RESEARCH LETTER
10.1029/2018GL081110

The Effect of Arctic Sea Ice Loss on the Hadley Circulation
R. Chemke1

Key Points:• Arctic sea ice loss affects the Hadleycell only through ocean-atmosphere
coupling• Arctic sea ice loss acts as a negativeinternal feedback in the responseof the Hadley cell width toanthropogenic emissions• Ocean heat transport opposes thethermodynamic effect of Arctic sea
ice loss on the Hadley circulation

Correspondence to:R. Chemke,
rc3101@columbia.edu

Citation:
Chemke, R., Polvani, L. M., &Deser, C. (2019). The effect of Arctic
sea ice loss on the Hadley circulation.
Geophysical Research
Letters, 46, 963–972.
https://doi.org/10.1029/2018GL081110

Received 26 OCT 2018
Accepted 12 JAN 2019
Accepted article online 16 JAN 2019
Published online 29 JAN 2019

, L. M. Polvani1,2, and C. Deser3

1 Department of Applied Physics and Applied Mathematics, Columbia University, New York, NY, USA, 2 Department ofEarth and Environmental Sciences and Lamont-Doherty Earth Observatory, Columbia University, Palisades, NY, USA,
3 National Center for Atmospheric Research, Boulder, CO, USA

Abstract One of the most robust responses of the climate system to future greenhouse gas emissions is
the melting of Arctic sea ice. It is thus essential to elucidate its impacts on other components of the climate
system. Here we focus on the response of the annual mean Hadley cell (HC) to Arctic sea ice loss using ahierarchy of model configurations: atmosphere only, atmosphere coupled to a slab ocean, and atmosphere
coupled to a full-physics ocean. In response to Arctic sea ice loss, as projected by the end of the 21st century,the HC shows negligible changes in the absence of ocean-atmosphere coupling. In contrast, by warming
the Northern Hemisphere thermodynamic coupling weakens the HC and expands it northward. However,dynamic coupling acts to cool the Northern Hemisphere which cancels most of this weakening andnarrows the HC, thus opposing its projected expansion in response to increasing greenhouse gases.

Plain Language Summary The climate's response to anthropogenic emissions comprises
different feedbacks of the different components in the climate system. One of the robust responses toincreased greenhouse gases is the melting of Arctic sea ice, which is found to have large effects on thehydrological circulation in the atmosphere. Here we examine the effect of Arctic sea ice loss on the tropicalcirculation. We find that under Arctic sea ice loss ocean heat transport acts to transfer the Arctic signal
to the tropics and to contract the tropical circulation. This contraction opposes the projected widening of
the tropical circulation and thus shows that Arctic sea ice loss acts as a negative internal feedback in the
response of the tropical circulation to increased greenhouse gases.

1. Introduction
The melting of Arctic sea ice in recent decades is one of the prominent instances of climate change. Overthe last decades, perennial Arctic sea ice has decreased its extent by 25–35% and with unabated emissionsof greenhouse gases is projected to nearly vanish by the end of the 21st century (Intergovernmental Panelon Climate Change, 2013). In spite of the substantial loss of Arctic sea ice in recent decades, its effects
on the atmospheric circulation remain unclear, mostly due to numerous confounding processes in the climate system, the short period of the observed record, and the large internal climate variability (e.g., Barnes,
2013; Barnes & Polvani, 2015; Blackport & Kushner, 2016; Cohen et al., 2014; Hassanzadeh & Kuang, 2015;
Overland et al., 2015; Screen & Simmonds, 2013; Sun et al., 2016; Vihma, 2014; Walsh, 2014).
At midlatitudes, the projected effects of Arctic sea ice loss on the zonal wind are found to oppose theeffects by increased greenhouse gases. In response to Arctic sea ice loss, the Northern Hemisphere (NH)jet weakens on its poleward flank, in concert with the reduced meridional temperature gradient accompanying polar amplification (e.g., Deser et al., 2015, 2016; Oudar et al., 2017; Peings & Magnusdottir, 2014;
Screen et al., 2018; Smith et al., 2017; Sun et al., 2015). Concomitantly, tropospheric eddy momentum fluxes
are also projected to weaken (in agreement with a reduction in baroclinicity; Oudar et al., 2017). The projected effects of Arctic sea ice loss on the position of the jet (its meandering), however, are less certain (e.g.,
Barnes & Polvani, 2015; Barnes & Screen, 2015; Hassanzadeh & Kuang, 2015; Oudar et al., 2017; Screen &Simmonds, 2013). And, in the tropics the Intertropical Convergence Zone (ITCZ) shifts equatorward andintensifies in response to the projected Arctic sea ice loss (e.g., Deser et al., 2015; Smith et al., 2017; Tomas
et al., 2016; Wang et al., 2018).
©2019. American Geophysical Union.
All Rights Reserved.

CHEMKE ET AL.

Interestingly, ocean-atmosphere coupling is found to play an important role in the above circulation
changes. Thermodynamic coupling (i.e., changes in sea surface temperature, SST, by radiative and turbulent
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Geophysical Research Letters10.1029/2018GL081110

heat fluxes) is found to warm the NH, mostly at high latitudes, and thus to reduce the meridional temperature gradient, to weaken the mean zonal wind on its poleward flank, and to push the ITCZ northward(similarly, cooling the NH was found to shift the ITCZ southward due to thermodynamic coupling; Chiang& Bitz, 2005; Kang et al., 2008). In contrast, dynamic coupling (i.e., the effects of ocean heat transport on
the SST) was found to cool the NH, by transferring heat to the Southern Hemisphere (SH), strengthen thejet on its equatorward flank, shift it equatorward, and to push the ITCZ equatorward (e.g., Deser et al., 2015,2016; Green & Marshall, 2017; Tomas et al., 2016; Wang et al., 2018). One example of a change in ocean circulation under Arctic sea ice loss is the weakening of the Atlantic meridional overturning circulation (e.g.,S‘evellec et al., 2017), which may then affect the tropical circulation (e.g., Zhang & Delworth, 2005).
The main focus in all the above studies is the impact of Arctic sea ice loss on the ITCZ and the extratropicalcirculation. The aim of this work, however, is to investigate the effects of the projected Arctic sea ice loss on
the Hadley cell (HC). While there is an extensive literature on the HC response to projected anthropogenic
emissions (e.g., Held & Soden, 2006; Kang et al., 2013; Lu et al., 2007; Merlis, 2015; Vallis et al., 2015), the specific impact of Arctic sea ice loss is largely unexplored. By the end of this century, climate projections show
a weakening of the HC along with an expansion of its vertical and meridional extents (Intergovernmental
Panel on Climate Change, 2013; Kang et al., 2013; Vallis et al., 2015). Recently, Tomas et al. (2016) and Wanget al. (2018) showed that in response to Arctic sea ice loss thermodynamic coupling also acts to weaken the
NH HC, while ocean dynamics acts to strengthen it, thus opposing its projected weakening. Building on thework of Tomas et al. (2016) and Wang et al. (2018), here we examine not only the HC strength but also its
northward edge and vertical extent and ask what fraction of the HC response to anthropogenic forcing is
caused by the melting of Arctic sea ice. In addition, we here elucidate the physical mechanisms behind the
HC response to Arctic sea ice loss. Since the circulation response to Arctic sea ice loss is more prominent in
the NH, we focus here on the NH HC response.

2. Methods
To study the response of the annual mean HC to Arctic sea ice loss, we make use of the set of simulations
presented in Deser et al. (2016). These simulations were conducted using the Community Climate System
Model version 4 (CCSM4; Gent et al., 2011), where all components (atmosphere, ocean, land, and ice) have
∼ 1◦ horizontal resolution.
Since ocean-atmosphere coupling plays an important role in transferring the Arctic sea ice signal to lower
latitudes, three configurations of the CCSM4 are used: (i) atmosphere only, with prescribed SST and sea ice
and no active ocean model (NOM), (ii) slab ocean model (SOM), which lacks any changes in ocean heattransport but accounts for ocean-atmosphere thermodynamic coupling, and (iii) full-depth ocean model(FOM), which accounts for both ocean-atmosphere thermodynamic and dynamic coupling.
The approach taken here for achieving a desired Arctic sea ice state is to add a spatially and seasonallyvarying longwave radiative flux (LRF) to the ice component in the SOM and FOM (see Deser et al., 2015 fordetails). Two experiments were conducted: one where the LRF is designed to reproduce the Arctic sea ice
thickness and concentration of the end of the 20th century (1980–1999) and one of the end of the 21st century(2080–2099), based on model simulations forced with the historical and RCP8.5 scenarios, respectively. Notethat since only the Arctic sea ice is different between the two experiments (i.e., radiative forcing is fixed atyear 2000), and the LRF is added solely to the ice component, with no heat conduction between the ice andocean components, any changes in the atmosphere and ocean stem from changes in Arctic sea ice alone.
For the NOM, the sea ice in both experiments is prescribed based on its corresponding FOM simulation. For
the NOM 21st century the SST in regions of Arctic sea ice loss is prescribed based on the FOM 21st century;
elsewhere the SST is prescribed based on the FOM twentieth century in both experiments. This accounts
for the local ocean warming due to sea ice loss (Deser et al., 2015; Screen & Simmonds, 2013; Screen et al.,2015). This procedure introduces discontinuities in SST at the edge of the region where sea ice is projected todisappear; however, these discontinuities are much smaller than those already present across the ocean-ice
boundary in the twentieth century. The results shown below for the NOM, SOM, and FOM are computed
using the last 260 years of a 260-, 300-, and 360-year run, respectively. Throughout the paper, Δ represents
the difference between the end of the 21st and 20th centuries Arctic sea ice simulations.
Finally, in order to assess the importance of Arctic sea ice loss in affecting the HC, ΔFOM is compared to
the response of the HC to the full anthropogenic forcing (RCP8.5). The latter is computed by averaging the
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six available CCSM4 runs of the historical and RCP8.5 scenarios at the end of the 20th (1980–1999) and21st centuries (2080–2099), respectively. This mean of all six runs isolates the forced response of the HC by
averaging out the internal variability.
Note that since the SST and sea ice in the NOM configuration are prescribed, the difference between ΔSOM
and ΔNOM isolates the effects of ocean-atmosphere thermodynamic coupling. In addition, since an identicalQ-flux and mixed-layer depth are used for the two LRF experiments in the SOM configuration, the difference
between ΔFOM and ΔSOM isolates the effects of ocean-atmosphere dynamic coupling.
To characterize the HC, following Chemke and Polvani (2018), the width, strength and height of the annual
mean HC are calculated as follows:(i) The northern edge of the HC (𝜑𝛹 500 ) is calculated at 500 mb as the latitude where the meridional mass
stream function (𝛹 ),Ψ(𝜙, p) =2πa cos 𝜙 pv(𝜙, p)dp′ ,
∫0
g

(1)

first changes sign northward of its maximum value, where p is pressure, v is meridional velocity, over-bar
represents zonal and time mean, g is gravity, and a is Earth’s radius.
(ii) The strength of the HC (𝛹max ) is calculated as the maximum value of 𝛹 at 500 mb in the NH.
(iii) The height of the HC (H) is calculated as the tropopause height averaged over 10◦ latitude centeredaround 𝛹max . The tropopause height is estimated as the lowest level where the temperature lapse rate reaches
2 K/km.
Throughout the paper all tropical quantities are averaged between the latitude of the ITCZ (defined as
the latitude where 𝛹 switches sign between the southern and northern HC's branches) and 𝜑𝛹 500 , and all
subtropical quantities between 30◦ N and 40◦ N.

3. Results
We start by comparing the temperature and circulation responses to sea ice melting in the NOM, SOM, andFOM configurations (Figure 1). For the sake of clarity, here we present the results for all model configurations and their differences in a single figure. While a few of these results have appeared in Deser et al. (2016),
Tomas et al. (2016), and Wang et al. (2018), aggregating these results allows us to make a clear comparison,
as was done for the extratropical NH circulation in Deser et al. (2016). As shown in Deser et al. (2016), since
the prescribed SST in the NOM 21st century is based on the FOM 21st century simulation only in regions
where Arctic sea ice loss occurs, the warming of the SST in ΔNOM is confined to the Arctic (Figure 1a). And,similar to Tomas et al. (2016), allowing thermodynamic ocean-atmosphere coupling, ΔSOM shows warmingof both hemispheres but mostly at NH high latitudes (Figure 1b). This effect of the thermodynamic coupling can also be seen by plotting the difference in SST response between ΔSOM and ΔNOM (Figure 1d).
By including both thermodynamic and dynamic ocean-atmosphere coupling, the SST in ΔNOM increases
more uniformly in both hemispheres (Figure 1c). Isolating the effects of dynamic coupling, by subtracting
the SST response in ΔSOM from ΔFOM, shows that ocean heat transport acts to transfer heat between thetwo hemispheres and thus to cool the NH and warm the SH (Figure 1e; Deser et al., 2016; Tomas et al., 2016).
The above temperature patterns are not confined to the surface but extend into the atmosphere as well
(middle row in Figure 1). Without any ocean-atmosphere coupling, atmospheric warming in ΔNOM is confined to high latitudes in the NH (Figure 1f). Ocean thermodynamic coupling, however, deepens the NH
high-latitude warming into the free troposphere, allowing the warming signal to reach into the upper tropical troposphere and into the SH (Figures 1g and 1i). Adding dynamic ocean-atmosphere coupling results
in a more symmetric warming around the equator, which resembles the pattern under global warming (i.e.,high-level tropical warming and surface-intensified Arctic warming; Figure 1h). Similar to the SST response,
dynamic ocean-atmosphere coupling acts to cool the troposphere in the NH and warm it in the SH (Figure 1j;
Deser et al., 2015, 2016).
In order to examine the response of the HC to Arctic sea ice melting, we start by showing the response of 𝛹in the ΔNOM, ΔSOM, and ΔFOM configurations (colors in bottom row in Figure 1, where black contours
show 𝛹 in the 20th century run). In ΔNOM, since the warming signal is confined to the pole, Arctic sea ice
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Figure 1. Response of the mean (a–e) SST (K), (f–j) zonal mean temperature (K), and (k–o) meridional mass stream function (kg/s) to late 21st century Arctic
sea ice loss in the (first column) NOM, (second column) SOM, (third column) FOM, and the difference (fourth column) between SOM and NOM and (fifth
column) between FOM and SOM. Black contours in panels k–m show the stream function at the end of the 20th century, with solid (dashed) contours
representing clockwise (counterclockwise) circulation. Green contours in panels k–m show the mean angular momentum lines, with 0.2 m2 /s spacing. The
black dots indicate the regions where the response is statistically significant at the 95% confidence level. SST = sea surface temperature; NOM = no active ocean
model; SOM = slab ocean model; FOM = full-depth ocean model.

loss has only a minor effect on the HC (Figure 1k). In ΔSOM, however, as in Tomas et al. (2016) and Wanget al. (2018), thermodynamic coupling weakens the NH HC (blue colors on solid contours in Figures 1l and
1n). The HC also weakens in ΔFOM (Figure 1m), but with a smaller magnitude than in ΔSOM, thus showing
the effect of the dynamic coupling in strengthening the NH HC (Figure 1o), as reported under CO2 doubling(Chemke & Polvani, 2018). To further examine the HC response to Arctic sea ice loss, we now analyze theresponses of the three HC metrics.
3.1. The Northern Edge of the HC
Without any ocean coupling 𝜑𝛹 500 in ΔNOM shows a minor shift of −0.16◦ , but with a large uncertainty(Δ𝜑𝛹 500 , yellow bar in Figure 2a). Adding thermodynamic coupling results in a clear northward shift of𝜑𝛹 500 of 0.85◦ in ΔSOM (blue bar). Dynamic coupling, however, overcomes this expansion and results in asouthward shift of 𝜑𝛹 500 of −0.32◦ in ΔFOM (red bar). Similar to the equatorward shift of the midlatitude
jet and contraction of the ITCZ under Arctic sea ice loss (e.g., Deser et al., 2015, 2016; Screen et al., 2018),
this southward shift opposes the projected northward shift of 𝜑𝛹 500 under the RCP8.5 scenario (0.75◦ purplebar) by ∼ 40%. This further emphasizes the importance of ocean heat transport in carrying the Arctic signal to lower latitudes and in reducing the atmospheric thermodynamic response, as was also found underincreased greenhouse gases (Chemke & Polvani, 2018).
Given the significant effect of Arctic sea ice loss on 𝜑𝛹 500 , we next seek to elucidate the mechanisms. Held
(2000) developed a theory for the HC width, which is able to explain the projected widening of the HC(e.g., Chemke & Polvani, 2019). In that theory, the edge of the HC (𝜑H00 ) is determined by the latitude
where the vertical shear of the mean angular momentum conserving flow at the upper branch of the HC
becomes baroclinically unstable and scales as follows:
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Figure 2. NH HC edge response to Arctic sea ice loss. (a) Latitudinal shift of the NH HC edge (Δ𝜑𝛹 500 , section 2); andthose predicted by the theory of Held (2000) with Ro and ITCZ taken from the simulations (Δ𝜙H00ITCZ+Ro , equation (4));
and with only Ro taken from the simulations (Δ𝜙H00Ro , equation (5)). (b) Relative contributions to the response ofΔ𝜙 H00Ro : subtropical tropopause height (Δ𝜙H00Ro |He ), static stability (Δ𝜙H00Ro |N ), and tropical Rossby number(Δ𝜙H00Ro |Ro ; equation (6)). (c) The relative contributions to the subtropical tropopause height response: subtropicalsurface temperature (ΔHe |Ts ), tropospheric lapse rate (ΔHe |𝛤 ), and stratospheric temperature and lapse rate (He |strat ).
(d) The response of the tropical eddy momentum flux divergence. In all panels yellow, blue, and red bars show ΔNOM,
ΔSOM, and ΔFOM, respectively, and the vertical error bars represent the 95% confidence interval. The purple bar inpanel a shows the RCP8.5 response. NH = Northern Hemisphere; HC = Hadley cell; ITCZ = Intertropical Convergence
Zone; RCP = Representative Concentration Pathway; NOM = no active ocean model; SOM = slab ocean model;
FOM = full-depth ocean model.

(
𝜙H00 ∝

NHe
Ωa

)1∕2
,

(2)

where He is subtropical tropopause height, N 2 = 𝜃 𝜕𝜃
is subtropical static stability (averaged between 400
𝜕z
and 800 mb), and 𝛺 is Earth's rotation rate. The angular momentum flow, however, is affected by both thepresence of eddies within the upper branch of the HC and the latitudinal position of the ITCZ (Kang & Lu,2012). Given the effects of Arctic sea ice loss on both eddy momentum fluxes (e.g., Oudar et al., 2017; Sunet al., 2015) and ITCZ position (e.g., Deser et al., 2015; Smith et al., 2017; Tomas et al., 2016; Wang et al.,2018), we next incorporate these effects in equation (2), as was done in Kang and Lu (2012).
g

Regarding the location of the ITCZ, since an air parcel starts to acquire angular momentum as it propagates
poleward of the equator, if the ITCZ is located further north of the equator, for example, it would act to push𝜑𝛹 500 further poleward, as it allows the mean flow to move further poleward before becoming baroclinically unstable. In addition, eddy momentum fluxes act to extract momentum from the mean flow, and thus
angular momentum is not entirely conserved within the HC. Neglecting friction and vertical advection, thesteady state zonal mean momentum equation can be written as follows:𝑓 (1 − Ro)v =CHEMKE ET AL.

1 𝜕u′ v′ cos2 𝜙,𝜕𝜙
acos2 𝜙THE EFFECT OF ARCTIC SEA ICE LOSS ON THE HADLEY CIRCULATION

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Geophysical Research Letters10.1029/2018GL081110

𝜕u cos 𝜙1
where f is the Coriolis parameter, Ro ≡ −𝜁 ∕𝑓 is the local Rossby number, 𝜁 = − a cos
is mean𝜙𝜕𝜙relative vorticity, u is zonal wind, and prime represents deviation from zonal and time mean. Since[]𝜕m𝑓 (1 − Ro) = a2 −1, where m is mean angular momentum (m ≡ u + Ωa cos 𝜙 a cos 𝜙), and v > 0
cos 𝜙 𝜕𝜙1
𝜕min the upper branch of the HC, angular momentum is conserved (i.e., a2 cos= 0) only if the eddies
𝜙 𝜕𝜙vanish in the HC (i.e., the right-hand side [RHS] of equation (3) is 0). However, due to the presence ofeddies within the HC, the angular momentum is not entirely conserved, as can be seen by the fact thatthe stream function crosses mean angular momentum lines in the upper branch of the HC (green lines in
Figures 1k–1m). Based on equation (3), Ro can be used to measure the importance of eddies in reducing
the mean angular momentum (Adam & Harnik, 2013; Walker & Schneider, 2006). As Ro approaches unity,
the flow approaches its angular momentum conserving solution, while as Ro approaches 0, eddies play animportant role in reducing angular momentum. Following Kang and Lu (2012; see their equation 8), one
can include the tropical Ro (averaged over the upper branch between 200 and 400 mb) in the Held (2000)
theory, as well as a northward displacement of the ITCZ of the equator (𝜑ITCZ > 0 for all NOM, SOM, andFOM simulations). Then, the HC width scaling can be written as follows:(⎧[] )1∕2 ⎫
NHe 2
⎪ 2
⎪
4
𝜙H00ITCZ+Ro ∝ 0.25⎨𝜙ITCZ + 𝜙 ITCZ +
⎬
1∕2
ΩaRo
⎪
⎪
⎩
⎭

1∕2

.

(4)

When Ro = 1 (i.e., when the flow conserves angular momentum) and 𝜑ITCZ = 0 (i.e., the ITCZ is on theequator), equation (4) reduces to equation (2). A decrease in Ro (i.e., strengthening of the eddies) pushes
𝜙H00Ro poleward, since the eddies extract momentum from the mean flow, which allows the mean flow tomove further poleward before becoming baroclinically unstable. Similar arguments can be applied for anorthward shift of 𝜑ITCZ .
Equation (4) (with a constant of proportionality of 1) qualitatively captures both the northward shift of𝜑𝛹 500 in ΔSOM (blue bar, 0.78◦ ) and the southward shift of 𝜑𝛹 500 in ΔFOM (red bar, −0.1◦ ; Δ𝜙 H00ITCZ+Ro ;Figure 2a). To elucidate which components in 𝜙H00ITCZ+Ro are responsible for these shifts in ΔSOM and
ΔFOM, we first examine the importance of changes in 𝜑ITCZ . This is done by recalculating equation (4) while
keeping 𝜑ITCZ = 0, which yields
(
)1∕2
NHe
𝜙H00Ro ∝.
(5)
ΩaRo1∕2Equation (5) gives results similar to equation (4) (compare Δ𝜙 H00Ro and Δ𝜙 H00ITCZ+Ro in Figure 2a), implying that ITCZ shifts have minor effects on the response of 𝜑𝛹 500 under Arctic sea ice loss. In order to further
examine which of the components in equation (5) is responsible for the HC edge changes, we take thelogarithm of equation (5) after diving it by its twentieth century value,
)
)
(
(
(
(
)
)
𝜙H00RoHeNRo= 0.5 log
− 0.25 log
log(6)+ 0.5 log.
𝜙H00RoN20th
He20th
Ro20th20th

The relative contributions of the RHS of equation (6) are shown in Figure 2b. Unlike the poleward shift of𝜑𝛹 500 under global warming that was found to occur due, primarily, to changes in subtropical static stability(Chemke & Polvani, 2019), here the northward shift of 𝜑𝛹 500 in ΔSOM (blue bar) is linked to both an increase
in He (Δ𝜙H00Ro |He ) and a decrease in Ro (Δ𝜙H00Ro |Ro ), whereas the southward shift of 𝜑𝛹 500 in ΔFOM (redbar) is linked to an increase in Ro. This shows that unlike 𝜙H00Ro (equation (5)), 𝜑H00 (equation (2)) alone
could not explain the shift of 𝜑𝛹 500 . These two variables (He and Ro) also show the largest difference between
ΔSOM and ΔFOM and thus capture the different roles of thermodynamic and dynamic ocean-atmosphere
coupling.
To gain further understanding on the physical processes that affect the response of He and Ro for both ΔSOM
and ΔFOM, we further analyze each of these components. Changes in He can be due to both changes in themean temperature and the temperature lapse rate (e.g., Thuburn & Craig, 2000; Vallis et al., 2015). Assuming
constant tropospheric (𝛤trop ) and stratospheric (𝛤strat ) lapse rates, these changes can be isolated from thestratospheric temperature (Tstrat ) equation,
Tstrat (z) = Ts + Γtrop He + Γstrat (z − He ),CHEMKE ET AL.

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Geophysical Research Letters10.1029/2018GL081110

where Ts is surface temperature. Isolating He in the above equation leads to an equation for ΔHe ,ΔHe = −He ΔΓtrop
ΔTs
ΔTstrat − ΔΓstrat (z − H)−+,Γtrop − Γstrat Γtrop − Γstrat
Γtrop − Γstrat(8)

which is similar to equation 9 in Vallis et al. (2015) but here also accounts for changes in a nonisothermal
stratosphere. The terms on the RHS in equation (8) account for changes in subtropical surface temperature,
tropospheric lapse rate, and stratospheric temperature and lapse rate, respectively. The relative contributionsof the different terms are plotted in Figure 2c. Changes in Ts (ΔHe |Ts ) are mostly responsible for the increase
in He in ΔSOM (blue bar) and for the reduced increase in He in ΔFOM (red bar). Thus, the cooling of the NH
due to ocean heat transport (Figure 1e) results in a weaker increase in He under Arctic sea ice loss, whichleads to a weaker HC poleward expansion.
Since Ro is defined using the mean zonal flow (−𝜁∕𝑓 ), any northward or equatorward shift of 𝜙H00Ro due tochanges in Ro may not be due to changes in eddies but might simply represent changes in the mean zonal
flow itself. To examine whether changes in Ro stem from changes in eddy momentum fluxes, changes in thedivergence of the tropical eddy momentum fluxes (Δu′ v′ 𝑦 ), averaged over the upper branch the HC between
200 and 400 mb, are shown in Figure 2d. Confirming previous studies (e.g., Oudar et al., 2017; Sun et al.,2015), the eddies within the HC weaken in both ΔSOM (blue bar) and ΔFOM (red bar). A weakening of theeddies implies an increase in Ro and thus a southward shift of 𝜙H00Ro (equation (5)). Hence, the decrease in
Ro in ΔSOM simply represents the changes in the mean zonal flow (partly associated with the shift of the
HC itself) and not the weakening of the eddies. That weakening, which acts to shift 𝜙H00Ro southward, does
not overcome the poleward shift of 𝜙H00Ro in ΔSOM due to the increased He (as discussed above). In ΔFOM,
however, the tendency of ocean heat transport to cool the surface, and thus to reduce the increase in He ,allows the weakening of eddy momentum fluxes to push 𝜙H00Ro southward.
3.2. The HC Strength
As was shown in Figures 1k–1o, the NH HC strength (Δ𝛹max ) shows minor changes in ΔNOM (−6.9·106 kg/s,
yellow bar in Figure 3a), strong weakening in ΔSOM (−6.7 · 109 kg/s, blue bar), and a small weakening in
ΔFOM (−0.91 · 109 kg/s, red bar). The latter, as also found under CO2 doubling (Chemke & Polvani, 2018),
reveals the opposite effects of the thermodynamic and dynamic ocean-atmosphere coupling, which weaken
and strengthen the HC under Arctic sea ice loss, respectively (Tomas et al., 2016; Wang et al., 2018). Note,also, that the weakening in ΔFOM is a relatively small fraction (∼ 12%) of the weakening of the HC under
the RCP8.5 scenario (−7.3 · 109 kg/s, purple bar).
To further analyze the weakening of the HC under Arctic sea ice loss, we investigate the stream function
equation (the Kuo-Eliassen equation, Kuo, 1956), which is derived using quasi-geostrophic approximationand thermal wind balance (section 14.5.5 in Peixoto & Oort, 1992),
g
g 1 𝜕
𝜕2 𝜓
1 𝜕𝜓
=
+ S2
2πa cos 𝜙 𝜕p2
2πa a 𝜕𝜙 a cos 𝜙 𝜕𝜙())(
𝜕 2 v′ T ′ cos 𝜙
R 1 𝜕Qdiab
1
1 𝜕 2 u′ v′ cos2 𝜙 𝜕X
− 2
−
,
+
𝑓
p a 𝜕𝜙𝜕p𝜕𝜙
𝜕pa cos 𝜙𝜕𝜙2
acos2 𝜙𝑓2

(9)is static stability in pressure coordinates, 𝜌 is density, R = 287 J·kg−1 ·K−1 is the gas
where S2 = − 𝜌𝜃1 𝜕𝜃𝜕pconstant of dry air, Qdiab is diabatic heating, v′ T ′ is eddy heat fluxes, and X is zonal friction. Several studies
have suggested that Qdiab and S2 are responsible for the weakening of the circulation in the future (e.g., Bonyet al., 2013; Knutson & Manabe, 1995; Merlis, 2015). Here we solve equation (9), with the RHS specified
from the model's output, using a successive overrelaxation method. The solution of equation (9) (ΔΨmaxEq )shows a similar response to Arctic sea ice loss as diagnosed from the model (Figure 3a): It captures the minorchanges in ΔNOM, the strong weakening in ΔSOM, and the small weakening in ΔFOM.
To gain further understanding on the HC strength responses to Arctic sea ice loss under the different configurations of ocean-atmosphere coupling, equation (9) is solved separately for each term on the RHS. The
contribution of each term in equation (9) along with that of the LHS operator (S2 ; cf. equation 12 in Kim& Lee, 2001a; calculated at 500 mb at the latitude of 𝛹max ) is plotted in Figure 3b. The weakening of the
HC in ΔSOM (blue bars) is accompanied with changes in all components, but mainly with diabatic heating (ΔΨ|Qdiab ). In ΔFOM (red bars), similar to the HC width response, the reduction in eddy momentum
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Figure 3. NH HC strength and height responses to Arctic sea ice loss. (a) The response of the NH HC strength (kg/s)
computed from equation (1) (Δ𝛹max ) and the Kuo-Eliassen equation (equation (9); ΔΨmaxEq ). (b) The relative
contribution of the different terms in equation (9) (kg/s): diabatic heating (ΔΨ|Qdiab ), eddy heat fluxes (ΔΨ|v′ T ′ ), eddy
momentum flux (ΔΨ|u′ v′ ), zonal friction (Δ𝛹 |X ), and static stability (ΔΨ|S2 ). (c) The contribution of the diabatic
heating term in equation (9) separated into contributions from radiative heating (ΔΨ|Qrad ) and latent heating(ΔΨ|Qlatent ). (d) The tropical tropopause height response to Arctic sea ice loss (ΔH, m; section 2). In all panels yellow,
blue, and red bars show ΔNOM, ΔSOM, and ΔFOM, respectively, and the vertical error bars represent the 95%
confidence interval. The purple bar in panels a and d show the RCP8.5 response. NH = Northern Hemisphere;
HC = Hadley cell; NOM = no active ocean model; SOM = slab ocean model; FOM = full-depth ocean model.
RCP = Representative Concentration Pathway.

fluxes (ΔΨ|u′ v′ ) together with zonal friction (Δ𝛹 |X ) and static stability (ΔΨ|S2 ) contribute to the weakeningof the circulation. The diabatic heating also accounts for the largest difference between ΔSOM and ΔFOM
responses (although the eddy fluxes also contribute to this discrepancy). Further decomposing the diabatic
heating to contributions from radiative (ΔΨ|Qrad ) and latent heating (ΔΨ|Qlatent ) shows that most of the difference between ΔSOM and ΔFOM comes from latent heating (Figure 3c). Similar to the response of the
HC strength under CO2 doubling (Chemke & Polvani, 2018), the cooling of the NH by ocean heat transport (Figure 1j) reduces the amount of water vapor available for condensation, which reduces the amountof latent heating, and thus acts to reduce the weakening of the HC under Arctic sea ice loss. Note that at
steady state the RHS terms are not independent from each other (e.g., Kim & Lee, 2001b). Hence, this effectof latent heating may not necessarily be a direct response to Arctic sea ice loss but may stem from changes
in the other terms in equation (9).
3.3. The HC Height
Unlike the above two metrics, Arctic sea ice loss has a very minor effect on the height (H) of the HC in ΔNOM
(5.6 m, yellow bar in Figure 3d), ΔSOM (36.5 m, blue bar), and ΔFOM (44.7 m, red bar). In comparison, H
increases by 1.1 km under the RCP8.5 scenario (purple bar in Figure 3d).

4. Conclusions
We have here examined the impact of future Arctic sea ice melting on the annual mean NH HC. Our findings
add to the large literature which has focused on the response of midlatitude circulation and the ITCZ to
Arctic sea ice loss (e.g., Barnes & Polvani, 2015; Barnes & Screen, 2015; Deser et al., 2015, 2016; Oudar et al.,2017; Peings & Magnusdottir, 2014; Screen et al., 2018; Sun et al., 2015; Smith et al., 2017; Tomas et al.,2016; Wang et al., 2018). Given the importance of ocean-atmosphere coupling in carrying the Arctic signal to
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lower latitudes, we used a hierarchy of model configurations (atmosphere only, slab ocean, and fully coupled
ocean-atmosphere) to simulate the Arctic sea ice state at the end of the 20th and 21st centuries.
We have found that the strength and poleward edge of the NH HC respond to Arctic sea ice loss only when
accounting for ocean-atmosphere coupling. In response to Arctic sea ice loss, the warming of the NH due
to thermodynamic ocean-atmosphere coupling increases the tropopause height, resulting in a northward
shift of the NH HC edge. The NH warming also increases the latent heating and decreases eddy momentum
fluxes, which together weaken the NH HC.
Dynamic ocean-atmosphere coupling, however, acts to cool the NH, which reduces latent heating, and cancels most of the NH HC weakening. The cooling induced by ocean heat transport changes also reduces theincrease in tropopause height, which together with the weakening of the eddy momentum fluxes overcomes
the thermodynamic northward expansion and acts to contract the NH HC. This contraction opposes theoverall projected widening in response to RCP8.5 radiative forcing by ∼ 40%. Hence, the melting of Arctic
sea ice acts as a negative internal feedback in the response of the tropical circulation to increased greenhousegases. This adds to the findings of previous studies and provides one more instance of Arctic sea ice loss
causing the atmospheric circulation to oppose its projected response, mostly through changes in ocean heattransport (e.g., Deser et al., 2015, 2016).
Our findings also confirm the results of previous studies which investigated the effects of high-latitude
forcing on the HC. In particular, previous studies showed that in both slab and full-depth ocean models
warming (cooling) the surface in NH high latitudes, in comparison to SH high latitudes, also results in aweakening (strengthening) of the HC (e.g., Chiang & Bitz, 2005; Green & Marshall, 2017; Kang et al., 2009).
More importantly, as previously reported, the effects of Arctic sea ice loss at lower latitudes occur throughocean-atmosphere coupling (e.g., Chiang & Bitz, 2005; Deser et al., 2015, 2016; Green & Marshall, 2017;
Tomas et al., 2016; Wang et al., 2018): This highlights the importance of accounting for this coupling whenassessing the response of the climate system to anthropogenic forcing (e.g., Armour et al., 2016; Chemke &Polvani, 2018; Deser et al., 2016; Lu & Zhao, 2012; Singh et al., 2017; Winton, 2003).
Ocean-atmosphere coupling not only affects the annual mean response of the HC but its seasonality as well.
The seasonality of the HC response is similar to the annual mean response, since sea ice loss occurs acrossall seasons (Deser et al., 2015). The magnitude of the response, however, does vary across seasons due tothe seasonal cycle of sea ice and the response time of ocean-atmosphere coupling. In future work we plan
to examine the effect of Antarctic sea ice loss on the HC, which was also found to result in atmosphericcirculation changes that oppose their response to increased greenhouse gases (England et al., 2018).
Acknowledgments
We thank Bob Tomas and Lantao Sun
for providing the data of thesimulations. R. C. is supported by the
NOAA Climate and Global Change
Postdoctoral Fellowship Program,administered by UCAR's Cooperative
Programs for the Advancement ofEarth System Science (CPAESS). LMP
is founded by a grant from the National
Science Foundation to Columbia
University. NCAR is sponsored by the
National Science Foundation.

CHEMKE ET AL.

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