Regime Transition between Eddy-driven and Moist-driven Circulationon High Obliquity Planets

Wanying KangSchool of Engineering and Applied Sciences Harvard University Cambridge, MA 02138, USA; wanyingkang@g.harvard.edu

Received 2019 June 11; revised 2019 August 11; accepted 2019 August 28; published 2019 October 14

Abstract

We investigate how the meridional circulation and baroclinic eddies change with insolation and rotation rate, underhigh and zero-obliquity setups, using a general circulation model. The total circulation is considered assuperposition of circulations driven by different physics processes, such as diabatic and adiabatic processes. Wedecompose the meridional circulation into diabatic and adiabatic components, in order to understand their differentresponses to changes of insolation and rotation rate. As insolation or rotation period increases, the meridionalcirculation tends to become more diabatically dominant, regardless of the obliquity. The low obliquity circulationis always dominated by diabatic processes, while the high obliquity configuration has two circulation regimes: anadiabatic-dominant regime in the limit of low insolation and fast rotation, and a diabatic-dominant regime in theopposite limit. This regime transition may be observable via its signature on the upper atmospheric zonal wind andthe column cloud cover. The momentum-driven circulation, the dominant circulation component in the weak-insolation and fast-rotating regimes is found to resemble that in a dry dynamic model forced by a reversedmeridional temperature gradient, indicating the relevance of using a dry dynamic model to understand planetarygeneral circulations under high obliquity.

Unified Astronomy Thesaurus concepts: Planetary atmospheres (1244); Exoplanet atmospheres (487); Exoplanetatmospheric variability (2020)

1. Introduction

While single column radiative convective equilibrium (RCE)models capture many dominant features of a climate system,they ignore the horizontal inhomogeneity, an important factorinvolved in most climate feedbacks. For example, theactivation of ice-albedo feedback is controlled by the lowest,rather than the average, surface temperature over the globe, andthe former is to a large extent affected by the temporal andspatial distribution of insolation, and the horizontal heattransport (e.g., Yang et al. 2014; Linsenmeier et al. 2015).Cloud cover and its radiative effects could change completelywhen the general circulation changes (Wang et al. 2016;Kang 2019a). Therefore, 3D general circulation models(GCMs) are necessary in order to account for these feedbackscorrectly.

High obliquity planets are expected to widely exist in theuniverse. In our solar system, for example, Mars has anobliquity chaotically varying from 0° to 60° (Laskar &Robutel 1993), and Venus and Uranus have obliquities closeto 180° and 90°, respectively (Carpenter 1966). Exoplanetsmay have a large obliquity or large obliquity variance,depending on the initial angular momentum of the nebulaethat formed the planet, continental movement (Williams et al.1998), gravitational interaction with other bodies (Correia& Laskar 2010), the history of orbital migration (Brunini2006) and the secular resonance-driven spin–orbit coupling(Millholland & Laughlin 2019).

Obliquity is one of the orbital factors that are missed in thesingle column picture. Although obliquity has no effect on theglobal-annual-mean insolation, it may have contributed tosetting the timing of the transitions between glacial and inter-glacial states during Pleistocene (Huybers & Wunsch 2005;Schulz & Zeebe 2006), especially via nonlinear phase locking(Tziperman et al. 2006). Under high obliquity, exoplanets are

found in GCMs to remain habitable under much lowerinsolation than their low obliquity equivalents (Armstronget al. 2014; Linsenmeier et al. 2015; Kilic et al. 2017, 2018;Rose et al. 2017), because permanent ice tends not to formunder high obliquity, (Linsenmeier et al. 2015; Kilic et al.2018), giving rise to lower planetary albedo. The moistgreenhouse state (Kasting & Pollack 1983) is more likely tooccur under high obliquity, due to the strong seasonal cycle andthe changes of the stratospheric circulation, ending thehabitable zone before the runaway greenhouse kicks in(Kang 2019b). Within the habitable zone, high obliquity statestend to be warmer than low obliquity states with all otherparameters fixed (Jenkins 2003), because ice cover is low(Linsenmeier et al. 2015; Kilic et al. 2018) and because clouds(surface temperature) lag behind the substellar point due to thesurface heat inertia, both leading to ineffective sunlightreflection (Kang 2019a).Meridional circulation and baroclinic eddies are crucial to

the understanding of climate. They carry heat, shaping thesurface temperature distribution, while the vertical motionscontrol cloud formation, affecting the planetary albedo. Cloudsmay be observable (e.g., Demory et al. 2013). Our purpose hereis to understand how the meridional circulation and barocliniceddies respond to changes in insolation, rotation rate andobliquity, and to find out potential ways to observe suchchanges. As far as we know, we are the first to investigate theresponse of the high obliquity meridional circulation to orbitalparameters, and also the first to understand the responsethrough circulation decomposition.The atmospheric general circulation under low obliquity has

been thoroughly studied in the Earth’s context. While for highobliquity planets, Linsenmeier et al. (2015), Kilic et al. (2017),and Kilic et al. (2018) simulated the atmospheric meridionalcirculation in both annual-mean and solstice season, but the

The Astrophysical Journal, 884:89 (13pp), 2019 October 10 https://doi.org/10.3847/1538-4357/ab3fa2© 2019. The American Astronomical Society. All rights reserved.

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https://orcid.org/0000-0002-4615-3702https://orcid.org/0000-0002-4615-3702https://orcid.org/0000-0002-4615-3702mailto:wanyingkang@g.harvard.eduhttp://astrothesaurus.org/uat/1244http://astrothesaurus.org/uat/487http://astrothesaurus.org/uat/2020http://astrothesaurus.org/uat/2020https://doi.org/10.3847/1538-4357/ab3fa2https://crossmark.crossref.org/dialog/?doi=10.3847/1538-4357/ab3fa2&domain=pdf&date_stamp=2019-10-14https://crossmark.crossref.org/dialog/?doi=10.3847/1538-4357/ab3fa2&domain=pdf&date_stamp=2019-10-14

circulation pattern is yet to be understood and how thecirculation changes with other orbital parameters is yet to beexplored. Kang et al. (2019, hereafter KCT) reversed themeridional temperature gradient in a dry dynamic core model,as inspired by Ferreira et al. (2014), to capture the key featureof high obliquity climate, and found that the meridionalcirculation under high obliquity becomes weak, bottomamplified, and found a thermally indirect Hadley after takingthe annual average. These features can be deduced from thefact that the baroclinic structure is bottom amplified, asexplained by a 1D linear baroclinic instability model (KCT).However, the relevance of such an idealized model study to thereal high obliquity world has not been shown, and that isanother main objective of this work.

In this study, we gradually change the insolation and rotationrate in a GCM, in order to study how the meridional circulationand baroclinic eddies respond, and to find potential observa-bles. The paper is organized in the following way. In Section 2,we introduce the 3D GCM setup, as well as a method used todecompose the meridional circulation into contributions bydifferent physics processes. Results are presented in Section 3.We first give an overview of the two-regime behavior(Section 3.1), then understand the high obliquity circulationpattern by connecting our finding to the previous dry modelstudy (KCT; Section 3.2), and finally provide some potentialobservables (Section 3.3). In Section 4, we summarize ourresults.

2. Methods

2.1. Models

The model used here is modified by Kopparapu et al. (2017,code are available on GitHub1) based on the Community EarthSystem Model version 1.2.1 (CESM, Neale et al. 2010), toinclude mainly the following two features: (1) more realisticradiation calculation resulting from increased spectral resolu-tion, updated spectral coefficients based on the HiTran 2012database (Rothman et al. 2013), and a new continuum opacitymodel (Paynter & Ramaswamy 2014), and (2) more frequentsub-step dynamic adjustment to improve numerical stability.The radiation transfer model does not include the CO2absorption, and thus we consider here an atmosphere madeof 1 bar N2 and condensible water vapor. Thanks to the finespectral resolution, this radiation scheme was shown to be morerobust at the high temperature end and to remain stable withglobal mean surface temperatures beyond 360 K (Kopparapuet al. 2017), while the default CESM radiative transfer modelunderestimates both longwave and shortwave water vaporabsorption (Yang et al. 2016). Other parameters are set to thevalues on Earth unless otherwise mentioned. The atmosphericcirculation is simulated by a finite-volume dynamic core, withapproximately 1°.9 horizontal resolution and 40 vertical layersextending to 0.8 mb. This atmosphere model is coupled with a50 meter deep slab ocean. Horizontal ocean heat transport isignored for simplicity, and it was also shown in Jenkins (2003)to play a minor role in the surface temperature, compared to therole of the large changes in obliquity. Sea ice is simulated usingCommunity Ice CodE (CICE) version 4, part of CESM 1.2.1.

We gradually increase the insolation under 0 deg obliquitysetup (OBL0-S) and under 80 deg obliquity setup (OBL80-S),

respectively. We attempt to cover the entire habitable range,with the lowest insolation corresponding to an almost snowballstate and the highest insolation corresponding to an almostrunaway greenhouse state. For zero-obliquity experiments, wevary the insolation from 1360 to 1760Wm−2 in 80 yr; and forhigh obliquity, from 1200 to 1750Wm−2 in 110 yr. There ismore than one equilibrium climate state for the part of theinsolation range we use here due to the positive ice-albedofeedback. By increasing the insolation instead of decreasing it,we here only explore the colder branch. Similar behavior isexpected for the warm branch.We also investigate the effects of the rotation rate, by

exploring the rotation rate from 5 times to 0.2 times the Earth’srotation rate. These experiments will be referred to as OBL0-Ωand OBL80-Ω, with the number following “OBL” to be theobliquity used in the simulation. Insolation is chosen to be1550Wm−2 and 1360Wm−2 for OBL80-Ω and OBL0-Ω,respectively, in order to maximize the probability of identifyinga regime transition (it turns out that the regime transition occursat these insolation levels in OBL0-S and OBL80-S; the reasonfor these choices will be clarified later). We initialize the modelusing the restart files from OBL0-S/OBL80-S simulationswhen the insolation reaches these levels, and increase anddecrease the rotation rate to 5 times and 0.2 times earth rotationrate in 40 yr, in order to keep the climate on the same branch asin OBL0-S and OBL80-S.The memory timescale of a slab ocean simulation can be as

high as 5–10 yr due to the high heat content in the ocean. Todemonstrate that the transient experiments almost reach theequilibrium state, we increase the insolation twice as fast, andfind the evolution of the surface temperature does not changesignificantly for most of the regime we explored (Figure 12(a)).The largest disagreement shows up toward the end of thetransient simulations. In particular, the high obliquity global-annual-mean surface temperature is about 20K warmer in theslow transient simulations compared to the fast one. We thenrun two steady-state simulations at 1750Wm−2 under low andhigh obliquity, respectively, and compare the steady-statetemperature field (Figures 12(e)–(g)) with that from the slowtransient simulations (Figures 12(b)–(d)). The similarityindicates that the slow transient simulations are almost inequilibrium state.We will also briefly refer to results from KCT using a dry

dynamic core model. This model is a Held–Suarez type model(Held & Suarez 1994), where the 3D Navier–Stocks equation isintegrated with temperature restored to a prescribed equilibriumstate. In KCT, we ran the dry model with the default setup as inHeld & Suarez (1994), and with a reversed the meridionaltemperature gradient (the poles are warmer than the equator).The case with a reversed temperature gradient was used tostudy the basic dynamics of high obliquity climate, as highobliquity planets receive more radiation over the pole than theequator on annual average.

2.2. Decomposing the Meridional Circulation

The meridional circulation dominantly driven by adiabaticprocesses is different from that driven by diabatic processes,and may have different observable consequences. Thus we tryto decompose the meridional circulation and understand thetwo regimes. We reconstruct the circulation associated withdiabatic/adiabatic processes by solving the Kuo–Eliassenequation (Kuo 1956; Chang 1996).

1 https://github.com/storyofthewolf/ExoRT and https://github.com/storyofthewolf/ExoCAM.

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The Astrophysical Journal, 884:89 (13pp), 2019 October 10 Kang

https://github.com/storyofthewolf/ExoRThttps://github.com/storyofthewolf/ExoCAMhttps://github.com/storyofthewolf/ExoCAM

The derivation of the Kuo–Eliassen equation is sketched herefor reference. Starting with the temperature and zonalmomentum equation averaged over ( )d+t t t, ,

( ) ( ) ¯ ¯ ( ¯ )

¯ ( ) ( ) ( )

dd q

q

qq w

+ -- = - ¶

- W¶ - ¶ ¢ ¢ - ¶ ¢ ¢ +

q

q

u t t u t

tfv

v

au

ua

u v u F

coscos

1

coscos 1p p2

2

( ) ( )¯ ¯ ¯

( ) ( ) ( )

dd

w

qq g g w

+ -- = - ¶

- ¶ ¢ ¢ - ¶ ¢ ¢ +

q

q-

T t t T t

tS

v

aT

av T T

Q

C

1

coscos , 2

p

pp

1

where F is the friction term, Q is the diabatic heating,¯

g= - ¶Q¶

Sp p is the static stability,¯ ¯ gQ = T , and ( )g = kp p0 .

(·) denotes seasonal climatology (the time derivative terms maynot vanish with a seasonal cycle), and prime denotesdeviations. Time average transfers the time derivative into thechanges during the time interval divided by the time interval(the first term in each equation). They are not necessarily smallwhen the time interval is a particular season. We cancel the twothese time derivative terms using the thermal wind balance,

¯ ¯= qpfu R aTp , and represent v̄ and w̄ with the meridionalstreamfunction defined below, to find

advective terms

⎛⎝⎜

⎞⎠⎟

⎛⎝⎜

⎞⎠⎟

( )

( ) ( )

( )

yq

q qyq

qq

qq

w

qq

qq

g q w qq

qg q

q

¶¶

+¶¶

¶¶

= -¶ ¢ ¢

¶ ¶-

¶ ¢ ¢¶

-¶¶

¶ ¢ ¢¶

-¶ ¢ ¢¶ ¶

+¶¶

+¶¶

+

q

f pp

R

a

S

f p

a

u v

pf p

u

p

a

v T R

a p

f pF

p

R

C a

Q

coscos

cos

coscos

cos 1

cos

cos cos

coscos

,

3

p

p

22

2 2

2

2

2 22

2

2

2

2

2

advective terms ⎜ ⎟⎛⎝

⎞⎠¯

¯

( ¯ ¯ ) ( ¯ ¯ ) ( )

qq

q wq

q

= -¶¶

¶¶

-¶¶

-¶¶

q

f p

a pv

u

f pp

ua

vT

cos

coscos

, 4p

2

22

where R is gas constant, a is the earth radius, and ψ is themeridional streamfunction defined as below:

¯ ( )q

y=

¶¶

vp

1

cos5

¯ ( )wq

yq

= -¶¶a

1

cos. 6

We solve for ψ forced by each individual term on the right-hand side (rhs) to decompose the meridional circulation. Sincethis is a Poisson equation, any initial ψ will finally converge tothe solution if it is updated using the tendency rhs–lhs.

Note again that by invoking the thermal wind balance, wenaturally have the time drift terms in Equations (1) and (2)canceled out without assuming ( ) ( ) ( )d d+ - = + -u t t u t T t t

( ) =T t 0. This allows us to decompose the meridional circulationfor one particular season. Also, because of the invoking of thethermal wind balance, the nonlinear advection terms of u and T

(Equation (4)) is also canceled to a large extent, as will be verifiedin the results section.The total meridional circulation is also diagnosed here from

a different perspective, by taking vertical integral of meridionalvelocity in pressure coordinate.

¯ ( ) ( )òyp q

= ¢ = -a

gv dp

2 cosunit: Sv 10 kg s . 7

p

0

9 1

To match the units of the previous calculation, the solution ofEquation (3) is multiplied by a factor, pa g2 . We then definethe projected circulation index (PCI) to evaluate how much ofthe total circulation is driven by a specific forcing component,by projecting the solution of Equation (3), ψ( i), onto thenormalized total streamfunction, ∣ ∣y y , from Equation (7):

( ) ( )

( )( )( )

( )ò ò

ò ò

y q y q q

y q qY =

p p d dp

p d dp

, ,

,, 8i

i

proj2

where i denotes the component being evaluated. In thediabatic/adiabatic decomposition, i could be the “diabatic”component forced by term associated with Q, or the “adiabatic”component forced by eddy transport terms and friction F (seeEquation (3)), or “advective” component forced by the terms inEquation (4). In the thermal/momentum decomposition, icould be the “thermal” component forced by the termsoriginated from the temperature equation (including the onesassociated with w q¢ ¢ ¢ ¢v T , and Q), or the “momentum”component forced by the terms originated from the momentumequation (including the ones associated with ¢ ¢u v , w¢ ¢u and F),or the “advective” component, whose definition is the same asbefore.If removing the square root in the denominator of

Equation (8), each ( )Y iproj would represent the percentage oftotal meridional streamfunction explained by a specificcomponent, and the sum of them would be 1. We, instead,multiply an additional factor ( )ò òy q qp d dp,2 to the abovedefinition, so that PCIs have the units of a streamfunction. Thisway, the relative magnitude of PCIs associated with differentphysical processes for a given climate state represents therelative importance of these processes, and meanwhile, thePCIs for a specific physical process can be compared acrossdifferent climate states to tell how the circulation strengthchanges.Equation (3) formulates a framework for evaluating the

meridional circulation driven by any specific momentum orthermal forcing. Except the circulation driven by the advectionterm (Equation (4)), solving it requires almost no knowledge ofthe climatological state ū and T̄ . The physical picture is asfollows. The planetary rotation creates a meridional gradient ofangular momentum (M̄ ), and latent heating release creates avertical gradient of potential temperature (Q̄). M̄ and Q̄conservations constrain air parcels from moving in themeridional plane without external momentum or thermalforcing. The solution of Equation (3) will be able to exactlycounterbalance the external forcings, while satisfying bothmass continuity and thermal wind balance. ū and T̄ areimplicitly determined: one can substitute Ψ back toEquations (2) and (1), and solve for ū and T̄ , provided properboundary conditions. For any given external forcing, there willbe such a pair of ū and T̄ , automatically satisfying the thermal

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wind relationship. When solving for a different externalforcing, the corresponding ū and T̄ will also change. This isan indication that the decomposition is not “clean.” Fullydecomposing the interactions among the mean circulation, theeddies and the diabatic terms is not possible.

3. Results

The results section is divided into two parts. We first show inSection 3.1 that on high obliquity planets, the meridionalcirculation has two regimes: an adiabatic-dominant/momen-tum-driven regime in the limit of low insolation and fastrotation, and a diabatic-dominant/thermal-driven regime in thelimit of high insolation and slow rotation. We then understandthe circulation by comparing it against the circulation in theidealized dry dynamic core model study by KCT in Section 3.2.Despite the sophisticated physics processes involved in theGCM here, the baroclinic eddies and the circulation driven inthe adiabatic-dominant regime share many common character-istics with those in the dry model, which, in turn, was shown tobe predicted by a 1D linear baroclinic instability model (KCT).We end with potentially observable diagnosis, including theupper atmospheric jet and the cloud distribution, discussed inSection 3.3.

3.1. Two-regime Behavior of the Meridional Circulation

The adiabatic and diabatic processes respond to externalforcings (such as orbital parameters) in different manners,despite the close coupling between them. This motivates us todistinguish between their roles in driving the meridionalcirculation. The diabatic processes include the radiative andlatent heating, and the latter enhances with temperature andthus insolation. The adiabatic processes, on the other hand,include friction and eddy transports, whose pattern andamplitude can be strongly affected by the rotation rate. Wehere investigate how the adiabatically driven and diabatically

driven meridional circulations change with insolation androtation rate.The circulation at different insolations. We measure the

circulation contributed by diabatic and adiabatic processes withthe PCI (Equation (8)) as insolation increases. The square rootof PCIs of the diabatic and adiabatic circulations under highobliquity are shown in Figure 1(a) for the annual mean, and inFigure 2(a) for boreal winter (Dec., Jan., Feb.; hereafter, DJF)season. For both seasons, the meridional circulation has tworegimes, with a transition near 1550Wm−2. In the lowinsolation end, the PCI of the adiabatic component is aroundfour times greater than that of the diabatic component, meaningthat adiabatic processes contribute four times more circulationthan diabatic processes, consistent with KCT. The dominanceof the adiabatic-driven circulation can also be clearly seen inthe circulation streamfunctions (panels (b), (c)). In the highinsolation end, the ratio reverses—diabatic processes contributefour times more than the adiabatic processes, as demonstratedin panels (e), (f).Under low obliquity, the diabatically driven circulation

always dominates in the tropics and adiabatically drivencirculation dominant elsewhere (Figure 3(a)). This is consistentwith the understanding of the atmospheric general circulationon Earth (Pfeffer 1987), but contradicts the results in drydynamic core study (KCT), where the adiabatic processes werefound to be dominant everywhere. This inconsistency occursprobably because the latent heating is fully represented in aHeld–Suarez type restoring physics.One common feature that is evident in all cases is that the

diabatic-driven circulation enhances significantly with insola-tion, whereas the amplitude of the adiabatic-driven circulationremains almost constant. Adiabatic processes include surfacefriction and eddy heat/momentum transport, none of which isdirectly affected by the insolation, explaining the lack ofsensitivity of adiabatic-driven circulation to insolation. How-ever, diabatic processes, composed of radiative heating/cooling and latent heating, are highly sensitive to insolation.

Figure 1. Regime transition of annual-mean meridional circulation as varying insolation for OBL80-S experiment. (a) The projected circulation index (PCI, defined inEquation (8)) as a function of insolation. The contribution from a specific component is measured by projecting the associated meridional streamfunction over the totalstreamfunction, and taking the sum over all grid points (see methods section for details). We show the sign preserved square root of PCIs ( ∣ ∣ · [ ]PCI sign PCI ), inorder to zoom in the regions with low PCI. Panels (b), (e), panels (c), (f), and panels (d), (g) are the meridional circulation driven by adiabatic processes, diabaticprocesses, and the total meridional streamfunction, respectively, plotted as a function of pressure and latitude. Panels (b)–(d) are for 1250 W m−2 insolation, andpanels (e)–(g) are for 1750 W m−2. Red indicates clockwise circulation and blue indicates counterclockwise circulation.

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Figure 2. Same as Figure 1, but for the boreal winter season (DJF).

Figure 3. Same as Figure 1, but for the zero-obliquity experiment (OBL0-S). Red indicates clockwise circulation and blue indicates counterclockwise circulation.

Figure 4. Same as Figure 1, except self rotation rate instead of insolation is varying here. Red indicates clockwise circulation and blue indicates counterclockwisecirculation.

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The Astrophysical Journal, 884:89 (13pp), 2019 October 10 Kang

Radiative heating/cooling rises proportionally to the insolationmagnitude, given a fixed latitudinal insolation profile. Latentheating surges up with temperature following the Clausius–Clapeyron relation.

The circulation at different rotation rates. We vary theplanet’s rotation rate, with insolation fixed at 1360 (1550)Wm−2 for the low (high) obliquity scenario, as this is the levelwhere the adiabatic and diabatic-driven circulations havesimilar magnitudes in OBL0-S and OBL80-S. The PCIs foradiabatic and diabatic-driven circulation are shown inFigures 4(a) and 5(a) for the high obliquity annual-mean andDJF season, and in Figure 6 for the low obliquity circulation.

The meridional circulation should get weaker and narrowerwith rotation rate, following Held–Hou scaling (Held &Hou 1980) or Held-2000 scaling (Held 2000). As expected,under high obliquity, both the diabatically and adiabaticallydriven circulations weaken with rotation rate (Figures 4(a) and5(a)). Thus the regime transition is less clear compared to that

in OBL80-S. Transition disappears for the DJF meridionalcirculation (Figure 4).Under low obliquity, the circulation response to rotation rate

change is not monotonic. The diabatic-driven circulation, inparticular, first weakens then strengthens, with a minimumaround one times the earth rotation rate (Figure 6(a)). Theadiabatic-driven circulation responds in a much subtler manner.The weakening of circulation with rotation rate is expected, asexplained above. The strengthening instead is associated withthe low-latitude melting. Fast rotation prohibits poleward heattransport beyond tropics (not shown), and leads to surfacewarming in the low latitudes, which in turn melts the tropicalsea ice, triggers convections and strengthens the circulationwithin tropics.The PCI of advection terms (Equation (4)) is plotted as a thin

black curve in panel (a) of Figures 1–3. It is substantiallysmaller than either diabatic or adiabatic PCI for mostcircumstances, and it is therefore negligible. We have

Figure 5. Same as Figure 2, except self rotation rate instead of insolation is varying here. Red indicates clockwise circulation and blue indicates counterclockwisecirculation.

Figure 6. Same as Figure 3, except self rotation rate instead of insolation is varying here. Red indicates clockwise circulation and blue indicates counterclockwisecirculation.

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The Astrophysical Journal, 884:89 (13pp), 2019 October 10 Kang

examined that the sum of the circulation forced by eachindividual component reproduces the total meridional circula-tion diagnosed by vertically integrating v (see the right twocolumns of Figure S7–12 in the supplementary figure filewhich is available fromhttps://www.dropbox.com/s/nsext5lc90hw6qe/supplementary_figures_high_obliquity_S0_Omega3.pdf?dl=0 or from Harvard dataversehttps://doi.org/10.7910/DVN/3JVBOS).

Another interesting decomposition is to separate thecirculation driven by eddy momentum transports and frictionfrom that driven by thermal effects (eddy heat transports anddiabatic heating). The same figures for the momentum/thermaldecomposition is availablehttps://www.dropbox.com/s/nsext5lc90hw6qe/supplementary_figures_high_obliquity_S0_Omega3.pdf?dl=0 (Figures S1–6), all of the above conclusionsstill hold, except that the momentum-driven circulation tends toplay a more important role in the annual mean than during DJF.

3.2. Understanding the Circulation Structure Changes Nearthe Transition Point

The circulation regime transition under high obliquity isaccompanied by the changes of the circulation structure. In thissubsection, we try to understand the dynamics driving thedifferent circulations. We particularly focus on the adiabatic/momentum-driven component, because it shows richer beha-vior than simply rising at warm latitudes and sinking at coldlatitudes, as it is for the diabatic/thermal component. The mainmessage here is that the eddies and the meridional circulation inthe high obliquity scenario resemble those in a dry dynamiccore model forced by a reversed meridional temperaturegradient used in KCT, and thus the dry model provides usefulinsights to understand the high obliquity climate.

Circulation structure’s response to insolation. Figures 7(a)–(c) show the momentum-driven2 circulation under differentinsolations. In panel (d), the total meridional circulation in thereverse gradient dry model used in KCT is reprinted to becompared with the circulation the realistic high obliquitysimulations here. Below 1670Wm−2, the momentum-drivencirculation under high obliquity remains remarkably similar tothat in the dry model. Both are characterized by a thermallyindirect cell within 45N/S, and a thermally direct cell in highlatitudes constrained near the surface. Since the momentum-driven circulation explains most parts of the total meridionalcirculation below 1550Wm−2 insolation, the total meridionalcirculations in this regime also resemble that in the dry model.The thermally indirect cell does not exist in most of the highobliquity simulations in Linsenmeier et al. (2015), probablybecause they constrain their simulation near the outer edge ofthe habitable zone, or because the baroclinic eddy activity isunderestimated due to the low resolution of their modeldecomposition.The similarity in the meridional circulation stems from the

similarity of baroclinic eddies, because eddies dominantly drivethe circulation.3

Shown in Figures 8(d)–(f) and (g)–(i), respectively, are theannual mean and DJF climatologies of ¢ ¢u v , ¢ ¢v T and w¢ ¢u under

Figure 7. Momentum-driven meridional streamfunction under different insolations. From (a) to (c), shown are for = -S 1250, 1670, 1730 W m0 2 in OBL80-S, andpanel (d) is the total meridional streamfunction in the dry dynamic core model with a reversed meridional temperature gradient. (e)–(g) are the same as (a)–(c) exceptfor DJF season. Momentum-driven circulation represents the circulation driven by meridional eddy momentum transport ¢ ¢u v , vertical eddy momentum transport w¢ ¢u ,and friction.

2 There is no unique “correct” way to decompose the circulation. To avoid thecancellation between the eddy heat transport and the diabatic processes, themeridional circulation here is decomposed into the momentum-driven andthermally driven components to avoid the cancellation between the eddy heattransport and the diabatic processes.3 Surface friction can also drive meridional circulation, however, it is slavedby the eddies. The surface wind will keep evolving until the surface friction canexactly counterbalance the column integrated eddy momentum conv-ergence ò ¶ ¢ ¢u v dpy .

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high obliquity forced by -1360 W m 2 insolation. They sharealmost all of the eddy characteristics with the dry model(Figures 8(a)–(c)). The similarity indicates that eddy character-istics are not qualitatively affected by the newly includedphysics processes (radiation, hydrological cycle etc.) and theseasonal cycle in ExoCAM. For both ExoCAM and the drymodel: ¢ ¢u v is concentrated near the surface rather than theupper troposphere as in the zero-obliquity situation(Figure 13(a)). ¢ ¢v T switches sign at the mid-troposphere,different from the zero-obliquity experiment which has twopeaks of the same sign (Figure 13(b)). w¢ ¢u is mostly positiverather than the opposite as in the zero-obliquity situation.

KCT attempts to understand the eddy characteristics using a1D linear baroclinic instability model, and explain why themeridional circulation is thermally indirect, shallow, and weakwith a reversed meridional temperature gradient using theseeddy characteristics. As discussed in KCT, eddies converge ina westerly momentum to the mid-latitude baroclinic zone,forming surface westerlies in the mid-latitudes and surfaceeasterlies elsewhere. The Ekman friction acting on the tropical

surface easterly leads to an upward motion and a thermallyindirect circulation in the tropics. Acceleration due to eddymomentum transport always counterbalances the surfacefriction; they together bound the vertical extension of themeridional circulation. Since the most unstable baroclinic modeis bottom amplified in the climatology of the reversed gradientcase, the circulation is shallower compared to the case with anormal meridional temperature gradient. Readers are referredto KCT for further details.The baroclinic eddy characteristics remain similar to that in

the dry model until 1670Wm−2, far beyond the circulationtransition point 1550Wm−2; so does the circulation driven bythese eddies. Beyond 1670Wm−2, the momentum-drivencirculation starts to become thermally direct from the bottom(Figure 7(c)). This circulation change coincides with thechanges of the baroclinic eddy features. The whole pattern ofw¢ ¢u shifts upward (not shown), consistent with Singh &

O’Gorman (2012). As a result, the westerly momentumaccumulation in the low latitudes peaks around 500 mb insteadof close to the surface, pushing the 500 mb air parcels

Figure 8. Eddy heat/momentum transports for (a)–(c) the dry dynamic model used in KCT, forced with reversed meridional temperature gradient, (d)–(f) the annualmean of 80° obliquity experiment, and (g)–(i) the DJF climatology of 80° obliquity experiment. All experiments are forced by = -S 1360 W m0 2. From left to right,shown are meridional eddy momentum transport ¢ ¢u v , meridional eddy heat transport ¢ ¢v T , and vertical eddy momentum transport w¢ ¢u .

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equatorward through Coriolis force, and leading to equatorialsink below that level.

The solstice meridional circulation under high obliquity is across-equator cell rising in the summer hemisphere and sinkingin the winter hemisphere, regardless of the insolation. Althoughthe circulation direction does not change, its vertical extensionincreases with insolation as the diabatic/thermal-drivencirculation expands to higher altitudes and starts to dominate(Figures 2(c), (f)). The adiabatic/momentum-driven circula-tion, on the other hand, is always limited below 300 mb (seeFigures 2(b), (e) for the adiabatic component and Figures 10(e)–(g) for momentum-driven component), until 1670Wm−2.Therefore, the vertical extension of the meridional circulationsuddenly starts to rise at 1550Wm−2, the transition point,where the diabatic/thermal component begins to dominate.

The shallowness of the adiabatic/momentum-driven circula-tion has its root in the shallowness of the baroclinic eddystructure, which can be seen from the meridional eddymomentum transport ¢ ¢u v in Figure 8(g). The DJF eddy heattransport ¢ ¢v T and vertical eddy momentum transport w¢ ¢u areshown together in panels (h) and (i). Even though the insolationdistribution during DJF is drastically different from that inannual mean, the eddies characteristics are not qualitativelydifferent from the annual mean (panels (d)–(f)), except that thesummer hemisphere has a stronger eddy activity. This is notsurprising given that the meridional surface temperaturegradient remains reversed in all seasons (Ferreira et al. 2014),and that the summer hemisphere has a stronger meridionalinsolation gradient and hence a stronger baroclinicity.

Circulation structure’s response to rotation rate. Themeridional circulation under high obliquity narrows with therotation rate, as seen in many low obliquity studies (e.g., Kaspi& Showman 2015). Concurrently, the annual-mean meridional

circulation also becomes more thermally direct (Figure 4). Thisis partially due to the rapid strengthening of the diabatic/thermal circulation component, and partially due to thetransition of the adiabatic/momentum-driven circulation froma thermally indirect one into a thermally direct one, which isshown in Figures 9(a)–(c). At five times Earth rotation rate, thecirculation is completely thermally indirect (i.e., rising at thecold, sinking at the warm). As rotation rate decreases,circulation expands meridionally, giving space to a thermallydirect circulation in the tropics. When the rotation rate dropsbelow 0.6 times earth value, the circulation becomes almostcompletely thermally direct. This change is mostly due to thereversal of vertical momentum transport w¢ ¢u (not shown). Atslower rotation rate, the upward westerly momentum transportin the tropics (Figure 8(f)) strengthens and expands, driving acirculation that sinks at the equator.

3.3. Observable Evidence for the Regime Transition UnderHigh Obliquity

The regime transition seen in the high obliquity simulations(OBL80-S and OBL80-Ω) has observable consequences.Regime transition due to insolation—Figure 10(a) shows the

10 mb zonal wind as a function of latitude and insolation. Zerowind speed is denoted by a black contour. Below the transitionpoint of 1550Wm−2, the extratropical zonal wind is mostlyeasterly, while the equatorial zonal wind in the upperatmosphere switches direction with season: westerlies prevailthe first half of a year and easterlies prevail the second half(Figure 10(b)). Beyond the transition point, upper air easterliesget stronger in most latitudes except the polar regions(Figure 10(c)). The strengthening of the tropical easterly acrossthe transition point is expected given a more thermally directmeridional circulation. As the poleward flow in the tropical

Figure 9. Same as Figure 7, but for different rotation rates. From left to right shown are Ω=5, 1, 0.6/earth day in OBL80-Ω. Upper panels are for annual mean, andlower panels are for DJF season.

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upper atmosphere is replaced by an equatorward flow(Figure 1(g)), extratropical air parcels with low angularmomentum are pumped toward the equator, accelerating theequatorial air near the tropopause toward the west. Startingfrom a more easterly base, the wind above will also be moreeasterly with a given meridional temperature gradient (thethermal wind balance constrains the vertical wind shear), unlessthere is a compensating momentum flux converging westerlymomentum back to the equator again. As demonstrated by theanalysis in Showman et al. (2012), different upper air windpatterns may be distinguishable in the transit phase curve,especially with the help of the future missions, such as JamesWebb Space Telescope, which can better resolve the infraredspectrum.

The vertically integrated cloud cover is shown inFigure 10(d). Below the transition point, the cloud cover ishigh (greater than 80%) all year round (Figure 10(e)). Thehighest cloud cover is located in the subtropics, supported bythe upward motion there (Figure 1(g)). Only outside thetropics, does cloud cover show a strong seasonal variation,oscillating between almost 0% and 80%. Beyond the transitionpoint, all latitudes show a strong seasonal variation, includingthe tropics (Figure 10(f)). In other words, the tropical cloudcover drops. This is expected given that the equatorial verticalmotion turns from upward to downward (Figure 1(g)). Thepeaks of the cloud cover through all seasons now move to45N/S, happening after the summer solstice. This temporalhigh cloud cover near 45N/S is supported by the strongupward motion there (Figure 2(g)). Cloud cover may bedetected through the albedo measurement (e.g., Demory et al.2013).

Regime transition due to rotation rate—Similar regimetransition of the annual-mean meridional circulation is alsoseen when changing rotation rate. Figure 11(a) shows the10 mb zonal wind as a function of rotation rate and latitude. Asthe meridional circulation expands meridionally (Figure 4), thewind pattern also expands. In addition, the tropical easterlyweakens, and finally starts to oscillate between easterly andwesterly when the rotation rate is lower than that of the earth

(Figure 11(a) upper parts). These changes can be understood asfollows. As circulation becomes more thermally direct at aslower rotation rate, more extratropical air with low angularmomentum is transported equatorward. However, this does notlead to a stronger equatorial easterly as it does in OBL80-S,because the meridional gradient of the planetary angularmomentum, which is induced by the self rotation, alsodecreases proportionally. As a result, the wider, stronger, andthermally direct meridional circulation at slow rotation rateends up transporting less easterly momentum equatorward.This may allow us to distinguish whether a thermal indirect(direct) circulation is induced by low (high) insolation or byfast (slow) rotation rate. A seasonal cycle of the upperatmospheric zonal wind is shown in Figures 11(b), (c) for thetwo most extreme conditions. In the fast rotating end, easterlywind is constrained within 30N/S, and the speed peaks in thelate spring (Figure 11(b)). In the slow rotating end, seasonalvariation is weak and wind tends to have a period longer thanone year (Figure 11(c), we verified this multi-year oscillation ina steady-state simulation), which might be similar to theequatorial eddy-mean flow interaction like the equatorial quasi-biennial oscillation on Earth.Figure 11(a) shows the cloud cover as a function of latitude

and rotation rate. Like the circulation and the wind pattern, thecloud pattern also expands meridionally as rotation ratedecreases. In the fast rotating end, the meridional circulationis dominated by adiabatic processes, with an annual-meanupward motion above the equator (Figure 4(g)). Supported bythis upward motion, the equatorial cloud cover is over 80% allyear round (Figure 11(e)). In the slow rotating end, as thecirculation becomes more diabatic-dominant, downwardmotions take over the equator (Figure 4(d)), and the equatorialcloud cover decreases in general. Concurrently, the meridionalcirculation becomes more seasonal varying (the ratio of theDJF circulation amplitude in Figure 5(a) over the annual-meancirculation amplitude in Figure 4(a) is larger when rotation isslow), and therefore the cloud cover also shows a strongerseasonal cycle.

Figure 10. The observables for the regime transition in OBL80-S. (a)–(c) are for the 10 mb zonal wind, and (d)–(f) are for the vertically integrated cloud cover. (a) and(d) show the whole progression of the zonal wind and cloud as insolation increases. While, (b), (e) and (c), (f) zoom in and show the seasonal cycle at the beginningand the end of the OBL80-S simulation, which corresponds to 1250 and 1750 W m−2 insolation. Zero wind speed is denoted with black contours in (a)–(c).

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4. Conclusions

In this work, we use a state-of-the-art GCM to investigatehow the meridional circulation and baroclinic eddies changewith insolation and rotation rate, under both high and zeroobliquity, and to find potential observable consequences ofthese changes. We separated the meridional circulation drivenby adiabatic processes from that driven by diabatic processes,to be able to study their different characteristics and responsesdifferently to changes in insolation and rotation rate.

We found a regime transition of the meridional circulationsin the high obliquity scenario when changing the insolation orthe rotation rate, and the regime transitions have observablesignatures in upper atmospheric wind and cloud cover. In thelimit of low insolation and fast rotation, the adiabatic processesand the momentum drag dominantly drive the meridionalcirculation (the adiabatic/momentum dominant regime); whilein the opposite limit, the diabatic processes and the thermalforcing dominate (the diabatic/thermal dominant regime).Fixing the rotation rate at 1 times the Earth rotation rate, theregime transition occurs when the insolation exceeds 1550 and1600Wm−2 for the solstice circulation and the annual-meancirculation, respectively, marked by a sudden strengthening ofthe tropical easterly in the upper atmosphere and a sudden dropof the tropical cloud cover. Fixing the insolation at1550Wm−2, the transition occurs around 0.7–1 times theEarth rotation rate as the rotation rate decreases, accompaniedwith a similar reduction of tropical cloud cover, but aweakening of the upper atmospheric easterly. The observablesignatures of the changes of the insolation and the rotationrate may be distinguishable, because unlike the cloud cover, theupper atmospheric zonal wind is affected by not only themeridional circulation but also the planet’s rotation rate.Therefore, observing both the cloud cover and the upperatmospheric zonal wind may help distinguish high (low)insolation from slow (fast) rotation. Under low obliquity, thediabatic/thermal circulation component always dominates inall of the parameter combinations we explored, consistent withthe understanding of the Earth’s climate (Pfeffer 1987).

Another key result is that the dry dynamic core model forcedby a reversed meridional temperature gradient in KCT can

explain most of the characteristics of the baroclinic eddies andthe momentum-driven meridional circulation in the realistichigh obliquity experiments. The baroclinic eddies under highobliquity are shallow and bottom amplified, driving ameridional circulation that is also shallow. In the regime thatthe adiabatic processes dominate, this characteristics arereflected in the total circulation. Therefore, the dry modelstudy (KCT) provides useful insights to the understanding ofthe high obliquity general circulation, especially the circulationon cool and fast-rotating planets.This work proposes potential pathways to observe the

circulation regime transition, and more needs to be done toevaluate the phase curves under different situations andcompare it with the instrumental accuracy. For simplicity, wehere do not discuss or explore the multiple equilibrium states.By gradually increasing the insolation, and reducing therotation rate, we keep the model in the cold branch. Morework is needed to examine whether the two-regime behavioralso exists in the other branch. Also, water vapor is the onlystrong greenhouse gas considered in the radiation scheme usedhere, and the robustness of our results to atmosphericcomposition needs to be examined.

The author thanks Professor Eli Tziperman and ProfessorMing Cai for the insightful and helpful discussion. This workwas supported by NASA Habitable Worlds program (grantFP062796-A/NNX16AR85G) and NSF climate dynamicsAGS-1622985. We would like to acknowledge high-perfor-mance computing support from Cheyenne provided byNCAR’s Computational and Information Systems Laboratory,sponsored by the National Science Foundation. The relevantmodel outputs are archived inhttps://www.dropbox.com/sh/ugkmaw4kjupx91a/AACXnBEylRoqyx2iqfe9QAH9a?dl=0and in Harvard Dataversehttps://doi.org/10.7910/DVN/XC4E1I.

Appendix

Figure 12 demonstrates the transient simulations are close toequilibrium. Figure 13 shows the eddy transports for the drydynamic models used in KCT.

Figure 11. Same as Figure 10, except for OBL80-Ω.

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ORCID iDs

Wanying Kang https://orcid.org/0000-0002-4615-3702

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Figure 12. Demonstrations to show that the transient simulations almost reach equilibrium. Panel (a) shows the global-annual-mean surface temperature evolution inthe slow (default) transient experiments (solid curves), compared with that in the fast transient experiments, where the insolation is turned up twice as fast (dashedcurves). Panel (b)–(d) show the zonal mean temperature profiles toward the end of the insolation varying simulation (1750 W m−2), for low obliquity annual mean,high obliquity annual mean, and high obliquity February. Panel (e)–(g) are the same plots for the steady-state experiments, where the insolation is fixed at1750 W m−2 for 40 yr.

Figure 13. Eddy heat/momentum transports for (a)–(c) the dry dynamic model used in KCT, forced with a normal meridional temperature gradient (equator is warmerthan poles), (d)–(f) the 0° obliquity experiment forced by = -S 1360 W m0 2 insolation. From left to right, shown are meridional eddy momentum transport ¢ ¢u v ,meridional eddy heat transport ¢ ¢v T , and vertical eddy momentum transport w¢ ¢u .

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1. Introduction2. Methods2.1. Models2.2. Decomposing the Meridional Circulation

3. Results3.1. Two-regime Behavior of the Meridional Circulation3.2. Understanding the Circulation Structure Changes Near the Transition Point3.3. Observable Evidence for the Regime Transition Under High Obliquity

4. ConclusionsAppendixReferences