Numerical study of the extended Kirchhoff approach and the lowest order small slope approximation for scattering from ocean-like surfaces: Doppler analysis

The validity of the lowest order small slope approximation (SSA(1)) and the extended Kirchhoff approach (EKA) (Elfouhaily et al., 1999) has been studied by comparing the Doppler spectra of the backscattered signals predicted by these models to their counterparts from exact integral equation-based numerical simulations. The study is conducted at L and S bands (electromagnetic wavelengths 23 and 10 cm); the rough ocean-like surfaces correspond to the wind speed of 5 m/s and were generated using both linear and nonlinear (Creamer) models. The incidence angle varies from normal to low grazing. Expressions for the two analytical models possess many similarities but contain different incidence/scattering angle-dependent factors. The analysis of the bistatic scattering cross sections predicted by the two models reveals that SSA(1) follows the exact numerical results more closely than the EKA. Moreover, at horizontal polarization the extended Kirchhoff bistatic cross section displays certain anomalies (unlimited growth at grazing scattering angles) that are indicative of the problems with this model. However, in the backscattering direction, the expressions for the two models are identical. Doppler analysis of the backscattered signals shows that in general, the analytical models provide better agreement with the numerical results for smaller incident angles. In addition, the agreement between the models and the exact numerical simulations is always better in the case of vertical polarization for which the analytical models give a satisfactory prediction of the Doppler spectrum for incident angles as large as 85/spl deg/ from the normal for both linear and nonlinear surfaces. For horizontal polarization, the models give increasingly poor predictions of the shape, magnitude, and location of the Doppler spectrum for incident angles in the range from 60/spl deg/ to low grazing. Doppler analysis proves to be a much more precise and sensitive tool in assessing the scattering model's validity than the usual comparison of cross sections.

[1]  Donald E. Barrick,et al.  First-order theory and analysis of MF/HF/VHF scatter from the sea , 1972 .

[2]  G. J. St-Cyr,et al.  A radar ocean imaging model for small to moderate incidence angles , 1986 .

[3]  D. Thompson,et al.  Calculation of radar backscatter modulations from internal waves , 1988 .

[4]  D. Jackson,et al.  The validity of the perturbation approximation for rough surface scattering using a Gaussian roughness spectrum , 1988 .

[5]  E. Thorsos,et al.  Acoustic scattering from a ‘‘Pierson–Moskowitz’’ sea surface , 1989 .

[6]  Dennis B. Creamer,et al.  Improved linear representation of ocean surface waves , 1989, Journal of Fluid Mechanics.

[7]  D. Thompson,et al.  Calculation of Microwave Doppler Spectra from the Ocean Surface with a Time-Dependent Composite Model , 1989 .

[8]  E. Thorsos,et al.  An investigation of the small slope approximation for scattering from rough surfaces. Part I. Theory , 1995 .

[9]  G. Brown,et al.  A new numerical method for rough-surface scattering calculations , 1996 .

[10]  Joel T. Johnson,et al.  A novel acceleration algorithm for the computation of scattering from rough surfaces with the forward‐backward method , 1998 .

[11]  Gary S. Brown,et al.  On the discretization of the integral equation describing scattering by rough conducting surfaces , 1998 .

[12]  Jakov V. Toporkov,et al.  Issues related to the use of a Gaussian-like incident field for low-grazing-angle scattering , 1999 .

[13]  K. L. Beach,et al.  What are the mechanisms for non‐Bragg scattering from water wave surfaces? , 1999 .

[14]  Bertrand Chapron,et al.  A new bistatic model for electromagnetic scattering from perfectly conducting random surfaces , 1999 .

[15]  Analysis of the iterative Kirchhoff approximation for rough surface scattering , 1999, IEEE 1999 International Geoscience and Remote Sensing Symposium. IGARSS'99 (Cat. No.99CH36293).

[16]  Jakov V. Toporkov,et al.  Numerical simulations of scattering from time-varying, randomly rough surfaces , 2000, IEEE Trans. Geosci. Remote. Sens..

[17]  Joel T. Johnson,et al.  A numerical study of backscattering from time-evolving sea surfaces: comparison of hydrodynamic models , 2001, IEEE Trans. Geosci. Remote. Sens..

[18]  Bertrand Chapron,et al.  A new bistatic model for electromagnetic scattering from perfectly conducting random surfaces: numerical evaluation and comparison with SPM , 2001 .