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MAPPING NEAR SHORE BATHYMETRY USING WAVE

KINEMATICS IN A TIME SERIES OF WORLDVIEW-2 SATELLITE IMAGES

Ron Abileah

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WorldView 2 Image Sequence

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WKBWorldView 2

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WKBWorldView 2 OSU Jetski

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2, / 2 , / 21 2( , ) ( ( , )) ( ( , ))z zJ x y I x y I x y

Image 1, propagated forward τ/2 seconds, at depth z

Image 2, propagated backward τ/2 seconds, at depth z

Depth Estimation Objective Function J – Evaluated pixel-by-pixel

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2, / 2 , / 21 2

A( , ) ( ( , )) ( ( , ))z zJ x y I x y I x y

Noise averaging over area A (e.g., 100m x 100m)

Objective Function – averaged over area A

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2, /2 , /21( , ) ( ( , )) ( ( , ))

N

z zn

AnJ x y I x y I x y

Noise averaging over area A and all image pairs in N

Objective Function – averaged over area A and all image pairs in set N

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Objective Function Minimization demonstrated with 1 image pair, A = 100m x 100m

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A = 100 x 100 m7 image pairs

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A = 100 x 100 m7 image pairs

Truth + tide datum corrected regression

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A = 100 x 100 m7 image pairs

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The ΔT Factor

Depth averaged over distance that waves travel in time interval ΔT. In shallow water limit

Wave refraction

210( ) 9. 1( ) 10( ), 100

mDi stance = T gz s m m

s

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Summary Depth mapping demonstrated at Agate Beach, OR

ΔT = 10 s 7 image pairs Haze Depth accuracy +1m with 100 m resolution ≤50 m resolution achievable at shallower depths

Possibility for greater depth mapping accuracy ΔT = 7 s with WV02 Up to 40 image pairs Better visibility

WBK method works in turbid waters

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Acknowledgements

Satellite imagery provided by Digital Globe under a data exchange agreement

DigitalGlobe's Gregory Miecznik, Dan Lester, and Chuck Chaapel provided much technical assistance throughout this study

Jet ski survey funded by Oregon's Department of Geology and Mineral Industries (DOGAMI) and The Northwest Association of Networked Ocean Observing Systems (NANOOS)

Peter Ruggiero, Oregon State University, provided the 2012 jet ski survey data

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Thank you

Ron Abileahabileah@jOmegak.com

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Appendix A Waimanlo Beach

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WKB vs. SHOALS depths

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Appendix B Coronado Beach

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Before depth can be estimated, WK estimates the ocean surface current. The color scale is

Red -1 m/s Green 0 m/sBlue +1 m/s

Positive x is to the right; positive y is up. Note strong outward jet at the San Diego Bay inlet.

WK Current

IKONOS image by SpaceImaging.

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WK Bathymetry

IKONOS image by SpaceImaging.

WK depths are average values over the area of a tile, 150m x 150m. The color scale is

Dark red 5mDark blue 25m

Blank tiles are areas where depth

could not be estimated reliably.

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San Diego bathymetry with IKONOS

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Appendix C WKB objective function in

deep water

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Appendix DAgate Beach with 1 image

pair, 200m x 200 m

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A = 200 x 200 m1 image pair

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A = 200 x 200 m1 image pair

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OSU Jet Ski Survey

Transects