ACPAtmospheric Chemistry and PhysicsACPAtmos. Chem. Phys.1680-7324Copernicus PublicationsGöttingen, Germany10.5194/acp-16-15485-2016An upper-branch Brewer–Dobson circulation index for
attribution of stratospheric variability and improved ozone and temperature trend analysisBallWilliam T.william.ball@env.ethz.chhttps://orcid.org/0000-0002-1005-3670KuchařAlešhttps://orcid.org/0000-0002-3672-6626RozanovEugene V.https://orcid.org/0000-0003-0479-4488StaehelinJohanneshttps://orcid.org/0000-0001-7861-1889TummonFionaSmithAnne K.https://orcid.org/0000-0003-2384-5033SukhodolovTimofeiStenkeAndreahttps://orcid.org/0000-0002-5916-4013RevellLaurahttps://orcid.org/0000-0002-8974-7703CoulonAncelinSchmutzWernerhttps://orcid.org/0000-0003-1159-5639PeterThomasInstitute for Atmospheric and Climate Science, Swiss Federal Institute of Technology Zurich, Universitaetstrasse 16, 8092 Zurich, SwitzerlandPhysikalisch-Meteorologisches Observatorium Davos World Radiation Centre, Dorfstrasse 33, 7260 Davos Dorf, SwitzerlandDepartment of Atmospheric Physics, Faculty of Mathematics and Physics, Charles University, V Holesovickach 2, 180 00 Prague 8, Czech RepublicNational Center for Atmospheric Research, Boulder, ColoradoBodeker Scientific, Alexandra, New ZealandWilliam T. Ball (william.ball@env.ethz.ch)15December20161624154851550025May20168July201628November201628November2016This work is licensed under a Creative Commons Attribution 3.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by/3.0/This article is available from https://acp.copernicus.org/articles/16/15485/2016/acp-16-15485-2016.htmlThe full text article is available as a PDF file from https://acp.copernicus.org/articles/16/15485/2016/acp-16-15485-2016.pdf
We find that wintertime temperature anomalies near 4 hPa and
50∘ N/S are related, through dynamics, to anomalies in ozone and
temperature, particularly in the tropical stratosphere but also throughout
the upper stratosphere and mesosphere. These mid-latitude anomalies occur on
timescales of up to a month, and are related to changes in wave forcing. A
change in the meridional Brewer–Dobson circulation extends from the middle
stratosphere into the mesosphere and forms a temperature-change quadrupole
from Equator to pole. We develop a dynamical index based on detrended,
deseasonalised mid-latitude temperature. When employed in multiple linear
regression, this index can account for up to 60 % of the total variability
of temperature, peaking at ∼ 5 hPa and dropping to 0 at ∼ 50
and ∼ 0.5 hPa, respectively, and increasing again into the mesosphere. Ozone
similarly sees up to an additional 50 % of variability accounted for, with
a slightly higher maximum and strong altitude dependence, with zero
improvement found at 10 hPa. Further, the uncertainty on all equatorial
multiple-linear regression coefficients can be reduced by up to 35 and
20 % in temperature and ozone, respectively, and so this index is an
important tool for quantifying current and future ozone recovery.
Introduction
Trend analysis, typically using multiple linear regression (MLR), is a key
approach to understand drivers of long-term changes in the stratosphere
e.g.. Ozone and temperature
have received most attention, partly because they have the longest
observational records. Temperature is important for understanding climate
change, while quantifying changes in the ozone layer is necessary to estimate
the impacts of elevated, or reduced, ultraviolet (UV) radiation reaching the
surface, especially following the implementation of the Montreal Protocol to
reduce halogen-containing ozone-depleting substances (ODSs).
Ozone and temperature variations in the stratosphere are directly modulated
by changes in solar flux, particularly in the UV
see e.g.and references therein. Ozone
concentration also responds to changes in the Brewer–Dobson circulation
(BDC), whereby air rises in the tropics, advects polewards either on a lower
shallow (below ∼ 50 hPa) or an upper deep branch, and descends at
mid-latitudes (less than ∼ 60∘) or over the poles
. The BDC is mainly driven by mid-latitude
upward-propagating planetary and gravity waves that break and impart momentum,
acting like a paddle to drive the circulation . Wave forcing depends on the mean state of
the flow, and vice versa ; changes
in either affect ozone transport by a change in the speed of the BDC that
leads to adiabatic heating, or cooling, and directly affects chemistry
through temperature-dependent reaction rates . As such, ozone and
temperature have an inverse relationship in the equatorial stratosphere above
10 hPa, which in turn has a dependence on dynamics , although this is not always the
case in the lower stratosphere . Ultimately, then, dynamical
perturbations at mid-to-high latitudes can directly influence the variability
of ozone and temperature .
The stratospheric ozone layer has been damaged by the use of ODSs, and,
following a ban through the 1987 Montreal Protocol ,
levels of ODSs have declined since their peak in 1998
, although the peak may be
earlier or later depending on the location of interest. However, the rate of
ozone recovery is latitude dependent, with southern mid-to-high latitudes
expected to recover from elevated ODSs . The increase in ozone
at mid-latitudes comes partly from ODS reductions but is also because the BDC
is expected to accelerate
, which will reduce
the time for ozone depletion to occur and lead to faster transport of ozone
from the equatorial region to higher latitudes. This in turn leads to a
reduction of ozone over the Equator and a prevention of a full recovery over
the tropics. Thus, the recovery of ozone at mid-to-high latitudes can be
understood as being partly due to less ozone destruction by lower ODS
concentrations and partly due to a faster redistribution of ozone-rich air
from the tropics. Additionally, the cooling stratosphere will slow ozone
depletion and further support the increase in ozone at mid-latitudes
. However, estimates of decadal trends in ozone since 1998
have a high level of uncertainty because various
long-term datasets provide different pictures , and
we do not understand much of the stratospheric variability on short
timescales. Anomalous monthly variability, like that at the Equator as shown
in Figs. 7 and 8 in , and which could be related to
high-latitude variability e.g., may simply be considered as noise in MLR trend
estimates (and other regressors) where it is not accounted for, which
increases the uncertainty.
In MLR analysis of the equatorial stratosphere, variability is usually
described with at least six regressors that represent the solar cycle UV flux
changes (e.g. with the F10.7 cm radio flux); volcanic eruptions
(stratospheric aerosol optical depth: SAOD); the El Niño Southern Oscillation
(ENSO) surface temperature variations; two orthogonal modes of the dynamical
quasi-biennial oscillation (QBO); and the equivalent effective stratospheric
chlorine (EESC), which describes the long-term influence of ODSs on ozone
concentration and temperature. A greenhouse gas (GHG) proxy is sometimes
also considered, or, alternatively to applying both GHG and EESC proxies, a
linear (or piece-wise linear) trend is considered.
At higher latitudes, other proxies have been used to represent dynamical
indices, e.g. in the Northern Hemisphere (NH), the North Atlantic Oscillation
(NAO) and Arctic Oscillation (AO), which are related to surface pressure
changes, though their relation is less anti-correlated with stratospheric
variability than, e.g., the tropopause pressure .
Trends in dynamically related quantities, such as horizontal advection and
mass divergence, contribute to long-term changes in ozone
. For short timescales,
note that tropospheric pressure is a physical
quantity directly responsible for changes in lower-stratospheric
temperatures but that it is nevertheless inferior to stratospheric
temperature when accounting for ozone and temperature variance in column
ozone and temperature; this can also depend on the location of tropospheric
blocking events . However, longer timescales render these
proxies unreliable due to additional radiative effects.
identified that the use of high-latitude temperature
at 10 hPa in winter–spring months, together with 200 hPa temperature at
mid-latitudes all year round, was most effective at reducing residuals,
though limited their study to total column ozone.
In fact, several studies have identified proxies, such as temperature in the
stratosphere, that can help improve MLR analysis
e.g.. However, these have tended to be focused on total
column ozone, the mid-to-lower stratosphere, or mid-latitude and polar
regions, and thus most attention on dynamical variability remains associated
with the lower branch of the BDC e.g.. Further, studies of dynamical
variability have also tended to focus on seasonal and inter-annual
timescales, and thus any fluctuations on monthly or shorter timescales may be
missed, underestimated, or driven by processes operating on different
timescales.
There are differing conceptual approaches to improve regression models
i.e. see: use of a statistical approach
e.g. or use of proxies that can be (at least
partly) physically understood e.g.. Both
approaches have their limitations, and the physical mechanisms may not be
fully understood in either case. As points out,
the use of (or lack thereof) unphysical or too many regressors could lead to
systematic errors – through the attribution of correlated variables – that
go unnoticed because error statistics do not change or, indeed, decrease. A
third approach simply considers dynamical variability as noise that leads to
enhanced uncertainties on trend analysis.
The identification of a correlation between two variables can be considered a
first step in identifying the physical mechanism that underlies the causal
link. A relationship between the proxies and processes that drive their
variability needs to be shown through additional information; it cannot be
done simply through statistical means alone as it needs information from a
physical understanding, either a priori or following further investigation.
Here, our aim is to find an index, or proxy, that represents rapid changes,
on timescales of a month or less, in the upper branch of the BDC by
investigating an identified association between temperature variation in the
mid-latitude upper stratosphere and planetary wave breaking. While
temperature alone does not represent a complete picture of the physical
driver of rapid BDC changes, we show that its variance is highly associated
with wave driving and that it can act as a proxy for such processes,
especially where the exact physical drivers remain unresolved; the use of
standard dynamical proxies is, as we shall show, not enough to capture this
variance. identified similar short-term dynamical
variability that we identify in monthly data here, but he applied it to
understand dynamical influences on upper-stratospheric variability relevant
to identifying 27-day solar irradiance variability – indeed showing that
27-day solar modulation was very difficult to identify due to large, rapid
dynamical fluctuations – and did not extrapolate this information to
improving MLR analysis, as we aim to do here. The drawback to using
temperature is that it mixes processes that might have different influences
on ozone . However, it is a simple and direct measure
of dynamical changes, at least on monthly or shorter timescales, that relate
to rapid dynamical adjustments within the stratosphere.
In summary, our aim here is to provide an index (Sect. ) to account
for sporadic, noise-like stratospheric variability in monthly time series that
represents rapid adjustments in the BDC and, therefore, better account for
residual variance, improve estimates of trends and regressor variability, and
reduce their uncertainties (Sect. ). We do this using model,
reanalysis, and observational data (Sect. ) to identify a
source for the short-term variability (Sect. ).
Data and modelsChemistry–climate model in specified-dynamics mode
To investigate temperature and ozone variability in the stratosphere and
mesosphere at all latitudes, without data gaps, we simulate historical ozone
and temperature variations using the chemistry–climate model (CCM) SOlar
Climate Ozone Links SOCOL, version 3; in
specified-dynamics mode, whereby the vorticity and divergence of the wind
fields and temperature, and the logarithm of surface pressure are “nudged”
using the ERA-Interim reanalysis between 1983 and 2012 and
up to 0.01 hPa; see for full nudging details. Note
that we use the Stratospheric–tropospheric Processes And their Role in Climate
(SPARC)/International Global Atmospheric Chemistry (IGAC) Chemistry–Climate
Model Intercomparison (CCMI) boundary conditions and external forcings
, except for the solar irradiance input, for which we
use the Spectral And Total Irradiance REconstruction – Satellite era (SATIRE-S) model . In the
following we focus on temperature and ozone variables; the former is nudged,
while the latter is simulated by the CCM SOCOL.
Observations
We verify that the nudged-model output fields ozone (not nudged) and
temperature (nudged) agree with observations. For ozone we use the
Stratospheric Water and OzOne Satellite Homogenized (SWOOSH) ozone composite
for 215–0.2 hPa (∼ 10–55 km) at all
latitudes. For temperature, we compare the nudged-model output with
independent measurements from the Sounding of the Atmosphere using Broadband
Emission Radiometry (SABER) instrument on the
Thermosphere, Ionosphere, Mesosphere, Energetics, and Dynamics (TIMED) satellite,
spanning 2002–2015 and for 100 to 0.00001 hPa (∼ 10–140 km) and
latitudes out to 52∘.
For the MLR analysis (Sect. ) we additionally consider
equatorial ozone from the Global OZone Chemistry And Related trace gas Data
records for the Stratosphere GOZCARDS;,
Solar Backscatter Ultraviolet Instrument Merged Cohesive
SBUV-Mer.;, SBUV Merged Ozone Dataset
SBUV-MOD; composites and temperature from the
Stratospheric Sounding Unit observations SSU;, and
Japanese 55-year Reanalysis (JRA-55)
and Modern-Era Retrospective analysis for Research and Applications (MERRA)
reanalyses. All observations are re-gridded onto the SOCOL model pressure
levels and latitudes. We consider monthly mean zonally averaged data.
Anomalous dynamical variabilityEquatorial ozone and temperature variability
We define short-term, “anomalous”, variability here to be that occurring on
monthly, or shorter, timescales. To identify this rapid variability, distinct
from behaviour on seasonal and longer timescales, we remove all long-term
variability by subtracting a time series that has been smoothed, with a
13-month running mean, and then deseasonalised, with monthly values, at each
latitude and pressure. We apply this pre-processing to all variables
described in Sects. and . An example equatorial
(20∘ S–20∘ N) ozone and temperature anomaly time series
from the CCM SOCOL at 2.5 hPa is shown in Fig. . SWOOSH ozone
from 1985 to 2012 and SABER temperature from 2002 to 2012
(Fig. ) show similar anomalies to the model and have correlation
coefficients (rc) of 0.72 and 0.83 with the nudged-model results,
respectively; the model, therefore, reproduces observations well. The monthly
temperature and ozone anomalies have a very strong relationship, especially
between 0.1 and 6.3 hPa, with negative rc reaching -0.96
(Fig. ) between 0.1 and 10 hPa, while being positive elsewhere.
Monthly anomalies of equatorial (20∘ S–20∘ N)
ozone (upper; %) and temperature (lower; degrees Kelvin) at 2.5 hPa,
following the subtraction of 13-month box-car smoothing and
monthly deseasonalising from the CCM SOCOL model in specified-dynamics mode.
SWOOSH ozone composite time series and SABER temperature measurements are
shown in light blue in the upper and lower plots, respectively. The dashed
blue and red horizontal lines are the thresholds shown in Fig. ;
thresholds for each coloured diamond are given in the right of the upper
panel. June–July–August (JJA) anomalies exceeding the thresholds have
orange (high T) and turquoise (low T) diamonds;
December–January–February (DJF) anomalies are identified by red (high T)
and blue (low T) diamonds.
To establish the coherency of the ozone–temperature relationship in the
tropics, we identify “extreme” anomalies (or “events”) as those at least
at the 90th percentile from the mean in temperature and at less than the 10th
percentile for ozone (and vice versa). We call “low-T” events those that
have low equatorial temperature at the same time as a high ozone
concentration (blue lines at 2.5 hPa, Fig. ), and “high T”
for the opposite situation (red lines); the low-T thresholds are -1.3 K
for temperature and +2.4 % for ozone, while high-T thresholds are
+1.1 K and -2.2 % (these are also given the upper plot of
Fig. ). We note that the ozone mixing ratio maximum in parts per
million (ppm) is at ∼ 10 hPa. We use 2.5 hPa as a reference here, but
other pressure levels at altitudes between 0.1 and 6 hPa give similar
results. The majority of the events (45/60) occur in
December–January–February (DJF; red/blue in Fig. ) and
June–July–August (JJA) (yellow/turquoise in Fig. ). High-T
and low-T months remain grouped above 10 hPa but mix and lose coherence
at altitudes below 10 hPa, implying that the events have a similar source at
all altitudes above 10 hPa but a different one below (i.e. rc
is high at 25 and 40 hPa, but the events at 25 hPa are well mixed). This
indicates a likely transition between BDC branches and that the driver of
variability is dynamical, which we confirm in the following.
Regression of equatorial (20∘N–20∘S) ozone and
temperature anomalies (following 13-month smoothing and monthly
deseasonalising) from the CCM SOCOL model in specified-dynamics mode for
pressure levels 0.01 to 40 hPa (∼ 80–22 km). Grey crosses are for
all other months in January 1983–October 2012. Coloured crosses in each plot
are determined at 2.5 hPa (lower left, and plotted as diamonds in
Fig. ) by those within regions defined by the red (high-T
events) and blue lines (low-T events); red crosses are for high-T events
in December, January, and February (DJF); yellow are for high-T events in June,
July, and August (JJA); and green are for “other” high-T events. Dark blue,
turquoise, and blue represent DJF, JJA, and “other” low-T months, respectively (see also
legends in 1.0 and 1.6 hPa plots). Correlation coefficients are given for
all crosses together. The y scale has been decreased by a factor of 30 and
5 at 0.01 and 0.05 hPa, respectively, as indicated in the plots.
Mid-latitude temperature variability
To identify and locate the source of the driver behind ozone and temperature
anomalies shown and described in the previous section, in Fig. we
correlate the 2.5 hPa equatorial temperature low-T and high-T events
with detrended and deseasonalised temperature at all latitudes and
pressure levels, for DJF and JJA months (Figs. a and b,
respectively). A quadrupole-like structure emerges with positive correlations
centred around 2.5 hPa at the Equator and in the winter-polar mesosphere
(<0.8 hPa), and negative correlations in the winter stratosphere at
mid-to-high latitudes and in the equatorial mesosphere. The inverse
correlation in the stratosphere for DJF extreme months peaks at
∼ 52∘ N (rc=-0.92), while JJA events peak at
∼ 43∘ S (rc=-0.93). We find similar results when
using other equatorial pressure levels near 2.5 hPa as a reference to
calculate correlations.
Correlation coefficient maps of zonal-mean
20∘ N–20∘ S 2.5 hPa temperature anomalies from the SOCOL
model with respect to latitude and altitude for all identified low- and
high-T(a) DJF and (b) JJA events, as defined in
Fig. . (c–f) Composite temperatures for (c)
DJF low-T, (d) JJA low-T, (e) DJF high-T, and
(f) JJA high-T events. Dashed (solid) contours are negative
(positive), with the bold line representing 0. Signals at the 2 and 3
standard deviations from 0 are given as yellow and blue contours,
respectively, in (c)–(f).
Figures c–f show temperature composites for each event type:
Fig. c for DJF low T, d for JJA low T,
e for DJF high T, and f for JJA high T; all show the same
temperature-quadrupole structure as in Fig. a–b (signals at 2
and 3 standard deviations from 0 are given as yellow and blue
contours, respectively). Equatorial temperature anomalies (∼ 2 K) are
smaller than at high latitudes (∼ 5 K or more). The maximum
temperature response at mid-to-high latitudes does not always reside at the
same location as the peak correlation. Although the statistics are less
robust, since the period is shorter, the quadrupole structure is also evident
in SABER observations (Fig. ). Thus, we can be confident that the
nudged model is giving a good representation of observations.
(a) SABER temperature data correlation coefficient map of
zonal-mean 20∘ N–20∘ S 2.5 hPa anomalies with all
latitudes and altitudes for all low- and high-T DJF events. Composite
temperatures for DJF (b) low-T and (c) high-T events,
as defined in Fig . Shading colours and black contours are the
same as in Fig. (dashed: negative; solid: positive; thick: 0).
Signals at 2 standard deviations from 0 are given as yellow contours in
(b) and (c).
The quadrupole structure is likely the result of (i) an acceleration of the
BDC that adiabatically cools the Equator during low-T events as more air
arrives at high latitudes and adiabatically heats there, and (ii) a
deceleration of the BDC that adiabatically heats the Equator during high-T
events as less air arrives at high latitudes, leading to cooling there; both
processes are associated with changes in wave activity.
We show that the mid-latitude temperature, the equatorial
temperature, and ozone anomalies are related to variations in wave activity
using the transformed Eulerian mean stream function (TEMS;
Fig. ), a measure of the mass flux (positive values imply
clockwise flow along contours, and negative values anti-clockwise) and the Eliassen–Palm
flux divergence (EPFD; Fig. ), which is a measure of the
resolved wave-induced forcing of the mean flow (positive values imply an
acceleration of the zonal-mean flow and a deceleration of the BDC, and
negative values the opposite). We used 6-hourly model output to calculate
the monthly means and use Eqs. (3.5.1) and (3.5.3) from
to perform the calculations. Using the events
identified in Figs. and , and used in
Fig. , we find clear EPFD and TEMS anomalies centred near
55∘, slightly poleward of the mid-to-high-latitude peak correlations
(Fig. a–b). As anomalies, they do not represent a reversal of
meridional air flow but a slowing or acceleration. When high-T anomalies
occur, the EPFD is positive, which implies zonal-mean westerly winds have
accelerated and the BDC has slowed, which is confirmed by the TEMS,
indicating increased equatorward flow. This will have the exact effect found:
that of adiabatically heating the equatorial region and cooling the mid-to-high
latitudes relative to the mean state. The opposite is the case for low-T
anomalies. These results confirm that equatorial anomalies are dynamically
driven, and we suggest that it appears to be mainly related to, at the
Equator, a shift in the ozone maximum upwards during low-T events that then
produces the anti-correlation seen in Fig. above 10 hPa, and
vice versa during high-T events. A further consequence of the circulation
changes for ozone is that a temperature increase should lead to faster
catalytic destruction and therefore a decrease of ozone, and vice versa for
temperature decreases, though these effects seem to be less important than
the rapid profile adjustment itself.
The median of the transformed Eulerian mean stream function (TEMS)
anomalies for (a) DJF low-temperature events, (b) JJA
low-T events, (c) DJF high-T events, (d) JJA high-T
events for the same months as in Fig. c–f. Contours lines (solid:
positive; dashed: negative) and colours are given in the legend. Positive
values indicate clockwise acceleration along the contour lines; negative are
anti-clockwise. Data are from the SOCOL model in specified-dynamics mode.
Upper-branch Brewer–Dobson circulation (UBDC) index
The link between anomalous mid-latitude temperature changes and equatorial
temperature and ozone provides a way to account for sporadic variability.
When performing, e.g., an MLR analysis to understand variability in the
stratosphere, such an index of monthly anomalies can account for a large
proportion of variability previously unaccounted for and drive down
uncertainties on regressor estimates. We focus here on the equatorial region,
but our results imply this index could be applied to other locations in the
stratosphere and mesosphere.
Below, we describe how we construct an UBDC index based on detrended and deseasonalised temperature averaged over
43–49∘ S and 2.5–6.3 hPa for June–October, and averaged over
52–57∘ N and 4–10 hPa for November–May. Our index utilises the
output from the CCM SOCOL in specified-dynamics mode, similar to ERA-Interim
and observations, but such an index could be constructed in a similar way for
any specific model.
As for Fig. but for EPFD. Negative
values indicate increased wave activity, and positive values decreased activity.
Construction
Constructing a useful UBDC index
requires the identification of maximum correlation between the Equator and
each hemisphere separately, followed by a combination of information from
these two regions. We have previously considered just the extreme events, but
we now consider all monthly anomalies between 1983 and 2012. While
wave activity drives the temperature changes, it is not an easily observable
quantity. Thus, temperature is a natural and simple quantity to build the
index with. Additionally, we have found that the CCM SOCOL in free-running
mode (i.e. without nudging) shows the same anomalous temperature-quadrupole
structure as in Fig. (not shown). Therefore, one can easily
construct an index using model data to represent anomalous behaviour in the
equatorial regions, and elsewhere where there is a quadrupole response.
We identify the maximum inverse temperature correlations at mid-latitudes in
both DJF and JJA by varying the reference equatorial pressure level. We find
that averaging over the nine grid cells centred on the mid-latitude peak
improves the relationship with the equatorial region. Therefore, we construct
the index with anomalous temperatures averaged over 43–49∘ S and
2.5–6.3 hPa in the Southern Hemisphere (SH) based on JJA months, and
52–57∘ N and 4–10 hPa in the NH based on DJF months.
The UBDC index from the CCM SOCOL model
in specified-dynamics mode using ERA-Interim from 1983 to 2012.
We complete the UBDC index by combining November–April NH anomalies with
May–October SH anomalies; this combination maximises the relationship with
equatorial temperature. We plot the index derived from the CCM SOCOL in
specified-dynamics mode using ERA-Interim in Fig. .
Figure shows the SH and NH mid-latitude temperature anomalies
versus the 4 hPa 20∘ S–20∘ N equatorial average (a and b,
respectively; grey crosses represent November–April, and black
May–October). The SH May–October temperature anomalies are inversely
correlated with equatorial temperatures (rc=-0.70), while
November–April are not (rc=0.05); the opposite is true for the
NH (rc=0.02 and -0.78, respectively). The ozone-temperature
events identified in Fig. are highlighted with coloured circles,
showing that the equatorial anomalies are related to mid-latitude
wave driving. Figure c shows the UBDC index plotted against all
equatorial temperature anomalies at 4 hPa (rc=-0.74). The lower
panels (Fig. d–f) show the equatorial ozone relationship with
respect to mid-latitude temperature and the UBDC index; the absolute
correlation coefficient is lower (rc=0.65) than for equatorial
temperature in the upper panels, but there is still a strong relationship.
(a–b) SOCOL equatorial temperature anomalies (4hPa,
20∘ N–20∘ S) plotted against (a) temperature
means from 2.5–6.3 hPa and 43–49∘ S and (b)
52–57∘ N and 4–10 hPa. (d–e) As for upper panels, but
equatorial ozone anomalies (4 hPa, 20∘ N–20∘ S) are
instead plotted against high-latitude temperature anomalies. Grey crosses are
for November–April months; black crosses for May–October; correlations for
both periods are given in each panel. Red and blue circles identify the DJF
high-T and low-T events in Figs. and ,
respectively; orange and light-blue circles similarly identify JJA events.
(c, f) May–October 43–49∘ S temperatures and
November–April 52–57∘ N temperatures are combined in the right
panel (UBDC index) and plotted against equatorial (c) temperature
and (f) ozone.
In Fig. we show the amount of variability the UBDC index can
account for in nudged-model temperature anomalies everywhere (1983–2012),
using the coefficient of determination rc2, or R2. It
ranges from 0 to 1; a value of 1 is synonymous with the index accounting for
100 % of the variability. In Fig. a the UBDC index can account
for >50 % of variability between 10 and 1 hPa, and above 0.05 hPa. The
variability accounted for at mid-latitudes is less (up to ∼ 30 %),
even at the index source locations (white circles), because the UBDC index
has almost zero agreement half of the time there (see Fig. ). In
Fig. b and c, the UBDC index accounts for much of the DJF/JJA
variability: above 20 hPa it can account for over 70 % of equatorial
variability, more than 60 % of polar mesospheric variability (80 % in the
SH), and much of polar stratosphere variability.
We briefly investigated if there was any indication of an association,
through correlation, between the UBDC index and proxies often considered to
represent precursors of, or be directly related to, dynamical drivers of
lower-stratospheric variability: the North Atlantic Oscillation (NAO)
; the Antarctic Oscillation (AAO) ;
ENSO; the QBO at both 30 and 50 hPa; and the 100 hPa (eddy) heat flux
averaged between 60–90∘ S,
60–90∘ N, 45–75∘ N, and 45–75∘ S. We consider
DJF and November–April periods for the Northern Hemisphere, and JJA and
May–October for the Southern Hemisphere. We considered the original
time series, and detrended and deseasonalised versions following the method
outlined in Sect. . We correlated these 32 “proxy”
time series with the UBDC index, which we have now shown to have high
agreement with short-term variability in the upper stratosphere and
mesosphere. Considering just the R2 values (i.e. coefficient of
determination), we found values exceeding 0.15 only for the 100 hPa heat
flux in three cases: DJF 60–90∘ N after deseasonalising and
detrending the data, and 0.18 and 0.19 for DJF 45–75∘ N,
respectively with or without deseasonalising and detrending; we also found
that the third case here has a similar value with a 1-month lag. Results for
proxies in the Southern Hemisphere all had values close to 0. While these
results suggest there is some possible relationship between the 100 hPa heat
flux and dynamical variability in the upper stratosphere, and we concede that
this was a simplistic set of tests, the implication is that very little of
the variance we see in temperature above 10 hPa is accounted for by these
proxies for stratospheric dynamics at lower altitudes. The source of the
upper-stratosphere and mesospheric variance warrants further investigation
beyond this publication, as our analysis clearly shows a relationship with
changes in temperature in the upper stratosphere and mesosphere related to
what appears to be a wave-forcing-like response in the EPFD and
stream functions (i.e. Figs. and ).
Coefficient of determination (R2) maps of the upper-branch
Brewer–Dobson circulation (UBDC) index with SOCOL model temperature at all
latitudes and altitudes for (a) all months, (b) DJF, and
(c) JJA. White circles represent the approximate region that
the UBDC index is derived from.
Improvement in MLR analysis using the UBDC index
Coefficient of determination summed over all regressors
(Rc2) and the reduction in the Student's t test-based error
on regressor coefficients (%) for equatorial profiles (positive values) for
(a) temperature from 1983 to 2005, for ozone between (b)
1985 and 1997, and for ozone between (c) 1998 and 2012 for various datasets (see
legends). For R2, dotted lines represent estimates without the UBDC
index, solid lines with, and the difference (without UBDC minus with UBDC) is
given as negative and dashed lines.
The UBDC index leads to a large uncertainty reduction in MLR analysis. To
show this, we consider MLR with or without the index focused on the
equatorial region (20∘ S–20∘ N). In both cases we use the
two QBO indices, SAOD, ENSO, a linear trend (mentioned in Sect. ),
and the F30 radio flux as a proxy for solar variability, as this is
superior to the F10.7 cm radio flux . We
consider the use of “AR2” auto-regressive modelling through the procedure
of in all cases; see for a
discussion of AR. The use of second-order auto-regression was determined
after assessing the regression analysis using a Durbin–Watson test, which
showed that AR1 was necessary but not sufficient to account for
auto-correlation in the residuals and that AR2 was sufficient. In
Fig. a, we show the combined ability of the regression model to
account for variance, i.e. the total R2 of all regressors, for
1983–2005 in SSU temperature observations (red), and JRA-55 (blue) and MERRA
(yellow) reanalyses. R2 without the UBDC index (dotted lines;
Fig. a) shows that only up to ∼ 45 % (R2=0.45) of the
stratospheric variability above 10 hPa can be accounted for. However, with
the UBDC index (solid lines) R2 is > 0.8 (MERRA ∼ 0.7), and, in
all cases, the use of the UBDC index peaks at ∼ 5 hPa, with R2 increasing by
0.45–0.60, or an improvement of up to 60 % (see negative values in the
left panel of Fig. a, i.e. Rw/oUBDC2-Rw/UBDC2). In the right panel of Fig. a, we show the relative
change in regressor uncertainty (σw/o UBDC2-σw/ UBDC2)/σw/o UBDC2×100,
where σ is based on Student's t test. The uncertainty estimates
on the regressors decrease by up to ∼ 35 (SSU), ∼ 35 (JRA-55), and
∼ 10 % (MERRA). In addition, the index increases R2 above
0.4 hPa in the mesosphere.
The full distributions of R2 from MLR of SSU equatorial
temperature (20∘ S–20∘ N, 1983–2005) without (w/o, blue) and
with (w, red) the UBDC index showing (a) 4.6 hPa R2 values for
all the regressors considered in the analysis, as well as the total; (b)
the annual and seasonal total R2 at 4.6 hPa; and (c) the
annual total R2 for the three SSU pressure levels. Distributions were
calculated from 10 000 bootstrapped samples for each of the possible (n=6)
720, or (n=7) 5040, order of regressors. Solid white lines are the median
values; dotted lines are the 68 % confidence intervals.
To check whether the UBDC index increases the amount of variance of the total
accounted for, in Fig. we calculate the relative importance of
each regressor without (blue) and with (red) the UBDC index by decomposing
R2seefor a comprehensive review of this technique,
which depends on the order in which regressors are considered, unless the regressors
are orthogonal, which is usually not the case for the 3 decades we
consider here see e.g.. We use the robust Lindeman–Gold–Merenda (LGM)
measure , which determines relative importance by
averaging over all possible, n!, ordering of
regressors (720 for six regressors, 5040 for seven). In Fig. a we show
the relative importance of each regressor, as well as the total, in representing the
variance in SSU temperature at 4.6 hPa; curves represent the complete
distributions resulting from 10 000 bootstrappings of averages over
orderings. At 4.6 hPa the UBDC index accounts for ∼ 61 % of
temperature variance when considered in addition to the others, partly at the
expense of decreasing the relative importance of the other regressors.
Together, the UBDC leads to a ∼ 44 % increase in the total variance
accounted for, from 38 to 82 % (peak values: solid white lines); we see
similar results at the other two pressure levels (Fig. c).
Figure b shows that seasonal MLR analysis is enhanced:
March–April–May (MAM), JJA, and DJF peaks increase by more than double the
68 % confidence intervals, i.e. by an additional ∼ 22, ∼ 40, and
∼ 33 %, respectively; September–October–November (SON) months do not
improve much (∼ 10 %).
Similar in format and method to Fig. a, the relative
importance of each regressor using the coefficient of determination
(R2), as well as the combined total, is shown from multiple linear regression
analysis of four ozone composite datasets at 1.6 hPa for
20∘ S–20∘ N and 1998–2012. The most-likely value is given
by the central, solid white line, and the dotted lines are the 68 %
confidence intervals. Distributions were calculated from 10 000 bootstrapped
samples of each of the possible 5040 regressor orderings.
Equatorial stratospheric decadal trend profiles for (left) SWOOSH
(light blue), GOZCARDS (blue), SBUV-Mer. (yellow), and SBUV-MOD (red) ozone
between 1998 and 2012, and (right) for SSU (red), MERRA (yellow), and JRA-55
(blue) temperature between 1983 and 2005. Thin lines and circles represent
profiles without the UBDC index; thick lines and filled circles are with the UBDC index. The
change in error bars are the same reduction in the error bar between using
and not using the UBDC index as in Fig. . Profiles have been offset
slightly from the actual pressure levels for clarity.
Similar results are found for ozone. Figure b and c show the ozone
composites (see Sect. ) split into 1985–1997 and 1998–2012 time
periods, reflecting those often used to investigate ozone trends
e.g.. There are significant differences in
R2 between the ozone composites from the MLR analysis, which reflects
the fact that different equatorial decadal trends are found between the ozone
datasets and in solar signal
profiles extracted with MLR, which may be related
to the way datasets in the composites have been merged together. While
smaller for ozone than temperature, an improvement is found in representing
variance (R2∼ 0.55), and errors reduce by up to ∼ 20 %
(smaller for the pre-1998 period). While the UBDC index leads to an increase
in the variance accounted for in equatorial temperature variability above
40 hPa (Fig. a), it only increases above 10 hPa for ozone; this
tallies with the strong relationship between temperature and ozone shown in
Fig. , which also breaks down at 10 hPa. Furthermore,
Fig. shows the relative importance of each regressor using violin
plots , as well as the total, for all four ozone composites for
the 1998–2012 period at 1.6 hPa. The format is the same as for
Fig. , though we only show relative importance for each regressor,
as well as the total, for the case that includes the UBDC index. We see that at this
pressure level most of the variance is given by QBO2 and UBDC indices. The
UBDC accounts for between 30 and 55 % of the variance in equatorial ozone,
depending on altitude and whether the composite is Stratospheric Aerosol and Gas Experiment (SAGE-II)-based (GOZCARDS
and SWOOSH) or SBUV-based; the results here suggest the data the composites
are based upon affect the relative contributions to the total variance (see
further discussion below).
We note that the UBDC index influences the relative importance of most of the
other regressors by less than the 68 % confidence interval (dashed white
lines in Fig. ), and only in the case of the trend does the
relative importance get decreased by a larger margin, albeit within 95 %.
Figure b shows that the mean values of the SSU MLR results are
almost completely unaffected (red dots are with the UBDC index; circles are
without), and the MERRA and JRA-55 are only marginally affected, and therefore
the UBDC index does not alias with the estimated trend in temperature. The
relative importance of regressors for ozone is affected only slightly in the
same way as temperature (not shown), so the larger effect on the SSU relative
importance may be data dependent.
In Fig. we show the equatorial decadal trend profiles of the
datasets considered in Fig. and the 2σ uncertainties
derived from multiple linear regression with (thick lines) and without (thin
lines) the UBDC index, between 25 and 0.2 hPa. A full discussion of the
differences in the ozone profiles is undertaken by
and , so we do not repeat that here. We simply note
that the mean decadal equatorial trends in temperature are affected only
slightly by the UBDC index (left panel of Fig. ). However, we see
that the influence of the UBDC index on the mean profile of ozone leads to a
decrease in the ozone trend of ∼ 0.5–1 % per decade in all the ozone
composites, at the altitudes where the index also performs best at reducing
uncertainties (Fig. a). This decrease may be a result of the
largest anomalies after 1998 being positive (see upper plot in
Fig. ), which might introduce a slight upward bias in the trend
analysis; once accounted for with the UBDC index, this bias is removed and
the trend is reduced slightly. Nevertheless, this result suggests that ozone
trend estimates that do not take the short anomalous variability into
account will overestimate the decadal trends, though it is clear that the
biggest uncertainties remain in the underlying datasets themselves
.
Conclusions
We have shown that detrended and deseasonalised ozone and temperature
anomalies in the tropics are strongly influenced by mid-latitude dynamical
perturbations that influence temperature throughout the upper stratosphere
and mesosphere of the perturbed hemisphere. The strongest correlations with
these anomalies occur at latitudes around 50∘ in the winter of both
hemispheres, which are linked to changes in wave forcing.
We develop a new upper-branch Brewer–Dobson circulation index, which
has the power to considerably improve the statistical significance of ozone
and temperature trends, and account for much larger fractions of the total
variability. Our results suggest that the index is able to improve the
uncertainty of equatorial temperature and ozone trend estimates by up to 35
and 20 %, respectively, between 0.5 and 50 hPa – and higher in the
mesosphere, although there is a strong altitude dependence – and up to 60 %
of the total variance can be accounted for. We also find that this result is
data dependent, with the reanalysis products seeing less improvement than the
observations. While we focus on improvements in equatorial temperature and
ozone, we suggest it could also be used in the analysis of other
stratospheric variables, and also in other regions as well as in the
mesosphere. The UBDC index should be employed in future investigations of
stratospheric trends in the upper stratosphere and mesosphere. For modelling
studies, this index can be extracted from pressure levels and latitudes
similar to those put forward here, though the exact peak is likely to be
model dependent; for future trends it may be necessary to determine the exact
peak again since the regions of wave propagation and breaking may change.
In all cases considered here, the UBDC index improves our ability both to
reduce uncertainties and to better account for equatorial stratospheric ozone
and temperature variability and, by extension, attain better estimates of
trends in stratospheric and mesospheric mid-to-high-latitude variability.
Data availability
We provide all MLR results on the Mendeley Data
portal . SABER/TIMED temperature data can be found at
http://saber.gats-inc.com/.
GOZCARDS ozone data can be found at https://gozcards.jpl.nasa.gov/.
SWOOSH ozone data can be found at
http://www.esrl.noaa.gov/csd/groups/csd8/swoosh/.
SBUV ozone data can be found at
http://acd-ext.gsfc.nasa.gov/Data_services/merged/.
ERA-Interim reanalysis data can be found at
http://www.ecmwf.int/en/research/climate-reanalysis/era-interim.
MERRA reanalysis data can be found at
http://disc.sci.gsfc.nasa.gov/mdisc/data-holdings/merra/merra_products_nonjs.shtml.
JRA-55 reanalysis can be found at
http://jra.kishou.go.jp/JRA-55/index_en.html.
SSU data can be found at
http://www.star.nesdis.noaa.gov/smcd/emb/mscat/products.php/.
The SOCOL model code is available on request.
Acknowledgements
We thank the reviewers A. Y. Karpechko and L. Hood
for very helpful suggestions that led to significant improvements in the
quality of the present work. We thank David Thompson for helpful discussion
and suggestions. We thank the GOZCARDS, SWOOSH, and SBUV teams for their ozone
products. We thank the Sounding of the Atmosphere using Broadband Emission
Radiometry (SABER/TIMED) science team for their data. We acknowledge the
Global Modeling and Assimilation Office (GMAO) and the GES DISC for the
dissemination of MERRA, and we acknowledge the Data Integration and Analysis
System (DIAS) for the use of JRA-55. We acknowledge SATIRE-S data from
http://www2.mps.mpg.de/ projects/sun-climate/data.html. William T. Ball
was funded by Swiss National Science Foundation (SNSF) grants 200021_149182
(SILA) and 200020_163206 (SIMA). Timofei Sukhodolov was funded by SNSF grant
200020_153302. Aleš Kuchař was funded by Charles University in
Prague, no. 1474314, and the Czech Science Foundation (GA CR), no. 16-01562J.
Eugene V. Rozanov was partially funded by SNSF grant CRSII2_147659
(FUPSOL-II). Fiona Tummon was funded by SNSF grant 20F121_138017. The
National Center for Atmospheric Research is sponsored by the National Science
Foundation. Edited by:
B. Funke Reviewed by: A. Y. Karpechko and L. Hood
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