Small-slope predictions of microwave backscatter from the sea surface

McDaniel, Suzanne T.

doi:10.1080/13616670109409789

Cited by 38 publications

(43 citation statements)

References 15 publications

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“…41 of [22]-to obtain spectra consistent with those shown in the figures of [22]. McDaniel [12] also provides an important caveat concerning air-sea interface scattering. She notes that for light wind speeds and radar in the C-and Ku-bands (wavelengths roughly comparable to those associated with underwater acoustic frequencies above 20 kHz-i.e., higher than those being considered here), the small slope approximation using the directional spectrum proposed by reference [22] gives poor agreement for out-of-plane (i.e., azimuthal) V-V scattering from the air-sea interface.…”

Section: Non-isotropic Spectrasupporting

confidence: 48%

“…It was developed by Voronovich in the early 1980s [4,5]. Since then, it has become a widely used and well-developed technique for calculating stochastic cross-sections for scattering from quasi-planar rough interfaces of the sort that occur, for example, on the ocean's airsea interface [6,7,8,9,10,11,12] or ocean bottom [13,14,15,16]. (See Section I of reference [6] for a discussion of how the small slope approximation incorporates largescale tilt.)…”

Section: Background and Motivationmentioning

confidence: 99%

“…Therefore, non-isotropic spectra must sometimes be used. (For an example of the measurement of non-isotropic spectra i As noted by McDaniel [12], an additional factor needs to be inserted on the right-hand side of her Eq. (3.9)-i.e., Eq.…”

Section: Non-isotropic Spectramentioning

confidence: 99%

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Stochastic Cross-Sections Based on the Small Slope Approximation: Theory

Wurmser¹

2005

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Standard Form 298 (Rev. 8-98)Prescribed by ANSI Std. Z39.18Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing this collection of information. The small slope approximation is widely used to model the incoherent scattering cross-section per unit area from stochastic rough interfaces. It consists of an integral multiplied by a prefactor. The prefactor involves a closed-form algebraic expression, but evaluation of the integral is nontrivial. This paper develops tractable methods for evaluating the integral. The rough-surface scenarios considered generally assume spectra that have tails that decrease according to a single specified power law. This assumption is typically valid for the air-sea interface and ocean bottom at frequencies below 10 and 40 kHz respectively. The scenarios involve various tradeoffs, but the most significant tradeoff involves tractability vs broad applicability. In the most tractable scenario, it is assumed that only the isotropic tail of the spectrum is relevant. Alternately, information about the spectral peak and the power-law tail can be used to generate an isotropic "difference spectrum" formed by taking the difference between two power laws. The difference spectrum peak can be sharpened either by grafting it to a decaying exponential at low-wavenumber, or by replacing it entirely with a Pierson-Moskowitz (isotropic) spectrum modified by substituting its exponential factor exp(-a/k^2) with exp (-a/k). The latter spectrum is tractable, and while incorporating very sharp spectral peaks, it is rather inflexible. A typical azimuthal dependence is also considered. REPORT TYPE 1. REPORT DATE (DD-MM-YYYY) TITLE AND SUBTITLE AUTHOR(S) PERFORMING ORGANIZATION REPORT NUMBER PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) SPONSOR / MONITOR'S ACRONYM(S) 9. SPONSORING / MONITORING AGENCY NAME(S) AND ADDRESS(ES) SPONSOR / MONITOR'S REPORT NUMBER(S) UnclassifiedUnclassified Unclassified

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Section: Non-isotropic Spectrasupporting

confidence: 48%

Section: Background and Motivationmentioning

confidence: 99%

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Stochastic Cross-Sections Based on the Small Slope Approximation: Theory

Wurmser¹

2005

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“…The advantage of this model is that it is easily applied. The predictions depend on how the surface is partitioned, and, together with difficulty in establishing the accuracy of the theory, these are the two drawbacks of this model [11]. Recently, Voronovich developed the small-slope approximation (SSA) [12,13], which overcame the above mentioned drawbacks.…”

Section: Introductionmentioning

confidence: 98%

Bistatic scattering from an anisotropic sea surface: Numerical comparison between the first-order SSA and the TSM models

Awada

Ayari

Khenchaf

et al. 2006

Waves in Random and Complex Media

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The first-order small-slope approximation (SSA-1) model is used for numerical predictions of the normalized radar cross section (NRCS) of an anisotropic ocean surface in bistatic configurations for the K u -band radar frequency. The calculations were made by assuming the Elfouhaily et al. surface-height spectrum for fully developed seas. In the forward-backward case, the SSA-1 presents an agreement with the geometric optics limit of the Kirchhoff approximation results in the near-specular directions where it is well known that the last model works well. In the fully bistatic case, SSA-1 numerical results are compared with those of the two-scale model in several configurations as a function of wind speed, wind direction, incident/scattering angles and for co-and cross-polarization states. Good agreement between the two models is noted in the co-and cross-polarization case with a small difference of about 1-2 dB. But in certain configurations, the SSA-1 model tends to overestimate the radar cross section peak behaviour. This irregularity is discussed and interpreted. The main purpose of this paper is to analyse NRCS predictions based on the SSA-1 model in a fully bistatic configuration.

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“…However [32] noticed that an additional term should be added. The spectrum employed in this study is as follows.…”

Section: Appendix a Elfouhaily Spectrummentioning

confidence: 99%

Comparison of the Two-Scale and Three-Scale Models for Bistatic Electromagnetic Scattering From Ocean Surfaces

Luo¹,

Du²

2013

PIER

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Abstract-With rapid development of satellite technology in monitoring the ocean, a good understanding of the physical processes involved in the electromagnetic ocean-surface interaction is required. The composite surface models are usually applied in the analysis of the interaction, hence a systematical check of their region of validity is desirable. Based on a generalized minimal residual procedure which is right preconditioned (GMRES-RP) that we have recently developed which has demonstrated the desirable properties of a numerical algorithm: robust and efficient, in this paper, for bistatic scattering from one dimensional ocean surfaces, we carry out a systematic assessment of the performance of the popular two-scale model and the advanced three-scale model under different conditions of ocean surface wind speeds, polarizations, frequencies, and incidence angles. It is found that the two-scale model in general captures the bistatic scattering pattern, yet the accuracy of geometrical optics (GO) for the large scale wave brings considerable impact on the overall accuracy. If the evaluation of the contribution of the large scale wave is instead using direct numerical integration for the corresponding Kirchhoff integral, impressive improvements are frequently observed, especially at low frequency (L and C bands) and low wind speed (3 m/s). But care should be taken when apply two-scale method with numerical integration, since there are cases where visible discrepancy with method of moment (MoM) are observed. On the other hand, the threescale model is found in very good agreement with MoM across the considered ocean surface wind speeds, polarizations, frequencies, and incidence angles, hence represents a much advanced model over the two-scale model.

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Small-slope predictions of microwave backscatter from the sea surface

Cited by 38 publications

References 15 publications

Stochastic Cross-Sections Based on the Small Slope Approximation: Theory

Stochastic Cross-Sections Based on the Small Slope Approximation: Theory

Bistatic scattering from an anisotropic sea surface: Numerical comparison between the first-order SSA and the TSM models

Comparison of the Two-Scale and Three-Scale Models for Bistatic Electromagnetic Scattering From Ocean Surfaces

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