microphysical modeling of ethane ice clouds in titan’s ... of ethane due to methane cloud ......

Microphysical modeling of ethane ice clouds in Titan’s atmosphere

Erika L. Bartha,* and Owen B. Toonb

a Department of Astrophysical and Planetary Science and Laboratory for Atmospheric and Space Physics,University of Colorado, Boulder, CO 80309, USA

b Program in Atmospheric and Oceanic Sciences and Laboratory for Atmospheric and Space Physics, University of Colorado, Boulder, CO 80309, USA

Received 11 June 2002; revised 18 October 2002

Abstract

A time-dependent microphysical model is used to study the evolution of ethane ice clouds in Titan’s atmosphere. The model simulatesnucleation, condensational growth, evaporation, coagulation, and transport of particles. For a critical saturation of 1.15 (a lower limit,determined by laboratory experiments), we find that ethane clouds can be sustained between altitudes of 8 and 50 km. Growth due tocoalescence is inefficient, limiting the peak in the size distribution (by number) to 10�m. These clouds vary with a period of about 20 days.This periodicity disappears for higher critical saturation values where clouds remain subvisible. Rainout of ethane due to methane cloudformation raises the altitude of the ethane cloud bottom to near the tropopause and may eliminate ethane clouds entirely if methane cloudformation occurs up to 30 km. However, clouds formed above the troposphere from other gases in Titan’s atmosphere could be sustainedeven with rainout up to 30 km. Although the optical depth of ethane clouds above 20 km is typically low, short-lived clouds with opticaldepths of order 0.1–1 can be created sporadically by dynamically driven atmospheric cooling. Ethane cloud particles larger than 25�m canfall to the surface before total evaporation. However, ethane clouds remain only a small sink for tholin particles. At the peak of their cycle,the optical depth of ethane clouds could be comparable to that of tholin in the near-infrared, resulting in a 5% increase in Titan’s albedofor wavelengths between 1 and 2�m. A number of factors limit our ablility to predict the ethane cloud properties. These factors includethe mixing time in the troposphere, the critical saturation ratio for ethane ice, the existence of a surface reservoir of ethane, the magnitudeand timing of dynamically driven temperature perturbations, and the abundance and life cycle of methane clouds.© 2003 Elsevier Science (USA). All rights reserved.

Keywords: Titan; Atmospheres; Structure; Clouds

1. Introduction

Titan’s temperature profile allows for the condensationof many of its atmospheric constituents throughout the tro-posphere and lower stratosphere. Sagan and Thompson(1984) showed that most of the known hydrocarbons andnitriles can condense in the stratosphere while methanecondensation could occur in the troposphere. The onlyknown nuclei for tropospheric clouds on Titan are aerosolparticles sedimenting from the stratospheric haze layers.However, cloud formation may be a sequential process inwhich condensation first starts in the stratosphere, proceedsthrough the addition of a series of hydrocarbons and nitriles,

and finally ends with methane condensation in the middletroposphere.

The first observational evidence for clouds in Titan’slower atmosphere was reported by Griffith et al. (1998).From ground-based near-infrared data they concluded thatincreases in reflectivity at several wavelengths observedduring 2 out of 18 sampling periods indicate the temporarypresence of methane clouds in the troposphere around 15km. Later Griffith et al. (2000) found similar evidence forshort-lived methane clouds at a higher tropospheric altitude,around 30 km. These clouds may be indicative of a methanecycle on Titan similar to the Earth’s hydrological cycle.

McKay (1996) found that tholin (laboratory producedanalogs for Titan’s haze particles) are virtually insoluble inpolar solvents such as methane and ethane, concluding thatlarge supersaturations must build up before tholin particles

* Corresponding author. Fax:�1-303-492-6946.E-mail address: [email protected] (E.L. Barth).

R

Available online at www.sciencedirect.com

Icarus 162 (2003) 94–113 www.elsevier.com/locate/icarus

0019-1035/03/$ – see front matter © 2003 Elsevier Science (USA). All rights reserved.doi:10.1016/S0019-1035(02)00067-2

could serve as acceptable condensation nuclei. However,observations of water ice clouds in the terrestrial atmo-sphere indicate that the ice nuclei involved are most com-monly solid, insoluble particles. Hence, the methane icenucleability of tholins, which needs to be measured, isprobably not related to the solubility of tholins.

The major hydrocarbon product of methane photolysis isethane. Gillett et al. (1973) used ground-based telescopes tomake the first detection of ethane in the 12-�m region. Laterobservations from Voyager IRIS (in the same spectral re-gion) identified the vg band of ethane in Titan’s stratosphereand set the ethane mixing ratio at 2 � 10�5 (Hanel et al.,1981). Calculations from more recent ground-based mea-surements give mole fractions ranging from 4 � 10�6 to 1.6� 10�5, depending on the thermal profile used (Kostiuk etal., 1997). If we were to assume this mixing ratio is inde-pendent of altitude, then comparison with the ethane vaporpressure curve shows that ethane would be supersaturatedbetween approximately 5 and 62 km.

Sagan and Thompson (1984) calculated that ethaneshould condense around an altitude of 58 km. This samestudy estimated a visible optical depth of about 200 for theresulting ethane clouds (assuming 1 �m particles in thegeometric limit).

Although definitive observations of ethane clouds havenot been made, Samuelson et al. (1997) believe ethaneclouds could provide some of the observed opacity between300 and 600 cm�1. By including scattering in their radiativetransfer modeling, they found, in addition to the condensedC4N2 at the north pole, a second component whose neutralwavenumber dependence was consistent with a thin, largerparticle hydrocarbon cloud. They assumed the cloud wascomposed of ethane in order to allow methane to remainsupersaturated and provide the rest of the opacity between300 and 600 cm�1. They compared several cloud modelsand found the best fit to the IRIS data called for an ethanecloud of � � 0.17 � 0.28 and r0 � 66 � 36 at 40 km (fixedaltitude), and a methane supersaturation of 1.48 � 0.11.

Despite the paucity of observations of lower atmosphericclouds, methane clouds have been considered in many ra-diative transfer models (Courtin et al., 1995; Samuelson etal., 1997). Ethane is the dominant product of methane pho-tolysis, and will condense at altitudes higher than that ofmethane. Condensed ethane could then serve to lower orraise the contact parameter necessary for methane nucle-ation on tholins. Given the impending Cassini/Huygensdata, we feel it is important to understand the processes thatcould lead to ethane cloud formation and to determine thelikely physical properties of these clouds. Some questionswe address are:

1. Can the removal of ethane and other vapors by meth-ane precipitation in the troposphere limit the produc-tion of clouds in the stratosphere?

2. What is the likely vertical extent of ethane clouds?

3. Will ethane clouds produce rain by either condensa-tional growth or coalescence? How does ethane pre-cipitation compare to that of methane raindrops asstudied by Lorenz (1993)? Could ethane precipitationreach the ground?

4. Are the cloud particle radii of 10 and 75 �m sug-gested by Samuelson and Mayo (1997) plausible?

5. Will nucleation or scavenging of tholin particles byethane change the tholin profile?

6. What level of temporal variability might there be incloud optical depth? Could Sagan and Thompson’s(1984) � � 200 be possible for even short periods?

7. What is the relaxation time for ethane cloud pertur-bations?

8. Can ethane clouds be observed from Earth or Cassini?9. What are the major unknowns limiting our ability to

predict or simulate ethane clouds on Titan?

The layout of this paper is as follows: Section 2 describesthe life cycle of a cloud starting with nucleation, conden-sational growth, coagulation, and destruction through rain-out or evaporation. Section 3 describes the microphysicalmodel; results of model simulations are given in Section 4and discussed in Section 5. Relevant Cassini and Huygensobservations are outlined in Section 6. We conclude byaddressing the questions above in Section 7.

2. Cloud formation & evolution

Nucleation or activation are the first steps in cloud for-mation (Pruppacher and Klett, 1997). Activation occurswhen liquid solution aerosols adsorb their solvent withrising humidity to become cloud droplets. No phase changeoccurs in this process, which is the dominant one for liquidwater in the terrestrial atmosphere (the latent heat release asa result of condensation is accounted for in the growthprocess). At Titan’s much lower temperatures, where ethanewill mostly exist in the solid state, this process is unlikely tooccur. This leaves nucleation, which requires much highersupersaturations to surpass the energy barrier. For ethane iceclouds at the low temperatures on Titan, it is most likely thatethane vapor condenses onto existing aerosol particles (het-erogeneous nucleation). Clusters randomly form on the sur-face of the aerosol. Some small fraction of these will belarge enough to reach the critical germ radius, given by

ag �2�svMw

RT�slnS, (1)

where �sv is the surface free energy of the solid–vaporinterface of the condensing species, Mw is the molecularweight of the condensing gas, R is the universal gas con-stant, T is the atmospheric temperature, �s is the density ofthe condensate, and S is the saturation ratio (explainedbelow). Once the germ reaches the critical size, it is ener-getically favorable for it to grow once a single molecule has

95E.L. Barth, O.B. Toon / Icarus 162 (2003) 94–113

been added. The nucleation rate is then determined from thenumber of aerosols present and the time it takes for onecluster to grow past this critical size by colliding with asingle molecule of the condensing vapor. Obviously, thenucleation rate depends on particle size, since more clustersare present on a larger aerosol.

The onset of nucleation is determined by the degree ofsaturation of the vapor. The saturation ratio, S, is the ratio ofthe partial pressure of the vapor to its saturation vaporpressure. The value of S determines which of three states thevapor is in: S � 1, subsaturated; S � 1, saturated; and S �1, supersaturated. We note that S is directly proportional torelative humidity, such that S � 1 corresponds to 100%relative humidity. Nucleation cannot occur until the vaporbecomes supersaturated, but how high S needs to be toobtain a given value of the nucleation rate depends on theparticular gas, the temperature and the ice nuclei (the aero-sol particles on which the cloud forms). Fig. 1 shows thesensitivity of the nucleation rate to variations in supersatu-ration.

By measuring the saturation ratio in the laboratory and

using the equations of classical nucleation theory, we cal-culate the contact parameter, m. The contact parameter isdetermined by the condition of mechanical equilibrium thatthere must be no net force component along the solid sur-face. This condition can be expressed through Young’srelation

cos� ��N/a � �N/i

�i/a� m, (2)

where � is the surface free energy for the air–substrate (N/a)interface, substrate–ice (N/i) interface, and ice–air (i/a) in-terface. We call cos � the contact parameter, m. The contactparameter characterizes the nucleability of the aerosols suchthat m � 1 indicates a perfectly wettable nucleus and m ��1 indicates an unwettable nucleus. It is important to notethat experimental evidence indicates nucleation onto solidsubstrates tends to favor nuclei with similar lattice spacingto that of the ice, and may occur in surface defects in thelattice. Nonetheless, the classical nucleation theory still ap-pears to be the best description for heterogeneous nucleationfor Titan conditions (Guez et al., 1997).

The contact parameter is related to the nucleation ratethrough the free energy of germ formation (Helmholtz freeenergy),

�Fg �4�ag

2�sv f

3, (3)

and f � (2 � m)(1 � m)2/4 for a planar substrate. In ourcase, we have nucleation onto spherical particles, so f be-comes a much more complicated function of the contactparameter and the ratio of the germ radius to the substrateradius. For simplicity of presentation, though, the planarsubstrate formula is used here in the derivation of thecritical nucleation rate. In our numerical model we use theactual form that contains the radius of the germ (see Prup-pacher and Klett (1997) for complete equation). Solving for�Fg at the critical radius gives the energy barrier to stableembryo formation. �Fg is 10�13 ergs and ag 0.05 �mfor nucleation of ethane vapor (onto tholin) at a saturation(S) of 1.15.

The rate (cm�2 s�1) at which nuclei appear at the surfaceof a single aerosol of radius r per unit area is

J � exp��Fg

kBT, (4)

where the prefactor (kinetic term) is given by � �Zsag2c1

and kB is Boltzmann’s constant. Zs is the Zeldovich factor,

Zs � � �Fg

3�kBT�2, (5)

which accounts for the nonequilibrium nature of the clustersize distribution (� is the ratio of the germ volume to that ofthe aerosol particle); the flux of monomers to the sphericalcap per unit surface area of the particle is

Fig. 1. Variation of the nucleation rate (s�1) at the tropopause as a functionof supersaturation (s � S � 1) and particle radius for a contact parameterof 0.986 (calculated from ethane measurements described in Section 3).The contours show the log10 of the nucleation rate. The zero level contouris defined to be the critical supersaturation value for a given radius, sincesuch nucleation rates are usually observable in the laboratory.

96 E.L. Barth, O.B. Toon / Icarus 162 (2003) 94–113

�pv

�2�mckBT, (6)

where pv is the vapor pressure and mc is the mass of acondensate molecule. In our model ranges from 1015 to1020 cm�2 s�1. The surface concentration of adsorbedmonomers is

c1 �pv

�2�mckBT�vs

exp��Fdes

kBT, (7)

where �Fdes is the desorption energy per molecule and vs isthe frequency of vibration of an adsorbed molecule normalto the surface. The nucleation rate is multiplied by anadditional factor of 4� rN

2 for nucleation onto a sphericalsubstrate of radius rN to get the rate at which the particlenucleates to form ice. The exponential term dominates the Jequation (Eq. (4)).

The critical saturation ratio (Scrit) marks the boundarybetween insignificant nucleation rates (S � Scrit) and thoseleading to visible particle formation (S � Scrit). Values ofScrit for homogeneous nucleation are often 10 or greater(Moses et al., 1992). Observations of the Earth’s atmo-sphere for heterogeneous nucleation of water ice crystalsshow Scrit is about 1.5 for nucleation (Heymsfield et al.,1998; Jensen et al., 2001). Once the critical saturation ratiois known, we can use the equations of nucleation theory,setting J � 1 cm2 s�1 at S � Scrit for nucleation onto aplanar substrate of area 1 cm2, to solve for the contactparameter. Then the contact parameter determines the nu-cleation rate for the modeled atmospheric conditions.

Homogeneous nucleation tends to be an inefficientmethod for the development of condensation, as the vaporpressure of the condensing gas must exceed its saturationvapor pressure by several hundred percent before conden-sation can begin. However, the presence of seed nuclei—heterogeneous nucleation—only requires S 1 or 2 forcondensation to begin. Titan tholin is a likely candidate forseed nuclei for ethane or methane. After being created in thephotochemical haze layer, it sediments down through theatmosphere. As it is falling, the tholin may become coatedwith other condensation products before reaching the alti-tudes of methane/ethane condensation.

Once a cloud particle has formed, it can grow through thecondensation of additional gas while the surrounding atmo-sphere remains supersaturated. The condensational growthof a cloud particle is described by

dM

dt�

g0pvS � AkAs�

1 � g0g1pv, (8)

where M is the particle mass, t is time, S is the saturationratio, and pv is the saturation vapor pressure. Ak is theKelvin correction to account for the effects of particle cur-vature on the vapor pressure

Ak � exp � 2mc�

�srRT� , (9)

where � is the surface tension and �s is the density of thecondensate (as in Eq. (1)). As is a solute term and is takento be equal to 1 in our case since tholins are not soluble inliquid ethane or methane. The gi terms are growth kernelsthat relate the growth to vapor diffusivity (D�), thermalconductivity ( �) of the atmosphere, and latent heat ofcondensation (L):

g0 �4�rD� fvmc

RT(10)

g1 �mcL

2

RT 2ft � 4�r. (11)

The f terms are ventilation factors to account for the motionof the particle through the air as condensation occurs. fv isthe mean ventilation coefficient and is proportional to(Sc�1/3Re�1/2)i, where i � 1 if the quantity in parenthesesis greater than unity or 2 otherwise (Sc is the Schmidtnumber and Re is the Reynolds number). For a motionlessdrop, fv � 1. ft is the ventilation effect on heat transfer andfollows the same convention as fv but with the Schmidtnumber replaced by the Prandtl number. The primes on Dand indicate a correction for the free molecular limit (thefull equations can be found in Pruppacher and Klett (1997),Chap. 13). Substituting in 4

3� r3 � for M in Eq. (8) shows that

the droplet size increases as the inverse of the radius. Soduring the growth phase, smaller drops will grow muchfaster and thus catch up to larger drops. Condensationalgrowth works to create a more monodisperse distribution ofcloud drops.

As the cloud particle grows, it will fall through theatmosphere with a velocity dependent on the particle sizeand mass and the atmospheric viscosity (for r � mean freepath),

Vfall �2B�sr

2g

9�, (12)

where �s is the particle density, g is acceleration due togravity, � is the dynamic viscosity of air, and r is the radiusof the particle. B is a correction for both particle shape andmean free path and is of order unity in the troposphere.Equation (12) applies only in the low Reynolds numberregime (Re � 10�2). For the large Reynolds number re-gime, the Reynolds number is calculated as described inChap. 10 of Pruppacher and Klett (1997). The fall speed canthen be derived using the definition of the Reynolds number.

As particles move through the atmosphere, they maycollide with other particles and so grow through coagula-tion,

dnv�

dt� 0.5�

0

v

Kcoagv�, v � v��nv��nv � v��dv�

� �0

Kcoag v�, v�nv�nv��dv�, (13)


where K is the coagulation kernel. The two terms in Eq. (13)represent the creation of particles of size v through thecoagulation of smaller particles and the loss of particles ofsize v as they coagulate to form larger particles, respec-tively. Toon et al. (1980) found that Brownian coagulationis the dominant coagulation process for tholin in Titan’satmosphere. The Brownian coagulation kernel is given by

KBr � 2�Dp1 � Dp2�D1 � D2�b, (14)

where Dpi is the diameter of the ith particle and Di is thediffusivity. The parameter b is a correction term for whenthe mean free path of the aerosol particle is comparable tothe radius of the absorbing particle. In the continuum re-gime, b � 1 and the diffusivities can be represented by theStokes–Einstein formula (where � is the atmospheric vis-cosity):

Di �kBT

3��Dpi. (15)

In our model Di is 10�2 cm2 s�1 at the bottom of theatmosphere and increases to 1 cm2 s�1 at 100 km. InTitan’s atmosphere the particles are subject to chargingbelow 300 km. This particle charging makes coagulationless efficient for small tholin particles. Brownian coagula-tion is not an important process for Titan cloud particles dueto their low number density and large size.

Coalescence is an accretional process. Falling largedrops overtake slower falling small drops, and collect thesesmaller drops with an efficiency defined by the ratio of theactual collision cross section to the geometric cross section(Seinfeld and Pandis, 1998). An additional efficiency, thecoalescence efficiency, describes whether drops on collisiontrajectories will coalesce or bounce off one another. Thenthe coagulation kernel is described by

Kcoal ��

4EcoalEcollDp1 � Dp2�

2vp1 � vp2�, (16)

where Dpi has the same meaning as described above and vpi

are particle velocities. We use terrestrial data from Hall(1980) and Beard and Ochs (1984) to determine the colli-sion and coalescence efficiencies, Ecoll and Ecoal, respec-tively. Once particles reach millimeter sizes, through eithergrowth or coalescence, they are considered raindrops.

Raindrops will either quickly fall to the surface or evap-orate in subsaturated regions of the atmosphere (evaporationis described by Eq. (8) when S � 1). Lorenz (1993) de-scribed evaporating methane raindrops in Titan’s atmo-sphere. The raindrops were modeled as spheroids subject tothe effects of aerodynamic drag and gravity. Growth wasdescribed by a simplified version of our Eq. (8), dM/dt �g0pv. Collisional growth was not treated (we show belowthat this type of growth is inefficient for our ethane clouds).Lorenz’s study concluded that for surface relative humidi-ties allowed by the Voyager data (maximum value of 70%),methane rain from a 3-km cloudbase cannot reach the sur-

face before total evaporation occurs. However, ethane con-densation nuclei, dubbed “ rain ghosts,” will remain after themethane clouds have evaporated. Lorenz’s calculations in-dicate extinctions of 0.5 km�1 for 1-�m-radius particles and104 times less for 10 �m particles (compare to our ethaneclouds which have extinctions ranging from 10�5 to 10�3 at3 km, particle sizes from 1–25 �m). Due to the lowervapor pressure of ethane and consequently its slower evap-oration rate, we find that ethane raindrops may reach thesurface, as we show below.

Samuelson and Mayo (1997) used methane condensationonto precipitating ethane ice crystals as the loss process intheir steady-state methane model (this was balanced byresupply from eddy diffusion). Maintaining methane super-saturation required a small ethane particle flux into themethane supersaturated region (to limit the number of nu-cleation sites). A small ethane particle flux implies largeethane particle radii (since the downward ethane transportrate is equal to the product of the number of ethane mole-cules per particle and the particle sedimentation flux at thetropopause). To match the latitudinal dependence of themethane supersaturations implied by the IRIS data simulta-neously with the ethane flux, they required ethane particleradii of 10 �m at the north pole and 75 �m in equatorialregions.

3. The microphysics model

The parameters described in this section are summarizedin Table 1. The table is divided into four sections: Atmo-spheric properties, Aerosol properties, Gas properties, andNucleation and growth properties.

The microphysics model simulates particle nucleation,condensational growth, evaporation, coagulation, sedi-mentation, eddy diffusion, and aerosol electrical charg-ing. The aerosol particles are created above the modeleddomain by unspecified photochemistry. The model ex-tends from the surface to 100 km altitude with 50 equallyspaced bins. Aerosol processes above this region areaccounted for by a flux of aerosol particles into the toplayer. This flux was determined based on a previousmodel of Titan’ s aerosols that covered the first 600 km ofTitan’ s atmosphere (Toon et al., 1992). Particles are lostto the surface by deposition. The steady-state aerosolprofile used to define the flux at the top of the model isshown in Fig. 2. Steady state in the aerosol model isdefined to be reached when the flux of particles out thebottom of the model is equal to the production rate.

The aerosol particles are segregated into 35 bins thatdouble in volume. The bin-mean radii range from 13 Å to3.35 �m. Fig. 3 shows the tholin size distribution at variousaltitudes used to initialize the cloud model and which themodel finds in steady state if no condensational clouds areallowed to form. Cloud particles are contained in 41 sizebins from about 0.1 �m to 1 mm. The aerosol particles grow


by coagulation, which is limited by charging (reducing thesticking coefficient to less than 1). They are removed byethane nucleating on them, by coagulating with ethanecloud particles, or by vertical transport. The cloud particlesgrow by both coagulation and condensation, and shrink dueto evaporation (we assume a thermal accommodation coef-ficient of unity).

The atmospheric temperature and density profiles (Table1) are from the Lellouch and Hunten (1987) recommendedmodel. The pressure profile is calculated from the ideal gaslaw, assuming a pure N2 atmosphere.

Recent data (Kostiuk et al., 1997) indicate an ethanemixing ratio 10�5 in the stratosphere. Assuming a con-stant mixing ratio to the surface leads to S values greater

Table 1Microphysics model equations

Parameter Formulaa Reference

Atmospheric properties

Temperature Recommended model (Fig. 4) Lellouch and Hunten (1987)Density Recommended model Lellouch and Hunten (1987)Pressure Ideal gas lawViscosity � � 1.718 � 10�5 � 5.1 � 10�8 (T � 273) Lorenz (1993)Thermal conductivityb � 0(T) � � R (�) Stephan et al. (1987)Eddy diffusionc Kdiff � 5000 below 90 km Toon et al. (1992)Rainout ratec,d 3.1688 � 10�8 s�1, 3.8580 � 10�7 s�1

Rainout altitudec,d 30 km, 20 km

Aerosol properties

Particle size rmin � 13 Å, bins double by mass Toon et al. (1992)Initial size distributionc Fig. 2 Toon et al. (1992)Particle flux (into model top) 1.22 � 10�14 g/cm2/s Toon et al. (1992)

Ethane vapor properties

Initial distribution Mixing ratio � 10�5 or 75% relativehumidity for 5–62 km

Kostiuk et al. (1997)

Vapor pressuree (ice) log(P) � 10.01 � 1085.0/(T � 0.561) Moses et al. (1992)Gas flux (into model top) 5.8 � 109 molecules/cm2/s Yung et al. (1984)

Nucleation and growth properties

Sticking coefficient � 1Thermal accommodation 1Shape SpheresDensity of ethane 0.5446 g/cm2 (liquid), 0.713 g/cm2 (ice)Diffusivity of ethane in N2 D � 0.148

1.01325 � 106

p � T

298.15�1.94

Boyd et al. (1951)

Latent Heat of ethane iceLe �

R

M��5.2514T � �1.1341 � 103

� 9.8774 � 10�11T 2 � 1.3466� 10�6T 3ln10�

From vapor pressure eqn.

Surface free energyC2H6 liquid–air

�lv � 21.157� 305.42 � T

305.42 � 153.2�11/9

Yaws (1992)

C2H6 ice–air�sv � �Lsub

Lvap�2

�lvGuez et al. (1997)

C2H6 ice–C2H6 liquid �sl � �sv � �lv

Critical saturationc Scrit � 1.15, 1.5 Measured for liquid ethane, solid butaneContact parameterc m � 0.986, 0.9589 Derived from Scrit at 72.7 KSurface concentration c1 � 1015 molecules/cm2

a All units are cgs unless otherwise noted.

b Thermal conductivity in W/m/K, valid for T � triple point � 3000 K, � � 1.09 g/cm3, 0 � 0.03926390�T exp��i�1

5 Ailog� kBT

138.0848 � 10�23��;

� R � 4.17�i�1

4 Ci��air

�crit�i

; Ai � [0.46649, �0.57015, 0.19164, �0.03708, 0.00241], Ci � [3.3373542, 0.37098251, 0.89913456, 0.16972505]; kB is

Boltzmann’s constant, T is temperature, � is density (of air, critical density of N2).c Variable parameters (not well constrained by observations).d Not included in base model.e Pressure in mmHg, valid 30–90 K.


than 1 over a substantial portion of the troposphere andlowermost stratosphere (Fig. 4). In order to initialize themodel with subsaturated conditions, the initial ethane pro-file follows the vapor pressure curve, but is reduced to 75%relative humidity for altitudes where the vapor pressurecurve would lead to supersaturation, and has a constantmixing ratio of 10�5 elsewhere. Ethane is continuouslyadded by a flux of 5.8 � 109 molecules cm�2 s�1 at the topof the model, based on the value of the flux at high altitudescalculated by Yung et al. (1984). We have no loss of ethanevapor at the bottom of the model.

An eddy diffusion coefficient controls the vertical trans-

port of gas in the model and is therefore of great importancein determining the supply of vapor to the regions of nucle-ation and growth. The diffusion coefficient used in thismodel, taken from Toon et al. (1992), is a constant 5000cm2 s�1 for the first 90 km of Titan’s atmosphere. Such adiffusion coefficient implies a mixing time of 57 years overa scale height of 30 km (Fig. 5). Titan’s diffusion coefficientis not heavily constrained by observations. Other modelsemploy different eddy diffusion profiles, as will be dis-cussed in Section 4.

Fig. 5 also shows typical fall times for Titan cloud andaerosol particles. These fall times give the particle sedimen-tation rate (i.e., the rate at which the particles settle underthe influence of gravity). For low Reynolds numbers theparticle fall velocities are calculated from the Stokes rela-tionship given in Eq. (12). Comparing diffusion and sedi-mentation times shows clearly that the vertical distributionsof particles larger than 1 �m are controlled by sedimenta-

Fig. 2. Number density plots for various tholin radii in the microphysicsmodel. The model was run for 500 years to achieve this steady-statedistribution. The tholin flux at 100 km in the ethane cloud model is takenfrom these results.

Fig. 3. Size distribution plots for tholin (at various altitudes) in the ethanecloud model, for a case in which ethane clouds are not allowed to form.

Fig. 4. Titan’s temperature profile. Shaded region indicates where ethane issupersaturated for an initial mixing ratio of 10�5. Diamonds indicatetemperatures at which ethane is frozen (below 90 K).

Fig. 5. Typical timescales for vertical movement of particles in Titan’satmosphere, over a scale height of 30 km. Particle sizes of 1 �m andsmaller are typical of the aerosol particles. Larger radii are typical of cloudparticles, where transport is dominated by sedimentation. Timelines aresuperimposed.


tion, while the distribution of smaller ones and of gases arecontrolled by diffusion.

Unfortunately, most nucleation parameters for ethane areunknown. The critical saturation value was obtained fromlab experiments (Curtis et al., in preparation) to be 1.15 forliquid ethane condensing on tholin. Most of the region ofTitan’s atmosphere in which we are interested actually liesbelow ethane’s freezing point of 89.9 K (Fig. 4). However,we do not yet have data on Scrit for ethane ice. However,based upon butane ice formation experiments (Curtis et al.,in preparation), the Scrit should actually be higher than 1.15.Because we have no information on the ethane desorptionenergy (see Eq. (7)), we assumed adsorption as a monolayeron the surface, giving a constant value for c1 of about 1015

molecules/cm2. As no experimental data can be found onthe surface free enthalpy for solid ethane (Eqs. (1)–(3)), wefollowed Guez et al. (1997). They show that the surface freeenthalpies of solids can be linked to material propertiesfor which laboratory measurements exist. Specifically, thesurface free enthalpy of the solid is shown to be a functionof the liquid enthalpy and the latent heats (as shown inTable 1).

4. Model results and sensitivity tests

4.1. Microphysics calculations for the formation andevolution of ethane clouds

Using the parameters specified in Section 3, the aerosolmodel was run to study ethane cloud formation and evolu-tion. We used a contact parameter of 0.986, which corre-sponds to Scrit � 1.15 at T � 72.7 K, the tropopausetemperature in our standard model. This value of m isrelatively large, so this calculation provides an upper limitto the nucleation rate for ethane.

Nucleation initially occurs about 40 days into themodel run, at 58 km. (The altitude values in the followingsection are for a layer bottom with 2 km resolution, i.e.,58 km means the bin ranging from 58 to 60 km.) This isthe same altitude where Sagan and Thompson (1984)predicted ethane would condense to form clouds! Theethane for the cloud particles is supplied by the initialethane just above 58 km as the timescale for mixingethane over a distance of 50 km is much longer than 40days (160 years). Over the course of the model run,nucleation occurs at all altitudes between 8 and 58 km.Nucleation at the higher altitudes and the net diffusion ofethane vapor to the tropopause reduces the ethane contentin the lower stratosphere to the extent that the atmospherebecomes subsaturated above 48 km by 100 years. Nucle-ation continues to occur between 8 and 46 km at steadystate. We consider steady state to have been reachedwhen the ethane flux out of a layer (including both ethanevapor and ethane ice in cloud particles) is equal to theethane flux at the top boundary of the model (given in

Table 1) within machine precision. It should be noted thatcloud formation is driven in this steady-state model byvapor transport driving S. However, an alternative growthmodel is for dynamically induced temperature declines todrive S up, by drawing the vapor pressure down. Thislatter process dominates terrestrial cloud formation, andwill be discussed later.

At steady state we see periodic cloud formation withmost of the activity confined to the troposphere (Fig. 6a).The greatest mass and number of cloud particles is locatedbetween 5 and 10 km. This mass is about the same order ofmagnitude as that of typical terrestrial subvisible cirrus(Jensen et al., 2001). Concentrations reach about 0.5 cm�3,which is at most one-tenth that of typical terrestrial subvis-ible cirrus clouds (Jensen et al., 2001).

Fig. 7 shows size distributions of cloud particles forvarious altitudes. Forty kilometers is near the top of thecloud-forming region where particles are smaller. As theparticles fall to lower altitudes, growth continues, as seen bythe peaks at increasingly larger sizes in the 10- and 20-kmcurves. The bimodal distributions result from both nucle-ation and growth occuring at the same altitude. The ethanebeing removed by the falling cloud particles is being con-stantly resupplied by an upward ethane vapor flux due toeddy diffusion. The largest particles formed are just belowSamuelson’s (Samuelson et al., 1997; Samuelson andMayo, 1997) requirement that ethane cloud particles haveradii between 30 and 100 �m.

The timescale for condensational growth can be esti-mated from Eq. (8). A coalescence timescale can be foundin a similar manner to the growth timescale. Accretionalgrowth of a drop of mass M can be found by multiplying Eq.(16) by the liquid water content (wL) of the small drops:

dM/dt ��

4EcoalEcollDp1 � Dp2�

2vp1 � vp2�wL. (17)

Fig. 8 shows coalescence times for some of the cloudparticle sizes in the model. The long timescales indicate thatthis process is not important for growth of ethane clouds inTitan’s atmosphere. (This conclusion was also confirmedthrough a model run with coalescence turned off.) There-fore, the maximum particle size achieved will be limited bythe efficiency of condensational growth of large particles.Thus, no significant number of millimeter-sized particlesform.

4.2. Radiative transfer modeling of ethane clouds

Since Titan’s haze obscures much of the lower atmo-sphere at visible wavelengths, it is interesting to look atwavelength-dependent optical depths in the near-infrared.We consider IR wavelengths where cloud observations havebeen reported. We used a plane-parallel radiative transfermodel (Toon et al., 1989) to determine albedos at variouswavelengths. Optical parameters (optical depth �, single-


scattering albedo �, asymmetry parameter g) were calcu-lated for the tholin and cloud particles using Mie theory.Table 2 shows the wavelength-dependent values used in thecalculation of the cloud and gas optical depths. Methane andtholin parameters were taken from Toon et al. (1992).

Ethane optical constants are not very well known. Valuesfor � 1 �m were taken from Quirico and Schmitt (1997).At shorter wavelengths, the ethane absorption was consid-ered negligible. The real part of the refractive index forethane was taken to be 1.45 for all wavelengths following

Fig. 6. Mass mixing ratio and number density for Titan’s ethane clouds. The contours are 0.1, 1, 10, 25, 50, 75, and 95% of the maximum value. (a) Forthe normal eddy diffusion coefficient, clouds appear within a period of 20 days at the tropopause and 40 days near 10 km. The periodicity of the cloudschanges for higher eddy diffusion coefficients: (b) 2 � Kdiff, (c) 5 � Kdiff and (d) 10 � Kdiff.


Pearl et al. (1991). The methane abundance was assumed tobe 1% above 30 km and to vary linearly to 4% at thesurface, following Toon et al. (1992). We take the groundalbedo to be 0.1. Rayleigh scattering is related to atmo-spheric pressure (p) as

�Ray � 0.0088p

1013 mbar �4.15�0.2 �. (18)

The optical depth of the ethane clouds, which is the sameorder of magnitude as that of terrestrial subvisible cirrus,

Fig. 7. Size distribution of ethane cloud particles at steady state, for various altitudes. The left plots correspond to a time when the optical depth was at aminimum at 10 km; the right plots are when optical depth was at its peak at 10 km.

Fig. 8. Growth times for various cloud particles. Dashed lines indicate times for condensational growth (long dashes) and evaporation (short dashes).Dashed–dotted lines indicate times for accretional growth. The saturation ratio used to calculate the condensational growth time (see Eq. (8) for S dependence)was taken from the cloud model; i.e., S is altitude dependent.


can exceed that of the tholin at some wavelengths and atsome times (Fig. 9). This opacity results in a 5–10% in-crease in Titan’s albedo for wavelengths between 1 and 2�m when the clouds are at peak optical depth. (Opticaldepths of cloud particles at the minimum of the cloud cycleare negligible compared to the tholin.) To increase thealbedo further requires a larger number of cloud particles tobe formed. If the number of cloud particles is uniformallyincreased by a factor of 10, a 50–150% increase in albedo( � 1 � 2 �m) results (Fig. 10).

Note that in the model atmosphere we have assumed thatmethane clouds do not form, so there is no rainout of theethane particles. In fact, the lower altitude ethane cloud maybe impacted by the formation of methane clouds. The cloudparticles produced in the model atmosphere are largeenough that we can approximate their visible wavelengthoptical depth in the geometric limit. Sagan and Thompson(1984) estimated the optical depth from

�v �3�Xpfc

2�� g�r, (19)

where � and �� are molecular weights for ethane and Titan’satmosphere, respectively; X is the ethane mole fraction; p isatmospheric pressure; g is Titan’s gravity, � and r refer tothe cloud particle density and radius; and fc is the ratio ofethane in the solid state to that in the gas state. From thisequation, their estimate of the ethane optical depth is about200; using results from our model we find a value closer to0.4, 103 times smaller! For their calculations, they assumedthat the amount of ethane present as cloud particles was

equal to that in the gaseous state ( fc � 1). This is the majordifference between our results and theirs; from our model-ing, we find fc � 10�3. In our model, the particles quicklyfall rather than remaining suspended as a cloud, resulting inthe small value of fc.

Another possible way to detect the presence of ethaneclouds would be by their effect on the tholin and ethaneprofiles. Changes to the tholin profile as a result of cloudformation are only evident in Titan’s troposphere. Eventhough clouds do deplete a significant amount of the largertholin particles, they do not exhaust the supply of availabletholin CN. The tholin loss reaches a maximum of about 30%at an altitude of 10 km (Fig. 11). This change in tholin isincluded in Fig. 10, and produces small drops in the albedo.If the amount of tholin condensation nuclei are decreased bya factor of 10 (to account for a similar increase in cloudparticles as described above, shown in Fig. 11) the albedodecreases between 10 and 50% for wavelengths less than 1�m (Fig. 10).

4.3. Sensitivity tests for the ethane cloud model

One of the factors controlling particle size and mass isthe atmospheric transport in our model. The mean transportis controlled by our eddy diffusion profile. The eddy diffu-sion coefficient of Toon et al. (1992) was based on a profileof Yung et al. (1984), modified so that a model without achemical sink agreed with the observed HCN profile (Tan-guy et al., 1990). The Voyager IRIS and UVS data pointsused as boundary conditions to constrain the HCN profilewere at 75 and 1125 km. Recently, McKay (1996) hasdetermined that haze production may be a significant sinkfor N in Titan’s atmosphere. Such a sink will affect theHCN profile and hence change the eddy diffusion profile.Lara et al. (1996) undertook a study of various eddy diffu-sion profiles and found that none could satisfactorally fitboth the HCN distribution and the mixing ratios of varioushydrocarbons. Their best-fit case KL was a combination ofthe profiles suggested by Toublanc et al. (1995), KT, and

Fig. 9. Optical depths of tholin and ethane cloud particles from the micro-physics model. Cloud optical depths are shown for a minimum and max-imum in the cloud cycle.

Table 2Methane, tholin, and ethane properties for RT calculations

Wavelength(�m)

CH4 absorptioncoefficients(km amagat)�1

Tholin refractiveindex

C2H6

k

k n

0.22245 0.0000 0.2100 1.660 0.00d � 00.35000 0.0000 0.1100 1.630 0.00d � 00.45000 0.0008 0.0590 1.720 0.00d � 00.55000 0.0030 0.0240 1.700 0.00d � 00.58000 0.0191 0.0190 1.695 0.00d � 00.61900 1.0130 0.0150 1.690 0.00d � 00.63600 0.0051 0.0130 1.685 0.00d � 00.72800 3.9500 0.0070 1.675 0.00d � 00.75000 0.0015 0.0060 1.675 0.00d � 00.79900 1.2300 0.0040 1.670 0.00d � 00.82700 0.0110 0.0033 1.665 0.00d � 00.84100 0.9180 0.0030 1.660 0.00d � 00.86200 5.2800 0.0023 1.660 0.00d � 00.88800 34.0000 0.0021 1.660 0.00d � 00.93500 0.0770 0.0017 1.655 0.00d � 01.07500 0.0000 0.0008 1.650 0.00d � 01.30000 0.0000 0.0005 1.645 2.06d � 51.60000 0.0000 0.0004 1.640 2.55d � 52.05000 0.0000 0.0008 1.630 3.25d � 52.16000 1436.6 0.0008 1.630 6.01d � 5


Strobel et al. (1992), KS, or, KL � (KT2KS)1/3. Below 100 km

Toublanc’s profile is constant, KT � 2000 cm2/s. Strobel’sprofile follows the form KS(z) � KS0 exp(�(z)/1.6), where�(z) � 1.76 � 105 km (z � Z0)/(R0(RT � z)) is the normal-ized geopotential height with respect to the homopause at Z0

� 985 km (RT is Titan’s radius and R0 � RT � Z0) and KS0

� 4 � 108 cm2/s. KL varies linearly on a log plot from about3000 to 4000 cm2/s over the altitude range of our model. Wesubstituted Lara’s profile for our constant profile, Kdiff �5000 cm2/s, and found that the altitude variation of thediffusion coefficient and the relatively small decrease in

Kdiff did not change the placement of the cloud layers ortheir optical depth significantly. The only substantialchanges were an increase in the amount (both mass andnumber) of cloud particles above the tropopause and non-variable cloud features above 30 km, as shown in Fig. 12.The size distribution of these particles did not change fromthat found with our original eddy diffusion coefficient.

It is noteworthy that both these alternative diffusioncoefficient profiles have values of Kdiff smaller than that inour model. To produce large cloud optical depths, largervalues of Kdiff are needed. With larger Kdiff values (increaseby factors of 2, 5, and 10), we see both an increase in themaximum optical depth and a change in the periodicity ofthe cloud features at 10 km. Figures 6b and 6c show that asthe eddy diffusion coefficient is increased, the length of timebetween cloud formation events decreases. However, due toless ethane vapor present near the tropopause in the highereddy diffusion cases, the optical depths of clouds featuresthere are an order of magnitude less than in the nominalcase.

The periodic cloud features result from the competitionbetween nucleation and growth in depleting the ethane va-por content of an atmospheric layer and transport resupply-ing vapor. When the relative humidity gets above 112% (fora critical supersaturation of 0.15 as in our base model),many cloud particles can be formed from nucleation beforecondensational growth becomes efficient (Fig. 13). Particleshave time to grow and fall before ethane is resuppliedthrough eddy diffusion. A higher eddy diffusion coefficientbrings in ethane faster; however; the majority of the excessvapor is then incorporated into the preexisting cloud parti-cles, rather than building up to form more cloud particles.

Fig. 11. Mass mixing ratio for tholin before and after clouds are added tothe model. The most noticeable effects occur in the bottom 25 km of thetroposphere with a maximum decrease of 30% at 10 km. The decrease isdue to a significant loss of particles of sizes greater than 2 �m. Also shownis how the tholin mass mixing ratio would appear if additional cloudformation removed 10 times more tholin.

Fig. 10. Albedo calculations from data produced by the microphysics model. The albedo values include contributions from Rayleigh scattering, methaneabsorption, and tholin. Shown is percent difference in albedo, comparing the cloud and no cloud cases. Also shown are the error bars from albedo data fromCourtin et al. (1991) (UV) and Neff et al. (1984) (visible). Error bars could not be found for the IR data. The curve marked with diamonds includes the effectsof ethane clouds from the peak in the cloud cycle; there is no significant change in Titan’s albedo when clouds from the minimum of the cycle are used. Muchlarger changes in Titan’s albedo are seen when ethane clouds with 10 times the optical depth of the normal model are added (squares). The curve markedwith triangles shows the change in Titan’s albedo that would occur if the tholins were removed at a rate 10 times greater than that which occurs in our model.


We believe that the periodicity is an artifact of the modelingprocess since eddy diffusion is an artificial process; how-ever, these results can be used to characterize cloud life-times.

While eddy diffusion may approximate the mean behav-ior of Titan’s atmosphere, there will in reality be organizedmean motions as well as waves propagating in the atmo-sphere. Such motions can lead to temporarily increasedsupersaturation via decreased vapor pressures due to low-ered atmospheric temperature. To partially investigate suchwaves we show a simulation of the cloud optical depth inFig. 14 and size distribution in Fig. 15 in which we alloweda sinusoidal temperature oscillation between 40 and 50 km,with an amplitude of 1 K and a period of 1 month. Theatmosphere responds to the first such wave by creating anethane cloud that has a significant optical thickness com-pared with the cloud that was present previously. The pres-ence of this cloud results in a 1% increase in Titan’s albedobetween wavelengths of 1 and 2 �m. However, subsequentwaves produce only very minor clouds since the first onedepletes the available vapor. Hence sporadic clouds of mod-erate optical thickness may occur but will probably be rare.The rarity is due to a fundamental mismatch in timescaleson Titan. Clouds are able to quickly remove vapor, onceformed. However, the sluggish dynamics on Titan makes itdifficult for the atmosphere to transport the vapor needed tocreate saturation. If a similar temperature wave is includedbetween 6 and 12 km, the area of highest cloud formation inthe base model, the maximum number of cloud particlesformed increases by a factor of nearly 100. A similar in-crease is seen in the optical depth, but effects are limited tothe region of the temperature changes. Fig. 16 shows thatthe 30-day timescale of the temperature wave becomes thedominant periodicity in the clouds.

Nucleation is a significant process controlling particlesize in our model. While results for liquid ethane suggest a

value of 1.15 for Scrit, this is likely to be somewhat low forice clouds. However, from running the model with higherScrit values, such as those measured for solid butane, we nolonger see periodic cloud formation (Scrit � 1.4 � 1.5).Once clouds reach a steady-state configuration, their maxi-mum optical depth is less than 0.03. At Scrit � 1.3 periodicclouds remain at 10 km. These clouds have a period of 11days at 10 km and an optical depth centering around 0.05(Fig. 17).

Ethane is just one of the many photolysis products thatwill condense in Titan’s atmosphere. We doubled the flux ofgas to simulate the addition of other similar hydrocarbons.The location of the clouds remains the same as that de-scribed above for the initial case. Fig. 18 shows that there isa significant increase in the amount of cloud particles abovethe tropopause, but comparable (to the base case) mixingratio and number in the troposphere. The periodicity ofclouds at 10 km is still about 40 days; however, clouds varyonly slightly with time above about 30 km. Despite theincreased amount of ethane being added to the atmosphere,the number of cloud particles formed in the troposphere isstill limited by the amount of ethane present, not the numberof tholin CN.

5. Discussion

5.1. Ethane precipitation

A comparison of the evaporation and sedimentationtimescales (Figs. 8 and 5) shows that particles larger than30 �m can fall from 6 km to the surface before totalevaporation. Our ethane particles can reach the surface,whereas the methane particles of Lorenz (1993) could notbecause the methane vapor pressure near Titan’ s surfaceis about 1000 times higher than that of ethane, so its

Fig. 12. Optical depth of ethane clouds above various altitudes for a model run with the eddy diffusion coefficient from Lara et al. (1996).


evaporation rate is correspondingly 1000 times greater.However, because most of the cloud particles only reach13

of this size, there is only a small flux of particles acrossthe bottom boundary of the model as shown in Fig. 19.This averages to a rate of about 2 � 10�5 cm perterrestrial year, which is much smaller than the averageterrestrial value of 1 m yr�1. Our calculated rainfall rate

is only a small fraction of the flux Titan is energeticallycapable of producing. Lorenz (2000) argues from plane-tary energetics that there is enough energy available onthe planet to drive about 1.5 cm of rainfall. Our modelinvolves a recycling of ethane. However, the loss ofethane through rainout of cloud particles to the ground isconsistent with the photochemical production of ethane.

Fig. 13. Comparison for nucleation and growth timescales in the cloud model at 10 and 40 km for different relative humidities.


A significant increase in the rainout rate (0.02 cm perterrestrial year) is seen in cases where a surface source ofethane is added (this case is described more fully inSection 5.4).

5.2. Influence of methane cloud formation on the ethaneclouds

Toon et al. (1988) described a case where, due to thescarcity of nucleation sites for methane condensation,any cloud formation would be followed by rapid growthand rainout. We simulate such a process by raining out allparticles (from the base model) in the bottom 30 km ofthe atmosphere (altitude chosen based on recent cloudobservations, Griffith et al. (2000)). A rainout time of 1year was chosen. By raining out the ethane in the bottom30 km of the atmosphere, the clouds above 30 km alsodisappear within 20 years, and the relative humidityaround the tropopause drops below 100%. This indicates

that the lower atmosphere is the important supplier ofethane to the clouds. Transport of air with a low ethanevapor content from the lower troposphere into the tropo-pause region reduces the mixing ratio of ethane at thetropopause, thereby preventing clouds from forming. Asteady-state model where ethane clouds remained at somealtitudes is found if rainout only occurs below 20 km(same rainout time). The resulting cloud profile (Fig. 20)shows clouds at the tropopause with a maximum concen-tration of 10�3 particles/cm3. These clouds have an ef-fective radius around 1 �m, but are too sparse to have asignificant optical depth (� 10�4).

5.3. Effects of rainout on the transport of gases

Assuming constant mixing ratios, as given by Cabaneand Chassefi ere (1995), we find that acetylene will besupersaturated below 62 km, propane will be supersatu-rated below 64 km, and hydrogen cyanide will be super-saturaed below 70 km. (Vapor pressures for these com-pounds are given in Table 3 and shown in Fig. 21. Notethat although all condensed forms of these compoundswill be frozen at Titan temperatures we were unable tofind data for the solid vapor pressure of propane.) Weused the microphysics model to look at the transport ofthese gases in Titan’ s atmosphere. For the purpose of thistest, the growth algorithms were turned off. Since each ofthese gases is soluble in methane, we studied the effectson the mixing ratios of rainout through methane cloudformation (Fig. 21). For comparison, we performed cal-culations with constant rainout rates at altitudes of 20 and30 km for all of the gases (1 year and 30 days). It isevident from the plots that ethane clouds cannot remainin the atmosphere for either choice of rainout times (if

Fig. 14. Optical depth (visible wavelengths) of Titan’s ethane clouds afterthe addition of a sinusoidal temperature perturbation (at 125 days).Optical depth values before the temperature change were 10�6 at thetropopause and 10�3 at 30 km.

Fig. 15. Size distributions of Titan’s ethane clouds corresponding to theoptical depth spikes in Fig. 14 (tropopause, dash dotted line; 30 km, longdashes). Size distributions before the temperature change are shown forcomparison (tropopause, dotted line; 30 km, short dashes).


there is no evaporation at altitudes surrounding the tropo-pause to resupply ethane, as was the case in the modeldescribed in Section 5.2). The vapor pressures of theother gases, however, are much lower than that of ethane,so that they may remain supersaturated in parts of thelower stratosphere. For a rainout time of a year, themixing ratios differ little between the 20- and 30-kmcases.

5.4. Addition of ethane from surface sources

We chose to study ethane sources further by adding asurface source such that the relative humidity of the bottomlayer remained at 75%. Even with a surface source ofethane, the cloud layers still form at the same altitudesdescribed above, the only difference being that nucleationcan now occur down to 6 km. It is evident from Fig. 22 thatthe surface ethane source is only effective for the bottom 10

km of the atmosphere, resulting in an increased number ofparticles (peaks in number concentration can increase by 3orders of magnitude when a surface source is added). Theaverage rainfall rate increases by about 3 orders of magni-tude as well. However, the greater number of cloud particlesis insufficient to raise the optical depth by an order ofmagnitude (Fig. 23). For this to occur, a much larger sourceof ethane is needed. Such a larger source might occur if theeddy diffusion coefficient near the surface were larger thanwe have assumed.

Fig. 16. Optical depth (visible wavelengths) of Titan’s ethane clouds afterthe addition of a sinusoidal temperature perturbation (at 125 days)between 8 and 11 km.

Fig. 17. Optical depth profiles for various critical saturation values. Theshaded regions show the variation in optical depth for periodic clouds. ForScrit � 1.15 (dark shaded region), the clouds are periodic over their entirevertical extent. Cloud features become constant with time above 20 kmwhen Scrit is raised to 1.3 (light shaded region). For higher values of Scrit

such as those measured for solid butane nucleation onto tholin (Scrit � 1.4,diamonds and Scrit � 1.5, squares), clouds are no longer periodic for anyaltitude.

Fig. 18. Particle number density and mass mixing ratio plots for compar-ison between different ethane fluxes. The profiles show a time-average overseveral cycles (120 days). Doubling the ethane flux only affects theclouds in the stratosphere.


5.5. Variations with latitude

Our model was run as a column using only the tem-perature profile from the Voyager radio occultation ex-periment. However, we can draw some conclusions as tohow our ethane clouds may vary with latitude. UsingIRIS data, Samuelson et al. (1997) extended the radiooccultation data from 7.8°N latitude to get a latitudinaldistribution of temperature at the surface, tropopause,and 1-mbar levels. At the tropopause they found varia-tions of about 1 K (as in our temperature perturbationcase). At the other altitudes temperature variations wereas great as a few Kelvin, symmetric about the equator.Since our ethane clouds form over about a 20-K range oftemperatures, the cloud profile at another latitude willmost likely not appear significantly different as thatshown in this paper. However, as shown by our sensitiv-

ity tests with the temperature perturbation, if a parcel iscarried horizontally, the 1 K temperature change isenough to enhance cloud formation such that the opticaldepth of the cloud will increase.

6. Cassini measurements

The Cassini spacecraft will reach the Saturn system in2004. The Composite Infrared Spectrometer and the Visibleand Infrared Mapping Spectrometer, both on the orbiter,will be capable of observing clouds below the haze layers.The Descent Imager/Spectral Radiometer on the Huygensprobe is equipped with upward and downward spectrome-ters and downward and side-looking imagers. The infraredspectrometer operates from 0.87 to 1.64 �m, a region wheresome ethane absorption features (distinguishable frommethane) exist. The tholin CN are optically thin, but theclouds may be thick enough to be seen by the side-lookingcamera. The best region to observe these clouds would bebetween the surface and 20 km, where the highest extinc-tions occur.

Another way to detect the presence of ethane in theclouds will probably be through the Aerosol Collector andPyrolyser on the Huvgens probe. Through heating at threeincreasing temperatures, this instrument will be capable ofdetecting the presence of an ethane layer around particlescollected from Titan’s atmosphere. Particle collection willoccur twice, at altitudes of 150–40 km and 23–17 km.Should optically thick ethane clouds be observed, it wouldindicate either a very lucky chance encounter or that Titan’slower atmosphere is dynamically much more active than iscurrently thought.

Fig. 19. Flux of ethane cloud particles at the ground. This gives an average rainfall rate of 2 � 10�5 cm year�1.

Fig. 20. Mixing ratios from the 20-km rainout model for a rainouttime of 1 year. Dashed lines indicate time-averaged profiles beforerainout.


7. Conclusions

Microphysical modeling has shown that conditions allowfor ethane cloud formation in Titan’s atmosphere. Unfortu-

nately, our poor knowledge of ethane physical chemistryand of Titan limit our ability to predict cloud properties. Themost important uncertainty is the contact parameter forethane forming on (possibly hydrocarbon-rich) tholins. The

Table 3Vapor pressures

Compound Vapor pressure equation Temperature range Reference

C2H2 30.895 �1645.9

T� 8.6252logT�

98 � T � 115 K 1

9.130 �1149

T � 3.84115 � T � 145 K

C3H8 8.16173 �1176

T105 � T � 165 K 2

HCN189044.86exp��27.3�1.38 � 1010

R260�1 � T�1�� 3

Note. Equations are for log(P) with P in mmHg except for HCN where P is in dynes/cm2. (1) Romani and Atreya (1988). (2) Moses et al. (1992). (3)Calculated from Clausius–Clapeyron, latent heat of sublimation from Stull (1947).

Fig. 21. Mixing ratio profiles for various gases in Titan’s atmosphere. Rainout occured up to 30 km (darker lines) or up to 20 km (lighter lines). The initialprofile follows the saturation vapor pressure at 75% relative humidity at altitudes where the initial mixing ratio value would result in saturation. Clouds willremain in the atmosphere where the rainout profiles are greater than the saturation vapor pressure.


results are also limited by not knowing the frequencies ofmethane cloud formation, the eddy diffusion coefficient inTitan’s lower atmosphere, the magnitude and timing ofdynamically driven temperature perturbations, and whetherthere is a surface reservoir of ethane on Titan. Assuming theonly source of ethane vapor is from methane photolysis, thenumber of cloud particles forming will be limited by theflux of vapor or the presence of temperature perturbationsrather than the abundance of condensation nuclei. Whetherclouds will be observable depends on the critical saturationat which ethane will nucleate onto tholin particles. For lowenough Scrit values we see a cloud cycle where enoughparticles are formed at peak production, to raise Titan’salbedo by about 5% at some infrared wavelengths. Themajority of the cloud particles remain in the troposphere,but clouds can exist at much smaller optical depths through-out the bottom 10 km of the stratosphere. The size distri-bution is generally bimodal, with peaks at 1 and 10 �m. Themaximum cloud particle size is limited by the inefficiencyof coalescence. Particles greater than 25 �m can fall to thesurface before total evaporation in the bottom 6 km of theatmosphere. The formation of ethane clouds has only asmall effect on the tholin profile. However, because theethane cloud particles tend to congregate in the lowest 20km of the atmosphere, they could provide sites for thenucleation of observable methane clouds. Depending on thealtitude of methane cloud formation, ethane vapor may beremoved near the tropopause to levels below saturation (butother hydrocarbon clouds can be sustained). Sporadicclouds with modest optical depths (0.1–1) may occur dueto temperature perturbations, but these must be very rareeven if the perturbations are common. Their frequency ofoccurance is limited by the low transport rates (diffusioncoefficients) in Titan’s lower atmosphere. Should currentestimates of these Kdiff values be much too low, then opti-cally thick clouds may occur.

Acknowledgments

We thank Larry Esposito for his helpful comments on thepaper and funding through Cassini and HST grants. We alsothank the Planetary Atmospheres Program, Grant NAG5-6900, for support. We also thank Ralph Lorenz and ananonymous reviewer for useful insights on the paper.

References

Beard, K.V., Ochs, H.T., 1984. Collection and coalescence efficiencies foraccretion. J. Geophys. Res. 89, 7165–7169.

Boyd, C.A., Stein, N., Steingrimsson, V., Rumpel, W.F., 1951. An inter-ferometric method of determining diffusion coefficients in gaseoussystems. J. Chem. Phys. 19, 548–553.

Cabane, M., Chassefiere, E., 1995. Laboratory simulations of Titan’s at-mosphere: organic gases and aerosols. Planet. Space Sci. 43, 47–65.

Courtin, R., Wagener, R., McKay, C.P., Caldwell, J., Fricke, K., Raulin, F.,Bruston, P., 1991. UV spectroscopy of Titan’s atmosphere, planetaryorganic chemistry and prebiological synthesis. Icarus 90, 43–56.

Courtin, R., Gautier, D., McKay, C.P., 1995. Titan’s thermal emissionspectrum: reanalysis of the Voyager infrared measurements. Icarus114, 144–162.

Gillett, F.C., Forrest, W.J., Merrill, K.M., 1973. 8–13 micron observationsof Titan. Astrophys. J. 184, L93–95.

Griffith, C.A., Owen, T., Miller, G.A., Geballe, T., 1998. Transient cloudsin Titan’s lower atmosphere. Nature 395, 575–578.

Griffith, C.A., Hall, J.L., Geballe, T.R., 2000. Detection of daily clouds onTitan. Science 290, 509–513.

Guez, L., Bruston, P., Raulin, F., Regnaut, C., 1997. Importance of phasechanges in Titan’s lower atmosphere. Tools for the study of nucleation.Planet. Space Sci. 45, 611–625.

Hall, W.D., 1980. A detailed microphysical model within a two- dimen-sional dynamic framework: model description and preliminary results.J. Atmos. Sci. 37, 2486–2507.

Hanel, R., Conrath, B., Flasar, F.M., Kunde, V., Maguire, W., Pearl, J.,Pirraglia, J., Samuelson, R., Herath, L., Allison, M., Cruikshank, D.,Gautier, D., Gierasch, P., Horn, L., Koppany, R., Ponnamperuma, C.,1981. Infrared observations of the saturnian system from Voyager 1.Science 212, 192–200.

Fig. 22. Particle number density and mass mixing ratio plots for compar-ison to a surface source of ethane. The profiles show a time-average overseveral cycles (120 days). Ethane from the surface only affects theprofiles up to 10 km.

Fig. 23. Optical depth profiles (time-averaged over 120 days) for two casesof the cloud model. The dashed line shows the case of no surface ethanesource, and the solid line describes the optical depth when the bottom of theatmosphere is kept at 75% relative humidity. These optical depth calcula-tions considered only the cloud particles in the geometric limit. For particlesizes of 1–1000 �m, this corresponds to visible and near-infrared wave-lengths. The optical depth above a given altitude is shown.


Heymsfield, A., Miloshevich, L., Twohy, C., Sachse, G., Oltmans, S.,1998. Upper-tropospheric relative humidity observations and implica-tions for cirrus ice nucleation. Geophys. Res. Lett. 25, 1343–1346.

Jensen, E., Toon, O., Vay, S., Ovarlez, J., May, R., Bui, T., Twohy, C.,Gandrud, B., Pueschel, R., Schumann, U., 2001. Prevalence of ice-supersaturated regions in the upper troposphere: implications for opti-cally thin ice cloud formation. J. Geophys. Res. 106, 17253–17266.

Kostiuk, T., Fast, K., Livengood, T.A., Goldstein, J., Hewagama, T., Buhl,D., Espenak, F., Ro, K.H., 1997. Ethane abundance on Titan. Planet.Space Sci. 45, 931–939.

Lara, L.M., Lellouch, E., Lopez-Moreno, J.J., Rodrigo, R., 1996. Verticaldistribution of Titan’s atmospheric neutral constituents. J. Geophys.Res. 101, 23261–23283.

Lellouch, E., Hunten, D.M., 1987. Titan atmosphere engineering model.Space Science Department of ESA, ESLAB 87/199.

Lorenz, R.D., 1993. The life, death and afterlife of a raindrop on Titan.Planet. Space Sci. 41, 647–655.

Lorenz, R.D., 2000. The weather on Titan. Science 290, 467–468.McKay, C.P., 1996. Elemental composition, solubility, and optical prop-

erties of Titan’s organic haze. Planet. Space Sci. 44, 741–747.Moses, J.I., Allen, M., Yung, Y.L., 1992. Hydrocarbon nucleation and

aerosol formation in Neptune’s atmosphere. Icarus 99, 318–346.Neff, J.S., Humm, D.C., Bergstralh, J.T., Cochran, A.L., Cochran, W.D.,

Barker, E.S., Tull, R.G., 1984. Absolute spectrophotometry of Titan,Uranus, and Neptune: 3500–10,500 Å. Icarus 60, 221–235.

Pearl, J., Ngoh, M., Ospina, M., Khanna, R., 1991. Optical constants ofsolid methane and ethane from 10,000 to 450 cm�1. J. Geophys. Res.96, 17477–17482.

Pruppacher, H.R., Klett, J.D., 1997. Microphysics of Clouds and Precipi-tation. Kluwer Academic, Norwell, MA.

Quirico, E., Schmitt, B., 1997. Near-infrared spectroscopy of simple hy-drocarbons and carbon oxides diluted in solid N2 and as pure ices:implications for Triton and Pluto. Icarus 127, 354–378.

Romani, P.N., Atreya, S.K., 1988. Methane photochemistry and hazeproduction on Neptune. Icarus 74, 424–445.

Sagan, C., Thompson, W.R., 1984. Production and condensation of organicgases in the atmosphere of Titan. Icarus 59, 133–161.

Samuelson, R.E., Mayo, L.A., 1997. Steady-state model for methane con-densation in Titan’s troposphere. Planet. Space Sci. 45, 949–958.

Samuelson, R.E., Nath, N.R., Borysow, A., 1997. Gaseous abundances andmethane supersaturation in Titan’s troposphere. Planet. Space Sci. 45,959–980.

Seinfeld, J.H., Pandis, S.N., 1998. Atmospheric Chemistry and Physics.Wiley, New York.

Stephan, K., Krauss, R., Laesecke, A., 1987. Viscosity and thermal con-ductivity of nitrogen for a wide range of fluid states. J. Phys. Chem.Ref. Data 16, 993–1023.

Strobel, D., Summers, M., Zhu, X., 1992. Titan’s upper atmosphere:structure and ultraviolet emissions. Icarus 100, 512–526.

Stull, D.R., 1947. Organic compounds. Ind. Eng. Chem. 39, 517.Tanguy, L., Bezard, B., Marten, A., Gautier, D., Gerard, E., Paubert, G.,

Lecacheux, A., 1990. Stratospheric profile of HCN on Titan frommillimeter observations. Icarus 85, 43–57.

Toon, O.B., Turco, R.P., Pollack, J.B., 1980. A physical model of Titan’sclouds. Icarus 43, 260–282.

Toon, O.B., McKay, C.P., Courtin, R., Ackerman, T.P., 1988. Methanerain on Titan. Icarus 75, 255–284.

Toon, O.B., McKay, C.P., Ackerman, T.P., Santhanam, K., 1989. Rapidcalculation of radiative heating rates and photodissociation rates ininhomogeneous multiple scattering atmospheres. J. Geophys. Res. 94,16287–16301.

Toon, O.B., McKay, C.P., Griffith, C.A., Turco, R.P., 1992. A physicalmodel of Titan’s aerosols. Icarus 95, 24–53.

Toublanc, D., Parisot, J.P., Brillet, J., Gautier, D., Raulin, F., McKay, C.P.,1995. Photochemical modeling of Titan’s atmosphere. Icarus 113,2–26.

Yaws, C.L., 1992. Thermodynamic and Physical Property Data, Vol. 1.Gulf Publishing, Houston.

Yung, Y.L., Allen, M., Pinto, J.P., 1984. Photochemistry of the atmosphereof Titan: comparison between model and observations. Astrophys. J.Suppl. 55, 465–506.


microphysical modeling of ethane ice clouds in titan’s ... of ethane due to methane cloud ......

Documents