2.1 Reanalysis datasets

Fujiwara et al. (2017) provide detailed descriptions of the models, assimilation systems, and data inputs for the reanalyses used here in their overview paper on S-RIP. We compare the four most recent high-resolution full-input reanalyses for all winters with data available from the beginning of the “satellite era” in 1979. All of our analyses are done using daily 12:00 UT fields from each reanalysis dataset (we have tested the sensitivity of our analyses to using 00:00 UT data and have found we get virtually identical results). Because of the importance of resolution, especially in the vertical dimension, in representing the polar lower stratosphere and threshold processes in general (see, e.g., Manney et al., 2017), we start our analyses from reanalysis data on the native model levels and at or (in the case of spectral models) near the native horizontal resolution. Please see Table 1 for a list of relevant acronyms that we use below to describe the instruments, radiative transfer models, etc., that are used by the reanalyses.

2.1.3 JRA-55

JRA-55 (Ebita et al., 2011; Kobayashi et al., 2015) is a global reanalysis that covers the period from 1958 to the present, and is produced using 4D-Var assimilation. The data from the JRA-55 T319L60 spectral model are provided on an approximately 0.56^∘ Gaussian grid corresponding to that spectral resolution. JRA-55 uses RTTOV version 9.3 for satellite radiance assimilation. The JRA-55 fields on the model vertical levels have a vertical resolution of ∼1.2 to 1.4 km in the lower stratosphere.

Figure 1Timeline for operational satellite instrument inputs to the reanalyses used herein: panels (a) through (d) show CFSR/CFSv2, ERA-I, JRA-55, and MERRA-2, respectively. Table 1 gives a list of the acronyms used here. Within the constraint of putting them in the same order for each reanalysis, the input datasets are stacked in approximately chronological order, with earliest on the bottom and latest on the top. The black vertical line is at the middle of 1998, near the time of the TOVS to ATOVS transition (see text). See Fujiwara et al. (2017) for a similar timeline but organized per instrument.

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2.2 Methods

The methods and diagnostics used herein are largely the same as those used by Lawrence et al. (2015). In the subsections to follow, we describe the reanalysis fields we use, and how we prepare them and derive the polar processing diagnostics from them. We also provide some information on additional analysis techniques that we use to help interpret our results.

2.2.1 Preparation of meteorological fields

The two meteorological fields necessary to derive most of the diagnostics used herein are temperatures and PV on isentropic surfaces. In the results we present later, we show temperature diagnostics on pressure surfaces, and vortex diagnostics on isentropic surfaces; as will be discussed, we also calculate and use some temperature diagnostics on isentropic levels.

Figure 2Potential temperature profiles of the reanalysis vortex edges determined from climatological maximum PV gradients expressed as scaled PV for the NH (a) and the SH (b) . Green, blue, purple, and red indicate CFSR/CFSv2, ERA-I, JRA-55, and MERRA-2, respectively.

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Of the four reanalyses described in Sect. 2.1, only MERRA-2 provides potential vorticity on its model levels. CFSR/CFSv2, ERA-Interim, and JRA-55 have isentropic PV available, but these products are only provided on a sparse set of isentropic levels, with very few common levels between the reanalyses. ERA-Interim provides absolute vorticity on model levels, and CFSR/CFSv2 provides relative vorticity; thus to get the vertically resolved PV fields that we need, we derive PV for these reanalyses using their provided vorticity, temperature, and pressure fields on the model levels. In the case of JRA-55, we use the zonal and meridional wind components to first calculate relative vorticity, which we then use in combination with temperature and pressure to calculate PV on the model levels. While a thorough evaluation of biases that may arise from using different types of PV calculations for different reanalyses would be valuable, it is beyond the scope of this paper. We think, however, that data users will most likely use the most direct calculation to get from the provided fields to the model level PV (as we have), and thus the fields we are comparing are those that are most likely to be used in practice. When calculating polar processing diagnostics, we scale the PV fields into vorticity units as in Dunkerton and Delisi (1986) by dividing the PV by a standard value of static stability calculated from assuming a vertical temperature gradient of 1 K km⁻¹ and a pressure of 54 hPa on the 500 K isentropic level. We use this scaling so that the scaled PV (sPV) values are of the same order of magnitude at different levels throughout the stratosphere.

Since the reanalyses are all on different model levels, we use the reanalyses' temperature and pressure fields to vertically interpolate their temperature and PV fields to a common set of fixed pressure and isentropic surfaces. We use a standard set of pressure and isentropic levels that have been used for several NASA satellite instrument datasets (see, e.g., https://cdn.earthdata.nasa.gov/conduit/upload/4849/ESDS-RFC-009.pdf, last access: 12 September 2018) including the Aura Microwave Limb Sounder (Livesey et al., 2015); these are 12 levels per decade in pressure, and their climatologically corresponding isentropic surfaces. For polar processing diagnostics, we limit our focus to 14 levels with pressures between approximately 120 and 10 hPa; these pressure levels and their corresponding isentropic surfaces are shown in Appendix A (Table A2).

2.2.2 Temperature and vortex diagnostics

The depletion of ozone in the lower stratosphere follows from a complex chain of processes that are highly dependent on meteorological conditions (see, e.g., Solomon, 1999; WMO, 2014, for reviews). The activation of chlorine requires the presence of PSCs, which form when temperatures are sufficiently low, and grow when temperatures stay low for sufficiently long periods of time (Hanson and Mauersberger, 1988; Solomon, 1999; WMO, 2014, and references therein). The catalytic ozone destruction cycles involving both chlorine and bromine further require sunlight, which is usually provided later in winter and spring when sunlight returns to the high-latitude polar regions. These chemical processes also require isolation from lower-latitude air, which is provided by the stratospheric polar vortex; the edge of the polar vortex acts as a barrier preventing transport and mixing, and thus the vortex acts as a containment vessel for the polar air where these processes take place (e.g., Schoeberl and Hartmann, 1991; Schoeberl et al., 1992). We thus examine polar processing diagnostics that primarily focus on lower stratospheric temperatures and the state of the polar vortex to assess the meteorological conditions conducive to ozone depletion. Unless specified otherwise, we focus on the months from December to March (DJFM) for the NH, and May to October (MJJASO) for the SH; these time periods cover roughly the full period during which polar processing takes place for most polar winters (see Sect. 3.1).

The temperature diagnostics that we use include minimum temperatures (T_min) poleward of ±40^∘ latitude, and the areas of temperatures (poleward of ±30^∘ latitude) below PSC formation thresholds (A_PSC, or area T≤T_PSC, where the subscript “PSC” may be replaced by “NAT” or “ice” to denote the specific type of PSC). For A_PSC, we specifically use the formation temperatures for solid nitric acid trihydrate (NAT; Hanson and Mauersberger, 1988) and ice particles on pressure levels, which we define using climatological profiles of HNO₃ and H₂O mixing ratios (see Appendix A and Table A1 for values). As a rule of thumb, the NAT threshold between 120 and 10 hPa ranges from roughly 198 to 187 K, respectively, and the ice threshold tends to be between 6 and 8 K below the NAT threshold. We stress that these thresholds are approximations, but they are convenient as proxies for PSC formation and chlorine activation. While most of the results we show herein for the temperature diagnostics are on pressure levels, we also calculate them on isentropic surfaces; for the diagnostics involving PSC thresholds, we assign the PSC thresholds on pressure levels to the isentropic surfaces that are roughly co-located (e.g., 520 K corresponds to 46.1 hPa). This is an additional approximation, but it allows us to keep the intercomparisons simple without having to calculate daily varying PSC thresholds for pressures/temperatures on isentropic levels or pre-computing climatological PSC threshold values from the reanalyses' fields. (Please see Appendix A and Table A2 for the pressure surfaces used, their corresponding isentropic surfaces, and the PSC threshold temperatures.) To mitigate issues with these approximations and test sensitivity to the thresholds, we also compute A_PSC with ±1 K offsets to the PSC formation temperatures.

The vortex diagnostics that we use include maximum gradients in sPV as a function of equivalent latitude (maximum sPV gradients, or MPVGs), which assess the strength of the vortex edge (e.g., Manney et al., 1994, 2011; Lawrence et al., 2015), and the area of the vortex exposed to sunlight (sunlit vortex area, or SVA). To calculate MPVGs, we bin sPV as a function of equivalent latitude (EqL, the latitude that would enclose the same area between it and the pole as a given PV contour; Butchart and Remsberg, 1986), numerically differentiate, and catalog the maximum value between ±30 and ±80^∘ EqL. We use ±30^∘ as a lower limit because relatively large PV gradients can be found in the tropics, which can dominate early/late in the season when the vortex is forming/decaying; we use ±80^∘ as an upper limit because the small areas represented by points poleward of ±80^∘ can vary much more dramatically than the lower EqLs, sometimes producing large gradients (e.g., Nash et al., 1996) that are not indicative of the vortex edge.

To calculate SVA, we calculate the area of the vortex that extends equatorward of the daily polar night latitude at 12:00 UT. The area of the vortex is determined by defining constant contours of sPV as the vortex edge over all years; herein we determined these vortex edges individually for each reanalysis from climatological seasonal averages of their maximum PV gradients (as determined above) from the extended periods of November through April for the NH, and April through November for the SH. We use periods that are longer than the DJFM and MJJASO periods we use for the intercomparisons because they help to include the formation and breakdown of the vortex. While constant vortex edges are a simplification, the ones we use here are defined for each reanalysis individually, and thus they inherently fold in any systematic differences that the reanalysis sPV fields may have. Furthermore, more common definitions of the vortex edge that provide daily varying values can be prone to giving spurious oscillations from day to day that could contaminate intercomparisons (e.g., Manney et al., 2007; Lawrence and Manney, 2018). Figure 2 shows the NH and SH profiles of vortex edges used for each reanalysis; it shows that the values obtained for each reanalysis and hemisphere are generally consistent, and that the largest differences between reanalyses below 850 K are around $\mathrm{0.2}\times {\mathrm{10}}^{-\mathrm{4}}$ s⁻¹.

Figure 3Time series of reanalysis ensemble mean (REM) (a, c, e) Arctic and (b, d, f) Antarctic climatological (1979/1980 through 2016/2017 in the NH, and 1979 through 2016 in the SH) minimum high-latitude (poleward of 40^∘ latitude) temperatures; panels (a) and (b) show contour plots (blue/purple shades represent low temperatures and reds high temperatures). The horizontal black lines mark the 30 hPa and 70 hPa pressure levels for which line plots are shown in panels (c) and (d) and in (e) and (f), respectively. The shading in the line plots shows the range of REM values on each date, and the black line shows the average values. Note that the time period shown is longer in the SH than in the NH. The same color range is used for each hemisphere, with values from 180 to 220 K shown (blues to reds; all values below/above 180/220 K are shown in the deepest blue/red).

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2.2.3 Derived diagnostics

Here, we describe some additional diagnostics that we examine later in the paper that are derived from the raw diagnostics we calculate (primarily those described above).

The winter mean volume of lower stratospheric air with temperatures below T_PSC (V_PSC) is a widely used diagnostic of polar processing potential. It is often expressed as a fraction of the vortex volume (V_PSC∕V_Vort) to provide a measure that is independent of the substantial interannual and interhemispheric variations in vortex size (e.g., Rex et al., 2004, 2006; Tilmes et al., 2006; Manney et al., 2011; Manney and Lawrence, 2016; WMO, 2014). (Again, we replace the subscript “PSC” with “NAT” or “ice” to denote specific PSC types.) Hence, V_PSC∕V_Vort represents the approximate fraction of the vortex (for a specified altitude range) in which temperatures are low enough for the formation of PSCs. Here, we calculate V_PSC and the volume of the vortex using A_PSC and the area of the vortex on isentropic levels between 390 and 550 K. A_PSC is calculated as described above in Sect. 2.2.2; the area of the vortex is calculated similarly to SVA but instead by finding the total area within the PV contours representing the vortex edge. To get volumes, we assume each isentropic level is nominally representative of the volume of air midway between each level; for example, the 410 K level comes after 390 K and before 430 K, so 410 K is assumed to be representative of the altitude “width” between 400 and 420 K. The altitude widths of these nominal levels are determined using the Knox (1998) approximation; for the levels from 390 to 550 K, the Knox approximation gives a mean altitude differential between levels of 1.13 km with a minimum of 0.98 km, and a maximum of 1.30 km. These altitude differentials are then multiplied by the area diagnostics on each isentropic level (which are converted to km²), and summed over the vertical range to get volumes. The volume fraction is then V_PSC∕V_Vort. In the results we show later on, we specifically show winter mean V_PSC∕V_Vort; these winter means are taken over DJFM for the NH and MJJASO for the SH.

The SH vortex breakup is of considerable concern because it results in the dispersal of ozone-depleted vortex air over midlatitudes (e.g., Ajtić et al., 2003, 2004; Manney et al., 2005c; Pazmino et al., 2005; WMO, 2007). While ozone depletion in the Arctic has not yet been large enough for this to be an ongoing concern, vortex evolution during the 2011 Arctic vortex breakup led to significant areas of ozone-depleted air over populated regions associated with increased surface UV (e.g., Manney et al., 2011; Bernhard et al., 2012). To examine the variability and representation in reanalyses of the vortex decay in the lower-to-middle stratosphere, we examine approximate vortex decay dates, which we derive using the vortex area diagnostic on isentropic levels from 460 to 850 K. Here, we calculate vortex area with $+\mathrm{0.1}\times {\mathrm{10}}^{-\mathrm{4}}$ s⁻¹ sPV offsets to the vortex edges shown in Fig. 2. To accomplish this, we examine NH vortex area between 1 December and 1 June, and SH vortex area between 1 May and 1 March; we have defined the decay date as the last day before which the vortex area is above 1 % of a hemisphere continuously for 30 days. We choose 1 % of a hemisphere as the limit because this threshold is only climatologically met at all levels at the beginning and end of the seasons when the vortex is forming or breaking down, which guarantees that any time the vortex is that small, it is either significantly disturbed or in the process of decaying. The 30-day limit was chosen to help guarantee that the vortex was sufficiently coherent beforehand. Finally, we use vortex edges with the positive sPV offset mentioned above to help remove the influence of small vortex fragments that can be present at the end of the season, which in some cases can add up to areas larger than 1 % of a hemisphere and lead to marginal scenarios that can skew the decay dates. The results we show herein are not highly sensitive to changing the area threshold or using vortex area with/without the sPV offset; except in some marginal cases that we discuss later on, adjusting the area threshold between 1 and 4 % only modifies less than 10 % of the cases (i.e., different years and levels) in all the reanalyses by more than 20 days in the NH and more than 10 days in the SH.

Figure 4SH winter season (MJJASO) (a, c, e, g) averages and (b, d, f, h) standard deviations of minimum temperature differences for each reanalysis from the reanalysis ensemble mean (REM) as a function of year and pressure for the 1979 through 2015 winters, concatenated from the individual years into pixel plots as described in the text. Columns of grey pixels indicate years with no data. Pixels with X symbols inside indicate years and levels where the differences from the REM are insignificant according to our bootstrapping analysis (see Sect. 2.2.4). Blues in the average difference panels show negative values (reanalysis less than the REM) and reds positive values (reanalysis greater than the REM); in the standard deviation panels, yellow/deep blue shades represent low/high standard deviations of the reanalysis differences, respectively.

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2.2.4 Analysis techniques

For most of the results shown herein, we compare the diagnostics derived from each of the reanalyses to an average across all of the reanalyses, which is referred to as the reanalysis ensemble mean (REM). In Sect. 3.1 and 3.2, the comparisons primarily take the form of reanalysis differences from the REM (i.e., reanalysis minus REM).

Our analysis also includes a statistical significance test to determine whether the average differences between the reanalyses and the REM are statistically different from zero over a winter season. To accomplish this, we use a non-parametric bootstrap resampling technique that is useful for time series datasets called the stationary bootstrap (Politis and Romano, 1994). Bootstrapping methods for time series have generally relied on resampling blocks of consecutive observations to construct many artificial time series so that accuracy estimates can be made for sample statistics/estimators (e.g., Lahiri, 2003, and references therein). Rather than resampling random fixed-size blocks (which may or may not overlap) to construct artificial time series, the stationary bootstrap constructs artificial time series by resampling random blocks with random sizes determined from a geometric distribution with specified mean. Herein, we bootstrap the time series of differences from the reanalyses and the REM; we treat the difference time series for each reanalysis, diagnostic, and year individually while the vertical levels are resampled together. In nearly all cases (see the NH A_NAT comparisons in Sect. 3.1 for the one exception), we perform stationary resampling with a specified geometric distribution mean of 10 (i.e., the expected block length is 10 days) and resample all the time series of differences 2×10⁵ times. We note that the results shown herein are not sensitive to the choice of the expected block length; we repeated our bootstrapping analysis for different expected block lengths between 5 and 15 days, and in all cases the results were nearly identical. Ultimately, we chose 10 days as a happy medium based on examinations of the decorrelation timescales of some of the difference time series. We then use the bootstrap percentile method to construct 99 % confidence intervals (CIs) of the average differences; the percentile method is known to have issues in cases with small sample sizes, but since we use a more strict 99 % CI and our time series are longer than 120 days, we expect that our estimates are robust (see discussion in DiCiccio and Efron, 1996, and references therein). When these 99 % CIs do not contain zero, we consider the average differences for the reanalysis minus the REM (for a specific level and year) to be indicative of persistent positive or negative differences. Thus, when statistical significance is mentioned hereinafter, we are referring to significance at the 99 % confidence level.

Figure 5As in Fig. 4 but for the NH winter seasons (DJFM) for 1979/1980 through 2015/2016. Note that different color ranges are used for the NH shown here than in Fig. 4 for the SH.

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3.1 Temperature diagnostics

Figure 3 shows the climatological values of minimum temperatures from the REM. The well-known difference in stratospheric temperatures between NH and SH (e.g., Andrews, 1989) is seen clearly, with the climatological period with temperatures below the NAT PSC threshold spanning approximately December through mid-February in the NH and mid-May through early October in the SH. The lowest temperatures are centered near 20 hPa at about the time of the solstice in the NH, and near 25 hPa approximately a month after the solstice in the SH. NH winter temperatures are lowest earlier in the season because of the prevalence of sudden stratospheric warmings (SSWs) in January and February in that hemisphere.

Figure 4 shows “pixel plots” of the winter mean differences in SH minimum temperatures from the REM (Fig. 4a, c, e, g), and the standard deviations of the differences (Fig. 4b, d, f, h) for each of the reanalyses. We use similar pixel plots herein for the other diagnostics and hemispheres discussed in Sect. 2.2.2. In these plots, each pixel represents a winter mean difference (i.e., reanalysis minus REM averaged over a winter period) or a standard deviation of the differences (i.e., the standard deviation of the reanalysis minus REM over the designated winter period) for a single year and vertical level.

The most striking feature shown in Fig. 4 is an overall improvement in the agreement around the turn of the century, particularly evident in MERRA-2 after 1998. This transition is also apparent in ERA-I, occurring between 1999 and 2001. In earlier years, ERA-I and MERRA-2 bracket the ensemble with differences up to ±3 K, which in later years drop to near 0.5 K. The SH CFSR/CFSv2 and JRA-55 minimum temperatures tend to reside between those of MERRA-2 and ERA-I and are generally close to the REM. In particular, the JRA-55 differences are marked as not statistically significant (at the 99 % confidence level, as described in Sect. 2.2) for many levels and years throughout the reanalysis period. The improvements after 1998 are largest at higher levels (where the differences and standard deviations are themselves largest), becoming less prominent, and less sudden, below about 50 hPa. MERRA-2 shows a change in sign of the differences in the upper levels (∼20–10 hPa). The overall convergence of the reanalyses after 1998–1999 is also seen as pronounced discontinuities in the standard deviations of the differences from the REM for ERA-I, JRA-55, and MERRA-2, with values frequently over 2 K before 1999 typically decreasing to below ∼0.8 K thereafter. The improvement is less evident in CFSR/CFSv2 with standard deviations greater than 1 K seen throughout the reanalysis period, particularly at pressures lower than ∼30 hPa. The 1998–1999 mark corresponds to the transition from assimilating TOVS to ATOVS radiances in all four reanalyses. In addition, in late 2002, MERRA-2 began assimilating the hyperspectral AIRS radiances, vastly increasing the number of data used in the Antarctic. ERA-I and CFSR/CFSv2 started ingesting AIRS data in 2004. Measurements of atmospheric thermal emissions in the 15 µm CO₂ absorption continuum provided by this sensor are strongly sensitive to stratospheric temperature variations as demonstrated, for example, by Hoffmann and Alexander (2009). In addition, all the reanalyses considered here have assimilated data from GPS-RO instruments starting from 2001 in ERA-I and CFSR/CFSv2, from 2004 in MERRA-2, and from 2006 in JRA-55. The GPS-RO data also affect stratospheric temperatures indirectly by anchoring bias correction of radiance observations (Fujiwara et al., 2017).

Figure 6As in Fig. 3 but for area with temperatures below the NAT PSC threshold. The color range in panels (a) and (b) goes from 0 % to 12 % of a hemisphere (blues to reds), with all values above 12 % shown in the deepest red.

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Figure 7As in Fig. 4 but for area with temperatures below the NAT PSC threshold in the SH.

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During the years including roughly 1993 through 1998, larger differences and standard deviations are seen above about 30 hPa in ERA-I and MERRA-2. These differences are positive in the former and negative in the latter reanalysis, leading to a partial cancellation in the REM. Between 1986 and 2001, ERA-I exhibited a layered structure of differences from the REM: positive at pressures greater than ∼50 hPa and less than ∼30 hPa and negative in between. A similar structure but with the signs reversed is seen in MERRA-2 where it extends back to 1980 and ends sharply in 1998. Investigations in progress (Long et al., 2018) show that both MERRA-2 and ERA-I temperatures in the SH polar stratosphere have oscillations of up to about 3 K that are in opposite directions, leading to the structure of the differences seen here. (Note that the absence of oscillations in the other reanalyses does not imply better agreement with sondes; Long et al., 2018). After 2000, both reanalyses show slightly positive (and, in the case of MERRA-2, largely statistically insignificant) differences from the REM at most pressure levels. CFSR/CFSv2 shows mostly positive differences between 1979 and 1986; afterward, the differences are primarily slightly negative at most of the pressure levels shown.

While the main sources of stratospheric information for all the reanalyses before 1998 are the SSU and MSU instruments, different reanalyses use different radiative transfer models to assimilate them and apply bias correction differently (Wright et al., 2018). It is particularly difficult to speculate about changes in CFSR/CFSv2, since it has multiple discontinuities and biases related to stitching together execution streams and applying a bias correction in a model with a warm bias (Long et al., 2017). Thus, while we cannot pin down particular changes that are associated with the differences among the reanalyses prior to the introduction of ATOVS data, there are numerous factors that could contribute to this behavior.

Average differences in minimum temperatures in the NH (Fig. 5) show more complicated patterns of changes over the years than those seen in the SH. The differences are much smaller throughout the 38-year period, with maximum absolute differences near 1.5 K at the highest levels shown (mainly in the period from about 1994 to 2004), and more frequent years/levels where the average differences are not statistically significant. From roughly 10 to 25 hPa, the standard deviations do decrease from above ∼1 K to less than ∼0.75 K after around 1999, though (as was the case in the SH) they remain larger in CFSR/CFSv2 than in the other reanalyses. While there are indications of changes around 1999, particularly in ERA-I and MERRA-2 they are less abrupt and of smaller magnitudes than those in the SH, and it is not as clear that there is a uniform trend towards better agreement. As in the SH, the CFSR/CFSv2 differences are primarily positive before 1987 and negative afterwards. ERA-I shows mostly positive differences except near 10 hPa. The opposite is true for JRA-55, except for the period between 1998 and 2006 when the differences are near zero, but slightly positive (and many of them not statistically significant), at pressures greater than about 30 hPa. Similar to the SH case, MERRA-2 exhibits a layered structure of differences prior to 1998: positive between roughly 60 and 30 hPa, and negative outside of this layer. After 1998, the MERRA-2 differences are mainly positive, except at pressures greater than about 50 hPa, where the differences gradually change from negative to positive between 2005 and 2010, except at the lowest levels.

Figure 6 shows the REM climatological values of the area with temperatures below the NAT PSC threshold (A_NAT) for the NH and SH winter seasons. As expected, these echo the patterns of minimum temperatures seen in Fig. 3, with the largest areas in the NH in early January, and in the SH in middle to late July. The great variability in the NH (see the grey envelopes in the line plots) results in the largest values being well above the climatological average, about 7 %–8 % of a hemisphere, but still much lower than the largest average values in the SH of over 10 % of a hemisphere.

Note that comparing differences in NH A_NAT among the reanalyses is more difficult than doing so for the SH or for the other NH diagnostics. Because there is significant interannual variability in the onset, termination, and magnitudes of low temperatures in the NH (see both Figs. 3 and  6), there are many NH winters with relatively few days having temperatures below T_NAT and thus many days with NH A_NAT being zero. Thus, comparing differences among the reanalyses for the full DJFM time period can often be unfairly biased by the high occurrence of zeros, which artificially decreases the average differences and standard deviations. To allay this issue such that we fairly compare NH A_NAT, we modify our analysis procedure as follows: we use time series of the REM NH A_NAT in November through April on 30, 50, and 70 hPa to define approximate start and end dates for the periods having non-zero A_NAT. We use 30 hPa to define the onset dates (because A_NAT usually first becomes non-zero around this level; e.g., Fig. 6a), and 50 or 70 hPa to define the termination dates. More specifically, we define the onset dates for each year as the first day at 30 hPa having non-zero A_NAT, and the termination dates as the latest day chosen by either 50 or 70 hPa having non-zero A_NAT; both 50 and 70 hPa are used because termination most often happens latest around 70 hPa as seen in Fig. 6a, but in some winters it happens later around 50 hPa. This process gives us individual “NAT seasons” between 1979/1980 and 2016/2017; these have a median length of 85 days, with the minimum and maximum number of days being 40 and 126, respectively. We then use these truncated time series to define the average differences and standard deviations thereof. This modifies the bootstrapping procedure described in Sect. 2.2.4; we still perform 2×10⁵ stationary bootstraps for each year, but because the lengths of the time series vary, we also vary the expected block size for each year by specifying them as the nearest integer to the cube root of the time series lengths plus a constant offset of +5 (which ranges from 8 to 10 days for time series lengths between 40 and 126 days). As was found for the regular bootstrapping procedure, using different expected block lengths with offsets between 0 (3 to 5 days) and 10 (13 to 15 days) had very little effect on the statistical significance results.

Figure 8As in Fig. 7 but for the NH. See text for explanation of date ranges used for the calculations.

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Figure 7 shows A_NAT differences from the REM for the SH winter seasons. There is a very apparent sudden decrease in the seasonal standard deviations of the differences at levels above ∼25 hPa after 1998 similar to but much more pronounced than in the case of minimum temperatures. The 1998–1999 boundary is less obvious in the average differences for CFSR/CFSv2 and JRA-55 but is apparent in ERA-I and MERRA-2. By these metrics, all four reanalyses converge toward better agreement following the TOVS/ATOVS transition. The patterns of differences largely mirror (in an opposite sense) the patterns shown in Fig. 4; that is, there tend to be positive/negative differences from the REM in A_NAT wherever there are negative/positive differences from the REM in minimum temperatures. ERA-I and MERRA-2 display layered difference structures prior to 1998; these layers of positive and negative differences are separated by approximately the 30 and 70 hPa pressure levels. As in the case of the minimum temperatures, the layered structures are more persistent in MERRA-2, extending between 1980 and 1998, whereas the one in ERA-I becomes apparent after 1986. JRA-55 and CFSR/CFSv2 are more often closer to the REM in terms of both the mean differences and the standard deviations. For CFSR/CFSv2, at pressures greater than 20 hPa, the differences are mostly negative (smaller A_NAT) prior to 1986, and mostly positive thereafter. No clear pattern is apparent for JRA-55, although after approximately 2005 each reanalysis generally has a uniform sign of the differences from the REM in the deep layer between 120 and 10 hPa. Overall, the largest mean differences tend to be at levels above (pressures lower than) ∼20 hPa prior to 1998, with mean differences as large as ±1.5 % of a hemisphere; at higher pressures in the lower stratosphere where the bulk of polar processing takes place, average differences are often well within ±1 % of a hemisphere during this time and within ±0.5 % of a hemisphere thereafter. Despite the better agreement, in later years, many of the differences remain statistically significant after 1998; given the low standard deviations, these results indicate small but persistent (i.e., roughly constant) differences relative to the REM.

Figure 9As in Fig. 3 but for maximum sPV gradients. The color range in panels (a) and (b) is from 0 to 20 scaled PV gradient units (PVGUs) (blues to reds), with all values over 20 shown in the deepest red.

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Differences in NH A_NAT from the REM (Fig. 8) show more complex patterns than those in the SH and less of an obvious convergence toward better agreement after 1998, similar to the corresponding T_min differences. The differences do decrease after about 2000, with most average differences being between ±0.25 % of a hemisphere. JRA-55 does show a narrow band of slightly larger positive differences continuing into the later years between about 30 and 15 hPa. MERRA-2 and ERA-I exhibit a pattern of opposing differences in this same layer between 1986 and 1998, but a layered structure of positive and negative differences at the lower levels is mostly only apparent in MERRA-2, consistent with the structure of the T_min differences seen in Fig. 5. Overall, the differences are mostly negative in CFSR/CFSv2 and ERA-I, and positive in JRA-55 and MERRA-2, but there is a considerable dependence on time and pressure for all the reanalyses. As was the case for the SH, the standard deviations decrease over time with the largest values seen before 2001. There is a considerable year-to-year variability in the standard deviations at the higher levels in the earlier period with some years especially standing out (1986 in CFSR/CFSv2 and MERRA-2, 1996 in ERA-I and MERRA-2, and 2000 in ERA-I). These highest levels tend to be where A_NAT is climatologically marginal (see Fig. 6).

Overall, the patterns of differences in A_NAT qualitatively follow those in T_min in both hemispheres: positive/negative differences in A_NAT correspond to negative/positive differences in the minimum temperatures, as expected. However, the patterns of statistical significance are often different. For example, broad patches of largely statistically insignificant differences in T_min in MERRA-2 and JRA-55 in both hemispheres after 1998 do not always translate into differences in A_NAT marked as not significant. Furthermore, the largest (most positive) values of one diagnostic do not always yield the smallest (most negative) ones in the other, and vice versa. Even more strikingly, the patterns of standard deviations, while overall similar, do not exhibit a simple monotonic relationship with those in T_min and generally display much more year-to-year variability before 2000. This is not unexpected as A_NAT differences depend not only on overall temperature biases but also on the morphology of the fields (e.g., spatial patterns or gradients), which varies from year to year and, to a certain extent, among the reanalyses. While closely related, the A_NAT and T_min statistics represent different diagnostics and elucidate different aspects of the reanalyses' differences in relation to polar processing.

Figure 10As in Fig. 4 but for maximum sPV gradients.

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3.2 Vortex diagnostics

Figure 9 shows the NH and SH climatologies of REM MPVGs. The evolution of MPVGs is quite similar in both hemispheres, particularly above 500 K; the gradients in sPV gradually increase over time, reaching maxima in roughly mid-February in the NH and early October in the SH. These patterns largely reflect two effects: one is the seasonal cycle of the vortex building up strength and subsiding. The other is the build-up effect from wave breaking and mixing/erosion of PV in the surf zone (the region of low-magnitude PV outside the vortex, e.g., McIntyre and Palmer, 1984) over the season, which can act to sharpen the gradients of PV in the vortex edge region. Generally, MPVGs provide a measure of the strength of the vortex edge as a transport barrier. For simplicity, in the discussion of results below, we will refer to $\mathrm{1.0}\times {\mathrm{10}}^{-\mathrm{6}}$ s⁻¹ deg⁻¹ as 1 scaled PV gradient unit, or 1 PVGU.

Figure 11As in Fig. 10 but for the NH.

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The averages and standard deviations of differences from the REM SH MPVGs are shown in Fig. 10. Through about 1998–2000, ERA-I and JRA-55 show similar patterns of differences from the REM, with a band of near-zero (for JRA-55) or small negative (for ERA-I, magnitudes up to ∼1.5 PVGUs) differences that are usually not statistically significant (at the 99 % confidence level, as described in Sect. 2.2) below about 460 K, positive differences between about 460 and 660 K, and negative differences above. The ERA-I differences are generally not statistically significant between 580 and 750 K. In the same time period, MERRA-2 shows an approximately opposite pattern, with negative differences from about 460 to 660 K and positive differences above and below; from about 1995 to 1999, MERRA-2 shows large average differences up to about 3.5 PVGUs above 700 K. In contrast to the banded structures in the other reanalyses, CFSR/CFSv2 generally shows small-magnitude negative differences across the levels and period, except during the period including 1985 through 1996 above about 700 K. The seasonal standard deviations of the differences are relatively small (usually on the order of 0.5–1.5 PVGUs), suggesting that statistically significant differences in the reanalyses typically represent differences that are more systematic in nature for MPVGs at these levels and times. The standard deviations tend to increase with height, especially at levels in the middle stratosphere above about 660 K where the differences can exceed 2.5–3 PVGUs. CFSR/CFSv2 and JRA-55 generally show slightly lower standard deviations than ERA-I and MERRA-2, and MERRA-2 shows a cluster of years between about 1994 and 1998 with large standard deviations above 700 K. After about 1998, there is a noticeable shift toward better agreement in most regions, similar to that seen in the SH temperature diagnostics. CFSR/CFSv2 and JRA-55 do not show an obvious improvement below about 550 K but already had close agreement with the REM there. In ERA-I and MERRA-2, most regions show small (magnitude less than 1 PVGU) differences that are not statistically significant after 1998. This shift toward better agreement is also reflected in the standard deviations, which markedly decrease in all the reanalyses, especially at levels above about 580 K. Similar to the temperature diagnostics, the TOVS to ATOVS transition most likely played a large role in this shift, with differences in the handling of this transition and the addition of AIRS radiances in 2002 also expected to be significant factors.

Differences in NH MPVGs from the REM (Fig. 11) indicate that CFSR/CFSv2 generally has smaller, and JRA-55 larger, PV gradients than the REM at levels up through about 750 K. ERA-I and MERRA-2 show smaller and less systematic patterns of differences that typically are not statistically significant. ERA-I does show a small vertical region with significant positive differences from the REM between 520 and 580 K until about 2001, similar to its pattern for the SH but with overall smaller differences. The standard deviations of the differences are largely consistent among the reanalyses; other than a few standout cases in ERA-I and MERRA-2 (1994/1995 in MERRA-2 and 2000/2001 in both), the standard deviations tend to increase consistently with height from less than 0.8 PVGUs at the lowest levels, to about 1.5+ PVGUs at the highest levels. There is some indication of convergence toward better agreement in MPVGs after roughly 2001 in MERRA-2 and ERA-I (when the reanalyses, except JRA-55, began assimilating AIRS radiances; Fig. 1), though most differences from the REM for these two reanalyses were not statistically significant even in the earlier years. No qualitative improvement in agreement with the REM is apparent in the CFSR/CFSv2 or JRA-55 differences, but the standard deviations of the differences do seem to decrease slightly above about 580 K for years after 2001.

Figure 12As in Fig. 9 but for sunlit vortex area. The color range in panels (a) and (b) is from 0 % to 13 % of a hemisphere (blues to reds), with all values over 13 % shown in the deepest red.

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Figure 12 shows the REM climatologies of SVA for both hemispheres. As was the case for MPVGs, the seasonal patterns of SVA for both hemispheres are similar. In this case, the patterns are largely due to the lack of sunlight early in the winter season, which gradually returns later on. However, there are notable differences between the hemispheres, particularly that SVA tends to be smaller in the NH; this is because the NH polar vortex is almost always smaller than its SH counterpart. The NH also shows relatively larger values in early winter above about 650 K, resulting from the NH vortex being more often disturbed and shifted to lower latitudes within sunlight. During individual winters, and given sufficiently low temperatures, the amount of vortex air exposed to sunlight at any time is generally indicative of the amount of air where ozone depletion can take place.

Figure 13As in Fig. 4 but for SH sunlit vortex area.

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The averages and standard deviations of differences of SH SVA from the REM are shown in Fig. 13. There are some persistent patterns of differences among the reanalyses; JRA-55 SVA is consistently smaller than that from the REM between about 430 and 700 K and larger above and below. Above about 700 K, JRA-55 differences are generally not statistically significant through about 2003, after which each of the other reanalyses evaluated had started assimilating AIRS radiances (see Fig. 1 and Fujiwara et al., 2017). The other reanalyses generally show sandwiched structures of negative and positive differences: MERRA-2 (ERA-I) shows positive (negative) values between 430 and 520 K, with negative (positive) values above and below. CFSR/CFSv2 shows positive values between about 490 and 660 K, and small (often not statistically significant) negative values at higher and lower levels; in this case, the band of positive differences extends to higher levels after 1998. In the top several levels (approximately 750 to 850 K), agreement of the reanalyses with the REM appears to degrade starting about 1999–2000: ERA-I and MERRA-2 show a decrease in the number of values that are not significantly different from zero, while JRA-55 shows a similar decrease starting around 2003–2004. MERRA-2 differences increase in magnitude in this region and time period, and those in JRA-55 change from negative to positive, while ERA-I shows increased differences, near/over 2.5 %, at the highest levels in 1999–2001. CFSR/CFSv2 shows an increase in the significance of the differences at these levels after 2010 (the time of the CFSR to CFSv2 transition). The standard deviations of the differences are the highest at levels above 660 K where they are often above 1 % of a hemisphere. These are more pronounced in ERA-I, which shows standard deviations often ranging above 1 %, with some years reaching over 2 % above 660 K. Some slightly larger (0.4 % to 0.8 %) standard deviations are also seen at the lowest levels (390 and 410 K), which are around the top of the subvortex region for the SH. After 2001, the standard deviations of differences are generally less than 0.4 % of a hemisphere at most of the levels between 390 and 750 K in all the reanalyses, suggesting a small shift towards more consistent SVA differences compared to the REM among the reanalyses. Examination of the reanalyses' differences in vortex area from those in the REM reveal they are nearly identical to those for SVA, indicating that the differences are largely dominated by differences in the area enclosed within the vortex edge contours.

The patterns of averages and standard deviations of differences in SVA for the NH (Fig. 14) are quite different from those in the SH: MERRA-2 and ERA-I show overall positive differences (except for narrow bands of small differences at the highest levels that are not significant), while JRA-55 shows overall negative values. CFSR/CFSv2 shows negative values below about 520 K and at 800 and 850 K, with positive values in between. There is no obvious indication of a decrease in the magnitude of the differences over the period compared. The standard deviations of NH SVA differences from the REM generally look consistent between the reanalyses, with the largest values greater than 0.7–1.2 % of a hemisphere usually confined to a band of levels between 700 and 850 K. At lower levels, however, the standard deviations are quite small throughout the period, generally on the order of 0.5 % of a hemisphere or less; CFSR/CFSv2 shows slightly higher values below about 460 K. As was the case for the SH, the SVA differences are dominated by differences in total vortex area among the reanalyses. Thus, while there is no consistent change in agreement over the years, our results indicate persistent differences in the size of the contours used to define the vortex edges and hence some persistent differences in the isentropic PV fields (reflected in differences in the PV values at which the maximum PV gradients are located).

Figure 14As in Fig. 13 but for the NH.

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3.3 Derived vortex–temperature diagnostics

The diagnostics shown in the following subsection are derived from the temperature and/or vortex diagnostics shown in the previous two subsections.

Figure 15Winter means of the fraction of vortex volume between the 390 and 580 K isentropic surfaces with temperatures below T_ice in the SH (a, c), and range of values obtained for the ±1 K sensitivity tests (b, d). The colored bars show the range of values obtained from the tests of sensitivity to the PSC threshold temperature used (see Sect. 2.2.2), while the black dots show the value for the “central” threshold temperature. The winter mean is calculated over the full MJJASO period. For each year, the reanalyses are ordered from smallest central value on the left to largest central value on the right; this order is also given as a text string at the top of the column for each year. The numbers at the bottom of each year's column indicate the difference in winter mean fraction between the largest and smallest central values for the winter season (i.e., between the rightmost and leftmost black dots). In the range panels (b, d), the range about the central value (black dots in a and c) is shown for each reanalysis. Green, blue, purple, and red indicate CFSR/CFSv2, ERA-I, JRA-55, and MERRA-2, respectively.

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Figure 15 shows the winter mean volume of temperatures below T_ice in the SH expressed as a fraction of the vortex volume, calculated for the central PSC threshold and the ±1 K sensitivity thresholds (see Sect. 2.2.2). Keeping in mind that T_ice was estimated assuming nominal pressure levels for isentropic levels (see Sect. 2.2.2), which can result in significant overestimates of areas/volumes, Fig. 15 shows that the volume fraction of cold air is relatively constant from year to year. Generally, the fractions of the vortex are between 0.20 and 0.30 each year, with sensitivities to the ice threshold offsets often less than ±0.05. During the winters of 1979 through 1986, there is a very persistent pattern with CFSR/CFSv2 having the lowest, and ERA-I having the highest, cold volume fractions of the vortex. During this period, CFSR/CFSv2 vortex fractions can individually be lower than the other reanalyses by nearly 0.025 to 0.03. These same years also have the largest inter-reanalysis spreads, with differences between the largest and smallest vortex fractions often greater than 0.04. For nearly all years between 1996 and 2016, ERA-I tends to have the lowest volume fractions, ranging from roughly 0.01 to 0.02 lower than the other reanalyses. For the years from 2007 to 2015, JRA-55 consistently has the highest volume fractions, but in these cases the inter-reanalysis differences are generally quite small. Differences among the reanalyses in the temperature threshold sensitivity envelopes are quite small, which indicates that there are not any persistent differences in temperature gradients among the reanalyses.

Figure 16As in Fig. 15 but for the NH and temperatures below T_NAT.

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Potential polar processing volumes in the NH are much lower and much more variable than those in the SH. The NH fraction of vortex volume below T_NAT (Fig. 16) shows values in the colder years that are comparable to those below T_ice in the SH. The lowest values are seen in 1984/1985, 1998/1999, 2001/2002, and 2003/2004, which are all years with very early (mid-December to the beginning of January) major SSWs that profoundly affected the entire stratosphere, including strongly disrupting the lower stratospheric vortex (e.g., Manney et al., 1999, 2005b; Naujokat et al., 2002); in these years, the fractional volumes are near 0.03, as opposed to nearly 0.30 in the coldest years (e.g., 1996, 2011, 2016). The range of values from the PSC threshold temperature sensitivity tests varies from about ±0.02 in the warmest years up to over ±0.05 in the coldest years, with differences between reanalyses indicating some differences in horizontal temperature gradients (especially in, e.g., 1997, 2009, and 2011). The interannual variability is well represented in all of the reanalyses. The central values usually vary more between reanalyses in colder years; e.g., 1996 and 2011 stand out as showing wide ranges of about 0.045. Between 1992/1993 and 2016/2017, ERA-I tends to have the smallest vortex fractions. In contrast, JRA-55 tends to have the overall largest NAT vortex fractions, having the largest values for 32 of the 38 years, with many cases being noticeably offset from the other reanalyses. While many of the recent years show smaller ranges of central values than the early years, there is not a monotonic progression, so any trend towards better agreement is masked by the larger influence of specific interannually varying conditions that affect the PSC volumes.

We note that the results of intercomparisons of V_PSC∕V_Vort outlined above are not very sensitive to the vortex volumes. When comparing these V_PSC∕V_Vort results having V_Vort determined from the reanalyses' individual vortex areas to V_PSC∕V_Vort calculated using the REM V_Vort (i.e., the reanalyses' V_PSC divided by the REM V_Vort), the reanalysis magnitudes and orderings remain generally consistent. However, using the REM V_Vort does tend to decrease the inter-reanalysis spreads and the sensitivities to the ±1 K PSC temperature thresholds.

Figure 17Pixel plots of (a) vortex decay dates (see text for the definition) based on the REM of vortex area, and (b–e) the difference between the vortex decay dates in each of the reanalyses from the REM (as reanalysis − REM).

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Figures 17 and 18 show pixel plots of the REM vortex decay dates and the differences from the other reanalyses (i.e., the reanalyses minus REM). For the SH, Fig. 17a shows that the vortex tends to decay fairly late in the year, and it does so earlier at the upper levels than at the lower levels; in other words, the vortex in the SH typically decays from the top down. The differences in decay dates among the reanalyses are generally less than 2 weeks; over 90 % of the differences are between ±7 days. The patterns of differences in each of the reanalyses generally follow their vortex area differences from the REM (which, while not shown, are very similar to differences shown in Fig. 13). That is, wherever the reanalyses have smaller/larger vortex areas than the REM, their vortices persist for less/more time. ERA-I shows some notable exceptions to this at levels above 700 K where its decay dates precede those of the REM by up to 14 days in the same region where ERA-I tended to have positive vortex area differences (see, e.g., 1980, 1981, 1987). Overall, because the differences in vortex area tend to be dominant and persistent, as shown in Fig. 13, so are the decay date differences, and thus there are no easily discernible changes in agreement over time.

Figure 18 shows that the NH vortex breakup is much more variable from year to year than that in the SH. Unlike the SH vortex, the NH vortex can decay nearly simultaneously over a wide range of levels (e.g., 1984 and 1999), or it can decay earlier at some low levels and later at higher levels (e.g., 2001 and 2009). Such variability in vortex decay is due to large variability induced by SSW disturbances to the vortex, as well as polar night jet oscillation events in which the middle and upper stratospheric vortex rapidly reforms following some major and minor disturbances (e.g., Hitchcock et al., 2013; Lawrence and Manney, 2018, and references therein). The reanalyses' differences from the REM are generally quite small; over 90 % of the differences are between ±4 days. With the exception of JRA-55, the reanalyses show no predominant patterns of differences (e.g., positive or negative bands). JRA-55 does seem to have a slightly more pronounced band of negative differences from about 620 to 700 K (with a band of small but positive differences above), in the same region where the JRA-55 vortex area differences tend to be the most negative (not shown directly but consistent with Fig. 14). There are also several outlier cases with absolute differences from the REM greater than 20 days (denoted by the white X symbols). Most of these cases are marginal scenarios when either the REM or the reanalyses' vortex areas oscillate above and below the specified 1 % of a hemisphere threshold at some levels, causing our algorithm to pick disparate decay dates. Many of these outlier cases occur at different singular levels and years in the reanalyses, but 460 K 2003/2004 does show up as a negative outlier in both CFSR/CFSv2 and JRA-55, while 660 K 2005/2006 shows up as a positive outlier in both CFSR/CFSv2 and ERA-I.