To evaluate the sensitivity of lower stratospheric water vapour over monsoon regions to different physical processes, we use the Chemical Lagrangian transport model CLaMS . This model simulates the three-dimensional trajectories of an ensemble of air parcels forward in time as well as the changes in the chemical composition of the air parcels along them. CLaMS has a modular structure that allows different parameterizations or new configurations to be easily implemented. Thus, the sensitivity of the water vapour distribution to each parameterization can be studied easily by switching them on and off.

The CLaMS model has been widely used to study the distribution of several tracers in the stratosphere , including recent studies on water vapour in the lower stratosphere . Previous studies have shown that the model properly simulates the variability of the stratospheric water vapour and the water vapour distribution over monsoon regions during boreal summer , highlighting the efficiency of these regions in transporting air masses and water vapour into the TTL .

All experiments performed for the present study use 6-hourly winds and temperature from the European Centre for Medium-Range Weather Forecasts (ECMWF) ERA-Interim reanalysis . The model uses a vertical hybrid coordinate that follows the orography with a σ coordinate at the ground that transforms into potential temperature in the upper troposphere. Above σ=0.3 (about 300 hPa in regions without strong orography), the vertical coordinate is purely isentropic. Cross-isentropic transport is simulated using total diabatic heating rates (considering all-sky radiation, latent heat release, and diffusive and turbulent heat transport as detailed by ) from ERA-Interim forecast data, as described in . For the sake of the analysis, simulated water vapour content of air parcels is daily gridded into maps with bin size 5∘ longitude × 2∘ latitude at a given pressure or potential temperature level with a thickness of 10 hPa or K, respectively. Hence, daily distributions of water vapour at 100 hPa are the result of averaging air parcels found between 105 and 95 hPa.

To create a common framework between previous studies focusing on the simulation of stratospheric water vapour and our CLaMS sensitivity experiments, we have implemented the forward domain-filling technique, here referred to as Lagrangian trajectory filling (LTF), in CLaMS. This set-up, introduced by , has been widely used to study different properties of water vapour in the stratosphere and UTLS region . In this approach, air parcels are continuously launched at a given level below the tropopause, and their trajectories are calculated forward in time until they leave the domain of interest, here bounded by the surfaces p=250 hPa (lower boundary) and θ=1800 K. After a spin-up time during which the number of tracked air parcels increases, an equilibrium state is reached in which the release of new air parcels balances removal at the boundaries. At that point, due to the structure of the large-scale stratospheric circulation, the whole domain is filled with air parcels.

Our set-up closely follows that of . Once a day (at 12:00 UTC), air parcels are released on a regular 5∘ longitude × 2∘ latitude grid spanning the 60∘ S–60∘ N latitudinal band. We initialize on the θ=360 K surface, which is, on average, above the level of zero radiative heating (LZRH) but below the tropical tropopause (∼375–380 K). We simulate the period from 2005 to 2016. The spin-up time is about 2 years, similar to . In pure LTF simulations, the equilibrium number of tracked air parcels is about 400 000 500 000 in, but in the case of experiments including small-scale mixing parameterizations, that number increases to 1.6 million (Table ) due to the spawning of new parcels inside the domain, which adds up to the release at θ=360 K.

We performed five LTF experiments with CLaMS. A summary of all experiments is provided in Table . This set of experiments is configured in such a way that the tested parameterizations are added cumulatively, increasing the complexity of the simulations and number of included processes step by step.

Satellite observations of water vapour mixing ratios in the LS from Aura Microwave Limb Sounder are used to further assess the results. We use version 4.2 of the water vapour data from MLS , which has been fully described in . These water vapour products have been validated in several studies and recently have been part of a climatological overview of the Asian Monsoon Anticyclone . Here, Aura MLS data and CLaMS data have been compiled on the same regular latitude–longitude grid as the one used by the experiments. In particular, we use the MLS data on 100 and 82 hPa pressure levels and compare them to the simulated water vapour distributions at 100 and 80 hPa, respectively. Since we are interested in differences between set-ups, we did not apply the averaging kernels to the model outputs to avoid potential smearing out of fine-scale patterns. We note that applying the averaging kernels of MLS does not change the pattern of water vapour in the lower stratosphere during boreal summer.

Figure a–g show the climatological water vapour distribution at 100 hPa during June–August (JJA) over the 2007–2016 period in the different CLaMS experiments and MLS observations (i.e. excluding the spin-up). A similar figure for 80 hPa is presented in Fig. . All experiments (Fig. b–f) reproduce the main characteristics of the water vapour distribution found in MLS. The contrast between the dry tropics and subtropics and the moister mid and high latitudes seen in MLS is present in all simulations. Furthermore, all experiments, including TRAJ, exhibit a local maximum in the Asian Monsoon Anticyclone (AMA). This consistency between the different experiments emphasizes the key role of transport through the large-scale temperature field in causing this feature as found in e.g.. However, there are also important differences between the experiments and with MLS observations. Compared with MLS (Fig. a), experiments with the LTF scheme (Fig. b–f) underestimate the water vapour content in the moistest regions. This underestimation reaches 1.5 to 2 ppmv in the case of TRAJ, pointing either to biases in large-scale transport and temperatures in ERA-Interim or to missing processes, as expected. The dry bias is reduced in the more sophisticated experiments which include more processes. In addition, there is a misrepresentation of the NAMA in all experiments, which tend to show a weaker maximum shifted towards the eastern and central Pacific with respect to observations. It should be noted that at 80 hPa the agreement between STANDARD and MLS is much better (Fig. ). Larger differences at 100 hPa are likely related to the fact that this lower pressure level is partly in the stratosphere and partly in the troposphere (e.g. in the Asian Monsoon where the tropopause is frequently above 100 hPa). Small biases in reanalysis tropopause height can therefore cause large biases in simulated water vapour at 100 hPa, while at 80 hPa their effect is marginal. Nevertheless, we focus our results at 100 hPa here as this is the most frequently considered level for investigating the monsoon UTLS, and further our goal is not to identify a best-case simulation scenario but to estimate the effects of different processes from the sensitivity simulations, and these estimates are very similar at 100 and 80 hPa.

In order to separate the effect of each parameterization, Fig. h–l display the differences between pairs of experiments which share the same configuration except for one single process parameterization. Thus, Fig. h (CHEM minus TRAJ) isolates the impact of methane oxidation, which is only included in CHEM (see Table ). Similarly, Fig. i–k show the impact of the simplified ice microphysics (cirrus) parameterization (CIRRUS-CHEM), small-scale mixing (SSMIX-CIRRUS) and enhanced tropospheric mixing (VMIX-SSMIX), respectively.

Regarding methane oxidation, Fig. h shows a water vapour increase of around +0.1 ppmv over the tropics and subtropics that reaches +0.2 ppmv over high latitudes, as expected. As methane oxidation occurs at mid-stratospheric levels , its impact on the water vapour distribution at 100 hPa (Fig. h) is a consequence of air parcels moving downward from those altitudes following the downwelling branch of the Brewer–Dobson circulation at high latitudes. During boreal summer, the downward circulation is stronger in the Southern Hemisphere, which explains the larger increase in water vapour in this region. Once air parcels reach the lower stratosphere at high latitudes, some of them may reach the troposphere below 250 hPa, where they are removed from the simulation, while others follow the residual meridional circulation giving rise to the observed subtropical and tropical enhancements of water vapour at 100 hPa. This weak meridional transport was also observed by and . A similar impact of methane oxidation can be found at 80 hPa in spite of the stronger meridional gradient at this pressure level (Fig. ).

Including our simplified representation of ice microphysics (Fig. i) results in a further moistening of the LS ranging from +0.4 to +0.6 ppmv over most regions. These values are in agreement with the global increase of +0.5 ppmv found by and exceed the effect related to methane. Moreover, Fig. i shows that the effects of ice are especially large in the AMA (about +0.8 ppmv at 100 hPa), enhancing the moisture anomaly in the monsoon UTLS. This signature is also found at 80 hPa but with slightly weaker values compared to 100 hPa (Fig. i).

Small-scale mixing has a similar impact (Fig. j), increasing water vapour at latitudes north of 30∘ S and especially in the AMA. Outside of the AMA, the water vapour increase linked to small-scale mixing is slightly weaker than that attributed to ice microphysics (+0.1 to +0.4 ppmv). The local impact on water vapour in the AMA region, however, is stronger and reaches values above +0.9 ppmv at 100 hPa. This strong moistening effect can be attributed to the fact that mixing processes are more frequent in regions with large-scale flow deformations, which are mainly located in the surroundings of the subtropical jet and hence in the AMA.

The effects of the enhanced mixing in the troposphere as represented in the VMIX experiment are shown in Fig. k. An increase in water vapour of up to +0.1 ppmv occurs almost everywhere north of 30∘ S, with again a relatively stronger impact in the AMA, with differences larger than +0.3 ppmv. This stronger influence in the AMA compared to other regions is also found at 80 hPa but is weaker than at 100 hPa. Compared to other processes, VMIX shows a weak increase in water vapour in the AMA related to the enhanced tropospheric mixing. The reason behind this increase in lower stratospheric humidity with the mixing parameterizations in SSMIX and VMIX ultimately lies in the bypassing of cold traps which air parcels would have otherwise encountered along their slow ascent and the associated horizontal wandering (for further details, see Appendix ).

The 80 hPa level shows a similar spatial distribution of water vapour differences to that at 100 hPa, with values peaking again in the AMA (Fig. j). However, the relative strength of this maximum (+0.5 ppmv) is weaker than at 100 hPa.

Since mixing changes the temperature encountered by air parcels, the impact of temperature-dependent processes, such as ice microphysics, is altered. To evaluate this effect, we have run a 2-year simulation, hereafter called “VMIXnocirrus”, in which all the water vapour in excess of saturation is instantaneously removed instead of being transferred to the ice phase. The difference between VMIXnocirrus and VMIX shows the impact of ice transport, as CIRRUS-CHEM, but with mixing being applied (see Fig. ). Comparing Fig.  with Fig. i, the moistening effect caused by the inclusion of a simple ice microphysics scheme is amplified with mixing. Nevertheless, the spatial pattern resembles that of the experiments without mixing and peaks in the AMA region (with +1 ppmv). We interpret this enhancement of the moistening as being caused by the vertical transport of both ice and a larger vapour content by mixing. By effectively bypassing cold traps, mixing favours ice sublimation, which (1) directly increases the water content and (2) decreases the size of the remaining ice particles and hence their settling velocity, thereby increasing their residence time and the possibility of subsequent sublimation in warmer regions. Together with the transport of the larger vapour background content associated with this set-up, this leads to an enhanced moistening.

Finally, the sensitivity of the LS water vapour to the boundary condition imposed in the LTF set-up is assessed by comparing SSMIX to the full-blown CLaMS STANDARD experiment. As a reminder, STANDARD uses the same parameterizations as SSMIX but calculates transport throughout the troposphere using ERA-Interim water vapour values as the lower boundary condition below about 500 hPa. Thus, contrary to the LTF initialization, the water vapour content of the air parcels at 360 K depends on the transport properties of the air parcels reaching that level. Figure  depicts the water vapour distribution obtained for the STANDARD simulation (panel g) and its differences with respect to SSMIX (panel l). The STANDARD simulation exhibits a much wetter stratosphere than SSMIX, which leads to a weak overestimation of the water vapour compared to MLS, in particular in the AMA region. However, at 80 hPa there is good agreement between the water vapour field simulated in STANDARD and MLS (Fig. g). Figure l shows that the main differences caused by the LTF scheme are not centered on the AMA region but on both the western and eastern parts of the North Pacific and in the 20–30∘ S latitude band. At 80 hPa, differences occur in the same latitude band and expand zonally. This implies that the global effect of the LTF set-up is to dry the stratosphere compared to the STANDARD simulation, in particular at the edges of the tropics, and with smaller differences in the AMA.

Concerning the water vapour maximum found over the NAMA in MLS observations, we found that its spatial pattern is not well reproduced in any of the experiments (Fig. ). The maximum is shifted to the west compared to MLS over the eastern Pacific and, except for the STANDARD simulation, which shows water vapour values in the NAMA close to the observations, all other experiments display much lower values. The mixing parameterization has a much weaker effect in the NAMA compared to the AMA, which suggests that the weaker anticyclonic monsoon circulation over that region produces a weaker deformation of the main flow leading to less mixing between air masses. The NAMA water vapour maximum seen in MLS is known to be more challenging to simulate than the AMA e.g..

Ice microphysics in the UTLS is a complex issue, which requires sophisticated models as well as a series of assumptions regarding the nature of ice nuclei, the shape of ice particles and their dynamical environment including convective detrainment and gravity waves. We have here considered a simple representation of the microphysics (in CIRRUS and related model experiments), in which the ice phase and water vapour are kept in thermodynamic equilibrium and ice particle sediment. However, both laboratory experiments and in situ observations e.g. show the common occurrence of large supersaturations under clear-sky conditions, which is related to a delay of ice nucleation to high supersaturations at low temperatures.

For a simple test of the sensitivity of our results to a potential supersaturation threshold required for ice formation, we performed a second CIRRUS (pure LTF) simulation, in which ice formation is delayed to a relative humidity of 150 %. If this value is reached, all vapour in excess of saturation is condensed into the ice phase (so that the parcel is at 100 % relative humidity). Figure  compares the distribution of water vapour during boreal summer averaged for the period 2005–2010 for CIRRUS with ice formation threshold 100 % and 150 %. Our results show that by allowing further transport of water vapour before ice formation, CIRRUS 150 % results in a more humid LS everywhere. This moistening effect of increasing the saturation level is proportional to the local saturation mixing ratio and especially large in regions in which ice microphysics has a strong signature, such as the AMA and NAMA.

It should be kept in mind that in situ ice formation, as represented here, is only one of the many processes through which ice influences the water vapour content. Ice may be detrained in the UTLS from deep overshooting convection and evaporate afterwards, resulting in a net hydration of the UTLS . However, concluded from observations that this effect is small, except in the NAMA, which may partly explain the poor model results there. On the other hand, convection also directly influences the vapour phase, an issue discussed in Sect. .

Another important process for the UTLS water vapour budget is ice and moisture transport by convection . Although some of the experiments presented here include processes whose particular parameterizations may contribute to convective moistening (e.g. small-scale mixing), a direct simulation of convection is not present in these simulations.

To further investigate the additional effects of convection on the monsoon water vapour budget, we performed a modified TRAJ experiment, hereafter called CONV, in which this process is taken into account, following an approach similar to that of . In CONV we use the trajectories of TRAJ to compute the LMR of the air parcels. At every time step a check is performed for whether an air parcel is located inside a cloud, i.e. at a pressure level below that of the cloud top. If this is the case, the air parcel's water vapour is set to the saturation mixing ratio (100 % relative humidity), according to the temperature that the ERA-Interim reanalysis attributes to the location of the air parcel. This process corresponds to hydration if the air parcel is initially subsaturated and dehydration if it is supersaturated see. We use ISCCP B1 (GridSat-B1) Infrared Channel Brightness Temperature combined with ERA-Interim data to determine cloud top heights , following the methodology of . Their approach is similar to the one employed by and assumes that the temperature at cloud top is equal to the temperature of the environment estimated from the reanalysis. The resulting altitude is shifted upward by 1 km to correct for biases in infrared cloud top temperature . There are a few differences, however, between the two methods: first, contrary to , do not distinguish convective cores from in situ formed cirrus clouds and include both for cloud top determination. The impact of this difference should be small as long as the cirrus clouds are sufficiently thin. Second, in the case of brightness temperatures lower than the local tropopause temperature, we assume that convective parcels rise adiabatically from 40 hPa below the tropopause, whereas take a mixture of tropopause (70 %) and environmental (30 %) air. Therefore, our estimated cloud top altitudes may be low biased compared to theirs. Finally, note that the ISCCP B1 has slightly lower horizontal resolution (∼8 km vs. 4 km) than the dataset of but similar temporal resolution (3-hourly). Figure  shows the water vapour distributions at 100 hPa of TRAJ (Fig. a), CONV (Fig. b) and the differences between both of them. The two experiments result in a very similar water vapour distribution, with a slight moistening effect caused by convection, mainly at mid and high latitudes. These results indicate that even when a convective event occurs, the water vapour is set by temperatures experienced by the air parcels after convection. This result is in agreement with but not in line with . However, it should be kept in mind that focused on the analysis of a single 7 d convective event during summer 2007, whereas we consider the entire summer (June–August) for 2005–2009. Thus, while their main conclusion is that infrequent deep convection reaching above 380 K causes a strong moistening of the LS, our results show that the climatological impact of these events is likely very weak.

We have also considered only the 7 d to check whether we were able to reproduce the same results with TRAJ and CONV as their simulations without and with convection, respectively. However, in our case TRAJ produces a maximum of water vapour in the AMA that is not observed in their non-convective experiment. This suggests that there are additional features, further than the differences mentioned before, that make the comparison between the experiments in and ours difficult. Another limitation of our approach in CONV is that we have not taken into account the role of convective ice. According to , the main impact of convection on the LS water vapour occurs through the injection of ice. The latter assertion, however, is contrary to the conclusions of . These differences between the different studies highlight the large existing uncertainty about the role of convection for LS water vapour. A deeper analysis of this issue should be considered in future studies.

In the LTF experiments previously described, we have used the same longitude–latitude grid to release new air parcels at the same initial potential temperature of 360 K. This configuration, which has been chosen following the procedure of , might have an effect on our results. In fact, and use 370 K as the initial potential temperature level for air parcels released in the Asian Monsoon region. They argue that because the LZRH is higher over the AMA than in other regions, many air parcels released at 360 K may descend and are removed from the simulation. Figure a shows the normalized distribution of air parcels in TRAJ at 100 hPa centered in the AMA for JJA in 2007. As we could expect from and , the AMA is characterized by a lower density of air parcels. Because a low number of air parcels could condition the robustness of the results, this raises the question of the possible impact of the number of air parcels in the AMA on the water vapour distribution in this region. To test this potential sensitivity to the number of air parcels, we have performed two additional TRAJ experiments in which either the number of air parcels newly released has been increased (TRAJ-denser) or the initial potential temperature (TRAJ-370 K) has been changed. In TRAJ-denser the number of air parcels is increased by releasing them on a higher-resolution grid (2.5∘ longitude × 1∘ latitude). By contrast, in TRAJ-370 K the initialization grid maintains the same resolution as in TRAJ, but air parcels are launched at the θ=370 K surface instead of at 360 K.

Figure b and c show the relative number of air parcels in the AMA at 100 hPa of TRAJ-denser and TRAJ-370 K with respect to TRAJ. In addition, Fig. d–f show the water vapour distributions of TRAJ, TRAJ-denser and TRAJ-370 K for the same season and year. In both experiments, the density of air parcels has increased notably with respect to TRAJ. There are 4 times more air parcels in TRAJ-denser (Fig. b) and 2 times more in TRAJ-370 K (Fig. c) than in TRAJ. As in TRAJ-denser more air parcels are released inside the AMA, a larger number of them reach the 100 hPa level. However, this larger number of air parcels is not accompanied by an enhancement of water vapour (Fig. e). Therefore, we conclude that increasing the resolution of the initialization grid used in our LTF experiments does not have an impact on our results, which means that the resolution and particle number of the TRAJ experiment are high enough to adequately capture the spatial variability of the temperature field and its impact on water vapour. By contrast, TRAJ-370 K exhibits a moister water vapour distribution in the AMA than the original TRAJ experiment (Fig. f). This might be explained by the fact that the AMA shows a stronger anticyclonic circulation at 370 K than at 360 K , giving rise to the uplift of more air parcels through the inner core of the AMA. The stronger confinement of this region can allow a greater number of air parcels to avoid the coldest regions, which are located at the south-eastern flank of the AMA. Thus, when the air parcels spawn to other regions at the 100 hPa level due to the weakening of the anticyclone circulation, they transport a larger water vapour content than air parcels reaching the same pressure level in TRAJ. This widening of the vertical transport conduit of air parcels when being uplifted in the Asian Monsoon Anticyclone is consistent with the main transport pathway proposed by .

These results show that our LTF experiments have a sufficient number of air parcels to be statistically significant. Furthermore, they point out that the selection of a higher initial potential temperature in the AMA has an impact on water vapour distributions, likely related to the larger exposure of the chosen potential temperature level to stronger confinement in the AMA. Thus, we conclude that the selection of the initial potential temperature should not only take into account the level of zero radiative heating, but also the strength and confinement of the AMA.

These sensitivity tests of the domain-filling technique to a different selection of arbitrarily chosen parameters do not cover possible impacts of the LTF scheme itself in our water vapour results. To study this we compare a LTF experiment, SSMIX, with a non-LTF experiment, STANDARD. Despite the similar set of parameterizations included, the STANDARD and SSMIX experiments significantly differ, and STANDARD agrees better with MLS regarding seasonal and intra-seasonal variability in the AMA and NAMA. The remaining discrepancies might be due to (i) the initial water vapour content of the air parcels and (ii) the filtering of air parcels below 250 hPa and above 1800 K, in particular the absence of a troposphere.

To test point (i), we performed an additional experiment configured as SSMIX but doubling the initial water vapour content of air parcels from 50 to 100 ppmv. Figure  in the Appendix shows that the distribution at 100 hPa is not affected by this change in the initial condition. Note however that this does not suggest that the water vapour is entirely insensitive to the lower boundary condition, as explained below.

In order to further investigate this result, Fig.  depicts the 360 K water vapour maps (corresponding to the level of initialization of SSMIX) for MLS observations, STANDARD and the two SSMIX experiments. Note that the water vapour mixing ratio in the SSMIX is significantly lower than the initialization value. This is due to the presence of older air parcels which have been released at earlier time steps, have undergone dehydration and have been transported into the 360 K layer from above. This stagnation and return of old air parcels is allowed as the filtering occurs at 250 hPa, which is below the initialization level. Therefore, we conclude that the initialization value in LTF experiments cannot be considered a lower boundary condition for LTF simulations in the Asian Monsoon.

It turns out that the water vapour variability at 100 hPa is, indeed, sensitive to this lower boundary condition. This is indicated by the high correlations between the water vapour at 360 K in the AMA region and local H2O at 100 hPa (Fig. e–h), which peak over the Asian Monsoon. The significantly different lower boundary conditions shown in (Fig. a–d) thus likely cause parts of the observed differences between STANDARD and SSMIX at 100 hPa. In the standard LTF approach, this boundary condition is not directly set because of the mixture of old and young air parcels making up the air masses at 360 K.

While this issue may be interpreted as a too dry lower boundary condition, it is in the end related to missing transport pathways in the lower part of the simulated domain. This interpretation is supported by Fig. a, which shows the relative percentage of air parcels simulated in STANDARD with respect to SSMIX. STANDARD shows a higher number of air parcels than SSMIX throughout the domain, and in particular in the AMA and the Southern Hemisphere subtropics (Fig. a). Not only does STANDARD simulate more air parcels in the AMA, but these parcels are also wetter, as shown in the probability density function (PDF) of the water vapour content of the air parcels (Fig. b). These differences suggest a lack of vertical transport of moist tropospheric air parcels from lower levels in the LTF initialization (where these air parcels are removed). Besides vertical transport, it is likely that inhibited horizontal entrainment also plays a role, since at the 360 K initialization level the inner anticyclone core is, to some degree, isolated from the surrounding areas, as shown in .