Data from 11 GCMs involved in PDRMIP have been used – details about PDRMIP and the participating models (except ECHAM-HAM – see Sect. S1 in the Supplement) are given in Myhre et al. (2017). The core PDRMIP experiments consist of one base experiment, representing present-day conditions (pre-industrial for HadGEM2), and five perturbation experiments relative to base: doubling of the CO2 concentration (hereafter denoted CO2x2), tripling of the CH4 concentration (CH4x3), total solar irradiance increased by 2 % (Sol+2%), 5 times increase in anthropogenic sulfate concentration or SO2 emissions (SO4x5), and 10 times increase in BC concentration or emissions (BCx10). Each experiment has been run with two model set-ups: with fixed SSTs and with a coupled model configuration, being run for at least 15 and 100 years, respectively. Analyses here are based on years 6–15 from the fixed SST experiments and years 51–100 from the coupled experiments. Each model has run one ensemble member, but the model-mean water vapour lifetime sensitivity (WVLS; see Sect. 2.3) for each experiment differs by only 3 % or less if results from years 51–75 or 76–100 are used instead of years 51–100 from the coupled experiments; this indicates a strong signal-to-noise ratio.

All the PDRMIP models include aerosol–radiation interaction (direct aerosol effect) and associated cloud changes through changes in humidity and stability (rapid adjustments). Most models (except GISS-E2-R and NCAR-CESM1-CAM4) include aerosol–cloud interactions (indirect aerosol effects), which involve aerosol influences on cloud microphysics and are connected with large uncertainties (Boucher et al., 2013).

All model data have been regridded to T42 horizontal resolution, and, in the case of 3-D data, to 60 vertical layers stretching from the surface to 0.1 hPa. In Fig. S1 in the Supplement, IWV in the PDRMIP base experiment has been compared with observations from MODIS Aqua and Terra level 3 data (downloaded from https://giovanni.gsfc.nasa.gov/giovanni/, last access: 2 May 2016), and the cycle 36 output from the European Centre for Medium-Range Weather Forecasts Integrated Forecast System model for the year 2010. Four of the PDRMIP models did not have 3-D fields with specific humidity available, but for these models the specific humidity was calculated based on temperature, pressure, and relative humidity in each grid box and for each month.

Data from 26 GCMs participating in CMIP5 (Taylor et al., 2011) were obtained (see Fig. 4 for model names) for the historical (1850–2005) and RCP8.5 (a high-emission pathway) (van Vuuren et al., 2011) (2006–2100) experiments and for the variables surface air temperature, evaporation, and water vapour path (here denoted integrated water vapour). The WVL was calculated by taking the global and 20-year mean IWV divided by evaporation (evaporation and precipitation are equal in the global mean).

The global-mean water vapour lifetime sensitivity follows the approach of Kvalevåg et al. (2013) and is calculated as WVLi=IWViPiΔWVL=WVLi-WVLbaseWVLS=ΔWVLΔTs, where WVLi is the lifetime (in days), IWVi is the global-mean integrated water vapour (kg m-2), and Pi is the global-mean precipitation (kg m-2 d-1) for a perturbation experiment i. The water vapour lifetime change, ΔWVL, is the difference between the lifetime in the perturbation and base experiments. The WVLS is the lifetime change divided by the global-mean surface temperature change, ΔTs. The ΔWVL due to fast responses has been split into contributions from IWV and P by calculating the ΔWVL twice, with the IWV and P terms held constant one at a time. This assumption involves nonlinear terms, but the model-mean difference between the actual ΔWVL and the sum ΔWVLIWV+ΔWVLP is less than 2 % for all drivers.

Table 1 shows that the slow responses of global-mean water vapour per kelvin of change in surface temperature are fairly close to the 7 % K-1 that we expect from the Clausius–Clapeyron relation. However, the numbers differ somewhat between drivers, ranging from 6.5±1 % K-1 for SO4x5 to 8.1±1 % K-1 for Sol+2%. These differences become larger when the fast response is included, which adds to the pure surface-temperature-related response. The fast response is largest for BCx10, which changes from 7.5±1 % K-1 to 9.8±2 % K-1 between the slow and total response.

Integrated water vapour increases much more than evaporation and precipitation at nearly all latitudes and for all five PDRMIP drivers (Figs. 1, S2–S3). However, the total global-mean increase in IWV differs strongly between each driver, with BCx10 at 9.8±2 % K-1 and SO4x5 at 6.4±0.9 % K-1 (Table 1). The estimated global IWV increase for BCx10 ranges from 6.8 to 13 % K-1 for the different PDRMIP models, while locally decreasing in some regions (Fig. S4). BCx10, and to some extent SO4x5, show steep north–south gradients in the IWV change, emphasizing the strong regional influences of these short-lived compounds (Figs. 1, S3–S4). The north–south gradient for BCx10 is steeper for the total response (Fig. 1b) than the slow response (Fig. 1a) due to strong influence of the fast response for this compound. In contrast to the other climate drivers, precipitation decreases and water vapour increases strongly for BCx10.

In order to explore reasons for differences in IWV between the drivers, we compare vertical profiles of specific and relative humidity and temperature for each of the climate drivers (Fig. 2). For the fast response from CO2x2, the change in the specific humidity profile differs considerably from what would be expected by the Clausius–Clapeyron relation when assuming that relative humidity stays constant (Figs. 2a, S5–S6), a common assumption in climate change studies (Allen and Ingram, 2002). This indicates that the changes are not only temperature-driven. The specific humidity change for CO2x2 is around half of the expected temperature-induced change throughout most of the lower troposphere, explained by a tropospheric relative humidity decrease that peaks near 800 hPa (Fig. 2c). This relative humidity decrease, and thus specific humidity decrease, contributes to the small fast IWV response for CO2x2 (Table 1). Over land, the lower-than-expected increase in specific humidity is particularly evident in the lower troposphere (Fig. S5), and could be explained by the physiological effect since increased CO2 leads to less evaporation from vegetation (Richardson et al., 2018a). CH4x3 shows some of the same tendency as CO2x2 (Fig. 2a) but without any considerable change in relative humidity (Fig. 2c). Sol+2% largely follows the temperature-induced change in specific humidity (Fig. 2a).

In contrast to the CO2x2 experiment, BCx10 mostly yields a small increase in relative humidity (Fig. 2c), especially close to the surface, and therefore the specific humidity change for BCx10 is larger than the temperature-induced change throughout most of the troposphere (Fig. 2a). This low-level relative humidity increase contributes to the large fast IWV response for BCx10 (Table 1). Additional contributions come from atmospheric solar absorption due to BC, which leads to rapid atmospheric temperature increase (Fig. 2d) and therefore increased water vapour availability. It is also worth noting the different lapse rates between the drivers, with temperature changes decreasing with height for CO2x2 and increasing with height for BCx10 (Figs. 2d, S6), and this has implications for atmospheric stability.

Changes in specific humidity profiles for the slow response (Fig. 2b) show that the assumption of constant relative humidity does hold. When normalized with ΔTs, the specific humidity profiles are similar between the drivers, with a small exception for SO4x5, which shows a smaller increase throughout the troposphere. One reason is that SO4x5 is the driver that gives the least change in the temperature profile (and lapse rate up to 300 hPa) when normalized with surface temperature change (Fig. S7, lower left), and therefore the least change in the water vapour availability. It is also worth noting the strong difference between land and sea in the temperature change profile for this driver. The small increase in vertical temperature profiles compared to the other drivers could explain why SO4x5 has the smallest slow IWV response (Table 1). Sol+2%, which has the largest slow IWV response, has the second strongest increase in temperature profile per kelvin of surface temperature change (Fig. S7). BCx10 gives the strongest increase in atmospheric temperature, but a decrease in relative humidity, especially over land (Fig. S7), leads to a discrepancy between the actual specific humidity change and the temperature-driven change between the surface and 800 hPa (Fig. 2b).

Earlier studies have shown a strong land–ocean contrast in the response of near-surface relative humidity to global warming, mainly due to greater warming over land than ocean (Byrne and O'Gorman, 2016). Inspection of near-surface relative humidity changes shows that patterns of reduced relative humidity over land and increased relative humidity over oceans are rather similar between drivers for the slow response (Fig. 3). However, the fast response constitutes a large part of the total response for all drivers. For CO2x2, fast responses amplify the land–ocean contrast considerably, while for BCx10, fast responses lead to strong increases in relative humidity over large land regions, and these outweigh the reductions over land in the slow response. Interestingly, Sol+2% shows much less land–ocean contrast than CO2x2 in the fast response, while their slow responses are very similar.

The CMIP5 pre-industrial multi-model mean value for the WVL is 7.8±0.5 d (Fig. 4a). All models show an increase over both the historical and future time period (a paired sample t test shows that the multi-model mean increases are significant). A substantial increase in the lifetime from a present-day (i.e. 1986–2005) value of 8.2±0.5 to 9.9±0.7 d towards the end of the century is projected by the mean of CMIP5 models assuming RCP8.5 because increases in IWV are larger than for precipitation (Fig. 4b). Also, nearly 75 % of the models show a stronger WVLS for the historical period than for the future, with model-mean values of 0.55±0.1 and 0.47±0.06 d K-1, respectively, and a paired sample t test shows that the two values are significantly different. The present-day lifetime of 8.2±0.5 d from CMIP5 is close to, but slightly lower than, a recent assessment using reanalysis data of 8.9±0.4 d (van der Ent and Tuinenburg, 2017).

To further understand these differences, it is instructive to investigate WVLS for each of the fast and slow responses, and for each of the five climate drivers studied in PDRMIP. The response to surface temperature changes (i.e. slow response) dominates the change for all drivers except BCx10 (Fig. 5a). However, the fast response is still a significant enhancement to the slow response for CO2x2 (27 % of the total). For CH4x3, the fast response is 30 % of the total, but with large differences between models (range of 8 %–58 %). All models (except HadGEM3) show that the fast response is more important than the slow response for BCx10 because BC is the driver with the strongest atmospheric temperature increase for the fast response. These results support earlier single-model findings (Kvalevåg et al., 2013). The slow response is remarkably similar between models and drivers, again with the exception of BCx10, which has an inter-model range of 0.10–0.45 d K-1. The total WVLS is more than twice as large for BCx10 than for any other driver, and this can be explained by the strong increase in integrated water vapour combined with a decrease in precipitation, in contrast to the other climate drivers which enhance precipitation (Fig. 1b).

Separating the fast response into contributions from changes in atmospheric water vapour and precipitation (keeping in mind that the lifetime is defined as global water vapour divided by precipitation) reveals that both terms are large for BCx10, but that reduced precipitation dominates the fast WVL changes (Fig. 5b). Interestingly, reduced precipitation also dominates the fast WVL changes for CO2x2, while increased atmospheric water vapour dominates for Sol+2%. For SO4x5, the small fast WVL change is dominated by reduced water vapour (note that increased sulfate leads to cooling) except for one model (NCAR-CESM1-CAM5), which has a different sign because it has perturbed emissions rather than concentrations and it includes the influence of sulfate on BC through coating. This leads to a heating of the atmosphere, and this effect dominates the direct sulfate effect because fast responses for sulfate are small.

By combining the PDRMIP results for individual drivers with radiative forcing since pre-industrial time, we can reproduce the pre-industrial to present-day WVL increase of 0.34±0.08 d from CMIP5 models within the uncertainties (Fig. 6a). There is an almost equal contribution from the slow temperature response and the fast response to the total lifetime change.

The PDRMIP estimate of historical lifetime change due to the slow (temperature) response in Fig. 6a was derived by first taking the mean of the slow lifetime change across all PDRMIP drivers in Fig. 5a. This value of 0.31 d K-1 was then multiplied with the multi-model mean CMIP5 historical surface temperature change of 0.64 K (not shown). The PDRMIP fast response contribution in Fig. 6a is the sum of the individual terms in Fig. 6b. These terms have been derived by combining the present-day radiative forcing for separate climate drivers from Myhre et al. (2013) with the radiative forcing and fast WVL change from PDRMIP models using the following equation for each PDRMIP model ΔWVLfast,historical,j=ΔWVLfast,PDRMIP,j×RFhistorical,jRFPDRMIP,j, where RF is the radiative forcing (W m-2) and j designates the climate driver and corresponding PDRMIP experiment, e.g. CO2 and CO2x2, respectively (see Table S1 in the Supplement for details and multi-model mean values). By scaling the fast ΔWVL with RF, we are able to estimate the historical contribution to ΔWVL from each driver, in a similar way to what has been done before for other quantities (e.g. sensible heat flux changes in Myhre et al., 2018b). The bars in Fig. 6b have further been split into contributions from changes in precipitation and water vapour using the numbers in Fig. 5b. All calculations were done for each PDRMIP model, and Fig. 6 shows the multi-model mean results.

Disentangling the fast response into contributions from the main historical climate drivers shows that increased CO2 concentrations constitute around half (∼0.1 d) of the net increase due to the fast response, with the reduced precipitation term being three times as large as the contribution from increased water vapour (Fig. 6b). For aerosols, a substantial lifetime increase due to BC is partly counteracted by scattering aerosols, which reduce the WVL. The impact of aerosols contributes to the stronger WVLS in the historical period compared to the future simulations in the CMIP5 models (Fig. 4b), since aerosol and aerosol precursor emissions are projected to decrease strongly towards the end of the century in the RCPs (Rogelj et al., 2014).

In atmospheric chemistry and aerosol science, the lifetime of a compound is a measure of how long the compound resides in the atmosphere after it is emitted or produced, e.g. through surface emissions or chemical production. Diagnosing this lifetime has proved useful in many aspects, and the most relevant example is probably the lifetime of BC. Several studies show that the BC lifetime in many global aerosol models is too long, and reducing the lifetime by altering the sinks (mainly wet removal for BC) has given substantial improvements in modelled vertical profiles compared with observations, with large implications for the climate effect of BC (e.g. Hodnebrog et al., 2014; Samset et al., 2014). In a similar way to chemical compounds, the changes in atmospheric water vapour lifetime (WVL) are the relationship between changes in the burden (i.e. IWV) and the sources or sinks (i.e. evaporation or precipitation). In the following we discuss the potential value of diagnosing changes in the water vapour lifetime in addition to examining changes in IWV and P separately.

Since the water vapour lifetime includes both IWV and P, it can be used to measure variations in the hydrological cycle and be an important indicator of climate change (Kao et al., 2018). However, the interpretation of changes in the hydrological cycle can be rather confusing and deserves some discussion. While the longer WVL induced by global warming means that the hydrological cycle is slowing down, the global-mean precipitation or evaporation fluxes are also commonly referred to as the strength of the hydrological cycle; because they both increase, this implies an intensification or acceleration of the hydrological cycle with global warming (e.g. Wu et al., 2013). Hence, when the global hydrological cycle is said to intensify or accelerate with warming, it should be made clear that this refers to the fluxes and not the cycle as a whole. Hence, as noted by Douville et al. (2002), the conclusion that the hydrological cycle is intensifying is somewhat misleading because it suggests faster turnover of water, which is not the case; instead they use the term amplification to indicate an increase in precipitation and evaporation rather than acceleration (which implies a decreased lifetime) of the hydrological cycle. While the terminology could be confusing, both the amplification (through intensification of fluxes) and the slowdown (through longer lifetime) are important indicators of changes in the hydrological cycle. The intensification of fluxes means more precipitation globally and higher water availability, with potential consequences for extreme precipitation and water vapour feedback. The slowdown, however, is an important sign of changing precipitation patterns since water vapour resides in the atmosphere for a longer time before precipitation, and this behaviour cannot be deduced based on analysing IWV and P separately. A longer water vapour lifetime implies an increased length scale of water vapour transport, so that the distance between evaporation and precipitation of moisture is greater, as has been shown in detail by Singh et al. (2016). They further mention implications of this increased transport length scale, such as the expansion of the Hadley circulation and a poleward shift of midlatitude precipitation maximum.

Another aspect of WVL is the link to isotopes. Stable water isotopes provide valuable knowledge on the evaporation and condensation history of atmospheric moisture, e.g. on proportions of convective and stratiform precipitation (Aggarwal et al., 2016) and past variability in high-latitude aerosol abundance (Markle et al., 2018). Singh et al. (2016) highlight, due to changes in water vapour lifetime and transport length scale, that caution is needed when interpreting isotope data. Also, a positive correlation between WVL and stable isotope ratio in precipitation has been found from daily measurements at stations representing a range of climate regimes (Aggarwal et al., 2012), and better diagnostics of the impact of WVL on isotopes have been called for by Dee et al. (2018). It is suggested that the relationship between isotope ratio and the WVL could be used to improve the parameterizations of vertical mass exchange (Aggarwal et al., 2012), which is currently one of the major uncertainties in GCMs (Bony et al., 2015). Therefore, understanding the WVL has the potential to contribute to improved quantification of the hydrological cycle and its climate-induced changes.

Among the most important caveats with our WVL findings is that climate models have known deficiencies, such as problems with representing vertical convective mass fluxes (Bony et al., 2015), surface moisture fluxes, and entrainment and detrainment rates. Part of the reason is that GCMs have relatively coarse resolution, and many processes, such as convection, need to be parameterized. The model spread in future WVL change is lower (relative standard deviation, RSD, of 22 %) than for precipitation change (RSD of 30 %) (Fig. 4), but the horizontal resolutions in the PDRMIP models range from 1.4∘×1.4∘ (MIROC-SPRINTARS) to 2.8∘×2.8∘ (CanESM2), where convection needs to be parameterized. This means that the uncertainty is larger if a decrease in convective mass fluxes is a major reason for the increase in WVL. Compared with present-day WVL from reanalysis, the climate models have too short WVLs (Trenberth et al., 2011; see also Sect. 3.3). Kao et al. (2018) compared trends in precipitation and column water vapour data from 13 CMIP5 models with observational datasets and also found differences in the moisture recycling rate between observations and the CMIP5 models, and concluded that this discrepancy was caused by relatively poor simulations of precipitation. However, the long-term trend and inter-annual variability of column water vapour was very well captured by nearly all models.

In conclusion, diagnosing changes in the water vapour lifetime reveals important changes in the hydrological cycle, and specifically changes in precipitation patterns since these are directly affected by how long water resides in the atmosphere. Since black carbon is the climate driver among those studied here with the by far strongest water vapour lifetime sensitivity, it is also the driver that is most efficient in increasing the distance between evaporation and precipitation per kelvin of global surface temperature change. However, the full potential of diagnosing the water vapour lifetime is most likely still unexplored. When inclusion of isotopes in GCMs becomes more common in the future, WVL and its changes can potentially prove extremely useful in constraining projections of the hydrological cycle and precipitation, in a similar way to how diagnosing and evaluating the lifetime of BC has helped constrain the climate effect of BC.