why is longwave cloud feedback positive?dennis/zelinka_hartmann...57 longwave cloud feedbacks. we...

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])

D R A F T January 5, 2010, 6:32pm D R A F T

X - 2 ZELINKA AND HARTMANN: WHY IS LONGWAVE CLOUD FEEDBACK POSITIVE?

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


ZELINKA AND HARTMANN: WHY IS LONGWAVE CLOUD FEEDBACK POSITIVE? X - 3

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



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



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



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



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



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



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



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



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



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



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



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



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



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



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)



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



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



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



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)



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



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



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



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



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



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



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



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



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



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



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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10−6

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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

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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.



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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.



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.



−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.



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.



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.



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.



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.



(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


−10

−5

0

5

10

(d) ∆fhi

∆OLRclr


−5

0

5

(e) −∆fhi

∆OLRhi


−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.



(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.



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.


why is longwave cloud feedback positive?dennis/zelinka_hartmann...57 longwave cloud feedbacks. we...

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