Exploring lakes and dune features
on Titan surface through
SAR images and electromagnetic
models
M. 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
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
VII Riunione Annuale CeTeM-AIT, Bari, 4-5 Dicembre 2012
The Cassini mission
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).
VII Riunione Annuale CeTeM-AIT, Bari, 4-5 Dicembre 2012
The Cassini Radar
Radar modes:
Instrument Description
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 W
Frequency: 13.78 GHz
Data rates: 1 kbps: Radiometer only
30 kbps: Altimeter and Scatterometer/Radiometer
365 kbps: SAR Imaging/Radiometer
VII Riunione Annuale CeTeM-AIT, Bari, 4-5 Dicembre 2012
Typical Titan’s flyby
VII Riunione Annuale CeTeM-AIT, Bari, 4-5 Dicembre 2012
Titan’s wide variety of surface features
VII Riunione Annuale CeTeM-AIT, Bari, 4-5 Dicembre 2012
T57-58-65: Ontario lake
In 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
VII Riunione Annuale CeTeM-AIT, Bari, 4-5 Dicembre 2012
Ontario lake bathymetry
Objective:
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
VII Riunione Annuale CeTeM-AIT, Bari, 4-5 Dicembre 2012
Modelling scattering from
liquid surfaces
Pi
i
air
lake
t
Total liquid
depth
l
ground
g
VII Riunione Annuale CeTeM-AIT, Bari, 4-5 Dicembre 2012
Electromagnetic models I
Integral Equation Model
 qps  S (J ,Js )
•
2
 
k
exp  s 2 k z2  k sz2
2
 s

n 1
2n
I
n 2
pq
W n k sx  k x , k sy  k y 
n!
 qps 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;
n
• I qp 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 .
VII Riunione Annuale CeTeM-AIT, Bari, 4-5 Dicembre 2012
Electromagnetic models II
Bragg scattering (incidence angles exceeding 20°)

r
pq
 8k cosJ a pq  12W 2k sin J ,0
4
2
2
where apq is the Fresnel’s coefficient;  1 W (2k sin J , 0) describes the normalized wave spectrum.
Facets scattering (low incidence angles)
r
 pp
J  
R pp  0 
2
 tan

e
2
J 2 2

2 2 cos 4 J
where Rpp is the Fresnel’s coefficient;  is the RMS slope.
VII Riunione Annuale CeTeM-AIT, Bari, 4-5 Dicembre 2012
Electromagnetic models III
Gravity-capillary wave description:
Donelan-Pierson model
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.
g
kp 
2


1
.
22
u
10
Gravity wave (k<10 k )
Capillary wave (k>10k )
p
p


3.24 103U 10
 g2
S k  
exp
 2
4
k 2.5 g 0.5
 k 1.2U 10 
2
2  0.194  a  U  k  
4k 

S k   3 
 1 



k  a  f  ck 
a
c
k


S k 
DN k ,  
k
Sk  k ,   is the directional spectrum ( = azimuth angle);  introduces kinematic viscosity; a is
S k  k ,   
function of surface tension, gravity and wave number describing the transition between gravity and
capillary regimes.
VII Riunione Annuale CeTeM-AIT, Bari, 4-5 Dicembre 2012
1
n
Electromagnetic models IV
Double 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.
cos J
2
0
 
T12 (J ,Jt )T21 (Jt , J ) exp( 
) gr
cos Jt
cos Jt
0
b
 J and Jt are respectively the incident and the transmitted angles;
 Tpp the Fresnel power transmission coefficient;
 0gr is the scattering from bottom surface that has been modelled by using the IEM model;
  is the liquid optical thickness:

x
dp
dp 

2 Re   tan 
tan  
Im(  )
Re( )
VII Riunione Annuale CeTeM-AIT, Bari, 4-5 Dicembre 2012
E:M: modelling and Bayesian inversion
application to lake depth estimation
Titan features
hyphoteses/
measurements
E.M. Models
Sensor
Acquisitions
0 (TB)
0 sim (TB, sim)
Comparison and
Possible ranges for
Surface parameters
Inversion
techniques
Probability density
functions for
surface parameters
and related
uncertaintes
VII Riunione Annuale CeTeM-AIT, Bari, 4-5 Dicembre 2012
Inversion algorithm
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 i |  i ) 
f (, s, l, ,... | (1 ), ( 2 ),...) 
f (S i )f ( i | S i )
f ( i )
f (, l, s, ,...)
 f ((1 ), ( 2 ),... | , s, l, ,...)
f ((1 ), ( 2 ),...)
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
VII Riunione Annuale CeTeM-AIT, Bari, 4-5 Dicembre 2012
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)
VII Riunione Annuale CeTeM-AIT, Bari, 4-5 Dicembre 2012
Optical thickness maps for Ontario lake
a
c
b
d
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)
VII Riunione Annuale CeTeM-AIT, Bari, 4-5 Dicembre 2012
Hypotheses on wind speeds and effect on
lake depth estimation
The 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).
VII Riunione Annuale CeTeM-AIT, Bari, 4-5 Dicembre 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 bed
It 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
VII Riunione Annuale CeTeM-AIT, Bari, 4-5 Dicembre 2012
…including uncertainties in pdf
VII Riunione Annuale CeTeM-AIT, Bari, 4-5 Dicembre 2012
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
VII Riunione Annuale CeTeM-AIT, Bari, 4-5 Dicembre 2012
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).
VII Riunione Annuale CeTeM-AIT, Bari, 4-5 Dicembre 2012
Dunes backscattering - Fensal
T29
Fensal
T28
T3
T17
T25
T17
T25
Dunes are visible also in a parallel acquisition with respect to dunes direction
Dunes 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 + sublayer scattering can exist).
VII Riunione Annuale CeTeM-AIT, Bari, 4-5 Dicembre 2012
Perpendicular acquisition
Samples extracted
from T17 and T3:
perpendicular
acquisition
VII Riunione Annuale CeTeM-AIT, Bari, 4-5 Dicembre 2012
Hypothesis: homogeneous material
signal
bright
dark
What is that angle (i.e tilt
angle = 2*slope of the
dunes) for which bright
and dark samples lie on
the same curve?
Tilt angle ≈ 30°
Slope = 15°
is it realistic?
VII Riunione Annuale CeTeM-AIT, Bari, 4-5 Dicembre 2012
Fit with electromagnetic models
GO:
ɛ=4.3
ms=4
IEM:
ɛ=5
s=0.5cm
L=3cm
For both GO and IEM the estimated values seem not realistic
VII Riunione Annuale CeTeM-AIT, Bari, 4-5 Dicembre 2012
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!
VII Riunione Annuale CeTeM-AIT, Bari, 4-5 Dicembre 2012
SAR acquisition over dunes with
different observation direction
Fly direction
dark
SAR
bright
dark
bright
dark
«material effect» only
dunes
dark
SAR
bright
dark
bright
dark
signal
«material» +
«geometric» effect
A
B
A
B
VII Riunione Annuale CeTeM-AIT, Bari, 4-5 Dicembre 2012
Backscattering angular behavior
Only parallel acquisition
with respect to dunes
direction are considered
The off-nadir angle is
the same on both sides
of the dune
fit
MAE bright
(dB)
MAE dark
(dB)
m = -0.29
1.20
0.96
m = -0.33
1.23
0.95
m = -0.23
1.18
1.04
–
0.93
VII Riunione Annuale CeTeM-AIT, Bari, 4-5 Dicembre 2012
Dunes height estimation
VII Riunione Annuale CeTeM-AIT, Bari, 4-5 Dicembre 2012
𝒎𝟏 = 𝒎𝟐 (each pixel of the two
acquisition correspond to the same
area)
In dB scale (with 𝑉 = 10
σ°2
log10 )
σ°1
𝒈𝒅𝑩 𝜽𝒏𝟐 + 𝜶 = 𝑽 + 𝒈𝒅𝑩 𝜽𝒏𝟏
signal
α
α<0
α>0
If 𝒈𝒅𝑩 𝒙 is known (e.g. linear fit) it is possible to compute 𝜶.
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
Parallel acquisition
pixel slope (α)
incremental pixel height (dh)
Perpendicular acquisition
integration
DTM
VII 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:
𝑏
𝐻𝑢𝑝 =
a
b
c
𝑖=𝑎
𝑑ℎ𝑖
𝑐
𝐻𝑑𝑜𝑤𝑛
𝐻𝑑𝑜𝑤𝑛 = −
𝑖=𝑏
𝑑ℎ𝑖
𝑑ℎ2
𝐻𝑢𝑝
𝑑ℎ1
𝐻=
𝐻𝑢𝑝 + 𝐻𝑑𝑜𝑤𝑛
2
pixel size
VII Riunione Annuale CeTeM-AIT, Bari, 4-5 Dicembre 2012
Compute single dune height
(example)
𝐻𝑢𝑝
𝐻𝑑𝑜𝑤𝑛
VII Riunione Annuale CeTeM-AIT, Bari, 4-5 Dicembre 2012
Pdf single dunes height
𝑔𝑑𝐵 𝜃 = 𝑚 ∙ 𝜃
mean = 86 m
std = 66 m
𝑚 = −0.29 is the value that assures
the best fit for the backscattering
samples:
mean = 117 m
std = 90 m
m
mean = 180 m
std = 138 m
MAE
bright
(dB)
MAE
dark
(dB)
-0.29
1.20
0.96
-0.19
1.21
1.11
-0.39
1.32
0.97
VII Riunione Annuale CeTeM-AIT, Bari, 4-5 Dicembre 2012
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
VII Riunione Annuale CeTeM-AIT, Bari, 4-5 Dicembre 2012