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 Titans Ontario lake bathymetry with SAR data using e.m. models and Bayesian inversion algorithms Analysis of Titans 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 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 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 Physical depth maps based on loss tangent estimation performed integrating SAR and altimeter data Error budget Error budget SAR data processing on Titans dune fields for physical-morphological parameter retrieval SAR data processing on Titans dune fields for physical-morphological parameter retrieval Discussion of the hypothesis of dune homogeneity Discussion of the hypothesis of dune homogeneity Estimation of physical-morphological dune field parameters merging information from SAR images acquired with different geometry 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 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 Saturnians system on July 1st, 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 Saturnians system on July 1st, 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: Radar modes: Altimeter: topographical profiles 4.25 MHz bandwidth, 24 to 27 km horizontal, 90 to 150 m vertical resolution Altimeter: topographical profiles 4.25 MHz bandwidth, 24 to 27 km horizontal, 90 to 150 m vertical resolution Scatterometer: radar reflectivity of Titans surface 0.1 MHz bandwidth, 10 to 200 km resolution Scatterometer: radar reflectivity of Titans surface 0.1 MHz bandwidth, 10 to 200 km resolution Radiometer: surface emissivity and dielectric constant of superficial features Radiometer: surface emissivity and dielectric constant of superficial features 135 MHz bandwidth, 7 to 310 km resolution 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 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: GHz Data rates: 1 kbps: Radiometer only 30 kbps: Altimeter and Scatterometer/Radiometer 30 kbps: Altimeter and Scatterometer/Radiometer 365 kbps: SAR Imaging/Radiometer 365 kbps: SAR Imaging/Radiometer Instrument Description Instrument Description The Cassini Radar VII Riunione Annuale CeTeM-AIT, Bari, 4-5 Dicembre 2012

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

Titans wide variety of surface features VII Riunione Annuale CeTeM-AIT, Bari, 4-5 Dicembre 2012

T : Ontario lake In the T57 an important lake area (16000 km 2 ) 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 Greens function; W (n) is the Fourier transform of the n-th power of the surface correlation coefficient; S( s ) is the bistatic shadowing function as defined by Sancer; is a function of k and of the field coefficients, f qp and F qp that are in turn function of the Fresnels coefficient, and. 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 Fresnels coefficient; is the RMS slope. Bragg scattering (incidence angles exceeding 20°) where pq is the Fresnels coefficient; describes the normalized wave spectrum. 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 k p ) Capillary wave (k>10k p ) is the directional spectrum ( = azimuth angle); introduces kinematic viscosity; 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 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. and t are respectively the incident and the transmitted angles; T pp 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: 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 0 ( T B ) Sensor Acquisitions E.M. Models 0 sim ( T B, 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

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 Bayes theorem allows to turn the probability of calculated trend (generated by models in the training phase) into probability of the associated parameters set. 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. 0 0 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 ε g = 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 ( ) 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] 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] Dunes material: [2] tholins sand (ε = [2, 2.5] and highly absorptive for the 2.2 cm wavelength signal) 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) over an icy bed-rock (ε 3.1, low absorption) Titan dunes height estimation: Titan dunes height estimation: Radarclinometry in case of material homogeneity [3]; Radarclinometry in case of material homogeneity [3]; Altimeter waveform analysis (in case of material homogeneity). 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), (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), (2010). VII Riunione Annuale CeTeM-AIT, Bari, 4-5 Dicembre 2012

Dunes backscattering - Fensal T25T17 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 dark signal 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 For both GO and IEM the estimated values seem not realistic IEM: ɛ =5 s=0.5cm L=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 bright dark bright dark A B AB 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 fit MAE bright (dB) MAE dark (dB) m = m = m = –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

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

DTM estimation pixel slope (α) Parallel acquisition Perpendicular acquisition integration incremental pixel height (dh) 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: pixel size abc VII Riunione Annuale CeTeM-AIT, Bari, 4-5 Dicembre 2012

Compute single dune height (example) VII Riunione Annuale CeTeM-AIT, Bari, 4-5 Dicembre 2012

Pdf single dunes height mean = 86 m std = 66 m mean = 117 m std = 90 m mean = 180 m std = 138 m m MAE bright (dB) MAE dark (dB) VII Riunione Annuale CeTeM-AIT, Bari, 4-5 Dicembre 2012

Conclusions Titans 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