Recent advances on InSAR temporal decorrela3on: theory and ......Recent advances on InSAR temporal...

Recent advances on InSAR temporal decorrela3on: theory and observa3ons using UAVSAR Marco Lavalle, Scott Hensley, Marc Simard

Jet Propulsion Laboratory, California Institute of Technology

1/18

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

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

3/18

JPL/UAVSAR L‐band airborne radar HV temporal coherence map

zero spatial baseline 45 min temporal baseline



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



Temporal decorrela3on model




6/18

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.



7/18

•  Temporal decorrelation depends on structure


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



8/18

•  physical and compact •  closed‐form expression •  4 structure + 2 motion = 6 parameters

temporal decorrelation depends on canopy height



Valida3on of temporal decorrela3on model

9/18

validation of dependence of temporal decorrelation on canopy height




lidar canopy height (LVIS) radar coherence (UAVSAR)



10/18

temporal decorrelation is sensitive to polarization

Similar concept of volume decorrelation loci



ground‐to‐volume scattering ratio

Valida3on of temporal decorrela3on model

11/18

validation of dependence of temporal correlation on wave polarization




optimized high coherence HV coherence


The general case: temporal‐volume decorrela3on model



Temporal‐volume decorrela3on model



structure function

temporal function

phase term

Temporal‐volume decorrela3on model

14/18

•  Closed‐form temporal‐volume coherence model, 4+2=6 model parameters



Applica3on to forest height es3ma3on

15/18

•  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)



Lidar (LVIS) forest height [m]

16/18

Forest height estimated by a repeat‐pass polarimetric radar interferometer



Applica3on to forest height es3ma3on

Radar (JPL/UAVSAR) forest height [m]

Consequences of our temporal decorrela3on model

17/18

•  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



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



Recent advances on InSAR temporal decorrela3on: theory and ......Recent advances on InSAR temporal...

Documents

Transcript of Recent advances on InSAR temporal decorrela3on: theory and ......Recent advances on InSAR temporal...