Spatially resolved methane band photometry of Jupiter: III. Cloud vertical structures for several axisymmetric bands and the Great Red Spot

We present cloud structure models for Jupiter's Great Red Spot, Equatorial Zone, North Tropical Zone, North and South Temperate Zones, North and South Polar Regions, and North and South Polar Hoods. The models are based on images of Jupiter in three methane bands (between 6190 and 8900 Å) and nearby continuum. Radiative transfer calculations include multiple scattering and absorption from three aerosol layers, the topmost of which is a high thin haze and the lower two are called clouds. All models are computed relative to a similar model for the South Tropical Zone which fits methane absorption data and Pioneer photometry data well. Outstanding features suggested by the model results are the transition in the upper-cloud altitude to about 3 km lower altitude from the tropical zones to temperate zones and polar regions, a N/S asymmetry in cloud thickness in the tropical and temperate zones, the presence of aerosols up to about 0.3 bar in the Great Red Spot and Equatorial Zone, the need for a significant (τ ～ 0.75 to 1.0) aerosol content in this region in the Equatorial Zone, and perhaps an even higher and thicker cloud in the South Polar Hood. The haze layer above both polar hoods may exhibit different scattering properties than the haze which covers lower latitudes. In comparing the present results with models derived from polarization and infrared observations we conclude that polarization data are sensitive to aerosols in and above the upper cloud layer but insensitive to deeper cloud structure, and the converse is true for infrared data.     

Galilean satellite eclipse studies II. Jovian stratospheric and tropospheric aerosol content

The Galilean satellite eclipse technique for measuring the aerosol distribution in the Jovian lower stratosphere and upper troposphere is described and applied using 30 color observations of 12 natural satellite eclipses obtained with the 200-in Hale telescope. These events probe the North and South Polar Regions, the North Temperate Belt, the South Equatorial Belt, the South Tropical Zone, the South Temperate Zone, and the Great Red Spot. Aerosol is found above the visible cloud tops in all locations. It is very tenuous and varies with altitude, increasing rapidly with downward passage through the tropopause. The aerosol extinction coefficient at 1.05 μm is 1.0 ± 0.05 × 10^?8 cm^?1 at the tropopause and the mass density is a few times 10^?13 g cm^?3. The observations require some aerosol above the tropopause but do not clearly determine its structure. The present analysis emphasizes an extended haze distribution, but the alternate possibility that the stratospheric aerosol resides in a thin layer is not excluded. The vertical aerosol optical depth above the tropopause at 1.05 μm exceeds 0.04 in the NPR, SPR, NTB, SEB, and StrZ, is ～0.006 ± 0.003 in the STZ, and is ～ 0.003 ± 0.001 above the GRS. The aerosol extinction increases with decreasing wavelength in the STZ and NTB and indicates a particle radius of 0.2–0.5 μm; a radius of ～0.9 μm is indicated in the STrZ.     

Spatially resolved absolute spectral reflectivity of Jupiter: 3390–8400 Å

Observational determinations of the absolute spectral reflectivities of visually distinct regions of Jupiter are presented. The observations cover the 3390–8400 Å region at 10 Å resolution, and they are compared with observations using 150–200 Å filters in the 3400–6400 Å range. The effective reflectivities for several regions (on the meridian) in the 3400–8400 Å range are: South Tropical Zone, 0.76±0.05; North Tropical Zone, 0.68±0.08; South Equatorial Belt, 0.63±0.08; North Equatorial Belt, 0.62±0.04; and the Great Red Spot, 0.64±0.09. Reflectivities near the limb are also observed. The appropriate blue and red reflectivities are tabulated in support of the Pioneer 10 and 11 imaging photopolarimeter experiments. For the regions listed above, equivalent widths of molecular bands vary as: CH₄ (6190 Å), 14–16 Å; CH₄ (7250 Å), 77–86 Å; and NH₃ (7900 Å), 87–95 Å. Significant differences from the results of C. B. Pilcher, R. G. Prinn, and T. B. McCord (“Spectroscopy of Jupiter: 3200 to 11200 Å,” J. Atmos. Sci.30, 302–307.)     

Spatially resolved reflectivities of Jupiter during the 1976 opposition

Spatially resolved absolute reflectivities of several regions of the Jovian disk in the wavelength region 3000 to 10760 Å are presented. Spectra were obtained of the central meridian and limbs of the Equatorial Region, North Equatorial Belt, and North Tropical Zone. Equivalent widths of several CH₄ and NH₃ bands are measured. The spatial variations of continuum reflectivity and absorption band profiles are shown in various ratio spectra.     

Infrared scans of Jupiter

We present spatial scans at eight wavelengths between 7.8 and 24 μm along Jupiter's meridian and along the Equatorial Zone, the North Equatorial Belt, and the South Tropical Zone. Some features of these scans are differences in brightness temperatures between the Great Red Spot and the surrounding South Tropical Zone, a higher temperature at high northern latitudes than high southern latitudes, equal or possibly higher temperatures of zones than belts at 7.8 μm in contrast to higher temperatures of belts at other observed wavelengths, very strong limb darkening at 8.9 μm possibly due to a large scale height or a nonuniform distribution of solid NH₃ particles, and inhomogenities within belts and zones.     

Voyager 1 imaging and IRIS observations of Jovian methane absorption and thermal emission: Implications for cloud structure

Images from three filters of the Voyager 1 wide-angle camera were used to measure the continuum reflectivity and spectral gradient near 6000 Å and the 6190-Å band methane/continuum ratio for a variety of cloud features in Jupiter's atmosphere. The dark “barge” features in the North Equatorial Belt have anomalously strong positive continuum spectral gradients suggesting unique composition, probably not elemental sulfur. Methane absorption was shown at unprecedented spatial scales for the Great Red Spot and its immediate environment, for a dark barge feature in the North Equatorial Belt, and for two hot spot and plume regions in the North Equatorial Belt. Some small-scale features, unresolvable at ground-based resolution, show significant enhancement in methane absorption. Any enhancement in methane absorption is conspicuously absent in both hot spot regions with 5-μm brightness temperature 255°K. Methane absorption and 5-μm emission are correlated in the vicinity of the Great Red Spot but are anticorrelated in one of the plume hot spot regions. Methane absorption and simultaneously maps of 5-μm brightness temperature were quantitatively compared to realistic cloud structure models which include multiple scattering at 5 μm as well as in the visible. A curve in parameter space defines the solution to any observed quantity, ranging from a shallow atmosphere and thin NH₃ cloud to a deep atmosphere with a thick ammonia cloud. Without additional constraints, such as center-to-limb information, it is impossible to specify the NH₃ cloud optical depth and pressure of a deeper cloud top independently. Variability in H₂ quadrupole lines was also investigated and it was found that the constancy of the 4-0 S(1)-line equivalent width is consistent with the constancy of the methane 6190-Å band equivalent width at ground-based resolution, but the much greater variability of the 3-0 S(1) line is inconsistent with either the methane band or 4-0 S(1) line. In hot spot regions the 255°K brightness temperature requires a cloud optical depth of about 2 or less at 5 μm in the NH₃ cloud layer. To be consistent with the observed 6190-Å methane absorption in hot spot regions, the NH₃ cloud optical depth in the visible is about 7.5, implying that aerosols in hot spot regions have effective radii near 1 μm or less.     

Five micron limb-darkening and the structure of the Jovian atmosphere

By observing the transit of various cloud features across the Jovian disk, Terrile and Westphal (1977) have constructed limb-darkening curves for three regions in the 4.6 to 5.1 μm band. Several models currently employed in describing the radiative or dynamical properties of planetary atmospheres are here examined to understand their implications for limb-darkening. The statistical problem of fitting these models to the observed data is reviewed and methods for applying multiple regression analysis are discussed. Analysis of variance techniques are introduced to test the viability of a given physical process as a cause of the observed limb-darkening. The intermediate flux region of the North Equatorial Belt appears to be in only modest departure from radiative equilibrium. The limb-darkening curve for the South Temperate Belt is rich in structure and cannot be satisfactorily ascribed to any single physical mechanism; a combination of several, as yet unidentified, processes is likely involved. The hottest areas of the North and South Equatorial Belts exhibit limb-darkening curves that are typical of atmospheres in convective equilibrium. In this case, we derive a measure of the departure of the lapse rate from the dry adiabatic value (η?1.68), which furnishes strong evidence for a phase transition at unit optical depth in the NEB and SEB. Although the system NH₃H₂S cannot be entirely ruled out, the freezing of an aqueous ammonia solution is shown to be consistent with the parameter fit and solar abundance data, while being in close agreement with Lewis' (1969a) cloud models.     

Silicon vidicon imaging of jupiter: 4100- to 8300-Å absolute reflectivities and limb darkening of spatially resolved regions

Jupiter was observed in six continuum wavelength channels in the region 4100–8300 Å, using a silicon vidicon imaging photometer. Spectral reflectivities and high spatial resolution limb-darkening curves for several belts and zones have been extracted from the data. Simple model fits to the data yield information regarding spectral and spatial variations in single-scattering albedos and shape of particle single-scattering phase functions. Belts appear to be more backscattering than zones, particularly in the blue. The data are in moderate agreement with limb-darkening predicted by models derived from the center-to-limb variation in equivalent width of the H₂ 4-0 S(1) quadrupole line (Cochran, 1976) in the South Tropical Zone, but strongly disagree with the results of such models for the North Equatorial Belt.     

On the nature of the blue and ultraviolet absorption in the Jovian atmosphere

Spatially resolved reflectivities from 3000 to 6600 Å of three positions from the center to the limb of the Jovian Equator, North Equatorial Belt, and North Tropical Zone are analyzed to determine the vertical distribution and wavelength dependence of various sources of blue and uv absorption. Six different models of the distribution of absorbing dust particles are examined. In each model, the variation of dust optical depth and cloud single-scattering albedo are determined. Only those models having dust above the upper NH₃ cloud layer will fit the data. The high altitude dust distribution is approximately uniform over the three regions examined. The contrast in reflectivity of the belts and zones may be modeled by a different cloud single-scattering albedo in the different regions.     

Spatially resolved methane band photometry of Jupiter: II. Analysis of the South Equatorial Belt and South Tropical Zone reflectivity

This work presents results and analysis of center-to-limb variations and absolute reflectivity measurements of Jupiter's South Equatorial Belt (SEBs) and South Tropical Zone (STrZ) in three narrowband methane filters and three nearby continuum filters. The observations and data reduction are reported in Paper I. The data were analyzed in terms of plane-parallel but vertically inhomogeneous atmospheric models. Diffuse reflecting-scattering models (RSM) and two-cloud models (TCM) with and without an additional high, thin haze layer (required from Pioneer observations) were computed. Computations of multiple scattering were performed with a doubling technique. Anisotropic phase functions derived from Pioneer 10 photometry were used. Observations in the strong 8900-Å band severely constrain the position of the upper cloud top. To fit both the center-to-limb variations and absolute reflectivity, the STrZ cloud top must lie between 0.55 bar total pressure, if the aerosols are concentrated (small scattering mean free path), and 0.43 bar for the RSM model with 8 to 10 m-am CH₄ per unit cloud optical depth. The 8900-Å data also constrain the cloud optical depth. If the cloud particles are concentrated, the top cloud must have optical depths between 1.5 and 2.5. The data at 7250 and 6190 Å are well suited to specify the level of the lower cloud. TCM models with concentrated aerosols have lower cloud-top pressure between 2.4 and 2.7 bars in the STrZ. To account for the small but significant differences between observations of the STrZ and SEBs, several configurations are allowed. An RSM model for the STrZ and a TCM model for the SEBs would constitute the greatest possible structural differences. RSM models were not satisfactory for the SEBs. If both the STrZ and SEBs are regions where the aerosols are concentrated, the upper cloud is slightly deeper (by 0.03 to 0.08 bar) in the SEBs; the cloud thickness is less (0 to 15%); and the lower cloud is deeper (by 0.4 to 0.8 bar). A forward scattering haze layer of the type derived from analysis of Pioneer 10 photometry is needed in the present STrZ and SEBs models at the 0.1-bar level to account for the limb darkening in the continuum. The haze could be concentrated in a thin layer or spread diffusely above the cloud top with little effect on the pressure level of the top cloud. A CH₄/H₂ mixing ratio of 1.2 to 1.5 × 10^?3 is estimated from computations by W. D. Cochran of the hydrogen quadrupole absorption strength for present models. The smaller value was used to assign pressure levels stated above.     

Estimates of methane and ammonia abundance in the Jovian atmosphere with allowance for scattering in the clouds

Results of photoelectric measurements of the intensity in CH₄ 5430, 6190, and 7250 Å absorption bands, CH₄ absorption lines in the 3ν₃ band, and the NH₃ 6457.1 Å line are examined from the point of view of a model which takes into account the role of multiple scattering inside a homogeneous semi-infinite cloud layer in the formation of absorption components in the Jovian spectrum. Introduced are a number of simple ratios between depths of lines and bands and the parameters which characterize the properties of the cloud layer and the atmosphere above the clouds for occurrence of the Henyey-Greenstein scattering phase function at various degrees of asymmetry in g. The CH₄ content inside the cloud layer is determined as an equivalent thickness on the mean free path between scattering events. The latter was found to be equal to A_L ? 10 ± 2 m-amagat at g = 0.75 or A_L ? 20 ± 3 m-amagat at g = 0.5 along all the above-mentioned CH₄ absorption bands. For NH₃ it is A_L ? 31 ± 4 cm-amagat at g = 0.75 and A_L ? 62 ± 8 cm-amagat at g = 0.5.The weakening of the CH₄ absorption bands toward the edges of the Jovian disc requires a volume scattering coefficient in the cloud layer of σ_a ～ 10^?6 cm^?1. The mean specific abundance of NH₃ obtained within the cloud layer does not contradict the calculated abundance of saturated gaseous ammonia.     

Detection of a CH4 atmosphere on Pluto

Using a low-resolution spectrograph and a CCD array, a spectrum of Pluto from 0.58 to 1.06 μm was obtained. The spectrum had a resolution of $\text{～25}\text{A}\text{?}$ and a signal-to-noise ratio of ～300. It showed CH₄ absorption bands at 6200, 7200, 7900, 8400, 8600, 8900 and 10,000 Å. The strongest of these bands was at 8900 Å with an absorption depth of 0.23. This band was heavily saturated, compared to the weaker bands, providing proof for the gaseous origin of the observed absorptions. By applying CH₄ band model parameters to our data, a total CH₄ abundance of 80 ± 20 m-am was derived. This translates into a one-way abundance of 27 ± 7 m-am and a CH₄ surface pressure of 1.5 × 10^?4 atm. An upper limit to the total pressure of ～0.05 atm could be set. First-order calculations on atmospheric escape showed that this methane atmosphere would be stable if the mass of Pluto is increased 50% over its current value and its radius is 1400 km. Alternatively a heavier gas mixed with the CH₄ atmosphere would aid its stability. The relatively large amount of gaseous CH₄ observed implies that the absorption bands recently reported at 1.7 and 2.3 μm are likely due to atmospheric CH₄ absorptions rather than surface frost as interpreted earlier.     

The thermal structure of Jupiter I. Implications of Pioneer 10 infrared radiometer data

Temperature profiles for low latitude regions of Jupiter in the 1.0-0.1 bar pressure regime are recovered from Pioneer 10 infrared radiometer data. The temperature near 0.1 bar is 108–117K, depending on the overlying thermal structure assumed. For the South Equatorial Belt, the temperature at 1.0 bar is 170 K, assuming an adiabatic lapse rate in the deep atmosphere. The South Tropical Zone temperature at this level is 155K if pure gaseous absorption is assumed. Alternatively, the temperature is much closer to that in the SEB, assuming the presence of an optically opaque cloud near the 0.6atm (145K) level. Such a cloud presence in the STrZ may be correlated with the visible and 5 micron appearance of the planet and with NH₃ saturation just below this position. The molar fraction of H₂ most consistent with the data is 0.91 ± 0.08. conditional on the perfect validity of the model and the lack of systematic errors in the data. The effective temperatures of the SEB and STrZ are 127.6 and 124.2K, respectively. These temperature profiles are generally consistent with data at other wavelengths and radiative-equilibrium models, but a discrepancy with the preliminary neutral atmosphere inversion of Pioneer 10 radio occultation data remains unexplained.     

High spatial and spectral resolution 10-μm observations of jupiter

Ten-micrometer spectra of the North Tropical Zone, North Equatorial Belt, and Great Red Spot at a spectral resolution of 1.1 cm^?1 are compared to synthetic spectra. These ground-based spectra were obtained simultaneously with the Voyager 1 encounter with Jupiter in March, 1979. The NH₃ vertical distribution is found to decrease with altitude significantly faster than the saturated vapor pressure curve and is different for the three observed regions. Spatial variability in the NH₃ mixing ratio could be caused by changes in the amount of NH₃ condensation or in the degree of the NH₃ photolysis. The C₂H₆ emission at 12 μm has approximately the same strength at the North Tropical Zone and North Equatorial Belt, but it is 30% weaker at the Great Red Spot. A cooler temperature inversion or a smaller abundance of C₂H₆ could explain the lower C₂H₆ emission over the Great Red Spot.     

Spectrophotometry of Pluto from 3500 to 7350 Å

We have obtained spectra of Pluto on six nights during February 1979 using the Cassegrain Digicon spectrograph on the 2.1-m Struve reflector and the IDS spectrograph on the 2.7-m reflector of McDonald Observatory. These spectra, with nominal resolution of 6–7 Å, have been reduced to relative fluxes. Relative albedos were then calculated using the solar irradiances of Arvesen et al. (1969). The spectra taken in the blue show no indication of the upturn in albedo at $\text{λ < 3800}\text{A}\text{?}$ previously reported by Fix et al. (1970). The lack of a uv upturn cannot be interpreted in terms of a Rayleigh scattering atmosphere unless the albedo of the underlying surface is known. From the lack of methane absorption at the wavelength of the 6190- or 7270-Å methane bands we derive an upper limit of 1–3 m-am of gaseous CH₄. The albedo curve has a constant slope between 3500 and 7300 Å. The only other solar system body which has this feature is an S-type asteroid.     

Longitudinal variability of methane and ammonia bands on Saturn

A total of 129 spectra of the center of the disk of Saturn were obtained in March 1980 in order to search for possible longitudinal variations in the CH₄ 6190 and NH₃ 6450 bands. The spectra were reduced to reflectivities, and the band equivalent widths were measured using a blind, automated continuum fitting technique. The methane and ammonia equivalent widths are well correlated with each other. There are some latitude regions in which both bands show enhanced absorption and some latitudes in which both bands are weaker than the average. The continuum reflectivity is quite constant with latitude and shows no apparent correlation with molecular band equivalent width. These data were analyzed by adopting the model of J. C. Buriez and C. de Bergh (1981, Astron. Astrophys.94, 382–390) and using a doubling-adding radiative transfer code. The observed variations may be explained by a longitudinal variation in the altitude of the top of the thick cloud of about ±2 km from the mean.     

Retrievals of jovian tropospheric phosphine from Cassini/CIRS

On December 30th, 2000, the Cassini-Huygens spacecraft reached the perijove milestone on its continuing journey to the Saturnian System. During an extended six-month encounter, the Composite Infrared Spectrometer (CIRS) returned spectra of the jovian atmosphere, rings and satellites from 10-1400 cm⁻¹ (1000-7 μm) at a programmable spectral resolution of 0.5 to 15 cm⁻¹. The improved spectral resolution of CIRS over previous IR instrument-missions to Jupiter, the extended spectral range, and higher signal-to-noise performance provide significant advantages over previous data sets.CIRS global observations of the mid-infrared spectrum of Jupiter at medium resolution (2.5 cm⁻¹) have been analysed both with a radiance differencing scheme and an optimal estimation retrieval model to retrieve the spatial variation of phosphine and ammonia fractional scale height in the troposphere between 60° S and 60° N at a spatial resolution of 6°. The ammonia fractional scale height appears to be high over the Equatorial Zone (EZ) but low over the North Equatorial Belt (NEB) and South Equatorial Belt (SEB) indicating rapid uplift or strong vertical mixing in the EZ. The abundance of phosphine shows a similar strong latitudinal variation which generally matches that of the ammonia fractional scale height. However while the ammonia fractional scale height distribution is to a first order symmetric in latitude, the phosphine distribution shows a North/South asymmetry at mid latitudes with higher amounts detected at 40° N than 40° S. In addition the data show that while the ammonia fractional scale height at this spatial resolution appears to be low over the Great Red Spot (GRS), indicating reduced vertical mixing above the ∼500 mb level, the abundance of phosphine at deeper levels may be enhanced at the northern edge of the GRS indicating upwelling.     

Kinematics of the Gould Belt based on open clusters

We have redetermined the kinematic parameters of the Gould Belt using currently available data on the motion of nearby young (log t < 7.91) open clusters, OB associations, and moving stellar groups. Our modeling shows that the residual velocities reach their maximum values of ?4 km s^?1 for rotation (in the direction of Galactic rotation) and +4 km s^?1 for expansion at a distance from the kinematic center of ≈300 pc. We have taken the following parameters of the Gould Belt center: R ₀ = 150 pc and l ₀ = 128°. The whole structure is shown to move relative to the local standard of rest at a velocity of 10.7 ± 0.7 km s^?1 in the direction l = 274° ± 4° and b = ?1° ± 3°. Using the derived rotation velocity, we have estimated the virial mass of the Gould Belt to be 1.5 × 10⁶ M _⊙.     

Galileo Photopolarimetry of Jupiter at 678.5 nm

Brightness and linear polarization measurements at 678.5 nm for four south-north strips of Jupiter are studied. These measurements were obtained in 1997 by the Galileo photopolarimeter/radiometer. The observed brightness exhibits latitudinal variations consistent with the belt/zone structure of Jupiter. The observed degree of linear polarization is small at low latitudes and increases steeply toward higher latitudes. No clear correlations were observed between the degree of linear polarization and the brightness. The observed direction of polarization changes from approximately parallel to the local scattering plane at low latitudes to perpendicular at higher latitudes. For our studies, we used atmospheric models that include a haze layer above a cloud layer. Parameterized scattering matrices were employed for the haze and cloud particles. On a pixel-wise basis, the haze optical thickness and the single-scattering albedo of the cloud particles were derived from the observed brightness and degree of linear polarization; results were accepted only if they were compatible with the observed direction of polarization. Using atmospheric parameter values obtained from Pioneer 10 and 11 photopolarimetry for the South Tropical Zone and the north component of the South Equatorial Belt, this analysis yielded acceptable results for very few pixels, particularly at small phase angles. However, for almost all pixels, acceptable results were found when the parameterized scattering matrix of the cloud particles was adjusted to produce more negative polarization for single scattering of unpolarized light, especially at large scattering angles, similar to some laboratory measurements of ammonia ice crystals. Using this adjusted model, it was found that the derived latitudinal variation of the single-scattering albedo of the cloud particles is consistent with the belt/zone structure, and that the haze optical thickness steeply increases toward higher latitudes.     

The albedo of Titan

The irradiance of Titan has been measured from 0.50 to 1.08μ in 30 Å band-passes spaced 0.01–0.02μ apart. Geometric albedos have been computed at the wavelenghts of measurement using a standard solar flux distribution after Labs and Neckel. The maximum value of p_λ(0) is 0.37 at 0.68, 0.75, and 0.834μ, the minimum value, in the centers of the strongest methane absorption bands, is 0.10 at 0.887 and 1.012μ.The brightness of Titan at the time of the present measurements has been compared with that of previous modern photoelectric measurements. Within the apparent consistency of the different photoelectric systems, the brightness of Titan appears to undergo changes with time.A provisional curve of the geometric albedo from 0.30 to 4.0μ has been made by combining the present results with those of other authors, i.e., relative measurements of Titan from 0.30 to 0.50μ, and measurements of Jupiter and Saturn from 1.08 to 4.00μ. The latter are used to estimate the strengths of the methane absorption bands of Titan in that spectral range. The bolometric geometric albedo, $\text{p}{}^1\text{(0)}$, is computed to be 0.21. A variety of current measurements of Titan indicate a substantial atmosphere, suggesting a value of the phase integral $\text{q}\text{= 1.30 ± 0.20}$. The bolometric Bond albedo, $\text{A}{}^1$, is then 0.27 ± 0.04, giving an effective radiative temperature T_e= 84 ± 2°K.The absorption band contours of Titan have been compared with those of Jupiter and Saturn at the same resolution. The bands of the planets are known to be due primarily to methane, and they show a very regular relationship, with those of Saturn being consistently deeper and wider. For Titan, the strengths of the bands are equal or less than those of Jupiter in the band centers, while the wings are stronger than those of Saturn.Previous photoelectric and photographic spectra have been examined for evidence of temporal variation of the methane path length in the atmosphere of Titan. Differences in measurement techniques prohibit detection of small differences. The only potential differences beyond experimental uncertainties are those of Kuiper (1944) and Harris (mid-fifties). Taking Kuiper's results at face value, Titan appears to have a shorter methane path length in 1972. Harris's results can be reconciled only by the doubtful hypothesis of an almost complete absence of methane at that time.