Revisiting the scattering greenhouse effect of CO2 ice clouds

3.5 MB·

by  Daniel Kitzmann

To appear in The Astrophysical Journal Letters
PreprinttypesetusingLATEXstyleemulateapjv.12/16/11
REVISITING THE SCATTERING GREENHOUSE EFFECT OF CO ICE CLOUDS
2
D. Kitzmann1
CenterforSpaceandHabitability,UniversityofBern,Sidlerstr. 5,3012Bern,Switzerland
To appear in The Astrophysical Journal Letters
Abstract
Carbondioxideicecloudsarethoughttoplayanimportantroleforcoldterrestrialplanetswiththick
CO dominated atmospheres. Various previous studies showed that a scattering greenhouse effect
2
by carbon dioxide ice clouds could result in a massive warming of the planetary surface. However,
all of these studies only employed simplified two-stream radiative transfer schemes to describe the
6
1 anisotropic scattering. Using accurate radiative transfer models with a general discrete ordinate
0 method,thisstudyrevisitsthisimportanteffectandshowsthatthepositiveclimaticimpactofcarbon
2 dioxide clouds was strongly overestimated in the past. The revised scattering greenhouse effect can
haveimportantimplicationsfortheearlyMars,butalsoforplanetsliketheearlyEarthortheposition
n
of the outer boundary of the habitable zone.
a
J Keywords: planets and satellites: atmospheres — astrobiology — radiative transfer

6

1. INTRODUCTION factorfortheimpactofCO cloudsonearlyMarsmight
] 2
P CloudsarecommonintheatmospheresofSolarSystem be the cloud coverage, which could be well below 100%
E planets and are likely ubiquitous in those of extrasolar (Forget et al. 2013).
Especially, the outer boundary of the classical habit-
. planets as well. They affect every aspect of a plane-
h able zone (HZ) might also be influenced by the forma-
taryatmosphere,fromradiativetransfer,toatmospheric
p tion of CO ice clouds and their corresponding climatic
- chemistryanddynamics,andtheyinfluence–ifnotcon- impact. Fo2r the Sun, Forget & Pierrehumbert (1997) re-
o trol–aspectssuchasthesurfacetemperatureand, thus,
portedanouterHZboundaryof2.4auforaplanetfully
r the potential habitability of a terrestrial planet (Marley
t covered with CO clouds, which is far larger than the
s et al. 2013). Understanding the impact of clouds is thus 2
cloud-free value of 1.67 au Kasting et al. (1993).
a instrumental for the study of planetary climates.
[ Clouds composed of carbon dioxide (CO ) ice parti- Thecompetingradiativecoolingandheatingeffectsare
cles are important for cold, CO -rich atmosp2heres. This individually large, but partly balance each other. That
1 2 meansthatsmallerrorsinthedescriptionofoneofthese
includes, for example, the present and early Mars (For-
v
radiativeinteractionscanleadtolargeerrorsinacloud’s
9 get & Pierrehumbert 1997), the early Earth (Caldeira
neteffect. Sofar,allpreviousstudiesontheclimaticim-
0 & Kasting 1992), or terrestrial exoplanets at the outer
pact of CO clouds used a simplified treatment for the
2 boundaryofthehabitablezone(Forget&Pierrehumbert 2
numerical solution of the radiative transfer equation to
1 1997; Kasting et al. 1993). Provided that condensation
determinetheatmosphericandsurfacetemperatures. In
0 nuclei are available, such clouds would form easily in a
particular, two-stream methods (Toon et al. 1989) have
. supersaturated atmosphere.
1 exclusively been used. With only two angular directions
Likeforwaterclouds(e.g. Kitzmannetal.(2010)),the
0 available to determine the radiation field, these methods
presenceofCO cloudswillfirstlyresultinanincreaseof
6 2 provide only limited means to describe e.g. the scatter-
theplanetaryalbedobyscatteringincidentstellarradia-
1
ing phase function of the CO ice particles well enough
: tionbacktospacewhichleadstoacoolingeffect(albedo 2
v effect). In contrast to liquid or solid water, CO ice is to yield accurate results for describing radiative effects
i mostly transparent with respect to absorption in2the in- based on anisotropic scattering.
X
In a numerical radiative transfer study by Kitzmann
frared (Hansen 1997, 2005). Thus, as argued by Forget
r et al. (2013), it was shown that these simplified two-
& Pierrehumbert (1997) or Kasting et al. (1993), a clas-
a
streammethodsunderestimatethealbedoeffectatshort
sical greenhouse effect by absorption and re-emission of
wavelengths and overestimate the back-scattering of
thermal radiation is unlikely to occur for a cloud com-
thermalradiationwhichformsthebasisofthescattering
posed of dry ice. On the other hand, CO ice particles
2 greenhouse effect. However, this previous study did not
canefficientlyscatterthermalradiationbacktotheplan-
use an atmospheric model and, thus, was unable to es-
etarysurface,therebyexhibitingascatteringgreenhouse
timate the impact of a more accurate description of the
effect. In their seminal study, Forget & Pierrehumbert
scattering greenhouse effect on the surface temperature.
Forget & Pierrehumbert (1997) showed that this scat-
In this study, I will therefore re-asses the climatic im-
tering greenhouse effect of CO ice clouds alone would
2 pactofCO cloudsusingasophisticatedradiativetrans-
have been efficient enough to allow for liquid water on 2
fer scheme. Since most of the studies related to the cli-
the surface of the early Mars. This strong heating effect
matic impact of CO ice clouds have been done for early
was also found in later studies by e.g. Pierrehumbert & 2
Mars, I will use the same modeling scenario to compare
Erlick(1998),Mischnaetal.(2000),orColaprete&Toon
my atmospheric model calculations with the previously
(2003). However,byusingthree-dimensionalgeneralcir-
published results.
culation models, it has been suggested, that a limiting
2 Kitzmann
2. MODELDESCRIPTION this study, eight streams are used for all model calcula-
tions. Doublingthenumberofstreamshasnoimpacton
To investigate the impact of CO ice clouds, I use a
2 the resulting radiation fluxes and surface temperatures.
one-dimensionalradiative-convectiveclimatemodel. The
The wavelength-dependent absorption by atmospheric
model incorporates a state-of-the-art radiative transfer
molecules and clouds is treated by the opacity sampling
treatment based on a discrete ordinate method (Hamre
method, which is one of the standard methods employed
etal.2013)whichisabletotreattheanisotropicscatter-
in cool stellar atmospheres (Sneden et al. 1976). In con-
ingbycloudparticlesaccurately(Kitzmannetal.2013).
The atmospheric model is stationary, i.e. it doesn’t trast to the k-distribution method with the correlated-k
assumption, opacity sampling still operates in the usual
contain an explicit time dependence, and assumes hy-
wavelength/wavenumberspace(Mihalas1978). Thisap-
drostatic equilibrium. About one hundred grid points
proach has the advantage, that absorption coefficients of
are used to resolve the vertical extension of the atmo-
all atmospheric constituents are fully additive. Essen-
sphere. The model currently considers N , CO and
2 2 tially, opacity sampling can be regarded as a degraded
H O. Ofthose,onlyCO andH Oare,however,usedin
2 2 2 line-by-line formalism. It is based on the fact that the
this study.
wavelength integral of the radiation flux converges al-
Thetemperatureprofileiscalculatedfromtherequire-
ready well before all spectral lines are fully resolved. At
ment of radiative equilibrium by a time-stepping ap-
each single wavelength, however, the solution with the
proach,aswellasperformingaconvectiveadjustment,if
opacity sampling method is identical to a corresponding
necessary. Theconvectivelapserateisassumedtobeadi-
line-by-line radiative transfer.
abatic,takingintoaccountthecondensationofH Oand
2 For this study, the distribution of the wavelength
CO . A surface albedo of 0.215 based on measurements
2 points at which the equation of radiative transfer is
of present Mars is used (Kieffer et al. 1977). A more de-
solved,istreatedseparatelyinthreedifferentwavelength
tailed model description will be presented in Kitzmann
regions. In the infrared, the points are sampled along
(2016).
the Planck black body curves for different temperatures.
ThismethodisadoptedfromHelling&Jorgensen(1998)
2.1. Radiative transfer
and guarantees an accurate treatment of the thermal ra-
In contrast to many other atmospheric models for ter-
diationwithasmallnumberofwavelengthpoints. Inthe
restrial exoplanets, the radiative transfer of this study
visibleandnearinfraredregion,10000wavelengthpoints
is not separated into two different wavelength regimes.
are distributed equidistantly in wavenumbers. This re-
Instead, one single, consistent radiative transfer scheme
gionismostimportantforthetemperatureprofileinthe
within the wavelength range from 0.1µm to 500µm is
upperatmospherewherethetemperaturesareessentially
used. At each distinct wavelength point, the plane-
determinedbyabsorptionofstellarradiationwithinwell-
parallel radiative transfer equation
separated lines. Beyond the visible wavelength region,
about 100 points are used to cover the smooth Rayleigh
dI
µ λ =I −S (τ ) (1) scattering slope and resolving the stellar Lyman alpha
dτ λ λ,∗ λ
λ emission line. In total about 12500 discrete wavelength
is solved, with the general source function points are used here. Tests by increasing the wavelength
resolution show virtually no change in the wavelength-
S (τ )=S (τ )+(1−ω )B
λ λ λ,∗ λ λ λ integrated flux. In fact, the high number of integration
ω (cid:90) +1 (2) pointsinthenearinfraredregioncouldalsobedecreased
+ 2λ pλ(µ,µ(cid:48))Iλ(µ(cid:48))dµ(cid:48) , if one is not interested in the temperatures near the top-
−1 of-the atmosphere.
where S is the contribution of the central star, B Absorption cross-sections for CO and H O are cal-
thePlanλck,∗function,ω thesinglescatteringalbedo,andλ culated as described in Wordswort2h & Pie2rrehumbert
λ
p (µ,µ(cid:48)) the scattering phase function. (2013), using the HITRAN 2012 database (Rothman
λ
The scattering phase function is represented as an et al. 2013). For these calculations, the open source
infinite series of Legendre polynomials (Chandrasekhar Kspectrum code (version 1.2.0) is used. In case of CO ,
1960) the sub-Lorentzian line profiles of Perrin & Hartman2n
(1989) are employed, while the contribution of collision
∞
(cid:88) induced absorption is taken from Baranov et al. (2003).
p (µ,µ(cid:48))= (2n+1)P (µ)P (µ(cid:48))χ (3)
λ n n λ,n The continuum absorption of H O is derived from the
n=0 MT-CKD description (Mlawer e2t al. 2012). Rayleigh
withtheLegendrepolynomialsP (µ)andthephasefunc- scatteringisconsideredforCO andH O(vonParisetal.
n 2 2
tion moments χ . In practice the series is truncated 2010).
λ,n
at a certain n = N . For discrete ordinate methods
max
the number of moments N is equal to the number of
ordinates (streams) considmeraexd in the radiative transfer 2.2. Cloud description
equation (Chandrasekhar 1960). The atmospheric model also takes the radiative effect
The equation of radiative transfer is solved by the dis- ofcloudsdirectlyintoaccount. FollowingForget&Pier-
crete ordinate solver C-DISORT (Hamre et al. 2013). In rehumbert (1997), the size distribution of the CO ice
2
contrasttotwo-streammethods,ityieldsthemathemat- particles is described by a modified gamma distribution
ically exact solution of the transfer equation for a given
sthetatofetnraonusgphorctocmopeffiutcaiteinotnsaalnsdtrpehaamsesfaurnectiinocnlus,dperdo.vidFeodr f(a)= (aΓeff(cid:0)ν1)−22−ν1(cid:1)/νa(ν1−3)e−aeaffν (4)
ν
Revisiting the scattering greenhouse effect of CO ice clouds 3
2
2
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att
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metry 0.5 aaeeffff==1500µµmm
asym aaeff==110000µ0µmm Fpeigruatruer2e.. SIumrfpacaecttemofpCerOat2ureicsearceloshuodwsnoansathfuencstuiornfaocfeoptteimca-l
eff
0 depth (at a wavelength of λ=0.1 µm) and effective particle size
10−1 100 101 102 103 of the CO ice clouds. The black contour lines are given in steps
of5K.Th2ewhitecontourlineindicatestheclear-skycase.
wavelength (µm)
Figure 1. Optical properties of CO2 ice particles. Re- present-day Martian Solar irradiance. A high-resolution
sults are shown for four different size distributions: a =10 µm spectrum of the present-day Sun from Gueymard (2004)
eff
(blue line), aeff =50 µm (green line), aeff =100.0 µm (red line), isusedforthespectralenergydistributionoftheincident
a = 1000 µm (black line). Upper diagram: optical depth (for
τe=ff 1), middle diagram: single scattering albedo, lower diagram: stellar flux.
asymmetryparameter. Because a supersaturated CO -rich atmosphere would
2
describedbytheeffectiveradiusa andaneffectivevari- provide a huge amount of condensible material, dry ice
eff
ance of 0.1 (Forget & Pierrehumbert 1997). particles would grow rapidly, thereby potentially reach-
Assumingsphericalparticles,theopticalpropertiesare ing large particle sizes under these conditions. The only
calculated via Mie theory, using the refractive index of detailed microphysical study for particle formation on
CO ice from Hansen (1997, 2005). The resulting op- early Mars obtained mean particle sizes of the order of
tica2l properties are shown in Fig. 1 for some selected 1000µm (Colaprete & Toon 2003). Thus, to cover this
valuesoftheeffectiveradiusandanopticaldepthofone. verywideparameterrange,theeffectiveparticlesizesare
Theopticaldepthτ ofthecloudsreferstotheparticular varied between 10µm and 1000µm in the following. A
wavelength of λ=0.1 µm throughout this study. total cloud coverage is assumed to obtain an upper limit
The Henyey-Greenstein function (Henyey & Green- fortheclouds’climaticimpact. Thecloudlayerisplaced
stein 1941) is used to approximate the scattering phase into the supersaturated region of the cloud-free atmo-
function. Although it lacks the complicated structure sphere around a pressure of 0.1 bar. This corresponds
and detailed features of the full Mie phase function, the roughly to the position of the cloud layer in Forget &
Henyey-Greenstein function preserves its average quan- Pierrehumbert (1997) and Mischna et al. (2000).
tities, suchastheasymmetryparameterg. TheHenyey- SincethepublicationofForget&Pierrehumbert(1997)
Greensteinphasefunctionisusuallyaverygoodreplace- orMischnaetal.(2000),severalupdatestothemolecular
mentoftheMiephasefunction,especiallyathigheropti- linelistsanddescriptionofthemolecule’scontinuumab-
caldepthsorifoneisonlyinterestedinangularaveraged sorptionwereintroduced. Whilethegreenhouseeffectof
quantities,suchastheradiationflux(vandeHulst1968; CO became less effective (Wordsworth et al. 2010), the
2
Hansen 1969). absorptivity of H O increased, especially due to changes
2
in the continuum absorption (Mlawer et al. 2012) and
3. EFFECTOFCO CLOUDSINTHEEARLYMARTIAN the line parameters (Rothman et al. 2013). Therefore,
2 ATMOSPHERE to limit the impact of the different molecular line lists
TocomparetheclimaticimpactofCO icecloudswith on the comparison, only CO is considered as an atmo-
2 2
previous model studies, I use the same model set-up as sphericgasinthefollowing. Thiscorrespondstothe“dry
inForget&Pierrehumbert(1997),whostudiedtheinflu- case” in Forget & Pierrehumbert (1997).
ence of CO clouds in the atmosphere of the early Mars. In the clear-sky case, the surface temperature is about
2
Thus,followingForget&Pierrehumbert(1997)orMis- 220Kandthusroughly8KsmallerthanreportedbyFor-
chna et al. (2000), a CO surface pressure of 2 bar is get & Pierrehumbert (1997) and Mischna et al. (2000).
2
used on a planet with the radius and mass of Mars. To This is caused by a revised collision induced absorption
simulate the conditions for early Mars with a less lumi- (CIA) of the CO gas, yielding a smaller greenhouse ef-
2
nous Sun, the incident stellar flux is set to 75% of the fect (Wordsworth et al. 2010).
4 Kitzmann
Theresultingsurfacetemperaturesforthecloudycases
80
are shown in Fig. 2 as a function of the cloud particle a =10 μm
eff
sizesandopticaldepth. Intotal,severalhundredsofindi- a =50 μm
vidualmodelcalculationshavebeenperformedtoobtain K) 60 eff
thIenreasgurletesminenFtigw.it2h. previous studies (Forget & Pierre- (ar−sky
humbert 1997; Pierrehumbert & Erlick 1998; Mischna Tcle40
geetffreeaeclnt.ih2vo0eu0rs0ae;dCeiiffolealacrptg.reertAtehn&aneTffiaocboioenuntt201g00r3eµ)em,nChcOoaun2serpeaserufftleitccliten,sahwoniwteht- T − cloudy20
ever, is only possible within a certain particle size range
and for medium values of the optical depth. Particles 0

larger than roughly 500µm are more or less neutral or - 0.11 2 4 6 8 10 12 14 16 18 20
at high optical depths - even exhibit a net cooling effect. Optical depth
These particles are too large to feature an efficient back- Fthigeusruer3fa.ceCtoemmppaerriastounreofwtihthe pimrepvaicotusofstCudOi2es.cloTuhdesdoian-
scatteringoftheupwellingthermalradiation. Theirlarge gram shows the changes of the surface temperature in the pres-
asymmetry parameters at thermal infrared wavelengths enceofCO iceclouds(T )withrespecttotheclear-skycase
2 cloudy
results in thermal radiation being predominantly scat- (T ), compared to the results of Forget & Pierrehumbert
clear−sky
tered in the upward direction and, thus, away from the (1997)andMischnaetal.(2000). Thickerlinesrefertosurfacetem-
peraturesabovethefreezingpointofwater. Theresultsareshown
surface. In order to obtain the highest possible green-
fortwoeffectiveradii: a =10µm(blue)anda =50µm(red).
houseeffect,theparticlesizesmustbecomparabletothe Solid lines denote the reesffults from this study, daesffhed-dotted lines
wavelength of the atmospheric thermal radiation below thedryatmosphereresultsfromForget&Pierrehumbert(1997)for
the cloud layer (cf. also Kitzmann et al. (2013)). This is comparison. Thesinglethreebluemarkerscompareresultsforan
atmosphere fully saturated with water (circle: this study, square:
only the case for aeff ≈ 25µm which therefore provides Mischnaetal.(2000),triangle: Forget&Pierrehumbert(1997)).
the largest net greenhouse effect.
In no case studied here, the freezing point of water is
reached-quiteincontrasttopreviousstudieswheresur-
face temperatures in excess of 300K had been found for -4
10
the same scenario (Forget & Pierrehumbert 1997). The eru 0.7
highest surface temperatures obtained for a pure 2 bar sse o
CO2 atmosphere are about 252K. Even considering the rp ro bed0.6
8enKcesdiiffnetrhenecreesduulteintgostuhrefacreevsitseemdpCeOra2tuCreIsAb,etthweeednifftehre- 10-3 pav n nd al0.5
different radiative transfer approaches are astonishingly oita Bo
large. However, it should be noted, that the lower colli- ruta 0.4
siincioeflAnupeiadnnridrcteieucccltteehsdceotaromebsaspuoaclrtrepiirnsttoigaoninsncooaefftxttttehhereenindCcg.lOigm2raemetinochleoimcuuspleeasecfftmewicgtihtohtfattlhhsoee sure (bar)10-2 s OC2 er freezing point
pMriesvcihonuasesttuadl.ie(s20o0f0F)oirsgsehto&wnPiinerFreigh.u3m.bNerotte(,1t9h9a7t)Faonrd- Pres Wat
get & Pierrehumbert (1997) only used two effective radii
(10 and 50µm), while Mischna et al. (2000) is limited 10-1 cloud layer
to a single value of 10µm and studies only atmospheres
clear-sky
saturated with water vapor.
a =10µm
The results in Fig. 3 clearly suggest that the cli- eff
a =25µm
matic impact of CO clouds was strongly overestimated eff
in the past. The clou2d-induced temperature changes de- 100 aeff=100µm
a =500µm
termined here are several tens of Kelvin smaller in most eff
cases. Foranopticaldepthof10andaneffectiveradiusof 100 150 200 250 300
10µm also the results for a water-saturated atmosphere Temperature (K)
are compared. Again, the temperature increases due to Figure 4. Atmospheric temperature-pressure profiles for
the scattering greenhouse effect are between 20 and 30 the dry case influenced by CO clouds. The resulting tem-
2
K smaller than those found in Forget & Pierrehumbert perature profiles are shown for the clear-sky case (black line) and
for several values of the effective radius of the particle size distri-
(1997) or Mischna et al. (2000) for this particular case.
bution(seelegend). Theopticaldepthis8ineachcase. Theeffect
Additionally, Colaprete & Toon (2003) also claimed a ofCO cloudsontheenergytransportismarkedbydifferentline-
strong greenhouse effect for particle sizes of several hun- styles.2Solidlinesindicateatemperatureprofileinradiativeequi-
librium, dashed lines dry convective regions, and dashed-dotted a
dred µm, which, as already shown in Fig. 2, is clearly
moist CO adiabatic lapse rate. The vertical dotted line denotes
not the case. thefreezin2gpointofwater. Thedashed-dottedlinemarksthesat-
The presence of CO clouds also has a profound im- uration vapor pressure curve of CO . The position of the cloud
pactonthetemperatur2eprofile,asshowninFig. 4. Due layerisdenotedbythegrey-shadeda2rea. Theinsetplotshowsthe
planetary Bond albedos affected by the presence of the CO ice
to their scattering greenhouse effect, they strongly in- clouds. Coloursrefertothesameeffectiveparticlesizesmenti2oned
crease the atmospheric temperature locally, just below above.
the cloud base. This inhibits convection and creates a
Revisiting the scattering greenhouse effect of CO ice clouds 5
2
temperature profile where the usual fully convective tro- andJ.Unterhinninghofenfortheirsuggestionsandcom-
posphere is changed into a lower convective region near ments and especially B. Patzer for the fruitful discus-
thesurfaceandasecondoneabovethecloudlayer. Both sions. D.K also gratefully acknowledges the support of
convectiveregionsareseparatedbyatemperatureprofile the Center for Space and Habitability of the University
determined by radiative equilibrium (see also Mischna of Bern.
et al. (2000)). The local heating due to the cloud parti-
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