accounted for with different O3 column classes. The second EOF (tripole) of an M2TCO3 covariance matrix describes the shrink or stretch of a profile, similar to the third EOF of an M2TPO3 matrix, while subsequent EOFs describe more complex rearrangement of the O3 profile.

Using the same binning schemes employed in the O3 profile climatologies, we create temperature profile climatologies from the MERRA-2 assimilated atmospheric temperature field. The resulting climatologies contain the mean and covariance of temperature profiles, paired with the respective M2TPO3 and M2TCO3 climatological O3 profiles.

Figure  shows sample MERRA-2 climatological temperature profiles corresponding to the sample M2TCO3 climatological O3 profiles shown in Fig. , and the O3–temperature correlation profiles for the sample month–latitude classes. These results illustrate the systematic behavior among O3 column amount, tropopause altitude, and atmospheric temperature: higher O3 column amounts occur with a warmer lower stratosphere and a colder troposphere, the condition for lower tropopause altitudes. This relationship, as well as its dependence on season and latitude, is captured in the MERRA-2 O3 and temperature climatologies and is consistent with the findings of long-term O3 and temperature profile measurements .

Results in Fig.  also reveal a significant north–south asymmetry in climatological temperature profiles. For instance, the stratospheric temperatures in the austral spring (e.g., see the October panel) in the southern polar region (90–80∘ S) are significantly lower than those in the boreal spring (e.g., see the April panel) in the northern polar region (80–90∘ N), and these temperature differences are associated with lower total O3 columns in the Antarctic than those in the Arctic.

The profile of correlation coefficient in each panel of Fig.  illustrates a mutual relationship between O3 concentration and atmospheric temperature. From the upper (Z*≳35 km) stratosphere to the lower mesosphere (Z*≲60 km), O3 and temperature are mainly negatively correlated because in this region O3 concentration is mostly governed by photochemical reactions, for which higher temperature speeds up the rate of O3 destruction. From the lower stratosphere down to the upper troposphere (10 km ≲Z*≲ 35 km) in which O3 concentration is controlled primarily by atmospheric motions , O3 and temperature are positively correlated since higher O3 concentrations likely occur from adiabatic air parcel compression, which increases the parcel temperature as well, and additionally higher O3 concentrations absorb more UV radiation, thus raising the atmospheric temperature. The positive correlation quickly becomes negative as the altitude descends into the lower troposphere (Z*≲ 10 km), but swings back and may become positive as the altitude falls further. In general, the degree of O3–temperature correlation is smaller in the lower troposphere than in the atmosphere above, indicating a weaker connection between them.

The pattern of negative correlation above the upper stratosphere and the positive correlation in the upper troposphere and lower stratosphere between O3 and temperature fields were elucidated with dynamical chemical models . The O3–temperature correlation profiles in Fig.  are consistent with those from numerical modeling  and observational data analysis , indicating that the MERRA-2 O3 and temperature climatologies represent O3 and temperature distributions and their interrelationship realistically.

The spatial distribution of O3 is controlled by the various chemical and dynamical processes that drive the production, destruction, and transport of atmospheric O3. Since the distributions of O3 sources and surface topography are inhomogeneous over the globe, systematic patterns with significant longitudinal variations are present in horizontal O3 distribution. The MERRA-2 baseline climatologies presented in previous sections focus on the latitudinal and altitudinal distribution of O3, with a coarse longitudinal resolution retained through the binning of the globe with equal size (15∘ longitude × 10∘ latitude) tiles. To better capture the spatial variation in O3 and to compare directly with previous global O3 climatologies referred to respectively as Ziemke2011 and GLiu2013 hereafter, we create a higher-spatial-resolution O3 profile climatology from MERRA-2 by reducing the tile bin size to 5∘ longitude × 5∘ latitude, which is the bin size for both Ziemke2011 and GLiu2013 climatologies. This higher-spatial-resolution MERRA-2 climatology consists of monthly statistics of O3 volume mixing ratio profile, tropopause pressure, stratospheric column O3 (SCO), and tropospheric column O3 (TCO) for 2592 (=36×72) 5∘ × 5∘ tiles. Here the SCO is an integration of an O3 profile from 0.01 hPa down to the tropopause and the TCO from the tropopause down to the surface.

For better comparisons with the Ziemke2011 climatology, we partition the MERRA-2 total O3 column into SCO and TCO using the climatological tropopause pressure provided in Ziemke2011, which is compiled from the National Centers for Environmental Prediction (NCEP) tropopause pressures. Figures  and show the spatial distributions of the NCEP-based MERRA-2 SCO and TCO, respectively, for 12 months of the year and their comparisons with Ziemke2011. Results in Figs.  and reveal excellent agreement between MERRA-2 and Ziemke2011 in the low-latitude zone (within ±30∘), with ΔSCO ≲±5 DU and ΔTCO ≲±6 DU for most months and tiles. This agreement becomes worse in the higher-latitude regions, mostly showing larger differences in SCO and TCO between MERRA-2 and Ziemke2011, likely due to higher longitudinal variability in stratospheric O3, degrading the accuracy of SCO from gap-filling interpolation of Aura MLS data . From September to May, MERRA-2 SCO in the polar latitudes is higher, while TOC is lower than the corresponding columns from Ziemke2011, with the broadest spread occurring in February–April. But more significantly, Figs.  and show that both spatial distributions of MERRA-2 SCO and TCO and their seasonal cycles closely resemble those of Ziemke2011.

MERRA-2 SCO displays a strong latitude dependence (see Fig. ) that is shaped primarily by the Brewer–Dobson circulation, showing low values in the tropics (∼220 DU) and elevated values in the middle and high latitudes, with the highest column amount exceeding 400 DU in the Northern Hemisphere (NH) (between 70 and 80∘ N) during February–April and exceeding 350 DU in the Southern Hemisphere (SH) (between 45 and 60∘ S) in September–October. The SCO longitudinal variability is low in the tropics but increases significantly along with higher columns at midlatitudes and high latitudes. In the midlatitude to high-latitude regions centered around 60∘ N, the longitudinal variation exhibits an oscillatory pattern with high SCO over North America that stretches across the Pacific Ocean to over eastern Asia. This pattern, which is influenced by the semipermanent atmospheric pressure systems resulting from the unique orography distribution in the NH, persists over the year with amplitude varying with the season and reaching its maximum during February. In the SH, a wavelike high-SCO pattern with longitude center near the dateline (the 180th meridian) also appears in the middle–high-latitude band (around 60∘ S), which evolves with the progression of the Antarctic O3 hole from formation to breakup, exhibiting SCO buildup and decay outside the stratospheric polar vortex and reaching its maximum in September–October when the O3 hole drops to its minimum (∼125 DU).

As illustrated in Figs.  and , TCO behaves differently from SCO, reflecting different sources and dynamical processes that affect its spatiotemporal distribution. The NH mean SCO rises in January, reaches its maximum during February–April, drops in May, and reaches its minimum in September. By comparison, the NH mean TCO starts to increase in March, maximizes in the summer months, and begins to drop in the fall, arriving at its minimum in January–February. These different seasonal cycles indicate a weak relationship between TCO and SCO in NH.

In the tropics, TCO is small (15 to 25 DU) in the Pacific but high (35 to 45 DU) in the Atlantic, exhibiting a stable wavelike pattern that detaches from the SCO distribution, which is almost longitudinally invariant in the same latitude zone. The small TCO in the tropical Pacific is likely due to atmospheric deep convection that uplifts marine boundary air, which is O3 poor, into the middle and upper troposphere. The elevated TCO in the tropical South Atlantic and the connected high-TCO band along the edge of the southern tropics (30∘ S) between 40∘ W and 80∘ E are contributed by regional O3 production, including lightning, biomass burning, fossil fuel combustion, and soil emissions, as well as influx from the stratosphere . This enhancement persists throughout the year, but it is strongest in September–November and weakest in March–May. Its longitudinal variation and seasonal dependence are influenced by large-scale atmospheric circulations . In the NH extratropics (between 20 and 40∘ N), TCO displays a zonal band elevation with strong longitudinal variability and the highest TCO occurs over the Mediterranean and eastern Asia in June–July. The TCO enhancement in this industrialized zonal band is significantly contributed from anthropogenic emissions .

Aura MLS and OMI O3 measurements are combined to create the Ziemke2011 climatology, and they are assimilated to generate the MERRA-2 O3 field. Consequently, the close resemblance described in this section between MERRA-2 and Zimeke2011 climatologies is expected, even though MERRA-2 uses a period that is twice as long as that of Zimeke2011. To further evaluate the MERRA-2 climatology, we compare it with the GLiu2013 climatology, which is created from trajectory mapping of the long-term ozonesonde record . Figure  shows monthly maps of O3 concentrations (i.e., mixing ratio in parts per million by volume) at 4.5 km altitude from GLiu2013 and at 4.5 km pressure altitude from MERRA-2 for 12 months of the year. These maps in Fig.  show similar O3 spatial distributions and temporal evolution between the two climatologies. For instance both exhibit persistent O3 concentration enhancements in the NH extratropics and in the tropical and subtropical South Atlantic. However, while GLiu2013 enhancements are located in roughly the same area as MERRA-2, they differ in shape, likely due to the spatial gaps of ozonesonde data. The seasonal cycles agree well with each other: both show the strongest NH enhancements in June–August and the weakest in January–March and the strongest SH enhancements in September–November and the weakest in March–May.

The close resemblances of O3 columns (both TCO and SCO) between MERRA-2 and Ziemke2011 and general similarities of O3 concentrations between MERRA-2 and GLiu2013 in terms of their spatial distributions and seasonal cycles demonstrate that the MERRA-2 climatology captures the spatiotemporal O3 distribution realistically.