Climate model simulations show an acceleration of the
Brewer–Dobson circulation (BDC) in response to climate change. While the
general mechanisms for the BDC strengthening are widely understood, there
are still open questions concerning the influence of the details of the wave driving. Mean age of stratospheric air (AoA) is a useful transport
diagnostic for assessing changes in the BDC. Analyzing AoA from a subset of
Chemistry–Climate Model Initiative part 1 climate projection simulations, we
find a remarkable agreement between most of the models in simulating the
largest negative AoA trends in the extratropical lower to middle
stratosphere of both hemispheres (approximately between 20 and 25 geopotential kilometers (gpkm) and 20–50
A global mass meridional circulation in the stratosphere, the Brewer–Dobson circulation (BDC), was discovered by Brewer (1949) and by Dobson (1956) through analysis of trace gas distributions. Climate model simulations robustly show that the BDC accelerates in connection to the greenhouse gas (GHG)-induced climate change (Shepherd and McLandress, 2011; Palmeiro et al., 2014), and this acceleration dominates the stratospheric changes in climate model projections (Butchart, 2014). Recently, Polvani et al. (2017, 2018) and Morgenstern et al. (2018) showed that ozone-depleting substances are key drivers of BDC trends with the potential to considerably reduce the trends in the future. However, the physical cause behind the BDC changes, in particular the role of various sources of wave driving for the circulation and its variations (Cohen et al., 2014), remains an open issue.
The BDC consists of two separate branches – a shallow branch in the subtropical lower stratosphere (LS) and a deep branch higher in the middle atmosphere (Andrews et al., 1987; Plumb, 2002; Birner and Bönisch, 2011). Both BDC branches are currently considered to be driven primarily by resolved waves of different scales (Plumb, 2002) plus contributions from gravity waves (GWs) in the upper stratosphere and mesosphere (Andrews et al., 1987) as well as above the subtropical jet (McLandress and Shepherd, 2009). Li et al. (2008), Okamoto et al. (2011) and Butchart (2014) highlighted the role of GW drag (GWD) and especially of orographic GWD (OGWD) changes for driving the trend of the shallow BDC branch. But there are also indications that changes in the unresolved wave drag are often compensated for by changes in the resolved wave driving (McLandress and McFarlane, 1993; Cohen et al., 2013, 2014; Sigmond and Shepherd, 2014), which makes it difficult to clearly separate the two effects (e.g., by the downward control (DC) principle, Haynes et al., 1991).
In this study, we analyze the mean age of stratospheric air (AoA; Hall and Plumb, 1994) trends and their causative factors in the REF-C2 scenario (see Eyring et al., 2013) from a subset of models participating in the Chemistry–Climate Model Initiative part 1 (CCMI-1; Morgenstern et al., 2017). AoA is a useful transport diagnostic and one of the best available tools for assessing the BDC change (Butchart, 2014). For different methods of definitions and a chemistry–climate model inter-comparison of age of air also in the troposphere refer to Krol et al. (2018). In the first part of our paper, we highlight a remarkable agreement between the majority of models in projecting the strongest negative AoA trends (global or local minimum) in the extratropical lower to middle stratosphere of both hemispheres. The extratropical regions of strongest AoA trend have previously been noted by Okamoto et al. (2011), Li et al. (2012) and Butchart (2014). Studying the full AoA spectrum, Li et al. (2012) have attributed the existence of strong AoA trends in the extratropics to the effect of a strengthening residual circulation and a weakening of the so-called “recirculation” (in-mixing of old stratospheric air into the tropical pipe).
The following sections comprise an in-depth analysis of the kinematic and dynamic changes corresponding with the regions of strongest AoA trends. For this analysis we use the Canadian Middle Atmosphere Model (CMAM; Scinocca et al., 2008) simulation. CMAM uses relatively advanced orographic (Scinocca and MacFarlane, 2010) and non-orographic (Scinocca, 2003) GW parameterization schemes and has been used in previous studies regarding BDC (McLandress and Shepherd, 2009) and wave-driving (Shepherd and McLandress, 2011) changes in response to climate change. Also, the issue of compensation between resolved and unresolved wave driving has been studied extensively for CMAM (Sigmond and Shepherd, 2014).
First, we illustrate that the minimal AoA trends in the extratropical lower to middle stratosphere in CMAM are connected with the climatological AoA distribution. In this region, the AoA distribution is sensitive to the vertical shift of the pressure levels under climate change (Lübken et al., 2009) as well as to the widening of the AoA isolines (Fig. 1). The isoline widening (not to be confused with the circulation widening) is due to a combination of the upward shift itself and a decrease in AoA. A decomposition of AoA into residual circulation transit times (RCTTs; Birner and Bönisch, 2011) and aging by mixing (AbM; Garny et al., 2014; Ploeger et al., 2015a) shows an additional contribution to the AoA isoline widening by the AbM reduction.
In the final section of the results, we investigate possible causative factors of AbM and RCTT trends with a focus on the hypothesis of a strengthening residual mean circulation in the shallow BDC branch (e.g., Li et al., 2012; Garny et al., 2014; Ploeger et al., 2015a) driven by changes in resolved and unresolved extratropical wave forcing (e.g., Okamoto et al., 2011; Shepherd and McLandress, 2011; Butchart, 2014). However, after the correction to the vertical shift of pressure layers, a clear connection between the acceleration of the residual circulation, stronger wave driving in the extratropical lower to middle stratosphere, net tropical upwelling, and the time evolution of the RCTT and especially AbM trends is not found. On this basis we argue that additional mechanisms may be acting. Namely, in the discussion section, we formulate a hypothesis about a possible impact of a variable shift of pressure levels in the stratosphere under climate change (stratospheric shrinkage; Lübken et al., 2009; Berger and Lübken, 2011) for the AoA (RCTT and AbM) trends.
Schematic illustration of the location and direction of the effects of the upward shift trend (A), the maximal AoA gradient (B) and the aging-by-mixing decrease (C) on the AoA trend. The colors indicate the climatological zonal mean AoA distribution of the 1960–2000 period in the CMAM REF-C2 simulation.
Our methodology is motivated by the intention to diagnose the effect of the vertical shift of the circulation due to tropospheric warming and stratospheric cooling (Shepherd and McLandress, 2011; Singh and O'Gorman, 2012; Oberländer-Hayn et al., 2016). For this goal, we have chosen to base our analysis on interpolation to the geopotential height vertical coordinate as an equivalent to the geometric height (for details on the difference between geometric and geopotential height, which is variable with altitude, refer to Andrews et al., 1987). The method of interpolation and vertical shift analysis is described in Sect. 2.2. Among the models that participate in the CCMI-1 project, we were able to apply this methodology to monthly mean data of five chemistry–climate models (CCMs): (1) CMAM; (2) the Goddard Earth Observing System CCM (GEOSCCM, Pawson et al., 2008); (3) the ECHAM/MESSy Atmospheric Chemistry model (EMAC; Jöckel et al., 2016) in two setups with different vertical resolution, L47 (r2i1p1 ensemble member) and L90; (4) HadGEM3-ES (Hardiman et al., 2017); and (5) the NIWA-UKCA (Morgenstern et al., 2009) ensemble of REF-C2 simulations. Basic information on these simulations is summarized in Eichinger et al. (2019; Table 1) and more details on the simulation setups can be found in Morgenstern et al. (2017). The selection of models is based on the availability of the required variables for our analysis and applicability of the method described in Sect. 2.2.
Following Dietmüller et al. (2018), the AoA data require additional
modification. For each time step, the AoA value at the tropical tropopause
(between 10
The studied period 1960–2100 has been divided into three parts in agreement with common periods of the REF-C2 model outputs: 1960–2000 (regarded as the reference period in our study; Ref), 2000–2050 (near future; NF) and 2050–2100 (future, F). Those periods correspond well with the ozone depletion and projected recovery (Dhomse et al., 2018; and Fig. S1 in the Supplement for the ozone evolution in the CMAM REF-C2 simulation), which has been highlighted to play a crucial role for driving the BDC trends (Polvani et al., 2017, 2018; Morgenstern et al., 2018). In Sect. 3.2, we analyze the mechanisms of the occurrence of the minimal AoA trends in the extratropical stratosphere and highlight the important role of decreasing RCTT and AbM for the AoA isoline widening. RCTTs are calculated according to the method of Birner and Bönisch (2011) based on residual circulation backward trajectories. AbM is estimated as the difference between AoA and RCTTs (see Garny et al., 2014; Dietmüller et al., 2017, 2018). This means that AbM includes all sorts of resolved and unresolved mixing (see Dietmüller et al., 2017). Due to the methodology of their computation (initialization of backward trajectories), RCTTs and therefore also AbM data are available starting from the year 1970.
For analysis of the causative factors of AbM and RCTT trends in Sect. 3.3,
we use CMAM REF-C2 monthly OGWD, non-orographic gravity wave drag (NOGWD),
Eliassen–Palm flux divergence (EPFD) and residual mean velocities (
Throughout the paper, we use information about the tropopause and turnaround latitudes as a measure for BDC widening (Hardiman et al., 2014). The tropopause is computed as a first lapse rate tropopause using the WMO (1957) definition. The turnaround latitudes are computed as the first latitude with a monthly mean vertical residual velocity being lower than or equal to zero going poleward from the Equator on the respective hemisphere and geopotential level.
Trends of all variables have been estimated by the Theil–Sen estimator
(Theil, 1950; Sen, 1968), and their significance has been computed using the
Mann–Kendall test (Mann, 1945; Kendall, 1975). Where applicable, the
statistical significance of differences and correlations has been computed
by a Student
The monthly mean data of all analyzed quantities (in the form
In Sect. 3.2, we estimate and subtract the effect of the vertical shift of
pressure levels on the computation of trends (the second term in Eqs. 1
and 2). Later in the text we call this procedure a correction to the
vertical shift of the pressure levels. The correction is based on
modification of the geopotential height field (to which we interpolate) so
that it does not have a trend (in the long-term sense
The interpolation to the geopotential height vertical coordinate has been
performed for monthly mean data (AoA, RCTT) or for zonal mean monthly mean
fields (EPFD, GWD, residual mean
velocities). From theory, the interpolation should be made on the finest
scale (spatiotemporal) possible. We tried to estimate an upper boundary of
the interpolation-connected error by considering an extreme case – we
confronted the zonal mean AoA climatology in the 1960–2000 period computed (1) from daily 3-D AoA data interpolated on a daily basis and (2) from
climatological zonal mean AoA data interpolated using the 1960–2000 mean
zonal mean geopotential data. This is an extreme case, because in our
analysis we are interpolating at least monthly mean zonal averages. The
difference of resulting AoA climatologies is at maximum around
Note that, in the process of changing to a different coordinate system, only
values of the original quantities are interpolated. This may be confusing
especially in the case of residual mean vertical velocity (
In Sect. 3.2 and 3.3 we analyze net tropical upwelling trends and trends
of spatially averaged local residual circulation and wave driving. Those
quantities in the form of mass fluxes or forces are computed from the
original pressure (log-pressure) data interpolated to the geopotential
height vertical coordinate. Unlike in pressure, in the geopotential height
vertical coordinate system, mass flux (force) has to be computed as a
product of velocity (acceleration) and density, which is not a standard
output in the CCMI-1 REF-C2 simulations. In our analysis, density is computed
using the state equation for dry air. However, the net upwelling mass flux
trend is dominated by the density trends (negative trends after the
correction for the vertical shift; see Fig. S2 and Table S3 in the Supplement). Therefore we
define a kinematic proxy for the mass flux in the form
The net tropical upwelling kinematical proxy (UP) is then computed by three
different methods: (1) direct integration of the mass flux proxy between the
turnaround latitudes (UP
The average density is also used to define the local residual circulation
strength (RC) in the form
In Fig. 2, the trends of zonal mean AoA for the subset of CCMI-1 simulations are shown for the three periods (Ref, NF and F). The contour lines display the climatological AoA distribution of the respective period. In all periods we see that the analyzed CCMI-1 REF-C2 simulations show the maximum AoA gradient in the region between the tropical LS and the extratropical lower to middle stratosphere (illustrated in Fig. 1).
Here, we focus on the inter-model agreement in projecting the largest
negative trend (global or local minimum) in the extratropical lower to
middle stratosphere of both hemispheres. The location of those minima does
slightly vary between the models but can be found in most cases
approximately between 20 and 25 gpkm and 20–50
The best agreement in projecting the minimal trend in the Ex regions is in the NF and F period (Fig. 2). In the NF period, the AoA trends from all analyzed simulations display a well-pronounced, localized Northern Hemisphere (NH) minimum (on the analyzed vertical domain) in the ExNH region. In the NF period, the ExSH AoA trend minima are only local extremes in NIWA and CMAM and have a different structure in GEOS and EMAC-L47. In the F period, there is a pronounced, localized AoA trend minimum in all simulations except EMAC-L47 in the ExNH region and EMAC-L47 and HadGEM in the ExSH region. Particularly in the EMAC-L47 simulation, the trend is strongest in the polar regions below/above 30 gpkm in the NH/SH (Southern Hemisphere). In the Ref period, the models agree only in projecting strong negative AoA trends in the ExSH region. In the NH, the trends are small or more widespread in a broader region with the minimum at the pole.
A localized minimum of the AoA trend in the ExSH region for the 1965–2000 period and in both Ex regions for the 2000–2080 period is visible also in Fig. 3 in Polvani et al. (2018) for their “All-forcings” simulation. In their study, Polvani et al. (2018) apply the Whole Atmosphere Community Climate Model (Marsh et al., 2013; Solomon et al., 2015; Garcia et al., 2017), which is forced as per the CCMI-1 specifications of scenario REF-C2. The localized and almost symmetric AoA trend features in the Ex regions (best pronounced in our analysis in CMAM, HadGEM and NIWA) are collocated with the maximum climatological AoA gradient. This suggests that the trend minima are a geometric consequence of the climatological AoA distribution and its future changes that are aligned with the direction of the gradient. We investigate this in the next subsection and propose possible causes for the changes in the AoA distribution.
Zonal mean AoA trends (days per decade) (colors) and AoA climatology (contours) of the analyzed CCMI-1 REF-C2 simulations. The left column shows the Ref period, the middle column the NF period and the right column the F period. The vertical axis is in geopotential kilometers (gpkm). The mean tropopause position is indicated by the bold black line. White regions mark where the significance level of the trends does not exceed 95 %.
The time evolution of the AoA trends is in agreement with the effect of the phasing out of the ozone-depleting substances, which will lead to a reduction of the BDC trends in future decades (Polvani et al., 2017, 2018; Morgenstern et al., 2018). In Fig. 2, except for the EMAC-L90 REF-C2 simulation, all analyzed simulations are in agreement with this (note that the color bar is different between the periods). The strongest negative AoA trends (globally as well as in the Ex regions) can be detected in the Ref period, and thereafter in the NF period the trend declines. In the F period (mature state of ozone recovery; see Fig. S1), the AoA trends are approaching the magnitudes of the Ref period. In the EMAC-L90 REF-C2 simulation the AoA trend shows the smallest magnitude in the Ref period and an increase in the NF and F periods. For a detailed inter-model comparison of the AoA changes, refer to Eichinger et al. (2019).
In the first part of this section we analyze the vertical shift of pressure levels and connect it with the net upward shift of the circulation (Shepherd and McLandress, 2011; Singh and O'Gorman, 2012; Oberländer-Hayn et al., 2016). In the second part we estimate the effect of the correction for the vertical shift of the pressure levels on AoA, AbM, and RCTT trends and analyze the processes leading to the minimal AoA trend in the Ex regions. This part of the analysis is based solely on the CMAM simulation. However, the findings of Eichinger et al. (2019) show that the AoA distribution and its change are governed by similar processes among the different CCMI-1 REF-C2 models. This suggests that our results can be considered robust also for other CCMI-1 simulations.
Observations and models have shown that the tropopause shifts upward (Santer et al., 2003; Añel et al., 2006) together with the whole tropospheric circulation pattern (Singh and O'Gorman, 2012) due to the tropospheric warming and stratospheric cooling in the course of climate change. The tropospheric warming also influences BDC wave driving by causing an upward displacement of the critical layers for wave breaking (Shepherd and McLandress, 2011). The effect of the upward shift of the circulation on the BDC trends has been highlighted recently by Oberländer-Hayn et al. (2016), where the shift has been divided between the shift of pressure levels and relative to pressure levels. Our methodology (see Sect. 2.2) is developed to diagnose (and subtract) the vertical shift of pressure levels, which is diagnosed as a trend of geopotential height of pressure levels (Fig. 3).
CMAM trend of geopotential height of pressure levels (gpm per decade) interpolated to the climatological geopotential height of the selected pressure levels in each period. The mean tropopause and turnaround latitude positions are marked with black lines. Only the trends in the regions where they exceed the statistical significance of 95 % confidence level are plotted.
In Fig. 3 we see that the tropopause is collocated with the region of the largest upward trend of pressure levels in all periods. The trend of the pressure levels in the vicinity of the tropopause in the tropics is around 40, 60 and 80 gpm per decade in the Ref, NF and F period, respectively. Above the tropopause, the trend decreases with altitude and it is not significant higher up. Starting in the middle stratosphere (above around 38 gpkm), the trend is negative. This vertical structure of the pressure level geopotential height trend characterizes the stratospheric shrinkage.
The vertical shift is not globally homogenous; it shows a maximum between
approximately 30
As described in Eq. (2), the height changes in the pressure levels result in a dependence of the AoA trend on the vertical coordinate system. Since the partial derivative of AoA with respect to the geopotential height is generally positive in the stratosphere (see Fig. 2), the sign of the second term in Eq. (2) is determined by the local derivative of the geopotential height of pressure levels (in our approximation by the trend of geopotential height of pressure levels). Hence, the AoA trend in the geopotential height vertical coordinate is smaller/larger than in pressure coordinates, where the pressure levels rise/sink. In the LS, the pressure levels rise and so the AoA trend is smaller (more negative) in geopotential height than in pressure coordinates. This can be easily illustrated by assuming a situation where the AoA trend in pressure coordinates is zero. But as the pressure levels rise, the fixed geopotential corresponds to increasing pressures over time. These are connected with smaller AoA, which yields a negative AoA trend in geopotential coordinates.
The second part of the vertical shift of the circulation, the vertical shift relative to the pressure levels, is diagnosed in the literature mainly with relation to the tropopause rise. For example, Abalos et al. (2017) assessed the shift by accounting for the tropopause rise by means of remapping to tropopause relative coordinates. The tropopause rise in the geopotential height vertical coordinate and relative to the surrounding pressure levels is shown in Fig. 4.
Time evolution of CMAM zonal mean geopotential height
(gpkm) of selected pressure levels and of a first lapse rate tropopause
averaged between 30
The tropopause trend in the geopotential height vertical coordinate can be used in our methodology (Sect. 2.2, Eq. 3) instead of the trend of geopotential height of pressure levels to diagnose the trends also in the tropopause relative coordinate. However, due to neglecting the variable vertical shift of pressure levels (see Fig. 3; stratospheric shrinkage, Lübken et al., 2009), the assumption of a uniform shift equal to the tropopause rise everywhere in the stratosphere may lead to an increasing overestimation of the upward shift effect with distance from the tropopause.
In the next section, we estimate the effect of the vertical shift of pressure levels on the computation of trends. Additional impact of the vertical shift relative to the pressure levels (included in the tropopause rise) on the trend computation is quantified for the trend of the net upwelling only, as the upwelling will undoubtedly reflect the tropopause rise (Oberländer-Hayn et al., 2016), but this is not as certain for the regions higher in the stratosphere.
In Fig. 5 we show the AoA, AbM, RCTT trends in the Ref, NF and F period
computed from spatial averages over the Ex regions (between 20 and 25 gpkm and 20–50
Trends of AoA (squares), AbM (crosses) and RCTTs (pluses)
averaged over the Ex regions (ExNH on the left, ExSH in the middle) in the
Ref, NF and F period in days per decade. Blue markers denote the trends in the geopotential
height vertical coordinates and red markers the trends computed after the
correction for the vertical shift of pressure levels. On the right
(tropics), bars represent UP
In Fig. 5, both before and after the correction for the pressure level shift, we can see the strongest negative AoA and AbM trends in both Ex regions in the Ref period. The AoA and AbM trends both have the same time evolution, decrease (in absolute values) from Ref to NF and increase again in the F period. On the contrary, both before and after the correction, the RCTT trends are not significant in the Ref period (significant at the 80 % confidence level before the correction in ExNH – see Table S1). In the NF period, the RCTT trends are slightly larger than in the F period both before and after the correction. The AoA trends in the Ex regions are dominated by RCTT trends in the NF period. The time evolution of AoA, AbM and RCTT trends is unchanged after the correction for the pressure level shift.
The difference between the directly computed trend value and the trend value
after the correction gives us an estimate of the influence of the pressure
level shift on the trend computation. The influence is determined by the
second term on the right side of Eqs. (1) or (2), which consists of the
vertical gradient of the given quantity and the rate of the pressure level
shift that is identical for all quantities but differs between periods. We
see in Fig. 5 that for the AoA and AbM trends, the influence grows in
future periods in accordance with the time evolution of the trend of
geopotential height of pressure levels (Fig. 3). Absolute values of the AoA
trend are reduced by 2, 6 and 8 d per decade (i.e., by 6 %, 35 % and 26 %) after
the correction in ExNH and by 3, 4 and 5 d per decade (7 %, 27 % and 15 %) in the ExSH
for the Ref, NF and F period respectively. The AbM trend is reduced by
maximally only 5 d per decade through the correction; however, the 3 d per decade reduction in the
ExNH region in NF already accounts for 50 % of the uncorrected trend. In
the ExSH region in NF the AbM
In the Ref period, the UP
It has been noted by Randel et al. (2008), Butchart et al. (2010) and
Butchart (2014) that the residual circulation changes mainly depend on
strengthening of the tropical upwelling. We find a good correspondence with
the RCTT and RCTT
We have also analyzed trends of spatial averages of RC in the Ex regions. RC (i.e., the residual circulation strength) is a local measure of acceleration of the residual circulation defined in Sect. 2.3. However, the RC trends are only sparsely significant at the 80 % confidence level and severely reduced in magnitude (see Table 1 in the next section or Table S1 in the Supplement) after the correction for the vertical shift of pressure levels. The possible link between the time evolution of AoA, AbM, and RCTT trends and the acceleration of the residual circulation together with a possible role of wave driving is analyzed also on a seasonal basis in Sect. 3.3.
With the methodology for correction to the vertical shift of pressure levels
(Eq. 3), we can now demonstrate the effect of vertical shift on the
occurrence of minimal AoA trends in the Ex regions. The distribution of
AoA
CMAM zonal mean AoA annual trend (days per decade) after the
correction of the pressure levels trend for the Ref
Figure 6 also shows the mean turnaround latitude positions. The mean turnaround latitude positions between the periods show only small differences in their meridional location. In the NH, there are some visible changes towards a narrowing of the upwelling region below about 26 gpkm and towards a widening above. This is in agreement with the results of Hardimann et al. (2014), who found that the tropical upwelling region narrows below about 20 hPa and widens above. This pattern also appears for turnaround latitude position changes in seasons (not shown), when changes in the SH are pronounced as well.
Time evolution of the meridional position of the zonal
mean AoA
Figure 7 shows that the AoA distribution in the Ex regions also widens
after subtraction of the vertical shift of pressure levels. This widening is
related only to AoA isolines and is completely independent of any
circulation widening. In Fig. 7 we show the time evolution of a meridional
position of intersection of the AoA
The widening of AoA isolines is partly a direct consequence of the AoA
distribution and the negative AoA
The Ex regions lie in the upper flank of the shallow BDC branch. There, AoA has been found to be controlled by both horizontal and vertical residual circulation tendencies and the horizontal mixing tendency (Ploeger et al., 2015b; see their Fig. B1). From Fig. 5 we know that the AoA trends in the Ex regions are dominated by the AbM trends in the Ref and F and by the RCTT trends in the NF period. Note that AbM is not a local quantity. Ploeger et al. (2015b; Lagrangian model study) found that AbM corresponds well with the local mixing integrated along the air parcel pathway. Garny et al. (2014) and Ploeger et al. (2015a) found that the AbM trends in the lowest part of the stratosphere are affected predominantly by changes in the local mixing intensity, but those further above are strongly coupled to the residual mean circulation. This complicates the analysis of possible AbM drivers in the Ex regions, because the Ex regions are located in the transition region between these two regimes. RCTTs are an integrated quantity with climatological values around 1 year in the Ex regions (Fig. 8), and hence they can be influenced by changes in seasonal UP and RC strength (this holds for AbM as well). To gain a better insight into these connections, we study how the RC, UP, local wave drag and vertically integrated drag trends correlate with each other and with the time evolution of AbM and RCTT trends in the Ex regions. The analysis on a seasonal basis is shown in the Appendix.
The Ex regions are located in a region characterized by domination of the
meridional residual mean velocity component
In Table 1 we provide annual trends of the spatial averages of total drag
(TD), RC, EPFD and GWD scaled by the climatological zonal mean density and
corrected for the vertical shift of pressure levels (
Upward-shift-corrected trend values (
Table 1 shows that in the ExNH neither TD
As shown in the Appendix (Table A1), seasonally, RC
To conclude, after the subtraction of the vertical shift of pressure levels,
the AbM
In several studies a physical connection between changes in AoA, AbM and
RCTTs; the speeding up of the residual mean circulation (see Birner and
Bönisch, 2011; Li et al., 2012; Garny et al., 2014; Ploeger et al.,
2015a); and increasing wave driving by changes in the resolved and unresolved
extratropical wave forcing (e.g., Okamoto et al., 2011; Shepherd and
McLandress, 2011; Butchart, 2014) has been postulated. In the present study,
after the correction to the vertical shift of pressure levels, we could not
find a simple link between trends of wave driving (TD
The trends computed in the geopotential height vertical coordinate after the
correction for the pressure level shift (
We would like to point out one particular result of our wave-driving
analysis – a weak correspondence between GWD
GWs are intermittent (e.g., Hertzog et al., 2012; Wright et al., 2013) and asymmetrically distributed (Hoffmann et al., 2013, 2016; Šácha et al., 2015; Pišoft et al., 2018) in nature. This intermittency and asymmetry of the spatial distribution of GWD (OGWD in particular) is to some extent present also in the CCMI-1 simulations. For example, a crucial role of the zonally asymmetric OGWD distribution for its interannual variability has been shown by Šácha et al. (2018) for a CMAM specified dynamics simulation (McLandress et al., 2013), which uses the same parameterization of orographic GWs as the CMAM REF-C2 simulation analyzed in this study. The zonal mean data can hide different effects on the residual circulation due to the zonally asymmetric distribution of the GWD (Šácha et al., 2016) present in the models, and monthly mean output can mask the extreme GWD values. Note that also the widely used DC principle relies on zonally symmetric forces (Haynes et al., 1991). Clearly, there is a need for provision of as-frequent-as-possible 3-D GWD output (complex, not only the induced zonal acceleration component) in connection with reporting of extreme values during the time window in addition to average values to properly diagnose the possible GW effects present in the models.
In Sect. 3.2.1 (Fig. 3) we analyzed the vertical shift of pressure
levels, which results in a so-called stratospheric shrinkage. Although our
methodology accounts for the effect of the vertical shift of pressure levels
(stratospheric shrinkage) in the process of trend computation, the effect of
decreasing geometrical distances between pressure levels in the course of
the model simulation, which can directly influence the AoA, RCTTs and AbM,
cannot be quantified in our analysis. To our knowledge, this effect has not
been mentioned in relation to the possible causative factors of the AoA
trend (or BDC acceleration) before. For example in Table 2 we show how the
mean distance between the 1 and 100 hPa levels will change between the
1960s and the 2090s. In the analyzed simulations, the 100 hPa level in the
tropics will be closer to the 1 hPa level by about 400–700 m in the
2090s than in the 1960s. Depending on the variable geopotential height of
pressure levels and distances between the two levels at the start of the
analysis in the simulations, the differences in Table 2 range from 2.33 % for CMAM to 1.3 % for NIWA of the original distance in the 1960s in
the tropics. Assuming a constant speed of advection in the vertical, this
directly reduces the RCTTs (for vertical velocity of an order of
The change in the mean distance (in geopotential meters) between the 1 and 100 hPa levels in the tropics between the 1960s and the 2090s for the analyzed REF-C2 CCMI-1 simulations.
As pointed out before, we also cannot account directly for the shift relative to the pressure levels. Typically in the literature (Oberländer-Hayn et al., 2016; Abalos et al., 2017), the tropopause is taken as a proxy for the upward shift relative to pressure levels. Otherwise, the possibly non-homogeneous shift relative to pressure levels in the stratosphere cannot be objectively assessed. Note also that the shift related to the tropopause can become very complicated to disentangle. The whole region changes its structure because of the increasing occurrence of double and multiple tropopauses due to increasing baroclinicity in the course of climate change (Castanheira et al., 2009; Castanheira and Gimeno, 2011; Wang and Polvani, 2011; Añel et al., 2012).
In Fig. 4 (Sect. 3.2.1) we show how the first lapse rate tropopause
in CMAM shifts relative to pressure levels between 30
Figure 4 also shows that the rate of the tropopause shift relative to pressure levels almost perfectly follows the division into the periods used in this study. The tropopause rises rapidly relative to pressure levels in the Ref and F period, when we found the biggest AbM and AoA trends (Fig. 5). In the NF period, there is no visible shift of the tropopause relative to pressure levels, which corresponds well with the small (ExNH) or insignificant (ExSH) AbM trends. The rate of the tropopause shift (and possibly of the net stratospheric shrinkage) thus correlates with the time evolution of AbM trends. However, at this stage we cannot provide a detailed or analytical description of the mechanism.
It has been shown before (i) by Shepherd and McLandress (2011) that the EPFD changes associated with GHG increases in the subtropics are largely controlled by the upward displacement of the critical layers for wave breaking and (ii) by McLandress and Shepherd (2009) and Okamoto et al. (2011) that the OGWD changes are linked to the upward shift of the subtropical jet (Son et al., 2009). Also, Eichinger et al. (2019) found that the mixing changes, as well as the inter-model spread, are connected to changes (upward shift) of the background potential vorticity (PV) gradient in the CCMI-1 simulations. All of those studies were based on pressure coordinates and so the shift they are referring to is the shift relative to pressure levels (tropopause shift).
The RCTT trends do not reflect the time evolution of the shift relative to pressure levels directly (i.e., the trend is larger in the NF period than in the F period). The reason can lie in the strong dependence of RCTTs on the tropical upwelling. Tropical upwelling is the only quantity (as explained in Sect. 3.2.1) for which we computed the trends also in coordinates corrected to the tropopause shift (Tables S2, S3 and S6 in the Supplement). After the correction to the tropopause shift, the net tropical upwelling shows the same time evolution of trends as RCTTs. This is caused by a missing vertical shift of the tropopause relative to pressure levels in NF in CMAM. Future research is needed regarding a possible cause and robustness of this feature between the models.
Finally, there are important consequences for trend analyses based on
log-pressure coordinates in connection to the stratospheric shrinkage.
Unlike in the pressure coordinates, the vertical shift of pressure levels is
reinstated in log-pressure coordinates due to the utilization of a constant
scale height (
In a subset of CCMI-1 REF-C2 simulations, we have pointed out a remarkable
pattern of similarity in the morphology of the stratospheric AoA trend,
especially in the future periods (2000–2050 and 2050–2100). These are the
regions of minimal AoA trends, which are located in both hemispheres between
20 and 25 gpkm and between 20–50
From the net upward shift of the circulation, the part connected with the vertical shift of the pressure levels has been diagnosed and the so-far-neglected stratospheric shrinkage pattern has been pointed out. We then showed that the AoA, AbM, RCTT (in the Ex regions) and the net tropical upwelling trends are reduced when accounting for the vertical shift of pressure levels. Moreover, the local residual circulation strength (RC) does not exhibit any trends when accounting for the shift (only at a weaker significance level). After the vertical shift correction, we could not find a direct relationship between the total zonal mean wave drag and its components (resolved and unresolved), the seasonal RC or upwelling trends, and the time evolution of the AbM and RCTT trends. This indicates that additional mechanisms may be involved. For example, we discuss a mechanism of how the stratospheric shrinkage can affect the AoA changes. Moreover, our diagnostic methods, in particular regarding the sparse spatiotemporal sampling of GWD effects, may not meet the needs for accurate analysis of the connections between the processes in the models, for which more detailed GWD output would be needed.
The analysis is based on geopotential height coordinates, but the argument that the upward shift (together with AoA isoline widening) is necessary for the visual pattern of localized AoA trend minima in the extratropical stratosphere holds also in pressure coordinates. The location of the minimal AoA trends is in the best vertical range for the AirCore measuring tool (Engel et al., 2017), and their easy visual detectability makes them the best regions for AoA trend observations. The detection of the localized trend minima in the Ex regions in observations could provide validation of the processes that lead to their formation in the models. Those are the upward shift of the circulation, the AoA decreasing trend and most importantly its aging-by-mixing (AbM) component that can be connected with the fine dynamical features of the model's lower stratosphere. To gain more insight in future climate projections, we particularly suggest inter-model analysis of the stratospheric shrinkage, including the time evolution of the vertical shift of the tropopause and its effect on the stratospheric circulation.
All data CCMI-1 used in this study can
be obtained through the British Atmospheric Data Centre (BADC) archive
(
There are indications that changes in the unresolved wave drag are often compensated for by changes in the resolved wave driving (McLandress and McFarlane, 1993; Cohen et al., 2013, 2014). This so-called “compensation mechanism” is present also in comprehensive climate model projections of the BDC change (Sigmond and Shepherd, 2014) and complicates the possibility of clearly separating the effects of individual wave drag components. The compensation needs to be taken into account to identify the areas where the individual drag components can influence the advection to the Ex regions. Therefore, we analyze the wave drag distribution and the occurrence of compensation near the Ex regions.
In Fig. A1a, we show the total drag (GWD
In the extratropical stratosphere, regions with the same sign of GWD and EPFD prevail (Fig. A1a, red and antique white colors). The ratio is shown for the Ref period and differs only slightly in the NF and F period when corrected to the pressure level shift (not shown). The regions of the lower stratospheric minima of GWD are collocated with the saddle-like regions in the EPFD distribution around 16 to 22 gpkm (Fig. A1b). Those regions are positioned on the upper flank of the subtropical jets of both hemispheres but are more pronounced in NH, where the GWD is stronger. The total drag distribution (contours in Fig. A1a) largely copies the EPFD distribution, but it is smoother in the lower stratosphere as the saddle-like pattern from the EPFD distribution is filled by GWD. This can be considered as a fingerprint of the compensation, and indeed this region includes the 70 hPa level, where Cohen et al. (2013) demonstrated the compensating effects between OGWD, EPFD and NOGWD for driving of the residual circulation.
Further information on the compensation is provided in Fig. A1d, e, f. Here
we show correlations between the drag components and
In Fig. A1d, the distribution of negative correlations, which indicate
compensation between the drag components, agrees well with the location of
regions of minimum (strongest) GWD (EPFD saddle regions). Otherwise, in the
extratropical stratosphere we find mainly positive GWD and EPFD
correlations. The localization of the compensation is confirmed also by
correlations of GWD and EPFD with
Due to the climatological distribution and occurrence of compensation, we do
not average the drag components over the whole Ex regions. Instead, EPFD
trends are computed from a spatial average between 18 and 25 gpkm and
15–30
As shown in Table A1, seasonally, RC
First, note that the seasonal TD
Upward-shift-corrected trend values (
Trends of UP (in
In the ExSH region, when significant, the seasonal RC
In Table A2 we show seasonal UP trends computed with different methodologies
after the correction for the vertical shift of pressure levels. The trends
of net upwelling (including time evolving density) are given in Table S6 in
the Supplement. Trends of another drag-based quantity (UP
From the three methodologies, two based on the residual mean velocities
(UP
The UP
To conclude, the UP
The supplement related to this article is available online at:
PŠ performed all the analyses and wrote the article together with RE. JAA, LdlT, PP and HG made substantial contributions to the conception of the study and interpretation of the results and participated in drafting the article. SD provided the RCTTs data, helped with their analysis and commented on the paper. In their role as CCMI model PIs, the other authors contributed information concerning the analyzed models, commented on the manuscript and helped to revise the paper.
The authors declare that they have no conflict of interest.
This article is part of the special issue “Chemistry–Climate Modelling Initiative (CCMI) (ACP/AMT/ESSD/GMD inter-journal SI)”. It is not associated with a conference.
We acknowledge the modeling groups for
making their simulations available for this analysis and the joint WCRP
SPARC–IGAC Chemistry–Climate Model Initiative (CCMI) for organizing and
coordinating this model data analysis activity. We thank the British
Atmospheric Data Centre (BADC) for hosting the CCMI-1 data archive. We
acknowledge the UK Met Office for use of the MetUM. The EMAC simulations
have been performed at the German Climate Computing Centre (DKRZ) through
support from the Bundesministerium für Bildung und Forschung (BMBF).
DKRZ and its scientific steering committee are gratefully acknowledged for
providing the HPC and data-archiving resources for the consortial project
ESCiMo (Earth System Chemistry integrated Modelling). The NIWA program
CACV was supported by the NZ Government's Strategic Science Investment Fund
(SSIF). The authors wish to acknowledge the contribution of NeSI high-
performance computing facilities to the results of this research. New
Zealand's national facilities are provided by the New Zealand eScience
Infrastructure (NeSI) and funded jointly by NeSI's collaborator institutions
and through the Ministry of Business, Innovation & Employment's Research
Infrastructure program (
The authors would like to thank the two anonymous referees and the co-editor Gabriele Stiller for all their help towards improving the manuscript.
This research has been supported by the Government of Spain (grant no. CGL2015-71575-P) and by the Czech Science Foundation (GAČR) under GA CR under grant nos. 16-01562J and 18-01625S.
This paper was edited by Gabriele Stiller and reviewed by two anonymous referees.