We carried out a number of sensitivity simulations using CLaMS in its 3-D version . CLaMS is a Lagrangian transport model based on 3-D forward trajectories and an additional parametrization of small-scale mixing. The time-dependent irregular model grid is defined by Lagrangian air parcels, which follow the flow. An advantage of the Lagrangian approach for simulating stratospheric transport is the ability to resolve small-scale features, which are often below the possible resolution of high-resolved Eulerian models . Such small-scale features are frequently observed in stratospheric trace gas distributions as elongated filaments, related to the stretching and differential advection in sheared flows .

The advection of forward trajectories in CLaMS is calculated based on a fourth-order Runge–Kutta scheme, as described by , using 6-hourly wind fields from meteorological reanalysis data. For vertical transport, CLaMS uses a hybrid vertical coordinate, which is an orography-following σ coordinate at the ground and transforms into potential temperature above . Above σ=0.3 (about 300 hPa), the vertical coordinate is purely isentropic, and vertical transport is driven by the reanalysis total diabatic heating rate . For the simulations considered here we use a horizontal resolution of about 100 km. The vertical resolution is defined via a critical aspect ratio α of 250 . This value expresses the ratio between horizontal and vertical scales and is about 400 m around the tropical tropopause, degrading below and above it . The simulations cover the atmosphere from the surface to about the stratopause, and the number of air parcels advected in the simulations is about 2 million at each time step.

The parametrization of small-scale mixing in CLaMS is based on the deformation rate in the large-scale flow. Hence, air parcels may be merged, or new air parcels may be inserted at each time step (every 24 h), depending on the critical distances between them. The strength of parametrized small-scale mixing can be controlled by choosing a critical finite-time Lyapunov exponent (λc), which, in turn, determines the critical distances between air parcels for details see. Whenever the nearest-neighbour air parcels move closer than a critical distance during one advection time step, they are merged into a single parcel. Whenever they become further separated than a critical distance, a new air parcel is inserted in between see.

A validation of the CLaMS mixing scheme was presented by in comparison to CRISTA-1 observations. Importantly, the CLaMS mixing parametrization affects both vertical and horizontal diffusivity. Horizontal diffusivity is largely associated with deformation in the horizontal flow, whereas the vertical mixing is mainly related to the vertical shear .

Stratospheric H2O in CLaMS is calculated using the CLaMS cirrus module. It includes freeze drying in regions of cold temperatures, which mainly occurs around the tropical tropopause (dehydration). This, in turn, causes formation and sedimentation of ice particles. The lower boundary for H2O in CLaMS is taken from the reanalysis (ERA-Interim or JRA-55) of specific humidity below about 500 hPa. If saturation along a CLaMS air parcel trajectory exceeds a critical saturation (100 % with respect to ice), then the H2O amount in excess is instantaneously transformed to the ice phase and partly sediments out. Such simple parametrization has been adopted in several global Lagrangian studies e.g.. The saturation mixing ratio is calculated as χH2O=ps/p for each air parcel trajectory, with the saturation pressure given by ps=10-2663.5/T+12.537 , where p is the ambient pressure e.g..

For sedimentation, a parametrization is based on a mean ice particle radius, a characteristic sedimentation length and the corresponding fall speed. When the fallen path of the ice particles is calculated from the fall speed and the computation time step Δt, it is compared with a characteristic sedimentation length of about the vertical grid size (here lc=300 m), which has been empirically optimized by comparison with observations . After this step, a respective fraction of ice will be removed. If the parcel is sub-saturated and ice exists, this ice is instantaneously evaporated to maintain saturation.

In addition, methane oxidation is included as a source of H2O in the middle and upper stratosphere. Therefore, hydroxyl, atomic oxygen, and chlorine radicals are taken from a model climatology for details see.

Note that the CLaMS H2O calculation gives meaningful results only above the tropopause due to the simple parametrization of ice microphysics and omission of a convection parametrization. In the stratosphere, however, CLaMS H2O has been shown to agree well with the observations e.g..

To study the sensitivity of simulated stratospheric H2O regarding different reanalysis temperatures, horizontal transport effects, and small-scale mixing, we carried out several CLaMS simulations. As a reference, we consider the run driven by ERA-Interim reanalysis data . To reach a steady state, we use a perpetuum technique, where the one year run (for 2011 conditions) is repeated several times. The initial values for the tracer fields at the first day of the simulation are taken from a long-term CLaMS simulation . After one year of the perpetuum calculation, tracer mixing ratios from 31 December 2011 are interpolated to the air parcel positions on 1 January 2011, and the calculation is repeated for 2011 again. After the fourth year, the maximum relative change of H2O mixing ratios between further years of the simulation is very small with the defined resolution and the time step (maximum year to year changes are below 1.0 %). Consequently, we use the fifth year of the perpetuum simulation for our further analysis. Restricting the analysis to a single year instead of calculating a multi-year climatology has no effect on our conclusions regarding the differences between different simulations, as shown in Appendix .

First, to assess the robustness of simulated H2O with respect to the meteorological datasets, we carry out another CLaMS simulation driven by the JRA-55 data and compare it to the ERA-Interim-based reference simulation. Second, to assess the effects of horizontal transport, we carry out sensitivity simulations with horizontal transport barriers along circles of latitude at the Equator, at 15 and at 35∘ N/S . The transport barriers are defined in the model and centred at the given latitude. Their thickness is 10∘ in latitude (to inhibit diffusive mixing transport), and the barriers extend from the ground to a potential temperature of 600 K. The two types of barriers, BAR-15 and BAR-35, are located at the edge of the subtropics. BAR-15 is located at the equatorward edge and BAR-35 at the poleward edge of the subtropics. As such, both of them inhibit the transport from the subtropics. BAR-15 suppresses horizontal transport from the subtropics into the tropics, and BAR-35 suppresses transport from the subtropics to the extratropics. Air parcels entering the barrier along their trajectories during one model time step are moved to their starting locations after Δt, as shown in Fig. . Air parcels which were mixed into the barrier after the mixing procedure are moved to the closer barrier edge after the time step. Because of the broad barrier width of 10∘, this technique inhibits all cross-barrier transport. The CLaMS mixing parametrization ensures that no unrealistic clustering of air parcels occurs at the barrier edges. Third, to investigate the effects of small-scale mixing, we vary the parametrized mixing strength in CLaMS. A discussion of the choice of the critical Lyapunov coefficient, controlling the strength of small-scale mixing in CLaMS, is given by . Hence, for a horizontal resolution of 100 km and a mixing step of 24 h, which were used also in our study, Lyapunov coefficients of 1.5 and 1.2 day-1 provide a good agreement between the observations and the simulation results, as indicated by the comparison of CLaMS simulations with observations from infrared limb sounding from the research aircraft Geophysica . In particular, using the value of 1.2 day-1 gives a better agreement with observations in the 2-D version of CLaMS . Furthermore, showed that the value of λc = 1.5 day-1 (corresponding to the critical deformation of γc=1.5) for the chosen horizontal resolution and time step here, turns out to be optimal for the 3-D version of CLaMS. Even for such a small difference in the small-scale mixing strengths, the annual mean H2O concentrations in the extratropical LS differs by about 10–15 % .

In our study we use a value of λc = 1.5 day-1 for the reference run, 2.0 day-1 to represent weak mixing, and 1.0 day-1 for modelling strong mixing to cover the range of realistic small-scale mixing strength. Furthermore, we carry out a simulation without small-scale mixing (mixing in CLaMS was switched off), which is equivalent to a critical Lyapunov exponent of infinity. The large range of chosen mixing parameters here (λc) enables an investigation of sensitivities throughout a large range of possible mixing strengths, including significantly changed mixing characteristics in a potential future climate. In addition, we estimated the vertical diffusivity coefficient for the TTL for the different model simulations. The result suggests a non-linear response of H2O to the small-scale mixing in CLaMS (details are considered in Sect. ).

Note again that small-scale mixing in CLaMS is parametrized in a physical way, by coupling the mixing intensity to deformations in the large-scale flow. The sensitivity of simulated H2O to the parametrized mixing strength can therefore be regarded representative of the response of changes in small-scale turbulence, as well as of the response of changes in numerical diffusion in climate models.

We use satellite observations from Aura Microwave Limb Sounder (MLS) and Atmospheric Chemistry Experiment-Fourier Transform Spectrometer (ACE-FTS) for validation of the CLaMS simulations. For MLS, we use Level 2 data of Version 4. Detailed information on the MLS instrument can be found in , and a general discussion of the microwave sounding technique is given in . The MLS instrument was launched on 15 July 2004 on the NASA Aura satellite and measured limb emissions in broad spectral regions. Vertical profiles are retrieved every 165 km along the suborbital track, covering 82∘ S to 82∘ N latitudes on each orbit. Generally, MLS measurements include around 15 atmospheric chemical species along with temperature geopotential height, relative humidity (deduced from the H2O and temperature data), cloud ice water content and cloud ice water path, all described as functions of pressure. All measurements are made simultaneously and continuously, during both day and night . The resolution of the retrieved data is strictly related to the averaging kernels , which describe both vertical and horizontal resolutions. Particularly, the vertical resolution for H2O is around 3 km in the UTLS region, whereas the along-track horizontal resolution is between 170 and 350 km .

As a second satellite observation we used ACE-FTS level 2 data of version 3.6. ACE-FTS is a part of a Canadian satellite mission for remote sensing of the Earth's atmosphere, SCISAT, which was launched into low-Earth circular orbit on 12 August 2003. ACE-FTS is a satellite instrument which covers the spectral region from 750 to 4400 cm-1, and works mainly in solar occultation. During sunrise and sunset, the ACE-FTS instrument measures sequences of atmospheric absorption spectra in the limb viewing geometry. In addition, the spectra are analysed and inverted into vertical profiles. Aerosols and clouds are being monitored using the extinction of solar radiation. The satellite provides the altitude profile information (typically from 10 to 100 km) for temperature, pressure, and the volume mixing ratios for several molecule species over the latitudes from 85∘ N to 85∘ S . Solar occultation instruments like the ACE-FTS could have a high vertical resolution as good as ∼ 1 km, but low horizontal resolution (∼ 300 km) in the limb direction . A detailed description of ACE-FTS is given by .

compare MLS H2O observations in the LS with balloon-borne Cryogenic Frost Point Hygrometer (CFH) and Frost Point Hygrometer (FPH) instruments, from 2004 to 2015. There is a potential drift between the two sets of measurements, with MLS H2O increasing at a rate of around 0.03–0.07 ppmv yr-1 relative to the hygrometer measurements, starting around 2009. In contrast, the comparisons with recent ACE-FTS data show no signs of such drift in MLS H2O, nor do comparisons of MLS upper stratospheric H2O with ground-based microwave measurements .

Zonal mean H2O mixing ratios for boreal winter (December-February, DJF) and summer (June–August, JJA) from MLS and ACE-FTS satellite observations, and from CLaMS simulations driven by ERA-Interim and JRA-55 are shown in Fig. . The comparison of the two different satellite datasets (first and second row) shows differences of about 0.5 ppmv (with ACE-FTS being moister), and even larger in the extratropical LS. Oscillations in MLS H2O at high latitudes are a known effect of the broad averaging kernel . At low latitudes the effects of the MLS averaging kernel on H2O are much smaller, and we do not apply it to the model data here in order not to smear out the structure in the simulated H2O.

A comparison of the two simulations, driven by either ERA-Interim or JRA-55 (third and fourth row), shows differences due to the used reanalysis dataset of about 0.5 ppmv, increasing towards the extratropical lowermost stratosphere. The main reason for JRA-55 causing a moister stratosphere when compared to ERA-Interim is the positive difference in the temperatures around the TTL (Fig. ). Zonal mean temperatures in this region are on average about 2 K higher for JRA-55 than for ERA-Interim. Remarkably, these differences only exist in a narrow layer around the tropical tropopause. In addition to the TTL temperature differences, the differences in winds and heating rates between the two reanalyses could also cause uncertainties in H2O mixing ratios; however, the temperature difference provides a self-evident explanation.

A detailed comparison of the LS H2O between MLS and CLaMS simulations driven by ERA-Interim or JRA-55 at 380 K is given in Fig. . Note that the 380 K surface may be located well below the tropopause in some regions (e.g. Asian monsoon). The patterns of dominant freeze-drying regions above the west Pacific and South America in boreal winter are consistent between the observations and the two simulations. Notably, the larger area of low H2O mixing ratios and colder temperatures for ERA-Interim when compared to JRA-55 is consistent with the drier global stratosphere, as discussed above. Also, in boreal summer, the H2O distributions for MLS observations and CLaMS, driven by the two reanalyses are similar in the tropics. Nevertheless, in the subtropics, the strength of summertime monsoon anomalies in MLS differs from CLaMS, with the Asian monsoon dominating in both simulations, while the American monsoon appears stronger in MLS data e.g.. Note that the long-term H2O time series from CLaMS driven by ERA-Interim reanalysis agrees well with the Halogen Occultation Experiment (HALOE) and MLS observations .

Overall, regarding the global H2O distributions and maps in the LS, CLaMS modelling results with ERA-Interim are drier when compared to JRA-55, resulting from lower TTL temperatures in ERA-Interim. The agreement between CLaMS based on ERA-Interim and JRA-55 with the observations strongly depends on the considered region and season. Furthermore, it is not possible to conclude from our analysis which reanalysis results in simulated H2O has the best agreement with the observations.

Probability density functions (PDFs) of H2O mixing ratio e.g. allow a simple comparison of the overall effects of horizontal transport on H2O (in the LS) by contrasting the various sensitivity simulations. Figure  shows these PDFs for the tropics and extratropics of both hemispheres for the different barrier simulations.

In the SH (Fig. a) the frequent very low mixing ratios are insensitive to horizontal transport, indicating the occurrence of local dehydration. This insensitivity reflects the fact that temperatures in the Antarctic polar vortex are so low that H2O mixing ratios are locally freeze-dried to the saturation value. However, there is a weak effect of transport from the NH on moistening the SH, indicated by a lowering of the PDF's tail without cross-equatorial transport. Suppressing transport from the tropics lowers the tail further, and suppressing transport from the SH subtropics (with the 35∘ S barrier) finally removes almost all mixing ratios higher than 5 ppmv.

In the tropics (Fig. b), the insignificant difference between the reference (REF) and an equatorial transport barrier (BAR-0) simulations shows that the interhemispheric transport is rather unimportant for tropical mean H2O mixing ratios. Similarly, in-mixing of mid- and high-latitude air (see BAR-35) has a very small impact on tropical mean H2O, which echoes the findings of . In contrast, transport from the subtropics into the tropics has a strong effect. Suppressing such transport by applying a barrier at 15∘ N/S (BAR-15) changes the PDF substantially, as evident from the difference between the simulation BAR-15 and the reference cases. The isolation of the tropics due to the lack of horizontal transport in the BAR-15 simulation (all the way from the surface to 600 K) between the Equator and the subtropics (both ways) causes dry air at the Equator. Thus, with the barrier at 15∘ N/S the fraction of dry air at the equatorial region increases. The comparison of BAR-15 with BAR-35 shows that transport from the subtropical region into the tropics increases H2O. Without transport from the subtropics, the tropical mean H2O PDF appears more strongly skewed towards low mixing ratios (blue line in Fig. b), and the mean H2O mixing ratio is shifted towards lower values by about 0.5 ppmv.

In the NH cross-equatorial transport from the SH has only a weak effect, as visible from the equatorial transport barrier (Fig. c). The introduction of a transport barrier in the subtropics at 15∘ N removes the low mixing ratios from the PDF, showing that these low mixing ratios result from transport out of the deep tropics. Moving the transport barrier further away from the Equator to 35∘ N changes the PDF drastically. In addition to the low mixing ratios, it also removes the tail of the PDF at high mixing ratios such that a very narrow extratropical H2O mixing ratio PDF remains. Hence, these high mixing ratios are the result of transport from the subtropics and are likely related to the Asian monsoon, as argued by . Accordingly, monsoon-driven H2O transport from the subtropics to the high latitudes is by far more pronounced for the NH than for SH.

The pure transport effects of a horizontal exchange between tropics and mid-latitudes are evident from the mean age of air (AoA), the mean transit time of air through the stratosphere for the different model experiments with horizontal transport barriers. Figure  shows CLaMS calculations of the AoA for the reference case (Fig. a) simulation with transport barriers in the subtropics at 35∘ N/S (Fig. b) and the absolute difference between them (Fig. c). These horizontal transport barriers at 35∘ N/S effectively isolate the tropical pipe from the in-mixing of older stratospheric air from mid-latitudes, significantly decreasing the AoA globally by more than a year. Hence, recirculation from mid-latitudes into the tropics has a strong ageing effect on the stratosphere globally, which reinforces findings by . Without recirculation (in the BAR-35 simulation) the global AoA distribution reflects mainly the pure effect of the residual circulation, resulting in oldest air in the extratropical lowermost stratosphere, and appears very similar to the distribution of residual circulation transit times e.g.. Older air in the NH is related to the deeper NH residual circulation cell.

In the tropics, the age distribution in Fig. b shows a weak double peak structure up to about 500 K, indicating that the subtropics are regions of particularly fast transport likely related to subtropical processes like monsoon circulations. Suppressing transport in the subtropics with barriers at 35∘ N/S therefore significantly increases AoA in the extratropical stratosphere (Fig. c). A similar result has recently been shown by . Furthermore, present a good explanation of the recirculation process, describing recirculation as a process when an air parcel enters the tropical stratosphere and travels along the residual circulation to the extratropics, where it can be mixed back into the tropics, and thus recirculates along the residual circulation again. In this way, the age of air of the parcels increases steadily while they are performing multiple circuits through the stratosphere.

Relating the pure horizontal transport effects seen in the age of air to H2O is not straightforward, as H2O is strongly controlled by TTL temperatures. Figure shows the annual zonal mean H2O mixing ratio for the different sensitivity simulations with transport barriers, and Fig.  highlights the differences between the simulations with largest H2O changes. The small differences between the reference (Fig. a) and the equatorial barrier (Fig. b) simulations indicate only a very weak effect of transport processes in the deep tropics and interhemispheric exchange on global stratospheric H2O. Similarly, the sensitivity simulation with a subtropical transport barrier at 35∘ N/S (Figs. c, c) shows that in-mixing of mid-latitude air has only a weak impact on global stratospheric H2O (except in the NH LS). In contrast, transport from the subtropics, between 10∘ and 30∘ N/S, as visible from the comparison of sensitivity simulation BAR-15 and BAR-35 (Figs. , c, d, a), has a strong effect on tropical entry H2O and hence on global H2O. Without such transport from the subtropics (Fig. a, d), the stratosphere becomes substantially drier (maximal differences through the entire stratosphere are up to about 1 ppmv). The fact that this drying occurs only with transport barriers at 15∘ N/S and not with barriers at 35∘ N/S shows that it is not related to the suppression of recirculation of aged air from mid-latitudes, which has been affected by methane oxidation. In fact, processes in the subtropics (e.g. monsoon circulations) have a strong effect in moistening the global stratosphere, and suppressing these processes in BAR-15 causes drying. The model experiments with transport barriers only in the NH or SH subtropics further show that the effect of the NH subtropics in moistening the global stratosphere is stronger compared to the SH subtropics (Fig. b).

Figure  shows the H2O seasonal cycle at 400 K and its latitudinal structure, sometimes termed the “horizontal tape recorder” e.g.. Consistent with the discussion above, a transport barrier at the Equator has only a very weak drying effect on the SH subtropics and mid-latitudes, indicating only a minor role of the NH in moistening the SH lowest stratosphere. Furthermore, the effect of horizontal transport on the SH is small in all simulations as H2O mixing ratios in the SH are strongly affected by local freeze drying at SH high latitudes. In the NH, horizontal transport moistens the extratropical LS in summer and dries this region in winter. In the tropics, the annual cycle is related to minimum tropopause temperatures during boreal winter and maximum tropopause temperatures during summer. Therefore, during winter, horizontal transport exports dry air out of the tropics into the NH and moist air during summer. Consequently, the entire annual cycle of the H2O in the NH extratropical LS is related to horizontal transport from low latitudes, as argued by . The boreal summer maxima are related to monsoonal circulations and transport out of the tropics along the eastern and western flanks .

The PDF of H2O mixing ratio in Fig.  shows that increased small-scale mixing in the model generally moistens the LS in the tropics, as well as in the extratropics of both hemispheres. Increased mixing causes both a decrease in the fraction of dry air and an increase in the fraction of moist air and therefore shifts the PDF to higher mixing ratios. In particular, for the NH extratropics, this effect is strong, substantially enhancing the tail of the PDF with simultaneously reducing the low values in the PDF. The mean H2O mixing ratio is also increasing towards higher values with increasing mixing strength (dashed lines in Fig. ).

Changes in the parametrized small-scale mixing strength, however, may affect different processes that are critical to the distribution of H2O in the LS region. Such processes are diffusive cross-tropopause moisture transport, recirculation of air masses, permeability of the tropical pipe, and vertical diffusion (for illustration see Fig. ). Therefore, interpreting the mixing effects in terms of processes is a challenging task.

Figure  shows annual zonal mean distributions of H2O (a–d) and total water (e–h). Similarly, Fig.  shows double methane mixing ratios (a-d) and AoA (e–h) from the CLaMS simulation without mixing (MIX-no) and their incremental differences between the sensitivity simulations with increasing mixing from the weak mixing case (MIX-weak) through the reference (REF) to the strong mixing case (MIX-strong), i.e. ((MIX-weak) – MIX-no), (REF – (MIX-weak)), and ((MIX-strong) – REF). Note that the simulation without small-scale mixing (MIX-no) should not be considered as a realistic case, as turbulent mixing processes always take place in the atmosphere. However, we show the results from this simulation for the sake of completeness when analysing the mixing effects, and for facilitating comparisons with pure trajectory studies e.g..

A clear response to mixing is found for the LS (below ∼ 430 K), which is moistened with increasing small-scale mixing. In the following, we consider total water above the tropical tropopause as an indicator of changes in transport because it is not affected by chemistry (here methane oxidation). As the moistening in the LS below 430 K is also evident in total water, but not in methane and mean age, it is largely related to enhanced diffusive cross-tropopause transport of moist air. This enhanced diffusive cross-tropopause transport, in turn, increases the probability to by-pass the regions of cold temperatures, rendering the freeze drying at the tropical tropopause less efficient. Consequently, H2O entering the stratosphere is enhanced with increased small-scale mixing. The response of total water to changes in mixing is largely independent from the reference mixing strength throughout the stratosphere, with total water always increasing with increased mixing (Fig. f, g, h), reflecting the fact that the efficiency of freeze drying at the tropical tropopause decreases with increasing mixing.

Above about 430 K, the response of the H2O mixing ratio to varying the mixing strength turns out to be more challenging to interpret and strongly depends on the reference strength of mixing, due to a complex interplay between horizontal and vertical mixing processes. First, increasing the mixing strength from no-mixing (MIX-no) to weak mixing (MIX-weak) causes significant drying in the NH (Fig. b). A related signal (above ∼ 430 K in the middle and upper stratosphere) is evident in methane (Fig. b) and mean age (Fig. f), but not in total water (Fig. f). Hence, the drying response in the NH is attributable to transport effects, most likely to an increased permeability of the tropical pipe with increasing mixing and related increased transport of dry air and enhanced methane out of the tropics and into the NH. Second, increasing the mixing strength from weak mixing (MIX-weak) to reference mixing (REF) and from reference mixing to strong mixing (MIX-strong) causes a moister stratosphere globally, related to enhanced diffusive cross-tropopause transport and less efficient freeze drying (see discussion above). For the former (increasing mixing from MIX-weak), a weak increase in methane in the NH (Fig. c) indicates a simultaneous increase in the permeability of the tropical pipe. For the latter (increasing mixing from REF), decreasing methane mixing ratios (Fig. d) and increasing mean age (Fig. h) throughout the stratosphere likely indicate a simultaneous increase in the strength of recirculation due to increasing mixing.

Figure  presents a zoomed-in view of the H2O response to mixing changes in the UTLS region, a critical region for global climate, for both summer (a, b) and winter (c, d). Clearly, enhanced small-scale mixing moistens the LS due to enhanced diffusive cross-tropopause moisture transport with maximum differences between the simulations of around 20 %. The moistening effects are particularly large in the region around the tropopause where the radiative effect is most sensitive e.g.. Furthermore, the moistening effect due to mixing is maximized in the summer hemisphere . In the SH, H2O in the subtropical jet regions appears to be most critical to changes in small-scale mixing. In particular, increasing H2O mixing ratios in the extratropical lowermost stratosphere causes a flattening of the H2O isopleths towards high latitudes.

Maps of the H2O distribution at 380 K for the different CLaMS simulations with different small-scale mixing strength show the regions most prone to mixing changes (Fig. ). Strongest moistening due to increased mixing, occur in the regions of subtropical jets. This is consistent with the findings of , who show that the subtropical jets are regions of intense mixing. Most intense moistening is always caused by mixing processes along the subtropical jet in the summer hemisphere. During boreal winter, the SH subtropical jet substantially moistens with increasing mixing, whereas during boreal summer the NH jet moistens. In particular, the moist anomaly of the Asian and American monsoons during boreal summer is affected by small-scale mixing. Without mixing, only a weak anomaly occurs in the Asian monsoon, while the moist anomaly in the American monsoon is absent. With increased mixing, the Asian monsoon moist anomaly first increases (MIX-weak and REF cases). When mixing becomes very strong (MIX-strong) the entire jet region is strongly moistened. Thus, the anomaly of the Asian monsoon relatively to the entire jet region decreases. It should be noted here that the 380 K potential temperature surface may well be located below the tropopause in the Asian monsoon region such that parts of the moist anomaly in Fig.  indicates tropospheric air rather than cross-tropopause transport. However, the response of the subtropical jet and monsoon moist anomalies to increased small-scale mixing remains comparable also at 400 K and hence appears to be related to enhanced diffusive upward moisture transport, particularly in regions of strongly deformed zonal flow. Overall, small-scale mixing in the CLaMS simulations and related diffusive cross-tropopause moisture transport seem crucial for the development of Asian and American monsoon moisture anomalies, in particular for the American monsoon (where no anomaly occurs without including small-scale mixing).

The comparison between the reanalysis own specific humidity products and H2O simulated with CLaMS driven by the meteorology of the same reanalysis reveals further insights into the control processes of H2O in the reanalyses. Figure shows H2O mixing ratios in the LS at 380 K for winter and summer, as provided by ERA-Interim and JRA-55 specific humidity. Although the two CLaMS simulations driven by either ERA-Interim or JRA-55 showed differences in the details of the patterns (Fig. ), both simulations agreed reliably well with the satellite observations. The reanalysis H2O products, on the other hand, show a very different pattern (Fig. ). Despite their success in describing the main dehydration regions in the deep tropics (mainly in the west Pacific, and over South America in boreal winter), they fail in representing the main moisture sources in the Asian and American monsoons during summer. ERA-Interim, for instance, shows highest summertime H2O mixing ratios above the Pacific.

The clearest difference to MLS and CLaMS, however, occurs for JRA-55 H2O in the middle and high latitude LS. In this region, JRA-55 H2O mixing ratios are about 1 order of magnitude higher than ERA-Interim. A similar result was recently noticed by , suggesting that JRA-55 strongly overestimates the amplitude of the seasonal H2O cycle, although this result depends on the considered level. Remarkably, using the reanalysis temperature and wind fields to drive CLaMS transport, our results show a good agreement of H2O distributions with MLS observations. Note that in CLaMS the calculation of stratospheric H2O is based on the CLaMS cirrus dehydration scheme based on the Clausius–Clapeyron relation and simplified fall-out of ice particles (see Sect. ) and is, therefore, largely related to the large-scale reanalysis temperature and wind fields. The different CLaMS simulations also show a moister stratosphere for JRA-55, compared to ERA-Interim, consistent with a warmer tropical tropopause in JRA-55, but with much smaller differences than for the reanalysis H2O products. Although both reanalysis assimilation systems are constrained by observational data to produce realistic temperatures, significant differences around the tropical tropopause still exist of about 2 K (see Sect. ). But these differences are not sufficient to explain the H2O differences between the reanalysis products, as presented in Fig. . Hence, the JRA-55 H2O products do not seem consistent with the simple Clausius–Clapeyron relation.

Figure  shows H2O PDFs for further insights into the processes causing the difference between ERA-Interim and JRA-55 H2O in the northern extratropical LS. Both CLaMS simulations, driven with either ERA-Interim or JRA-55 data, and ERA-Interim reanalysis H2O products show a skewed PDF with a tail at high values, particularly strong in boreal summer. JRA-55 H2O mixing ratios, conversely, show a PDF with a totally different shape and a much higher mean value by about a factor of 5. This behaviour is the clearest at around 370 K (Fig. ), but it is also visible at levels below and above (not shown). The different shape of the JRA-55 PDFs with the peak at much higher mixing ratios suggests that high H2O mixing ratios are deposited in the extratropical LS, from potential temperature levels of about 350 K up to at least about 400 K, which is potentially related to the convective scheme in the reanalysis. JRA-55 shows a higher frequency of high and optically thick clouds, when compared with ERA-Interim e.g., which might also indicate a critical role of differences in convection for causing the differences in H2O e.g..

Recent studies have emphasized the overall qualitatively positive agreement between the large-scale climatological features in the UTLS in different reanalysis datasets; however, important quantitative differences remain e.g.. This qualitative agreement among the reanalysis in many regions of the UTLS and different seasons points to the robustness of the representation of related transport and chemistry in the reanalysis datasets . As the stratospheric H2O in the reanalysis is not assimilated directly, the treatment of H2O in the particular reanalysis product plays an important role. For instance, JRA-55 does not contain a parametrization of methane oxidation unlike ERA-Interim . further showed that the JRA-55 mean H2O values are much too large at 100 hPa. Our results of excessively high H2O values in the JRA-55 data product in the extratropical LS agree well with the findings of . Furthermore, point out that there is still a lack of assimilated observations and that significant uncertainties remain in the representation of the relevant physical processes in the reanalyses.

Although it is clear qualitatively that a decreasing critical Lyapunov exponent enhances mixing, it is also desirable, at least for comparison purposes, to quantify this effect. Because of the similarity between the mixing procedure in CLaMS and physical diffusion, the vertical mixing intensity can be quantified by computing the induced vertical diffusivity Kz (in m2 s-1) . We estimated Kz for each air parcel in CLaMS following , i.e. Kz=cΔz2Δt, if mixing occurs during Δt time step, and Kz=0, if mixing did not happen.

Here Δz is the model layer depth (in m), Δt=1 day is the mixing time step and c is taken to be 1/24 to account for the random position of the air parcels within the layer. The average diffusivity can be computed as the mean of the local diffusivity of the air parcels.

In the tropical LS (between 380 and 420 K), we estimate the vertical diffusivity of the simulations with a critical Lyapunov exponent of 2.0 day-1 (MIX-weak), 1.5 day-1 (REF), and 1.0 day-1 (MIX-strong) to be respectively 0.005, 0.02, and 0.065 m2 s-1 (Fig. ). This range of about 1 order of magnitude difference for the parametrized Kz in the tropical LS matches the uncertainty in that coefficient e.g.. Indeed, the value parametrized in the reference run (REF) is similar to the one estimated by (0.02 m2 s-1) from a satellite tracer measurements, or to results from a recent study by based on small-scale in situ wind measurements. rather suggest an average Kz of 0.08 m2 s-1, which is closer to the value in the MIX-strong simulations.

Figure also shows the annual average H2O concentration in the tropical LS as a function of the estimated annual average Kz in the same region. The increase in vertical diffusivity by 1 order of magnitude, from MIX-weak to MIX-strong, results in a moistening of ∼ 0.6 ppmv. This sensitivity is of the same order as suggested by , although those authors varied the diffusivity by 2 orders of magnitude (from 0.001 to 0.1 m2 s-1) and found a moistening effect of ∼ 0.5 ppmv. The discrepancy might be partly due to the non-linear dependence of mean H2O on diffusivity; although there are only three points in Fig. , the impact of increasing vertical diffusivity appears to saturate, which is probably due to the limitation of transport effects by dehydration.

Finally, it should be noted that the mixing in CLaMS induces both vertical and horizontal diffusion. However, given the larger vertical gradients of H2O compared to horizontal gradients in the UTLS, the impact of small-scale horizontal diffusion is assumed to be much smaller than the impact of vertical diffusion, especially in the tropics.