S. Haimov

Sea Spikes at Moderate Incidence and Their Relation to Position on the Waves

Most models of radar backscatter from the sea ignore sea spikes, the nonlinear effects that result in large excursions above the local mean signal. They are strong enough to change the mean scattering level significantly, and they may cause streaks in synthetic aperture radar (SAR) ocean images. A threshold based on short signal excursions above the local mean is used to identify spikes. With this method, spikes can be found in regions of low signal level. An autoregressive spectral method is used to identify the locations of the spikes on the dominant waves. Sample results from Ka-band measurements in the North Sea made during the SAXON-FPN experiment are given. It is shown that spikes can occur anywhere on the dominant wave, although they are most prevalent on the front face.

Calculation of ocean environmental parameters from a Ka-Band scatterometer using the Longuet-Higgins approach

During the SAXON-FPN experiment in the North Sea off the coast of Germany, The University of Kansas operated a 35-GHz FM-CW Vector Slope Gauge (VSG) that simultaneously measured the range to three locations on the ocean surface. This enabled it to determine a time series of wave heights and time series of two orthogonal components of wave slopes. With this information, the wave-height spectrum, the directional spectrum, and the angular width spectrum can be determined. The authors calculate these parameters using the standard pitch-and-roll buoy technique and the VSG data [Longuet-Higgins et al., 1963]. They show simulations to illustrate inherent errors in the VSG measurements. The VSG measures the distance to a point along the radar beam, so the intersection with the surface does not move vertically. This introduces a phase shift in the time series of wave height and slope. Use of the average distance for the three beams to produce a single wave-height time series reduces the phase shift error. However, the slopes depend on differences in separate measurements of each range, so multibeam averages are impossible. In addition, the slope measurement is only a first-order approximation of the true slope, so errors result. Noiseless simulations of VSG performance for a simple ocean surface show that errors in the wave-height time series are relatively small. Similar simulations illustrate the errors in slope. Pitch-and-roll buoys also are subject to errors. The horizontal motion of the buoy must be accounted for, an effect similar to the slant-range errors of the VSG. The diameter of the buoy limits the length of ocean waves that can be accurately measured, a problem present with the VSG because of the finite size and spacing of the beams.<<ETX>>

The tail of sea-surface radar backscatter distribution and its dependence on the long waves

A technique for studying radar sea backscatter modulation and non-Bragg scattering is developed. It is based on simultaneous measurements of the radar backscattered field and the surface elevation from the same location on the sea surface. Instantaneous ocean wave frequencies are determined from the surface elevation using a parametric auto-regressive (AR) model. They are used to calculate the average received power and the radar power distribution tail contribution (sea spikes) with respect to the phase of the long (12- to 150-m) ocean waves. The analysis shows that sea spikes are the result of different non-linear phenomena and are present at every wave location, not only at the crest.

Statistics of radar sea spikes at moderate angles of incidence

The distribution functions for radar backscatter from the sea are important for various detection problems. Sea spikes affect these distributions, and the distributions of the spikes themselves are important. The authors studied distributions from Ka-band radar signals measured in the SAXON experiment. Distributions are bilinear on Weibull paper when modulation due to underlying waves is present, but also when the modulation is removed. The low-energy part of the CDF for power is exponential, but the tail extends to higher signal levels than for exponential. The fact that both modulation and sea spikes extend the distribution makes separation of the effects difficult.<<ETX>>

Comparison of Slope, Wave Height, and Radar Spectra, Slope and Hydrodynamic Modulation of Radar Scatter from the Sea

Description of Ocean waves usually depends on point measurements of wave height. The important vector slope of the ocean must usually be derived either from point measurements and linear assumptions or from pitch-and-roll buoys that cannot be in the radar footprint. We developed a 35-GHz vector slope gaugehat- terometer using a single switched-beam antenna. It can measure three adjacent height profiles of the ocean, from which we can derive two orthogonal components of the slope. We used the vector slope gauge during the SAXON-FFN experiment in November, 1990. Simultaneous measurements of the orthogonal components of the long-wave slopes and the backscattered power permit determination of the relative contribution to the overall modulation of the radar signal by slope modulation and hydrody- namic modulation of Bragg-resonant ripple amplitude.

Ka-band ocean wave/radar modulation transfer function: a comparative study

For radar systems looking at moderate angles of incidence most scattering theories assume that the prime scatterers are ripples. Various mechanisms relate the modulation of radar returned power to the long ocean waves. The most important contributors to the radar-signal modulation for real-aperture radars are the tilt and aero-hydrodynamic modulation. The tilt modulation is a purely geometric effect and can be evaluated from the ocean wave slope. The hydrodynamic modulation that results from the nonuniform distribution of the ripples on the long waves is less well understood. In this paper the authors compare the radar backscatter modulation measured by two different Ka-band radar systems to gain more insight into the modulation process. One system is a Ka-band unmodulated continuous-wave (CW) radar that measured radar cross section at HH and VV polarizations and Doppler frequency. The other is a Ka-band frequency-modulated CW Vector Slope Gauge (VSG) that combines a vertically polarized scatterometer with range measurements at three closely located spots on the surface, thus permitting measurement of surface elevation and two orthogonal components of the 2D wave slope. The modulation transfer function often used to describe radar/ocean interaction, depends on the assumption that the microwave signal power depends linearly on the long-wave slope. If linear wave theory applies, the slope can be extracted from measurements of either the surface elevation or the horizontal component of the orbital velocity.<<ETX>>

Slope and hydrodynamic modulation of radar scatter from the sea

Microwave backscatter from the ocean surface is largely due to Bragg scattering from short surface ripples. Modulation of the signal results from changes in the local angle of incidence as the local slope changes, and from variations in Bragg ripple amplitude. The slope (tilt) modulation can be modeled as a memoryless nonlinear system. The hydrodynamic modulation results from a nonuniform distribution of the amplitude of the small-scale ripples over the large-scale waves. For azimuthally traveling waves the hydrodynamic modulation dominates, while for waves propagating in other directions, both tilt and hydrodynamic modulation are significant. The authors developed a 35-GHz radar vector slope gauge (VSG) to measure the orthogonal components of the surface slopes within the radar footprint. Simultaneous measurements of the surface slope and radar cross section permit determination of the relative contribution of slope and hydrodynamic modulations to the overall fluctuation of the radar signal. The authors present a method for separating effects due to the surface tilting from hydrodynamic effects. They include a sample result based on this approach with data from the SAXON-FPN experiment in November, 1990.<<ETX>>

Comparison of slope-derived and height-derived modulation transfer functions for radar return and ocean waves

Use of a radar vector slope gauge at the SAXON experiment allowed new types of studies of the modulation-transfer function (MTF) between ocean waves and radar signals. The MTF calculated from slopes shows less coherence than that using heights, suggesting flaws in the usual application of linear, long-crested wave theory to MTF determination. In complex situations with multiple wave trains, the slope-derived MTF is related the most to the wave train traveling nearly toward the radar, regardless of wind direction, but coherence is low. This low coherence with slope and phase of the height MTF suggest that cross-wave radar signal modulation is largely hydrodynamic.<<ETX>>

Autoregressive modeling for ocean wave — radar modulation transfer function

The standard technique for computing ocean wave — radar modulation transfer functions (MTFs) depends on nonparametric fast Fourier transform (FFT) methods. In this paper we suggest a new approach applying an autoregressive (AR) parametric spectral estimator. The analysis shows that the two-channel autoregressive model produces smooth estimates of the MTF and permits better frequency resolution than FFT techniques. The feed-across effect inherent in the methods developed to evaluate the multichannel AR coefficients causes a negligible effect on MTF. The AR-based MTF depends weakly on the record length; for steady meteorological conditions the AR model of the MTF for a 2-min data run is comparable with ones calculated using 10 min or more of data. In the same situation the FFT technique is unreliable for records of less than 10 min. The appropriate order of the multichannel AR model can vary without causing significant change in the MTF. In most cases any order between 8 and 16, depending on radar system parameters and meteorological conditions, will give acceptable results.