Radiation Laboratory Quantifying the Effects of Wind on polarimetric SAR & InSAR Tree height estimation Michael L. Benson Dr. Leland E. Pierce Prof. Kamal Sarabandi

Radiation Laboratory Overview Motivation Tree Model Wind Model InSAR Simulator SAR Image Coherence InSAR Height Estimate Future Work

Radiation Laboratory Motivation InSAR is often used over forested areas to obtain information on forest structures Repeat-pass InSAR over forests suffers from poor coherence due to changes in a forests physical attributes (exact position, motion of branches, leaves, etc) and moisture which affects the dielectric constant of the scatterers. Is there a way to obtain high-coherence repeat-pass InSAR data using models of these effects? Could we then produce reliable, high-quality forest structure estimates including canopy height? This research presents a detailed model of the effects of wind on SAR image formation coherence and the associated effect on tree height retrieval through the scattering phase center.

Radiation Laboratory Overview Motivation Tree Model Wind Model InSAR Simulator SAR Image Coherence InSAR Height Estimate Future Work

Radiation Laboratory Use our existing Lindenmayer system based fractal tree generator [Lin + Sarabandi, IGRS, 1999] Trees defined by a DNA file Consists of basic parameters such as leaf radius, leaf thickness, and maximum branch angle. Different DNA for each species. DNA is iterated a set number of times to form a complex, semi- random tree realization. DNA sub-string re-writing rules are used to generate realistic branching structures, with needles / leaves. Current study uses a deciduous red maple stand only. Tree Generation

Radiation Laboratory Generate both coniferous and deciduous trees including: Red Maple Red Oak Red Pine Sugar Maple White Ash White Pine White Spruce DNA files only specify tree structure. InSAR parameters are specified elsewhere. Tree Generation (2)

Radiation Laboratory Overview Motivation Tree Model Wind Model InSAR Simulator SAR Image Coherence InSAR Height Estimate Future Work

Radiation Laboratory Modelling Wind Branches Need to know: Mechanical Parameters Length, l Center (x, y, z) Orientation (Θ,Φ) Parent & Children Young’s Modulus, E Need to Find: Moment of Inertia, I Resonant Frequency, f r Deflection angle, α

Radiation Laboratory Modelling Wind Stems & Leaves Need to know: Mechanical Parameters Stem length, l Center (x, y, z) Orientation (Θ,Φ) Family (branch  stem  leaf) Young’s Modulus, E Leaf thickness, t Need to Find for each stem-leaf pair: Moment of Inertia, I Resonant Frequency, f r Deflection angle, α

Radiation Laboratory Modelling Wind a single branch m

Radiation Laboratory Modelling Wind multiple branches W Θ = 80° Θ = 45° Θ = 90° z ⌃ y x ⌃ ⌃ WaN = WaN = 0.5 WaN = 1.0

Radiation Laboratory Modeling Wind A steady wind force on the branch causes a vibration with frequency: Moment of Inertia, I is determined by the mass distribution in the branch as well as the mass of branches attached to its end: Young's Modulus, E, is a measure of the stiffness of the branch, measurements of E for different species are available. Tree motion composes each branch motion using movement of lower branches to alter locations of upper branches.

Radiation Laboratory Modelling Wind: Branch Motion A steady wind force on the branch causes a vibration with frequency: How far should each branch move? Depends on the wind velocity and the branch’s physical parameters Assuming T = 25  C and average moisture content in each branch, calculate the maximum deflection for each branch as: Under SHM approximation branch will be directly moved along the direction of the wind field a maximum of ½  max in any direction. However, branches may move more than ½  max relative to their original (rest) position as a result of their parents’ motion.

Radiation Laboratory Modelling Wind: Branch Motion (2) Where does Φ max come from? Pressure due to wind is [ axia.com/knowledge/handbook/section1/windflow.asp ] Branch surface area (SA) presented to wind is ~ Maximum deflection for a cantilever is defined as [ ] Use of simple trigonometric relationships yield Φ max as y max Φ max L L

Radiation Laboratory Modelling Wind: Constant Breeze Movie

Radiation Laboratory Overview Motivation Tree Model Wind Model InSAR Simulator SAR Image Coherence InSAR Height Estimate Future Work

Radiation Laboratory InSAR Simulator (1) Divide stand into several horizontal slabs In each slab estimate the mean field using Foldy's approximation [Lin + Sarabandi, IGARSS, 1996] Also estimate attenuation through each slab For each branch or leaf in the tree, calculate the backscattered field as : E scat = E inc · Se i ɸ where S is the scattering matrix of the object, and ɸ is the relative phase of the scattering, due to the relative position of this object in the tree. The scattering matrix is estimated using four (4) scattering mechanisms: –Direct Scattering, S t –Ground-Object scattering S gt –Object-Ground scattering S tg –Ground-Object-Ground S gtg

Radiation Laboratory InSAR Simulator (2) Use Δk Approach [Sarabandi, TGRS, 1997]. Approximate InSAR baseline with a small change in frequency Measured phase can be calculated as For each polarization, calculate a scattering phase center as:

Radiation Laboratory Overview Motivation Tree Model Wind Model InSAR Simulator SAR Image Coherence InSAR Height Estimate Future Work

Radiation Laboratory Combined InSAR and Wind Produced 5 instances of a single red maple, without the influence of wind and placed them in a 625 m 2 region. Applied wind to these trees and saved all geometries for each time step in the simulation. –Δt = 0.02s, total time = 1s Use InSAR simulator to produce a single-look complex (SLC) image of a one-pixel forest stand for each geometry at each time step. This includes the no-wind case. Now can produce a coherence estimate between pairs of SLC images: Where u 1 is the no-wind tree and u 2 is one sample from a wind- blown tree sequence Can plot this as a function of time.

Radiation Laboratory Forming a SAR Image A SAR image formed with multiple looks in practice will be collected over a period of time, often under 1 second. Wind Speeds below vary from a strong breeze to a sustained hurricane force wind.

Radiation Laboratory Forming a SAR Image A SAR image formed with multiple looks in practice will be collected over a period of time, often under 1 second. Wind Speeds below vary from a strong breeze to a sustained hurricane force wind.

Radiation Laboratory Overview Motivation Tree Model Wind Model InSAR Simulator SAR Image Coherence InSAR Height Estimate Future Work

Radiation Laboratory Coherence and Height Estimation This Coherence measurement can also be thought of as a measure of similarity between two SAR images taken at different times. The only difference between the two images is a wind induced motion.

Radiation Laboratory Coherence and Height Estimation At L-band, the principal contributor to the VV-polarization from the target will be the tree trunks. As the wind height increases, the mean scattering phase center height decreases at a nearly consistent rate. mean SPC Strong Breeze: m Stronger Breeze: m Storm Gust: m

Radiation Laboratory Coherence and Height Estimation The physical description of the wind’s effect on higher frequency (C-band) tree height estimate is not as straight forward as the L- band VV case. We have observed that the co-polarized mean SPC increases with an increasing wind force while the mean cross-polarized SPC decreases. Mean Scattering Phase Center Height [m] Strong BreezeStorm Gust VV C-Band HH C-Band VH C-Band

Radiation Laboratory Overview Introduction Tree Model Wind Model ifSAR Simulator SAR Image Coherence InSAR Height Estimate Conclusions and Future Work

Radiation Laboratory Conclusions and Future Work Developed a realistic wind model for trees including branches, stems, leaves, and needles and demonstrated it on a red maple stand. Applied SAR and InSAR model to the stand with and without wind. Calculated coherence between wind / no-wind cases to simulate repeat-pass InSAR. Showed poor coherence for both L-band and C-band. –This is only due to the movement of the branches and leaves. Showed wind effect on IfSAR Tree Height estimation Future Work: –Different moisture conditions in branches and leaves. –Large database generation

Radiation Laboratory Questions

Radiation Laboratory Extra Slides

Radiation Laboratory Coherence due to Wind inc angle = 43.6° L-band coherence drops below 0.7 at 2.39s, 1.01s C-band coherence drops below 0.7 at 1.6s, 0.7s C-band has significantly more scattering from the tree's upper branches than does L-band and so their movement will create greater decorrelation at C-band than L-band

Radiation Laboratory Wind’s effect σ 0 comparison At both L and C bands, variations in σ 0 are minimal. σ 0 is relatively unaffected by wind motion. L-Band C-Band σ0σ0