Water vapor and lapse rate feedbacks in the climate system

Water vapor is a greenhouse gas that dominates Earth’s terrestrial radiation absorption. As the planetary temperature warms, forced by increasing ${\mathrm{CO}}_2$ and other greenhouse gases, water vapor content of the atmosphere increases, thereby producing the strongest positive feedback in the climate system. At the same time, the rate at which atmospheric temperature drops with height (the “lapse rate”) is expected to decrease with warming. This represents a smaller, but significant, negative feedback since it enables the planet to radiate more effectively to space. The two feedbacks are closely coupled to each other, and the combined result represents the foundational net positive feedback in the climate system, mandating substantial global warming in response to increased greenhouse gases. This review summarizes the published work that has provided an ever deepening understanding of these critical feedbacks. The historical context, beginning with the 19th century awakening to the importance of water vapor in the climate, is outlined before the review’s focus shifts to the theoretical, observational, and modeling work in recent decades that has transformed our understanding of the feedbacks’ role in climate change. It is shown that the evidence is now overwhelming that combined water vapor and lapse rate processes indeed provide the strongest positive feedback in the climate system. However, important challenges remain. This review provides physicists with a deeper understanding of these feedbacks and stimulates engagement with the climate research community. Together the scientific community can facilitate further rigor, understanding, and confidence in these most fundamental Earth system processes.

Figure 1

John Tyndall (top), Thomas Chamberlin (bottom left), and Svante Arrhenius (bottom right). Tyndall performed laboratory measurements of the absorption spectrum of water vapor in the mid-19th century. Thomas Chamberlin articulated the fundamental process controlling water vapor feedback. Arrhenius in the late 19th century laid out a coherent framework of ${\mathrm{CO}}_2$-induced climate change, as amplified by water vapor feedback.

Figure 2

Schematic illustrating how additions to atmospheric greenhouse gases, such as a doubling of ${\mathrm{CO}}_2$ concentration, change surface temperature. Assuming an unchanged lapse rate, additional longwave absorbers, and unchanged emission temperature ($T_e$) forces radiation to space to come from a higher altitude, increasing the surface temperature ($T_s$). From [160].

Figure 3

(a) CMIP3 multimodel mean surface temperature change $\mathrm{\Delta }{T}_s^e$ [equivalent to $\mathrm{\Delta }{T}_s$ in Eq. (5)] under a doubling of ${\mathrm{CO}}_2$. The thick and thin lines represent the 1 and 2 standard deviation ranges. Colored bars show the multimodel mean contribution to $\mathrm{\Delta }{T}_s^e$ from each of the feedbacks listed, according to gain factors in Eq. (5). (b) Contribution to the range in $\mathrm{\Delta }{T}_s^e$ of the different feedbacks, calculated as the standard deviation of the contribution to temperature change normalized by $\mathrm{\Delta }{T}_s^e$. From [100].

Figure 4

Feedback parameters associated with water vapor or the lapse rate predicted by CMIP3 GCMs, with boxes showing interquartile range and whiskers showing extreme values. At left is the total radiative response including the Planck response. The darker-shaded region shows the traditional breakdown of this into a Planck response and individual feedbacks from water vapor (labeled WVMR) and lapse rate (labeled Lapse). The lighter-shaded region at the right depicts the equivalent three parameters calculated in the alternative, RH-based framework. In this framework all three components are both weaker and more consistent among the models. Data are from [159]. From [32].

Figure 5

Absorption spectra for total atmosphere and water vapor, ${\mathrm{CO}}_2$, and other atmospheric gases as a function of wavelength. Also shown are the blackbody curves of downward solar (SW) radiation and upward terrestrial (LW) radiation. Adapted from [134].

Figure 6

Zonal mean distributions of relative humidity as a function of latitude and height in the European Centre for Medium-Range Weather Forecasts (ECMWF) reanalysis of July 1987 (left panel) and in a single GCM (right panel), that of the Geophysical Fluids Dynamics Laboratory. Vertical units are in hPa. From [160].

Figure 7

Top panel: calculations of the spectrally resolved OLR as a function of temperature for idealized atmospheric profiles in radiative-convective equilibrium with constant relative humidity ($r=100\%$). Red curves show the surface’s blackbody emission at 240 and 280 K. Bottom panel: spectrally resolved transmission between the surface and the top of atmosphere for each profile. From [216].

Figure 8

Zonal mean radiative “kernels” (see Appendix pp1), in height (hPa) and latitude (deg), calculated using the Geophysical Fluids Dynamics Laboratory GCM. Shown are (left column) the LW TOA impact of 1 K temperature increases at each point and (center and right columns) the LW and SW TOA impacts of moisture increases corresponding to a 1 K temperature rise with fixed relative humidity. The top row shows “all-sky” conditions, i.e., those including the effect of clouds, while the bottom row shows “clear-sky” conditions, i.e., those with the removal of clouds at all levels. Units are in ${\mathrm{W}\mathrm{m}}^{-2}{\mathrm{K}}^{-1}100{\mathrm{hPa}}^{-1}$. The importance of the tropical upper troposphere for LW water vapor feedback is apparent, whereas low levels and high latitudes are most important for the SW. From [381].

Figure 9

Geographical distributions of water vapor (top panel) and lapse rate (bottom panel) feedbacks under $2\times {\mathrm{CO}}_2$ forcing, as calculated using the PRP methodology (see Appendix pp1) applied to the CCSR/NIES/FRCGC/MIROC3.2(medres) Model for Interdisciplinary Research on Climate 3.2, medium-resolution version ([154]). From [451].

Figure 10

Schematic of key processes involved in moisture transport in the tropics and subtropics. From [361].

Figure 11

Ensemble mean change in relative humidity per kelvin of surface warming under ${\mathrm{CO}}_2$ forcing, calculated from 18 CMIP5 GCMs. Axes are height (hPa) vs latitude (deg). Dashed contours indicate negative values, and shading represents areas of agreement on the sign of change by at least 90% of the models. From [359].

Figure 12

Results from an advection-condensation (AC) simulation of annual average water vapor mixing ratio ($\approx \text{specific}$ humidity) at 346 and 547 hPa using 50 day moisture advection trajectories. Thick solid lines represent AIRS satellite data. The three thin solid lines represent different configurations of the AC model, with different specified microphysics, in this case different convective thresholds whereby parcels mix with other sources of convection of different temperatures within rising plumes. Dashed lines show the AC model but with assumed relative humidity saturation limit of 90% instead of 100%. The close overall agreement with moisture distribution between the AC model and observations is apparent, as is the insensitivity of the AC model simulations to either microphysics specification, or even the precise definition of saturation. From [93].

Figure 13

(a) The relationship between global effective (viz., standardly defined) water vapor and lapse rate feedbacks for CMIP5 models. Each data point represents a GCM, and the correlation coefficient is shown. (b) Water vapor and lapse rate feedbacks plotted against the ratio of tropical to global surface temperature change. Note the discontinuity on the $y$ axis. This shows the strong anticorrelation between water vapor and lapse rate feedbacks globally, and the close dependence of both feedbacks on the relative warming between the tropics and extratropics. From [297].

Figure 14

(a) Relationship between global effective (viz., standardly defined) water vapor and lapse rate feedbacks for the CMIP5 models in the tropics (latitude $<30°$) and extratropics. (b) Tropical water vapor feedback shown against tropical relative humidity feedback [${{\lambda }^{\prime }}_H$ in Eq. (8)], here denoted as ${\tilde{\lambda }}_{\mathrm{rh}}$. From [297].

Figure 15

Feedbacks derived from the Model for Interdisciplinary Research on Climate 3.2, medium-resolution version [MIROC3.2(medres)] GCM under $2\times {\mathrm{CO}}_2$ forcing above current climate, as well as from Last Glacial Maximum (LGM) changes, compared with the current climate. LGM forcing includes ice sheets over northern continents and ${\mathrm{CO}}_2$ levels of 185 ppm ($\sim 65\%$ of the current value) along with reduced values of ${\mathrm{CH}}_4$ and ${\mathrm{N}}_2\mathrm{O}$. LGMGHG denotes an experiment with current climate ice sheets, but with LGM-level greenhouse gases. Feedback notation is as in Eq. (4), with the addition of “A” for surface albedo. Error bars represent 1 standard deviation of different ten-year samples that are calculated using PRP; see Appendix pp1. This shows the weakened water vapor feedback in the colder climate, and a small positive lapse rate feedback due to low latitude ice sheets; however, the combined feedback is close to that of $2\times {\mathrm{CO}}_2$. From [451].

Figure 16

Latitude mean, annual radiative feedbacks defined at the TOA (solid lines) and at the surface (dashed lines) calculated for a GCM forced by SSTs from a equilibrium warming $4\times {\mathrm{CO}}_2$ forcing experiment (4SST) for the (a) LW and (b) SW. Notation for feedbacks is as in Eq. (4), except that $T$ denotes the Planck feedback $P$ and is scaled by a factor of 0.5 for display purposes. This shows that at the surface (compared with TOA) SW water vapor feedback is reversed in sign, lapse rate feedback is close to zero except at high latitudes, and LW water vapor feedback is consistently stronger. From [64].

Figure 17

Surface temperature change from 14 CMIP5 models as a function of latitude, in years 100–150 after an abrupt $4\times {\mathrm{CO}}_2$ forcing, showing the “amplification” in surface warming that occurs in the high latitudes, particularly in the Arctic. The thick black line is the model average, and the shading shows the full model range. Box-whisker plots from left to right denote the warming averaged over the Arctic poleward of $70°\mathrm{N}$, the Antarctic poleward of $70°\mathrm{S}$, and the tropics $20°\mathrm{N}–20°\mathrm{S}$. Box whiskers represent 25th to 75th percentile and minimum, median, and maximum values. From [23].

Figure 18

(a) Contribution to Arctic warming vs tropical warming in 16 CMIP5 models from diagnosed TOA feedbacks (lapse rate, water vapor, Planck, surface albedo, and cloud) from changes in atmospheric transport and ocean uptake or transport, and from the latitudinal dependence of ${\mathrm{CO}}_2$ forcing. Values to the top left of the gray dashed line increase polar amplification, and those to the bottom right decrease it. The importance of lapse rate feedback is apparent from its warming of the Arctic vs tropical cooling, whereas water vapor feedback warms the tropics more. (b) Seasonal variation shown by winter vs summer warming from each of the processes in (a). The contrasting seasonal roles of lapse rate (winter) and water vapor (summer) are apparent. The gray dot represents the residual from total warming minus the addition of the individual components. From [296].

Figure 19

Radiative feedbacks diagnosed using 2000–2014 Clouds and the Earth’s Radiant Energy System (CERES) ([437]) TOA SW and LW fluxes combined with surface temperature and vertical profiles of temperature and humidity taken from ERA-Interim reanalyses ([84]). Values shown are calculated using linear regression of TOA fluxes with regional surface temperature and kernels applied to temperature and moisture profiles to diagnose individual feedbacks. Error bars show the standard error from regressions combined with estimated CERES uncertainties. Clear sky represents results with all cloud effects removed. The importance of lapse rate feedback is apparent in regional warming, whereas water vapor contributions are diagnosed as small. From [176].

Figure 20

Graphic attributing observed water vapor feedback to anthropogenic greenhouse gas emissions. Bars show water vapor feedback between the periods 1979–1988 and 1989–1998 from CMIP5 experiments forced by natural forcing agents due to solar and volcanic changes only (HistNat) and anthropogenic greenhouse gases and aerosols as well as natural forcings (Historical). A third calculation (Hist UTWV only) is derived from the historical runs but uses only humidity changes occurring above 600 hPa. One estimate of water vapor feedback from reanalyses ([88]) is marked in purple. Differences between Historical and HistNat show that models do not match observational estimates of water vapor feedback unless anthropogenic greenhouse gas forcing is included: i.e., this feedback can be attributed to anthropogenic emissions. Differences between Historical and Hist UTWV only values demonstrate the dominance of the upper troposphere, in that around 80% of the feedback strength can be attributed to upper humidity changes in this region. See Tables 1 and 3 for other estimates of water vapor feedback from unforced variability and climate change. From [54].

Figure 21

(a)–(c) Planck, water vapor, and lapse rate feedbacks from CMIP5 models for transient (i.e., secular) response to increased ${\mathrm{CO}}_2$ (Trans) and from unforced decadal (Dec), interannual (I/A), and seasonal (Seas) variability. In (d) the seasonal feedback is broken up into separate Northern and Southern hemispheres. Box-whisker plots show median 25th–75th percentiles, ranges within 1.5 interquartiles, and outliers (stars). X’s (plus signs) show results calculated from ERA-40 (MERRA) reanalyses. From [67].

Figure 22

(a) Longitudinally averaged TOA flux responses (positive is increased downward flux) from water vapor changes over an ENSO cycle as depicted by 12 CMIP3 models (gray lines) and derived from two reanalyses: MERRA (dashed black line) and ERA-40 (solid black line). (b) Flux changes (in ${\mathrm{W}\mathrm{m}}^{-2}100{\mathrm{hPa}}^{-1}$) from water vapor perturbations as a function of altitude. From [96].

Figure 23

Estimated specific humidity variations with temperature averaged over the tropics from MERRA ([317]), Atmospheric Infrared Sounder (AIRS) satellite retrievals, and 1.2–1.6 GHz Global Positioning System Radio Occultation (GPSRO) measurements at 250 hPa during the period 2007–2010. This shows close agreement among the three observational measurements. The values of $dq/d{T}_s$ indicate moistening with temperature at slightly below the rate implied by unchanged relative humidity. Error bars represent 1 standard deviation estimation uncertainty from linear regressions. Also shown are calculations from a single GCM, the Community Atmosphere Model (CAM) ([129]). The solid line and the region between the horizontal dotted lines represent the mean and spread of $dq/d{T}_s$ in 42 CMIP5 GCMs from [262] and show overall consistency between models and observations, albeit with wide model spread and a mean model value that is slightly larger than observational estimates. From [423].

Figure 24

Water vapor feedback calculated from interannual variability from CMIP5 GCMs forced by observed SSTs over the period 1979–2008. Red (larger) dots show feedbacks calculated over the entire 30-year period, black dots from 19 different 12-year segments within this period, and blue dots the mean of all 12-year segments. Shading shows AIRS-MLS sounding observations from 2004 to 2016. It is clear that an enormous spread of results from estimation of water vapor feedback can be expected if taken from relatively short (approximately decadal) time periods of models or observations. From [238].

Figure 25

Top panel: changes in global mean $6.7\mu \mathrm{m}$ brightness temperatures from High-Resolution Infrared Radiation Sounder (HIRS) observations (black line) and as simulated by the Geophysical Fluid Dynamics Laboratory GCM (blue line) following the Mount Pinatubo eruption. Anomalies are expressed relative to preeruption values (January–May 1991). The green line represents the GCM with unchanged relative humidity, and the red line represents the GCM with unchanging specific humidity (corresponding to no upper tropospheric drying). Thick lines are seven month running means. This shows that unchanging relative humidity, not specific humidity, enables the model to match observations. Bottom panel: observed global cooling in the lower troposphere following the Mount Pinatubo eruption as measured by the microwave sounding unit (MSU) (black lines) and model predicted temperature (blue line). The red line shows the temperature trace of the GCM with suppressed water vapor feedback. This shows that strong positive water vapor feedback was necessary for the GCM to reproduce observed cooling. From [384].

Figure 26

Comparisons of CMIP6 model vertical temperature trends ($20°\mathrm{N}/20°\mathrm{S}$) to observations from two radiosonde datasets (RICH1.7 and RAOBCORE1.7) and the $\mathrm{ERA}5/5.1$ reanalysis (black lines) for the period 1979–2014. Box-whisker plots show the 25%–75% intermodel range, while bars and crosses represent the 1.5 quartile range and then outliers beyond that. Red (upper) boxes represent 48 fully coupled ocean-atmosphere CMIP6 GCMs forced by anthropogenic greenhouse gases and aerosols as well as estimated natural forcing, and blue (lower) boxes represent a subset of 28 atmosphere-only GCMs forced by observed SST changes. Blue (lower) lines are displaced vertically for plotting purposes. In the troposphere, models show much less spread, and better agreement with observations when forced by SSTs that match observed, rather than those simulated under a “freewheeling” experiment, indicating that much of the apparent disagreement between model and observed lapse rate changes may be due to different trends in model surface temperatures. From [263].

Figure 27

Values of (a) water vapor, (b) lapse rate, and (c) combined water vapor plus lapse rate feedbacks taken from the studies listed in Table 3. Error bars show a $\pm 1\sigma$ range of the estimates (where available). Assess. refers to an evaluation carried out from published literature. Experiments referred to are $4\times$, $4\times {\mathrm{CO}}_2$; Hist, CMIP Historical simulations; 8.5, CMIP RCP8.5 experiments. Shaded areas denote CMIP-based analyses, with the vertical lines differentiating CMIP2, 3, 5, and 6. AIRS are determinations from Atmospheric Infrared Sounder observations of interannual feedback, scaled by the ratio between climate change and interannual feedbacks derived from model ensembles. AR6 water vapor values are the average of the reported model and observational estimates.