IGARSS 2010 IGARSS 2010 Session: Ocean Radar Remote Sensing at Grazing Incidence Paper: FR3.LO2.2 r: FR3.LO2.2 Session: Ocean Radar Remote Sensing at Grazing Incidence Pape SHALLOW WATER BATHYMETRY WITH AN SHALLOW WATER BATHYMETRY WITH AN INCOHERENT X- -BAND RADAR USING SMALL BAND RADAR USING SMALL INCOHERENT X (SMALLER) SPACE- -TIME IMAGE CUBES TIME IMAGE CUBES (SMALLER) SPACE 1 Ron Abileah 1 Ron Abileah Dennis B. Trizna 2 2 Dennis B. Trizna 1 1 jOm egak jOm egak 2 I m aging Science Research I nc 2 I m aging Science Research I nc .
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
…… S , …… 3D Image Cube, S = {S S = {S 1 , S 2 S N } 3D Image Cube, 1 , S 2 , N } x t y 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
Inversion of a 3D Image Cube into Depth Inversion of a 3D Image Cube into Depth � 3 D Fourier 2 ω = ℑ transform of ( , ) [{ }] P k S 3 im age cube S � � � � ∑ ∑ = ω − ω ω 2 Least-square argmin ( ) ( ( | , )) ( , ) J W k k d u P k � d u , 3 D 0 solution for ω , k k depth ( d) and x y current ( u) [ Tang et al., � � � � 2 0 0 8 ] ω = − ⋅ ( | , ) tanh( ) where k d u g k k d k u 0 Shallow w ater gravity w ave dispersion equation
First Depth Inversion With X- -band Radar band Radar First Depth Inversion With X 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 Dw ell tim e Paper used ( sec) From Piotrow ski From Piotrow ski and Dugan, 2 0 0 2 Hoogeboom 1 0 0 and Dugan, 2 0 0 2 et al., 1 9 8 6 Dugan et al. 7 0 1 9 9 6 Bell, 1 9 9 9 1 6 0 Dugan, 1 2 8 2 0 0 0
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 Dw ell tim e Paper used ( sec) This plot is from This plot is from Hoogeboom 1 0 0 Piotrow ski and Piotrow ski and et al., 1 9 8 6 Dugan, 2 0 0 2 Dugan, 2 0 0 2 Dugan et al. 7 0 1 9 9 6 Bell, 1 9 9 9 1 6 0 Dugan, 1 2 8 2 0 0 0 This paper 1 0
Reformulated with 2D Fourier Transforms Reformulated with 2D Fourier Transforms � 2 D Fourier transform s = ℑ ( ) [ ] F k S of im age S1 , S2 , … 2 n n Least-square solution � 2 − 1 N ∑ ∑ for depth ( d) and = − Φ argmin ( ) J W k F F � Δ + current ( u) using N , 1 d u n n N ≥ = , 1 2 k k n im ages, x y 2 D FT of im age n+ 1 2 D FT of im age n propagated to tim e n+ 1 � � ± ω τ Propagation kernel for Φ ≡ 0 ( , | , ) i k k d u ( , | , ) . where k k d u e x y linear gravity w aves ± x y
Simulation with P- -M Wave Spectrum M Wave Spectrum Simulation with P Propagated At 7m depth Propagated At 7m depth N = 2 � 2 − 1 N ∑ ∑ = − Φ ( ) ( ) J d W k F F Δ + n 1 n = k , k n 1 x y � 2 N ∑ ∑ = Φ − n ( ) ( ) J d W k F ∏ n = , 1 k k n x y
X- -Band Radar Test Data Band Radar Test Data X 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- -Band Radar Bathymetry Band Radar Bathymetry X Bathym etry w ith T = 1 0 s T = 8 1 s
Depth vs. Cross- -Shore Distance Shore Distance Depth vs. Cross Historical Duck depth profile Joint Density Function T = 1 0 s T = 8 1 s
Depth Error vs. Dwell Time (at 7 m depth) Depth Error vs. Dwell Time (at 7 m depth) [ Piotrow ski and [ Piotrow ski and Dugan, 2 0 0 2 ] Dugan, 2 0 0 2 ] Results using 2 D algorithm on Duck pier radar data
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
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