In order to put the improvements discussed later into the context of the pre-existing retrieval scheme, we recapitulate the main features of the MIPAS temperature retrieval scheme here. MIPAS spectra are analyzed with a constrained nonlinear least-squares fit. The updated guess of the state vector xi+1 at iteration i+1 is calculated from the previous estimate xi as follows: 1xi+1=xi+KTSy,noise-1K+R-1KTSy,noise-1y-F(xi)-Rxi-xa.

Here K is the Jacobian containing the partial derivatives ∂ym∂xn, superscript “T” indicates transposed matrices, Sy,noise is the covariance matrix representing measurement noise, R is a regularization matrix, y is the vector of measurements under consideration, F(xi) is the vector of the respective simulated measurements based on the Karlsruhe Optimized and Precise Radiative Transfer Algorithm (KOPRA, ), and xa is the vector of prior information on x. The vertical grid for the retrieval of the temperature profile is 0, 4[1]50, 52[2]70, 72.5[2.5]80, 85[5]110, 120 km (i.e., lower altitude [altitude step] upper altitude). MIPAS measurements are analyzed limb profile by limb profile in a global-fit mode in a sense that all fitting residuals related to an entire limb scan are minimized simultaneously rather than in sequence . Contrary to the original global-fit approach, which was an un-regularized maximum likelihood retrieval, we do use regularization (Sect. ). Adequate a priori information above the uppermost MIPAS tangent altitude proved to be of particular importance (Sect. ). Also contrary to the original global-fit method, our retrieval scheme supports consideration of horizontal variability along the line-of-sight direction (Sect. ), where the respective element of x associated with a certain altitude is a scaling factor for the horizontal temperature distribution. Temperature is fitted jointly with a correction of the tangent altitude of the line of sight in order to minimize mutual error propagation. During each iteration, a hydrostatic atmosphere is constructed using the current guess of the temperature profile and pointing information. For this purpose, a reference point from the a priori temperature profile is used for which geometrical altitude, pressure, and temperature are available see Sect.  andfor further details. The temperature and tangent altitude fit uses spectral lines of CO2 because excellent prior knowledge on the vertical distribution of this gas is available and because no rapid changes in its mixing ratios are expected. The retrieval relies on specific parts of the spectra, called “microwindows”, which contain maximum information on the target quantities with minimal contributions from gases of unknown abundance (see Sect. ). This means that y contains only a subset of the available spectral measurements. However, CO2 lines are not perfectly isolated but are interfered with by a background continuum and some signal of mainly H2O and O3. To avoid propagation of uncertainties of the a priori uncertainties of these gases and the background continuum, these parameters are jointly fitted with the temperature and tangent altitude information, i.e., they are part of the x vector (Sect.  and , respectively). In addition, an additive offset calibration correction is retrieved, which is frequency-independent for each microwindow (Sect. ). An accurate retrieval depends crucially on the choice of reliable spectroscopic data (Sect. ). Consideration of non-local thermodynamic equilibrium emission improves the retrieval at higher altitudes (Sect. ). Adequately chosen numerical accuracy parameters are important for a sound trade-off between the accuracy of the results and computational efficiency (Sect. ).

Previous MIPAS temperature and tangent altitude retrievals were described in for FR measurements and in for RR nominal-mode version 4 measurements. The RR upper troposphere–lower stratosphere measurements mode version 4 retrievals were documented by . RR version 5 nominal-mode retrievals were presented by . Version 3 temperatures were validated by , while version 5 temperatures were validated by .

Prior to the retrieval of atmospheric state variables, a frequency shift scale is determined from the spectra. In principle, the level-1b data are already frequency-calibrated, but frequency calibration and instrument line shape modeling are intertwined. For our retrieval we need an adjustment of the frequencies that also accounts for any frequency shift implied by the modeling of the instrument line shape.

A technical change with respect to the frequency calibration has been implemented in the level-1b processing. Instead of one spectral calibration per four scans, spectral calibration in version 8 is performed once per day, relying on measurements of one full orbit. The mean spectral shift scale is then applied to all measurements of the respective day. The MIPAS spectral accuracy of ESA's frequency calibration is estimated to 0.00065 cm-1 at 2410 cm-1 . The described modification of the frequency calibration scheme leads to very small differences in the retrieved atmospheric state variables and is of minor relevance to the IMK/IAA MIPAS processing because a spectral shift correction is performed as the first step of the retrieval chain anyway.

The calculation of the spectral shift within the IMK-IAA processing is made by minimizing the residual between simulated and measured spectra using Eq. () and then fitting a linear regression function to the shift values, which are calculated for the single microwindows. Differences between calculated shift values and the values represented by the fitted line range from -0.00065±0.00029 cm-1 to 0.00032±0.00032 cm-1 with a root of the mean square value over all frequencies of 0.00039 cm-1. The microwindows used for the frequency shift retrieval are shown in Table . Line selection criteria were sufficient line strength, good separation of the target lines, and a good coverage of the MIPAS A, AB, B, and C bands. The MIPAS D band was not used because sufficiently strong D-band transition would require consideration of non-local thermodynamic equilibrium in the respective radiative transfer calculations, which was considered too costly for this purpose.

For the frequency scale correction, we use spectra at a tangent altitude of 38 km, where the lines are narrow enough to allow for a good spectral calibration and where the signal is still strong enough to avoid large random error in the spectral shift correction. Under some polar winter conditions, and particularly in the case of an elevated stratopause, however, the shift retrieval from a single spectrum is by far not precise enough. In order to reduce large fluctuations due to noise, the spectral shift retrieval is constrained towards its temporal mean, where separate means were used for the high-resolution measurement period and the reduced-resolution measurement period. The reason for this choice was the use of different instrument line shapes for these measurements.

Inclusion of NO2 proved to be essential, particularly because of a sizable signal of mesospheric NO2. Omission of this gas would lead to artificial diurnal variations of the spectral shift.

The fit is carried out using a maximum a posteriori scheme using the mean of the spectral calibration scale over the entire FR and RR period, determined in a previous step as a priori. A priori variances of (0.00035 cm-1)2 for the FR and (0.0007 cm-1)2 RR measurements are used. The actual spectral correction for any wavenumber can be determined using the linear regression function.

According to the retrieval vector x, R has a block-diagonal structure, and the choice of the regularization can be made independently for each group of variables.

In general we use a regularization term, which is composed of a smoothing component Rsmooth and a diagonal component Rdiag: 2R=Rsmooth+Rdiag. Here the diagonal component Rdiag is formally equivalent to the inverse of an a priori covariance matrix without information on inter-altitude correlations. For the regularization term Rsmooth the following implementation of the altitude dependence has replaced the approach by , which has been used in our retrievals up to version 5. 3Rsmooth=LTγ10…00⋱0⋮⋱⋮0…0γN-1L

Here L is an (N-1)×N first-order finite-difference operator as suggested by , , and but scaled with the respective grid width to yield difference quotients. The γ values control the altitude dependence of the strength of the regularization.

The regularization term used for the parameter temperature is RT=Rsmooth with the values of all γi being set to 0.49 K-2 in the entire altitude range.

The tangent altitudes are constrained towards the line-of-sight engineering information. The respective block of R can be understood as an inverse a priori uncertainty covariance matrix describing both the relative pointing uncertainties between adjacent tangent altitudes and the absolute pointing uncertainty of the entire limb scan as a whole. The relative pointing a priori uncertainties were assumed to be 60 m in the RR measurement mode and 150 m in the FR measurement mode, in terms of 1σ standard deviations. The standard deviation of the absolute pointing uncertainty, representing the possible altitude shift of the entire limb scan, was assumed to be 900 m.

In older nominal-mode retrieval versions problems occurred which could be traced back to the use of inadequate a priori temperature distributions for altitudes above the uppermost MIPAS tangent altitude. Here, reliable analysis data are not available, and MIPAS cannot vertically resolve the temperature profile. Older retrieval versions used the NRLMSISE-00 climatology at these altitudes. However, this climatology has systematic biases and does not capture short-term variations occurring in dynamically active episodes such as elevated stratopause events. Due to missing MIPAS measurement information at related altitudes, this error propagated into the MIPAS temperatures in the nominal scan range. These temperature retrieval errors further propagated noticeably into retrievals of trace species, e.g. ozone .

For IMK/IAA MIPAS version 8 temperature retrievals, ECMWF ERA-Interim analysis fields were used as a priori at altitudes up to 43 km because ERA-5 was not available for the MIPAS time period when the processing was started. A priori temperatures above 53 km are based on Whole Atmosphere Community Climate Model (WACCM, ) Version 4 (WACCM4) fields of a specified dynamics run , which provided output specifically for the MIPAS measurement geolocations and times. Since a specified dynamics run was used, the actual atmospheric conditions, including stratospheric warming events and elevated stratopauses, were sufficiently well reproduced. The WACCM temperatures were bias-corrected using MIPAS version 5 middle and upper atmosphere measurements, which cover an altitude range of 18–102 km but are performed less frequently . Multi-annual averages of MIPAS-colocated WACCM differences were used to construct an altitude- and latitude-dependent seasonal correction, independently for day and night observations. The transition between ECMWF and bias-corrected WACCM takes place between 43 and 53 km. In this altitude region the temperature is calculated as the average of the two contributing profiles with altitude-dependent weights. The pressure above 43 km is calculated by numerical integration of the hydrostatic equation starting with the ECMWF value at 43 km. The integration uses the mixed temperature profile up to 53 km and the bias-corrected WACCM temperature above, as well as the corresponding given geometric altitudes. The pressure–altitude relation at 20 km altitude (or at the lowest tangent altitude above 20 km with valid spectral information), which is assumed to be fixed for the calculation of the pressure profile by the hydrostatic equation during the retrieval iterations, is taken from this a priori profile for details, see Sect. 2.2. of.

CO2 distributions are imported from an SD-WACCM4-based climatology. From MIPAS V5 data, gas profiles are generated for interfering species and for initial guess profiles for O3 and H2O, which both are jointly fitted together with target state variables. The a priori of the latter is a zero profile, while the regularization is of Tikhonov type.

Typically, a locally spherically symmetric atmosphere is assumed in profile retrievals. That is to say, within one profile retrieval the atmospheric state is assumed to be a function of altitude only and does not vary with latitude or longitude. However, for MIPAS limb measurements the range where 95 % of the information originates from varies from about 260 to 440 km . Hence, the horizontal homogeneity assumption is not without problems. Depending on the computational effort spent on accurate radiative transfer modeling, a fully tomographic retrieval as suggested by or is often beyond reach. As a first step, horizontal inhomogeneities of temperature have been considered in the trace gas retrievals since MIPAS version 4 by retrieving a horizontal temperature gradient applicable in a range of ±400 km around the tangent point . For retrievals based on level-1b spectra of version 7 onwards, we go a step further and consider a full a priori 3D temperature field generated from ECMWF ERA-Interim data with latitude and longitude resolutions of approx. 1.1∘, extended by NRLMSISE-00 data above 60 km. During the retrieval, the temperatures of this 3D a priori field are scaled at each altitude in a way that the horizontal structure is provided by the a priori while the vertical structure comes from the measurements. The respective component of the retrieval vector x is the 1D vector of scaling factors. Roughly speaking, the result is a temperature profile which provides the best spectral fit under the assumption that the a priori horizontal structure of the temperature field is correct. The information on the horizontal temperature variability enters through the a priori, but the vertical structure is provided by the MIPAS temperature retrievals.

Additionally, the retrieval of a horizontal gradient directly from the spectra of a single limb sequence is performed. However, the horizontal gradients are strongly regularized towards zero below 60 km, where ECMWF ERA-Interim temperature fields are available, and above 70 km, the topmost tangent altitude of MIPAS nominal measurement mode. In between, the regularization of the temperature gradient is chosen to be weaker in order to better exploit the information on the horizontal temperature gradient provided by the measurements.

The retrieval does not use all of the measurement data but only parts of the spectra that are particularly sensitive to the target species, so-called “microwindows” (see , for the rationale behind this approach). For the combined temperature and tangent altitude retrieval CO2 lines are used because the mixing ratio distribution of CO2 is well known and only weakly structured. This reduces the number of unknowns in the retrieval.

In order to have more information on temperature at high altitudes, additional microwindows were included since data version 5. These are 686.8125–689.7500, 689.8750–692.6250, 699.4375–702.3750, 719.6250–722.5000, 740.3750–742.8750, and 791.1875–792.6875 cm-1 (given for the wavenumber grid of the RR measurements). The full list of microwindows for FR and RR measurements is presented in Table . The inclusion of CO2 Q branches, on the one hand, implies the consideration of line mixing (omitted in previous data versions) but, on the other hand, allows the use of the same microwindow selection for analysis of MIPAS nominal and middle-atmosphere measurements . Thus, apart from the increased information gain for higher altitudes, this choice will lead to a better inter-consistency between the two datasets. Depending on the tangent altitude, certain data points within a microwindow can be discarded to avoid interference by spectral lines of gases other than CO2.

Joint-fitting of a background radiance continuum has always been a standard feature of all MIPAS retrievals e.g.,. The purpose of this is to account for all radiance contributions that are included neither in the line-by-line calculation of absorption cross sections nor the pressure–temperature interpolation of pre-tabulated laboratory measurements of absorption cross sections of heavy molecules. These contributions are caused by (a) the far-wing contributions of transitions spectrally distant from the analysis window under investigation, which add up to a continuum-like background signal whose line-by-line modeling would be inefficient; (b) continuum emission of trace gases by, e.g., dimers in the case of H2O; (c) differences between the idealized modeled line shapes and the true super- or sub-Lorentzian pressure broadening; and (d) the emission by non-gaseous components of the atmosphere like clouds, aerosols, volcanic ash, or meteoric dust. Since these non-line-by-line effects are mostly important in the lower atmosphere, the background continuum contribution was only fitted up to 33 km altitude in previous data versions and set to zero above. It turned out, however, that consideration of the background continuum up to altitudes of 58 km significantly improved the robustness of the retrievals and removed known biases in retrieved state variables. The cause of the continuum signal from high altitudes is possibly meteoric dust . The relevance of a high-reaching continuum signal was first discovered by in the context of the retrieval of SF6.

Only a smoothing constraint is applied to the continuum retrieval up to 58 km without any diagonal term. Above, the continuum is regularized exclusively by a diagonal term and an a priori of zero. Formally, an individual continuum profile is retrieved per microwindow, but the continuum values are not only constrained in the altitude domain but also in the frequency domain. The latter smoothing constraint avoids unrealistic jumps of the value of the background continuum between adjacent microwindows.

Besides the background continuum, we also retrieve a radiance offset profile that is meant to correct the radiance zero-level calibration. While the continuum is additive to the absorption coefficient and appears in the exponent of Beer's law, the offset correction is directly additive in the radiance space. When radiative transfer is linear, which is the case for high tangent altitudes, the offset correction and the background continuum cannot be distinguished and the simultaneous retrieval of both leads to a null-space of solutions. This problem is solved by strongly constraining the background continuum to zero above 58 km, while the vertical offset profile is strongly regularized towards an empirically determined offset correction profile , which is used as a priori for the fit of the zero-level correction. The actual offset value per microwindow and per altitude is retrieved using both Rsmooth. and Rdiag.. The diagonal term corresponds to a variance that is roughly a factor of 2 larger than the offset uncertainty obtained by , in order to account for possible unknown uncertainties. No regularization of the offset in the frequency domain has been applied, i.e., the offset can vary independently between microwindows.

Ideally, microwindows contain only signal of the target species and are free of any interfering signal. In general, however, such microwindows do not exist. In particular, H2O and O3 have sizable contributions in the microwindows of the temperature retrieval. Since the temperature retrieval is the first step in the retrieval chain, no actual information on the highly variable trace gas abundances is available.

To avoid the mapping of inadequate assumptions on the actual H2O and O3 abundances, these species' mixing ratio profiles are jointly retrieved with temperature. Since the microwindows of the temperature retrieval have not been optimized for joint retrieval of H2O and O3, the resulting mixing ratios are discarded. The only purpose of this joint-fit approach is to avoid related error propagation.

The HITRAN 2016 spectroscopic database was used for CO2, whose lines provide the information on temperature and the tangent altitude, as well as for most interfering species. Exceptions are O3 and HNO3, for which the dedicated MIPAS spectroscopic database provided by was used.

Typically, radiative transfer in the stratosphere is calculated assuming that the atmosphere is in local thermodynamic equilibrium (LTE). Test calculations, however, have provided evidence that the consideration of non-LTE (NLTE) populations of vibrational states involved in the contributing CO2 bands also makes a difference for temperature retrievals in the MIPAS nominal observational altitude range. NLTE populations of the CO2 states emitting around 15 µm, driven by absorption of upwelling radiation and insufficient collisional thermalization, occur predominantly above the nominal tangent altitude range (> 70 km); however, their emissions contribute to the radiances measured below. The non-LTE effects are only moderate here and thus a full-blown non-LTE retrieval using all the machinery developed by seems undue. Instead we use a non-LTE parameterization that accounts for the temperature dependence of vibrational non-LTE populations in an approximate manner (manuscript in preparation), which is briefly explained in the following.

Considering a simple two-level system under non-LTE conditions, upper- and ground-state populations n1 and n0, respectively, are related by 4n1=P+RL+An0, with the collisional productions and losses P and L, respectively, radiative losses A, and non-thermal productions R (e.g., radiative production by solar absorption). In this equation, only P=Lexp⁡(-ΔE/kT), with ΔE being the energy difference between upper and ground state, is temperature dependent. Hence, Eq. () can be separated into a temperature-dependent term aexp⁡(-ΔE/kT) and a temperature-independent term b with a=L/(L+A)n0 and b=R/(L+A)n0.

The radiative transfer algorithm uses population ratios r=nNLTE/nLTE with nLTE=n0exp⁡(-ΔE/kT). Using Eq. () and the identity bexp⁡(ΔE/kT)=r-a, the population ratio r(T,z) can be expressed as function of the ratio r(T0,z) at a reference temperature T0 as 5r(T,z)=U(z)+r(T0,z)-U(z)exp⁡E(z)k1T(z)-1T0(z), with U=a and E=ΔE for the simple case described above. An updated version of the Generic RAdiative traNsfer AnD non-LTE population algorithm (GRANADA) computes the parameter profiles U(z) and E(z) for realistic and more complex situations (i.e., multi-level systems, nonlinear interactions by vibration–vibration collisions, etc.), allowing for a temperature parameterization of non-LTE population ratios in a local approximation. A seasonal and latitudinal climatology of r(T0,z), U(z) and E(z) for the local times of MIPAS ascending and descending overpasses has been calculated offline with GRANADA and is considered by the KOPRA radiative transfer model in the forward calculations to estimate the non-LTE population ratios of vibrational states 01101, 02201, 10011, and 11101, involved in the observed 16C12O2 bands for the actual temperatures at each line-of-sight path segment during the retrieval iterations. This approach seems to be a fair compromise between rigor and efficiency.

The accuracy of the numerical integration in the radiative transfer modeling has been improved in several places. In order to achieve a more accurate numerical integration of the radiance over the field of view, now five pencil beams are used throughout, while older retrievals (up to version 5) used only three pencil beams at some tangent altitudes. In addition, in order to improve the numerical accuracy, a finer wavenumber grid is used for calculation of the monochromatic absorption cross sections (0.00048828125 cm-1 instead of 0.001 cm-1). The convolution of the spectrum with the apodization function now includes a wider wavenumber range. Additionally, a more conservative rejection threshold for lines so small that they are deemed not to contribute in any sizable way to the total signal has been chosen. Further, it was found that it is advantageous to recalculate the absorption cross sections during each iteration in the first seven layers above each tangent altitude. Formerly, this costly line-by-line calculation was performed only during the first iteration and the cross sections were re-used in all layers except the layer above the tangent altitude of the respective line of sight. However, when the temperature profile varies from iteration to iteration, the mass-weighted mean temperatures and pressures of the respective layer change, which is better accounted for by the new approach.

In the retrieval code an “oscillation detection” has been activated which identifies failure of convergence in the sense that the iteration flips back and forth between two minima of the cost function according to xi+1≈xi-1 and xi≈xi-2. In this case xi+1 is set to xi+1+xi2, and one further iteration step is performed.

In version 8, 99.95 % of the retrieval converged successfully. This is an improvement compared to versions 5 and 7, with 99.37 % and 99.85 % convergence rate, respectively.

Following the terminology of , we distinguish measurement errors, parameter errors, and model errors. Measurement errors include measurement noise and all uncertainties related to less than perfect knowledge of the instrument state. Parameter errors are uncertainties of atmospheric state parameters which are assumed to be sufficiently well known and thus not treated as unknowns of the retrieval. Model errors include deficiencies in the way the radiative transfer model describes radiative transfer through the atmosphere and uncertainties in constants such as spectroscopic data. We consider all error sources as independent from each other and thus add them quadratically to obtain the total error. We do not evaluate the smoothing error because we conceive the retrieval as an estimate of the smoothed true state rather than a smoothed estimate of the true state see,Sect. 3.2.1, for a discussion of this issue. Furthermore, we provide information on error correlations in various domains (Sect. ) and averaging kernels (Sect. ).

When comparing measurements of the same state variable by two different instruments, random errors are errors that contribute to the intrinsic variability (standard deviation) of the differences. The main sources of random errors of MIPAS temperature are measurement noise, spectral shift, gain calibration uncertainties, and the uncertainties of CO2 mixing ratios. Measurement noise is random by nature. Spectral shift originally has a more systematic characteristic, but the residual frequency calibration error after correction is random. According to our definition, gain calibration uncertainties are also random. While they are obviously systematic within one gain calibration period, they contribute in the long run rather to the standard deviation of differences between measurement systems than to the bias. Similar considerations apply to the uncertainties in CO2 mixing ratios, which we consider as random, although they are presumably positively correlated among subsequent measurements. The adequacy of this classification of uncertainties in random and systematic components will be critically tested in a dedicated validation study. None of the other random error components, e.g., mixing ratios of interfering species, makes a sizable contribution to the error budget.

For most atmospheric conditions and altitudes, the random temperature uncertainty varies between 0.4 and 1 K. Occasional excursions up to 1.3 K are encountered above 60 km altitude (Tables – and Figs. –).

As a rule of thumb, measurement noise is – everything else unchanged – larger for colder and smaller for warmer atmospheres. For the other random error components, no such simple dependence of the error on the atmospheric state can be provided.

For some applications the error covariances are relevant. These depend both on the structure of the Jacobian of the inverse problem and on the covariances of the ingoing uncertainties. While it is hard to fully quantify the latter, we present a sample error correlation matrix that characterizes the former in the Appendix (Table ). The correlation matrix allows the construction of an approximate covariance matrix for any given retrieval noise.

Systematic errors are, regardless of their origin, errors which explain the bias between measurements of the same state variable by different instruments observing the same part of the atmosphere. The main sources of systematic error in MIPAS temperatures below the mid-mesosphere are uncertainties in spectroscopic data and instrument line shape uncertainties. To classify these as systematic is admittedly an idealization because the actual conditions will somehow modulate the actual resulting errors; e.g., the impact of the uncertainty of the line intensity of an interfering gas depends on the abundance of the interfering species, which may vary randomly. Since, however, the CO2 lines chosen for the temperature retrieval are strong lines and only weakly interfered by transitions of other species, this random modulation of systematic errors is deemed negligible and the classification of related temperature uncertainties as chiefly systematic seems justified.

The other source of systematic error in MIPAS temperatures is uncertainties in the instrument line shape. Since the same set of coefficients is used for all measurements, this error is clearly systematic in nature. However, it must be kept in mind that modulations of the related initially systematic error by the variable sensitivity of the retrieval that depends on the actual state of the atmosphere will generate a certain random component.

In all altitudes except the uppermost ones, the error budget is dominated by these systematic errors. With this in mind, it can be considered a particularly grave deficit that uncertainties in spectroscopic data are so vaguely characterized with respect to their confidence limits and correlation characteristics.

Since our retrieval decomposes the inverse problem profile by profile, vertical correlations of measurement noise are represented by the respective covariance matrix. Related correlation coefficients are represented in Table . Errors due to spectral shift are expected to be almost fully correlated in the altitude domain because the frequency calibration correction is performed individually for entire limb scans. Since frequency calibration corrections are constrained towards the long-term mean, a positive error correlation in the time domain also has to be expected.

As stated above, positive correlations are expected for gain calibration errors of measurements recorded within one gain calibration period. This leads to positive error correlations in altitude and between subsequent limb scans. The typical length of a gain calibration period is 1 d and occasionally 2 d. Errors due to uncertain mixing ratios of CO2 are also expected to be correlated in altitude and between subsequent limb scans. Correlation lengths depend on the actual spatial and temporal extension of the CO2 anomalies.

The vertical resolution of the temperature profiles, estimated as the full width at half maximum of the respective row of the averaging kernel matrix, varies around 3 km in the altitude range up to 40 km (Fig. ). Above, it gradually deteriorates towards 7 km at 70 km. A local maximum of vertical resolution values of approx. 3.3 km is typically found at the tropical tropopause layer (around 15 km altitude) and is attributed to particularly low temperatures. The actual values of the vertical resolution are provided for each limb scan along with the data on the MIPAS data server (http://www.imk-asf.kit.edu/english/308.php, last access: 21 May 2021).

The averaging kernels are generally well behaved in the sense that they peak at their nominal altitude. That is to say, the temperature retrieval at altitude z is most sensitive to the true temperature at altitude z. Further, the kernels are fairly symmetric. This rules out major information displacement by the retrieval. The pronounced side-wiggles are a typical feature of a retrieval on a grid that is much finer than the measurement grid. This does not point at a weakness of the retrieval setup. Instead, the often smoother averaging kernels of retrievals on coarser retrieval grids just do not represent these features because the Jacobians do not resolve them. Understanding the column of an averaging kernel matrix as the response of the retrieval to a delta perturbation of the true profile, the so-called delta perturbation on a coarse grid perturbs a much wider part of the atmosphere and thus is not comparable to our fine-grid averaging kernels.

Preceding versions of MIPAS temperature data were already quite a mature and well-validated data product e.g.. It has already been shown that MIPAS sees the expected temperature features in the middle atmosphere e.g.,. Thus, it does not come as a surprise that, for most parts of the atmosphere, the differences between the new improved temperature data and the previous ones are small. (Fig. ). Only near the stratopause and above are major differences observed. These are attributed to the use of the extended set of microwindows (see Sect. ) and to the new WACCM-based prior information (see Sect. ), which is expected to represent the actual conditions much better than the climatology used previously.

In this section we concentrate on improvements with respect to the previous data version for cases where problems with the older data had already been identified, and we investigate to which degree MIPAS provides additional information with respect to pre-existing knowledge on temperature and line-of-sight pointing.

MIPAS is able to reveal structures in temperature profiles independently of the a priori information. We demonstrate this by using two examples of features in temperature profiles that might be attributed to gravity waves. In the left-hand panels of Fig. , temperature profiles for MIPAS retrievals (black lines) and the corresponding ECMWF-based a priori (red lines) are shown, while the right-hand panels show the differences between temperature profile minus the respective vertically smoothed temperature profile for retrieval and a priori data. Smoothing is done with a boxcar of 10 km width.

We rule out that the retrieved wave structure is a numerical artifact of the retrieval caused by too weak regularization because the MIPAS result agrees well with the ECMWF ERA-interim analysis, which shows very similar structure. The upper panels in Fig. 10 show an example. The example shown in the lower panel demonstrates that MIPAS is able to retrieve such structures independently from the a priori information. There (as in many other cases) we find wave structures in both datasets (MIPAS and ECMWF analyses) with similar vertical wavelengths but different phases. The retrieval scheme chosen does not employ any mechanism that would be able to map a vertically shifted structure in the prior information onto the result. Therefore, these results prove that structures in vertical profiles, and in particular these wave structures, are independent MIPAS measurement information.

Contrary to other MIPAS data processors (, , and http://eodg.atm.ox.ac.uk/MORSE/, last access: 21 May 2021), the IMK/IAA processor retrieves the pointing information in terms of tangent altitudes from the spectra see Sect. 2.2 of, using the engineering information only as a Bayesian constraint and not as a hard constraint (see Sect. ). The comparison between the retrieved data and the level-1b engineering information has been used in the past to characterize the MIPAS pointing and to improve the algorithm involved in the calculation of the line of sight . Meanwhile, several improvements of this algorithm have been implemented, and now the comparison reveals the following information.

The engineering information on the tangent altitudes has changed in a noticeable manner between data versions V5 and V8. Mean changes between engineering tangent altitudes can reach and exceed 600 m at most altitudes for FR data and -400 m for the RR period (signs according to V5 minus V8). The impact of the inclusion of atmospheric refraction in the calculation of the engineering tangent altitudes for level-1b versions after V5 is clearly visible as a difference below 20 km.