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where Ss is the surface scattering strength (dB), Q the grazing angle (degrees), v the wind speed (knots) and f the frequency (Hz).

Chapman and Scott (1964) later validated these results over the frequency range 0.1-6.4kHz for grazing angle below 80°. Figure 8.2 presents curves computed using Equation (8.2) at several frequencies with wind speed as a parameter.

McDaniel (1993) reviewed recent advances in the physical modeling of monostatic sea-surface reverberation in the frequency range 200 Hz-60 kHz (also see the extensive review by Fortuin, 1970). Three sources of surface reverberation were considered: rough-surface scattering, scattering from resonant bubbles and scattering from bubble clouds (or plumes).

In the absence of subsurface bubbles, rough-surface scattering is adequately explained by the composite-roughness model (e.g. Thorsos, 1990). This model partitions treatment of surface scattering into two regimes according to the wind-wave spectrum: large-scale waves (using the Kirchhoff approximation) and small-scale waves (using a modified Rayleigh

Figure 8.2 Low-frequency scattering strengths of the sea surface (Ss) computed from the empirical expressions given by Chapman and Harris (1962). (Urick, 1983; Principles of Underwater Sound, 3rd edn; reproduced with permission of McGraw-Hill Publishing Company.)

Figure 8.2 Low-frequency scattering strengths of the sea surface (Ss) computed from the empirical expressions given by Chapman and Harris (1962). (Urick, 1983; Principles of Underwater Sound, 3rd edn; reproduced with permission of McGraw-Hill Publishing Company.)

approximation). McDaniel (1993) summarized recent advances in surface reverberation modeling according to acoustic frequency:

High-frequency reverberation (3-25 kHz). Backscattering at grazing angles above 30° is in agreement with rough-surface scattering theories. At lower grazing angles, anomalously higher backscattering strengths are assumed due to scatter from resonant microbubbles. Backscattering in coastal waters is higher (by an order of magnitude) than in the open ocean under similar wind conditions. This effect is attributed, in part, to the greater generation of microbubbles in coastal waters. McDaniel (1993) also observed that many recent backscattering-strength measurements are lower than would be predicted using the Chapman and Harris (1962) empirical model.

Low-frequency reverberation (<1kHz). Anomalous scatter similar to that observed at higher frequencies is evident, apparently due to entrained air. However, the nature of the physical processes governing the scattering at these lower frequencies is not evident from an examination of the available data.

Extensive measurements of low-frequency (70-950 Hz) sea-surface backscat-tering strengths were made during the critical sea test (CST) experiments for grazing angles ranging from 5° to 30°, and for wind speeds ranging from 1.5 to 13.5 m s-1 (Ogden and Erskine, 1994a). Analyses of these measurements revealed several regimes in the frequency-versus-wind speed (f-U) domain corresponding to at least two different scattering mechanisms. Perturbation theory (Thorsos, 1990) was found to provide adequate descriptions of the data at high frequencies for calm seas, and at lower frequencies for all wind speeds, where air-water interface scattering is the dominant mechanism. The Chapman-Harris empirical relationship adequately described surface backscattering for rougher seas at higher frequencies where scattering from bubble clouds is presumed to dominate the scattering process. In the transition region where these two effects are competing, the scattering strengths depended upon the details of the surface and wind characteristics.

Ogden and Erskine (1994a) proposed a formula for computing the total scattering strength at the sea surface (Stotal) as a combination of perturbation theory (Spert) and the Chapman-Harris empirical relationship (Sch):

Spert = 10log10

f 2U4 cos2 0

where Sch is the Chapman-Harris empirical formula (Equation (8.2))

UCH - Upert

This formula is valid for grazing angles (0) less than 40° for wind speeds (U) less than 20 ms-1 (measured at a height of 19.5 m above the sea surface) over the frequency range (f) 50-1,000 Hz.

For practical applications, the algorithm used a minimum wind speed of 2.5 ms-1 since, at lower wind speeds, swell is likely to dominate the scattering process. Also, an arbitrary cutoff of 1° has been specified for the

No CST SUS data available above 13.5ms"

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