Principally, we considered observations from two data sets as coincident when the following criteria were satisfied:

a maximum temporal separation of 24 h

When different versions of the ACE-FTS, MIPAS, SCIAMACHY solar occultation and the SMILES data sets were compared with each other these coincidence criteria were not invoked. In these cases the exact same observations were compared. For SMR the different data sets are obtained on different measurement days, so that this exception does not apply. The same is true for MIPAS observations in the nominal mode (NOM) and the middle atmosphere (MA) mode. Also, the different SCIAMACHY observation geometries did not provide simultaneous measurements among them.

To apply the equivalent latitude criterion a scalar value was assigned to every observation. This value was based on an average of equivalent latitudes within the altitude range from 425 to 2000 K potential temperature, which essentially covers the entire stratosphere. The equivalent latitude information was derived from MERRA (Modern Era Retrospective-Analysis for Research and Applications, ) reanalysis data of potential vorticity.

To determine the coincidences we went through the individual observations of the first data set and determined the observations of the second data set that fulfilled the coincidence criteria. If multiple coincidences were found we chose the coincidence closest in spatial distance. This choice is optimised for the stratosphere, where the diurnal variation is small . Close to the tropopause and towards the middle mesosphere the diurnal variation in water vapour becomes more relevant. Once an observation of the second data set was determined to be a coincidence it was not considered any further as a possible coincidence for other observations of the first data set. Inherent in this approach is that the final coincidence pairs are dependent on the choice of the first data set: comparing ACE-FTS and HALOE, for example, can result in different coincidences than when comparing HALOE and ACE-FTS. To avoid inconsistent results based on this aspect, we only derived coincidences for the lower half of the data set comparison matrix and used those results for the upper half of that matrix. According to the sorting of the data sets in Table , the ACE-FTS v2.2 data set has been used as first data set in all comparisons. The SMR 489 GHz data set was considered as first data set only in the comparison with the SOFIE data set, while the latter never served as the first data set. We investigated the influence of the first data set choice based on test comparisons with the HALOE, ACE-FTS v2.2 and MIPAS-IMKIAA V5H data sets. Typically the differences in the biases were smaller than 0.05 ppmv or 1 % in absolute and relative terms, respectively. Larger deviations were mostly found at the lower-altitude limits of the comparisons.

The data sets considered in our comparisons have different vertical resolutions. A summary figure and a description of how the resolutions have been estimated is provided in the data set overview paper by . Differences in the vertical resolution only play a role for the comparisons at altitudes where the vertical distribution exhibits distinct structures; elsewhere the data sets can be compared directly regardless of the resolution differences. In our work this concerns first and foremost the hygropause region in the lowermost stratosphere. To decide in which comparisons a consideration of differences in the vertical resolution is necessary, we categorised the data sets into various classes according to their vertical resolution dz around the hygropause, using some reasonably selected resolution intervals. These classes are given by the first four columns in Table . The lower the class number, the better the vertical resolution of the data sets around the hygropause. The differences in the vertical resolution were considered in those comparisons where the two data sets were in different classes. The data set in the lower class was degraded to the vertical resolution of the data set in the higher class. In the table columns some data sets have been marked by an asterisk, indicating that these data sets have a limited observational coverage of the hygropause. Some retrieved profiles will include the hygropause, while others do not. Hence, some comparisons to these data sets may not necessarily need the consideration of differences in the vertical resolution in this altitude range. Yet, they have been taken into account for completeness.

The water vapour maximum in the vicinity of the stratopause is relatively broad and can accordingly be considered less problematic. Yet, some data sets exhibit a strong degradation of their vertical resolution in this altitude region, in particular in the lower mesosphere. To check any influence of this degradation we considered a fifth convolution class that includes data sets with a vertical resolution exceeding 6 km anywhere above 1 hPa in the resolution summary figure presented by . The differences in the vertical resolution are considered in the comparisons to those data sets that are not part of this convolution class and which cover altitudes up to at least 1 hPa. The GOMOS, HIRDLS, MAESTRO, SCIAMACHY limb, SMILES-NICT band A, SMILES-NICT band B and SMR 544 GHz data sets do not fulfil the latter criterion.

Due to the focus on differences in the vertical resolution in two different altitude regions, hybrid cases are possible, i.e. comparisons between data sets where one data set is better vertically resolved around the hygropause but worse than the other data set at high altitudes and vice versa. In total there have been 19 such cases in which we made two comparisons considering the differences around the hygropause and at high altitudes individually. The results will be presented later as a combination of these two comparisons. Up to 10 hPa, data from the comparison considering the differences in the vertical resolution around the hygropause are taken into account. Above, the results from the comparison focusing on the resolution differences at the stratopause and the lower mesosphere are used.

The degradation of the higher vertically resolved data sets followed the approach by . Using the averaging kernel A and the a priori profile xapriori of the lower-resolved profile, which we denote collectively as convolution data, the degradation of the higher-resolved profile xhigh can be achieved as follows: 1xdeg=xapriori+A⋅(xhigh-xapriori).

The degraded profile xdeg can then be compared directly to the lower vertically resolved data set. According to the equation the degradation is performed on the grid of the lower-resolved profile. The regridding of the higher-resolved profile to this grid follows the work of . For some data sets the averaging kernel considers the log space, i.e. A=Aln, based on a different retrieval approach. In these cases Eq. () has to be adapted to e.g.: 2xdeg=exp⁡{ln⁡xapriori+Aln⋅ln⁡xhigh-ln⁡xapriori}.

The third column of Table , which lists the sources and characteristics of the convolution data employed in our comparisons, indicates the data sets for which this aspect had to be considered. Please note that this is specific to the convolution data employed here. For example, the retrievals of the MIPAS-Oxford V5H and V5R MA data sets are performed in log space. But for these data sets we had to generate the convolution data ourselves (as described below, see the second column of Table ), which simply assumed a linear space. The degradation of the vertically higher-resolved data sets has been performed in the natural domain of the lower-resolved data sets, as specified in the fourth column of Table . Most data sets have volume mixing ratio (VMR) as a natural domain, and only some SCIAMACHY data sets use number density. Again this is specific to the convolution data used in this work. The retrievals of the GOMOS and SCIAMACHY solar Onion data sets, for example, use number density as the natural domain, but once more we needed to generate the corresponding convolution data which assumed volume mixing ratio as the natural domain. Temperature and pressure data for the conversion between volume mixing ratio and number density have been provided by all data set teams, either retrieved from the same set of measurements or from an auxiliary data source as reanalysis. provide a comprehensive summary of the retrieval spaces and domains of the individual data sets as well as the sources of the additional temperature and pressure information.

Another aspect is that the convolution data often exceed the altitude range covered by the particular profile to be degraded. This can be handled by either reducing the altitude range of the convolution data or extending the altitude range of the profile to be degraded. For that, a priori or other climatological data as well as model simulations can be employed. In practice the latter approach is often the better choice, leading to more reasonable results at the vertical boundaries of the degraded profile. After the degradation the extension data are removed again. Here, we utilised offset-corrected, climatological data from HAMMONIA (Hamburg Model of the Neutral and Ionized Atmosphere, ) as a function of month and latitude.

The second column of Table  lists the sources of the convolution data that have been employed in the comparisons. For most MIPAS data sets and the SCIAMACHY limb data set, the complete set of averaging kernels and the corresponding a priori data were available. A single characteristic averaging kernel and observation-dependent a priori data were provided for the MLS, SCIAMACHY lunar and solar OEM data sets. For the MIPAS-Oxford V5R NOM data set and both SMR data sets, collections of characteristic averaging kernels were supplied. They are dependent on time and latitude band. For the SMR 544 GHz data set there is also a dependency on the tropopause altitude. This data set only covers the upper troposphere and lower stratosphere, and the tropopause altitude is the main source of kernel variability. Since for the SMR data sets the convolution data are not saved by default, we re-retrieved the convolution data from at least 20 (50) observations that fell into the individual bins (monthly and 20∘ latitude; see Table ) for the 544 GHz (489 GHz) data set. For those bins where overall fewer observations exist we re-retrieved all of them. From this set we selected the convolution data for which the averaging kernel minimised the following quantity as being the most representative: 3∑j=lstartlendAd(j)-Ad‾(j)2.

Here, Ad denotes the averaging kernel diagonal that has been interpolated on a regular altitude grid prior to the analysis. Ad‾ is the average averaging kernel diagonal over the entire set of re-retrieved data for a particular bin and j is the index over the altitude levels lstart, …, lend that were considered. For the 544 GHz data set we took into account the altitude range between 10 and 25 km, while for the 489 GHz data set the altitude range between 15 and 50 km was considered.

For the remaining data sets averaging kernels are typically not part of their retrieval or were not provided to us. The latter applies to the MIPAS-Oxford V5H and V5R MA data sets. In these cases we generated averaging kernels ourselves based on Gaussian functions, using volume mixing ratio as the natural domain (as noted above) and kept the a priori constant at zero. The averaging kernel row Ar(j) for a given altitude index j was calculated as follows: 4Ar(j)=G(j)∑j=1naG(j), with 5G(j)=exp⁡-4⋅ln⁡(2)⋅[z-z(j)]2dz(j)2.

In the equation na represents the number of altitudes contained in the altitude vector z. Accordingly z(j) is the altitude for which the averaging kernel row is calculated and dz(j) describes the vertical resolution at this altitude. The vertical resolutions that have been used to generate the averaging kernels of the individual data sets are also given in the second column of Table . For the MIPAS-Oxford V5H and V5R MA data sets the vertical resolutions have been assumed, while for the other data sets they are typically based on the field of view. The only exceptions are the GOMOS and the SCIAMACHY solar Onion data sets. For the latter the vertical resolution is based on the smoothing of the absorption profiles, while the estimate for the GOMOS data set relied on actual averaging kernels. As altitude vector we considered the altitudes given in the data files for the individual observations. For the ACE-FTS data sets we used the data files with the tangent altitude grid and not those with the interpolated regular 1 km grid. When generating the averaging kernel for a given observation we set rows to zero for those altitudes where data were missing, either due to a lack of coverage or screening.

The comparisons essentially followed the approach outlined by , which compared various ozone data sets. The bias b‾(t,ϕ,z) between two coincident data sets for a given time period t and latitude band ϕ and for a specific altitude z has been calculated as 6b‾(t,ϕ,z)=1nc(t,ϕ,z)⋅∑i=1nc(t,ϕ,z)bi(t,ϕ,z), where nc(t,ϕ,z) denotes the corresponding number of coincident measurements and bi(t,ϕ,z) are the individual differences between them. These differences were considered both in absolute, 7bi(t,ϕ,z)=bi,abs(t,ϕ,z)=xi(t,ϕ,z)1-xi(t,ϕ,z)2, and relative terms 8bi(t,ϕ,z)=bi,rel(t,ϕ,z)=xi(t,ϕ,z)1-xi(t,ϕ,z)2[xi(t,ϕ,z)1+xi(t,ϕ,z)2]/2⋅100%, where xi(t,ϕ,z)1 are the individual water vapour abundances of the first data set and xi(t,ϕ,z)2 are the abundances of the second data set. As reference for the relative bias, several options were possible, like the first data set, the second data set in a comparison or the mean of the two data sets. In our work we used the last option. A reason for the decision was that satellite observations can have larger uncertainties and thus the mean may be a more appropriate choice . Another aspect was simply convenience. For a specific comparison there is no need to know which data set acted as reference. Eventual inconsistencies based on the combination of which data set was chosen to be the first data set in the comparison (see Sect. ) and which one was used as reference can be avoided. Finally, we also wanted to intentionally avoid any preference towards using a certain data set as reference but to compare all data sets on equal terms. Accordingly, the relative biases presented here are not comparable to those shown in the first SPARC water vapour assessment , where the HALOE data set was always used as reference. In general, any a posteriori attempt to relate the relative bias to the first or the second data set (instead of the mean among the data sets) is not meaningful nor appropriate, because there is some non-intuitive behaviour involved according to Eq. (). A simple example for that is provided in the Appendix.

Before the mean bias b‾(t,ϕ,z) was derived we performed an additional screening on the individual biases bi(t,ϕ,z) using the median and median absolute deviation (MAD, e.g.). After screening profiles with data points outside a reasonable abundance range, as described in Sect. , this is a second attempt to ensure meaningful bias estimates. We preferred this method over a screening using the mean and standard deviation due to its superior robustness with respect to larger outliers. Individual biases outside the interval 〈median[bi(t,ϕ,z)] ± 10 × MAD[bi(t,ϕ,z)]〉, with i=1, …, nc(t,ϕ,z), were discarded. For a normally distributed set of data, 10 × MAD corresponds roughly to 7.5 standard deviations. Hence this has not been a very strict screening, aiming to remove the most prominent outliers of individual biases bi(t,ϕ,z).

As indicated by Eqs. ()–() the biases were calculated for various sets of coincidences covering different time periods t and latitude bands ϕ as listed below:

time t: MAM, JJA, SON, DJF and all seasons together

The comparisons were performed on pressure as altitude scale and biases have been derived in the volume mixing ratio space. For this all data sets were interpolated on a common grid with 32 levels per pressure decade. Tropospheric data were intentionally removed using MERRA tropopause information. Comparisons in the troposphere will be presented by . Due to the finite vertical resolution of the individual data sets the removal of tropospheric data has not been perfect and at the lower boundary volume mixing ratios still remain that are associated with tropospheric conditions. In comparisons where differences in the vertical resolution among the data sets had to be considered, the tropospheric data were removed after the convolution to obtain optimal results. In the following figures, we only show bias results that are based on at least 20 coincidences to avoid spurious results. This primarily targets the lower and upper vertical limits of the comparisons, where typically the smallest numbers of coincidences tend to occur.

Given the large number of data sets, this work yields a large number of comparisons. Even though every comparison is unique, some sort of combination is needed to be able to present the results in a reasonable way. To summarise the bias results for a given data set considering a specific time and latitude band, we chose the median over all available comparisons (with an aggregation of the MIPAS results as described later in Sect. ). We tested other approaches but the median appeared to be the optimal choice for multiple reasons. It provides robust statistics in the presence of outliers (avoiding the need for additional screening) and it does not require any assumption of a certain probability distribution or a specific weighting of the individual comparisons.

Besides the bias estimation we performed an analysis of drifts among the different data sets. Unlike for the bias comparisons, we do not separate the drift comparisons by season. The drift analysis was based on monthly averaged biases derived from a minimum of five coincidences. Drifts were only calculated if the overlap period between the two data sets compared was at least 36 months. This period is defined as the time between the first and the last month where sufficient coincidences were found between the two data sets. The estimation of the drifts was done with a regression model that contained an offset, a single linear term for the drift as well as terms for the semi-annual (SAO), annual (AO) and quasi-biennial oscillation (QBO): 9f(t,ϕ,z)=Coffset(ϕ,z)+Cdrift(ϕ,z)⋅t+CSAO1(ϕ,z)⋅sin⁡(2⋅π⋅t/pSAO)+CSAO2(ϕ,z)⋅cos⁡(2⋅π⋅t/pSAO)+CAO1(ϕ,z)⋅sin⁡(2⋅π⋅t/pAO)+CAO2(ϕ,z)⋅cos⁡(2⋅π⋅t/pAO)+CQBO1(ϕ,z)⋅QBO1(t)CQBO2(ϕ,z)⋅QBO2(t).

In the equation, f(t,ϕ,z) represents the fit of the regressed bias time series b‾(t,ϕ,z); however here t describes all months in which the data sets that are compared have sufficient overlap (i.e. five coincidences; see above). C are the regression coefficients of the individual model components and Cdrift describes the drift that is sought. The SAO and AO are parameterised by orthogonal sine and cosine functions, while for the QBO the normalised winds at 50 hPa (QBO1) and 30 hPa (QBO2) observed over Singapore (1∘ S, 104∘ E) are used. These winds are closely orthogonal and have been compiled by Freie Universität Berlin (web page: http://www.geo.fu-berlin.de/met/ag/strat/produkte/qbo/qbo.dat, last access: 16 April 2019). pSAO and pAO represent the time periods of the semi-annual (0.5 years) and annual variation (1 year), respectively. The regression coefficients were derived following the method by using the standard mean error of the monthly averaged biases as statistical weights. In the regression autocorrelation effects and empirical errors are also considered, using the same approach as outlined by .

In our work we consider drifts as statistically significant when they exceed the 2σ uncertainty level. σ is defined as the absolute ratio between the drift estimate Cdrift and its uncertainty ϵdrift: 10σ=Cdriftϵdrift.

The previous WAVAS-II papers often received comments on the large number of MIPAS data sets (here 13 out of 33; see Table  for example) included in the assessment. As described in these publications the different MIPAS data sets are based on different measurement modes (with different vertical sampling) and, more prominently, are derived by four different processors with varying retrieval choices, as microwindows, vertical grid regularisation, spectroscopic database or a priori, for example. Here, we want to provide general results in the form of percentiles and histograms using all comparison results as well as summaries of data-set-specific biases as described at the last paragraph of Sect. . In general such results will always depend on the data sets that are considered. One of the WAVAS-II goals was to involve as many data sets as possible to provide a complete and realistic picture. There are, however, limits. For example, if all data sets in such an assessment were experimental (i.e. test or research versions), any general result derived from the combination of them would be rather meaningless. Also, the large number of MIPAS data sets in our assessment may be such a limit. Accordingly, we asked ourselves if our intended results may be influenced or skewed by the large number of MIPAS data sets. The typical biases among the different MIPAS data sets are significantly smaller than among the non-MIPAS data sets. They amount to roughly 0.1 ppmv (0.5 ppmv) for the MIPAS (non-MIPAS) data sets, considering large parts of the stratosphere. A similar picture is found in terms of typical drifts. In the stratosphere they are approximately 0.1 ppmvdecade-1 for the MIPAS data sets, while for the non-MIPAS data sets they correspond to 0.3 ppmvdecade-1. This indicates a relative similarity among the different MIPAS data sets in contrast to the non-MIPAS data sets. This can clearly affect our intended general results based on all comparison results. In addition, the summary biases (based on the median over all comparisons to the other data sets; see Sect. ) for any randomly picked MIPAS data set will be small because this data set is compared with many relatively similar ones. In contrast, a single non-MIPAS data set has to be compared with the bulk of the MIPAS data sets. If these comparisons disagree, the summary biases for this non-MIPAS data set will be large. Given these considerations we decided to aggregate the MIPAS results. For percentiles, histograms and full matrix plots, the aggregation has been performed as follows:

All MIPAS comparison results to a given non-MIPAS data set are combined using the median.

For the summary bias b‾S(t,ϕ,z) of a given data set, described in Sect.  and shown in Figs.  and   in the main paper as well as in Fig. S9 in the Supplement, the following approach has been chosen: (a)

For a non-MIPAS data set, like HALOE11b‾St,ϕ,z,HALOE=median〈b‾t,ϕ,z,ds1,medianb‾t,ϕ,z,ds2〉,where b‾(t,ϕ,z,ds1) represents all biases of the HALOE data set to the remaining non-MIPAS data sets and b‾(t,ϕ,z,ds2) describes the HALOE biases relative to all MIPAS data sets.

In numerous figures we supply as auxiliary information the number of comparisons or data points contributing to the results presented. Even when the MIPAS results are aggregated we still count the contributing results individually and do not condense them into a single contribution. For example, in Fig.  the bias summaries for the ACE-FTS v3.5 data set are presented. This data set could be compared with all 13 MIPAS data sets if coincidences at all seasons and latitudes are considered. Hence the number of comparisons contributing to these summary biases given in that figure (i.e. 31) includes these 13 comparisons.

We will show some results with and without the aggregation of the MIPAS results for the sake of comparison. In the main paper this concerns Figs. ,  and . In the Supplement, Figs. S2, S5 and S10 show percentiles and histograms without the aggregation of the MIPAS results that correspond to Figs. ,  and  in the main paper which take this aggregation into account. The two ACE-FTS and SCIAMACHY solar occultation data sets are also based on the same set of measurements. Therefore an aggregation of these results could also be considered. However, due to the small number of the data sets concerned (in relation to the MIPAS data sets), this has not further been pursued.

Figure  shows exemplarily biases of the SCIAMACHY solar OEM data set, considering coincident observations during all seasons and at all latitudes. The upper row considers biases in absolute terms, while the lower row focuses on biases in relative terms. Figure a and c show the biases to the individual data sets (i.e. SCIAMACHY solar OEM minus the other data set; see Sect. ). Figure b and d shows the corresponding summary biases. The red profile is based on the median over all comparisons (see Sect. ). The blue profile, additionally, considers the aggregation of MIPAS results as described in Sect. 3.5 and is also used for the summary of the data-set-specific results presented later in Sect.  and the Supplement. The legend provides information on the actual temporal and spatial coverage of the individual comparisons as a complement. Even though all latitudes are considered in the analysis, the comparisons are limited to the latitude range between 49 and 69∘ N according to the coverage of the SCIAMACHY solar OEM data set.

The comparisons indicate biases of the SCIAMACHY solar OEM data set that are typically within ±1 ppmv or ±20 % in relative terms. In most cases the biases are positive, but in some comparisons also negative biases are found. These negative biases are visible in the lower (roughly between 100 and 50 hPa) and upper stratosphere (between 3 and 1 hPa) as well as in the lower mesosphere (roughly above 0.2 hPa). In the uppermost altitude range this behaviour is systematically observed in comparisons to the MIPAS-Bologna data sets derived from the nominal mode observations, i.e. MIPAS-Bologna V5H and MIPAS-Bologna V5R NOM. For the other altitude ranges no such data-set-specific behaviour is observed. Beyond that, these example biases indicate more issues with specific data sets that will be presented more comprehensively in Sect.  and the Supplement.

In accordance with the individual bias results presented in Fig. a and c, the summary profiles shown in Fig. b and d generally indicate positive biases for the SCIAMACHY solar OEM data set compared with the other data sets. From the summary biases we find that the results are clearly influenced by the summary approach in the altitude range between 30 and 0.6 hPa. Here, the median over all comparisons yields consistently lower biases than the median considering the aggregation of the MIPAS results. Differences between these two profiles become as large as 0.4 ppmv, corresponding to 6 % in relative terms. This highlights the influence that the large number of MIPAS data sets can have in the comparisons, as discussed in Sect. . The summary profiles considering the aggregation of the MIPAS results exhibit the smallest biases below 25 hPa (around 0.25 ppmv or 5 %) and at 0.1 hPa (about 0.1 hPa or 2 %–3 %). At 10 hPa, and more prominently at 0.25 hPa, the biases maximise. At 10 hPa the bias amounts to 0.75 ppmv or 12 %, while the maximum in the lower mesosphere (also notable in the summary profiles without aggregation) exhibits smaller values (0.6 ppmv or 10 %). On average, the biases amount to 0.5 ppmv (about 8 %) in the stratosphere.

Figure a and c show the biases from the full matrix of comparisons. Here, the comparisons that include coincident observations during all seasons and at all latitudes are considered. Figure a and b show the results for the absolute biases. In Fig. c and d the results for the relative biases are given. Based on our comparison approach (see Sect. ) the results for the full matrix are symmetric around zero. In grey the comparison results without the aggregation of the MIPAS results are shown. With 33 data sets, theoretically 33×32=1056 comparisons (of which 528 are unique) are possible. But since not all data sets overlap with each other the actual number decreases to 862 comparisons (of which 431 are unique; see Fig. ). For eight comparisons (four unique) the biases are based on less than 20 coincidences at all altitudes and were thus not considered any further (see Sect.  or description of Fig.  in the beginning of this section). Hence, the unaggregated results are effectively based on 854 comparisons (427 unique). In blue the comparison results considering the aggregation of the MIPAS results are shown. As described in Sect.  the aggregation omits comparisons among the MIPAS data sets, reducing the amount of available comparisons to 770. After combining all MIPAS results in comparisons to non-MIPAS data sets, 348 comparisons remain for the full matrix.

Overall, the left column of Fig.  provides a good first impression of the typical envelope of biases in the observational database. Above 30 hPa the biases are typically within ±2 ppmv (or ±40 %). Below this altitude the biases can get significantly larger and even exceed ±5 ppmv or ±100 % on some occasions.

Based on the positive biases shown in (a, c) of Fig. , (b, d) show the corresponding 50 % (i.e. median, blue), 80 % (green) and 95 % (red) percentiles without (lighter colours) and with (darker colours) the aggregation of the MIPAS results. In general, the 50 % and 80 % percentiles are quite constant above 70 hPa, while the 95 % percentile shows much more variation in this altitude range. At altitudes below there is a distinct increase in the corresponding values. In addition, the percentiles considering the aggregation of the MIPAS results are larger than without this aggregation. At stratospheric altitudes the differences amount to 0.1 ppmv (2 %) for the 50 % percentile, 0.2 ppmv (5 %) for the 80 % percentile and 0.5 ppmv (7 %) for the 95 % percentile. Prominent exceptions from this behaviour are observed close to 0.1 hPa, below 200 hPa (except for 50 % percentile of the absolute biases) or between 2 and 1 hPa for the 95 % percentile of the absolute biases. In the following description we focus on percentiles considering the aggregation of the MIPAS results. The 50 % percentile is around 0.5 ppmv above 100 hPa and minimises at 60 hPa with 0.35 ppmv. Below 200 hPa the 50 % percentile exceeds 2 ppmv. In relative terms, the 50 % percentile is smaller than 10 % around 60 hPa and between 25 and 0.3 hPa. From 100 to 250 hPa the 50 % percentile increases from 12 % to 40 %. Below, the percentile actually decreases again to reach a pronounced minimum of 23 % at about 340 hPa. The 80 % percentile, considering the absolute biases, averages to 1.1 ppmv for altitudes above 100 hPa. A distinct minimum is again observed at 60 hPa (0.8 ppmv). Also, in the altitude range between 10 and 3 hPa, as well as around 0.5 and 0.1 hPa, pronounced minima of about 1 ppmv are visible. At 100 hPa the 80 % percentile amounts to 1.5 ppmv. With decreasing altitude it quickly increases and exceeds 5 ppmv slightly below 200 hPa. For the relative biases the 80 % percentile varies between 20 % and 35 % in the altitude range between 100 hPa and 10 hPa. Higher up, it is below 20 % with a few exceptions. Below 200 hPa the 80 % percentile ranges from 50 % to 70 %. Again a pronounced minimum is observed close to 370 hPa, similar to that observed for the 50 % percentile. The 95 % percentile is generally smaller than 2 ppmv with three noticeable exceptions. One concerns the altitude range below 70 hPa, in a similar fashion to that observed for the other two percentiles. Another exception is observed around 30 hPa, where a localised maximum of more than 5 ppmv is found. This behaviour can be attributed to the MAESTRO data set that is close to its upper boundary and exhibits high positive biases at these altitudes. The third exception is visible at 0.7 hPa, primarily attributed to the two SAGE data sets. In relative terms, the 95 % percentile ranges from 20 % to almost 80 % above 70 hPa. Below 100 hPa there are large variations and the values exceed 100 % occasionally.

To provide a more quantitative statement on how variable these percentiles are we applied a jackknife approach . Randomly we left out five data sets and recalculated the percentiles. We repeated this until every data set had been left out at least once. This approach yields a set of results (typically about 25 for the non-aggregated data and a dozen for the aggregated data) for a given percentile. From this set of results a standard deviation can be calculated. Given our random approach many different sets of results (and corresponding standard deviations) are possible. One characteristic realisation is shown in the Supplement in Fig. S1. Overall, standard deviations are in general around 0.05 ppmv (1 %) for the 50 % percentile without the aggregation of the MIPAS results. With this aggregation the standard deviations are typically twice as large in the stratosphere. Close to 0.1 hPa standard deviations around 0.25 ppmv (4 %) are observed. For the 80 % percentile the standard deviations amount roughly to 0.1 ppmv (1 %–5 %) and 0.2 ppmv (2 %–10 %) without and with the aggregation of the MIPAS results, respectively. For the 95 % percentile the standard deviations vary typically between 0.05 and 0.5 ppmv (2 %–10 %) when no aggregation of the MIPAS results is considered. If the aggregation is taken into account a larger variation is observed with peak values exceeding 1 ppmv (20 %).

In Fig.  the characterisation of the typical biases is extended by considering the 50 % percentile (median) for different seasons and latitude bands. These results take into account the aggregation of the MIPAS results and are again based on the positive biases only, as the percentile results shown in the previous figure. The left column of the figure considers the absolute biases, the right column focuses on the relative biases. The different rows focus on different seasons or their combination. The results for the different latitude bands are colour coded. On the right side of the individual panels the number of (unique) comparisons contributing to the results are given. As described in Sect. , the comparisons to the different MIPAS data sets are counted individually. In general, the 50 % percentiles exhibit a rather common altitude dependence for the different seasons and latitude bands. Below about 70 hPa the 50 % percentiles increase considerably and the highest values are observed in the tropics and subtropics. Below 200 hPa the values are typically beyond the upper limits of the x axes considered here, i.e. 1 ppmv in absolute terms and 20 % in relative terms. The 50 % percentiles are typically lowest in the altitude range from roughly 70 to 5 hPa. The values here vary between 0.25 and 0.5 ppmv in absolute terms and between 5 % and 10 % in relative terms. In this altitude region, the lowest values generally occur outside the polar regions. Higher up, there is a distinct increase of the 50 % percentiles, i.e up to about 1 hPa. At this altitude the 50 % varies approximately between 0.6 and 0.8 ppmv (roughly 8 % to 12 %). In JJA the values are a bit smaller, while in DJF there is a much larger variation among the latitude bands (percentiles minimise for the Arctic and maximise for the latitude band from 30 and 60∘ N). Higher up, the 50 % percentiles vary considerably with altitude and among the latitude bands, comprising values from 0.3 to 1 ppmv (4 % to 20 %). The smallest values are typically observed between 0.5 and 0.4 hPa. In MAM, SON and all seasons combined, the latitude band from the Equator to 30∘ N stands for these minimum values. In DJF this occurs prominently in the Arctic. The largest values are observed at 0.1 hPa, with pronounced variations among seasons and latitude bands.

Figure S2 in the Supplement shows the results corresponding to Fig.  without the aggregation of the MIPAS results. Overall, the altitude dependence is quite similar to the results shown here. However, without the aggregation, the values for the 50 % percentiles are smaller (like in Fig. ), as is the variation among the different latitude bands and seasons (a prominent exception occurs at 0.1 hPa). To further complement Fig. , the results for the 80 % and 95 % percentiles, again considering the aggregation of the MIPAS results, are shown in the Supplement (Figs. S3 and S4). For these larger percentiles the altitude dependence is somewhat different, in particular for the 95 % percentile, where less pronounced differences between stratospheric and lower mesospheric values are visible. Pronounced differences among the latitude bands occur in the lower stratosphere rather than the lower mesosphere.

For a last characterisation of the biases in the observational database we use histograms, as shown in Fig. . These results again use the positive biases only, consider data from all altitudes and take into account the aggregation of the MIPAS results. The histograms for the absolute biases (left column) use bins of 0.1 ppmv. For the relative biases (right column), bins of 2 % are considered. As in the previous figure the different panels consider different seasons or their combination. The different latitude bands are again colour coded. On the right side of the individual panels the number of data points contributing the results are given (again comparisons to different MIPAS data sets are counted individually; see Sect. ). Overall, the histograms exhibit a similar picture for the different seasons and latitude bands. The occurrence rates typically maximise within the first bin that ranges from 0 to 0.1 ppmv (between 11 % and 13 %). The decrease in occurrence towards larger biases (up to 0.8 ppmv) is steepest in DJF. For biases around 1 ppmv the occurrence has dropped to 2.5 % to 4.5 %. Biases beyond 3 ppmv occur in 2 % to 7 % of the comparisons. The lowest occurrences for these biases are observed in the Antarctic and tropics. In relative terms the occurrence of biases within the first bin from 0 % and 2 % varies between 10 % and 14 % depending on season and latitude band. A bias of 10 % occurs in about 6 % to 9 % of the comparisons. For biases beyond 50 % the occurrence is typically between 2 % and 8 %. The lower limit is observed for the latitude band between 30∘ S and the Equator in JJA. In contrast, the upper limit occurs in the Antarctic in DJF.

As for the previous figure we present the results without the aggregation of the MIPAS results, corresponding to Fig. , in the Supplement (Fig. S5). The results without the aggregation exhibit larger occurrence rates for the smallest biases (between 14 % and 19 %). Besides that, the variation among the different latitude bands is smaller. In addition, in the Supplement we present histograms that focus separately on data in the altitude ranges 100–10 hPa, 10–1 hPa and 1–0.1 hPa (see Figs. S6, S7 and S8), again considering the aggregation of the MIPAS results. The picture in the altitude range from 100 to 10 hPa is relatively similar to that observed in Fig. . In the altitude range from 10 to 1 hPa, the maximum occurrence rates occur over a larger bias range (roughly up to 0.5 ppmv or 10 %). Occasionally there are pronounced peaks in the occurrence rate, often involving data in the tropics and subtropics. Biases beyond 3 ppmv or 50 % occur more rarely than in the altitude range from 100 to 10 hPa. This behaviour is even more obvious in the altitude range from 1 to 0.1 hPa. Here, the histograms exhibit a pronounced variation among the different latitude bands. The smallest biases often show very high occurrence rates. Within the next bins a steep decrease in the occurrence rates is observed. Pronounced secondary maxima in the occurrence rates occur for biases beyond 0.5 ppmv or 10 %, depending on season and latitude.

Finally, we want to note that the consideration of differences in the vertical resolution among the data sets, as done in this work (see Sect. ), yields an improvement of the biases in 55 % of the comparisons (all data sets, times, latitude bands and altitudes). This primarily concerns altitudes above 70 hPa, and pronounced improvements are visible around 30 hPa in the stratopause and above 0.2 hPa. They can reach several tenths of a ppmv (or a few percent) in these altitude regions. Below 70 hPa there are both improvements and deteriorations, but with a clear tendency to the latter and as large as 100 % in relative terms. This indicates that differences in the vertical resolution are not the primary cause of the pronounced biases in this altitude region.

In this section an overview of data-set-specific results is presented. Figure  shows the summary biases for all data sets, based on the comparisons that consider coincidences during all seasons and at all latitudes. The absolute biases are given in the left column and the relative biases in the right column. For the sake of better visibility the results have been split into three panels. In the legend this separation is also reflected by the columns. In addition, the legend contains the information on the number of comparisons contributing to the individual summary biases (using the aggregation of the MIPAS results). As described in Sect.  these results consider the aggregation of the MIPAS results. Overall the smallest biases are observed in the middle and upper stratosphere. The largest biases occur below 100 hPa (larger than ±2 ppmv or ±50 %). On occasion pronounced summary biases are also visible in the lower mesosphere close to 0.1 hPa.

The first row comprises the results for the ACE-FTS, GOMOS, HALOE, HIRDLS, ILAS-II, MAESTRO and some MIPAS data sets (Bologna and one from ESA). Here, the biases are relatively small with ±0.4 ppmv, corresponding to relative biases of ±10 %. Larger (negative) biases are found for the GOMOS, HALOE (above 2 hPa) and ILAS-II data sets. Among them, the GOMOS data set shows the absolute largest biases. The GOMOS biases get more negative with increasing altitude above 75 hPa and reach values of -1.4 ppmv at 20 hPa. Up to 2 hPa the biases of the GOMOS data set vary between -1.7 and -1.1 ppmv (roughly -35 % to -25 %). Above 2 hPa the biases decrease again in size; however this is close to the upper limit at which water vapour information can be retrieved from the GOMOS observations. The biases for the ILAS-II data set generally do not exceed -0.8 ppmv, corresponding to less than -15 % in relative terms. For the HALOE data sets the biases vary between -0.5 and -0.2 ppmv (-5 % to -10 %) in the altitude range from 70 to 5 hPa. Towards the lower mesosphere the biases increase in size, where they are around -1 ppmv (-15 %). At 0.1 hPa the biases for the data sets shown in the first panel range from -0.9 (-20 %) to 0.4 ppmv (10 %). Below 100 hPa the absolute biases increase significantly in size. All data sets exhibit biases larger than ±2 ppmv at some altitude. Also, in relative terms, a large variation is observed; however the biases for ACE-FTS v2.2 and MAESTRO data sets remain largely within ±10 %.

In the second panel results for numerous MIPAS (ESA, IMKIAA and Oxford) data sets are shown, plus those from the MLS and POAM III data sets. For these data sets the biases are generally within -0.3 to 0.6 ppmv, corresponding roughly to relative biases between -5 % and 10 %. Larger biases are found for the MIPAS-ESA V5R MA, MIPAS-Oxford V5H and MIPAS-Oxford V5R MA data sets around the stratopause. Some data sets exhibit a pronounced increase in their biases above 0.3 hPa. This concerns the MIPAS-Oxford and the MLS data sets. At 0.1 hPa biases range, overall, from -0.4 to more than 2 ppmv, corresponding to relative biases of -10 % to 45 %. Below 100 hPa again large biases are visible, with a tendency towards negative values. Data sets for which the biases exceed -50 % below 100 hPa are MIPAS-ESA V7R, MIPAS-Oxford V5H and MIPAS-Oxford V5R NOM. The MIPAS-ESA V5R NOM (-25 % to 0 %), MIPAS-IMKIAA (-20 % to 5 %), MLS (±20 %) and POAM II (5 % to 15 %) data sets show typically smaller biases here.

The third panel of Fig.  presents results for data sets from the following instruments: SAGE, SCIAMACHY, SMILES, SMR and SOFIE. Here, some data sets exhibit quite pronounced biases. This concerns, on one hand, the experimental SMILES data sets. They cover the altitude range from slightly above 200 to 50 hPa and show good agreement between 70 and 60 hPa. Higher up, distinct positive biases (exceeding 1 ppmv or 20 %) are observed, while below negative biases of even larger size are visible. The summary biases for the SMR 544 GHz data set are almost entirely negative. Around 30 hPa they amount to -1.8 ppmv (exceeding -50 %). Above 15 hPa they get significantly smaller and switch sign at above 10 hPa, close to the upper limit of this data set. The biases for the SMR 489 GHz data set are quite low up to 10 hPa but start to increase significantly higher up. In the lower mesosphere this data set exhibits biases around -1.2 ppmv in absolute terms and -25 % in relative terms. In the lower half of the stratosphere the SAGE II, SAGE III, SCIAMACHY lunar and SOFIE data sets show very good agreement (typically within ±0.2 ppmv or ±5 %). Towards higher altitudes, biases increases to some extent, most prominently for the SAGE II data set above 3 hPa. The SCIAMACHY solar occultation data sets exhibit low biases in the lower stratosphere (around 5 %). Above 30 hPa they vary typically between 0.3 and 0.7 ppmv (5 % to 12 %).

Figure  shows the summary biases for the ACE-FTS v3.5 data set as a function of season and latitude, using the same layout as in Figs.  and . For all other data sets the corresponding figures are provided in the Supplement (Fig. S9). The comparisons to the ACE-FTS v3.5 data set show a rather consistent picture above about 100 hPa with relatively small variations among the different seasons and latitude bands. Between about 80 and 5 hPa the biases are typically within ±0.2 ppmv or ±5 %, with a clear preference towards negative biases. Towards higher altitudes the biases get more negative. They peak between 2 and 1 hPa with values from -0.8 (-10 %) to -0.2 ppmv (-2 %), depending on season and latitude. Above 1 hPa, the biases decrease again and switch sign at around 0.4 to 0.3 hPa. At 0.1 hPa there is a larger bias variation with season and latitude band. Here, the biases range between 0 and 0.9 ppmv (0 % to 15 %). Below 100 hPa a wide range of biases is observed, occasionally exceeding ±2 ppmv. The vast majority of the biases are negative. In relative terms they vary roughly between -40 % and 10 %.

As an example we consider the drift of the SMR 489 GHz data relative to other data sets in the latitude range from 30 to 60∘ N. The drift estimates are shown in Fig. a. Fig. b shows the corresponding significance levels, defined as the absolute ratio between the drift estimates and their associated uncertainties (see Eq. 10). In the legend, for every data set, two numbers are provided. The first number indicates the overlap period of the two data sets in months. As described in Sect. , a minimum overlap period of 36 months was required for a drift to be calculated. The second number shows during how many months the two data sets actually have a sufficient number of coincidences. Since this information is altitude dependent, the legend considers the maximum values over all altitudes. The example indicates mostly positive drifts for the SMR 489 GHz data set, which means that its trends in water vapour are more positive or less negative than the trend estimates derived from the other data sets. The drifts are clearly systematic. Even though the comparisons consider different time periods, and thus the estimates can vary, a very consistent picture of their altitude dependence is obtained. Pronounced drifts are observed around 50 hPa, which is close to the lower altitude limit where water vapour retrievals from SMR observations are possible. The drifts are as large as 2 ppmvdecade-1 and many of those are also statistically significant at the 2σ uncertainty level. Towards 20 hPa the drift estimates decrease to values smaller than 0.5 ppmvdecade-1. The comparisons with a few data sets even indicate negative drift estimates for the SMR 489 GHz data set. Above 20 hPa, the drifts increase again and maximise at around 0.5 hPa. Here, the drift estimates typically range from 1 to 1.75 ppmvdecade-1 and are in most cases statistically significant. Exceptions are the HALOE and SAGE II data sets, for which drift estimates are even larger than 2 ppmv. Above 0.5 hPa the drift estimates generally decrease again.

Figure  shows the drift estimates from the full matrix of comparisons, similarly to the bias results shown in Fig. . Again, these results consider the comparisons that incorporate coincidences during all seasons and at all latitudes. The upper panel shows the picture without the aggregation of the MIPAS results. The picture in the lower panel takes this aggregation into account. Overall, from the 862 comparisons (see Sect. ) in the full matrix, 470 comparisons yield drift results (see Fig. ), with the chosen minimum overlap period of 36 months. In 450 comparisons drift estimates that are statistically significant at the 2σ uncertainty level are found. The estimates that are significant are marked in light blue in the figure. The picture without the aggregation of the MIPAS results indicates a wide range of drifts, in particular below 30 and at 0.1 hPa. Some of the extreme values can be assigned to specific data sets. Between 30 and 10 hPa the envelope of the drifts is smallest. Here, they are generally within ±0.4 ppmvdecade-1. Also, based on the median, in this altitude range the smallest drifts are observed. Beyond that, we find that there is some dependence between the overlap period and the absolute drift size. Based on results above 100 hPa, the drift size typically decreases with increasing overlap period for periods up to 70 months. Beyond that overlap period, there is no obvious connection.

The picture with the aggregation of the MIPAS results is clearly sparser than that without the aggregation. Most prominently this is visible in the lower mesosphere, similarly to the corresponding picture for the biases shown in Fig. . In contrast to the unaggregated picture, a notable widening of the drift range at 0.1 hPa is not observed. At lower altitudes the picture is rather similar and the envelope of drifts exhibits a similar minimum region in the middle stratosphere. The typical drift sizes (based on the median) are typically larger for the picture with the aggregation of the MIPAS results, except above 0.2 hPa. Below 30 hPa the difference is of the order of 0.3 ppmvdecade-1. Above 20 hPa the difference is roughly 0.1 ppmvdecade-1.

In Fig.  drift histograms are shown for the different latitude bands, taking into account the aggregation of the MIPAS results. They consider the positive estimates from all altitudes that are statistically significant at the 2σ uncertainty level. In the upper-right corner of the figure the number of available data points is indicated. Bins of 0.1 ppmvdecade-1 are used for the histograms. The smallest drifts have the lowest occurrence rate in the Antarctic (about 2.5 %) and Arctic (4 %). In contrast, the largest occurrence rates are observed in the latitude bands from the Equator to 30∘ N (9.25 %) and from 15∘ S to 15∘ N (10.25 %). Beyond the smallest drift bin, the occurrence rates quickly rise. In fact, the maximum occurrence rates are observed for drifts between 0.1 and 0.2 ppmvdecade-1, consistently for all latitude bands. They vary between 12.25 % (60 to 30∘ S and Antarctic) and 18 % (30∘ S to Equator and 30 to 60∘ N). Towards larger drifts the occurrence rates generally decrease. However, there are some prominent additional maxima, for example in the Antarctic for drifts between 0.4 and 0.5 ppmvdecade-1 (occurrence rate of 12 %). For drifts of 1 ppmvdecade-1 the occurrence rate is between 2.75 % and 4.25 %, except for the latitude bands from 15∘ S to 15∘ N and from the Equator to 30∘ N. In those latitude bands again pronounced additional maximum in the occurrence rate (7 % to 7.5 % for the bin between 1.0 and 1.1 ppmvdecade-1) are visible. For drifts of 2 ppmvdecade-1 the occurrence rate is smaller than 1.5 % and minimises for the Antarctic. Drifts larger 3 ppmvdecade-1 occur in 2 % to 7.5 % of the comparisons with the highest occurrence rate for the latitude band from 60 to 30∘ S and the lowest occurrence rate for the latitude band between 15∘ S and 15∘ N.

In the Supplement, in Fig. S10, the corresponding picture without the aggregation of the MIPAS results is shown. In contrast to Fig. , the maximum occurrence rates are larger (between 14.5 % and 19.25 %). Prominently, the maximum occurrence rate in the Antarctic is found first for drifts between 0.3 and 0.4 ppmvdecade-1. Also, for the latitude band from 30 to 60∘ N and the Arctic, the maximum occurrence rate is observed at larger drifts than for the aggregated results. Note that secondary maxima in the occurrence rate are not visible in the results without the MIPAS aggregation. The occurrence rates for drifts larger than 1 ppmvdecade-1 are on average smaller than for the picture with the aggregation of the MIPAS results. Also, the variation with increasing drifts and among the latitude bands is smaller in Fig. S10.

In this section we provide a summary of data-set-specific drift results, focusing on the MIPAS-ESA V7R (Fig. ) and the MLS data sets (Fig. ). All remaining results can be found in Fig. S11 in the Supplement. No results are available for the ILAS-II, MIPAS V5H and SMILES data sets. These cover a too-short time period for a drift analysis according to our criteria defined in Sect. . A summary figure for given data set shows all drifts that are statistically significant at the 2σ uncertainty level relative to this data set. For better distinction between the data sets, results are only plotted at every second altitude, i.e. with a sampling of ∼1 km (see Sect.  as well as Figs.  and ). The different panels focus on different latitude bands, as indicated in the upper left. For some of the data sets (e.g. GOMOS, HALOE, POAM III; see the Supplement) there are occasionally no results for any of the latitude bands. In these cases there will be information explaining why, in accordance with the list below:

No comparisons. No comparisons to other data sets could be made due to missing overlap (at least 20 coincidences; see Sect. ).

In the legend all possible data sets are listed. Colour coding is used to convey extra information to which data sets may or may not contribute results (on a global scale):

Dark grey means no comparisons.

The comparisons to the MIPAS-ESA V7R data set exhibit predominantly negative drifts as visible in Fig. . These negative drifts minimise in size, typically around 20 to 10 hPa (up to -0.3 to -0.4 ppmvdecade-1), and increase towards lower and higher altitudes. Around 50 hPa large negative drifts (beyond -1 ppmvdecade-1) are observed relative to the SMR 489 GHz data set in all latitude bands. Below 100 hPa drifts of similar size are found more frequently relative to a number of data sets. In the mesosphere the comparison to SMR 489 GHz data set again yields large negative drifts. They often peak in size around 0.5 hPa (in the polar regions a bit higher up) with values between -2 and -1.2 ppmvdecade-1. At 0.1 hPa the negative drifts vary between -1.6 and -0.3 ppmvdecade-1, based on the comparisons to the other MIPAS V5R NOM, MLS and SMR 489 GHz data sets. Notable positive drifts (beyond 1 ppmvdecade-1) are found below 20 hPa relative to the HIRDLS, GOMOS, MAESTRO data sets at selected latitudes. Smaller positive drifts occur in the comparisons to the MIPAS V5R NOM data sets derived with the Bologna, IMKIAA and Oxford processors as well as some SCIAMACHY data sets. In the latitude bands from 90 to 60∘ S and 60 to 30∘ S, drifts up to 0.5 ppmvdecade-1 are observed in the altitude range from 8 to 1 hPa in the comparisons with the ACE-FTS, MLS and SCIAMACHY lunar (only Antarctic) data sets. Close to 0.1 hPa pronounced positive drifts are often found relative to the any of MIPAS-Bologna data sets (except in the latitude from 15∘ S to 15∘ N and 60 to 90∘ N).

The MIPAS V5 data sets are prone to a small drift since the correction coefficients for the non-linearity in the detector response function have changed over time and this is not accounted for in the V5 calibration . In the MIPAS V7 calibration a time dependence of these coefficients is considered and, thus, data sets derived from this calibration are expected to show fewer drifts. Compared with its predecessor data set, i.e. MIPAS-ESA V5R NOM, the MIPAS-ESA V7R data set indeed exhibits a reduced number of significant drifts. Considering the comparisons with non-MIPAS data sets, the number is reduced by 4.6 %. If only comparisons with the ACE-FTS v3.5 and MLS data sets are taken into consideration, the reduction amounts to 25 %. In contrast to the MIPAS-ESA V7R data set, the MIPAS-ESA V5R NOM data set shows a predominance of positive drifts (see Fig. S11 in the Supplement). This might be a hint that the correction coefficients used in the MIPAS V7 calibration overcompensate for the original issue in the V5 calibration.

The comparisons with the MLS data set (Fig. ) yield both negative and positive drifts with a slight prevalence of the former. Typically the drift estimates are within ±0.5 ppmvdecade-1. Larger drifts are prominently found in the comparisons with the GOMOS (negative), HIRDLS (primarily positive) and SMR 489 GHz data sets, which highlight issues with these data sets rather than with the MLS data set itself. Positive drifts are consistently found relative to the ACE-FTS data set (around 0.2 ppmvdecade-1). A similar picture is observed in the comparisons with the SCIAMACHY solar occultation data sets. In the lower stratosphere the comparisons with the MIPAS-ESA V5R NOM (roughly up to about 60 hPa), MIPAS-IMKIAA V5R NOM (up to about 10 hPa) and MIPAS-Oxford V5R NOM (up to about 30 to 20 hPa) exhibit positive drift estimates. In the lower mesosphere the drifts are positive relative to the MIPAS-Bologna, MIPAS-ESA V7R (not in the Antarctic and from 60 to 30∘ S) and the MIPAS-IMKIAA V5R NOM (except in the Antarctic) data sets. In addition, the comparisons with the SOFIE data set indicate positive drifts in the Antarctic (with a gap between 9 and 1.5 hPa) and the Arctic lower mesosphere. In contrast, negative drifts are found relative to the MIPAS-Bologna data sets below about 1 hPa, the MIPAS-ESA data sets (except those positive drifts mentioned before), the V5R MA data sets derived with the IMKIAA and Oxford processors, the MIPAS-Oxford V5R NOM data set above about 30 to 20 hPa as well as the SMR 489 GHz data set.

In this work we present drift results based on coincident observations. In a preceding WAVAS-II work we presented drift estimates among the different data sets based on the comparison of their zonal mean time series . The latter approach has the advantage that more data can be used, typically also allowing more comparisons. The disadvantage of the zonal mean time series approach is that it is more prone to sampling errors (in time and space) and does not take into account differences in vertical resolution among the data sets, which, under circumstances, may influence the drift estimates. Here, we want to compare the results from these two comparison methods and assess how often the drift estimates differ or not. For that, Fig.  shows the drift estimates among the different data sets, calculated using the profile-to-profile method, in a matrix form considering data in the latitude band from 80 to 70∘ S at 80, 10, 3 and 0.1 hPa (from top to bottom). The drift estimates are based on the difference time series between the data sets given at the x axis and the data sets given at the y axis. Data sets are only shown if they yield any result at a given altitude to optimise the available space. The drift estimates are colour coded. In addition to that, different types of auxiliary information are provided in the result boxes. In the upper left, the overlap period of the two data sets is given as well as the number of months the data sets actually overlap. A non-significant drift (at the 2σ uncertainty level) is indicated by a slant. For contrast a significant drift is marked by a green frame and the significance level is noted in the lower-right corner. As such the figure is directly comparable with Fig. 11, shown in the work of . Both figures exhibit a number of similar patterns. At 0.1 hPa the drift size is the largest among the four altitudes with prominent examples in the comparisons relative to the MIPAS-Bologna V5R MA and SMR 489 GHz data sets. At 3 hPa the large drifts relative to SMR 489 GHz are again a common feature among the two drift estimation methods. Smaller drift sizes are observed both at 10 and 80 hPa with exceptions attributed to the same data sets.

For a more quantitative comparison, Fig.  shows the actual drift differences ΔCdrift between the two approaches, i.e. 13ΔCdrift(ϕ,z)=Cdriftp2p(ϕ,z)-Cdriftzmts(ϕ,z) in the same style as Fig. . Here, Cdriftp2p represents the drifts derived from the profile-to-profile comparisons (this work) and Cdriftzmts the drifts based on the comparisons of the zonal mean time series . The uncertainty of this difference εdrift is given by 14εdrift(ϕ,z)=εdriftp2p(z)2+εdriftzmts(ϕ,z)2, where εdriftp2p and εdriftzmts are the drift uncertainties from the two approaches and any covariance among them is neglected. The characteristic numbers in the result boxes of Fig.  correspond to the profile-to-profile comparisons. Differences not statistically significant at the 2σ uncertainty level are again marked by a slant, while for significant differences the significance level is once more provided in the lower-right corner. The largest differences between the drift estimates from the two approaches occur at 0.1 hPa and amount to 0.4 ppmvdecade-1 on average. Prominent examples are visible in comparisons with the ACE-FTS v3.5, SMR 489 GHz and SOFIE data sets. Also, some comparisons among MIPAS data sets exhibit large differences in the drift estimates. In contrast, at 3 hPa the drift differences minimise among the four altitudes shown in Fig.  (on average 0.15 ppmvdecade-1). Also, at 10 and 80 hPa, relatively small differences in the drift estimates from the two approaches are found. A few noteworthy exceptions occur in comparisons with the SMR 544 GHz and SOFIE data sets. Even though the drift estimates derived from the profile-to-profile and zonal mean time series comparisons occasionally exhibit larger differences, they are only statistically significant (at the 2σ uncertainty level) in 2.6 % of the comparisons shown in Fig. .

In addition, the zonal mean time series comparisons presented by consider the latitude bands from 15∘ S to 15∘ N and from 50 to 60∘ N. For these latitude bands the figures corresponding to Figs.  and  are shown in the Supplement (see Figs. S12, S13 and S14, S15). In summary, for the tropical band, the drift differences maximise on average at 80 hPa, close the top of the highly variable tropical tropopause layer. The minimum differences are observed at 3 hPa for the latitude band from 80 to 70∘ S. In total, in 6.0 % of the comparisons, the drift estimates from the two approaches differ significantly. For the latitude band from 50 to 60∘ N the differences are largest at 0.1 hPa and smallest at 3 hPa. In 3.8 % of the comparisons the drift differences are significant at the 2σ uncertainty level in this latitude band.

For the eight latitude bands primarily considered in this work and altitudes above 100 hPa, overall, in 3.2 % of the comparisons the drift estimates derived with the profile-to-profile and zonal mean time series comparisons differ at the 2σ uncertainty level. On average, the differences in the drift estimates are largest for comparisons among occultation data sets (i.e. ACE-FTS, GOMOS, HALOE MAESTRO, POAM, SAGE, SCIAMACHY occultation and SOFIE). For the remaining data sets with more dense temporal and spatial sampling (i.e. HIRDLS, MIPAS, MLS, SCIAMACHY limb, SMR) the differences are clearly smaller. At the same time the percentage of significant differences in the drift estimates is smallest for comparisons between the occultation data sets and largest for comparisons between more dense data sets. Comparisons between occultation and more dense data sets yield statistics in the middle.

Overall, the differences in the drift estimates from the two approaches minimise in the altitude range between 5 and 2 hPa (typically, based on the median, between 0.05 and 0.1 ppmvdecade-1). The largest differences are observed towards 100 and 0.1 hPa (typically beyond 0.15 ppmvdecade-1 median-wise). For individual comparisons the differences between the drift estimates derived with the profile-to-profile and zonal mean time series comparisons can be significantly larger, as visible in the example shown in Fig. .