SHALLOW WATER BATHYMETRY WITH AN SHALLOW WATER BATHYMETRY WITH AN - - PowerPoint PPT Presentation

SHALLOW WATER BATHYMETRY WITH AN SHALLOW WATER BATHYMETRY WITH AN INCOHERENT X INCOHERENT X-

• BAND RADAR USING SMALL

BAND RADAR USING SMALL (SMALLER) SPACE (SMALLER) SPACE-

• TIME IMAGE CUBES

TIME IMAGE CUBES

Ron Abileah Ron Abileah 1

1

Dennis B. Trizna Dennis B. Trizna 2

2 1 1 jOm egak

jOm egak

2 2 I m aging Science Research I nc

I m aging Science Research I nc.

IGARSS 2010 IGARSS 2010 Session: Ocean Radar Remote Sensing at Grazing Incidence Pape Session: Ocean Radar Remote Sensing at Grazing Incidence Paper: FR3.LO2.2 r: FR3.LO2.2

Outline Outline

Space-tim e im age cubes Traditional bathym etry ( depth inversion) algorithm Motivation for sm aller cubes Alternative algorithm Test on radar data Sum m ary

3D Image Cube, 3D Image Cube, S = {S S = {S1

1, S

, S2

2,

, …… …… S SN

N}

}

Typical cube dim ension used for bathym etry are 1 0 0 m x 1 0 0 m x 1 0 0 s Credit: Miros x y t

Inversion of a 3D Image Cube into Depth Inversion of a 3D Image Cube into Depth

2 3

( , ) [{ }] P k S ω = ℑ

• 2

, 3 ,

argmin ( ) ( ( | , )) ( , ) ( | , ) tanh( )

x y

d u D k k

J W k k d u P k where k d u g k k d k u

ω

ω ω ω ω = − = − ⋅

∑ ∑

• 3 D Fourier

transform of im age cube S Shallow w ater gravity w ave dispersion equation Least-square solution for depth ( d) and current ( u) [ Tang et al., 2 0 0 8 ]

First Depth Inversion With X First Depth Inversion With X-

• band Radar

band Radar Reported By Hoogeboom et al. in IGARSS 1986 Reported By Hoogeboom et al. in IGARSS 1986

Hoogeboom et al., 1986 Hoogeboom et al., 1986

Depth Error vs. Dwell Time Depth Error vs. Dwell Time

From Piotrow ski From Piotrow ski and Dugan, 2 0 0 2 and Dugan, 2 0 0 2

1 2 8 Dugan, 2 0 0 0 1 6 0 Bell, 1 9 9 9 7 0 Dugan et al. 1 9 9 6 1 0 0 Hoogeboom et al., 1 9 8 6 Dw ell tim e used ( sec) Paper

Motivation for smaller cubes Motivation for smaller cubes

Bathym etry from low earth orbiting satellites E.g., I KONOS - tw o im ages 1 1 -1 3 s apart [ Abileah 2 0 0 6 , 2 0 0 7 ] Notional airborne radar surveying coastlines 2 0 0 kt speed, 1 0 0 0 m altitude, 5 -1 0 km range, 5 -1 0 o grazing angle Entire CONUS coastline surveyed in 1 0 0 flight hours Dw ell tim e ~ 1 0 s

Depth Error vs. Dwell Time Depth Error vs. Dwell Time

This plot is from This plot is from Piotrow ski and Piotrow ski and Dugan, 2 0 0 2 Dugan, 2 0 0 2 1 2 8 Dugan, 2 0 0 0 1 6 0 Bell, 1 9 9 9 7 0 Dugan et al. 1 9 9 6 1 0 0 Hoogeboom et al., 1 9 8 6 Dw ell tim e used ( sec) Paper 1 0 This paper

Reformulated with 2D Fourier Transforms Reformulated with 2D Fourier Transforms

2

( ) [ ]

n n

F k S = ℑ

• 0 (

, | , )

( , | , ) .

x y

i k k d u x y

where k k d u e

ω τ

±

±

Φ ≡

• 2

1 , 1 , 1

argmin ( )

x y

N d u n n k k n

J W k F F

− Δ + =

= − Φ

∑ ∑

• 2 D Fourier transform s
• f im age S1 , S2 , …

Propagation kernel for linear gravity w aves Least-square solution for depth ( d) and current ( u) using N im ages, 2 D FT of im age n+ 1 2 D FT of im age n propagated to tim e n+ 1

2 N ≥

Simulation with P Simulation with P-

• M Wave Spectrum

M Wave Spectrum Propagated At 7m depth Propagated At 7m depth

2 1 1 , 1

( ) ( )

x y

N n n k k n

J d W k F F

− Δ + =

= − Φ

∑ ∑

• 2

, 1

( ) ( )

x y

N n n k k n

J d W k F

− ∏ =

= Φ

∑ ∑

• 2

N =

X X-

• Band Radar Test Data

Band Radar Test Data

From the I m aging Science Research experim ental radar at Duck Pier, NC Date: Novem ber 2 9 , 2 0 0 9 1 2 -kW Koden radar ( I ncoherent) Antenna 6 ’ Pulse length 8 0 ns Rotation 1 .2 5 -s SW H 0 .3 3 m w ave period 7 s w ind speed 3 .8 m / s

X X-

• Band Radar Bathymetry

Band Radar Bathymetry

Bathym etry w ith T = 1 0 s T = 8 1 s

Depth vs. Cross Depth vs. Cross-

• Shore Distance

Shore Distance

T = 1 0 s T = 8 1 s Joint Density Function Historical Duck depth profile

Depth Error vs. Dwell Time Depth Error vs. Dwell Time (at 7 m depth)

(at 7 m depth)

Results using 2 D algorithm on Duck pier radar data

[ Piotrow ski and [ Piotrow ski and Dugan, 2 0 0 2 ] Dugan, 2 0 0 2 ]

Differences From Satellite Algorithm Differences From Satellite Algorithm

No w hitecaps editing Low grazing angle nonlinearities Radar did not resolve short w ind w aves ( λ≤d) for current estim ation

Summary Summary

W ith the 3 D FTs errors~ ( dw ell tim e) -1

• typical dw ell tim es are ~ 1 0 0 s

W ith 2 D m ethod errors~ ( SNR) - 1

• 1 0 s dw ell tim e is feasible

2 D m ethod enables depth inversion w ith Satellite im agery Airborne X-band radar

Concluding remarks Concluding remarks

Softw are available 2 4 / 7 on server

Rem ote Desktop Connection host: 7 4 .2 0 8 .1 3 .1 5 2 user: jguest passw ord: jguest

Future w ork: test algorithm w ith actual airborne radar data

Mahalo Mahalo