In this paper, we analyze nine models from the Precipitation Driver and Response Model Intercomparison Project (PDRMIP) (Samset et al., 2016; Myhre et al., 2017; Tang et al., 2018, 2019). These are Coupled Model Intercomparison Project phase 5 (CMIP5) era models (Table 1), and each performed a baseline and multiple climate perturbation experiments (Table 1). This subset of the CMIP5 ensemble has a multi-model mean equilibrium climate system (ECS) of 3.6 K, close to the ensemble average ECS of the entire CMIP5 ensemble (3.3 K) (Zelinka et al. 2020).

In the perturbation experiments, perturbations on a global scale are applied abruptly at the beginning of the model simulation. The five core experiments include a doubling of CO2 concentration (2×CO2), a tripling of CH4 concentration (3×CH4), a 2 % increase in solar irradiance (2%Solar), an increase in present-day black carbon concentration or emission by a factor of 10 (10×BC), and an increase in present-day SO4 concentration or emission by a factor of 5 (5×SO4). In addition to the five core experiments, a subset of models also performed additional perturbation experiments: an increase in CFC-11 concentration from 535 ppt to 5 ppb (hereafter, 10×CFC-11), an increase in CFC-12 concentration from 653.45 ppt to 5 ppb (hereafter, 10×CFC-12), an increase in N2O concentration from 316 ppb to 1 ppm (hereafter, 3×N2O), an increase in tropospheric O3 concentration used in MacIntosh et al. (2016) by a factor of 5 (5×O3), and an increase in present-day black carbon with a shorter lifetime by a factor of 10 (10×BCSLT). We note that indirect chemical effects are not included in the 3×CH4 experiment. Table 1 provides details about the models and the perturbations each one simulated.

The perturbations in GHGs and solar irradiance are relative to the models' baseline simulations, in which the concentrations of GHGs and solar irradiance are either at present-day levels or preindustrial levels. The perturbations in the aerosols depend on whether it is possible to prescribe aerosol concentrations in the models. For models that are able to prescribe aerosol concentrations, the aerosol perturbations are based on a multi-model mean baseline aerosol concentration in 2000 obtained from the AeroCom Phase II initiative (Myhre et al., 2013a). For those that are only able to produce aerosols through emissions, the perturbation is applied by increasing the emissions by the factors listed above. The 10×BCSLT experiment is performed only by models that are able to prescribe aerosol concentrations.

Each perturbation experiment is performed in two configurations: a fixed sea surface temperatures simulation (“fixed SST”) and a fully coupled (slab ocean for CAM4 only) simulation. The fixed SST simulations use the SST climatology at either the present-day or preindustrial level. The fixed SST simulations are at least 15 years, and the coupled simulations are at least 100 years.

When available, the SWV mixing ratio is obtained directly from the specific humidity output by each model simulation. For the models that do not output specific humidity (CAM5, GISS-E2-R, and MIROC-SPRINTARS), we calculate specific humidity by multiplying the models' relative humidity by the saturation mixing ratio with respect to ice calculated using model temperature and pressure. Responses of specific humidity and relative humidity in the PDRMIP have been investigated by Hodnebrog et al. (2019), but they focused on water vapor in the troposphere.

We define ΔSWV, the change in the SWV mixing ratio in response to a particular perturbation, to be the difference between SWV in the perturbed coupled run and that in the baseline coupled run. As discussed above, the ΔSWV can then be broken down into the two components: the fast response (ΔSWVfast) and slow response (ΔSWVslow). We compute results in the tropical lower stratosphere (70 hPa, 30∘ N–30∘ S, hereafter, TLS), in the northern hemispheric (NH) lowermost stratosphere (50–90∘ N at 200 hPa, hereafter, NH LMS), and in the southern hemispheric (SH) lowermost stratosphere (50–90∘ S at 200 hPa, hereafter, SH LMS). Most previous studies have focused on the response of water vapor in the TLS (e.g., Gettelman et al., 2010; Shu et al., 2011; Smalley et al., 2017). But recent studies report that the climate is most sensitive to changes in water vapor in the LMS (Solomon et al., 2010; Dessler et al., 2013; Banerjee et al., 2019), so we also investigate that region.

We use the fixed SST simulations to get ΔSWVfast, the rapid adjustment in SWV before sea surface temperature changes. ΔSWVfast is the difference between the SWV mixing ratio averaged over the last 10 years in the fixed SST run with the forcing perturbation and the SWV mixing ratio averaged over the last 10 years in the fixed SST baseline simulation. The fixed SST runs have some warming of the land surface, meaning that our fast response includes a contribution from a warming land surface. We expect this will have a small impact on our results, but it remains one of the uncertainties in our analysis.

We calculate ΔSWVslow as ΔSWV minus ΔSWVfast. To estimate the time series of ΔSWVslow, we use annual mean ΔSWV time series over the entire coupled run period (at least 100 years) minus the 10-year average ΔSWVfast. To estimate equilibrium ΔSWVslow, we use a regression method similar to the methodology introduced by Gregory et al. (2004). The basic concept is that we regress the annual mean global average net downward radiative flux (R) at the top of the atmosphere (TOA) against the annual mean ΔSWV averaged at TLS, NH LMS, or SH LMS. The equilibrium ΔSWV is where the linear fit intercepts at R=0. Then we simply subtract ΔSWVfast from the equilibrium ΔSWV to estimate equilibrium ΔSWVslow.

These regressions can be very noisy and yield highly uncertain parameters, particularly for perturbations with relatively small amounts of radiative forcing and warming. To account for this, we first fit the R and ΔSWV time series using an exponential function (y(t)=b+a1⋅e-t/τ1+a2⋅e-t/τ2) and then do the regression using the fitted time series. For fully coupled models, we constrain τ1 to be within the range of 4±2 years and τ2 to be within the range of 250±70 years; for CAM4, in which the atmosphere is coupled to a slab ocean, we constrain τ1 to be within the range of 4±2 years. We then compute the best fit of all parameters. The ranges for the time constants are based on previous estimations of climate system timescales (Geoffroy et al., 2013). We estimate the ΔSWV intercept at R=0 by regressing the fitted R and ΔSWV data over the last 30 years, since the relation between R and ΔSWV is not necessarily linear over the entire 100-year period. The slow and fast responses of other variables, such as global average surface temperatures and cold-point temperatures, are computed using the same method.

We tested this method in a climate model that nearly reaches the equilibrium climate state. We analyzed runs of the fully coupled Max Planck Institute Earth System Model version 1.1 (MPI-ESM1.1) (Maher et al., 2019), which has a transient climate response and an effective climate sensitivity near the middle of the CMIP5 ensemble range (Adams and Dessler, 2019; Dessler, 2020). It includes a 2000-year preindustrial control run and a 2614-year abruptly quadrupled CO2 run. The values of ΔSWV averaged over the last 30 years of the 4×CO2 run relative to the control run are 4.60 ppmv in the TLS, 22.40 ppmv in the NH LMS, and 9.69 ppmv in the SH LMS. We expect this to be close to equilibrium ΔSWV because the trend in global average surface temperature over the last 500 years of the 4×CO2 run is 0.02 K per century. We use the regression method to estimate the equilibrium ΔSWV using MPI-ESM1.1 water vapor mixing ratio time series over the first 100 years and obtain estimates of 4.38 ppmv in the TLS, 20.01 ppmv in the NH LMS, and 9.07 ppmv in the SH LMS; these yield differences of 0.22 ppmv in the TLS, 2.39 ppmv in the NH LMS, and 0.62 ppmv in the SH LMS. Thus, our method underestimates the true equilibrium value by 5 % in the TLS, 11 % in the NH LMS, and 6 % in the SH LMS.

Uncertainty for slow and fast responses of different quantities shown in this paper is obtained from Monte Carlo samples as follows: for each perturbation, we randomly sample with replacement 100 000 times for each model that performed that perturbation and from these samples compute the 2.5–97.5 percentiles.

We show equilibrium ΔSWVslow and its percentage contribution to the total equilibrium ΔSWV in Fig. 1. We show results in the TLS (Fig. 1a and d), in the NH LMS (Fig. 1b and e), and the SH LMS (Fig. 1c and f). In evaluating the absolute magnitude of ΔSWVslow in the first column of Fig. 1, we normalize the equilibrium ΔSWVslow using effective radiative forcing (ERF) so that differences in the magnitude of the forcing do not confound our results.

ERF values used in the construction of Fig. 1 are plotted in Fig. 2a; they are calculated as the difference in net radiation at the top of the atmosphere (TOA) averaged over the last 10 years between the fixed SST perturbed and baseline simulation. Previous studies have computed the ERF in the PDRMIP using various methods (Richardson et al., 2019; Tang et al., 2019). The ERF calculation in our paper uses the same method as the ERFsst in Richardson et al. (2019). We directly compared our ERF with the ERFsst listed in Richardson et al. (2019), which shows good agreement and can be found in the Supplement (Table S3). The equilibrium global averaged surface temperature changes (ΔTs), estimated using the regression method described in Sect. 2.2 and normalized by ERF, are plotted in Fig. 2b. The multi-model mean ΔTs / ERF shows general agreement across different perturbations. This quantity is the inverse of the feedback parameter λ (e.g., Dessler and Zelinka, 2015), so Fig. 2b implies that the climate sensitivity to these different perturbations is similar, which also agrees with Richardson et al. (2019). We list the ERF and ΔTs quantities for each model and perturbation in Table S1.

In each region, the magnitude of multi-model mean ΔSWVslow / ERF shows general agreement for different perturbations. The magnitudes of ΔSWVslow / ERF in the LMS are larger than those in the TLS (Fig. 1b–c). This is consistent with previous studies, which showed that the long-term trend in SWV over the century in climate models is largest near the LMS tropopause (Dessler et al., 2013; Huang et al., 2016; Banerjee et al., 2019). This reflects different transport pathways into the LMS, including downward transport by the Brewer–Dobson circulation, quasi-horizontal isentropic mixing from the tropical troposphere, and convective influence (Dessler et al., 1995; Holton et al., 1995; Plumb, 2002; Gettelman et al., 2011).

In the LMS, the multi-model mean ΔSWVslow / ΔSWV ratio is close to 100 % for many perturbations (Fig. 1e–f). The latitude band (50–90∘) we choose is somewhat arbitrary, so in the Supplement (Fig. S1), we also show ΔSWVslow / ERF and ΔSWVslow / ΔSWV ratios for water vapor averaged at 200 hPa between 30∘ and 50∘ latitudes in the Northern Hemisphere and Southern Hemisphere, respectively, which also show that the ΔSWVslow plays a dominant role and contributes to close to 100 % of the total ΔSWV for most perturbations. In the TLS, the multi-model mean ΔSWVslow / ΔSWV ratio is generally above 50 %, with a few exceptions. We will discuss this in detail in Sect. 3.3.

We note that inter-model variability in ΔSWVslow / ERF and ΔSWVslow is generally consistent for different perturbations. For example, HadGEM3 produces larger responses than the rest of the models for most perturbations (Fig. 1a–c, Table S1). GISS-E2-R and MIROC-SPRINTARS have ΔSWVslow / ERF and ΔSWVslow values generally below the rest of the models (Fig. 1a–c, Table S1). We have not further investigated the causes of these differences among models; this clearly warrants further investigation.

We also note that CAM5, CanESM2, and MIROC-SPRINTARS produce negative TLS ΔSWVslow / ERF for 10×BC. These negative values are partly contributed by artifacts of the method we use to estimate equilibrium ΔSWVslow, which is the residual of the total equilibrium ΔSWV minus ΔSWVfast. When differencing two numbers with similar magnitudes, the residual may be quite uncertain. So, the negative values here do not necessarily mean that a BC-induced surface warming results in a negative SWV slow response. The direct regression between ΔSWVslow and surface temperature change described in the next section more accurately describes the relationship for these cases.

Our results show that, in most climate perturbations analyzed in this study, the equilibrium response of water vapor in both the TLS and the LMS is dominated by ΔSWVslow, which is the component mediated by sea surface temperature change. To directly quantify how SWV responds to surface temperature across a range of different climate change mechanisms, we linearly regress the time series of annual mean ΔSWVslow over the entire period of the coupled simulations (at least 100 years) against the time series of annual mean global averaged surface temperature change (ΔTs). We do this regression for each model and perturbation separately. This is similar to the analysis of Banerjee et al. (2019), who did this for quadrupled CO2 perturbation, but we do this for multiple perturbations.

The scatter plot for each perturbation and model is shown in the Supplement (Figs. S3–S5). For most perturbations and models, the ΔSWVslow time series in both the TLS and the LMS is positively correlated with the ΔTs time series, supporting the hypothesis that the surface temperature change contributes to the long-term trend in SWV for most cases.

Figure 3 shows the slopes of the regression for all perturbations and models. The corresponding slope values are listed in Table S4. We also list slopes in the unit of percent per Kelvin (% K-1) in Table S5. The uncertainty of the slopes is obtained from Monte Carlo samples: for each model and perturbation, we first randomly sample the slope 100 000 times, assuming a Gaussian distribution. Then, for each perturbation, we sample from the slope distributions with replacement 100 000 times for each model that performed that perturbation and from these samples compute the 2.5–97.5 percentiles.

In both the TLS and LMS, the slopes from different perturbations show general agreement (Fig. 3); this is also true for water vapor averaged at 200 hPa between 30∘ and 50∘ latitudes in the Northern Hemisphere and Southern Hemisphere (Fig. S2). In the TLS, the multi-model and multi-perturbation average slope is 0.35 ppmv K-1, with a 95 % confidence interval of 0.28–0.44 ppmv K-1 (Fig. 3a). The LMS ΔSWVslow time series has stronger correlations with the ΔTs time series (Figs. S3–S5) and produces larger sensitivities (Fig. 3b–c). Specifically, the multi-model and multi-perturbation mean slope is 2.1 ppmv K-1 in the Northern Hemisphere and 0.97 ppmv K-1 in the Southern Hemisphere, with 95 % confidence intervals of 1.82–2.39 ppmv K-1 and 0.79–1.15 ppmv K-1, respectively. Our results are similar to those of Dessler et al. (2013) and Smalley et al. (2017) despite the fact that they used 500 hPa temperature as their regressor.

We show that the relation between ΔSWVslow and ΔTs time series can be extended to the entire stratosphere (Fig. 4a). We regridded the zonal mean ΔSWVslow from all models and perturbations onto the same pressure–latitude grid (10 hPa above 100 hPa and 50 hPa below 100 hPa, 4∘ latitude) and regressed the ΔSWVslow time series at each grid point against global average ΔTs time series. The multi-model and multi-perturbation average slope of the linear fit at each grid point is shown in Fig. 4a (figures for each individual perturbation are shown in Fig. S6). Since the vertical gradient of water vapor is large, we plot the percentage change in the mixing ratio per Kelvin relative to the baseline. Lapse rate tropopause, the lowest level where the lapse rate decreases to 2 K km-1, also plotted, is obtained using the atmospheric temperatures from the baseline coupled run and multi-model mean.

We clearly see the larger sensitivity of ΔSWVslow to ΔTs in the LMS than in the overworld. In the LMS, the slope has a hemispheric asymmetry, with larger values in the Northern Hemisphere. This is consistent with previous studies, which showed that isentropic transport brings more tropospheric water vapor to the NH than the SH (Pan et al., 1997, 2000; Dethof et al., 1999, 2000; Ploeger et al., 2013). In addition, convective moistening may be more important to the NH due to more land in the Northern Hemisphere and, consequently, more convection (Dessler and Sherwood, 2004; Smith et al., 2017; Ueyama et al., 2018; Wang et al., 2019). We also see large responses in the tropical upper troposphere, which is the main part of the tropospheric water vapor feedback. The sensitivity declines as one ascends through the TTL. Once above the TTL, the sensitivity in the overworld is relatively uniform with altitude.

Figure 1 also shows the ΔSWVfast normalized by the ERF (Fig. 1g–i) and its contribution to total equilibrium ΔSWV (Fig. 1j–l). As discussed previously, ΔSWVfast is the rapid adjustment in SWV before the sea surface temperatures respond. For most perturbations, especially in the LMS, ΔSWVfast / ERF is smaller than ΔSWVslow / ERF, with a magnitude of a few tenths of a part per million by volume per watt per square meter (ppmv (W m-2)-1).

For 2×CO2, the near-zero TLS ΔSWVfast / ERF is the result of cancellation between cooling by a strengthening Brewer–Dobson circulation and increased local radiative heating (Lin et al., 2017). Some other GHG forcing agents, however, produce larger TLS ΔSWVfast / ERF and contributions in the TLS. For both 10×CFC-12 and 10×CFC-11 the multi-model mean ΔSWVfast contributes about half of the total ΔSWV (Fig. 1j). This is a consequence of halocarbons producing more TTL warming per watt per square meter (W m-2) by efficiently absorbing upwelling longwave radiation from the troposphere in the atmospheric window (Forster et al., 1997; Jain et al., 2000; Forster and Joshi, 2005). Figure 5 shows the fast temperature response per unit ERF due to different perturbations, and it shows heating in the TTL for both 10×CFC-12 and 10×CFC-11.

The 3×CH4 also includes some models that produce large TLS ΔSWVfast / ERF magnitudes. This is likely due to TTL heating (Fig. 5) by CH4 shortwave absorption, which is explicitly treated in some models, including CAM5, CanESM2, MPI-ESM, and MIROC-SPRINTARS (Smith et al., 2018). These models are also the ones that produce the largest TLS ΔSWVfast contributions (Fig. 1g and j).

Increases in tropospheric O3 (in the 5×O3 experiment) reduce the upwelling longwave radiation, which cools the stratosphere (Ramaswamy and Bowen, 1994; Berntsen et al., 1997; Forster et al., 1997). The longwave radiation absorbed heats the TTL region (Fig. 5), resulting in larger TLS ΔSWVfast / ERF magnitude than ΔSWVslow / ERF and larger contributions to total equilibrium ΔSWV (77 %) (Fig. 1g and j). There is also heating in the LMS, resulting in larger LMS ΔSWVfast / ERF magnitude than ΔSWVslow / ERF (Fig. 1h–i and k–l). We note that our conclusion on 5×O3 is based on only one model, MIROC-SPRINTARS.

ΔSWVfast from 10×BC dominates total equilibrium ΔSWV in the TLS, with a multi-model mean contribution of 84 %. The magnitude of the multi-model mean ΔSWVfast / ERF from 10×BC is also larger than any other perturbations in each region. This occurs because the 10×BC strongly absorbs shortwave radiation, causing large heating of the tropopause region in both the tropics and extratropics. Figure 5 shows that the 10×BC gives by far the most warming per unit ERF, which is consistent with the vertical profile of fast temperature response shown in Stjern et al. (2017).

The 10×BC ΔSWVfast / ERF in the NH and SH LMS contributes about 50 % of the total equilibrium ΔSWV, with smaller magnitudes in the Southern Hemisphere (Fig. 1h–i and k–l). This is because the total amount of black carbon is smaller in the Southern Hemisphere (Myhre et al., 2017), since black carbon is a combustion product and is predominantly emitted over the NH continents (Ramanathan and Carmichael, 2008). The 10×BCSLT ΔSWVfast also contributes about 50 % of the total 10×BCSLT ΔSWV. The 10×BCSLT does not produce as strong a ΔSWVfast / ERF as 10×BC, since the reduction in BC lifetime leads to less BC in the TTL and therefore less heating per unit ERF.

We quantify control of TLS ΔSWVfast by the fast TTL temperature adjustments across a range of different climate perturbations by regressing the TLS ΔSWVfast against the fast response of the cold-point temperature (ΔTCPfast). To estimate ΔTCPfast in the models, we first find the minimum temperature in the profile at each grid point in the fixed SST runs (no interpolation is done; we simply find the minimum temperature on the output model levels). These minimum temperatures are then averaged between 30∘ N and 30∘ S to yield TCPfast in each run. ΔTCPfast is the difference between TCPfast in the perturbed model run and that in the baseline runs.

We find that TLS ΔSWVfast is strongly correlated with ΔTCPfast across all perturbations and models (Fig. 6a), with a slope of 0.52 ppmv K-1 and a 95 % confidence interval of 0.43 to 0.61 ppmv K-1. Randel and Park (2019) pointed out that the slope from the Clausius–Clapeyron relationship evaluated near the tropical tropopause is close to this value, about 0.5 ppmv K-1. We also tested the relationship between TLS ΔSWVslow and the slow response of the cold-point temperature (ΔTCPslow) across all perturbations and models, yielding a slope of 0.72 ppmv K-1. However, for the slow response, correlation does not necessarily prove causality, since Dessler et al. (2016) showed that, in two climate models at least, a significant fraction of the long-term trend was due to increases in convective moistening, which bypasses the TTL cool trap. Therefore, this relationship for the slow response could arise from either TCP control, a process that correlates with it, such as deep convective injection of ice, or some combination.

We also separately plot the slopes between ΔSWVfast and ΔTCPfast for each perturbation (Fig. 6d–f). For the perturbations that have more than five participating models, including 2×CO2, 3×CH4, 2%Solar, 10×BC, 5×SO4, and 10×CFC-12, we calculate the linear regression between ΔSWVfast and ΔTCPfast from the models and show the slopes and 95 % confidence intervals. For the perturbations that have fewer participating models, including 10×CFC11, 3×N2O, 5×O3, and 10×BCSLT, we plot the ratio ΔSWVfast / ΔTCPfast and show only the multi-model mean. The slopes produced by different perturbations show general agreement (Fig. 6d). The larger uncertainty in the slopes produced by 2%Solar and 10×CFC-12 occurs because both the ΔTCPfast and ΔSWVfast produced by different models are similar, and therefore the slope of the linear regression is uncertain. Overall, we find that the fast response of TTL temperature is a good predictor for the TLS ΔSWVfast across a range of different climate mechanisms and across multiple models.

For the LMS ΔSWVfast, the ΔTCPfast does not show a control as strong as that in the TLS (Fig. 6b–c) due to the fact that TTL temperatures are only one factor that influences the LMS. In addition, the regression between ΔSWVfast and ΔTCPfast across all perturbations at each grid point in the pressure–latitude domain shows that the slope (% K-1) follows the transport pattern of the Brewer–Dobson circulation (BDC) (Fig. 4b). The slope is large in the tropical overworld stratosphere and becomes weaker as one moves poleward and downward in the extratropics below 150 hPa. The value is lower in the LMS, again consistent with the fact that water vapor in the LMS is controlled by several processes, not just TTL cold-point temperature. Clearly, more work on this is warranted.