We begin by analysing the spatial distribution of the stratospheric CH4 column abundance and identifying regions where the total column is most sensitive to stratospheric column variability. We compute the pressure-weighted column averaged dry air mole fraction of CH4 using the CH4 fields from the C-IFS model for the year 2010. The profile is then separated into two parts and the tropospheric and stratospheric partial column averaged mole fractions are computed for which we use the 6-hourly tropopause information from the C-IFS model. Figure 1 shows the column-averaged abundance of CH4 for the stratospheric and tropospheric partial columns as well as the total column for the months June to August, 2010. This figure shows that for the tropical regions, the spatial variability in the total column XCH4 is largely driven by the tropospheric CH4 column abundance, which can be attributed to spatial variability in surface fluxes. In the Northern Hemisphere, the equator-to-pole gradient of the stratospheric CH4 column is opposite to that of the tropospheric CH4 column such that the stratosphere acts to smooth the overall tropics–pole gradient in the total column.

Figure 2 shows the variability in the two partial columns and the total column CH4 over the 3-month period. We see that the tropospheric column variability is largest around the Tibetan Plateau region. The highlands of the Tibetan Plateau are regions of high tropopause variability due to their high elevation (between 3000 and 8848 m above sea level) which cause strong stratosphere–troposphere interaction events like tropopause folds to occur. These events can cause stratospheric air to be transported into the troposphere, which is responsible for the variability in the tropospheric and stratospheric partial column. The tropospheric column variability in this region is as high as 40 ppb, while in most other regions of the world the tropospheric CH4 values remain comparatively constant where the variability is less than 15 ppb. The variability in the tropospheric column is also large for regions that form the CH4 hotspots such as wetlands and rice-growing regions of Bangladesh, India, and China, and anthropogenic emissions, possibly exacerbated by wildfires in 2010, in western Russia.

The stratospheric column variability, on the other hand, has a zonal distribution. This is because the variability in the stratospheric column is directly linked to the tropopause height (Fig. 3). As expected, the mean tropopause height is higher in the tropics (90–100 hPa) than at extratropical and polar latitudes (> 150 hPa). In the high- and mid-latitudes, especially in areas at the edge of the Southern Hemisphere polar vortex, the spatial gradient of the tropopause is at its maximum. The tropopause, therefore, interacts with the jet stream and extratropical weather systems, causing it to move up and down. The vertical movement of the tropopause results in areas of high tropopause height variability during the austral winter months (Fig. 3b), which therefore impact the variability in the stratospheric column. During months of boreal winter (not shown), this effect is shifted to the Northern Hemisphere. On the other hand, since the tropical tropopause is rather flat and has a weak spatial gradient, it causes little or no variability in the stratospheric partial column except in the Tibetan highland region (90 ppb).

The impact of the stratosphere on the total column CH4, XCH4, is largely linked to two factors: (i) the mass of CH4 in the stratosphere relative to that in the total column and (ii) its associated variability due to dynamical processes in the atmosphere such as the movement of the tropopause. This means that the contribution of the uncertainties in the stratospheric CH4 to the total column abundance of CH4 is likely to be significant in regions where at least one of the two driving factors is high. For regions where both these factors are low, the XCH4 value is less sensitive to uncertainties in the stratospheric CH4 component. We perform a qualitative analysis of how these two driving factors vary spatially during the different seasons of the year to identify regions where the stratospheric processes directly influence the total column and regions where the impact is not significant.

We define two quantities: CH4mass fraction(fstr)=mass ofCH4in the stratospheric column (in kg)mass ofCH4in the total column (in kg),CH4mass fraction variability(σstr)=standard deviation offstr. In the context of extending the aircraft measured profiles into the stratosphere, it can be said that if an aircraft profile is present in regions having both low fstr and low σstr, the total column is likely to be less sensitive to the choice of data source used as an assumption for the stratosphere. Figure 4 shows the C-IFS stratospheric CH4 mass fraction fstr plotted against its variability σstr for five different latitude bands during the different seasons. It can be seen that, overall, the tropics are regions with both low fstr and low σstr throughout the year, while the extratropical and high-latitude regions have high values for either one or both of these factors, making the computed value of the total column in these regions more sensitive to the CH4 variability in the stratosphere. During the austral winter months, the Southern Hemisphere shows particularly high variability in the stratospheric CH4, which is likely to be due to the impact of the polar vortex dynamics.

The latitudinal distribution of airports visited by the MOZAIC fleet during 1 year (2004), reflecting the typical yearly MOZAIC flight statistics shows that while almost all the profiles are measured in the Northern Hemisphere, they are mostly concentrated in the mid-latitude region (between 40 and 55∘ N). This is because of the large air traffic between Europe and North America by the airlines participating in MOZAIC. Of all the MOZAIC profiles measured in 1 year, only a small fraction falls within the tropical region (about 17 %). It is thus reasonable to infer that for the passenger aircraft profiles with sampling comparable to MOZAIC, the stratospheric variability is critical to determining the total column CH4 abundance and needs to be accounted for using an appropriate method of profile extension into the stratosphere.

In the following sections, we compute and compare the uncertainty introduced in the total column at the MOZAIC airport locations using the model output, climatology data and a priori profile as stratospheric extensions.

We compare the model profiles from C-IFS and TOMCAT models to coincident satellite observations from MIPAS. These measurements are independent since these are not assimilated into the models. The 6-hourly model profiles are interpolated to the time and location of the satellite observed soundings – linear in time and closest neighbour in space. The MIPAS profiles are then interpolated onto the coarser model vertical grids. We do not apply averaging kernel information to the coincident model profiles since the impact is not expected to be significant (Laeng et al., 2015; Ridolfi et al., 2011). In order to make a true comparison between the stratospheric levels of the profile simulated by the two models we use the C-IFS tropopause height for identifying and analysing the stratospheric levels for the TOMCAT model. Because the TOMCAT model is driven by winds from ERA-Interim, this definition of the tropopause height should be consistent with the transport of TOMCAT.

Comparison of zonal mean model profiles and coincident satellite observations for the months September to November is shown in Figs. 5 and 6. We see that the C-IFS is biased high compared to the observed value from MIPAS in the lower stratosphere just above the tropopause (at around 100 hPa) by about 80–100 ppb during the months of September to November (Fig. 5d). This bias reverses in sign and increases to about 200 to 300 ppb in the middle stratosphere (10 hPa pressure level). In the tropical latitudes this bias shifts to the upper layers of the stratosphere (around 1 hPa). Furthermore, a comparison between Fig. 5a and b shows that the C-IFS model simulates a steeper vertical gradient in the CH4 concentration in the stratosphere as compared to that observed by MIPAS.

The comparison between TOMCAT and MIPAS for the same period shows that TOMCAT is biased high by about 100 ppb compared to the MIPAS soundings in the lower stratosphere (100 hPa). In the middle stratosphere (10 hPa) the bias reverses in sign (-100 to -200 ppb in the Southern Hemisphere and around -50 ppb in the Northern Hemisphere mid-latitudes) and again becomes positive (∼ 100 ppb) in the upper stratospheric layers. Thus, the positive and negative bias patterns in the stratospheric levels occur alternately. Also, the gradient in the CH4 concentration in the stratospheric levels as simulated by TOMCAT is more comparable to the observations and is not as steep as that modelled by C-IFS.

In order to further investigate the spatial patterns of the stratospheric bias, we evaluate the satellite observed CH4 concentrations and the models sampled at the locations of the satellite measurements at a given pressure level. We chose 10 hPa, since the observed biases are highest around this pressure. From Figs. 7c, d and 8c, d, we find that, for both instruments, the bias in the C-IFS model forms zonal bands with little variability. Since the data density from MIPAS is much higher, these patterns are more clearly seen in Fig. 7. From Figs. 7e and 8e we see that the TOMCAT model bias in the middle stratosphere with reference to the two satellite instruments compare well with each other, with the highest bias during September–November 2010 being around the North Pole (∼ 400 ppb). The spatial distribution of the bias is not quite as zonal as is seen in the C-IFS and is more irregular in structure. This difference in the bias pattern between the two models can be attributed to the fact that the TOMCAT simulation used here fails to capture the observed zonal structure of the CH4 distribution (Fig. 7c), while the C-IFS does a much better job at simulating the longitudinal patterns (Fig. 7b) in the satellite data from MIPAS or ACE-FTS measurements.

A similar comparison was made for the two models for the other seasons of the year (not shown) and it was seen that these biases are a constant feature throughout the year with the magnitude and distribution being almost the same for all seasons. We also compared the CH4 profiles from the ACE-FTS instrument and the C-IFS fields to investigate if the biases obtained by comparison with MIPAS are in agreement (Fig. 6). Although MIPAS has much better data coverage than ACE-FTS, with measurements made at all latitudes and the number of MIPAS profiles measured per day being significantly larger than those measured by ACE-FTS, we find that the model bias as observed by ACE-FTS is similar in magnitude and distribution to that observed by MIPAS and the two comparisons are in good agreement with one another. The CH4 gradient in the vertical as observed by ACE-FTS is also much shallower than that simulated by C-IFS, a feature consistent with that seen by MIPAS.

We further compute the column-averaged bias for the stratospheric levels in the C-IFS and TOMCAT models. Comparing the bias allows us to evaluate the sources of model error in the stratospheric extension of aircraft profiles. Here, we make an implicit assumption that the aircraft profiles reach the altitude of the tropopause and that the entire column above the tropopause height is unmeasured and has to be extended artificially using the model data. Since the MIPAS instrument offers the advantage of more complete global coverage over ACE-FTS, we use it as our reference for the subsequent analysis of stratospheric column bias. We compute the overall bias in the stratospheric column by carrying out a mass-weighted integration of the bias in each model with respect to the satellite soundings from MIPAS for each pressure level above the tropopause. We restrict our analysis to only those latitudes where the aircraft profiles are likely to be measured – i.e. we do not consider the latitudes poleward of 60∘ S and 80∘ N. Thus, we exclude the polar regions, over which no commercial aircraft are likely to fly and it is reasonable to exclude those latitudes from the analysis for the purposes of this study.

Figure 9 shows the zonally averaged stratospheric column bias relative to MIPAS for C-IFS and TOMCAT. We see that the overall absolute magnitude of the bias in the stratospheric column of the C-IFS is less than 15 ppb. This bias translates to less than 1 % of the total column CH4 abundance. The bias magnitude changes with season and latitude. Overall, in the Northern Hemisphere the bias is lowest during the autumn months (SON) and highest in spring (MAM). The opposite is observed in the Southern Hemisphere. The errors in the Southern Hemisphere could be partly due to the inability of the model to capture the dynamics of the polar vortex and the extratropical storm track that develops in the Southern Ocean during autumn–winter months. These are associated with tropopause folds in the development of synoptic weather systems which are generally not as well captured as those in the Northern Hemisphere due to a sparser observing system (Bauer et al., 2015; Haiden et al., 2015). The summer and winter bias values lie intermediate to the spring and autumn bias globally. The zonal mean bias in TOMCAT has a similar seasonally and latitudinally varying nature as C-IFS albeit with a smaller magnitude. The bias throughout lies between ±5 ppb, which translates to 0.2 % of the total column value, which is much smaller than the C-IFS model bias. This is likely to be due to the fact that these values are averages over all longitudes and, therefore, any variation in the bias along the longitude will be smoothed out.

We further analyse the stratospheric column bias at actual aircraft profile locations to get a realistic estimate of the bias from both models. For comparison, we use MIPAS profiles measured on the same day as the aircraft profiles and within ±2∘ longitude and latitude in space. We find that, for real aircraft profile locations, both models have the same mean bias (about -9 ppb) in the stratosphere (Fig. 10, Table 1). The C-IFS bias, however, has a higher precision (standard deviation of 6.5 ppb) compared to TOMCAT (standard deviation of 12.8 ppb). As per the random error (precision) and systematic error (accuracy) requirements specified in Buchwitz et al. (2011), the errors from both models are lower than the minimum (“threshold”) accuracy and precision requirements for XCH4. In addition, the C-IFS model random error also meets the targeted precision (“goal”) requirement (9 ppb).

We now explore the potential of climatology-based approaches as stratospheric extensions for the aircraft profiles that, for instance, could be based on balloon-based measurements, satellite limb soundings or those from AirCore. Climatology-based measurements are typically long-term averages having a much sparser global coverage compared to global model output. For this part of the study, no real observations are used and we only evaluate the contribution of sparse data coverage and temporal averaging to the stratospheric column uncertainty. In order to do this, we analyse two main cases:

mmC-IFS: in this case, we use monthly mean C-IFS fields for our stratospheric assumption instead of full C-IFS fields with 6-hourly output (the FULL C-IFS case). This means that we do not account for the synoptic scale variability in the CH4 vertical distribution. This helps us examine the impact of temporal variability in the data source on the stratospheric column bias.

We find that the mean bias increases slightly to -14 ppb in the case where only monthly mean fields from C-IFS (mmC-IFS) are used, and increases to -32 ppb in mmC-IFS@ACE-FTS. The variability increases strongly to 49 and 200 ppb for the two cases. In mmC-IFS@MIPAS, the mean reduces to 3 ppb which is better than the mean bias in the FULL C-IFS (-9 ppb). However, since the variability in the stratospheric column error is still about 10 times larger than that of the FULL C-IFS (around 57 ppb), it cannot be deemed fit for estimating the stratosphere well. As expected mmC-IFS@ACE-FTS performs poorly as compared to mmC-IFS@MIPAS both in terms of the bias and variability, owing to the fact that the monthly sampling from ACE-FTS is much sparser than that of MIPAS.

Finally, we evaluate the possibility of using a priori profiles used in satellite data retrievals to extend aircraft profiles into the stratosphere. For this, we use the University of Leicester GOSAT Proxy XCH4 retrieval (Parker et al., 2011). The a priori profile used in this retrieval is based on a CH4 simulation using the TM3 transport model. Figure 12 shows the distribution of the stratospheric column bias at the MOZAIC airport locations, with respect to collocated MIPAS CH4 profiles. We see that the mean error in the stratospheric column is about -14.7 ppb while the random error amounts to 53 ppb (Table 1). These values are comparable to those obtained from the mmC-IFS case in Sect. 3.4 but are still much higher than the bias and random error obtained from the C-IFS and TOMCAT models.