Quantifying the Effects of Wind on polarimetric SAR & InSAR Tree height estimation

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

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

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.

Tree Generation • 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 (2) • 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.

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, fr • Deflection angle, α

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, fr • Deflection angle, α

Modelling Winda single branch m

Modelling Windmultiple branches Θ = 80° WaN = 0.889 W Θ = 45° WaN = 0.5 Θ = 90° ⌃ z WaN = 1.0 ⌃ y ⌃ x

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.

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.

Modelling Wind: Branch Motion (2) • Where does Φmax come from? • Pressure due to wind is [http://www.vent-axia.com/knowledge/handbook/section1/windflow.asp ] • Branch surface area (SA) presented to wind is ~ • Maximum deflection for a cantilever is defined as [http://darkwing.uoregon.edu/~struct/courseware/461/461_lectures/461_lecture40/461_lecture40.html ] • Use of simple trigonometric relationships yield Φmax as ymax L L Φmax

Modelling Wind: Constant Breeze Movie

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 : Escat = Einc· Seiɸ 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, St • Ground-Object scattering Sgt • Object-Ground scattering Stg • Ground-Object-Ground Sgtg

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:

Combined InSAR and Wind • Produced 5 instances of a single red maple, without the influence of wind and placed them in a 625 m2 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 u1 is the no-wind tree and u2 is one sample from a wind-blown tree sequence • Can plot this as a function of time.

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.

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.

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: • 3.9777m • Stronger Breeze: • 3.5758m • Storm Gust: • 2.9520m

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.

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

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

Questions

Extra Slides

Coherence due to Windinc 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

Wind’s effectσ0 comparison L-Band C-Band • At both L and C bands, variations in σ0 are minimal. • σ0 is relatively unaffected by wind motion. σ0

Quantifying the Effects of Wind on polarimetric SAR & InSAR Tree height estimation