JOURNAL OF GEOPHYSICAL RESEARCH, VOL. ???, XXXX, DOI:10.1029/,
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Why is Longwave Cloud Feedback Positive?
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Mark D. Zelinka and Dennis L. Hartmann
Department of Atmospheric Sciences
University of Washington, Seattle, Washington, USA.
Corresponding Author: Mark D. Zelinka, Department of Atmospheric Sciences, University of
Washington, Box 351640, Seattle, Washington 98195, USA. ([email protected])
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Abstract.
Longwave cloud feedback is systematically positive and nearly the same
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magnitude across all global climate models used in the IPCC AR4. Here it
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is shown that this robust positive longwave cloud feedback is caused in large
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part by the tendency for tropical high clouds to rise in such a way as to re-
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main at nearly the same temperature as the climate warms. Furthermore,
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it is shown that such a cloud response to a warming climate is consistent with
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well-known physics, specifically the requirement that, in equilibrium, tropo-
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spheric heating by convection can only be large in the altitude range where
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radiative cooling is efficient, following the fixed anvil temperature (FAT) hy-
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pothesis of Hartmann and Larson [2002].
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Longwave cloud feedback computed assuming that high cloud tempera-
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ture follows upper tropospheric convergence-weighted temperature, which
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we refer to as proportionately higher anvil temperature (PHAT), gives an
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excellent prediction of the longwave cloud feedback in the AR4 models. The
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ensemble-mean feedback of 0.5 W m−2 K−1 is much larger than that calcu-
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lated assuming clouds remain at fixed pressure, highlighting the large con-
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tribution from rising cloud tops to the robustly positive feedback. An im-
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portant result of this study is that the convergence profile computed from
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clear-sky energy and mass balance warms slightly as the climate warms, in
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proportion to the increase in stability, which results in a longwave cloud feed-
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back that is slightly smaller than that calculated assuming clouds remain at
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fixed temperature.
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1. Introduction
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In the present climate, clouds strongly cool the planet, reducing the net downwelling
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radiation at the top of the atmosphere by about 20 W m−2 . Comparing this number
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with the radiative forcing associated with a doubling of CO2 , 4 W m−2 , it is clear that
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even tiny changes in clouds can have dramatic effects on the climate and can act as a
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positive or negative feedback on climate change. It is for this reason that understanding
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how clouds respond to a warming planet is of vital importance for accurately predicting
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how the climate will change.
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Cess et al. [1990], Colman [2003], Soden and Held [2006], and Webb et al. [2006] show
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that the largest uncertainty in global climate model (GCM) projections of future climate
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change is caused by the responses of clouds to a warming climate. Whereas other feedbacks
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are similar among the models, the cloud feedback varies between 0.14 and 1.18 W m−2
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K−1 (Soden and Held [2006]) and little progress has been made in reducing this spread.
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Bony et al. [2006] point out several reasons why progress has been slow in evaluating
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cloud feedbacks and narrowing this range. It is difficult to use observations to evaluate
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cloud feedback because observable climate variations are not good analogues for climate
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change due to increasing greenhouse gases and because it is nearly impossible to isolate the
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unambiguous role of clouds in causing a change in net radiation at the top of atmosphere.
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Additionally, the radiative impact of clouds is large, so even subtle changes to their
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characteristics (height, amount, thickness, etc.) can have dramatic effects on the climate.
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Finally, clouds are not actually resolved in GCMs but are instead parameterized; thus a
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variety of plausible and self-consistent cloud responses to global warming can be produced
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in models.
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Though estimates of cloud feedback vary significantly among the AR4 models (Soden
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and Held [2006]), this large spread is primarily due to the shortwave (SW) component,
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which can be attributed to uncertainties in simulations of the response of marine boundary
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layer clouds to changing conditions (Bony and Dufresne [2005]). Generally speaking,
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the models which predict a reduction in low cloud fraction exhibit greater 21st Century
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warming because the reduction in the area of such clouds with large negative net cloud
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forcing represents a strong positive cloud feedback. Conversely the models that predict
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increases in low clouds have very low climate sensitivity.
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Whereas estimates of SW cloud feedback vary considerably such that even the sign
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is uncertain, estimates of longwave (LW) cloud feedback are systematically positive in
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all AR4 models and exhibit half as much spread (B. J. Soden, personal communication,
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2009). In this study we address the question of why all the AR4 models exhibit positive
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LW cloud feedbacks. We show that the robust positive LW cloud feedback is largely due to
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tropical high clouds, which remain at approximately the same temperature as the climate
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warms. Furthermore, we show that this cloud response should be expected from basic
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physics and is therefore fundamental to Earth’s climate.
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We demonstrate this by making use of the clear-sky energy budget, which requires
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balance between subsidence warming and radiative cooling. Because radiative cooling
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by water vapor becomes very inefficient at very low temperatures, subsidence rapidly
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decreases with decreasing pressure in the tropical upper troposphere. This causes large
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convergence into the clear-sky upper troposphere, which, by mass conservation, implies
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large convective detrainment and abundant high cloudiness at that level. Thus the im-
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plied clear-sky upper tropospheric convergence calculated from clear-sky mass and energy
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balance provides a convenient marker for the level of high clouds and a diagnostic tool for
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understanding how that level changes as the climate warms.
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As described in the fixed anvil temperature or FAT hypothesis of Hartmann and Larson
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[2002], this level should remain at the approximately the same temperature as the climate
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warms because it is a fundamental result of radiative convective equilibrium: The tropo-
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sphere can only be heated by convection where it is being sufficiently cooled by radiation,
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resulting in an equilibrium near neutral stability. Because the altitude range of suffi-
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cient radiative cooling by water vapor is primarily determined by temperature through
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the Clausius-Clapeyron relation, the temperature that marks the top of the convective
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cloudiness should remain approximately constant as the climate warms.
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In the cloud resolving model simulations of Kuang and Hartmann [2007], high clouds
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migrate upward for higher values of SST, but do so in such a way as to remain at the same
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temperature. The clear-sky upper tropospheric diabatic convergence calculated from the
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clear-sky energy balance as described above shows an identical constancy in temperature
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for all simulations. Kubar et al. [2007] showed, using MODIS observations, that the
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level of abundant anvil cloud tops and its seasonal and regional variability is accurately
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predicted by clear sky energy budget considerations, indicating that the real atmosphere
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is also subject to such constraints. Xu et al. [2005], Xu et al. [2007] and Eitzen et al.
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[2009] showed, using observations from the CERES instrument on the TRMM satellite,
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that the distribution of tropical cloud top temperatures for clouds with tops greater than
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10 km remains approximately constant as SSTs vary over the seasonal cycle, lending
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observational support to the FAT hypothesis. Conversely, Chae and Sherwood [2010]
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showed that cloud top temperatures observed by MISR exhibit appreciable fluctuations
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(∼5K) that can be attributed to lapse rate changes in the upper troposphere.
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Here we show that, as in observations and cloud resolving models, clouds in the AR4
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GCMs remain at approximately the same temperature as the climate warms, and that
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this feature is well-diagnosed by the clear-sky energy budget explained above. This is
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perhaps unsurprising given that it is a result that arises directly from tropical radiative-
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convective equilibrium that GCMs must approximately maintain, regardless of the details
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of their individual convective and cloud parameterizations. What is less appreciated is
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that this important result gives rise to a robustly positive LW cloud feedback that can be
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explained from the fundamental principles of saturation vapor pressure, radiative transfer,
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and energy balance.
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In the first part of the paper, we assess the degree to which the model cloud fields
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are in agreement with the basic physics described above, both in the mean sense and
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as the climate warms. In the second part, we decompose the LW cloud feedback into its
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individual components to show that the systematic tendency for GCMs to maintain nearly-
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constant tropical high cloud temperature causes a robust positive LW cloud feedback.
2. Data
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We make use of monthly mean model diagnostics from the IPCC SRES A2 scenario
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simulations that are archived at the Program for Climate Model Diagnosis and Intercom-
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parison (PCMDI). We calculate decadal-mean quantities between the years 2000 and 2100,
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but maintain the monthly mean resolution such that the radiative calculations are more
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accurate. LW and SW radiative fluxes at both the surface and top of atmosphere and for
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both clear and all-sky conditions are used, as well as profiles of temperature (T ), specific
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humidity (q), and cloud amount. We interpolate all quantities onto the same latitude,
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longitude, and pressure grid as that of the radiative kernels of Soden et al. [2008].
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Unfortunately cloud optical thickness or effective cloud top temperature as would be
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seen from satellites are not standard model diagnostics available in the PCMDI archive.
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Only a small number of modeling centers have participated in the Climate Feedback Model
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Intercomparison Project (CFMIP), in which ISCCP-simulators are run in the models to
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better compare with observations. We instead make use of the basic cloud field that all
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modeling centers are required to output, the height-resolved cloud fraction within each
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pressure bin. This gross cloud field may include cloud types that are not relevant to this
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study (e.g., subvisible tropopause cirrus) as well as clouds that are not directly influencing
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the OLR (e.g., interior of clouds rather than cloud tops). Nevertheless, the cloud changes
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in this study are quite coherent in the sense that the entire cloud profile tends to shift
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to higher altitudes as the climate warms rather than exhibiting a fundamental change in
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shape. Thus we can make reasonable assumptions about the cloud top properties without
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actually making use of optical depth or cloud top information.
3. Methodology
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Before assessing how realistically high clouds are being simulated in the models, we
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first demonstrate a method of calculating the altitudes of convective detrainment and
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implied abundant cloudiness using the tropospheric mass and energy budget equations.
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We adopt the same one-dimensional diagnostic model employed by Minschwaner and
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Dessler [2004], Folkins and Martin [2005], Kuang and Hartmann [2007], and Kubar et al.
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[2007]. The tropical atmosphere is divided into a convective domain and a clear-sky
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domain. The cloudy domain is assumed to cover a small fraction of the Tropics (as active
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convection does in reality), with the majority of the Tropics being convection-free. We
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shall refer interchangeably to the convective (nonconvective) region as the cloudy (clear-
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sky) region, though these are used very loosely simply to distinguish between regions
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that are undergoing active deep convection and those that are not. Most likely there are
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boundary layer clouds and/or nonconvective high clouds in the clear-sky region.
One can write the dry static energy (s = cp T + gz) budget of the troposphere as
∂s
= −∇· (sU) − cp QR + SH + LP,
∂t
(1)
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where cp is the specific heat of air at constant pressure, QR is the net (LW plus SW)
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radiative cooling of the atmosphere, SH is the surface sensible heat flux, L is the latent
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heat of vaporization, and P is the precipitation rate. We calculate QR using each model’s
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T and q profiles as input to the Fu-Liou radiation model, which uses the delta-four-stream
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approximation and correlated k-distribution scheme (Fu and Liou [1992]). Although we
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use T and q profiles from regions that are both cloudy and clear, the radiative transfer
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calculation is performed assuming no clouds. Because the presence of clouds alters cooling
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rates substantially (e.g., Ackerman et al. [1988], Stephens et al. [1994], Bergman and
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Hendon [1998], Sohn [1999], L’Ecuyer and McGarragh [2010]), it is preferable to take
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into account clouds in the nonconvective regions. It would be very difficult to do this,
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however, because there is inadequate cloud property information provided by the modeling
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centers (e.g., particle size, phase, ice water content). Thus we do not attempt to account
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for the effect of clouds on QR and acknowledge a small degree of uncertainty in the cooling
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profiles.
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Considering only regions of the free-troposphere that are not actively convecting (such
that we can ignore SH and LP ), and assuming no tendency or horizontal transport gives
ω=
QR
σ
(2)
where σ is the static stability, having various equivalent forms, including
σ=−
T ∂θ
κT
∂T
Γd − Γ
=
−
=
,
θ ∂p
p
∂p
ρg
(3)
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where θ is potential temperature, κ = Rd /cp , Γd is the dry adiabatic lapse rate, and Γ is the
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lapse rate. We will refer to ω as the diabatic vertical velocity (positive downward). From
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Equation 2, we see that QR is balanced by diabatic subsidence in the clear-sky regions of
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the tropical free-troposphere. The stronger the radiative cooling or the weaker the static
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stability, the larger the diabatic subsidence that is required to maintain energy balance.
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The energy equivalent of this diabatic subsidence is provided by convective heating.
Assuming mass continuity, the diabatic convergence profile in the clear-sky region is
calculated by
−∇H · U =
∂ω
∂p
(4)
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where −∇H · U is the horizontal diabatic convergence, hereafter referred to as conv. As-
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suming a closed mass budget between convective and nonconvective regions, convergence
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into the nonconvective region is balanced at the same altitudes by divergence out of the
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convective region, and vice versa. Note that using this system of equations we can calculate
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the implied convective detrainment simply from mass and energy conservation without
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invoking any complex moist physics or assumptions about parcel entrainment. This is
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a simple and elegant method for diagnosing the level of detrainment and abundant high
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clouds in the model and for understanding the changes in high clouds that accompany
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climate change.
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Rather than computing QR profiles corresponding to 24 solar zenith angles for each
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latitude and longitude in every month in every model, we instead linearize the computation
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about a mean QR profile to increase efficiency. A mean QR profile is calculated at each
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latitude and month using the ensemble-mean, monthly-mean, zonal-mean T and q profiles
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averaged over the first decade of the 21st Century. Then, perturbed QR profiles are
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calculated at each latitude and month for small perturbations at each pressure level of
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the T and q fields. The perturbations are as in Soden et al. [2008], namely, a T increase
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of 1 K and an increase of q equal to that which is necessary to maintain constant RH in
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the presence of a 1 K increase in T . The actual T and q fields at any location and time
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within any model are then multiplied by the appropriate T - and q-perturbed QR profiles
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and summed to calculate the actual QR profile for that location. A sample of randomly-
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selected QR profiles calculated using this procedure are nearly identical to those calculated
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by running the Fu-Liou code.
4. Results
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The tropical-mean ensemble-mean q, T , radiative cooling, σ, and diabatic ω profiles are
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plotted as functions of pressure in Figure 1 for averages over three decades, 2000-2010,
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2060-2070, and 2090-2100. Here, ensemble mean refers to the average over the 15 models
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that run the A2 scenario. Note that q is plotted on a logarithmic scale.
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Tropospheric temperatures are nearly moist adiabatic (Xu and Emanuel [1989]), de-
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creasing modestly with decreasing pressure in the lower troposphere, then decreasing more
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dramatically with decreasing pressure in the mid and upper troposphere (not shown). Wa-
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ter vapor concentrations are fundamentally limited by temperature through the Clausius-
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Clapeyron relation, thus q decreases exponentially with decreasing pressure throughout
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the troposphere (Figure 1a). The radiative cooling rate, QR , is approximately constant
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with pressure throughout most of the troposphere at about 1.5 K dy−1 (Figure 1b). At
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the very low temperatures characteristic of the upper troposphere, water vapor concentra-
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tions become so low that QR dramatically falls off until reaching a level of zero radiative
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heating. Consistent with the sharp drop in water vapor radiative cooling, Hartmann et al.
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[2001] show that the radiative relaxation time sharply increases near 200 hPa, implying a
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dramatic reduction in the ability of water vapor to radiate away any temperature pertur-
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bations. Above this level, radiative processes provide net warming to the atmosphere. It
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is important to note that QR falls off to zero well below the cold-point tropopause.
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Static stability is small and nearly constant throughout most of the well-mixed tro-
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posphere as the T profile closely follows the moist adiabat (Figure 1c). At pressures
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less than about 200 hPa, the T profile becomes increasingly more stable than the moist
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adiabat as radiative cooling by water vapor becomes increasingly less efficient and radia-
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tive convective equilibrium is no longer the dominant balance. Additionally, the inverse
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pressure-dependence of σ (Equation 3) becomes especially pronounced at these low pres-
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sures. Diabatic ω, which is directly proportional to QR and inversely proportional to σ,
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very closely mimics the QR profile: It is nearly constant with pressure at about 25 hPa
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dy−1 throughout the troposphere, then falls off rapidly to zero in the region where QR
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falls off rapidly and σ increases rapidly (Figure 1d).
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Because the diabatic ω is nearly constant with pressure above and below the range of
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altitudes where it falls off rapidly with decreasing pressure, conv (vertical derivative of
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ω) exhibits a clear peak in the upper troposphere around about 200 hPa (Figure 2). It
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is in this region of large upper tropospheric conv that net convective detrainment and its
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associated cloudiness should be maximum. Indeed, the ensemble-mean cloud amounts also
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exhibit a peak at the same altitude as the conv peak (Figure 2). We interpret this peak
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in the cloud field as due to the abundance of high clouds detrained from deep convection
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near the top of the region of efficient radiative cooling. The same correspondence between
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conv and cloud fraction is verified in MODIS observations (Kubar et al. [2007]) and in a
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cloud resolving model (Kuang and Hartmann [2007]).
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In Figure 3 we plot the change in these quantities between the beginning and end of the
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21st Century. Overlain in light lines are the average profiles for 2000-2010 and 2090-2100.
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Water vapor mixing ratios increase at all levels in step with the warming climate so as
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to retain nearly constant relative humidity through the 21st Century (Figure 3a). The
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amplification of warming aloft where water vapor concentrations are very low results in
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large fractional increases of q and thus very large increases in QR between 200 hPa and
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the tropopause, peaking at 150 hPa (Figure 3c). Thus the level at which QR falls off
229
rapidly shifts upward as the climate warms, as expected from the FAT hypothesis.
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Whereas QR increases everywhere throughout the mid- and upper-troposphere, the
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change in σ is positive at pressures greater than 200 hPa and negative at pressures less
232
than 200 hPa (Figure 3d). Convection keeps the T profile close to the moist adiabat at
233
pressures greater than 200 hPa; thus the warming profile is accompanied by an increase in
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σ. The warming of the upper troposphere, which maximizes at about 200 hPa, combined
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with the CO2 -induced cooling of the stratosphere cause stability to decrease at pressures
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less than 200 hPa.
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At pressures greater than about 250 hPa, the fractional increase in σ exceeds that of
238
QR (not shown), so the diabatic ω is reduced (Figure 3e). This reduction in clear-sky
239
ω is consistent with several other studies that have pointed out the robust slow-down
240
of the tropical circulation in a warmer climate (Knutson and Manabe [1995], Held and
241
Soden [2006], Vecchi and Soden [2007], Gastineau et al. [2009]). Because the fractional
242
increase in σ is larger than that of QR at these altitudes, less ω is required in the clear-sky
243
atmosphere to balance the enhanced QR . In other words, a given descent rate achieves
244
greater warming in the presence of enhanced σ.
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At pressures less than 200 hPa, the reduction in σ and increase in QR result in an
246
enhancement in the diabatic ω, or an upward shift in the ω profile. The combination of
247
enhanced ω above due to enhanced QR and diminished ω below due to increased σ reduces
248
the vertical gradient of diabatic ω in the warmer climate, and thus causes a reduction in
249
the upper tropospheric conv (Figure 3f). In the end, the conv profile shifts upward along
250
with the QR profile and becomes smaller in magnitude – most dramatically at its peak –
251
due to the competing changes in the QR and σ profiles.
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In summary, the warming climate is associated with two main changes to conv and
253
implied convective detrainment. First, the location of peak conv shifts toward lower
254
pressure. The upward shift of peak conv is consistent with upward shift in QR because
255
the temperature is sufficiently “high” that there is appreciable QR from water vapor.
256
As will be shown below, the upward shift is nearly isothermal, but the peak conv level
257
warms slightly due to the significantly increased σ. Secondly, the upper tropospheric conv
258
systematically decreases at all but the lowest pressures in association with the decrease
259
in the tropical overturning circulation. Because the ω falls off to zero less dramatically
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with decreasing pressure in the warmer climate as explained above, the implied upper
261
tropospheric conv also decreases. Clearly, both the reduction in total conv and the shift
262
towards higher altitude of peak conv are mimicked in the cloud fractions. Such a cloud
263
response is also present in cloud resolving model simulations of Tompkins and Craig [1999],
264
who noted higher but slightly warmer cloud tops as well as decreased high cloud fractional
265
coverage for runs at higher temperature.
266
The quantities plotted in Figure 1 are plotted again in Figure 4, but now as a function
267
of T . The three water vapor mixing ratio curves now lie on top of one another throughout
268
most of the troposphere, indicating an essentially unchanged relative humidity as the
269
climate warms (Figure 4a). Associated with this nearly unchanged relative humidity is
270
a nearly unchanged QR profile, when plotted in T coordinates (Figure 4b). This clearly
271
indicates the strong and fundamental dependence of QR on T through its exponential
272
limit on the water vapor concentrations. Static stability, on the other hand, is a function
273
of pressure and the vertical gradient of T rather than its absolute value. Thus, as the
274
climate warms and the T profile remains locked to the moist adiabat, the σ at a given
275
T increases (Figure 4c). Furthermore, σ is inversely dependent on pressure (Equation 3),
276
so at a fixed temperature it increases dramatically simply because the isotherms move
277
towards lower pressure in the warming climate.
278
The shift towards higher σ at all temperatures results in a systematic decrease in di-
279
abatic ω at all temperatures as the climate warms (Figure 4d). Although the level of
280
peak conv shifts upward in space, it does not do so in such a way as to remain at fixed
281
temperature. Rather, the level gets slightly warmer due to the strong increase in σ gener-
282
ated by the models (Figure 5). Similarly, the level of abundant high clouds shifts towards
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slightly warmer temperatures rather than staying fixed in T as would be expected from
284
FAT (Figure 5). Modelled conv and clouds do not shift isothermally because of the strong
285
increase in σ relative to QR that is not explicitly accounted for in the FAT mechanism.
286
The importance of static stability changes for preventing observed cloud top tempera-
287
tures from remaining constant was also emphasized in Chae and Sherwood [2010]. It is
288
important to note that the clouds warm only slightly, and certainly much less than the
289
upper troposphere. This near-constancy of cloud temperature is largely the cause of the
290
positive LW cloud feedback, as will be shown in Section 5.
291
Trenberth and Fasullo [2009] assert that the main warming in AR4 models comes from
292
the increase in absorbed solar radiation due to decreases in tropical cloud cover. In
293
the Tropics, the cloud fraction reduction is most evident in high clouds (their Figure
294
3). Here we offer an explanation for the decrease in cloud cover, namely, the decrease in
295
upper tropospheric conv that accompanies warming. As described above, the combination
296
of enhanced ω at pressures less than 250 hPa due to enhanced QR and diminished ω
297
at pressures greater than 250 hPa due to increased σ reduces the vertical gradient of
298
diabatic ω in the warmer climate, and thus causes a reduction in upper tropospheric
299
conv (Figure 3f). These changes to QR and σ can be directly attributed to the upper
300
tropospheric warming that peaks around 200 hPa, implying that models with greater
301
upper tropospheric warming (i.e., those models with large negative lapse rate feedback)
302
have larger decreases in tropical high clouds. Furthermore, if a portion of the SW cloud
303
feedback is due to changes in tropical high cloud coverage, one would expect that portion
304
of SW cloud feedback to be anti-correlated with the lapse rate feedback: the larger the
305
upper tropospheric warming, the larger the reduction in high cloud amount, and the
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smaller in magnitude the (negative) SW cloud feedback. This would allow one to define a
307
combined lapse-rate SW cloud feedback that would have less inter-model spread than the
308
two taken separately, in a similar way to the combined lapse rate - water vapor feedback.
309
This is is the subject of ongoing work that will be addressed in a subsequent paper. The
310
remainder of the paper will focus on the implications of rising high cloud tops for longwave
311
cloud feedback.
312
In Figure 6 we show tropical mean conv and cloud fraction profiles for each of the 15
313
models used in this study. Assessing the degree to which the models exhibit a correspon-
314
dence between their high cloud fractions and the location of peak upper tropospheric conv
315
is difficult because the model output available in the PCMDI archive is only the cloud
316
fraction in the model vertical bins, with no information about optical depth or cloud top
317
information similar to what a satellite sensor would retrieve in reality. It is also probable
318
that each model defines cloud fraction differently. Thus a lack of perfect correspondence
319
between cloud fraction and upper tropospheric conv is not necessarily an indication that
320
our diagnosis technique is flawed, nor is perfect correspondence a validation of our diag-
321
nosis technique. It is our hope that, in the future, modeling centers will archive more
322
detailed cloud diagnostics that will be more useful than the cloud amounts shown here.
323
Nonetheless, the models collectively produce a peak in high cloud amount that is con-
324
sistent with the level diagnosed from the clear-sky energy and mass balance. Notable
325
exceptions are the miroc3 2 medres model, where a large peak in cloud amount appears
326
at the tropopause, most likely very thin tropopause cirrus that is disconnected from deep
327
convection, and the mri cgcm2 3 2a model, whose cloud fraction exhibits a very broad
328
upper tropospheric peak that is rather different from its much sharper conv peak. In
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329
general, conv peaks are sharper and located at a slightly lower pressure than the cloud
330
fraction peaks. It is reasonable that a plot of cloud tops would exhibit a peak that is
331
both sharper and located at lower pressures than the peak shown here for cloud amount.
332
Thus, it is likely that a better correspondence exists between the level of abundant conv
333
and the level of abundant high cloud tops, the emission from which is more relevant for
334
LW cloud feedback.
335
Additionally, it is clear that all models produce cloud and conv profiles that remain
336
nearly fixed in temperature. The models generally exhibit a slight decrease in upper
337
tropospheric conv and cloud amount, though it appears as though the signal is larger in
338
the conv profile.
To assess the degree to which the upward migration of model clouds agrees with the
upward migration of calculated conv in each model, we calculate the high cloud-weighted
pressure and upper tropospheric clear-sky diabatic convergence-weighted pressure as
phicld =
Pp at
trop
p at T =270K f
Pp at trop
p at T =270K
∗p
f
(5)
and
pconv =
Pp
at trop
p at T =270K conv ∗
Pp at trop
p at T =270K conv
p
,
(6)
339
where f is the cloud fraction at each pressure. Scatterplots of decadal-mean tropical-mean
340
pconv and phicld are shown for each model and for the ensemble mean in Figure 7. While the
341
degree of correspondence between the location of abundant high cloud amount and upper
342
tropospheric conv varies from model to model (Figure 6), the correspondence between the
343
shift in pconv and the shift in upper tropospheric phicld as the climate warms is remarkably
344
consistent from model to model, closely following a one-to-one relationship. In general,
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345
the decrease in phicld is slightly larger than the decrease in conv weighted pressure. In
346
other words, the clouds migrate slightly more than conv does.
347
High cloud weighted-temperature (Thicld ) and upper tropospheric clear-sky diabatic
348
convergence-weighted temperature (Tconv ) are calculated as in Equations 5 and 6, but
349
with T substituted for p. Scatterplots of decadal-mean tropical-mean upper tropospheric
350
Tconv and Thicld are shown for each model and for the ensemble mean in Figure 8. Each
351
number in the plot represents its respective decadal mean.
352
As in the previous figure, the dashed line has slope one but nonzero y-intercept. In
353
T space, the shift in Tconv and Thicld is very small (on the order of a degree) indicating
354
that both the high clouds and the upper tropospheric conv shift upward in altitude as
355
the climate warms, but do so in such a way that they remain at approximately the same
356
T . Because the conv profile migrates upward slightly less than the cloud profile, there is
357
slightly greater warming of Tconv than of Thicld. This is especially the case in the GFDL
358
models, whose Thicld s remain remarkably constant in the face of relatively large increase
359
of their Tconv s. Overall, the very slight shift towards warmer Thicld and Tconv is related to
360
the increase in σ as the climate warms, as explained above. In summary, all models in
361
the IPCC AR4 archive exhibit a clear shift in high cloud amount towards lower pressures
362
that is remarkably well-explained by the upper tropospheric conv inferred from radiative
363
cooling. The shift occurs nearly isothermally, as expected from the FAT hypothesis.
364
Figure 9, which plots the ensemble mean Tconv , Thicld , and the T at 200 hPa as a function
365
of surface T over the course of the 21st Century, concisely illustrates the main conclusions
366
from the first part of this paper. Whereas the tropical upper troposphere warms 6 K,
367
approximately twice as much as the mean tropical surface T (lapse rate feedback), the
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368
Thicld and Tconv warm only about 1 K. Tropical high clouds much more closely follow the
369
isotherms rather than the isobars, as expected from the FAT hypothesis. This represents
370
a strong positive feedback because the clouds are not warming in step with the surface
371
or atmosphere; in other words the planet cannot radiate away heat as easily as it could
372
if the high clouds warmed along with the upper troposphere. In the following section we
373
make a quantitative estimate of the contribution of this nearly-fixed Thicld to the total LW
374
cloud feedback.
5. Estimating Actual and Hypothetical LW Cloud Feedbacks in the Models
375
Though the tendency for clouds to shift upward as the climate warms has been noted in
376
several previous studies (e.g., Hansen et al. [1984], Wetherald and Manabe [1988], Mitchell
377
and Ingram [1992], Senior and Mitchell [1993]), no study has explicitly shown to what
378
extent this effect is giving rise to the positive LW cloud feedback. Here we make an
379
estimate of the contribution to LW cloud feedback of the nearly constant Thicld. We first
380
decompose the change in LW cloud forcing into its components, then calculate LW cloud
381
feedback using the radiative kernel technique of Soden et al. [2008].
5.1. Contributors to the Change in LW Cloud Forcing
The outgoing LW radiation (OLR) can be written as the sum of contributions from the
clear and cloudy regions, denoted by the subscripts cld and clr, respectively:
OLR = ftot OLRcld + (1 − ftot )OLRclr
(7)
where ftot is the total cloud fraction output by the model. Note that this cloud fraction
is the total (i.e., vertically integrated with overlap assumptions) cloud fraction to be
distinguished from f which is the cloud fraction in each vertical bin. Because OLR,
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OLRclr , and ftot are model diagnostics, OLRcld is calculated using this equation. Note
that OLRcld is the LW radiation that is emerging from only the cloudy portion of the
scene whereas OLR is the LW emerging from the entire scene including cloudy and clear
sub-scenes. This allows us to define the LW CF as
LW CF = OLRclr − OLR = ftot (OLRclr − OLRcld ).
(8)
The change in LW CF , which we calculate as the difference between the 2090-2100
mean and the 2000-2010 mean, can be written as
∆LW CF = ∆ftot (OLRclr − OLRcld ) + ftot ∆OLRclr − ftot ∆OLRcld + C.
(9)
382
The first term on the right hand side is the contribution from the change in cloud fraction
383
assuming no change in clear minus cloudy OLR. This term is generally negative because
384
cloud fraction decreases slightly. The second term is the change in clear sky OLR assuming
385
no change in cloud fraction. This term is generally positive in the extratropics and negative
386
in the Tropics, as the atmosphere becomes more opaque to LW radiation. The third term
387
is the change in cloudy sky OLR assuming no change in cloud fraction. This term is
388
strongly positive throughout most of the tropical oceans and negative elsewhere. That
389
this term is so strongly positive throughout much of the Tropics implies that the cloudy
390
sky OLR decreases dramatically in many regions as the climate warms. However, upon
391
close inspection of the regions that show large values of ∆OLRcld , it is clear that the
392
large changes are caused not by clouds cooling or warming but simply by increases or
393
decreases in the relative amount of high versus low clouds. Because of this, we perform
394
a slightly different decomposition below. The fourth term, C, is a covariance term, equal
395
to ∆ftot ∆OLRclr − ∆ftot ∆OLRcld . It is negative on average throughout the Tropics.
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To better assess the relative roles of high and low clouds in affecting ∆LW CF , we
decompose OLRcld into components due to high and low clouds in the Tropics:
ftot OLRcld = fhi OLRhi + flo OLRlo ,
(10)
fhi + flo = ftot
(11)
where
Rather than attempting to calculate the high and low cloud fractions from the cloud
amount profiles, we assume that the high cloud weighted temperature (Thicld ) is a reasonable estimate of the high cloud emission T and that the cloud is a blackbody such
that
4
OLRhi = σThicld
.
(12)
We also assume that the low cloud OLR is the same as the clear-sky OLR, OLRlo =
OLRclr . This allows us to calculate fhi as
fhi = ftot
OLRcld − OLRclr
OLRcld − OLRlo
= ftot
.
OLRhi − OLRlo
OLRhi − OLRclr
(13)
The decomposition of the change in LW cloud forcing is now
∆LW CF = ∆fhi (OLRclr − OLRhi ) − fhi∆OLRhi + fhi ∆OLRclr + C.
(14)
396
Thus the change in LW CF is due to the change in fhi assuming a constant difference
397
between clear-sky OLR and high cloud OLR, the change in high cloud OLR and clear sky
398
OLR assuming no change in fhi , and the covariance between changes in fhi , high cloud
399
OLR, and clear sky OLR. ∆LW CF calculated here is exactly equal to that calculated
400
directly.
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401
In Figure 10 we show the contribution of each of these components to the change
402
in ensemble-mean LW CF . Note that the color scale varies among the panels to make
403
the features more apparent. Henceforth, ensemble-mean refers to the average over the
404
12 models that run the A2 scenario and that archived enough information to compute
405
cloud feedbacks. (Three of the models used previously do not output enough clear-sky
406
diagnostics to compute cloud feedbacks.) Large regional changes in fhi occur as the
407
tropical circulation changes over the course of the century. Most notably, fhi increases
408
along the equatorial Pacific and Indian Oceans are nearly compensated by fhi decreases
409
in the subtropics and over tropical land masses (Figure 10a). Maps of both the mean
410
and change in fhi are very similar to maps of the mean and change in precipitation (not
411
shown), lending credence to our method of extracting the fhi using Equation 13. Overall,
412
the redistribution of tropical high clouds tends to increase the LW CF in the Tropics
413
(Figure 10a).
414
In the Tropics, clear-sky OLR decreases between the beginning and end of the century
415
as the atmosphere becomes more opaque (Figure 10b). This is especially true in convective
416
regions that are moist in the free troposphere like over the Western Pacific warm pool,
417
resulting in a largely negative fhi ∆OLRclr term. Because high cloud temperatures do not
418
stay perfectly constant with climate change as explained above, the −fhi ∆OLRhi term
419
is negative over most of the Tropics (Figure 10c). This is especially pronounced over the
420
West Pacific warm pool and Indian Ocean. Taken together, the terms in panels (b) and
421
(c) represent a decrease in the difference between clear and cloudy OLR as the cloud tops
422
warm slightly and the clear-sky OLR decreases slightly; thus they contribute to a decrease
423
in LW CF .
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424
Both covariance terms (Figure 10d and e) are very small (note the color scale range) and
425
systematically negative throughout the Tropics. These are due to the concurrent increase
426
in fhi in regions where both the high clouds are warming slightly and the clear-sky OLR
427
is decreasing slightly.
428
∆LW CF is negative throughout most of the Tropics, with two main regions of positive
429
change, namely, the equatorial Pacific and off the east coast of Africa (Figure 10f). These
430
two regions exhibit large increases in fhi that outweigh the other terms contributing to
431
∆LW CF . Over the maritime continent, the increase in high cloud OLR and decrease
432
in clear-sky OLR result in a decrease in LW CF . Over the tropical continents, the main
433
cause of the decrease in LW CF is due to the decrease in fhi as the climate warms.
5.2. From ∆LW CF to LW Cloud Feedback: Applying the Radiative Kernels
434
The change in LW CF is not equal to the LW cloud feedback, though they are corre-
435
lated (Soden et al. [2004], Soden and Held [2006]). Whereas ∆LW CF is equal to the
436
change in clear- minus all-sky OLR, the LW cloud feedback is the change in OLR due
437
to clouds alone. Thus, we calculate the LW cloud feedback by adjusting ∆LW CF using
438
the radiative kernel technique (Soden et al. [2008]). Briefly, radiative kernels represent
439
the LW or SW radiative response at the top of atmosphere to temperature, humidity,
440
or surface albedo perturbations at each latitude, longitude, pressure (if applicable), and
441
time. For each model we calculate the clear and all-sky T and q feedbacks by convolving
442
the appropriate radiative kernels with the change in T and q between the first and last
443
decade of the 21st Century. LW cloud feedback is estimated by adjusting the change in
444
LW CF by the magnitude of cloud masking in the T and q feedbacks. The cloud masking
445
is calculated by differencing the clear- and all-sky radiative responses and adding a term
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446
due to the cloud masking of the radiative forcing in the A2 scenario (Eqn. 25 of Soden
447
et al. [2008]). Assuming clouds mask the radiative forcing in the SRES A2 scenario (cal-
448
culated by summing the A2 radiative forcing terms given in Tables 6.14 and 6.15 of the
449
IPCC Third Assessment Report (Ramaswamy et al. [2001])) by the same proportion as
450
in the A1B scenario (Soden et al. [2008]), this term is 1.03 W m−2 .
5.3. Three Hypothetical LW Cloud Feedback Cases: FAT, FAP, and PHAT
451
Here we compare three hypothetical scenarios to the actual ∆LW CF to illustrate the
452
contribution of nearly-fixed high cloud temperatures to the LW cloud feedback. We con-
453
sider two cases that can be thought of as upper and lower bounds on ∆LW CF , the
454
fixed anvil temperature (FAT) and the fixed anvil pressure (FAP) cases, respectively. We
455
also consider an intermediate case, the proportionately higher anvil temperature (PHAT)
456
case, in which the change in Thicld is set equal to the change in upper tropospheric Tconv .
457
(Recall that the increase in Tconv is proportional to the increase of static stability that
458
accompanies warming.) As will be shown, PHAT does the best job of matching the LW
459
cloud feedback in the models. Note that we use the term“anvil” very loosely to include
460
all tropical high clouds, simply to maintain consistent terminology with Hartmann and
461
Larson [2002].
The change in LW CF assuming FAT is given by
∆LW CFF AT = ∆fhi (OLRclr − OLRhi ) + fhi ∆OLRclr + C,
(15)
where the ∆OLRhi term in Equation 14 is neglected because Thicld is assumed fixed. The
change in LW CF assuming FAP is given by
F AP
∆LW CFF AP = ∆fhi (OLRclr − OLRhi ) − fhi ∆OLRhi
+ fhi ∆OLRclr + C,
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F AP
where ∆OLRhi
is the change in high cloud OLR assuming the clouds remain at the
same pressure – the initial high cloud weighted pressure – as the climate warms. The
change in LW CF assuming PHAT is given by
P HAT
∆LW CFP HAT = ∆fhi (OLRclr − OLRhi ) − fhi ∆OLRhi
+ fhi ∆OLRclr + C, (17)
462
P HAT
where ∆OLRhi
is the change in high cloud OLR assuming the change in Thicld is
463
equal to the change in tropical-mean Tconv . As we have seen, the change in Tconv is
464
small but generally positive, so it represents a small but important correction to the
465
FAT assumption. For all three cases, we compute ∆LW CF , then apply the cloud mask
466
corrections described above to calculate LW cloud feedback.
467
In Figure 11 we plot maps of the ensemble mean LW cloud feedback estimated for each
468
case, along with the difference between the actual LW cloud feedback and that computed
469
for each case. Note that we use the term “actual” to refer to the model’s LW cloud
470
feedback, not to the actual LW cloud feedback in nature. The decomposition of ∆LW CF
471
was only done for the Tropics, where it is easier to separate high and low clouds; thus
472
the FAT, FAP, and PHAT assumptions differ only in the Tropics, due to the fhi ∆OLRhi
473
term. Strictly, the maps show the spatial structure of the LW cloud feedback, which is
474
defined by globally-integrating the local contributions.
475
Unlike ∆LW CF , the LW cloud feedback is positive throughout the Tropics, except in
476
the FAP case where it is only positive over the equatorial Pacific and off the east coast of
477
Africa where large increases in high clouds occur (Figure 11c). In the FAP feedback, the
478
large increase in Thicld results in a large negative contribution due to the change in OLRhi .
479
The FAP feedback is essentially that which would occur if the cloud profile did not shift
480
upward as the climate warmed. Thus, the difference between the actual feedback and
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481
the FAP feedback shown in Figure 11d gives the contribution of changing cloud height to
482
the LW cloud feedback. Here we find that the contribution to LW cloud feedback of the
483
tendency for clouds not to warm as much as the upper troposphere is 0.95 W m−2 K−1
484
in the tropical-mean. Without this contribution, the tropical-mean LW cloud feedback
485
would be negative, as shown in the FAP case.
486
The FAT feedback is slightly larger than the actual feedback because tropical high
487
clouds do not stay at a fixed T as the climate warms (Figures 11a and b). Thus, a slight
488
overestimate of the feedback occurs in all regions that have climatologically abundant high
489
clouds. In the tropical mean, the FAT assumption overestimates the LW cloud feedback
490
by 0.27 W m−2 K−1 .
491
Allowing tropical high clouds to warm along with the tropical-mean Tconv (i.e., PHAT)
492
predicts a tropical-mean LW cloud feedback that is only slightly greater than the actual
493
feedback by 0.04 W m−2 K−1 (Figure 11f). Because we apply a spatially-invariant tropical-
494
mean warming to the high clouds in the PHAT assumption, there are some regions where
495
we underestimate the feedback (i.e., over the continents and in the subtropics) and some
496
regions where we overestimate the feedback (i.e., over the west Pacific warm pool and In-
497
dian Ocean). Where we overestimate the feedback, the high clouds warm more than does
498
the tropical-mean upper tropospheric Tconv . Nevertheless, the feedback calculated assum-
499
ing PHAT agrees quite well with the actual LW cloud feedback, and properly accounts
500
for the physics that govern the shift in the high cloud profile.
501
In Figure 12, we show bar plots of tropical- and global-mean LW cloud feedback along
502
with the three cases FAP, PHAT, and FAT in each model and in the ensemble mean. Note
503
that the feedback scenarios differ only in the Tropics, having the same LW feedback in the
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504
extratropics; the global-mean feedback is provided for completeness. Clearly the feedback
505
calculated assuming clouds remain at fixed pressure (FAP) greatly underestimates the
506
actual LW cloud feedback. It is small in all models, with the spread being caused by dif-
507
ferences the other terms in the decomposition, most notably the change in fhi . For nearly
508
every model, the global- (tropical-) mean difference between FAP and actual feedback
509
magnitude is about 0.5 (1.0) W m−2 K−1 . This is entirely due to the fact that clouds do
510
not stay at fixed pressure as the climate warms, but rather rise nearly isothermally.
511
On the other hand, the feedback calculated assuming Thicld does not change (i.e., FAT)
512
slightly overestimates the LW cloud feedback in every model. The magnitude of overesti-
513
mation varies from model to model depending on the degree to which the shift in cloud
514
profile deviates from isothermal. In models with less pronounced upward enhancement
515
of warming in the Tropics, the LW cloud feedback is closer to the value given by the
516
FAT assumption because the reduction in pressure and corresponding increase in static
517
stability at a fixed temperature is less, preventing clouds from warming as much. FAT
518
remains a considerably better approximation to the actual LW cloud feedback than FAP.
519
The PHAT feedback very closely tracks the actual LW cloud feedback in all the models
520
but can over- or underestimate the actual LW cloud feedback depending on how much
521
each model’s Tconv changes. In the ensemble mean, it is a slight overestimation, but is
522
remarkably close to the actual value. The PHAT feedback is always positive, as there is
523
a large contribution from the fact that the clouds do not warm nearly as much as if they
524
stayed at fixed pressure. PHAT is a slightly better predictor of the LW cloud feedback
525
magnitude than FAT because it accounts for the change in σ that accompanies modeled
526
climate change, thereby incorporating a slight increase of Thicld . Thus we have a physically
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527
consistent and robust predictor of each model’s LW cloud feedback, and therefore high
528
confidence that the systematically positive LW cloud feedback produced by the models is
529
indeed correct.
6. Conclusions
530
We have shown that tropical high clouds in models shift upward as the climate warms
531
over the 21st Century and that this upward shift is accompanied by a very modest increase
532
in cloud top temperature. Because the clouds are not warming in step with the surface
533
temperature, the warming Tropics become less efficient at radiating away heat and thus
534
the clouds are acting as a positive feedback on climate.
535
The negligible temperature response of tropical high clouds to climate change can be
536
understood through the principles of the fixed anvil temperature (FAT) hypothesis of
537
Hartmann and Larson [2002]. The essential physics are simply that the troposphere can
538
only be heated by convection where it is being cooled by radiation. Thus clouds are
539
only abundant in altitude ranges where the temperatures are high enough for appreciable
540
water vapor to radiatively cool to space. If the entire troposphere warms, the tropical-
541
mean cloud tops will be located at a higher altitude that is now warm enough that water
542
vapor near saturation has substantial LW emissivity.
543
Assuming a mass-conserving circulation connects the convective and non-convective re-
544
gions of the Tropics, the altitude of convective detrainment and abundant high cloud
545
amount must be co-located with the altitude of strong radiatively-driven convergence,
546
conv. One can calculate the conv profile in a relatively straightforward manner by com-
547
puting the vertical gradient of the diabatic subsidence, ω, required to balance radiative
548
cooling, QR . Because of the rapid fall-off of QR and rapid increase of static stability,
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549
σ, with decreasing pressure, diabatic ω decreases rapidly with decreasing pressure in the
550
upper troposphere, creating a region of enhanced conv. We have shown good qualitative
551
agreement between this level of enhanced upper tropospheric conv and the high cloud
552
amount in each model.
553
As the climate warms over the course of the 21st Century, pconv and phicld decrease in a
554
nearly one-to-one fashion, and do so in such a way as to remain at approximately the same
555
T . Because the vertical structure of changes to the QR profile differs from that of the σ
556
profile, the diabatic ω decreases below and increases above the level of peak conv, causing
557
a decrease in conv that is mimicked by slight decreases the upper tropospheric cloud
558
fraction. Both the clouds and conv tend to warm slightly over the course of the century,
559
and this is due to an increase in σ that prevents the clouds from rising isothermally.
560
To assess the contribution of nearly constant cloud top temperatures to the LW cloud
561
feedback, we first decomposed the change in LW CF into components. This allowed
562
us to create three cases, one in which Thicld (and therefore high cloud OLR) does not
563
change (FAT), one in which Thicld increases as much as does the temperature at a fixed
564
pressure level (FAP), and one in which Thicld increases along with the tropical-mean upper
565
tropospheric Tconv (PHAT).
566
Assuming that clouds do not rise as the climate warms (i.e., FAP) results in a near-zero
567
LW cloud feedback in every model. The global- (tropical-) mean LW cloud feedback is
568
systematically about 0.5 (1.0) W m−2 K−1 larger than that calculated assuming FAP,
569
and this is entirely because high clouds rise in such a way as to warm only slightly in
570
every model. The LW cloud feedback calculated assuming FAT slightly overestimates the
571
actual LW cloud feedback because the Thicld does increase slightly over the course of the
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572
century. That calculated assuming PHAT is very close to the actual LW cloud feedback
573
in all models and represents an improved estimate over FAT because it allows for the
574
slight increase in Thicld due to the increase in static stability. Thus, we show that the
575
robust positive LW cloud feedback can be well-explained by the fundamental physics of
576
FAT, with a slight modification (PHAT) to take into account the modeled static stability
577
changes. Tropical high clouds are fundamentally constrained to emit at approximately
578
the same temperature as the climate warms, and we have shown here that this results in
579
a LW cloud feedback that is robustly positive in climate models.
580
Acknowledgments. This research was supported by NASA Earth and Space Science
581
Fellowship NNX06AF69H and NASA Grant NNX09AH73G. We acknowledge the inter-
582
national modeling groups for providing their data for analysis, the Program for Climate
583
Model Diagnosis and Intercomparison (PCMDI) for collecting and archiving the model
584
data, and B. J. Soden for providing the radiative kernels. We thank Chris Bretherton,
585
Rob Wood, Andrew Dessler, and two anonymous reviewers for useful suggestions for im-
586
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100
100
200
200
Pressure (hPa)
Pressure (hPa)
ZELINKA AND HARTMANN: WHY IS LONGWAVE CLOUD FEEDBACK POSITIVE?
300
400
500
600
400
500
600
700
−6
10
−5
10
−4
−3
−2
10
10
10
(a) Specific humidity (kg kg−1)
700
−0.5
−1
10
100
100
200
200
Pressure (hPa)
Pressure (hPa)
300
300
400
500
600
0
Figure 1.
0.1
0.2
0.3
0.4
(c) Static Stability (K hPa−1)
0.5
0.5
1
1.5
(b) Radiative Cooling (K day−1)
2
300
400
500
600
700
0
700
−5
2000−2010
2060−2070
2090−2100
0
5
10
15
20
25
(d) Diabatic ω (hPa day−1)
30
35
Tropical-mean ensemble-mean specific humidity (a), radiative cooling (b), static
stability (c), and diabatic subsidence (d) for 2000-2010 (thin solid), 2060-2070 (thick dashed),
and 2090-2100 (thick solid). Ensemble-mean refers to the average over the 15 models that run
the A2 scenario. Note that the specific humidity is plotted on a logarithmic scale.
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ZELINKA AND HARTMANN: WHY IS LONGWAVE CLOUD FEEDBACK POSITIVE?
0
5
Gray: Cloud amount (%)
10
15
20
100
Pressure (hPa)
200
300
400
500
2000−2010
2060−2070
2090−2100
600
700
−0.05
Figure 2.
0
0.05
0.1
0.15
0.2
0.25
Black: Diabatic convergence (day−1)
0.3
Tropical-mean ensemble-mean clear-sky diabatic convergence (black) and cloud
amount (gray) for 2000-2010 (thin solid), 2060-2070 (thick dashed), and 2090-2100 (thick solid).
Ensemble-mean refers to the average over the 15 models that run the A2 scenario.
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ZELINKA AND HARTMANN: WHY IS LONGWAVE CLOUD FEEDBACK POSITIVE?
Light: Specific Humidity (kg kg−1)
−6
−4
10
−2
10
200
300
−0.5
50
100
100
150
150
150
200
200
200
250
300
350
Pressure (hPa)
100
250
300
350
300
350
400
400
450
450
450
0
0
500
−2
50
100
150
(a) Thick: Percentage Change
500
0
2
4
(b) Thick: Absolute Change
6
0
Light: Diabatic ω (hPa dy−1)
Light: Static Stability (K hPa−1)
0.1
0.2
0.3
0.4
0
10
20
30
100
100
100
150
150
150
200
200
200
350
Pressure (hPa)
50
Pressure (hPa)
50
300
250
300
350
300
350
400
400
450
450
450
500
−0.15
500
−4
Figure 3.
0.05
−2
0
2
(e) Thick: Absolute Change
0.4
250
400
−0.1
−0.05
0
(d) Thick: Absolute Change
0.1
0.2
0.3
(c) Thick: Absolute Change
Light: Diabatic Convergence (dy−1)
0
0.1
0.2
0.3
50
250
Light: Radiative Cooling (K dy−1)
0
0.5
1
1.5
2
250
400
500
Pressure (hPa)
Light: Temperature (K)
250
50
Pressure (hPa)
Pressure (hPa)
10
50
4
500
−0.05
0
(f) Thick: Absolute Change
0.05
Tropical-mean ensemble-mean change in specific humidity (a), temperature (b),
radiative cooling (c), static stability (d), diabatic subsidence (e), and clear-sky diabatic convergence (f) calculated as a difference between the 2000-2010 mean and the 2090-2100 mean.
Overlain in each panel are the 2000-2010 mean (light dashed line) and 2090-2100 mean (light
solid line). Ensemble-mean refers to the average over the 15 models that run the A2 scenario.
Note that the mean specific humidity is plotted on a logarithmic scale and its change is expressed
as a percentage.
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March 26, 2010, 3:20pm
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ZELINKA AND HARTMANN: WHY IS LONGWAVE CLOUD FEEDBACK POSITIVE?
190
190
200
200
210
210
Temperature (K)
Temperature (K)
X - 38
220
230
240
230
240
250
250
260
260
270
−6
10
−5
10
−4
−3
−2
10
10
10
(a) Specific humidity (kg kg−1)
270
−0.5
−1
10
190
190
200
200
210
210
Temperature (K)
Temperature (K)
220
220
230
240
240
260
260
Figure 4.
0.1
0.2
0.3
0.4
(c) Static Stability (K hPa−1)
0.5
2
230
250
0
0.5
1
1.5
(b) Radiative Cooling (K day−1)
220
250
270
0
270
−5
2000−2010
2060−2070
2090−2100
0
5
10
15
20
25
(d) Diabatic ω (hPa day−1)
30
35
Tropical-mean ensemble-mean specific humidity (a), radiative cooling (b), static
stability (c), and diabatic subsidence (d) for 2000-2010 (thin solid), 2060-2070 (thick dashed),
and 2090-2100 (thick solid) as a function of temperature. Ensemble-mean refers to the average
over the 15 models that run the A2 scenario. Note that the specific humidity is plotted on a
logarithmic scale and that temperature increases downward in each panel.
D R A F T
March 26, 2010, 3:20pm
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ZELINKA AND HARTMANN: WHY IS LONGWAVE CLOUD FEEDBACK POSITIVE?
0
5
Dashed: Cloud amount (%)
10
15
X - 39
20
190
200
Temperature (K)
210
220
230
240
250
2000−2010
2060−2070
2090−2100
260
270
−0.05
Figure 5.
0
0.05
0.1
0.15
0.2
0.25
Solid: Diabatic convergence (day−1)
0.3
Tropical-mean ensemble-mean clear-sky diabatic convergence (black, bottom axis)
and cloud amount (gray, top axis) for 2000-2010 (thin solid), 2060-2070 (thick dashed), and
2090-2100 (thick solid) as a function of temperature. Ensemble-mean refers to the average over
the 15 models that run the A2 scenario. Note that temperature increases downward.
D R A F T
March 26, 2010, 3:20pm
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ZELINKA AND HARTMANN: WHY IS LONGWAVE CLOUD FEEDBACK POSITIVE?
mpi_echam5
10
20
0
30
0
miroc3_2_medres
10
20
30
ukmo_hadcm3
10
20
30
0
ipsl_cm4
10
20
0
30
gfdl_cm2_1
10
20
0
30
Temperature (K)
200
220
240
260
0
0.1
0.2
gfdl_cm2_0
10
20
0
0
30
0
0.1
0.2
giss_model_e_r
10
20
30
0
0.1
0.2
inmcm3_0
10
20
0
0
30
0.1
0.2
0
cccma_cgcm3_1
10
20
30
0
0
0.1
0.2
mri_cgcm2_3_2a
10
20
30
Temperature (K)
200
220
240
260
0
0.1
0.2
ncar_pcm1
10
20
0
0
30
0.1
0.2
ncar_ccsm3_0
10
20
30
0
0
0.1
0.2
bccr_bcm2_0
10
20
30
0
0
0.1
0.2
csiro_mk3_5
10
20
0
0
30
0.1
0.2
ingv_echam4
10
20
30
0
Temperature (K)
200
220
240
260
0
0.1
0.2
0
0.1
0.2
0
0.1
0.2
0
0.1
0.2
0
0.1
0.2
Figure 6. Tropical-mean clear-sky diabatic convergence (black, bottom axis) and cloud amount
(gray, top axis) for 2000-2010 (thin solid), 2060-2070 (thick dashed), and 2090-2100 (thick solid)
for the 15 IPCC AR4 models used in this study. The units for convergence are day−1 and for
cloud amount are %. Note that temperature increases downward in each panel.
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March 26, 2010, 3:20pm
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ZELINKA AND HARTMANN: WHY IS LONGWAVE CLOUD FEEDBACK POSITIVE?
mpi_echam5
miroc3_2_medres
10
200
9
210
7
4
23
210
200
190
180
High Cloud−Weighted Pressure (hPa)
250
8
23
210
200
180
8
230
9
4
3
12
250
210
200
230
cccma_cgcm3_1
250
5
4
6
200
210
6
45
123
200
190
180
300
210
10
290
32
1
300
200
230
210
200
45
6 7
250
8
260
34
12
270
190
180
210
7
56
1234
220
190
180
200
170
230
220
160
56
9
8
7
210
10
200
ncar_ccsm3_0
8
210
910
220
230
1
190
9
7
3
12
4
5
190
180
170
200
ingv_echam4
10
23
4
5
6
7
9
8
10
6
190
180
190
4
3
2
1
5
6
7 8
9
170
Ensemble Mean
170
180
8
220
10
9
230
4
23
1
240
200
220
220
200
csiro_mk3_5
210
310
170
240
200
7
56
4
3
12
7
9
8
180
inmcm3_0
230
bccr_bcm2_0
280
190
200
10
290
2
1
180
ncar_pcm1
9
8
280
3
280
190
9
mri_cgcm2_3_2a
270
7
240
250
7
270
200
240
210
6
200
210
230
5
220
123
45
8
10
10
10
9
8
260
190
giss_model_e_r
67
240
9
180
34
220
4
220
190
220
9 10
1
230
2
1
10
170
8
7
6
5
240
gfdl_cm2_0
7
6
5
260
280
7
250
gfdl_cm2_1
270
56
230
170
1
230
34
12
ipsl_cm4
10
9
10
9
8
160
56
220
220
150
8
ukmo_hadcm3
140
5
6
7
10
8
250
210
200
190
180
200
190
180
170
210
200
190
180
Upper Tropospheric Convergence−Weighted Pressure (hPa)
Figure 7.
Scatterplots of tropical-mean decadal-mean upper tropospheric clear-sky diabatic
convergence-weighted pressure and high cloud-weighted pressure for the 15 IPCC AR4 models
used in this study as well as the ensemble mean. Each number identifies the respective decade
within the 21st Century. Note that pressure increases downward and to the left. The dashed line
is a 1:1 line with a nonzero y-intercept passing through the mean of both quantities.
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March 26, 2010, 3:20pm
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ZELINKA AND HARTMANN: WHY IS LONGWAVE CLOUD FEEDBACK POSITIVE?
mpi_echam5
miroc3_2_medres
222
220
218
216
219
220
231
211
226
218
230
210
225
217
229
209
224
ipsl_cm4
228
208
223
219 218 217 216 215
gfdl_cm2_1
High Cloud−Weighted Temperature (T)
ukmo_hadcm3
227
207
221
222
gfdl_cm2_0
220
218
219 218 217 216 215
giss_model_e_r
inmcm3_0
231
225
229
230
232
226
230
231
233
227
231
232
234
228
232
233
235
229
233
234
224
222
220
224
cccma_cgcm3_1
233
234
235
236
237
222
220
224
225
235
226
236
223
227
237
224
228
238
225
229
218
216
214
217 216 215 214 213
226
235
227
236
228
237
229
238
228
226
220
ingv_echam4
225
234
224
222
220
ncar_ccsm3_0
222
csiro_mk3_5
216
216
221
bccr_bcm2_0
218
218
ncar_pcm1
234
221 220 219 218 217
220
220
mri_cgcm2_3_2a
218
216
Ensemble Mean
218
225
219
226
220
227
221
228
222
229
221 220 219 218 217
221 220 219 218 217
Upper Tropospheric Convergence−Weighted Temperature (T)
Figure 8.
Scatterplots of tropical-mean decadal-mean upper tropospheric clear-sky diabatic
convergence-weighted temperature and high cloud-weighted temperature for the 15 IPCC AR4
models used in this study as well as the ensemble mean. Each cross represents one decadal mean
within the 21st Century. Note that temperature increases downward and to the left. The dashed
line is a 1:1 line with a nonzero y-intercept passing through the mean of both quantities.
D R A F T
March 26, 2010, 3:20pm
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ZELINKA AND HARTMANN: WHY IS LONGWAVE CLOUD FEEDBACK POSITIVE?
X - 43
229
228
Temperature (K)
227
Thicld
226
225
224
Tconv + 5K
223
222
221
T200 hPa
220
219
298.5
Figure 9.
299
299.5
300
300.5
301
Surface Temperature (K)
301.5
Tropical-mean ensemble-mean high cloud-weighted temperature (thick solid line),
upper tropospheric clear-sky diabatic convergence-weighted temperature (thick dashed line), and
200 hPa temperature (thin solid line) plotted against tropical-mean ensemble-mean surface temperature for the 21st Century. Ensemble-mean refers to the average over the 15 models that run
the A2 scenario.
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March 26, 2010, 3:20pm
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ZELINKA AND HARTMANN: WHY IS LONGWAVE CLOUD FEEDBACK POSITIVE?
Ensemble Mean
∆LWCF Terms
(a) ∆f (OLR −OLR )
hi
clr
hi
(b) fhi∆OLRclr
5
10
5
0
0
−5
−2
−10
Tropical Mean = 0.05 W m
(c) −f ∆OLR
hi
−5
−2
Tropical Mean = −0.29 W m
(d) ∆f ∆OLR
hi
hi
clr
5
10
5
0
0
−5
−2
−10
Tropical Mean = −0.46 W m
(e) −∆f ∆OLR
hi
−5
−2
Tropical Mean = −0.13 W m
(f) Sum of Terms
hi
10
5
5
0
0
−5
−2
Tropical Mean = −0.31 W m
Figure 10.
−5
−2
Global Mean = −0.84; Tropical Mean = −1.14 W m
−10
Terms contributing to the change in ensemble-mean LW CF : ∆fhi (OLRclr −
OLRhi ) (a), fhi ∆OLRclr (b), −fhi ∆OLRhi (c), ∆fhi ∆OLRclr (d), −∆fhi ∆OLRhi (e), and the
sum of all terms, including the contribution from the extratropical terms that are not shown
(f). Ensemble-mean refers to the average over the 12 models that run the A2 scenario and that
archived enough information to compute cloud feedbacks. Note that the color scale varies from
panel to panel.
D R A F T
March 26, 2010, 3:20pm
D R A F T
ZELINKA AND HARTMANN: WHY IS LONGWAVE CLOUD FEEDBACK POSITIVE?
Ensemble Mean
LW Cloud Feedback
(a) FAT
X - 45
(b) FAT minus Actual
2.5
5
2
1.5
1
0.5
0
0
−0.5
−1
−1.5
−2
−2
−1
Global Mean = 0.67; Tropical Mean = 0.96 W m K
−5
−2
−1
Global Mean = 0.13; Tropical Mean = 0.27 W m K
−2.5
(d) FAP minus Actual
(c) FAP
2.5
5
2
1.5
1
0.5
0
0
−0.5
−1
−1.5
−2
−2
−1
Global Mean = 0.06; Tropical Mean = −0.26 W m K
−5
−2
−1
Global Mean = −0.48; Tropical Mean = −0.95 W m K
−2.5
(f) PHAT minus Actual
(e) PHAT
2.5
5
2
1.5
1
0.5
0
0
−0.5
−1
−1.5
−2
−2
−1
Global Mean = 0.55; Tropical Mean = 0.74 W m K
Figure 11.
−5
−2
−1
Global Mean = 0.02; Tropical Mean = 0.04 W m K
−2.5
Ensemble-mean LW cloud feedback for three cases, FAT, FAP, and PHAT (left
column) as well as the difference between the actual LW cloud feedback and the three cases (right
column). Ensemble-mean refers to the average over the 12 models that run the A2 scenario and
that archived enough information to compute cloud feedbacks. Note the different color scales
between columns.
D R A F T
March 26, 2010, 3:20pm
D R A F T
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ZELINKA AND HARTMANN: WHY IS LONGWAVE CLOUD FEEDBACK POSITIVE?
Figure 12. Estimates of tropical-mean (a) and global-mean (b) LW cloud feedback along with
the three hypothetical cases FAP, FAT, and PHAT, in each model and in the ensemble mean.
D R A F T
March 26, 2010, 3:20pm
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