Stratospheric water vapor is well known to be a greenhouse gas e.g.,. Because of this, understanding the processes that control the humidity of air entering the tropical lower stratosphere (hereafter [H2O]entry) has been a high priority of the scientific community since first described stratospheric circulation.

It is now well established that the fundamental control over [H2O]entry comes from the cold temperatures found in the tropical tropopause layer (TTL) , and that variability in these temperatures translates into variability in [H2O]entry. The most well-known example of this is the so-called “tape recorder”, in which the seasonal cycle in TTL temperatures is imprinted on tropical stratospheric water vapor .

On interannual timescales, variability in [H2O]entry originates from variability in the Brewer–Dobson circulation (BDC) and the quasi-biennial oscillation (QBO; ; ; ; ; ; ; ; ; ; ). suggest that the temperature of the troposphere also exerts an influence on [H2O]entry based primarily on an analysis of satellite measurements of [H2O]entry. This is mainly caused by radiative heating of the TTL from increased upwelling radiation from a warming troposphere . In addition to this mechanism, demonstrated in two CCMs that a warming climate also increases the amount of water directly injected into the stratosphere via deep convection, providing another mechanism for tropospheric temperature to affect [H2O]entry.

Putting these factors together, demonstrated that observed [H2O]entry anomalies could be accurately reproduced with a simple linear model: [H2O]entry=β0+βΔTΔT+βBDCBDC+βQBOQBO+ϵ, where ΔT is the temperature of the troposphere, BDC is the strength of the Brewer–Dobson circulation, QBO represents the phase of the QBO, and ϵ is the residual. analyzed the 21st century trend in one chemistry–climate model (hereafter, CCM; similar to general circulation models, but with a more realistic stratosphere and higher vertical resolution in the TTL) and found that the regression model worked well in reproducing the CCM's [H2O]entry trend over the 21st century. They concluded that the increase in [H2O]entry was driven by the increase in tropospheric temperatures, which was partially offset by a strengthening BDC.

The regression method provides a novel way to examine the regulation of [H2O]entry in CCMs and compare it to observations. The purpose of this paper is to see whether this linear decomposition of [H2O]entry variability holds in most CCMs and whether the same factors dominate.

We analyze model output from six CCMs participating in Phase 2 of the Chemistry–Climate Model Validation Project (CCMVal-2; ) and output from six CCMs participating in Phase 1 of the Chemistry-Climate Model Initiative (CCMI-1; ). Table  lists the model specifics and documentation.

We use simulations from the REF-B2 scenario of CCMVal-2. In this scenario, greenhouse gas concentrations during the 21st century come from the A1B scenario, which lies in the middle of the Special Report on Emissions Scenarios (SRES; ). Ozone-depleting substances come from the halogen emission scenario A1 . Specifics on CCMVal-2 can be found in and . We use the refC2 scenario of the CCMI-1. In this scenario, greenhouse gas concentrations come from the RCP6.0 scenario and ozone-depleting substances come from the halogen emission scenario A1 . CCMI-1 model specifics can be found in . In order to maintain a consistent reference period between models, our analysis covers 2000–2097, which we will hereafter refer to as “the 21st century”.

For each model, we fit CCM [H2O]entry using the multivariate linear regression (MLR) model described above. We use tropical average 80 hPa water vapor volume mixing ratio as a proxy for [H2O]entry (all tropical averages in this paper are averages over 30∘ N–30∘ S).

For our BDC index, we use 80 hPa diabatic heating rate (see , for details). Within models, studies have shown that the strength of the BDC increases throughout the 21st century, primarily resulting from increasing greenhouse gases e.g.,. Observations generally confirm that tropical upwelling into the lower stratosphere has strengthened . However, the BDC is not a directly observable circulation, and different variables including trace gas abundances, residual velocity, mean age of the air, and diabatic heating have been used . Thus, depending on the variable used, the strength of the connection between the BDC term and [H2O]entry may change.

The tropospheric temperature index is the 500 hPa tropical average temperature. For the few CCMI-1 simulations that only produce variables on hybrid pressure levels (CMAM-CCMI, CCSR/NIES-MIROC3.2, and MRI-ESM1r1), we choose a hybrid pressure level close to the 500 hPa pressure surface (See Table ). For the QBO index, we take the standardized anomaly of equatorial 50 hPa zonal winds (anomalies in this paper are calculated by subtracting the mean seasonal cycle). By examining 21st century 50 hPa zonal winds (shown in the figures in the Supplement), we find that only 5 of the 12 models simulate a QBO (Table ). As a result, we do not expect the QBO to significantly impact [H2O]entry in many of the models.

All of these choices are similar to those used by . The MLR returns the coefficients for each regressor in Eq. (), along with an uncertainty for each coefficient. Unless otherwise noted, we use 95 % confidence intervals in this paper. Autocorrelation in the residuals is accounted for in the uncertainties following . Finally, we will illustrate results with the MRI model; figures showing results derived from the other models can be found in the Supplement.

We first analyze the long-term trend in [H2O]entry over the 21st century. To do this, we calculate annual average values of [H2O]entry and perform an MLR against annual averages of the indices for BDC, QBO, and ΔT. For consistency, all annual average time series have had the 2000–2010 mean subtracted out. Most models simulate [H2O]entry increasing during the 21st century . However, recent observational studies have concluded that no significant historical trend in water vapor entering the lower stratosphere exists .

Figure shows that the fits to most of the models generate adjusted R2 values greater than 0.8. The NIWA-UKCA 21st century MLR has the lowest adjusted R2, with a value of approximately 0.6. Overall, this result confirms the result of that the regression model does a good job reproducing the CCMs' [H2O]entry. Because we have left long-term trends in the time series, we will refer to this as the “trended analysis”.

Ideally, we would compare the results of the last section to observations. Unfortunately, we do not have 100 years of observations to test the models against. Instead, we will compare regressions of 10-year segments from the CCMs to regressions of 10 years of observations. This will help us evaluate how good the models are and provide us with an indication of how representative a single decade is.

To do this, we split the 21st century of each CCM run into 10 decades (2000–2010, 2010–2020, 2020–2030, 2040–2050, etc.) and fit each individual decade using the regression model (Eq. ). The regression calculation used on each 10-year segment is identical to the century analysis, except monthly averaged anomalies of all quantities are used instead of annual mean anomalies. Following , decadal regression terms are lagged in order to maximize MLR fit: we lag ΔT by 3 months, the BDC by 1 month, and the QBO by 3 months. These lags reflect the time between changes in each index and the impact on [H2O]entry.

Figure shows the median ± 1 standard deviation of the 10 decadal adjusted R2 values generated by each CCM. The ensemble average is 0.61±0.25, with some spread among the models. Also plotted are the adjusted R2 values from two regressions of the tropical average Aura Microwave Limb Sounder (MLS) 82 hPa water vapor mixing ratio observations from 2004–2014 . One regression uses Modern-Era Retrospective Analysis for Research and Applications reanalysis (MERRA) and the other uses European Centre for Medium-Range Weather Forecasts interim reanalysis (ERAI) for the ΔT and BDC indices; the QBO index in both regressions are from observations, as calculated in .

Many of the models have a range of adjusted R2 values that overlap with the observational regression. However, the models producing the smallest decadal adjusted R2 values, CCSR/NIES, CNRM-CM5-3, and NIWA-UKCA, are also the models that produced the poorest fits to long-term detrended [H2O]entry. This provides some evidence that analysis of just a decade of [H2O]entry can provide insight into the long-term behavior of that quantity.

Figure shows the median and 1 standard deviation of each coefficient (values are listed in Table ), along with the coefficients from the regression of the MLS data (taken from Table 1 of ). We find that the CCMs agree unanimously that increases in ΔT are associated with increased [H2O]entry, though the CCM ensemble tends to underestimate the observational estimate. The only models that do not fall within both observational ranges are CCSR/NIES, CMAM-CCMI, and CNRM-CM5-3.

In addition, the spread between the different decades for a single model tends to be small. The coefficient for individual models ranges from 0.01 to 0.4 ppmv K-1, with an average of 0.15 ppmv K-1 and a standard deviation of 0.11 ppmv K-1. This provides additional confidence that the comparison between the CCMs and 1 decade of observations is meaningful.

Figure shows that there exists significant spread in the CCMs' decadal BDC regression coefficients. The coefficient for individual models ranges from -8.4 to +2.9 ppmv (K/day)-1, with an average of -3.55 ppmv (K/day)-1 and a standard deviation of 3.58 ppmv (K/day)-1. On all timescales, we expect a strengthening BDC to cool the TTL and reduce [H2O]entry, so the coefficient should be negative. We see that the median is indeed negative for all CCMs except for the CNRM-CM5-3 and NIWA-UKCA (these models also generated positive BDC coefficients for the century analysis).

When comparing with observations, we find that the model ensemble does well. The CCSR/NIES, CCSR/NIES-MIROC-3.2, CMAM, CMAM-CCMI, LMDZrepro, MRI-ESM1r1, and WACCM decadal BDC regression coefficients fall within 95 % confidence of MERRA, and the CCSR/NIES-MIROC-3.2, LMDZrepro, and WACCM fall within 95 % confidence interval of ERAI. As with the ΔT coefficient, the spread between the different decades for a single model tends to be small.

Figure shows that, for all CCMs, the ensemble average decadal QBO coefficient is approximately 0 ppmv. For those CCMs that do simulate a QBO, the ensemble average coefficient is 0.02±0.03 ppmv. This is significantly smaller than the response to the QBO in the observations. Only CCSR/NIES-MIROC3.2 and CMAM-CCMI decadal regressions produce QBO coefficients approaching those from both observational regressions. Again, CMAM-CCMI does not simulate a QBO, and it is not clear to us why the model does so well in this aspect of our analysis.

Previous studies found that the QBO significantly influences TTL temperatures and subsequently [H2O]entry , so the lack of response in the model ensemble appears to be a problem in the models. Previous studies have investigated this issue, finding that a higher vertical resolution within the stratosphere can help resolve the QBO's impact on the lower stratosphere . Clearly, this needs to be investigated further.

Similar to both the trended and detrended regression analysis, we calculated the regression coefficients using standardized variables of the decadal analysis, and the values are listed in Table 4. Within most models, we see that the BDC, on decadal timescales, has the largest impact on [H2O]entry, with ΔT having a smaller impact.

One interesting question is whether or not the regression coefficients from the decadal analyses are related to regression coefficients from century regressions. To answer this, Fig.  shows the coefficients from the trended century regressions of each CCM plotted against the median of the decadal regressions from the same CCM. Also shown is a linear least-squares fit to the points. For the ΔT coefficient, the best-fit line is β(ΔT,century)=1.21±0.44β(ΔT,decade)+0.13±0.08. All uncertainties are 95 % confidence intervals. Thus, the ΔT coefficients from the trended MLRs are slightly larger than those from the decadal MLRs. Using values of β(ΔT,decade) from MLS observations and this fit, we predict β(ΔT,century) of 0.50±0.06 and 0.55±0.08 ppmv K-1 for MERRA and ERAI regressions, respectively.

For the BDC coefficient, the best-fit line is β(BDC,century)=1.16±0.32β(BDC,decade)+0.56±1.56. The BDC coefficients from the trended MLRs also have a slightly larger magnitude than those from the decadal MLRs. By fitting the observed values of β(BDC,decade) through Eq. (), we predict β(BDC,century) values of β(BDC,century) of -3.45±1.09 and -2.34±1.09 ppmv (K/day)-1 for MERRA and ERAI regressions, respectively.

For the QBO coefficient, the best-fit line is β(QBO,century)=0.75±0.40β(QBO,decade)+0.004±0.01. The QBO coefficients from the trended MLRs are slightly smaller than those from the decadal MLRs. Again, using Eq. (), we predict β(QBO,century) values of 0.09±0.03 and 0.09±0.02 ppmv for MERRA and ERAI regressions, respectively.

Climate models predict that tropical lower-stratospheric humidity ([H2O]entry) will increase as the climate warms, with important implications for the chemistry and climate of the atmosphere. We demonstrate in this paper that the regression used by can be used to quantify the physical processes underlying these model trends and variability in an ensemble of CCMs. Our method is based on regressing CCM [H2O]entry time series against three processes that have been shown to be important to [H2O]entry: tropospheric temperature (ΔT), the strength of the Brewer–Dobson circulation (BDC), and the phase of the QBO. Our approach provides insight into model processes not available by simply comparing [H2O]entry to TTL temperatures.

We do this on two separate timescales: (1) the 21st century and (2) on decadal timescales. Considering all of our analyses, we find that long-term increase in [H2O]entry, in the CCMs, is primarily driven by warming of the troposphere. This is partially offset in most CCMs by an increase in the strength of the Brewer–Dobson circulation, which tends to cool the tropical tropopause layer (TTL) . For shorter-term internal variability, we find variability in the Brewer–Dobson circulation is of greater importance to the variability of [H2O]entry, consistent with and . The models show little impact from the QBO.

The coefficients from regressions of individual decades in the CCMs can be compared to coefficients from regressions of observations covering a decade. Overall, the CCM ensemble reproduces [H2O]entry observations well, except for the fact that the CCMs simulate little response to the QBO, in disagreement with the observations ; this appears to be a deficiency in the models.

That said, the good agreement of the ensemble average hides some spread among the models, particularly in the response to the BDC. Of particular note, the CNRM-CM5-3 and NIWA-UKCA regressions generate positive BDC regression coefficients, contrary to the other models and contrary to our expectations.

Our overall conclusions are encouraging – the models appear to respond to the factors that control [H2O]entry in realistic ways, providing some confidence in their simulations of [H2O]entry. Nevertheless, our work has pointed out issues that should be resolved. Some models have clear problems, e.g., the models that predict [H2O]entry will increase with a strengthening BDC. In addition, nearly the entire ensemble does not reproduce the observed variations of [H2O]entry with the phase of the QBO. This analysis should help the modeling groups refine their models' simulations of the 21st century.