The Odin satellite, a Swedish-led project in collaboration with Canada, France and Finland, was launched on 20 February 2001 into a 600 km sun-synchronous orbit with inclination 97.77∘ and 18:00 LT ascending node. Its observation time was shared between astronomical and atmospheric observations until 2007, when the astronomical part of Odin's mission was concluded. After that, the instruments on board Odin have been used exclusively for limb sounding of the atmosphere. These instruments are OSIRIS (Optical Spectrograph and InfraRed Imaging System) and SMR. In this article, we are using the latter. The four sub-millimetre receivers in SMR can be tuned to cover frequencies between 486–504 and 541–581 GHz, thus to observe emission due to rotational transitions for species such as O3, H2O, CO, NO, ClO, N2O and HNO3 in the stratosphere and mesosphere e.g.. There is also a millimetre receiver to observe the 118 GHz O2 transition. The cold sky and a hot load are repeatedly observed for calibration purposes (see Fig. ). A Dicke switch allows us to quickly change the source of the signal between the main beam and the calibrators. The signal is thereafter split according to polarisation and injected into the mixer through a Martin–Puplett interferometer. Here the source signal is converted to longer wavelengths by combining it with a local oscillator (LO) signal, also injected through the Martin–Puplett interferometer. The frequency of the LO is fine tuned with the use of a PLL. The output signal of the mixer is a function of the sum and difference of the frequencies of the input signals, therefore consisting of two sidebands. SMR is however run in single sideband mode so, of the two sidebands, only the one containing the signal of interest will be detected and the other one suppressed. This is achieved, before mixing, by accordingly setting the length of the arms of the Martin–Puplett interferometer. The resulting signal can then be amplified and routed to the autocorrelator spectrometers (AC1 and AC2, as indicated in Fig. ).

Measurements are performed during both upward and downward vertical scanning with a vertical sampling of ∼6 km in the mesosphere. The scanning is continuous, with a constant speed of 0.75 km s-1. Odin/SMR L1 data are organised in scans, each of them consisting of a group of spectra collected during a single upward (or downward) scanning. Each spectrum corresponds to a single mean tangent altitude in the range 7–72 km (stratospheric scans), 7–110 km (strato-mesospheric scans) or 60–110 km (mesospheric scans) .

Odin/SMR measures CO, with a 3–7 km vertical resolution, from the thermal emission line corresponding to the J=5→4 rotational transition at 576.268 GHz. In Fig. a we show an illustrative scan of spectra obtained in normal conditions where both a CO line and an O3 line are measured. The SMR receivers can be adjusted to different configurations called frequency modes (FMs), each of which corresponds a certain observed frequency band and a scheduled observation time. There are three FMs that cover bands in which the above-mentioned CO transition is observed. Their characteristics are summarised in Table . All these measurements are carried out by using the B1 front end (the set of components thus denoted in Fig. ), whose PLL element was working correctly for a year only, between 8 October 2003 and 8 October 2004. The measurements made during the rest of the Odin operational time, from 2001 until today, have all been affected by a malfunctioning of this PLL, leading to a shift of the LO frequency from its nominal value . Consequently each scan presents a different frequency shift. In extreme cases like the one shown in Fig. b, the frequency shift causes the CO line to fall outside the observed bandwidth, and thus the data are unrecoverable.

In order to correct the frequency shift, as a first step, the centre frequency of the CO line in the scan's average spectrum has been compared with the theoretical centre frequency. The resulting difference is then applied to the LO frequency. To do that, the correction algorithm first needs to distinguish the CO line from the O3 line. In Fig. a it is shown how peak brightness temperatures of CO and O3 lines vary with altitude. Here it can be noticed that the CO and O3 slopes are most different between 40 and 60 km, allowing us to discern between the two species. In Fig. b, averaging of observations during the PLL working period show that, in this altitude range, a -0.0004±0.001 K m-1 slope corresponds to the CO line, while the value -0.009±0.003 K m-1 identifies the O3 line, where the uncertainties on slopes correspond to 3σ. Thus, the correction algorithm associates peak Tb gradients with a value higher than -0.0045 K m-1 to the CO line. The LO frequency can then be corrected for the whole altitude range under consideration in this study, as explained above. If no line or only the O3 line is found, the scan is not considered for further processing.

Despite the application of this first correction to the data, they still present artefacts that need to be corrected. In fact, as can be seen in Fig. a, all spectra in a single scan, each corresponding to a different altitude, present a different frequency shift. This suggests that the PLL malfunctioning affects the observation at a timescale smaller than the scanning timescale (∼2 min). Thus applying the same correction to each spectrum in a scan is not sufficient. To solve this problem, we modified the pre-correction algorithm by considering each single-altitude spectrum and estimating the observed centre frequency of each CO line by fitting them with a Gaussian function. We then compared these values to the theoretical centre frequency and therefore applied a different shift to each spectrum. An example of result obtained from this correction is shown in Fig. b. Including this altitude-dependent correction resulted in a significantly increased amount of data that could be recovered, i.e. from which CO concentration profiles could be derived (as shown in Fig.  in Sect. ). The frequency shifts, of which we presented the corrections in this section, appear to be random and not follow any trend with time. No dependency on satellite temperature was observed either.

The Atmospheric Radiative Transfer Simulator (ARTS) retrieval algorithms are based on the optimal estimation method from which statistical errors on the retrieved quantities originate. A new version of the ARTS operational processing system has been developed for SMR retrievals. The data produced by this system will be denoted as version 3.x. The new retrieval system will be described in detail in a forthcoming publication, but a summary is provided below. The CO data discussed in this work have been assigned version number 3.0.

The new processing system is based on a MySQL database and is capable of distributing the calculations over multiple clusters. The actual retrievals are based on ARTS . For the moment ARTS version 2.3.564 is applied. Besides atmospheric radiative transfer, the forward simulations consider the sensor's antenna response, double-sideband characteristics and spectrometer frequency response, using the approach of . ARTS provides the needed weighting functions (mainly using analytical expressions), while the inversion of optimal estimation type is made in MATLAB by code taken from .

The L2 data provided contain a characterisation of the retrieval, following . As described in , when retrieving multiple quantities in parallel, the “smoothing error” includes terms that describe the interference between the quantities. The retrieval error reported in SMR v3.0 data incorporates this cross-quantity interference but excludes the classical smoothing error internal to the quantity. For example, the error reported for CO considers that the retrieval of instrumental parameters is nonideal but excludes the direct smoothing of the CO profile due to limitations in vertical resolution. In this way, the reported error matches the standard one that would be obtained if the instrumental parameters would instead be treated as forward model uncertainties (though strictly true only for a totally linear inversion problem).

Specifics for the retrievals presented in this paper include that only spectra recorded at tangent altitudes between 40 and 100 km are considered to form a mesospheric retrieval mode. The spectroscopic data for the frequency range of concern is solely taken from HITRAN 2012 (but the system allows us to incorporate data from other sources). The set of variables retrieved is specified for each mode separately. In this case, the CO profile and off-sets for pointing, frequency and brightness temperature zero level (baseline) are retrieved.

The a priori dataset previously used for Odin/SMR CO retrievals was found outdated and inaccurate. As a consequence, for the new inversions, a new CO climatology was formed, based on MIPAS zonal means averaged over the years separately for each month. For this purpose, we are using the product V5R_CO_521, which at the moment is the most recent data version from MIPAS middle atmosphere observation mode (see Sect. ). The monthly a priori is divided into 10∘ latitude bins. As a temperature model for the retrieval, ERA-Interim reanalysis data are used up to 60 km and the Mass Spectrometer Incoherent Scatter model (version NRLMSISE-00; ) is used from 70 km upwards. Between 60 and 70 km, a spline interpolation of the two is applied.

In Fig.  the retrieval for a typical scan is shown. Despite the fact that spectra above 40 km tangent altitude are considered in the inversion, only measurements above 50 km are reliable since at lower altitudes it is not possible to discern the CO line from the noise. Moreover, data with a measurement response lower than 0.75 are discarded, where the measurement response is a measure of the degree to which the result may be contaminated by the a priori. It is defined as the sum over the row of the averaging kernel matrix . Values lower than 0.75 occur for the retrieved profile above 100 km which is dominated by the a priori and is here shown out of completeness, together with the averaging kernel extending to higher altitudes, to display how retrieved concentrations between 90 and 100 km are also influenced by higher altitudes.

The fits of the CO line performed during the inversion process – which have the shape of a Gaussian function due to Doppler broadening – have significantly different amplitude and width compared to the observed line, causing an underestimation of the concentration. This suggests that the PLL malfunctioning even has an effect within the integration time, causing the observed line to be broadened with respect to what it would be in normal instrumental conditions. To take into account this broadening issue during the inversion, the original response function, a Gaussian function with σ=0.8 MHz, has been replaced with a Gaussian function with a higher σ value. The response function wchi(ν) of a spectrometer's channel i represents how the power of a signal I(ν) is weighted: 1yi=∫0∞I(ν)wchi(ν)dνwith∫0∞wchi(ν)dν=1, where yi is the final, calibrated antenna temperature of the channel i .

Figure a shows the relative difference between the Gaussian area beneath the observed CO line and the Gaussian area beneath the fit, for a scan in the period when the PLL was working. Here there is no need for correction, and the lower values of the relative area difference are obtained with the original response function. As an example, in Fig. b the relative area difference for one scan in the PLL malfunctioning period after 8 October 2004 is plotted. During this period, the most suitable response function is a Gaussian function with σ=1.1 MHz. This is indeed the one resulting in the lowest overall relative area differences; therefore, this same response function has been used in the whole period aforementioned.

Note that the original response function is still the one giving the best results during the period before 8 October 2003. Consequently, the new response function has been applied only to inversions after 8 October 2004. This suggests that the PLL malfunctioning before 8 October 2003 is of a different nature than the one after 8 October 2004, with the former causing only frequency shifts and the latter causing both line broadenings and frequency shifts, i.e. having effects both within the integration time and at longer timescales.

The Michelson Interferometer for Passive Atmospheric Sounding (MIPAS) is a mid-infrared spectrometer which was launched on board Envisat on 1 March 2002 and was operating until April 2012, when an unexpected loss of contact with the satellite occurred. The satellite travelled at 800 km altitude on a sun-synchronous orbit with a 98.55∘ inclination and a 22:00 LT ascending node. The concentration profiles that we use for comparison in this study are retrieved from measurements of 12C16O roto-vibrational emissions in the v=1→0 band around 4.7 µm, using the retrieving processor developed at the Institute of Meteorology and Climate Research (IMK) in Karlsruhe and the Instituto de Astrofisica de Andalucia (IAA) in Granada e.g.. The forward model used for CO retrieval takes into account non-LTE effects. We consider data from the most recent MIPAS datasets, as specified in Table  . All recommendations about the quality filtering of the data have been followed .

The Fourier Transform Spectrometer (FTS) is an instrument which is part of the Canadian-led Atmospheric Chemistry Experiment (ACE) on board SCISAT-1, launched on 12 August 2003 (and still operating) into a 74∘ inclination orbit at 650 km altitude . ACE-FTS performs solar occultation measurements in the mid-infrared. In particular, CO concentrations are retrieved from the roto-vibrational absorption bands around 4.7 µm (v=1→0) and 2.3 µm (v=2→0). CO retrievals are performed between 5 and 105 km altitude, with a 3–4 km vertical resolution . In this study we use ACE-FTS v3.6 dataset for comparison. The data have been quality filtered according to the guidelines from the instrument team .

A total of 12 925 coincident CO measurements between ACE-FTS and SMR were found between February 2004 (first available ACE-FTS CO measurements) and March 2019. The number of coincidences found is lower compared with any of the MIPAS modes, despite the longer period considered. This is due to the fact that ACE-FTS is a solar occultation instrument, thus scanning the limb only twice per orbit, while both SMR and MIPAS are measuring almost continuously. The spatial and temporal average comparison with ACE-FTS is shown in Fig. . The relative difference decreases almost monotonically with altitude, from a maximum of +15 % at 50 km to a minimum of almost -15 % at the highest altitudes. In particular, the difference decreases more quickly between 50 and 60 km from 15 % to near 0 %. SMR and ACE-FTS are in extremely good agreement with each other between 60 and 75 km, with a relative difference close to zero. The difference then slowly decreases with altitude up to about -15 % at 90 km and finally increases almost imperceptibly between 90 and 100 km. Looking at seasons separately, the relative differences present generally low values, almost always within ±20 %. Values only increase to more than +40 % between 60 and 70 km during northern autumn around +25∘ and during southern winter at the Equator and around -25∘. The latter difference is similar to the one observed from ACE with respect to MIPAS . Moreover, strong negative differences of about -40 % are observed at the Equator at 80 km altitude during northern spring and also at +25∘ during northern autumn between 80 and 90 km (see Fig. ). Note that the majority of ACE-FTS measurements occur at latitudes higher than 60∘ and that the above-mentioned differences at low latitudes are probably related to averaging on a smaller number of coincidences.

The Microwave Limb Sounder (MLS) is an instrument on board the Aura satellite, still operating since its launch on 15 July 2004. Aura/MLS was launched on a 98∘ sun-synchronous orbit with 13:45 LT ascending node at an altitude of 705 km. It performs measurements between 118 GHz and 2.5 THz with a 1.5–3 km vertical resolution . In this study we use MLS CO concentrations from the v4 dataset, retrieved from the J=2→1 rotational transition emission line at 230.5 GHz, which are considered to be reliable between 0.0046 and 215 hPa. Also, the suggested quality filtering has been performed . A previous comparison between SMR and MLS CO retrievals was presented in , based on older versions of the datasets. A validation study of the MLS CO v2 dataset has been performed by , and the differences between v2 and v4 datasets are documented in .

Because MLS uses the same observation technique as SMR, and because it has been functioning since 2004, a great number of coincident measurements could be used for this validation study. Indeed, 227 820 coincidences were found between the beginning of MLS mission and March 2019. The overall average comparison of these measurements with the ones from SMR is shown in Fig. . A negative difference of SMR with respect to MLS characterises all of the altitude range. The relative differences are oscillating between -40 % and -10 % and are characterised by a significant variability. This is due to MLS CO profiles being rather jagged, as reported in , where the MLS bias described is in accordance with what we obtain in this study. Also, the MLS–ACE bias which is reported in – although referring to older versions of the two datasets – is consistent with the one we measure. The difference we measure varies significantly with latitudes and seasons: between -40 and +40∘ and below 70 km, there are peaks of -150 % and -80 % during northern spring and autumn, respectively; while marked negative differences are registered during local summertime in both hemispheres, getting more pronounced toward high latitudes, especially around 50 and 70 km altitude with peaks of -120 %, as shown in Fig.  (this is also observed in the ACE–MLS comparison in ).

Odin/SMR CO data are compared with data measured by a ground-based remote-sensing instrument at the Onsala Space Observatory, OSO (57.4∘ N, 11.9∘ E), during 2002–2007. The recommended quality filtering has been followed.

The OSO instrument is a frequency-switched microwave radiometer for observations of the CO 1→0 transition at 115.27 GHz. During 2002–2007, a cooled Schottky single sideband mixer was used as the first stage. In 2014 the instrument was modified to a double-sideband system with a low-noise amplifier, at ambient temperature, as the first stage. During 2002–2007 a spectrometer with 20 MHz bandwidth and a resolution of 25 kHz was used. The optimal estimation method together with the forward model ARTS, the Atmospheric Radiative Transfer Simulator , has been used to retrieve vertical CO profiles from the measured spectra. The OSO instrument, the calibration and retrieval methods are described in .

Daily averages for 2002–2007 of CO profiles are retrieved from the OSO spectra. Only the 24 h average CO spectra with a signal-to-noise ratio larger than 2 are used in the retrievals. SMR data are regarded as coincident with OSO if the differences in latitude and longitude do not exceed ±5 and ±10∘ respectively and if the SMR data are taken within the OSO time average periods mentioned above. For the period 2002–2007, there are 89 coincident SMR profiles ( see Fig. ).

Figure  shows the mean vertical CO profiles for the coincident SMR and OSO datasets. The limb sounding SMR has a much higher vertical resolution than the upward-looking OSO instrument. To compensate for this difference, the SMR profiles, xsat, were convoluted with the averaging kernels, A, of the OSO instrument . 5xs=xa+A(xsat-xa), where xa is the OSO a priori and xs the smoothed SMR profile. The measurement response of SMR is very close to 1 in the 50–100 km range. The altitude range in Fig.  is more narrow since it is given by the range where the measurement response of the OSO instrument is >0.75.

OSO data from 2002–2007 have been compared to data from the satellite instruments ACE-FTS, MIPAS and MLS in a previous study . As seen in Fig. , during this period, the difference between SMR data and the coincident averaged data from OSO was found to be of 30 % at 50 km, decreasing with altitude to reach -10 % at 60 km and remaining constant up until 90 km altitude. The standard error of the mean, σx‾, for the average difference between SMR and OSO is about 5 % above 55 km (see Fig. ).