Numerical simulation of random rough surface finds wide applications in scientific disciplines, e.g., radar remote sensing of terrain and sea. In scattering simulation of rough surface, not only energy conservation must be ensured, but also, perhaps equally important, the surface inherent properties must be preserved. However, the proper choice of surface and grid sizes that are statistically representative poses a problematic issue. This study applied the entropy measure to determine such parameter settings by examining the relative error of sample entropy associated with roughness parameters and by noticing the fact that a rough surface with certain roughness parameters, including power spectrum density function, must have unique sample entropy. It is found that if the two criteria are met, proper choice of surface length and grid size is attainable to warrant minimum uncertainties of rough surfaces and maximum information content for different roughness spectra density functions under different correlation lengths. The feasibility and superiority of the proposed entropy-based method are validated in terms of minimum error of roughness parameters and also the energy conservation in bistatic scattering coefficients of rough surfaces generated using obtained simulation parameters.

中文翻译：

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用于波浪散射数值模拟的随机粗糙表面的熵测度

随机粗糙表面的数值模拟在科学学科中有着广泛的应用，例如地形和海洋的雷达遥感。在粗糙表面的散射模拟中，不仅必须确保能量守恒，而且，也许同样重要的是，必须保留表面固有特性。然而，正确选择具有统计代表性的表面和网格大小会带来问题。本研究通过检查与粗糙度参数相关的样本熵的相对误差，并注意到具有某些粗糙度参数（包括功率谱密度函数）的粗糙表面必须具有独特的样本熵，从而应用熵测量来确定此类参数设置。发现如果满足这两个条件，可以获得正确选择的表面长度和电网尺寸，以根据不同的相关长度的不同粗糙度谱密度函数保证粗糙表面的最小不确定性和最大信息含量。所提出的基于熵的方法的可行性和优越性在粗糙度参数的最小误差以及使用获得的模拟参数生成的粗糙表面的双基地散射系数的能量守恒方面得到验证。