Numerical implementation of local unified models for backscattering from random rough sea surfaces

Abstract

In the context of electromagnetic wave backscattering from ocean-like surfaces, by using the lowest order of the SSA (SSA-1) model, Bourlier et al. proposed an original technique to reduce the number of numerical integrations to two for easier numerical implementation. To be consistent with microwave measurements, closed-form expressions of the Fourier coefficients with respect to the wind direction of the backscattering normalized radar cross-section (NRCS) are obtained. For Gaussian statistics, previous work is extended in this paper to kernels of unified models expanded up to second order, like full SSA and full LCA. Thus, with the help of Bessel functions and by analytical integrations over the azimuthal angles, the secondorder backscattering (BNRCS) is expressed in terms of two-fold integrations and another independent integration instead of four-fold integrations, if no analytical integration is made. This approach allows us to obtain fast results (less than one second). Numerical results are then presented for different microwave frequencies and wind speeds.

Sea Wind Retrieval by Analytically-Based Geophysical Model Functions and Sentinel-1a Sar Images

“…For the Gaussian sea surfaces, the backscattering coefficients of Eq. (4) in the SSA1 can be expressed as [17] σ pq 0 (θ;…”

“…where Q z = q 0 + q k , and −q 0 and q k are the vertical projections of the incident and scattered wave vectors, respectively. B 1 is the first-order Bragg kernel and depends on the scattering geometry and dielectric constant of the medium [17]. J m denotes the Bessel function of the first kind and of order n, and I m denotes the modified Bessel function of the first kind and of order m. k B = 2K 0 sin θ is the Bragg wavenumber (K 0 is free space wavenumber).…”

“…However, these methods are not efficient for electrically large surfaces (high wind speeds). The approximate analytical methods are small perturbation method (SPM) [10,11], Kirchhoff approximation (KA) [10,11], AIEM [12], two-scale model (TSM) [13], and small-slope approximation (SSA) [14][15][16][17][18][19][20]. SPM and KA calculate the scattering of small and large-scale roughness, respectively, while TSM, AIEM and SSA, so-called unified models, describe the scattering of both types.…”

“…Various functions have been proposed in the literature based on in-situ and laboratory measurements for both parts such as the directional spectra proposed by Apel [21], Romeiser et al [22], Elfouhaily et al [23], the omnidirectional spectrum proposed by Hwang et al [24][25][26][27], and the angular spreading function proposed by McDaniel [14]. Elfouhaily spectrum is the most common sea spectrum used for simulating the sea surface scattering in the literature [16][17][18][19]. Hwang spectrum is the newest spectrum for sea waves that includes swell effects on sea roughness.…”

Spectral Decomposition Method for Large Sea Surface Generation and Radar Backscatter Modeling

“…Arguably, this model is relevant due to an easy‐to‐use expression, and it provides accurate results. Indeed, regarding more complex models like the full SSA, the SSA1 model can predict the NRCS with a precision of 1 and 2 dB for the VV and HH polarizations, respectively (Bourlier, ; Bourlier & Pinel, ; McDaniel, ; Voronovich & Zavorotny, ). However, the SDM remains applicable for more complex scattering methods anyways.…”