International Journal of Antennas and Propagation

Volume 2015, Article ID 815913, 8 pages

http://dx.doi.org/10.1155/2015/815913

## The Fast Simulation of Scattering Characteristics from a Simplified Time Varying Sea Surface

^{1}School of Physics and Optoelectronic Engineering, Xidian University, Xi’an 710071, China^{2}State Key Laboratory of Integrated Services Networks, Xidian University, Xi’an 710071, China

Received 29 December 2014; Revised 2 April 2015; Accepted 7 April 2015

Academic Editor: Claudio Curcio

Copyright © 2015 Yiwen Wei et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

This paper aims at applying a simplified sea surface model into the physical optics (PO) method to accelerate the scattering calculation from 1D time varying sea surface. To reduce the number of the segments and make further improvement on the efficiency of PO method, a simplified sea surface is proposed. In this simplified sea surface, the geometry of long waves is locally approximated by tilted facets that are much longer than the electromagnetic wavelength. The capillary waves are considered to be sinusoidal line superimposing on the long waves. The wavenumber of the sinusoidal waves is supposed to satisfy the resonant condition of Bragg waves which is dominant in all the scattered short wave components. Since the capillary wave is periodical within one facet, an analytical integration of the PO term can be performed. The backscattering coefficient obtained from a simplified sea surface model agrees well with that obtained from a realistic sea surface. The Doppler shifts and width also agree well with the realistic model since the capillary waves are taken into consideration. The good agreements indicate that the simplified model is reasonable and valid in predicting both the scattering coefficients and the Doppler spectra.

#### 1. Introduction

The calculation of electromagnetic (EM) scattering from a time varying surface is important in many fields such as radar surveillance, target tracking, and ocean remote sensing [1]. Useful techniques have already been developed to provide realistic results. They can be based on exact numerical methods (MoM, FEM, FDTD, and so on [2–5]) or approximate approaches [6]. Because numerical methods are unfortunately not efficient, the approximate approaches are widely used for the moment to calculate the scattered field from a large time varying surface. Among them, PO [7, 8] is most employed because it is simple and easy to implement.

However, the PO method is still limited by the number of unknowns when dealing with large time varying sea surface. When dealing with the scattering problem form the sea, it should be noted that the sea surface should be divided into small segments whose length of each segment on the realistic sea surface should be 1/8~1/10 wavelength of the incident wave to accurately reflect the geometry characteristics of the sea. Since each segment is that small, the number of the segments form the realistic sea surface will be very large. To reduce the number of segments, one can divide the sea surface into larger segments. However, the larger the segment is, the more inaccuracy will be shown in the scattering coefficient and Doppler spectrum. The inaccurate results may be caused by two reasons. Firstly, the phase difference on one segment will be neglected in this case. This will lead to the inaccuracy of the integration on each segment. Secondly, the capillary waves superimposed on each segment are not taken into consideration. This will cause the fact that the Doppler value in some spectrum regions cannot be detected by the radar. Since the segment cannot be larger than 1/8~1/10 wavelength, the number of the unknowns will be tremendous especially when dealing with time varying large sea surface, which will limit the efficiency of PO method.

In order to get accurate results with larger segments, as well as promote the efficiency of conventional PO method, we add capillary waves [9]. The capillary wave considered to be sinusoidal line superimposing on each segment. The wavenumbers of the sinusoidal waves are supposed to satisfy the resonant condition of Bragg waves which are predominant in the scattered short wave component. In this way, we substitute the simplified sea surface for the realistic sea surface approximately. Since the capillary wave is periodical within one facet, the analytical expression of the induced currents can be given after we get the currents on the first period of the sinusoidal wave.

This paper is organized as follows. In Section 2, the PO method is introduced and applied on the simplified sea surface model. All the formulas are derived and all the expressions are given in this part; both horizontal (HH) polarization and vertical (VV) polarizations are considered. Several numerical simulations are exhibited in Section 3 to show the validity and efficiency of the new model compared with the realistic sea surface. Then, this model is used to investigate the characteristic of the Doppler spectrum of time varying sea surface. Section 4 ends with a summary of the new model and a proposition for further pertinent investigation.

#### 2. Formula

##### 2.1. The Physical Optics Formulation

The initial point of physical optics is the surface currents produced by an incoming electromagnetic wave (). Considering a 1D sea surface, the induced electric currents and magnetic currents on each segment (the length of each segment is set as 1/8~1/10 wavelength of the incident wave to meet the division criterion) are given by where is the unit normal vector of the surface and indicates the position of each segment. and are, respectively, the total electric and magnetic fields at the surface. For TE case, the horizontal polarization vector of the incident wave is along , is the wavenumber of the incident wave, and the vertical polarization vector is . The scattering problems in the global coordinate system and the local coordinate system are shown in Figures 1(a) and 1(b), respectively. Given the slop of one segment, the local coordinate system can be built as , and each coordinate component can be expressed as