Mathematical Models for Combined Refraction-Diffraction of Waves on Non-Uniform Current and Depth

Two mathematical models for combined refraction-diffraction of regular and irregular waves on non-uniform current in water of slowly varying topography are presented in this paper. Model I is derived by wave theory and variational principle separately. It has two kinds of expressions including the dissipation term. Model n is based on the energy conservation equation with energy flux through the wave crest lines in orthogonal curvilinear coordinates and the wave kinematic conservation equation. The analysis and comparison and special cases of these two models are also given.     

东中国海HYCOM模式垂向坐标对比研究

基于挪威南森环境遥感中心改进的NERSC-HYCOM 模式, 利用单向嵌套技术与欧洲中心提供的2008 年ERA-I 高分辨率强迫场针对东中国海及其邻近海区进行了不同垂向坐标配置的四个敏感性试验。通过分析东中国海区域的温度、盐度, 流速的分布和变化, 探讨了HYCOM 模式中不同垂向坐标设置对东中国海近岸区域的影响以及黑潮流速及路径对不同坐标设置的响应, 期望对HYCOM 模式更深入的研究提供参考。结果表明: (1)在东中国海区上层并不适于采用等密度坐标方案, 也就是说应该采用z坐标或σ坐标用以表征此处混合层的季节性变化特征; (2)针对东海大陆架区给出了10 个位置上的模式与浮标观测资料的温、盐平均误差(ME)、均方根差(RMS)及相关系数(R)指标, 发现对于不同区域, 每种试验的适用性都不同; (3)使用高频资料时, 模拟的流速普遍偏高, 东海黑潮冬夏路径的异同指出了σ-z-iso 与z-iso 试验模拟效果较好, 但模拟的日本岛南岸的弯曲流场位置偏南; 而z-only 试验模拟的日本岛以南的黑潮路径是有所改观的, z坐标的分辨率对表层的黑潮路径影响很大; σ-only 试验模拟的整个黑潮路径的效果最差。     

排序对模糊度解算中降相关性能的影响分析

针对不同排序算法对模糊度解算存在降相关性能影响的问题,从理论上分析了自然升序法、对称旋转法及扰动升序法的降相关原理,并基于模拟数据和实测数据,从降相关时间、搜索时间、总体耗时、Bootstrapping成功率及条件数5个方面对3种算法进行对比分析。结果表明,降相关效率与搜索椭球压缩程度呈负相关关系,搜索椭球压缩程度越高,降相关效率越低;对于不同的排序算法,提高降相关性能的关键在于减少降相关时间及对条件方差按一定方向排序,进而提高搜索效率。     

Spurious diapycnal mixing in terrain-following coordinate models: The problem and a solution

In this paper, we identify a crucial numerical problem in sigma coordinate models, leading to unacceptable spurious diapycnal mixing. This error is a by-product of recent advances in numerical methods, namely the implementation of high-order diffusive advection schemes. In the case of ROMS, spurious mixing is produced by its third-order upwind advection scheme, but our analysis suggests that all diffusive advection schemes would behave similarly in all sigma models. We show that the common idea that spurious mixing decreases with resolution is generally false. In a coarse-resolution regime, spurious mixing increases as resolution is refined, and may reach its peak value when eddy-driven lateral mixing becomes explicitly resolved. At finer resolution, diffusivities are expected to decrease but with values that only become acceptable at resolutions finer than the kilometer. The solution to this problem requires a specifically designed advection scheme. We propose and validate the RSUP3 scheme, where diffusion is split from advection and is represented by a rotated biharmonic diffusion scheme with flow-dependent hyperdiffusivity satisfying the Peclet constraint. The rotated diffusion operator is designed for numerical stability, which includes improvements of linear stability limits and a clipping method adapted to the sigma-coordinate. Realistic model experiments in a southwest Pacific configuration show that RSUP3 is able to preserve low dispersion and diffusion capabilities of the original third-order upwind scheme, while preserving water mass characteristics. There are residual errors from the rotated diffusion operator, but they remain acceptable. The use of a constant diffusivity rather than the Peclet hyperdiffusivity tends to increase these residual errors which become unacceptable with Laplacian diffusion. Finally, we have left some options open concerning the use of time filters as an alternative to spatial diffusion. A temporal discretization approach to the present problem (including implicit discretization) will be reported in a following paper.     

地心坐标反解大地坐标的非线性方程组牛顿迭代法分析

目前的一些地心坐标向大地坐标的转换模型在计算速度,稳定性或精度方面存在一定的局限性。本文探讨了非线性方程组数值迭代的求解方法及其在MATLAB 7.0中的编程实现,并将结果与基于一元三次方程求解的严密方法做了比较分析,结果证明该方法是可以在实际中参考应用的。     

双重投影在高速铁路测量中的应用分析

针对目前我国高速铁路测量采用的高斯投影独立坐标系每个投影带可控制范围太小,给施工带来很多不便的问题,提出了首先将椭球面经纬度投影至球面后再沿铁路线方向进行斜墨卡托投影的原理、方法和计算步骤,并通过算例分析其在高速铁路测量应用中的可行性,该投影方法与目前施工单位正在使用的高斯投影相比较具有明显的优点。     

图形坐标转换方法与实现

图形坐标转换是CAD和GIS开发与应用的基本问题,涉及基础地理数据标准的统一、共享程度的提高和服务面的拓宽等重要问题,是地图制图输出、基础地理信息系统和专业信息系统建设中的重要功能。本文以CAD和GIS的图形坐标转换与配准为例,介绍了相关的数学模型和实现方法。     

旋转椭球面上的应变与转动张量表达

以旋转椭球体面上某点为原点建立一个大地坐标单位活动坐标架. 通过平移, 使活动坐标架的原点与以椭球中心为原点的笛卡尔单位标架的原点相重合. 然后再通过两次标架旋转, 使活动坐标架与笛卡尔单位标架完全重合. 本文给出了使两个单位标架相重合的转换关系式, 以及该点位移在两个单位标架中的坐标转换式; 在此基础上, 考虑该点的位移及活动坐标架皆为该点大地坐标的函数, 经复杂推导, 分别给出了该点位移向量的微分在大地坐标系中的分量以及该点分别沿坐标曲线的弧微分表达式, 继而导出了该点的位移梯度矩阵; 最后推导出了椭球坐标系的应变张量与转动张量表达式, 并对转动张量的几何含义进行了较详细的解释, 且采用曲面理论对球面与椭球面的应变张量间的内在关系进行了讨论.      

Descriptive statistics for N -dimensional closed arrays: A spherical coordinate approach

Recent publications have demonstrated that the composition of a system can be described by the angles which define the vector resulting from the projection of the composition onto the unit hypersphere. Although published trigonometric relationships allow determination of the angles in any number of dimensions, no general hyperdimensional recursive formulae exist for the calculation of these quantities and their variances and covariances. A general methodology for calculating the angles which describe the compositions of systems in any number of dimensions is presented. These angles can be used to calculate statistics (central moments and resultant vectors) describing the central tendency and dispersion among rock compositions, as well as to quantify the angular differences between compositions. Equations that relate the variances and covariances of these angular variables to the variances and covariances of the actual component proportion variables are presented, allowing projection of these measurements from one reference frame to another (cartesian to spherical and vice versa).