Titan’s Ontario Lacus: Smoothness Constraints from Cassini RADAR

Lauren Wye, Howard ZebkerStanford University

with contributions from members of the Cassini RADAR Team

L. Wye 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

12/02/2009

3Image Credit: NASA

98% Nitrogen

100% cloud cover

200-880 km

Atmosphere

77% Nitrogen

50% cloud cover

100 km

Atmosphere

1 g

1.0 bars

290 K (60 F)

Surface Surface

Earth

Titan

5,150 km

12,715 km

0.14 g

1.5 bars

94 K (-290F)

4

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

Frequency (Wavelength) 13.78 GHz (2.18 cm) Power Transmitted 48.084 W Peak Gain 50.7 dB Beamwidth (one-way) 0.373º High-Gain Antenna Area 4.43 m2 Polarization same-sense linear (SL)

Cassini RADAR Instrument Parameters

The RADAR operates in four primary modes.

Scatterometry Mode: Backscatter response and mappingRadiometry Mode: Brightness temperatures and emissivity

SAR Mode: Imaging at resolutions 350 – 1000 m Altimetry Mode: Heights with vertical resolution 35-50 m

Janssen et al., Icarus 2009.

6

Erosion and Channels Dunes

Craters

Cryovolcanic flows

Mountain Chains

Credit: NASA/JPL

7

Liquid Hydrocarbons

North Polar Region

Credit: NASA/JPL

L. Wye 812/02/2009

Lakes are prevalent in Titan’s north polar region.

Credit: NASA/JPL/USGS

About 10% of mapped area appears to be

liquid.

About 55% of the north has been mapped.

Kraken Mare

Ligeia Mare90°W

0°W

90°N

80°N

70°N

9

About 60% of the south polar region has been imaged, but only 0.4% appears to be liquid.

Ontario Lacus

12/02/2009

Credit: A. Hayes

180°W

10

Asymmetric distribution of lakes

12/02/2009 Aharonson et al., Nature Geoscience, 2009.

10%0.7%1.0%

0.40%0.10%0.36%

NORTH

SOUTH

Asymmetry in Titan’s seasons may cause dichotomy: hotter, shorter southern summers may drive volatiles to north

11

Ontario Lacus was discovered by ISS in Jun 2005 and imaged by VIMS in Dec 2007.

22,000 km2

235 km x 73 km

Barnes et al., Icarus 2008

Cassini ISS

Annuli interpreted as past shorelines: time-dependence requires presence of liquid methane (in addition to the liquid ethane present in the spectra).

L. Wye 12

0

0.005

0.01

0.015

0.02

RADAR imaged Ontario Lacus in June (T57) and July (T58) 2009, revealing a complex

shoreline and non-uniform surface.

25 30 35 40 450

0.005

0.01

0.015

0.02

Incidence Angle

Sigm

a-0

SAR Beam Footprint

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.

T57T58

12/02/2009

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RADAR Ontario Observations

12/02/2009

Wall et al., submitted to GRL.A: Flooded valleysC: Wave-generated raised beachD: River ValleyE: Alluvial FanF: Recently flooded diapiric structureI: 1km wide river channelJ,K: Delta lobesL: Flooded valley system

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).

18,700 km2

T49 data

88.5K Tb→90-92 K Ts

<10m over 100 m

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

173 km

198 kmOntario Lacus

Liquid Smooth Surface

No signal received

i

Specular reflection away

from radar

Strong signal received (diffuse)

Solid or Liquid Rough Surface

i

Small specular reflection away

from radar

12/02/2009 14

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By observing near-nadir (T49), where surface scattering dominates, we can constrain the

roughness of the surface.

Liquid Smooth Surface

i → 0° Specular reflection towards radar

Liquid Smooth Surface

No signal received

i

Specular reflection away

from radar

Strong signal received (diffuse)

Solid or Liquid Rough Surface

i

Small specular reflection away

from radar

Small specular reflection towards radar and diffuse reflection

Solid or Liquid Rough Surface

i → 0°

Very strong signal received

Extremely strong signal

received

12/02/2009

L. Wye 16

0.37°

12 km

0.37°

R=1850 km

12 km109 m

Rough Surface Smooth Surface

Fresnel radiation pattern

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.

Gaussian Histogram

Like that of a single point scatterer, the received echo is a replica of the transmitted waveform, with reduced amplitude and modified phase.

Sinusoid Histogram

12/02/2009

L. Wye 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.

-150 -100 -50 0 50 100 1500

0.2

0.4

0.6

0.8

1

Histogram Bin

Burst 103 (Lake) Burst 300 (Surface)

The Lake echo is saturated: discrete quantization effect and asymmetry from DC bias.12/02/2009

L. Wye 18

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

Histogram Bin

T49

Alti

met

ry B

urst

Inde

x

-100 -50 0 50 100

50

100

150

200

250

300

350

400

4500

200

400

600

800

1000

Histogram Bin

Alti

met

ry E

cho

Inde

x

-100 -50 0 50 100

100

150

200

250

0

200

400

600

800

1000

12/02/2009

L. Wye 19

The received pulse echo looks like a chirped sinusoid...

12/02/2009

0 200 400 600 800 1000 1200 1400 1600 1800 2000-150

-100

-50

0

50

100

150

Sample Index

Mea

sure

d Vo

ltage

(dn)

Receive Window for First Pulse Echo

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0 200 400 600 800 1000 1200 1400 1600 1800 2000-150

-100

-50

0

50

100

150

Sample Index

Mea

sure

d Vo

ltage

(dn)

Receive Window for First Pulse Echo

Only it is severely clipped.

12/02/2009

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

12/02/2009

0 0.5 1 1.5 2 2.5 3x 104

0

50

100

150

Sample Index

Mea

sure

d Vo

ltage

Am

plitu

de (d

n)

Receive Window for T49 burst 2040

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The received lake signal is saturated: all 15 pulse echoes are clipped to 145.8 dn

12/02/2009

Sample Index within Pulse

Puls

e In

dex

Measured Voltage Amplitude (dn)

500 1000 1500 2000

2

4

6

8

10

12

14

0

20

40

60

80

100

120

140

0 0.5 1 1.5 2 2.5 3x 104

0

50

100

150

Sample Index

Mea

sure

d Vo

ltage

Am

plitu

de (d

n)

Receive Window for T49 burst 2040

0 500 1000 1500 20000

50

100

150

Mea

sure

d Vo

ltage

Am

plitu

de (d

n)

Sample Index

First Pulse Echo

The Block Adaptive Quantization algorithm is based on Gaussian sample statistics and a periodic echo profile.

8-2 BAQ Decode8-2 BAQ Encode

BAQX0 X8 bits 8 bits

(2 bits, Th)

12/02/2009 23L. Wye

X

The algorithm is similar for 8-4 bits but with 16 levels.

If echo profile is periodic, then similar blocks (red) are sampling the same surface and can calculate standard deviation (threshold).

L. Wye 24

Typical altimetry data utilizes all 16 encoded words.

0 0.5 1 1.5 2 2.5 3x 104

0

5

10

15

Received sample

Enco

ded

4-bi

t val

ue

12/02/2009

25

By simulating the BAQ algorithm, we show that a saturated signal will only utilize 10 encoded words.

0 0.5 1 1.5 2 2.5 3x 104

0

5

10

15

Received sample

Enco

ded

4-bi

t val

ue

And because the threshold is fixed to its maximum value (255), the 10 levels will always be the same, no matter the signal.

12/02/2009

L. Wye 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).

50 100 150 200 250 300 350 400 4500

10

20

30

40

50

60

70

80

90

100

T49 Altimetry Burst Index

Perc

ent S

inus

oida

l

12/02/2009

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0 100 200 300 400 5000

10

20

30

40

50

60

70

80

T49 Altimetry Burst Index

Mea

sure

d Si

gma-

0

Sigma-0 assuming range/area/attenuation dependence

CFAdSGNP

RCE

rptxt

adnr

22)(

0

4

The jump is due to an attenuation change and the slope is from range and area

variations.

(Issue 3) The saturated signal does not show a dependence on range, area, or attenuation.

12/02/2009

L. Wye 29

We consider the most saturated sinusoidal bursts (red) as candidates for the ‘true’ sigma-0 levels.

0 100 200 300 4000

10

20

30

40

50

60

70

80

T49 Altimetry Burst Index

Sigm

a-0

0 100 200 300 4000

10

20

30

40

50

60

70

80

T49 Altimetry Burst Index

Sigm

a-0

The lowest s0 level is obtained using from burst 125 (gray circle), right before the attenuator jump.

The highest s0 level is obtained using the parameters from burst 126 (black circle), right after the attenuator jump.

12/02/2009

L. Wye 30

BAQ

To correct for saturation error, we must understand the effect of the receiver on the output signal.

Modified from West et al., 2008

Quantizes to 8 bits

Compresses to 4 bits

The saturating signal may incur some distortion in here.

12/02/2009

L. Wye 31

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

12/02/2009

L. Wye 32

-500 -400 -300 -200 -100 0 100 200 300 400 500-150

-100

-50

0

50

100

150Soft Clip Limiter Model

Input Amplitude

Out

put A

mpl

itude

Hard ClipSoft Clip (p=10)Soft Clip (p=5)Soft Clip (p=2)

pp

Kx

xy 1

1

0 20 40-200

-150

-100

-50

0

50

100

150

200

time

sign

al

Effect on Sinusoid

Hard Clip vs. Soft Clip Limiter Model

12/02/2009

L. Wye 33

The saturated lake histograms cannot be reproduced with a simple hard clipper; signal

distortion is required.

-150 -100 -50 0 50 100 1500

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Histogram Bin

Hard Clip Model fit to T49 b2000

-150 -100 -50 0 50 100 1500

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Histogram Bin

Soft Clip Model (P1P2K1K2post) fit to T49 b2000

A = 395.8DC offset = 57.6P1 = 2.72P2 = 0.82K1 = 248.7K2 = 354.4SSE = 1.1e-4

A = 298.6DC offset = 47.7SSE = 2.9e-3

12/02/2009

L. Wye 34

50 100 150 2000

200

400

600

800

1000

T49 altimetry echo burst index

Peak

vol

tage

am

plitu

de (d

n)

Using these models, we estimate the original input signal levels of the saturated lake echoes (for echoes

with >50% sinusoidal histogram indicator).

12/02/2009

L. Wye 35

To make sense of this, we have engineering data from T56. As we decrease the

attenuation, the signal begins to saturate.

Histogram Bin

Bur

st In

dex

T56 8-4 BAQ Histograms (Normalized, Logarithmic)

-100 -50 0 50 100

15

20

25

30

-25

-20

-15

-10

-5

0

Histogram Bin

Bur

st In

dex

T56 8-8 Histograms (Normalized, Logarithmic)

-100 -50 0 50 100

1

2

3

4

5

6

7

8

9

10 -35

-30

-25

-20

-15

-10

-5

0-61 dB

-43 dB

-61 dB

-43 dB

12/02/2009

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100 200 300 400 500 600

200

400

600

800

1000

1200

1400

Mod

eled

Out

put A

mpl

itude

Theoretical Input Amplitude

T56 8-4 BAQ Soft Clip (P1P2K1K2pre) Model Response

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)

12/02/2009

L. Wye 37

Using the amplitude correction algorithm from T56, we estimate the lower bounds of the T49 lake

amplitudes (yellow).

1.57x increase in lower bound s0

12/02/2009

50 100 150 2000

200

400

600

800

1000

T49 altimetry echo burst index

Peak

vol

tage

am

plitu

de (d

n)

Measured AmplitudesHard Clip ModelSoft Clip ModelBound Corrected Amplitudes

L. Wye 38West Longitude

Latit

ude

195 190 185 180 175 170

-67.5

-70

-72.5

-75

-77.50

10

20

30

40

50

60

70

80

1002003004000

20

40

60

80

Along Track Distance (km)

Sigm

a-0

Normalized radar cross section (0 )

0

10

20

30

40

50

60

70

80

Normalized by beam-illuminated area

Sigma-0 Results (Lower Bound)

12/02/2009

L. Wye 39

From geometric optics, we expect the radar cross section to be:

2

22

RaRa

2

11

R = ~1900 kma = 2575 km

24

2

22

heRaRa

If the surface is not perfectly smooth, the cross section will be exponentially reduced.

12/02/2009

L. Wye 40

0.37°

12 km109 m

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.

Fresnel radiation pattern

0 2 4 6 8 100

0.2

0.4

0.6

0.8

1

RMS surface height (mm)

Nor

mal

ized

mea

sure

d am

plitu

de

The measured amplitude falls off exponentially with increasing roughness.

tj

kjtj

eeS

deeS

h

h

2

e

2

22

8

h

2-2

12/02/2009

L. Wye 41

100150200250300

2.4

2.6

2.8

3

3.2

3.4

Along Track Distance (km)

RM

S Su

rfac

e H

eigh

t (m

m)

West Longitude

Latit

ude

195 190 185 180 175 170

-67.5

-70

-72.5

-75

-77.52.8

2.85

2.9

2.95

3

3.05

3.1RMS Surface Heights

( = 1.9)

= 2.4

= 1.9

= 1.6

2.8

2.85

2.9

2.95

3

3.05

3.1

RMS Heights for Specular-only points

12/02/2009

L. Wye 42

100150200250300

2.4

2.6

2.8

3

3.2

3.4

Along Track Distance (km)

RM

S Su

rfac

e H

eigh

t (m

m)

West Longitude

Latit

ude

195 190 185 180 175 170

-67.5

-70

-72.5

-75

-77.52.8

2.85

2.9

2.95

3

3.05

3.1RMS Surface Heights

( = 1.9)

= 2.4

= 1.9

= 1.6

2.8

2.85

2.9

2.95

3

3.05

3.1

RMS Heights (for Specular-only points) must be less than 3 mm over ~100 m

Suggests waves are not present

24

2

22

heRaRa

12/02/2009

L. Wye 43

Photometric models fit to VIMS brightness (5 μm) suggest Ontario is quiescent and smooth, free of

scattering centers larger than a few μm.

12/02/2009

Brown et al., Nature 2008

Lake Interior

Adjacent area outside of Lake

Lake has ~zero reflectivity at zero airmass

L. Wye 44

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

12/02/2009

45

Liquid hydrocarbons (with low viscosity and low density) and the higher Titan air pressure should facilitate significant capillary wave generation.

12/02/2009

Lorenz et al., Icarus 175, 2005.“Sea-surface wave growth under extraterrestrial atmospheres:

Preliminary wind tunnel experiments with applications to Mars and Titan.”

L. Wye 46

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

12/02/2009

This combined with morphological evidence of wave action at some time in the past on one shore of Ontario Lacus

L. Wye 47

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

12/02/2009

L. Wye 48

Winds are low (<0.5 m/s) during radar observations of Ontario Lacus

Lorenz, Newman, Lunine, Threshold of Wave Generation on Titan’s Lakes and Seas: Effect of Viscosity and Implications for Cassini Observations, submitted to Icarus.

TitanWRF by Claire Newman

12/02/2009

49

Winds should pick up in upcoming northern observations.

12/02/2009

Lorenz, Newman, Lunine, Threshold of Wave Generation on Titan’s Lakes and Seas: Effect of Viscosity and Implications for Cassini Observations, submitted to Icarus.

VIMS specular detection (July, 2009): Stephan et al. AGU Fall09.

L. Wye 50

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)

12/02/2009

L. Wye 51

0 0.1 0.2 0.3 0.4 0.50

10

20

30

40

50

60

70

80

Volume Fraction of Suspended Particles

Scal

ed D

ynam

ic V

isco

sity

Lab data: As the volume fraction of suspended particles approaches 45-50%, the viscosity

diverges (increases to >50x original velocity).

12/02/2009

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.”

Liquid: Polydimethyl siloxane (PDMS) - 21.21, 32.47 poise

Suspended Particles: - powdered silicon (1 μm)- powdered glass (14 μm)

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.

L. Wye 52

Summary of Results• We’ve detected a reflected signal from the lake that mirrors the

transmitted signal. A very smooth surface is needed to produce such a specular reflection.

• We’ve estimated a lower bound on radar cross section.• We’ve developed a scattering model that relates the attenuated

echo to the rms surface roughness (upper bound) for candidate materials.

• The surface is smooth to the order of 3 mm, possibly further evidence for a liquid material.

• These results are consistent with the low wind speeds predicted by global circulation models and do not necessarily require increased viscous damping

12/02/2009