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Coupled high-latitude climate feedbacks and their impact on atmospheric
heat transport
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Nicole Feldl⇤
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Department of Earth and Planetary Sciences, University of California, Santa Cruz, California
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Simona Bordoni
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Environmental Science and Engineering, California Institute of Technology, Pasadena, California
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Timothy M. Merlis
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Department of Atmospheric and Oceanic Sciences, McGill University, Montreal, Quebec,
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Canada
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⇤ Corresponding
author address: University of California, Santa Cruz, 1156 High Street, Earth and
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Planetary Sciences, Santa Cruz, CA 95064
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E-mail: [email protected]
Generated using v4.3.2 of the AMS LATEX template
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ABSTRACT
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The response of atmospheric heat transport to anthropogenic warming is de-
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termined by the anomalous meridional energy gradient. Feedback analysis
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offers a characterization of that gradient and hence reveals how uncertainty
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in physical processes translates into uncertainty in the circulation response.
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However, individual feedbacks do not act in isolation. Anomalies associated
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with one feedback may be compensated by another, as is the case for the pos-
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itive water vapor and negative lapse rate feedbacks in the tropics. Here we
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perform a set of idealized experiments in an aquaplanet model to evaluate the
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coupling between the surface albedo feedback and other feedbacks, including
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the impact on atmospheric heat transport. In the tropics, the dynamical re-
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sponse manifests as changes in the intensity and structure of the overturning
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Hadley circulation. Only half of the range of Hadley cell weakening exhibited
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in these experiments is found to be attributable to systematic variations in the
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surface albedo feedback. Changes in extratropical clouds that accompany the
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albedo changes explain the remaining spread. This finding has implications
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for the efficacy with which the climate system, including tropical circulation
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and the hydrological cycle, adjusts to high latitude feedbacks, over climate
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states that range from perennial or seasonal ice to ice-free conditions in the
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Arctic.
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1. Introduction
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Climate feedbacks have long been recognized as a key piece to understanding the Earth’s cli-
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mate sensitivity. Climate sensitivity is the amount of global-mean surface temperature change
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for a given external forcing, typically defined as a doubling of CO2 . On time scales relevant
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to anthropogenic warming, feedbacks include atmospheric processes, such as changes in clouds,
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water vapor, atmospheric lapse rate, and sea ice, which in turn either amplify or damp the cli-
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mate response to a forcing (Charney et al. 1979; Hansen et al. 1984; Schlesinger 1985). While
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conventionally defined relative to the globally averaged case, these processes exhibit rich spatial
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structures and are arguably activated by regional rather than global-mean warming (Armour et al.
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2012). An emerging emphasis in the field of climate dynamics is to understand how the spatial
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pattern of climate feedbacks controls the spatial pattern of climate change.
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In addition to amplifying or damping the climate response, climate feedbacks exhibit two ad-
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ditional characteristic behaviors: nonlinearities and remote impacts. Firstly, from a Taylor series
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perspective, nonlinearities may be understood as higher-order terms in the energy balance (Colman
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et al. 1997; Roe 2009). For instance, both longwave radiative fluxes (Stefan-Boltzmann law) and
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atmospheric moisture content (Clausius-Clapeyron relation) are nonlinear functions of tempera-
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ture. However, nonlinearities may also enter as interactions among feedbacks, which introduces
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bias in the first-order linear approximation. Secondly, remote impacts are a consequence of pos-
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itive feedbacks amplifying the local energy balance (or negative feedbacks damping it), which
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the atmosphere then accommodates by diverging and converging energy flux meridionally (Feldl
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and Roe 2013b; Roe et al. 2015; Zelinka and Hartmann 2012). Hence it is probable that regional
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interactions between feedbacks affect remote climate responses in a nonlinear manner.
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Perturbations to the energy balance, caused directly and indirectly by enhanced greenhouse gas
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concentrations, affect the meridional energy flux and may manifest as changes in the strength or
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position of the tropical Hadley circulation or the large-scale extratropical eddies. In a previous
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study, we characterized the response of the tropical atmospheric circulation in CMIP5 in terms
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of climate feedbacks, radiative forcing, ocean heat uptake, atmospheric eddies, and gross moist
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stability (Feldl and Bordoni 2016). For the most part these effects are large and competing. At
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the level of individual feedbacks, it becomes difficult to grasp intuitively how any single feedback
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affects the circulation response given their interactive nature. For example, compensation between
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lapse rate and water vapor feedbacks is well known (Bony et al. 2006; Cess 1975). Assuming
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the feedbacks act in isolation, we can quantify the contribution of the temperature feedback as a
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5-10%/K weakening of the Hadley cell and of the lapse rate feedback as a 5-10%/K strengthening.
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But does that level of specificity matter when the net result is no change at all?
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Naturally, such results are still useful for understanding uncertainty amongst climate change
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projections, and moreover any particular coupled model is not required to cancel so neatly. Herein
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we present a series of idealized modeling experiments designed to reveal the coupling between
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regional climate feedbacks at a mechanistic level. This is conceptually similar to a perturbed
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physics ensemble (e.g., Sanderson et al. 2008). In contrast to studies such as Kang et al. (2009),
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which forces the high latitudes by applying an ocean heat source and sink, or Graversen and Wang
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(2009), which suppresses the surface albedo feedback, we modify the sensitivity of sea ice to
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warming. Specifically, we manipulate the strength of the surface albedo feedback in order to (1)
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identify compensating behavior in other feedbacks and (2) assess the efficacy of the net impact on
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the remote climate response.
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2. Methods
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We employ the Geophysical Fluid Dynamics Laboratory Atmospheric Model (GFDL AM2.1;
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Delworth et al. 2006) in its aquaplanet configuration with daily mean solar zenith angle. Sea-
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sonally varying insolation corresponds to modern day parameters in the control runs, except for
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eccentricity, which is set to zero. The model is coupled to a slab ocean of fixed depth (30m) with no
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oceanic heat transport. Sea-ice formation is enabled by introducing an ocean albedo dependence
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on surface temperature; the surface albedo is increased where surface temperatures are less than
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270 K. Elsewhere, ocean albedo remains a function of zenith angle (Taylor et al. 1996). Control
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CO2 concentration is 330 ppm. The surface albedo a is systematically varied (0.3, 0.4, 0.45, 0.5)
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in each CO2 quadrupling experiment to manipulate the strength of the surface albedo feedback.
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The eight simulations are integrated for 40 years, with the exception of IcyAqua05 (i.e., a = 0.5),
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which is run for 45 years (including 15 years of spin up), to serve as a run from which the others
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are branched. Monthly climatologies are computed from 30-year periods.
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Feedbacks are calculated using the radiative kernel technique (Shell et al. 2008; Soden and Held
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2006; Soden et al. 2008). Individual feedback parameters are the product of the radiative kernel
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for the relevant climate variable, Ki = ∂ R/∂ xi , and the climate change anomaly, Dxi , normalized
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by the local (i.e., zonal-mean seasonal-mean) surface air temperature response DTs to give units of
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Wm
2
K 1:
li =
∂ R Dxi
∂ xi DTs
(1)
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where R is the net radiative flux at the top of the atmosphere. Note that the conventional approach
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for global feedbacks is to instead normalize by the global-mean surface warming, however, the
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regional feedbacks offer a number of advantages where spatial patterns of warming are of interest
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(Armour et al. 2012; Feldl and Roe 2013a). We consider the Planck, lapse rate, surface albedo,
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water vapor, and cloud feedbacks. The Planck feedback is associated with a vertically uniform
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warming of the surface and troposphere (x = Ts ), the lapse rate feedback with tropospheric warm-
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ing that deviates from the vertically uniform profile (x = T 0 ), and the surface albedo feedback with
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changes in surface albedo (x = a). For the water vapor feedback, the specific humidity anomaly
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(x = ln(q)) is given relative to the standard anomaly for a 1 K warming assuming no change in
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relative humidity. Finally, we compute the cloud feedback from the change in cloud radiative ef-
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fect, DCRE, with corrections for cloud masking of non-cloud feedbacks, following Soden et al.
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(2008). Radiative kernels are those of Soden and Held (2006) for the GFDL model, but zon-
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ally averaged, the northern hemisphere mirrored in the south, and with a six-month lag to create
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pseudo-seasonal-cycle-aquaplanet kernels.
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The sum of the energy adjustments due to individual feedbacks, along with the radiative forcing
of CO2 , R f , characterizes the anomalous atmospheric energy balance,
DR = Â li DTs + R f + O(DTs2 )
(2)
i
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Higher-order terms account for the nonlinearity, which is estimated as a residual. In an aqua-
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planet without ocean dynamics and for equilibrium climate states, anomalous surface fluxes are
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negligible. To maintain balance, latitudes of amplified atmospheric energy anomalously diverge
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atmospheric heat flux, and those of damped energy converge atmospheric heat flux (hereafter heat
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indicates moist static energy). Thus we can write the northward energy flux as the zonal and
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meridional integral of feedbacks and forcing, and further split the total atmospheric flux into con-
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tributions due to stationary and transient eddies, DFe , and the mean meridional circulation, DFHC ,
DFHC = DFe +
Z f Z 2p
p
2
0
(Â li DTs 0 + R f 0 ) a2 cos f dl df .
(3)
i
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Primes (0 ) denote deviations from the global mean; a uniform feedback or forcing does not alter
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tropical transports.
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The tropical mass flux ymax and energy flux can further be related via the gross moist stability,
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H = FHC /ymax , i.e., the effective energy stratification of the tropics. Combining Equation 3 with
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gross moist stability and assuming small perturbations, we arrive at the following expression for
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the fractional change in mass flux by the Hadley cell:
Dymax
=
ymax
RR
RR
Âi (li DTs )0 +
FHC
Rf 0
DFe
DH
.
H
(4)
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Integrals are as in Equation 3. For a lengthier derivation, see Feldl and Bordoni (2016). Changes in
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Hadley cell strength are thus quantified in terms of contributions from feedbacks, radiative forcing,
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atmospheric eddies, and gross moist stability. Since we focus on fractional changes, the response
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at latitudes of zero energy flux by the Hadley circulation (i.e. the cell edges) is ill-defined. Instead,
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this analysis best captures the region of the streamfunction extrema. In the following section,
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we perform a detailed evaluation of changes in circulation strength for each albedo experiment,
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following Equation 4.
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3. Results
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a. Climate feedbacks and atmospheric heat transport
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The four experiments, in which the albedo magnitude is specified but areal extent freely interac-
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tive, exhibit a wide range of polar amplification under 4⇥CO2 (Figure 1a). High-latitude surface
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temperature change is 5 K in the low-albedo experiment (IcyAqua03) and up to 24 K in the high-
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albedo experiment (IcyAqua05). All of the simulations reside in the same ice-free equilibrium
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climate state at 4⇥CO2 , and hence differences in surface warming reflect differences in the initial
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mean state. In particular, the high-albedo experiment starts from the coldest climatology, with
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year-round sea-ice cover to nearly 50 degrees latitude, and must warm substantially to reach the
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same end point as the low-albedo experiment, which only ever forms seasonal (not perennial) sea
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ice.
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The different climate responses are reflected in the different climate feedbacks among the ex-
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periments (Figure 1b). In the tropics, the net feedbacks are more similar, though small differences
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in positive subtropical feedbacks may have a substantial effect on divergence of atmospheric heat
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flux. However, striking differences in the feedbacks occur at high latitudes: the net feedback is
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weakly negative (i.e., stabilizing) in the high-albedo experiment and strongly negative in the low-
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albedo experiment. Naively, one might expect this difference to equal the magnitude of the surface
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albedo feedback, since it is the surface albedo that was perturbed as the experimental design.
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Figure 2 shows the annual-mean zonal-mean feedback parameters. The surface albedo feedback
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varies in magnitude and location, with the high-albedo experiment extending the farthest equator-
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ward (a signature of extensive sea ice retreat) and the low-albedo feedback being both weak and of
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limited areal extent. The feedback magnitude ranges from 0-1.5 Wm 2 K 1 , consistent with cou-
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pled models despite its idealized nature (Feldl and Bordoni 2016). Already, we see this difference
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is not large enough to account for the spread in the net feedback in Figure 1b. The Planck feedback
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is the same in all experiments, because DTs /DTs is unity so this is simply the temperature kernel.
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The lapse rate feedback is positive in the high-albedo experiments and negative in the low-albedo
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experiments, which we discuss in more detail later in the section. The well-known compensation
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between water vapor and lapse rate feedbacks (Soden and Held 2006) leads to only small variabil-
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ity in the combined temperature and water vapor feedback. This combined feedback is neutral for
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the low-albedo experiment at high latitudes (not shown).
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The cloud feedback is the only remaining feedback capable of contributing to the differences in
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net feedbacks. Unlike the case for temperature and water vapor feedbacks, the combined effect
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of surface albedo and cloud feedbacks increases rather than decreases the spread among the net
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feedback (a positive covariance). This is evident in the high-albedo experiment having the most
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positive surface albedo and net cloud feedback, whereas the low-albedo experiment has the most
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negative of both feedbacks. At high latitudes, the SW cloud feedback is negative and the LW cloud
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feedback is positive (not shown), resulting from complex interactions among clouds of different
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thicknesses, heights, and optical properties (Ceppi et al. 2015; Zelinka et al. 2012).
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Figure 3 shows the anomalous northward atmospheric energy fluxes implied by the spatial pat-
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terns of feedbacks, radiative forcing, and atmospheric eddies, following Equation 3. The fluxes
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are scaled by global-mean surface temperature change. Positive high latitude feedbacks pro-
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duce anomalous energy divergence and an equatorward flux (lapse rate, surface albedo feedback)
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whereas positive tropical and/or negative high latitude feedbacks (water vapor, net cloud feed-
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backs) produce a poleward energy flux. Feldl and Bordoni (2016) show the same result for CMIP5.
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As anticipated based on the structure of the feedbacks (Fig. 2), the surface albedo feedback and
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the cloud feedback promote opposing tendencies in atmospheric heat flux, however, they do so in
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a way that adds to rather than subtracts from the spread among feedbacks. At 45 N, for instance,
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the spreads in the northward fluxes implied by the surface albedo and net cloud feedbacks are
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comparable, 0.07 PW K
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by temperature and water vapor feedbacks to 0.1 PW K 1 .
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and 0.06 PW K
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respectively. That combined spread is then reduced
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The bottom panel of the figure shows the role of transient atmospheric eddies (stationary eddies
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are nonexistent in the zonally symmetric aquaplanet) and radiative forcing. The anomalous flux
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by eddies is poleward in all experiments in the tropics, but the extratropics show equatorward flux
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in the high-albedo simulations, consistent with anomalous divergence from the sea-ice margin.
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In not prescribing ocean heat flux divergence, the atmosphere bears the full brunt of transporting
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heat meridionally. We anticipate the eddy heat flux to be an overestimate compared to coupled
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atmosphere-ocean models. Finally, our choice of radiative forcing estimate contributes anomalous
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divergence from the tropics and poleward heat flux, consistent with Huang and Zhang (2014),
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which we discuss in more detail in Section 4.
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In order to evaluate the impact of the coupled climate feedbacks on the strength of the mean
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meridional atmospheric circulation, it is first helpful to understand the climatological mass and
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energy fluxes in the aquaplanet simulations. Figure 4a shows the mass flux by the Hadley circu-
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lation, ymax , in the 1⇥CO2 (solid lines) and 4⇥CO2 (dashed lines) climates. The peak mass flux
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occurs in the subtropics, and the poleward edges of the Hadley cells are indicated by the latitudes
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of zero mass flux (near 30 degrees). The high-albedo experiment has the strongest mean tropi-
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cal circulation, and also weakens the most. The Hadley cell does expand under increased CO2 ,
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consistent with theory and modeling (Held and Hou 1980; Korty and Schneider 2008; Levine and
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Schneider 2015; Lu et al. 2007), however, the widening is the same in all four experiments (2 de-
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grees). Hence the experimental setup induces variability in strength but not position of the Hadley
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cell. The Intertropical Convergence Zone (ITCZ) remains at the equator in the annual-mean, on
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account of the hemispherically symmetric model configuration. The northward energy flux by the
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mean meridional circulation, FHC , is shown in solid lines in the lower panel.
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A characteristic feature of the aquaplanet model is that, without the zonal asymmetries asso-
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ciated with continents, stationary eddies do not form and cannot transport momentum, heat, or
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moisture. In the absence of stationary eddies, transient eddy energy flux (dotted lines in Fig. 4b)
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is calculated as the difference between the total atmospheric energy flux and the energy flux by the
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mean meridional circulation.
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Following Equation 4, the fractional changes in circulation strength are calculated as the ratio of
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anomalous fluxes in Figure 3 to the climatological energy flux in Figure 4b (solid lines). Results
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are averaged over the subtropical latitudes where the Hadley cell, and its changes, maximizes.
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Figure 5a shows the circulation changes associated with feedbacks, radiative forcing, gross moist
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stability, and atmospheric transient eddies. Total decreases (leftmost column) range from 1.1-1.9%
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K 1 , with the high-albedo experiment exhibiting the largest changes in Hadley cell strength. The
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greatest contributors to the circulation changes are feedbacks (strengthening tendency) and eddies
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(strong weakening tendency). The other contributions are small and positive in most experiments.
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The increase in eddy heat flux in the tropics (Fig. 3) is a consistent response to a positive net
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feedback in the tropics. In previous work, the main compensation occurred instead between at-
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mospheric eddies and ocean heat uptake (Feldl and Bordoni 2016). Here, in the absence of ocean
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dynamics, that relationship is precluded.
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Evaluating the response of the tropical circulation demonstrates the remote impact of coupled
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climate feedbacks. Given our four experiments are differentiated only by their sea ice albedo
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formulation, a null hypothesis would have been that the experiments differ only in their surface
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albedo feedbacks and consequently that the 2.9% K
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net feedback may be accounted for by the spread in circulation change due to the surface albedo
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feedback alone. However, in Figure 5b we see that is not at all the case. The combined temperature
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and water vapor feedback collapses to a strengthening tendency with minimal contribution to the
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spread. The surface albedo feedback is a weakening tendency on the tropical circulation, consistent
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with the equatorward anomalous energy flux evidenced in Figure 3. Notably, the spread in the
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surface albedo feedback contribution is only 1.4% K
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of circulation response. The remaining half is made up by the cloud feedback, a strengthening
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tendency of 1.2-3.6% K 1 . In other words, the spread–or uncertainty–in surface albedo produces
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changes in polar clouds that are additive with respect to the uncertainty in the tropical circulation
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response.
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Nonlinear processes account for 3 Wm
2
1
1
spread in circulation change due to the
and insufficient to explain the total range
of the global energy balance in the high-albedo exper-
iment. As a result, the effective climate sensitivity from the sum of the feedbacks underestimates
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actual global-mean surface warming by 3 degrees (9.4 compared to 12.4 K). Largest nonlinearities
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are found in the IcyAqua05 experiment. Since this experiment is most comparable to the climate
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used to generate the radiative kernels, it is unlikely that the nonlinearity stems from a kernel-
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simulation mismatch. Rather, we attribute the nonlinear term to interactions between feedbacks,
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discussed in more detail below, as well as to processes that are nonlinear functions of surface tem-
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perature. The nonlinearity is zero in IcyAqua03, which in addition to not having an appreciable
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surface albedo feedback also exhibits the least warming.
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b. Polar clouds and sea ice albedo
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A documented relationship exists between clouds and sea ice, but the mechanisms involved
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remain ambiguous. In an intermodel comparison, Huybers (2010) reports a negative covariance
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between surface albedo and cloud feedback, though the cloud feedback is estimated as a residual
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and may be biased. Mauritsen et al. (2013) similarly find that cloud and water vapor changes
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dampen the effect of the surface albedo feedback. One interpretation of these previous studies is
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that increased cloud fraction masks surface albedo changes, such that the positive surface albedo
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feedback is weakened relative to clear-sky conditions. One might then anticipate the opposite
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relationship (i.e., a positive covariance) to develop if the clouds are instead reduced.
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Under a quadrupling of CO2 , we find that polar boundary layer clouds decrease strongly in
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the high-albedo experiments (Figure 6). Climatologically in this region, the surface is cold and
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the atmosphere, stable. Low cloud fraction is high (black lines). By contrast, the low-albedo
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simulations are relatively warm, lack atmospheric temperature inversions, and have much weaker
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cloud decks in the initial mean state. The decrease in low clouds, which becomes more pronounced
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from the low- to high-albedo experiments, is a positive shortwave cloud radiative effect. Enhanced
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liquid water path in all four experiments ensures an overall negative shortwave cloud feedback,
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consistent with Ceppi et al. (2015).
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The lower tropospheric stability, estimated as the difference in potential temperature between
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700 hPa and the surface, further elucidates this response (Figure 7). As previously mentioned, the
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mean 4⇥CO2 climate is identical among simulations (dashed lines). The low-albedo experiments
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start from a weakly stable atmosphere that increases in stability to reach equilibrium. The high-
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albedo experiments start from a strongly stable atmosphere that decreases in stability to reach the
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final state. That decrease in stability is marked by a strong cloud response as the capping inver-
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sion at the top of the boundary layer is eroded. The correlation between cloud fraction and lower
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tropospheric stability is consistent with common cloud parameterizations (Rasch and Kristjánsson
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1998; Slingo 1987). For reference, the AM2.1 model uses the cloud and convective parameteriza-
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tions of Tiedtke (1993) and Moorthi and Suarez (1992), respectively.
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The decrease in planetary albedo associated with these cloud changes is analogous to, and acts
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in concert with, the decrease in surface albedo due to sea ice retreat. In both cases, the resulting
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increase in absorbed shortwave radiation warms the boundary layer, contributing to the charac-
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teristic bottom-heavy polar warming profile. In both cases, where clouds and sea ice are initially
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more extensive, potential decreases may also be larger. And in both cases, uncertainty in the mag-
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nitude of the response contributes to the total uncertainty in atmospheric heat transport. Critically,
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while the SW cloud feedback is negative, the mechanisms described above render it less nega-
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tive in the high-albedo experiment relative to the low-albedo experiment. Polar cloud and sea ice
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changes thus amplify the energy imbalance at high latitudes, requiring less poleward heat transport
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under enhanced CO2 . In the high-albedo experiments, that decrease is accomplished by decreases
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in energy flux by both transient eddies and the mean meridional circulation. In the low-albedo
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experiments, the weakening of the Hadley cell alone is sufficient.
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4. Summary and Discussion
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Feedbacks do not act in isolation. When we turn a positive feedback off, the net feedback be-
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comes more negative than can be accounted for based on the strength of the missing feedback
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alone. In the experiments presented herein, the effect of manipulating the surface albedo feed-
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back is investigated. By restricting the formation of sea ice—in actuality a simple ocean albedo
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dependence on surface temperature—we simulate the transition from perennial or seasonal ice
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to ice-free conditions. For a warm initial mean state, the characteristic bottom-heavy structure of
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Arctic warming is inhibited, and boundary layer clouds show slight increases rather than the strong
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decreases that occur when the lower troposphere is destabilized. Importantly, while the coupled
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climate feedbacks explored are extratropical in nature, the impacts are global. The net feedback
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has a stronger meridional gradient in the low-albedo experiment, which reinforces the existing
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pole-to-equator temperature gradient and promotes an anomalous poleward flux of energy. The
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high-albedo experiment of IcyAqua05 behaves in the opposite manner. The strong surface albedo
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feedback provokes an anomalous divergence of heat flux from the sea ice margin, the signature of
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which is a decrease in energy flux by extratropical eddies as well as by the tropical Hadley cell.
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Taken as a whole, the range in tropical circulation responses can thus be understood in terms of
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the spatial pattern of coupled climate feedbacks.
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An important result from the analysis is added insight into the interactive nature of surface
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albedo and cloud feedbacks. Temperature and water vapor feedbacks are affected as well, though
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to a lesser degree. In particular, we find that the lapse rate feedback is positive in the high-albedo
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experiments, contributing to the evident polar amplification as other studies have also shown (Feldl
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and Roe 2013b; Graversen et al. 2014; Pithan and Mauritsen 2014), and neutral/negative in the
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low-albedo experiments. The sign change of the lapse rate feedback is consistent with work by
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Cronin and Jansen (2016), in which the lapse rate feedback was found to be positive in the presence
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of surface forcing and negative in the presence of warming by atmospheric heat transport. In our
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case, boundary-layer warming is provided by the surface albedo feedback; in the absence of a
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strong albedo feedback, the polar warming structure is instead dominated by meridional transport.
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Ongoing research is aimed at uncovering the mechanisms responsible for the varying amounts of
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polar amplification in the aquaplanet experiments.
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Previous work by the authors has demonstrated that polar amplification persists (albeit in a
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reduced form) even in the absence of a surface albedo feedback. In contrast, here we show that
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warming in the low-albedo experiment is relatively uniform, with maxima at the equator and poles
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(Fig. 1b). It is tempting to declare the discrepancy a consequence of the inclusion of a seasonal
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cycle in the present study, however, the feedback structures and mean climates are different enough
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to render a direct comparison challenging. Regardless, the combination of an extreme feedback
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gradient and uniform warming pattern in Figure 1 is evidence of an atmosphere highly effective
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at redistributing heat between latitudes. If this were not the case, the dominant response would be
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one of tropical amplification, i.e., greatest warming where feedbacks are most positive.
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The inclusion of a seasonal cycle also impacts the radiative forcing estimate (Fig. 8). Merlis
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(2015a,b) has shown that time-independent and seasonally varying radiative forcing can have
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different impacts on the annual-mean circulation response. Here we estimate the CO2 radiative
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forcing as the ensemble-mean, zonal-mean, symmetrized and six-month-lagged forcing from the
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CMIP5 sstClim4⇥CO2 minus sstClim experiments. This fixed-SST forcing includes seasonality,
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which results in heat flux divergence from the equator. Were a time-invariant forcing instead used,
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a localized region of convergence due to cloud masking would develop along the equator. Since
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discussion of tropical circulation within the present study focuses on the regions of streamfunction
327
extrema, this distinction between time-invariant or seasonally varying forcing largely has little ef15
328
fect. For instance, the partial circulation changes due to radiative forcing are 0.2-0.5%/K for the
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time-invariant forcing, compared to 0.3-0.9%/K for seasonally varying forcing.
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We have emphasized the coupling between high-latitude cloud and surface albedo feedbacks.
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Resulting differences in atmospheric heat transport are felt globally, including by the tropical
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circulation, which must in turn mediate tropical clouds (Seo et al. 2014; Voigt and Shaw 2015).
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At the edge of the tropics, the decrease in poleward heat flux implied by the extratropical cloud
334
feedback is 0.1 PW K
335
(Fig. 3). The edge of the tropics (i.e., 30 degrees) also exhibits differences in low-latitude cloud
336
feedbacks. Since the Hadley cell widens by the same amount in all four albedo experiments, the
337
spread is not due to a differential expansion of the subtropics. Rather, decreases in subsidence
338
are consistent with decreases in tropospheric cloud fraction, and both changes are greatest in the
339
high-albedo experiments.
1
and 0.06 PW K
1
in the low- and high-albedo experiments, respectively
340
Interactions among climate feedbacks have been implied based on documented nonlinearities.
341
Here, we demonstrate in a controlled modeling environment how perturbing one feedback, surface
342
albedo, affects the other feedbacks and atmospheric heat transport. Although nonlinear feedback
343
interactions and feedbacks that are nonlinear functions of temperature enter the energy balance at
344
the same order, we may be confident that the former dominates here: (1) The increase is longwave
345
emission with temperature, following Stefan-Boltzmann law, is a negative nonlinear feedback,
346
and our nonlinearity is positive. (2) The structure of the nonlinearity reveals a peak at approxi-
347
mately 60 degrees latitude, in a region of active sea ice and atmospheric processes. We express
348
the degree of coupling between feedbacks in terms of uncertainty in circulation response. For
349
instance, variability in the surface albedo feedback does indeed contribute to the weakening of the
350
Hadley cell, however the impact is larger than would be expected based on the magnitude of the
351
albedo feedback alone. The implication is that the strength of a feedback cannot be accurately
16
352
quantified in isolation. Hence decompositions that emphasize the climate response to individual
353
feedbacks must account for the energy balance residual, which captures the effect of the nonlinear
354
interactions among feedbacks.
355
Acknowledgments. NF was supported by the National Science Foundation (AGS-1524569).
356
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465
LIST OF FIGURES
466
Fig. 1.
467
468
469
Fig. 2.
470
471
472
Fig. 3.
473
474
475
Fig. 4.
476
477
478
479
480
Fig. 5.
481
482
483
484
485
486
487
488
489
490
491
498
499
500
501
502
.
25
Anomalous northward atmospheric energy fluxes, integrated from the south to north pole.
Each experiment is normalized by its global-mean surface temperature change to give units
of PW K 1 . Simulations are color-coded as in the legend of Fig. 1. . . . . . . .
.
26
(a) Mass flux in the 1⇥CO2 (solid lines) and 4⇥CO2 (dashed lines) climates. Mass flux is
calculated as the signed maximum magnitude of the meridional mass streamfunction. (b)
Energy flux by the mean meridional circulation (solid lines) and transient eddies (dotted
lines) in the 1⇥CO2 climate. Due to the absence of zonal asymmetries, stationary eddies do
not occur in the aquaplanet. Simulations are color-coded as in the legend of Fig. 1. . . .
. 27
(a) Changes in circulation strength implied by net feedback (fdbk), radiative forcing (forc),
gross moist stability (gms), and transient atmospheric eddies (eddy) averaged between 1525 degrees in both hemispheres. The total change (tot) is in the leftmost column and the
portion of the net feedback due to nonlinearities (nonl) in the rightmost column. The nonlinear contribution is estimated as the residual
RR between the anomalous TOA radiative flux
and the sum of feedbacks and forcing, FHC 1 DR0 (Si li DTs 0 + R f 0 ). Each experiment is
normalized by its global-mean surface temperature change to give units of %K 1 . CMIP5
results reproduced from Feldl and Bordoni (2016) are in grey. (b) The same but for individual climate feedbacks: temperature (T), water vapor (WV), combined temperature and water
vapor (T+WV), surface albedo (A), net cloud (C), and the longwave (LW C) and shortwave
(SW C) components of the cloud feedback. . . . . . . . . . . . . .
.
28
.
29
Fig. 7.
Annual-mean zonal-mean lower tropospheric stability calculated as the difference in potential temperature between 700 hPa and the surface in the 1⇥CO2 (solid lines) and 4⇥CO2
(dashed lines) climates. Simulations are color-coded as in the legend of Fig. 1. . . . .
.
30
Annual-mean zonal-mean radiative forcing for 4⇥CO2 . Stratosphere-adjusted radiative
forcing (dashed line) calculated as 2 ⇥ R f from the GFDL radiative transfer model based on
the perpetual equinox aquaplanet simulations of Feldl and Roe (2013b). Fixed-SST radiative forcing (solid line) calculated from the seasonally varying CMIP5 sstClim4⇥CO2 and
sstClim experiments. Symmetrized fixed-SST radiative forcing used in the present study
(dotted line); the global mean is 7.6 W m 2 . See Hansen et al. (2005) for more on forcing
definitions. . . . . . . . . . . . . . . . . . . . . . .
.
31
495
497
Annual-mean, zonal-mean regional feedbacks (Wm 2 K 1 ) for the four aquaplanet experiments. Simulations are color-coded as in the legend of Fig. 1. See Feldl and Bordoni (2016)
for the CMIP5 version of this figure. . . . . . . . . . . . . . . .
Annual-mean, zonal-mean change in cloud fraction (shading) and 1⇥CO2 climatology (lines
at 0.1 intervals) for the four aquaplanet experiments. . . . . . . . . . . .
494
496
. 24
Fig. 6.
492
493
a) Annual-mean zonal-mean change in near-surface temperature (K) under 4⇥CO2 for the
four aquaplanet experiments. Surface albedo values are 30% (purple), 40% (blue), 45%
(green), and 50% (yellow). (b) Zonal-mean net feedback in Wm 2 K 1 . . . . . . .
Fig. 8.
23
Surface temperature change
a
K
20
15
10
5
-60
-30
0
Latitude
30
60
Net feedback
1
b
W m -2 K -1
0
-1
-2
IcyAqua03
IcyAqua04
IcyAqua045
IcyAqua05
-3
-4
-5
-60
-30
0
Latitude
30
60
503
F IG . 1. a) Annual-mean zonal-mean change in near-surface temperature (K) under 4⇥CO2 for the four aqua-
504
planet experiments. Surface albedo values are 30% (purple), 40% (blue), 45% (green), and 50% (yellow). (b)
505
Zonal-mean net feedback in Wm 2 K 1 .
24
Planck
Temperature plus water vapor
0
W m -2 K -1
W m -2 K -1
0
-2
-4
-6
-4
-6
-60 -30
2
-2
0
30
60
-60 -30
Lapse rate
0
30
60
Surface albedo
W m -2 K -1
W m -2 K -1
4
0
-2
2
0
-4
-60 -30
30
60
Water vapor
-60 -30 0 30
Latitude
Net cloud
60
-60 -30
60
2
W m -2 K -1
W m -2 K -1
6
0
4
2
0
-2
0
-60 -30
0
30
60
0
30
506
F IG . 2. Annual-mean, zonal-mean regional feedbacks (Wm 2 K 1 ) for the four aquaplanet experiments.
507
Simulations are color-coded as in the legend of Fig. 1. See Feldl and Bordoni (2016) for the CMIP5 version of
508
this figure.
25
Planck
Temperature plus water vapor
0.05
PW/K
PW/K
0.1
0
-0.1
-0.05
PW/K
0
30
Latitude
Lapse rate
60
0.1
PW/K
-60 -30
0.1
0
0
-0.1
0
30
Latitude
Surface albedo
60
-60 -30
60
0
-0.1
-60 -30
0
30
Latitude
Water vapor
60
0
30
Latitude
Net cloud
0.1
PW/K
0.1
PW/K
-60 -30
0
-0.1
0
-0.1
-60 -30
0.2
0
30
Latitude
Eddy
60
-60 -30
0
30
Latitude
Forcing
60
-60 -30
0
30
Latitude
60
PW/K
PW/K
0.02
0
0
-0.02
-0.2
-60 -30
0
30
Latitude
60
509
F IG . 3. Anomalous northward atmospheric energy fluxes, integrated from the south to north pole. Each
510
experiment is normalized by its global-mean surface temperature change to give units of PW K 1 . Simulations
511
are color-coded as in the legend of Fig. 1.
26
Northward mass flux (10
9
kg s -1 )
a
200
100
0
-100
-200
-60
-30
0
Latitude
30
60
Northward energy flux (PW)
b
5
0
-5
-60
-30
0
Latitude
30
60
512
F IG . 4. (a) Mass flux in the 1⇥CO2 (solid lines) and 4⇥CO2 (dashed lines) climates. Mass flux is calculated as
513
the signed maximum magnitude of the meridional mass streamfunction. (b) Energy flux by the mean meridional
514
circulation (solid lines) and transient eddies (dotted lines) in the 1⇥CO2 climate. Due to the absence of zonal
515
asymmetries, stationary eddies do not occur in the aquaplanet. Simulations are color-coded as in the legend of
516
Fig. 1.
27
Partial circulation changes
12
a
10
8
6
4
% K -1
2
0
-2
-4
-6
-8
-10
-12
tot
fdbk
forc
gms eddy
ohu
nonl
IcyAqua03
IcyAqua04
IcyAqua045
IcyAqua05
cmip5
10
b
8
6
4
2
% K -1
0
-2
-4
-6
-8
-10
-12
-14
T
WV T+WV
A
C
LW C SW C
28
526
527
F IG . 6. Annual-mean, zonal-mean change in cloud fraction (shading) and 1⇥CO2 climatology (lines at 0.1
intervals) for the four aquaplanet experiments.
29
Lower tropospheric stability
22
20
18
K
16
14
12
10
8
-90
-60
-30
0
Latitude
30
60
90
528
F IG . 7. Annual-mean zonal-mean lower tropospheric stability calculated as the difference in potential tem-
529
perature between 700 hPa and the surface in the 1⇥CO2 (solid lines) and 4⇥CO2 (dashed lines) climates. Sim-
530
ulations are color-coded as in the legend of Fig. 1.
30
Radiative forcing
10
W m -2
8
6
4
2
-90
-60
-30
0
Latitude
30
60
90
531
F IG . 8. Annual-mean zonal-mean radiative forcing for 4⇥CO2 . Stratosphere-adjusted radiative forcing
532
(dashed line) calculated as 2 ⇥ R f from the GFDL radiative transfer model based on the perpetual equinox
533
aquaplanet simulations of Feldl and Roe (2013b). Fixed-SST radiative forcing (solid line) calculated from the
534
seasonally varying CMIP5 sstClim4⇥CO2 and sstClim experiments. Symmetrized fixed-SST radiative forcing
535
used in the present study (dotted line); the global mean is 7.6 W m 2 . See Hansen et al. (2005) for more on
536
forcing definitions.
31