m. callegari (1) , d. casarano (2 ) , c. notarnicola (1 ) ,

Exploring lakes and dune features on Titan surface

through SAR images and

electromagnetic modelsM. Callegari(1), D. Casarano(2) , C. Notarnicola(1) ,

L. Pasolli(1), B.Ventura (1), (1)Institute for Applied Remote Sensing, EURAC Bolzano, Italy.

(2)CNR-IRPI, Via Amendola 122 I, Bari, Italy,

VII Riunione Annuale CeTeM-AIT, Bari, 4-5 Dicembre 2012

http://images.google.it/imgres?imgurl=http://www.tesaf.unipd.it/dmt/images/IRPI.gif&imgrefurl=http://www.tesaf.unipd.it/dmt/span/dEFAULT.HTM&h=113&w=113&sz=4&hl=it&start=20&tbnid=fSPQCL8TqS-4FM:&tbnh=86&tbnw=86&prev=/images?q=cnr+irpi&gbv=2&svnum=10&hl=it&sa=G

Outline Analysis of Titan’s Ontario lake bathymetry with SAR data

using e.m. models and Bayesian inversion algorithms Estimation of optical thickness with Bayesian inversion methods also

allowing to obtain incertitude estimation Study of the effect of the hypotheses on wave motion, with the

possibility to constrain likely wind speed ranges Physical depth maps based on loss tangent estimation performed

integrating SAR and altimeter data Error budget

SAR data processing on Titan‘s dune fields for physical-morphological parameter retrieval Discussion of the hypothesis of dune homogeneity Estimation of physical-morphological dune field parameters merging

information from SAR images acquired with different geometry


The Cassini mission is a cooperative project between NASA (National Aeronautics and Space Administration), ESA (European Space Agency) and Italian Space Agency (ASI).

Cassini was launched on October 15th, 1997 by a TitanIV/Centaur Rocket.

Cassini has travelled at an average speed of about 16.4 kilometres per second and covered a distance of about 3474 million kilometres In order to reach the Saturnian’s system on July 1st, 2004.

The Cassini Mission initially foreseen until 2008, has been extended to 2012 (XX) and now until 2018 (Solstice Mission).

The Cassini mission


Radar modes: Altimeter: topographical profiles 4.25 MHz bandwidth, 24 to 27 km horizontal, 90 to 150 m vertical resolution Scatterometer: radar reflectivity of Titan’s surface 0.1 MHz bandwidth, 10 to 200 km resolution Radiometer: surface emissivity and dielectric constant of superficial features 135 MHz bandwidth, 7 to 310 km resolution SAR: construction of visual images of the target surface 0.45 MHz and 0.85 MHz bandwidth, 0.35 to 1.7 km resolution Peak power: 86 WFrequency: 13.78 GHzData rates: 1 kbps: Radiometer only 30 kbps: Altimeter and Scatterometer/Radiometer 365 kbps: SAR Imaging/Radiometer

Instrument Description

The Cassini Radar


Typical Titan’s flyby


Titan’s wide variety of surface features


T57-58-65: Ontario lakeIn the T57 an important lake area (16000 km2) was first detected in the Southern polar region.

Altimetry data offer strong evidence that Ontario Lacus is a basin filled with liquid. Detected heights reveal a flat lake surface. Individual echoes show very strong specular reflection, thus an extremely flat lake surface, with <3 mm rms height variation over 100‐meter lengths [Wye et al., 2009].

If wind‐wave generation theories [e.g., Ghafoor et al., 2000; Notarnicola et al., 2009; Lorenz et al., 2005] apply under Titan conditions, then either the winds were very weak (<0.3 m/sec [Notarnicola et al., 2009] during the altimetry observation, or the liquid material is much more resistant to wave generation than previously thought [Wye et al., 2009].

From Wall et al., 2010


Ontario lake bathymetryObjective:

To investigate lake bathymetry considering the effect of the hypotheses on boundary conditions, to retrieve also possible constraint to these parameters, in particular wind speed


Modelling scattering from liquid surfaces

ground

lake

Total liquid depth

g

l

air

Pi

i

t


Electromagnetic models I

• is the bistatic single-scatter surface model for pp polarization based on the integral equations with simplified Green’s function;

• W(n) is the Fourier transform of the n-th power of the surface correlation coefficient;

• S(J,Js) is the bistatic shadowing function as defined by Sancer; • is a function of k and of the field coefficients, fqp and Fqp that

are in turn function of the Fresnel’s coefficient, J and j .

sqp

nqpI

!,

exp2

),(2

1

22222

nkkkkW

IskkskS ysyxsxn

npq

n

nszzs

sqp

JJ

Integral Equation Model


Electromagnetic models II

Facets scattering (low incidence angles)

where Rpp is the Fresnel’s coefficient; is the RMS slope.

2 22 tan 2

2 4

0

2 cosppr

pp

R eJ

JJ

Bragg scattering (incidence angles exceeding 20°)

where apq is the Fresnel’s coefficient; describes the normalized wave spectrum.

0,sin2cos8 21

24 JaJ kWk pqrpq

21 (2 sin ,0)W k J


Electromagnetic models III

To model the electromagnetic scattering from this liquid layer, wave spectra have been described with Donelan-Pierson model.Kinematic viscosity, density, surface tension, needed for the capillary wave description are taken into account.

Gravity wave (k<10 kp)

,, kDkkSkS Nk

42

2

5.05.2

3

102.1exp101024.3

Ukg

gkUkS

21022.1 ugk p

n

f

a

kck

kckU

kkS

12

3

41194.02

a

a

Capillary wave (k>10kp)

,kS k is the directional spectrum ( = azimuth angle); introduces kinematic viscosity; a is function of surface tension, gravity and wave number describing the transition between gravity and capillary regimes.

Gravity-capillary wave description: Donelan-Pierson model


Electromagnetic models IVDouble layer scattering:

- the first component, derived from liquid surface, is modelled considering Bragg and facets scattering;- the second is determined by non-coherent scattering from bottom

boundary surface attenuated by the liquid layer, approximated by using the IEM model and by accounting for crossing of the top surface boundary and attenuation due to propagation loss through the layer.

02112

0 )cos

2exp(),(),(coscos

grt

ttt

b TT JJJJJ

JJ

J and Jt are respectively the incident and the transmitted angles; Tpp the Fresnel power transmission coefficient; 0

gr is the scattering from bottom surface that has been modelled by using the IEM model;

is the liquid optical thickness:

tanRe2pd

pdx

)Re()Im(tan


E:M: modelling and Bayesian inversion application to lake depth

estimation

Titan features hyphoteses/measurement

s

0

(TB)

SensorAcquisitions

E.M. Models

0 sim

(TB,

sim)

Comparison and

Possible ranges for

Surface parameters

Inversion techniques

Probability density

functions forsurface

parameters and related uncertaintes


The estimation of noise (error) functions is the main objective of the training phase. In fact, the noise function, due to the presence of the natural target variability, the experimental uncertainties and the approximation of the assumptions in the e.m. scattering models and target properties, inferred in this phase is assumed valid also in the test phase

),...)(),((f,...),l,s,),...(),((f,...),s,l,(

),...)(),(|,...,l,s,(f21

|21f21

Bayes’ theorem allows to turn the probability of calculated trend (generated by models in the training phase) into probability of the associated parameters set.

)(f)S|(f)S(f

)|S(fi

iiiii

Inversion algorithm


It can be assumed that the associated targets can be classified in different groups, each one characterized by homogeneous properties. In this case, the objective is to obtain surface parameters pdfs estimate for each target class.

For Titan lakes of T16-T19, it was assumed (as stated by the e.m. model results) that the capillary wave contribution was smaller with respect to the bottom contribution, and the 0 values were depending only on the incidence angle and the optical thickness. Lakes were grouped in three classes, based on their 0 values in each interval of incidence angles (it was assumed that the optical thickness distribution was independent on the incindence angle)


Optical thickness maps for Ontario lake

Optical thickness map obtained with Notarnicola et al., (2009) model when εg= 3.1, vwind=0, 0.5, 0.8 and 1.0 m/s a, b,c,d)

a

d

b

c


Hypotheses on wind speeds and effect on lake depth

estimationThe hypothesis of v>0.7 m/s leads to optical thickness estimates corresponding to total attenuation of scattering from lake bottom, also on areas with scattering coefficients significantly higher than the lake innermost areas A maximum limit of 0.7 m/s is compatible with the outputs of circulation models (Schneider et al., 2012).


Ontario lake bathymetry

Depth map of Ontario lake obtained using the Pb model when null wind speed and =3.1 (a); wind speed of 0.7 m/s and =4.5 (b). These two extreme cases indicates that the higher is the wind speed the weaker is the scattering response from the bedIt is assumed the loss tangent value estimated by Paillou et al. (2008) and also confirmed by Hayes et al. (2010) obtained with the integration of SAR and altimeter data (3.7-8.7 10-4)VII Riunione Annuale CeTeM-AIT, Bari, 4-5 Dicembre 2012

Error estimation on lake bathymetry


…including uncertainties in pdf


Next steps

• Loss tangent estimation using altimeter data and bayesian algorithm in order to derive an independent value

• Bathymetry maps on other lake areas

• Complete evaluation of error budget using all the major componenets such as bayesian inversion techniques, constrains on physical parameters.

• Possible change detection from new acquisitions on lakes including synergy between SAR and radiometric data


Titan dunes Titan dunes are mainly confined around the equatorial line,

between -30° and 30° latitude and covering about 12.5% of the total Titan surface [1]

Dunes material: [2] tholins sand (ε = [2, 2.5] and highly absorptive for the 2.2 cm

wavelength signal) over an icy bed-rock (ε ≈ 3.1, low absorption)

Titan dunes height estimation: Radarclinometry in case of material homogeneity [3]; Altimeter waveform analysis (in case of material

homogeneity).

[1] Le Gall, et al.,"Cassini SAR, radiometry, scatterometry and altimetry observations of Titan's dune fields," Icarus 213(2), 608-624 (2011).[2] Rodriguez, et al., P., "Impact of aerosols present in Titan's atmosphere on the CASSINI radar experiment," Icarus 164(1), 213–227 (2003).[3] Neish, et al., "Radarclinometry of the sand seas of Africa's Namibia and Saturn's moon Titan," Icarus 208(1), 385-394 (2010).


Dunes backscattering - Fensal

T25 T17

Dunes are visible also in a parallel acquisition with respect to dunes directionDunes material is not homogeneous:

• Dark stripes: tholins sand (ε ≈ 2.2)• Bright stripes: sand-free (or thin layer of tholins sand)

interdunes. The icy bedrock is more reflective (ε ≈ 3.1) and less absorptive than sand (volume + sub-layer scattering can exist).

T25

T28

T29

T17

T3

Fensal


Perpendicular acquisition

Samples extracted from T17 and T3: perpendicular acquisition


Hypothesis: homogeneous material

What is that angle (i.e tilt angle = 2*slope of the dunes) for which bright and dark samples lie on the same curve?

bright darksignal

Tilt angle ≈ 30°

Slope = 15°

is it realistic?VII Riunione Annuale CeTeM-AIT, Bari, 4-5 Dicembre 2012

Fit with electromagnetic models

GO:ɛ=4.3ms=4

For both GO and IEM the estimated values seem not realistic

IEM:ɛ=5s=0.5cmL=3cm


Dunes height estimation

Considering an interdune spacing S ranging from 1 to 4 km we obtain mean dunes height H equal to:

The estimated dunes result too high!


SAR

Fly direction

dunes

SAR

dark bright dark bright dark

dark bright dark bright dark

A

BA B

SAR acquisition over dunes with different observation direction

«material effect» only

«material» + «geometric» effect

signal


Backscattering angular behavior

fit MAE bright (dB)

MAE dark (dB)

m = -0.29 1.20 0.96m = -0.33 1.23 0.95m = -0.23 1.18 1.04

– 0.93

Only parallel acquisition with respect to dunes direction are considered

The off-nadir angle is the same on both sides of the dune


Dunes height estimation


(each pixel of the two acquisition correspond to the same area)

signal

α

α<0 α>0

In dB scale (with )

If is known (e.g. linear fit) it is possible to compute . Then (𝒅𝒉 pixel height) can be computed and thus a Digital Terrain Model (DTM) can be estimated VII Riunione Annuale CeTeM-AIT, Bari, 4-5 Dicembre 2012

DTM estimation

pixel slope (α)

Parallel acquisition

Perpendicular acquisition

integration

incremental pixel height (dh)

DTMVII Riunione Annuale CeTeM-AIT, Bari, 4-5 Dicembre 2012

Compute single dune height

For each dunes profile compute the dune height for each single dune:

pixel size

h𝑑 1

h𝑑 2𝐻𝑢𝑝

𝐻𝑑𝑜𝑤𝑛

𝐻=𝐻 𝑢𝑝+𝐻 𝑑𝑜𝑤𝑛

2

𝐻𝑢𝑝=∑𝑖=𝑎

𝑏

h𝑑 𝑖

𝐻𝑑𝑜𝑤𝑛=−∑𝑖=𝑏

𝑐

h𝑑 𝑖

a b c


Compute single dune height (example)

𝐻𝑢𝑝𝐻𝑑𝑜𝑤𝑛


Pdf single dunes height

mean = 86 mstd = 66 m

mean = 117 mstd = 90 m

mean = 180 mstd = 138 m

𝑔𝑑𝐵 ( 𝜃 )=𝑚 ∙𝜃

is the value that assures the best fit for the backscattering samples:

mMAE bright (dB)

MAE dark (dB)

-0.29

1.20 0.96

-0.19

1.21 1.11

-0.39

1.32 0.97


Conclusions • Titan’s Ontario lake bathymetry maps were obtained from

SAR images using scattering and wave spectum models and a Bayesian inversion algorithm

• The dependence of depth estimates on the hypotheses on the wind speed alloed to pose realistc constraints on this parameter

• Hypothesis of Fensal dunes homogeneous in composition and roughness is not verified

• A simple model for separating the effects of acquisition geometry and surface constituents is suggested where both parallel and perpendicularSAR acquisitions are available on the same area

• Altimeter data on the intersection area of parallel and perpendicular SAR acquisition could validate the results and allow to improve the dune model


m. callegari (1) , d. casarano (2 ) , c. notarnicola (1 ) ,

Documents

cassini presentation

flat lake surface

surface emissivity

target surface

resolution sar

resolution radiometer

dicembre 2012t57

space administration