Near‐nadir, quasi‐specular backscatter data obtained with a 14‐GHz airborne radar altimeter are analyzed in terms of the surface mean square slope (mss) parameter. The raw mss data, derived from a least squares fitting of a ray optical scattering model to the return waveform, show an approximately linear wind speed dependence over the wind speed range of 7–15 m s−1, with a slope of about one half that of the optically determined mss. Further analysis based on a simple two‐scale scattering model indicates that, at the higher wind speeds, ∼20% of this apparent slope signal can be attributed to diffraction from waves shorter than the estimated diffraction limit of ∼0.10 m. The present slope data, as well as slope and other data from a variety of sources, are used to draw inferences on the structure of the high wavenumber portion of the wave spectrum. The data support a directionally integrated model height spectrum consisting of wind speed dependent k−5/2 and classical Phillips' k−3 power law subranges in the range of gravity waves, with a transition between the two subranges occurring around 10 times the peak wavenumber, and a Durden and Vesecky wind speed dependent spectrum in the gravity‐capillary wave range. With a nominal value of the spectral constant Au = 0.002 in the first k−5/2 subrange, this equilibrium spectrum model predicts a mss wind speed dependence that accords with much of the available data at both microwave and optical frequencies.
A microwave radar technique for remotely measuring the vector wave number spectrum of the ocean surface is described. The technique, which employs short‐pulse, noncoherent radars in a conical scan mode near vertical incidence, is shown to be suitable for both aircraft and satellite application. The technique has been validated at 10 km aircraft altitude, where we have found excellent agreement between buoy and radar‐inferred absolute wave height spectra.
Non-Gaussian ocean wave statistics are accounted for in a simple model of the reflection of radar impulses from the sea at near-vertical incidence. In the geometrical optics approximation to microwave backscatter, the impulse response of the sea surface is proportional to the joint probability density function (pdf) of wave height and slope, where the wave height corresponds to the appropriate propagation delay time and the slope satisfies the condition for specular reflection. The joint pdf is calculated according to the theory of Longuet-Higgins (1963) on the distributions of variables in a 'weakly nonlinear' random sea. The long-crested approximation is made, a Phillips wave spectrum is assumed, and the Gram-Charlier series is truncated after skewness terms. It is found that the height and heightslope skewness coefficients bear the ratio 1:2 and that consequently, the impulse response of the sea at vertical incidence is very nearly equal to wave height pdf. The mean of the distribution, however, is not located at true mean water level but is negatively biased in an amount equal to the height skewhess coefficient times the rms wave height. The derived impulse response and conditional cross section versus wave height are in excellent agreement with the Yaplee et al. (1971) observations. It is suggested that the empirically determined and theoretically predicted sea state bias be corrected for in the routine processing of satellite radar altimeter data.
or alternatively, by composite surbe* theory (Brown,1978^ hasiqft, thougl4 the situation is one of specoar reflection, and the Tadar baehacatter problem on be compared to that of sun t observation in the cue whom the sun is anti-parallel to the observer's line of eight.I am concentrating here on small angle, specular backscatter for two rend t One is t. I believe that the p~ mechanisms involved in the reflectivity modulation by Marge waves are simpler than in the case of largeangle Bragg diffraction backscstter. At large angles these is, in add} tion to a purely geometrical tilting effect, a very strong sensitivity of the electmmagnetle (am) MO& ulation to the datails of the hydrodynamic modulation of the centimetric Bragg-diffraetlng wavelets by the atmospheric and large ocean wave flow fields, While the hydrodynamic contribution-to the large-angle reflectivity modulation has been treated theoretically (Alpers and Homelmann,1978;Valenzuela and Wright, 1979), theory is hard premed to deal with the hydrodynamic complexities and actual field observations (Valenzuela and Wright, 1979;Wright et aL, 1980). In the specular scatter regime, however, there is no special sensitivity to a particular small water wavelength. RMhOt, the entire ensemble of water waves is contributing to the population of specularly reflecting facets, (excluding of course those wavelets smaller than the diffraction limit). For this large ensemble of waves, an assumption of Gaussian surface statistics seems to be a reasonable one, at least in the first order of approximation.The second reason for concentrating on the near-vertical is a more practical one. It is desirable to make the nadir angle as small as posbible in order that the radius of the azimuth scan circle on the ocean surface not exceed the distance over which the wave field can be expected to be homogeneous (cf. Fig. 1).We have said that the radars need Not actually image the surface to measure wave spectra. The idea behind the non-imaging radar measurement is simple: we let the broad em phase front on the surface (i.e., broad compared to the correlation scale of the waves) function to isolate or resolve plane Fourier surface contrast waves travelling in (or contrary to) the direction of radar look. The
The directional spectrum of a fully arisen ∼3 m sea as measured by an experimental airborne radar, the NASA Ku‐band radar ocean wave spectrometer (ROWS), is compared to reference pitch‐roll buoy data and to the classical SWOP (stereo wave observation project) spectrum for fully developed conditions. The ROWS spectrum, inferred indirectly from backscattered power measurements at 5‐km altitude, is shown to be in excellent agreement with the buoy spectrum. Specifically, excellent agreement is found between the two nondirectional height spectra, and mean wave directions and directional spreads as functions of frequency. This agreement is found despite certain discrepancies between the radar and buoy angular harmonics which are believed to be due to buoy instrumental effects. A comparison of the ROWS and SWOP spectra shows the two spectra to be very similar, in detailed shape as well as in terms of the gross spreading characteristics. Both spectra are seen to exhibit bimodal structures which accord with the Phillips' resonance mechanism. This observation is thus seen to support Phillips' contention that the SWOP modes were indeed resonance modes, not statistical artifacts.
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