ACPAtmospheric Chemistry and PhysicsACPAtmos. Chem. Phys.1680-7324Copernicus PublicationsGöttingen, Germany10.5194/acp-17-5677-2017The radiative role of ozone and water vapour in the annual temperature cycle in the
tropical tropopause layerMingAlisona.ming@damtp.cam.ac.ukhttps://orcid.org/0000-0001-5786-6188MaycockAmanda C.HitchcockPeterhttps://orcid.org/0000-0001-8993-3808HaynesPeterDepartment of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, UKSchool of Earth and Environment, University of Leeds, Leeds, UKNational Center for Atmospheric Research, Boulder, Colorado, USAAlison Ming (a.ming@damtp.cam.ac.uk)8May20171795677570125October201622November20167April201713April2017This 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/17/5677/2017/acp-17-5677-2017.htmlThe full text article is available as a PDF file from https://acp.copernicus.org/articles/17/5677/2017/acp-17-5677-2017.pdf
The structure and amplitude of the radiative contributions of the annual
cycles in ozone and water vapour to the prominent annual cycle in
temperatures in the tropical tropopause layer (TTL) are considered. This is
done initially through a seasonally evolving fixed dynamical heating (SEFDH)
calculation. The annual cycle in ozone is found to drive significant
temperature changes predominantly locally (in the vertical) and roughly in
phase with the observed TTL annual cycle. In contrast, temperature changes
driven by the annual cycle in water vapour are out of phase with the latter.
The effects are weaker than those of ozone but still quantitatively
significant, particularly near the cold point (100 to 90 hPa) where
there are substantial non-local effects from variations in water vapour in
lower layers of the TTL. The combined radiative heating effect of the annual
cycles in ozone and water vapour maximizes above the cold point and is one
factor contributing to the vertical structure of the amplitude of the annual
cycle in lower-stratospheric temperatures, which has a relatively localized
maximum around 70 hPa. Other important factors are identified here:
radiative damping timescales, which are shown to maximize over a deep layer
centred on the cold point; the vertical structure of the dynamical heating;
and non-radiative processes in the upper troposphere that are inferred to
impose a strong constraint on tropical temperature perturbations below
130 hPa. The latitudinal structure of the radiative contributions to
the annual cycle in temperatures is found to be substantially modified when
the SEFDH assumption is relaxed and the dynamical response, as represented by
a zonally symmetric calculation, is taken into account. The effect of the
dynamical response is to reduce the strong latitudinal gradients and
inter-hemispheric asymmetry seen in the purely radiative SEFDH temperature
response, while leaving the 20∘ N–20∘ S average response relatively
unchanged. The net contribution of the annual ozone and water vapour cycles
to the peak-to-peak amplitude in the annual cycle of TTL temperatures is
found to be around 35 % of the observed 8 K at 70 hPa, 40 % of
6 K at 90 hPa, and 45 % of 3 K at 100 hPa. The primary
sensitivity of the calculated magnitude of the temperature response is
identified as the assumed annual mean ozone mixing ratio in the TTL.
Climatology of the annual temperature cycle in ERA-Interim
constructed by averaging from 1991 to 2010: (a) between
20∘ N and 20∘ S, (b) at 70 hPa, (c) at 90 hPa, and
(d) at 100 hPa. The marks for the months indicate the first day of
each month. The values of the temperature are shown by solid contours with
contour values labelled explicitly. The coloured contours are shown at
intervals equal to half of the solid contour interval. These conventions are
followed in all of the figures in the paper.
Introduction
The tropical tropopause layer (TTL), spanning from 150 to 70 hPa or 14 to
18.5 km, is the main entry region for air into the stratosphere from
the troposphere e.g.. The properties of this
region are influenced by the presence of a prominent annual cycle in
temperatures which is clear in, for example, radiosonde measurements
and GPS radio occultation measurements .
Figure shows the structure of the annual temperature cycle in a month-by-month climatology from the ERA-Interim reanalysis dataset
, constructed using data from 1991 to 2010. Consistent with
earlier studies, the annual cycle in temperatures is coherent over the layer
from 130 to 40 hPa (Fig. a), with relatively cold
temperatures in Northern Hemisphere (NH) winter, relatively warm temperatures
in NH summer only and early autumn, and weak latitudinal gradients over the
tropics (20∘ N–20∘ S; Fig. b–d). The maximum
peak-to-peak amplitude of the annual cycle is 8 K near 70 hPa,
decreasing to 6 K at 90 hPa and 3 K at 100hPa, below
which the amplitude reduces very rapidly (Fig. a). Above
about 30 hPa (not shown), temperature variations are dominated by the
semi-annual oscillation.
The temperature variations at the tropical cold point near 100 to 90 hPa
regulate the water vapour entering the stratosphere on annual and
interannual timescales by modulating the freeze drying of upwelling air
e.g.. In
particular, the regular annual cycle in temperatures shown in
Fig. c at 90 hPa and panel (d) at 100 hPa leads to
a substantial annual cycle in water vapour. The additional effect of upward
transport in the lower-stratospheric Brewer–Dobson circulation creates the
well-known water vapour tape recorder signal e.g.. Note that the larger annual temperature cycle at 70 hPa
(Fig. b) does not have a direct effect on water vapour
because overall temperatures are higher than at the cold point below.
Despite the potential significance of the annual cycle in TTL temperatures,
both in its role in determining stratospheric water vapour mixing ratios and
also simply as a conspicuous and persistent aspect of temperature variation,
the mechanisms responsible for the cycle are not yet completely clear.
Furthermore, state-of-the-art climate models, e.g. within the CMIP5 dataset,
still exhibit large inter-model differences in the amplitude of the annual
cycle at 100 hPa with peak-to-peak amplitudes ranging from ∼1 to
∼5 K compared to ∼4 K for the 15∘ N–S average in
ERA-Interim . This indicates that many current climate models
do not capture correctly the processes that drive the TTL annual temperature cycle. Moreover, the lack of an understanding of the quantitative impact of different physical mechanisms on TTL temperatures precludes the development of a
set of general principles for improving models .
To consider the annual cycle further, it is useful to begin by introducing
the thermodynamic equation in the transformed Eulerian mean framework
, neglecting eddy terms:
∂tT‾=Q‾rad-w‾∗S‾-v‾∗∂yT‾=Q‾rad+Q‾dyn;
this predicts the rate of change of zonal mean temperature, T‾,
with time, t, where (.)‾ represents a zonal mean. The dynamical
heating, Q‾dyn, is defined by the second equality in
Eq. (). v‾∗ and w‾∗ are the
horizontal and vertical components of the mean residual velocity
respectively. y is the meridional coordinate. S‾=∂zT‾+κT‾/H is a measure of the static stability, where z is the log-pressure height. z=-Hlog(σ), where H is a
scale height taken to be 7 km, and σ=p/p0, where p is pressure and
p0=1000 hPa. κ=R/cp≃2/7, where R is the gas
constant for dry air and cp is the specific heat at constant pressure. The
radiative heating, Q‾rad, depends in general on the
temperature and the distributions of various radiatively active components
including clouds, aerosols, and trace gases.
Combined with the equations for zonal wind, continuity, and thermal wind
balance, Eq. () determines the zonally symmetric response to
imposed heatings and mechanical forcing Chap. 3. This is
particularly important in considering the response to an imposed forcing on
the right-hand side of Eq. () or indeed an imposed forcing
term in one of the other equations.
Many studies have focused on the role of wave-induced forces in driving the
annual cycle in temperature through their effects on upwelling in the TTL and
hence on Q‾dyn in Eq. (), although
uncertainty remains about what types of waves are the most important
and references therein. However, radiative
contributions to the annual cycle have also been suggested, principally in
connection with the strong annual cycle in TTL ozone mixing ratios
. The quantitative effect of ozone on TTL
temperatures was first investigated by , who used a
one-dimensional radiative convective model representing a tropical average
profile. They concluded that at 70 hPa, about 3 K of the observed
8 K peak-to-peak variation in temperature might be caused by the radiative
effects of the annual cycle in ozone, reducing to about 1 K of the
observed 3 K peak-to-peak variation at 100 hPa.
used a seasonally evolving fixed dynamical heating
(SEFDH; see Sect. ) calculation and found a slightly smaller
contribution from ozone of 2 K at 70 hPa.
Both and asserted that annual
variations in TTL water vapour mixing ratios only have a small role in
determining the annual cycle in temperatures; quantitative details, however,
were omitted. There has been recent significant interest in the radiative
effect of variations in stratospheric water vapour, both in the effect on the
radiative balance of the troposphere e.g. and also in the effect on the lower stratosphere. For example,
used a set of radiative calculations to show that a
uniform increase in stratospheric water vapour gives rise to a cooling that
is largest in the lower stratosphere at all latitudes.
In this work, we investigate, first using the SEFDH approach, the individual
and combined radiative effects of the annual cycles in ozone and water vapour
on TTL temperatures, including at 70 hPa where the amplitude of the annual
cycle is at a maximum and at 90 hPa near the cold point which is crucial
for determining stratospheric water vapour mixing ratios. The radiative
calculations required for this investigation also allow us to examine
carefully how vertical structure in the background radiative environment
combines with the variations in radiative and dynamical heating to determine
the vertical structure of the annual cycle in temperatures. All the
calculations presented here neglect any cloud effects and assume clear-sky
conditions.
For a more complete assessment of the effect of seasonal variations in ozone
and water vapour on the annual cycle in TTL temperatures, which goes beyond
the simplifying assumptions of the SEFDH approach, it is necessary to take
account of dynamical changes. The seasonal cycle in radiative heating induced
by ozone and water vapour variations will in part be balanced by a change in
the meridional circulation e.g.. This is shown in Sect. below to modify
strongly the latitudinal structure of the temperature response.
The structure of the paper is as follows. Section describes
the data and the radiative calculations. Section describes
the results of SEFDH calculations to quantify the effect of annual variations
in ozone and water vapour on the annual cycle of temperature in the TTL. This
section includes a detailed discussion of the radiative effects of water
vapour variations omitted by previous authors. These calculations are
complemented by a set of illustrative fixed dynamical heating (FDH) radiative
calculations in Appendix . The SEFDH temperature changes are also
sensitive to the background ozone mixing ratios and a set of further
calculations is presented in Appendix . (The results
presented in Sect. are in broad agreement with those from
similar work by , which we became aware of during the
review process.) Section discusses the vertical
structure of the annual cycle in temperature, distinguishing the role of the
background radiative environment from that of the radiative and dynamical
heating in determining this structure. Details regarding the estimates of
uncertainty associated with the calculations in Sects. and
are given in Appendix .
Section then goes beyond the SEFDH calculation reported
in Sect. to consider how the temperature response to
variations in ozone and water vapour is modified by the zonally symmetric
dynamical response to the radiative heating. The final section discusses the
results and their implications and reviews the various simplifying
assumptions that have been made.
Data and radiative method
We use temperature and dynamical fields from the ERA-Interim reanalysis
dataset covering the period 1991 to 2010, using data at a horizontal
resolution of 1∘, at 6-hourly analysis time intervals (00:00, 00:06,
00:12, and 00:18 UTC) and at 60 model levels. The mean residual vertical
velocity in the transformed Eulerian mean framework, calculated using the
same method as , and the dynamical heating used in
Sect. are both computed on the original grid from the
ERA-Interim data and then smoothed by linearly interpolating the monthly
averages to daily values. The temperatures are also linearly interpolated to
the grids relevant for the calculations described below and in
Sect. .
Ozone and water vapour mixing ratios are obtained from the Stratospheric
Water and OzOne Satellite Homogenized dataset SWOOSH;. This record is formed from a combination of
measurements from various limb and solar occultation satellite instruments
from 1984 to 2015, namely SAGE-II/III, UARS HALOE
, UARS MLS, and Aura MLS
instruments. The measurements are homogenized by applying corrections that
are calculated from data taken during time periods of instrument overlap.
Using the same data, SWOOSH also provides combined monthly climatologies of
ozone and water vapour which we make use of in this work. SWOOSH is chosen
for this study because it provides a homogenized record useful for climate
studies and has been used previously to study both stratospheric water vapour
and stratospheric ozone variability.
The pressure at the lowest altitude level in SWOOSH is 316 hPa. The results
presented in this paper are not sensitive to mixing ratios of water vapour
and ozone below 316 hPa (within plausible limits), and for convenience the
vertical profiles below 316 hPa were simply defined by linear interpolation
between the SWOOSH values at 316 hPa and the surface values taken from
ERA-Interim.
The radiative calculations were performed using a modified version of the
radiation scheme, which includes updates to the
longwave absorption properties of water vapour . All
calculations were performed on zonal mean data at 5∘ intervals in
latitude and at 100 pressure levels (which are the same as those listed in
Appendix for the FDH calculations). Shortwave heating rates are
calculated as diurnal averages and the surface albedo is taken from
ERA-Interim data. Carbon dioxide is assumed to be well mixed and the volume
mixing ratio is set to 360 ppmv. All calculations in this study assume
clear-sky conditions (i.e. neglecting radiative effects of clouds).
To study the radiative contributions of seasonal variations in ozone and
water vapour to the annual cycle in TTL temperatures, we make use of the
seasonally evolving fixed dynamical heating calculation .
This method calculates the time-varying temperature change due to a specified
radiative perturbation (e.g. a change in a trace gas) and takes into account
the specified time dependence of temperature and trace gas concentration
profiles in a background state to which the perturbation is applied.
Given time-varying background profiles (at a specified latitude) of
temperatures, T‾0, and mixing ratios of trace gases,
χ‾O30 and χ‾H2O0
(where (⋅)0 denotes the background state), the dynamical heating,
Q‾dyn0, is first calculated by assuming the balance in
Eq. (), i.e.
∂tT‾0=Q‾rad(T‾0,χ‾O30,χ‾H2O0)+Q‾dyn0.
A perturbation is applied to the trace gas mixing ratios (Δχ‾O3,Δχ‾H2O), and the new time evolving equilibrium temperature state, T‾0+ΔT‾, is obtained from
∂t(T‾0+ΔT‾)=Q‾rad(T‾0+ΔT‾,χ‾O30+Δχ‾O3,χ‾H2O0+Δχ‾H2O)+Q‾dyn0.
Equation () is integrated forward in time with a daily time
step until the perturbed temperature field, T‾0+ΔT‾, is also annually repeating. Five years is found to be
sufficient for accurate convergence (see Appendix for the
criteria for convergence). The radiative transfer calculation couples
vertical levels but not latitudes so that each calculation is local in
latitude. Following a similar method to ,
Eq. () is applied to update the temperature only above a
certain level taken here to be 130 hPa, on the basis that there are
distinct processes determining temperature variations in the troposphere
below. The choice of this level is further justified in
Sect. . In setting up the calculation we verified that
the results could be reproduced. The SEFDH technique
reduces to the more standard and widely used FDH technique if the imposed
background temperature and species mixing ratios are constant in time and
Eq. () is integrated to a steady state
(Appendix ).
Ozone volume mixing ratio (ppmv) from the SWOOSH dataset plotted as
a difference from the annual mean (a) averaged between
20∘ N and 20∘ S and (b) at 70 hPa. (c) The total change
in heating rate (longwave and shortwave) due to the annual ozone cycle, assuming that temperatures are fixed at the annual average values.
The background state is taken to be the annual average ERA-Interim
temperature (which implies ∂tT‾0=0) and the annual
mean SWOOSH constituent mixing ratios. The latter are then perturbed to their
annually varying climatologies. One could alternatively use the annually
varying temperature climatology as the base state
e.g., but this was found to have a negligible
impact on the simulated temperature response. The use of a time-independent
background state was also easier to implement in the dynamical calculations
reported in Sect. .
SEFDH calculations of temperature responseTemperature response due to annual ozone cycle
Figure shows differences in ozone mixing ratios from
the annual mean over the tropics. The annual cycle in tropical lower-stratospheric ozone mixing ratios, and in particular the large amplitude of
the annual cycle relative to annual mean values, is well known on the basis
of ozonesondes e.g. and satellite data
e.g.. The height and latitude structure
of the annual ozone cycle at low latitudes from SWOOSH is shown in
Fig. a, and the corresponding latitudinal structure
at 70 hPa is shown in Fig. b. Ozone mixing ratios
are lowest across the tropics in NH winter and spring and highest in NH
summer and autumn. The cycle has a broad latitudinal structure, but the amplitude
is substantially larger in the NH subtropics than in the SH subtropics
. Whilst the amplitude of the annual cycle in ozone
mixing ratio increases with height (Fig. a), the
amplitude as a proportion of the annual mean mixing ratio (i.e. the
“relative amplitude”) is largest at about 80 hPa and decreases upward
above that level e.g. their Fig. 3.
SEFDH temperature change (K) due to the annual cycle in ozone. All
other trace gases are kept at their annual mean values.
(a) Temperature change averaged between 20∘ N and 20∘ S.
(b) Temperature change at 70 hPa. (c) Temperature changes
at 70 hPa and averaged between 20∘ N and 20∘ S calculated with the annual
cycle in ozone imposed within different pressure ranges. Outside of each
range and including the pressure level at the lower bound (in terms of
height) of the range, the ozone mixing ratio is kept at the annual mean
value.
The factors that determine the temperature response to a change in ozone
mixing ratio in the TTL are explained in detail in Appendix .
The main effect of a reduction in ozone in a particular shallow layer is to
decrease heating in that layer through both decreased shortwave absorption
and decreased absorption of upwelling longwave radiation, with the latter
being the dominant effect in the TTL. The decreased opacity of the perturbed
layer also leads to increased longwave heating in overlying layers. As an
illustration, Fig. c shows the change in heating rate
at 70 hPa due to the annual ozone cycle, assuming that temperatures are fixed at
the annual average values. (The quantity plotted is
Q‾rad(T‾0,χ‾O30+Δχ‾O3,χ‾H2O0)-Q‾rad(T‾0,χ‾O30,χ‾H2O0).)
The temperature response associated with the ozone anomalies in
Fig. predicted by the SEFDH calculation is shown in
Fig. . A significant annual cycle in temperature is
simulated across the tropics (averaged between 20∘ N and 20∘ S), with
cooler temperatures when ozone mixing ratios are relatively low, in NH
winter, and warmer temperatures when ozone mixing ratios are relatively high,
in NH summer.
In the vertical, the temperature response to ozone is largest between 90 to
70 hPa with a peak-to-peak amplitude over the annual cycle of about
3.5±0.4 K at 70 hPa and about 3.3±0.5 K at 90 hPa
(Fig. a; values are quoted with 95 % confidence
intervals; see Appendix for details). The simulated
temperature response has a lag of about 1.5 months compared to the annual
cycle in ozone. The response essentially has the same sign at all levels because the change in ozone mixing ratios occurs over a relatively deep layer
so that, at a given level, any effects of the reduction in upwelling
radiation by increased ozone in the levels below are dominated by the
increased absorption by ozone at that level. The latitudinal structure of the
simulated temperature response at 70 hPa is shown in
Fig. b. Within the tropics, the latitudinal
structure closely matches that of the ozone variations shown in
Fig. b. Both are stronger in the NH subtropics than
in the SH subtropics.
The temporal and latitudinal structure of the temperature response to ozone
at 70 hPa is similar to those presented by , who
used ozone from the HALOE dataset and the Edwards and Slingo radiation code.
However, the peak-to-peak amplitude we obtain, 3.5±0.4 K, is
substantially larger than they report (∼2 K). The 3 K amplitude found
by is closer to our result and provides a useful comparison
since the assumptions underlying the time-dependent 1-D radiative–convective
calculation from which it was obtained are very similar to those in the SEFDH
approach. The recent study of , which used the same SEFDH
approach with a different radiation code and ozone climatology, finds an
amplitude of 3.1 K, which is more consistent with the present results.
There are several possible causes for the quantitative differences between
results, including differences in the satellite ozone datasets employed
(which reflect real observational uncertainties) and differences in radiation
schemes. Our quoted uncertainties for the magnitude of the annual cycle in
temperature at different levels (refer to previous text and/or
Appendix ) are intended to estimate the effect of the
uncertainty in the precision of the observational data. While we have not
been able to isolate the specific reason for the different results, it is
also clear from further sensitivity tests, reported in
Appendix , that the quantitative temperature response to
the annual ozone cycle has significant sensitivity to the annual mean
background ozone concentrations. For example, if the background ozone
concentration is reduced at each level by about 10 % (which corresponds
to about 2 standard deviations of the estimated uncertainty in the annual
mean ozone mixing ratio), the peak-to-peak amplitude of the annual cycle is
reduced by about 5 %.
To investigate the role of ozone variations in different layers of the TTL
for the observed annual cycle, the SEFDH calculation was repeated with the
annual cycle in ozone imposed only within a set of sub-layers: 1000 to 90, 90
to 50, 50 to 30, and 30 to 1 hPa (see Fig. c).
Outside the given layer, and including the pressure level at the lower bound
of the range (in height), ozone is left at the annual mean value. The annual
cycle in ozone in the region 90 to 50 hPa accounts for about 80 % of the
annual temperature cycle at 70 hPa. A similar result is found at 90 hPa,
where about 60 % of the temperature variation is driven by ozone
variations in the 100 to 80 hPa layer, 30 % by those in the 80 to
50 hPa layer, and 8 % by those in the 50 to 30 hPa layer, with the
remainder coming from the other layers (not shown). The relation between
ozone variations and the resulting temperature variations in the TTL region
is therefore primarily local in the vertical.
Water vapour volume mass mixing ratio (ppmv) from SWOOSH plotted as
a difference from the annual mean (a) averaged over the region
20∘ N–20∘ S, (b) at 70 hPa, (c) at 90 hPa, and
(d) at 100 hPa.
Temperature change (K) due to the annual water vapour cycle in an
SEFDH calculation (a) averaged between 20∘ N and 20∘ S,
(b) at 70 hPa, (c) at 90 hPa, and (d) at
100 hPa.
To summarize the results of this subsection, we have shown using an SEFDH
calculation that the annual ozone cycle can account for 3.5±0.4 K of the
8.2±0.3 K observed peak-to-peak amplitude of the annual cycle in
tropical averaged temperature at 70hPa. The response amounts to an
even larger fraction of the observed annual cycle near the cold point,
accounting for 3.3±0.5 K of the 5.8±0.2 K amplitude at 90 hPa and
2.6±0.2 K of the 3.4±0.1 K amplitude at 100 hPa.
Temperature response due to annual water vapour cycle
Figure shows the annual cycle in tropical water
vapour mixing ratio anomalies from the SWOOSH dataset. The tropical average
water vapour mixing ratios show a clear tape recorder signal of tilted bands
of positive and negative anomalies in the vertical
(Fig. a). Above the tropopause, the amplitude of the
annual water vapour cycle is largest at around 90 hPa where temperatures are
coldest, consistent with the fact that water vapour is directly controlled by
temperature. The amplitude of the annual cycle increases substantially below
150 hPa.
Annual cycle temperature changes (K) at 90 hPa calculated using
SEFDH with the annual cycle in water vapour imposed within different pressure
ranges. Outside of this range and on the pressure level at the lower bound
(in terms of height) of the range, the water vapour mixing ratio is kept at
the annual mean value. The plots are averaged between 20∘ N and 20∘ S. The
contributions from each layer add up linearly to reproduce the total change (not
shown). The temperature change (K) for the case in (a) where the annual water vapour cycle is imposed only from 100 to 130 hPa is shown in
(b) averaged between 20∘ N and 20∘ S and in (c) at
90 hPa.
Since the vertical structure of the annual water vapour cycle is quite
complex relative to that of ozone, we show the latitudinal structure at
several different levels, 70, 90, and 100 hPa
(Fig. b–d). Some hemispheric differences are
apparent, especially at 100 hPa. The amplitude in the annual cycle in water
vapour is greater in the NH, with the largest values near the cold point in
September.
The radiative factors that determine the temperature response to a change in
water vapour in the TTL are described in detail in Appendix .
The main effect of a reduction in water vapour within a particular shallow
layer is cooling below the layer and heating within and above it. The
reduction in water vapour implies less local emission of longwave radiation
and therefore reduced absorption above and below (hence the cooling),
together with less absorption of upwelling radiation within the layer and
increased absorption above. Within the layer the effect of reduced local
emission is stronger, so the net effect is heating. Above the layer the
effects of increased absorption of upwelling radiation dominate, leading to
net heating.
Figure a shows the temperature response from the
SEFDH calculation for the water vapour changes in
Fig. . The temperature response peaks near 90 hPa,
i.e. at a lower altitude than the maximum response to ozone (see
Fig. a). The peak-to-peak amplitude averaged
between 20∘ N–S is 0.9±0.1 K at 70 hPa, 1.1±0.1 K at
90 hPa, and 1.0±0.05 K at 100 hPa. In contrast to the ozone
response, the water vapour response has a phase lag of about 1 month
between 90 hPa and 70 hPa. Note the phase lag of about 2 months between
the annual cycle in water vapour mixing ratios at these levels
(Fig. a). These phase lags result from the
non-locality of the radiative response and the fact that the effect of one
layer on another is being communicated in part by changes in temperature, and
hence changes in radiation, in the intermediate layers. The temperature
response in the range 100 to 70 hPa is, broadly speaking, opposite in
phase to the observed annual cycle in temperatures
(Fig. a) and the response to ozone
(Fig. a).
Temperature changes (K) calculated using the SEFDH method with
annual cycles in ozone and water vapour and from the modified SEFDH method
(Sect. ) for the dynamical heating. The plots are
averaged between 20∘ N and 20∘ S at (a) 70 hPa and
(b) 90 hPa. The ERA-Interim annual temperature cycle is also shown.
Note that the vertical axes are different in (a, b).
(c) The peak-to-peak amplitude of the temperature change averaged
between 20∘ N and 20∘ S. Note that there is a phase difference between the
temperature from the annual water vapour and ozone cycles. Shadings show
95 % confidence intervals arising from uncertainties in the datasets (see
Appendix for more details).
Figure b–d show that the water vapour response is
largest in the NH subtropics at all three levels (70, 90, and 100 hPa). In
each case, the latitude of the maximum response is further north than the
latitude of the maximum amplitude in the water vapour mixing ratios at that
level. The fact that there is no simple relation between the latitude–time
structure of the SEFDH-predicted annual cycle in temperature at a given level
and the latitude–time structure of the water vapour mixing ratios at that
level is further evidence for important non-local contributions in the
vertical from water vapour to the temperature variations.
As in the previous section, we examine these non-local contributions further
by imposing the water vapour changes only within a set of sub-layers: 1000 to
200, 200 to 130, 130 to 100, 100 to 80, 80 to 60 hPa, and 60 to 1 hPa.
Typical results are illustrated by Fig. a, which shows
the response at 90 hPa for each calculation. The total peak-to-peak
amplitude is 1.1±0.1 K, which consists of a local contribution from
the 80 to 100 hPa layer of 0.7 K and a substantial non-local
contribution of 0.4 K from the 100 to 130 hPa layer. Contributions from
above 80hPa and from below 130 hPa are small. The net
contribution from the 130 to 200 hPa layer is small in the
20∘ N–20∘ S average as a result of cancellations between the Northern
and Southern Hemisphere temperature changes. There is also a large meridional
gradient in water vapour, resulting in a larger temperature change in the
Northern Hemisphere which is about 15 % of the temperature change at
90 hPa and 20∘ N (not shown).
Further illustration is given in Fig. b, which shows
the time evolution of the temperature response at all levels when the water
vapour perturbation is confined to 130 to 100 hPa. In this layer, the water
vapour anomaly is at a minimum in February–March and at a maximum in
September–October. The features of the response described above are all
visible except that there is no cooling below 130 hPa due to the SEFDH
temperature constraint. Figure c shows the same
temperature response plotted at 90 hPa. Comparing it to
Fig. c (note the different contour interval), the
100 to 130 hPa region contributes up to about 35 % of the total response
at 90 hPa. The peak response is centred at around 25∘ N,
demonstrating that the maximum response at 90 hPa
(Fig. c) is shifted northwards by non-local
effects. Further sensitivity tests show that, unlike the case with ozone, the
temperature response is not very sensitive to changes in the background value
of water vapour (considering changes typical of interannual variations within
the range of years covered by the SWOOSH dataset).
find a response to water vapour changes with a
peak-to-peak amplitude of 0.6 K at 70 hPa, 0.9 K at 85 hPa, and 0.5 K at
100 hPa. These values are smaller than the amplitudes (respectively 0.9 K and 1.1 K for 90 hPa and 1.0 K) we report above, particularly at 100 hPa
but the difference may be in part explained by the fact that our calculations
include water vapour variations down to 130 hPa. When, following
, we include water vapour variations only above 117 hPa,
we obtain peak-to-peak amplitudes of 0.8, 1 (for 85 hPa), and 0.8 K closer to their results.
Temperature response to annual cycle in both constituents and dynamical heating
Figure a, for 70 hPa, and
Fig. b, for 90 hPa, show the combined effects
of the annual ozone and water vapour cycles on temperature in an SEFDH
calculation. These figures also show the observed annual cycle in
temperature, the estimated annual cycle in temperature due to the annual
cycle in dynamical heating (based on ERA-Interim data; see
Sect. for further details), and the estimated annual
cycle due to the combined effects of ozone, water vapour, and dynamical
heating. To a good approximation the combined effect of ozone and water
vapour is simply the sum of the individual effects discussed in
Sects. and .
At 70 hPa (Fig. a), ozone and water vapour
together can account for an annual cycle in temperature of about
2.8±0.3 K peak-to-peak, i.e. about 35 % of the observed annual
cycle in temperature. The cancellation between the effects of ozone and water
vapour on temperature is strongest at 90 hPa
(Fig. b), with the combined amplitude being
about 2.3±0.4 K peak-to-peak, i.e. again about 40 % of the observed
annual cycle. At 100 hPa, the combined amplitude is about 1.5±0.4 K
peak-to-peak or about 45 % of the observed annual cycle (not shown).
Thus, while the estimated contribution of dynamical heating to the annual
cycle in temperatures is substantially smaller than the observed annual cycle
(Fig. a–c), when the contributions from
dynamical heating, ozone, and water vapour are combined the result is in
remarkably good agreement with the observed annual cycle, both in amplitude
and in phase.
In summary, the combined effects of ozone and water vapour variations exert a
substantial radiative influence on the annual cycle in TTL temperatures and
the lower stratosphere above. The estimated radiative effect of ozone and
water vapour and the observed annual cycle both peak in amplitude at 70 hPa.
The fractional effect of ozone and water vapour relative to the annual cycle
is substantial throughout the TTL, including at the cold point, where
temperatures control the entry values of stratospheric water vapour.
Vertical structure of the annual temperature cycle
The annual cycle in tropical lower-stratospheric temperature is largest over
a shallow layer from 100 to 50 hPa, with a maximum amplitude at 70 hPa
(Fig. c). This vertical structure has been attributed by
to the presence of long radiative timescales in this
region. In this section, we reconsider the question of whether the location
of the maximum variation in tropical temperatures over the annual cycle is
due to the structure of the major radiative and dynamical forcings and/or to
the structure of the background radiative environment.
Data from ERA-Interim averaged between 1991 to 2010 and
20∘ N–20∘ S. Monthly averages are interpolated to daily values to
smooth out the noise in the upwelling field. (a) Mean residual
vertical velocity, w‾∗. (b) Dynamical heating term
w‾∗S‾(=-Q‾dyn).
(c) Same as (b) but with the annual mean removed.
(d)(w‾∗-〈w‾∗〉)〈S‾〉 component of the dynamical heating.
(e)〈w‾∗〉(S‾-〈S‾〉) component of the dynamical heating.
Figure a shows the variation in tropical averaged
w‾∗, in height and time, and reveals a systematic decrease in
amplitude with increasing height from 150 to 50 hPa.
Figure b shows the full dynamical heating term,
w‾∗S‾, and Fig. c shows the
same quantity with the annual mean,
〈w‾∗S‾〉, removed. The annual cycle in
dynamical heating is larger above 100 hPa compared to below and rather
uniform in amplitude over a deep layer that extends from 90 hPa up to about
40 hPa (Fig. c). This behaviour is strongly
influenced by the annual cycle in upwelling (Fig. d),
and in the region 120 to 90 hPa, it is further modified by the annual cycle in
static stability (Fig. e), which causes a reduction
in the annual cycle in dynamical heating around 100 hPa. The peak-to-peak
amplitude of the annual cycle in dynamical heating in the lower stratosphere
is around 0.15 to 0.2 K day-1. This amplitude does not decrease below
the tropopause as rapidly as does the observed peak-to-peak amplitude of
temperature (Fig. a).
Temperature change from the annual mean averaged between
20∘ N and 20∘ S. (a) An SEFDH-like calculation with a perturbation
of -0.1cos(2πt/365) K day-1 is added to the dynamical heating
with annual mean ozone and water vapour. (b) The temperature change
from the annual cycle in the ERA-Interim dynamical heating,
w‾∗S-〈w‾∗S〉, shown in
Fig. c. (c) Temperature change due to the
annual cycle in the ERA-Interim dynamical heating but assuming a constant radiative relaxation rate of
1/40 days-1. (d) ERA-Interim annual mean temperature averaged
between 1991 to 2010 (same as Fig. a).
(e) Similar to (b) but with temperature held fixed at the
annual mean below 130 hPa. (f) Similar to (e) but with the
additional perturbation from the annual cycle in ozone and water vapour
included.
To probe the effects of these heating structures on the annual temperature cycle, we now consider a set of SEFDH-like calculations forced by a set of
specified dynamical heating structures. This is achieved by imposing an
additional dynamical heating, ΔQ‾dyn, on the right-hand side of Eq. (). To determine whether the localization of
temperature variation is a result of the structure of the radiative
environment, we first consider an idealized dynamical heating perturbation
with no vertical structure: ΔQ‾dyn=-0.1cos(2πt/365) K day-1. For this and the next few calculations, we remove the
constraint on temperatures below 130 hPa, permitting them to evolve freely
in response to the radiative perturbations. Any vertical dependence in the
response to this heating will therefore be solely determined by vertical
structure in the temperature-dependent part of the radiative heating.
The resulting temperature change for this case is shown in
Fig. a. The amplitude of the response is largest in a
layer centred on 100 hPa. The phase lag with respect to the imposed heating
is also largest in this layer and equal to about 60 days. This is consistent
with a Newtonian cooling model in which the radiative relaxation timescale
was a maximum of about 60 days at 100 hPa, roughly at the cold point,
consistent with theoretical expectations . The
implied radiative timescales peak over a broader height range than those
found by and in particular do not show such a strong
reduction below 100 hPa. inferred damping timescales
from the cross-correlation between the annual components of analysed
T‾ and w‾∗, which implicitly includes non-local
effects such as those of non-radiative processes operating in the upper
troposphere. This is also true of the supporting radiative calculations they
performed on the basis of observed temperature anomalies. As demonstrated
below, the tropospheric processes have a substantial effect on the relaxation
of temperature anomalies even in the lower stratosphere, in part because of
the strong dependence of radiative timescales on the vertical scale of the
imposed temperature perturbation .
The response to the annual cycle in w‾∗S‾ from
ERA-Interim (Fig. c) is now considered. For
convenience, we set the dynamical heating below 450 hPa to have the same
value as at 450 hPa. This does not affect the main conclusions of this
calculation. The corresponding temperature response is shown in
Fig. b. The vertical structure in the dynamical heating
significantly modifies the vertical structure in the temperature response. In
particular, the fact that the dynamical heating is larger at 70 hPa than at
100 hPa leads to a larger temperature response at 70 hPa than at 100 hPa,
in contrast to the response to the uniform dynamical heating shown in
Fig. a. Therefore, the vertical structure in amplitude of
the annual temperature cycle driven by dynamical heating is determined by
both the background radiative environment and by the vertical structure of
the dynamical heating itself.
To further illustrate this, Fig. c shows the temperature
response to the ERA-Interim dynamical heating assuming a constant radiative
relaxation timescale of 40 days. The response is a good approximation to
that in Fig. b around 70 hPa, suggesting that the
radiative timescale appropriate for the dynamical heating perturbation is
around 40 days, somewhat shorter than that inferred from
Fig. a and consistent with the smaller vertical length
scale of the imposed perturbation. However, there remains below 100 hPa a
peak-to-peak amplitude in the temperature that is significantly larger than
is observed. If we assume that this calculation of the dynamical heating
provides a reasonable estimate of the magnitude of the dominant terms in the
thermodynamic budget of the upper troposphere, this suggests that upper-tropospheric processes provide a stronger constraint on temperature
perturbations than do clear-sky radiative processes. Further calculations
(results not shown) suggest (subject to the preceding assumption) that the
effective timescale of this constraint is approximately 10 days.
To illustrate the implications of the observed tropospheric constraint on
temperatures, we reintroduce the clamp on the temperatures below 130 hPa in
the SEFDH calculation as a simple representation of these processes.
Figure e shows the resulting temperature response to the
same dynamical heating perturbation imposed in Fig. b.
The tropospheric constraint causes the maximum amplitude of the response to
shift upwards from around 80 hPa to about 70 hPa and reduces the magnitude
of the peak response compared to Fig. b. It is clear,
therefore, that this upper-tropospheric constraint has a significant
radiative effect on the region above.
We now add the radiative heating perturbations from the annual ozone and water
vapour cycles to the ERA-Interim dynamical heating to produce
Fig. f. The net effect of the annual ozone and water vapour cycles, as shown in Sect. , is to increase
the amplitude of the temperature response. This produces an annual cycle with
a structure that is in better agreement than that in
Fig. e with the ERA-Interim annual cycle,
Fig. d, with a more pronounced peak at 70 hPa.
In summary, the calculations reported in this section suggest that the
vertical structure of the peak-to-peak amplitude in the annual cycle of
temperatures arises from a combination of several effects. In the absence of
the implied upper-tropospheric constraint, we find that clear-sky radiative
processes produce long radiative timescales over a deep layer centred around
100 hPa and would, in the absence of other effects, imply a similarly deep
structure in the amplitude of the annual cycle. The vertical structure in the
dynamical heating and radiative heating from constituent changes, both of
which exhibit a peak in the region around 80 to 70 hPa, combined with the
tropospheric constraint, lead to a shallower vertical structure with a
stronger response at 70 than at 100 hPa.
The effect of zonally symmetric dynamical adjustment
We will now consider the temperature response to annual cycles in ozone and
water vapour, relaxing the SEFDH assumption to include zonally symmetric
dynamical adjustment. This approach assumes no change in the zonally averaged
wave force, which might well be a significant part of the full dynamical
response in a three-dimensional atmosphere, even if the imposed annual cycles
in ozone and water vapour are zonally symmetric. We discuss the implications
of this simplifying assumption in Sect. below. The zonally
symmetric dynamical response problem has been considered in many previous
papers e.g.. The
expectation from this previous work is that the response to the heating
implied by an imposed change in constituents will occur in part through
dynamical heating, modifying the vertical and latitudinal structure of the
temperature response. One important difference in our approach from these
previous studies is that, rather than approximating the temperature-dependent
part of the radiative heating by Newtonian cooling, we continue to use the
modified Morcrette–Zhong and Haigh radiation code.
Model description
For the dynamical calculations, we use the University of Reading IGCM 3.1
which is a hydrostatic primitive equation model based on
the original spectral dynamical model. This is set up
with a minimal configuration that only includes the dynamical core and the
radiation code. Only the coefficients of the zonally symmetric spherical
harmonics are retained, up to the total wave number 42, resulting in an
approximate latitudinal resolution of 3∘. There are 60 levels equally
spaced in log-pressure coordinates in the vertical with the model top at
50 km. The velocities in the layer near the surface σ>0.7 are
linearly damped as described in .
The temperature tendency in the model is set to be
∂tT‾+[…]=(1-G(ϕ,σ))(Q‾rad(T‾(t),χ‾(t))-Q‾rad(T‾0,χ‾0))-G(ϕ,σ)α(T‾-T‾0),
where the […] represents other advective processes in the model and
G(ϕ,σ)=0.5(1+tanh(50(σ-σtrop(ϕ)))). The
notation Q‾rad(T‾(t),χ‾(t)) is
used to denote the instantaneous radiative heating rate, calculated from the
radiation code, given vertical profiles of temperature, T‾(t),
and concentration, χ‾(t), of radiatively active species
(meaning here ozone and water vapour, with the single symbol χ for
brevity used to indicate both). The use of G(ϕ,σ) in
Eq. (), with σtrop(ϕ) set to 0.13,
implies that the heating terms calculated from the radiative code dominate
above 130 hPa, i.e. in the stratosphere, and the Newtonian cooling term
dominates below 130 hPa, i.e. in the troposphere, with a smooth transition
between the two regimes. The Newtonian cooling timescale is taken to be
1/α=10 days. The radiative calculation is implemented in exactly the
same way as in the SEFDH calculations in Sects. and
. We have verified that the stand-alone radiation code and
the version in the model produce consistent longwave and shortwave heating
rates.
The term Q‾rad(T‾0,χ‾0) is
included so that with the annual mean species concentrations,
χ‾0, and the ERA-Interim annual mean temperature,
T‾0, the heating term on the right-hand side of
Eq. () is 0. Therefore, T‾0 is in principle
an equilibrium state of the model. In practice, the effect of dissipative
dynamical processes such as surface drag and hyper-diffusion means that if
the model is initialized in state T‾0, it evolves towards a
slightly different state T‾c0. Differences between
T‾c0 and T‾0 are very small (e.g. less than 2 K
in the tropical stratosphere), and we have verified that this does not affect
the results presented below.
(a) Monthly temperature changes showing the annual cycle at
70 hPa calculated using the idealized dynamical model (IGCM) with an annual
cycle in ozone. (b) Figure b is reproduced
here for comparison and shows the corresponding SEFDH calculation at 70 hPa.
(c) Difference in temperature change (K) between SEFDH calculation
(b) and the IGCM calculation (a). (d) Change in
upwelling in idealized dynamical model. (e) Temperature change at
70 hPa calculated by imposing the term Δ(w‾S‾)
from the dynamical model as a perturbation to the SEFDH calculation. See main
text for more details.
The dynamical response to the annual cycles in ozone and water vapour is
calculated by considering the difference between a “perturbed” integration
in which the annual cycles are included in χ‾(t)) in
Eq. () and a “control” integration in which they are
not; so χ‾(t)=χ‾0. Both integrations are for
5 years, with T‾0 set as initial condition for each. The first
4 years is allowed as a spin-up period, during which there is an evolution
from the state T‾0 to T‾c0 as noted above and, in
the case of the perturbed integration, an evolution of T‾ towards
a time-periodic annual cycle. The response, as presented in the remainder of
Sect. below, is then taken to be the difference between
the two integrations during the final year. (Note that the responses are
shown at the nearest model levels to 70, 90, and 100 hPa, which are 68.8,
87.3, and 98.3 hPa respectively.) The label IGCM will be used throughout the
remainder of the paper, in the text and the figures, to denote the dynamical
calculation, as just described, and to distinguish it from the SEFDH
calculation.
Temperature response to annual ozone cycle
Figure a and b compare the temperature change at
70 hPa caused by the annual cycle in ozone in the dynamical model and in the
SEFDH calculation respectively (Fig. b is
identical to Fig. b but is included here for ease
of comparison). Figure c shows the difference
between the two. The figures show the importance of including the dynamical
adjustment, which tends to broaden the temperature response in latitude in
the tropical region, making it more symmetric about the Equator. Note, in
particular, the effect on the off-equatorial maximum at about 10∘ N
in the SEFDH calculation, which is no longer a distinct isolated feature in
the dynamical calculation.
Temperature changes (K) calculated using the idealized
dynamical model (IGCM) with an annual cycle in water vapour at
(a) 70 hPa, (b) 90 hPa, and (c) 100 hPa.
Temperature change from the SEFDH calculation (same as
Fig. b–d) at (d) 70 hPa,
(e) 90 hPa, and (f) 100 hPa for comparison.
This difference between the dynamical and SEFDH calculations is as expected
from the previously cited theoretical work on the zonally symmetric dynamical
response adjustment problem. In the dynamical calculation there is a change
in vertical velocity, w‾∗, and in consequence, the applied
heating is balanced in part by ∂tT‾ and
Q‾rad (the “temperature part” of the response), and in
part by a response in dynamical heating (principally
w‾∗S‾). In considering the annual cycle in the
TTL, timescales are comparable to or somewhat larger than the radiative
damping time, implying that the change in the temperature-dependent part of
Q‾rad is substantial (but not necessarily dominant) in
the temperature part of the response. On the basis of simple scaling
arguments which follow as a corollary to those presented, for example in
or , the dynamical heating response is
then expected to dominate over the temperature part of the response when
the latitudinal scale, L, is less than (ND/(2Ωsinϕ))(ωa/α)1/2, where N is the buoyancy frequency, D is
the vertical scale of the heating, Ω is the rotation rate, and
ωa is the annual frequency. This condition holds when the
latitudinal scale L is sufficiently small or at sufficiently low latitudes.
Close to the Equator, this criterion is modified to L being less than
(NDa/(2Ω))1/2(ωa/α)1/4, where a
the radius of the Earth. (Note that this condition can be rewritten in terms
of β=2Ω/a, the gradient of the Coriolis parameter at the
Equator.) Since the ratio of ωa/α is close to 1
(recall that in Sect. , the relevant value of the radiative
relaxation time was deduced to be about 40 days), it follows from the latter
expression, assuming a vertical scale, D, of 4 km, that the dynamical
heating response will dominate on latitudinal scales of less than about
2000 km or 20∘.
Temperature changes (K) calculated using the idealized dynamical
model (IGCM) with annual cycles in both ozone and water vapour shown at
(a) 70 hPa and at (b) 90 hPa. Temperature changes
averaged between 20∘ N and 20∘ S at (c) 70 hPa and
(d) 90 hPa and showing the effects of ozone and water vapour in the
dynamical model (thick lines) as well as the corresponding SEFDH temperature
changes from Fig. a and b (thin lines).
The w‾∗ response at 70 hPa to the annual ozone cycle
variations is shown in Fig. d. Consistent with
the dynamical scaling argument, the w‾∗ field tends to
emphasize the smaller latitudinal-scale features in the heating field shown
in Fig. c, e.g. the two regions of strong cooling
near 30∘ S and 10∘ N in January and February and the
regions of strong heating at about 20∘ S in September and October
and at about 10∘ N in August and September. On the other hand,
between these regions there tends to be an oppositely signed dynamical
response. We have verified consistency by applying the dynamical heating
corresponding to the vertical velocity field shown in
Fig. d, extracted from the IGCM calculation, as a
perturbation heating in an SEFDH calculation using the same procedure
described in Sects. and . The
resulting temperature response shown in Fig. e is
a very good match to the difference in temperature in
Fig. c and reassures us that the difference
between SEFDH and dynamical calculations can indeed be interpreted as
resulting from the effect of dynamical heating and is not due to differences
in detail in the implementation of the two calculations.
The temperature difference at 70 hPa between the SEFDH and IGCM calculations
(Fig. c) is, therefore, that forced by a heating
anomaly equal to the dynamical heating response. The overall effect of the
dynamical adjustment is to smooth the SEFDH-predicted temperature response in
latitude, eliminating features of latitudinal scale (in this particular
problem) less than about 20∘. The amplitude of w‾∗
between 20∘ N and 20∘ S is typically about 20 % of the amplitude of the
annual cycle in upwelling in ERA-Interim, implying that the ozone heating
plays a non-negligible role in determining the latitudinal structure of the
overall annual cycle in w‾∗.
Temperature response to annual water vapour cycle
The temperature response of the dynamical model to a perturbation from annual
average water vapour to annually varying water vapour is now considered in a
similar way to the ozone perturbation just discussed. Given the substantial
radiative interactions in the water vapour response between different
vertical layers, the temperature responses at each of the levels 70, 90, and
100 hPa are displayed respectively in Fig. a–c. The
corresponding SEFDH temperature responses at 70, 90, and 100 hPa are shown
respectively in Fig. d, e, and f. As was the case for ozone,
the temperature responses in the dynamical model are broader and smoother
than the corresponding SEFDH temperature responses. The prominent maxima in
heating in March and April at 20∘ N at 70 hPa and about
25∘ N at 90 and 100 hPa, and in cooling in September to November at
the same locations, are reduced in magnitude, but over the Equator and
extending into the SH there is increased heating in March and April and
increased cooling in September to November. The resulting structure in the
tropics is much more symmetric across the Equator than the SEFDH temperature
response.
Temperature response to annual ozone and water vapour cycles
The combined effect of the annual ozone and water vapour cycles in the
dynamical calculation is now considered. Their effects, to very good
approximation, add up linearly. The latitudinal structure of the combined
response is shown for 70 hPa (Fig. a) and for 90 hPa
(Fig. b). Figure c and d show
the temperature responses in the dynamical model averaged between
20∘ N and 20∘ S, to ozone and water vapour individually and their combined
response, at 70 and at 90 hPa respectively. Also shown in these figures are
the SEFDH results for comparison (same as
Fig. a and b). By this tropical average
measure, there is virtually no change in the peak-to-peak amplitudes of the
individual and combined temperature responses to ozone and water vapour
variations between the SEFDH and dynamical calculations. Any reduction in
local latitudinal maxima in the temperature response is offset by the
broadening effect, leaving the tropical average essentially the same.
However, we reiterate that important changes in the structure of the
temperature responses across the tropics occur as a result of including the
zonally symmetric dynamical adjustment.
The non-locality in latitude in the dynamical problem means that the
temperature response in the tropics, shown in Fig. a
and b, is potentially determined in part by the change in trace gases in the
extratropics. To quantify this effect, we restricted both the annual ozone and water
vapour cycle perturbations to the tropical region between
30∘ N and 30∘ S. The net
effect of the annual variation in trace gases in the extratropics is to
increase the amplitude of the temperature response in the tropics from 2.6 to
2.8 K peak to peak (not shown). The dominant contribution to the annual
cycle change in temperature in the tropics is therefore due to ozone and
water vapour variations in the tropics.
Discussion
We have analysed radiative aspects of the prominent annual cycle in
temperature in the TTL and tropical lower stratosphere, which has a maximum
peak-to-peak amplitude at 70 hPa of ∼8 K. Building on previous work
, we have applied the seasonally evolving
fixed dynamical heating (SEFDH) method to calculate the temperature response
to the annual cycle variations in zonal mean ozone and water vapour, derived
here from the SWOOSH satellite dataset . We extend the
previous work by presenting explicit results for the effects of water vapour
variations and by paying particular attention to the vertical structure of
the temperature response and the role of variations in the trace gas mixing
ratios in different vertical layers. In our first approach, we have used an SEFDH calculation in which the temperature response to annual variations in a
trace gas is calculated independently at each latitude, assuming that the
dynamical heating at each height is unchanged from its value in a control
state in which the trace gas mixing ratios are constant (and equal to their
annual mean values).
We find substantial contributions to the peak-to-peak amplitude of the
tropical average (20∘ N–20∘ S) annual cycle in temperatures from ozone (3.5±0.4 K at 70 hPa, 3.3±0.5 K at 90 hPa, and 2.6±0.2 K at
100 hPa) and from water vapour (0.9±0.1 K at 70 hPa, 1.1±0.1 K at
90 hPa, and 1.0±0.03 K at 100 hPa). Whilst the ozone contribution
maximizes around 70 hPa and is roughly in phase with the observed
annual temperature cycle, the water vapour contribution maximizes around
90 hPa and is of the opposite phase. Despite the cancellation, the net
effect of variations in ozone and water vapour together is substantial and
amounts to about 35 % of the observed annual cycle at both 70 and 90 hPa
and about 45 % at 100 hPa (Fig. ). Our
results are broadly consistent with the recent independent work of
.
Further SEFDH calculations showed that in the region where the ozone has the
largest temperature change, 70 hPa, the ozone-induced temperature variation
is caused primarily (80 %) by local ozone variations
(Fig. ). In contrast, the water-vapour-induced
temperature variation is largest at 90 hPa and is caused by both local and
non-local water vapour variations. Overall, 60 % of
the water-vapour-induced temperature variation at this level comes from water
vapour variation in the region 100 to 80 hPa and 40 % from the region
130 to 100 hPa (Fig. ). This upward non-local
radiative effect is seen throughout the lower stratosphere and has important
implications for cold point temperatures. For example, if the amplitude of
the annual cycle in water vapour below the cold point was to increase, then
the radiative effect would reduce the amplitude in the annual cycle in cold
point temperatures and hence reduce the amplitude of the annual cycle in
water vapour at and above the cold point.
All of the calculations make use of a clear-sky assumption. A rough SEFDH
calculation taking into account an estimate of the annual mean climatological
high cloud cover shows that the peak-to-peak annual cycle temperature change
due to ozone at 70 hPa decreases by 5–10 % at all latitudes between
20∘ N and 20∘ S. The effect on the annual water vapour cycle at the same level is negligible. The clouds lead primarily to a
reduction in the amount of upwelling longwave radiation reaching 70 hPa of
about 0.05 K day-1, which in turn decreases the ozone temperature
response. A full assessment of the cloud effect is beyond the scope of this
work and further work is needed to establish its precise contribution.
We also examined the factors controlling the vertical structure of the
amplitude of the annual cycle in temperatures. The observed maximum centred
on 70 hPa and, largely restricted to the 50 to 100 hPa layer, arises from a
combination of several factors. The vertical structure cannot be explained by
clear-sky radiative damping timescales alone, which maximize over a deep
region, centred near the cold point at 100 hPa. However, both the dynamical
and radiative forcings maximize above the cold point, and in combination with
an inferred upper-tropospheric constraint active below 130 hPa, these lead
to the observed maximum at 70 hPa. We have not attempted to provide an
explanation for the inferred upper-tropospheric constraint and highlight this
as an area for further study.
Finally, we investigated the effect on the temperature response of relaxing
the SEFDH assumption, thereby going beyond the work of
and . We do this by incorporating
the radiative code used for the SEFDH calculations within a 2-D
(height–latitude) dynamical model. Consistent with dynamical expectations,
part of the heating associated with annual cycle variations in both ozone and
water vapour drives an annual cycle in the upwelling and that may play a
non-negligible role in determining the latitudinal structure of the observed
annual cycle in upwelling. This has the effect of reducing latitudinal
gradients in the SEFDH-predicted temperature response, particularly across
the tropics. However, this modification of the response leaves the tropical
(20∘ N–20∘ S) average temperature response essentially unchanged.
Therefore, the conclusion that the net effect of ozone and water vapour
contributes about 35 % of the annual cycle peak-to-peak amplitude at 70
and 90 hPa from the SEFDH calculations is robust to including the dynamical
adjustment. The detailed latitudinal structure predicted by the SEFDH
calculation, however, is not robust to this adjustment.
As explicitly illustrated by Fig. d (for ozone),
the differences between the temperature responses to ozone and water vapour
calculated through the SEFDH approach and those calculated using the 2-D
dynamical model demonstrate that low-latitude temperature features with small
latitudinal scales predicted by SEFDH calculations are unlikely to be
reproducible when the SEFDH assumption is relaxed because these features
will be smoothed out by the dynamical response. (When considering annual
variations in the TTL, “small latitudinal scales” means less than about
20∘ of latitude.) This applies to Figs. b
and b–d in this paper, to previous SEFDH
calculations of the temperature response to annual variations in ozone
their Fig. 5b, and to similar calculations of the
effect of recent interannual variations in ozone and water vapour
their Fig. 6.
Within the 2-D zonally symmetric dynamical formalism presented here, we do
not take account of changes in wave-induced forces. This effect has been
discussed by several authors over the last 30 years or so, including
and , usually making the assumption that
the wave force can be represented by Rayleigh friction (so that the local
wave force is proportional to and opposite of the local zonal velocity).
However, it is generally accepted that Rayleigh friction is a poor
representation of the wave forces that operate in the upper troposphere and
stratosphere. analyse the effect of the change in wave
force in the response to imposed steady localized zonally symmetric heating
in a simple 3-D model (where the waves are resolved and no Rayleigh friction
assumption is necessary) and argue that the effect is to broaden the
temperature response, particularly at low latitudes. Latitudinal structure in
the imposed heating tends to be balanced by the dynamical heating associated
with the meridional velocity response, and the change in wave force provides
the necessary angular momentum balance. A similar effect is seen in the
zonally symmetric problem with Rayleigh friction e.g. their
Fig. 6. There is an analogous effect in the time-dependent
zonally symmetric response problem, without any change in wave force or
Rayleigh friction, considered in Sect. , with the angular
momentum balance including the zonal acceleration. Therefore, the effect of
including the change in wave force in the dynamical problem is, broadly
speaking, expected to be similar; in addition to that already seen in the
time-dependent zonally symmetric problem, at low latitudes, the dynamical
adjustment will smooth the temperature response to latitudinally varying
heating. If the change in wave force is weak then the additional effect will
be small. If the change in wave force is strong then the result will be that
the smoothing is over a larger range of latitudes. The fact that the observed
annual cycle in temperature is coherent over the latitude range
20∘ N–20∘ S (Fig. b–d), but no more
than that, suggests that the wave force effect cannot be too
strong. Therefore, we expect that our conclusions
from the zonally symmetric dynamical problem studied here would not be
changed too much if the change in wave force was included. Furthermore, we
expect that similar dynamical principles will allow extension to the fully
three-dimensional case, implying that an SEFDH calculation will have limited
ability to predict geographical (i.e. latitudinal and longitudinal)
variations in temperature resulting from geographical latitudinal variations
in radiatively active gases or in other relevant quantities such as clouds or
aerosol.
Current comprehensive global (chemistry–)climate models show a large spread
in the amplitude of the TTL annual cycle in temperature
e.g., but the quantitative causes of these differences
are not well understood. The results of this study show that an erroneous
representation of the climatology of ozone and water vapour, as is
commonplace amongst such models e.g., is likely to
be a major contributor to poor model performance for capturing the TTL
annual temperature cycle. Similar conclusions are likely to apply to
interannual variations, e.g. in the 2010–2013 period investigated by
using SEFDH calculations. Progress in improving the
representation of the TTL in comprehensive global models therefore requires
consideration of the coupling through transport and radiative effects between
dynamics, ozone, and water vapour in the TTL. Specific aspects highlighted by
our results include a strong sensitivity of ozone radiative effects to mean
ozone mixing ratios in the 90 to 70 hPa region, for which models with
interactive chemistry simulate a range of values and
for which a range of observation-based gridded datasets exist for climate
models that do not include chemistry .
Furthermore, because of the importance shown here of non-local radiative
effects for water vapour in the TTL, modelled cold point temperatures are
also likely to be sensitive to the representation of water vapour mixing
ratios in the upper tropical troposphere.
The ERA-Interim dataset is described in and
available from http://apps.ecmwf.int/datasets/data/interim-full-daily/.
The SWOOSH dataset is described in and available at
.
FDH calculations
A first-order estimate of the effect of specified perturbations to radiative
trace gases on temperatures in the TTL and the stratosphere can be made using
a fixed dynamical heating (FDH) calculation where it is assumed that the
dynamical heating remains constant from the unperturbed to the perturbed
state, i.e. that no changes in circulation occur as a result of the
perturbation . The timescale for
stratospheric adjustment to the perturbation is essentially the stratospheric
radiative damping time. This is about 40 days in the tropical lower
stratosphere and less than a week near the stratopause, although different
techniques estimate different values and furthermore the timescale is
dependent on the vertical scale of the heating perturbation
e.g.. These
stratospheric timescales are relatively short compared to that required for
tropospheric temperatures to adjust to the perturbation because these are
strongly constrained to surface temperatures, which particularly in oceanic
regions, will evolve only on timescales of months or years. Hence, in FDH
calculations, temperatures are held fixed below some level, often
corresponding to the (radiative) tropopause. We choose this level to be
130 hPa, consistent with previous calculations. The reasons for this choice
are justified in Sect. .
The FDH calculation is a simplified version of the SEFDH calculations and the
equations below can be compared to Eqs. () and
(). Given the background profiles of temperatures and mixing
ratios of trace gases (T‾0, χ‾O30,
χ‾H2O0), the dynamical heating,
Q‾dyn0, is first calculated by assuming the balance
Q‾rad(T‾0,χ‾O30,χ‾H2O0)+Q‾dyn0=0.
The dynamical heating is not a function of time, unlike in the SEFDH
calculations. A perturbation is then applied to trace gas mixing ratios (Δχ‾O3,Δχ‾H2O) and the equilibrium temperature state,
T‾0+ΔT‾, is obtained from
Q‾rad(T‾0+ΔT‾,χ‾O30+Δχ‾O3,χ‾H2O0+Δχ‾H2O)+Q‾dyn0=0.
Time-averaged profiles of ozone and water vapour from the SWOOSH dataset and
the annual mean temperature from ERA-Interim at the Equator are used as the
base profile, and the trace gases are then perturbed. The calculation is done
at the Equator on 1 January and the albedo is set to 0.085. The 100 pressure
levels used in all radiative calculations are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10,
11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 22, 25, 27, 30, 35, 40, 45, 50, 55,
60, 65, 70, 75, 80, 85, 90, 93, 95, 97, 100, 103, 105, 107, 110, 113, 115,
117, 120, 123, 125, 127, 130, 133, 135, 137, 140, 145, 150, 155, 160, 165,
170, 175, 180, 185, 190, 200, 205, 210, 215, 220, 225, 230, 235, 240, 245,
250, 255, 260, 265, 270, 275, 280, 285, 290, 295, 300, 320, 330, 340, 350,
370, 400, 450, 500, 600, 700, 800, 900, and 1000 hPa.
(a) Left: ozone reference profile (solid) and perturbed
profile (dashed) used in the FDH calculation. Right: instantaneous change in
heating rate from perturbation. (b) Temperature change resulting
from the ozone perturbation. The calculation is done at the Equator on
1 January. The lines correspond to perturbations of A0=-0.2, -0.1,
-0.07 (black line), -0.05, 0.05, 0.07, 0.1, and 0.2 ppmv from left to
right at the maximum temperature change (see text for more details). For the
perturbation of -0.07 ppmv, (c) shows total longwave heating rate from
all the constituents, (d) longwave heating rate due to ozone,
(e) longwave heating rate due to carbon dioxide, and
(f) longwave heating rate due to water vapour.
Numerically, the FDH calculation is done by iterating the temperatures
forward with a time step of 1 day using the longwave heating rates to find
the new equilibrium temperature. The values are considered to have converged
when the temperature change and the fluxes between pressure levels after
consecutive time steps fall below 5×10-4 K and
1×10-7 K m-1 respectively. In practice, these thresholds are
reached after about 500 days, which is much larger than any radiative timescales in the stratosphere; hence, they ensure that the temperatures in the
stratosphere have converged.
In Sects. and below, we describe in detail
the temperature response to example perturbations in ozone and in water
vapour. These provide helpful background for understanding the response to
the annual cycle in these two gases reported in Sect. .
Ozone perturbation
The example perturbation applied to ozone mixing ratios is a reduction in
mixing ratios in the lower stratosphere (solid line in
Fig. a, left). This is a simple representation of lower-stratospheric mixing ratios in NH winter, relative to the annual mean. The
perturbation is a Gaussian of the form A0exp[-0.5((z-18.6)/2)2], where A0=-0.07 (ppmv) and z=-7log(p/1×105) km. Removing
ozone in the lower stratosphere leads to an instantaneous local decrease in
the longwave and shortwave heating (Fig. a, right) and
results in a local decrease in the temperature in an FDH calculation (Fig. b, where “local” refers to the vertical region in
which the perturbation in mixing ratios is applied).
The time evolution of various components of the longwave radiative heating
after the perturbation is applied is shown in Fig. b, c, d, and e; these show respectively total longwave heating and then the individual contributions
from ozone, carbon dioxide, and water vapour. The instantaneous effect of the
reduction in ozone mixing ratios is to cause a decrease in both the shortwave
heating and the local longwave heating because of a reduction in local
longwave absorption. The shortwave change, which has peak amplitude
-1.1×10-2 K day-1, occurs because of reduced shortwave
absorption and is essentially proportional to the local change in mixing
ratio. The instantaneous longwave change is significantly larger, with peak
amplitude of -4×10-2 K day-1, and, in addition to the local
decrease, there is an increase, with similar peak amplitude in the region
above the mixing ratio perturbation (see Fig. d). The
explanation for this vertical structure is that, because ozone mixing ratios
are small in the troposphere, in the lower stratosphere there is a
substantial upwelling flux of longwave radiation of wavelength relevant to
ozone (9.6 µm-band), and the imposed perturbation in ozone mixing
ratios leads to less local absorption of this upwelling radiation with correspondingly increased absorption above the perturbation. Note that
another potential effect of the perturbation to ozone mixing ratios is
reduced local emission, which would imply local heating.
Figure d shows that any effect of change in emission is
dominated by the changed absorption of upwelling radiation.
Similar to the plots in Fig. but for water vapour.
(a) Left: water vapour profile (solid) and perturbation (dashed)
used in the FDH calculation. Right: instantaneous change in heating rate from
perturbation. (b) Temperature change resulting from the water vapour
perturbation for B0=2.0, 1.0, 0.5, 0.2, -0.2, -0.5, -1.0 (thick
black line), and -2.0 ppmv from left to right at the maximum temperature
change for the solid lines. For comparison, a perturbation in water vapour of
a similar form to the ozone perturbation with A0=0.2 ppmv is also
included (dashed grey line) (see text for more details). For the perturbation
B0=-1.0 ppmv, (c) is total longwave heating rate from all the
constituents, (d) is longwave heating rate due to ozone,
(e) is longwave heating rate due to carbon dioxide, and
(f) is longwave heating rate due to water vapour.
In the response to the instantaneous change in heating just described, the
temperature and hence the longwave fluxes change, with both carbon dioxide
(Fig. e) and to a lesser extent water vapour
(Fig. f) contributing significantly. Note that changes in the
ozone longwave heating, after the instantaneous change resulting from the
perturbation to ozone mixing ratios, are weak, suggesting that it plays
little role in the temperature adjustment. An equilibrium is reached where
the net longwave heating (Fig. c) balances the reduction in
shortwave heating. The equilibrium temperature change is dominated by a local
decrease centred on 70 hPa (i.e. the centre of the region where ozone
mixing ratios were perturbed). Several timescales are involved in the
adjustment process and Fig. c shows that the heating rates
and hence the temperature are still evolving after 100 days. This justifies
the use of an SEFDH rather than an FDH calculation when studying the annual
cycle in temperatures.
Further experiments show that the FDH temperature response varies
approximately linearly with the peak value of the Gaussian perturbation in
the range -0.1 to 0.1 ppmv (thin grey lines in
Fig. b), so that the detailed time evolution described above
continues to hold if heating and temperature anomalies are multiplied by the
appropriate factor. In particular a modest increase in ozone mixing ratios
will lead to a local temperature increase, in which the net (negative) change
in longwave heating balances an increase in shortwave heating. For mixing
ratio anomalies with peak values of ±0.2pmmv, substantial
non-linear effects appear.
Water vapour perturbation
Following the approach in Appendix above, a corresponding
calculation is now described in which water vapour is perturbed by removing a
Gaussian of the form B0exp[-0.5((z-16.9)/1.5)2)], where
B0=1.0 (ppmv) (Fig. a, left) which leads to an
instantaneous local decrease in the shortwave and a local increase in the
longwave radiation (Fig. a, right). This is also a very
simple representation of lower-stratospheric mixing ratios in NH winter,
relative to the annual mean. As in Appendix ,
Fig. c, d, e, and f respectively show the total longwave heating and
then the individual contributions from ozone, carbon dioxide, and water
vapour during the evolution in response to the water vapour perturbation.
The abundance of water vapour in the troposphere means it is relatively
opaque to upwelling longwave radiation in the main water vapour absorption
bands. This means that, in contrast to ozone, the dominant instantaneous
effect in the longwave of locally reducing the water vapour in the lower
stratosphere is to cause less local emission, i.e. local heating, and,
correspondingly, less non-local absorption in neighbouring regions, i.e.
non-local cooling, rather than any effect on the absorption of upwelling
radiation. This can be seen in the water vapour longwave heating shown in
Fig. f. Note that the change in non-local absorption is seen
primarily in the upper troposphere below the region where the mixing ratios
are reduced because background water vapour mixing ratios are relatively
large there compared to those in the stratosphere. The reduction in water
vapour mixing ratio also leads to a reduction in shortwave absorption, as was
the case for ozone, but the magnitude (-0.3×10-2 K day-1)
is smaller than the corresponding change in longwave heating (4.3×10-2 K day-1).
In the evolution following the initial instantaneous change in heating, the
longwave heating contributions due to carbon dioxide, water vapour, and
ozone all play a role to limit the temperature response and redistribute it
in the vertical (Fig. d–f). In particular the initial local
increase in temperatures is transmitted in the vertical through longwave
fluxes in the carbon dioxide bands to give subsequent temperature increases
substantially above the layer in which water vapour mixing ratios were
perturbed. This sort of behaviour is not captured by a local Newtonian
cooling approximation. As was the case for ozone, the longwave heating (and
hence the temperatures) continue to evolve beyond 100 days. This suggests
that a sequence of quasi-steady FDH calculations would be inadequate for
studying the annual cycle in temperatures and again justifies the use of the
SEFDH approach.
Experiments with different amplitudes of perturbation to water vapour mixing
ratio (Fig. 19b) show that the response is linear for peak values up to ±1.0 ppmv, with non-linear effects visible at ±2.0 ppmv. Note that a
similar amplitude and shape of perturbation as the ozone perturbation with
A0=0.2 ppmv are shown for comparison as a dashed grey line in
Fig. b and the magnitude of the temperature change is small
(0.14 K at 70 K) compared to that for the equivalent ozone perturbation
(2.8 K at 70 K).
Statistical methods
Estimates of the 95 % confidence intervals are shown for the SEFDH
calculations in Fig. . For ozone and water
vapour in the SWOOSH dataset, a combined uncertainty arising from the
uncertainties in the various instruments and a standard deviation arising
from interannual variability can be obtained. These two quantities are
provided as part of the SWOOSH dataset and are of similar magnitude in the
region of interest. A 95 % confidence interval is obtained for each month
by summing these two uncertainties in quadrature and assuming that each year
in the dataset is independent. This assumption has been checked and is
adequate. The uncertainty is dominated by the interannual variability for
ozone. The SEFDH calculation for each constituent is then repeated to give
bounds for the temperature change given the uncertainty in that constituent
only. For example, the water vapour uncertainty in
Fig. is small and only reflects that coming
from the water vapour dataset and not from differences in ozone, which will
also affect the temperature change from water vapour. However, the combined
effect of both uncertainties is present in the calculation of the temperature
change from both ozone and water vapour. When calculating the peak-to-peak
amplitude, the uncertainties at the maximum amplitude and minimum amplitude
are added in quadrature.
The residual mean vertical velocity in reanalysis datasets has a large
interannual variability and this is the only source of uncertainty taken into
account in the calculation in Fig. . Again, in
estimating this quantity, we assume that each year of the dataset is
independent. This leads to a peak-to-peak amplitude from the dynamical
heating averaged over 20∘ N–20∘ S at 70 hPa of 5.6±0.6 K and of
1.5±0.6 K at 90 hPa. In addition, there are other large discrepancies
in estimates of the dynamical heating which are not taken into account in
this calculation. For example, the difference between calculating the
dynamical heating directly from w‾∗S‾ and from
the thermodynamic equation can be as high as about 40 % in certain
months. A full treatment of all the sources of uncertainty in this
calculation is beyond the scope of this work.
Background ozone mixing ratio
The greatest sensitivity of the temperature changes calculated in the SEFDH
calculations is to the background value of ozone. A set of illustrative SEFDH
calculations is presented below to show how this affects the temperature
change for the annual ozone cycle. Figure a shows an
illustrative perturbation (third line from the left, solid grey) to the
annual mean ozone profile (middle line, solid black) used in the SEFDH
calculations in Sect. . (The illustrative
perturbation is calculated as a decrease of twice the standard deviation of
the sample mean, σ^μ=s^ne^-1/2, where
s^ is the standard deviation of the time series of annual mean values
in the SWOOSH dataset and n^e is the effective number of degrees of
freedom in this time series. This method is used to obtain a sensible ozone
perturbation.) This decrease in the annual mean ozone leads to an increase in
the peak-to-peak amplitude of the temperature change due to ozone at 70 hPa
by about 0.16 K (Fig. b). Similarly, an increase in
the annual mean ozone leads to a smaller-amplitude ozone annual
(a) Annual mean ozone profile averaged between
20∘ N and 20∘ S (middle solid black line). Solid dark grey line to the left
of the middle line shows an illustrative perturbation to the annual mean
profile where the ozone background value is decreased. Solid grey lines
represent negative perturbations 2 times and 3 times this perturbation.
Corresponding positive perturbations are shown as dashed lines.
(b) Difference to the SEFDH temperature change at 70 hPa for the
annual ozone cycle due to the different annual mean ozone values
in (a). The darker solid grey line shows the temperature change for
the illustrative perturbation. The lighter grey lines and dashed lines
correspond to the increasingly larger negative and positive perturbations
respectively, as shown in (a). (c) The contribution of
different ranges of pressure levels to the temperature change for the
illustrative perturbation.
cycle. Further experiments show that the change in the
peak-to-peak amplitude varies roughly linearly with the change in the
background ozone mixing ratio within the range of values shown in
Fig. a. These values are of a magnitude comparable to
those seen in other ozone datasets. For instance, quote a
spread of about ±10 % in the annual mean ozone in the lower
stratosphere between seven newly available merged satellite ozone profile
datasets. The spread in individual satellite instruments is larger with
differences of up to ±20 % from the multi-instrument mean
.
Figure c shows the contribution from different
pressure ranges to the change in the annual temperature cycle from the
illustrative perturbation. A decrease in the annual mean ozone increases the
upwelling longwave radiation reaching 70 hPa leading to a larger annual temperature cycle response at 70 hPa. This can be seen from the largest
contributions coming from the regions 90 to 70 hPa and below 90 hPa.
The authors declare that they have no conflict of
interest.
Acknowledgements
The authors wish to thank Stephan Fueglistaler for helpful discussions,
Manoj Joshi for assistance with the IGCM3.1 model, and Sean Davis and
Karen Rosenlof for help with the SWOOSH dataset. We also acknowledge helpful
comments from the two referees. Alison Ming, Amanda C. Maycock, and
Peter Hitchcock were supported by an ERC ACCI grant (project no. 267760). In
addition, Amanda C. Maycock was supported by an AXA Postdoctoral Research
Fellowship and a NERC Research Fellowship (grant NE/M018199/1), and
Peter Hitchcock was supported by an NSERC postdoctoral fellowship.
Peter Haynes acknowledges support from the IDEX Chaires d'Attractivité
programme of l'Université Fédérale de Toulouse,
Midi-Pyrénées. Edited by: Q.
Fu Reviewed by: S. Solomon and one anonymous referee
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