Sea Surface Microwave Scattering at Extreme Grazing Angle: Numerical Investigation of the Doppler Shift

Abstract

Abstract-We present a numerical investigation of horizontally polarized microwave scattering from 1-D sea surfaces at extreme grazing angles. Rigorous electromagnetic calculations are performed with a specific integral formalism dedicated to grazing angles. Sample sea surfaces are simulated using a classical Pierson-Moskowitz elevation spectrum together with weakly nonlinear hydrodynamic models, namely, the Creamer solution, the "choppy wave model," and a recent improved version thereof. For this, the electromagnetic integral formalism is extended to surfaces with irregular sampling. For the different nonlinear surface models and assuming no large-scale current, we evidence a dramatic increase, followed by a saturation of the mean Doppler shift in the last few grazing degrees, with a limiting value depending quasilinearly on the significant wave height. Our numerical investigations confirm that breaking events are not necessary to produce fast scatterers but tend to show that they are necessary to reproduce the elevated level of backscattered power. The results of this study also support the hypothesis that the blow-up of the mean Doppler shift at grazing angle is associated to an electromagnetic sharp edge effect on the large surface crests rather than geometrical shadowing of the troughs.Index Terms-Doppler effect, method of moments, sea surface.

The Properties of the Electromagnetic Scattering From a Sinusoidal Water Wave

“…Thus, it is necessary to investigate the scattering field from a sinusoidal water wave in order to understand the properties of electromagnetic scattering from sea surface. Up to now, many analytic and numerical methods, such as Kirchhoff approximation (KA), small perturbation method (SPM), and method of moment (MoM), have been developed to evaluate NRCS and Doppler spectrum [1][2][3][4][16][17][18][19][20][21][22][23][24][25] of the electromagnetic scattering from an oceanic surface. Although MoM is an exact numerical method to calculate electromagnetic scattering from rough surface, and the Doppler spectra of the scattering fields from water surfaces can be well simulated by it, the theoretical spectral model cannot be derived directly by MoM.…”

Two‐Dimensional Spectra of Radar Returns From Sea: 2. Analysis of the Group Line From Experimental Data

“…Space‐time series of the backscattered signal have also been generated with a numerical solver based on a rigorous boundary integral formalism Miret, Soriano, Nouguier, et al (). In those simulations, ocean surfaces are described by a Pierson‐Moskowitz spectrum combined with Creamer's approach Creamer et al (), and an analysis of Doppler spectra has been performed Miret, Soriano, and Saillard ().…”

Doppler Spectrum of Scattered Wave From Two-Dimensional Time-Varying Nonlinear Sea Surfaces Under Right-Hand Circularly Polarized Wave Incidence

“…That is, there is a peak separation between HHand V V -polarized Doppler spectra at low-grazing angles. Many efforts have been made to determine its causes by theoretical analysis as well as rigorous numerical simulations [13,17,18]. Among these efforts, to our knowledge, Toporkov et al first demonstrated that HH-and V V -polarized Doppler spectra of linear sea surface model almost overlap and shrink to Bragg frequency at low-grazing angles [13].…”

“…To overcome the drawbacks of linear sea surface model, several nonlinear hydrodynamic models have been proposed, such as Creamer model [19] as well as its simplified version (Creamer model at second-order) [12], choppy wave model (CWM) [20] as well as its improved version (C2WM) [18], West model [21], narrow-band Lagrange model [22], and nonlinear fractal sea surface model [23]. These models have been extensively utilized to better predict Doppler spectra of sea echoes for both 1-D [13,17,18,[22][23][24][25] and 2-D sea surfaces [12,[26][27][28][29] with analytical models or numerical algorithms, in particular for low-grazing case. Not surprisingly, the Doppler spectra obtained by nonlinear sea surface models are more consistent with measurements in comparison with linear sea surface model.…”