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JOURNAL OF GEOPHYSICAL RESEARCH, VOL. ???, XXXX, DOI:10.1029/,
Why is Longwave Cloud Feedback Positive?1
2
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.3
Global climate models predict a longwave cloud feedback that is system-4
atically positive and nearly the same magnitude across all models. Here it5
is shown that this robust positive longwave cloud feedback is caused in large6
part by the tendency for tropical high clouds to remain at nearly the same7
temperature as the climate warms. Furthermore, it is shown that such a cloud8
response to a warming climate is consistent with well-known physics, specif-9
ically the requirement that, in equilibrium, tropospheric heating by convec-10
tion can only be large in the altitude range where radiative cooling is effi-11
cient, following the fixed anvil temperature hypothesis of [Hartmann and Lar-12
son, 2002].13
Estimates of longwave cloud feedback assuming clouds remain at fixed pres-14
sure as the climate warms under predict the model feedback by about 1 W15
m−2 K−1, highlighting the large contribution from nearly-constant cloud top16
temperature to the robustly positive longwave cloud feedback. The conver-17
gence profile computed from clear-sky radiative cooling warms slightly as the18
climate warms in the AR4 models. Longwave cloud feedback computed as-19
suming that the high cloud temperatures follow the upper tropospheric convergence-20
weighted temperature gives an excellent prediction of the longwave cloud feed-21
back in the models.22
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1. Introduction
In the present climate, clouds strongly cool the planet, reducing the net downwelling23
radiation at the top of the atmosphere by about 20 W m−2. Comparing this number24
with the radiative forcing associated with a doubling of CO2, 4 W m−2, it is clear that25
even tiny changes in clouds can have dramatic effects on the climate and can act as a26
positive or negative feedback on climate change. It is for this reason that understanding27
how clouds respond to a warming planet is of vital importance for accurately predicting28
how the climate will change.29
Cess et al. [1990], Colman [2003], Soden and Held [2006], and Webb et al. [2006] show30
that the largest uncertainty in global climate model (GCM) projections of future climate31
change is caused by the responses of clouds to a warming climate. Whereas other feedbacks32
are similar among the models, the cloud feedback varies between 0.14 and 1.18 W m−233
K−1 (Soden and Held [2006]) and little progress has been made in reducing this spread.34
Bony et al. [2006] point out several reasons why progress has been slow in evaluating35
cloud feedbacks and narrowing this range. It is difficult to use observations to evaluate36
cloud feedback because observable climate variations are not good analogues for climate37
change due to increasing greenhouse gases and because it is nearly impossible to isolate the38
unambiguous role of clouds in causing a change in net radiation at the top of atmosphere.39
Additionally, the radiative impact of clouds is large, so even subtle changes to their40
characteristics (height, amount, thickness, etc.) can have dramatic effects on the climate.41
Finally, clouds are not actually resolved in GCMs but are instead parameterized; thus a42
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variety of plausible and self-consistent cloud responses to global warming can be produced43
in models.44
Though estimates of cloud feedback vary significantly among the AR4 models (Soden45
and Held [2006]), this large spread is primarily due to the shortwave component, which46
can be attributed to uncertainties in simulations of the response of marine boundary47
layer clouds to changing conditions (Bony and Dufresne [2005]). Generally speaking,48
the models which predict a reduction in low cloud fraction exhibit greater 21st Century49
warming because the reduction in the area of such clouds with large negative net cloud50
forcing represents a strong positive cloud feedback. Conversely the models that predict51
increases in low clouds have very low climate sensitivity.52
Whereas estimates of shortwave cloud feedback vary considerably such that even the53
sign is uncertain, estimates of longwave cloud feedback are systematically positive in all54
AR4 models and exhibit half as much spread (B. J. Soden, personal communication,55
2009). In this study we address the question of why all the AR4 models exhibit positive56
longwave cloud feedbacks. We show that the robust positive longwave cloud feedback is57
largely due to tropical high clouds, which remain at approximately the same temperature58
as the climate warms. Furthermore, we show that this cloud response should be expected59
from basic physics and is therefore fundamental to Earth’s climate.60
We demonstrate this by making use of the clear-sky energy budget, which requires61
balance between subsidence warming and radiative cooling. Because radiative cooling by62
water vapor becomes very inefficient very low temperatures, subsidence rapidly decreases63
with decreasing pressure in the tropical upper troposphere. This causes large convergence64
into the clear-sky upper troposphere, which, by mass conservation, implies large convective65
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detrainment and abundant high cloudiness at that level. Thus the implied clear-sky upper66
tropospheric convergence calculated from clear-sky mass and energy balance provides a67
convenient marker for the level of high clouds and a diagnostic tool for understanding how68
that level changes as the climate warms.69
As described in the fixed anvil temperature or FAT hypothesis of Hartmann and Larson70
[2002], this level should remain at the approximately the same temperature as the climate71
warms because it is a fundamental result of radiative convective equilibrium: The tropo-72
sphere can only be heated by convection where it is being sufficiently cooled by radiation,73
resulting in an equilibrium near neutral stability.. Because the altitude range of suffi-74
cient radiative cooling by water vapor is primarily determined by temperature through75
the Clausius-Clapeyron relation, the temperature that marks the top of the convective76
cloudiness should remain approximately constant as the climate warms.77
In the cloud resolving model simulations of Kuang and Hartmann [2007], high clouds78
migrate upward for higher values of SST, but do so in such a way as to remain at the same79
temperature. The clear-sky upper tropospheric diabatic convergence calculated from the80
clear-sky energy balance as described above shows an identical constancy in temperature81
for all simulations. Recent work by Eitzen et al. [2009] shows, using observations from82
the CERES instrument on the TRMM satellite, that the distribution of tropical cloud top83
temperatures for clouds with tops greater than 10 km remains approximately constant84
as SSTs vary over the seasonal cycle, lending further observational support to the FAT85
hypothesis.86
Here we show that, as in observations and cloud resolving models, clouds in the AR487
GCMs remain at approximately the same temperature as the climate warms, and that this88
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feature is well-diagnosed by the clear-sky energy budget explained above. This is perhaps89
unsurprising given that it is a result that arises directly from tropical radiative-convective90
equilibrium that GCMs must approximately maintain, regardless of the details of their91
individual convective and cloud parameterizations. What is less appreciated is that this92
important result gives rise to a robustly positive longwave cloud feedback that can be93
explained from fundamental principles.94
In the first part of the paper, we assess the degree to which the model cloud fields95
are in agreement with the basic physics described above, both in the mean sense and96
as the climate warms. In the second part, we decompose the LW cloud feedback into its97
individual components to show that the systematic tendency for GCMs to maintain nearly-98
constant tropical high cloud temperature causes a robust positive LW cloud feedback.99
2. Data
We make use of monthly mean model diagnostics from the IPCC SRES A2 scenario100
simulations that are archived at the Program for Climate Model Diagnosis and Intercom-101
parison (PCMDI). We calculate decadal-mean quantities between the years 2000 and 2100,102
but maintain the monthly mean resolution such that the radiative calculations are more103
accurate. LW and SW radiative fluxes at both the surface and top of atmosphere and for104
both clear and all-sky conditions are used, as well as profiles of temperature (T ), specific105
humidity (q), and cloud amount. We interpolate all quantities onto the same latitude,106
longitude, and pressure grid as that of the radiative kernels of Soden et al. [2008].107
Unfortunately cloud optical thickness or effective cloud top T as would be seen from108
satellites are not standard model diagnostics available in the PCMDI archive. Only a109
small number of modeling centers have participated in the Climate Feedback Model In-110
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tercomparison Project (CFMIP), in which ISCCP-simulators are run in the models to111
better compare with observations, and no SRES scenarios were run. We instead make112
use of the basic cloud field that all modeling centers are required to output, the height-113
resolved cloud fraction within each pressure bin. This gross cloud field may include cloud114
types that are not relevant to this study (e.g., subvisible tropopause cirrus) as well as115
clouds that are not directly influencing the OLR (e.g., interior of clouds rather than cloud116
tops). Nevertheless, the cloud changes in this study are quite coherent in the sense that117
the entire cloud profile tends to shift to higher altitudes as the climate warms rather than118
exhibiting a fundamental change in shape. Thus we can make reasonable assumptions119
about the cloud top properties without actually making use of optical depth or cloud top120
information.121
3. Methodology
Before assessing how realistically high clouds are being simulated in the models, we122
first demonstrate a method of calculating the altitudes of convective detrainment and123
implied abundant cloudiness using the tropospheric mass and energy budget equations.124
We adopt the same one-dimensional diagnostic model employed by Minschwaner and125
Dessler [2004], Folkins and Martin [2005], Kuang and Hartmann [2007], and Kubar et al.126
[2007]. The tropical atmosphere is divided into a convective domain and a clear-sky127
domain. The cloudy domain is assumed to cover a small fraction of the Tropics (as active128
convection does in reality), with the majority of the Tropics being convection-free. We129
shall refer interchangeably to the convective (nonconvective) region as the cloudy (clear-130
sky) region, though these are used very loosely simply to distinguish between regions131
that are undergoing active deep convection and those that are not. Most likely there are132
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boundary layer clouds and/or high clouds that are disconnected from deep convection in133
the clear-sky region.134
One can write the dry static energy (s = cpT + gz) budget of the troposphere as
∂s
∂t= −∇· (sU) + cpQR + SH + LP, (1)
where cp is the specific heat of air at constant pressure, QR is the net (longwave plus135
shortwave) radiative heating of the atmosphere, SH is the surface sensible heat flux, L136
is the latent heat of vaporization, and P is the precipitation rate. We calculate QR using137
the Fu and Liou [1993] delta-four-stream, k-distribution scheme, with each model’s T138
and q profiles as input. Although we use T and q profiles from regions that are both139
cloudy and clear, the radiative transfer calculation is performed assuming no clouds.140
Because the presence of clouds alters cooling rates substantially, it is preferable to take141
into account clouds in the nonconvective regions, however it is very difficult to do this,142
both because there is inadequate cloud property information provided by the modeling143
centers (e.g., particle size, phase, ice water content), and because a QR profile would need144
to be calculated for every scene at every timestep, which is computationally unrealistic.145
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
∂θ
∂p=
κT
p−
∂T
∂p=
Γd − Γ
ρg, (3)
where θ is potential temperature, κ = Rd/cp, Γd is the dry adiabatic lapse rate, and Γ is the146
lapse rate. We will refer to ω as the diabatic vertical velocity (positive downward). From147
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Equation 2, we see that QR is balanced by diabatic subsidence in the clear-sky regions of148
the tropical free-troposphere. The stronger the radiative cooling or the weaker the static149
stability, the larger the diabatic subsidence that is required to maintain energy balance.150
The energy equivalent of this diabatic subsidence is provided by convective heating.151
Assuming mass continuity, the diabatic convergence profile in the clear-sky region is
calculated by
−∇H · U =∂ω
∂p(4)
where −∇H ·U is the horizontal diabatic convergence, hereafter referred to as conv. As-152
suming a closed mass budget between convective and nonconvective regions, convergence153
into the nonconvective region is balanced at the same altitudes by divergence out of the154
convective region, and vice versa. Note that using this system of equations we can calculate155
the implied convective detrainment simply from mass and energy conservation without156
invoking any complex moist physics or assumptions about parcel entrainment. This is157
a simple and elegant method for diagnosing the level of detrainment and abundant high158
clouds in the model and for understanding the changes in high clouds that accompany159
climate change.160
Rather than computing QR profiles corresponding to 24 solar zenith angles for each161
latitude and longitude in every month in every model, we instead linearize the computation162
about a mean QR profile to increase efficiency. A mean QR profile is calculated at each163
latitude and month using the ensemble-mean, monthly-mean, zonal-mean T and q profiles164
averaged over the first decade of the 21st Century. Then, perturbed QR profiles are165
calculated at each latitude and month for small perturbations at each pressure level of166
the T and q fields. The perturbations are as in Soden et al. [2008], namely, a T increase167
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of 1 K and an increase of q equal to that which is necessary to maintain constant RH in168
the presence of a 1 K increase in T . The actual T and q fields at any location and time169
within any model are then multiplied by the appropriate T - and q-perturbed QR profiles170
and summed to calculate the actual QR profile for that location. A sample of randomly-171
selected QR profiles calculated using this procedure are nearly identical to those calculated172
by running the Fu-Liou code.173
4. Results
The tropical-mean ensemble-mean q, T , radiative heating, σ, and diabatic ω profiles are174
plotted as functions of pressure in Figure 1 for averages over three decades, 2000-2010,175
2060-2070, and 2090-2100. Here, ensemble mean refers to the average over the 15 models176
that run the A2 scenario. Note that q is plotted on a logarithmic scale.177
Tropospheric temperatures are nearly moist adiabatic (Xu and Emanuel [1989]), de-178
creasing modestly with decreasing pressure in the lower troposphere, then decreasing more179
dramatically with decreasing pressure in the mid and upper troposphere (not shown). Wa-180
ter vapor concentrations are fundamentally limited by temperature through the Clausius-181
Clapeyron relation, thus q decreases exponentially with decreasing pressure throughout182
the troposphere (Figure 1a). Because temperature decreases with decreasing pressure and183
q falls off exponentially, QR is approximately constant with pressure throughout most of184
the troposphere at about 1.5 K dy−1 (Figure 1b). At the very low temperatures char-185
acteristic of the upper troposphere, water vapor concentrations become so low that QR186
dramatically falls off until reaching a level of zero radiative heating. Consistent with the187
sharp drop in water vapor radiative cooling, Hartmann et al. [2001] show that the radia-188
tive relaxation time sharply increases near 200 hPa, implying a dramatic reduction in the189
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ability of water vapor to radiate away any temperature perturbations. Above this level,190
radiative processes provide net warming to the atmosphere. It is important to note that191
QR falls off to zero well below the cold-point tropopause.192
Static stability is small and nearly constant throughout most of the well-mixed tropo-193
sphere as the T profile closely follows the moist adiabat (Figure 1c). At pressures below194
about 200 hPa, the T profile becomes increasingly more stable than the moist adiabat195
as radiative cooling by water vapor becomes increasingly less efficient. Additionally, the196
inverse pressure-dependence of σ (Equation 3) becomes especially pronounced at these197
low pressures. Diabatic ω, which is directly proportional to QR and inversely propor-198
tional to σ, very closely mimics the QR profile. It is nearly constant with pressure at199
about 25 hPa dy−1 throughout the troposphere, then falls off rapidly to zero in the region200
where QR falls off rapidly and σ increases rapidly (Figure 1d). Because the diabatic ω201
is nearly constant with pressure above and below the range of altitudes where it falls off202
rapidly with decreasing pressure, conv (vertical derivative of ω) exhibits a clear peak in203
the upper troposphere around about 200 hPa (Figure 2). It is in this region of large upper204
tropospheric conv that net convective detrainment and its associated cloudiness should205
be maximum. Indeed, the ensemble-mean cloud amounts also exhibit a peak at the same206
altitude as the conv peak (Figure 2). We interpret this peak in the cloud field as due to207
the abundance of high clouds detrained from deep convection near the top of the region208
of efficient radiative cooling. The same correspondence between conv and cloud fraction209
is verified in MODIS observations (Kubar et al. [2007]) and in a cloud resolving model210
(Kuang and Hartmann [2007]).211
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One may question why we do not diagnose the level of abundant high clouds based212
on where boundary layer parcels reach neutral buoyancy in the models. In order to do213
this, one would have to assume details about the entrainment profile during parcel ascent.214
Indeed, air parcels undergoing convective ascent will eventually detrain at their level of215
neutral buoyancy, and the level at which the majority of parcels reach neutral buoyancy216
must be consistent with the level at which conv peaks (Folkins and Martin [2005]). Using217
the clear-sky mass and energy budget, however, requires no a priori assumptions about218
how entrainment rates affect parcel buoyancy. It also does not require a priori assumptions219
about how entrainment rates will change or not change with a warming climate.220
In 3 we plot the fractional change in these quantities between the beginning and end of221
the 21st Century. Overlain in light lines are the average profiles for 2000-2010 and 2090-222
2100. Water vapor mixing ratios increase at all levels in step with the warming climate223
so as to retain nearly constant relative humidity through the 21st Century (Figure 3a).224
Associated with the warming planet is an increase in the QR. The level at which QR falls225
off rapidly in the upper troposphere rises over the course of the century because T and q226
increase at all pressure levels (Figure 3c).227
Static stability increases throughout most of the troposphere through the 21st century228
due to the nearly moist adiabatic temperature structure of the Tropics (Frierson [2006]),229
but this increase is confined below about 200 hPa (Figure 3d). Likewise, the warmer230
and more moist atmosphere emits more to space and so the QR also increases in time231
(Figure 3c). There are important differences in the vertical structures of their fractional232
changes. Whereas QR increases everywhere throughout the mid- and upper-troposphere,233
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the change in σ is positive at pressures greater than 200 hPa and negative at pressures234
less than 200 hPa.235
The amplification of warming aloft where water vapor concentrations are very low results236
in large fractional increases of q and thus very large fractional increases in QR between237
200 hPa and the tropopause, peaking at 100 hPa. This is essentially an upward shift in238
the QR profile as the climate warms, as expected from the FAT hypothesis.239
The fractional change in σ changes sign at about 200 hPa (Figure 3d). At pressures240
greater than 200 hPa, convection keeps the T profile close to the moist adiabat. Thus,241
the warming profile is accompanied by increases in σ. At pressures less than 200 hPa,242
radiative convective equilibrium is no longer the dominant balance, as QR becomes small243
and dynamically-forced ascent becomes more relevant. At these altitudes, the T profile is244
much more stable than the moist adiabat, but σ decreases in time because the moistening245
makes longwave cooling more efficient (a destabilizing effect).246
Where the fractional increase in σ exceeds that of QR (i.e., at pressures greater than247
about 250 hPa), the diabatic ω is reduced (Figure 3e). This reduction in clear-sky ω is248
consistent with several other studies that have pointed out the robust slow-down of the249
tropical circulation in a warmer climate (Knutson and Manabe [1995], Held and Soden250
[2006], Vecchi and Soden [2007], Gastineau et al. [2009]). Because the fractional increase251
in σ is larger than that of QR at these altitudes, less ω is required in the clear-sky252
atmosphere to balance the enhanced QR. In other words, a given descent rate achieves253
greater warming in the presence of enhanced σ.254
At pressures less than 200 hPa, the reduction in σ and increase in QR result in an255
enhancement in the diabatic ω, or an upward shift in the ω profile. The combination of256
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enhanced ω above due to enhanced QR and diminished ω below due to increased σ reduces257
the vertical gradient of diabatic ω in the warmer climate, and thus causes a reduction in258
the upper tropospheric conv (Figure 3f). In the end, the conv profile shifts upward along259
with the QR profile and becomes smaller in magnitude due to the competing changes in260
the QR and σ profiles.261
In summary, the warming climate is associated with two main changes to conv and262
implied convective detrainment. First, the location of peak conv shifts toward lower263
pressure. The upward shift of peak conv is consistent with upward shift in QR because264
the T is sufficiently “high” that there is appreciable QR from water vapor. As will be265
shown below, the upward shift is nearly isothermal, but the peak conv level warms slightly266
due to the significantly increased σ. Secondly, the upper tropospheric conv systematically267
decreases at all but the lowest pressures in association with the decrease in the tropical268
overturning circulation. Because the ω falls off to zero less dramatically with decreasing269
pressure in the warmer climate as explained above, the implied upper tropospheric conv270
also decreases. Clearly, both the reduction in total conv and the shift towards higher271
altitude of peak conv are mimicked in the cloud fractions.272
The quantities plotted in Figure 1 are plotted again in Figure 4, but now as a function273
of T . The three water vapor mixing ratio curves now lie on top of one another throughout274
most of the troposphere, indicating an essentially unchanged relative humidity as the275
climate warms (Figure 4a). Associated with this nearly unchanged relative humidity is276
a nearly unchanged QR profile, when plotted in T coordinates (Figure 4b). This clearly277
indicates the strong and fundamental dependence of QR on T through its exponential278
limit on the water vapor concentrations. Static stability, on the other hand, is a function279
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of pressure and the vertical gradient of T rather than its absolute value. Thus, as the280
climate warms and the T profile remains locked to the moist adiabat, the σ at a given281
T increases (Figure 4c). Furthermore, σ is inversely dependent on pressure (Equation 3),282
so at a fixed temperature it increases dramatically simply because the isotherms move283
towards lower pressure in the warming climate. For example, the tropical-mean 230 K284
isotherm moves from 245 hPa to 220 hPa over the century. Taken alone, this inverse285
pressure dependence causes a 50% increase in σ at 230 K.286
The shift towards higher σ at all T levels results in a systematic decrease in diabatic ω287
at all T levels as the climate warms (Figure 4d). Although the level of peak conv shifts288
upward in space, it does not do so in such a way as to remain at fixed temperature. Rather,289
the level gets slightly warmer due to the strong increase in σ generated by the models290
(Figure 5). Similarly, the level of abundant high clouds shifts towards slightly warmer291
temperatures rather than staying fixed in T as would be expected from FAT (Figure 5).292
The change in cloud T is consistent with that predicted from conv. The reason that293
conv and clouds in models do not exhibit a strict FAT response is because of the strong294
increase in σ relative to QR that is not explicitly accounted for in the FAT mechanism.295
It is important to note that the clouds warm only slightly, and certainly much less than296
the upper troposphere. This near-constancy of cloud T is largely the cause of the positive297
longwave cloud feedback, as will be shown below.298
Trenberth and Fasullo [2009] assert that the main warming in AR4 models comes from299
the increase in absorbed solar radiation due to decreases in tropical cloud cover. In300
the Tropics, the cloud fraction reduction is most evident in high clouds (their Figure301
3). Here we offer an explanation for the decrease in cloud cover, namely, the decrease302
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in upper tropospheric conv due to the competing effects of enhanced clear-sky QR and303
enhanced upper tropospheric σ. If the mechanism explained above is the cause for the304
decrease in high cloudiness, then one would expect models with greater upper tropospheric305
warming (i.e., those models with large negative lapse rate feedback) to also be models with306
larger decreases in tropical high clouds. Furthermore, if a portion of the shortwave cloud307
feedback is due to changes in tropical high cloud coverage, one would expect that portion308
of shortwave cloud feedback to be well correlated with the lapse rate feedback: the larger309
the upper tropospheric warming, the larger the reduction in high cloud amount, and the310
smaller in magnitude the (negative) shortwave cloud forcing. This would allow one to311
define a combined lapse-rate shortwave cloud feedback that would have less inter-model312
spread than the two taken separately, in a similar way to the combined lapse rate - water313
vapor feedback.314
In Figure 6 we show tropical mean conv and cloud fraction profiles as a function of T315
for the three decades 2000-2010, 2060-2070, and 2090-2100 for each of the 15 models used316
in this study. Here we assess the degree to which the models exhibit a correspondence317
between their high cloud fractions and the location of peak upper tropospheric conv. This318
is difficult because the model output available in the PCMDI archive is only the cloud319
fraction in the model vertical bins, with no information about optical depth or cloud top320
information similar to what a satellite sensor would retrieve in reality. It is also probable321
that each modeling center defines clouds differently from each other. Thus a lack of perfect322
correspondence between cloud fraction and upper tropospheric conv is not necessarily an323
indication that our diagnosis technique is flawed, nor is perfect correspondence a validation324
of our diagnosis technique.325
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Nonetheless, the models collective produce a peak in high cloud amount that is con-326
sistent with the level diagnosed from the clear-sky energy and mass balance. Notable327
exceptions are the miroc medres model, where a large peak in cloud amount appears at328
the tropopause, most likely very thin tropopause cirrus that is disconnected from deep329
convection, and the mri cgcm model, whose cloud fraction exhibits a very broad upper330
tropospheric peak that is rather different from its much sharper conv peak. In general,331
conv peaks are sharper and located at a slightly lower pressure than the cloud fraction332
peaks. It is reasonable that a plot of cloud tops would exhibit a peak that is both sharper333
and located at lower pressures than the peak shown here for cloud amount, so it is likely334
that a better correspondence exists between the level of abundant conv and the level of335
abundant high cloud tops.336
Additionally, it is clear that all models produce cloud and conv profiles that remain337
nearly fixed in temperature. The models generally exhibit a slight decrease in upper338
tropospheric conv and cloud amount, though it appears as though the signal is larger in339
the conv profile.340
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 =
∑p at tropp at T=270K f ∗ p∑p at trop
p at T=270K f(5)
and
pconv =
∑p at tropp at T=270K conv ∗ p∑p at trop
p at T=270K conv, (6)
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where f is the cloud fraction at each pressure. Scatterplots of decadal-mean tropical-mean341
pconv and phicld are shown for each model and for the ensemble mean in Figure 7. While the342
degree of correspondence between the location of abundant high cloud amount and upper343
tropospheric conv varies from model to model (Figure 6), the correspondence between the344
shift in pconv and the shift in upper tropospheric phicld as the climate warms is remarkably345
consistent from model to model, closely following a one-to-one relationship. In general,346
the decrease in phicld is slightly larger than the decrease in conv weighted pressure. In347
other words, the clouds migrate slightly more than conv does.348
High cloud weighted-temperature and upper tropospheric clear-sky diabatic convergence-
weighted temperature are calculated as
Thicld =
∑p at tropp at T=270K f ∗ T∑p at trop
p at T=270K f(7)
and
Tconv =
∑p at tropp at T=270K conv ∗ T∑p at trop
p at T=270K conv. (8)
Scatterplots of decadal-mean tropical-mean upper tropospheric Tconv and Thicld are shown349
for each model and for the ensemble mean in Figure 8. Each number in the plot represents350
its respective decadal mean.351
As in the previous figure, the dashed line has slope one but nonzero y-intercept. In352
T space, the shift in Tconv and Thicld is very small (on the order of a degree) indicating353
that both the high clouds and the upper tropospheric conv shift upward in altitude as354
the climate warms, but do so in such a way that they remain at approximately the same355
T . Because the conv profile migrates upward slightly less than the cloud profile, there is356
slightly greater warming of the Tconv than that of the Thicld. This is especially the case357
D R A F T January 5, 2010, 6:32pm D R A F T
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in the GFDL models, whose Thiclds remains remarkably constant in the face of relatively358
large increase of their Tconvs. Overall, the very slight shift towards warmer Thicld and Tconv359
is related to the increase in σ as the climate warms, as explained above. In summary,360
all models in the IPCC AR4 archive exhibit a clear shift in high cloud amount towards361
lower pressures that is remarkably well-explained by the upper tropospheric conv inferred362
from radiative cooling. The shift occurs nearly isothermally, as expected from the FAT363
hypothesis.364
Figure 9, which plots the ensemble mean Tconv, Thicld, and the T at 200 hPa as a function365
of surface T over the course of the 21st Century, nicely illustrates the main conclusions366
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), the368
Thicld and Tconv warm only about 1 K. Tropical high clouds much more closely follow the369
isotherms rather than the isobars, as expected from the FAT hypothesis. This represents370
a strong positive feedback because the clouds are not warming in step with the surface or371
atmosphere; in other words the planet cannot radiate away heat as easily as it could if the372
high clouds warmed along with the upper troposphere. In the following section we make373
a quantitative estimate of the contribution of this nearly-fixed Thicld to the total longwave374
cloud feedback.375
5. Estimating Model and Hypothetical Cloud Feedbacks
Though the tendency for clouds to shift upward as the climate warms has been noted in376
several previous studies (e.g., Wetherald and Manabe [1988], Mitchell and Ingram [1992],377
Senior and Mitchell [1993]), no study has explicitly shown to what extent this effect is378
giving rise to the positive longwave cloud feedback. Here we make an estimate of the379
D R A F T January 5, 2010, 6:32pm D R A F T
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contribution to longwave cloud feedback of the nearly constant Thicld. We first decompose380
the change in longwave cloud forcing into its components, then calculate longwave cloud381
feedback using the radiative kernel technique of Soden et al. [2008].382
The outgoing longwave 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 = ftotOLRcld + (1 − ftot)OLRclr (9)
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,
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 LWCF as
LWCF = OLRclr − OLR = ftot(OLRclr − OLRcld). (10)
The change in LWCF , which we calculate as the difference between the 2090-2100
mean and the 2000-2010 mean, can be written as
∆LWCF = ∆ftot(OLRclr − OLRcld) + ftot∆OLRclr − ftot∆OLRcld + C. (11)
The first term on the right hand side is the contribution from the change in cloud fraction383
assuming no change in clear minus cloudy OLR. This term is negative in the ensemble384
mean because cloud fraction decreases slightly. The second term is the change in clear385
sky OLR assuming no change in cloud fraction. In the ensemble mean, this term is386
generally positive in the extratropics and negative in the Tropics, as the atmosphere387
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becomes more opaque to longwave radiation. The third term is the change in cloudy388
sky OLR assuming no change in cloud fraction. In the ensemble mean this term is389
strongly positive throughout most of the tropical oceans and negative elsewhere. That390
this term is so strongly positive throughout much of the Tropics implies that the cloudy391
sky OLR decreases dramatically in many regions as the climate warms. However, upon392
close inspection of the regions that show large values of ∆OLRcld, it is clear that the393
large changes are caused not by clouds cooling or warming but simply by increases or394
decreases in the relative amount of high versus low clouds. Because of this, we perform395
a slightly different decomposition below. The fourth term, C, is a covariance term, equal396
to ∆ftot∆OLRclr − ∆ftot∆OLRcld. It is negative on average throughout the Tropics.397
To better assess the relative roles of high and low clouds in affecting ∆LWCF , we
decompose OLRcld into components due to high and low clouds in the Tropics:
ftotOLRcld = fhiOLRhi + floOLRlo, (12)
where
fhi + flo = ftot (13)
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 rea-
sonable estimate of the high cloud emission T and that the cloud is a blackbody such
that
OLRhi = σT 4
hicld. (14)
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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 − OLRlo
OLRhi − OLRlo
= ftot
OLRcld − OLRclr
OLRhi − OLRclr
. (15)
The decomposition of the change in longwave cloud forcing is now
∆LWCF = ∆fhi(OLRclr − OLRhi) − fhi∆OLRhi + fhi∆OLRclr + C. (16)
Thus the change in LWCF is due to the change in fhi assuming a constant difference398
between clear-sky OLR and high cloud OLR, the change in high cloud OLR and clear sky399
OLR assuming no change in fhi, and the covariance between changes in fhi, high cloud400
OLR, and clear sky OLR. ∆LWCF calculated here is exactly equal to that calculated401
directly.402
In Figure 10 we show the contribution of each of these components to the change403
in ensemble-mean LWCF . Note that the color scale varies among the panels to make404
the features more apparent. Henceforth, ensemble-mean refers to the average over the405
12 models that run the A2 scenario and that archived enough information to compute406
cloud feedbacks. (Three of the models used previously do not output enough clear-sky407
diagnostics to compute cloud feedbacks.) Large regional changes in fhi occur as the408
tropical circulation changes over the course of the century. Most notably, fhi increases409
along the equatorial Pacific and Indian Oceans are nearly compensated by fhi decreases410
in the subtropics and over tropical land masses (Figure 10a). Maps of both the mean411
and change in fhi are very similar to maps of the mean and change in precipitation412
(not shown), lending credence to our method of extracting the fhi using Equation 15.413
Overall, the redistribution of tropical high clouds tends to increase the LWCF in the414
D R A F T January 5, 2010, 6:32pm D R A F T
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Tropics (Figure 10a). Interestingly, the tropical-mean change in fhi is slightly negative415
(not shown), indicating an overall contraction of high cloudiness that is consistent with416
the decrease in upper tropospheric conv.417
In the Tropics, clear-sky OLR decreases between the beginning and end of the century418
as the atmosphere becomes more opaque (Figure 10b). This is especially true in convective419
regions that are moist in the free troposphere like over the Western Pacific warm pool,420
resulting in a largely negative fhi∆OLRclr term. Because high cloud temperatures do not421
stay perfectly constant with climate change as explained above, the −fhi∆OLRhi term422
is negative over most of the Tropics (Figure 10c). This is especially pronounced over the423
West Pacific warm pool and Indian Ocean. Taken together, the terms in panels (b) and424
(c) represent a decrease in the difference between clear and cloudy OLR as the cloud tops425
warm slightly and the clear-sky OLR decreases slightly; thus they contribute to a decrease426
in LWCF .427
Both covariance terms (Figure 10d and e) are very small (note the color scale range) and428
systematically negative throughout the Tropics. These are due to the concurrent increase429
in fhi in regions where both the high clouds are warming slightly and the clear-sky OLR430
is decreasing slightly.431
∆LWCF is negative throughout most of the Tropics, with two main regions of positive432
change, namely, the equatorial Pacific and off the east coast of Africa (Figure 10f). These433
two regions exhibit large increases in fhi that outweigh the other terms contributing to434
∆LWCF . Over the maritime continent, the increase in high cloud OLR and decrease435
in clear-sky OLR result in a decrease in LWCF . Over the tropical continents, the main436
cause of the decrease in LWCF is due to the decrease in fhi as the climate warms.437
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The change in LWCF is not equal to the longwave cloud feedback, though they are438
correlated (Soden et al. [2004], Soden and Held [2006]). Whereas ∆LWCF is equal to439
the change in clear- minus all-sky OLR, the longwave cloud feedback is the change in440
OLR due to clouds alone. If clouds fraction remained perfectly constant at all levels as441
the climate warmed, ∆LWCF would be negative because the clouds would be warming442
and emitting more and the clear-sky atmosphere would become more opaque, causing a443
reduction in the contrast between clear and cloudy OLR. However, the longwave cloud444
feedback would – by definition – be zero because the change in OLR due to changes in445
clouds alone would be zero. Similarly, if total cloud fraction remained unchanged but446
the cloud profile shifted upward such that it exactly compensated the change in clear-sky447
emission temperature, ∆LWCF would be zero. However, because the clouds rose to a448
higher altitude, the reduction in OLR due to clouds alone (the longwave cloud feedback)449
would be positive. Thus, ∆LWCF must be adjusted to calculate the longwave cloud450
feedback. We do so using the radiative kernel technique (Soden et al. [2008]), as described451
below.452
5.1. From ∆LWCF to LW Cloud Feedback: Applying the Radiative Kernels
Briefly, radiative kernels represent the net radiative response at top of atmosphere to453
small perturbations of given variables at each latitude, longitude, pressure, and time.454
They are matrices containing the partial derivative of net radiation at the top of the455
atmosphere with respect to T , humidity, or surface albedo perturbations. Feedback mag-456
nitude is calculated by convolving the kernel with the response of T , q, or albedo to a457
change in surface T . This technique is especially useful because one can calculate feed-458
backs using model output without having to run a radiative transfer model or perform459
D R A F T January 5, 2010, 6:32pm D R A F T
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several simulations, as in the partial radiative perturbation method. Because the radia-460
tive transfer calculation is already performed in the construction of the kernel, it also can461
be convolved with observational humidity or T changes to estimate feedbacks (Dessler462
et al. [2008]). The kernels are also useful in their own right for illustrating the regions463
of the atmosphere that are especially important for feedbacks (e.g., the tropical upper464
troposphere for water vapor feedback).465
There is no cloud radiative kernel because the linearity assumptions that are required466
for the technique are invalid for perturbations to cloud fields. However, one can estimate467
cloud feedback by adjusting the change in cloud forcing by the magnitude of cloud masking468
in the T , q, and albedo feedbacks. The cloud masking terms are calculated by differencing469
the clear-sky radiative responses and all-sky radiative responses (Eqn. 25 of Soden et al.470
[2008]).471
For each model we calculate the clear and all-sky feedbacks due to T , q, and surface472
albedo by convolving the appropriate radiative kernels with the change in T , q, and473
surface albedo between the first and last decade of the 21st century. The cloud masking474
is calculated by differencing the clear- and all-sky feedbacks and adding a term due to475
the cloud masking of the change in radiative forcing in the A2 scenario. If we assume476
the same proportionality of cloud masking occurs in the SRES A2 scenario as in the A1B477
scenario (Soden et al. [2008]) and sum the A2 radiative forcing terms given in Tables 6.14478
and 6.15 of the IPCC Third Assessment Report (Ramaswamy et al. [2001]), this term is479
1.03 W m−2.480
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5.2. Three Hypothetical LW Cloud Feedback Cases: FAT, FAP, and PHAT
Here we compare three hypothetical scenarios to the model ∆LWCF to illustrate the481
contribution of nearly-fixed high cloud temperatures to the longwave cloud feedback. We482
consider two cases that can be thought of as upper and lower bounds on ∆LWCF , the483
fixed anvil temperature (FAT) and the fixed anvil pressure (FAP) cases, respectively. We484
also consider an intermediate case, the proportionately higher anvil T (PHAT) case, in485
which the change in Thicld is set equal to the change in upper tropospheric Tconv. As will be486
shown, PHAT does the best job of matching the longwave cloud feedback in the models.487
Note that we use the term“anvil” very loosely to include all tropical high clouds, simply488
to maintain consistent terminology with Hartmann and Larson [2002].489
The change in LWCF assuming FAT is given by
∆LWCFFAT = ∆fhi(OLRclr − OLRhi) + fhi∆OLRclr + C, (17)
where the ∆OLRhi term in Equation 16 is neglected because Thicld is assumed fixed. The
change in LWCF assuming FAP is given by
∆LWCFFAP = ∆fhi(OLRclr − OLRhi) − fhi∆OLRFAPhi + fhi∆OLRclr + C, (18)
where ∆OLRFAPhi 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 LWCF assuming PHAT is given by
∆LWCFPHAT = ∆fhi(OLRclr − OLRhi) − fhi∆OLRPHAThi + fhi∆OLRclr + C, (19)
where ∆OLRPHAThi is the change in high cloud OLR assuming the change in Thicld is490
equal to the change in tropical-mean Tconv. As we have seen, the change in Tconv is491
small but generally positive, so it represents a small but important correction to the492
D R A F T January 5, 2010, 6:32pm D R A F T
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FAT assumption. For all three cases, we compute ∆LWCF , then apply the cloud mask493
corrections described above to calculate longwave cloud feedback.494
In Figure 11 we plot the LWCF estimated for each case, along with the difference495
between the model LWCF and that computed for each case. Note that the decomposition496
of ∆LWCF was only done for the Tropics, where it is easier to separate high and low497
clouds; thus the FAT, FAP, and PHAT assumptions only differ in the Tropics, due to the498
fhi∆OLRhi term. This is why a sharp discontinuity is clear at 30 ◦N and 30 ◦S, especially499
in the FAP feedback map.500
Unlike ∆LWCF maps, the longwave cloud feedback is positive throughout the Tropics,501
except in the FAP case where it is only positive over the equatorial Pacific and off the502
east coast of Africa where large increases in high clouds occur (Figure 11c). In the FAP503
feedback, the large increase in Thicld results in a large negative contribution due to the504
change in OLRhi. The FAP feedback is essentially that which would occur if the cloud505
profile did not shift upward as the climate warmed. Thus, the difference between the506
model feedback and the FAP feedback shown in Figure 11d gives the contribution of507
changing cloud height to the longwave cloud feedback. Equivalently, this difference is508
the contribution to longwave cloud feedback of the tendency for clouds not to warm as509
much as the upper troposphere. It is about 1 W m−2 K−1 in the tropical-mean. Without510
this nearly constant high cloud contribution, the tropical-mean longwave cloud feedback511
would be negative, as shown in the FAP case.512
The FAT feedback is slightly larger than the model feedback because tropical high513
clouds do not stay at a fixed T as the climate warms (Figures 11a and b). Thus, a slight514
overestimate of the feedback occurs in all regions that have climatologically abundant515
D R A F T January 5, 2010, 6:32pm D R A F T
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high clouds. In the tropical mean, the FAT assumption overestimates the model longwave516
cloud feedback by 0.28 W m−2 K−1.517
Allowing the tropical high clouds to warm slightly in proportion to the amount that the518
tropical-mean Tconv warms (i.e., the PHAT assumption) predicts a tropical-mean longwave519
cloud feedback that is only slightly greater than the model feedback by 0.04 W m−2520
K−1 (Figure 11f). Because we apply a spatially-invariant tropical-mean warming to the521
high clouds in the PHAT assumption, there are some regions where we underestimate522
the feedback (i.e., over the continents and in the subtropics) and some regions where523
we overestimate the feedback (i.e., over the west Pacific warm pool and Indian Ocean).524
Where we overestimate the feedback, the high clouds warm more than does the tropical-525
mean upper tropospheric Tconv. Nevertheless, the feedback calculated assuming PHAT526
agrees quite well with the model longwave cloud feedback, and properly accounts for the527
physics that govern the shift in the high cloud profile.528
In Figure 12, we show a bar plot of the model, FAT, FAP, and PHAT tropical-mean529
longwave cloud feedback for each model and for the ensemble mean. Clearly the feedback530
calculated assuming clouds remain at fixed pressure (the FAP feedback) greatly under-531
estimates the longwave cloud feedback in every model. As expected, it is nearly zero in532
all models, with the spread being caused by differences the other terms in the decompo-533
sition, most notably the change in fhi. For nearly every model, the difference between534
FAP and model feedback magnitude is near 1 W m−2 K−1. This is entirely due to the535
fact that clouds do not stay at fixed pressure as the climate warms, but rather rise nearly536
isothermally.537
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On the other hand, the feedback calculated assuming Thicld does not change (the FAT538
feedback) slightly overestimates the longwave cloud feedback in every model. The mag-539
nitude of overestimation varies from model to model depending on the degree to which540
the shift in cloud profile deviates from isothermal. FAT remains a considerably better541
approximation to the model cloud feedback than FAP.542
The feedback calculated assuming that Thicld increases in a manner proportional to543
the tropical-mean upper tropospheric Tconv (the PHAT feedback) very closely tracks the544
model longwave cloud feedback in all the models. Depending on the degree to which545
each model’s Tconv changes, the feedback calculated assuming PHAT can over- or under-546
estimate the model longwave cloud feedback. In the ensemble mean, it is a slight over-547
estimation, but is remarkably close to the model value. The PHAT feedback is always548
positive, as there is a large contribution from the fact that the clouds do not warm nearly549
as much as if they stayed at fixed pressure. PHAT is a slightly better predictor of the550
longwave cloud feedback magnitude than FAT because it accounts for the slight increase551
of Thicld. The PHAT assumption works better because it incorporates the change in σ that552
accompanies modeled climate change, which is ignored in the FAT hypothesis. Thus we553
have a physically consistent and robust predictor of each model’s longwave cloud feedback,554
and therefore high confidence that the systematically positive longwave cloud feedback555
produced by the models is indeed correct.556
6. Conclusions
We have shown that tropical high clouds in models shift upward as the climate warms557
over the 21st Century and that this upward shift is accompanied by a very modest increase558
in cloud top temperature. Because the clouds are not warming in step with the surface559
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temperature, the warming Tropics become less efficient at radiating away heat and thus560
the clouds are acting as a positive feedback on climate.561
The negligible temperature response of tropical high clouds to climate change can be562
understood through the principles of the fixed anvil temperature (FAT) hypothesis of563
Hartmann and Larson [2002]. The essential physics are simply that the troposphere can564
only be heated by convection where it is being cooled by radiation. Thus clouds are565
only abundant in altitude ranges where the temperatures are high enough for appreciable566
water vapor to radiatively cool to space. If the entire troposphere warms, the tropical-567
mean cloud tops will be located at a higher altitude that is now warm enough to support568
sufficient water vapor and QR.569
Separating the Tropics into convective and non-convective regions and assuming a mass-570
conserving circulation connecting them, the altitude of convective detrainment and abun-571
dant high cloud amount must be co-located with the altitude of upper tropospheric conv.572
One can calculate the conv profile in a relatively straightforward manner by computing573
the vertical gradient of the diabatic ω required to balance QR. Because of the rapid574
fall-off of QR with decreasing pressure and rapid increase of σ with decreasing pressure,575
diabatic ω decreases rapidly with decreasing pressure in the upper troposphere, creating576
a region of enhanced conv. We have shown good qualitative agreement between this level577
of enhanced upper tropospheric conv and the high cloud amount in each model. This578
method of diagnosing the level of high cloud amount is preferred over that which calcu-579
lates the level of neutral buoyancy for a rising boundary layer parcel because it requires580
no assumptions about parcel entrainment, which is poorly constrained.581
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As the climate warms over the course of the 21st Century, the pconv and phicld decrease582
in a nearly one-to-one fashion, and do so in such a way as to remain at approximately583
the same T . Because the vertical structure of changes to the QR profile differs from584
that of the σ profile, the diabatic ω decreases below and increases above the level of585
peak conv, causing a decrease in conv that is mimicked by slight decreases the upper586
tropospheric cloud fraction. Both the clouds and conv tend to warm slightly over the587
course of the century, and this is due to an increase in σ that prevents the clouds from588
rising isothermally.589
To assess the contribution of nearly constant cloud top temperatures to the longwave590
cloud feedback, we first decomposed the change in LWCF into components. This allowed591
us to create three cases, one in which the contribution due to changing high cloud OLR592
is zero (FAT), one in which the Thicld increases in proportion to the T at a fixed pressure593
level (FAP), and one in which the Thicld increases in proportion to the amount that the594
tropical-mean upper tropospheric Tconv increases (PHAT).595
Assuming that clouds do not rise as the climate warms (i.e., FAP) results in a near-zero596
tropical longwave cloud feedback in every model (by definition). The model longwave597
cloud feedback is about 1 W m−2 K−1 larger than that calculated assuming FAP, and this598
is entirely because the clouds rise in such a way as to warm only slightly. That calculated599
assuming FAT slightly overestimates the model longwave cloud feedback because the Thicld600
does increase slightly over the course of the century. That calculated assuming PHAT is601
very close to the model longwave cloud feedback in the models, and represents an improved602
estimate over FAT because it allows for the slight increase in Thicld due to the increase in σ.603
Thus, we show that the robust positive longwave cloud feedback can be well-explained by604
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the fundamental physics of FAT, with a slight modification (PHAT) to take into account605
the modeled σ changes. Tropical high clouds are fundamentally constrained to emit at606
approximately the same T as the climate warms, and we have shown here that this results607
in a longwave cloud feedback that is robustly positive in climate models.608
Acknowledgments. This research was supported by NASA Earth and Space Science609
Fellowship NNX06AF69H and NASA Grant NNX09AH73G. We acknowledge the interna-610
tional modeling groups for providing their data for analysis and the Program for Climate611
Model Diagnosis and Intercomparison (PCMDI) for collecting and archiving the model612
data. We thank Chris Bretherton and Rob Wood for useful discussion and suggestions613
for improvement, as well as Marc Michelsen for computer support.614
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D R A F T January 5, 2010, 6:32pm D R A F T
X - 36 ZELINKA AND HARTMANN: WHY IS LONGWAVE CLOUD FEEDBACK POSITIVE?
10−6
10−5
10−4
10−3
10−2
10−1
100
200
300
400
500
600
700
(a) Specific humidity (kg kg−1)
Pre
ssur
e (h
Pa)
−0.5 0 0.5 1 1.5 2
100
200
300
400
500
600
700
(b) Radiative Cooling (K day−1)
Pre
ssur
e (h
Pa)
0 0.1 0.2 0.3 0.4 0.5
100
200
300
400
500
600
700
(c) Static Stability (K hPa−1)
Pre
ssur
e (h
Pa)
−5 0 5 10 15 20 25 30 35
100
200
300
400
500
600
700
(d) Diabatic ω (hPa day−1)
Pre
ssur
e (h
Pa)
2000−20102060−20702090−2100
Figure 1. 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.
D R A F T January 5, 2010, 6:32pm D R A F T
ZELINKA AND HARTMANN: WHY IS LONGWAVE CLOUD FEEDBACK POSITIVE? X - 37
−0.05 0 0.05 0.1 0.15 0.2 0.25 0.3
100
200
300
400
500
600
700
Black: Diabatic convergence (day−1)
Pre
ssur
e (h
Pa)
2000−20102060−20702090−2100
0 5 10 15 20
100
200
300
400
500
600
700
Gray: Cloud amount (%)
Figure 2. 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.
D R A F T January 5, 2010, 6:32pm D R A F T
X - 38 ZELINKA AND HARTMANN: WHY IS LONGWAVE CLOUD FEEDBACK POSITIVE?
0 50 100 150
50
100
150
200
250
300
350
400
450
500
(a) Thick: Percentage Change
Pre
ssur
e (h
Pa)
10−6
10−4
10−2
50
100
150
200
250
300
350
400
450
500
Light: Specific Humidity (kg kg−1)
−1 0 1 2 3
50
100
150
200
250
300
350
400
450
500
(b) Thick: Percentage Change
Pre
ssur
e (h
Pa)
200 250 30050
100
150
200
250
300
350
400
450
500
Light: Temperature (K)
−100 0 100 200
50
100
150
200
250
300
350
400
450
500
(c) Thick: Percentage Change
Pre
ssur
e (h
Pa)
−0.5 0 0.5 1 1.5 250
100
150
200
250
300
350
400
450
500
Light: Radiative Cooling (K dy−1)
−20 0 20 40
50
100
150
200
250
300
350
400
450
500
(d) Thick: Percentage Change
Pre
ssur
e (h
Pa)
0 0.1 0.2 0.3 0.450
100
150
200
250
300
350
400
450
500
Light: Static Stability (K hPa−1)
−100 0 100 200
50
100
150
200
250
300
350
400
450
500
(e) Thick: Percentage Change
Pre
ssur
e (h
Pa)
0 10 20 3050
100
150
200
250
300
350
400
450
500
Light: Diabatic ω (hPa dy−1)
−200 −100 0 100 200
50
100
150
200
250
300
350
400
450
500
(f) Thick: Percentage Change
Pre
ssur
e (h
Pa)
0 0.1 0.2 0.350
100
150
200
250
300
350
400
450
500
Light: Diabatic Convergence (dy−1)
Figure 3. Tropical-mean ensemble-mean change in specific humidity (a), temperature (b),
radiative cooling (c), static stability (d), diabatic subsidence (e), and clear-sky diabatic conver-
gence (f) calculated as a percentage 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 sce-
nario. Note that the mean specific humidity is plotted on a logarithmic scale and that the x-axis
limits on percentage changes vary from panel to panel.
D R A F T January 5, 2010, 6:32pm D R A F T
ZELINKA AND HARTMANN: WHY IS LONGWAVE CLOUD FEEDBACK POSITIVE? X - 39
10−6
10−5
10−4
10−3
10−2
10−1
190
200
210
220
230
240
250
260
270
280
(a) Specific humidity (kg kg−1)
Tem
pera
ture
(K
)
−0.5 0 0.5 1 1.5 2
190
200
210
220
230
240
250
260
270
280
(b) Radiative Cooling (K day−1)
Tem
pera
ture
(K
)
0 0.1 0.2 0.3 0.4 0.5
190
200
210
220
230
240
250
260
270
280
(c) Static Stability (K hPa−1)
Tem
pera
ture
(K
)
−5 0 5 10 15 20 25 30 35
190
200
210
220
230
240
250
260
270
280
(d) Diabatic ω (hPa day−1)
Tem
pera
ture
(K
)
2000−20102060−20702090−2100
Figure 4. 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 January 5, 2010, 6:32pm D R A F T
X - 40 ZELINKA AND HARTMANN: WHY IS LONGWAVE CLOUD FEEDBACK POSITIVE?
−0.05 0 0.05 0.1 0.15 0.2 0.25 0.3
190
200
210
220
230
240
250
260
270
280
Solid: Diabatic convergence (day−1)
Tem
pera
ture
(K
)
2000−20102060−20702090−2100
0 5 10 15 20190
200
210
220
230
240
250
260
270
280
Dashed: Cloud amount (%)
Figure 5. 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 January 5, 2010, 6:32pm D R A F T
ZELINKA AND HARTMANN: WHY IS LONGWAVE CLOUD FEEDBACK POSITIVE? X - 41
0 0.1 0.2
200
220
240
260
Tem
pera
ture
(K
)
0 10 20 30
200
220
240
260
mpi_echam5
0 0.1 0.2
0 10 20 30miroc3_2_medres
0 0.1 0.2
0 10 20 30ukmo_hadcm3
0 0.1 0.2
0 10 20 30ipsl_cm4
0 0.1 0.2
0 10 20 30gfdl_cm2_1
0 0.1 0.2
200
220
240
260
Tem
pera
ture
(K
)
0 10 20 30
200
220
240
260
gfdl_cm2_0
0 0.1 0.2
0 10 20 30giss_model_e_r
0 0.1 0.2
0 10 20 30inmcm3_0
0 0.1 0.2
0 10 20 30cccma_cgcm3_1
0 0.1 0.2
0 10 20 30mri_cgcm2_3_2a
0 0.1 0.2
200
220
240
260
Tem
pera
ture
(K
)
0 10 20 30
200
220
240
260
ncar_pcm1
0 0.1 0.2
0 10 20 30ncar_ccsm3_0
0 0.1 0.2
0 10 20 30bccr_bcm2_0
0 0.1 0.2
0 10 20 30csiro_mk3_5
0 0.1 0.2
0 10 20 30ingv_echam4
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.
D R A F T January 5, 2010, 6:32pm D R A F T
X - 42 ZELINKA AND HARTMANN: WHY IS LONGWAVE CLOUD FEEDBACK POSITIVE?
180190200210
200
210
220
230
mpi_echam5
123
456
78
910
180190200210
140
150
160
170
miroc3_2_medres
1 23456
78
910
180190200210
220
230
240
250
ukmo_hadcm3
12
3456
78
910
160170180190
170
180
190
200
ipsl_cm4
12345
67
89
10
200210220230
250
260
270
280
gfdl_cm2_1
1
234
567
8910
200210220230
220
230
240
250
gfdl_cm2_0
1 234
567
89
10
170180190200
220
230
240
250
giss_model_e_r
1234 56 7
89
10
200210220230
240
250
260
270
inmcm3_0
123456
78
9 10
180190200210
250
260
270
280
cccma_cgcm3_1
12
345
67
89
10
180190200210
270
280
290
300
mri_cgcm2_3_2a
12345 6
789
10
170180190200
200
210
220
230
ncar_pcm1
123456
78
910
170180190200
210
220
230
240
ncar_ccsm3_0
123
45 6
78
910
200210220230
280
290
300
310
bccr_bcm2_0
123
4567
89
10
180190200210
190
200
210
220
csiro_mk3_5
1234 5
67
89
10
170180190200
170
180
190
200
ingv_echam4
12345
67 8
9 10
180190200210
220
230
240
250
Ensemble Mean
1234
567
89
10
Upper Tropospheric Convergence−Weighted Pressure (hPa)
Hig
h C
loud
−W
eigh
ted
Pre
ssur
e (h
Pa)
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.
D R A F T January 5, 2010, 6:32pm D R A F T
ZELINKA AND HARTMANN: WHY IS LONGWAVE CLOUD FEEDBACK POSITIVE? X - 43
216218220
222
223
224
225
226
mpi_echam5
215216217218219
207
208
209
210
211
miroc3_2_medres
218220222
227
228
229
230
231
ukmo_hadcm3
215216217218219
217
218
219
220
221
ipsl_cm4
220222224
231
232
233
234
235
gfdl_cm2_1
220222224
225
226
227
228
229
gfdl_cm2_0
216218220
229
230
231
232
233
giss_model_e_r
220222224
230
231
232
233
234
inmcm3_0
217218219220221
233
234
235
236
237
cccma_cgcm3_1
214216218
234
235
236
237
238
mri_cgcm2_3_2a
213214215216217
221
222
223
224
225
ncar_pcm1
216218220
225
226
227
228
229
ncar_ccsm3_0
216218220
234
235
236
237
238
bccr_bcm2_0
224226228
225
226
227
228
229
csiro_mk3_5
217218219220221
218
219
220
221
222
ingv_echam4
217218219220221
225
226
227
228
229
Ensemble Mean
Upper Tropospheric Convergence−Weighted Temperature (T)
Hig
h C
loud
−W
eigh
ted
Tem
pera
ture
(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 January 5, 2010, 6:32pm D R A F T
X - 44 ZELINKA AND HARTMANN: WHY IS LONGWAVE CLOUD FEEDBACK POSITIVE?
298.5 299 299.5 300 300.5 301 301.5219
220
221
222
223
224
225
226
227
228
229
T200 hPa
Tconv
+ 5K
Thicld
Surface Temperature (K)
Tem
pera
ture
(K
)
Figure 9. 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 tem-
perature for the 21st Century. Ensemble-mean refers to the average over the 15 models that run
the A2 scenario.
D R A F T January 5, 2010, 6:32pm D R A F T
ZELINKA AND HARTMANN: WHY IS LONGWAVE CLOUD FEEDBACK POSITIVE? X - 45
(a) ∆fhi
(OLRclr
−OLRhi
)
Tropical Mean = 0.05 W m−2
−10
−5
0
5
10
(b) fhi
∆OLRclr
Tropical Mean = −0.29 W m−2
−5
0
5
(c) −fhi
∆OLRhi
Tropical Mean = −0.46 W m−2
−10
−5
0
5
10
(d) ∆fhi
∆OLRclr
Tropical Mean = −0.13 W m−2
−5
0
5
(e) −∆fhi
∆OLRhi
Tropical Mean = −0.31 W m−2
−5
0
5(f) Sum of Terms
Global Mean = −0.84; Tropical Mean = −1.14 W m−2
−10
−5
0
5
10
Ensemble Mean∆LWCF Terms
Figure 10. Terms contributing to the change in ensemble-mean LWCF : ∆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 January 5, 2010, 6:32pm D R A F T
X - 46 ZELINKA AND HARTMANN: WHY IS LONGWAVE CLOUD FEEDBACK POSITIVE?
(a) FAT
Global Mean = 0.64; Tropical Mean = 0.91 W m−2 K−1
−5
0
5
(c) FAP
Global Mean = 0.01; Tropical Mean = −0.36 W m−2 K−1
−5
0
5
(e) PHAT
Global Mean = 0.52; Tropical Mean = 0.67 W m−2 K−1
−5
0
5
(b) FAT minus Model
Tropical Mean = 0.28 W m−2 K−1
−2.5
−2
−1.5
−1
−0.5
0
0.5
1
1.5
2
2.5
(d) FAP minus Model
Tropical Mean = −0.99 W m−2 K−1
−2.5
−2
−1.5
−1
−0.5
0
0.5
1
1.5
2
2.5
(f) PHAT minus Model
Tropical Mean = 0.04 W m−2 K−1
−2.5
−2
−1.5
−1
−0.5
0
0.5
1
1.5
2
2.5
Ensemble MeanLW Cloud Feedback
Figure 11. Ensemble-mean longwave cloud feedback for three cases, FAT, FAP, and PHAT
(left column) as well as the difference between the model 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 January 5, 2010, 6:32pm D R A F T
ZELINKA AND HARTMANN: WHY IS LONGWAVE CLOUD FEEDBACK POSITIVE? X - 47
Figure 12. Estimates of tropical-mean longwave cloud feedback for the three cases FAP, FAT,
and PHAT, as well as the model longwave cloud feedback for each model and for the ensemble
mean.
D R A F T January 5, 2010, 6:32pm D R A F T