[1] Multiscale composite models based on the Bragg theory are widely used to study the normalized radar cross-section (NRCS) over the sea surface. However, these models are not able to correctly reproduce the NRCS in all configurations and wind wave conditions. We have developed a physical model that takes into account, not only the Bragg mechanism, but also the non-Bragg scattering mechanism associated with wave breaking. A single model was built to explain on the same physical basis both the background behavior of the NRCS and the wave radar Modulation Transfer Function (MTF) at HH and VV polarization. The NRCS is assumed to be the sum of a Bragg part (two-scale model) and of a non-Bragg part. The description of the sea surface is based on the short wind wave spectrum (wavelength from few millimeters to few meters) developed by Kudryavtsev et al. [1999] and wave breaking statistics proposed by Phillips [1985]. We assume that non-Bragg scattering is supported by quasi-specular reflection from very rough wave breaking patterns and that the overall contribution is proportional to the white cap coverage of the surface. A comparison of the model NRCS with observations is presented. We show that neither pure Bragg nor composite Bragg model is able to reproduce observed feature of the sea surface NRCS in a wide range of radar frequencies, wind speeds, and incidence and azimuth angles. The introduction of the non-Bragg part in the model gives an improved agreement with observations. In Part 2, we extend the model to the wave radar MTF problem.

[1] A new radar imaging model of ocean current features is proposed. The simulated normalized radar cross section (NRCS) takes into account scattering from ''regular'' surfaces (by means of resonant Bragg scattering and specular reflections) and scattering from breaking waves. The description of background wind waves and their transformation in nonuniform medium is based on solution of the wave action conservation equation. Wave breaking plays a key role in the radar imaging model. Breaking waves scatter radio waves (thus directly contributing to the NRCS), provide energy dissipation in wind waves (thus defining the wave spectrum of intermediate scale waves), and generate short surface waves (thus affecting Bragg scattering). Surface current, surfactants accumulated in the convergence zone, and varying wind field are considered as the main sources for the NRCS manifestations of current features. The latter source can result from transformation of atmospheric boundary layer over the sea surface temperature front. It is shown that modulation of wave breaking significantly influences both radar returns and short wind waves. In the range of short gravity waves related to Ku-X-, and C-bands, the modulation of Bragg waves through wave breaking is the governing mechanism. The model is tested against well-controlled experiments including JOWIP, SARSEX, and CoastWatch-95. A reasonably good agreement between model and observations is obtained.

Abstract. A wind over waves coupling scheme to be used in a coupled wind waves-atmosphere model is described. The approach is based on the conservation of momentum in the marine atmospheric surface boundary layer and allows to relate the sea drag to the properties of the sea surface and the properties of the momentum exchange at the sea surface. Assumptions concerning the local balance of the turbulent kinetic energy production due to the mean and the wave-induced motions, and its dissipation, as well as the local balance between production and dissipation of the mean wave-induced energy allow to reduce the problem to two integral equations: the resistance law above waves and the coupling parameter, which are effectively solved by iterations. To calculate the wave-induced flux, the relation of Plant [1982] for the growth rate parameter is used. However, it is shown by numerical simulations that the local friction velocity rather than the total friction velocity has to be used in this relation, which makes the growth rate parameter dependent on the coupling parameter. It is shown that for light to moderate wind a significant part of the surface stress is supported by viscous drag. This is in good agreement with direct measurements under laboratory conditions. The short gravity and capillary-gravity waves play a significant role in extracting momentum and are strongly coupled with the atmosphere. This fact dictates the use of the coupled short waves-atmosphere model in the description of the energy balance of those waves.

Abstract. A physical model of the short wind wave spectrum in the wavelength range from a few millimeters to few meters is proposed. The spectrum shape results from the solution of the energy spectral density balance equation. Special attention is paid to the description of the capillary range of the short wave spectrum. It is assumed that in this range the spectrum shape is determined mainly by the mechanism of generation of parasitic capillaries. This is described as the cascade energy transfer from the gravity to the capillary waves. Thus the capillary wave spectrum results through the balance between generation of capillaries and their viscous dissipation. The short gravity wave spectrum results through the balance between wind input and dissipation due to wave breaking. A parameterization of wind input is obtained in part i of the present paper. To describe the dissipation due to wave breaking, the approach developed by Phillips [1985] is used. The spectral rate of energy dissipation is presented in the form of a power dependence of the ratio of the saturation spectrum to some threshold level. It is further shown that the threshold level depends on the drift current shift in the water viscous sublayer, which affects the energy losses by wave breaking. To obtain a short wave spectrum which is valid in the whole wavenumber domain, the capillary and the short gravity wave spectra are patched in the vicinity of the wavenumber corresponding to the minimum phase velocity. This short wave spectrum is incorporated into the wind over waves coupled model developed in part i of the present paper. The measured statistical properties of the sea surface related to the short waves, such as the spectral shape of omnidirectional and up-wind spectra, their wind speed dependence and angular spreading, and the wind speed dependence of integral mean square slope and skewness parameters, are well reproduced by the model. Also the model well reproduces the measured wind speed dependence of the drag coefficient and of the coupling parameter.

[1] Previous analysis of Advanced Synthetic Aperture Radar (ASAR) signals collected by ESA's Envisat has demonstrated a very valuable source of high-resolution information, namely, the line-of-sight velocity of the moving ocean surface. This velocity is estimated from a Doppler frequency shift, consistently extracted within the ASAR scenes. The Doppler shift results from the combined action of near surface wind on shorter waves, longer wave motion, wave breaking and surface current. Both kinematic and dynamic properties of the moving ocean surface roughness can therefore be derived from the ASAR observations. The observations are compared to simulations using a radar imaging model extended to

[1] New field measurements of 2-D wave number short wind wave spectra in the wavelength range from few millimeters to few decimeters are reported and discussed. The measurement method is based on stereophotography and image brightness contrast processing. As found, the spectra of decimeter waves are almost isotropic and weakly dependent on the wind speed. Both directional anisotropy and wind sensitivity rapidly increase at wave numbers larger than 100 rad/m. These aspects are consistent with other previously reported optical and radar data. Following these new in situ measurements, a revision of a semiempirical model of short wind wave spectrum is suggested. This revised model can readily be implemented in other studies (radar scattering, air-sea interaction issues) where detailed knowledge of short wind wave spectra is crucial.Citation: Yurovskaya, M. V., V. A. Dulov, B. Chapron, and V. N. Kudryavtsev (2013), Directional short wind wave spectra derived from the sea surface photography,

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