submitted to ApJPreprint typeset using LATEX style emulateapj v. 11/10/09

ATMOSPHERIC DYNAMICS OF TERRESTRIAL EXOPLANETS OVER A WIDE RANGE OF ORBITAL ANDATMOSPHERIC PARAMETERS

Yohai Kaspi1 Adam P. Showman2,

submitted to ApJ

ABSTRACT

The recent discoveries of terrestrial exoplanets and super Earths extending over a broad rangeof orbital and physical parameters suggests that these planets will span a wide range of climaticregimes. Characterization of the atmospheres of warm super Earths has already begun and will beextended to smaller and more distant planets over the coming decade. The habitability of theseworlds may be strongly affected by their three-dimensional atmospheric circulation regimes, sincethe global climate feedbacks that control the inner and outer edges of the habitable zone—includingtransitions to Snowball-like states and runaway-greenhouse feedbacks—depend on the equator-to-poletemperature differences, pattern of relative humidity, and other aspects of the dynamics. Here, usingan idealized moist atmospheric general circulation model (GCM) including a hydrological cycle, westudy the dynamical principles governing the atmospheric dynamics on such planets. We show howthe planetary rotation rate, planetary mass, surface gravity, heat flux from a parent star, opticalthickness and atmospheric mass affect the atmospheric circulation and temperature distribution onsuch planets. Our simulations demonstrate that equator-to-pole temperature differences, meridionalheat transport rates, structure and strength of the winds, and the hydrological cycle vary stronglywith these parameters, implying that the sensitivity of the planet to global climate feedbacks willdepend significantly on the atmospheric circulation. We elucidate the possible climatic regimes anddiagnose the mechanisms controlling the formation of atmospheric jet stream, Hadley and Ferrel cellsand latitudinal temperature differences. Finally, we discuss the implications for understanding howthe atmospheric circulation influences the global climate.

1. INTRODUCTION

Since the mid-1990s, nearly 2000 planets have beendiscovered around other stars. The first to be discov-ered were giant planets with short orbital periods, andsince then, many smaller planets with longer orbital pe-riods have been identified. The planets can generallybe divided into two types: planets close to their par-ent star that become synchronously locked, resulting inone side constantly being heated from their parent star,and asynchronously rotating planets with a diurnal cy-cle — similar to Earth and most solar system planets.In this study we focus on the latter type, and withinthese, we focus on terrestrial planets, i.e., those in whichthe atmospheric dynamics are limited to a thin spher-ical shell overlying a solid surface. These planets spana large range of masses, radii, densities, incident stellarfluxes, orbital periods, and orbital eccentricities. Thegoal of this study is to characterize the range of possi-ble climatic regimes these planets might encompass, andcharacterize how the climate and habitability depend onthese orbital, planetary, and atmospheric parameters.

Although exoplanet discovery and characterization be-gan with giant planets, emphasis is gradually shifting tosmaller worlds. Approximately 100 planets with massesless than ∼ 10 Earth masses have been discovered 3, withmany hundreds of additional candidates identified by the

1 Department of Earth and Planetary Sciences, WeizmannInstitute of Science, 234 Herzl st., 76100, Rehovot, Israel;yohai.kaspi@weizmann.ac.il

2 Department of Planetary Sciences and Lunar and PlanetaryLaboratory, The University of Arizona, 1629 University Blvd.,Tucson, AZ 85721 USA3 www.exoplanet.eu

NASA Kepler spacecraft (Borucki et al. 2011). Planetstoward the upper end of this mass range may typicallyconstitute mini Neptunes with no solid surfaces (e.g., Va-lencia et al. 2007; Adams et al. 2008; Rogers et al. 2011;Nettelmann et al. 2011; Fortney et al. 2013), but planetstoward the lower end are more likely terrestrial planetswith solid surfaces and relatively thin atmospheres. Im-portantly, discoveries to date include a number of plan-ets with masses and/or radii less than those of Earth(e.g., Fressin et al. 2012; Muirhead et al. 2012; Boruckiet al. 2013; Barclay et al. 2013 see review by Sinukoffet al. 2013), as well as numerous planets ∼ 1 − 3 Earthradii in size. This overall population of super Earthsand terrestrial planets includes not only hot, inhabitableobjects blasted by starlight (CoRoT-7b and Kepler-10bbeing prominent examples; Léger et al. 2011; Batalhaet al. 2011), but also many planets receiving ∼ 0.2 toseveral times the incident stellar flux Earth receives fromthe Sun, with effective temperatures of ∼ 200 − 400 K(Muirhead et al. 2012; Dressing & Charbonneau 2013;Quintana et al. 2014; see Figure 7 in Ballard et al. 2013for a visual summary). Depending on atmospheric com-position, these moderate stellar fluxes put these planetsin or near the classical habitable zones around their stars.

Atmospheric characterization of super Earths, whiledifficult, has already begun. Attention to date has fo-cused on GJ 1214b, a 6.5-Earth-mass, 2.7-Earth-radiussuper Earth orbiting a nearby M dwarf (Charbonneauet al. 2009). Transit spectroscopy in visible and near-infrared (IR) wavelengths indicates a relatively flat spec-trum, ruling out hydrogen-dominated, cloud-free atmo-spheres and favoring instead a high-molecular-weight(e.g., water-dominated) atmosphere and/or the presence

2 Kaspi and Showman

of clouds that obscure spectral features (e.g., Bean et al.2010, 2011; Désert et al. 2011; Berta et al. 2012; de Mooijet al. 2012; Fraine et al. 2013; Teske et al. 2013; Kreid-berg et al. 2014). The secondary eclipses of this rel-atively cool (∼ 500 K) planet have recently been de-tected by Spitzer (Gillon et al. 2013). The NASA Tran-siting Exoplanet Survey Satellite (TESS, to be launchedin 2017) and European Space Agency’s Planetary Tran-sits and Oscillations of Stars (PLATO, to be launchedin 2024) will search for additional, observationally favor-able super Earths, and upcoming platforms including theJames Webb Space Telescope (JWST) and the ground-based Thirty Meter Telescope (TMT) will be capable ofcharacterizing their atmospheres. These developmentsindicate that, in the coming decade, observational tech-niques currently used to characterize the atmospheres ofhot Jupiters will be applied to super Earths and terres-trial planets, placing constraints on their atmosphericcomposition, thermal structure, and climate. In princi-ple, visible and infrared light curves, ingress/egress map-ping during secondary eclipse, and shapes of spectrallines during transit could lead to constraints on longi-tudinal temperature variations, latitudinal temperaturevariations, cloud patterns, and vertical temperature pro-files.

These observational developments provide a strongmotivation for investigating the possible atmospheric cir-culation regimes of terrestrial exoplanets over a widerange of conditions. Such an investigation—as we carryout here—can provide a theoretical framework for in-terpreting future measurements of these planets and as-sessing their habitability. Moreover, such an effort canhelp to answer the fundamental, unsolved theoreticalquestion of how the atmospheric circulations of terres-trial planets—broadly defined—vary with incident stellarflux, atmospheric mass, atmospheric opacity, planetaryrotation rate, gravity, and other parameters. While gen-eral circulation model (GCM) studies of Mars, Venus,Titan, and especially Earth provide insights into the rel-evant dynamical mechanisms, these models are typicallyconstructed for a narrow range of conditions specific tothose planets, and thereby provide only limited under-standing of how the circulation regimes vary across thecontinuum of possible conditions. More recently, severalauthors have carried out GCM studies of terrestrial ex-oplanets, emphasizing synchronously locked, slowly ro-tating planets (Joshi et al. 1997; Joshi 2003; Merlis &Schneider 2010; Heng & Vogt 2011; Wordsworth et al.2011; Selsis et al. 2011; Yang et al. 2013, 2014; Hu &Yang 2014). Despite the insights provided by these stud-ies, only a small subset of possible conditions have yetbeen explored, especially for planets that are not syn-chronously rotating. It thus remains unclear, for exam-ple, how the equator-pole temperature differences, ver-tical temperature profiles, wind speeds, and propertiesof the Hadley cell, jet streams, instabilities, and wavesshould vary with the atmospheric mass, atmosphericopacity, planetary rotation rate, and other parameters.

In addition to its inherent interest, knowledge of howthe atmospheric circulation varies over a broad range ofparameters will aid an understanding of how the circu-lation interacts with global-scale climate feedbacks tocontrol planetary habitability. For example, the con-ditions under which planets enter globally glaciated or

runaway greenhouse states depend on the equator-to-pole temperature difference, the 3D distribution of hu-midity, and other aspects of the circulation (e.g., Voigtet al. 2011; Pierrehumbert et al. 2011; Leconte et al. 2013;Wordsworth & Pierrehumbert 2013; Yang et al. 2013).See Showman et al. (2014) for a review of our current un-derstanding of the atmospheric circulation of terrestrialexoplanets.

In this study we focus on the leading order mecha-nisms controlling the general circulation. We refer to thegeneral circulation (Lorenz 1967) as the longitudinallyaveraged circulation of the atmosphere, assuming thereare no longitudinal asymmetries on the planets (e.g., con-tinents, topography). This allows us to keep the analy-sis as simple as possible while maintaining the leading-order forcing of the climate system. While longitudinalasymmetries in the surface can modify the circulation,this is often a second-order effect; for example, even onEarth which has significant longitudinal and hemispher-ical differences in continental distribution, the leadingorder climate is zonally symmetric. As will be discussed,for Earth this is a consequence of the rapid planetaryrotation, but even on slower rotating planets or moons(e.g., Titan) similar hemispherical asymmetry is found toleading order (e.g., Mitchell et al. 2006; Aharonson et al.2009; Schneider et al. 2012). For simplicity, we performall experiments at perpetual equinox conditions, ignor-ing effects of obliquity and therefore seasonal variations,which also bring a hemispherical asymmetry to the cli-mate system.

Section 2 introduces our model and presents controlsimulations for modern-Earth conditions, which providesa reference against which to compare our parameter vari-ations. Section 3 describes our main results, where everysubsection presents a separate set of simulations wherethe dependence on one parameter is explored; namelywe study the dependence on planetary rotation rate, in-cident stellar flux, atmospheric mass, planetary meandensity (hence gravity), atmospheric optical depth, andplanetary radius. For each, we present detailed descrip-tion of the general circulation, particularly focusing onthe equator-to-pole temperature difference, the polewardheat transports, Hadley and Ferrell cells and the jetstreams. Section 4 concludes and summarizes implica-tions for observables and habitability.

2. MODEL

2.1. Model description

To explore the sensitivity of the general circulation tothe basic characteristics of the planet we use an ide-alized General Circulation Model (GCM). The ideal-ized GCM is based on the Flexible Modeling System(FMS) of NOAA’s Geophysical Fluid Dynamics Labora-tory (GFDL) (GFDL 2004; Held & Suarez 1994; Friersonet al. 2006). It is a three-dimensional model of a spher-ical aquaplanet4, and solves the primitive equations forfluid motion on the sphere for an ideal-gas atmosphere in

4 An aquaplanet is defined as a terrestrial planet with a (rela-tively) thin atmosphere, a global liquid-water ocean with no conti-nents, and a discrete interface between the ocean and atmosphere;this is to be distinguished from the term “ocean planet” (Légeret al. 2004) which sometimes is used to denote fully fluid planets(mini-Neptunes) composed predominantly of H2O.

Atmospheric dynamics of terrestrial exoplanets 3

the reference frame of the rotating planet with rotationrate Ω. The primitive equations in spherical coordinatesare given, using pressure as a vertical coordinate, by

Du

Dt− 2Ωv sin θ − uv

atan θ=− 1

a cos θ

∂Φ

∂λ− Σu, (1)

Dv

Dt+ 2Ωu sin θ +

u2

atan θ=−1

a

∂Φ

∂θ− Σv, (2)

0 =− ∂Φ∂ ln p

−RdTv, (3)

∇ · u = 0, (4)DT

Dt− RdTω

cpp=Qr +Qc +Qb, (5)

where u, v, and ω are the longitudinal (λ), latitudinal (θ)and pressure (p) velocities respectively, Φ is geopotential,T is temperature and Tv is the virtual temperature

5. Thematerial derivative is given by DDt =

∂∂t + u · ∇, where

u = (u, v, ω) and t is time. Σu, Σv are the surface stressterms from the boundary layer (see below), Rd = 287J kg−1 K−1 is the dry gas constant for air, cp = 1004J kg−1 K−1 is the specific heat of air, a is the planetaryradius and Qr, Qc and Qb are the radiative, convectiveand boundary layer heating per unit mass, respectively(see below). In Eq. (1–3) we have made the traditionalassumptions for terrestrial atmospheres that due to theshallowness of the atmosphere compared to the radiusof the planet the horizontal Coriolis terms and some ofthe metric terms are negligible (Vallis 2006). Note that,because pressure is the vertical coordinate, Eq. (4) doesnot imply that density is constant; indeed, we use theideal-gas equation of state, which allows significant den-sity variations vertically and horizontally.

The primitive equations are solved in vorticity-divergence form using the spectral transform methodin the horizontal and finite differences in the vertical(Bourke 1974). We mostly use a horizontal resolutionof 42 spectral modes (T42), which corresponds to about2.8◦ × 2.8◦ resolution in longitude and latitude, but forcases where eddy length scales become small (e.g., highrotation rates) we increase the horizontal resolution upto T170 (0.7◦×0.7◦). The vertical coordinate is σ = p/ps(pressure p normalized by surface pressure ps). It is dis-cretized with 30 levels, unequally spaced to ensure ade-quate resolution in the lower troposphere and near thetropopause. The uppermost full model level has a meanpressure of 0.46% of the mean surface pressure. All simu-lations have been spun up to statistically steady state forat least 1500 simulation days, and the results presentedhere have been then averaged over at least the subse-quent 1500 simulation days, and are all in a statisticallystable state.

2.1.1. Radiative transfer

Radiative transfer is represented by a standard two-stream gray radiation scheme (Held 1982; Frierson et al.

5 The virtual temperature is defined as Tv = Tmd/m, wheremd and m are the mean molecular mass of dry and moist air,respectively; e.g., Bohren & Albrecht (1998). Virtual temperaturemeasures density as a given pressure; high Tv implies low densityand vice versa.

2006) given by

dU

dτ=U − σSBT 4, (6)

dD

dτ=σSBT

4 −D, (7)

where U is the longwave6 upward flux and D is the long-wave downward flux, with the boundary condition atthe surface being U (τ (z = 0)) = σSBT

4s , where Ts is

the surface temperature (see below), and D (τ = 0) = 0at the top of the atmosphere. σSB = 5.6734 × 10−8W m−2 K−4 is the Stefan-Boltzmann constant. The long-wave optical thickness τ is given by

τ =[flσ + (1− fl)σ4

] [τe + (τp − τe) sin2 θ

], (8)

where fl, τe, and τp are constants; this implies that thelongwave and shortwave optical depths only depend onlatitude and pressure. The longwave optical thickness atthe equator and pole τe = 8.4 and τp = 2.2 respectively,and fl = 0.2, are chosen to mimic roughly an Earth likeequinoctial meridional and vertical temperature distribu-tion (Fig. 1). The quartic term in (8) represents the rapidincrease of opacity near the surface due to water vaporunder Earth-like conditions (Frierson et al. 2006). Notethat, because the constants in Eq. (8) are specified, ourexperiments do not include the water-vapor feedback inwhich variations in water vapor cause variations in opac-ity. The radiative source term in the atmospheric interioris then given by

Qr =p

cpRdT

∂ (U −D)∂z

. (9)

Insolation is imposed equally between hemispheres withthe top-of-atmosphere insolation Rs set as

Rs=S04

[1 +

∆s4

(1− 3 sin2 θ

)]e−τsσ

2

, (10)

where S0 = 1360 W m−2, ∆s = 1.2, and the parameter

τs = 0.08 controls the vertical absorption of solar radia-tion in the atmosphere. These parameters have also beenset to mimic an Earth-like climate (Fig. 1).

2.1.2. Surface boundary layer

Our surface boundary-layer scheme is similar to thatof Frierson et al. (2006). The lower boundary of theGCM is a uniform water covered slab, with an albedoof α = 0.35. A planetary boundary layer scheme withMonin-Obhukov surface fluxes (Obukhov 1971), whichdepend on the stability of the boundary layer, links at-mospheric dynamics to surface fluxes of momentum, la-tent heat, and sensible heat. The roughness length formomentum, moisture and heat fluxes is 1× 10−3 m, andan additive gustiness term of 1 m s−1 in surface velocitiesto represent subgrid-scale wind fluctuations. These val-ues yield energy fluxes and a climate similar to Earth’s inthe aquaplanet setting of our simulations (Fig. 1). Ourresults are not very sensitive to the choice of these pa-rameters.

6 Here, longwave refers to the long-wavelength infrared radiationassociated with planetary emission; this is to be distinguished fromshortwave radiation which represents the stellar flux.

4 Kaspi and Showman

Pre

ssu

re [

hP

a]

a10

250

500

750

1000

b

−10

0

10

20

30

Pre

ssu

re [

hP

a]

Latitude

c

−80 −40 0 40 80

10

250

500

750

1000

Latitude

d

−80 −40 0 40 80200

220

240

260

280

300

Fig. 1.— The zonal mean zonal wind (m s−1) (top), and zonal mean temperature distribution (K) (bottom) from NCEP reanalysis dataaveraged over the years 1970-2012 (left) and the reference simulation (right).

The lower boundary is a “slab ocean”, comprising avertically uniform layer of liquid water of depth H, heretaken to be 1 m thick, with no dynamics and a horizon-tally varying temperature evolving as

cpoρ0H∂Ts∂t

=Rs (1− α)−Ru − LeE − S, (11)

where cpo = 3989 J kg−1 K−1 is the surface heat capacity,

ρ = 1035 kg m−3 is the effective density of the slab ocean,Le = 2.5× 106 J kg−1 is the latent heat of vaporizationand Ru is the net upward longwave flux from the oceansurface. E and S and Σ are the surface evaporative heatflux, sensible heat flux7 and surface stress respectivelywhich are given by

E=ρaC |ua| (qa − q∗s ) , (12)S=ρacpC |ua| (Ta − Ts) , (13)Σ =Cρa |ua| |ua| , (14)

where ρa,ua, Ta and qa are the density, horizontal wind,temperature and humidity at the lowest atmosphericlevel. q∗a is the saturation specific humidity at the low-est model layer (see below), and C is a drag coefficientwhich decays with height following Monin-Obhukov the-ory (Obukhov 1971; Frierson et al. 2006). For furtherdetails see GFDL (2004). The neglect of horizontal mix-ing and heat transport in the ocean is a reasonable as-sumption in the Earth climate regime, since only one-third of Earth’s meridional heat transport occurs in theocean, with the remaining two-thirds occurring in theatmosphere. Nevertheless, there may be some exoplanetregimes in which this assumption breaks down (e.g., Hu& Yang 2014).

7 Sensible heat refers to energy stored, i.e., thermal energy (asdistinct from latent heat). Here, the sensible heat flux is the con-ductive heat flux from the slab ocean to the atmosphere.

Above the boundary layer, horizontal ∇8 hyperdiffu-sion in the vorticity, divergence, and temperature equa-tions is the only frictional process. The hyperdiffusioncoefficient is chosen to give a damping time scale of 12 hrsat the smallest resolved scale.

2.1.3. Hydrological cycle

We include a hydrological cycle involving the evapora-tion, condensation, and transport of water vapor. Mois-ture is calculated at every grid point and depends on thesurface evaporative fluxes and the convection giving themoisture equation

Dq

Dt= g

∂E

∂p− QcLe. (15)

A large-scale (grid-scale) condensation scheme ensuresthat the mean relative humidity in a grid cell does not ex-ceed 100% (Frierson 2007; O’Gorman & Schneider 2008).Only the vapor-liquid phase change is considered, and thesaturation vapor pressure es is calculated from a simpli-fied Clausius-Clapeyron relation given by

es (T ) = e0 exp

[−LeR

(1

T− 1T0

)], (16)

where Rv = 461.5 J kg−1K−1 is the gas constant for

water vapor, e0 = 610.78 Pa and T0 =273.16 K. The sat-uration specific humidity is then calculated by qs =

RvesRdp

.

Moist convection is represented by a Betts-Miller likequasi-equilibrium convection scheme (Betts 1986; Betts& Miller 1986), relaxing temperatures toward a moistadiabat with a time scale of 2 hours, and water vapor to-ward a profile with fixed relative humidity of 70% relativeto the moist adiabat, whenever a parcel lifted from thelowest model level is convectively unstable. Large-scalecondensation removes water vapor from the atmosphere

Atmospheric dynamics of terrestrial exoplanets 5

0 30 60 90

0

2

4

6

En

erg

y F

lux (

PW

)

Latitude

Total

Eddy

Dry

Moist

Fig. 2.— The total (full) and eddy (dashed) poleward moist staticenergy flux (PW). The eddy flux is divided to its dry (blue) andmoist (red) components.

when the specific humidity on the grid scale exceeds thesaturation.

2.2. Reference climate

Before presenting the dependence of the climate on theorbital and atmospheric parameters, we begin by present-ing below the reference climate against which all exper-iments are compared. We choose this to be a climatesimilar to Earth’s climate, which to leading order is awell-understood regime, and allows us to check the va-lidity of our model by comparing it to observations. Ourstrategy is to perform systematic parameter space sweepsall in reference to this single reference climate. With theparameter choice presented above the model referenceclimate is set to represent an Earth like annual-mean cli-mate. Fig. 1 shows the zonally averaged temperatureand wind fields for this reference climate (right), and theannually averaged climate for Earth from the NationalCenters for Environmental Prediction (NCEP) reanaly-sis data averaged over 40 years (1970-2010, left). Despitethe simplicity of the model the resulting mean climaterepresents well Earth’s annual mean climate. The tropicsare dominated by Hadley cells reaching nearly latitude30◦ with a generally weak westward zonal flow, and mid-latitudes are dominated by an eastward jet streams withwind velocities reaching about 30 m s−1 at latitude 45◦

and 200 hPa. Of course the model results are hemispher-ically symmetric, in contrast to the Earth data whichvaries considerably between hemispheres. In addition,our model does not have a seasonal cycle, which affectsthe climate despite not appearing directly in the annualaveraged climate. Despite these differences, the choiceof parameters given in section 2.1 yields a mean climatesimilar to observations. Fig. 3 (upper right) shows thesurface temperature map resembling that of Earth’s ob-servations with wave number five Rossby waves dominat-ing the midlatitude climate.

A main focus of this paper will be on what controls theequator-to-pole temperature difference on terrestrial exo-planets. For Earth, if the planet had no atmospheric andoceanic dynamics and the planet were in pure radiativeequilibrium, the equator-to-pole temperature differencewould be much larger than the actual value (Hartmann

1994). The existence of dynamics in the atmosphere,and particularly the fact that the atmosphere is turbu-lent, leads to a net poleward heat flux, which results inthe cooling of the lower latitudes and heating of high lat-itudes, and therefore a much more equable climate thana planet in pure radiative equilibrium. This results inthe reduction of the mean equator-to-pole temperaturedifference. The total heat transport can be described interms of the moist static energy (MSE) defined as

m= cpT + gz + Leq, (17)

where all symbols were defined in section 2.1. For Earth’sclimate the global moist static energy flux is poleward inboth hemispheres and peaks at about 5×1015 W in mid-latitudes (Fig. 2). The total flux can be divided intoa time mean component and a variation from the timemean coming from the turbulence in the atmosphere. Ifwe divide the meridional velocity into a time mean de-noted by an over-line and deviations from the time mean(eddies) with a prime so that v = v+v′, and do similarlyfor the moist static energy then

vm= vm+ v′m′. (18)

Fig. 2 shows the zonal averaged total flux (vm) and theeddy flux (v′m′), divided into the dry static energy com-ponent v′s′, where s = cpT + gz, and the latent energy

component Lev′q′. It shows the dominance of the eddyterm within the total flux (in midlatitudes it is even big-ger since the mean component is negative), and the factthat the dry and moist components contribute roughlyequally to this flux. For Earth, the moist componentis more dominant in low latitudes and the dry compo-nent in high latitudes. This reflects the strong nonlineardependence of the saturation vapor pressure on temper-ature (Eq. 16), meaning that warmer climates will havestronger heat transport due to latent heating (see sec-tion 3.2).

3. RESULTS

3.1. Dependence on the rotation rate

We begin with a series of experiments where we varythe rotation rate of the planet (e.g., Williams & Hol-loway 1982; del Genio & Suozzo 1987; Williams 1988;Navarra & Boccaletti 2002; Schneider & Walker 2006;Chemke & Kaspi 2014). The main effect of increasingthe rotation rate is that the eddy length scales decrease(we refer to eddies as the deviation from the time meanflow). This results from the fact that the primary sourceof extratropical eddies is from baroclinic instability (e.g.,Pedlosky 1987; Pierrehumbert & Swanson 1995), and thedominant baroclinic length scale scales inversely with ro-tation rate (e.g., Schneider & Walker 2006). This is illus-trated in Fig. 3, which shows instantaneous snapshots ofthe surface temperature of experiments with the proper-ties of the our reference climate, but where the rotationrate is varied between half and four times that of Earth.The waves in the temperature field are Rossby waves(e.g., Vallis 2006), resulting from the latitudinal depen-dence of the Coriolis forces in the horizontal momentumequations (Eq. 1,2). The smaller eddies in the rapidly ro-tating models, demonstrated also by the mean zonal wavenumber in Fig. 4, are less efficient in transporting MSE

6 Kaspi and Showman

Ω/2

250 260 270 280 290 300

Ω

250 260 270 280 290 300

2Ω

250 260 270 280 290 300

4Ω

250 260 270 280 290 300

Fig. 3.— Surface temperature (colorscale, in K) illustrating the dependence of temperature and eddy scale on rotation rate. Modelsare performed with rotation rates from half (upper left) to four times that of Earth (lower right). Baroclinic instabilities dominate thedynamics in mid- and high-latitudes, leading to baroclinic eddies whose length scales decrease with increasing planetary rotation rate.

meridionally, leading to a greater equator-to-pole tem-perature difference for those cases. A similar dependencehas been found in other studies as well (e.g., Schneider& Walker 2006; Kaspi & Schneider 2011, 2013).

The strong dependence of the atmospheric circulationon rotation rate is because of the dominance of theCoriolis acceleration in the momentum balance. Thiscan be quantified in terms of the Rossby number whichis the ratio between the typical velocity and the ro-tation rate times a typical length scale uΩL (Pedlosky1987). Typically, away from the equator for Earth’s at-mosphere and ocean the Rossby number is smaller thanone, meaning that in Eq. (1–3), the leading order bal-ance is geostrophic, and thus between the Coriolis andpressure forces in the horizontal momentum equations.However, planetary atmospheres are not necessarily inthat regime (e.g., Showman et al. 2014). Solar system

10−1

100

101

100

101

102

Rotation rate (Ωe)

Zo

na

l w

ave

nu

mb

er

Fig. 4.— The mean zonal wave number as function of the rotationrate of the planet, compared to Earth’s rotation rate (Ωe).

examples are Venus and Titan which have rotation ratesof 243 days and 16 days respectively, and therefore arecharacterized by larger Rossby numbers. This is demon-strated in Fig. 5, where we show the zonal winds, temper-ature, meridional streamfunction, and meridional zonal-momentum fluxes (u′v′) for cases of 1/16, 1/8, 1/4, 1/2,1, 2, 4 and 8 times the rotation rate of Earth. Simu-lation results presented here and throughout the paperhave been both zonally (longitudinally) and time aver-aged.

As rotation rate is increased the Rossby numberbecomes smaller and more jets (regions of localizedzonal velocity) develop (e.g., Williams & Holloway 1982;Williams 1988; Schneider & Walker 2006; Chemke &Kaspi 2014). These jets are generated by two distinctmechanisms, which we can categorize as thermally, andeddy, driven. In the former, the differential heating be-tween low and high latitudes causes air to rise at theequator, flow poleward aloft, and sink at higher latitudesforming Hadley cells (colors on the left column of Fig. 5).Air flowing polewards within the upper branch of theHadley cell moves closer to the axis of rotation of theplanet, and therefore to conserve angular momentum itmust develop eastward velocity (contours in the left sideof Fig. 5). Within the Hadley cells meridional tempera-ture differences are weak, creating a strong temperaturegradient on the poleward side of the Hadley cell. For thecases of small Rossby number (rapidly rotating) geostro-phy then implies that the atmosphere must be in thermalwind balance, meaning that

f∂u

∂p=Rdp

1

a

(∂T

∂θ

)p

, (19)

thus that the vertical wind shear is proportional to the

Atmospheric dynamics of terrestrial exoplanets 7

Ωe/16

200

800

Ωe/8

200

800

Ωe/4

200

800

Ωe/2

200

800

Ωe

Pre

ss

ure

(h

Pa

)

200

800

2Ωe

200

800

4Ωe

200

800

8Ωe

Latitude

−60 −30 0 30 60

200

800

Ωe/16

Ωe/8

Ωe/4

Ωe/2

Ωe

2Ωe

4Ωe

8Ωe

Latitude

−60 −30 0 30 60

Fig. 5.— Zonal-mean circulation for a sequence of idealized GCM experiments ranging from 1/16th to eight times the rotation rate ofEarth from top to bottom, respectively. Left column: Thin black contours show zonal-mean zonal wind with a contour interval is 5 m s−1,and the zero-wind contour is shown in a thick black contour. In color is the mean-meridional streamfunction, with blue denoting clockwisecirculation and orange denoting counterclockwise circulation. Maximum streamfunction values correspond to 8.7, 5.1, 4.2, 3, 1.9, 1.2, 0.6,0.2 ×1011 m2 s−1, from top to bottom, respectively. Right column: colorscale shows zonal-mean temperature, with colorscale rangingbetween 210 K to 290 K. Contours show zonal-mean meridional eddy-momentum flux, u′v′. Contour spacing grows from 9 m2 s−2 in theslowly rotating cases to 1 m2 s−2 in the fast rotating cases. Black and gray contours denote positive and negative values, respectively(implying northward and southward transport of eastward eddy momentum, respectively).

8 Kaspi and Showman

0

20

40

60

Latitu

de

a

10−1

100

101

101

102

Rotation rate

Jet velo

city [m

s−

1]

(Ωe)

b

Fig. 6.— (a) The latitude of the Hadley cell maximum (red),Hadley cell width (black) and the latitudinal location of the max-imum jet. The dashed line shows the Hadley cell width followingthe axisymmetric theory of Held & Hou (1980). (b) The magni-tude of the subtropical jet (blue), the magnitude of an angularmomentum conserving wind (uM ) at the latitude of the maximaljet (red) the strength of the Hadley Cell streamfunction (black) tothe power of 2/5.

latitudinal temperature gradients along isobars. Thisthen implies that the strong temperature gradient at thepoleward side of the Hadley cell must be balanced bystrong local wind shear, which then results in a localmaxima of eastward velocity (Fig. 5). This jet is referredto as the subtropical jet (due to its location on Earth— at the edge of the Hadley cell), and is evident in thefaster rotation cases in Fig. 5. For the slower rotationcases (Rossby number & 1), the eastward jets are a con-sequence of the conservation of angular momentum ofpoleward moving air in the upper branch of the Hadleycell, and therefore the jet magnitude is closer to thatexpected simply by conservation of angular momentum

given by uM = Ωasin2 θcos θ (Held & Hou 1980; Vallis 2006).

Figure 6 shows both the magnitude of the subtropical jetand the magnitude of uM for a series of simulations withdifferent rotation rates ranging from 1/24 to 12 timesthe rotation rate of Earth. It shows that the slowly ro-tating cases develop stronger jets which are close to theangular momentum conserving value, while for the fastrotating cases the geostrophically balanced jets (Eq. 19)are much weaker than uM . The strength of the sub-tropical jet scales nicely with the Hadley cell strength tothe 2/5 power following Held & Hou (1980), as shown inFig. 6b.

The other type of jets — eddy driven jets — appearin the rapidly rotating cases. Here, breaking of Rossbywaves in the extratropics results in eddy momentum fluxconvergence in the extratropics8, and the formation ofjets due to this convergence of momentum. This canbe seen in Fig. 5 showing multiple zonal jets (left side)corresponding to areas where there is momentum flux

8 We define extratropics as regions of the atmosphere withRossby number � 1, (e.g., Showman et al. 2014).

convergence (Fig. 5, right side). The resulting jets fromthis mechanism have a more barotropic structure thenthe subtropical jets (Vallis 2006). For the Earth rotationrate case the subtropical and eddy-driven jets appear al-most merged in Fig. 5 (and Fig. 1, but are then clearlyseparable for the cases with faster rotation rates. Thenumber of jets in each hemisphere is then related to thetypical eddy length scale, and the inverse energy cascadelength scales (Rhines 1975, 1979; Chemke & Kaspi 2014).

At slow rotation rates, the Hadley cells are nearlyglobal, the subtropical jets reside at high latitude, andthe equator-pole temperature difference is small (Fig. 5).The low-latitude meridional momentum flux is equa-torward, leading to equatorial superrotation (eastwardwinds at the equator) in the upper troposphere (Mitchell& Vallis 2010), qualitatively similar to that on Venus andTitan. At faster rotation rates, the Hadley cells and sub-tropical jets contract toward the equator, and simultane-ously an extratropical zone, with eddy-driven jets, devel-ops at high latitudes, and the equator-pole temperaturedifference is large. The low-latitude meridional momen-

0

2

4

6

Ωe/16

Ωe/8

Ωe/4

Ωe/2

Ωe

2Ωe

4Ωe

8Ωe

v ′m ′

En

erg

y F

lux (

PW

)

−2

0

2

4

6v m

En

erg

y F

lux (

PW

)

0 30 60 90

0

2

4

6

8

En

erg

y F

lux (

PW

)

Latitude

vm

Fig. 7.— The eddy (top), mean (middle) and total (bottom)poleward MSE flux as function of latitude for simulations withdifferent planetary rotation rates.

Atmospheric dynamics of terrestrial exoplanets 9

tum flux is poleward, resulting from the absorption ofequatorward-propagating Rossby waves coming from theextratropics. It is also evident from Fig. 5 that as therotation rate is increased the equator to pole tempera-ture difference increases. This is a result of the combi-nation of the facts that as rotation rate increases, thedecreases in eddy length scale results in less eddy trans-port polewards, and that the slower rotation rate caseshave large planetary scale Hadley cells which increase theheat transport by the mean meridional circulation.

These two effects are shown in Fig. 7, which showsvm, v′m′ and vm as function of latitude for different ro-tation rate cases. It shows that the turbulent heat fluxv′m′ has a nonmonotonic response to change of rotationrate. For slow rotation rates there is weak baroclinic in-stability and therefore the atmosphere is less turbulentresulting in weaker eddy heat transport (v′m′), while forfast rotation rate the atmosphere is strongly baroclini-cally unstable but baroclinic zones are narrow and ed-dies are small resulting in weak v′m′. Thus the maxi-mum eddy poleward heat transport in these experimentsis for rotation rates roughly similar to Earth’s (of coursewe should remember that our reference climate is tunedto Earth’s observed dynamics). On the other hand, themean fluxes decrease monotonically with the increase ofrotation rate (Fig. 7b), and this is because the Hadleycells become smaller for faster rotation (Fig. 6a). Themajority of the contribution of the mean fluxes is at lowlatitudes (within the Hadley cell), and becomes a global

10−1

100

101

0

2

4

6

En

erg

y f

lux [

PW

]

b

Rotation rate (Ωe)

20

40

60

80

Eq

ua

tor−

to−

po

le t

em

p d

iff.

[K

]

a

Fig. 8.— (a) The equator-to-pole surface temperature differenceas function of the rotation rate of the planet. (b) The maximum

value of the poleward eddy heat transport, v′m′, (red) and meantransport, vm, (blue) as function of the rotation rate of the planet.Fast rotation rate simulations are dominated by the decrease ineddy length scale with rotation rate resulting in less eddy heattransport poleward. Slower rotation rate experiments are domi-nated by large Hadley cells resulting in large mean heat transportand therefore smaller equator-to-pole temperature differences.

0

2

4

6

8

10

2500

2000

1600

1360

1200

1000

750

500 W m−2

En

erg

y F

lux (

PW

)

a

0 30 60 90−2

0

2

4

6

8

10

En

erg

y F

lux (

PW

)

b

Latitude

Fig. 9.— (a) The eddy MSE transport (×1015 W) for experimentsat different distances from the parent star, ranging from 0.6 to 2AU. (b) Three cases from above (solar constant of 500, 1360 and2500 W m−2) showing the latent heat transport (dash-dot) and drystatic energy transport (dash). This shows the strong nonlineareffect of water vapor on the MSE transport.

heat transport only for the very slowly rotating caseswhere the Hadley cell becomes of the order of the sizeof the planet. In fact, for rotation rate cases faster than1/4 Ωe the heat transport in the extratropics is nega-tive because of the existence of Ferrel cells, and it dom-inates the overall mean transport (vm). Only for theextremely slow rotation planets when the Hadley cell isglobal does the extratropical heat transport by the meanbecome positive (Fig. 7b). An axisymmetric picture pre-dicts that the Hadley cell width should be proportionalto Ω−1 (Held & Hou 1980), however this is complicatedby the existing of eddies leading to more complex theo-ries regarding where exactly the Hadley cells terminate(e.g., Levine & Schneider 2010). The clear dependenceof the Hadley cell width on the rotation rate is shown inFig. 6a, with the Ω−1 line as a reference.

The sum of the eddy and the mean transports, givingthe total heat transport, results in an overall larger heattransport for slower rotating planets; and therefore, plan-ets with faster rotation to have larger equator-to-poletemperature differences (Fig. 8a). For the fast rotatingcases this total is dominated by the eddies (even for theextreme fast rotation cases because the mean transportin those cases is negligible), and dominated by the meantransport for the less turbulent, slowly rotating cases.The transition between eddy- and mean-flow dominatedtransport occurs at a rotation rate of 0.2Ωe (locationwhere red and blue points cross in Fig. 8b). Interest-ingly, however, the dependence of equator-pole temper-ature difference on rotation rate (i.e., the slope of theline in Fig. 8a) exhibits a clear kink at larger rotationrates of Ωe. This occurs because the dependence of eddy

10 Kaspi and Showman

0.6AU

200

800

0.8AU

200

800

Pre

ss

ure

(h

Pa

)

1AU

200

800

1.5AU

200

800

2AU

200

800

3AU

Latitude

−60 −30 0 30 60

200

800

0.6AU

0.8AU

1AU

1.5AU

2AU

3AU

Latitude

−60 −30 0 30 60

Fig. 10.— Zonal-mean circulation for a sequence of idealized GCM experiments with solar flux values of 3800, 2100, 1360, 607, 342 and 152W m−2, which correspond to a distance of 0.6, 0.8, 1, 1.5, 2 and 3 AU from their parent star (for Solar like luminosity) from top to bottom,respectively. Left column: Thin black contours show zonal-mean zonal wind with a contour interval is 5 m s−1, and the zero-wind contouris shown in a thick black contour. In color is the mean-meridional streamfunction, with blue denoting clockwise circulation and orangedenoting counterclockwise circulation. Maximum and minimum streamfunction values correspond to ±2.2 × 1011 m2 s−1 respectively, forall panels. Right column: colorscale shows zonal-mean temperature. Due to the large range of temperatures colorscale is different for eachof the panels: maximum values are 354, 318, 301, 257, 222 and 183 K, and minimum values are 270, 233, 211, 173, 159 and 124 K fromtop to bottom, respectively. Contours show zonal-mean meridional eddy-momentum flux, u′v′. Contour spacing is 3 m2 s−2. Black andgray contours denote positive and negative values, respectively (implying northward and southward transport of eastward eddy momentum,respectively).

energy flux on rotation rate changes sign at Ωe. At rota-tion rates smaller than Ωe, eddies transport more energywhen rotation rate is larger, but at rotation rates largerthan Ωe, they transport less energy when rotation rateis larger (Fig. 8a, red points). By comparison, the meanflow transports less energy when rotation rate is largeracross the entire parameter range explored (Fig. 8b, bluepoints). The sum of the red and blue points implies thatthe total energy transport is rather insensitive to rotationrate when Ω < Ωe but depends strongly on rotation whenΩ > Ωe. In turn, this leads to a relatively flat dependenceof equator-pole temperature difference on rotation at lowrotation rate but a strong dependence at high rotationrate, explaining the kink in Fig. 8a.

3.2. Dependence on distance to parent star

Next we look at the dependence of the circulation onthe distance from its parent star. For all experimentswe assume the star is similar in luminosity to the Sun,so that the distance to the star corresponds to the heatflux received by the planet. As far as we treat the staras a point source of energy, we could have equivalentlyvaried the heat flux of the star and left the distance con-stant to achieve the same type of analysis. As in thereference case which resembles Earth, the poleward heattransport for all cases with different solar heat fluxes isdominated by the eddy transport. Fig. 9a shows thatplanets closer to their parent star have a larger poleward

Atmospheric dynamics of terrestrial exoplanets 11

0

4

8

12

16

20

En

erg

y f

lux (

PW

)

Ha

dle

y S

tre

am

fun

ctio

n

0

1

2

3

4

5

×1011

a

20

30

40

50

Eq

ua

tor−

to−

po

le t

em

p d

iff.

(K

)

b

102

103

0.05

0.1

0.15

0.2

Norm

alized e

qua

tor−

to−

pole

tem

p d

iff.

Solar Flux (W m−2

)

c

Fig. 11.— (a) The maximum value of the Hadley cell stream-

function (red) and eddy latent heat flux, Lv′q′, (blue) as functionof the solar heat flux. (b) The equator-to-pole surface temperaturedifference and (c) the equator-to-pole surface temperature differ-ence normalized by the mean surface temperature as function ofthe solar heat flux. Strongly irradiated planets which are warmertherefore have moister atmospheres, have a stronger equator-to-pole MSE flux which reduces the equator-to-pole temperature dif-ference.

heat flux, which results in reduction of the equator-to-pole temperature difference (Fig. 10, Fig. 11b). The mainreason for this increase in v′m′ is the non-linear depen-dence of the Clausius-Clapeyron relation on temperature(Eq. 16). Warmer climates have greater atmospheric wa-ter vapor abundances, and therefore the relative effect oflatent heating in the total MSE transport becomes moresignificant.

Fig 9b shows the dry (cpv′T ′ + gv′z′) and latent

(Lv′q′) components of the eddy MSE transport for threecases with different solar fluxes. For the cooler case(500 W m−2), the latent heat transport is very smallcompared to the dry component, while in the Earth casethey are very similar in magnitude (with the latent com-ponent more dominant in the tropics and the dry compo-nent more dominant in the extratropics, Fig. 2). On the

other hand in the very warm case (2500 W m−2) the la-tent component becomes much larger than the dry com-ponent (Fig. 9b). The strong non-linearity is expressedin the fact that the difference in heating between the twosets of cases is similar (500, 1360 and 2000 W m−2), butthe increase in total heat flux has more than quadrupled.

The zonal mean climate for five cases ranging in dis-tance from 0.6 to 2 AU (solar flux ranging between be-tween 342 to 5470 W m−2) is shown in Fig. 10. Obviouslythe closer-in planets are much warmer (Fig. 10, rightside). The meridional streamfunction however showsnonmonotonic behavior (Fig. 10, left side). Planets faraway from their parent star have less forcing, and there-fore Hadley and Ferrel cells get weaker as the stellar fluxdecreases. However, also as the planet becomes signifi-cantly warmer the strength of the Hadley and Ferrel cellsbecomes weaker. This is due to the nonlinear depen-dence of water vapor on temperature, where the increasein latent heating allows transporting heat with a weakercirculation, resulting in weaker circulation cells in thewarmer climates. The nonlinear increase in water vaporfluxes is also evident in Fig. 11a. For Earth like planets,the peak in the strength of the Hadley and Ferrel cells ap-pears at about 1.5 AU (Fig. 10, left side). Quantitativelythese results depend on the temperature dependence ofthe saturation vapor pressure, which can be different forplanets with different atmospheric masses since then theratio of latent to sensible heat will be different. However,despite the fact that the turning point may be different(Fig. 11a), we expect the general behaviour to be similarto the results presented here.

The domination of the moist component of the MSEflux results in that warmer planets have a smallerequator-to-pole temperature differences as long as mois-ture plays an important role in the transport as in thewarm example in Fig. 9b. However, we find that oncemoisture is less important (cooler climates), this rela-tion reverses and then as the distance to the star is in-creased the equator-to-pole temperature difference de-creases again (Fig. 11b). Thus, despite the decreasein MSE flux with increasing distance to parent star(Fig. 9a), the equator-to-pole difference decreases lead-ing to the nonmonotonic dependence in Fig. 11b. Mostly,this is due to the fact that for the cooler planets the meantemperature is smaller, and therefore even if the relativetemperature difference would not have changed the abso-

102

103

8

10

12

14

16

Solar Flux (W m−2

)

Zonal w

avenum

ber

Fig. 12.— The mean zonal wave number as function of the solarheat flux to the planet.

12 Kaspi and Showman

0.1Bar

20

80

0.3Bar

60

240

Pre

ss

ure

(h

Pa

)

1Bar

200

800

3Bar

600

2400

10Bar

2000

8000

30Bar

Latitude

−60 −30 0 30 60

6000

24000

0.1Bar

0.3Bar

1Bar

3Bar

10Bar

30Bar

Latitude

−60 −30 0 30 60

Fig. 13.— Zonal-mean circulation for a sequence of idealized GCM experiments with surface pressure ranging from 0.1 to 30 bars from topto bottom, respectively. Left column: Thin black contours show zonal-mean zonal wind with a contour interval of 5 m s−1. The zero-windcontour is shown in a thick black contour. In color is the mean-meridional streamfunction, with blue denoting clockwise circulation andorange denoting counterclockwise circulation. Maximum and minimum streamfunction values correspond to ±3×1011 m2 s−1, respectivelyfor all panels. Right column: colorscale shows zonal-mean temperature, with colorscale ranging between 210 K to 290 K. Contours showzonal-mean meridional eddy-momentum flux, u′v′. Contour spacing grows from 6 m2 s−2 in the less massive cases to 1 m2 s−2 in the moremassive cases. Black and gray contours denote positive and negative values, respectively (implying northward and southward transport ofeastward eddy momentum, respectively).

lute temperature difference between equator and pole issmaller. However, even the normalized equator-to-poletemperature difference (normalizing by the average sur-face temperature) shows a small decrease of tempera-ture difference with reduction of solar flux (Fig. 11c),which is due to the increase in radiative time constantfor the colder planets. Note that for these simulations theenergy containing wavenumber generally decreases withsolar flux (Fig. 12). Therefore unlike the rotation rateexperiments (section 3.1) where the eddy length scaledecreased with rotation rate (Fig. 4), limiting the ed-dies ability to transport heat poleward and causing anincrease in equator-to-pole temperature difference withrotation rate, here the reduction of eddy length scaledoes not result in increased equator-to-pole temperature

difference. Thus, for the cooler planets, despite the de-crease of eddy length scale with larger distance to theparent star, the equator-to-pole temperature differenceis reduced.

3.3. Dependence on atmospheric mass

Atmospheric masses can vary considerably based onthe planetary composition and history. Even in our closeneighbours in the solar system atmospheric masses varyby orders of magnitude from an atmosphere of 92 barson Venus, to an atmosphere of 0.006 bars on Mars. Theother terrestrial type atmosphere in the solar system, Ti-tan, has an atmospheric surface pressure similar to Earthof 1.5 bar. In this section we experiment with the atmo-spheric mass of the planet, by keeping all other param-eters constant as in our reference climate, and varying

Atmospheric dynamics of terrestrial exoplanets 13

only surface pressure. We use no convection scheme anddo not vary optical thickness despite increasing atmo-spheric mass, to allow an even comparison between thesimulations. Fig. 13 shows that as the atmospheric massis increased the Hadley and Ferrell cells become strongerand narrower, resulting also in the subtropical jet beingcloser to the equator. Eddy momentum flux convergenceis aligned with the jet location and also becomes closerto the equator and weaker with increasing atmosphericmass. Note that the contour interval of u′v′ decreaseswith atmospheric mass in Fig. 13.

Planets with more massive atmospheres also havestronger equator-to-pole MSE flux (Fig. 14a), which re-duces the equator-to-pole temperature difference (Fig. 13right side), and therefore the jet strength. In all casesthe mass flux is dominated by the eddy component(as in the Earth case in Fig. 2), and the increase inMSE flux follows monotonically with the increase in at-mospheric mass. However, the increase in MSE fluxwith atmospheric mass becomes more gradual beyond10 bars, likely because of the strong decrease in eddylength scale (Fig. 15b) for the extremely massive atmo-spheres. Thus the two competing effects of more effi-cient heat transport due to more atmospheric mass, andless efficient transport because of smaller eddies levelout the equator-to-pole heat transport in very massiveatmospheres. Nonetheless the general trend of smallerequator-to-pole temperature differences with increasingatmospheric mass is obvious in Fig. 13 (right column),14b, and 15c.

Fig. 14b shows that as planetary mass increases surfacetemperatures increases as well. This is a consequence ofthe fact that although horizontal eddy fluxes increasein magnitude with increasing atmospheric mass, vertical

0

2

4

6

8

a

Energ

y F

lux (

PW

)

0 30 60 90

250

270

290

310b

Latitude

Tem

pera

ture

(K

)

0.1

0.3

1

3

10

30

100 Bar

Fig. 14.— (a) The poleward eddy MSE flux and (b) the surfacetemperature as function of latitude for simulations with differentsurface pressure ranging from 0.1 bar to 100 bar. More massiveatmospheres generally have a larger poleward MSE flux resultingin a reduced equator-to-pole temperature difference.

0

4

8

En

erg

y f

lux [

PW

]

Ha

dle

y S

tre

am

fun

ctio

n

0

1

2

×1011

a

10−1

100

101

102

20

30

40

50E

qu

ato

r−to

−p

ole

te

mp

diff.

[K

]c

Surface pressure (bar)

8

10

12

14

16

18

Zo

na

l w

ave

nu

mb

er

Ve

rtic

al e

dd

y h

ea

t flu

x

0

2

4

×10−6

b

Fig. 15.— (a) The maximum value of the Hadley cell streamfunc-

tion (red) and eddy MSE flux, v′m′, (blue) as function of surfacepressure. (b) The vertical eddy heat flux averaged over the tropo-sphere (red), and the mean zonal wave number (blue) as function ofsurface pressure. (c) The equator-to-pole surface temperature dif-ference as function of surface pressure. More massive atmospheresgenerally have a larger poleward MSE flux resulting in a reducedequator-to-pole temperature difference. The two competing effectsof more efficient heat transport due to more atmospheric mass,and less efficient transport because of smaller eddies level out theequator-to-pole heat transport in very massive atmospheres.

eddy fluxes reduce in magnitude (Fig. 15b). Thus moremassive atmospheres allow less efficient vertical eddyheat transport, which results in the surfaces accumulat-ing more heat (the optical thickness in these simulationsdepends only on σ and therefore is equally distributedin height in all simulations). These differences are largerin midlatitudes than in the tropics since at midlatitudesthe eddies play a larger role in the heat transport. Thisresults in the fact that more massive atmospheres havelarger extratropical lapse rates, which acts to destabi-lize the atmosphere. However, this increase of horizontalheat fluxes with atmospheric mass has the opposite effect(thus stabilizing the atmosphere), and is more dominantin our simulations, resulting in weaker eddy momentumfluxes and weaker jets as can be seen in Fig. 13.

14 Kaspi and Showman

g = 1

20

80

g = 2

40

160

Pre

ss

ure

(h

Pa

)

g = 4

80

320

g = 8

160

640

g = 16

Latitude

−60 −30 0 30 60

320

1280

g = 1

g = 2

g = 4

g = 8

g = 16

Latitude

−60 −30 0 30 60

Fig. 16.— Zonal-mean circulation for a sequence of idealized GCM experiments ranging in mean planetary density from 562 kg m−3 to7,874 kg m−3 (corresponding to surface gravity ranging from 1 m s−2 to 16 m s−2. Left column: Thin black contours show zonal-meanzonal wind with a contour interval is 5 m s−1, and the zero-wind contour is shown in a thick black contour. In color is the mean-meridionalstreamfunction, with blue denoting clockwise circulation and orange denoting counterclockwise circulation. Maximum and minimumstreamfunction values grow with the gravity, and thus correspond to ± (1, 2, 4, 8, 16)×1010 m2 s−1, from top to bottom respectively. Rightcolumn: colorscale shows zonal-mean temperature, with colorscale ranging between 210 K to 290 K. Contours show zonal-mean meridionaleddy-momentum flux, u′v′. Contour spacing is 5 m2 s−2. Black and gray contours denote positive and negative values, respectively(implying northward and southward flux of eastward eddy momentum, respectively).

3.4. Dependence on planetary mean density

Terrestrial type exoplanets likely span a wide range ofmean densities ranging from ice-rich planets to heavyplanets composed primarily of rock and iron. Herewe explore the effect of varying the planetary meandensity between the extremes of a relatively light ice-planet (1000 kg m−3), to that of a heavy iron-planet(7,874 kg m−3), while keeping the atmospheric mass con-stant. Thus, in these simulations the planet radius is keptfixed to that of Earth, and we also keep Earth’s atmo-spheric mass by varying the surface pressure hydrostati-cally given the varying surface gravity, where g = 4π3 Gρ(Fig. 17). Fig. 16 shows that Hadley and Ferrel cellstrength increases with the gravity coefficient (note thatthe color scale changes between the panels). For theHadley cell case the increase in width and strength isconsistent with Held & Hou (1980) suggesting a g1/2 in-crease in Hadley cell width and g3/2 in Hadley cell inten-sity. In our simulations, despite showing the same trends,the increase in Hadley cell width and intensity is moremodest likely due to the role of eddies. Concurrently,

the jets become more subtropical in nature (thus morebaroclinic and closer to the edge of the Hadley cell). Inthe water-density planet the midlatitude jets are mainlyeddy driven, weaker and more barotropic, while in thedenser planets due to the dominance of the Hadley cell,and despite the strengthening of the eddies, the jets peaknear the edge of the Hadley cells. On the other hand, theincrease in Ferrel-cell strength is likely due to strongerbaroclinic instability in midlatitudes (see below).

Unlike the rotation and atmospheric-mass experiments(sections 3.1 and 3.3), here the increased Hadley cellstrength also results in an increase in equator-to-poletemperature differences, which shows roughly a triplingof the equator-to-pole surface temperature between theice-density planet and the iron-density planet (Fig. 18a).The reason for this variation is that as the mean den-sity increases, so do the buoyancy frequency and verticalshear which both affect the Eady growth rate

σ ∼ Ω sin θN

∂u

∂z, (20)

representing the growth rate of baroclinic eddies in the

Atmospheric dynamics of terrestrial exoplanets 15

+o

Raduis [km]

Ma

ss [

kg

]

ice

rock

iron

1000 10000 100000

1e+23

1e+24

1e+25

1e+26

1e+27

0.001

0.1

10

1000

Fig. 17.— The surface gravity (colorscale, m s−2) as functionof planetary mass and radius. Black lines denote planets with amean density of ice (1000 kg m−3), rock (5520 kg m−3) and iron(7,874 kg m−3). The ⊕ symbol denotes the location of Earth inthis phase space.

atmosphere (Eady 1949; Lindzen & Farrell 1980). Thestatic stability and vertical shear exert opposite effectson the Eady growth rate and both depend on gravity.The static stability, N2 = gΘ

∂Θ∂z , has a dependence on

gravity both because of the direct dependence on grav-ity and the fact that the vertical gradient of potentialtemperature becomes larger for larger mass (again, be-cause of the reduction of the vertical eddy heat flux).The vertical shear has a linear dependence since for asimilar forcing by a temperature gradient thermal windimplies that the vertical shear will grow linearly withgravity (Eq. 19). Taking into account both dependen-cies (Fig. 18b), we find that heavier planets will have alarger Eady growth rate implying stronger baroclinic ed-dies and eddy kinetic energy (Fig. 18c). However, thisdoes not cause stronger eddy heat fluxes (Fig. 18d, bluepoints), but rather the larger eddy activity in midlati-tudes strengthens the eddy-driven Ferrel cell that drivesa stronger equatorward mean circulation (Fig. 18d, redpoints) that weakens the overall poleward heat transport(Fig. 18d, black points). The reduced overall polewardheat transport then results in an increased equator-to-pole temperature difference (Fig. 18a). The heavier plan-ets therefore have stronger Ferrel cells and eddies in theextratropics, which is also evident when looking at thestrength of the eddy kinetic energy, 12g

∫ (u′2 + v′2

)dp,

integrated over the troposphere (Fig. 18c). On the otherhand, if atmospheric surface pressure, rather than atmo-spheric mass, is held constant while the gravity is vary-ing (not shown), then the simulations would resemblethose of varying atmospheric mass where the equator-to-pole temperature differences decreases with increasingthe gravity.

3.5. Dependence on optical thickness

In all previous sections optical thickness (Eq. 8) hasbeen kept fixed, set to the parameters that give an Earth-like climate in the reference simulation (Fig. 1). Increas-ing the optical thickness while keeping other parametersfixed (including atmospheric mass) results in an atmo-sphere that absorbs more of the emitted longwave ra-diation and therefore is warmer. How this effects eddymomentum transport in the atmosphere and the equator-

20

30

40

50

60

Eq.−

to−

pole

∆T

[K

]

a

10

−3

10−2

10−1

Sta

tic s

tability [s

−1]

Vert

ical shear

[s−

1]

10−3

10−4

10−5

b

2

4

6

8x 10

−6

Eady g

row

th r

ate

[s

−1]

Eddy k

inetic e

nerg

y [M

J m

−2]

0.2

0.4

0.6

0.8c

0 4000 8000 12000−2

2

6

Mean density [kg m−3

]

Energ

y flu

x [P

W]

d

Fig. 18.— (a) The equator-to-pole surface temperature differ-ence as function of the mean density of the planet ranging betweendensity of an ice-planet to that of a heavy lead-planet (Fig. 17).(b) Static stability (red) and vertical wind shear (blue) as functionof the mean density of the planet. (c) Eady growth rate (Eq. 20,blue), and eddy kinetic energy (red) (d) Eddy MSE flux (blue),mean MSE flux (red) and total MSE flux (black) as function of themean planetary density.

to-pole temperature difference is less straight forward;we explore this issue here. Over this series of simula-tions we increase τp and τe (Eq. 8) by the same factor,thus increasing the optical thickness linearly over all lat-itudes. In the series of experiments presented here theoptical thickness was varied between 0.1 to 15 times thereference case, which corresponds to mean surface tem-peratures of 253 K to 319 K respectively. In resemblanceto the case of varying the distance to the parent star(section 3.2), the results are dominated by the nonlinearresponse of temperature to the atmospheric water-vaporabundance. For the cases with low optical thickness theatmosphere is cold resulting in dry static energy domi-

16 Kaspi and Showman

0 30 60 90

0

2

4

6

254 K

286 K

318 K

Energ

y F

lux [P

W]

Latitude

a

260 280 300 32020

30

40

50

60

70

Mean surface temperature [K]

Equato

r−to

−pole

tem

p d

iff. [K

]

b

Fig. 19.— (a) The eddy moist (solid) and dry (dashed) staticenergy fluxes as function of latitude for three cases different op-tical thicknesses which correspond to a mean surface temperatureof 254, 286 and 318 K. (b) The equator-to-pole surface temper-ature difference as function of the mean surface temperature ofthe planet corresponding to experiments with 0.1 to 15 times theoptical thickness of the reference case, which correspond to meansurface temperatures of 253 K to 319 K respectively.

nating the moist static energy fluxes (Fig. 19a), and thusless overall poleward heat transport resulting in a largeequator-to-pole temperature difference (Fig. 19b). Asthe optical depth is increased the moist component of theMSE becomes larger resulting in stronger MSE transportand therefore smaller equator-to-pole temperature differ-ences. Note that in our simple model as optical thicknessdoes not vary with the amount of water vapor, this modeldoes not allow for a runaway effect as perhaps relevantto Venus.

3.6. Dependence on planetary mass (radius)

In this set of experiments we keep the planetary meandensity constant at the density of Earth (5520 kg m−3),and vary the radius and correspondingly the mass andsurface gravity of the planet (along the “rock” line inFig. 17). If gravity would not have been changing thenreducing the radius of the planet has a similar effect toincreasing the rotation rate, since the Rossby numberbecomes smaller (u/ΩL), where L is the typical lengthscale. However, for a rocky planet changing the radius,results in a change of mass and surface gravity. Again, inthis experiment we keep the mass of the atmosphere (perunit area) constant by consistently varying the surfacepressure. Fig. 20 shows that larger planets have a smallermean equator-to-pole temperature gradient due to theMSE transport increasing with planet size (in Fig. 20aMSE flux is normalized by planetary radius). For all sim-ulations the MSE fluxes, in similar to the reference case,are dominated by the eddy fluxes, with the mean con-

tributing negatively in midlatitude (as in Fig. 2). Similarto increasing the rotation rate of the planet (section 3.1,as the planet size is increased, the typical eddy lengthscale becomes smaller compared to the size of the planetand therefore is less efficient in heat transport. This re-sults in a larger equator-to-pole temperature difference(Fig. 20b.

4. DISCUSSION AND CONCLUSION

To date, nearly a hundred terrestrial exoplanets havebeen identified, and this number is expected to grow sig-nificantly over the next few years as more Earth-sizedand sub-Earth-sized planets are discovered. These plan-ets span a wide range of orbital parameters and incidentstellar fluxes, and they likely also span a wide range ofclimatic regimes. In this work, we have attempted tocharacterize the basic features of the general circulationof these atmospheres, focusing on planets that are farenough away from their parent star so that they arenot tidally locked, and therefore to leading order, likeEarth, have an zonally symmetric climate. In this sensethis study is different than many recent studies focus-ing on the atmospheric dynamics of tidally locked ter-restrial exoplanets (e.g., Joshi et al. 1997; Joshi 2003;Merlis & Schneider 2010; Heng & Vogt 2011; Wordsworthet al. 2011; Selsis et al. 2011; Yang et al. 2013, 2014;Hu & Yang 2014). For simplicity we have attempted tokeep the model configuration as simple as possible (aqua-planet, no seasons, no ice, simplified radiation), and wepresented several series of numerical GCM simulationsexperiments exploring one parameter at a time. Beingone of the first studies that are addressing such planetaryregimes, we have attempted to address only the basic fea-tures of these diverse planetary atmospheres. We there-fore focus on the equator-to-pole temperature difference,and the size and intensity of the Hadley cells, Ferrel cellsand extratropical jet streams. We focus on six uniquesystematic experiments which contain in our view someof the more interesting characteristics of the planetaryatmospheres: rotation rate, distance to the parent star,atmospheric mass, surface gravity, optical thickness andplanetary radius. Of course, these six encompass onlya small subset of possible explorable parameters. Analternate approach would be to nondimensionalize theequations and vary only the nondimensional parameters.However, in order to give better intuition we decided topresent our integrations using the real physical parame-ters.

The key results for the six sets of simulations presentedin section 3 are given below:

• Planets with faster rotation rates will be charac-terized by smaller and weaker Hadley cells, andsmaller eddy length scales. This results in a largerequator-to-pole temperature difference, and weakerjets. The number of jets grows with rotation rate.Slowly rotating planets will have an equatorialeddy momentum flux convergence resulting in a su-perrotating state (e.g., Venus, Titan).

• The distance to the parent star has a nonmono-tonic response in most aspects we have examined,due to the strong nonlinear dependence of water va-por abundance on temperature. Warmer and closer

Atmospheric dynamics of terrestrial exoplanets 17

planets will have smaller equator-to-pole tempera-ture gradients due to enhanced eddy MSE trans-port due to the latent heat component, which in-creases significantly with temperature. However,planets which are far enough from the their parentstar, so that for their abundance of water vapor theatmospheres are dry, will also have smaller equator-to-pole temperature differences due to the overalllower temperatures and larger radiative time scales.Hadley and Ferrel cells exhibit the same nonmono-tonic behavior.

• Planets with larger atmospheric masses will gener-ally have larger horizontal fluxes but lower verticalfluxes, resulting in reduced equator-to-pole temper-ature differences and higher surface temperatures.Hadley and Ferrel cells increase in strength withatmospheric mass due to the increased mass trans-port.

• Planets with larger mean densities and thereforelarger surface gravity have stronger Hadley andFerrel cells. For these cases despite the growthof eddy energy with surface gravity, the maincontroller of the extratropical temperature is thestrengthening of the Ferrel cells, and therefore theequator-to-pole temperature difference increaseswith mean planetary density.

• Planets with larger optical thickness are warmeracross all latitudes, and the equator-to-pole tem-perature difference decreases with the increase ofoptical thickness due to enhanced poleward eddyMSE transport (due to increased latent heat trans-port) in the warmer climates.

• Planets with larger radii and consequently largergravity show a decrease in equator-to-pole temper-ature gradient with increasing radius due to en-hanced poleward eddy MSE transport. However,despite the reduction in temperature gradients, thiseffect does not compensate for the increase in dis-tance between the equator and the pole and there-fore overall the equator-to-pole temperature differ-ence increases.

• The dependence of the equator-to-pole tempera-ture difference on rotation rate, atmospheric mass,and other parameters implies that dynamics mayexert a significant effect on global-mean climatefeedbacks such as the conditions under which aplanet transitions into a globally frozen, ”SnowballEarth” state. Thus, our results imply that the dy-namics influences planetary habitability, includingthe width of the classical habitable zone.

A key result, which has important implication for thehabitability of these planets, is the equator-to-pole tem-perature difference response to the variation in orbitaland atmospheric parameters. As we have discussed,large-scale atmospheric turbulence attempts to homoge-nize latitudinal temperature differences, mainly throughpoleward transport of moist static energy. In the simu-lations presented here, we find that the equator-to-poletemperature difference increases for larger rotation rates,

0 30 60 90

0

1

2

Energ

y F

lux [G

W m

−1]

Latitude

a

106

107

108

20

40

60

80

Equato

r−to

−pole

tem

p d

iff. [K

]

Equato

r−to

−pole

tem

p g

rad. [K

m−

1]

0

8

16

24×10

−6

b

Radius (km)

1000 km

5000 km

20000 km

Fig. 20.— (a) The eddy moist (solid) and dry (dashed) staticenergy fluxes as function of latitude for three cases with differ-ent planetary radius of 1000 km, 5000 km and 20000 km (b) Theequator-to-pole surface temperature difference (blue) and meanequator-to-pole surface temperature gradient (red) as function ofthe planetary radius.

planets with larger surface gravity (density) and largerradius planets, while the equator-to-pole temperaturedifference decreases with atmospheric mass, larger ther-mal opacity and for cooler or warmer planets (dependingon water vapor). Varying the distance to the parent starhas a nonmonotonic response in the equator-to-pole tem-perature difference due to the nonlinear dependence ofwater vapor on temperature. Despite the fact that theseresults have been obtained in respect to an Earth likereference atmosphere, the combination of experimentsrepresent the general trends we expect to find in anyatmosphere. Known examples which are consistent withour results are the terrestrial type atmospheres of Venus,Mars and Titan. The slow rotating Venus has a verysmall equator-to-pole temperature difference and strongjets, despite having a massive atmosphere (92 bars). Ti-tan has a large global Hadley cells due to its slow rota-tion, and Mars has a similar rotation rate to Earth butan atmosphere of only 0.006 bar and therefore has largeequator-to-pole temperature differences.

Moreover, this analysis has implications for the un-derstanding of solar system planetary atmospheres aswell. The observed equator-to-pole temperature differ-ence on Venus is only a few degrees Kelvin (Prinn & Fe-gley 1987), and it is unclear if this is because of Venus’sslow rotation or its massive atmosphere with a result-ing long radiative time scale. Extrapolating from ourresults for varying atmospheric mass and rotation rate,which both give smaller equator-to-pole temperature dif-ferences for a 92 bar atmosphere rotating at ∼ 0.004Ωe,respectively (Figs. 8a, 15b), implies that both slow rota-tion and a massive atmosphere are necessary for such asmall equator-to-pole temperature difference.

18 Kaspi and Showman

As more detailed exoplanet observations become avail-able, we will be able to provide more constraints to theseplanetary atmospheres to better constrain the models.This paper provides a first attempt to characterize theseatmospheres, focusing on the main drivers of the atmo-

spheric circulation and the resulting climate. Developingthis mechanistic understanding of what controls the cli-mate, will allow to better provide constraints on whatinfluences habitability on these planets.

REFERENCES

Adams, E. R., Seager, S., & Elkins-Tanton, L. 2008, Astrophys.J., 673, 1160

Aharonson, O., Hayes, A. G., Lunine, J. I., et al. 2009, NatureGeoscience, 2, 851

Ballard, S., Charbonneau, D., Fressin, F., et al. 2013, Astrophys.J., 773, 98

Barclay, T., Rowe, J. F., Lissauer, J. J., et al. 2013, Nature, 494,452

Batalha, N. M., Borucki, W. J., Bryson, S. T., et al. 2011,Astrophys. J., 729, 27

Bean, J. L., Miller-Ricci Kempton, E., & Homeier, D. 2010,Nature, 468, 669

Bean, J. L., Désert, J.-M., Kabath, P., et al. 2011, Astrophys. J.,743, 92

Berta, Z. K., Charbonneau, D., Désert, J.-M., et al. 2012,Astrophys. J., 747, 35

Betts, A. K. 1986, Q. J. R. Meteorol. Soc., 112, 677Betts, A. K., & Miller, M. J. 1986, Q. J. R. Meteorol. Soc., 112,

693Bohren, C. F., & Albrecht, B. A. 1998, Atmospheric

thermodynamics (Oxford University Press)Borucki, W. J., Koch, D. G., Basri, G., et al. 2011, Astrophys. J.,

736, 19Borucki, W. J., Agol, E., Fressin, F., et al. 2013, Science, 340, 587Bourke, W. 1974, Mon. Weath. Rev., 102, 687Charbonneau, D., Berta, Z. K., Irwin, J., et al. 2009, Nature, 462,

891Chemke, R., & Kaspi, Y. 2014, J. Atmos. Sci., submittedde Mooij, E. J. W., Brogi, M., de Kok, R. J., et al. 2012,

Astronomy and Astrophys., 538, A46del Genio, A. D., & Suozzo, R. J. 1987, J. Atmos. Sci., 44, 973Désert, J.-M., Bean, J., Miller-Ricci Kempton, E., et al. 2011,

Astrophys. J. Let., 731, L40Dressing, C. D., & Charbonneau, D. 2013, Astrophys. J., 767, 95Eady, E. T. 1949, Tellus, 1, 33Fortney, J. J., Mordasini, C., Nettelmann, N., et al. 2013,

Astrophys. J., 775, 80Fraine, J. D., Deming, D., Gillon, M., et al. 2013, Astrophys. J.,

765, 127Fressin, F., Torres, G., Rowe, J. F., et al. 2012, Nature, 482, 195Frierson, D. M. W. 2007, J. Atmos. Sci., 64, 1959Frierson, D. M. W., Held, I. M., & Zurita-Gotor, P. 2006, J.

Atmos. Sci., 63, 2548GFDL. 2004, J. Climate, 17, 4641Gillon, M., Demory, B.-O., Madhusudhan, N., et al. 2013, ArXiv

e-prints, arXiv:1307.6722Hartmann, D. L. 1994, Global Physical Climatology (Academic

Press)Held, I. M. 1982, J. Atmos. Sci., 39, 412Held, I. M., & Hou, A. Y. 1980, J. Atmos. Sci., 37, 515Held, I. M., & Suarez, M. J. 1994, Bull. Am. Meteor. Soc., 75,

1825Heng, K., & Vogt, S. S. 2011, Mon. Not. of the Roy. Astro. Soc.,

415, 2145Hu, Y., & Yang, J. 2014, Proc. Natl. Acad. Sci. U.S.A., 111, 629Joshi, M. 2003, Astrobiology, 3, 415Joshi, M. M., Haberle, R. M., & Reynolds, R. T. 1997, Icarus,

129, 450Kaspi, Y., & Schneider, T. 2011, J. Atmos. Sci., 68, 2459—. 2013, J. Atmos. Sci., 70, 2596Kreidberg, L., Bean, J. L., Désert, J.-M., et al. 2014, Nature, 505,

69

Leconte, J., Forget, F., Charnay, B., et al. 2013, Astronomy andAstrophys., 554, A69

Léger, A., Selsis, F., Sotin, C., et al. 2004, Icarus, 169, 499Léger, A., Grasset, O., Fegley, B., et al. 2011, Icarus, 213, 1Levine, X. J., & Schneider, T. 2010, J. Atmos. Sci., in prep.Lindzen, R. S., & Farrell, B. 1980, J. Atmos. Sci., 37, 1648Lorenz, E. N. 1967, The Nature and Theory of the General

Circulation of the Atmosphere (World MeteorologicalOrganization)

Merlis, T. M., & Schneider, T. 2010, ArXiv e-prints,arXiv:1001.5117

Mitchell, J. L., Pierrehumbert, R. T., Frierson, D. M. W., &Caballero, R. 2006, Proc. Natl. Acad. Sci. U.S.A., 103, 18421

Mitchell, J. L., & Vallis, G. K. 2010, J. Geophys. Res., 115, 12008

Muirhead, P. S., Hamren, K., Schlawin, E., et al. 2012,Astrophys. J. Let., 750, L37

Navarra, A., & Boccaletti, G. 2002, Clim. Dyn., 19, 467Nettelmann, N., Fortney, J. J., Kramm, U., & Redmer, R. 2011,

Astrophys. J., 733, 2Obukhov, A. M. 1971, Boundary-Layer Meteorology, 2, 7O’Gorman, P. A., & Schneider, T. 2008, J. Climate, 21, 3815Pedlosky, J. 1987, Geophysical Fluid Dynamics (Spinger)Pierrehumbert, R. T., Abbot, D. S., Voigt, A., & Koll, D. 2011,

Ann. Rev. Earth Planetary Sci., 39, 417Pierrehumbert, R. T., & Swanson, K. L. 1995, Ann. Rev. Fluid

Mech., 27, 419Prinn, R. G., & Fegley, B. 1987, Ann. Rev. Earth Planetary Sci.,

15, 171Quintana, E. V., Barclay, T., Raymond, S. N., et al. 2014,

Science, 344, 277Rhines, P. B. 1975, J. Fluid Mech., 69, 417—. 1979, Ann. Rev. Fluid Mech., 11, 401Rogers, L. A., Bodenheimer, P., Lissauer, J. J., & Seager, S. 2011,

Astrophys. J., 738, 59Schneider, T., Graves, S. D. B., Schaller, E. L., & Brown, M. E.

2012, Nature, 481, 58Schneider, T., & Walker, C. C. 2006, J. Atmos. Sci., 63, 1569Selsis, F., Wordsworth, R. D., & Forget, F. 2011, Astronomy and

Astrophys., 532, A1Showman, A. P., Wordsworth, R. D., Merlis, T. M., & Kaspi, Y.

2014, Atmospheric Circulation of Terrestrial Exoplanets (TheUniversity of Arizona Press), 277–326

Sinukoff, E., Fulton, B., Scuderi, L., & Gaidos, E. 2013, SpaceSci. Rev.

Teske, J. K., Turner, J. D., Mueller, M., & Griffith, C. A. 2013,Mon. Not. of the Roy. Astro. Soc., 431, 1669

Valencia, D., Sasselov, D. D., & O’Connell, R. J. 2007, Astrophys.J., 656, 545

Vallis, G. K. 2006, Atmospheric and Oceanic Fluid Dynamics(pp. 770. Cambridge University Press.)

Voigt, A., Abbot, D. S., Pierrehumbert, R. T., & Marotzke, J.2011, Clim. of the Past, 7, 249

Williams, G. P. 1988, Clim. Dyn., 2, 205Williams, G. P., & Holloway, J. L. 1982, Nature, 297, 295Wordsworth, R., & Pierrehumbert, R. 2013, Science, 339, 64Wordsworth, R. D., Forget, F., Selsis, F., et al. 2011, Astrophys.

J. Let., 733, L48Yang, J., Boué, G., Fabrycky, D. C., & Abbot, D. S. 2014,

Astrophys. J. Let., 787, L2Yang, J., Cowan, N. B., & Abbot, D. S. 2013, Astrophys. J. Let.,

771, L45