The Mean-Square Slope of Ocean Surface Waves and Its Effects on Radar Backscatter

Yuguang Liu College of Marine Studies, University of Delaware, Newark, Delaware

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Ming-Yang Su Oceanography Division, Naval Research Laboratory, Stennis Space Center, Mississippi

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Xiao-Hai Yan College of Marine Studies, University of Delaware, Newark, Delaware

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W. Timothy Liu Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California

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Abstract

The mean-square slope (MSS) of the sea surface for upwind and crosswind is derived, based on Phillips’ equilibrium spectrum and the model herein on gravity–capillary wave spectrum. The MSS integrated from the above two spectra over high-frequency dissipation length (1 mm) fits the optical observations very well. The radar backscatter cross section (RBCS), calculated from specular reflection theory using the Ku-band filtered MSS, is in keeping with the empirically based Ku-band models by Brown for the GEOS-3 13.9-GHz altimeter, and by Witter and Chelton for the Geosat 13.5-GHz altimeter. Also, the RBCS, calculated using the C-band filtered MSS, is in keeping with the ERS-1/-2 scatterometer empirically based algorithms CMOD3 and CMOD4.

The physics included in this model on gravity–capillary wave spectrum is also illustrated. The short-wave dissipation due to wave–drift interactions has the effect of suppressing the spectral density at high wind condition, which further influences the directional spreading rate. This effect can be denoted by c2/U210 or c2/c2p dependence of short-wave spectrum. It is suggested that the kp/k dependence observed in the range of gravity waves should not be extended to the region of short waves. The parasitic capillary wave dissipation due to molecular viscosity can be balanced by the energy supply from the underlying waves, hence it is removed from the model. The eddy viscosity is due to turbulence at the wind-drift layer, which suppresses the spectrum of high-frequency waves with wavelengths on the order of millimeters.

Corresponding author address: Dr. Yuguang Liu, College of Marine Studies, University of Delaware, Newark, DE 19716.

Email: yuguang@newark.cms.udel.edu

Abstract

The mean-square slope (MSS) of the sea surface for upwind and crosswind is derived, based on Phillips’ equilibrium spectrum and the model herein on gravity–capillary wave spectrum. The MSS integrated from the above two spectra over high-frequency dissipation length (1 mm) fits the optical observations very well. The radar backscatter cross section (RBCS), calculated from specular reflection theory using the Ku-band filtered MSS, is in keeping with the empirically based Ku-band models by Brown for the GEOS-3 13.9-GHz altimeter, and by Witter and Chelton for the Geosat 13.5-GHz altimeter. Also, the RBCS, calculated using the C-band filtered MSS, is in keeping with the ERS-1/-2 scatterometer empirically based algorithms CMOD3 and CMOD4.

The physics included in this model on gravity–capillary wave spectrum is also illustrated. The short-wave dissipation due to wave–drift interactions has the effect of suppressing the spectral density at high wind condition, which further influences the directional spreading rate. This effect can be denoted by c2/U210 or c2/c2p dependence of short-wave spectrum. It is suggested that the kp/k dependence observed in the range of gravity waves should not be extended to the region of short waves. The parasitic capillary wave dissipation due to molecular viscosity can be balanced by the energy supply from the underlying waves, hence it is removed from the model. The eddy viscosity is due to turbulence at the wind-drift layer, which suppresses the spectrum of high-frequency waves with wavelengths on the order of millimeters.

Corresponding author address: Dr. Yuguang Liu, College of Marine Studies, University of Delaware, Newark, DE 19716.

Email: yuguang@newark.cms.udel.edu

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