Observations indicate methane in Titan's atmosphere may be both highly supersaturated and condensed in clouds. In this paper, we present simulations of methane clouds which show that supersaturation and condensation can be compatible given certain conditions. Cloud formation is limited by lack of suitable nuclei as it is for terrestrial cirrus. The simulations suggest much of the troposphere contains optically thin clouds composed of methane which have formed on ethane coated cores. Optically thick methane clouds form in regions where atmospheric dynamics pushes the supersaturation beyond a threshold value. Horizontal quasi-barotropic motions are more likely to drive the supersaturation creating these clouds than are vertical motions.
 Methane condensation in Titan's atmosphere has long been an area of speculation. A methane meteorological cycle was initially proposed by Tyler et al. , as the Voyager radio science data indicated a surface temperature near methane's triple point of 90.7 K. Analysis of other Voyager (IRIS) data led Courtin et al. , and subsequently Samuelson et al. , to conclude that Titan's upper troposphere was supersaturated with respect to methane with the saturation, S, near 1.5 (although recent measurements by Lemmon et al.  indicate much lower methane abundances). Sagan and Thompson  found that methane should condense out near 40 km while many other minor species will condense out at higher altitudes. Toon et al.  concluded that the large abundance of methane combined with long haze particle fall times and hence limited abundances of the haze particles would result in a scenario of rapid cloud growth producing rain without clouds. Lorenz  calculated that though methane raindrops could grow larger than terrestrial raindrops, they tend to evaporate before reaching the surface, with the possibility of ethane rain ghosts being left behind.
 The observations point to infrequent large cloud systems covering about 10% of Titan's disk and lasting several days [Griffith et al., 1998] and more frequent short-lived clouds at ∼25 km [Griffith et al., 2000]. Recent images locate Titan's optically thick clouds at the south pole [Roe et al., 2002; Brown et al., 2002]. These polar clouds vary in appearance over several hours, but are seen across several nights of observations.
 Generally, cloud modeling has focused on the dynamics of their formation. Awal and Lunine  predicted convective plumes with vertical velocities of 1–13 m/s, but these were only small localized phenomena. Tokano et al.  created methane clouds in their time-dependent convective cloud model by condensing methane when S exceeded 150%. An artificial updraft pulse initiated moist convection, producing clouds with a mixing ratio of 5 g/kg and vertical extent of up to 28 km. However, the clouds quickly dissipated, leaving behind slowly falling precipitation.
 The microphysics of ethane clouds was explored in the model of Barth and Toon . They treated the nucleation of ethane onto a size distribution of tholin particles; then monitored the growth, evaporation and transport of these cloud particles in a column of atmosphere.
 Here, we expand our ethane microphysics model to allow methane nucleation, condensation, and evaporation. Our goal is to understand the compatibility of high methane supersaturation with the optically thick polar clouds.
 We use the Community Aerosol & Radiation Model for Atmospheres (CARMA). Aerosol processes include coagulation with electrical charging and sedimentation. The cloud lifecycle includes nucleation, condensation, coalescence, and loss through sedimentation and/or evaporation. The model equations are described by Barth and Toon .
 The model domain covers a column of atmosphere from the surface to 100 km with 2 km layer spacing. Particles are grouped by composition and modeled over size bins doubling in mass. Table 1 lists the cloud groups and nucleation parameters. Relevant nucleation measurements were made with laboratory created tholin particles which have spectral properties similar to Titan's haze particles, and hence we refer to the aerosol particles in our model as tholin. Tholin radii range from 13 Å to 3.35 μm with the majority at 0.1 μm. Tholin as small as 0.01 μm can serve as cloud condensation nuclei; maximum cloud radii are ∼1 mm.
 The nucleation barrier (Scrit) for ethane ice nucleation onto tholin has not been measured to date. We use 1.15 as a lower limit as this is similar to the methane-ethane Scrit (1.1) and so could represent ethane nucleation onto a hydrocarbon coated tholin. From analogy to the high Scrit of terrestrial ice clouds and that measured for butane ice nucleation onto tholin [Curtis et al., 2000], we also consider the case where ethane nucleation has a Scrit of 1.4.
3. Description of Results
3.1. Steady State
 Our previous modeling [Barth and Toon, 2003] showed that, due to its low gas phase abundance, ethane was able to nucleate on only a small fraction (∼5%) of the tholins supplied by high altitude photochemistry (additional factors limiting nucleation included slow ethane resupply by eddy diffusion such that condensation of ethane onto preexisting cloud particles became more efficient than nucleation of additional cloud particles, and predominantly small tholin particles which require a higher S for efficient nucleation). Likewise, it would be expected that all other condensable hydrocarbons [Sagan and Thompson, 1984] will nucleate on only a small subset of tholins. Methane nucleation occurs in our model on all of the ethane cloud particles in the tropospheric regions where methane is supersaturated. Only small methane supersaturations remain (≤0.07) in steady state. These mixed cloud particles grow with methane to sizes of 600–900 μm in radius. They are found between 10 and 30 km with a maximum number of ∼10−5 cm−3 at 30 km and a maximum mixing ratio of ∼1 ppm at 10 km.
 The lack of optically thick clouds in these “steady state simulations” is a direct result of mass balance. Given an eddy diffusion coefficient of 5000 cm2/s [Toon et al., 1992], Titan's troposphere mixes vertically over century timescales. Hence the downward transport by sedimentation is limited by the slow upward transport of vapor by the dynamics and only optically thin clouds form.
3.2. Non–Steady State for Low Ethane Scrit
 The lack of tropical clouds and the slow turnover time of the troposphere suggests convection there is a rare phenomenon. Clouds will more likely form from horizontal transport due to quasi-barotropic motions (where nearly adiabatic motion occurs along constant potential temperature surfaces with planetary scale thermal gradients of a few Kelvin). If vertical ascent in the mean overturning circulation slowly brings the atmosphere to saturation, the horizontal movement of air to the lower temperatures at the poles provides sufficient cooling to form clouds. For a parcel of air near saturation, we can derive the equivalent of dS/dT from the temperature derivative of the log of the saturation vapor pressure. Figure 1 shows this quantity as a function of temperature for values typical of Titan's troposphere and lower stratosphere (up to 60 km). Voyager inferred latitudinal temperature variations point to a 2–3 K change near the surface and ≤1–2 K variations at the tropopause [Flasar et al., 1981; Samuelson et al., 1997]. For a parcel near 25 km, a 2–3 K latitudinal T change from equator to pole results in a 40–60% increase in S, comparable to our threshold for the nucleation of methane onto bare tholins (Table 1).
 To simulate the cooling of an air parcel due to poleward transport, we introduced a sinusoidal temperature oscillation between 24 and 28 km. Details of Titan's tropospheric circulation are unknown, but haze horizontal transport scales (from GCM models) may be ∼10 days [Tokano et al., 2001]. We look at timescales of 1 month and 1 week, and amplitudes up to 3 K, the maximum cooling allowed by the Voyager data. For a 3 K wave with a 1 week period, we see short (2–3 days) episodes of high optical depth (Figure 2, solid curve). Since these clouds are less frequent than those in our steady state simulations, they can have a higher optical depth or mass and remain in long term mass balance. However, these clouds still only have modest values of S (Figure 2, solid curve).
3.3. Non–Steady State for High Ethane Scrit
 The methane supersaturation in the non–steady state simulation described above is small. To allow higher supersaturations we introduce the same temperature wave to a model where the ethane nucleation barrier was raised to 1.4. At these S values, methane is likely to start nucleating onto bare tholin. We studied the effects of these ‘pure’ methane clouds by running this case twice, once allowing methane nucleation onto tholin for a critical saturation of 1.5 and a second time excluding this cloud group. Figure 2 compares the optical depths and methane saturations found from these cases with those from the low ethane Scrit case described above. Methane clouds formed on bare tholins contribute to the optical depth, but the clouds formed on ethane coated tholins are optically thick. At these supersaturations, nucleation of methane onto bare tholin forms about 10−4 particles/cm3. Figure 2 shows that cloud formation is enough to keep the methane supersaturation from rising as much as indicated by the dS/dT calculation (Figure 1), but S reached is comparable with Samuelson et al. .
 The methane saturation is controlled by the temperature wave even though clouds form. The methane mass on the cloud particles is only about 2% of the methane vapor mass. These clouds must be in long term mass balance such that the mass they remove by sedimentation equals the upward vapor flux by atmospheric motions. The mixed clouds have limited cloud particle numbers due to the small number of ethane cloud particles. Since the surface area (optical depth, Figure 2) falls slightly compared with the low ethane Scrit case, these clouds are not very effective in limiting the methane supersaturation. To bring the methane down to saturation would require the clouds to remove 4.5 × 10−6 g/cm3 of methane. Even assuming the maximum number of cloud particles created in the model, 3 × 10−4 cm−3, the particles would need to be almost 2 mm in radius to remove this much mass. However, a methane cloud particle can grow to only a few 100 μm before falling out of the altitude layer (i.e., falling 2 km), and so they don't limit S.
 General cloud properties - optical depth, particle size and cloud duration - are controlled by the wave period, number of particles formed and eddy diffusion coefficient. For fixed eddy diffusion the upward vapor flux is determined. This must be balanced by the downward sedimentation flux which is proportional to cloud number density times particle radius to approximately the fifth power. A higher ethane Scrit leads to fewer particles, and consequently slightly lower optical depth (Figure 2), but such particles are also less able to reduce the methane supersaturations (Figure 2). The duration of the cloud events is basically limited by sedimentation, but that in turn can be controlled by the period of the temperature oscillation. For the 1 week temperature wave, the cloud rains out in about half a day whereas for a period of 1 month the clouds last about 3 1/2 days, due to a longer period of supersaturation. Since the rise in S is more gradual in the 1 month period case, nucleation occurs continuously for a period of time before the temperature begins to rise, resulting in a longer lasting cloud. Optically thick clouds also appear for 1 and 2 K amplitude temperature waves applied to the low ethane Scrit case. A 1 K temperature change applied to the high ethane Scrit case produces clouds with optical depth ∼0.1.
4. Conclusions and Predictions
 We predict optically thin, large particle hydrocarbon clouds are likely to form in a broad region of Titan's atmosphere. Even with little nucleation barrier methane clouds formed on an ethane core are optically thin if clouds are allowed to form continuously. These clouds allow only a small methane supersaturation. Ethane (and other hydrocarbon) clouds are gas limited; they nucleate at/near their critical saturation but only on a small fraction of haze particles. They may grow to large size, but do not have enough surface area to be optically thick. Ethane haze will occur near the tropopause and surface. Elsewhere, on average, ethane together with methane forms a methane rain without clouds.
 Most of Titan's methane clouds probably form around an ethane core, as the barrier for nucleation in this case is low. With the Huygens descent site near equatorial latitudes, the probe is unlikely to descend through optically thick clouds. If a limited amount of ethane coated haze particles are present here, the majority of the (optically thin and sparse) methane cloud particles will be of the mixed (i.e., layered coating of ethane ice and other hydrocarbon ices around the tholin core) variety as these have a lower threshold to nucleation than pure methane clouds which nucleate on bare haze particles. The optically thick clouds seen in recent observations and those most likely to be observed by the Cassini orbiter, are most likely driven by a temperature decrease as the air parcel moves poleward. The best place to find the optically thick clouds is at the poles, where horizontal quasi-barotropic motions are most likely to yield high S air. Cloud properties should provide clues to atmospheric mixing rates, dynamical processes, and modes of nucleation.
 We thank Larry Esposito for funding through Cassini science grant JPL 961196 and Chris McKay and an anonymous reviewer for helpful feedback.