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Titan’s Ontario Lacus: Smoothness Constraints from Cassini RADAR

Titan’s Ontario Lacus: Smoothness Constraints from Cassini RADAR. Lauren Wye, Howard Zebker Stanford University. with contributions from members of the Cassini RADAR Team. Outline. Titan, Lakes and Ontario Lacus Radar scattering theory for lake surfaces

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Titan’s Ontario Lacus: Smoothness Constraints from Cassini RADAR

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  1. Titan’s Ontario Lacus: Smoothness Constraints from Cassini RADAR Lauren Wye, Howard Zebker Stanford University with contributions from members of the Cassini RADAR Team

  2. Outline • Titan, Lakes and Ontario Lacus • Radar scattering theory for lake surfaces • T49 Altimetry Observation (Dec 21, 2008) • T49 backscatter and roughness results • Implications for lake material and winds L. Wye

  3. Atmosphere Atmosphere Earth 100 km 200-880 km 77% Nitrogen 98% Nitrogen 50% cloud cover 100% cloud cover Titan Surface Surface 290 K (60 F) 94 K (-290F) 1.0 bars 1.5 bars 5,150 km 1 g 0.14 g 12,715 km Image Credit: NASA

  4. The Cassini RADAR uses 2.2 cm-λ signals to penetrate the haze and explore the surface. Cassini RADAR Instrument Parameters

  5. The RADAR operates in four primary modes. SAR Mode:Imaging at resolutions 350 – 1000 m Altimetry Mode:Heights with vertical resolution 35-50 m Scatterometry Mode:Backscatter response and mapping Radiometry Mode:Brightness temperatures and emissivity Janssen et al., Icarus 2009.

  6. Erosion and Channels Dunes Craters Mountain Chains Cryovolcanic flows Credit: NASA/JPL

  7. Liquid Hydrocarbons North Polar Region Credit: NASA/JPL

  8. Lakes are prevalent in Titan’s north polar region. About 55% of the north has been mapped. About 10% of mapped area appears to be liquid. Ligeia Mare 90°W 90°N 80°N Kraken Mare 70°N L. Wye Credit: NASA/JPL/USGS 0°W

  9. About 60% of the south polar region has been imaged, but only 0.4% appears to be liquid. Ontario Lacus Credit: A. Hayes 180°W Due to asymetry in seasons from Saturn’s orbital configuration? (Aharonson, et al.)

  10. NORTH 10% 0.7% 1.0% Asymmetric distribution of lakes SOUTH Asymmetry in Titan’s seasons may cause dichotomy: hotter, shorter southern summers may drive volatiles to north 0.40% 0.10% 0.36% Aharonson et al., Nature Geoscience, 2009.

  11. Ontario Lacus was discovered by ISS in Jun 2005 and imaged by VIMS in Dec 2007. 235 km x 73 km 22,000 km2 Barnes et al., Icarus 2008 Annuli interpreted as past shorelines: time-dependence requires presence of liquid methane (in addition to the liquid ethane present in the spectra). Cassini ISS

  12. RADAR imaged Ontario Lacus in June (T57) and July (T58) 2009, revealing a complex shoreline and non-uniform surface. The nearly-flat slope of the dark section implies that there is very little diffuse scattering in the liquid itself, but these values are near the noise-equivalent sigma-0 level and are suspect. T57 T58 SAR Beam Footprint L. Wye

  13. RADAR Ontario Observations T49 data <10m over 100 m Wall et al., submitted to GRL. A: Flooded valleys C: Wave-generated raised beach D: River Valley E: Alluvial Fan F: Recently flooded diapiric structure I: 1km wide river channel J,K: Delta lobes L: Flooded valley system 18,700 km2 88.5K Tb→90-92 K Ts Shoreline receded by 10 km over 4 years since ISS image; 1 m/year flux in depth consistent with GCM methane evaporation rates (Hayes et al., submitted to Icarus). L. Wye

  14. Radar imaging is typically acquired at angles > 20°. For smooth surfaces (e.g. lakes), this means that the signal is reflected away from the radar and is never received. 72° S, 184° W i Specular reflection away from radar No signal received Liquid Smooth Surface 198 km Ontario Lacus Small specular reflection away from radar Strong signal received (diffuse) i Solid or Liquid Rough Surface 173 km

  15. By observing near-nadir (T49), where surface scattering dominates, we can constrain the roughness of the surface. i Extremely strong signal received Specular reflection away from radar i→ 0° Specular reflection towards radar No signal received Liquid Smooth Surface Liquid Smooth Surface Small specular reflection away from radar i→ 0° Small specular reflection towards radar and diffuse reflection Strong signal received (diffuse) i Very strong signal received Solid or Liquid Rough Surface Solid or Liquid Rough Surface L. Wye

  16. The near-nadir echo from a surface that is rough at wavelength and larger scales comprises quasi-specular scatter radiated by all illuminated facets facing the radar. The near-nadir echo from a surface that is very smooth comes primarily from the first Fresnel zone (~1% of the beam diameter); All other zones will cancel out. The total echo is the sum of the scattered signals over the entire beam; this tends toward a Gaussian distribution via central limit theorem. Like that of a single point scatterer, the received echo is a replica of the transmitted waveform, with reduced amplitude and modified phase. Gaussian Histogram Sinusoid Histogram 0.37° 0.37° First Fresnel zone radius Planar surface R=1850 km Curved surface a = 2575 km Fresnel radiation pattern 109 m 12 km 12 km L. Wye Rough Surface Smooth Surface

  17. A lake burst’s histogram is very different from the surrounding surface’s histogram: it has a sinusoidal shape, which corresponds to a perfect coherent reflection of the transmitted chirp signal. Burst 103 (Lake) Burst 300 (Surface) The Lake echo is saturated: discrete quantization effect and asymmetry from DC bias. L. Wye

  18. The stacked T49 data histograms illustrate the unique sinusoidal characteristic of the lake (Bursts 100-200). L. Wye

  19. The received pulse echo looks like a chirped sinusoid... L. Wye

  20. Only it is severely clipped. L. Wye

  21. The received lake signal is saturated: all 15 pulse echoes are clipped to ±145.8 dn L. Wye

  22. The received lake signal is saturated: all 15 pulse echoes are clipped to 145.8 dn First Pulse Echo L. Wye

  23. The Block Adaptive Quantization algorithm is based on Gaussian sample statistics and a periodic echo profile. BAQ X0 X (2 bits, Th) 8 bits 8 bits 8-2 BAQ Encode 8-2 BAQ Decode X If echo profile is periodic, then similar blocks (red) are sampling the same surface and can calculate standard deviation (threshold). The algorithm is similar for 8-4 bits but with 16 levels. L. Wye

  24. Typical altimetry data utilizes all 16 encoded words. L. Wye

  25. By simulating the BAQ algorithm, we show that a saturated signal will only utilize 10 encoded words. And because the threshold is fixed to its maximum value (255), the 10 levels will always be the same, no matter the signal.

  26. We model the bursts that show a strong sinusoidal signature (>50% of their echo falls within the 10 histogram bins characteristic of a quantized sinusoid). L. Wye

  27. (Issue 3) The saturated signal does not show a dependence on range, area, or attenuation. The jump is due to an attenuation change and the slope is from range and area variations. L. Wye

  28. We consider the most saturated sinusoidal bursts (red) as candidates for the ‘true’ sigma-0 levels. The highest s0 level is obtained using the parameters from burst 126 (black circle), right after the attenuator jump. The lowest s0 level is obtained using from burst 125 (gray circle), right before the attenuator jump. L. Wye

  29. To correct for saturation error, we must understand the effect of the receiver on the output signal. The saturating signal may incur some distortion in here. Quantizes to 8 bits BAQ Compresses to 4 bits L. Wye Modified from West et al., 2008

  30. We use histogram matching to correct for some of the saturation error. Simulate transmitted signal: Sinusoid with amplitude (A) Subtract dc Offset (DCoffset) Apply input-output receiver transformation (maybe more params) Clip signal to + 127.5 (8-bit quantized) Apply 8-4 BAQ Compare output histogram to data histogram L. Wye

  31. Hard Clip vs. Soft Clip Limiter Model Hard Clip Soft Clip (p=10) Soft Clip (p=5) Soft Clip (p=2) Effect on Sinusoid L. Wye

  32. The saturated lake histograms cannot be reproduced with a simple hard clipper; signal distortion is required. A = 298.6 DC offset = 47.7 SSE = 2.9e-3 A = 395.8 DC offset = 57.6 P1 = 2.72 P2 = 0.82 K1 = 248.7 K2 = 354.4 SSE = 1.1e-4 L. Wye

  33. Using these models, we estimate the original input signal levels of the saturated lake echoes (for echoes with >50% sinusoidal histogram indicator). L. Wye

  34. To make sense of this, we have engineering data from T56. As we decrease the attenuation, the signal begins to saturate. -61 dB -61 dB -43 dB -43 dB L. Wye

  35. Using the T56 best-fit model results, we develop a method of correcting and bounding the overestimated amplitudes. We linearly map the estimated amplitudes from 149 to 850 to their corresponding input amplitudes For estimated amplitudes > 850, where the estimator “plateaus”, we bound to the highest unambiguous input amplitude (245) L. Wye

  36. Using the amplitude correction algorithm from T56, we estimate the lower bounds of the T49 lake amplitudes (yellow). Measured Amplitudes Hard Clip Model Soft Clip Model Bound Corrected Amplitudes 1.57x increase in lower bound s0 L. Wye

  37. Sigma-0 Results (Lower Bound)  0 Normalized by beam-illuminated area Normalized radar cross section (0 ) L. Wye

  38. From geometric optics, we expect the radar cross section to be: R = ~1900 km a = 2575 km If the surface is not perfectly smooth, the cross section will be exponentially reduced. L. Wye

  39. A smooth surface can be slightly roughened (up to ~1/4  rms height) and still maintain its coherent specular nature. As the surface roughens, the transmitted sinusoid will reflect from points of different heights (phase delays) within the Fresnel zone. These reflected sinusoids will interfere, reducing the perceived amplitude of the received signal. 0.37° The measured amplitude falls off exponentially with increasing roughness. Fresnel radiation pattern 109 m 12 km L. Wye

  40.  = 2.4  = 1.9 RMS Heights for Specular-only points  = 1.6 RMS Surface Heights ( = 1.9) L. Wye

  41. RMS Heights (for Specular-only points) must be less than 3 mm over ~100 m  = 2.4  = 1.9 Suggests waves are not present  = 1.6 RMS Surface Heights ( = 1.9) L. Wye

  42. Photometric models fit to VIMS brightness (5 μm) suggest Ontario is quiescent and smooth, free of scattering centers larger than a few μm. Adjacent area outside of Lake Lake has ~zero reflectivity at zero airmass Lake Interior Brown et al., Nature 2008 L. Wye

  43. Waves should be easy to generate on Titan: • Higher air density of Titan (4x denser than Earth) lowers the threshold wind speed to 0.5-1 m/s (Lorenz et al., submitted Icarus) • Low density and low viscosity liquid hydrocarbons should facilitate wave generation • Lower gravity (14% of Earth’s) should allow 7x larger wave heights for fully developed seas of a given wind speed (Ghafoor et al., JGR 2000) • For 1 m/s winds, models suggest rms wave heights > 2.5 cm (Ghafoor; Notarnicola et al. 2009); 0.3 m/s needed to generate our upper limit L. Wye

  44. Liquid hydrocarbons (with low viscosity and low density) and the higher Titan air pressure should facilitate significant capillary wave generation. Lorenz et al., Icarus 175, 2005. “Sea-surface wave growth under extraterrestrial atmospheres: Preliminary wind tunnel experiments with applications to Mars and Titan.”

  45. Waves should be easy to generate on Titan: • Higher air density of Titan (4x denser than Earth) lowers the threshold wind speed to 0.5-1 m/s (Lorenz et al., submitted Icarus) • Low density and low viscosity liquid hydrocarbons should facilitate wave generation • Lower gravity (14% of Earth’s) should allow 7x larger wave heights for fully developed seas of a given wind speed (Ghafoor et al., JGR 2000) • For 1 m/s winds, models suggest rms wave heights > 2.5 cm (Ghafoor; Notarnicola et al. 2009); 0.3 m/s needed to generate our upper limit This combined with morphological evidence of wave action at some time in the past on one shore of Ontario Lacus L. Wye

  46. Implications for winds and material properties (from Lorenz et al., submitted to Icarus) • Threshold wind speed for capillary wave generation on Earth: 1-2 m/s • On Titan (scaling by air density only): ~0.5-1 m/s for pure methane/ethane/nitrogen • These winds (over >20 km fetch) should lead to gravity waves of 20 cm height. • Threshold can be increased by factor of 2 or more from change in liquid properties L. Wye

  47. Winds are low (<0.5 m/s) during radar observations of Ontario Lacus TitanWRF by Claire Newman Lorenz, Newman, Lunine, Threshold of Wave Generation on Titan’s Lakes and Seas: Effect of Viscosity and Implications for Cassini Observations, submitted to Icarus. L. Wye

  48. Winds should pick up in upcoming northern observations. VIMS specular detection (July, 2009): Stephan et al. AGU Fall09. Lorenz, Newman, Lunine, Threshold of Wave Generation on Titan’s Lakes and Seas: Effect of Viscosity and Implications for Cassini Observations, submitted to Icarus.

  49. Viscosity likely higher than predicted for clean liquid hydrocarbons: affect wave generation threshold by factor >2 (Lorenz et al, submitted) • Deposits of dissolved heavy hydrocarbons expected (Cordier et al., submitted) which have viscosities 5x larger than pure liquid hydrocarbons. • Suspended sediment (such as fine-grained tholin haze with low sedimentation velocity) may increase bulk viscosity • Possible that Ontario may be more viscous than northern lakes (transport of methane/ethane) L. Wye

  50. Lab data: As the volume fraction of suspended particles approaches 45-50%, the viscosity diverges (increases to >50x original velocity). Hydrodyamic interaction between the particles (independent of size and shape) will begin to arrest the flow as the number of particles increases. Fluid Immobilized at a volume fraction near 0.53. Results seem independent of liquid. • Liquid: Polydimethylsiloxane (PDMS) • 21.21, 32.47 poise • Suspended Particles: • powdered silicon (1 μm) • powdered glass (14 μm) Halder et al., J. Phys.: Condens. Matter 9, 8873-8878, 1997. “The change of viscosity with concentration of suspended particles and a new concept of gelation.” L. Wye

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