Letter


Nature Geoscience 2, 851 - 854 (2009)
Published online: 29 November 2009 | doi:10.1038/ngeo698

Subject Category: Planetary science

An asymmetric distribution of lakes on Titan as a possible consequence of orbital forcing

O. Aharonson1, A. G. Hayes1, J. I. Lunine2, R. D. Lorenz3, M. D. Allison4 & C. Elachi5


A set of lakes filled or partially filled with liquid hydrocarbon and empty lake basins have been discovered in the high latitudes of Saturn's moon Titan1. These features were mapped by the radar instrument on the Cassini orbiter1, 2, 3, 4. Here we quantify the distribution of the lakes and basins, and show a pronounced hemispheric asymmetry in their occurrence. Whereas significant fractions of the northern high latitudes are covered by filled and empty lakes5, the same latitudes in the southern hemisphere are largely devoid of such features. We propose that in addition to known seasonal changes, the observed difference in lake distribution may be caused by an asymmetry in the seasons on Titan that results from the eccentricity of Saturn's orbit around the Sun. We suggest that the consequent hemispheric difference in the balance between evaporation and precipitation could lead to an accumulation of lakes in one of Titan's hemispheres. This effect would be modulated by, and reverse with, dynamical variations in the orbit. We propose that much like in the Earth's glacial cycles, the resulting vigorous hydrologic cycle6 has a period of tens of thousands of years and leads to active geologic surface modification in the polar latitudes.


The liquid hydrocarbon accumulations on the surface of Titan were discovered and mapped by the Cassini Orbiter's RADAR system1, 2, 3, 4. Interpretation of radar imaging data shows that poleward of about 55° N these lakes and seas are in a range of states, from filled to intermediate (radar granular), to empty5. In the south, available data indicate a significant paucity in lakes relative to the north (Fig. 1). Hemispheric differences in the atmosphere were also apparent in past telescopic observations7, 8.

Figure 1: Geographic distribution of lakes.

Figure 1 : Geographic distribution of lakes.

a,b, Maps of the northern (a) and southern (b) hemispheres. The lakes are colour coded according to their morphologic type (filled, intermediate, empty)5. Shades of brown indicate SAR backscatter brightness.

Full size image (95 KB)

We separately map the distribution of filled, intermediate and empty lakes5 as described in the Methods section. Figure 2 shows the latitudinal distribution of the resulting sets where the identification is considered confident according to the method. Polewards of 55°, where the areal coverage is 55% in the north and 60% in the south, a dichotomy is present in all lake types: filled lakes represent 10% compared with 0.4% of the coverage area in the north and south respectively, empty lakes cover 1.0 and 0.36% of the sampled area in each hemisphere, and intermediate lakes 0.7 and 0.1%. The data used include Cassini Titan passes up to and including T59. Future RADAR coverage will further modify these fractions, as well as help constrain their seasonal dependence.

Figure 2: Lake latitudinal distribution.

Figure 2 : Lake latitudinal distribution.

Surface area covered by various lakes normalized by the surface area sampled by Cassini SAR, as a function of latitudinal position in 3° bins. The southern hemisphere shows a statistically significant paucity in lakes (all types) relative to the north. The fractional surface area of Titan sampled by SAR swaths (dashed line) indicates that significant fractions of both hemispheres are sampled by existing coverage.

Full size image (35 KB)

The asymmetry in lake distribution has been suggested to be a seasonal effect driven by methane evaporation and condensation over the course of a Titan year8, 9, 10, 11, or persistent owing to inherent differences in the south versus north polar terrains, but aspects of both of these mechanisms remain problematic. In particular, the seasonal mechanism requires significant changes to occur over the relatively short timescale of a Saturn year, that is, 29.5 Earth years. Empty lake basins are significantly less abundant and appear highly degraded in the south relative to the north. Combined with their expected persistence for durations longer than the seasonal period, seasonal variations now seem less likely to explain the overall asymmetry, which is expressed not just in the volatile distribution, but also in the topography. Whereas spatially localized surface liquid changes have been detected over timescales of years3, 12, models13 show the peak evaporative energy flux available is approx2 W m-2, lower than previously estimated9, reducing the potential for extensive transport over seasonal timescales.

Furthermore, the asymmetric distribution of empty lakes requires an extra resurfacing process. If seasonal, the process must effectively degrade and at least partly conceal these features from synthetic-aperture radar (SAR) observations on a very short timescale of several years. Fluvial erosion cannot be invoked as the primary mechanism because most, if not all, of the liquid methane has disappeared from the lake before it must be modified.

A topographic, or subsurface lithologic asymmetry in the icy crust could be responsible for hemispheric differences in precipitation, drainage and infiltration rates, but such asymmetries are absent in global shape models from direct altimetry and SAR-Topo techniques14. Likewise, an impermeable boundary may alter the interaction of surface methane with subsurface reservoirs in each hemisphere, but no evidence for such a boundary has been offered10, nor are there global trends in radiometric properties that would reveal porosity differences15.

Although the current seasonal state is responsible for transport of methane, the total magnitude of which is yet to be determined, we propose that components of the observed asymmetry in lake distribution are inherited from the asymmetry in Titan's seasons owing to Saturn's orbit. Saturn's obliquity is 26.7° (Titan's inclination and obliquity to Saturn's equatorial plane are 0.33° and 0.6°, respectively), its current longitude of perihelion passage is16Ls,p=277.7° near northern winter solstice and its orbital eccentricity is e=0.054. Hence, southern summers are shorter and more intense than their northern counterparts and the asymmetry in insolation is about 24% at the top of the atmosphere, peak-to-peak. This asymmetry has previously been suggested7, 8 to cause an asymmetry in the seasonal cycle of haze transport in Titan's stratosphere. In the scenario proposed here, an enhancement in insolation-driven evaporation, precipitation, or both, would account for the current preferential accumulation of hydrocarbon lakes in the north relative to the south. The candidate liquids, methane and ethane, have a volatility ratio of nearly 104 at the relevant approx92 K near-polar surface temperature15, and correspondingly different transport timescales. Methane, therefore, may be moved more rapidly between the polar reservoirs whereas the ethane distribution reflects a longer-term history. Indeed, with possible recession from previous highstands of Ontario Lacus17, the persistence of significant amounts of liquid in this southern lake is consistent with the spectroscopic observation of ethane there18. Ethane is not expected to evaporate appreciably on seasonal timescales (neither from Ontario nor from other lakes).

When averaged over an annual period, the insolation is latitudinally symmetric. Hence, it is only through the many known nonlinear climate mechanisms (notably the exponential Clausius–Clapeyron relation) that the insolation asymmetry may translate to hemispheric volatile transport. Evidence for such a process of net methane transport has been seen in general circulation models of Titan's atmospheric dynamics19, 20. At the peaks of the current seasonal cycle, the top of the polar atmosphere receives 1.5 W m-2 greater solar flux in southern summer than northern summer. As an upper limit, if this entire excess energy were used for vaporization of methane (neglecting atmospheric heat redistribution), using a latent heat value21 of 546 kJ kg-1, and liquid density of 422 kg m-3, the energy corresponds to vaporization of approx0.2 m yr-1. As haze and methane in Titan's atmosphere absorb approx90% of the sunlight before it reaches the ground22, the energy budget at the surface would differ from this upper limit on the theoretical evaporation rate. As noted earlier, stricter constraints on the seasonal surface methane budget are obtained from circulation models13, 20, which show that the difference between peak north- and south-polar evaporative energy flux is approximately 0.5–1 W m-2 (that is, approximately 0.07–0.14 m yr-1).

The asymmetry described would reverse, much like the (Croll) Milankovitch cycles on Earth and their analogue on Mars, here with Saturn's precession of perihelion passage, eccentricity variations and position of spin axis. The rate of Saturn's perihelion precession is -19.4889 arcsec yr-1 at present, which together with the remaining orbital variations leads to an approximately 45 kyr period in the driving function that is also modulated in amplitude. The insolation function may be computed in past epochs by integrating the orbital parameters backwards in time23, 24 (Fig. 3). At present, the solar energy incident at the top of the atmosphere at the south and north poles is, respectively, 7.48 W m-2 and 6.04 W m-2. Note, that for example when the seasonal angle of perihelion passage Ls,p was 180° away from the present, the south and north polar fluxes were, respectively, 6.47 and 7.75 W m-2, an excess of approx20% in the north owing to the smaller eccentricity at the time. During the past hundreds of kiloyears, the peak polar insolation contrast both reversed and changed in amplitude. Over a million years, a variation of period approx270 kyr is present, and more periods exist over longer times. The orbital cycles induce a smaller energy difference than the seasonal ones by a factor of a few, but they operate over timescales of greater than three orders of magnitude longer.

Figure 3: Incoming solar radiation.

Figure 3 : Incoming solar radiation.

a,b, The insolation function at the top of Titan's atmosphere (contours in W m-2). Two cases are contrasted: a, the present day (t=0, Ls,p=277.7°, e=0.054) and b, the time at which Ls,p was 180° away from the present (t=-31.5 kyr,Ls,p=97.7°,e=0.046). c, Peak annual insolation incident at the top of the polar atmosphere over the past 100 kyr. d, Peak annular insolation difference between the north and south poles over the past 1 Myr.

Full size image (96 KB)

Neglecting seasonal albedo variations and small sensible heat, the asymmetry in net radiation at the top of the atmosphere will be expressed in differences in annual average evaporation13 minus precipitation (E-P) in the atmospheric column20, through the nonlinearity of the phase change. We propose one mechanism as a heuristic, recognizing the detailed dynamics are more complex and alternative mechanisms are possible. If E-P increases, net drying of the more intensely heated pole (recently, the south) would result. In an atmosphere where the methane humidity is supply- (rather than transport-) limited, the control by the surface reservoirs would induce unequal absolute humidity gradients in each season. Atmospheric dynamics would mix these gradients over timescales that are short compared with the period of the orbital cycles19, 25. As the gradients are unequal in opposite seasons, their equilibration would lead to net transport (reminiscent of the situation on Mars). Note, however, that increased insolation may also lead to enhanced summer precipitation. The net effect on E-P is hence an important target for models.

Evaporation, transport and deposition of tens to hundreds of metres of material (the approximate depth of lakes5) on a timescale of 45 kyr is well below the suggested upper limit of 10 cm yr-1 on winter precipitation placed by RADAR observations26. If the volatile transport timescales are such that the lake distribution indeed records the forced seasonal asymmetry in addition to the annual effects, then the lake regions on Titan, poleward of approx55° in both hemispheres, experience surface modification that masks the appearance of empty lakes in SAR observations. Radar altimetry observations indicate the depths of empty depressions are5 200–300 m. This entire topography need not necessarily disappear every cycle, but two prominent characteristics of empty lakes do not appear abundantly in the south: the sharp radar contrast resulting from the lake boundary topography is usually absent in the south, and the interior bright return relative to the surroundings, interpreted to be due to volume scattering and compositional effects5, is relatively muted. The process responsible is difficult to identify. Possibilities include fluvial erosion or deposition of a mantle of porous atmospheric fallout. With a typical loss tangent approx10-3 at Titan temperatures27, several metres of material is required.

The implied resurfacing is rapid, especially when considering the recognition of several craters on the surface. The five accepted crater identifications have led to a crater retention age estimate of between 200 Myr and 1 Gyr (ref. 28). However, intriguingly, these craters occur in the low latitudes. Several dozen further putative crater identifications exist29. The mapping shows the geographic distribution of these is again biased towards the equator. Hence, the distribution of small craters known, sparse as it is, supports the notion of high-latitude active surface modification. Only those craters of comparable size to the empty lakes that show the asymmetry (tens of kilometres) must be masked on the timescale of the orbital cycles; much larger craters can survive from one cycle to the next.

The proposed mechanism of seasonal asymmetry of insolation driving the lake dichotomy requires Titan to sustain an active methane hydrologic cycle that redistributes the volatiles globally. It is consistent with the filled and empty geographic lake distribution, the approximate energetic budget of the insolation function, the spectroscopic detection of ethane remaining in Ontario Lacus18 and the latitudinal gradients in the crater distribution. If indeed the lake distribution is determined by the mechanism proposed, the strongly asymmetric surface volatile distribution and empty lakes would not entirely reverse over half of an annual period on Titan, that is, over approx15 yr. Surface hydrocarbons, primarily methane, are transported over that timescale, but the overall dichotomy in various lake types would not entirely reverse. It is notable that three planetary bodies in our solar system with atmospheres, observable surfaces and substantial obliquity may bear records of their astronomically driven climate history in their landscapes.

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Methods

The distribution of filled, intermediate and empty lakes follows the classification scheme previously proposed5. To minimize subjectivity, we first map all putative lake features. Once identified, the backscatter ratio of the interior to exterior return from the lake determines its class. Second, we individually assign a confidence score to the empty lake identification in a double-blind procedure (that is, without knowledge of the feature's geographic position or context). The identification of filled lakes is robust because their radar backscatter returns are typically so low that there are no other known features with which they may be mistaken. Empty and intermediate lakes can be more ambiguous, and hence the criteria for their identification include their boundary morphology as well as topographic evidence for a steep-sided local depression in the SAR image.



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Acknowledgements

We would like to thank E. Schaller, M. Brown, M. Richardson, C. Newman, T. Schneider and K. Lewis for helpful discussions. This work was partially supported by the Cassini Project. O.A. would like to thank R. Sari, Y. Erel and the Hebrew University of Jerusalem, Israel, for hosting him while carrying out this work.

Author Contributions

O.A., A.G.H., J.I.L. and R.D.L. contributed data analysis and development of the hypothesis; M.D.A. and A.G.H. carried out the computation of the orbital elements; C.E. is the Cassini Radar instrument principal investigator.

Received 29 June 2009; Accepted 26 October 2009; Published online 29 November 2009.

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  1. Department of Geological Planetary and Sciences, California Institute of Technology, Pasadena, California 91125, USA
  2. Lunar & Planetary Laboratory, University of Arizona, Tucson, Arizona 85721, USA
  3. Space Department (SRE), Applied Physics Laboratory, Johns Hopkins University, Laurel, Maryland 20723-6099, USA
  4. NASA Goddard Institute for Space Studies, New York, New York 10025, USA
  5. Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California 91109, USA

Correspondence to: O. Aharonson1 e-mail: oa@caltech.edu

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