The distribution of ozone in the upper troposphere and lower stratosphere (UTLS) region is crucial for Earth's radiation budget e.g., and for modulating air quality near Earth's surface e.g.,. Despite its importance and the decades of satellite, aircraft, balloon-borne, and ground-based measurements, confidence in the long-term ozone trends in the UTLS remains low e.g.,. The difficulty in quantifying trends arises because the UTLS is a transition region between the ozone-poor troposphere and the ozone-rich stratosphere . UTLS ozone also exhibits high spatial and temporal variability driven primarily by variations in the UTLS jets and the tropopauses e.g.,. Measurements available in this region are spatially and temporally limited, resulting in inhomogeneous sampling of this variability. Moreover, the tropopause and the jets act as dynamical barriers to mixing, accompanied by strong changes in static stability (e.g., Birner, 2004) or strong isentropic potential vorticity (PV) gradients e.g.,. Both lead to strong ozone and tracer gradients at the tropopause . Thus, tropopause e.g., or jet-relative e.g., coordinate systems have often been used to segregate air masses influenced by different dynamical processes (e.g., tropospheric versus stratospheric or poleward versus equatorward of the subtropical jet).

Another way of segregating air masses is by using coordinates that account for adiabatic conservation laws, i.e., PV–potential temperature (θ)-related coordinates. Rossby and smaller-scale waves lead to meridional displacements of air parcels that are mostly adiabatic and largely reversible in nature. PV–θ coordinates leverage the meridional distortions of PV contours as well as the movement of adiabatic parcels on surfaces of constant θ to account for these displacements e.g.,. It is important to note that irreversible processes (diabatic processes such as radiative cooling or heating, turbulent mixing and stirring) modify PV on different timescales. These processes are associated with transport that leads to mixing and irreversible tracer exchange, likewise introducing ozone variability that cannot be accounted for by adiabatic coordinate transformations. Analyzing datasets in geometric coordinate systems (e.g., latitude–pressure grids) generally results in higher binned variability, as these coordinates do not account for the variability caused by changes in the positions of the jets or the tropopauses or for wave-induced air parcel displacements.

As part of the Observed Composition Trends And Variability in the UTLS (OCTAV-UTLS) Stratosphere-troposphere Processes And their Role in Climate (SPARC) activity, in this study we analyze how well different coordinate systems separate ozone measurements taken in atmospheric regimes dominated by different processes. Coordinate systems that effectively achieve this are expected to segregate observations into bins with reduced variability because measurements influenced by different (reversible) dynamical processes will not be averaged together. The datasets used include observations from the Aura Microwave Limb Sounder (MLS) and the Atmospheric Chemistry Experiment Fourier Transform Spectrometer (ACE-FTS) satellite instruments as well as high-resolution measurements from aircraft (including those from various research campaigns and the Civil Aircraft for the Regular Investigation of the atmosphere Based on an Instrument Container – CARIBIC-2), lidars, and ozonesondes.

Each data point from our observational datasets (see Sect. ) comes with temporal and geolocation information. The geolocation information includes longitude and latitude in the horizontal and either altitude or pressure (or both) in the vertical. While these basic coordinates are essential for measurement retrievals and data processing, dynamically defined coordinates often facilitate interpretation of the data. Coordinate systems designed to show relationships with atmospheric phenomena are typically established with reference to the specific phenomenon itself, such as tropopause-relative coordinates. Conversely, dynamical coordinates such as potential temperature in the vertical or equivalent latitude (i.e., PV on isentropes) in the horizontal provide a framework (based on conservation laws for atmospheric motions) that aligns with the adiabatic movement of the air parcels.

Each of these coordinates remaps the data with respect to different aspects of dynamics, transport, or location. Thus, the coordinates that are most helpful for studying geophysical and transport properties of the data may be different for different regions and/or phenomena that are of interest. A key metric used to evaluate the impact of binning the data in each coordinate system is the binned variability. Depending on the coordinate system and its ability to account for tracer gradients at transport barriers between different air masses (e.g., at the tropopause or jet cores), the binning process can induce artificial variability on top of the inherent atmospheric variability (e.g., induced by nonconservative processes).

For example, discussed this enhanced variability when comparing datasets binned using tropopause-relative coordinates to those binned using altitude. This comparison revealed increased variability when the influence of the tropopause (and the tracer gradients associated with its location) was not accounted for, thereby highlighting the significance of dynamical variability. Since dynamical variability is an inherent property of the atmosphere, different representations of the data, i.e., coordinate systems that segregate dissimilar air masses, can minimize its effects on values grouped together in a bin, making it a useful metric for coordinate system comparison. We emphasize that neither the dynamical variability itself nor the atmospheric trace gas variability can be removed or minimized by any means – and indeed it is exactly this variability and the mechanisms for it that we ultimately want to isolate and study.

The choice of coordinate can, however, facilitate combination of measurements in each bin that are primarily affected by the same processes (thus reducing the variability in that bin) by accounting for transport history and/or the locations of transport barriers and thus strong tracer gradients. In other words, process-related coordinates can reduce binned variability, highlighting a more interpretable representation of the geophysical and trace gas variability and thus helping to elucidate the physical processes controlling it in different regions. The goal of this study is to show the effect of different coordinate systems on the binned variability. To achieve this, we use a variety of observational datasets together with reanalysis data.

Several abbreviations are used throughout this paper; all are defined the first time they appear in the text. However, to improve readability, a list of the abbreviations is provided in Appendix A (Table ).

Before conducting a comparison involving all 33 coordinate systems, we assess the RSTD and the underlying properties for the coordinate systems illustrated in Fig.  through Fig. . The RSTD equivalents of those figures are shown in Fig.  through Fig. . It is important to note that the aircraft, ozonesonde, and lidar datasets have much sparser coverage, particularly for the latter two, in latitude-based coordinates than ACE-FTS and MLS. Additionally, ACE-FTS and lidar observations are limited to clear-sky conditions due to their inability to penetrate most clouds. MLS has the coarsest vertical resolution, causing smearing of both observations and the variance . The aircraft measurements are mostly limited to flight levels but allow for the detection of more variability in the measurement region due to the high temporal sampling. By examining these diverse datasets, the impacts of each individual limitation in resolution or sampling can be assessed and ozone variability characteristics that are robust across all the datasets can be identified. As a reference, Fig.  showcases the number of measurements per bin available for each observation system and for several coordinate systems used in this study.

Figure  shows the influence on the relative standard deviation of using different traditional vertical coordinates versus latitude. The tropopause region can be clearly identified as a region of high ozone variability in all five datasets. In altitude and pressure coordinates, the variability associated with this feature extends well into the troposphere, particularly for MLS as a consequence of its coarser vertical resolution. However, when employing potential temperature, which effectively captures rapid quasi-isentropic transport and accounts for vertical displacements of the adiabats in altitude or pressure coordinates, a decrease in the vertical extent of this high binned variability (high RSTD values) becomes apparent. This effect is particularly evident in the MLS, ACE-FTS, and aircraft datasets but can be inferred from the ozonesonde and lidar plots as well. Thus the potential temperature vertical coordinate helps account for some of the geophysical variability seen when binning the data at altitude or pressure.

Moreover, MLS and ACE-FTS display particularly high RSTD values around the northern STJ, which constitutes a stronger transport barrier in DJF compared to summer. Specifically, the STJ separates tropical and midlatitude air, leading to intense ozone gradients near the jet location. Variability in this region manifests itself as high RSTD values resulting from variations in the latitude of large ozone gradients. In altitude and pressure coordinates, the jet-associated variability mostly falls along the tropopause. However, when employing potential temperature, the jet-induced variability manifests itself more prominently as a distinct lobe of variability located mostly above the STJ. Overall, as a function of latitude, potential temperature not only reduces the overall binned variability, but also clarifies the structure of the two main sources of variability (i.e., tropopause and STJ variations), which cannot be separated when using altitude or pressure coordinates.

When changing the vertical coordinate to potential temperature relative to the tropopause(s), as shown in Fig. , it is apparent that the effect of remapping to tropopause-referenced coordinates tends to agglomerate the variability in the bins along the transport barriers, i.e., where gradients are strong enough to make for substantial changes within one bin. MLS and ACE-FTS display high RSTD lobes around 30° S and 30° N (also hinted at by the lidars), which correspond to the regions where double tropopauses e.g., associated with tropospheric and stratospheric intrusions are preferentially found. In these regions, the choice of one reference surface leads to high variability in a fixed latitude framework. The location of the double tropopauses varies with latitude, longitude, and time. The binning process then mixes measurements within latitude bins where vertical profiles are taken relative to the lower (primary) and upper (secondary) tropopause at different longitudes, resulting in the large RSTD at the jet location high into the lower stratosphere. Moreover, in between the primary and secondary tropopause, only accounting for the vertical distance relative to the tropopause fails to account for the presence of air masses of tropospheric and stratospheric origin that are quasi-horizontally (i.e., quasi-isentropically) advected between these levels e.g.,, leading to high RSTD values.

By intercomparing the panels in Fig. , it is evident that the RSTDs are overall smaller when binning with respect to either the 2 PVU (PV2θ) or 4.5 PVU dynamical tropopause (PV4θ) than when binning with respect to the WMO tropopause (WMOθ). In particular, this is noticeable in the lobes of high RSTDs around 30° S and 30° N seen in MLS and ACE-FTS and hinted at in the ozonesonde and lidar panels. Further, the RSTD also displays smaller values for the aircraft datasets in the extratropics, with the PV4θ coordinate generally accounting for variability better than the PV2θ coordinate. This is because the 2 PVU surface better represents the tropopause at the middle and high latitudes , while higher PV values best represent the tropopause for the subtropics . In general, Fig.  suggests that dynamical tropopause-based coordinates resolve the ozone gradients across the tropopause region better than the WMO tropopause-based coordinate. This is not unexpected as the WMO tropopause results in breaks and multiple tropopauses between the tropics and the extratropics e.g., rather than a continuous transition as provided by the dynamical (PV) tropopauses. Compared to other datasets, MLS displays larger RSTD values in the northern extratropics and smaller values in the southern extratropics in the tropopause-based coordinates. Despite its coarse vertical resolution potentially failing to properly resolve the tropopause, this RSTD value might be related to its better coverage of the region; i.e., MLS might sample more variability.

Figure  shows the influence on the RSTD of using different horizontal coordinates with potential temperature as the vertical coordinate. The similarity between binning in latitude and binning in STJ-referenced latitude in the MLS and ACE-FTS panels is striking, though the STJ-L panels do show variability along the STJ, with a narrower peak (especially for ACE-FTS). This similarity likely arises from the relatively dense sampling of these datasets and the climatological averaging; it also likely arises partly from the fact that the jets have a strong influence on transport only in the region within about 20–30° latitude of the jet, meaning that distributions are expected to be very similar away from the jets. A similar effect is seen for the aircraft data, albeit with slightly higher RSTD values in the extratropics, again suggesting that the limited latitude region of influence of the jets is an important factor.

For MLS, ACE-FTS, and the aircraft datasets, binning in equivalent latitude leads to a reduction in the RSTD. For example, the lobe of the high RSTD above the northern STJ in latitude and at 0° in the STJ-L coordinate system is greatly reduced when binning the data using equivalent latitude. This is also evident in the ozonesonde and lidar datasets, which show higher RSTD values when binned in latitude with respect to the STJ compared to binning using equivalent latitude. The high RSTD values are greatly reduced when using equivalent latitude, which accounts for the different dynamical regimes and isentropic PV gradients away from the STJ. This illustrates that a portion of the variability is related to reversible processes, in this case primarily the undulation of planetary and synoptic-scale waves. In contrast, binning with respect to the STJ leads to pronounced RSTD values at the jet core location (i.e., 0° with respect to the STJ) due to the strong ozone gradient across the jet, but further from the jet, the variability is higher than that observed with the other horizontal coordinates.

Overall, Fig.  indicates that all datasets benefit from the use of equivalent latitude. This coordinate implicitly includes the dynamical tropopause and accounts for dynamics on the typical timescale of planetary wave activity by accounting for the reversible part of the planetary-wave-induced air mass excursions in the mean, especially in the lower stratosphere. However, it is important to exercise caution when using equivalent-latitude coordinates in the upper troposphere. Adiabatic PV conservation is violated, particularly by phase transitions of water, regional turbulence (especially near jet cores), radiative cooling in anticyclones e.g., or above clouds e.g.,, and the absence of a connected circumpolar transport barrier e.g.,. STJ-relative coordinates are more appropriate for processes in the region immediately surrounding the jet and for studies where identifying and quantifying the strength and sharpness of the jet is critical.

We now discuss the DJF RSTD for MLS (Fig. ), ozonesondes (Fig. ), and aircraft measurements (Fig. ) to illustrate the differences between the various coordinate systems. These datasets were chosen to exemplify satellite observations (MLS) with relatively coarse vertical and horizontal resolutions but with global coverage as well as examples of in situ data with fine vertical resolution (ozonesondes) and horizontal resolution (aircraft) but with limited geographical coverage. The equivalent figures for ACE-FTS and lidars are shown in the Appendix (Figs.  and ).

Despite their different sampling and data densities, all datasets show broad areas of agreement (i.e., consistency in the change) when comparing the various binned coordinate systems in Figs. , , and . Comparing the typically used vertical coordinates (altitude, pressure, and potential temperature) versus latitude, equivalent latitude, and latitude relative to the STJ (top three rows in these figures), all the datasets show a significant reduction in binned variability in the equivalent latitude–potential temperature coordinate system. For example, the binned variability directly at the extratropical tropopause (including the subtropics) is greatly reduced. Further, the lobes of variability above the northern STJ as seen in MLS (Fig. ) almost disappear in this coordinate system.

This result may not be too surprising since equivalent latitude and potential temperature constitute a purely adiabatic coordinate system combining isentropes (i.e., adiabats) with PV, which is materially conserved for adiabatic and frictionless flow. Equivalent latitude facilitates identification of a reversible adiabatic transport component (which can be appropriately accounted for using suitable coordinates) and a non-adiabatic component related to irreversible mixing. The latter cannot be fully accounted for by coordinate mapping and constitutes part of natural atmospheric variability. In contrast, minimizing the impact of the former is contingent upon the selection of suitable coordinates.

Regarding tropopause-relative coordinates, we subdivided the data into two categories using geometric altitude and potential temperature relative to the tropopause. Across all the datasets, the use of tropopause-relative altitude coordinates consistently results in higher binned variability than tropopause-relative potential temperature coordinates, regardless of the horizontal coordinate used. This again highlights the quasi-isentropic stratospheric distribution of ozone. Overall, the binned variability is lower for all the horizontal coordinates when using either the 2 PVU tropopause or the 4.5 PVU tropopause as a reference than when using the WMO tropopause. Further, the 2 PVU relative coordinate in general leads to higher binned variability in the subtropics than the 4.5 PVU coordinate but with very similar binned variability elsewhere. The enhanced tropical variability when using the 2 PVU tropopause is in line with the findings of and , which concluded that the subtropical tropopause is better represented by the ∼ 4–5.5 PVU surfaces, depending on the season.

As discussed in Sect. , double tropopauses associated with the STJ manifest themselves as regions of enhanced ozone variability (around 30° S and 30° N) since a vertical coordinate with respect to the primary tropopause cannot account for mixing measurements taken relative to the lower (primary) and upper (secondary) tropopause and air mass references with tropospheric and stratospheric origins that are quasi-horizontally advected between the primary and secondary tropopauses. These lobes of binned variability are somewhat reduced when using STJ-referenced latitude. However, away from the STJ core, the binned variability increases since the jet is a primary factor (i.e., a transport barrier) in controlling the flow only in a narrow latitude band around the jet core, and thus the flow away from this region is better represented by a dynamical coordinate such as equivalent latitude.

Binning in an equivalent latitude–tropopause-referenced coordinate results in high binned variability near the South Pole during DJF (and near the North Pole during JJA; see the Appendix). In fact, it leads to higher binned variability than using latitude or STJ latitude at all times. This is related to the thermal structure in the polar regions, where both WMO and dynamical tropopauses are often ill-defined and/or very broad e.g.,.

Regarding vertical STJ coordinates, the data are again shown for coordinates relative to both altitude and potential temperature. As expected, across all the datasets, the use of STJ coordinates relative to altitude results in larger RSTD values than for STJ coordinates relative to potential temperature, regardless of the horizontal coordinate used. Examining the RSTD values across the coordinate systems which use STJθ as the vertical coordinate, it is evident that the binned variability is minimized when using STJ-L as the horizontal coordinate. That is, referring to the STJ in both the vertical and horizontal leads to the lowest binned variability within the STJ-based coordinates.

All of the findings discussed in this section also hold for ACE-FTS and lidar datasets (see Figs.  and ) as well as for the other seasons (see Figs. – for JJA examples).

To further quantify the impact of using the various coordinate systems on variability, we use the binned climatological values of latitude and pressure in the different coordinate systems to remap the variability to the “traditional” latitude–pressure coordinate system. The accuracy of this remapping depends on how representative the climatological latitude and pressure values are in the different coordinate systems. Consequently, it only offers a broad overview of the impacts of these coordinate systems. The difference between the RSTD of the reference coordinate system (RSTDref) and that of each of the remapped climatologies (RSTDclim) is calculated as 2RSTDdiff=RSTDclim-RSTDrefRSTDref, which yields a direct metric for assessing the effect of these coordinate systems on the binned variability.

Figure  displays the result of remapping and comparing the MLS DJF data. Notably, the use of equivalent latitude–potential temperature (EqL /θ) coordinates leads to the most substantial reduction in binned variability across the upper troposphere and lowermost stratosphere. Equivalent latitude effectively accounts for the reversible short-term variability at the extratropical tropopause, while potential temperature accounts for the vertical variability of isentropic surfaces and thus isentropic vertical displacement of air parcels. To highlight this further, Fig.  displays the same MLS DJF data comparison using the climatological values of equivalent latitude and θ, i.e., remapping into EqL /θ. In all the other coordinates, there is enhanced binned variability, except in small regions, emphasizing the global utility of this coordinate pairing. Given the importance of equivalent latitude, other methods to calculate it e.g., could be explored in the future.

Figure  also highlights that any tropopause-based coordinate leads to reduced binned variability around the tropopause, consistent with the results of . It is important to note that, at greater distances from the respective tropopauses, tropopause coordinates in altitude tend to increase variability for all horizontal coordinates. This confirms earlier results by and indicates that using tropopause-based altitude coordinate systems may not be physically meaningful farther away from the tropopauses. Similarly, STJ coordinates lead to reduced binned variability only around the STJ, consistent with the results of .

The reduction in variability observed in tropopause-based coordinates relative to potential temperature, especially in the winter hemisphere when the Brewer–Dobson circulation dominates vertical movement via advection, supports this interpretation e.g.,. Unlike altitude, potential temperature accounts for at least some of the large-scale adiabatic movements driven by the stratospheric circulation in the deeper stratosphere on shorter timescales e.g.,. Finally, some of this enhanced variability in all the tropopause-based coordinates is generally further reduced when using latitude with respect to the STJ.

As part of the OCTAV-UTLS SPARC activity, we have mapped multiplatform ozone datasets to different coordinate systems to systematically evaluate the influence of these coordinates on the binned climatological variability, unifying the disparate work of numerous prior studies on individual coordinate system variability in the most complete assessment of this topic that we are aware of. Coordinate systems that do not consider transport barriers can induce artificial variability when binning across ozone gradients at transport barriers, increasing the binned variability. By comparing the relative standard deviation in different coordinate systems, we evaluated the ability of each coordinate to account for variations arising from changes in the subtropical upper-tropospheric jet, changes in tropopause height, and wave-induced air parcel displacements. We thus evaluated the ability of each coordinate system to identify different regimes separated by transport barriers and to group air parcels appropriately into those regimes.

We found the following:

Across all the datasets, referring to the tropopause or STJ core in the vertical leads to greater binned variability in altitude-based coordinates compared to potential temperature-based coordinates, irrespective of the horizontal coordinate used. This highlights the largely quasi-isentropic distribution of upper-tropospheric and lower-stratospheric ozone.

These conclusions were drawn using a variety of ozone measurements (i.e., ozonesondes, lidars, and satellite and in situ aircraft measurements) with a plethora of vertical and horizontal resolutions as well as sampling characteristics. Therefore, we anticipate that these results will be applicable to other datasets not included in this study, such as OMPS, OSIRIS, IAGOS-CORE, and additional ozonesondes and lidar data available elsewhere.

We note that each coordinate system has its strengths and weaknesses, and thus different coordinate systems may be most effective for times and regions dominated by variability from different atmospheric processes. In this study, we identified coordinate systems that most help to reduce binned variability over broad regions in an effort to facilitate more robust UTLS composition trend analyses. The use of multiple datasets with different samplings and resolutions enables us to identify commonalities among them, ensuring conclusions that are independent of the specific measurement techniques. We are aware that several questions regarding the binned variability are still open, and some of them will be addressed in upcoming studies. For example, a future OCTAV-UTLS study will evaluate the impact of using those coordinates that most reduce binned variability in quantification of long-term ozone trends. Another study will analyze how differences in sampling patterns and resolution (both vertical and horizontal) can affect the representation of the datasets as well as the trend quantification.