Post on 28-Mar-2015
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
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 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
VII Riunione Annuale CeTeM-AIT, Bari, 4-5 Dicembre 2012
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 W
Frequency: 13.78 GHzData rates: 1 kbps: Radiometer only 30 kbps: Altimeter and Scatterometer/Radiometer 365 kbps: SAR Imaging/Radiometer
Instrument Description
The Cassini Radar
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 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
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
ground
lake
Total liquid depth
g
l
air
Pi
i
t
VII Riunione Annuale CeTeM-AIT, Bari, 4-5 Dicembre 2012
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
!
,exp
2),(
2
1
22222
n
kkkkWIskks
kS ysyxsx
nnpq
n
nszzs
sqp
Integral Equation Model
VII Riunione Annuale CeTeM-AIT, Bari, 4-5 Dicembre 2012
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 e
Bragg scattering (incidence angles exceeding 20°)
where apq is the Fresnel’s coefficient; describes the normalized wave spectrum.
0,sin2cos8 21
24 kWk pqrpq
21 (2 sin ,0)W k
VII Riunione Annuale CeTeM-AIT, Bari, 4-5 Dicembre 2012
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)
,, kDk
kSkS Nk
42
2
5.05.2
3
102.1exp
101024.3
Uk
g
gk
UkS
21022.1 u
gk p
n
f
a
kc
k
kc
kU
kkS
12
3
41
194.02
Capillary wave (k>10kp)
,kS k is the directional spectrum ( c = azimuth angle); n 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
VII Riunione Annuale CeTeM-AIT, Bari, 4-5 Dicembre 2012
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(),(),(
cos
cosgr
ttt
tb TT
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:
tanRe2pd
pd
x
)Re(
)Im(tan
VII Riunione Annuale CeTeM-AIT, Bari, 4-5 Dicembre 2012
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
VII Riunione Annuale CeTeM-AIT, Bari, 4-5 Dicembre 2012
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,(f
21
|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(f
i
iiiii
Inversion algorithm
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
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
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
T25 T17
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 + sub-layer scattering can exist).
T25
T28
T29
T17
T3
Fensal
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
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
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
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
VII Riunione Annuale CeTeM-AIT, Bari, 4-5 Dicembre 2012
Backscattering angular behavior
fitMAE 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
Only parallel acquisition with respect to dunes direction are considered
The off-nadir angle is the same on both sides of the dune
VII Riunione Annuale CeTeM-AIT, Bari, 4-5 Dicembre 2012
Dunes height estimation
VII Riunione Annuale CeTeM-AIT, Bari, 4-5 Dicembre 2012
(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
VII Riunione Annuale CeTeM-AIT, Bari, 4-5 Dicembre 2012
Compute single dune height (example)
𝐻𝑢𝑝𝐻𝑑𝑜𝑤𝑛
VII Riunione Annuale CeTeM-AIT, Bari, 4-5 Dicembre 2012
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
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