Latitudinal and seasonal models of stratospheric photochemistry on Saturn: Comparison with infrared data from IRTF/TEXES

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1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 110,, doi: /2005je002450, 2005 Correction published 10 June 2006 Latitudinal and seasonal models of stratospheric photochemistry on Saturn: Comparison with infrared data from IRTF/TEXES J. I. Moses and T. K. Greathouse Lunar and Planetary Institute, Houston, Texas, USA Received 14 April 2005; revised 22 June 2005; accepted 27 June 2005; published 20 September [1] The variation of hydrocarbon abundances with altitude, latitude, and season in Saturn s stratosphere is investigated using a one-dimensional, time-variable, photochemical model. The results indicate that hydrocarbon abundances at pressures less than 0.01 mbar are extremely sensitive to solar flux variations due to changes in season, latitude, orbital radius, solar cycle, and ring shadowing. Long vertical diffusion times in the mbar region introduce phase lags in the response to insolation changes. At pressures greater than 1 mbar, vertical diffusion timescales are longer than a Saturnian year. Therefore, relatively long-lived hydrocarbons like C 2 H 2,C 2 H 6, and C 3 H 8 exhibit little seasonal variation in the lower stratosphere, and the yearly averaged solar insolation combined with vertical diffusion control species abundances in this region. Species with short photochemical lifetimes (e.g., CH 3,C 2 H 4 ) continue to experience seasonal variations, even at low altitudes. The model results are compared with infrared observations from the TEXES spectrometer at NASA s Infrared Telescope Facility. We find that the observed C 2 H 2 mixing-ratio variation with latitude is reasonably well predicted, whereas the C 2 H 6 distribution is poorly predicted by the models. Meridional transport is likely affecting the distribution of C 2 H 6, which has a long photochemical lifetime, whereas the distribution of shorter-lived C 2 H 2 is controlled by photochemistry and vertical diffusion. Given the different observed behavior of C 2 H 2 and C 2 H 6,we constrain meridional transport timescales at 2 mbar on Saturn to be in the range years, corresponding to meridional wind or diffusion speeds of cm s 1. Citation: Moses, J. I., and T. K. Greathouse (2005), Latitudinal and seasonal models of stratospheric photochemistry on Saturn: Comparison with infrared data from IRTF/TEXES, J. Geophys. Res., 110,, doi: /2005je Introduction [2] Saturn, with its eccentric orbit and 26.7 obliquity, experiences seasons in much the same way as the Earth. Moreover, Saturn s ring system casts shadows on the planet and attenuates incident solar radiation for portions of the year. Both the ring attenuation and seasonal dependence of ultraviolet radiation affect the chemical production and loss rates of atmospheric constituents in the upper atmosphere. These effects have been considered in ionospheric chemistry models [e.g., Moore et al., 2004; Waite, 1981] and in seasonal models of atmospheric temperatures on Saturn [e.g., Barnet et al., 1992; Bézard and Gautier, 1985; Bézard et al., 1984; Carlson et al., 1980; Cess and Caldwell, 1979], but not in models of neutral atmospheric photochemistry. Previous studies of stratospheric hydrocarbon photochemistry on Saturn have been limited to one (vertical) dimension for a fixed season and a restricted number of investigated Copyright 2005 by the American Geophysical Union /05/2005JE latitudes [e.g., Moses et al., 2005, 2000a, 2000b; Atreya and Romani, 1985; Atreya et al., 1984; Strobel, 1983, 1975]. Such modeling has been appropriate and useful to date because observations of hydrocarbon constituents generally have been averaged over large geographical areas on Saturn or were limited to a few specific latitude/longitude locations. However, with the Cassini Composite Infrared Spectrometer (CIRS) poised to map hydrocarbon distributions across Saturn [Flasar et al., 2004, 2005] and with ground-based infrared observations now providing information about latitude distributions of temperatures and hydrocarbon abundances [e.g., Greathouse et al., 2005a; Livengood et al., 2004; Kostiuk et al., 2003], more complex and realistic photochemical models are needed. [3] We have developed a one-dimensional, seasonal model for stratospheric photochemistry on Saturn that couples hydrocarbon and oxygen photochemistry, vertical diffusion, condensation, and radiative transport (including multiple Rayleigh scattering). The model accounts for variations in ultraviolet flux due to orbital position, solar cycle variations, latitude and season, and ring-shadowing 1of16

2 effects. The results for two Saturnian years, starting at solar longitude L s =0 (northern vernal equinox) in September 1950 and running until the upcoming vernal equinox in August 2009 are presented for numerous latitudes. The predicted latitude variations of C 2 H 2 and C 2 H 6 from the model are compared with the observations of Greathouse et al. [2005a] acquired from the Infrared Telescope Facility (IRTF) with the TEXES spectrometer [Lacy et al., 2002] in October 2002 (at which time L s 268 for Saturn). The purpose of the model-data comparisons is to determine whether realistic, one-dimensional photochemical models can provide reliable predictions of constituent distributions or whether 2-D models that include meridional transport will be needed to explain the observations. 2. Model Inputs [4] We use the Caltech/JPL KINETICS code [Allen et al., 1981] to solve the coupled one-dimensional continuity equations for hydrocarbon and oxygen species in Saturn s stratosphere. Transport effects are assumed to occur solely by vertical eddy and molecular diffusion, and we adopt diurnally averaged chemical production and loss rates. Our reaction list, photolysis cross sections, boundary conditions, temperature profile, and eddy diffusion coefficient profile are identical to the Saturn Model C of Moses et al. [2005]. However, rather than allowing the model to reach steady state for a fixed latitude and season, as was the case with the Moses et al. model, we now track the time variation of the solar flux (including ring shadowing, seasonal variation, and solar cycle variations) to derive the resulting time-variable photochemistry. [5] Owing to a lack of observational constraints, we assume that the vertical profiles of temperature and eddy diffusion coefficient are constant with latitude. Little information is available regarding eddy diffusion coefficient variations across Saturn. Lower-stratospheric temperatures are observed to vary with latitude by ^15 K between the equator and pole at certain seasons [e.g., Greathouse et al., 2005a, 2005b; Flasar et al., 2005; Ollivier et al., 2000; Gezari et al., 1989; Conrath and Pirraglia, 1983; Orton and Ingersoll, 1980; Tokunaga et al., 1978; Gillett and Orton, 1975; Rieke, 1975]; the theoretical models of Bézard and Gautier [1985], Carlson et al. [1980], and Cess and Caldwell [1979] predict an even greater possible variation. However, models and observations do not agree in detail [Greathouse et al., 2005a, 2005b; Flasar et al., 2005], and the observations are sparse in time and have limited horizontal and vertical coverage. Lower-stratospheric temperature variations of ^15 K slightly affect the photochemical model results; however, until the model-data mismatch regarding the latitude variation is better understood and/or until thermal -structure observations span a wide range of time and space, the assumption of constant temperature profiles with latitude is reasonable. In section 3.3, we explore the sensitivity of the model results to assumptions about stratospheric temperatures. [6] We solve the hydrostatic equilibrium equation to determine the background atmospheric structure, using the Moses et al. [2005] Model C mean molecular mass and temperature variation with pressure. Because of Saturn s oblate shape, the background pressure-temperature-densityaltitude grid differs for each latitude in the model. Information on the planetary shape, gravity parameters (e.g., J 2 and J 4 ), and zonal winds needed to solve the hydrostatic equilibrium equation are taken from Lindal et al. [1985], Campbell and Anderson [1989], and W. B. Hubbard (personal communication, 2004). [7] Saturn s orbital position during the time period of the calculations is taken from the Jet Propulsion Laboratory s Horizons ephemeris calculator [Giorgini et al., 1996] ( The calculations begin at L s =0 at 22 September 1950 and end two Saturnian years later, at L s =0 on 11 August 2009 (note that one year on Saturn equals 29.5 Earth years). The vertical diffusion timescales in Saturn s lower stratosphere are much longer than a Saturnian year. Time-variable effects that are initiated at high altitudes take hundreds of years to propagate through the lower stratosphere. The initial conditions could therefore affect the results if we were to allow the model to run only for the two Saturnian years under consideration. To get around this problem, we repeated the same two years over and over again until the solution converged; i.e., the results for northern spring at the end of the second year were used as the initial conditions for northern spring at the beginning of the new calculation, and so on, until there was no difference in the results between one two-year run and the next to within one part in a thousand. For the stratospheric region of interest, full convergence occurred after 28 Saturn years (825 Earth years, or s) Solar Flux [8] The Lyman alpha flux in our model is taken from the 81-day, running-average Ly a proxy from the daily historical irradiances of the SOLAR2000 model [Tobiska et al., 2000; Tobiska and Bouwer, 2004] (see Figure 1). At other wavelengths, we use the solar minimum and maximum ultraviolet spectra presented by Woods and Rottman [2002], in combination with our own 81-day running boxcar averaging of the E10.7 proxy from the SOLAR2000 historical irradiances [Tobiska et al., 2000; Tobiska and Bouwer, 2004], to predict the flux at any wavelength and any point in time during the simulation. Specifically, the 1-AU solar ultraviolet flux F(l, t) at any time t and wavelength l (other than Lyman alpha) is determined by Fðl; tþ ¼ F min ðlþþ ðþf t ½ max ðlþ F min ðlþš; ð1þ where F min (l) and F max (l) are the values of the solar minimum and maximum ultraviolet fluxes presented by Woods and Rottman [2002] and (t) is a normalized function that describes the variation of solar flux with time (see Figure 2) and is derived from the E10.7 proxy from the SOLAR2000 model. The 1-AU fluxes are then scaled to the instantaneous Sun-Saturn distance. When we performed these calculations, SOLAR2000 historical irradiance proxies were only available up to 30 August 2004; proxies for times beyond this date were estimated by simply repeating the values from the end of solar cycle Ring Shadowing [9] Brinkman and McGregor [1979] were the first to publish calculations of the effects of ring shadowing on the solar insolation at the top of the atmosphere of an oblate planet like Saturn. However, we have found errors in the 2of16

3 Figure 1. The Lyman alpha flux at 1 AU, outside the Earth s atmosphere, as derived from the 81-day average proxy from the SOLAR2000 daily historical irradiances [Tobiska et al., 2000; Tobiska and Bouwer, 2004]. The dotted curve represents an estimate of the future Lyman alpha irradiance values for the time period following 30 August 2004 and is simply a repeat of the irradiances from the end of solar cycle 19. formulation of their equation (2), we did not follow their reasoning for a couple of the later equations, and the form of the equations (in x-y-z coordinates rather than latitude and longitude) makes them somewhat difficult to use. We therefore have adopted the formulation of Bézard [1986] for our calculations. We consider only the direct absorption of solar radiation by the ring particles and ignore scattering (see Barnet et al. [1992] for a description of the latter); note that Moore et al. [2004] demonstrate that absorption by ring gas plays a negligible role in the attenuation of solar radiation at Saturn. [10] From the analysis of 1989 data of the star 28 Sgr being occulted by Saturn s rings, Nicholson et al. [2000] have confirmed that ring particle sizes are in the centimeterto-meter range and that the ring structure does not change on decade timescales. The ring optical depth therefore has little wavelength dependence in the ultraviolet, visible, and near infrared, and the ring structure derived during the Voyager encounter should hold roughly constant during our two-saturnian-year simulation. For the purposes of our calculations, we divide the rings into five separate regions, each with a constant assumed normal optical depth. The average normal optical depth hti within these regions was derived from Voyager Ultraviolet Spectrometer (UVS) data at an effective wavelength of 0.11 mm [Sandel et al., 1982; Holberg et al., 1982] and Photopolarimeter Subsystem (PPS) data at 0.26 mm [Esposito et al., 1983]. The detailed optical depth profiles were obtained from the Planetary Data System s Ring Node ( nasa.gov), and the averaging was performed such that 2Z r2 3 e t dr r hti ¼ ln Z r2 7 5 ; ð2þ dr r 1 where r is the radial distance from Saturn s center, r 1 and r 2 are the inner and outer radii of the ring regions, and t is the optical depth normal to the ring plane. Table 1 provides the ring parameters used in our calculations. We used the UVS optical depths for the photochemistry calculations described in section 3 and the PPS optical depths for the insolation calculations described below. [11] Figure 3 shows how the mean daily solar insolation is affected by ring shadowing, latitude, and season. Several interesting effects can be noted from Figure 3. First, ringshadowing effects are pronounced from 10 to 40 latitude and become progressively less important at high latitudes and toward the equator. Second, daily mean insolation values are relatively constant with latitude in the summer hemisphere near summer solstice because the increase in the length of daylight hours with increasing latitude counteracts the increasing solar zenith angle. Latitude gradients are larger at other times of the year. Third, the fact that Saturn s orbit is eccentric and that perihelion occurs near southern summer solstice causes an asymmetry in the daily mean insolation between the northern and southern hemispheres: southern summer experiences higher daily mean insolation values than northern summer. By the same token, seasonal variation in daily mean insolation values is greater in the southern hemisphere than in the northern hemisphere. Finally, seasonal variations in insolation have a large amplitude at high latitudes and are more muted at low latitudes. Figure 2. An 81-day boxcar average of the E10.7 index from the SOLAR2000 model [Tobiska et al., 2000; Tobiska and Bouwer, 2004], normalized such that the minimum E10.7 index from the whole time period is scaled to zero and the maximum E10.7 index from the last two solar cycles is scaled to unity. We do not use the whole time period for normalizing the latter because the solar maximum values from Woods and Rottman [2002] relate only to the last couple solar cycles. Minimum values are relatively constant for the different cycles, but maximum values vary greatly. The dotted curve represents an estimate of the future E10.7 index values for the time period following 30 August 2004 and is simply a repeat of the indices from the end of solar cycle 19. 3of16

4 Table 1. Ring Parameters Radial Distance From Saturn Center, km Average Normal Optical Depth hti Ring Region r 1 r 2 UVS PPS C Inner B Outer B Cassini Div A [12] When averaged over an entire year (Figure 4), the insolation asymmetry between the northern and southern hemispheres disappears due to Kepler s second law. Although the instantaneous solar flux is higher at perihelion, the planet sweeps through perihelion more quickly than at aphelion, and equal areas in equal times maintains insolation symmetry between hemispheres. Figure 4 illustrates the pronounced effects of ring shadowing at low-to-middle latitude in a yearly averaged sense. In the absence of Figure 4. Yearly average of the daily mean solar insolation (W m 2 ) as a function of planetocentric latitude for models that include (dotted line) and do not include (solid line) the effects of ring shadowing. meridional atmospheric transport, the signature of ring shadowing might appear in the record of the latitudinal variation of photochemically produced species. Figure 3. Daily mean solar insolation (W m 2 per planetary day) incident on a unit horizontal surface at the top of Saturn s atmosphere as a function of planetocentric latitude and season (where season is represented by solar longitude L s ), assuming (top) no ring shadowing or (bottom) with the inclusion of ring shadowing. The shaded regions indicate polar night. A solar constant of W m 2 was used for these calculations; the solar constant does not vary with solar cycle. 3. Results and Discussion [13] The production and loss rates of the photochemically produced hydrocarbon species are strongly affected by changes in solar flux due to varying seasons, solar cycle, orbital position, and ring shadowing. Figure 5 shows how the acetylene (C 2 H 2 ) and ethane (C 2 H 6 ) mixing ratios vary with time during the simulation. The results are for high altitudes (3 mbar), where the response to the changing solar flux is rapid. Note from Figure 5 that seasonal variations are much more pronounced at high latitudes than at low latitudes; a close examination of Figure 3 reveals that this behavior is directly related to the solar insolation variation as a function of latitude and season. Both the ring-shadowing effects and the solar cycle effects show up clearly in the mixing-ratio variations with time; the effects of attenuation by the rings are especially prominent at lower latitudes. In the southern hemisphere, the simultaneous effects of solar cycle maximum and summer solstice near perihelion late the second year (all occurring within the time frame of January 2002 to July 2003) combine to create a maximum in the C 2 H 2 and C 2 H 6 abundances at that time. [14] Throughout the rest of this section, we focus on the converged model results from Saturn Year 2 of our simulation (from March 1980 to August 2009), unless otherwise stated. All latitudes quoted throughout this paper are planetocentric. A full discussion of the chemical production and loss mechanisms for the observable hydrocarbons can be found in the work of Moses et al. [2005, 2000a]. That discussion will not be repeated here Results From the Current Epoch: Saturn Year 2 [15] In Figure 6, the mixing-ratio profiles for the observed hydrocarbons on Saturn are plotted for four different seasons. At high altitudes (pressures less than 0.01 mbar), hydrocarbon abundances are generally greatest near summer 4of16

5 Figure 5. The variation in the mixing ratios of C 2 H 6 (thick solid line) and C 2 H 2 (thin solid line) at mbar, as a function of time (Saturn year) in our converged two-saturnian-year model run for (a) 8, (b) 22, (c) 59, and (d) 24. Other pertinent time periods are marked as labeled, such as perihelion (stars), aphelion (triangles), solar cycle maximum (ss max), season (vertical dotted lines for L s =0, 90, 180, and 270 ), and times during which the latitude experiences ring shadowing (horizontal markings labeled ring shadow ). All latitudes are planetocentric. solstice, trail off in spring and autumn, and become lowest during the winter. This behavior results from the short photochemical production and loss timescales of the hydrocarbons and short vertical diffusion timescales at high altitudes; the abundances respond relatively quickly to insolation changes, and the hydrocarbons quickly diffuse downward to 0.01 mbar. The behavior in the mbar region is more complicated because longer vertical diffusion timescales and longer photochemical lifetimes can introduce phase lags. For example, note that the C 2 H 2 and C 2 H 6 mixing ratios at 0.03 mbar are greater at autumnal equinox than they are near summer solstice, whereas the high-altitude abundances peak at summer solstice. It has taken roughly a Saturnian season for the high-altitude, summer-produced C 2 H 2 and C 2 H 6 to diffuse down into the 0.03-mbar region. At pressures greater than 1 mbar, vertical diffusion timescales are much longer than a Saturnian year. Photochemical production and loss timescales also tend to be longer at these lower altitudes, so the mixing-ratio profiles of the stable hydrocarbons tend to exhibit little seasonal variation, and the yearly average solar insolation combined with vertical diffusion control the abundances. [16] Exceptions to this behavior are species with short production and/or loss timescales (e.g., C 2 H 4,CH 3 C 2 H, and radicals like CH 3 ) that continue to exhibit seasonal variation in the lower stratosphere. For instance, the photochemical loss timescale of C 2 H 4 at 1 mbar and 36 is 2 years at L s =94, but only 20 days at L s = 273. The production rate of C 2 H 4 actually exceeds the loss rate in the lower stratosphere during the winter because the reduction in atomic H and the reduced photolysis rates with reduced insolation make C 2 H 4 destruction less effective. As a result, unlike the other hydrocarbons, the abundance of C 2 H 4 at 1 mbar is greater in winter than during other seasons. [17] To better illustrate these effects, Figure 7 shows some timescales of interest as a function of pressure. The 5of16

6 Figure 6. The model-derived mixing-ratio profiles of the observed constituents (a) CH 4, (b) CH 3, (c) C 2 H 2,(d)C 2 H 4,(e)C 2 H 6, (f) CH 3 C 2 H, (g) C 3 H 8,(h)C 4 H 2, (i) C 6 H 6, and ( j) H as a function of season for 36 planetocentric latitude in the second year of our model run. The dotted lines represent L s = 94.2 ( just past southern winter solstice), the dashed lines represent L s = ( just before southern vernal equinox), the dot-dashed lines represent L s = (just past southern summer solstice), and the solid lines represent L s = 360 (southern autumnal equinox). The data points with associated error bars represent various observations, as labeled. Note that many of the data points are from globally averaged observations; only the Greathouse et al. [2005a] data, open squares in (c) and (e), pertain to 36 and L s 268. diffusion timescale for ethane is defined as H 2 /D, where the generalized diffusion coefficient D equals the molecular diffusion coefficient D e plus the eddy diffusion coefficient K, and the generalized scale height H is given by H ¼ D e H e þ De ð 1þae Þ T D dt dz þ K H a þ K T ; ð3þ dt dz where H e is the ethane scale height, a e is the thermal diffusion factor for ethane, T is the atmospheric temperature at altitude z, and H a is the average atmospheric pressure scale height. The diffusion timescale for acetylene is similar to that for ethane; for the sake of clarity, it has been omitted from the figure. Also plotted are photochemical time constants n/(dn/dt), where n is the species concentration (cm 3 ) and dn/dt is the rate of change of the concentration 6of16

7 Figure 6. (continued) (cm 3 s 1 ) due purely to chemical processes. The photochemical loss timescale, defined as n divided by the loss rate L (cm 3 s 1 ), and the photochemical production timescale, defined as n divided by the production rate Q (cm 3 s 1 ), are plotted separately to give an indication of whether production or loss processes are dominating the rate of change of species concentrations. Although many researchers quote only the photochemical loss time scale when discussing species stability, it is the net photochemical time constant, defined as n divided by dn/dt = jq Lj that provides the most appropriate measure of the time constant for chemical change. For instance, a high loss rate L may suggest a short photochemical lifetime; however, if Q L, the species will survive much longer than the loss timescale would indicate. Therefore it is the net photochemical time constants (solid lines in Figure 7) that provide the appropriate indicators for species stability. The photochemical lifetimes are dependent on latitude and season; we provide results only for 36 at L s = [18] One thing that should be noted from Figure 7 is that although C 2 H 6 is short lived near its peak production region near mbar, its lifetime increases dramatically a couple scale heights below this region because methane, which is more abundant than ethane, helps shield the ethane from photolysis. The photochemical lifetime for C 2 H 6 is greater than a Saturnian year throughout the middle and lower stratosphere for all seasons. Note, however, that the vertical diffusion timescale is much less than the photochemical lifetime of C 2 H 6 throughout the stratosphere, so vertical transport plays a major role in controlling the ethane mixing-ratio profile. Ethane that is produced in its peak Figure 7. The photochemical time constants for C 2 H 2 (thin lines) and C 2 H 6 (thick lines) for 36 at L s = The dashed lines are the photochemical loss timescales, the dotted lines are the photochemical production timescales, and the solid lines are the net photochemical time constants defined as the concentration (cm 3 ) divided by jq Lj, where Q and L are the production and loss rates (cm 3 s 1 ). The vertical dot-dashed line marks Saturn s orbital period of 29.5 years and is included for reference. The points marked by stars represent estimates of the timescale for meridional transport, assuming the effective meridional eddy diffusion coefficients K yy on Saturn are similar to those derived for the 0.3- and 30-mbar regions on Jupiter. The triple-dot-dashed line represents the vertical diffusion timescale. 7of16

8 Figure 8. The column abundance of C 2 H 2 above different pressure levels as a function of planetocentric latitude and season: (a) above mbar, (b) above 0.01 mbar, (c) above 0.1 mbar, and (d) above 1 mbar. The contour interval and overall scale changes for each figure (note the scale bars at the bottom). production region is transported rapidly to lower altitudes. Because the photochemical lifetimes are short in the peak production region, seasonal variations are large, and the short diffusion timescale allows these changes to propagate to lower altitudes than one might expect based solely on an examination of chemical lifetimes. The importance of vertical diffusion is apparent in Figure 6, in which obvious phase lags in the seasonal response for ethane appear at a few hundredths to a few tenths of a mbar, just where the diffusion timescale approaches a Saturnian season; similarly, no seasonal response is apparent at pressures greater than 0.8 mbar, where the diffusion timescale exceeds a Saturnian year. [19] The seasonal behavior of acetylene is similar to that of ethane. In contrast to ethane, acetylene has an appreciable photolysis cross section at longer ultraviolet wavelengths than either ethane or methane, and C 2 H 2 is not well shielded by other atmospheric constituents. Its photochemical loss time scale in the middle and lower stratosphere (e.g., 4 years at L s = 273 and 130 years at L s =94 at 1 mbar for 36 ) is therefore much shorter than that of ethane. However, acetylene is efficiently recycled in the middle and lower stratosphere once it is destroyed photochemically. As is discussed by Moses et al. [2000a], the effective chemical lifetime for C 2 H 2 is longer than is indicated by the loss timescale, and the net photochemical time constant (thin solid line in Figure 7) is a more realistic measure of the time it would take acetylene to respond to changes in solar insolation. The net photochemical time constant for C 2 H 2 in Saturn s middle and lower stratosphere is longer than the vertical diffusion timescale. Therefore, as with C 2 H 6, vertical diffusion plays a major role in controlling the C 2 H 2 mixing-ratio profile and its seasonal variation. [20] Figure 8 further illustrates the effects of time lags. In this figure, the column density of C 2 H 2 above pressure level P is plotted as a function of latitude and season at four different pressure levels. For the highest altitude plotted, P = mbar, the column density is clearly very sensitive to the solar flux variation with time. Winter polar night shows up prominently, and the effects from ring shadowing (recall Figure 3) can be seen. The coincidence of solar maximum, 8of16

9 assume they are representative of all latitudes; during their analyses, the whole profile is often allowed to change by a multiplicative factor while the overall slope remains the same. This practice could clearly cause problems with the inferred hydrocarbon abundances at specific pressure levels if the adopted slope is quite different from the actual slope. Figure 9. The column abundance of C 2 H 4 above 1 mbar as a function of planetocentric latitude and season. Note the difference between this figure and Figure 8d. perihelion, and summer solstice in the southern hemisphere near L s = 270 causes the column densities to reach maximum values in the southern hemisphere near that time (note that solar maximum occurs before solstice, which is why the column density peak precedes solstice). The solar cycle clearly plays an important role in the chemistry, as prominent column density maxima appear at solar maximum, even when solar maximum is not ideally aligned with seasons. For example, note that the column density maximum in the northern hemisphere significantly postdates the 90 summer solstice there and aligns instead with solar maximum. At P = 0.01 mbar, phase lags are readily apparent in the location of the column density maxima, and seasonal differences are beginning to be muted. An asymmetry between northern and southern hemispheres still exists, but this asymmetry is being washed out by P = 0.1 mbar and has almost completely disappeared by P = 1 mbar. Because of the long vertical diffusion timescales, the latitude variation of the C 2 H 2 column density above 1 mbar mimics the yearly average solar insolation rather than daily average for the current season, and seasonal effects are no longer important. Ethane and some of the other relatively long-lived species exhibit a similar behavior. Ethylene (C 2 H 4 ) and some less photochemically stable species exhibit seasonal variation even at low altitudes. As can be seen from Figure 9, the influence of the sun and its variation with seasons still plays a major role in controlling C 2 H 4 abundances at pressures as high as 1 mbar. [21] Figure 10 shows how the hydrocarbon mixing-ratio profiles change with latitude for a specific season, L s = 273, near southern summer solstice and northern winter solstice. The northern hemisphere profile is obviously different from those from the southern hemisphere. More importantly, the shapes of the mixing ratio profiles within the southern hemisphere change with latitude in interesting and unusual ways. This result needs to be emphasized because observers often take theoretical profiles from a photochemical model relevant to a single latitude and 3.2. Comparison With Observations [22] The latitudinal variation of the C 2 H 2 and C 2 H 6 mixing ratios at southern summer solstice are plotted in Figure 11 for a few different pressure levels. As with many of our previous figures, Figure 11 demonstrates that the high-altitude atmosphere responds relatively quickly to insolation changes, and the hydrocarbon abundances at mbar have a latitude variation that mimics that of the mean daily solar insolation at 273 (recall Figure 3). The variation with latitude at lower altitudes is more complicated because long vertical diffusion timescales can introduce phase lags. At altitudes below 1 mbar, the vertical diffusion timescale is much greater than a Saturnian year, and the predicted latitudinal variation for both C 2 H 2 and C 2 H 6 resembles that of the yearly average mean daily insolation (recall Figure 4) rather than that of the insolation for the current season. [23] In Figure 11, our predictions regarding the latitudinal variation of C 2 H 2 and C 2 H 6 at southern summer solstice are also compared with results from high-resolution, groundbased, thermal-infrared observations acquired with the TEXES grating spectrograph at the IRTF [Greathouse et al., 2005a]. The model predicts that the acetylene mixing ratio should decrease from the equator to the south pole by a factor of 1.9 at 1.2 mbar and by a factor of 2.6 at 0.12 mbar. The data indicate an equator-to-south-pole drop of a factor of 3.7 at 1.2 mbar and a factor of 3.8 at 0.12 mbar. Although the altitude distribution of C 2 H 2 in the model is somewhat different from that of the data (i.e., the model tends to underpredict the C 2 H 2 mixing ratio at 0.12 mbar) and fine structure apparent in the data does not have a correspondence in the model, the overall trend of the observed latitudinal distribution is similar to that of the model: both show that the C 2 H 2 mixing ratio falls off with increasing latitude from the equator to the south pole, and the latitudinal gradient of the model is consistent with that of the data in the 20 to 80 region. The C 2 H 6 mixing ratios at 2.3 mbar, on the other hand, are observed to remain roughly constant or even increase from the equator to the south pole, whereas the model predicts a decrease of a factor of 3.5 from the equator to 81. An examination of the timescales in Figure 7 may reveal a possible reason. [24] The net photochemical time constant of ethane is very long in the region probed by the observations (e.g., 2-mbar timescale of 700 years at 36 and L s = 273 ). In addition, the long vertical diffusion timescales in Saturn s stratosphere prevent the dramatic seasonal changes from propagating into the lower stratosphere. Therefore, although the C 2 H 6 mixing ratio at high altitudes is expected to be roughly constant with latitude in the summer hemisphere, the mixing ratio at 2.3 mbar should more closely follow the average yearly solar insolation latitudinal profile, which would suggest a decrease from the equator to the pole. 9of16

10 Figure 10. The model-derived mixing-ratio profiles of the observed constituents (a) CH 4, (b) CH 3,(c) C 2 H 2,(d)C 2 H 4,(e)C 2 H 6, (f) CH 3 C 2 H, (g) C 3 H 8,(h)C 4 H 2, (i) C 6 H 6, and (j) H as a function of latitude for L s = 273 (southern summer, northern winter, January 2003). The dashed lines represent 8, the solid lines represent 36, the dot-dashed lines represent 69, the dotted lines represent 32 latitude, and the triple-dot-dashed lines represent 80 latitude. The model-data differences here suggest that atmospheric motions with meridional transport timescales less than that of the ethane photochemical lifetime are operating on Saturn to transport C 2 H 6 across latitudes. Shorter-lived acetylene is apparently not as affected by atmospheric transport; its mixing ratio decreases with increasing southern latitude as expected due to solar forcing and vertical diffusion. The similarity in the seasonal behavior of C 2 H 2 and C 2 H 6 in the model at lower stratospheric pressures (see Figure 6 and resulting discussion) indicates that the effective acetylene photochemical lifetime is greater than its loss timescale would indicate because of efficient recycling. The net photochemical time constant (100 years at 2 mbar for L s = at 36 ) provides a good measure of this effective lifetime. Together, these pieces of evidence suggest that the meridional transport timescale t v at 2 mbar on Saturn is between the 100-year net photochemical lifetime for C 2 H 2 and the 700-year net photochemical lifetime for C 2 H 6, at least during southern summer solstice. The time constants vary with time and with latitude. If we take 90,000 km (roughly the equator-to-pole distance) as an effective length scale L, large-scale meridional winds (L/t v ) would then be constrained to be in the 0.4 to 2 cm s 1 range at 2 mbar. 10 of 16

11 Figure 10. (continued) [25] The latitudinal distribution of C 2 H 2 and C 2 H 6 on Jupiter was observed by Cassini CIRS [Kunde et al., 2004; C. A. Nixon et al., Meridional variations of C 2 H 2 and C 2 H 6 in Jupiter s atmosphere from Cassini CIRS infrared spectra, submitted to Icarus, 2005 (hereinafter referred to as Nixon et al., submitted manuscript, 2005)] to be quantitatively simililar to that of Saturn. Acetylene on Jupiter during the Cassini flyby in December 2000 was observed to decrease from the equator to either pole; ethane, in contrast, remained roughly constant in the northern hemisphere and increased from the equator to the pole in the southern hemisphere. As with our Saturn model-data comparisons above, Kunde et al. [2004] and Nixon et al. (submitted manuscript, 2005) concluded that the observed behavior on Jupiter is caused by meridional transport with a timescale between that of the photochemical lifetimes of C 2 H 2 and C 2 H 6. Note, however, that Kunde et al. and Nixon et al. quote the strict photochemical loss timescale for C 2 H 2 in their arguments, whereas the net photochemical time constant described above would be a more appropriate measure for the effective photochemical lifetime on Jupiter, as well as on Saturn. [26] No observations are currently available that could help us determine meridional transport timescales or wind/ diffusion velocities at relevant stratospheric altitudes on Saturn. The spreading of the Shoemaker-Levy 9 debris after the 1994 impact of the comet with Jupiter [e.g., Sanchez-Lavega et al., 1998; Friedson et al., 1999; Lellouch et al., 2002; Moreno et al., 2003; Griffith et al., 2004; Kunde et al., 2004] has been used to constrain meridional transport in the Jovian stratosphere. From these references, we take K yy cm 2 s 1 at 0.3 mbar and K yy cm 2 s 1 at 30 mbar as effective meridional diffusion coefficients for Jupiter. If K yy s on Saturn are similar, and if large-scale quasi-geostrophic eddies dominate meridional transport, then effective largescale meridional transport timescales on Saturn would be 10 years at 0.3 mbar and 100 years at 30 mbar. These values suggest that our estimated meridional transport timescale of years at 2 mbar on Saturn is not unreasonable, although meridional transport may be slower on Saturn than Jupiter Sensitivity to Stratospheric Temperatures [27] As was discussed in section 2, we have assumed that the stratospheric thermal structure does not vary with latitude or time, whereas observations and theory suggest that temperatures can vary by more than 15 K from equator to pole and as a function of season. In this section, we examine the consequences of different assumptions regarding the temperature structure. Our adopted stratospheric temperature profile (see Figure 12) derives largely from global-average observations taken in from the ISO satellite [Lellouch et al., 2001]. More recent observations [Greathouse et al., 2005a, 2005b; Flasar et al., 2005; Orton and Yanamandra-Fisher, 2005] indicate much warmer temperatures in the southern hemisphere near summer solstice. To examine the effect of warmer temperatures on the hydrocarbon photochemistry, we repeat the previously described calculations for specific latitudes using temperature profiles consistent with the observations of Greathouse et al. [2005a]. We select a relatively warm 11 of 16

12 C 2 H 4. However, as is clear from comparing Figures 6 and 13, the mixing ratios are less sensitive to temperature changes than they are to changing solar insolation. Our assumption of a constant thermal structure with time and latitude will introduce mole-fraction errors of a few percent but will not affect our overall conclusions. For example, with our constant (cold) profiles from our nominal model, the ratio of the 1-mbar C 2 H 2 mole fraction at 29 versus that at 81 is at L s = 273. The equivalent comparison for the more realistic warmer profiles is 1.454, a difference of less than 1%. Therefore the observed difference in the temperature structure at 29 versus 81 (see Figure 12) does not have much effect on the predicted latitudinal variation of C 2 H 2 abundances. The same is true for C 2 H 6. [29] Note that the warmer temperatures not only affect the chemistry but also the atmospheric structure and homopause level. The methane homopause is located at lower altitudes as stratospheric temperatures increase, which reduces hydrocarbon abundances in the uppermost portions of the stratosphere. On the other hand, the entire stratosphere expands when temperatures increase. Thus, even if the mole-fraction profiles remain constant with pressure as the temperatures increase, the hydrocarbon column densities (which are found by integrating the mole fractions over altitude) increase owing to the expanded altitude scale. In our case, this effect turns out to be more important than the altered chemistry. The 1-mbar column density of C 2 H 2 is 18% higher in our warm -atmosphere simulation than in our nominal model at 81 (for L s = 273 ), and 8% higher at 29. Figure 11. The latitudinal variation of the mixing ratios of (top) C 2 H 6 and (bottom) C 2 H 2 at L s = 273 (near southern summer solstice) at different pressure levels, as labeled. The model-derived latitudinal profiles (solid lines) are compared with mixing ratios inferred from the ground-based infrared observations of Greathouse et al. [2005a] (open diamonds): top, C 2 H 6 mixing ratios at 2.3 mbar (red); bottom, C 2 H 2 mixing ratios at 0.12 mbar (red) and 1.2 mbar (black). The observations were acquired at L s 268. profile from Greathouse et al. [2005a], characteristic of 81 at L s 268, and a more moderate profile, characteristic of 29 at L s 268, for these calculations (see Figure 12); both profiles are warmer than our previously adopted profile throughout the stratosphere. As with the old calculations, these new temperature profiles do not vary with time in the calculations: the stratosphere is assumed to be as warm in winter as it is in summer. The object here is simply to determine the sensitivity of the results to temperature. [28] The results from the new calculations for the C 2 H 2 and C 2 H 6 mole fractions at summer solstice in the second year of the calculations are shown Figure 13. The increased temperatures have a slight effect on both the magnitude and slope of the mole fractions. Temperature-sensitive reaction rates can affect the production and loss rates and overall recycling efficiencies of the hydrocarbons. Some key reactions that drive the changes include CH + CH 4,CH 3 +CH 3, C 2 H+H 2,C 2 H+CH 4,C 2 H+C 2 H 6,H+C 2 H 3, and H + 4. Summary and Conclusions [30] Using a realistic, one-dimensional, time-variable model of stratospheric photochemistry, we track the varia- Figure 12. The temperature profiles adopted in our nominal model (solid line) and in our sensitivity tests for 29 (dashed line) and 81 (dotted line). The latter two profiles are from the TEXES/IRTF observations of Greathouse et al. [2005a], except the temperatures above 10 4 mbar have been estimated. Our nominal profile is derived from the golbal-average ISO observations of Lellouch et al. [2001]. 12 of 16

13 Figure 13. The (top) C 2 H 2 and (bottom) C 2 H 6 mixing ratios at L s = 273 from our nominal model (solid lines) versus models with warmer temperature profiles (dotted lines) at 29 (thick lines) and 81 (thin lines). The temperature profiles corresponding to these models are shown in Figure 12. By comparing these results with those from Figure 6, one can see that the hydrocarbon mixing ratios are less sensitive to stratospheric temperature than they are to solar flux. tion in hydrocarbon abundances with latitude and season on Saturn. Winds and horizontal eddy diffusion are not considered in the model, and both the eddy diffusion coefficient profile and temperature profile are assumed to be latitude invariant. Latitude variations in the model are therefore solely caused by changes in solar insolation. Our model results are compared with spatially resolved, highspectral-resolution, thermal-infrared observations from IRTF/TEXES [Greathouse et al., 2005a]. We find that the model does a reasonable job of reproducing the acetylene mixing-ratio variation with latitude; however, the observed ethane meridional variation is quite different from the model. Ethane has a photochemical lifetime greater than the estimated meridional transport times scales in Saturn s stratosphere and is therefore very sensitive to transport effects. C 2 H 6 should act as a good tracer for atmospheric motions. One-dimensional photochemical models, even ones that accurately track the variation in ultraviolet flux due to seasons, orbital position, solar cycle, and ring shadowing, will not provide reliable predictions of the latitudinal variations of long-lived species. Two- or three-dimensional models will be needed to explain the observed latitudinal/seasonal behavior. However, realistic 1-D models like the one presented here can be used to reliably predict and explain the latitudinal/seasonal behavior of moderate- or short-lived hydrocarbons like CH 3,C 2 H 2, C 2 H 4, CH 3 C 2 H, and C 4 H 2. Photochemistry and vertical diffusion dominate over meridional transport for these species. [31] Our model-data comparisons can help us place constraints on meridional transport in Saturn s stratosphere. The different observed latitudinal behavior of C 2 H 2 and C 2 H 6 suggest that the meridional transport timescale at southern summer solstice lies somewhere between the photochemical lifetimes of C 2 H 2 and C 2 H 6. Kunde et al. [2004] and Nixon et al. (submitted manuscript, 2005) reached a similar conclusion for Jupiter from an examination of the Cassini CIRS observations of the latitude distribution of C 2 H 2 and C 2 H 6 acquired during the Cassini Jupiter flyby in December Nixon et al. and Kunde et al. found that the C 2 H 2 column abundance decreased by a factor of 4 from the equator to either pole, whereas C 2 H 6 remained constant with latitude in the northern hemisphere and increased with latitude in the southern hemisphere. On Saturn, the C 2 H 6 loss timescale at 2 mbar, the level at which the observations are most sensitive, is 700 years at L s = 273 for 36. The C 2 H 2 loss timescale is 4 years at 2 mbar for the same conditions; however, the effective C 2 H 2 photochemical lifetime is considerably longer due to the fact that C 2 H 2 is efficiently recycled in the stratosphere once it is destroyed. The net photochemical lifetime for C 2 H 2 at 2 mbar in our model for 36 and L s = is 100 years. Therefore the meridional transport timescale is estimated to be between years, corresponding to large-scale meridional wind/diffusion velocities in the 0.4 to 2 cm s 1 range at 2 mbar. Propane has a lifetime intermediate between that of ethane and acetylene in the lower stratosphere, and observations of the latitudinal variation of C 3 H 8 on Saturn would be interesting and might help to further constrain meridional transport timescales. [32] Hydrocarbons located at pressures less than 0.01 mbar will respond rapidly to changes in solar insolation; seasonal and latitudinal variations will be pronounced at these high altitudes, and the ring shadow (and polar night) will strongly affect species abundances. In the middle stratosphere ( mbar), the latitude and seasonal distribution of hydrocarbons will be less pronounced and will depend on the relative magnitudes of the photochemical production/loss timescales, the vertical diffusion timescale, and the meridional transport timescale. Owing to long vertical diffusion timescales in the lower stratosphere, stable hydrocarbons residing at pressures greater than 1 mbar will be unaffected by the changing seasons unless the net photochemical lifetimes are noticeably less than a Saturnian year. [33] More modeling and observations are needed to test the above claims. Cassini will map hydrocarbon distributions for the next several years, and these maps will provide good tests for our models, as well as good constraints for 13 of 16

14 future 2-D models that include atmospheric transport. If the nominal Cassini mission time frame is extended as proposed, then coverage through the southern summer and into autumn will be provided. Such seasonal information will greatly aid model-data comparisons. Ground-based infrared observations will continue to provide valuable information for seasons other than those encountered during the Cassini era and for altitudes different from those probed by the Cassini experiments. All infrared observations, whether from spacecraft or Earth-based telescopes, need nearly simultaneous observations of the temperature structure (e.g., through the n 4 methane band) in order to obtain reliable abundance information. [34] Several caveats to our models and their interpretation need to be mentioned. Our assumption of constant temperatures with latitude is certainly incorrect. More realistic models that either self-consistently calculate temperatures using radiative forcing arguments or that use observations to constrain temperatures as a function of latitude and season (if such information ever becomes available) should be attempted. In addition, the assumption of a constant eddy diffusion coefficient profile with latitude is of unknown veracity. Because ethane is very long-lived, its lower stratospheric abundance is particularly sensitive to the adopted eddy diffusion coefficient profile. It is possible that an eddy diffusion coefficient profile that varies with latitude could contribute to the observed ethane distribution with latitude; that is, horizontal transport alone may not explain the observed distribution. This suggestion deserves to be better quantified, and 2-D models that include realistic atmospheric circulation would certainly address this problem. Finally, analyses of observations that provide spatially resolved information on hydrocarbon abundances on Saturn should make allowances for the fact that the shape of the mixing-ratio profiles likely change with latitude and season. [35] By the same token, seasonal climate models such as those presented by Conrath et al. [1990] and Bézard and Gautier [1985] need to consider the fact that the important stratospheric coolants C 2 H 2 and C 2 H 6 will have mixing ratios that are not constant with latitude, altitude, or season. More realistic models that consider these mixing-ratio variations may greatly affect our understanding of radiative time constants and seasonal behavior of temperatures on Saturn. For example, Conrath et al. [1990] have inferred radiative relaxation times of 9 years at 1 mbar on Saturn, resulting in phase lags of nearly a season in the response of atmospheric temperatures to changing solar insolation. Bézard and Gautier [1985] also predict a phase lag of roughly a Saturnian season. Observations, however, show that stratospheric temperatures at the south pole are much warmer than those at the equator in and that temperatures in the 1-mbar region vary on relatively short timescales [e.g., Flasar et al., 2005; Greathouse et al., 2005a, 2005b; Orton and Yanamandra-Fisher, 2005]; the fact that the observed behavior is not consistent with the models has led to general confusion. The dominant coolants in this region of the stratosphere are C 2 H 6 and C 2 H 2 [see Yelle et al., 2001]. Conrath et al. [1990] do not state what values they have assumed for the C 2 H 6 and C 2 H 2 mixing ratios in their modeling, so it is difficult to evaluate their claim. Bézard and Gautier [1985] assume constant mixingratio profiles with altitude and adopt C 2 H 2 and C 2 H 6 mixing ratios that are even smaller than those derived by the Voyager infrared spectrometer [Courtin et al., 1984]. As can be seen from Figures 6 and 10, the actual C 2 H 2 and C 2 H 6 mixing ratios are not likely constant with altitude, and the Courtin et al. [1984] values are considerably lower than current measurements of the C 2 H 2 and C 2 H 6 mixing ratios at 1 mbar and above. Bézard and Gautier [1985] (and probably Conrath et al. [1990]) are therefore likely underestimating C 2 H 2 and C 2 H 6 cooling rates and overestimating the radiative relaxation times at P < 1 mbar by a considerable factor. Note also that the radiative relaxation time will change with latitude and season as the C 2 H 2 and C 2 H 6 profiles change. More realistic radiative modeling is needed to resolve this model-data mismatch. [36] In all, one-dimensional photochemical models are still useful for predicting the stratospheric composition of Saturn and the other giant planets. They can fail, however, for long-lived species like ethane. Given the increasing amount of spatially resolved information about the Saturnian atmosphere, the development of more sophisticated multidimensional models that include atmospheric dynamics is warranted. [37] Acknowledgments. We thank Yuk Yung and Mark Allen for writing a powerful and flexible kinetics code that can smoothly handle the seasonal variations and other time-variable phenomena investigated in this paper. We also thank Mark Allen for sending his notes on diurnal averaging so that the code could be modified for oblate planets, and we thank Mike Flasar for reminding us of the effects of Kepler s second law. Thorough and constructive reviews by Conor Nixon and an anonymous reviewer improved the manuscript. The JPL Horizons ephemeris calculator was of immense use for this project, as were the daily historical irradiances from the SOLAR2000 model, provided courtesy of W. Kent Tobiska through funding from the NASA UARS, TIMED, and SOHO projects. 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