1 Introduction

It is increasingly recognized that stratospheric water vapor plays an important role in the Earth’s energy budget (Forster and Shine 2002), stratospheric temperature and chemistry (Stenke and Grewe 2005), and surface climate (Solomon et al. 2010). Stratospheric water vapor is projected to increase as climate warms in the simulations of the general circulation models (Gettelman et al. 2010). This increase of stratospheric water vapor potentially feeds back to and amplifies global warming (Dessler et al. 2013; Huang et al. 2016).

It is widely accepted that stratospheric water vapor is predominantly controlled by the tropical tropopause temperature (TTT) (Fueglistaler and Haynes 2005), which itself is determined by the radiative, chemical, and dynamical processes in the tropical tropopause layer (Fueglistaler et al. 2009; Gettelman et al. 2004). Stratospheric water vapor mainly comes from transport of water vapor itself in the troposphere through upwelling in the tropics, which is the upward branch of the Brewer–Dobson circulation (BDC). It is widely agreed that the water vapor that enters the stratosphere primarily in the tropics is limited to a few parts per million by volume (ppmv) by the strong dehydration process in the tropical tropopause layer due to extremely cold temperatures there (Fueglistaler et al. 2005). Moreover, BDC propagates methane and hydrogen into the stratosphere, which can also contribute to water vapor in the middle and upper stratosphere by oxidative degradation (Brasseur and Solomon 2005). Methane oxidation is the primary reason for the increase of water vapor with altitude from the tropical tropopause to the upper stratosphere (le Texier et al. 1988). Several studies have demonstrated that penetrating deep convection systems can contribute to lower stratospheric water vapor (Fueglistaler et al. 2009; Herman et al. 2017; Lei and Jin 2012).

The TTT is projected to increase during the greenhouse warming and this warming is mainly driven by the radiative effect from tropospheric warming and the direct radiative heating of CO2, despite of some compensating effects, such as that resulting from the strengthening of the BDC (Lin et al. 2017; Thuburn and Craig 2002). Based on the TTT control theory, such warming of the TTT would lead to a moistening of the stratosphere. However, because of the strong coupling between the radiation, chemistry, and dynamics in the stratosphere (Hartmann 1981), such radiative heating may impact not only the local temperature but also the stratospheric circulation and chemical constituents and consequently stratospheric water vapor. Hegglin et al. (2014) merged satellite water vapor data sets with the help of a chemistry-climate model, and the new record extends back to the late 1980s. They indicate that lower and mid-stratospheric water vapor long-term trends are negative. Upper-stratospheric water vapor instead shows a long-term increase. The contributions of the stratospheric entry values of water vapor and methane are quantified and shown not to be sufficient to explain the observed water vapor trends, particularly the difference in the trends between the upper and lower stratosphere. The long-term trends of the stratospheric water vapor may be mainly resulted from the changes in the stratospheric circulation. Although the relationship between the TTT and the stratospheric water vapor has been extensively diagnosed in the global models and observations [e.g., Gettelman et al. (2010) on the results of coupled chemistry-climate models; Dessler et al. (2013) on observation], there is a lack of understanding of the indirect effects of the TTT warming and how they modify the transport of water vapor into the stratosphere and then collectively control the stratospheric water vapor. To address this problem and mechanistically investigate the consequences of TTT warming, in this study, we use the Specified Dynamics version of the Whole Atmosphere Community Climate Model (SD-WACCM) to investigate the consequences of the tropical tropopause heating and their overall impact on the stratospheric water vapor. In the following sections, we will describe the design of the experiments and the results in order.

2 Model and experiment design

The SD-WACCM, compiled from the Community Earth System Model version 1.2 (CESM 1.2) derived from the National Center for Atmospheric Research (NCAR), is a fully coupled chemistry-climate model (Lamarque et al. 2012). The model domain of WACCM extends from the Earth’s surface to the lower thermosphere (~ 145 km or 4.5 × 10−6 hPa). The SD-WACCM used here is performed with the Goddard Earth Observing System Model, Version 5 (GEOS-5) meteorological fields of NASA’s Global Modelling and Assimilation Office (GMAO) (Rienecker et al. 2008) to constrain the dynamics and temperature in the troposphere and stratosphere (below ~ 50 km). The meridional and zonal winds, temperature, and surface pressure are relaxed to the reanalysis data at every model time step (30 min) using the approach described in Kunz et al. (2011):

$${T_n}=(1 - \alpha ){T_{predicted}}+\alpha {T_{met}},$$

where \({T_n}\) is the temperature at the nth model time step, \({T_{predicted}}\) is the predicted temperature by the integration from the previous time step \({T_{n - 1}}\), and \({T_{met}}\) is the GEOS-5 meteorological temperature field used for nudging. \(\alpha\) is the nudging factor, which is the weighting factor of the meteorological data. In this paper, \(\alpha\) is set to 10%. This strength of the relaxation is linearly reduced between 0.79 hPa (about 50 km) and 0.19 hPa (~ 60 km), such that the model meteorological fields become fully interactive above 60 km. The vertical resolution in the troposphere is higher in SD-WACCM. So, SD-WACCM has more vertical levels (88 levels) than the standard version of WACCM (66 levels). SD-WACCM is widely used to study the particular meteorological events (Chandran et al. 2013; Marsh 2011; Yuan et al. 2012), their impacts on the chemistry and microphysics (Sakazaki et al. 2013; Tweedy et al. 2013; Wegner et al. 2013), and the distribution of trace gases in the stratosphere and above (Garcia et al. 2014; Straub et al. 2012).

In order to isolate the impact of the tropical tropopause warming on the stratospheric water vapor, three experiments are conducted here. In the control (CNTL) experiment, we use the original GEOS-5 meteorological fields without any modification. In the two TTT warming experiments, the meteorological temperature fields are uniformly increased by 1 K in the tropical tropopause layer. In the first perturbation experiment, the temperature increases are added within 12°S and 12°N between 120 and 80 hPa, since the tropical-mean lower stratospheric water vapor is found to be most sensitive to the cold point tropopause (around 100 hPa) temperature in the deep tropics (Fueglistaler and Haynes 2005; Liang et al. 2011; Randel et al. 2004). In the other perturbation experiment, the warming perturbation is added in a broader region, between 120 and 80 hPa within 25° latitude which is similar to the simulated TTT warming under greenhouse warming (Collins et al. 2013). These two experiments are denoted as the tropical tropopause temperature perturbation experiment a (TTTa) and experiment b (TTTb) in the following, respectively. All the three experiments are integrated for 5 years from 2007 to 2011. By comparing the two perturbation experiments to the CNTL experiment, we can assess the impact of the tropical tropopause warming on the stratospheric water vapor.

3 Results

Figure 1 shows the annual and zonal mean temperature, methane, and water vapor concentration in the CNTL experiment and the corresponding responses in the TTTa and TTTb experiments. The TTT perturbations of the meteorological fields lead to significant warming within 12° latitude and 25° latitude in the tropical cold-point tropopause in the TTTa and TTTb experiments, respectively (Fig. 1a–c). These warming patterns are consistent with the temperature perturbations added in the meteorological data in the two experiments. Although the meteorological temperature fields are uniformly increased by 1 K, the responses are spatially non-uniform. The maximum of the warming, which are ~ 0.79 K and 0.94 K in the TTTa and TTTb experiments, occurs in the lower latitudes where the climatological temperature is the coldest.

Fig. 1
figure 1

Annual and zonal mean climatology in the CNTL experiment (the left column) and responses in the TTTa and TTTb experiments (the middle and right columns) of a–c temperature, units: K, d–f methane, units: ppbv, and g–i water vapor concentration, the units are ppmv in g and % in h and i. Regions with dots are the places where differences have statistical significant levels higher than the 95% confidence level (student’s T test). The black lines indicate the tropopause in the CNTL experiment

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The stratospheric methane significantly increases in both experiments (Fig. 1e, f). The increase of methane rises with the increasing altitude in the stratosphere, which reaches 240 and 280 ppbv in the TTTa and TTTb experiments, respectively. Methane oxidation contributes to moistening of the stratosphere, and the inferred contribution to the increase of the stratospheric water vapor could be about 0.5 ppmv (one CH4 molecule creates two H2O molecules) in the middle stratosphere in both experiments.

The TTT warming results in an increase of water vapor in the lower stratosphere and a significant reduction above 60 hPa in the middle stratosphere in the TTTa experiment (Fig. 1h), and stratospheric moistening especially in the lower stratosphere in the TTTb experiment (Fig. 1i). The increase of the water vapor in the tropical tropopause layer, which reaches about 18% in both experiments, has the similar pattern to the warming in this area (Fig. 1b, c). This is induced by the less dehydration associated with the increase of the saturated water vapor by the warming. This positive signal propagates vertically into the stratosphere and horizontally toward poles. Although the warmer tropical tropopause allows more water vapor to penetrate the tropopause into the stratosphere and the increase of methane contributes to moistening of the middle stratosphere, it is a significant reduction (~ 9%) of water vapor in the middle stratosphere in the TTTa experiment, which may be caused by the change of circulation. The largest reduction occurs in the NH tropics at about 20 hPa, which may be associated with the seasonal changes of BDC.

Stratospheric water vapor can be impacted by the change in the BDC which determines the transport speed (efficiency) of water vapor from tropopause to stratosphere in the tropics. To characterize the variation of the BDC, we examine the Eliassen–Palm (EP) flux and the vertical component (speed) of the transformed Eulerian-mean residual circulation \({\overline {w} ^*}\) (Andrews et al. 1987). Here, 3-hourly output data are used to calculate the EP flux and \({\overline {w} ^*}\). Figure 2 shows the annual and zonal mean zonal wind, EP flux and its divergence, \({\overline {w} ^*}\), and ozone concentration in the CNTL experiment and the responses in the TTTa and TTTb experiments. According to the thermal wind balance, vertical shear of zonal wind is proportional to the horizontal temperature gradient. The increases of the TTT (Fig. 1b, c) result in the westerly-wind anomalies above the subtropical tropopause in both experiments (Fig. 2b, c). These westerly-wind anomalies over the upper flanks of the subtropical jets, which are favourable for the vertical propagation of the wave activities, lead to the upward shift of the Rossby-wave critical layer (Garcia and Randel 2008; Lin and Fu 2013; Shepherd and McLandress 2011). So, more eddy heat fluxes propagate from the troposphere into the stratosphere through the subtropical tropopause, which results in the convergence of eddy flux above the tropopause (Fig. 2e, f). Following the “downward control” principle (Haynes et al. 1991), this convergence of eddy flux results in a strengthening of the shallow branch of the BDC at the edge of the warming region. On the other hand, since the warming is located in the low latitudes where rotation effect is weak, the strengthening of the BDC including both the upwelling anomaly between 12°S and 12°N and downwelling in the subtropics in the TTTa experiment is mainly contributed by the change in the zonal mean meridional circulation (the vertical velocity, w) (Fig. 2h, k). Similar results can also be seen in the TTTb experiment, with the broader upwelling anomaly between 25°S and 25°N and downwelling on both sides (Fig. 2i, l). The change of the meridional overturning circulation is mainly driven by the increase of the meridional temperature gradient over the warming region in the tropical tropopause layer (Fig. 1b, c). Because the temperature gradient within 20° latitude in the tropics is stronger in the TTTa experiment than that in the TTTb experiment, the upward velocity in the deep tropics is stronger in the TTTa experiment than that in the TTTb experiment. The stronger tropical upwelling propagates more air with less ozone from the troposphere into the stratosphere, which reduces the ozone concentration in the tropical lower stratosphere in both experiments (Fig. 2k, l). The strengthening of the BDC propagates more methane from the troposphere to the stratosphere and results in the increase of stratospheric methane (Fig. 1e, f).

Fig. 2
figure 2

Similar to Fig. 1, but for a–c zonal wind, units: m/s, d–f EP flux (vectors) and its divergence (shading), g–i\({\overline {w} ^*}\), units: mm/s, j–l vertical velocity, w units: mm/s, and m–o ozone concentration, the units are ppmv in j and % in k and l. Regions with dots are the places where differences have statistical significant levels higher than the 95% confidence level (student’s T test). The black lines indicate the tropopause in the CNTL experiment

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The impact of the strengthening of the BDC on the stratospheric water vapor is sensitive to the amount of water vapor concentration in the tropical tropopause layer. Figure 3 shows the time-height distributions of the daily mean water vapor averaged over 10°S to 10°N in the CNTL, TTTa, and TTTb experiments and their differences. The water vapor in the tropical tropopause layer has very strong seasonal variation, from 3 ppmv during December, January and February (DJF) to 5 ppmv during July, August, and September (JAS) in the CNTL experiment (Fig. 3a). Both the dry and moist air are propagated by the tropical upwelling from the tropical tropopause upward into the stratosphere. This so-called tropical “tape recorder” phenomenon (Mote et al. 1996) is impacted by the strengthened tropical upwelling in the TTTa and TTTb experiments (Fig. 3b, d). Following Jiang et al. (2015), the mean vertical transport flux velocities of the water vapor in the tropics between 10°S and 10°N is calculated via the cross-correlations method based on the daily mean water vapor data. Compared to the CNTL experiment, the inferred mean vertical velocity from 19 to 25 km (about 100–20 hPa) is about two times faster in the TTTa experiment and one and a half times faster in the TTTb experiment. The stronger BDC transports more dry/moist air from the tropopause to the stratosphere during DJF/JAS. This leads to enhancements of both negative and positive water vapor anomalies in the stratosphere in the TTTa and TTTb experiments although the water vapor increases for all year in the tropopause layer (Fig. 3c, e). The negative anomaly is stronger in the TTTa experiment than that in the TTTb experiment, which is consistent with the reduction of water vapor in the middle stratosphere in the TTTa experiment.

Fig. 3
figure 3

Time-pressure distributions of the water vapor averaged over 10°S–10°N in the a CNTL, b TTTa, and d TTTb experiments and the differences between c TTTa and CNTL experiments and e TTTb and CNTL experiments. Units: ppmv. The black lines indicate the position of 380 K potential temperature

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Similar to the water vapor, the vertical speed \({\overline {w} ^*}\) in the stratosphere averaged between 10°S and 10°N also has strong seasonal variation (Fig. 4a). The vertical upward speed is stronger during the DJF than that during JAS in all the three experiments (Fig. 5a), which is mainly because the planetary wave is stronger in the Northern Hemisphere winter than that in the Southern Hemisphere winter. It is interesting to note that the upward velocity increase is stronger in boreal winter than that in boreal summer in the stratosphere, especially in the TTTa experiment (Figs. 4b, c, 5b), which coincides with the phase of the dry signal in the tropopause (Fig. 3a). The seasonal difference of the vertical upward velocity between DJF and JAS reaches its maximum at 17 km, which are 0.46, 0.65, and 0.53 mm/s in the CNTL, TTTa, and TTTb experiments, respectively (Fig. 5b). It is stronger by about 40% in the TTTa experiment than that in the CNTL experiment. This means that the strengthening of the BDC would propagate more dry air from the tropopause into the stratosphere in DJF in the TTTa experiment. Thus, although the water vapor increases in the tropical tropopause layer, the total effect of the stronger BDC is to dry the stratosphere above 60 hPa in the TTTa experiment. On the contrary, the increase of the seasonal difference (by ~ 10%) in the TTTb experiment, which is confined between 16 and 18 km, is weaker than that in the TTTa experiment. The drying effect of the BDC is counteracted by the moistening processes induced by the TTT warming and methane oxidation in the TTTb experiment.

Fig. 4
figure 4

Time-pressure distributions of the \({\overline {w} ^*}\) averaged over 10°S–10°N in the a CNTL experiment, and the differences between b TTTa and CNTL and c TTTb and CNTL experiments. Units: mm/s

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Fig. 5
figure 5

Vertical profile of the vertical velocity \({\overline {w} ^*}\) averaged between 10°S and 10°N in the CNTL (the black lines), TTTa (the red lines), and TTTb (the blue lines) experiments. a The solid lines indicate the mean vertical velocity during JAS, and the dotted lines denote the mean vertical velocity during DJF. b The difference of the vertical velocity between DJF and JAS

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4 Conclusions and discussions

In this study, we analyze the impact of tropical tropopause warming on the stratospheric water vapor with the simulations by the SD-WACCM. By comparing the TTTa and TTTb experiments to the CNTL experiment, we find that the tropical tropopause warming results in a strengthening of the stratospheric BDC. This is mainly caused by the change in the zonal mean overturning circulation which is driven by the increase of the meridional temperature gradient over the warming region in the tropical tropopause layer (Fig. 1b, c). The increase of the tropical upwelling velocity in the stratosphere is stronger in boreal winter than that in boreal summer, especially in the TTTa experiment, which is consistent with the previous studies on the trends of the BDC under greenhouse warming (Lin and Fu 2013; Oberländer et al. 2013). The seasonal difference of the tropical upward velocity between DJF and JAS increases by about 40% in the TTTa experiment compared to the CNTL experiment, which means that the strengthening of BDC propagates more dry air in winter from the tropopause into the stratosphere (Fig. 3c). Hence, although the tropical tropopause warming results in an increase of water vapor in the tropical tropopause layer and the lower stratosphere, the stronger seasonal difference of BDC leads to a reduction of water vapor in the middle and upper stratosphere. On the contrary, the increase of the seasonal difference of the vertical velocity in the TTTb experiment, with a broader (25°S to 25°N) tropical tropopause warming similar to those in the CO2-increase experiments, is much smaller than that in the TTTa experiment (Fig. 5b). So, the BDC induced drying effect is counteracted by the moistening effects of TTT warming and methane oxidation in the stratosphere. Finally, the tropical tropopause warming results in stratospheric moistening in the TTTb experiment.

These results have important implications for understanding the stratospheric water vapor bias in the reanalysis data and inter-model differences. Here, we use the stratospheric water vapor data from Microwave Limb Sounder (MLS) on Aura satellite. A strict quality control process is conducted following Yan et al. (2015). Compared to the annual mean MLS observation, the ERA-interim reanalysis (ERAi) data (Dee et al. 2011) overestimates the water vapor in the tropical tropopause layer and the lower stratosphere but underestimates the water vapor in the middle and upper stratosphere (Fig. 6a, b). It is consistent with the results in Jiang et al. (2015). Here, we use 9-years (from 2005 to 2013) average for both the observation and reanalysis data. The distribution of the difference of stratospheric water vapor (Fig. 6b) resembles the difference between the TTTa and CNTL experiment (Fig. 1h). As shown in Fig. 6c, the tropical mean (between 10°S and 10°N) vertical velocity \({\overline {w} ^*}\), calculated with the 6-hourly ERAi data, is stronger in DJF than that in JAS. And the seasonal difference between DJF and JAS is very large, which reaches 0.7 and 0.6 mm/s at 16 and 17 km, respectively (Fig. 6d). Interestingly, the magnitude of the seasonal difference is similar to that in the TTTa experiment (Fig. 5b). In analogy, the BDC in the ERAi propagates more dry air from the tropopause to the stratosphere in boreal winter, which may result in dryer stratosphere accompanied by moister tropical tropopause layer than the observation (Fig. 6b).

Fig. 6
figure 6

Annual and zonal mean water vapor from a Aura MLS observations and b the fractional change between the ERA interim reanalysis and MLS averaged from 2005 to 2013. The units are ppmv in a and % in b, respectively. c Vertical profile of the vertical velocity \({\overline {w} ^*}\) averaged from 10°S to 10°N in the ERA Interim reanalysis during DJF (black line) and JAS (red line) and d the difference of vertical velocity between DJF and JAS, units: mm/s

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The results here call into attention the complex mechanisms via which TTT controls the stratospheric water vapor and indicate a possible negative impact. The warming of TTT results in more water vapor entering the stratosphere through the tropical tropopause, which is consistent with the results in Fueglistaler and Haynes (2005), but the associated strengthening of the BDC and its seasonal difference leads to the reduction of stratospheric water vapor in the higher altitudes. It reveals the importance of the change of the seasonality of the BDC on the variation of stratospheric water vapor.

A caveat worth noting is that the results reported here are based on the simulations by SD-WACCM using one ensemble member for each experiment. To fully understand the impact of the tropical tropopause warming on the stratospheric water vapor, it is important to perform TTT perturbation experiments in a fully coupled model in future studies.