Oxygen is a well-mixed gas whose fractional concentration is independent of altitude below approx. 80 km, so the microwave radiation from it contains information primarily on atmospheric temperature. The retrievals of stratospheric temperature profiles from TEMPERA are based on the measurements of two oxygen emission lines centred at 52.54 and 53.06 GHz (see Fig. ). The shape of these lines is governed by a pressure broadening mechanism up to 60 km of altitude; therefore, the measured spectra can provide vertical information. The wings of the emission lines provide information of the radiation coming from low altitudes (higher broadening caused by higher pressure) while the line centres give information of the radiation coming from upper altitudes (smaller broadening and lower pressure). Both emission lines measured by TEMPERA are used at the same time with a bandwidth of 200 MHz around the first line and of 160 MHz around the second. Only measurements at the highest elevation angle (60∘) are used for stratospheric measurements with the digital FFT spectrometer. This limits the integration time with the FFT spectrometer to 15 s in each minute measurement cycle. In order to get a low enough noise level the measurements are integrated for half an hour, which requires 2 h of measurement time, since only a quarter of the measurement time is used for the digital FFT spectrometer . Therefore, the time resolution of the stratospheric temperature profiles from the TEMPERA radiometer is 2 h.

Obtaining temperature profiles from the calibrated brightness temperature spectrum, an example of which is shown in Fig. , requires a solution to the radiative transfer equation. A unique solution does not exist, so some statistical constraints are needed in order to obtain physically meaningful solutions. In our case we use the optimal estimation method (OEM) by means of the radiative transfer model ARTS/QPack . The method is based on Bayes' probability theorem and a detailed description of its application to TEMPERA measurements can be found in .

The ARTS package implements the radiative transfer equation (forward model), simulating the brightness temperature as y=F(x,b)+ϵ, where F denotes the forward model, the vector y corresponds to the measured spectrum (brightness temperature), x is the true temperature profile, b contains some additional forward model parameters and ϵ is the measurement noise.

The solution to the inverse problem is obtained by using the Gauss–Newton iterative method, whose solution can be expressed in a matrix notation as follows: xi+1=xi+Sa-1+KiTSϵ-1Ki-1KiTSϵ-1y-Fxi-Sa-1xi-xa, where the vector x is the true temperature profile, y is the measured spectrum (brightness temperature), xa is the a priori temperature profile, Sa is the a priori covariance matrix and Sϵ is the observation error-covariance matrix. The forward model is denoted by F, and the vector K is the weighting function (K=∂F/∂x).

An important tool used very often in the OEM is the averaging kernel matrix A . This matrix describes the response of the retrieved temperature profile x^ to the true temperature profile x and is defined as A=DyKx=∂x^∂x, where Kx is the weighting function already defined, and Dy=∂F/∂x is the so-called contribution function.

The rows of A are called the averaging kernels (AVKs) and they describe the sensitivity of the retrieval for a certain height level to a perturbation at other levels. The sum of the AVKs is called the measurement response (MR), which describes the contribution of measurements to the retrieved profile at a certain height.

The method needs an a priori temperature profile in order to constrain the solutions to physically meaningful results. As a priori profiles, monthly mean temperature profiles from radiosonde measurements at Payerne from 1994 to 2011 are used in the lower part (ground to 15 km) and mean MLS temperature profiles from a climatology are used in the upper part. As a priori covariance matrix, Sa a function decreasing exponentially with a correlation of 3 km is used, assuming a standard deviation of 2 K. For the observation errors the residuals of the inversion are considered (difference between the integrated spectra and the fit of the spectra). Under regular conditions these errors range between 0.5 and 1.5 K .

In the radiative transfer calculations (F(x,b)) the absorption coefficients of the different species are calculated using different models: for H2O, for O2 and for N2. The density profiles of oxygen (O2) and nitrogen (N2) are incorporated by ARTS assuming standard atmospheric profiles for summer and winter . In the case of tropospheric water vapour, a profile with an exponential decrease is considered. This profile is calculated with the measured surface water vapour density from a weather station and assuming a scale height of 2000 m .

Figure  shows an example of temperature inversion from TEMPERA measurements using the OEM result obtained on 1 October 2015 for the time interval from 22:00 to 00:00 UTC. In Fig. a we can observe that the forward model brightness temperatures (red lines) agree well with the measured brightness temperatures (black lines), except for around the line centre. The larger differences observed in the centre of the emission lines (see Fig. 4b) are mainly due to a different binning used in the centre of the lines and on the wings of the lines . In addition, the Zeeman effect could explain some small differences in the centre of the lines, because it is not incorporated in the forward model . Figure c presents the a priori temperature profile used in the inversion (black dashed line) and the retrieved temperature profile (blue line). Figure d shows the AVKs (black lines), the measurement response (red line) and the height resolution, which is defined as the full width at half maximum (FWHM) of the AVKs (blue line). We can observe that for this inversion the height resolution ranges between 13 and 16 km. The MR shows values larger than 0.8 in the range between 20 and 43 km, meaning that 80 % of the contribution to the retrieved temperature profile comes from the measurements. These values decrease with altitude reaching 0.5 at 47 km for this case. We would like to point out that the altitude range of the stratospheric temperatures from the TEMPERA radiometer used in this study correspond to levels with a high MR (higher than 0.8 at most of the altitudes). Finally, the total, observational (random error due to measurement noise) and smoothing errors are also calculated with this method and are shown in Fig. e.

In order to compare the temperature profiles from the different instruments (RS, MLS satellite, lidar) and also from the WACCM model with those from the TEMPERA radiometer, the profiles are first interpolated to the pressure grid of TEMPERA, and then are convolved with the AVK of this radiometer in order to take into account the different height resolutions. Equation () gives the expression for calculating the convolved temperature profiles: x^r=xa+Axr-xa, where xa is the a priori profile of the radiometer, A is the AVK and xr is the interpolated reference profile.

Stratospheric temperature profiles from TEMPERA have been compared with the ones from RS measurements for the period from January 2014 to September 2016. As indicated in previous sections, radiosondes have been launched twice a day (11:00 and 23:00 UTC) at the aerological station at Payerne since 1954. The TEMPERA profiles closest in time to the RS launches have been selected in order to do this comparison. A total of 1489 pairs of profiles are used in these statistics, which were measured under all weather conditions except for rainy cases. The RS profiles were interpolated to the altitude grid of TEMPERA radiometer, and completed in the upper part with the TEMPERA measurements, since RSs usually do not reach altitudes higher than 30–35 km. Afterwards, the profiles were convolved using the AVKs of TEMPERA.

Figure  shows the temporal evolution of the stratospheric temperature at different altitudes from TEMPERA and RS for the campaign period. The interpolated temperatures from RS have also been plotted (green lines) in order to visualize the smoothing effect on them when they are convolved with the AVKs of TEMPERA. In addition, the a priori temperature used for the TEMPERA inversions is shown. The temperature deviations along this period between TEMPERA and the convolved measurements from RS are shown in the lower panels (black lines). We can observe in general a very good agreement between both instruments for the displayed altitudes with correlation coefficients higher than 0.9. An annual pattern is observed in the stratospheric temperature with higher temperatures in summer than in winter. Again in this plot we can observe that the variability of the temperature is higher during winter than in other seasons, and some interesting events with a strong increase in temperature have been detected (January 2014 and 2015, February 2016). The temperature deviations between TEMPERA and RS are in general small with most of the values below 3 K, although some short periods with larger discrepancies are also found (e.g. February 2015). We can also observe from these plots that the deviations at 27 km altitude are larger and noisier than for the other two altitudes. A remarkable feature observed in the temperature deviation lines at all the profiles is a small step in the summer of 2015. This step is more evident in the two higher altitudes (27 km and 33 km), where the deviations changed from positive to negative. The effect is smaller at the lowest altitude (21.5 km), where it looks to have an opposite behaviour, changing from negative or almost zero deviations to positive deviations after the step occurs. This change of tendency could be due to the fact that an attenuator in the FFT spectrometer was repaired in summer 2015. It seems that after this repair the brightness temperature spectra measured by the FFT were slightly affected and some small differences in the retrieved temperatures are observed.

In order to take into account this instrumental modification and characterize possible changes in the accuracy and precision of the TEMPERA radiometer, the statistical analysis between TEMPERA and the other measurements (RS, MLS, lidar and WACCM) is carried out over two different measurement periods. From here on, period 1 will refer to the period before the attenuator in the FFT spectrometer was changed (January 2014–June 2015) and period 2 will refer to the period after this repair (July 2015–September 2016). In addition, the measurements have been split by season into winter and summer, with summer referring to April–September and winter October–March, inclusive. It is useful to make this distinction because there is a greater level of atmospheric variability in winter, which could produce larger deviations between the different measurements than those due to fundamental differences in the measurement techniques.

Figure  shows the mean and the standard deviations between TEMPERA and RS which have been calculated for all the measurements in each period (black lines) and also for winter and summer seasons of the different periods (blue and red lines, respectively). From this plot we can observe that there is a clear change in the mean bias between TEMPERA and RS for periods 1 and 2. The mean bias for period 1 ranged between -0.3 K at 20 km and 2.6 K at 28.5 km, showing in general a positive deviation at most of the altitudes. The mean bias in period 2 showed negative values for most of the altitudes, with values ranging between 0.9 K (20 km) and -2.3 K (32 km). There is also a clear difference in the standard deviation observed for both periods. Period 1 showed much larger standard deviations than period 2, with values that range between 1.9 K (21 km) and 3.5 K (28.5 km). The standard deviations for period 2 were smaller and much more constant in height, with values ranging between 1.3 K (34 km) and 1.7 K (26.5 km). These results show a change in the sign of the bias between TEMPERA and RS when the attenuator of the FFT spectrometer was repaired in June 2015, although in terms of absolute values the differences were not very significant. However, the standard deviations for period 2 were smaller than for period 1, indicating a higher precision of the TEMPERA radiometer after the repair with respect to the reference RS measurements. If we look at the seasonal behaviour of the bias for both periods we can observe that there are small differences between winter and summer. In the case of period 1, the maximum difference between winter and summer is 0.9 K and it is observed in the lower part, while for period 2 the differences are lower than 0.7 K. Much larger differences are found for the standard deviation between the two seasons for period 1 (dashed lines). While the standard deviation ranges between 0.9 and 1.8 K in summer, the values range between 2 and 4.5 K in winter, reaching the maximum standard deviation at 28.5 km. Although during period 2 the standard deviations in winter were also larger than in summer, the differences were not so remarkable (smaller than 0.5 K). These results show that there was a larger variability in the temperature deviations between TEMPERA and RS during the winters of period 1. This is something that could be expected from the temperature evolution in Fig. , which showed larger discrepancies, especially during winter 2015.

The stratospheric temperature profiles from TEMPERA have also been compared with those obtained from the MLS instrument on board the Aura satellite. As indicated in Sect. 2, the temperature profiles used for MLS correspond to the version 4 retrievals. In order to select the temperature profiles from MLS to be used in the comparison we chose those that were collocated with the measurement site, which by our criteria meant that the MLS measurements were within ±1∘ (±110 km) of the measuring site in latitude and ±5∘ (±460 km) in longitude. The data were also restricted to cases with near time coincidence between TEMPERA and MLS, which means that the MLS profiles were taken during the period of the spectral integration for the TEMPERA measurements. A total of 367 profiles were obtained under these criteria and for all weather conditions excluding rainy cases. The MLS temperature profiles were interpolated to the pressure grid of TEMPERA, and these profiles were convolved using the AVKs of TEMPERA as described in Sect. 3.

Figure  shows the evolution of the stratospheric temperatures and the deviations between TEMPERA and MLS at three different altitude levels. Similar patterns to those observed in Fig.  are found in this plot (although with fewer data), observing an annual cycle with higher temperatures in summer than in winter and with a larger variability during winter. We can observe from these plots a very good agreement between both instruments despite the very different type of observations that we are comparing (ground-based against satellite measurements). This good agreement is also observed when strong variations in temperature occur in a short time interval, as can be seen in the winter of 2016, and is confirmed by the high correlation coefficient (larger than 0.92) found at the different altitudes. The temperature deviations (TEMPERA-MLS) observed are in general small, although we observe some larger discrepancies for some measurements (reaching deviations of 10 K) mainly during wintertime. Differences between TEMPERA and MLS retrievals can arise from several factors, including differences due to spatio-temporal inhomogeneities arising from synoptic variability, which can be more important during winter, differences in vertical resolution, interpolation techniques, or measurements errors from both instruments.

The mean and the standard deviations of the difference between the TEMPERA and MLS measurements for both periods described in the previous section and also for the different seasons have been plotted in Fig. . From this comparison, a clear change in the mean bias is again observed between both periods in the lower part of the stratosphere (from 20 to 37 km). In that range, the mean bias in period 1 was 2.5±1.3 K, reaching a maximum deviation of 4.1 K at 28.5 km, while for period 2 the mean bias was -0.4 ± 0.9 K with a maximum negative deviation of -1.4 K at 30 km. In the upper part (between 38 and 50 km) the differences in the biases were not so significant, with a mean value of 1.7±0.5 K for period 1 and 2.3±0.7 K for period 2. The standard deviations again show higher values for period 1 than for period 2, although the differences were smaller than in the comparison with RS. The mean standard deviations in the range between 20 and 50 km were 2.4±0.6 K for period 1 and 2.0±0.4 K for period 2.

This comparison also shows a seasonal behaviour for the mean and the standard deviation of the temperature differences between TEMPERA and MLS for both periods. For period 1 there was a positive bias for both seasons in almost the whole column, with larger values in winter than in summer. The mean bias in the lower part (20–35 km) was 3.3±1.2 K in winter and 1.9±1.4 K in summer. The discrepancies were even larger in the upper part (35–50 km), showing a much lower bias in summer (0.4±0.4 K) than in winter (2.8±0.7 K). During period 2 the differences between the biases in winter and summer were quite constant in altitude, and they were always lower than 1.6 K. The standard deviations of the temperature differences showed higher values in winter than in summer for both periods. For period 1 the mean standard deviation for the whole range (20–50 km) was 2.5±0.5 K in winter reaching a maximum value (3.1 K) at 28.5 km, while for period 2 the mean standard deviation was 2.1±0.5 K with a maximum value of 2.6 K at 32 km. The standard deviations in summer for both periods were very similar, with mean values for the whole altitude range (20–50 km) of 1.8±0.6 K in period 1 and 1.7±0.5 K in period 2. These results again show the lower temperature discrepancies observed between TEMPERA and the MLS satellite during summertime. The biases found in this comparison are similar to those reported by for a comparison between MLS version 2.2 retrievals and different analyses and observations (GEOS-5, ECMWF, radiosondes, AIRS/AMSU, etc.), where the biases ranged between -2.5 and 1 K.

The MLS measurements have also been compared with the ones from RS in the range where they were comparable (lower stratosphere). Only collocated MLS profiles (according to the criteria as used above) and measured within 4 h of the RS launch were selected for the comparison. A total of 323 pairs of profiles fulfilled these criteria and were used for these statistics. The RS profiles were interpolated to the pressure grid of MLS in order to perform the direct comparison of their profiles. Figure  shows the mean and the standard deviation for this comparison. It can be seen that the mean bias ranges from -1.7 K at 19 km to +1.4 at 15 km. The standard deviation of the temperature differences between MLS and RS was quite constant with altitude, with a mean value of 1.7±0.2 K and a maximum value of 2.2 K reached at 31 km. Note that the bias and the standard deviation observed between MLS and RS are very similar to the values observed in the comparison between TEMPERA and RS in period 2 (biases ranging between -2.3 and 0.9 K and the standard deviations between 1.3 and 1.7 K). The slight underestimation of the temperature in most of the altitudes found for MLS versus RS in this study agrees with the results obtained by between MLS and different sources.

The TEMPERA radiometer has also been compared with an active remote sensing instrument, a Rayleigh lidar. This lidar is operated at Hohenpeißenberg station (Germany), around 400 km northwest of Payerne. Despite the distance between the two instruments, we wanted to evaluate the agreement in the stratospheric temperature between these very different techniques. A total of 192 profiles were compared for all weather conditions (except for rainy cases) for the period from January 2014 to July 2016. As in the previous comparisons, the lidar profiles were interpolated to the pressure grid of the TEMPERA radiometer and then these profiles were convolved using the AVK of TEMPERA. Since the Rayleigh lidar only provides temperature information above approximately 28 km (below this the measurements would be affected by stratospheric aerosol), the gap below this altitude was filled with coincident measurements from TEMPERA in order to avoid modifying the AVK used by TEMPERA for the convolution.

Figure  shows the stratospheric temperature evolution from TEMPERA and the lidar at three different altitude levels. For the lowest altitudes shown here (29.5 km a.s.l.), the temperature from RS has also been plotted, since at this altitude there were measurements from the three instruments. We can observe from this figure that there is good agreement between TEMPERA and the lidar in the upper stratosphere, with correlation coefficients larger than 0.94 for the two highest altitudes. This coefficient is lower (0.9) for the lowest altitude (29.5 km a.s.l.). The agreement between the lidar and the RS in this lowest altitude is better than for TEMPERA, with a correlation coefficient of 0.96. The evolution of the temperature deviations between TEMPERA and lidar at the three altitudes shows small discrepancies for both techniques over the measurement period, with values in most measurements below 5 K. The biggest differences were found at the lowest altitude (29.5 km a.s.l.), where a clear change of bias was observed after summer 2015.

Figure  shows the mean bias and the standard deviation for all the measurements in periods 1 and 2 in addition to seasonal profiles. Mean bias profiles show again a clear change in the tendency of the biases of both periods, being more evident in the lower stratosphere (below 35 km). In this lowest altitude range the mean biases were 2.7±1.3 K for period 1 and -1.2 ± 0.4 K for period 2. Above 35 km the differences between the biases were smaller, with a larger bias for period 2 (2.3 ± 0.9 K versus 1.3 ± 0.4 K in period 1). Similar behaviour to the other comparisons was observed for the standard deviation, with larger values during period 1 than during period 2. The mean values for the whole altitude range were 2.9 ± 0.3 K for period 1 and 2.5 ± 0.2 K for period 2. Seasonal behaviour is observed in the bias and standard deviation for both periods. The seasonal biases showed a vertical oscillation with different tendencies for both periods in the lower and upper part of the stratosphere. For the lower part (28–35 km) the mean biases for period 1 (period 2) were 3.2 ± 1.1 K (-0.7 ± 0.4 K) in winter and 1.9 ± 1.5 K (-2.1 ± 0.3 K) in summer. In the upper part (35–50 km), a general positive bias was observed between TEMPERA and the lidar, where the mean biases for period 1 (period 2) were 2.2 ± 0.6 K (2.9 ± 1.1 K) in winter and -0.3 ± 0.3 K (1.1 ± 0.9 K) in summer. The standard deviations showed larger values in winter for both periods than in summer. The highest standard deviations were again observed in the winter of period 1. The mean standard deviations in the whole column for period 1 (period 2) were 3.1 ± 0.4 K (2.6 ± 0.3 K) in winter and 2.0 ± 0.3 K (1.7 ± 0.4 K) in summer.

A first validation of the stratospheric temperature from SD-WACCM (Whole Atmosphere Community Climate Model with Specified Dynamics) has also been carried out in this study. SD-WACCM is the whole-atmosphere component of CESM (Community Earth System Model) . CESM is a coupled climate model, which means that it consists of separate models for different parts of the climate system, which interact via the coupler module. There are models for ocean, atmosphere, land, sea ice, land ice and rivers. CESM allows us to combine the above models into a component set for the simulation.

The specified dynamics (SD) used in these simulations mean that the model is nudged by meteorological analysis fields by 10 % at every internal time step up to an altitude of 50 km. This means that 90 % of the model and 10 % of the nudging data are taken. The fields that are nudged are temperature, horizontal winds, surface wind stress, surface pressure and heat fluxes from the surface. The nudging data are from the Goddard Earth Observing System version 5.0.1 (GEOS-5) Data Assimilation and are provided every 6 h; in between the data are interpolated.

The altitude range for SD-WACCM is from ground to 140 km a.s.l. The altitude resolution ranges from 0.5 to 4 km (with lower resolution at higher levels) and with a total of 88 layers in the whole atmosphere. The grid resolution is 1.9∘ latitude by 2.5∘ longitude.

The stratospheric temperatures from SD-WACCM have been compared with the almost continuous stratospheric temperature profiles measured by the TEMPERA radiometer for the period from January 2014 to April 2016. A total of 6868 profiles were selected for comparison under all weather conditions except rainy conditions. Figure  shows the stratospheric temperature evolution along this period for TEMPERA and WACCM. Good agreement is observed in general between both temperature sets. We can observe that the temperature from the model follows the same pattern as TEMPERA, with the same annual cycle and detecting the same structures in time and also in altitude. Note the good agreement observed during winters, where strong increases in temperatures are produced for short periods and can be observed in both data sets. The differences between TEMPERA and WACCM are more evident above 50 km a.s.l., but above this altitude the measurement response for TEMPERA is low (lower than 0.6) since the weight of the measurements is small and so it should not be considered in the comparison.

The temperature profiles from SD-WACCM have been interpolated and convolved as described in Sect. 3 to allow comparison with those from TEMPERA. Figure  shows the evolution of the temperature at three altitude levels and the differences between both (TEMPERA–WACCM). The good agreement observed from these plots is particularly shown by the low temperature deviation values (lower than 5 K most of the time) and the large correlation coefficient (larger than 0.92). Despite this good agreement, we also find some periods with larger discrepancies between the measurements and the model, especially during winter, most markedly in winter 2015. Note that the statistics shown in this section are particularly robust, since almost 7000 pairs of temperature profiles are compared.

We have also calculated the bias and the standard deviation for this comparison between the TEMPERA radiometer and the WACCM model (Fig. ). It is again very obvious from these statistics that there is a strong change in the biases between periods 1 and 2, with a very different tendency in the lower stratosphere than in the upper. The mean biases for the lower part (20–35 km) were 1.4 ± 1.1 K for period 1 and -1.0 ± 1.3 K for period 2, whilst the mean biases for the upper stratosphere (35–50 km) were 1.0 ± 0.7 K for period 1 and 1.7 ± 1.1 K for period 2. The seasonal behaviour observed in the biases was almost negligible for both periods.

From the standard deviation figure (Fig. , right) we can observe that much larger values are obtained for period 1, with a mean value in the whole column of 2.9 ± 0.6 K and a maximum standard deviation of 3.8 K at 29 km. These large standard deviations observed during period 1 are strongly influenced by the large values observed during winter (blue dashed line), when a maximum mean standard deviation of 4.7 K at 29 km was reached. The rest of the standard deviation profiles show very similar values between them, increasing slightly in the lower part (up to 30 km), and keeping close to constant values above this altitude. The smallest values are found in summer with a mean bias in the whole column of 1.8 ± 0.4 K for period 1 and 1.5 ± 0.3 K for period 2.

In order to summarize the intercomparison carried out between TEMPERA and the different measurement techniques and model we have plotted the biases and the standard deviations for all the comparisons together (Fig. ). Because we are interested in evaluating the accuracy and precision of TEMPERA radiometer against other measurements in this study we have only displayed in Fig.  the biases and the standard deviations obtained for the summer season, since it is less affected by atmospheric variability than the winter measurements.

The mean bias plot (Fig. , left) shows a clear change of biases between TEMPERA and all the other measurements between the first (dashed lines) and the second (solid lines) period (before and after the repair of the FFT spectrometer's attenuator). We can observe that there is a persistent vertical oscillation for all the profiles in both periods, causing a different behaviour of the biases in the lower and upper stratosphere. This oscillation has an amplitude of around 2 K and a periodicity of roughly 20 km. Similar behaviour was observed for the MLS measurements when they were compared with different sources . The change of tendency in the bias between both periods is more evident in the lower stratosphere (below 35 km), where we can observe that for almost all the altitude levels the biases change from positive to negative in all the comparisons. Another remarkable point is the consistency between the different biases in each period, showing small differences between them (below 1 K) for most of the altitudes, especially for period 2. For period 1, the maximum deviation was found at 28.5 km, with a maximum value of 3.6 K for the comparison with the MLS satellite. Below this altitude, an almost identical bias between the comparison with RS and WACCM model is found. In the upper stratosphere the biases were between -0.6 K and 1.5 K, and the smallest bias was found in the lidar comparison. For period 2 the values of the different biases ranged between -2.4 K (at 32 km) and a maximum positive bias of 2.9 K (at 43 km), the latter being found with the comparison with WACCM. As already mentioned, the differences between the different comparisons for period 2 were smaller than for period 1, showing consistency between the RS, MLS, lidar measurements and also WACCM simulations.

Figure  (right) shows the standard deviations of the differences between TEMPERA and the different measurements and model. In general, there was a reduction in the standard deviations for all the comparisons in period 2, indicating that the precision of TEMPERA improved after the attenuator was repaired. Next, we focus our discussion on period 2, when we consider that TEMPERA was operating optimally. For this period, we observe that standard deviations were always lower than 2.2 K, with this maximum value being reached at 45 km in the comparison with the lidar. The lowest standard deviation in the lower stratosphere (<35 km) was found for the comparison with RS, with the mean value in this range being 1.3 ± 0.1 K. The highest standard deviations in the lower stratosphere were found in the comparison with MLS (1.3 ± 0.1 K). These results evidence a better precision from the TEMPERA radiometer when it is compared with the in situ reference technique of RS in the lower stratosphere. This result makes sense, because RS is the technique with the lowest errors (0.2 K for temperature) and the comparison between TEMPERA and RS is the one that should present lower atmospheric variability between both measurements since the RS are launched from the same location where TEMPERA is operated.

In the middle stratosphere (between 30 and 40 km) the lowest standard deviations were found for the comparison with lidar with a mean value of 1.4 ± 0.2 K. However, above this altitude (40 km) the standard deviation with respect to lidar is the largest (2.2 ± 0.3 K). In this upper part the lowest standard deviations were found for the comparison with MLS and WACCM. A common pattern observed in all the comparisons is that the standard deviations decrease slightly with altitude in the last kilometres of the stratosphere. This behaviour is due to a greater weight of the a priori temperature profile used in the TEMPERA retrievals and also to the convolved profiles at these altitudes since the measurement response presents lower values for high altitudes (around 0.6 at 48 km).

Table  presents the different biases and standard deviations obtained in the lower and upper stratosphere for all the comparisons during summertime in period 2. These values are the most representative way of characterizing the accuracy and precision of the TEMPERA radiometer since they correspond to the period when TEMPERA was running with the repaired attenuator (period 2) and also when the measurements were least affected by atmospheric variability (summertime).

We end by highlighting the consistency found between the standard deviations of the different comparisons and the observation errors of the TEMPERA retrievals. As mentioned in Sect. 3.1, the OEM also estimates the observation, smoothing and total errors of the TEMPERA inversions (Fig. e). The standard deviations found in the different comparisons are partly related to the observation error of TEMPERA but also to the errors associated with the other measurements and the atmospheric mismatches. If we assume that the random errors in TEMPERA (D1), in the other instruments (D2) and in the atmospheric mismatching (D3) are independent, then the observed standard deviation (DT) should be given by DT2=DT12+DT22+DT32. For example, if we consider the observation error of TEMPERA provided by OEM (0.8 K), the errors for the lidar (0.7 K) and the mean observed standard deviation for the comparison between TEMPERA and the lidar (1.1 K), we would conclude that the errors associated with atmospheric mismatches should be 0.3 K, which is a realistic value and shows the consistency between the observed standard deviations and the observation errors of the different measurements.