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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WorldView 2
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WKB
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WorldView 2
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WKB
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OSU Jetski
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Depth Estimation Objective
Function J – Evaluated pixel-by-pixel
Image 1, propagated forward
seconds, at depth z
J (x, y )  
z, /2
τ/2
(I1(x, y ))  
z, /2
(I 2(x, y ))
2
Image 2, propagated backward
τ/2 seconds, at depth z
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Objective Function –
averaged
over area A
J (x, y ) 

z, /2
(I1(x, y ))  
z, /2
(I 2(x, y ))
2
A
Noise averaging over area A
(e.g., 100m x 100m)
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Objective Function –
averaged
over area A and all image pairs in set N
J ( x, y) 

z , /2
( I n ( x, y))  
z ,  /2
( I n1 ( x, y))
2
A N
Noise averaging over area A
and all image pairs in 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 m
7 image pairs
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A = 100 x 100 m
7 image pairs
Truth + tide datum
corrected regression
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A = 100 x 100 m
7 image pairs
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The ΔT Factor

Depth averaged over distance that waves
travel in time interval ΔT. In shallow water limit
m
Distance = T gz  10(s) 9.1( 2 ) 10(m),  100 m
s

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Wave refraction
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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 Abileah
abileah@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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WK Current
Before depth can be estimated, WK estimates
the ocean surface current. The color scale is
Red -1 m/s
Green 0 m/s
Blue +1 m/s
Positive x is to the right; positive y is up. Note
strong outward jet at the San Diego Bay inlet.
IKONOS image by SpaceImaging.
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WK Bathymetry
WK depths are average values over
the area of a tile, 150m x 150m. The
color scale is
Dark red
Dark blue
5m
25m
Blank tiles are areas where depth
could not be estimated reliably.
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IKONOS image by SpaceImaging.
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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 D
Agate Beach with 1 image
pair, 200m x 200 m
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A = 200 x 200 m
1 image pair
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A = 200 x 200 m
1 image pair
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OSU Jet Ski
Survey
Transects
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