Composite Model and Hydrodynamic Modulation in .NET

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Composite Model and Hydrodynamic Modulation
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In studying the electromagnetic wave interactions with ocean waves, a customary way is to divide the spectrum given by W(k, ) into large-scale waves and small-scale waves. To do that, one has to define a two-scale cutoff kd
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Wl(k, </J) = {:(k, </J)
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if k < kd otherwise if k < kd otherwise
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(4.8.27)
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Ws(k, </J) = {
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~(k, </J)
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where WI denotes the large-scale spectrum and W s denotes the small-scale waves. The cutoff kd is dependent on the frequency of the electromagnetic Wave because large-scale or small-scale is from the point of view of the wavelength of the electromagnetic wave. Thus kd is not an intrinsic parameter of the ocean but is instead a parameter used in electromagnetic scattering. For a particular electromagnetic wave frequency, the results of scattering and emission should not be too dependent on the choice of kd for the electromagnetic model to be useful. Let q be the correlation function of the large-scale roughness (4.8.29) The variance of the slope in the x and y directions are, respectively,
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dk y k; Wl(k x, k y )
(4.8.31) and let Sy = respectively, (4.8.32)
</J Wl(k, </J)
ft(x, y) be the large-scale height function, let Sx = aft/ax, aft!ay; then the correlation functions of height and slope are,
(f1(X, y)fl(X', y')} = a 2q(x - x', y - y')
given by
4 CHARACTERISTICS OF DISCRETE SCATTERERS AND ROUGH SURFACES
if Wl(k, ) depends on cosm only. The joint probability density function of the slope of the large-scale structure is
p(sx, Sy)
1r(J Sx (J Sy
(s2 - -+ --f
(J Sx (J Sy
s2 )
(4.8.34)
The hydrodynamic modulation creates short scales that are more concentrated on the leeward faces of large-scale waves. A hydrodynamic smallscale spectrum W;h)(k, ,sx) is thus used instead of Ws(k, ). The relation is [Yueh, 1997]
(4.8.35)
where
0.5 sgn(sx)
::x I > 1.25
(4.8.36)
1- 0.4 2
a sx
if 12 \ S a
where sgn( sx) = 1 if Sx is positive and sgn( sx) = -1 if Sx is negative. This h h gives a larger ) when Sx is negative, and it gives a smaller ) when Sx is positive giving stronger ripple on the leeward side of large waves. The introduction of hydrodynamic modulation further adds asymmetry to the ocean surface.
REFERENCES
REFERENCES AND ADDITIONAL READINGS
Ambach, W. and A. Denoth (1980), The dielectric behavior of snow:a study versus liquid water content, NASA Workshop on the Microwave Remote Sensing of Snowpack Properties, NASA CP-2153, Ft. Collins, Colorado. Apel, J. R. (1994), An improved model of the ocean surface wave vector spectrum and its effects on radar backscatter, J. Geophys. Res., 99, 16269-16291. Battan,L. J. (1973), Radar Observation of the Atmosphere, Univ. of Chicago Press, Chicago, 11. Blanchard, D. C. (1972), Bentley and Lenard: Pioneers in cloud physics, Am. Sci., 60, 746. Bottcher, C. J. F. (1952), Theory of Electric Polarization, Elsevier, Amsterdam. Chu, T. S. and D. C. Hogg (1968), Effects of precipitation on propagation at 0.63, 3.5 and 10.6 microns, Bell System Tech. J., 47, 723-759. Colbeck, S. C. (1972), A theory of water percolation in snow, J. Glaciology, 11, 369-385. Colbeck, S. C. (1979), Grain clusters in wet snow, J. Colloid Interface Sci., 72, 371-384. Colbeck, S. C. (1982), The geometry and permittivity of snow at high frequencies, J. Appl. Phys., 20, 45-61. Cox, C. S. and W. H. Munk (1954), Measurement of the roughness of the sea from photographs of the sun's glitter, J. Opt. Soc. Am., 44, 838-850. Cox, G. F. N. and W. F. Weeks (1983), Equations for determining the gas and brine volumes in sea-ice samples, Journal of Glaciology, 29,306-316. Cumming, W. A. (1952), The dielectric properties of ice and snow at 3.2 cm, J. Appl. Phys., 23, 768-773. de Loor, G. P. (1968), Dielectric properties of heterogeneous mixtures containing water, J. Microwave Power, 3,67-73. Durden, S. 1. and J. F. Vesecky (1985), A physical radar cross-section model for a wind driven sea with swell, IEEE J. Ocean. Eng., 10, 445-451. Evans, S. (1965), Dielectric properties of ice and snow ~ a review, Journal of Glaciology, 5, 773-792. Frankenstein, G. E. and R. Garner (1967), Equations for determining the brine volume of sea ice from -0.5 to -22.9 , Journal of Glaciology, 6, 943-944. Fraser, K. S., N. E. Gaut, E. C. Geifenstein, II, and H. Sievering (1975), Interaction mechanisms ~ within the atmosphere, Manual of Remote Sensing, I, R. G. Reeves, Ed., 5, 207-210, American Society of Photogrammetry, Falls Church, Virginia. Fung, A. K. (1994), Microwave Scattering and Emission Models and Their Applications, Artech House, Norwood, Massachusetts. Fung, A. K. and K. K. Lee (1982), A semi-empirical sea spectrum model for scattering coefficient estimation, IEEE J. Ocean. Eng., 7, 166-176. Fung, A. K. and F. T. Ulaby (1978), A scatter model for leafy vegetation, IEEE Trans. Geosci. Electronics, 16, 281-285. Gradshteyn, I. S. and I. M. Ryzhik (1980), Table of Integrals, Series, and Products, Academic Press, New York. Havelka, U. D. (1971), The effect of leaf type, plant density,and row spacing on canopy architecture and plant morphology in grain sorghum, Doctoral Dissertation, Texas A&M University, College Station, Texas. Lane, J. and J. Saxton (1952), Dielectric dispersion in pure liquids at very high radio frequencies, Proc. Roy. Soc., A213, 400-408.