\def\FIGURES{\local/FIGURES} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{Introduction} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% The atmosphere of Titan, which will be soon observed by the Cassini/Huygens mission, is one of the most mysterious and exciting climate systems of the solar system. Titan's dense nitrogen atmosphere (1.4 atm at the surface for a gravity of 1.35~m~s$^{-2}$) is thought to be dominated by a strong zonal flow, peaking in the stratosphere at around 200-300~km. At these altitudes, the atmosphere is rotating about 10 times faster than the solid body, itself locked in phase around Saturn, with a 16-day period. Composed mainly of nitrogen (90-98\%) and methane (2\% above tropopause), Titan's atmosphere is also the site of an intense photochemistry, initiated between 600 and 1000 km by dissociation of molecules by magnetospheric electrons and UV photons. Laboratory experiments suggest that compounds as complex as ``ammono" analogs to amino acids could be present \cite[]{Raul:02}. About 20 different species have been detected thus far, either by Voyager or from ground based observations. This rich photochemistry yields polymerization of hydrocarbons and nitriles, with formation of a dense aerosol layer in the stratosphere, that gives Titan its orange color on Voyager visible images. The details of this polymerization are not yet understood, and both experimental and theoretical studies are in progress on this point \cite[]{Coll:99,Tran:03I,Lebo:02,Wils:03}. Almost all the gaseous species show a strong enrichment in the northern polar latitudes at the time of Voyager encounter, shortly after northern spring equinox. If defined as the ratio between the average concentration at 50-70 N and that at 0-30 N, this enrichment varies from a factor of 1.4 to more than 20 depending on the particular chemical compound. In a review of the composition of Titan's atmosphere from a meteorological viewpoint, \cite{Flas:98} suggests that the meridional transport and subsidence of stratospheric species could play a significant role in enhancing the polar concentration. From meridional winds of 4~m~s$^{-1}$ and a dynamical time scale $\sim 4$~terrestrial years, he estimated an HCN enhancement of a factor of 2, and concluded that some additional factor, such as a localized meridional circulation, was necessary to explain the observations. He also discusses the possibility of the circumpolar vortex becoming dynamically and compositionally isolated from the remainder of the atmosphere during late winter and early spring. In a speculative analogy with Earth's ozone hole, the isolation would end with the breaking of the vortex by planetary waves, which would mix constituents, heat and vorticity across the boundary. Combining a photochemical model and transport of atmospheric compounds by meridional circulation, \cite{Lebo:01} have clearly attributed the enrichment of northern high latitudes at the time of Voyager to the downward advection of chemical compounds from the production zone, in the downward branch of a global pole-to-pole Hadley cell which prevails almost until northern spring equinox. Without additional factors, the coupled model was able to reproduce even the large value observed for the polar enrichment of HCN. No clear explanation was given however for the wide range observed for the magnitude of this polar enrichment. \cite{Lebo:01} suggested that this magnitude could be partly controlled by chemistry: a stronger contrast on the vertical, due for instance to a stronger source in the upper atmosphere relatively to the sinks, could produce, through downward advection in high latitudes, a stronger polar enrichment. The present paper casts a new light on this question. For most species, the magnitude of the latitudinal contrast does not depend in fact on the actual chemistry but only on the altitude at which they condense. We show that the very same latitudinal contrasts can be obtained either with a full chemical model forced by the GCM dynamics or with a very simple tracer fixed to one in the upper stratosphere and undergoing advection and condensation at a given level. It is shown also that advection in the meridional plane and latitudinal mixing by waves is controlling the vertical gradient of chemical compounds. If atmospheric transport is responsible for the latitudinal and vertical variations of the stratospheric composition, then observations of composition can also provide valuable information on the atmospheric circulation. In particular, the good agreement of model results and observations in terms of polar enrichment and vertical profiles provides a strong validation of the atmospheric dynamics given that this polar enrichment is quite sensitive to the model dynamics. In fact, polar enrichment in itself is evidence for the existence of the Hadley circulation on Titan. This fundamental component of the dynamics has never been directly observed on Titan. Observations of the latitudinal and time variations of atmospheric composition by the Cassini orbiter will thus contain very important constraints on the atmospheric circulation. The paper begins with a synthesis of previous modelling work on the simulation of the atmospheric composition and dynamics of Titan's atmosphere including a description of the version of the coupled model used in this study (section 2). We then discuss what controls the vertical and latitudinal variations of atmospheric chemical compounds (section 3) and how their simulation depends on the accuracy of the simulated atmospheric dynamics (section 4). Seasonal variations are discussed in section 5. We finally present some predictions of what Cassini should observe during the mission and underline the importance an extended mission covering a longer fraction of a Titan year could have (section 6) before some concluding remarks. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{Titan Climate Modelling} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \subsection{Atmospheric Superrotation} \cite{Goli:75} was the first to suggest that, like Venus, Titan may be the site of an intense atmospheric superrotation. Observations of latitudinal temperature contrasts by the Voyager~1 probe \cite[]{Flas:81} as well as the shape of Titan's atmosphere %[reconstructed from ground based observations of the occultation of a %very bright star, {\em Hubbard et al.}, 1993] \cite[reconstructed from ground based observations of the occultation of a very bright star, ][]{Hubb:93} both suggested a strong zonal flow, but with no constraint on its direction. The prograde nature of winds was first predicted theoretically and simulated numerically with a general circulation model adapted from the climate model of the Laboratoire de M\'et\'eorologie Dynamique \cite[]{Hour:92b,Hour:95b}, LMDZ. It has since gained mounting observational confirmation \cite[]{kostiuk2001, moreno2003, bouchez2003, luzdps2003}. The adaptation of the climate model from Earth to Titan mainly consisted in turning off the water cycle and replacing the radiative transfer computation by the code developed for Titan by \cite{Toon:89} for the solar range (UV and IR) and \cite{McKa:89} for the thermal IR. In this first study \cite[]{Hour:95b}, the radiative effect of latitudinal variations of the atmospheric composition was ignored. The 3-dimensional dynamical core, based on the primitive equations of meteorology, was kept unchanged except for parameters such as gravity or the thermodynamic gas constant. Those simulations have been preceded by simpler studies \cite[]{Hour:92b,Del:93,Hour:96estec} for idealized planetary conditions in which superrotation has been obtained for planets rotating much slower than the Earth, at zero obliquity (as on Venus) and increased absorption of solar radiation in the visible. Both for the realistic Titan case and for the simpler simulations mentioned above, the simulated superrotation is explained by the so-called Gierasch-Rossow mechanism \cite[]{Gier:75}. The net upward transport of angular momentum (product of the absolute zonal velocity and the distance to the polar axis) by global equator-to-pole Hadley cells is able to create and maintain an excess of angular momentum in the upper atmospheric layers, if the angular momentum is larger in low than in high latitudes (this is the case for instance for an atmosphere at rest with respect to the surface). Once superrotation sets in, there is also more angular momentum transported into high latitudes in the upper branches of the Hadley cells than equatorward near the surface. This net poleward transport of angular momentum is balanced by equatorward transport by non-axisymmetric eddies as originally suggested by \cite{Gier:75} and \cite{Ross:79} in the context of Venus. In the numerical simulations, those eddies were identified as planetary waves forced by barotropic and inertial instabilities on the equatorward flank of the strong high latitude jets created, like the jet stream on Earth, by the poleward transport of angular momentum from the equator. In this context, the slow planetary rotation rate is important to allow the Hadley circulation to extend up to the pole \cite[]{Hunt:79,Del:87} while the increased static stability reduces the coupling between the surface and the superrotating atmosphere. The main difference between Titan simulations \cite[]{Hour:95b} and the above mentioned simulations of atmospheric superrotation is the strong seasonal cycle arising from Titan's large obliquity (26.7$^\circ$): during almost half a year around solstice, the meridional circulation is dominated by a Hadley cell extending between both poles, with rising motion in the summer hemisphere. This meridional circulation creates an intense circumpolar jet in the winter hemisphere, analogous to the jet stream on Earth. It is only close to the equinoxes or on an annually averaged view that the meridional circulation is dominated by two equator-to-pole Hadley cells. For more details see the introduction of \cite{Luz:03I}. \subsection{Coupling with Atmospheric Composition} Those first simulations of Titan's atmospheric circulation strongly underestimated the latitudinal temperature contrasts measured by Voyager in the stratosphere as well as the intensity of the circumpolar jet inferred from the stellar occultation. \cite{Hour:95b} suggested that this deficiency could be due to the fact that the radiative computations did not take into account the latitudinal contrasts in atmospheric composition or haze opacity. Modelling work and analysis of Voyager observations did confirm the strong coupling between chemistry, microphysics and stratospheric dynamics. By forcing a microphysical model of Titan's haze by the meridional circulation predicted with the Titan's GCM, it was shown that meridional transport alone could explain the order of magnitude of the observed hemispheric and seasonal contrasts in Titan's albedo \cite[]{Hutz:95}. With a similar approach, the polar enrichment in gaseous compounds at the time of the Voyager encounter was attributed to downward advection from source regions in the subsiding branch of the Hadley cell \cite[]{Lebo:01}. Finally, from radiative computations, it was shown that the latitudinal variations of atmospheric composition and haze opacity, as deduced from Voyager observations, were able to modulate significantly the radiative balance of Titan's stratosphere \cite[]{Beza:95}. \subsection{The 2-Dimensional Coupled Model} \begin{figure*} \centerline{ \includegraphics[angle=-90,width=5.5cm]{\FIGURES/profils_a.eps} \includegraphics[angle=-90,width=5.5cm]{\FIGURES/profils_b.eps} \includegraphics[angle=-90,width=5.5cm]{\FIGURES/profils_c.eps} } \caption{Comparison between simulated and observed stratospheric composition at solar longitude L$_s$=9 (Voyager 1 fly-by). Model results including full chemistry is plotted with solid lines. Dashed lines are for the linearized chemistry (see text). Black circles are observations from Voyager 1 (Coustenis and B\'ezard, 1995). Pressure levels correspond to the maximum of the contribution function (at equator) for each compound. For the model, concentrations are extracted at this particular pressure level. Observations for HC$_3$N at low to mid latitudes are upper limits. \label{fg:compo}} \end{figure*} For the reasons above, it was then decided to develop a climate model for Titan, coupling dynamics, chemistry and haze microphysics. Because of the prohibitive numerical cost of the 3-dimensional Titan GCM, the model was developed based on a restriction to axi-symmetric component. The microphysical model by \cite{Caba:92} was introduced in the climate model based on a description of the haze particles in terms of 10 bins in radius (instead of the 45 bins of the original 1-dimensional model). %\cite[instead of 45 bins in the original 1-dimensional model, ][]{Caba:92}. The smallest size is for the freshly created macromolecules ($r_1=1.64\times 10^{-9}\mbox{ m}$), the other radii being given by $r_{n+1}=16^{1/3}r_n$. The monomer radius is $r_m=66\mbox{ nm}$ and the volume ratio between two adjacent bins is 16. Particles larger than $r_m$ are represented as fractal aggregates. %The first five bins correspond to spherical particles. %The fifth one serves as a monomer for aggregates particles represented %as fractals (5 last bins). The radiative code was upgraded to account for the coupling with the new aerosol description \cite[]{Rann:04}. The atmospheric composition is handled by a module consisting essentially of the photochemical model of \cite{Lebo:01}, which has been integrated in the GCM. This yields a stratospheric composition in rather good agreement with available observations, as shown in Fig.~\ref{fg:compo}. A detailed analysis of the most significant discrepancies (C$_2$H$_6$, C$_3$H$_8$, C$_4$H$_2$, HC$_3$N), and comparison with the previous results of \cite{Lebo:01} is not in the scope of this paper, and will be published in a forthcoming study. As in \cite{Lebo:01}, linear tracers can also be used for C$_2$H$_6$, C$_2$H$_2$ and HCN (thereafter named linearized chemistry). The chemical production and loss terms are replaced by relaxation toward a reference profile with a given photochemical time constant, both taken from a 1-dimensional photochemical model. The advantages of this simplified chemistry are twofold: 1) the code is faster and 2) the model can be tuned so as to reproduce the observed mean stratospheric concentrations. This is important when evaluating the effect of chemical composition on atmospheric dynamics. Latitudinal profiles obtained with the linearized chemistry for these three compounds are also shown in Fig.~\ref{fg:compo}. In the present study, both the full and linearized chemistry are used. When using the full chemistry, the upper boundary has to be chosen for all species. Chemistry taking place above the GCM limits has a crucial role for most constituents, which are produced in the mesosphere and then transported downward. For the simulations used in this paper, we decided to fix the exchange flux between the upper atmosphere and the upper layer of the GCM. These fluxes are calculated using a 1-dimensional model of Titan's atmosphere in equatorial conditions \cite[see ][]{Lebo:02,Lebo:03a}. As a first approximation, these fluxes are fixed, both in time and as a function of latitude. A second option is to fix the composition in the upper layer of the GCM. This option was also tested, again with no temporal or latitudinal variations, and it gives results very similar to our first option. For the linearized chemistry, the upper boundary condition is handled in a different way: the concentration is forced to stay close to the 1-dimensional reference profile in the three upper layers by imposing arbitrarily short chemical time constants (1 Titan day in the top layer, 10 days in the second and 100 days in the third layer from the top). The upper condition essentially controls the mean stratospheric concentration without affecting latitudinal contrasts, as will be shown below. To avoid difficulties related to the possible impact of temperature errors, condensation is computed for each species (both for the full and linearized chemistry) from a concentration at saturation estimated once at the beginning of the simulation using the temperature profile of \cite{Lell:89}. One important point when reducing the model to a 2-dimensional latitude-altitude version, is to parametrize the effect of latitudinal transport of momentum, heat, or tracers by planetary waves. For this, a specific parametrization was developed \cite[]{Luz:03II}. In this parametrization, latitudinal mixing by waves is prescribed as an eddy diffusion. The eddy diffusivity $K_y$ itself is parametrized as a function of the explicit variables of the axi-symmetric model (closure). This parametrization was developed and tuned based on a series of simulations of planetary waves in Titan-like conditions with a global shallow water model \cite[]{Luz:03I}. The diffusivity $K_y$ mainly depends on the barotropic instability of the mean zonal flow. For the simulations presented here, the model discretization is based on 48 latitude bands of equal width spread from pole to pole with 55 vertical layers of which the last three serve as a sponge layer to dump down the wind and prevent spurious reflection of waves. Level 52 is at approximately 480~km above the surface. The vertical resolution is about 3~km in the troposphere, 5~km at the tropopause and 10-15~km in the stratosphere, which corresponds to one half to one third of a scale height. The dynamical equations are integrated with a time step of 3 minutes. The radiative transfer is computed ten times per Titan day. Additional informations can be found in \cite{Luz:03II} and \cite{Rann:04}. All the simulations presented here were started from an initial state inherited from previous pluriannual simulations. The model was integrated for several Titan years and it was checked at the end, by comparing two successive years, that the results presented were identical. It appears in fact that the time constants involved when studying the stratospheric dynamics and composition are relatively short. In particular, the time constants for composition are not determined by the reaction rates themselves, which can correspond to very long time constants, but rather by transport and condensation close to the tropopause as analyzed in detail below. Finally, the results presented below for sensitivity experiments correspond to year 6, which is more than enough to obtain stable results from one year to the other. \subsection{Impact of Coupling on the Dynamics} \begin{figure} \centerline{ \includegraphics[width=8cm]{\FIGURES/tcoust.eps} \includegraphics[width=8cm]{\FIGURES/uhubb.eps} } \caption{Stratospheric temperature (at 1~hPa, L$_s$=9) and zonal winds (at 0.25~hPa, L$_s$=128). Comparison between observations and simulations with and without coupling with the atmospheric chemistry and haze microphysics. Temperatures were retrieved from infrared remote sounding by Voyager shortly after northern spring equinox. The observed wind profile was deduced from the 1989 stellar occultation. The symmetric shape is imposed by the retrieval procedure but observations are only reliable in the shaded area. \label{fg:Voyager}} \end{figure} The first important result of the coupled model was to explain the origin of the detached haze layer observed in Voyager images above the main haze layer and to predict a strong accumulation of haze in the polar night \cite[]{Rann:02}. This accumulation in turn increases radiative cooling to space in high latitudes, enforcing the meridional forcing of the general circulation \cite[]{Rann:04} and hence latitudinal temperature contrasts and the zonal circumpolar jet, in better agreement with observations. The coupling with chemistry has a similar effect but occurs higher in the atmosphere, and is less sensitive for comparison with available observations \cite[]{Lebo:03}. As an illustration, we show in Fig.~\ref{fg:Voyager} the comparison between the simulated and observed zonal wind profiles %[comparison with the occultation %profiles close to northern summer solstice, {\em Hubbard et al.}, 1993] \cite[comparison with the occultation profiles close to northern summer solstice, ][]{Hubb:93} and latitudinal temperature profiles at 1~hPa \cite[compared with Voyager retrieval close to northern spring equinox by][]{Flas:81,Flas:90,Cous:95}. The comparison is shown for two simulations, one without coupling and another with the dynamics coupled with both haze and chemistry. The temperature contrasts in winter mid latitudes and the jet speed are in much better agreement for the coupled case. \subsection{North/South Temperature Asymmetry} Note also that the coupled simulation tends to produce a north/south asymmetry of temperatures (upper panel of Fig.~\ref{fg:Voyager}) consistent with Voyager observations. Voyager observed, shortly after northern spring equinox, a warmer southern hemisphere. This observation was a surprise since radiative time constants were estimated to be much shorter than a season at the pressure levels sounded by the methane bands. It was first suggested that this asymmetry could be due to a phase lag in the latitudinal redistribution of angular momentum by the mean meridional circulation \cite[]{Flas:90}. Full simulations with a radiative convective model plus seasonal cycle showed in fact that the radiative time constants were long enough to explain the observed asymmetry. However, latitudinal redistribution of heat by dynamics would reduce instead of increase the asymmetry \cite[]{Hour:95b}. Based on radiative computations, it was then suggested that the latitudinal variations in atmospheric composition and the north-south asymmetry in the haze distribution could cause the observed asymmetry \cite[]{Beza:95}. The results obtained with the coupled and uncoupled models favor the second explanation. The coupling with dynamics, and the enrichment in haze and chemical compounds in the winter hemisphere, clearly contribute to the seasonal lag in atmospheric temperatures. However, the model still slightly underestimates the temperature at southern latitudes. So some additional dynamical or radiative effects, not well resolved by the model, can not be completely ruled out. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{On Polar Enrichment} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{figure} \centerline{ \includegraphics[height=8cm]{\FIGURES/hcnz.eps} \includegraphics[height=8cm]{\FIGURES/ktrack.eps} } \caption{Meridional transport of HCN during northern winter. {\bf a:} Meridional cross section of HCN concentration (in ppmv) (shaded) with stream lines of the mean meridional circulation (black arrows). {\bf b:} zonal wind (shaded) and latitudinal eddy diffusivity $K_y$ (contour, 10$^{-6}$~m$^2$~s$^{-1}$). With these particular units, the same contours can be interpreted as well as iso-values of a meridional eddy velocity in m~s$^{-1}$ for a mixing length of 1000~km. All the quantities are averaged from northern winter solstice to northern spring equinox. \label{fg:fig1}} \end{figure} The rationale behind enrichment in most chemical compounds in northern high latitudes at the time of the Voyager encounter (close to northern spring equinox) is as follows, and is illustrated in Fig.~\ref{fg:fig1}. During almost half a year around solstice, the mean meridional circulation is dominated by a global pole-to-pole Hadley cell with the rising branch in the summer (southern) hemisphere and subsiding motions in the winter (northern) latitudes (arrows in panel {\bf a} of Fig.~\ref{fg:fig1}). The downward advection of chemical compounds from the production zone in the upper stratosphere or mesosphere is responsible for the strong polar enrichment \cite[]{Lebo:01} as illustrated for HCN in panel {\bf a} of Fig.~\ref{fg:fig1} (shaded). This Hadley circulation also creates an intense circumpolar jet in northern high latitudes (shaded in panel {\bf b} of Fig.~\ref{fg:fig1}). This jet is unstable on its equatorward flank leading the development of planetary waves. Those waves, parametrized in the model \cite[]{Luz:03II}, are responsible for the erosion of the polar bulge. Values of the parametrized eddy diffusivity $K_y$ averaged for northern winter are shown in panel {\bf b} of Fig.~\ref{fg:fig1} (contours). Figure~\ref{fg:schema} summarizes these mechanisms. \subsection{Composition of the Polar Vortex} \begin{figure} \centerline{ \includegraphics[height=7cm]{\FIGURES/pole.eps} } \caption{ A sketch of the essential mechanisms responsible for the observed contrasts in Titan's stratospheric composition.\label{fg:schema}} \end{figure} \begin{figure*} \includegraphics[width=5.cm]{\FIGURES/tauA1C1Kiid.eps} \includegraphics[width=5.cm]{\FIGURES/wtauA1C1Kiid.eps} \includegraphics[width=5.cm]{\FIGURES/hcnA1C1Kiid.eps} \caption{Time constants and vertical profiles in the winter polar vortex. {\bf a:} time constants (in Titan days) for vertical advection in the core of the vortex ($-h/w$, with $h=150$~km, averaged between 70 and 90N), and meridional circulation ($l/v$, with $l=$1000~km, averaged between 50 and 80N) and latitudinal mixing by waves ($l^2/K_y$, averaged between 50 and 80N) at the edge of the vortex. The grey curve corresponds to meridional advection toward the equator ($-v$ instead of $v$). The vertical lines correspond to 1~day and 1~year. {\bf b:} associated scale height (km) for meridional advection, $-wl/v$, latitudinal mixing $-wl^2/K_y$ and the total scale height $H=-w/(v/l+K_y/l^2)$. {\bf c:} vertical profiles of the mole fraction of HCN (in log scale) at different latitudes (linearized chemistry). The thin oblique line corresponds to a constant scale height of 100~km. \label{fg:scaleh}} \end{figure*} For the simulations with linearized chemistry, the time evolution of the mass concentration $c$ of a given chemical compound is simply given by \begin{eqnarray} \frac{\partial c}{\partial t}+ v\frac{\partial c}{a\partial \phi}+ w\frac{\partial c}{\partial z}=\nonumber\\ \frac{c_0-c}{\tau_{\mbox{chem.}}} +\frac{1}{a^2\rho\cos\phi}\frac{\partial }{\partial \phi} \left( \cos\phi\rho K_y \frac{\partial c}{\partial \phi} \right) \label{EQ1} \end{eqnarray} where $\phi$ is the latitude, $z$ is the altitude, $\rho$ is the air density, $a$ is the radius of Titan, $v$ and $w$ are the meridional and vertical wind components, $K_y$ is the lateral eddy diffusivity defined above, $c_0$ is a 1-dimensional vertical profile determined from a 1-dimensional simulation of Titan's photochemistry and $\tau_{\mbox{chem.}}$ is a time constant from the same simulation which also depends on altitude only \cite[]{Lebo:01}. For chemical species subsiding in the polar vortex down from the production zone, the concentration decreases under the combined effects of meridional advection of clear air from low latitudes and latitudinal mixing by waves. By denoting by $c_{\mbox{eq}}$ the typical concentration at low latitudes, the erosion of the polar vortex concentration $c$ by latitudinal eddy diffusion (last term in equation~\ref{EQ1}) %\begin{equation} %\frac{1}{a^2\rho\cos\phi}\frac{\partial }{\partial \phi} %\left( \cos\phi\rho K_y \frac{\partial c}{\partial \phi} \right) %\end{equation} can be roughly estimated as \begin{equation} \frac{K_y}{l^2} \left( c_{\mbox{eq}}-c\right) \end{equation} where $l\simeq$~1000~km is the typical length scale associated with latitudinal contrasts in atmospheric composition. Similarly, the effect on the polar vortex concentration $c$ of advection of clear air from low latitudes by a meridional wind $v$ (assumed positive in the northern hemisphere), $(-v/a) \partial c / \partial \phi$, %\begin{equation} %-v\frac{\partial c}{a\partial \phi} %\end{equation} can be approximated as \begin{equation} \frac{v}{l} \left( c_{\mbox{eq}}-c\right) \mbox{.} \end{equation} Assuming a steady state regime, the transport equation can be approximated as \begin{equation} w\frac{\partial c}{\partial z}\simeq\frac{c_0-c}{\tau_{\mbox{chem.}}}+ \left( c_{\mbox{eq}}-c\right) \left( \frac{K_y}{l^2}+\frac{v}{l} \right) \end{equation} For a large number of species, the polar enrichment is such that the hypothesis that $c_0 << c$ and $c_{\mbox{eq}} << c$ can be made. In such conditions, and for a positive meridional wind $v>0$, the vertical gradient of $c$ in the polar vortex is given by \begin{equation} w\frac{\partial c}{\partial z}\simeq -c\left( \frac{1}{\tau_{\mbox{chem.}}}+\frac{K_y}{l^2}+\frac{v}{l} \right) \end{equation} corresponding to a total atmospheric scale height for the mass concentration of \begin{equation} H=\left( \frac{d \ln c }{dz} \right)^{-1}\simeq w\left( \frac{1}{\tau_{\mbox{chem.}}}+\frac{K_y}{l^2}+\frac{v}{l} \right)^{-1} \end{equation} For species with large chemical time constants (compared to dynamical time constants), the shape of the vertical concentration profile is controlled by a competition between vertical advection (with faster advection from the upper stratosphere reducing vertical contrasts) and relaxation toward the weak concentrations found in low latitudes in the mid stratosphere by either mean meridional transport or latitudinal mixing by waves (which accentuates the vertical contrasts). The relative importance of meridional advection and latitudinal mixing can be quantified either in terms of time constants, $\tau_{\mbox{mmc}}=l/v$ and $\tau_{\mbox{mix}}=l^2/K_y$ or in terms of the associated scale height $-w\tau_{\mbox{mmc}}$ and $-w\tau_{\mbox{mix}}$. In Fig.~\ref{fg:scaleh}, panel {\bf a}, we show for northern winter (quantities averaged between northern winter solstice and northern spring equinox) the time constants for the vertical and meridional advection as well as for latitudinal mixing by waves. The meridional advection dominates latitudinal transport only in the upper branch of the Hadley cell (above 400~km) as well as in the lower stratosphere, between 100 and 150~km were the meridional wind is negative. This region corresponds to the lower branch of the stratospheric Hadley cell. Typical values for dynamical time constants vary from about one Titan year at 120~km to less than one Titan day above 350~km. As discussed below, those time constants are shorter or much shorter than chemical time constants for most species. The associated dynamical scale height (panel {\bf b}) is of the order of 100~km in the mid-stratosphere, where it is essentially determined by the balance between downward advection and latitudinal mixing by waves. Panel {\bf c} shows, at the same season, simulated vertical profiles of HCN (obtained with the linearized chemistry) for different latitude ranges in the northern hemisphere. The straight line in the same panel corresponds to a scale height of 100~km. This is very close to the scale height for HCN profiles above 250~km at 45-60N, at the edge of the polar vortex, in the region of mixing. Between 100 and 150~km, the scale height is much larger due to the weaker mixing there. For the 45-60N profile, a local maximum is even obtained in this altitude range, due to meridional advection of rich air from the polar vortex. The shape of the vertical profiles, with three distinct slopes and a very well mixed region in the mid-stratosphere, between 150 and 400~km, is consistent with recent observations by \cite{Mart:02}. Numerical simulations with 1-dimensional chemical models show much larger vertical variations in this region due to a much weaker vertical transport \cite[see e.g. Figure~1 of ][]{Hida:02}. The vertical advection by the stratospheric Hadley cell is in fact much more efficient in transporting chemical species over long distances than turbulent mixing by small scale eddies. For a vertical eddy diffusivity $K_z$ and a vertical scale $h$, the time scale for diffusive mixing is $h^2/K_z$ instead of $h/w$ for advection. Between 250 and 150~km, the time constant associated with vertical advection varies from about 10 to 100~Titan days. Very large values of $K_z$ of typically 100-5000~m$^2$~s$^{-1}$ would be required (assuming $h\simeq$200~km) to obtain similar time constants. This is consistent with the study by \cite{Lebo:03a} in which an eddy diffusion coefficient of 100~m$^2$~s$^{-1}$ was adopted in this region to emulate mixing by the general circulation. % h^2=2.25e10 / tau=10*16*86400 1.3e7 = 1.7e2 \subsection{Magnitude of Latitudinal Contrasts} \begin{figure} \includegraphics[angle=-90,width=8cm]{\FIGURES/compo.eps} \caption{Latitudinal profiles of chemical species as computed with the 4 options (full, linearized or null chemistry as well as idealized tracers) compared to Voyager observations. Curves are normalized to the observed equatorial value to focus on latitudinal variations.\label{fg:chim}} \end{figure} \begin{table*} \caption{Condensation level, polar enrichment (ratio of the averaged concentrations at 50-70N and 0-30N) and chemical time constants for various chemical compounds. \label{tab:chem}} \begin{center} \begin{tabular}{ccccccccc} & C$_2$H$_2$ & C$_2$H$_4$ & C$_2$H$_6$ & CH$_3$CCH & C$_3$H$_8$ & C$_4$H$_2$ & HCN & HC$_3$N \\\hline \multicolumn{9}{c}{Condensation level}\\\hline winter polar vortex, km & 64 & - & 57 & 64 & 54 & 77 & 86 & 63 \\ winter polar vortex, hPa & 35 & - & 50 & 35 & 60 & 20 & 15 & 36 \\ retained for idealized tracers, hPa & 40 & - & 80 & 40 & 100 & 20 & 20 & 40 \\\hline % niveaux detectes a partir du script levels.x sur SEB %winter polar vortex & 28 & - & 36 & 28 &28 & 16 & 12 & 28 \\ %idealized tracers & 40 & 200 & 60 & 40 &40 & 30 & 20 & 40 \\\hline \multicolumn{9}{c}{Level of maximum of the weighting function for Voyager IRIS observations}\\\hline km & 152 & 190 & 160 & 85 &125 & 100 & 107 & 103 \\ hPa & 2.5 & 1 & 2 & 13 &5 & 10 & 8 & 9 \\\hline %SEB \multicolumn{9}{c}{Polar enrichment}\\\hline Observations & 2.1 & 8.3 & 1.4 & 6.4 & 1.9 & 16.8 & 7.6 & 19.6 \\ Full chemistry & 2.7 & 3 & 1.9 & 9.9 & 1.6 & 5.9 & 7.8 & 6.2 \\ Linearized chemistry & 2.3 & - & 1.3 & - & - & - & 7.5 & - \\ Null chemistry & 2.6 & 2.6 & 1.9 & 9.6 & 1 & 10.1 & 9.2 & 5.2 \\ Idealized tracers & 2.4 & - & 2 & 5.6 & 2.6 & 9.3 & 9.3 & 4.2\\\hline \multicolumn{9}{c}{Chemical time constant (Titan year)}\\\hline 0.5-1 hPa (190-200~km) & 0.5-100 & 0.03-4 & $>$40 & 2-100 & $>$10 & 0.001-1 & 2-200 & 0.05-10 \\ 2-5 hPa (125-160~km) & $>$2.5 & 0.2-5 & $>$200 & 2-200 & $>$80 & 0.01-3 & 2-300 & 0.2-50 \\\hline \end{tabular} \end{center} \end{table*} \begin{table*} \caption{Characteristics of the various chemical schemes.\label{tb:sims}} \begin{center} \begin{tabular}{|c|c|c|c|}\hline Simulation name & Chemistry & condensation & upper boundary condition \\\hline Full chemistry & realistic & realistic & prescribed flux \\ Null chemistry & no & realistic & prescribed flux \\ Linearized chemistry & Relaxation & realistic & relaxation \\ Idealized tracers & no & removal below a given pressure level & relaxation\\\hline \end{tabular} \end{center} \end{table*} The enriched subsiding air generally reaches saturation when approaching the tropopause level, explaining the sharp decrease observed in panel {\bf c}\ of Fig.~\ref{fg:scaleh} for HCN at all latitudes. For most species, the concentration at saturation at the very cold tropopause of Titan ($T\simeq70$~K) is orders of magnitude smaller than the concentrations observed in the polar vortex. So the air which is recycled in low latitudes rises from the troposphere with a very low concentration. It is then replenished either by latitudinal advection from the polar vortex or by latitudinal mixing by waves. The latitudinal contrast observed for altitudes ranging from 80 to 200 km thus essentially represents the efficiency of mixing and latitudinal transport to carry chemical species into the clear air rising from the troposphere. As is visible in Fig.~\ref{fg:scaleh}, meridional advection dominates this latitudinal transport below 150~km (grey curve in panel {\bf a}). This simple idea of the build-up of latitudinal contrasts was checked by simulating chemical compounds as very simple atmospheric tracers (thereafter named idealized tracers). In the three upper layers, those tracers are relaxed (with the same time constants as for the linearized chemistry) toward a concentration of unity. The tracers undergo both the mean meridional circulation and latitudinal mixing, but not chemistry. The tracers are completely removed below a given level, close to the tropopause. The various tracers only differ by the pressure level at which they are removed. We consider 8 idealized tracers corresponding to condensation levels of: 100., 80., 60., 40., 30., 20., 15. and 10. hPa. The idealized tracers can only be compared to real chemical compounds in terms of relative latitudinal or vertical variations. Also, because the idealized tracers disappear suddenly at the condensation level whereas the actual concentration is decreasing gradually in the condensation region, the level retained for the condensation of the idealized tracer must be somewhat lower than the real condensation level of the chemical compound to which it is compared (typically at the level where the concentration has decreased by one order of magnitude, which generally occurs at a little bit less than twice the pressure of the actual condensation level). The actual level of condensation in the winter polar vortex was computed from the simulation with full chemistry, as the upper layer where the given species condenses (note that this level depends on the concentration simulated for that species in the polar vortex). This level as well as the level retained for the idealized tracer is given for a certain number of species in Table~\ref{tab:chem}. Table~\ref{tab:chem} also shows the polar enrichment, defined as the ratio of the averaged concentrations at 50-70N and 0-30N. First, the comparison of the observed polar enrichment with the results of the model with full chemistry shows an agreement for most species, except C$_2$H$_4$ -- the enrichment appears closer to the pole than observed -- C$_4$H$_2$ and HC$_3$N -- which may be affected by chemical processes not included in the model (e.g. pathways producing haze precursors). For most species (C$_2$H$_2$, C$_2$H$_6$, C$_3$H$_8$, HCN, HC$_3$N), the polar enrichment obtained for the full chemistry and idealized tracers differ by less than 50$\%$. This general agreement clearly shows that the level at which species are removed by condensation is controlling for a large part the magnitude of polar enrichment. The secondary role played by either chemistry or specifications of the model upper boundary conditions is detailed below. In order to estimate the relative importance of chemistry for the various species, we computed a chemical time constant $\left( d\mbox{ln}c/dt \right)^{-1}$, where the tendency is computed for all the chemical reactions acting as a sink for the given species. Values are given for two pressure ranges in Table~\ref{tab:chem}. We also ran the full chemical model but replacing all chemical rate constants by zero (thereafter named null chemistry, see Table~\ref{tb:sims}). Values of the polar enrichment obtained by the full and null chemistry depart by less than 20\% except for C$_4$H$_2$ and C$_3$H$_8$. The disagreement between null and full chemistry for C$_4$H$_2$ is consistent with the relatively short chemical time constants obtained for this species. In the case of C$_3$H$_8$, the discrepancy between full and null chemistry, despite very long chemical time constants, is probably due to the fact that the flux at the upper boundary is very close to zero. This flux is probably underestimated by the 1-dimensional photochemical model, leading to an underestimated equatorial value in the GCM. The photochemical reactions, though occurring on long timescales, may then explain the difference between both simulations (Table~\ref{tab:chem}). As a consequence also, the simulation of C$_3$H$_8$ as an idealized tracer, with an upper condition prescribed as a relaxation toward a fixed value, also departs from the null chemistry. For the other species, the agreement between the null chemistry and idealized tracer is very good, in spite of the different treatment of the upper boundary condition and of the condensation (see summary of the different simulations in Table~\ref{tb:sims}). This good agreement reinforces the confidence in the results presented above. In particular, the upper boundary condition which, for a given species, controls its mean level in the lower stratosphere, does not affect its latitudinal variations. Finally, it clearly appears that the level of condensation is the main determinant of the magnitude of polar enrichment for most species. The higher the condensation occurs the stronger the polar enrichment. If the observational contribution function peaks just above the condensation level, the observed polar enrichment will also be larger than if the contribution function peaks much higher in the atmosphere. This for instance explains the small polar enrichment of C$_2$H$_2$ when compared to CH$_3$CCH which both condensate at the same levels. The same processes explain not only the magnitude of the polar enrichment but also the shape of the latitudinal profiles. To illustrate this point, we show in Fig.~\ref{fg:chim} for the three radiatively active species the latitudinal profiles normalized to the observed equatorial value for the various simulations. We compare normalized rather than absolute profiles to focus on latitudinal variations and also because comparison of absolute values does not make sense for the idealized tracers which are arbitrarily relaxed toward a concentration of unity at the model top (comparisons of absolute profiles are shown in Fig.~\ref{fg:compo} for the full and linearized chemistry). The agreement between all those profiles, from the most complex with full chemistry to the simple idealized tracer, clearly confirms the very weak control by chemistry of those latitudinal variations. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{Constraints on Winds} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{figure} \centerline{\includegraphics[angle=-90,width=8cm]{\FIGURES/chim.eps}} \centerline{\includegraphics[angle=-90,width=8cm]{\FIGURES/T.eps}} \centerline{\includegraphics[angle=-90,width=8cm]{\FIGURES/u.eps}} \caption{Sensitivity experiments. Polar enrichment in C$_2$H$_2$ and HCN obtained with the full coupled model, or with uncoupled chemistry (No chem) or uncoupled haze (No haze) or both (uncoupled) or with weakened (0.3xKy) or enhanced (3xKy) dissipation by waves or modified advection field for chemical compounds (mean meridional circulation multiplied by 0.3 or 3). The error bars correspond to the Voyager data. \label{fg:sensitiv}} \end{figure} \begin{figure} \centerline{\includegraphics[width=9cm]{\FIGURES/couple.eps}} \caption{Effect of the coupling with the haze on the latitude-altitude distribution of HCN ({\bf a}) and C$_2$H$_2$ ({\bf b}) and associated impact on the mean meridional circulation (MMC, {\bf c}) and latitudinal eddy diffusivity $K_y$ ({\bf d}, 10$^{-6}$~m$^2$~s$^{-1}$) at the time of the Voyager encounter. \label{fg:couple}} \end{figure} If the latitudinal contrasts depend primarily on dynamics as well as on the level of removal by condensation for each species, what does observation of the composition tells us about winds? Or, to which degree is the agreement with observations sensitive to the simulated circulation? To answer that question, we made a series of sensitivity experiments by varying the intensity of either the meridional advection or latitudinal mixing. A factor was applied either on both $v$ and $w$ or on the eddy diffusivity $K_y$, with two values~: 0.3 and 3. The factor was applied for the transport of the three linear chemical species only. We also performed simulations with and without coupling with chemistry or haze microphysics. The coupling with haze is turned off by applying a strong latitudinal mixing on haze particles to obtain almost no latitudinal contrasts. In those simulations, the production rate of haze must be strongly reduced to obtain the same geometric albedo of Titan \cite[see ][for additional details]{Rann:04}. In the radiative computation, coupling with chemistry is turned off by using the \cite{Lell:89} vertical profile of the methane abundance, and values taken from \cite{Cous:89} for ethane and acetylene above their condensation level. In this simulation however, the chemical compounds are transported as in the coupled version. Note that, to avoid complex feedbacks which would complicate the analysis, the simulations with modified meridional circulation or latitudinal mixing are performed without coupling with chemistry. In Fig.~\ref{fg:sensitiv}, we compare the polar enrichment for C$_2$H$_2$ and HCN obtained in the various sensitivity experiments and in Voyager observations (with associated error bars). For the nominal version, the latitudinal contrast is very well reproduced for both species. The ratio is much larger (respectively weaker) if the meridional advection ($v$ and $w$ components) is increased (respectively decreased) or if the latitudinal mixing is weakened (respectively strengthened). So observations of the composition actually contain strong constraints on the combined intensity of advection and mixing. The results suggest that those components are predicted at a factor of typically less than two with the nominal version of our coupled Titan GCM. Coupling with chemistry tends to degrade a little bit the agreement but keeps the results in the error bars. Without haze coupling, the agreement is significantly reduced, the contrast for HCN being much too low and that of C$_2$H$_2$ too high. The difference in sensitivity of these two species is due to the level at which they are observed. In Fig.~\ref{fg:couple}, we show a latitude-altitude cross-section of the ratio of the concentrations of HCN (panel {\bf a}) and C$_2$H$_2$ (panel {\bf b}) in the coupled and uncoupled simulations at the time Voyager encounter. The sensitivity is in fact very similar for the two species, with a decrease by about 30$\%$ in the polar vortex near 160~km and an increase by about 50$\%$ near 100~km, and can be interpreted as follows. The main effect of coupling with haze is a reinforcement of the subsidence in the winter polar region, due to a larger infrared cooling to space due to the accumulation of haze in the polar night \cite[]{Rann:04}. This reinforcement of the meridional circulation is illustrated by the stream-lines in panel {\bf c} of Fig.~\ref{fg:couple}. It is responsible for the increase in concentration in the low stratosphere, near 100~km. At the same time, the stronger jet in the coupled version leads to stronger wave activity (panel {\bf d}). The latitudinal eddy diffusivity is much larger in the coupled version. This reinforcement is particularly strong near 150~km and explains the weaker polar enrichment in this altitude range in the coupled model. C$_2$H$_2$ which is observed at 2.5~hPa, close to 160~km, has a smaller polar enrichment in the coupled version while it is the opposite for HCN which is observed close to 100~km. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{Seasonal Variations} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{figure*} \centerline{\includegraphics[angle=-90,width=18cm]{\FIGURES/season.eps}} \caption{The seasonal evolution of the concentration of HCN (ppmv) at (a) 50-70N and (b) 0-30N as well as the corresponding polar enrichment (c) are shown, together with the various components of atmospheric transport: vertical wind in the polar vortex (d) and meridional wind (e) and latitudinal mixing (f) at the edge of the polar vortex. WS is for winter solstice, SE for spring equinox, SS for summer solstice and FE for fall equinox. \label{fg:season}} \end{figure*} \begin{figure*} \centerline{\includegraphics[width=18cm]{\FIGURES/seasonhcn.eps}} \caption{ \label{fg:clouds} Six snapshots of the meridional structure for HCN and associated mean %SEB meridional circulation for seasons going from northern fall to northern spring equinox. Seasons are labeled according to the solar longitude $L_s$ with $L_s$=180 for northern fall equinox, $L_s=270$ for northern winter solstice and $L_s=0$ for northern spring equinox. Concentration of HCN (grey scales) is in ppmv. The condensation rate of HCN is shown as shaded squares with the same bar chart but for $10^{9}$ m$^{-3}$ s$^{-1}$.} \end{figure*} We have focused up to now on the mean winter conditions for interpreting the physics of the transport of chemical compounds and on northern spring equinox for the comparison with Voyager observations. In Fig.~\ref{fg:season} we present how the northern polar enrichment in HCN, as well as the associated components of atmospheric transport, evolve with seasons in the mid stratosphere (80-240~km). Soon after fall equinox in this altitude range, the high-latitude concentration grows very fast under the effect of downward advection (panel {\bf a}). At the same time, the jet is not yet established so that the latitudinal contrasts with low latitudes grow very fast, reaching a first maximum (panel {\bf c}). The polar enrichment then decreases under the combined effect of mixing by waves and latitudinal advection from the vortex toward low latitudes. Close to northern spring equinox, the meridional advection reverses above 150~km. The chemically rich air of the polar vortex is then rapidly advected toward the other hemisphere, explaining both the rapid decrease of concentrations at 50-70N above 180~km (panel {\bf a}) and the local maximum observed at 0-30N, in the upper part of the domain of panel {\bf b}. In the lower part, the polar high concentrations persist much longer, both because the time constants are longer there, and because the vertical and meridional advection do not change their signs in high latitudes. Around equinox on the other hand, the ascending branch of the stratospheric Hadley cell migrates from the hemisphere coming out of summer to the other hemisphere, bringing clear tropospheric air to the lower stratosphere at low latitudes. This upward advection of clear air explains the decrease observed below 150~km at 0-30N (panel {\bf b}) and the associated maximum in polar enrichment (panel {\bf c}). At this season also, the intensity of latitudinal mixing reaches a minimum in the lower stratosphere. But, as already stated, it is essentially the mean meridional advection which controls the polar enrichment below 150~km (compare panel {\bf e}\ and {\bf f}). The time constant of about 5 terrestrial years which can be deduced from the decrease of the first maximum of polar enrichment (panel {\bf c}) is also the time it takes to travel 1000~km at a speed of 5~mm~s$^{-1}$, which is the typical meridional velocity encountered in the lower branch of the stratospheric Hadley cell, near 120~km (panel {\bf e}). This seasonal evolution is illustrated in a series of 6 snapshots running from northern fall to northern spring equinox (Fig.~\ref{fg:clouds}). At both equinoxes (first and last panels) the upward advection of clear air by the low latitude branch of the two equator-to-pole Hadley cells is clearly visible. At fall equinox (panel {\bf a}), the southern polar vortex is still strongly enriched while the rich air from the upper stratosphere starts to sink in the northern high latitudes. Then the global pole-to-pole Hadley cell sets in (panels {\bf b} to {\bf d}), with an ascending branch in the south and subsidence in the north. Between 80 and 200~km, a secondary Hadley cell appears in the summer hemisphere which persists until the next equinox. This secondary cell clearly contributes to maintain a strong enrichment in the summer hemisphere, in the lower stratosphere. Note that this secondary cell is much more intense in the simulations with coupling to both atmospheric composition and haze. Because of this secondary cell also, the air keeps on sinking into the troposphere during summer, producing condensation at high latitudes (condensation is shown as shaded squares close to 80~km altitude in Fig.~\ref{fg:clouds}), even close to summer solstice when insolation is maximum at the pole. Exactly the same picture is obtained with C$_2$H$_6$ and C$_2$H$_2$ (not shown). The secondary cell coupled to condensation is in fact the sink of polar enrichment of the lower stratosphere during summer. This may also explain the cloudy features observed around the pole during summer from ground based observations \cite[]{Grif:98,Grif:00,Brow:02,Roe:02} and more recently from the T0 Cassini flyby of Titan. Our results clearly show that there is no contradiction between the season (summer) and a stratospheric origin of the observed clouds, so that a convective origin from the troposphere is not required. From our computation, it appears that clouds are as likely in the summer as in the winter hemisphere. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{What should Cassini Observe?} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{figure} \includegraphics[width=8cm]{\FIGURES/cassini.eps} \caption{ Time evolution of some observable quantities. {\bf a}: polar enrichment for HCN (at an altitude of 107~km) and C$_2$H$_2$ (at 152~km). {\bf b}: zonal wind at the equator (20S-20N) and in the northern high latitude jet (40-70N) at an altitude of 250~km. {\bf c}: Equator to high latitude (60N) temperature contrast and north south asymmetry (temperature difference between 60N and 60S) at 190~km. \label{fg:cassini} } \end{figure} Most that is known about the composition and dynamical state of Titan's mid stratosphere (pressure range 10-0.1 hPa) comes from the Voyager observations, at northern spring equinox. The vertical temperature profile, from the surface up to 200~km was reconstructed from radio occultation measurements \cite[]{Lind:83}. From there upward it is mainly constrained by the model by \cite{Yell:91}. For stratospheric dynamics, an estimate of the zonal flow was inferred through geostrophic balance \cite[]{Flas:81} from the temperatures retrieved for two pressure levels (0.4 and 1~hPa) from observations of the Q and P branches of the $\nu_4$ band of methane by the Voyager Infrared Spectrometer (IRIS). Since then, ground-based observers have tried to measure zonal winds with two main techniques: stellar occultations \cite[]{Hubb:93,Bouc:03}, which provide the speed but leave the wind direction undetermined, and from the Doppler shifts of either ethane and nitrile emission lines \cite[]{kostiuk2001,moreno2003} or of the backscattered solar spectrum \cite[]{luzdps2003}. The stratospheric composition is also constrained from Voyager IRIS observations. The equatorial composition has been obtained in the region 80-200 km for several hydrocarbons and nitriles (C$_2$H$_2$, C$_2$H$_4$, C$_2$H$_6$, CH$_3$C$_2$H, C$_3$H$_8$, C$_4$H$_2$, HCN), and latitudinal variations of their abundances could be retrieved thanks to the latitudinal resolution of IRIS \cite[]{Cous:89,Cous:95}. Ground-based observations made since only give access to a mean stratospheric value (C$_2$H$_6$ \cite[]{Live:02}; C$_3$H$_8$ \cite[]{Roe:03}) or to a mean stratospheric vertical profile (HCN, CH$_3$CN, HC$_3$N \cite[]{Mart:02}), which as mentioned above contains also information on atmospheric dynamics. Latitudinal contrasts in haze also contain information on dynamics. They have been monitored by Voyager \cite[]{Srom:81} and, since then, by the Hubble Space Telescope \cite[]{Lore:99,Lore:01,Youn:02} and ground-based observatories with adaptive optics and speckle imaging \cite[]{RoeN:02,Gend:04,Gibb:04}. Transient cloud features have been detected from disk-integrated infrared spectra \cite[]{Grif:00}, and from resolved adaptive optics \cite[]{Brow:02,Roe:02} and speckle imaging \cite[]{Gibb:04}. Haze aspects of our simulations are already published \cite[]{Rann:02,Rann:04}. Although strongly coupled to dynamics, the distribution of haze and clouds are much more sensitive to the way the microphysics is handled than chemical composition. Thus constraints on the dynamics are less direct than for chemical compounds. The Cassini orbiter has been placed in Saturn's orbit on the 1st of July 2004. During four years it will make several Titan fly-bys, which will be used to modify the orbits around Saturn. It will monitor at least a part of the seasonal cycle. Information on the dynamics of the mid-stratosphere will be provided essentially by observations of thermal contrasts by the composite infrared spectrometer (CIRS), but recent observations by the Imaging Science Subsystem (ISS) indicate that cloud tracking may become a possibility. The Doppler Wind Experiment (DWE) onboard the Huygens probe will measure the speed and direction of the winds to better than 1~ms$^{-1}$ accuracy during the descent \cite[]{Bird:02}, but only below 160 km and in a very limited time span. Both the Descent Imager/Spectral Radiometer (DISR) and the Huygens Atmospheric Structure Instrument (HASI) data sets will also allow to corroborate DWE measurements \cite[]{Alli:04,Fulc:02}. Here we propose some predictions of what we expect Cassini-Huygens to observe in Titan's mid stratosphere. Of course the model could predict a number of things. In Fig.~\ref{fg:cassini}, we show predictions concerning quantities which were observed by Voyager but at a different season. We first show the seasonal evolution of polar enrichment for HCN and C$_2$H$_2$, for altitudes corresponding to the maximum of the weighting function of Voyager infrared retrievals (107 and 152~km respectively). The two-peak maximum described above is clearly visible for the polar enrichment of HCN (panel {\bf a}). For C$_2$H$_2$, the second maximum is not visible not because of their different condensation heights, but rather because of the higher altitude probed. Note also that the enrichment for HCN increases with a phase lag of 1-3 terrestrial years with respect to C$_2$H$_2$, at the beginning of fall. This phase lag is directly related to the difference in altitude of the two weighting functions (50~km lower for HCN). The corresponding downward velocity in the polar vortex is of the order of 0.5-1.5~mm~s$^{-1}$, which is consistent with the values given in Fig.~\ref{fg:season}. Here, the vertical wind can be deduced almost directly from the observation of the atmospheric composition. In the second panel, we show the time evolution of the stratospheric jet speed (40-70N) and equatorial zonal wind velocity at 250~km. It is not clear whether Cassini will succeed in measuring directly the winds by tracking clouds or other structures, since, except for recent ground-based detections of clouds at the south pole, Titan's disk seems featureless. However, the 250~km-altitude range is interesting because it can be probed by stellar occultations (including the 2003 occultation, B. Sicardy, priv. comm.) and by heterodyne infrared spectroscopy \cite[]{kostiuk2001}. The time evolution of the stratospheric jet presents similarities with that of HCN, with a two-maxima structure and a long winter season with an intense circumpolar jet, contrasting with a shorter season where the wind speed is less than the equatorial velocity. The time evolution of the latitudinal temperature contrast at 1~hPa or 190~km, which will be easily monitored by Cassini, is still more complex. The polar latitudes are generally colder than the equator except during a short season around the summer solstice. The curves shown in Fig.~\ref{fg:cassini} are relative to the northern hemisphere but the situation is, to first order, symmetric for the southern hemisphere (not exactly because of the eccentricity of Titan's orbit around the Sun) so that the situation at the time of arrival is given by year 2005 for the northern hemisphere and 2020 for the southern hemisphere. According to those figures, Cassini should arrive at the time at which the zonal winds are weakest in the southern hemisphere, with southern high latitudes warmer than the equator. As shown in panel {\bf f}\ of Fig.~\ref{fg:season}, it should be a period of intense wave activity. From Fig.~\ref{fg:scaleh}, it is seen that the time constants of latitudinal mixing and vertical advection are of the order of tens of Titan days in the mid stratosphere. According to the simulations of latitudinal mixing by planetary waves presented by \cite{Luz:03I}, longitudinal contrasts less than 10\% of the latitudinal contrasts are expected, which could be monitored as well by Cassini's CIRS. Many other quantities will be observed by remote sounding by Cassini and {\em in situ} measurements by the Huygens descent module. A database based on a reference simulation performed with the coupled model is now distributed to the scientific community \footnote{http://www.lmd.jussieu.fr/titanDbase}, so that it will be possible to check a posteriori if the observations confirm or not other components of the simulations. \section{Concluding Remarks} The results presented above have been obtained with a state-of-the-art comprehensive climate model of Titan, including coupling with both chemistry and haze microphysics. This model, however, presents a number of approximations and limitations which must be kept in mind when discussing the results. First, the model is reduced to an axi-symmetric version. Latitudinal mixing by waves is handled through a parametrization which obviously only partially and imperfectly reproduces the physics of these waves. In particular, there was no attempt to predict mixing by baroclinic waves which may become significant at high latitudes. Also, because of the 2-dimensional nature of the model as well as of the lack of information on surface conditions, longitudinal forcing, as could occur from the presence of mountains, is not included. Subgrid scale gravity waves, which could be parametrized as in many terrestrial or Martian GCMs, are not accounted for either, once again essentially because of the lack of information on the possible sources. The dynamical core of the model is based on the primitive equations of meteorology, which assume the thin layer approximation, whose validity becomes doubtful at altitudes as high as 400~km on Titan. The thin layer approximation could in particular affect the magnitude of superrotation since the altitude with respect to the surface is not taken into account when computing the distance to the polar axis which enters in the definition of angular momentum. Because of this approximation, an overestimation by 10\% of the zonal wind can be expected at the peak altitude for superrotation, near 300~km. At the model upper boundary also, the hypothesis of Local Thermodynamic Equilibrium is probably violated \cite[above a few tens of Pa, ][]{Yell:91a}. As for the composition, the mean stratospheric concentrations strongly depend on the top boundary conditions and on the chemistry occurring above, for which we rely on the results of a 1-dimensional photochemical model (with no latitudinal nor seasonal variations). The haze production rate is not coupled to the chemistry, although some attempts are under way to include a parametrization of polymerization. Condensation/sublimation of methane, which has been shown to significantly affect the tropospheric circulation \cite[]{Toka:01} is not accounted for. Nor is the possible effect of gravity tides from Saturn \cite[]{Toka:02}. Finally, we had to make an assumption on the thermal inertia of the surface. This thermal inertia was fixed to a low value, typical of continental surfaces on Earth. However, tests done with a much larger thermal inertia, typical of an ocean of water, do not change the results, except slightly in the lower troposphere (results not shown). Despite all those limitations, the coupled model provides a comprehensive and consistent view of the main observations made by Voyager, and since then by ground based observations, concerning the composition and dynamics of the stratosphere. In particular, the polar enrichment in chemical compounds in the mid stratosphere caused by downward advection of air coming from the source region \cite[]{Lebo:01} is remarkably well reproduced with the nominal version of the model. For most species, this polar enrichment has little to do with chemistry. It is due to the contrast between rich air in the polar vortex and uprising clear air having undergone condensation when approaching the tropopause. The amplitude of the polar enrichment is controlled by the competition between vertical advection and latitudinal transport by either the mean meridional wind or parametrized eddies. The modulation of the observed polar enrichment for the various species comes from the different altitudes at which they are removed by condensation and from the altitude of the peak of the observational contribution function. The vertical gradient of atmospheric composition in the polar vortex is also controlled by the balance between vertical advection and latitudinal mixing with the clear air of equatorial latitudes. Since latitudinal and vertical contrasts are primarily dependent on atmospheric dynamics, it also means that observations of the composition provide a strong constraint on the stratospheric circulation. In particular, the good agreement with available observations for the nominal version provides an indirect but strong validation for the atmospheric regime obtained in the general circulation model (for the mean meridional circulation as well as for the parametrization of latitudinal mixing by waves) and in turn for the explanation put forward for explaining Titan's atmospheric superrotation in previous studies \cite[]{Hour:95b,Luz:03II}. Note that there is some analogy with the description of humidity contrasts in the Earth's troposphere. For humidity, the source is at the surface and the value at saturation decreases with increasing altitudes up to the tropopause. In the absence of mixing, the specific humidity of a given air parcel corresponds to the smallest humidity at saturation encountered along the parcel trajectory (more or less corresponding to the highest point). There also, water vapor can be used to monitor atmospheric transport and assess transport models \cite[e.~g.][]{Pier:98}. It is not clear yet whether Cassini will be able to monitor cloud motions. It is clear however that the time evolution of stratospheric temperature and composition will provide a strong constraint on the atmospheric dynamics and on the validity of the coupled model which we will continue to develop. An extended mission beyond the nominal 4 years will probably add a lot to our understanding of the complex machinery of Titan's stratosphere. For instance, the transition period after equinox will bring substantial information on vertical advection in the polar vortex.