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Previous calculations of the strength of the stratospheric circulation from data have relied on indirect measures. Observational estimates of the strength of the overturning have been limited to qualitative descriptions based on tracer distributions1,2,3,4 or quantitative measures of limited regions, such as the vertical velocity over a narrow range in the tropics5,6,7. Free-running climate models vary widely in stratospheric circulation metrics, including the tropical upwelling mass flux at 10 hPa and 70 hPa, although the multimodel mean is relatively close to some reanalysis products8. Reanalyses, meanwhile, differ substantially in their mean tropical upwelling velocity, with the magnitude of the mismatch depending on how it is computed9. Here we consider the diabatic circulation of the stratosphere; because the stratosphere is stratified, vertical motion moves air across potential temperature surfaces and thus must be associated with warming/cooling in the ascending/descending branches. Hence, the net meridional overturning of mass is tightly linked to diabatic processes. We use potential temperature as our vertical coordinate, and the meridional overturning becomes explicitly the diabatic circulation in this framework.

The diabatic circulation has been shown to be related to the idealized tracer ‘age of air’10,11, which is a measure of how long an air parcel has spent in the stratosphere12. The difference between the age of the air that is upwelling and downwelling through an isentropic surface is inversely proportional to the strength of the diabatic circulation through that surface, in steady state and neglecting diabatic diffusion.

In this paper, we apply this age difference theory to calculate the mean magnitude and vertical structure of the global overturning circulation of the stratosphere using observations of sulfur hexafluoride (SF6) and nitrous oxide (N2O). We demonstrate the validity of the theory and explore limitations of the tracer data with a coupled chemistry–climate model. We calculate the global overturning directly from the diabatic vertical velocity from three reanalyses to compare with the data and model results. Information on the data products, model, and reanalyses is given in Table 1.

Table 1 Data, reanalyses, and model output used in this study.
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Age of air observations and model

A trace gas that is linearly increasing in time in the troposphere and has no stratospheric sinks can be converted to age following age of air theory12. Carbon dioxide (CO2) and SF6 are both approximately linearly increasing in the troposphere and have minimal sinks in the stratosphere. We use age derived from SF6 measurements (henceforth SF6-age) from the Michelson Interferometer for Passive Atmospheric Sounding (MIPAS) on Envisat4. We interpolate SF6-age onto isentropic surfaces using simultaneously retrieved pressure and temperature from MIPAS13,14. The resulting SF6-age on the 500 K surface is shown in Fig. 1a. Age is young in the tropics, older in the extratropics, and oldest at the winter poles, consistent with the pattern of upwelling in the tropics and the majority of downwelling in the winter polar region. The SF6-age at high latitudes in wintertime is older than observations of age based on CO2 measurements15,16. SF6 is not conserved in the mesosphere, and its sink will result in a high bias in SF6-age in areas with mesospheric influence17, such as the poles and the upper stratosphere.

Figure 1: Age of air on the 500 K surface.
figure 1

a–d, The different panels show age calculated from SF6 from MIPAS (a), N2O from GOZCARDS (b), SF6 from WACCM (c) and WACCM ideal age tracer (d). Contours are every half year, and the ages in the Southern Hemisphere winter for MIPAS get above 8 years old.

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To explore the limitations of using SF6-age, we compare SF6-age to ideal age of air in a coupled chemistry–climate model, the Community Earth System Model 1 Whole Atmosphere Community Climate Model (WACCM). This fully coupled state-of-the-art interactive chemistry–climate model18,19 includes the physical parameterizations and finite-volume dynamical core20 from the Community Atmosphere Model, version 4 (ref. 21). The model domain extends from the Earth’s surface to the lower thermosphere (140 km). The WACCM simulations are based on the Chemistry–Climate Model Initiative REF-C1 scenario22. WACCM models only one of the two sinks of SF6 in the mesosphere; photolysis at Lyman-alpha wavelengths is included, but associative electron attachment, recently shown to be the dominant loss mechanism for SF6 below 105 km (refs 23,24), is not. The impact of the mesospheric sink of SF6 on stratospheric SF6 will be determined by the strength of the dynamical coupling between the stratosphere and the mesosphere. We calculate SF6-age using the same methods as were used to calculate MIPAS SF6-age1 (for details see Methods). Although WACCM is missing the dominant SF6 loss mechanism, the difference between SF6-age and ideal age will qualitatively illustrate the sense and location of any bias introduced by using SF6 as an age tracer.

Age on the 500 K surface between 2002 and 2012 is shown for WACCM SF6-age in Fig. 1c, and for WACCM ideal age of air in Fig. 1d. The agreement between ideal age and SF6-age on the 500 K surface suggests that SF6-age is a good proxy for ideal age at this level in the model. The temporal correlation at each latitude on the 500 K surface is high (r = 0.93), and only at the poles is SF6-age older than ideal age by up to half a year. Where there is more mesospheric influence the correlation is weaker and no longer one to one: higher in the stratosphere and at the highest latitudes (r = 0.52 and age has only 35% of the magnitude of variations of SF6-age at 1,200 K, 85° N). Since WACCM is missing the dominant sink of SF6, these differences represent a lower bound on the bias from using SF6-age as a proxy for ideal age.

The difference between the MIPAS SF6-age and WACCM SF6-age is substantial. MIPAS SF6-age has been shown to be consistently older than in situ CO2 and SF6 age observations, although typically within error estimates1,4 (see Supplementary Information). In the tropics, these known high biases are almost the same as the difference between WACCM SF6-age and MIPAS SF6-age. In the polar region, a similar amount of bias exists at low levels, and at upper levels there are no in situ measurements for comparison. In WACCM, the dynamical coupling of the stratosphere and mesosphere has been shown in certain events to be too weak25,26, and in another case to be accurate16, and so the reliability of the model’s transport of mesospheric air into the stratosphere is unclear.

Given the potential biases of SF6-age and the MIPAS data, other age tracers are desirable to corroborate the circulation strength calculations from SF6-age. CO2 is currently not retrieved from satellites with enough accuracy and spatial coverage to calculate age of air differences27. Instead, we determine age from N2O, which demonstrates a compact relationship with age, like other long-lived stratospheric tracers28. We use a relationship between age of air and N2O calculated empirically from balloon and aircraft measurements29, accounting for the linear growth in tropospheric N2O. Following the procedure outlined in the Methods, we calculate age of air from the Global OZone Chemistry And Related trace gas Data records for the Stratosphere (GOZCARDS) N2O data for 2004–201330. Because of the range of tracer values over which the empirical relationship holds, global coverage exists for a small range in potential temperature (about 450 K–500 K, Supplementary Fig. 8). An additional empirical relationship31 is explored in the Supplementary Information.

The age on the 500 K surface calculated from its empirical relationship with N2O is shown in Fig. 1b. The Southern Hemisphere winter polar coverage is limited because N2O concentrations are below 50 ppb, the lower limit of the empirical fit. Age from the N2O data is generally younger than MIPAS SF6-age, although older than age from WACCM. The temporal correlation of MIPAS SF6-age and N2O-age at every latitude on the 500 K surface is around r = 0.5, except in the Northern Hemisphere mid-latitudes, where the correlation is not significant.

Age difference and the diabatic circulation

In steady state, the diabatic circulation () through an isentropic surface wholly within the stratosphere can be calculated as the ratio of the mass above the surface (M) to the difference in the mass-flux-weighted age of downwelling and upwelling air on the surface (ΔΓ, or age difference)11.

is the total mass flux upwelling (or downwelling, as in steady state these must be equal) through the isentropic surface. (See Figure 1 of ref. 11 for a diagram.) Intuitively this reflects the idea of a residence time; the age difference is how long the air spent above the surface, and it is equal to the ratio of the mass above the surface to the mass flux passing through that surface.

The real world is not in steady state, and so averaging is necessary for this theory to apply. A minimum of one year of averaging was necessary for the theory to hold in an idealized model11. As the MIPAS instrument has five years of continuous data, the longest average possible for this study is five years. To test the validity of applying the steady-state theory to five-year averages, we have calculated the 2007–2011 averages of ideal age difference and the ratio of the total mass above each isentrope to the mass flux through that isentrope from WACCM output. These are shown in the blue lines (solid and dotted, respectively) in Fig. 2. The total overturning strength is calculated from the potential temperature tendency, , which is the total all-sky radiative heating rate interpolated onto isentropic surfaces. The upwelling and downwelling regions are defined where is instantaneously positive or negative, and the mass fluxes through these regions are averaged to obtain the total overturning mass flux, . If the age difference theory held exactly, the two blue lines in Fig. 2 would be identical. In the upper stratosphere, these two calculations agree closely; in the lower stratosphere, the ratio of the mass to the mass flux is greater than the ideal age ΔΓ. This behaviour is consistent with the neglect of diabatic diffusion, which is greater in the lower stratosphere32. Using area weighting of ideal age, since mass-flux weighting is not possible with data, results in about a 10% low bias of ΔΓ compared to the mass-flux weighting shown here.

Figure 2: The average age difference between downwelling and upwelling age of air on each isentrope between 2007–2011.
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ΔΓ is plotted in solid lines: MIPAS SF6-age in purple, GOZCARDS N2O-age in black, WACCM SF6-age in green, and WACCM ideal age of air in the blue. The blue dotted line shows the ratio of the total mass above each isentrope to the mass flux through the isentrope (M/) from WACCM. The shading shows one standard deviation of the five annual averages that are averaged to get the mean. The mean height of each isentrope in the tropics (calculated from MIPAS pressure and temperature) is on the right y-axis. Where the line for the MIPAS SF6-age difference is thinner, we believe there is a bias in either the data or the SF6 to age conversion (see discussion in Supplementary Information).

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We calculate the five-year average (2007–2011) of the difference in area-weighted age of air in the regions poleward and equatorward of 35° from the SF6-age from both MIPAS and WACCM, and from the N2O-age. (See Supplementary Information and Supplementary Fig. 1 for a discussion of this latitudinal extent.) The results of this are shown in Fig. 2. The MIPAS SF6-age ΔΓ is different from the other estimates except around 450 K. At 400 K, it is smaller, in part because of older tropical air at that level (see Supplementary Fig. 10). Above 500 K, MIPAS SF6ΔΓ is much greater than the model ΔΓ using either ideal age or SF6-age. Age difference for N2O is calculated only where data is available over the entire surface at almost all times, 450–480 K (extended in Supplementary Fig. 9). In this limited range, the age difference from N2O-age is greater than the age difference from WACCM and agrees with the age difference calculated from MIPAS SF6-age.

To gain insight into the role of the mesospheric sink, we compare the ideal age ΔΓ with SF6-age ΔΓ in WACCM. The ideal age ΔΓ is the mass-flux-weighted age difference between upwelling and downwelling regions, and the SF6-age ΔΓ from WACCM is calculated in the same way as the MIPAS SF6-age ΔΓ. Because of the area weighting, we expect the SF6-age ΔΓ to be 10% lower than the ideal age ΔΓ. This is true from 450–550 K, but above that, the SF6-ageΔΓ is either equal to or greater than the ideal age ΔΓ, and at 1,200 K SF6-age ΔΓ is 50% greater. Since WACCM does not include the dominant sink of SF6 for the mesosphere, we cannot estimate an upper bound on the true bias.

All three calculations of ΔΓ from the model as well as the ΔΓ from MIPAS SF6-age show a peak in the middle stratosphere. This peak indicates a relative minimum of the diabatic velocity at that level, and so this provides evidence that there are indeed two branches of the circulation33.

Circulation from reanalyses, model, and age

Figure 3 shows the total overturning circulation strength calculated using the ratio of the total mass above the isentrope to ΔΓ for the MIPAS SF6-age and the N2O-age. Total mass is determined from the simultaneously retrieved pressure in the former case and from pressure from the Modern Era Retrospective analysis for Research and Applications (MERRA34) for N2O. Also shown is the directly calculated overturning circulation strength from the three reanalysis products MERRA, Japanese 55-year Reanalysis (JRA 55 (ref. 35)) and the ECMWF Reanalysis Interim (ERA-Interim36), and from WACCM. The total overturning strength is calculated from the potential temperature tendency, , from the total diabatic heating rates from JRA 55 and ERA-Interim forecast products and from total temperature tendency provided by MERRA, and then following the same procedure as above for WACCM.

Figure 3: The strength of the total overturning circulation through each isentrope averaged between 2007–2011.
figure 3

The solid lines are for the data-based estimates MIPAS SF6 in purple and GOZCARDS N2O in black. Reanalyses are shown in dashed lines: JRA 55 in light blue, MERRA in green and ERA-Interim in gold. The dotted blue line is WACCM. The shading shows one standard deviation of the five annual averages. The details of the calculation for each data product, the model and the reanalyses are described in the text. The mean height of each isentrope in the tropics (calculated from MIPAS pressure and temperature) is on the right y-axis. Where the line for the MIPAS SF6-age difference is thinner, we believe there is a bias in either the data or the SF6 to age conversion (see discussion in Supplementary Information).

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These six estimates of the strength of the circulation are quite different, as can be seen by examining the circulation at individual levels. At the lowermost levels, the reanalyses tend to agree, while the MIPAS SF6-age circulation estimate is much greater because of its very low ΔΓ. In the range where we have estimates from both observational data sets, they agree closely and are flanked by the reanalyses, which vary more widely (see Supplementary Information for more details). At 500 K and above, the MIPAS SF6-age-based circulation strength has the lowest value, and at 900 K and above, it is lower by a factor of three. The circulation strength from MIPAS SF6-age ΔΓ is biased low, consistent with the sink of SF6 in the mesosphere24. The disagreement at 1,200 K would require that the bias be nearly 300% for the model and reanalyses to agree with the data. In addition to the disagreement of MIPAS SF6-age circulation strength with the model and reanalyses, there is significant disagreement between different reanalyses. MERRA has a distinct vertical structure, with weaker circulation in the lower stratosphere and stronger circulation in the mid-stratosphere. JRA 55 and ERA-Interim have a similar vertical structure; JRA 55 is stronger by around 3 × 109 kg s−1, except above 800 K, where it decreases more quickly with potential temperature than ERA-Interim so that they converge by 1,200 K. The shading is the standard deviation of the annual averages that make up the five-year average, and it shows the small interannual variability.

A benchmark and the need for more data

The strength of the stratospheric circulation helps determine transport of stratospheric ozone, stratosphere–troposphere exchange, and the transport of water vapour into the stratosphere37. Stratospheric water vapour has been demonstrated using both data38 and a model39 to impact the tropospheric climate. The stratospheric ozone hole recovery is also influenced by the strength of the circulation40.

We have calculated the strength of the overturning circulation of the stratosphere from observations, reanalyses, and a model. We find that at 460 K (about 60 hPa or 20 km in the tropics), the total overturning circulation of the stratosphere is 7.3 ± 0.3 × 109 kg s−1, based on the agreement of two independent global satellite data products to within 4% and including interannual variability estimated from WACCM (see Methods). Accounting for the potential high bias induced by the method, this estimate becomes 6.3–7.6 × 109 kg s−1. Despite this wide range, two of the three reanalysis products lie outside of this range, suggesting deficiencies in their lower stratospheric transport (see Supplementary Table 1). This value can be used as a metric to determine the accuracy of the mean transport of climate models. Because the diabatic circulation and not the residual circulation is used, the computational demands for this metric are minimal, requiring only monthly mean total diabatic heating and temperature on pressure levels.

The global SF6 data have enabled this quantitative calculation of the diabatic circulation in the middle and upper stratosphere. However, the interpretation of age from SF6 is limited because we cannot quantify the impact of the mesospheric sink of SF6, which is important above 550 K. This makes the age difference a minimum of 60% too high at 1,200 K, which would imply a 35% low bias in the overturning strength at 1,200 K, and we cannot estimate an upper bound on the bias. The reanalyses may correctly represent the stratospheric circulation where they agree at the uppermost levels, although the data becomes more limited there41. Beneath 900 K, however, the reanalyses disagree with each other as well as with the circulation strength implied by data; it is clear that the data assimilated into these reanalyses are not sufficient to constrain estimates of the circulation.

Climate models predict an increase in the strength of the Brewer–Dobson circulation of about 2% per decade42,43, and much effort has recently gone towards calculating trends in the stratospheric circulation based on observations and reanalyses to see if such a trend can be detected2,9,44,45. However, the mean diabatic circulation strength is not known except at one level. At upper levels, the circulation is uncertain to within at least 100%. We suggest cautious interpretation of trends in light of this uncertainty. More global age of air tracer data, in particular CO2, would provide an independent estimate of age difference and thus the strength of the diabatic stratospheric circulation. High-altitude balloon and aircraft measurements could be very useful; further characterization of compact relationships between age and long-lived tracers, such as N2O or methane, would provide additional constraints on the circulation in the lower stratosphere by enabling more complete utilization of current global satellite data.

Methods

MIPAS SF6.

For more details on validation and methods, we refer the readers to the papers on this product1,4,47. We note that the vertical resolution is 4 to 6 km at 20 km, 7 to 10 km at 30 km, and 12 to 18 km at 40 km altitude. Noise error on individual profiles is of the order of 20%, but because of the many profiles, meaningful SF6 has been obtained by using monthly and zonal mean averages in 10° bins.

N2O.

An empirical fit between N2O and age from an extensive record of NASA ER-2 aircraft flights and high-altitude balloons from 1992–1998 has been calculated29. Age is based on CO2, and for details of the conversion from CO2 to age, we refer the reader to the original study29. The fit holds well for 50 ppbv < N2O < 300 ppbv and is given by the equation Γ(N2O) = 0.0581(313 − N2O) − 0.000254(313 − N2O)2 + 4.41 × 10−7(313 − N2O)3, where 313 ppbv was the average tropospheric mixing ratio for 1992–1998. Although different tracer–tracer relationships are expected in the tropics and the extratropics31,48, the limited tropical data used to calculate this relationship were not treated separately. To account for the increase in tropospheric N2O, we calculate the trend from the data product provided by the EPA Climate Indicators46, a combination of station measurements from Cape Grim, Australia; Mauna Loa, Hawaii; the South Pole; and Barrow, Alaska. The slope is 0.806 ± 0.014 ppbv yr−1. (One standard error on the slope is reported. Using only Mauna Loa, the tropical station, does not change the fit much, since N2O is fairly well mixed in the troposphere.) We linearly adjust the GOZCARDS N2O data using this slope to account for the growth in tropospheric N2O, although simply subtracting the mean difference in tropospheric N2O between 2009 and 1995 yielded very similar results. Then we apply the empirical relationship between 2004 and 2012 to obtain age estimates. Age difference is calculated only on those levels for which there are very few gaps in age. Only 460 and 470 K have no gaps at all. This method relies on several potentially problematic assumptions: the compact relationship from the 1990s is assumed to be applicable over a decade later; the tropics are assumed be represented by this relationship well enough to obtain unbiased estimates of age difference; and linearly adjusting the data is assumed to sufficiently account for the changing tropospheric source.

WACCM SF6.

The method to calculate age from SF6 in WACCM is as follows: the SF6 on pressure levels is zonally averaged and then averaged in the same latitudinal bins that were used for MIPAS. That zonally averaged SF6 is then converted to age1. The reference curve for SF6 is the zonal mean value in the tropics at 100 hPa just north of the equator (0.5° N) with a one-year low-pass fourth-order Butterworth filter applied to remove the weak seasonal cycle. Results are insensitive to the filtering provided the filter is sufficient to obtain a strictly increasing reference curve. We use the same method for correcting the age of air for the nonlinear tropospheric growth, with a Newtonian iteration (see ref. 1 equation 3). The nonlinearity correction is insensitive to the choice of constant parameter used to describe the relationship of the width of the age spectrum with the age. Once the age is determined, it is interpolated to isentropic levels using zonal mean temperatures that have also been binned by latitude according to the MIPAS grid. No attempt is made in this work to adjust the age for the mesospheric sink.

Statistics for 460 K overturning.

To calculate the average overturning circulation strength where the two data estimates agree most closely (within 5% at 460 K), we average them. The error estimate is based on the variability in the total overturning circulation strength from WACCM calculated using SF6-age to infer the circulation (M/SF6-age ΔΓ). We take the average of five annual averages chosen randomly from the annual averages from 1999–2014 100,000 times. The standard deviation of the 100,000 resulting mean circulation strength estimates (0.14 × 109 kg s−1) is taken to be half of the error. We repeated this procedure using the true overturning circulation strength () and found smaller variations in the standard deviation (0.09 × 109 kg s−1). This error estimate assumes that WACCM represents the variability of the true circulation. The standard deviations of the five annual averages that were averaged for each data estimate were considerably smaller than these reported error bars. We therefore believe this is a conservative representation of the uncertainty in the diabatic circulation strength.

Code availability.

Codes used to generate the primary figures in this article is available at https://figshare.com/articles/NGeo2017_plots_m/5229844/1, and any additional code can be obtained from the corresponding author upon request.

Data availability.

The data for the primary figures in this article are available at https://figshare.com/articles/NGeo2017_plots_m/5229844/1, and any additional data can be obtained from the corresponding author upon request.

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