The middle atmosphere (MA: stratosphere and mesosphere, 12 to 90 km altitude) is a transition region between the troposphere, which is heavily influenced by anthropogenic activity, and the upper atmosphere (thermosphere and ionosphere), at the edge of the space and strongly impacted by solar activity. The MA is a unique environment for fundamental research as it is subject to the conjugated influence of climate change due to anthropogenic activities and natural solar-driven variability.

The increase in GHGs (greenhouse gases) induces global warming at the surface and of the troposphere at large but also causes global cooling in the MA (e.g. ). The cooling occurs as thermal infrared radiation emitted by GHGs escapes directly into space due to the low optical thickness of the atmosphere above.

The mesosphere is a region where temperature and wind observations are sparse or not well resolved. Recent studies have demonstrated the role of MA dynamics in both tropospheric weather and climate (). In addition, weather and climate-chemistry models are currently moving towards a more comprehensive representation of the MA (). Atmospheric observations in this region can also be used as a benchmark for climate change studies due to the MA having a high sensitivity to the increase in GHGs and to the external solar forcing. Furthermore, technical and scientific questions relating to applications, such as the re-entry of space and sub-orbital vehicles, the impact of meteors on the atmosphere, and infrasound propagation modelling in the atmosphere, require an accurate understanding of the mesospheric mean state and its variability on different scales.

There are insufficient observations of the temperature in the upper portions, given that the upper limit of radiosondes is about 30 km. The GNSS (Global Navigation Satellite System) radio occultation technique provides accurate measurements of temperature up to about 35 km with high vertical resolution. Nadir-viewing satellite sensors making observations in the thermal infrared (e.g. SSU is Stratospheric Sounder Unit) and at microwave wavelengths (e.g. AMSU is Advanced Microwave Sounding Unit) extend measurements of brightness temperature into the upper stratosphere (around 45 km) but often have very broad vertical weighting functions (≈10 km). These coarsely resolved operational satellites provide the only temperature observations assimilated into NWP (numerical weather prediction) models. Limb viewing satellite sounders, such as MLS (Microwave Limb Sounder on the Aura satellite) and SABER (Sounding of the Atmosphere using Broadband Emission Radiometry on the TIMED mission), provide temperature profiles up to the upper mesosphere with good vertical resolution. However these datasets are not assimilated into the NWP models because MLS and SABER are not operational meteorological satellites.

The scattering of sunlight (near the UV and visible wavelengths) by the Earth's atmosphere above the top of the stratospheric layer (30–35 km) is solely due to Rayleigh scattering by atmospheric molecules. The elastic scattering intensity is directly proportional to the atmospheric density. It is thus possible to retrieve an absolute temperature profile using the hydrostatic equation and the perfect gas law. The temperature is initialised at the top of the measurement profile from a climatological model. This inversion technique has been applied to Rayleigh lidar observations for more than 40 years . Approximately 10 Rayleigh lidars are operated routinely in the NDACC (Network for the Detection of Atmospheric Composition Changes). These ground stations are limited in number (approximately 10 distributed globally) but routinely produce local observations of the atmospheric temperature profile between 30 and 80–90 km with good accuracy and vertical resolution . They have been used for trend analysis () and/or validation of satellite data and identification of possible biases and trends due to orbital changes and instrument ageing ().

The observation from space of Rayleigh scattering at the atmospheric limb during the daytime may be also used to derive density and temperature profiles in the upper stratosphere and mesosphere (US-M). This technique has been applied by , who derived temperature profiles from 40 to 92 km for the period 1982–1986 using Solar Mesosphere Explorer bright limb observations at 304, 313 and 442 nm. determined temperature profiles from 65 to 90 km during the period of March 1992–January 1994 by analysing WINDII/UARS data at 553 nm. More recently retrieved temperature profiles using OSIRIS/Odin bright limb observations at 318.5 and 347.5 nm in the altitude range 45–85 km. In the frame of the ESA-funded MesosphEO project, a new data set of temperature profiles in the altitude range 35–85 km was created from the analysis of GOMOS/ENVISAT bright limb observations in the spectral band 420–480 nm. A data set of more than 309 000 profiles from June 2002 to April 2012 is now available for climatological and dynamical studies.

The paper is organised as follows: in Sect. , the principle of the method is explained and the data processing is described. Section  is dedicated to the validation of the GOMOS temperature profiles using Rayleigh lidar observations from OHP. Section  presents the first scientific results with a focus on the evolution of equatorial temperature profiles. Finally, a summary is given in Sect. .

A validation exercise has been made using the Rayleigh lidar located at Observatoire de Haute Provence (OHP; 43.9∘ N, 5.7∘ E). This lidar has been part of the Network for Detection of Atmospheric Composition Change (NDACC; http://www.ndaccdemo.org; last access: 30 January 2019) since its creation in 1991 and has participated in several satellite validation experiments for instruments on board the UARS satellite (; ; ; ; ), and more recently for MLS-Aura and SABER-TIMED . For the present study, 554 collocated GOMOS profiles were selected in a geographic region around OHP (40∘ N, 9∘ E); (48∘ N, 21∘ E). The nightly mean lidar profiles are smoothed down to a 3 km vertical resolution for comparison with the GOMOS profiles. A maximum of 12 h difference between GOMOS and lidar measurements was accepted for the time coincidence. When several GOMOS profiles reached the coincidence criteria, as shown in Fig. , the median profile was used for statistical comparison.

The statistical median difference between the OHP lidar and GOMOS temperatures (Fig. ) is close to zero below 46 km. There is a negative relative bias between 46 and 73 km with a maximum difference of -5 K between 55 and 60 km and a positive relative bias above 73 km with a maximum difference of +7 K at 85 km. The dispersion of the differences remains relatively constant with altitude and has an approximate value of ±5 K over the entire altitude range. The positive relative bias in the upper part of the profile may be at least partially due to a warm bias in OHP temperature above 75 km as reported by using a comparison with SABER-TIMED. Below 75 km, the alternation between positive and negative relative biases with altitude may indicate a contribution of the atmospheric thermal tides, as the temperature measurements are not obtained simultaneously. The tidal effect has been previously observed in comparisons between measurements obtained at different solar times . GOMOS measurements above OHP are performed during the daytime at around 11:00 solar time, while lidar operations are conducted during the first part of the night for several hours, with an estimated average mid-sequence time around 21:00 solar time.

To evaluate the potential effect of the thermal tides, tidal characteristics above the lidar site have been extracted from the Global Scale Wave Model (GSWM; ) and used to provide an estimate of the tidal contribution to the observed temperatures differences. The model has been optimised to provide the migrating thermally forced tides on a global scale throughout the atmosphere on a monthly mean basis. The amplitude and phase of the diurnal and the semi-diurnal components can be calculated from the outputs of the GSWM-00 tidal model (http://www.hao.ucar.edu/modeling/gswm/gswm.html, last access: 30 January 2019), which is an extension of the GSWM-98 . This model has previously been used in comparisons with observations. While the vertical shape of the observed lidar–GOMOS relative temperature bias is well reproduced using this model, the amplitude is often smaller than those reported by . In this study, the amplitude (Fig. , left panel) and the phase (Fig. , middle panel) of the diurnal component of the tides have been extracted from the GSWM for 45∘ N during the month of August). In the summer, the middle atmospheric component of the diurnal tide is dominant and the expected difference between the lidar and GOMOS temperatures is represented in Fig. , right panel. In the middle mesosphere, we observe a +3 K difference, while in the vicinity of the mesopause, we note a reverse effect of -3 K. The expected tidal contribution does not fully reproduce the observed temperature difference between the OHP lidar and GOMOS but, considering uncertainties associated with the amplitude and phase of the tidal effect, and the fact that non-migrating tides were not taken into account, it appears that at least some part of the observed differences may be explained by local time differences. Further work would be needed to confirm this hypothesis. The comparison of OHP lidar temperature profiles with MLS-Aura and SABER-TIMED indicated systematic differences and suggested non-linear distortions in the satellite altitude retrievals . In order to better understand these differences, we plan to compare our new GOMOS temperature data set with MLS and SABER in a future work.

The monthly climatology of GOMOS temperature has been built by averaging the data into 10∘ bins from 80∘ S to 80∘ N. For each monthly latitude bin, the average value is only considered if at least 15 valid profiles are kept. The results are presented in Fig. . At the stratopause the warmest temperatures are observed at the North Pole from April to September and at the South Pole from November to January. The equatorial stratopause temperature shows a relative maximum throughout the year. As expected, the coldest temperatures are observed in the upper mesosphere at high latitudes during the summer months, from May to August in the Northern Hemisphere and from November to February in the Southern Hemisphere. The deep temperature minimum in the summer mesopause is due to adiabatic cooling of ascending air.

In order to better visualise the main features of the GOMOS climatology, the temperature difference between the climatology and an external model is represented in Fig. . The external model used for processing the GOMOS data relies on the retrieval of different atmospheric species as described by . For each occultation the external atmospheric profile is built by using ECMWF analysis up to 1 hPa (about 48 km), with a smooth transition to NRLMSISE-00 climatological model above 1 hPa, preserving the hydrostatic equilibrium at all altitudes.

Figure  shows the average temperature difference between GOMOS and the external model, averaged over all latitudes and months. Below 48 km, where the external model is based on ECMWF analysis, the agreement is very good and is almost always better than 5 K and on average better than 2 K. The only exception is at 35 km in the equatorial region where GOMOS presents a cold bias compared to the model. In particular, from January to May, a cold bias of about -10 K is seen. We attribute this cold bias to a contamination of the Rayleigh scattering profile by Mie scattering due to the presence of aerosols in the lower stratosphere. These aerosols may reach altitudes of 35 km at the equator . Above 48 km the external model is driven by NRLMSISE-00 and between 48 and 80 km the GOMOS temperature is warmer than the external model. Near 60 km the temperature difference is on average +10 K. Above 80 km GOMOS is colder than the external model.

An interesting characteristic of the measurement which arises from the geometry of observation is that for a given line of sight, parallel to the Earth's polar axis, the tangent point in the atmosphere is exactly at the Equator. The occultation of the Polar Star, at approximately 89.5∘ declination, provides a year-round tangent reference point between 0.8∘ S and 0.8∘ N in bright limb conditions. More than 22 000 occultations of the Polar Star have been performed during the 10 years of the ENVISAT record, providing a quasi-continuous survey of the temperature evolution at the Equator (Fig. , left panel). The temperature at the stratopause exhibits a semi-annual variation, while in the mesosphere we observe the descent of cold layers from 80 to 70 km over the course of 1 month. Several intense cold layers occurred in April–May 2007 and the vertical profile for the first week of May (Fig. , right panel) shows that this cold layer corresponds to a so-called mesospheric inversion layer (MIL) in the vertical temperature profiles.

MILs have been observed by rocketsondes and Rayleigh lidars at midlatitudes (), high latitudes and low latitudes . Satellite observations showed the global extent of MILs (). Several explanations have been proposed to explain the formation of MILs, including gravity wave breaking (), planetary wave structure and thermal tides . Explanations of the long duration and the global longitudinal extent of the observed equatorial MILs are beyond the scope of this paper and will be the topic of a future publication.

Polar Star profiles have been used to build a seasonal climatology of equatorial temperatures Fig. . In the upper stratosphere, the dominant feature is the semi-annual temperature oscillation, which has maxima during the equinoxes (February to April and September–October) and minima during the solstices (June–July and December). The altitude of the stratopause, taken at the altitude with warmest temperature, varies between 47 and 54 km during the year with a primary maximum in December–January and a secondary maximum in July. In the mesosphere, the temperature evolution is dominated by the annual oscillation, which has a maximum in December–January, corresponding to the period with an elevated stratopause, and a long minimum from April to October.

A database of more than 309 000 temperature profiles from 35 to 85 km, covering the period June 2002 to April 2012, has been created within the framework of the ESA-funded MesosphEO project using the daytime Rayleigh scattering at limb observed by GOMOS.

Comparisons of the GOMOS temperature profiles with night-time Rayleigh lidar temperature profiles measured at OHP show some differences, which possess a vertical structure that may be partially explained by the contribution of the thermal diurnal tides. The GOMOS data set was used to build a temperature climatology as a function of latitude and month. Subsequent comparison with the GOMOS external model has yielded an agreement, which is better than 2 K in the upper stratosphere (below 48 km (1 hPa) where the model is driven by ECMWF), and between 5 and 10 K in the mesosphere (from 50 to 80 km where the model follows NRLMSISE-00 climatology). The evolution of the temperature at the Equator shows the occurrence of temperature MILs with global longitudinal extension, descending in the period of approximately 1 month from 80 to 70 km. The equatorial climatology also shows a semi-annual temperature oscillation in the upper stratosphere, a stratopause altitude varying between 47 and 54 km, and an annual temperature oscillation in the mesosphere.

The technique outlined in this paper to derive temperature profiles from Rayleigh scattering at the limb can be applied to any other limb-scatter sounder observing in the spectral range 350–500 nm, where the Rayleigh scattering is efficient and the absorption by ozone and other stratospheric constituents are not overly important. The technique is also a good candidate for application to future missions involving small satellite constellations due to the simplicity of the principle.