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Icarus
journalhomepage:www.elsevier.com/locate/icarus
The circulation pattern and day-night heat transport in the
atmosphere of a synchronously rotating aquaplanet: Dependence on planetary rotation rate
S. Noda
a,1,∗, M. Ishiwatari
b,c, K. Nakajima
d, Y.O. Takahashi
a,c, S. Takehiro
e, M. Onishi
a,2, G.L. Hashimoto
f, K. Kuramoto
b,c, Y.-Y. Hayashi
a,caDepartment of Planetology, Kobe University, Kobe 657-8501, Japan
bDivision of Earth and Planetary Sciences, Hokkaido University, Sapporo 060-0810, Japan
cCenter for Planetary Science, Kobe University, Kobe 650-0047, Japan
dDepartment of Earth and Planetary Sciences, Kyushu University, Fukuoka 819-0395, Japan
eResearch Institute for Mathematical Sciences, Kyoto University, Kyoto 606-8502, Japan
fDepartment of Earth Sciences, Okayama University, Okayama 700-8530, Japan
a rt i c l e i n f o
Article history:
Received 29 September 2015 Revised 21 August 2016 Accepted 6 September 2016 Available online 1 October 2016 Keywords:
Astrobiology Atmospheres, dynamics Atmospheres structure Extra-solar, planets Meteorology
a b s t r a c t
Inordertoinvestigateapossiblevarietyofatmosphericstatesrealizedonasynchronouslyrotatingaqua- planet,anexperimentstudyingtheimpactofplanetaryrotationrateisperformedusinganatmospheric generalcirculationmodel(GCM)withsimplifiedhydrologicalandradiativeprocesses.Theentireplane- tarysurfaceiscoveredwithaswampocean.Thevalueofplanetaryrotationrateisvariedfromzeroto theEarth’s,whileotherparameterssuchasplanetaryradius,meanmolecularweightandtotalmassof atmosphericdrycomponents,andsolarconstantaresettothepresentEarth’svalues.Theintegrationre- sultsshowthattheatmospherereachesstatisticallyequilibriumstatesforallruns;noneofthecalculated casesexemplifiestherunawaygreenhousestate.Thecirculationpatternsobtainedareclassifiedintofour types:Type-Icharacterizedbythedominance ofaday-nightthermallydirectcirculation, Type-IIchar- acterizedbyazonalwavenumberoneresonantRossbywaveoverameridionallybroadwesterlyjeton theequator,Type-IIIcharacterizedbyalongtimescalenorth-southasymmetricvariation,andType-IV characterizedbyapairofmid-latitudewesterlyjets.Withtheincreaseofplanetaryrotationrate,thecir- culationevolvesfromType-ItoType-IIandthentoType-IIIgraduallyandsmoothly,whereasthechange fromType-IIItoType-IVisabruptanddiscontinuous.Overafiniterangeofplanetaryrotationrate,both Types-III and -IVemerge as statistically steady states, constitutingmultiple equilibria.In spite ofthe substantialchangesincirculation,thenetenergytransportfromthedaysidetothenightsideremains almostinsensitivetoplanetaryrotationrate,althoughthepartitionintodrystaticenergyandlatentheat energytransportschanges.Thereasonforthisnotableinsensitivityisthattheoutgoinglongwaveradia- tionoverthebroadareaofthedaysideisconstrainedbytheradiationlimitofamoistatmosphere,so thatthetransporttothenightside,whichisdeterminedasthedifferencebetweentheincomingsolar radiationandtheradiationlimit,cannotchangegreatly.
© 2016TheAuthors.PublishedbyElsevierInc.
ThisisanopenaccessarticleundertheCCBYlicense(http://creativecommons.org/licenses/by/4.0/).
1. Introduction
A numberof recentsystematic surveyshavediscovered many earth-sized exoplanets (e.g., Torres et al., 2015). Many of those
∗ Corresponding author. Fax: +81 75 753 3715.
E-mail address: [email protected] (S. Noda).
1 Present address: Division of Earth and Planetary Sciences, Kyoto University, Ky- oto 606-8502, Japan
2 Present address: Department of Earth Sciences, Okayama University, Okayama 700-8530, Japan
planetsexistinsidethetidallockradiusoftheircentralstars,and are thought to be synchronously rotating (e.g., Von Bloh et al., 2007). Evenwhen the globalmean incoming heat flux from the central star is comparableto that of the presentEarth’s, the in- cidentflux onthe perpetualdayside ofa synchronouslyrotating planetcaneasilyexceedtheradiationlimitofamoistatmosphere, whichistheupperlimitofoutgoinglongwave(infrared)radiation atthetop oftheatmosphere(OLR)definedbyaone-dimensional radiative–convective equilibrium model of an atmosphere with a sufficient amount of liquid water on its bottom surface (Nakajima et al., 1992). So, a synchronously rotating planet may http://dx.doi.org/10.1016/j.icarus.2016.09.004
0019-1035/© 2016 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY license ( http://creativecommons.org/licenses/by/4.0/ ).
2 S. Noda et al. / Icarus 282 (2017) 1–18
easilyentertherunawaygreenhousestateifthedayside tonight side(hereafter,day-night)energytransportisinsufficient.
However, inprevious studiesonatmospheresofsynchronously rotatingplanetsusinggeneralcirculationmodels(GCMs),therun- awaygreenhousestatedoesnotemergeforseveraldifferentvalues ofplanetaryrotationratewiththepresentvalueoftheEarth’sso- larconstant (e.g.,Joshi, 2003; MerlisandSchneider, 2010;Edson etal.,2011). Evenwiththea solarconstant 1.9timesthat ofthe Earth,Yang etal.(2013) obtains statisticallyequilibriumstates in anaquaplanetGCMexperiment,inwhichhighcloudalbedointhe regionsaroundthesubsolarpointpresumablypreventsarunaway greenhousestate. These results suggest that themechanism that determinestheamountofday-nightenergytransportstillremains tobeunderstoodanditsdependenceonplanetaryrotationrateto berevealed.Theseissuesmaybe crucialinconsideringthehabit- abilityofsynchronouslyrotatingexoplanets.
The atmosphericcirculationstructure,whichshouldbe related today-night energytransport,has beenshowntodepend onthe planetaryrotation rate (e.g., Showman et al., 2013), which is, in this paper, represented by ∗, the value divided by that of the presentEarth:7.272×10−5 s−1. Using aGCM witha slab ocean, MerlisandSchneider (2010) obtains a day-night thermally direct circulation in the case with ∗=1/365, whereas high-latitude westerliesemerge inthe casewith ∗=1.The latter circulation pattern is similar to that obtained earlier by Joshi (2003) with ∗=1. Merlis and Schneider (2010) names the two circulation regimes the “slowly rotating regime” and the “rapidly rotating regime”, respectively. However, there is little information on the transitionbetweenthesetworegimes.Edsonetal.(2011)explores the ∗ dependence of the atmospheric circulation structures of bothdryandmoistplanets,andshowsthat,inadditiontothetwo regimessimilartothoseidentifiedbyMerlisandSchneider(2010), aregime witha strong westerlyzonal wind inlow latitudes ap- pearswithintermediatevaluesof∗.Itisalsoshownthat,forthe dryplanetcondition,an abruptchangeofzonalwindvelocityoc- cursandmultipleequilibriawithhystereticbehaviorexistbetween ∗=0.109and∗=0.25.However,correspondingmultipleequi- libriafortheaquaplanethavenotbeendescribedclearly.
As for day-night energy transport, Merlis and Schneider (2010)showsthattheamountsofmoiststaticenergytransportare almostthe sameforthe twocases with∗=1/365 and∗=1, butthereisnoinformationaboutenergytransportforintermedi- atevaluesof∗.Edson etal.(2011)describes∗ dependencesof minimum,maximum,andgloballyaveragedmeansurfacetemper- ature,butdoesnot present that ofenergy transport. Thedepen- denceofday-nightenergytransporton∗,togetherwithpossible constraintsonit,remaintobeexplored.
Recently, GCMexperimentshavealsobeenperformedinorder toexaminepossibleclimatesonsynchronouslyrotatingterrestrial exoplanetswithparticularparametersetupsestimatedfromobser- vations(e.g.,HengandVogt,2011;Wordsworth etal.,2011).Nat- urally, detailed parameter dependence is not examined in these works,sincetheyfocusonexplorationofclimatesfortheparame- tersofparticularexoplanets.
In thispaper, a series of GCM runs with ∗ incremented by smallstepsisperformedunderasimplesetupconsideringamoist planetthatrotatessynchronously.Wewillattempttoconfirmthat, forthe same value of incomingsolar flux asthat ofthe present Earth’s, statistically equilibrium statesare obtainedand the run- awaygreenhousestatedoesnotoccurforvariousvaluesof∗in- cludingthosethatarenot closelyexaminedintheprevious stud- ies.We alsoexamine how ∗ affects theatmospheric circulation structure andday-night energy transport, andconsider what de- terminestheamountofday-nightenergytransport.Thesamesim- ple model configuration as used in Ishiwatari et al. (2002) and Ishiwatari etal. (2007)is adopted, namelycloud-free conditions,
grayradiation, swampocean andso on.This choice allows usto compare the results of the experiment directly with our previ- ousstudiesshowingthatthethree-dimensionalmoistatmosphere evolvesintotherunawaygreenhousestate whentheglobalmean insolationexceedstheradiationlimit.Using theswampcondition allows the system to reach a statistically equilibrium state in a shorter time than with a slab ocean, andis convenient forexe- cutionofalargenumberofrunswithvarious ∗ andinitialcon- ditions.Varying theseinitialconditionsis necessaryto searchfor possiblemultipleequilibriumsolutions.
The specification of the GCM and the experimental setups are describedinSection 2. Therealization ofstatisticallyequilib- rium statesis confirmed, andan overview of the dependenceof the structure of the atmospheric circulation on ∗ are given in Section3.Fourtypicalcaseswithdifferentvaluesof∗arechosen andtheir associatedstructures ofatmospheric circulationare de- scribedinSection4.Thedependenceofday-nightenergytransport on ∗ isanalyzed, and itis argued that day-night energytrans- portisconstrainedbytheradiationlimitofamoistatmospherein Section5.DiscussionsandconclusionsaregiveninSection6. 2. Modelandexperimentalsetup
The GCM utilized in this study is DCPAM5 (the Dennou-Club Planetary AtmosphericModel, http://www.gfd-dennou.org/library/
dcpam/index.htm.en), which is reconstructed from GFD-Dennou- ClubAGCM5 usedin Ishiwatarietal.(2002) andIshiwatarietal.
(2007)withadesignconvenientfornumericalexperimentsonvar- iousplanetaryatmospheres.WithDCPAM5,itisconfirmedthatthe runawaygreenhousestate emerges underthe sameconditionsas thoseofIshiwatarietal.(2002).Hereweusethesamemodelcon- figurationasthat ofIshiwatari etal.(2002).Thegoverning equa- tions fordynamicalprocesses arethe primitiveequations.Simple parameterizationschemesare adoptedforphysicalprocesses.The atmosphereconsistsofwatervapor anddryair. Bothdryairand watervaporare transparenttoshortwaveradiation,andonlywa- tervaporabsorbslongwaveradiationwithconstantabsorptionco- efficient(0.01m2 kg−1). Themoistconvectiveadjustmentscheme (Manabeetal.,1965)isusedasacumulusparameterization.Con- densed water is immediately removed from the atmosphere as rain.There isno cloud;absorption andscatteringofradiation by cloudsare not incorporated. The surfaceof theplanet isentirely coveredwiththeswampocean,anoceanwithzeroheatcapacity.
Itis assumedthattheocean doesnottransport heathorizontally anddoesnotfreeze. Thesurfacealbedo issettozero.Abulkfor- mula(Louisetal.,1982)isusedforsurfacefluxcalculation.
Inorderto drawon existingknowledge ofthepresentEarth’s atmosphere,the valuesofparameters usedinourexperimentare basicallythoseoftheEarthexceptforplanetaryrotationrateand obliquity.Thevaluesofmolecularweightandspecificheatofdry airaresetto28.964×10−3kgmol−1 and1004.6 JK−1kg−1,re- spectively.Thevaluesofmolecularweightandspecificheatofwa- tervapor aresetto18.0×10−3 kgmol−1 and1810.0 JK−1 kg−1, respectively.TheplanetaryradiusRp issetto6.371×103 km.The accelerationofgravityis9.80665 ms−2,andglobalmeansurface pressureis105Pa.Thesynchronouslyrotatingplanetisconfigured withtheobliquitysettozero,andthedistributionofsolarincident fluxfixedtotheplanetarysurface(Fig.1)accordingto
Ssolar=S0max[0,cos
φ
cos( λ
−λ
0)
], (1)where
φ
is latitude andλ
is longitude, with subsolar longitudeλ
0=90◦ and solar constant S0=1380 W m−2, which is about 88% ofthethresholdvalue (S0=1570W m−2 ) toenter therun- away greenhouse state obtained by the non-synchronously rotat- ing aquaplanet experiment by Ishiwatari et al. (2002). We use 16 values of∗: ∗ = 0, 0.05, 0.1, 0.15,0.2, 0.25, 0.33, 0.5, 0.6,Fig. 1. Horizontal distribution of the incident solar flux [W m −2] given by Eq. (1) . Contour interval is 300 W m −2.
0.67,0.7,0.75,0.8,0.85, 0.9,and1.Hereaftereachcasewillbere- ferredtoascharacterfollowedbythevalueof∗.Forexample, 0.05isthe casewithorbital periodof20 Earthdays.Notethat changing ∗ withfixed solarconstant means changingthe lumi- nosityofthecentralstar.Althoughnoplanetwith∗=0existsin reality,weexaminethecirculationstructureofthisidealizednon- rotatingplanetasthelimitingcaseofsmall∗.
Forthehorizontaldiscretization,we usethespherical spectral transformmethodwithtriangulartruncationattotalwavenumber 21 (T21), giving 64 grid-points for the longitudinal axis and 32 grid-pointsforthelatitudinalaxis.Astheverticalcoordinate,
σ
≡ p/psisadopted,wherepsissurfacepressure.Thenumberofverti- cal levelsis setto16.Themodeltop levelissettoσ
=0.02.We performedtest runsforseveralvalues of∗employing32 verti- cal levels withthe top level ofσ
=9.2×10−5. The results show noqualitativechangeineithertheatmosphericcirculationcharac- teristicsortheenergybudgetcomparedwiththosewith16verti- cal levels;thechangeindaysideaveraged OLRisatmost10 W m−2 (figures not shown), which is negligibly small compared to the value ofOLR itself. Wealso conducteda highresolution test experimentuptoT341with∗=1,andconfirmedthatthelarge scale circulationandthe surfacetemperature patternsare mostly unchanged. Thesesensitivitytestsshowthattheverticalandhor- izontal resolutions are adequate for the present purpose. Some aspects of the resolution dependence are demonstrated later in AppendixA.Foreach ∗, weperform 10runs. As will bediscussed inthe following sections, we have recognized that initial condition de- pendenceappearsforcertainvaluesof∗;differenttypesofcircu- lationpatternsresultfromslightlydifferentinitialconditions.The initial condition foreach run is an isothermal (280K) resting at- mosphere with a small temperature perturbation in the formof randomnoisewithamplitudeof0.1Kaddedtoallgrid-points;we preparetendifferentperturbationfieldsforthetenruns.Eachrun isintegratedfor2000Earthdays,andthedatafromthelast1000 daysareusedforanalysis.
3. Dependenceofatmosphericcirculationcharacteristicson planetaryrotationrate
In all runs the atmosphere reaches a statistically equilibrium state;therunawaygreenhousestatedoesnotemerge.Fig.2shows temporalchangesoftheglobalmeanvaluesofsurfacetemperature andOLRobtainedinfourtypicalrunswithdifferentvaluesof∗. In every case, theatmospheresettlesdown after about300days toa statisticallyequilibriumstateinwhichbothglobalmeansur-
Fig. 2. Time series of global mean quantities. (a) Surface temperature [K] and (b) OLR [W m −2]. Green, light-blue, black, and red lines indicate 0.0, 0.15, 0.75, and 1.0, respectively. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
facetemperatureandOLR fluctuatearound their equilibriumval- ues.Thetemporalmeanvaluesofglobalmeansurfacetemperature andthemagnitudesoftemperaturefluctuationdifferamongruns.
The structure of the atmospheric circulation varies with ∗. Fig.3summarizesthevarietyofglobaldistributionsoftimemean surface temperature for various values of ∗. For each value of ∗,theresultofasinglerunarbitrarily chosenfromthetenruns is plotted. In Fig. 3, we can identify at least three features that characterize the variety of surface temperature. First, an equato- rialwarmbeltinthenighthemisphereispresentin0.05−0.8 (Fig.3b–m),whileitisabsentintheothercases.Second,theequa- torialregionisgenerallywarmerin0.0−0.8(Fig.3a–m),while the mid-latitude regions are warmer in the other cases. These twofeaturesabovereflectthemeridionalstructuresofzonalmean zonalwind,aswillbeshownlater.Third,anorth-southasymmetry isevident in 0.6−0.8 (Fig. 3i–m),whileit is absent orweak intheothercases.Thislastfeaturereflectsthepresenceofnorth- southasymmetricvariabilitywithlong timescales,aswillbede- scribedinSection4.3.
Fora morequantitative descriptionofthegeneraldependence of the atmospheric circulation structure on ∗, bearing in mind the three features of the surface temperature fields identified above,we examine the∗-dependences offourquantities. These arethesurfacetemperaturesatthe subsolarandantisolarpoints, theuppertroposphericzonalmeanzonalwindattheequator,and a measure ofnorth-south asymmetry in the surfacetemperature
4 S. Noda et al. / Icarus 282 (2017) 1–18
Fig. 3. Horizontal distributions of 10 0 0-day mean surface temperature for all of the computed values of ∗. Contour interval is 5 K.
withshorttimescaletransientsfilteredoutdefinedby
NS[Ts]≡ 1 2
π
π/2 0
2π 0
T˜s( λ
,φ )
−T˜s( λ
,−φ )
dλ
cosφ
dφ
, (2) where T˜s is the 50 day running average of surface temperature, andtheoverbarmeansthetemporalaverageover1000days.Fig.4 showsthe∗dependencesofthesefourquantities.Notethatthe tenrunsforeachvalue of∗ areplottedseparately.Now wecan identifytwoseparatebranchesofatmosphericstates:oneextend- ingfrom∗=0to ∗=0.8(hereafter, thesmall-branch),and theotherfrom∗=0.7to∗=1(hereafter,thelarge-branch).Between∗=0.7and∗=0.8,thesetwo branchescoexist, giv- ingmultipleequilibria. Thepreferencebetweenthetwo branches in the range of the multiple equilibria seems to depend on the valueof∗;theratioofrunsonthelarge-branchincreasesfrom 10%for∗=0.7to80% for∗=0.8.Thebranchtakenbyapar- ticularrundependson smalldifferencesin theinitial conditions.
Itis determined inthe first ∼500 daysof themodel integration,
andthereisnoswitchingtotheother branchafterthat.Notethat thoseshowninFig.3k–mbelongtothesmall-branchbychance;
therearealsorunsbelongingtothelarge-branchforthisrange of∗,withsurfacetemperaturestructuresimilar tothoseshown inFig.3n–p.
In Fig. 4 we observe that the atmosphericcirculation charac- teristicschangecontinuouslybutmarkedlyonthesmall-branch.
When∗=0,bothzonalmeanzonalwindandnorth-southasym- metry are negligible.As ∗ increases,the westerlywind intensi- fies rapidly, andthe night side surfacetemperature rises rapidly, both ofwhichare tiedtothe appearanceofthe equatorialwarm beltidentifiedinFig.3b–m.Thetemperatureatthesubsolarpoint fallsatfirst,thenrises.Thenorth-southasymmetryremainssmall.
Around∗=0.5, thenorth-southasymmetryincreases,andcon- tinuesto increaseswithincrease of∗.Theasymmetry hasbeen identified in Fig. 3i–m, but is not evident in cases 0.2–0.5 (Fig. 3e–h), where, aswill be shown later, the temporal scale of the variability is short compared with the averaging period of
Fig. 4. ∗dependences of (a) surface temperature [K] at the subsolar point, (b) surface temperature [K] at the antisolar point, (c) zonal mean equatorial zonal wind [m s −1]
at σ= 0 . 17 , and (d) degree of north-south asymmetry of surface temperature defined by Eq. 2 in the text [K]. The values are temporal averages between day 10 0 0 and day
20 0 0. All 10 runs for each ∗case are plotted. Red and blue lines are ensemble averages for the small- and the large- branches, respectively. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
1000-days. Until the end of the small- branch at ∗=0.8, the values of temperature at the subsolar and antisolar points re- main high, and the zonal mean wind at the equator maintains its strength.Onthelarge-branch,theuppertroposphericzonal meanwind iseasterly. Thetemperatureislower than thatofthe small- branch at both the subsolar and antisolar points, and north-south asymmetry is weak. Changes in the four circulation characteristicsarerathersmallovertheentirerange(0.7࣠∗࣠1) ofthelarge-branch.
4. Typicalatmosphericcirculationstructures
Inorderto understandtheatmosphericcirculationandits de- pendence on∗ onthe synchronouslyrotatingplanet,we exam- ine here the spatialstructures andtemporal variation of the so- lutions indetail.Althoughthe circulationstructure changesmore orlesscontinuously as∗ changesonthesmall-branchasim- plied in Figs. 3 and 4, we can classify the circulation structures into three types according to the zonal wind structure and the temporal variability. They are, in order of the planetary rotation ratewheretheyappear,Type-I,characterizedbyday-nightconvec- tion,Type-II,characterized bya broadequatorialwesterlyjet and a north-south symmetric stationary wave-like pattern that turns out tobeastationaryRossbywave, andType-III,characterizedby longtimescalenorth-southasymmetricvariability.Inthelarge- branch we can classifythe circulationstructure asType-IV, char- acterized by a pair of mid-latitude deep westerly jets. For each of the four types, we choose one case and examine it in detail below.
4.1. Type-I:day-nightconvection(case0.0)
TheType-I circulationappearsincases withvery smallvalues of∗,andischaracterizedbyday-nightconvection;itissimilarto thoseobtainedwithsmall∗inearlierstudies(Edsonetal.,2011;
MerlisandSchneider,2010).Weexaminecase0.0asarepresen- tativecaseofType-I.
Thetime meanstructureoftheatmosphericcirculationincase 0.0 is shown in Fig. 5. Upper tropospheric horizontal flow di- verges towardthe nightside (Fig.5b) fromthe concentrated up- ward motion at the subsolar point, where intense precipitation develops(Fig.5e).Theoutflowisstrongnotonlyintheuppertro- posphere(
σ
∼0.23)butalsoatthemiddlelevelsaroundσ
∼0.55 (Fig. 5c). In the middle troposphere, the entire planet except at thesubsolarpointiscoveredwithawidespread,weak,andalmost homogeneous downwardflow (Fig.5c). In the lower troposphere (σ
∼ 0.9), the air flow divergesfrom the antisolarpoint and re- turnstothedayside,connectedtotheflowconvergingtowardthe subsolarpoint.The surface temperature distribution (Fig. 5h) closely follows theincidentsolarflux distribution(Fig.1).The nightsidesurface temperature is almost homogeneous; its variation is as small as 10 K, being by far the smallest among all the experiments. The surfacepressuredistribution(Fig.5a)canbeinterpretedasadirect responsetothesurfacetemperaturedistribution;anotablefeature isthe heatlow inthe lower troposphereofthe dayside (Fig. 5a andc).Temperature on thenight side isgenerallyhighestin the middlelevels(
σ
∼0.6)andlower nearerthesurface(Fig.5c).In contrast,temperature in the heat low around the subsolar point (20°≤λ
≤160°),increaseswithdecreasingaltitude.6 S. Noda et al. / Icarus 282 (2017) 1–18
Fig. 5. Day 10 0 0 to day 20 0 0 temporal mean fields for case 0.0. (a) Surface pressure (color shading) [Pa] and horizontal wind vectors [m s −1] at the lowest level. Contour interval of surface pressure is 5 ×10 2Pa, and the unit vectors of zonal and meridional wind are 20 m s −1. (b) Horizontal wind vector [m s −1] and geopotential [J kg −1] at σ= 0 . 17 . Unit vector indicates 25 m s −1. Contour interval of geopotential is 500 J kg −1. (c) Vertical wind −σ˙ [s −1] and zonal wind [m s −1] (vector), and temperature [K] (color) in the equatorial vertical section. Unit vectors of vertical wind and zonal wind are 1 . 67 ×10 −5s −1and 50 m s −1, respectively. Contour interval of temperature is 5 K. (d) Specific humidity at the equator. Contour interval is 2 ×10 −3. (e) Condensation heating [W m −2]. Color interval is 50 W m −2. White area represents heating over 20 0 0 W m −2. (f) Horizontal distribution of surface evaporation [W m −2]. Color interval is 50 W m −2. (g) Vertically integrated water vapor flux [m s −1] and vertically integrated water vapor mass [kg m −2]. Unit vector is 0.3 m s −1. Contour interval is 10 kg m −2. (h) Surface temperature [K]. Contour interval is 5 K. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Thehydrologicalcycleisgovernedbythedirectday-nightcircu- lation.Surfaceevaporationhasitsmaximumatthesubsolarpoint, andisverysmalloverthewholenightside(Fig.5f).Rainfalloccurs almostexclusivelyaround thesubsolar point(Fig.5e).The middle level outflow from the subsolar point (Fig. 5c) advects moist air into thenightside, producing relativelymoist tongues(0.45≤
σ
≤0.65,
λ
<210°andλ
>320°)(Fig.5d).However,themagnitude oftheverticallyintegratedwatervaporflux(Fig.5g)isfairlysmall comparedtothosefortheothercirculationtypes.4.2. Type-II:stationaryRossbywaveonbroadequatorialwesterlyjet (case0.15)
The Type-II atmospheric circulation structure appears for 0.05 ࣠∗ ࣠0.2 and is characterized by a warm region on the night side(Fig.3b–d) belowan intensebroadequatorialwesterly wind as shownin Fig. 4c,andlarge amplitude wavenumber one stationary waves in the higher latitudes. These features are also seen in thecirculations obtainedin an intermediate range of∗ byEdsonetal.(2011).Weexaminecase0.15asarepresentative caseofType-II.
Thetimemeanstructureoftheatmosphericcirculationincase 0.15 is shownin Fig. 6. The mostnotable feature is the emer- gence ofa broadanddeep westerlywind that coversalmost the wholedepthofthetroposphere(Fig.6c)ofthelow-latitudinalre- gion (Fig. 6b). In the bottom layer near the surface, a trace sig- natureofday-nightcirculationcanstillbe noted(Fig.6a).Thelo- cation of maximum rainfall andthe associated deep updraft are shiftedeastwardfromthesubsolarpointbyabout20°(Fig.6cand e),possiblyduetomoistureadvectionbythedeepwesterlywind.
The surface temperature peak is also shifted eastward from the subsolar point by 25° (Fig. 6h). Asimilar eastward shift emerges alsointheothercasesonthesmallbranch,explainingthedrop insubsolarpointsurfacetemperatureat∗∼0(Fig.4a).Thepeak ofevaporationremains atthesubsolar point(Fig.6f). Infact,the latent heat flux around the equator on the dayside changes lit- tle overtherangeof∗examined inthisstudy.The insensitivity to ∗ results fromtheemployment ofthe swampsurfacecondi- tion and cloud free condition; the incoming shortwave radiation reaching the ground surface has fixed geographical distribution, andmustbeapproximatelybalancedby theenergylossbylatent heat of evaporation. The surfacepressure minima are located at (
λ
,φ
) ∼ (120°,±15°);theseare not onlyto theeast of thesub- solar point,butalso off the equator (Fig. 6a). Thehigher-latitude regions are characterized by intense wavenumber one stationary wavesmanifested astheridgearoundλ
∼150°andthecyclones around(λ
,φ
)∼(330°,±60°)(Fig.6b).Thepressuresignaturesare generally geostrophic, and have an equivalent barotropic vertical structure suggestedby thelow surfacepressuresignaturesbelow theupperlevellowpressurearea(Fig.6a).The deep, broad equatorial westerly wind transports a large amount of sensible and latent heat to the night side, which is manifested as the warm and moist tongue in the lower to the middletroposphereextendingeastwardcrossingtheterminatorat
λ
=180◦(Fig. 6cand d).Aconsiderable portion(about one fourth) of the watervapor transported to the night side atλ
=180◦ re- turnstothedaysideatλ
=360◦ (figurenotshown).Atλ
=180◦, watervaportransporttothenightsideismoreintenseinthehigh- latitudinal regions than in the equatorial region, resulting from themeandering oftheeastwardwindassociatedwiththeintense wavenumber one stationary waves and near surface westward windneartheequator.Rainfallisnolongerfocusedatthesubso- larpoint,asitisassociatedwiththemoisturetransport,andsome amount of rainfalloccurs even in thenight hemisphere (Fig. 6e) despite the negligibly small amount of surface evaporation. Also duetotheenhancedwatervaportransport,thecolumnintegratedmoisture content around the antisolar point reaches about three timesthatincase0.0(Fig.6g).Actually,columnintegratedmois- turecontentincreasesconsiderablyalsoonthedayside;thepeak valuenearthesubsolarpointincase0.15isabout1.5timesthe valueofthatincase0.0,anditsassociatedgreenhouseeffectre- sults in the rise of surfacetemperature following the drop near ∗∼0(Fig.4a).
Itisnotablethatthehorizontaldistributionofsurfacetemper- aturecloselyfollowsthatofcolumnmoisturecontentonthenight side (Fig.6g and h);in an extensive region of highcolumn wa- tervaporcontentinthelowlatitudes,surfacetemperatureishigh, whereasit isverylow inthedryregions located aroundthelow pressurecentersofwavenumberonestructureathigherlatitudes.
The energy budget at the ground surface explains this close re- lationship; because incident solar flux is absent and both latent (∼2 W m−2) and sensible (∼ −4 W m−2) heat fluxes are negli- gibly smallon the night side, the upward thermal radiationflux (∼230 Wm−2)atthesurfacealmostbalancesthedownwardlong- waveradiationfromtheatmospherethatisexclusivelyemittedby watervapor,theonlyradiativelyactivecomponentinthismodel.
Whenall Type-II casesare compared,the broadequatorialjet is stronger forthe cases with larger value of ∗ as indicated in Fig.7,wherethevaluesofmassweightedglobalmeanzonalwind velocity in Type-II are shown. Moreover, for ∗ ࣡0.2, thewind speedis closetotheabsolutevaluesof theintrinsicphasespeed ofthe normalmode Rossbywave of Longuet-Higgins(1968). The thinlinein Fig.7 showsthe intrinsicphase speed ofthe merid- ionallygravestnormalmodeRossbywavewithwavenumberone, whichwe calculatewiththe spectral methodof Kasahara(1976). ConsideringtheverticalstructureofthewavesappearinginType- II,weassumeanequivalentdepthof10000 m,whichisthevalue for the barotropic mode in an isothermal atmosphere of 245 K.
The rough coincidenceof thespeed of thebroad eastwardequa- torial jet andthat ofthe intrinsically westward propagating nor- malmodeRossbywaveforeach∗suggeststhatthewavenumber oneplanetaryscalestationarywaveinType-IIisresonantlyexcited on the broad westerly jet. Other evidence for the resonant exci- tation is the ∗-dependence of the amplitudeand phase of the stationarywavenumberonewaves.Thecyclonicregionsassociated withthewavesare expressed asthenorth-southsymmetriccold regionsinthenightsidemidtohighlatitudes(Fig.3).For∗from 0.05to0.2,theamplitudeofthecyclonicregionsisgenerallylarge.
Thelongitudinalphase difference betweenthe precipitationmax- imumandthe cycloniccenters is about270°for ∗= 0.05. This isthe largest eastwardphase shift ofthe upperRossby wave re- sponse to a wavenumber one thermal forcing in a westerlyflow fasterthantheresonant speed.As ∗ increases,thephase differ- encedecreases,droppingbelow180°for∗=0.25and0.33.Pos- siblemechanismsforthe accelerationofthe broadwesterlywind anditsresonantrelationtothenormalmodeRossbywaveswillbe discussedinmoredetailinSection6.3,referringtoearlierstudies.
For∗ ࣡ 0.25, the westerlywind doesnot reach the normal modeRossbywavespeed.Ourpreliminaryanalysisrevealsthat,in thesecases,mid-latitudetransientdisturbances, which mayorig- inatefrombaroclinic instability giventhedevelopmentof merid- ional temperature gradient (not shown), transport westerly mo- mentumpolewardanddeceleratethe broadwesterlyjet. Detailed analysisonthenatureofthetransientdisturbancesandtheir pos- sibleroleasthe“governor” oftheequatorialjetremainstobeper- formed.
4.3.Type-III:longtimescalenorth-southasymmetricvariability (case0.75)
The Type-III atmospheric circulation structure appears on the small- branch for 0.5 ࣠ ∗ ࣠ 0.8. The temporally averaged
8 S. Noda et al. / Icarus 282 (2017) 1–18
Fig. 6. Same as Fig. 5 but for case 0.15, except that the unit vector in (b) is 50 m s −1and the unit vector of vertical wind in (c) is 2 . 5 ×10 −6s −1.
characteristicsofType-III aresimilar to thoseof Type-IIin terms ofthestrongeastwardequatorialjet,but,asshowninFig.4d,dif- ferinthepresenceofsignificantnorth-southasymmetriclongtime scalevariability.
Before considering the Type-III circulation structure in detail, wesummarizethe∗dependencesoftheamplitudeandthetyp- ical oscillation period of the north-south asymmetric variability.
Fig.8comparesthetime seriesofzonalmeansurfacepressurein
fourcaseswithdifferentvaluesof∗.Incase0.2,whereType- II structure develops,a quasi periodic oscillation withamplitude of∼20hPa anda temporal scale of∼10 days isnotable. In case 0.5,inadditionto anoscillationwith∼20dayperiod,aslower, north-southasymmetricvariability isevident; its periodandam- plitudeare∼40–100daysand∼45hPa,respectively.Incaseswith larger∗,theslow,north-southasymmetricvariabilityismorein- tense and its characteristic period is longer; in case 0.67, the
Fig. 7. Mass weighted global mean zonal wind velocity for cases with ∗from 0.0 to 0.33 (circles). Absolute value of westward phase velocity of the zonal wavenum- ber one gravest Rossby normal mode is indicated by the thin line for comparison.
amplitudeis∼80hPa,andtheperiodis∼1000days.Incase0.75, the amplitudeisaslarge as∼160 hPa,and, looks almost perma- nent in Fig. 8d. However, by conductingseveral extended exper- iments, we have confirmed that the asymmetry does change its sign over a long time;the pressure deviationreverses at around t=25000 days for the run shown in Fig. 8d. Furthermore, the sign ofthe asymmetry is determined by chance;inthe ten runs conductedfor0.75, Type-IIIstructure appears infourruns(not shown), and, during the period shown in Fig. 8d, two of them have a positive pressure anomaly in the northern highlatitudes, andtheremainingtwoarenegative.Weconcludethat,despitethe developmentofthedistinctlongtimescalenorth-southasymmet- ric variation, the structure ofthe atmosphericcirculation is,in a
statisticalsense, north-southsymmetric,consistentwiththesym- metryoftheappliedsolarflux.
Consideringthecharacteristicsofthenorth-southvariation,we examinecase0.75asrepresentativeofType-III,wherethenorth- southasymmetry appearsasaquasistationarystructurethatper- siststhroughoutthe1000daysofthetemporalaverage.Asshown inFig.8d,northern(southern)highlatitudesareoccupiedbyhigh (low) pressure throughoutthe averaging period. The north-south asymmetricfeaturesdiscussedbelowarenaturallyreversedinthe timeperiodwhenthesurfacepressureinthenorthern(southern) hemisphereislow(high).Wealsonotethatthenorth-southasym- metricatmosphericcirculationfeaturesdevelopalsoinGCMexper- imentswithhigherhorizontalresolution(T42 andT85),although theyappearinslightlydifferentrangesof∗(seeAppendixA),so webelievetheiremergenceitselfisinsensitivetomodelresolution.
Thetime meanstructureoftheatmosphericcirculationincase 0.75isshowninFig.9.Thedeepwesterlyflowalong theequa- tor(Fig.9bandc),andtheassociatedeastwardadvectionofwater vapor (Fig.9d andg) resultingin awarm belt along theequator inthenighthemisphere (Fig.9h), arefeatures similarto thosein Type-II (Fig. 6). However, except for the distribution of evapora- tion,whichisstronglyconstrainedby insolationaswasdiscussed forType-II,mostoftheoff-equatorialfeaturesexhibitnorth-south asymmetry in contrast to the north-south symmetry in Type-II.
Northern(southern) highlatitudes are covered withsurfacehigh (low) pressure (Fig. 9a). The low pressure area inthe day hemi- spherealsoexhibitsnorth-southasymmetry;thelowpressurecen- ter in the southern hemisphere is much more intense than its counterpartinthenorthernhemisphere.Beingingeostrophicbal- ancewiththepressuregradientaroundthepolarpressureanoma- lies,north-easterly(north-westerly)windprevailsatthesurfacein northern (southern) mid latitude (arrows in Fig. 9a). This brings dry(moist)airintothemidlatitudesoftheday(night)hemisphere (Fig.9g)crossingtheday-nightboundaryat
λ
=180◦,inducingtheFig. 8. Latitude–time distribution of zonal mean surface pressure [Pa] for (a) 0.2, (b) 0.5, (c) 0.67, and (d) 0.75.
10 S. Noda et al. / Icarus 282 (2017) 1–18
Fig. 9. Same as Fig. 6 but for case 0.75, except that the unit vector of vertical wind in (c) is 1 . 3 ×10 −6s −1.
north-westward(south-eastward)developmentofthemid-latitude precipitationzone(Fig.9e)andthenorth-southasymmetryofsur- facetemperatureinboth thedayandnighthemispheres(Fig.9h) throughtheanomalyindownwardthermalradiation.
Twoadditional featurescharacterize thenorth-southasymme- try. First, the westerly region extends farther poleward in the
southern hemisphere thanin thenorthern hemisphere (Fig. 10a), where intense baroclinic disturbances develop (not shown here), presumablytransportingwesterly momentumdownward. Second, there is a baroclinic zonal wavenumber one feature (Fig. 9ab) whichhasmarkedlynorth-southasymmetricmeridionalphasetilt (Fig. 10b); the phase lines tilt from northwest to southeast in
Fig. 10. Structure of the atmosphere averaged from day 10 0 0 to day 20 0 0 for case 0.75: (a) zonal mean zonal wind, and (b) eddy stream function at σ= 0.17.
a wide latitudinal zone from the northern high latitudes (
φ
∼ +70◦) tosouthern midlatitudes(φ
∼ −40◦),crossing theequator.The phase tilt of the zonalwavenumber one feature, which im- plies southward transport of westerly momentum from northern to southern hemispheres, presumably contributes to driving the mid-latitudewesterlyjetinthesouthernhemispherenotedabove (Fig.10a).
According to our preliminary analysis (not shown here) of the vorticity sources following the formulation of Sardeshmukh andHoskins(1988),themeridionally tilted wavenumberone fea- tureseems to be forcedjointlyby tropical andextratropical pre- cipitation (Fig. 9e); the heating near the subsolar point, which is distributed mainly in the northern tropics around (
λ
,φ
)= (120◦,+12◦),canbe regarded as anexcitation source ofa Rossby wave that contributes the northern half of the wavenumber one structure.Meanwhilethelatentheatingassociatedwiththeprecip- itationbandinsouthernmidlatitudesdistributedaround(λ
,φ
)= (180◦,−30◦),canbe regardedasan excitationsourceofaRossby wave thatcontributesthesouthern half.Upwardcascadeofbaro- clinic eddies developingin the westerlyjet could also contribute to the southern half. The distribution of mid-latitude precipita- tion seems to be, in turn, induced by the north-south asymme- tryofmoisture fluxassociatedwithsurfacepressureasdescribed in the previous paragraph. Combining these features, the north- south asymmetry maypossibly be maintainedthrough a positive feedbackloop,sothattheasymmetrytendstohavelonglifetime.Quantitativeexaminationofthedynamicsofthispossiblefeedback loopremainsforfuturestudies.
4.4. Type-IV:mid-latitudewesterlyjets(case1.0)
TheType-IVatmosphericcirculationstructureisfoundoverthe entirelarge-branchfor∗࣡0.7, and ischaracterized bysome- whatEarth-like mid-tohigh- latitudeswesterlyjets.Thisissimi- lartothestructures obtainedby MerlisandSchneider(2010) and Edsonetal.(2011)with∗=1,althoughseveralpointsofdiffer- encecan be noted (See Section 6.1). We examine case1.0asa representativecaseofType-IV.
Thetimemeanstructureoftheatmosphericcirculationincase 1.0isshowninFig.11.Themidlatitudesare occupiedbywest- erly windsthrough thewhole depth ofthe troposphere (Fig. 11a andb).The lowlatitudesare occupiedbyeasterlywind, butonly intheuppertroposphere.Thelowertroposphericcirculationalong theequator(Fig.11c)ismorestronglycontrolledbytheday-night contrast; zonalwind near the surfaceconverges to formthe up- ward motion at the subsolar point, and diverges around the an- tisolarpointcompensatedby thebroaddownwardmotion.Inthe off-equatoriallatitudes,latitudinaltiltingofzonalwavenumberone wavefeatures arenotable,butthesehavegenerallybaroclinicver-
ticalstructure,incontrasttothebarotropicRossbywaveinType-II.
Polarregionsarecoveredwithdeeplowpressureareas.
Theprecipitationandwatervapordistributionsaremorecom- plicatedthanthoseonthesmall-branch.Precipitation(Fig.11e) is most intense in a zonally aligned V-shaped region extending from the equatorial point (
λ
,φ
) ∼ (110°, 0°) to (λ
,φ
) ∼ (30°,±25°), loosely overlapping the low pressure area in the western part of the day hemisphere (contours in Fig. 11a). The wings of theV-shapedprecipitationregionintrudeintothenightsidefrom theregions around
φ
=±25◦ atλ
=360◦. There isalso a pairof zonallyelongatedprecipitationzoneinthehigherlatitudes,which startat(λ
,φ
) ∼ (45°,±45°)andextendto(λ
,φ
)∼ (330°,±80°) onthenightside.Thedistributionofcolumnintegratedwaterva- porcontentroughlyfollowsthatofprecipitation(Fig.11g),butthe areasofgreatestmoisture content arelocated farfromtheequa- tor,polewardofthehigh-latitudepartsoftheequatorialV-shaped strongprecipitationareaat(λ
,φ
)∼(50°,±30°).The distribution of night side surface temperature (Fig. 11h) closely follows that of the atmospheric water vapor content (Fig.11g)asinthecasesonthesmall-branch.However,reflect- ing the complex structure ofhumidity, temperature varieslongi- tudinally;it iswarmer tothe eastalong
φ
∼ ±30°,whereasit is warmertothewestalongφ
∼ ±50°.Alsothedistributionofsur- facetemperatureonthedaysideisaffectedbythedistributionof watervapor content; the highest surfacetemperature appears at (λ
,φ
)∼(80°,±40°),thelocationsthatarequitefarfromthesub- solarpointandbelowthebeltsoflarge watercontent(deep blue colorsof Fig.11g).The valuesofsurfacetemperature atthesub- solarandantisolarpointsare lower thantherespective valuesin Types-IIor-III(Fig.4aandb),resultingfromthereductionofat- mosphericwatercontentcomparedtothosecases.5. Day-nightenergytransport 5.1. Dependenceon∗
In this section, we examine how day-night energy transport changeswith ∗,respondingto theconsiderable variationof the atmosphericcirculationstructuredescribedintheprevioussection.
WeanalyzeOLRonthenightside,FOLR,day-nightdrystaticenergy transport,Tsens,andday-nightlatentenergytransport,Tlat,which, inequilibriumstates,satisfytheenergybalanceofthenightside:
Tsens+Tlat−2
π
R2pFOLR=0. (3) TsensandTlat arecalculatedassumingtheapproximatebalancesof heat and moisture budgets in the night side atmosphere, which are2
π
R2p(
FSLR+Fsens−FOLR+LP)
+Tsens=0, (4)12 S. Noda et al. / Icarus 282 (2017) 1–18
Fig. 11. Same as Fig. 9 but for case 1.0 except that unit vector of the vertical wind in (c) is 2 . 5 ×10 −6s −1.
2
π
R2p(
Fevap−P)
+Tlat/L=0, (5) whereFevap is surface evaporation flux, FSLR is net upward long- wave radiation flux at the surface, Fsens is surface sensible heat flux,P isprecipitation,andL islatentheat ofwatervapor. All of the termsare 1000-day mean values spatially averaged over the nightside.Fig. 12a shows ∗ dependences of FOLR, Tsens/(2
π
R2p), and Tlat/(2π
R2p). All 10 runs are plotted for each value of ∗. Themost remarkable feature is that total energy transport is almost unchangedregardlessofthebranchofthesolution andthe value of∗, whilethe partition intoTsens andTlat changes. For∗∼0, where the Type-I structure appears, Tlat is negligible, as atmo- sphericwatervaporcontentisverysmall(Fig.5g).As∗increases andthe Type-IIstructure appears,Tlat rapidly increases,butTsens
decreases correspondingly,keeping thesumof the two (FOLR) al- mostunchanged.TheincreaseofTlat resultsfromthedevelopment of the deep broad westerly wind (Fig. 6b and c) together with theincrease ofmoisture inthe dayhemisphere (Fig.6d). Further
Fig. 12. (a) ∗dependences of outgoing longwave radiation on the night side, F OLR( ), day-night dry static energy transport per unit area, T sens/ (2 πR 2)( ), and day-night latent energy transport per unit area, T lat/ (2 πR 2) ( ×). Units are [W m −2]. All 10 runs for each ∗case are plotted. Blue and red lines represent ensemble averages for the small- and the large- branches, respectively. (b) Same as (a) but for global mean ( ), day side mean ( ×), and night side mean ( ) of surface temperature [K]. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
increaseofTlat anddecreaseofTsens continueforlarger∗asthe Type-III withnorth-southasymmetricvariability appears.Tlat ex- ceeds Tsens at∗=0.33andTlat reachesabouttwice Tsens atthe large- end of the small- branch (∗=0.8). Still, the sum of thetwo (FOLR)is keptalmost constant.Atthe transitionfromthe small-branchtothelarge-brancharound∗∼0.75,Tlat sud- denly reduces by about half. Nevertheless, an equally abruptin- creaseofTsensmeansthattotalheattransportchangesonlyalittle.
ThedeclineofTlatatthetransitionresultsfromtheassociateddis- appearanceofthebroadwesterlywindatlowlatitudes.Thetype- IVstructurehasapairofdeepmid-latitudewesterlyjetsblowing throughthedayandnightsides(Fig.11b),buttheycannottrans- portasmuchwatervaporasthebroadequatorialwesterlywindin the Type-IIorType-III cases,becausethewater vapormixingra- tiointhemidlatitudesissmallerthaninthelowerlatitudes.The variation oftotal day-night energy transport islessthan 2% over thewiderangeof∗,whiletheatmosphericcirculationstructure varies considerably. Day-nighttotal energy transport scarcely de- pendsontheatmosphericcirculationstructure.
We have already seen in Fig. 4b that surface temperature at the antisolar point changes greatly with the change of ∗. This seemsperplexing,sinceday-nighttotalenergytransportisalmost constant. However, if we examine the hemispherically averaged temperature, the change is only modest. Fig. 12b shows ∗ de- pendences of surface temperature averaged over the night side, the dayside, and thewhole globe. The rangeof the variation of night side average temperature is around 10 K, which is much smaller than thevariation atthe antisolar point ofalmost 50 K (Fig.4b).Thisresultsfromthecompensationbetweenthetemper- ature variationsin thelower andhigherlatitudes; inType-II and Type-III,surfacetemperatureinthelowlatitudesincludingthean- tisolarpointishigh, whileregions oflowsurfacetemperatureap- pear in the higher latitudes associated with the large amplitude Rossbywaves(Fig.3b–m).Theremainingmodestchangesofaver- agedtemperaturescanbeexplainedmainlybythechangeofmean columnwatervaporcontent.
5.2. Moistatmosphereradiationlimitconstraint
As described in the previous subsection, the total amount of day-nightenergytransportisfoundtobeinsensitivetothechange of ∗ and to the associated change of atmospheric circulation structure. The invariance of day-night total energy transport is equivalenttotheinvarianceofdaysideOLR,becausetheday-night total energytransport isequalto thedifference betweenthe day side OLRandtheincident solarflux; thelatterisconstant inthe presentstudy.Ithasbeenrecognized that,inthe frameworkofa
Fig. 13. Relationships between surface temperature and OLR obtained by the GCM and by the one-dimensional (vertical) radiative-convective equilibrium model. The GCM results are shown as colored dots: purple, light blue, green, and pink dots indicate runs 0.0, 0.15, 0.75, and 1.0, respectively. Data are from the grid points in the 120 °×120 °rectangular region centered on the subsolar point. Crosses in black circles indicate the values at the subsolar point. Black lines are the one-dimensional model results with tropospheric relative humidity of (in order from the top) 50, 60, 70, 80, 90, and 100%, respectively. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
one-dimensionalradiativeconvectiveequilibriummodel,thevalue of OLR fromthe atmosphere on a water covered planet can not exceedtheradiationlimit.Inthefollowing,weattempttounder- stand the invariance of day-night energy transport in relation to the constrainton the dayside OLR fromthe radiation limit of a moistatmosphere.
Fig.13showstherelationshipbetweensurfacetemperatureand OLR on the day side obtained by the present GCM calculations superposedonthe relations obtainedby theone-dimensional ra- diative convective equilibrium model described in Section 4 of Ishiwatari et al. (2002) with several specified values of tropo- spheric relative humidity. The relationship betweensurface tem- peratureandOLRissampledatthegridpointswithinthe120°× 120° rectangularregion centered on the subsolar point from the runforeach∗describedintheprevioussection.
InalltheGCMruns,themaximumvaluesofOLRarebetween 400 and430 W m−2, andlie under the valuesof the radiation limitsintheone-dimensionalcalculation,giventhatthevaluesof relative humidityaveraged overthe troposphere on the dayside oftheGCMrunsare withinthe range60–80%.Moreover,ineach oftheGCMresults,therelationshipbetweensurfacetemperature and OLR roughly follows those obtained in the one-dimensional calculations. These results imply that the day side OLR in the
14 S. Noda et al. / Icarus 282 (2017) 1–18
presentGCMcalculationsis constrainedby the radiation limit of amoistatmosphereonawatercoveredplanet.Nowrecallingthat the system is in a statistically equilibrium state, the amount of day-nighttotalenergytransportshouldbeequaltothedifference betweentheincidentsolarfluxandtheradiationlimitofamoist atmosphere.TheresultsofourGCMcalculationsindicatethatthe change in atmospheric circulation structure associated with the changeof ∗ doesnot modify drastically the mean value of at- mospheric humidity, and hence doesnot affect the value ofthe radiationlimit.Thisexplainsthegeneralinsensitivityofday-night energytransportto∗obtainedinthepresentGCMcalculations.
6. Concludingremarks
6.1.Summaryofresultsandcomparisonwithpreviousstudies
Numerical experiments are performed using a cloud-free, swamp aquaplanet GCM with a gray absorption coefficient for longwaveradiationandwiththeEarth’ssolarconstant. Thevalue ofplanetaryrotation ratenormalizedby the Earth’svalue, ∗, is variedfrom0to1.Forall∗cases,statisticallyequilibriumstates areobtained;therunawaygreenhousestatedoesnot emerge.The circulationstructuresobtainedareclassifiedintofourtypes:Type- Icharacterized by day-night convection, Type-II characterized by a broad equatorial westerly jet and a stationary Rossby wave, Type-IIIcharacterizedbyalongtimescalenorth-southasymmetric variability,andType-IV characterized by a pairof mid-latitudinal westerlyjets. Types-I, II, andIII evolve continuously fromone to anotheras ∗ increases, constituting one branch ofthe solution referred to as the small- branch, whereas Type-IV belongs to a differentbranch referred to asthe large- branch (Fig. 4). For 0.7࣠ ∗ ࣠0.8, multiple equilibriumstates emerge; both Type- III and Type-IV are allowed. The dependence of the amount of day-nightenergytransporton∗isanalyzed.Itisconfirmedthat theamount is large enough to prevent the day side atmosphere fromentering arunawaygreenhousestate.Moreover,theamount isfoundtobe almostinsensitiveto∗despitethedrasticchange inthestructure ofthe atmosphericcirculation,although thepar- tition into latent andsensible energy transports varies. Day side OLRintheexperimentsisanalyzedandcomparedwiththevalues obtainedwitha one-dimensionalradiative convective model.The resultsstronglysuggestthatdaysideOLRisconstrainedbythera- diationlimitofamoist atmosphere;thedetails ofthe circulation structuredonotgreatlychangeatmospherichumidity,sothevalue oftheradiationlimitisunchanged.Thisexplainstheinvarianceof day-nightenergytransport,asitisequaltothedifferencebetween incomingsolarfluxanddaysideOLR.Theformerisaconstantpre- scribedamountinthisstudy,andthelatterisconstrainedby the radiationlimit.
Itshouldbeusefultore-examinethecirculationcharacteristics obtainedinpreviousstudiesfromthepresentviewpoint,sincethis studyhasperformeda morecompleteinvestigation ontheir sen- sitivityto∗ thanprevious studies. The “slowlyrotatingregime”
andthe“rapidlyrotatingregime” identifiedbyMerlisandSchnei- der(2010)presumablycorrespondtothesmall-branchandthe large- branch in the present study, respectively. However, the correspondenceis not certain because they present the horizon- tal distributions of atmospheric variables for only two values of ∗.Circulation structures similar to those of Type-I andType-IV are obtained forthose two values of ∗, but it remains unclear whetherthey obtained atmospheric structures similar to Type-II andType-III. The dependence of the circulation structure on ∗ obtained by Edson et al. (2011) can be compared with the re- sults of the present study withmore confidence.They observed two separate branches of solutions with multiple equilibria, and solutions withplanetarywaves of zonalwavenumber one super-
posedonbroadwesterlywindinthelow latitudesforintermedi- ate valuesof ∗.These features are similar to those obtainedin thepresentstudy.
However, more carefulcomparisonsuggests afew differences.
Oneisthe differenceofthedirectionsofthe zonalmeanequato- rial upper tropospheric wind obtained
