Simulations of Superrotation on Slowly Rotating Planets: Sensitivity to Rotation and Initial Condition

We use a simplified terrestrial general circulation model as a nonlinear process model to investigate factors that influence the extent of equatorial superrotation in statically stable atmospheres on slowly rotating planets such as Titan and Venus. The possibility of multiple equilibria is tested by running the same model to equilibrium from vastly different initial conditions. The final state is effectively independent of initial state, reinforcing the impression that equatorial superrotation is inevitable on slowly rotating planets with stable radiative equilibrium structures. Of particular interest is the fact that at Titan rotation, the model equilibrates with strong prograde winds even when initialized with strong retrograde winds. This suggests that reliable remote sensing inferences of latitudinal temperature gradients on Titan can unambiguously be interpreted as evidence for superrotation. We also demonstrate for the first time that significant equatorial superrotation can be produced at Venus' rotation rate in such models, given sufficient numerical precision. The strength of superrotating zonal winds increases with rotation rate in the slowly rotating regime when other parameters are held fixed. However, the efficiency of superrotation relative to the angular momentum of an atmosphere corotating with the solid planet increases with decreasing rotation rate instead, because the Hadley cell strengthens and expands poleward. This allows for the formation of stronger high latitude jets, which ultimately serve as the source for equatorial superrotation via barotropic instability. Estimates of relevant parameter settings for Triton and Pluto tentatively imply that their atmospheres may marginally be in the superrotating regime, but only if temperature decreases with height near the surface.     

On the maintenance of thermal wind balance and equatorial superrotation in Titan's stratosphere

Titan's atmospheric winds, like those on Venus, exhibit superrotation at high altitudes. Titan general circulation models have yielded conflicting results on whether prograde winds in excess of 100 m s⁻¹ at the 1 mbar level are possible based on known physical processes that drive wind systems. A comprehensive two-dimensional (2D) model for Titan's stratosphere was constructed to systematically explore the physical mechanisms that produce and maintain stratospheric wind systems. To ensure conservation of angular momentum in the limit of no net exchange of atmospheric angular momentum with the solid satellite and no external sources and sinks, the zonal momentum equation was solved in flux form for total angular momentum. The relationships among thermal wind balance, meridional circulation, and zonal wind were examined with numerical experiments over a range of values for fundamental input parameters, including planetary rotation rate, radius, internal friction due to wave stresses, and net radiative drive. The magnitude of mid-latitude jets is most sensitive to a single parameter, the planetary rotation rate and results from the conversion of planetary angular momentum to relative angular momentum by the meridional circulation, whereas the strength of meridional circulation is mainly determined by the magnitude of the radiative drive. For Titan's slowly rotating atmosphere, the meridional temperature gradient is vanishingly small, even when the radiative drive is enhanced beyond reasonable magnitudes, and can be inferred from zonal winds in gradient/thermal wind balance. In our 2D model large equatorial superrotation in Titan's stratosphere can be only produced through internal drag forcing by eddy momentum fluxes, which redistribute angular momentum within the atmosphere, while still conserving the total angular momentum of the atmosphere with time. We cannot identify any waves, such as gravitational or thermal tides, that are sufficiently capable of generating the required eddy forcing of >50 m s⁻¹ Titan-day⁻¹ to maintain peak prograde winds in excess of 100 m s⁻¹ at the 1 mbar level.     

Westward rotation of the atmospheric angular momentum vector of Titan by thermal tides

The orientation of the atmospheric angular momentum vector of Titan and its temporal variation predicted by a general circulation model are analysed and interpreted. The atmospheric angular momentum vector is tilted by a few degrees from the polar axis and the vector rotates (precesses) westward with a constant period of 1 Titan day. The fast westward rotation is likely to be caused by migrating diurnal thermal tides. The tilt is almost cancelled out in the troposphere by the wavenumber 2 pattern of Saturn's gravitational tide, but is more pronounced in the stratosphere, where thermal tides are significant. The predicted tilt angle and the equatorial angular momentum vary with season and maximize when the hemispheric asymmetry of the axial angular momentum or superrotation attains its peak.     

Stratospheric superrotation in the TitanWRF model

TitanWRF general circulation model simulations performed without sub-grid-scale horizontal diffusion of momentum produce roughly the observed amount of superrotation in Titan’s stratosphere. We compare these results to Cassini-Huygens measurements of Titan’s winds and temperatures, and predict temperature and winds at future seasons. We use angular momentum and transformed Eulerian mean diagnostics to show that equatorial superrotation is generated during episodic angular momentum ‘transfer events’ during model spin-up, and maintained by similar (yet shorter) events once the model has reached steady state. We then use wave and barotropic instability analysis to suggest that these transfer events are produced by barotropic waves, generated at low latitudes then propagating poleward through a critical layer, thus accelerating low latitudes while decelerating the mid-to-high latitude jet in the late fall through early spring hemisphere. Finally, we identify the dominant waves responsible for the transfers of angular momentum close to northern winter solstice during spin-up and at steady state. Problems with our simulations include peak latitudinal temperature gradients and zonal winds occurring ∼60 km lower than observed by Cassini CIRS, and no reduction in zonal wind speed around 80 km, as was observed by Huygens. While the latter may have been due to transient effects (e.g. gravity waves), the former suggests that our low (∼420 km) model top is adversely affecting the circulation near the jet peak, and/or that we require active haze transport in order to correctly model heating rates and thus the circulation. Future work will include running the model with a higher top, and including advection of a haze particle size distribution.     

Maintenance of equatorial superrotation in the atmospheres of Venus and Titan

This paper extends Leovy's theory on Venus’ equatorial superrotation by analytically examining additional terms in the mean zonal momentum equation that stably balances the momentum source of pumping by thermal tides. The general analytical solution is applied to the atmospheres of both Venus and Saturn's moon Titan. The main results are: (i) Venus’ equatorial superrotation of 118 m s⁻¹ results primarily from a balance between the momentum source of pumping by thermal tides and the momentum sink of meridional advection of wind shear by horizontal branches of the Hadley circulation; (ii) no solution is found for Titan's stratospheric equatorial superrotation centered at the 1-hPa level; (iii) however, if the main solar radiation absorption layer in Titan's stratosphere is lifted from 1 hPa (∼185 km) to 0.1 hPa (∼288 km), an equatorial superrotation of ∼110 m s⁻¹ centered at 0.1-hPa could be maintained. Titan's equatorial superrotation results mainly from a balance between the momentum source of tidal pumping and the momentum sink of frictional drag.     

A tidal explanation for the Titan haze layers

Though Titan is in synchronous rotation around Saturn, it experiences gravitational tides as a consequence of its eccentric orbit. It is proposed that the vertical transport of aerosols by these tides produces the haze layers in Titan's upper atmosphere. Analysis shows that the zonal winds in Titan's superrotating atmosphere have a profound influence on which tidal components are effective in establishing the multiple detached-haze layers. If the Huygens Doppler winds are representative of the equatorial global superrotation, then the westward propagating s=2 mode is the responsible tidal component even though its forcing is significantly weaker than that of the s=0 and eastward s=2 components. The eastward s=2 tidal mode is eliminated by critical levels while the s=0 mode is viscously damped in the strong high altitude winds. At polar latitudes, however, the gravest s=0 mode is the one most likely to produce layering. It is also suggested that the atmospheric gravitational tides could be responsible for decelerating the superrotating atmosphere as seen in the Huygens Doppler wind velocity profile at about 80 km altitude.     

Seasonal variation of Titan's atmospheric structure simulated by a general circulation model.

The seasonal variation of Titan's atmospheric structure with emphasis on the stratosphere is simulated by a three-dimensional general circulation model. The model includes the transport of haze particles by the circulation. The likely pattern of meridional circulation is reconstructed by a comparison of simulated and observed haze and temperature distribution. The GCM produces a weak zonal circulation with a small latitudinal temperature gradient, in conflict with observation. The direct reason is found to be the excessive meridional circulation. Under uniformly distributed opacity sources, the model predicts a pair of symmetric Hadley cells near the equinox and a single global cell with the rising branch in the summer hemisphere below about z = 230 km and a thermally indirect cell above the direct cell near the solstice. The interhemispheric circulation transports haze particles from the summer to the winter hemisphere, causing a maximum haze opacity contrast near the solstice and a smaller contrast near the equinox, contrary to observation. On the other, if the GCM is run under modified cooling rate in order to account for the enhancement in nitrites and some hydrocarbons in the northern hemisphere near the vernal equinox, the meridional cell at the equinox becomes a single cell with rising motions in the autumn hemisphere. A more realistic haze opacity distribution can be reproduced at the equinox. However, a pure transport effect (without particle growth by microphysics, etc.) would not be able to cause the observed discontinuity of the global haze opacity distribution at any location. The stratospheric temperature asymmetry can be explained by a combination of asymmetric radiative heating rates and adiabatic heating due to vertical motion within the thermally indirect cell. A seasonal variation of haze particle number density is unlikely to be responsible for this asymmetry. It is likely that a thermally indirect cell covers the upper portion of the main haze layer. An artificial damping of the meridional circulation enables the formation of high-latitude jets in the upper stratosphere and weaker equatorial superrotation. The latitudinal temperature distribution in the stratosphere is better reproduced.     

Decadal variations in a Venus general circulation model

The Community Atmosphere Model (CAM), a 3-dimensional Earth-based climate model, has been modified to simulate the dynamics of the Venus atmosphere. The most current finite volume version of CAM is used with Earth-related processes removed, parameters appropriate for Venus introduced, and some basic physics approximations adopted. A simplified Newtonian cooling approximation has been used for the radiation scheme. We use a high resolution (1° by 1° in latitude and longitude) to take account of small-scale dynamical processes that might be important on Venus. A Rayleigh friction approach is used at the lower boundary to represent surface drag, and a similar approach is implemented in the uppermost few model levels providing a ‘sponge layer’ to prevent wave reflection from the upper boundary. The simulations generate superrotation with wind velocities comparable to those measured in the Venus atmosphere by probes and around 50-60% of those measured by cloud tracking. At cloud heights and above the atmosphere is always superrotating with mid-latitude zonal jets that wax and wane on an approximate 10 year cycle. However, below the clouds, the zonal winds vary periodically on a decadal timescale between superrotation and subrotation. Both subrotating and superrotating mid-latitude jets are found in the approximate 40-60 km altitude range. The growth and decay of the sub-cloud level jets also occur on the decadal timescale. Though subrotating zonal winds are found below the clouds, the total angular momentum of the atmosphere is always in the sense of superrotation. The global relative angular momentum of the atmosphere oscillates with an amplitude of about 5% on the approximate 10 year timescale. Symmetric instability in the near surface equatorial atmosphere might be the source of the decadal oscillation in the atmospheric state. Analyses of angular momentum transport show that all the jets are built up by poleward transport by a meridional circulation while angular momentum is redistributed to lower latitudes primarily by transient eddies. Possible changes in the structure of Venus’ cloud level mid-latitude jets measured by Mariner 10, Pioneer Venus, and Venus Express suggest that a cyclic variation similar to that found in the model might occur in the real Venus atmosphere, although no subrotating winds below the cloud level have been observed to date. Venus’ atmosphere must be observed over multi-year timescales and below the clouds if we are to understand its dynamics.     

A transposable planetary general circulation model (PGCM) and its preliminary application to Titan

We present in this work an application to Titan, Saturn's satellite of the transposable planetary general circulation model (PGCM), which was developed based on the second version of the Community Atmosphere Model (CAM2) of NCAR. The PGCM is a spectral model with the sigma coordinate (where σ is the pressure normalized to its surface value, commonly used as a vertical coordinate in general circulation models) and is integrated in time using the semi-implicit leapfrog scheme. The horizontal resolutions of the model are based on 128 points in longitude and 64 points in latitude, and the vertical discretization is of 26 σ-levels. In Titan's conditions we apply the PGCM to simulate Titan's general circulation in this study. Some interesting phenomena such as equatorial superrotation, vertical meridional circulations, vertical structure, etc. are well replicated. This demonstrates the good performance and applicability to Titan of our model and provides a foundation for further studies on simulating and understanding Titan's general circulation and its variability by coupling the physical processes. The features of Titan's circulation under the condition of the Earth's rotation rate are also investigated. The results suggest that different rotation rates can significantly affect the dynamical structure of Titan's circulation.     

Hadley circulations and Kelvin wave-driven equatorial jets in the atmospheres of Jupiter and Saturn

We propose a dynamical mechanism that can plausibly explain the origin of the broad prograde equatorial winds observed on Jupiter and Saturn, and examine the feasibility of this mechanism using two- (2D) and three-dimensional (3D) numerical simulation models. The idea is based on combining a narrow Gaussian jet peaking at the equator, which is induced by the momentum transfer from an upward propagating equatorial Kelvin-wave, and a pair of off-equatorial jets due to a meridional-vertical circulation similar to the tropical Hadley circulation on Earth. We employ for this feasibility study a 2D mechanistic mean-flow model which incorporates the influence of prescribed waves, and a 3D general circulation model, based on the generalised primitive equations of atmospheric motion. We then confirm that the dynamical models of both kinds can successfully reproduce theoretically expected flows of a reasonable magnitude, and that when two mechanisms are combined, a broad super-rotating jet is produced with off-equatorial maxima in zonal velocity for both Jupiter and Saturn, approximately in accordance with observations.     

Atmospheric dynamics on the outer planets and some of their satellites

A short review of the atmospheric dynamics for the outer planets and some of their satellites with atmospheres is presented. Their physical properties are discussed. A survey of observational data for atmospheric motions on the large planets is presented and similarity parameters are given for all objects. General problems of the vertical structure of atmospheres are then considered with some detailed discussion for rarefied atmospheres on Io and Ganymede. The low densities of these atmospheres make their dynamics similar to those of the thermospheres of the terrestrial planets but with a specific boundary layer. The atmospheric temperature regime must be strongly coupled to that of their surface, and so winds should be of the order of the velocity of sound. Similarities and differences are noted between the dynamics of Titan and possibly of Pluto and the circulation on Venus. For large and rapidly rotating planets, some analogies with the oceans are pointed out. The “soliton” hypothesis is discussed in some detail for circulation perturbations observed on Jupiter's disk. Finally, it is noted that the bimodal rotation period found for Neptune [D.P. Cruikshank, Astrophys. J. 220, 157–159 (1978)] may be interpreted as an indication of an equatorial jet on the planet with a relative velocity of about 140 m sec^?1.     

About Superrotation in Venus

In this work we study in a general view slow rotating planets as Venus or Titan which present superrotating winds in their atmospheres. We are interested in understanding what mechanisms are candidates to be sources of net angular momentum to generate this kind of dynamics. In particular, in the case of Venus, in its atmosphere around an altitude of 100 km relative to the surface, there exists winds that perform a full rotation around the planet in four terrestrial days, whereas the venusian day is equivalent to 243 terrestrial ones. This phenomenon called superrotation is known since many decades. However, its origin and behaviour is not completely understood. In this article we analise and ponderate the importance of different effects to generate this dynamics.     

Diagnostics of Titan's stratospheric dynamics using Cassini/CIRS data and the 2-dimensional IPSL circulation model

The dynamics of Titan's stratosphere is discussed in this study, based on a comparison between observations by the CIRS instrument on board the Cassini spacecraft, and results of the 2-dimensional circulation model developed at the Institute Pierre-Simon Laplace, available at http://www.lmd.jussieu.fr/titanDbase [Rannou, P., Lebonnois, S., Hourdin, F., Luz, D., 2005. Adv. Space Res. 36, 2194-2198]. The comparison aims at both evaluating the model's capabilities and interpreting the observations concerning: (1) dynamical and thermal structure using temperature retrievals from Cassini/CIRS and the vertical profile of zonal wind at the Huygens landing site obtained by Huygens/DWE; and (2) vertical and latitudinal profiles of stratospheric gases deduced from Cassini/CIRS data. The modeled thermal structure is similar to that inferred from observations (Cassini/CIRS and Earth-based observations). However, the upper stratosphere (above 0.05 mbar) is systematically too hot in the 2D-CM, and therefore the stratopause region is not well represented. This bias may be related to the haze structure and to misrepresented radiative effects in this region, such as the cooling effect of hydrogen cyanide (HCN). The 2D-CM produces a strong atmospheric superrotation, with zonal winds reaching 200 m s⁻¹ at high winter latitudes between 200 and 300 km altitude (0.1-1 mbar). The modeled zonal winds are in good agreement with retrieved wind fields from occultation observations, Cassini/CIRS and Huygens/DWE. Changes to the thermal structure are coupled to changes in the meridional circulation and polar vortex extension, and therefore affect chemical distributions, especially in winter polar regions. When a higher altitude haze production source is used, the resulting modeled meridional circulation is weaker and the vertical and horizontal mixing due to the polar vortex is less extended in latitude. There is an overall good agreement between modeled chemical distributions and observations in equatorial regions. The difference in observed vertical gradients of C₂H₂ and HCN may be an indicator of the relative strength of circulation and chemical loss of HCN. The negative vertical gradient of ethylene in the low stratosphere at 15° S, cannot be modeled with simple 1-dimensional models, where a strong photochemical sink in the middle stratosphere would be necessary. It is explained here by dynamical advection from the winter pole towards the equator in the low stratosphere and by the fact that ethylene does not condense. Near the winter pole (80° N), some compounds (C₄H₂, C₃H₄) exhibit an (interior) minimum in the observed abundance vertical profiles, whereas 2D-CM profiles are well mixed all along the atmospheric column. This minimum can be a diagnostic of the strength of the meridional circulation, and of the spatial extension of the winter polar vortex where strong descending motions are present. In the summer hemisphere, observed stratospheric abundances are uniform in latitude, whereas the model maintains a residual enrichment over the summer pole from the spring cell due to a secondary meridional overturning between 1 and 50 mbar, at latitudes south of 40-50° S. The strength, as well as spatial and temporal extensions of this structure are a difficulty, that may be linked to possible misrepresentation of horizontally mixing processes, due to the restricted 2-dimensional nature of the model. This restriction should also be kept in mind as a possible source of other discrepancies.     

Tidal Winds on Titan Caused by Saturn

The influence of Saturn's gravitational tide on the atmosphere of Titan is investigated by means of a three-dimensional general circulation model. Titan's orbital eccentricity of 0.0292 gives rise to time-dependent radial and librational tide whose potential circles eastward on Titan. Unlike atmospheric tides on terrestrial planets, Saturn's tide on Titan has a large impact on the dynamic meteorology down to the surface. The surface pressure oscillates by up to 1.5 hPa through the orbit. Near the surface the tidal wind dominates the atmospheric flow and exhibits strong temporal and spatial variation. The superposition of the annually present, thermally forced latitudinal pressure gradient and tidally caused pressure variation produces a unique wind pattern near the surface characterized by equatorward flow and high-latitude whirls. At higher levels the tidal wind manifests itself as eastward traveling planetary-scale wave of wavenumber 2 superposed on the background wind. In general tidal winds are more significant in the troposphere, where other forcing mechanisms are weak. Meridional tidal winds become as fast as 5 m s⁻¹ in the troposphere and change direction periodically through the orbit and along the parallel of latitude. Except in the lower troposphere, zonal winds always remain prograde because the tidal wind amplitude is usually smaller than the mean zonal wind. The tide also has a large impact on the mean zonal circulation in the stratosphere. A meridional drift of the descending Huygens Probe in the troposphere would be the easiest way to verify the tidal wind on Titan, but more complete observations of tropospheric wind and surface pressure by a future mission would be required to unveil the complete details of the tidal wind.     

Venusian middle-atmospheric dynamics in the presence of a strong planetary-scale 5.5-day wave

The middle atmospheric dynamics on Venus are investigated using a middle atmosphere general circulation model. The magnitude of the superrotation is sensitive to the amplitude of the planetary-scale waves. In particular, the critical level absorptions of the forced planetary-scale waves might contribute to the maintenance of the superrotation near the cloud base. In the case of strong 5.5-day wave forcing, the superrotation with zonal wind speed higher than 100 m s^?1 is maintained by the forced wave. Four-day and 5.5-day waves are found near the equatorial cloud top and base, respectively. The planetary-scale waves have a Y-shaped pattern maintained by the amplitude modulation in the presence of strong thermal tides.The polar hot dipole is unstable and its dynamical behavior is complex near the cloud top in this model. The dipole merges into a monopole or breaks up into a tripole when the divergent eddies with high zonal wavenumbers are predominant in the hot dipole region. A cold collar is partly enhanced by a cold phase of slowly propagating waves with zonal wavenumber 1. Although such a complex dipole behavior has not been observed yet, it is likely to occur under a dynamical condition similar to the present simulation. Thus, the dynamical approach using a general circulation model might be useful for analyzing Venus Express and ground-based observation data.     

Titan global climate model: A new 3-dimensional version of the IPSL Titan GCM

We have developed a new 3-dimensional climate model for Titan’s atmosphere, using the physics of the IPSL Titan 2-dimensional climate model with the current version of the LMDZ General Circulation Model dynamical core. Microphysics and photochemistry are still computed as zonal averages. This GCM covers altitudes from surface to 500 km altitude, with barotropic waves now being resolved and the diurnal cycle included. The boundary layer scheme has been changed, yielding a strong improvement in the tropospheric zonal wind profile modeled at Huygens descent position and season. The potential temperature profile is fairly consistent with Huygens observations in the lowest 10 km. The latitudinal profile of the near-surface temperature is close to observed values. The minimum of zonal wind observed by the Huygens probe just above the tropopause is also present in these simulations, and its origin is discussed by comparing solar heating and dynamical transport of energy. The stratospheric temperature and wind fields are consistent with our previous works. Compared to observations, the zonal wind peak is too weak (around 120 m/s) and too low (around 200 km). The temperature structures appear to be compressed in altitude, and depart strongly from observations in the upper stratosphere. These discrepancies are correlated, and most probably related to the altitude of the haze production. The model produces a detached haze layer located more than 150 km lower than observed by the Cassini instruments. This low production altitude is due to the current position of the GCM upper boundary. However, the temporal behaviour of the detached haze layer in the model may explain the seasonal differences observed between Cassini and Voyager 1. The waves present in the GCM are analyzed, together with their respective roles in the angular momentum budget. Though the role of the mean meridional circulation in momentum transport is similar to previous work, and the transport by barotropic waves is clearly seen in the stratosphere, a significant part of the transport at high latitudes is done all year long through low-frequency tropospheric waves that may be baroclinic waves.     

Latitudinal transport by barotropic waves in Titan's stratosphere.: II. Results from a coupled dynamics-microphysics-photochemistry GCM

We present a 2D general circulation model of Titan's atmosphere, coupling axisymmetric dynamics with haze microphysics, a simplified photochemistry and eddy mixing. We develop a parameterization of latitudinal eddy mixing by barotropic waves based on a shallow-water, longitude-latitude model. The parameterization acts locally and in real time both on passive tracers and momentum. The mixing coefficient varies exponentially with a measure of the barotropic instability of the mean zonal flow. The coupled GCM approximately reproduces the Voyager temperature measurements and the latitudinal contrasts in the distributions of HCN and C₂H₂, as well as the main features of the zonal wind retrieved from the 1989 stellar occultation. Wind velocities are consistent with the observed reversal time of the North-South albedo asymmetry of 5 terrestrial years. Model results support the hypothesis of a non-uniform distribution of infrared opacity as the cause of the Voyager temperature asymmetry. Transport by the mean meridional circulation, combined with polar vortex isolation may be at the origin of the latitudinal contrasts of trace species, with eddy mixing remaining restricted to low latitudes most of the Titan year. We interpret the contrasts as a signature of non-axisymmetric motions.     

A coupled dynamics-microphysics model of Titan's atmosphere

We have developed a coupled general circulation model of Titan's atmosphere in which the aerosol haze is treated with a microphysical model and is advected by the winds. The radiative transfer accounts for the non uniform haze distribution and, in turn, drives the dynamics. We analyze the GCM results, especially focusing on the difference between a uniform haze layer and a haze layer coupled to the dynamics. In the coupled simulation the aerosols tend to accumulate at the poles, at latitudes higher than ±60°. During winter, aerosols strongly radiate at thermal infrared wavelengths enhancing the cooling rate near the pole. Since this tends to increase the latitudinal gradients of temperature the direct effect of this cooling excess, in contrast to the uncoupled haze case, is to increase the strength of the meridional cells as well as the strength of the zonal winds and profile. This is a positive feedback of the haze on dynamics. The coupled model reproduces observations about the state of the atmosphere better than the uniform haze model, and in addition, the northern polar hood and the detached haze are qualitatively reproduced.     

Speckle imaging of Titan at 2 microns: surface albedo, haze optical depth, and tropospheric clouds 1996-1998

We present results from 14 nights of observations of Titan in 1996-1998 using near-infrared (centered at 2.1 microns) speckle imaging at the 10-meter W.M. Keck Telescope. The observations have a spatial resolution of 0.06 arcseconds. We detect bright clouds on three days in October 1998, with a brightness about 0.5% of the brightness of Titan. Using a 16-stream radiative transfer model (DISORT) to model the central equatorial longitude of each image, we construct a suite of surface albedo models parameterized by the optical depth of Titan's hydrocarbon haze layer. From this we conclude that Titan's equatorial surface albedo has plausible values in the range of 0-0.20. Titan's minimum haze optical depth cannot be constrained from this modeling, but an upper limit of 0.3 at this wavelength range is found. More accurate determination of Titan's surface albedo and haze optical depth, especially at higher latitudes, will require a model that fully considers the 3-dimensional nature of Titan's atmosphere.     

Simulations of Titan's brightness by a two-dimensional haze model

We have used a 2-D microphysics model to study the effects of atmospheric motions on the albedo of Titan's thick haze layer. We compare our results to the observed variations of Titan's brightness with season and latitude. We use two wind fields; the first is a simple pole-to-pole Hadley cell that reverses twice a year. The second is based on the results of a preliminary Titan GCM. Seasonally varying wind fields, with horizontal velocities of about 1 cm sec-1 at optical depth unity, are capable of producing the observed change in geometric albedo of about 10% over the Titan year. Neither of the two wind fields can adequately reproduce the latitudinal distribution of reflectivity seen by Voyager. At visible wavelengths, where only haze opacity is important, upwelling produces darkening by increasing the particle size at optical depth unity. This is due to the suspension of larger particles as well as the lateral removal of smaller particles from the top of the atmosphere. At UV wavelengths and at 0.89 micrometers the albedo is determined by the competing effects of the gas the haze material. Gas is bright in the UV and dark at 0.89 micrometers. Haze transport at high altitudes controls the UV albedo and transport at low altitude controls the 0.89 micrometers albedo. Comparisons between the hemispheric contrast at UV, visible, and IR wavelengths can be diagnostic of the vertical structure of the wind field on Titan.