The Odin satellite was launched in 2001 with a dual mission: at first the observation time was split between astronomy and aeronomy, but since 2007 has purely been dedicated to atmospheric measurements. It flies in a approximately 600 km sun-synchronous orbit with an inclination of 98∘ and the ascending node at 18:00 LT. The satellite carries two instruments: the SMR and the OSIRIS. The instruments are co-aligned and scan the atmosphere in a limb-scanning configuration, and during standard operation scan tangent altitudes between roughly 8 and 120 km .

The Odin satellite and its instruments have many different modes of operation. In this study we use measurements taken in a special “tomographic” mode. These measurements were performed during 3 consecutive days in each of June, July and August 2010 and 2011 (see Table ). In this mode the two instruments only scan the atmosphere at altitudes between 75 and 90 km to specifically target the summer mesopause region. The tomographic mode is activated as the satellite crosses the equator, and measurements are made across the Northern Hemisphere. Figure  shows the coverage of the SMR tomographic mode during 1 day. As can be seen from the figure, large parts of the Northern Hemisphere are sampled by Odin over the course of a day.

Since the tangent altitudes of the tomographic mode are limited to 75–90 km, the distance between each scan through the atmosphere is reduced from 1000 to 200 km, compared to previous Odin measurements of water vapour in the mesopause . The shorter distance between scans means that the line-of-sight through the atmosphere for each scan will overlap. Figure b shows the line-of-sight from a set of SMR measurements as a function of altitude and angle along orbit, where 0∘ is the ascending node and 180∘ the descending node. The overlap between the scans can clearly be seen. The line-of-sight overlap means that in order to optimally retrieve information from these measurements, a tomographic retrieval approach should be used, hence the name “tomographic” mode.

This paper focuses on the tomographic mode measurements made by SMR. It measures radiation in five bands at around 118 and between 480–581 GHz, and can operate in several different frequency modes depending on the species of interest . The tomographic mode uses either the A1 or B2 front-end, operating in the ranges 541–558 and 547–564 GHz, respectively, to measure the H2O spectral line at 556.9 GHz. This is achieved by setting the LO frequency to 553.05 and 553.302 for A1 and B2 frontends, respectively. The resulting frequency modes are labelled mode 19 and mode 13. A tunable Martin–Pupplet interferometer is used for single sideband (SSB) filtering. Pre-flight measurements show a nominal sideband suppression of better than 19 dB across the image band, with a maximum suppression of 35 dB . However, post-launch analysis of spectra indicates that the true suppression rather is 11–15 dB for the frequency modes used in this study.

The spectra are recorded using one of the two autocorrelator spectrometers among the SMR backends. Each autocorrelator has four sub-bands of 200 MHz, and provides a total bandwidth of 800 MHz. For mesospheric studies of the 557 GHz line only a part of full bandwidth is needed, and just the 200 MHz sub-band covering the line is used in the retrieval process. The effective channel resolution of the spectrometer is 2 MHz, and the channel separation 1 MHz. Furthermore, post-launch analysis of the instrument has revealed that the autocorrelators have problem measuring spectra with large dynamic ranges, i.e. large differences in brightness temperature across the bandwidth of the instrument. This results in a low bias in the recorded brightness temperature, which becomes especially apparent in high-altitude measurements . To compensate for this, the measured spectra in this study are scaled by 1.03 before they are inverted.

The amount of noise in each channel is determined by the noise temperature of the system, the effective channel resolution, and the integration time. For the frequency bands used in this study, SMR has a noise temperature of roughly 3000–3500 K. For the tomographic mode measurements, an integration time of 1.8 s is used. Due to the time used switching between calibration measurements and atmospheric measurements, SMR is only measuring the atmosphere about half of the total time. Taking this into account, the resulting thermal noise (1σ) is of the order of 2.6 K for the measured spectra.

To relate the measured radiation to a physical brightness temperature a calibration must be performed. The SMR measurements are calibrated by switching between the cold sky (space) and the atmosphere, with a hot-load calibration performed at the end of each scan. In this study the newest version (V8) of the calibrated Odin spectra is used. This version was prepared during the autumn of 2013, and beside improving the treatment of known instrumental artefacts, it corrected an error related to the transition between orbits, which previously had made the tomographic observations unusable.

The vertical resolution of the measurements depends on the size and shape of the antenna pattern. For SMR the antenna is a 1.1 m Georgian telescope which provides a half-power beam width better than 0.035∘ . This results in a vertical resolution at the tangent point of ∼1.6 km. However, due to the telescope continuously scanning vertically during the integration time of 1.8 s the angular resolution is reduced to 0.04∘ (∼1.8 km) in the tomographic mode.

In addition to presenting the results from the SMR tomographic mode retrievals, this paper also includes some comparisons with the PMC brightness retrieved from the optical spectrograph of OSIRIS. The spectrograph is a modified Erbert–Fastie grating spectrometer with a CCD backend, and can measure light scattered from the atmosphere between 280 and 800 nm with a spectral resolution of around 1 nm. The entrance slit of OSIRIS is aligned parallel to the horizon, and subtends a region 30 km wide and 1 km high at the tangent point.

To retrieve PMC properties from the scattered light, the measured radiation in the wavelength region of 302.8 to 305.9 nm is compared to a purely Rayleigh scattering background field calculated using the MSIS climatology. The differences between the measured and simulated spectra are then used as inputs to a tomographic retrieval scheme based on a modified version of the Multiplicative Algebraic Reconstruction Technique MART,. The retrievals return the scattering coefficient of the clouds with a 330 km horizontal resolution and 1 km vertical resolution, and an accuracy of 4×10-11 m-1str-1. For a detailed description of the observations and retrieval process the reader is referred to .

In order to illustrate the viability of the tomographic methodology, a simulated retrieval was performed. In this way the sensitivity of the retrievals to changes in water vapour and temperature can be investigated. The mean temperature and water vapour retrieved from the tomographic measurements was used as the atmospheric a priori in the simulation. Since the purpose of this study is to look at small-scale variations of water vapour and temperature around PMCs, a water vapour enhancement of 50 % was simulated in three small regions of the atmosphere. One such region was centred at 79 ∘ AAO and 82 km in altitude. This region was given a size of 200km×3km, which roughly corresponds to the estimated resolution of the tomographic measurements (see Sect. ). A smaller region (100km×1km) was positioned at ∼ 74 ∘ AAO, to test the limits of the method. Finally, a region with a small horizontal (100 km), but large vertical (15 km) extent was simulated at ∼ 67 ∘ AAO to investigate the effect of horizontal inhomogeneities. Using this atmosphere, a set of simulated measurements was generated. This test atmosphere might not be realistic, but should be a useful tool for qualitatively evaluating the performance of the methodology. The retrieval was performed as described in Sect. . No noise was added to the simulated data, but the simulated retrievals were done using a noise covariance matrix describing a thermal noise with a σ of 2.6 K.

Figure a shows the retrieved water vapour, relative to the a priori atmosphere, from the simulated retrieval. The areas with enhanced water vapour are shown by the black contours, and the retrieved water vapour is shown by the colour of each pixel. Looking at the area around 79 ∘ it is clear from the results that the retrievals can reproduce the water vapour enhancement, though some smoothing is seen. This smoothing is expected, as the enhanced area is of the same size as the 67% centred quantile resolution derived in Sect. .

The values retrieved for the enhanced area at ∼ 67 ∘ show that inhomogeneities with an even smaller horizontal extent can be retrieved at the correct position. The vertical edges of the inhomogeneity are accurately reproduced by the retrievals. However, a large effect of the limited spatial resolution can be seen as the retrieved enhancement is around 15–25 % rather than the true value of 50 %. This is also the case for the smallest area at 74 ∘ AAO where an enhancement of less than 10 % is retrieved. Thus, this small area of 100km×1km indicates the smallest regions of change we can expect our measurements to be sensitive to, although it should noted that retrieved values from such small areas in most cases will be overshadowed by the random variations from noise in the data.

In addition to water vapour, the tomographic retrieval returns the temperature field of the atmosphere. Due to the nature of the measurement method, the Jacobian matrix is not completely block diagonal with respect to the two atmospheric variables. This means that the two retrieved quantities will not be independent of each other. As a result an increase in water vapour will influence the retrieved temperature field. Figure b shows the change in retrieved temperature due to the simulated water vapour enhancements, and variations of ±1 K are seen in the retrieved data around the water vapour enhancements.

To test the temperature retrievals, another simulation was set up. In this simulation (not shown) the water vapour distribution was set equal to the measured mean, and the temperature was perturbed by reducing it by 10 K in the same manner as with the test simulation for water vapour. For the temperature the perturbed areas were reproduced in the correct position, but the retrieved values were up to 5 K warmer than the true value. The reason for this is that the temperature resolution, in particular the 95% quantile resolution, is worse than resolution of the retrieved water vapour, thus a larger smoothing effect is seen. For further discussion on this see Sect. . The influence that changes in temperature had on the retrieved water vapour field were up to 8 % in the retrieved water vapour within the perturbed areas, and no change outside of them.

These simulated tests are not a complete validation of the retrievals, but meant to illustrate some of the capabilities and limitations of the method. The final test of the abilities of the measurements to estimate the true atmosphere will be done by comparing the retrieved data to other instruments. A further discussion of this along with possible sources of uncertainties and errors in the retrievals can be found in Sect. .

To exemplify the results of the tomographic measurements, two orbits (51221 and 51226) recorded on 15 July 2010 are selected as example orbits. Orbit 51221 is selected as collocations between Odin-SMR and both ACE-FTS and AIM-SOFIE can be found along this orbit. Orbit 51226 is used since it is an orbit recorded soon after, where SMR is using the other frontend.

Figure  shows some example spectra from orbit 51226 at different tangent altitudes. The saturation of the line at the lower altitudes is seen, as the brightness temperature of the line centre is lower than the line wings, reflecting the negative temperature gradient of the mesosphere. The spectra fitted by the retrievals are shown as dashed lines showing how they reproduce the general shape and amplitude of the measured spectra. To get a better view of the fit, the residuals from all spectra in orbit 51226 are shown in Fig. b. Ideally the residuals should be white noise with a standard deviation equal to that of the thermal noise of the receiver. For most of the spectrometer channels this is true; however, for the channels closest to the line centre some non-white noise can be seen in single measurements.

Spatial resolution of retrieved data is usually described by the rows of the averaging kernel matrix (AKM), A. Each element in this matrix, Aij, gives the change in the retrieved state vector element x^i from a change in the true state vector element xj. We calculate the AKM by assuming that the final step in the Levenberg–Marquardt iteration has a Levenberg–Marquardt parameter of 0, i.e. A=Sa-1+(KTSϵ-1K)-1KTSϵ-1K.

Note that for these batches where the final ML-parameter differs from zero, A is still calculated with an ML-parameter of 0 (i.e using Eq. ). The reason for this is that the final solution (and hence the AVK) is independent of γ (for further discussion see e.g. and the discussion thereof, and ).

For non-linear retrievals A will depend on the atmospheric state, and will vary between measurements. Thus, in order to give the most representative picture of the capabilities and limitation of the retrievals, we have chosen to show the averaging kernels calculated using the mean retrieved state from all the measurements in this paper.

The plots in Fig. show a single row of the AKM, separated into the columns covering water vapour and temperature respectively. This row can be referred to as the 2-D averaging kernel (AVK), for the retrieval point considered (positioned at 94.5 ∘ AAO and 82 km altitude).

The 2-D averaging kernel for water vapour is relatively symmetric around the retrieval point. However, since this point is not placed directly in a line of sight, all contributions to the retrieved value will come from measurements of the adjacent grid points, thus the peak of the AVK will not be in the centre. We have chosen this point to illustrate a “worst case” scenario for the analysis of the averaging kernels. For retrieval grid points where several lines of sight intersect, the 2-D averaging kernels have their peak at the grid point.

Just as for water vapour, the temperature averaging kernel has peaks located at the measurement points surrounding the retrieval point, rather than at the retrieval point. Additionally the temperature AVK displays an asymmetry, weighting the information along the line of sight more than information from adjacent scans. If the centroid (first moment) position is calculated it is still placed at the retrieval point.

There are several possible sources of errors in the retrievals. Random errors come from thermal noise in the measurements (retrieval noise), from the limited resolution of the measurements (smoothing error), and pointing error in the satellite. Additionally, the results have systematic errors related to uncertainties in modelling of the instrument, modelling of the atmosphere, and uncertainties in the spectral line parameters. Just as with the averaging kernels, the effect of uncertainties and errors will depend on the true atmospheric profile. Thus, to give an indication of the average error expected in the retrievals, the error analysis is based around a case linearised around the mean retrieved state of the measurements.

The smoothing error and retrieval noise can be calculated using the covariance matrices, Sa and Sϵ respectively, as described in . The retrieval noise for the measurements presented in this study is ∼ 0.2 ppmv for water vapour and 2–3 K for temperature. It should be noted that the errors arising from thermal noise in the data will be correlated in both the vertical and horizontal direction. From investigation of the retrieval noise covariance matrix, the correlation length of the retrieval noise is 2–3 km in altitude and 2–3 ∘ in angle along orbit for both temperature and water vapour from 75 to 90 km. An accurate estimation of the smoothing error requires that the atmospheric covariance matrix is known with certainty, which is not the case for these retrievals. As such we will not use the smoothing errors for the error analysis, but rather consider the retrieved result as the smoothed version of the true atmosphere, with a resolution given by the averaging kernels.

For the systematic errors, their influence is estimated by performing a simulated retrieval on the mean retrieved state with the forward model perturbed to the ±1σ estimate of the investigated parameter. The parameters investigated are the line strength I0, which is perturbed ± 2 %, based on the JPL uncertainty, and the pressure broadening parameter γ, which is perturbed 5 %, based on differences between the measurements reported in . Errors in the altitude of the HSE reference pressure level (2.9 Pa), Pressure, are estimated by moving the pressure level ± 2 km, based on differences between MSISE-90 and CIRA86 at 70 km. Additionally uncertainties related to the properties of the SMR instrument are simulated. The instrumental parameters investigated are an offset in the pointing of ± 0.02∘ , and uncertainties in the sideband suppression of ± 2 % (11–15 dB).

It should be noted that the presence of PMCs will not affect the retrieval of water vapour and temperature from SMR. The radiance emitted from ice particles is of the order of 0.1 K, and will be very uniform across the bandwidth of the spectrometer. As such, it will be completely overshadowed by any baseline in spectrometer, and thus corrected for in the polynomial baseline fit performed on each spectrum.

Figure  shows the random and systematic errors estimated around the mean atmospheric state. The plotted value, ΔE, is the mean absolute value of the difference between the perturbed, x(±σ), and unperturbed, x(0), retrievals given by ΔE=|x(σ)-x(0)|+|x(-σ)-x(0)|2.

The two largest sources of uncertainties in the retrievals are the pressure–altitude relationship (red line) and errors in pointing of the satellite (cyan line). The reason for this is that the weighting function for a change in water vapour is similar to the weighting function from the changing of the pointing angle of the satellite, or from a change in ambient pressure at different altitudes. Since the water vapour line is dominated by Doppler (compared to pressure-) broadening at the observed altitudes, and the number density of molecules decrease exponentially with altitude, any pointing error (or errors in altitude of the HSE reference point) will give rise to a large-scale change in the retrieved water vapour mixing ratio, and vice versa. The errors arising from assuming the wrong altitude of the 2.9 Pa pressure level can be adjusted for by ensuring that comparisons to other instruments or models are done with respect to a common pressure vs. altitude profile, in effect comparing number density- rather than mixing ratio profiles. If this is done, the estimated systematic error from this uncertainty is lowered to ∼2 ppmv (red-dashed curve in Fig. ).

The uncertainties from the two aforementioned errors (Pointing and Pressure) are however highly correlated across each orbit and will mainly affect the mean water vapour field retrieved in each orbit, and not the variations around this field. For these variations the other systematic errors will dominate, and these are of the order of 0.5 ppmv. Thus the measurements can reliably retrieve small-scale variations, despite the poor accuracy of the mean field. It should also be noted that the systematic errors introduced from the pointing and pressure uncertainties do not necessarily lead to a bias as both errors may vary across the measurement period.

As a final test of the ability of the observations to retrieve water vapour and temperature, the results are compared to measurements from other satellite instruments. The solar occulting instruments Atmospheric Chemistry Experiment-Fourier Transform Spectrometer (ACE-FTS) on board the SCISAT satellite and Solar Occultation for Ice Experiment (SOFIE) on board the AIM satellite provide water vapour and temperature measurements with high vertical resolution in the area covered by the tomographic retrievals during the time period of the tomographic measurements.

ACE-FTS is a Fourier transform spectrometer which measures solar radiation between 750–4400 cm-1 and retrieves water vapour and temperature profiles between 5–90 km with an altitude resolution of 3–4 km and a precision of ∼300 ppbv for water vapour statistical fitting error and “form-factor” error and ∼2 K for temperature comparison to LIDAR. In this study we use version 3.0 of the water vapour data , which provides data during July 2010 in the time period covered by tomographic retrievals.

SOFIE uses differential absorption spectroscopy at 11 different wavelengths between 0.292 to 5.316 µm to determine the temperature and the atmospheric composition. It retrieves water vapour and temperature between 20 and 95 km with a vertical resolution of 1–2 km. The precision for water vapour is estimated to be better than 0.2 ppmv across the mesopause , and for temperature the precision is estimated to 0.1 K at 80 km increasing up to 0.5 K at 95 km . In this study we use version 1.2 of the data which covers the entire time period of the tomographic Odin measurements.

The measurements are collocated by finding the retrieved SMR profile at the latitude of ACE-FTS/SOFIE measurements and comparing it to the closest (spatially) ACE-FTS/SOFIE during the same day. Due to the different orbits of the satellites there is some distance between the collocated measurements, but 90 % of the collocations are within 350 km. This means that some differences between the profiles due to natural variability should be expected. Another reason for discrepancies between the measurements is that, while SOFIE and ACE-FTS perform measurements at ∼ 23:00 and ∼ 01:00 LT due to their solar occultation technique, SMR measurements are performed around 17:00 LT. Furthermore, the occultation measurements are made perpendicular to the orbit, i.e. east–west, while SMR measures along the orbit, i.e. north–south. The differences due to sampling different air, however, should largely average out (except possible diurnal variations) when comparing data over the entire PMC season.

The result from SMR orbit 51226 (15 July 2010) is compared to AIM-SOFIE and ACE-FTS in Fig. . The position of the collocations are showed by the vertical black lines in Fig. . The solid and dashed lines in Fig.  are the collocations at AAO=70∘ and AAO=110∘ respectively. The data from the three instruments are interpolated onto a common altitude grid for intercomparison to minimise the effect of the retrieved pressure differences between the instruments. For water vapour the agreement between the instruments is good, but SMR seems to show too low values below 80 km. The retrieved temperature of the three instruments have larger differences above 85 km. For the profile measured at 63∘ W (dashed lines) SMR and ACE-FTS places the mesopause at the same altitude (90 km), while the profile from SOFIE shows the mesopause at 86 km. SMR does however measure a significantly lower mesopause temperature (<130 K) than the two other instruments. At 81∘ E (solid lines), SMR places the mesopause at a higher altitude than both ACE-FTS and SOFIE. These differences might be, as previously mentioned, due to different sampling time/location. In conclusion, the comparison of the single measurement points show that the tomographic measurements successfully can retrieve water vapour and temperature structures in the area of interest.

To look at the systematic errors in the tomographic retrievals, the mean of all measurements collocated with SOFIE is analysed. A total of 198 collocations are investigated, and Fig. 13a and b show the result of this comparison with respect to each of the two frequency modes of SMR. The measurements using mode 19 show a low bias compared to SOFIE in both water vapour (>0.5 ppmv) and temperature (>15 K). The estimated accuracy of SOFIE is ∼5 %/0.8 K at 80 km and 15 %/9.9 K at 95 km for water vapour and temperature respectively. Taking this into account the agreement between SMR and SOFIE is good for mode 13, but not for mode 19. Above 85 km a large difference in mean temperature can be seen (>30 K). This is partially explained by a known high bias in SOFIE . However, comparing SMR and ACE-FTS for July 2010 (not shown), a similar, albeit smaller (5 K), cold bias is seen above 85 km, and SMR places the mesopause about 2 km higher than ACE-FTS. Thus, we cannot rule out the possibility of a cold bias of ∼ 5 K above 85 km even in the frequency mode 13 measurements, though these differences are within combined accuracy of the two instruments.

The comparison of the mean profiles can be extended by looking at the mean profile from each month for SOFIE and SMR. Figure 11c shows the mean water vapour profiles from both instruments for June, July and August averaged over 2010 and 2011. Only the collocations from the frequency mode 13 measurements are used. In June, SOFIE (blue-dashed line) shows a higher water vapour concentration below 82 km than SMR (blue line), while in August (red lines) the reverse is true. The reason for the larger seasonal variation in water vapour in SMR is unknown, but it could be linked to systematic errors in the pressure a priori used for the retrievals. The mean temperature (Fig. 13d) is very similar for both SMR and SOFIE for June and July, while for August SOFIE retrieves a much higher mesopause temperature (155 K) compared to SMR (140 K).

It should be noted that the measured water vapour mixing ratios are first converted to number density, before they are rescaled using a common pressure and temperature profile during the comparisons. This means that in principle number density profiles are compared rather than mixing ratios. Doing this mitigates errors arising from the lack of pressure information in the SMR measurements.

In conclusion, the overall agreement between the SMR tomographic measurements and the two solar occulting instruments are within the accuracy estimations from Sect.  for the measurements made with frequency mode 13. For the measurements made with mode 19 however there is a clear systematic low bias in both water vapour and temperature. The measurements from SMR also show a larger seasonal variance of water vapour, with lower concentrations than SOFIE in June and higher concentrations in August.

As previously mentioned, one of the reason for doing the tomographic SMR measurements is that measurements by OSIRIS are able to retrieve PMC coverage at the same time. Figure  shows some example results combining measurements from both instruments. The left panels show the water vapour distribution around PMCs from two different orbits recorded on 15 July 2010. The white contours show the volume scattering coefficient from the PMCs measured by OSIRIS. The most striking feature is the strong depletion of water vapour above the clouds. This is seen particularly well above each of the three cloudy areas at 80, 90 and 100∘ AAO in Fig. 14c. At 82 km, there are areas with higher water vapour concentrations between the clouds, indicating possible cloud deposition. In Fig. 14a the water vapour is concentrated in a single area at 80∘ AAO. The reason for this feature cannot be explained by looking at the cloud distribution alone, but probably arises as a combination of air movement as well as cloud formation and particle sedimentation.

The atmospheric temperatures are shown in the rightmost panels in Fig. . In general, the existence of clouds seem to correlate with the cold areas at 82 km. In particular the warmer area seen at 90–100∘ AAO in Fig. 14d has a noticeable lack of clouds compared to the areas around it. This fits well with the water vapour analysis, indicating that this as a possible area of PMC sublimation. In some areas, however, the clouds penetrate into areas of higher temperature (>150 K); explaining these intrusions requires further analysis taking into account both cloud microphysics and the dynamics of the atmosphere.