For equilibrium arid near-equilibrium sea states, the Wave.slope variance is a function of wind speed U and of the sea maturity. The influence of both factors on the altimeter measurements of wind speed, wave height, and radar cross section cr ø is studied experimentally. The necessary theoretical background, both on wave statistics and on the near-nadir radar backscatter, is outlined. It is based on a recently proposed view that the effective fractal dimension for a surface patch corresponding to the equilibrium range of wave spectra increases as the wave field matures. The experimental part is based on ! year's worth of Geosat altimeter observations colocated with in situ wind and wave measurements by 20 NOAA buoys. Errors and biases in altimeter wind speed and wave height measurements are investigated. A geophysically significant error trend correlated with the sea maturity (i.e., with Co/U, where Co is the phase velocity of waves corresponding to the spectral peak and U is the mean wind speed well above the surface) is found in wind speed measurements. This trend is explained by examining the effect of the generalized wind fetch, X oc gH•/3/U 2, on the curves of the observed dependence cr ø =f(U, X). We conclude, in particular, that unambiguous measurements of wind speed by altimeter, in a wide range of sea states, are impossible without accounting for the actual degree of wave development. An approach to a more accurate retrieval of wind speeds is suggested as based on accounting for the actual degree of wave development, which can be achieved through processing the total radar cross section simultaneously with the significant wave height information contained in altimeter waveforms. The potential capability of a satellite altimeter to estimate wave age and similar measures of wind-wave coupling is discussed. This capability expands the use of satellite altimeters for air-sea interaction studies. lated with errors in microwave radiometer-and scatterometer-reported winds [Glazman, 1987; Glazman et al., 1988; Glazman and Pilorz, 1989]. An explanation of the error trend in the scatterometer data was proposed based on the notion of a non-Bragg ("spike") component ors ø of the total radar return, cr ø = o'• ø + o'•, arising at oblique incidence. Here o-• ø is due to the Bragg-type scattering from small tipples, while cr• o• o-iv accounts for an impact of wedgelike cusps and breaking wavelets [e.g., Kwoh and Lake, 1984; Glazman et al., 1988]; o 'l represents the mean contribution due to an individual, spike-generating wavelet, and v is the rate of steep wavelet occurrence. This rate is a strong function of the surface slope variance 72 = (IV•r12): v oc 7 -2 exp (-F2/272) where F is the threshold wave steepness causing a radar spike [Glazman, 1985, 1986; Glazrnan et al., 1988; Glazrnan and Welchman, !989]. Since the scales of the spike-producing wavelets pertain to the equilibrium range of the wave spectrum, the rms s16pe •/of these gravity waves is influenced by the degree of wave development. In the case of the a...

The effect of the degree of wave development on the sea state bias (SSB) in Geosat altimeter height measurement is evaluated. Theoretical considerations suggest that the altimetric SSB is generally not a linear function of significant wave height but depends also on other factors of wave development. Of particular interest is its dependence on wave age, defined as the ratio of the phase speed of the dominant ocean waves to ocean wind speed. We estimate wave age rather crudely, on the basis of the significant wave height (H1/3) and wind speed measured by the altimeter. Under general conditions when the sea is not in equilibrium with the wind, this estimate may not correspond to the wave age in a strict sense and hence is called "pseudo wave age" in this paper. Nevertheless, the pseudo wave age is a rough indicator for the degree of wave development. The general trend in the dependence of the SSB on pseudo wave age, as found by analyzing 2.7 years' worth of Geosat data, agrees well with the theoretical prediction: for a given H1/3, the SSB decreases as the degree of the wave develop. ment (measured by the pseudo wave age) increases. This empirical trend is modeled as SSB=A(•m)•HI/3, where s • and S•m are the pseudo wave age and its average value, respectively; A = 0.013 -+ 0.005, and M = -0.88 _+ 0.37. Statistically, this model performs slightly better than a standard model (i.e., SSB = [•H1/3 with • being a constant). In terms of the global rms error the improvement is by 1.6 cm. However, because the degree of wave development varies with the season and geographical location, this small improvement could become important for more accurate altimetric missions in the future when the centimetric, basin-scale signals are the focus of the study.

Statistics of two dimensional wave groups, of steep wave events, and of a cascade pattern manifested in the surface geometry in a developed sea state are derived. However, mathematical theories used to parameterize these as well as many other features of random surfaces have very limited ranges of validity. For example, high-order moments of wave spectra appearing in the calculations of wave slope statistics cannot be evaluated because of divergence of the corresponding integrals. In the present paper the restrictions are reviewed and the difficulties are shown to be due to a pseudo-fractal geometry of the sea surface whose spectrum is known only within a limited range of frequency (characterized by either the resolution of a measuring technique or the constraints of a theoretical model). An approach is presented that solves the problem: treating the surface elevation field as specified on a spatial (temporal) running grid, an averaging procedure is developed employing the Ta_ylor microscale as the mesh size. The technique is illustrated by first exposing errors in direct calculations of the effective surface impedance for a coherently reflected L band radio wave. The errors arise from the use of wave spectra whose highfrequency tail is identified with the Phillips saturation range. The technique is then employed in the study of wave groups and steep waves for a Gaussian, two-dimensional, time-varying surface. In particular, it is found that wave groups are not observable in a developed sea. Finally, the theory is applied to estimating breaking wave statistics. A comparison with field observations is presented.

Recent analyses of wind speed measurements by the Geosat altimeter showed that the radar cross section is affected by oceanographic factors, particularly by the degree of sea development, which are not directly accounted for in the geophysical model functions (GMF). In the present work, two new GMFs which account for the effects of the actual degree of sea development are proposed. Along with the radar cross section, these models use significant wave height information. One particular version is recommended for applications in oceanographic and climate studies where wind speed (or wind stress) data have to be binned (i.e., averaged over time and/or space intervals). The accuracy of this GMF (overall bias of 0.1 m/s and rms error of about 1.6 m/s) is higher than the accuracy of commonly employed GMFs, while the wave-age-related trend is reduced to a geophysically insignificant level. Finally, the wind speed histograms for the collocated data set are derived and compared with the ground truth data as well as with the histograms yielded by presently known GMFs. It is also shown that the accuracy of altimeter measurements could be increased even further if some additional information on the wave field were available from independent sources (e.g., the dominant wavelength from synthetic aperture radar images).

Adsorption films’ mechanical properties are discussed. With regard to a problem of bubble oscillations in a surfactant solution, dynamical boundary conditions at the bubble wall are modified by including a new term to account for a normal force component caused by dilational elasticity of an adsorbed film. Consequently, the Rayleigh–Plesset equation acquires a term which affects the restoring force of bubble oscillations. A linearized theory (for small-magnitude oscillations) is developed which shows that the film dilational elasticity induces a change in the mean radius and a shift in the natural frequency of bubble oscillations. These effects become extremely important when a capillary component 2σ/R0 accounts for at least 20% of the total pressure inside the bubble.