Statistical Properties of Low-Grazing Range-Resolved Sea Surface Backscatter Generated Through Two-Dimensional Direct Numerical Simulations

Statistical properties of the X-band sea clutter are studied using 2-D direct numerical simulations. Surfaces are modeled as realizations of a Gaussian random process with the Pierson-Moskowitz or Elfouhaily spectrum. The Creamer transform is further applied to account for the lowest-order surface nonlinearities. Backscattered field at a given frequency is found using the first-principles boundary integral equation (BIE) technique. Calculations are repeated at a number of frequencies, which allows synthesizing the surface response to a pulse as short as 2.2 ns (the corresponding spatial resolution is 0.33 m). Large-scale Monte Carlo trials are used to evaluate the correlation properties and to obtain the probability distributions for the vertically- and horizontally-polarized clutter. This paper concentrates on the incident angle of 85deg (5deg grazing), with a few results for moderate 60deg incidence also reported for comparison. The effects of variations in wind speed (sea state) and radar resolution on the clutter statistics are investigated. An L-band example (with proportionally longer pulse) helps explore the role of a different electromagnetic (e/m) wavelength. The simulation technique also allows for the isolation and examination of the impacts of certain e/m and hydrodynamic approximations, including the replacement of rigorous solution to the BIE by a simpler analytical scattering model. The amplitude statistics of the simulated backscatter are compared to the Weibull and K distributions that are often used to describe surface clutter

[1]  W. Pierson,et al.  A proposed spectral form for fully developed wind seas based on the similarity theory of S , 1964 .

[2]  Joel T. Johnson,et al.  Radar images of rough surface scattering: comparison of numerical and analytical models , 2002 .

[3]  Bruno O. Shubert,et al.  Random variables and stochastic processes , 1979 .

[4]  Bruce J. West,et al.  A new numerical method for surface hydrodynamics , 1987 .

[5]  D. Thompson,et al.  Application of iterative moment-method solutions to ocean surface radar scattering , 1998 .

[6]  H. Nagaoka Propagation of Short Radio Waves , 1926 .

[7]  Aarnout Brombacher,et al.  Probability... , 2009, Qual. Reliab. Eng. Int..

[8]  C. L. Rino,et al.  Numerical simulation of low-grazing-angle ocean microwave backscatter and its relation to sea spikes , 1998 .

[9]  Mark A. Sletten,et al.  Radar scattering behavior of estuarine outflow plumes , 2004, IEEE Transactions on Geoscience and Remote Sensing.

[10]  Harold Guthart,et al.  Numerical simulation of backscatter from linear and nonlinear ocean surface realizations , 1991 .

[11]  K. Katsaros,et al.  A Unified Directional Spectrum for Long and Short Wind-Driven Waves , 1997 .

[12]  D. Trizna Statistics of low grazing angle radar sea scatter for moderate and fully developed ocean waves , 1991 .

[13]  M. Sletten,et al.  Multipath scattering in ultrawide-band radar sea spikes , 1998 .

[14]  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..

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

[16]  James C. West,et al.  Numerical calculation of electromagnetic scattering from measured wind-roughened water surfaces , 1998 .

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

[18]  James C. West,et al.  Low-grazing scattering from breaking water waves using an impedance boundary MM/GTD approach , 1998 .

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

[20]  J. V. Toporkov,et al.  Simulation of coherent radar backscatter from dynamic sea surfaces , 2003, 2003 User Group Conference. Proceedings.

[21]  Jakov V. Toporkov,et al.  Numerical study of the extended Kirchhoff approach and the lowest order small slope approximation for scattering from ocean-like surfaces: Doppler analysis , 2002 .

[22]  D. Thompson,et al.  Ocean microwave backscatter distributions , 1994 .

[23]  Zhiqin Zhao,et al.  Electromagnetic modeling of multipath scattering from breaking water waves with rough faces , 2002, IEEE Trans. Geosci. Remote. Sens..

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

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

[26]  I. Ostrovsky,et al.  Very high frequency radiowave scattering by a disturbed sea surface Part I: Scattering from a slightly disturbed boundary , 1968 .

[27]  F. Posner,et al.  Spiky sea clutter at high range resolutions and very low grazing angles , 2002 .

[28]  Joel T. Johnson,et al.  On the canonical grid method for two-dimensional scattering problems , 1998 .

[29]  Joel T. Johnson,et al.  A Numerical Study of the Modulation of Short Sea Waves by Longer Waves , 2006, 2006 IEEE International Symposium on Geoscience and Remote Sensing.

[30]  Irene A. Stegun,et al.  Handbook of Mathematical Functions. , 1966 .

[31]  Necip Doganaksoy,et al.  Weibull Models , 2004, Technometrics.

[32]  Leung Tsang,et al.  Monte Carlo simulations of large-scale one-dimensional random rough-surface scattering at near-grazing incidence: Penetrable case , 1998 .

[33]  Joel T. Johnson,et al.  Formulation of forward-backward method using novel spectral acceleration for the modeling of scattering from impedance rough surfaces , 2000, IEEE Trans. Geosci. Remote. Sens..

[34]  Mark A. Sletten,et al.  Radar investigations of breaking water waves at low grazing angles with simultaneous high-speed optical imagery , 2002, IEEE International Geoscience and Remote Sensing Symposium.

[35]  C. Swift,et al.  An improved model for the dielectric constant of sea water at microwave frequencies , 1977, IEEE Journal of Oceanic Engineering.

[36]  Gabriel Soriano,et al.  Doppler Spectra From a Two-Dimensional Ocean Surface at L-Band , 2006, IEEE Transactions on Geoscience and Remote Sensing.

[37]  C. Guérin,et al.  A critical survey of approximate scattering wave theories from random rough surfaces , 2004 .

[38]  Shirley Dex,et al.  JR 旅客販売総合システム(マルス)における運用及び管理について , 1991 .

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

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

[41]  J. Toporkov,et al.  Numerical Study of Low Grazing Range-Resolved Radar Backscatter from the Sea Surface , 2005, 2005 Users Group Conference (DOD-UGC'05).

[42]  G. Brown,et al.  Guest Editorial - Special Issue On Low-grazing-angle Backscatter From Rough Surfaces , 1998 .

[43]  R. D. Chapman,et al.  Doppler Spectra and Backscatter Cross Section Over 45 °-85 ° Incidence , .

[44]  Joel T. Johnson,et al.  Further numerical studies of backscattering from time-evolving nonlinear sea surfaces , 2003, IEEE Trans. Geosci. Remote. Sens..

[45]  I. Ostrovsky,et al.  Very high frequency radiowave scattering by a disturbed sea surface Part II: Scattering from an actual sea surface , 1968 .

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

[47]  James C. West Low-grazing-angle (LGA) sea-spike backscattering from plunging breaker crests , 2002, IEEE Trans. Geosci. Remote. Sens..

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

[49]  D. Wehner High Resolution Radar , 1987 .

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

[51]  Joel T. Johnson,et al.  Time statistics of propagation over the ocean surface: a numerical study , 2000, IEEE Trans. Geosci. Remote. Sens..

[52]  Alexander D. Poularikas,et al.  The handbook of formulas and tables for signal processing , 1998 .

[53]  G. Brown,et al.  Backscattering from a Gaussian-distributed perfectly conducting rough surface , 1978 .

[54]  D. B. da Costa,et al.  Joint statistics for two correlated Weibull variates , 2005, IEEE Antennas and Wireless Propagation Letters.

[55]  Jakov V. Toporkov,et al.  Study of Electromagnetic Scattering from Randomly Rough Ocean-Like Surfaces Using Integral-Equation-Based Numerical Technique , 1998 .

[56]  Athanasios Papoulis,et al.  Probability, Random Variables and Stochastic Processes , 1965 .

[57]  Joel T. Johnson,et al.  Radar image study of simulated breaking waves , 2002, IEEE Trans. Geosci. Remote. Sens..

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

[59]  K. Ward,et al.  Sea clutter: Scattering, the K distribution and radar performance , 2007 .

[60]  E Jakeman,et al.  K-Distributed Noise , 1999 .

[61]  J. Toporkov,et al.  Numerical study of wide-band low-grazing HF clutter from ocean-like surfaces , 2005, 2005 IEEE Antennas and Propagation Society International Symposium.

[62]  D. Thompson,et al.  Comparisons of model predictions for radar backscatter amplitude probability density functions with measurements from SAXON , 1994 .

[63]  Joel T. Johnson,et al.  A numerical study of low-grazing-angle backscatter from ocean-like impedance surfaces with the canonical grid method , 1998 .

[64]  H. Ward Radar reflectivity of land and sea , 1976, Proceedings of the IEEE.