Winebrenner and Hasselmann (1988) incorporated geometric-optics specular point scattering into the Hasselmann et al. (1985) model of the mean synthetic aperture radar (SAR) image of the ocean surface, deriving closed-form expressions for the specular reflectivity variance spectrum (RVS), its short coherence time and Doppler offset, the resulting azimuthally smeared and displaced mean specular image, and a strongly nonlinear long-wave tilt modulation of the specular cross section. Their numerical estimates rested on simplified Phillips-type spectra with idealized directional spreading, and their conclusions explicitly state as future work the coupled program that defines this problem: determine under what conditions (incidence angle, wind, spectral directional spreading, currents) specular point scattering significantly contributes to the backscattered signal and measurably alters the total SAR image spectrum, through a coupled investigation of the specular and Bragg RVS with realistic two-dimensional wave spectra, including nonlinear specular-Bragg interactions and harmonic generation, SAR processor focus and bandwidth effects, and the speckle statistics of the specular image, and validate such a model against small-incidence-angle data. The direct successor Monte Carlo studies (Bruening et al. 1990) remained explicitly in the Bragg scattering regime, and later work absorbed pieces of the agenda into adjacent frameworks - non-Bragg (wave-breaking) cross-section and modulation-transfer-function models, empirical non-Gaussian image statistics, small-incidence-angle Doppler-spectrum models, and modern full-link SAR sea-surface simulators - without performing the coupled Bragg-plus-specular image-spectrum quantification with realistic spectra, processor effects, and data validation. The coupled regime quantification and validation for small-incidence-angle SAR therefore remains open.

Background

Synthetic aperture radar (SAR) is a coherent microwave radar that forms high-resolution images of the ocean surface by exploiting the Doppler history of the backscattered signal along the platform track; the along-track (azimuthal) image coordinate is therefore tied to the Doppler frequency of the scatterers. Ocean surface waves imprint on SAR imagery through several mechanisms: modulation of the local backscatter by long-wave tilt and by hydrodynamic interaction with the short resonant waves, and motion effects - long-wave orbital velocities shift the apparent azimuthal position of scatterers (velocity bunching), orbital accelerations defocus the image, and the finite Doppler bandwidth of the moving, decorrelating sea limits the achievable azimuthal resolution. In the theory of Hasselmann et al. (1985), developed from the Marine Remote Sensing (MARSEN) field experiment of 1979 in the North Sea, the ensemble-mean SAR intensity image is expressed as a mapping of the reflectivity variance spectrum (RVS) - the temporal spectrum of the second-order statistics of the complex surface reflectivity - under the assumption that distinct scattering regions are spatially uncorrelated (the spatial whiteness assumption).

Electromagnetically, sea-surface backscatter at moderate incidence angles is dominated by Bragg resonant scattering: constructive interference from ocean wave components whose wavenumber matches the horizontal projection of the radar wavenumber onto the surface (centimeter-scale Bragg waves). Composite (two-scale) roughness theory predicts an additional geometric-optics specular point contribution: mirror-like reflections from facets of the intermediate-scale roughness (wavelengths between the SAR-resolvable scale and the electromagnetic-hydrodynamic partition scale) whose local slope satisfies the specular reflection condition. This contribution grows relative to Bragg scattering as the incidence angle decreases below roughly 20 degrees and under some high-wind conditions.

Winebrenner and Hasselmann (1988) incorporated the specular point mechanism into the Hasselmann et al. (1985) imaging model. For a Gaussian intermediate-scale surface they derived closed-form expressions for the specular RVS - characterized by a short coherence time τs\tau_s (computed as about 0.09 s for Seasat, the 1978 oceanographic satellite carrying the first civilian spaceborne SAR; about 0.11 s for SIR-B, the 1984 Shuttle Imaging Radar-B; and about 0.03 s for a representative airborne X-band SAR) and a mean Doppler offset ωD\omega_D proportional to the mean motion of the specular points - and for the mean SAR intensity image as a superposition of a Bragg image and a specular image. Because specular points move fast and decorrelate quickly, the specular image is azimuthally smeared (azimuthal resolution degraded by factors of order 6.6 for Seasat and 29 for the airborne X-band case), displaced from the true surface by several resolution cells, and often exceeds the SAR processor bandwidth, losing mean intensity. The local specular cross section is modulated by long-wave tilt through a strongly nonlinear exponential factor (about 437 dB per radian of range-directed slope in their SIR-B example at 18 degrees incidence): a 5-degree slope tilted toward the radar raises the local specular cross section from about -48 dB to about -10 dB, exceeding the Bragg return of about -20 dB. Taken together these effects plausibly explain azimuthally oriented streaks observed in Seasat imagery of high-wind areas. The paper concluded that for incidence angles greater than about 15 degrees the specular contribution to the mean image intensity is small, but its contribution to image contrast can be significant at smaller angles, and it stated as future work the coupled program of quantification and validation that defines the present problem. All of its numerical estimates used simplified Phillips-type (∣K⃗∣−4|\vec K|^{-4}) intermediate-scale spectra with idealized cos-squared or isotropic directional spreading and sharp spectral cutoffs. The paper notes that the coupled program of quantification and validation it left open can in principle be pursued with nonlinear Monte Carlo simulation.

Problem Statement

Complete the quantification and validation of specular point scattering effects in SAR imaging of the ocean surface, with the objective stated in the source paper's conclusions: 'to further quantify the conditions (e.g., incidence angle, wind, and current conditions) under which specular point scattering significantly contributes to the backscattered signal and to further quantify imaging conditions under which the SAR image spectrum is affected by this mechanism.' The source enumerates the following further studies that advance these goals:

(1) Coupled investigation with realistic spectra. Investigate the effects of specular point scattering on the total (Bragg plus specular) SAR image spectrum, combining the derived specular reflectivity variance spectrum (RVS) with the Bragg RVS and with realistic, observation-based two-dimensional intermediate- and long-wave spectra (replacing the simplified Phillips-type spectra with idealized directional spreading), in order to determine under what combinations of incidence angle, wind speed, spectral directional spreading, and current conditions specular point scattering measurably alters the total SAR image spectrum, to characterize the resulting image statistics, and to establish the generality of the previously estimated coherence times, Doppler offsets, azimuthal degradation ratios, and modulation depths.

(2) Nonlinear interaction. Quantify the interaction (nonlinear coupling) between the specular and Bragg contributions in the image spectrum, including possible harmonic generation of the dominant ocean wavelength arising from the strong, nonlinear tilt modulation of the specular cross section.

(3) Processor effects. Determine the effects of SAR processor focus adjustments and filter bandwidth choices on the recovery of broadband specular returns, and the speckle statistics of the specular point image.

(4) Validation. The quantification would enable an analytic comparison of the complete imaging model including specular point effects (Bragg plus specular, including tilt, advection, and acceleration) against already-published small-incidence-angle observations under characterized wind and wave conditions; the source suggests that results from the Tower Ocean Wave and Radar Dependence (TOWARD) experiment, which extend to small incidence angles, and small-incidence-angle Seasat/SIR-B imagery should prove useful for such a comparison, so as to assess the theoretical predictions and establish the incidence-angle and processor-bandwidth regimes in which specular-point scattering should be avoided or corrected for when the objective is remote sensing of the ocean surface wave spectrum.

The common objective binding these studies is the regime question - under what conditions does specular point scattering measurably alter SAR ocean wave imagery. The open program comprises the coupled investigation of the total image spectrum with realistic spectra (1), the nonlinear specular-Bragg interaction and harmonic generation (2) it entails, the SAR processor focus, bandwidth, and speckle analysis (3), and the comparison with small-incidence-angle observations (4). The comparison in (4) is an analytic comparison of the model's predictions, and of the incidence-angle and processor-bandwidth regimes it implies, against already-published small-incidence-angle observations, so that no dataset beyond the published literature is required. The source's remaining goals center on the coupled image-spectrum quantification and its consequences for imaging rather than on the isolated recomputation of the coherence time, Doppler offset, degradation ratio, or modulation depth for new wave spectra.

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