The Leibniz-Institute Middle Atmosphere Model LIMA is used to study mesospheric temperature trends in summer during the last 5 decades (1961–2009). In order to account for realistic atmospheric conditions LIMA adapts several observational data sets, namely a) tropospheric and stratospheric temperatures and winds from ECMWF at heights 0–35 km, b) daily Lyman-α fluxes, c) monthly carbon dioxide concentrations since 1961, and d) annual total ozone from ground-based data for 1964–1978 and monthly ozone profiles up to 0.60 hPa from satellites since 1979. This paper presents a comparison of simulated temperature trends with a) ground-based observations of lidar temperatures at 44°N, b) phase height measurements at mid-latitudes (51°N), and c) temperature trends derived from satellite data. In general there is excellent agreement between trends from LIMA and observations. Cooling in the mesosphere is on the order of 2–4 K/decade. The magnitude of the mesospheric temperature trend varies during the last five decades. In particular, the period from 1979–1997 shows large mesospheric cooling of 3–5 K/decade. This large cooling is primarily caused by long-term changes of ozone in the upper stratosphere in combination with a CO2 increase. For the first time, modeling of mesospheric temperature trends confirm the extraordinarily large trends from observations.
 It has been suggested since many years that an increase of greenhouse gases results in a cooling in the middle atmosphere [Roble and Dickinson, 1989]. Since carbon dioxide and ozone are the main radiative cooling gases in this region it is expected that temperatures have decreased in the stratosphere and mesosphere in recent decades. In the lower stratosphere observed cooling trends and simulations with climate models are generally consistent [Austin et al., 2009]. In the upper stratosphere some inconsistencies between observed and modeled temperature trends were reported by Steinbrecht et al. . Observations show that in the period 1985–2008 upper stratospheric temperatures are almost constant, whereas chemistry climate models show an ongoing temperature decline. In the mesosphere, however, there are even much larger uncertainties and also discrepancies between observations and modeling (see review by Beig et al. ). Global satellite observations of stratospheric temperatures started in the 1970s with the Stratospheric Sounding Units (SSU) which provide the only global decadal data set for trend analysis in the upper stratosphere (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 (∼50 km) with a maximum weight at pressures near 0.60 hPa [Shine et al., 2008]. For the mesosphere, no direct multi-decadal measurements of temperatures by satellites are available. Instead we have to rely on single station ground based observations. Temperature trends detected at a lidar station at mid-latitudes show exceptional large cooling rates in the mesosphere and stratosphere [see recent update by Keckhut et al., 2011]. Another piece of evidence for large trends in the middle atmosphere comes from multi-decadal measurements of the reflection height of radio waves near 82 km which is presumably the longest data record from the mesopause region based on active sounding. This reflection height has decreased by ∼1.5 km in the last 50 years which relates to a cooling in the mesosphere of up to 4–5 K/decade [Bremer and Berger, 2002; Bremer and Peters, 2008]. Several model studies have shown that increasing CO2 and decreasing O3 indeed cause a cooling in the middle atmosphere [e.g., Bremer and Berger, 2002; Akmaev et al., 2006; Schmidt et al., 2006; Garcia et al., 2007]. However, the magnitude of the effect in models is much smaller compared to observations [Beig et al., 2003].
 In this paper we study the effect of CO2 increase and O3 changes on trends in the middle atmosphere, in particular in the mesosphere. Tropospheric and stratospheric effects are implicitly taken into account. We concentrate on summer at mid-latitudes because natural variability is small in summer and some long-term observations are available here (see above). We present trend simulations from the LIMA model for the period 1961–2009 and compare our results with observations from lidar, phase heights, and SSU.
2. Model Description
 The LIMA model (Leibniz-Institute Middle Atmosphere) is a global circulation model of the middle atmosphere (0–150 km, Δz = 1.1 km) which especially aims at representing the thermal structure around mesopause altitudes in order to simulate the morphology of polar mesospheric ice clouds [Lübken and Berger, 2011]. LIMA uses a triangular horizontal grid with an almost uniform horizontal resolution of 110 km. LIMA takes into account major processes of radiation, chemistry, and transport [Berger, 2008]. The model has recently been upgraded to include additional radiation parameterizations which improve simulations of solar irradiance variations, e. g., during the 11-y solar cycle. In the new version of LIMA daily Lyman-α 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 Lyman-α radiation at 121.6 nm by photolysis of O2 is calculated using the method described by Chabrillat and Kockarts . Variable solar activity also alters the strength of solar absorption from the near infrared to the UV-spectrum [Lean et al., 1997]. Infrared cooling by CO2, including effects from non-local thermodynamic equilibrium conditions (non-LTE) above heights of 75 km, is calculated using the parametrization of Fomichev et al. , recently upgraded by A. A. Kutepov et al. . Finally we added a parametrization of IR cooling by water vapor in the rotational and the 6.3 μm vibrational bands according to Zhu .
 LIMA adapts several observational data sets. In order to account for realistic lower atmosphere conditions LIMA uses tropospheric and lower stratospheric data with complete global coverage from ECMWF (European Centre for Medium-Range Weather Forecasts, Reading, United Kingdom). LIMA loads the 40-yr ECMWF reanalysis data set (ERA-40) for the period from August 1960 to August 2002, and ECMWF operational analysis fields after August 2002. The ECMWF data used by LIMA are extracted with 1° × 1° latitudinal/longitudinal resolution at 21 pressure levels from 1000 to 1 hPa and every 6 hours at 0, 6, 12, and 18 UT. LIMA adapts these data in the following way: at every model time step forcing functions are added to the governing model equations to gradually nudge the model toward observations of temperature, zonal wind, meridional wind, and surface geopotential. The nudging coefficient is constant from the ground to the middle stratosphere (35 km), and decreases linearly to zero from 35–45 km.
 Global monthly changes of CO2 are taken from http://www.esrl.noaa.gov/gmd/ccgg/trends. Ozone as the second major greenhouse gas is quantified by monthly, latitudinal, longitudinal, and altitude-dependent profiles available from SBUV (Solar Backscatter in the Ultraviolet) satellite data from 1979 to 2009 (http://acdb-ext.gsfc.nasa.gov/Data_services/merged). The uppermost level of SBUV ozone data corresponds to a pressure of 0.5 hPa. Above this level LIMA interpolates and fits the SBUV ozone fields within one scale height to the standard ozone climatology used in LIMA. For the period 1964–1978 we adapt annual total ozone data from ground-based measurements for 1964–1978 published in the WMO report 2011 [Douglass and Fioletov, 2011]. The years 1961–1963 have been extrapolated from 1964. Three different simulations have been performed with LIMA to assess the sensitivity of mesospheric temperature trends: 1) taking into account long term changes of CO2 in the entire atmosphere and O3 changes up to approximately 55 km (see above), 2) same, but keeping O3 constant from year to year, and 3) keeping CO2 and O3 constant from year to year. We note that long term changes of CO2 and O3 in the troposphere and stratosphere are implicitly taken into account in all three runs by the nudging procedure described above. Unless noted otherwise, we show trends from run 1. Lübken  has shown mean temperatures at a latitude section 40°–90°N in the mesopause region for summer conditions (mean from 1997–2007 for July) from run 1. Temperatures in the mesosphere are in good agreement with satellite observations as, e. g., from SABER [Garcia et al., 2007].
3. Temperature Trends at Midlatitudes
 In Figure 1a we show summer temperature anomalies in the period 1979–2005 from lidar temperatures at the Observatory of Haute-Provence (OHP) in southern France (44°N, 7°E) [Keckhut et al., 2011]. We also show temperatures from SSU channel 47X at approximately 50 km. Unless noted otherwise we define ‘summer’ as the mean of June to August. LIMA results are taken at the geographical position of OHP with a vertical weighting according to SSU (including the CO2/instrumental effect discussed below). SSU data comprise zonal mean temperatures in the latitudinal band 35°–55°N at a pressure level of 0.60 hPa. No attempt has been made to remove any solar cycle signal in the curves shown in Figure 1a. There is excellent agreement between LIMA and SSU anomalies, whereas the lidar data show somewhat larger deviations in some years. We have also selected LIMA temperatures with geographic sampling according to SSU and find negligible changes relative to the results from OHP latitude. This suggests that local observations are indeed representative for trends in an entire latitude band, which is presumably not true in winter when planetary waves may contribute to longitudinal variation of trends.
 We investigated in detail the potential effect of vertical sampling on temperature trends. SSU measures temperatures at weighted pressure levels, for example at 0.60 hPa for channel 47X. Furthermore, the weighting function increases to higher altitudes with increasing CO2 due to an instrumental effect [Shine et al., 2008]. We mimicked these sampling scenarios with LIMA. More precisely, we sampled a) at a fixed geometric altitude of 50 km, b) at a fixed pressure level of 0.60 hPa, c) applying the SSU weighting function for channel 47X according to Shine et al. , and d) modifying the weighting function considering the instrumental effect mentioned above. All sampling methods result in almost identical temperature anomalies (deviations smaller than 0.5 K) and give very similar trends. The agreement between SSU and LIMA trends is perhaps not surprising since the nudging region within LIMA is only ∼10 km below SSU channel 47X. The good agreement is also based on the quality of the SBUV ozone data set. This statement comes from a sensitivity test where we have replaced SBUV ozone (in run 1) by ozone climatology not varying from year to year (in run 2 and 3). This indeed results in somewhat worse agreement between LIMA and SSU temperatures. For example, for run 3 the anomalies are ∼2 K lower (∼0.5–1 K higher) at the beginning (end) of the period shown in Figure 1a.
 In Figure 1b vertical profiles of temperature trends for the period 1979–1997 derived from LIMA and from lidar measurements at the geographical position of OHP are shown. Lidar trends are taken from Keckhut et al. [2011, Figure 10a]. LIMA trends are obtained from a multiple regression fit considering solar cycle effects. Above 30 km large cooling trends of ∼3–5 K/decade are obtained in LIMA and also in observations which reduce and even turn to warming around the mesopause. Modeled and observed trends are consistent at almost all altitudes. For the first time, modeling of mesospheric temperature trends confirm the extraordinarily large trends observed by lidar. As will be discussed later such large trends are confined to the period 1979–1997.
 We also compare LIMA trends with long-term measurements of radio wave reflection heights performed since 1959 at the IAP in Kühlungsborn [Bremer and Peters, 2008]. Radio waves at 162 kHz transmitted from Allouis (France) are reflected in the ionosphere and detected at IAP. The reflection occurs at a pressure level of ∼0.006 hPa (corresponding to an altitude of ∼82 km) at the mid point position which is at 50.7°N, 6.6°E. More details on the phase height technique and potential effects of long term trends of electron densities are presented by Bremer and Berger . In Figure 2a long-term changes of these reflection heights are shown for summer (data are taken from Bremer and Peters [2008, Figure 5a]). Solar cycle and geomagnetic influences have been removed from the observations. We also show LIMA results, namely the height variation of the 0.00576 hPa pressure level averaged during summer. Again, the solar cycle influence is removed from the LIMA data, but it is rather small anyway (typically less than 0.05 km). As can be seen from Figure 2a there is excellent agreement between LIMA and observations. Regarding long term variations we concentrate on the period 1961–1997 since trends are much smaller thereafter. Observations show a height decrease of −338 m/decade in this period. LIMA gives a very similar result (−300 m/decade) considering combined uncertainties.
 We have performed various LIMA runs to elucidate the physics behind the trends, in particular the role of CO2 and O3 trends in the mesosphere, and the impact of the stratosphere. In Figure 2b we present trend calculations from the three model runs introduced in section 2. Run 3 is labeled ‘stratosphere only’ because it still adapts ECMWF data and therefore implicitly includes long-term changes in the troposphere and stratosphere. Temperature anomalies shown in Figure 2b are derived at 70 km altitude for summer conditions at the geographic position of phase height reflection (51°N,7°E). Temperature anomalies are largest in run 1, decrease by up to 50% if the effect of O3 is ignored (run 2), and are smallest if stratospheric effects only are considered (run 3). The CO2 effect alone (without any interference by O3) can be indirectly inferred from the difference between run 2 and run 3. The temperature difference is about +2 K in 1961 and declines almost linearly to −2.75 K in 2009 which corresponds to a cooling trend of about 1 K/decade. In all runs there are pronounced year-to-year variations, for example a steep decrease from the mid 1980s to the mid 1990s. For comparison we show ozone anomalies at 0.70 hPa from SBUV for the period June–August and averaged in the latitude band 50 ± 20°N. As can be seen from Figure 2b year-to-year variations of stratospheric ozone and temperatures in the mesosphere are rather similar for all runs. We have already shown [Lübken et al., 2009] that stratospheric shrinking can cause temperature changes in the mesosphere. Ozone anomalies in the mesosphere may add to this effect as shown in run 1. We repeat that stratospheric effects in LIMA come from adaptation to ECMWF temperatures which includes (through assimilation) ozone trends. Accidently, this effect is demonstrated in the years 1975 and 1976 where ECMWF temperatures are too high due to an erroneous bias in satellite data. As can be seen in Figure 2b this offset copies into the mesosphere through expansion. As can be expected, the effect disappears if temperatures at a constant pressure level are considered.
 Stimulated by the evolution of stratospheric ozone as presented by World Meteorological Organization (WMO)  we grouped our trend studies into three time periods, namely 1961–1979, 1979–1997, and 1997–2009. Temperature trends from LIMA show a corresponding change of trends in these periods. We determined trends for run 1 from a multiple regression fit which includes solar cycle variations. For the period 1961–1979 (ignoring 1975 and 1976) a rather weak cooling trend of ∼0.5 K/decade is observed. For the period 1979–1997 we find large cooling trends of ∼4–5 K/decade, and for the period 1997–2009 a warming of ∼1 K/decade. A similar warming is observed from phase height (see Figure 2a), lidar and SSU observations (see Figure 1a). We summarize that mesospheric temperature trends change with time and are significantly influenced by stratospheric ozone. They are therefore analogue to stratospheric temperature trends [Randel et al., 2009; Steinbrecht et al., 2009].
 In Figure 2b we also compare (for run 1) trends at a fixed geometric altitude (70 km) and at a fixed pressure level (0.0487 hPa) which on average is located near 70 km. While year-to-year variations are rather similar, long term trends in the mesosphere are significantly larger at geometric altitudes (compared to pressure altitudes) since it includes atmospheric shrinking [Lübken et al., 2009]. The latter effect depends on the background temperature gradient: in the mesosphere (negative gradient) cooling trends at geometric altitudes are enhanced (relative to constant pressure level), whereas in the thermosphere (positive gradient) the effect is vice versa. This also explains why the difference between trends at geometric versus pressure altitudes is small at 50 km since here the pressure trend at a constant geometric height is only ∼50 m/decade [Lübken and Berger, 2011]. Furthermore, the vertical gradient of background temperatures at stratopause heights is close to zero, hence small geometric height changes do not induce differences in trend derivations.
 We put our trend analysis into a broader perspective by analyzing mesospheric temperature trends on global scales. Motivated by the results shown in previous sections we show in Figure 3 temperature trends from LIMA for summer conditions for two periods, namely 1979–1997 and 1997–2009. Note, that we have obtained the trends in LIMA from a multiple regression fit considering solar cycle effects. For the first period strong cooling of up to ∼3–4 K/decade occurs in the middle mesosphere. Additional cooling peaks of similar magnitude occur in the equatorial and northern stratosphere near 40 km, presumably in response to a strong negative ozone forcing [WMO, 2011]. In the southern winter hemisphere, enhanced cooling is observed in the mesosphere at mid and high latitudes, whereas stratospheric cooling is substantially smaller.
 Temperature trends are generally small in magnitude in the mesopause region in winter and summer which is consistent with observations and other model results [Beig et al., 2003; Akmaev et al., 2006; Schmidt et al., 2006; Garcia et al., 2007]. At polar latitudes in summer, heating is observed around the mesopause which is caused by radiative effects and atmospheric shrinking. Trends are entirely different for the second period 1997–2009. In many regions, for example in the summer mesosphere and at the equatorial stratopause, positive temperature trends dominate. Our analysis suggests that this is to due to stratospheric ozone recovery which over-compensates the enhanced cooling caused by increasing carbon dioxide. As mentioned in the previous section, Figure 3 emphasizes the importance of stratospheric ozone trends for the entire mesosphere and even the lower thermosphere. It also shows that the trend reversal is not restricted to mid-latitudes but occurs on global scales. It will be interesting to validate this result with long-term records of mesospheric temperatures available in the near future.
5. Summary and Conclusions
 Our LIMA model reproduces large temperature trends deduced from satellites measurements, radio wave reflection height detections, and lidar observations. To the best of our knowledge this is first time that models can reproduce such large trends in the mesosphere. We show that mesospheric cooling in summer is not uniform in time but is strong in the period 1979–1997 and small (or even heating) before and after that period. At mid latitudes and in the period 1979–1997 the lower stratosphere cooled by ∼0.5–1 K/decade, whereas further up (∼35–75 km) much larger cooling of up to ∼3–5 K/decade occurs. Mesospheric temperature trends are in general about a factor of 10 larger (and of opposite sign) compared to trends at Earth's surface (global mean of ∼ + 0.2 K/decade). In the period 1961–1978 both the stratosphere and mesosphere cooled significantly less. After 1997 cooling becomes negligible and even changes to heating. The altitude profile of cooling/heating is rather complex. In general terms, trends at geometric heights are larger compared to trends at constant pressure levels, which is explained by atmospheric shrinking. Temperature trends in the mesosphere are mainly forced by long-term changes of CO2 and O3. We find that stratospheric ozone evolution in the past 50 years has a major impact on mesospheric temperature trends. Our model results suggest that the differences of mesospheric temperature trends in the periods 1961–1979, 1979–1997, and 1997–2009 originate from long term ozone changes in the upper stratosphere. Any cooling in the stratosphere leads to a shrinking and a corresponding trend in the meso- and thermosphere. Our results emphasize the importance of considering the entire atmosphere and to specify conditions (geometric/pressure altitude, time period, season, etc.) when presenting observational or model results regarding temperature trends in the mesosphere.
 We appreciate the continuing financial support from the DFG for the SOLEIL project. The European Centre for Medium-Range Weather Forecasts (ECMWF) is gratefully acknowledged for providing ERA-40 and operational analysis data. We thank Philippe Keckhut for providing the OHP lidar data.
 The Editor thanks Jan Lastovicka and an anonymous reviewer for their assistance in evaluating this paper.