Observations and modeling of angular compression and spatial coherence in sea surface forward scattering Peter H. Dahl Applied Physics Laboratory and Mechanical Engineering Dept. University of Washington Seattle, Washington, USA Spatial coherence in forward scattering from single (time resolved) interaction with sea surface from Shallow Water 06 Environment: Wind speed ~ 6 m/s, Waveheight ~ 0.15 m, stationary > 6 h Comparative influence of sea surface C(Z) [thermocline] Research sponsored by U.S. Office of Naval Research
Experimental site: off the New Jersey Continental Shelf, Water Depth 80 m Shallow Water 06 (SW06) August 2006 Moored Receiver Acoustic Source & Data Telemetry 200m R/V Knorr 25 m 40m 50 m 80m
August 10 2006 measurements: R/V Knorr holds station at four source locations each at range 200 m from the receiver and separated in bearing angle by 90 o Time: 0830-1500 UTC Receiver moored here R/V Knorr 200m 25 m 40m 80m 50 m Two, time resolved surface bounce paths studied
0 10 20 Derived from WHOI Shark Temperature 30 mooring 15 min avg. 0830 UTC Depth (m) Derived from WHOI Shark Temperature 40 mooring 15 min avg. 1330 UTC R/V Knorr CTD cast 1107 UTC 50 60 70 80 1490 1500 1510 1520 1530 1540 Sound Speed (m/s)
upper receiver eigenrays and corresponding arrival structure complex envelope 5 for i th ping x i 0 RELATIVE LEVEL (dB) - 5 20-ping avg - 1 0 - 1 5 - 2 0 - 2 5 - 3 0 Surface Bott-Surf Surf-Bott - 3 5 Direct Bottom - 4 0 0 1 0 2 0 3 0 4 0 5 0 6 0 RELATIVE TIME (ms)
Moored Receiver Spatial coherence between (d) vertically-separated x channels based on 20 ping avg 0.2 m * xy 25 m Γ xy = y 0.3 m * * xx yy 50 m 4 receiver pairs and frequency (k) 0.9 m 6 combinations of kd
Average air-sea conditions for 0830-1500 UTC. Wind speed 6 m/s +/- 1 m/s 0 160 o WAVE DIRECTION FROM (deg) 220 o 100 APL-UW wave buoy 200 300 0.1 0.2 0.3 0.4 0.5 0.6 FREQUENCY (Hz) 0 10 APL-UW 2 /Hz SPECTRAL DENSITY m wave buoy -1 10 (loan from ARL-PSU) -2 10 0.12 Hz 0.34 Hz -3 10 0.1 0.2 0.3 0.4 0.5 0.6 U. Miami FREQUENCY (Hz) ASIS buoy
~0.34 Hz wind waves 300 o 1035 UTC from 220 o 14 U Miami Shark AUG 10 1000 m 500 m 10 6 2 1000 m 210 o 030 o 15 11 7 3 1 5 9 13 A2 M 1215 UTC 0835 UTC 4 8 12 16 120 o 1445 UTC ~0.12 Hz swell from 160 o
Absolute value of vertical coherence vs normalized separation (kd) at 16 kHz 1 Bearing 210 0.9 Bearing 120 0.8 Bearing 030 0.7 Bearing 300 0.6 | Γ | (n=20) 0.5 0.4 0.3 0.2 0.1 0 0 20 40 60 80 100 kd
Absolute value of vertical coherence vs normalized separation (kd) at 16 kHz 1 Bearing 210 0.9 Bearing 120 0.8 Bearing 030 0.7 Bearing 300 0.6 | Γ | 0.5 (n=80) 0.4 0.3 0.2 0.1 0 0 20 40 60 80 100 kd
Modeling of coherence will proceed with directional-averaged 2 sea surface wavenumber spectrum F(K) 10 Buoy 0 10 Combination used in -2 bistatic scattering computation 10 F(K) (m 4 ) -4 10 Plant model -6 10 6 m/s, 20000 m fetch (Plant 2002) -8 10 -2 -1 0 1 2 10 10 10 10 10 WAVE NUMBER K (radian/m)
PDF for vertical arrival angle sea surface bistatic cross section via small slope approximation & wave number spectrum F(K) (Dahl, 1999) θ Α RECEIVER region producing same θ Α SOURCE
iso-speed analysis 200m 25 m 9 40m 50 m 8 7 PROBABILITY DENSITY FUNCTION 6 mean vertical arrival angle close to specular angle ~18 o 5 Variance = 0.0078 rad 2 4 3 2 1 0 0 5 10 15 20 25 30 35 40 45 50 VERTICAL ARRIVAL ANGLE (deg)
Analysis using measured c(z) with thermocline 9 c(z) 8 7 PROBABILITY DENSITY FUNCTION 6 c o c(z) 5 mean: 18 o 21 o 4 Variance: 0.0078 rad 2 0.0042 rad 2 iso-speed 3 c o 2 1 0 0 5 10 15 20 25 30 35 40 45 50 VERTICAL ARRIVAL ANGLE (deg)
The PDF for vertical arrival angle is readily converted to spatial coherence Γ (kd) Alternatively, the van Cittert-Zernike Theorem can utilized to estimate Γ (kd) (Dahl 2002, 2004) kd* for c(z) ~ 21 kd* for c 0 ~ 14 define kd* as | Γ | at exp(-1/2) − Γ = 1 / 2 e
Range of magnitude coherence for modeled spectrum: 4 – 10 m/s 1 Refraction conditions of SW06 0.9 0.8 Range of magnitude coherence for modeled spectrum: 4 – 10 m/s 0.7 Iso-speed conditions 0.6 | Γ | 0.5 0.4 4 m/s 10 m/s 0.3 0.2 4 m/s 10 m/s 0.1 0 0 10 20 30 40 50 60 70 80 kd
C=1530 m/s θ S n = 1485/1530 − θ = θ cos 1 ( n cos ) A S θ A C=1485 m/s f is a smooth function relating surface-to-arrival angle ∴ ∂ f θ ≈ θ 2 var( ) ( | ) var( ) A θ S ∂ θ S S − θ n sin( ) S 2 cos Vertical angular compression factor − θ 2 1 n S
Vertical Angular Compression Large change in kd* predicted by the angular compression factor ⇒ ↑ Compression does not intensity SW06 geometry: TL increased by 1.5 dB (confirmed by ray and PE analysis) θ n sin( ) σ * σ = σ kd ~ 1 / S θ 2 cos θ θ A − θ 2 A A 1 n iso-speed SW06 S ∴ ↑ * thermocline kd should by ~ 4/3 0.72
Model comparison with data (14-16-18-20 kHz) plotted verus kd Re Γ and | Γ | for SWO6 measured 1 sea surface conditions and c(z) 0.8 Re Γ and | Γ | for SWO6 measured sea surface conditions and iso-speed c o 0.6 0.4 Re Γ AND | Γ | 0.2 0 -0.2 -0.4 -0.6 -0.8 -1 0 10 20 30 40 50 60 70 80 kd
Summary •Spatial coherence in sea surface forward scattering with strong thermocline •Vertical angular compression: dominate effect greater than that linked to sea surface roughness and slope •Vertical angles compressed while TL increased over spherical spreading (angle expansion in upward paths not balanced by downward paths) •Mild refraction effects (influencing phase of Γ ) observed in ASIAEX data (Dahl 2004) SWO6 : strong refraction effects influencing both magnitude and phase •Predictive model based on Snell’s mapping of angular variances
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