JOURNAL OF GEOPHYSICAL RESEARCH: ATMOSPHERES, VOL. 118, 13,347–13,360, doi:10.1002/2013JD020576, 2013
Temperature trends in the midlatitude summer mesosphere
F.-J. Lübken,1 U. Berger,1 and G. Baumgarten1
Received 18 July 2013; revised 21 October 2013; accepted 18 November 2013; published 16 December 2013.
[1] We have performed trend studies in the mesosphere in the period 1961–2009 with
Leibniz-Institute Middle Atmosphere (LIMA) model driven by European Centre for
Medium-Range Weather Forecasts reanalysis below approximately 40 km and adapts
temporal variations of CO2 and O3 according to observations. Temperatures in the
mesosphere/lower thermosphere vary nonuniformly with time, mainly due to the
influence of O3 . Here we analyze the contribution of varying concentrations of CO2 and
O3 to the temperature trend in the mesosphere. It is important to distinguish between
trends on pressure altitudes, zp , and geometrical altitudes, zgeo , where the latter includes
the effect of shrinking due to cooling at lower heights. For the period 1961–2009,
temperature trends on geometrical and pressure altitudes can differ by as much as
–0.9 K/dec in the mesosphere. Temperature trends reach approximately –1.3˙0.11 K/dec
at zp 60 km and –1.8˙0.18 K/dec at zgeo 70 km, respectively. CO2 is the main driver
of these trends in the mesosphere, whereas O3 contributes approximately one third, both
on geometrical and pressure heights. Depending on the time period chosen, linear
temperature trends can vary substantially. Altitudes of pressure levels in the mesosphere
decrease by up to several hundred meters. We have performed long-term runs with LIMA
applying twentieth century reanalysis dating back to 1871. Again, trends are nonuniform
with time. Since the late nineteenth century, temperatures in the mesosphere have dropped
by approximately 5–7 K on pressure altitudes and up to 10–12 K on geometrical altitudes.
Citation: Lübken, F.-J., U. Berger, and G. Baumgarten (2013), Temperature trends in the midlatitude summer mesosphere,
J. Geophys. Res. Atmos., 118, 13,347–13,360, doi:10.1002/2013JD020576.
1. Introduction
[2] Temperature trends in the mesosphere have gained
increasing attention in recent years since there is substantial evidence that trends are much larger here compared to
the troposphere and stratosphere. Major progress has been
achieved by analyzing long-term data records from groundbased, in situ, and satellite-borne measurements [see, for
example, She et al., 2009; Keckhut et al., 2011; Kubicki
et al., 2006; Keating et al., 2000]. Since the pioneering
work of Roble and Dickinson [1989], extensive modeling
has helped to identify the main reasons responsible for these
trends, namely the increase of greenhouse gasses (GHG)
[e.g., Akmaev et al., 2006; Schmidt et al., 2006; Garcia et
al., 2007]. Several reviews have been published in recent
years which summarize the observational and theoretical
status of understanding these trends (some recent examples are Beig [2011], von Zahn and Berger [2011], and
Laštovička et al. [2012]).
1
Leibniz-Institute of Atmospheric Physics, Rostock University,
Kühlungsborn, Germany.
Corresponding author: F.-J. Lübken, Leibniz-Institute of Atmospheric
Physics, Rostock University, Schloss-Str. 6, DE-18225 Kühlungsborn,
Germany. (luebken@iap-kborn.de)
©2013. American Geophysical Union. All Rights Reserved.
2169-897X/13/10.1002/2013JD020576
[3] Most model results regarding mesospheric temperature trends include the troposphere and stratosphere, which
potentially introduces uncertainties due to the complicated physics and chemistry involved. In our LeibnizInstitute Middle Atmosphere (LIMA) model, we nudge to
observations in the lower atmosphere available from
European Centre for Medium-Range Weather Forecasts
(ECMWF), Reading, United Kingdom. LIMA incorporates
the 40 year ECMWF reanalysis data set (ERA-40) from
1960 to 2002 and ECMWF operational analysis thereafter. We thereby avoid model uncertainties in the troposphere/stratosphere but are somewhat sensitive to any
potential error in ECMWF.
[4] Trends in the mesosphere are not uniform in time
but may vary from one period to the other [Berger and
Lübken, 2011, hereafter referred to as B&L11]. In addition to a mostly linear trend caused by CO2 , we found that
O3 imposes a variation on time scale of decades. In this
study we concentrate on summer at midlatitudes because
natural variability in summer is small and there exist some
long-term observations in the mesosphere here. We present
trend simulations from the LIMA model for the period
1961–2009 and compare our results with observations. The
main idea of this paper is to quantitatively evaluate longterm variations of temperatures in the mesosphere and to
identify the role of carbon dioxide, ozone, Ly˛ (as a proxy
for solar UV), and atmospheric shrinking (i.e., the difference between geometrical and pressure altitudes). These
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LÜBKEN ET AL.: SUMMER MESOSPHERE TEMPERATURE TRENDS
Figure 1. Sketch of LIMA. (left) Height dependence of nudging coefficient (in arbitrary units) relevant
for the transition from ECMWF (blue) to the free-running part of LIMA (red). (right) The temporal
and height-dependent variations of ozone (green) and carbon dioxide (orange). Dashed lines indicate
height regions where the temporal variations of O3 and CO2 have basically no impact on mesospheric
temperature trends (see text for more details).
quantification and separation of various effects go beyond
our previous work. We have performed a sensitivity study
to clarify the potential role of mesospheric ozone trends on
temperature trends in the mesosphere. We realize that trends
also exist in other quantities, such as winds, circulation patterns, waves, and such. We will only briefly discuss these
trends in this paper. In LIMA the altitude variation of the
effects mentioned above is partly determined by the implementation of ECMWF (at lower altitudes) and to a large
extent by trace gas changes in LIMA (at higher altitudes).
2. LIMA Model
[5] LIMA is a model of the middle atmosphere which
especially aims to represent the thermal structure around
mesopause altitudes [Berger, 2008]. LIMA is a fully nonlinear, global, and three-dimensional Eulerian grid point
model which extends from the ground to the lower thermosphere (0–150 km), taking into account major processes of
radiation, chemistry, and transport.
[6] We shortly summarize the parameterizations of radiative transfer used in our model calculations. Daily Ly˛ fluxes
from August 1960 until June 2011 are taken as a proxy for
solar activity (ftp://laspftp.colorado.edu/pub/SEE-DATA/
composite-lya). The absorption of solar Ly˛ radiation at
121.6 nm by photolysis of O2 is calculated using the method
described by Chabrillat and Kockarts [1998]. Solar heating
rates are calculated with a parametrization of solar absorption by O2 and O3 [Strobel, 1978]. The actual energy available from direct solar heating is scaled by the stored potential
of chemical energy and the energy loss due to air glow
emission [Mlynczak and Solomon, 1993]. Near-infrared CO2
heating is parameterized as discussed in Ogibalov and
Fomichev [2003]. Variable solar activity also alters the
strength of solar absorption from the near infrared to the
UV and is parameterized following Lean et al. [1997]. We
also take into account heat release by exothermic chemical
reactions [see Berger, 2008; Sonnemann et al., 2007, for
more details].
[7] Cooling rates by terrestrial fluxes are computed
with parameterizations of ozone in the range 30–80 km
[Fomichev and Shved, 1988], water vapor in the range
30–100 km [Zhu, 1994], and atomic oxygen and nitric oxide
in the lower thermosphere [Kockarts, 1980]. Infrared cooling by CO2 including effects from nonlocal thermodynamic
equilibrium conditions (non-LTE) above 75 km is calculated
using the parametrization of Fomichev et al. [1998], recently
upgraded by Kutepov et al. [2007]. The vibrational modes of
CO2 are effectively activated by collisions with atomic oxygen. We use a CO2 -O collisional deactivation rate constant
of 6.010–12 cm3 /s which is consistent with values applied in
the satellite retrieval community [see, for example, Feofilov
et al., 2012].
[8] LIMA applies a triangular horizontal grid structure with 41,804 grid points in every horizontal layer
(x y 110 km) and nudges to tropospheric and lower
stratospheric data from ECMWF. The nudging coefficient
˛n is altitude dependent with a constant value of ˛n =
1/300, 000 s–1 from the ground (0 km) to the middle stratosphere (35 km). Above 35 km, the coefficient linearly
decreases to 0 up to 45 km. The nudging of ECMWF
data introduces short-term and year-to-year variability. As
is shown in Figure 1 the transition from ECMWF to LIMA
occurs gradually in the height range 38.5 to 46.5 km (pressure altitudes). In this paper we will frequently refer to
pressure (zp ) and geometrical (zgeo ) altitudes. The former is
defined as
zp = H loge (po /p)
(1)
where H = 7 km is the pressure scale height and po =
1013 hPa is the pressure close to the surface. We calculate the geometrical altitude according to the formula given
in USSA76 [1976] which is valid for midlatitudes with
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Figure 2. Temperature climatology from LIMA (run 7)
on pressure heights for the summer months (June–
August) averaged over the most recent solar cycle period
(1998–2009).
sufficient accuracy:
zgeo =
ro Zgeopot
;
ro – Zgeopot
Zgeopot =
ˆ(zp )
;
go
Z
zp
ˆ(zp ) =
0
R T(z‘p )
m0 (z‘p ) H
dz‘p
(2)
where ˆ(zp ) is the geopotential, Zgeopot is the geopotential
altitude, ro is the Earth’s effective radius (ro = 6356.766 km),
go is sea level value of the acceleration of gravity
(go = 9.80665 m/s2 ), R is the gas constant, T(zp ) is temperature, and m0 (zp ) is the relative molecular mass:
m0 (zp ) = m(zp )/m(0–50 km), where m is the mean
molecular mass.
[9] In Figure 2 we show the mean temperature climatology in pressure heights averaged over the summer months
(June–August) and the latest solar cycle, i.e., 1998–2009.
There is only little difference to the same climatology in
geometrical altitudes. LIMA clearly shows very low temperatures typical for the polar summer mesosphere. In an
extended version, LIMA also determines mesospheric ice
cloud parameters (noctilucent clouds, NLC) which have successfully been compared with various observations [e.g.,
Lübken et al., 2008; Lübken and Berger, 2011]. Since ice
clouds are very sensitive to temperature, this agreement
implies a verification of the mesospheric thermal structure
in LIMA.
[10] Above approximately 40 km, carbon dioxide and
ozone concentrations in LIMA vary with time. For CO2 (t),
we have used the monthly mean time series for the
entire year and the entire period (1961–2009) as measured
at Mauna Loa (from http://www.esrl.noaa.gov/gmd/ccgg/
trends). From this time series CO2 (t), we have constructed
c 2 (t) by averaging over the summer months
a fit function CO
and calculating normalized fluctuations as follows:
c 2 (t) =
CO
CO2 (t) – CO2 (t)
max{CO2 (t)} – min{CO2 (t)}
from the latest World Meteorological Organization (WMO)
report for 1961–1978 [Douglass and Fioletov, 2011]. This
variation is extrapolated to the ozone concentration in the
lower mesosphere up to 72 km. Above this altitude, the
ozone concentration is held constant in time (see Figure 1).
For the fitting function, we have used a similar normalization
procedure as described for CO2 and also a similar procedure
for the Ly˛ time series. This normalization guarantees a similar chance for all three functions to influence the fit. The
normalized fit functions are shown in Figure 3.
[12] The ozone time series shown in Figure 3 exhibits
a rather complicated temporal variation with very little
trend up to 1980, a rather steep decrease from approximately 1980 to 1995 and an increase thereafter. Note that
this function includes a linear trend of –0.125 /dec (error:
˙0.023/dec) considering the entire time period 1961–2009.
Once the ozone function has been fitted to temperatures,
several trend characteristics can be obtained from the fit
coefficients, such as the mean temperature trend, the maximum and the actual temperature deviation, and such. We
have considered ozone variations in different months (May,
June, July, and August) which turn out to be rather similar.
We therefore decided to average over the summer months
(June–August), not only for ozone but also for the temperatures from LIMA. It turns out that most of the variation in the
mesosphere can be characterized by a combination of variations caused by carbon dioxide and ozone and a small and
quasi-regular variation with Ly˛ . Ly˛ will not be considered further in this paper since it has basically no influence
on trends.
[13] We have performed several runs with LIMA which
are explained in more detail in Lübken et al. [2012] (see
also Table 1). In short, three runs are of major interest here
which (i) consider the influence of the stratosphere only
(run 5, no greenhouse gas increase in LIMA), (ii) include
the effect of CO2 increase (run 6), and (iii) include the
increase of both CO2 and O3 (run 7). The isolated influence
of greenhouse gas increase in LIMA (i.e., without influence of ECMWF reanalysis) can be studied by calculating
the difference between runs. Note that each run contains the
(3)
where CO2 (t) is the mean and max{...} and min{...} are the
maximum and minimum values.
[11] For ozone we have used the temporal variation in the
upper stratosphere. More precisely, we have used relative
anomalies at 0.5–0.7 hPa from 1979 to 2009 as measured
by solar backscatter ultraviolet (SBUV) and the ozone data
Figure 3. Normalized time variations of carbon dioxide
(green), ozone (blue), and Ly˛ (orange). See text for details.
The straight lines and the inlet give the slopes of the time
series.
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Table 1. LIMA Runs
Run 5
Run 6
Run 7
Run 7 – run 6
Run 7 – run 5
Run 6 – run 5
ECMWF + Ly˛
ECMWF + CO2 + Ly˛
ECMWF + CO2 + O3 + Ly˛
O3 effect only
CO2 + O3 effect
CO2 effect only
influence of ECMWF and the difference between any two
runs eliminates this influence. For example, the difference
between run 6 and run 5 isolates the effect of carbon dioxide
in LIMA, i.e., in the mesosphere and lower thermosphere.
[14] If at lower altitudes, e.g., in the stratosphere, a temperature trend causes a shrinking of the atmosphere, this will
shift the pressure levels at higher altitudes downward. Such a
shift causes a temperature change at fixed altitudes which is
negative if the temperature gradient is negative and positive
if the temperature gradient is positive. Any change of temperatures due to other effects, for example, GHG increase,
comes on top of this change.
3. Temperature Trends in the Mesosphere
[15] In Figure 4 we show the temporal evolution of temperatures in the upper stratosphere (zgeo = 43 km) and upper
mesosphere (zgeo = 82 km). It is obvious that there are some
significant similarities between these time series. For example, the temperature minimum in the mid-1990s and the
increase thereafter appear at both altitudes. This similarity
has motivated us to study the influence of the stratosphere
and greenhouse gas variations on mesospheric temperatures
(see B&L11). We realize that there are also some differences,
in particular at the beginning of the time series. There are
several potential explanations, for example, some inconsistencies regarding O3 (t) and T(t) in ERA-40 at the beginning
of the time series (1961–1978), i.e., before reliable satellite
measurements became available. Since these differences are
of secondary importance for our analysis, they will not be
evaluated in this paper. Note that in the years 1975 and 1976,
ECMWF temperatures are too high due to an erroneous bias
in satellite temperatures in the stratosphere [Gleisner et al.,
2005]. More details regarding the ECMWF data sets are
described in Dee et al. [2011].
[16] In Figure 5 we show an example of mesospheric temperature variations from LIMA. For comparison we show
the ozone variation O3 (t) introduced above. It is obvious that
the temperature series show striking similarities to the ozone
variation caused by the influence of ozone on temperatures.
We have performed a multivariate fit consisting of carbon
dioxide, ozone, and Ly˛ functions shown in Figure 3. The
results of these fits are also shown in Figure 5. The temporal variation of temperatures is nearly perfectly described by
this multivariate fit. This is true both for temperature variations on geometrical and on pressure altitudes. For the results
on pressure altitudes, the overall squared correlation coefficient is R2 = 91.1% which indicates that the data are well
represented by the fit. We note that the CO2 and O3 functions
shown in Figure 3 are partly correlated. The squared correlation coefficient is R2 = 0.343 which fortunately is small
enough to separately evaluate the influence of CO2 and O3
on temperature trends. The variance inflation factor (VIF)
for O3 is 1.562 which implies that the
p standard error for the
fit coefficient for O3 is a factor of 1.562 = 1.25 larger as
it would be if the ozone fit function were uncorrelated with
the carbon dioxide fit function. This is well acceptable. The
VIF for O3 and CO2 are much smaller than critical values
stated in the literature, indicating that multicollinearity does
not severely impact our conclusions. The overall F statistic is
F = 152.6 for the example shown in Figure 5 which indicates
that the null hypothesis can basically be discarded. Finally,
the distribution of residuals, namely data minus fit, follows
a normal distribution as expected from randomly distributed
deviations (not shown). We note that fits are less reliable
around the mesopause as will be discussed in section 3.2.
[17] We have performed such a fit procedure at all altitudes. Since the influence of greenhouse gasses on temperatures varies with altitude, the magnitude and relative
importance of the fit components vary as well. As can be
seen in Figure 5, the offset of the 1975/1976 stratospheric
temperatures transfers into the mesosphere through expansion, i.e., it is visible on geometrical heights. As can be
expected, the effect disappears if temperatures at a constant
pressure level are considered. The 1975 and 1976 data points
are ignored when calculating fits. We have considered error
bars when determining the fit coefficients, assuming that
temperatures from LIMA have an uncertainty of T =
˙1 K. The reduced 2 values are on the order of 1, which
confirms that the fit is an appropriate description of the
original time series.
[18] In Figure 6 we show time series of temperatures
in the mesosphere in a latitude band 45ı N–55ı N for the
three runs introduced in section 2. Obviously, the combination of ECMWF and CO2 introduces the largest contribution
to the total variation, whereas the influence of ECMWF is
minor at this height. Temporal changes on geometrical altitudes are significantly larger compared to pressure altitudes,
which is caused by the cumulative shrinking due to trends at
lower altitudes.
[19] As has been mentioned above, the isolated influence of GHG increase in LIMA (i.e., without influence
of ECMWF) can best be studied by calculating the difference of runs (Figure 7). Run 6 – run 5 clearly shows
Figure 4. Temperatures on geometrical altitudes in the
stratosphere (43 km) and in the mesosphere (82 km) over
Kühlungsborn (54ı N, 12ı E). Note the different temperature
scales. The orange curve shows the variation of Ly˛ and the
cyan curve the variation of ozone (right axis; see text for
more details).
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Figure 5. Temperature variations in the latitude band 45ı N–55ı N on a (left) pressure and (right) geometrical altitude of 70 km for run 7. LIMA temperatures (black lines) are compared with a multivariate
fit (red lines) consisting of carbon dioxide, ozone, and Ly˛ variations as shown in Figure 3. For comparison, a linear fit over the entire time period is also shown (green line). The orange curve shows the
variation of Ly˛ and the cyan curve the variation of ozone (right axis; see text for more details). The two
squares mark temperatures in 1975 and 1976 which are ignored when fitting (see text).
the nearly linear trend caused by CO2 which contributes
approximately half of the total variation, both on geometrical
and pressure altitudes. The combination of carbon dioxide
and ozone trends explains most of the temporal variation
observed in LIMA if the influence of ECMWF is eliminated
by subtracting different runs.
3.1. Variation of Greenhouse Gas Influence
With Altitude
[20] The temporal variation of CO2 in LIMA is almost linear in time, as is the reaction of the atmosphere in terms of
temperature change, as can be seen in Figure 8 (run 6 – run
5). The CO2 effect is largest in the middle mesosphere and
decreases at higher altitudes. We repeat that the zero effect
below approximately 40 km is caused by eliminating the
effect of ECMWF in this analysis. Figure 8 (right) shows
the difference of run 7 and run 5, i.e., the combined influence of CO2 and O3 . We concentrate on trends on pressure
levels since this isolates the physical cause and avoids confusion due to shrinking. The effect of ozone on temperatures is
clearly visible. The combination of CO2 and O3 maximizes
in the middle mesosphere, namely around 55–65 km.
[21] We noted already that LIMA run 7 takes into account
ozone anomalies which have been taken from SBUV
satellite observation at pressure levels of 0.5 hPa and 0.7 hPa
close to 55 km (see Table 1). Long-term measurements of
ozone are not available above these heights. We have considered various model studies (some with coupled chemistry) of
long-term trends of greenhouse gasses in the summer mesosphere [Schmidt et al., 2006; Garcia et al., 2007; Fomichev
et al., 2007; Langematz et al., 2013; Rienecker et al., 2011;
Stenke et al., 2012]. Unfortunately, there is not a common
and simple picture regarding ozone trends in the summer
mesosphere. We have therefore performed a sensitivity study
of long-term variations of ozone in the mesosphere. We use
the available observations from SBUV data (0.5–0.7 hPa)
and extrapolate these ozone anomalies to higher altitudes
applying seven different weighting functions varying with
height. The altitude variation of the ozone weighting functions and their effects on temperature trends in the mesosphere for July conditions are shown in Figure 9. Chemical
heating rates and long-term trend of CO2 are included in
all seven cases. Note that our standard scenario being used
throughout this paper is case 2 (identical to run 7 in Table 1),
and the scenario of no ozone trends (in the mesosphere) is
considered in case 7 (identical to run 6 in Table 1).
[22] Temperature trends in the mesosphere generally
depend on ozone trend profiles but converge near 85 km.
Figure 6. Temperature variations for runs 5, 6, 7 at a (left) pressure altitude and (right) geometrical
altitude of 70 km. The orange curve shows the variation of Ly˛ and the cyan curve the variation of ozone
(right axis; see text for more details). The two squares mark temperatures in 1975 and 1976 (see text).
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LÜBKEN ET AL.: SUMMER MESOSPHERE TEMPERATURE TRENDS
Figure 7. Temperature difference between various LIMA runs according to Table 1, for a (left) pressure
and (right) geometrical altitude of 70 km in the latitude band 45ı N–55ı N. Differences are shown for run
6 – run 5 (CO2 only), run 7 – run 6 (O3 only), and run 7 – run 5 (CO2 plus O3 ). In Figure 7 (right), we also
show the temperature difference (for run 7) at pressure altitude minus geometrical altitude (orange line).
Concentrating on pressure altitudes and considering those
cases which are in agreement with SBUV measurements
(cases 1–3 and case 6), temperature trends in the mesosphere
(above 65 km) are very similar, independent of the altitude
profile (cases 1–3) or the strength (case 6) of the ozone trend
in the mesosphere. On the other hand, ozone changes at
stratopause heights (more precisely at 40–55 km) significantly influence temperature trends in the mesosphere (cases
4 and 5). The main reason for this behavior is stratospheric
cooling by reduced ozone and the connection of mesospheric
temperatures to stratopause levels through radiative transfer, mainly by CO2 . The shrinking effect further emphasizes
stratospheric effects on mesospheric temperatures as can be
seen when comparing temperature trends on geometrical and
pressure altitudes in Figure 9 (see section 4).
[23] In summary, our sensitivity study for midlatitudes
and summer conditions has shown that ozone trends in the
stratopause region dominate temperature trends in the mesosphere, whereas ozone trends in the mesosphere play a minor
role. We therefore take our standard scenario (case 2 in
Figure 9) as being representative for many potential cases
of ozone trends in the mesosphere. Note that we concentrate
on ozone trends below 85 km where long-term variations of
chemical heating rates are negligible (not shown).
[24] It is well known that radiative coupling is nonlocal.
We have therefore considered temporal variations of carbon
dioxide and ozone in the entire atmosphere, including the
stratosphere, following the procedure described in Fomichev
et al. [1998] and Fomichev and Shved [1985], respectively.
Note that at ECMWF altitudes, radiative effects do not
impact temperatures (see Figure 1). It turns out, however,
that the impact of trace gasses variations at ECMWF heights
on mesospheric temperatures trends through radiative coupling is negligible. Potential uncertainties regarding ozone
time variations in the middle and lower stratosphere are
therefore not relevant in this study.
3.2. Altitude Variation of Temperature Trends
[25] In Figure 10 we show temperature trends for
1961–2009 as a function of pressure and geometrical altitudes. At each altitude, the carbon dioxide contribution to the
total linear trend is determined as follows: The fit coefficient
for CO2 is multiplied by the linear trend of the carbon dioxide fit function shown in Figure 3. A similar procedure is
performed for ozone and for Ly˛ . We do not show trends due
to Ly˛ in Figure 10 since its contribution is negligible at all
altitudes. The total trend (also shown in Figure 10) is given
as the sum of all three contributions. This sum is identical to
Figure 8. Temperature difference relative to the year 1961 at pressure heights zp (in kilometers) caused
by (left) CO2 trends only and by (right) the combined effect of CO2 and O3 . The cyan curve in Figure 8
(right) shows the variation of ozone (right axis; see text for more details).
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LÜBKEN ET AL.: SUMMER MESOSPHERE TEMPERATURE TRENDS
Figure 9. Case studies of temperature trends in the mesosphere with seven different ozone variations.
(left) The ozone anomalies from SBUV multiplied with seven different weighting functions. The two
red asterisks show the SBUV data points at the two uppermost pressure levels (0.5 and 0.7 hPa). Zonal
mean temperature trends according to these cases are shown as (middle) pressure heights and (right)
geometrical heights for the month of July at 50ı N and the period 1961–2009. Profiles are smoothed by a
running mean over 3 km.
the linear trend calculated from the entire temperature series,
without decomposition. The error bars shown in Figure 10
are determined from the errors of the fit coefficients and the
errors of the slopes of the fit functions.
[26] In the mesosphere, CO2 constitutes the largest part
to temperature trends. Still, ozone contributes approximately
one third both on pressure and geometrical altitudes. The
CO2 -induced negative temperature trends are in agreement
with former studies [for example, Roble and Dickinson,
1989; Akmaev et al., 2006]. In particular, they are largest
(negative) around 55–65 km (65–75 km) in pressure (geometrical) altitudes. Around the mesopause, they are smallest
Figure 10. Temperature trends in a latitude band 45ı N–55ı N for the period 1961–2009 on (left) pressure altitudes and on (right) geometrical altitudes. Slopes are derived from the fit coefficients for carbon
dioxide (green) and ozone (blue). See text for more details. Total temperature trends are shown in red.
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Figure 11. Total temperature trends (mtotal ) in K/dec for the period 1961–2009 on (left) pressure altitudes
and on (right) geometrical altitudes as a function of latitude. The definition of mtotal is given in the text.
Note the different color scales. Typical error bars are shown in Figure 10 and the statistical significance
is discussed in section 3.2.
and even turn from negative to positive. This effect is more
pronounced in geometrical altitudes compared to pressure
altitudes because the reversal of background temperature
gradient at the mesopause reverses the impact of shrinking
on temperature trends (see above). We show results above
the stratopause only because this is the height range where
results stem from the prognostic part of LIMA. Total trends
on geometrical altitudes in the mesosphere are more than
twice as large compared to pressure altitudes. This highlights
the importance of the shrinking effect which involves lower
heights including the stratosphere [Lübken et al., 2009].
Fits are reliable in a statistical sense in the entire mesosphere (R2 above 80–90%) but less so at altitudes above
80 km. This is mainly because natural variations increase
in the upper mesosphere. Figure 10 indicates that the ozone
contribution to temperature trends disappears in the upper
mesosphere, in agreement with our detailed study shown
in Figure 9.
[27] The isolated influence of ECMWF on mesospheric
temperatures is demonstrated by analyzing run 5 (Figure 6).
The influence of ECMWF alone on pressure levels (here:
close to 70 km) is practically negligible. The effect is
significantly larger on geometrical altitudes and is mainly
caused by shrinking. Higher up in the mesosphere, the
effect of ECMWF alone may become significant even on
pressure levels.
[28] Temperature trends in the mesosphere depend on latitude. We have therefore repeated the fit procedure described
above for several latitude bands, namely 5ı N–15ı N, 15ı N–
25ı N, ... 75ı N–85ı N. In Figure 11 we show the result of
this analysis for the total temperature trend mtotal . As can
be seen, trends are generally negative and largest (negative)
in the middle mesosphere. There is a small region around
the mesopause at high latitudes where the total trend is no
longer negative but positive. The height range of positive
trends is restricted to polar latitudes in pressure altitudes
but extends to rather low latitudes (35ı N) in geometrical
altitudes. This is important, for example, when studying temperature and ice layer trends at middle latitudes [Gerding et
al., 2013].
[29] We have repeated the analysis shown in Figure 11
using July temperatures only and not the average of June to
August. We find substantially larger positive trends at 80–
90 km and an extension to lower latitudes. This is due to
the fact that July temperatures in this height range are somewhat lower (up to 10 K) than the June–August average and
the stratopause is warmer. Radiative heating due to radiative
coupling with lower altitudes is therefore more important for
trends. In general, our analysis confirms earlier results from
other models which also show a heating region around the
summer mesopause [Roble and Dickinson, 1989; Akmaev et
al., 2006; Schmidt et al., 2006; Garcia et al., 2007; Fomichev
et al., 2007].
4. Height Shift of Pressure Levels
[30] Most physical processes in the atmosphere, such as
the absorption of solar radiation, radiative transfer, or the
excitation of hydroxyl molecules, can best be described on
pressure levels. Therefore, most models work on pressure
Figure 12. Shift of geometrical altitudes at pressure
heights zp (in kilometers) given in the inlet. Results are presented for LIMA run 7 in the latitude band 45ı N–55ı N.
Shifts are shown relative to the mean of the first 6 years
(1961–1966). Mean values in the time periods 1994–1997
and 2006–2009 are indicated by horizontal lines, respectively.
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Figure 13. Shift of geometrical altitudes in layers between
certain pressure levels defined by pressure altitudes zp given
in the inlet. Shifts are shown relative to the mean of the first
6 years (1961–1966). The total shift is also shown (black
solid line) together with the sum of the contributions from
the three layers (yellow dashed line). Note that these two
lines are practically identical.
levels. On the other hand, some instruments measure the signal from certain geometrical altitudes, e.g., radars, lidars,
sounding rockets, and some satellite instruments. It is therefore important to distinguish between physical processes
acting in a certain pressure level and the height shift of this
level caused by, for example, trends at lower altitudes.
[31] In Figure 12 we show the height shift of pressure
levels at various altitudes. In general, the shift is negative
(shrinking) which increases (in magnitude) with altitude corresponding to an accumulated shrinking because of cooling
in most of the stratosphere and mesosphere. At noctilucent
cloud altitudes (82 km) and near the mesopause, maximum
shrinking appears in the mid-1990s and reaches 1 km.
Since then the atmosphere is expanding again and the
shrinking at, for example, 82 km reduces to approximately
600–800 m up to present time.
[32] We have analyzed the shrinking contribution of various height layers defined by (i) the ground and the uppermost
level of unrestricted ECMWF influence zECMWF = 38 km, (ii)
the latter altitude and the uppermost altitude of the transition
region (i.e., above which there is unrestricted LIMA influence, zLIMA = 47 km), and (iii) the latter altitude and an altitude close to the mesopause (92 km) where total shrinking
is maximal (see also Figure 12). The contribution from each
of these layers is shown in Figure 13. We also show the total
shift at 92 km (black solid line) and compare this with the
sum of all contributions from the layers introduced above.
These two curves are practically identical, which demonstrates the self-consistency of our calculations. Shrinking
in the entire stratosphere is small (sum of blue and green
curves: maximum of approximately –200 m) compared
to shrinking in the mesosphere (maximum approximately
–900 m).
[33] We have further investigated the reasons for atmospheric shrinking by studying the height shifts for various
LIMA runs introduced in section 2. The results are shown
in Figure 14 in terms of the total shift from the early 1960s
to the mid-1990s (more precisely from 1961 to the mean
shift in the period 1994–1997, h90s ) and the total shift up
to today (htoday), respectively. For h90s , ECMWF alone
(“GHG constant”) contributes approximately 40–60% to the
Figure 14. Accumulated geometrical altitude shift of pressure levels from the early 1960s to the mid1990s ((left)= mean of 1994 to 1997) and to recent years ((right)= mean of 2006 to 2009) for run 5 (blue),
6 (green), and 7 (red) at the latitude band 45ı N–55ı N.
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LÜBKEN ET AL.: SUMMER MESOSPHERE TEMPERATURE TRENDS
Figure 15. Accumulated geometrical altitude shift of pressure levels from the early 1960s to the mid-1990s (= mean
of 1994 to 1997, solid lines) and to recent years (= mean
of 2006-2009, dashed lines) for 45ı N–55ı N (blue, zonal
average), Kühlungsborn (green, 54ı N), and for 55ı N–65ı N
(red, zonal average). All curves are based on run 7.
total shift in the mesosphere, whereas CO2 and O3 contribute
approximately 20–25% each. For the actual shift (htoday),
the relative contribution of ECMWF is smaller (20–40%)
whereas the CO2 effect is more important (60%) and
the ozone effect is nearly negligible (<10%). We conclude
that the height region of dominant shrinking is the lower
mesosphere (45–70 km). The shrinking effect is amplified with height by mesospheric CO2 cooling. The decadal
variation of shrinking seen at mesopause heights is modified by the decadal evolution of upper stratosphere/lower
mesosphere ozone.
[34] Does the shrinking effect vary with longitude? In
Figure 15 we compare the maximum and actual shrinking
at a particular location, namely Kühlungsborn (54ı N, 12ı E)
to the mean in the latitude band 45ı N–55ı N. The shrinking effect is basically the same, i.e., there is no evidence
for strong longitudinal variation. Please note that we analyze summer conditions in this paper. We have also briefly
studied latitudinal variation by including results from 55ı N
to 65ı N. As can be seen from Figure 15, the difference
in shrinking at middle and polar latitudes is small compared to the shrinking itself. In the mesosphere, the present
day shrinking has recovered to approximately 60% of the
maximum value in the mid-1990s.
5. Comparison With Observations
[35] Long-term temperature measurements in the summer
mesosphere are very limited. We have therefore compared
our results with indirect measurements of the mesospheric
thermal structure based on radio reflection heights hrefl. .
These measurements exist in Kühlungsborn since the late
1950s and have extensively been used to study trends in
the middle atmosphere [see, e.g., Bremer and Berger, 2002;
Bremer and Peters, 2008, for some recent examples]. The
reflection height is basically determined by a fixed electron number density, which in turn is given by a particular
pressure present at 81–82 km. This reflection height has
decreased by more than 1 km in the last 50 years which
has been attributed to shrinking at lower heights caused
by cooling. The potential influence of ozone trends in the
stratosphere on reflection heights has also been considered
[Bremer and Peters, 2008; Berger and Lübken, 2011]. We
have compared LIMA results with reflection height measurements in B&L11 (Figure 2). There is general agreement
between phase height observations and LIMA modeling.
The total shift of pressure levels and the contribution from
various layers shown in Figures 12 and 13, respectively,
demonstrate that the mesosphere causes most of the shift, but
the stratospheric contribution (20%) cannot be neglected,
as has been shown in earlier studies.
[36] In Figure 16 we show a comparison of LIMA temperatures with observations from the Stratospheric Sounding
Units (SSU) (see ftp://ftp.cpc.ncep.noaa.gov/wd53rl/ssu/)
[Randel et al., 2009]. The uppermost altitude (“channel
47X”) from SSU provides data for the lower mesosphere
(52 km) with a maximum weight at pressures near 0.6 hPa.
This plot is similar to Figure 1 in B&L11, except that in this
paper we have averaged SSU in the latitude band of 35ı N–
65ı N to get a value representative for Kühlungsborn (54ı N)
(note that SSU data are given in latitude bands of 10ı ). For
this comparison, we have weighted the LIMA results similar to the rather broad weighting function of SSU. There
is excellent agreement between LIMA and SSU anomalies.
For example, both SSU and LIMA show a temperature minimum in the mid-1990s and an increase thereafter. It should
be noted that the height of comparison is just above the
lowermost altitude where LIMA runs freely. We therefore
Figure 16. Time series of summer temperature anomalies
from SSU channel 47 and from the LIMA model (run 7)
at a pressure of 0.6 hPa (52 km). Anomalies are relative to the mean of 1979–2005. SSU values are derived from
zonal mean temperatures in the latitude band 35ı N–65ı N.
The orange curve shows the Ly˛ variation (right axis).
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LÜBKEN ET AL.: SUMMER MESOSPHERE TEMPERATURE TRENDS
published by She et al. [2009] turns out to be more complicated since annually mean trends on geometrical altitudes for
the period 1990–2007 are derived which makes it difficult to
disentangle the geometrical/pressure altitude effect on trends
in a height range where the background temperature gradient
varies substantially with time and altitude. Rocket borne
studies of trends have recently been updated by Kubicki et al.
[2006]. We have mentioned earlier that temperature trends
are not uniform in time. This may help to explain some of
the discrepancies between temperature trends observed from
rocket sondes in the period 1969 to 1995 compared to other
techniques, as noted in Kubicki et al. [2006].
6. Simulations Over More Than a Century
Figure 17. Temperature anomalies (=deviations from the
mean) at zgeo =70 km at Kühlungsborn (54ı N) from 1871 to
2008 (black line). The result of a multivariate fit (red) consisting of CO2 (t) (green), O3 (t) (blue), and Ly˛ (t) (orange) is
also shown. Temperatures are marked at the beginning and
at the end of the time series and around 1960 where the trend
changes markedly (red dots).
expect some impact from ERA-40. The agreement shown
in Figure 16 can therefore only partly be considered as an
independent validation of LIMA.
[37] In B&L11 we have performed a detailed comparison with lidar measurements at the Observatory of HauteProvence in southern France (44ı N) [Keckhut et al., 2011]
and found very good agreement. Comparison with temperature trends derived from lidar measurements in the upper
mesosphere/lower thermosphere at Fort Collins (41ı N)
[38] We have expanded our trend calculations by adapting temperatures in the lower atmosphere back to the end
of the nineteenth century. Here we use a reanalysis from
NOAA Earth System Research Laboratory and University
of Colorado Cooperative Institute for Research in Environmental Science (NOAA/CIRES) called “Twentieth Century
Reanalysis” which provides estimates of global tropospheric
and lower stratospheric variability spanning the period from
1871 to 2010 with a resolution of 6 h [Compo et al., 2011,
QJRMS]. In Figure 17 we show temperatures from LIMA
at zgeo = 70 km based on this lower atmosphere data set.
Similar to what was discussed above, we have performed
a multivariate fit based on three functions (also shown in
Figure 17), namely CO2 (t), O3 (t), and Ly˛ (t). The largest
contribution to the long-term temperature trend comes from
CO2 , whereas O3 has an impact in the last 30 years only
(by construction), and Ly˛ (t) causes a quasi-periodical modulation. Obviously, temperature trends are not uniform in
Figure 18. Temperature trends for the location of Kühlungsborn (54ı N) as a function of (left) pressure
and (right) geometrical altitudes. Black lines show the trend over the entire period (1871–2008), whereas
blue and red lines show trends in the subperiods 1871–1960 and 1960–2008, respectively.
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LÜBKEN ET AL.: SUMMER MESOSPHERE TEMPERATURE TRENDS
time but accelerate since approximately the 1960s. Comparison with CO2 (t) clearly shows that this acceleration is
due to an increase of carbon dioxide. We have calculated
temperature trends in three periods, namely from the beginning of the time series (1871) to 1960, from 1960 to present
time (2008), and over the entire period. The results are
shown in Figure 18. As expected, trends are larger in the
second period. In pressure coordinates, total temperature
trends are largest in the upper stratosphere and mesosphere,
more precisely at 40–70 km. Trends are minimal around
the mesopause. In geometrical heights, trends are generally
larger and, for the second period 1960–2008, clearly maximize in the mesosphere, where trends can be as large as
–1.8 K/dec. We note that this trend is very similar to our
detailed analysis of the ECMWF+LIMA runs presented in
section 3.1 (see Figure 10 (right)) .
7. Discussion and Summary
[39] In the troposphere and stratosphere, LIMA relies on
data from ECMWF, more precisely on ERA-40 and the operational analysis. There are indications that ERA-interim provides a more reliable time series of temperatures and other
atmospheric parameters. We have tentatively used ERAinterim in LIMA and indeed find some differences which,
however, do not effect the main conclusions in this paper.
Since ERA-interim is only available since 1979 (because
satellite temperatures are only available since then), we
decided to stay with ERA-40 in this paper.
[40] We noted earlier that we do not separate the influence
of dynamics in this paper. The potential importance of largescale (Brewer-Dobson circulation, planetary waves) and
small-scale (gravity waves and such) dynamics for trends is
elaborated in various studies [see, for example, Schmidt et
al., 2006; Cnossen et al., 2009; Becker, 2009]. Trends due
to dynamics are automatically included in LIMA as long as
they are adequately presented in ECMWF. It is not the purpose of this paper to analyze the reasons for trend effects
in the troposphere and stratosphere and what the potential
contribution of dynamics (relative to radiation) might be.
In the mesosphere we estimate the trend effect of dynamics
introduced by ECMWF by studying LIMA run 5 (no GHG
increase in the mesosphere). Indeed, in the mesosphere we
find a small and barely significant negative trend (on pressure altitudes) of typically –0.1 to –0.2 K/dec, which is much
smaller compared to the radiative induced trends presented
in this paper. At the mesopause, however, the trends from
run 5 are positive and significantly larger (up to +1 K/dec
at zp 90 km, not shown). We cannot exclude trends in
dynamical parameters which are not present in LIMA, e.g.,
by small-scale gravity waves or turbulent heating. On the
other hand, if such trends were substantial, this would
presumably destroy the satisfying agreement of LIMA
trends with observations of temperatures (lidar), phase
heights, and NLC parameters [Berger and Lübken, 2011;
Lübken et al., 2012].
[41] Comparison with general circulation model studies is
not straightforward since scenarios are either different from
LIMA (e.g., assuming a doubling of CO2 ) or the nonuniform
nature of trends is not taken into account [Schmidt et al.,
2006; Garcia et al., 2007]. Akmaev et al. [2006] have studied
the effect of GHG (CO2 , O3 , and H2 O) cooling on trends in
the mesosphere and lower thermosphere (MLT) in the period
1980–2000. Their study covers the entire globe, but potential nonuniform trends are not considered. They confirm that
ozone has a substantial effect on trends in the MLT and find
that water vapor is of minor importance. This is an important result because it implies that ignoring H2 O trends (as
we have done in this paper) has only little effect on temperature trends in the MLT. In the summer hemisphere Akmaev
et al. [2006] find a maximum trend of –2 K/dec in the
mesosphere. This is in general agreement with our results,
in particular since in 1980–2000 trends are somewhat larger
compared to the entire time period considered by LIMA
(see Figure 5). They also study shrinking effects (called
“hydrostatic contraction”) and emphasize their importance
for density variations in the thermosphere.
[42] We have performed trend studies in the period 1961–
2009 with LIMA which is based on ECMWF below approximately 40 km and adapts temporal variations of CO2 and
O3 according to observations, whenever possible. There is
general agreement of temperature trends with observations
such as trends derived from SSU, lidars, and phase height
measurements. Temperatures in the MLT vary nonuniformly
with time, mainly due to the influence of the complicated temporal variation of ozone. It is therefore somewhat
ambiguous to define “trends” as a linear temperature change
over the entire period. Instead, we have separated the influence of CO2 (t), O3 (t), and the effect of Ly˛ (t).
[43] We find that CO2 is the main driver of temperature trends in the mesosphere with maximum values of
–0.74 K/dec at zp 60 km and –0.91 K/dec at zgeo 70 km,
respectively. It is more complicated to evaluate the influence of ozone on trends since the temporal variation of O3 (t)
is nonuniform. Taking into account the ozone trend over
the entire period 1961 to 2009, ozone contributes approximately one third (both on geometrical and pressure heights)
to the total trend in the mesosphere of –0.5 to –1.3 K/dec
(–1.0 to –1.8 K/dec) on pressure (geometrical) altitudes.
Depending on the time period chosen, the ozone effect on
trends can be significantly smaller or larger. It is important
to distinguish trends on pressure and geometrical altitudes.
Differences in total temperature trends can easily be as
large 0.4–0.9 K/dec in the mesosphere, depending on altitude (Figure 10). Note that the role of various trace gasses
for temperature trends in the stratosphere/lower mesosphere
has also been discussed in WMO-2002 . A comparison to
our results is not straightforward, however, since global and
annual means for a different time periods are considered in
WMO-2002.
[44] We have studied in detail the height shifts of pressure levels in the mesosphere caused by shrinking. At
mesopause altitudes, this shift accumulates to more than
1 km in the mid-1990s and recovers somewhat thereafter.
Most of the shrinking occurs in the mesosphere and a
smaller fraction (20%) in the stratosphere. The relative
contributions of CO2 , O3 , and stratospheric effects vary
with time and altitude. There is no indication that shrinking depends substantially on longitude (during summer).
We note that the variation of shifts with altitude and time
period is larger compared to differences between middle and
polar latitudes.
[45] We have performed long-term runs with LIMA,
applying the Twentieth Century Reanalysis from NCEP/
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LÜBKEN ET AL.: SUMMER MESOSPHERE TEMPERATURE TRENDS
NCAR which goes back to 1871. Again, trends are not uniform with time but depend significantly on the time period
considered. Since the late nineteenth century, temperatures
in the mesosphere have dropped by approximately 5–7 K on
pressure altitudes and even more (up to 10–12 K) on geometrical altitudes. This is substantially more than typical trends
in the troposphere and stratosphere. Since these changes are
very likely due to anthropogenic activities affecting carbon
dioxide and ozone, we summarize that the mesosphere (at
least in summer and at middle latitudes) reacts substantially
more sensitive to climate change than lower altitudes. In the
near future we will come back to our original motivation of
trend studies in the mesosphere and will study the effect of
these long-term changes on mesospheric ice layers.
[46] Acknowledgments. The project is partly funded by the Deutsche
Forschungsgemeinschaft under CAWSES SPP grant LU 1174/3 (SOLEIL).
The European Centre for Medium-Range Weather Forecasts (ECMWF) is
gratefully acknowledged for providing ERA-40 and operational analysis
data. Support for the Twentieth Century Reanalysis Project dataset is provided by the U.S. Department of Energy, Office of Science Innovative and
Novel Computational Impact on Theory and Experiment (DOE INCITE)
program, and Office of Biological and Environmental Research (BER), and
by the National Oceanic and Atmospheric Administration Climate Program
Office.
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