recent advances on insar temporal decorrela3on: theory and ......recent advances on insar temporal...
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Recent advances on InSAR temporal decorrela3on: theory and observa3ons using UAVSAR Marco Lavalle, Scott Hensley, Marc Simard
Jet Propulsion Laboratory, California Institute of Technology
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Outline
• Background and motivation
• Physical model of temporal decorrelation
• Model validation with JPL/UAVSAR data
• Application to forest height estimation
• Conclusions
2/18 Jet Propulsion Laboratory, California Institute of Technology
FRINGE Workshop • September 2011
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What we know about temporal decorrela3on
• Temporal decorrelation • exponential model (Zebker and Villasenor, 1992)
• further extended to Brownian motion (Lombardini, 1994) and birth‐and‐death processes (Rocca, 2007)
• Missing features • temporal decorrelation and target structure • temporal decorrelation and polarization
• complex‐valued temporal decorrelation
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JPL/UAVSAR L‐band airborne radar HV temporal coherence map
zero spatial baseline 45 min temporal baseline
Jet Propulsion Laboratory, California Institute of Technology
FRINGE Workshop • September 2011
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Why we need a refined model of temporal decorrela3on
• InSAR over vegetation • estimation of vegetation structure • forest biomass
• Two‐layer models of volume coherence • polarimetric InSAR • RVoG model (Cloude and Papathanassiou, 1998)
• Temporal decorrelation
• signi\icantly affects the model‐based inversion of RVoG model
4/18 Jet Propulsion Laboratory, California Institute of Technology
FRINGE Workshop • September 2011
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Temporal decorrela3on model
5/18 Jet Propulsion Laboratory, California Institute of Technology
FRINGE Workshop • September 2011
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Temporal decorrela3on model
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scatterer’s displacement depends on initial vertical position
M. Lavalle, M. Simard and S. Hensley, “A temporal decorrelation model for polarimetric radar interferometers”, IEEE TGRS 2011.
Jet Propulsion Laboratory, California Institute of Technology
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Temporal decorrela3on model
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• Temporal decorrelation depends on structure
M. Lavalle, M. Simard and S. Hensley, “A temporal decorrelation model for polarimetric radar interferometers”, IEEE TGRS 2011.
SUBMITTED FOR PEER REVIEW 8
Fig. 4: Temporal coherence versus ground-to-volume ratio µ. For a fixed radar wavelength, µ changes with the polarization.Large values of µ correspond to higher correlation because the scatterer motion at ground is smaller than the motion in the
canopy. Fixed values of the model are λ = 0.23 m, θ = 45 deg, κe = 0.3 dBm−1, hv = 15m, σg = 1 cm, hr = 15m.
B. Dependence on wave polarization
We use the RVOG model to see how polarization affects temporal decorrelation. This model is an extension of the
random volume model with the scattering contribution from an underlying dielectric surface located at z = zg [13].
The structure function, valid within the interval zg ≤ z ≤ zg + hv , becomes
ρgv(z) = ρv(z) + "g exp(− 2κe
cos θhv
)δ(z − zg) , (15)
where δ(z − zg) is the Dirac’s delta located at the ground reference z = zg and "g is the effective attenuated
backscatter per unit length of the ground, which accounts for direct-ground and ground-canopy interactions.
The temporal coherence model is obtained by solving (8) using (15) and (9) and may be written as
γtgv =µ γtg + γtv
µ + 1(16)
where the real positive parameter µ is the effective ground-to-volume scattering ratio defined as
µ =σ0dg + σ
0gv
"vcos θ2κe
[1− exp
(− 2κe
cos θhv
)] , (17)
where σ0dg and σ0gv are the total average backscatter of the direct-ground and double-bounce returns, respectively.
Since µ changes with the wave polarization, the model (16) can be used to study radar data acquired with arbitrary
polarization.
In Fig. 4, the temporal coherence is plotted against the ground-to-volume ratio µ for various levels of canopy
motion. All curves increase monotonically with µ because the motion standard deviation increases from the ground
(high values of µ) to the top of the canopy (low values of µ) according to (9). For a given value of µ, the
coherence is lower if the differential motion is larger. For very large values of µ, all curves approach the fixed
June 30, 2011 DRAFT
SUBMITTED FOR PEER REVIEW 7
A. Dependence on structural parameters
The dependence of temporal decorrelation on structural parameters, such forest height, can be examined using a
basic model of a forest canopy, namely the random volume model [13]. The forest is modeled as a layer of uniform
and randomly distributed scatterers that extend between zg and zg +hv , where hv is the thickness of the layer. The
structure function is an exponential function in the interval zg < z ≤ zg + hv , and may be written as
ρv(z) = "v exp[
2κecos θ
(z − zg − hv)]
, (11)
where "v is the average backscatter per unit length of the volume layer and κe is the mean wave extinction coefficient
in the canopy.
The temporal coherence associated with a random volume is obtained by solving (8) using (11) and (9), and may
be written as
γtv = γtgp1
[e(p1+p3)hv − 1
]
(p1 + p3)(ep1hv − 1
) , (12)
where
γtg = exp
[−1
2
(4πλ
)2σ2g
](13)
is the ground-level temporal coherence, and
p1 =2κecos θ
, p3 = −∆σ2
2hr
(4πλ
)2. (14)
Eq. (12) is a model of temporal decorrelation that applies to forest canopies when the scattering contribution from
the underlying ground is negligible. The temporal decorrelation changes with the height of the canopy layer hv and
the wave extinction κe. If ∆σ2 = 0, then p3 = 0, and γtv reduces to the exponential model published in [4].
In Fig. 3 the temporal coherence (12) is plotted against the differential motion ∆σ for different values of forest
height and extinction. The model parameters are set to λ = 0.23 m, θ = 45 deg, κe = 0.3 dB m−1, hv = 15m,
σg = 1 cm and hr = 15m. The values of radar wavelength and look angle are typical for an airborne radar, whereas
the wave extinction is taken from literature [14]. The motion standard deviation at the ground-level is calculated
using (12) with hv = 0 and γtv = γtg = 0.87. This value of temporal coherence is chosen as an example to
illustrate the model. Note that, in [4, Fig. 8], it is shown that any value between 0.7 and 1 is reasonable for the
ground-level coherence caused by random motion at moderate temporal baseline.
All curves in Fig. 3 start from a fixed value of ground-level decorrelation (γtg = 0.87). Then they decrease
monotonically with the differential motion, expressing a lower correlation induced by a larger motion variance. For
a given value of differential motion, the temporal coherence is lower if the extinction is lower and the canopy layer
is taller. This follows from the expression (9) of the motion variance, which states that the scatterers located at
the upper part of the canopy experience a larger motion than those located at the bottom. As an example, 1 cm
of motion standard deviation at ground-level and 3.5 cm of motion standard deviation at top of the canopy are
sufficient to reduce the coherence to 0.3 at L–band in the presence of 15 m high canopies.
June 30, 2011 DRAFT
temporal function structure function
Jet Propulsion Laboratory, California Institute of Technology
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Temporal decorrela3on model
8/18
• physical and compact • closed‐form expression • 4 structure + 2 motion = 6 parameters
temporal decorrelation depends on canopy height
M. Lavalle, M. Simard and S. Hensley, “A temporal decorrelation model for polarimetric radar interferometers”, IEEE TGRS 2011.
Jet Propulsion Laboratory, California Institute of Technology
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Valida3on of temporal decorrela3on model
9/18
validation of dependence of temporal decorrelation on canopy height
M. Lavalle, M. Simard and S. Hensley, “A temporal decorrelation model for polarimetric radar interferometers”, IEEE TGRS 2011.
JPL/UAVSAR L‐band airborne radar HV temporal coherence map
zero spatial baseline 45 min temporal baseline
lidar canopy height (LVIS) radar coherence (UAVSAR)
Jet Propulsion Laboratory, California Institute of Technology
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Temporal decorrela3on model
10/18
temporal decorrelation is sensitive to polarization
Similar concept of volume decorrelation loci
Jet Propulsion Laboratory, California Institute of Technology
FRINGE Workshop • September 2011
ground‐to‐volume scattering ratio
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Valida3on of temporal decorrela3on model
11/18
validation of dependence of temporal correlation on wave polarization
M. Lavalle, M. Simard and S. Hensley, “A temporal decorrelation model for polarimetric radar interferometers”, IEEE TGRS 2011.
JPL/UAVSAR L‐band airborne radar HV temporal coherence map
zero spatial baseline 45 min temporal baseline
optimized high coherence HV coherence
Jet Propulsion Laboratory, California Institute of Technology
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The general case: temporal‐volume decorrela3on model
12/18 Jet Propulsion Laboratory, California Institute of Technology
FRINGE Workshop • September 2011
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Temporal‐volume decorrela3on model
13/18 Jet Propulsion Laboratory, California Institute of Technology
FRINGE Workshop • September 2011
structure function
temporal function
phase term
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Temporal‐volume decorrela3on model
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• Closed‐form temporal‐volume coherence model, 4+2=6 model parameters
Jet Propulsion Laboratory, California Institute of Technology
FRINGE Workshop • September 2011
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Applica3on to forest height es3ma3on
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• Temporal‐volume model inversion • real JPL/UAVSAR data with simulation of interferometric phase
• temporal parameters, forest height, topography phase and ground‐to‐volume ratio from real data
• Gaussian noise added
motion at ground‐level [mm]
motion at canopy‐level [mm]
coherence amplitude (high ground‐to‐volume ratio)
coherence amplitude (low ground‐to‐volume ratio)
Jet Propulsion Laboratory, California Institute of Technology
FRINGE Workshop • September 2011
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Lidar (LVIS) forest height [m]
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Forest height estimated by a repeat‐pass polarimetric radar interferometer
Jet Propulsion Laboratory, California Institute of Technology
FRINGE Workshop • September 2011
Applica3on to forest height es3ma3on
Radar (JPL/UAVSAR) forest height [m]
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Consequences of our temporal decorrela3on model
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• temporal decorrelation depends on system wavelength through ground‐to‐volume ratio
• temporal decorrelation depends on full structure, including wave extinction
• product of temporal and volume coherence is not generally valid ( de\inition of temporal factor)
• temporal factor is complex‐valued and affects the scattering phase center position
Jet Propulsion Laboratory, California Institute of Technology
FRINGE Workshop • September 2011
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Conclusions
18/18
• Designed a new temporal decorrelation model based on differential random motion
• Differential random motion explains new properties of temporal decorrelation
• Model validated with zero spatial baseline L‐band JPL/UAVSAR airborne data
• Derived an invertible temporal‐volume coherence model for forest canopies
• Attractive avenue for estimating forest parameters using repeat‐pass polarimetric interferometry
Jet Propulsion Laboratory, California Institute of Technology
FRINGE Workshop • September 2011