A three-dimensional coastal barotropic model in generalized curvilinear grids

INTRODUCTIONThemethodofautomaticallygeneratinggeneralizedcurvilinearmeshesisaneffectivetoolforobtainingnumericalsolutionsofpartialdifferentialequationsinaregionwitharbitraryboundaries.Thegrids,calledadaptivemesh ,canbeadaptedtotheshapeoftheboundaryortothespatialdis tributionofthesimulatedfield .Insteadofthetraditionalequidistantgrids,automaticallyproducedcurvilineargrids,whichcanbeadaptedtotheequationsolutions’featuresandtotheirregularshapeofthelateralboundary,areused .Thenumericalcalcul…     

An Evaluation of Publicly Available Global Bathymetry Grids

We evaluate the strengths and weaknesses of six publicly available global bathymetry grids: DBDB2 (Digital Bathymetric Data Base; an ongoing project of the Naval Research Laboratory), ETOPO2 (Earth Topography; National Geophysical Data Center, 2001, ETOPO2 Global 2’ Elevations [CD-ROM]. Boulder, Colorado, USA: U.S. Department of Commerce, National Oceanic and Atmospheric Administration), GEBCO (General Bathymetric Charts of the Oceans; British Oceanographic Data Centre, 2003, Centenary Edition of the GEBCO Digital Atlas [CD-ROM] Published on behalf of the Intergovernmental Oceanographic Commission and the International Hydrographic Organization Liverpool, UK), GINA (Geographic Information Network of Alaska; Lindquist et al., 2004), Smith and Sandwell (1997), and S2004 (Smith, unpublished). The Smith and Sandwell grid, derived from satellite altimetry and ship data combined, provides high resolution mapping of the seafloor, even in remote regions. DBDB2, ETOPO2, GINA, and S2004 merge additional datasets with the Smith and Sandwell grid; but moving from a pixel to grid registration attenuates short wavelengths (<20 km) in the ETOPO2 and DBDB2 solutions. Short wavelengths in the GINA grid are also attenuated, but the cause is not known. ETOPO2 anomalies are offset to the northeast, due to a misregistration in both latitude and longitude. The GEBCO grid is interpolated from 500 m contours that were digitized from paper charts at 1:10 million scale, so it is artificially smooth; yet new efforts have captured additional information from shallow water contours on navigational charts. The S2004 grid merges the Smith and Sandwell grid with GEBCO over shallow depths and polar regions, and so is intended to capture the best of both products. Our evaluation makes the choice of which bathymetry grid to use a more informed one. The U.S. government right to retain a non-exclusive royalty-free license in and to any copyright is acknowledged.     

Gravitational mode calculation of basins discretized by orthogonal curvilinear grids

This paper presents a simple and straightforward method for carrying out the direct numerical solution of the eigenvalue problem associated to the homogeneous linear shallow-water equations expressed using orthogonal curvilinear coordinates, when ‘adiabatic’ boundary conditions apply. These equations, together with the boundary conditions, define a self-adjoint problem in the continuum. The method presented here, which is thought for calculating the 2-D theoretical gravity modes of both natural and artificial basins, relies on a change of basis of the dependent variable vector. This preliminary transformation makes it, in fact, possible to formulate two different numerical approaches which guarantee the self-adjoint property of the discrete form of the system consisting of the governing equations and the boundary conditions. The method is tested using a square and a fully circular domain, both of which allow comparisons with well-known analytical and numerical solutions. Discretizing the physical domain of a fully circular basin by a cylindrical coordinate grid makes it possible to show the actual efficiency of the method in calculating the theoretical gravity modes of basins discretized by a boundary-following coordinate grid which allows laterally variable resolution.     

Numerical modeling of wind waves generated by tropical cyclones using moving grids

A version of the WAVEWATCH III wave model featuring a continuously moving spatial grid is presented. The new model option/version is intended for research into wind waves generated by tropical cyclones in deep water away from the coast. The main advantage of such an approach is that the cyclones can be modeled with spatial grids that cover much smaller areas than conventional fixed grids, making model runs with high spatial resolution more economically feasible. The model modifications necessary are fairly trivial. Most complications occur due to the Garden Sprinkler effect (GSE) and methods used to mitigate it. The basic testing of the model is performed using idealized wind fields consisting of a Rankine vortex. The model is also applied to hurricane Lili in the Gulf of Mexico in October 2002. The latter application shows that the moving grid approach provides a natural way to deal with hurricane wind fields that have a high-resolution in space, but a low resolution in time. Although the new model version is originally intended for tropical cyclones, it is suitable for high-resolution modeling of waves due to any moving weather pattern.     

A Finite Volume Method with Unstructured Triangular Grids for Numerical Modeling of Tidal Current

The finite volume method （FVM） has many advantages in 2-D shallow water numerical simulation. In this study, the finite volume method is used with unstructured triangular grids to simulate the tidal currents. The Roe scheme is applied in the calculation of the intercell numerical flux, and the MUSCL method is introduced to improve its accuracy. The time integral is a two-step scheme of forecast and revision. For the verification of the present method, the Stoker＇s problem is calculated and the result is compared with the mathematically analytic solutions. The comparison indicates that the method is feasible. A sea area of a port is used as an example to test the method established here. The result shows that the present computational method is satisfactory, and it could be applied to the engineering fields.     

Horizontal Pressure Gradient Errors of the Monterey Bay Sigma Coordinate Ocean Model with Various Grids

A coastal ocean -coordinate model of Monterey Bay (MOB) with realistic bottom topography and coastlines is developed using the Princeton Ocean Model (POM) and grid generation technique (GGT) to study the horizontal pressure gradient errors associated with the MOB steep topography. The submarine canyon in MOB features some of the steepest topography encountered anywhere in the world oceans. The MOB grids are designed using the EAGEAL View and GENIE⁺⁺ grid generation systems. A grid package developed by Ly and Luong (1993) is used in this study to couple grids to the model. The MOB model is tested with both orthogonal and curvilinear nearly-orthogonal (CNO) grids. The CNO grid has horizontal resolution which varies from 300 m to 2 km, while the resolution of the orthogonal grid is uniform with x = 1.25 km and y = 1.38 km. These grids cover a domain of 180 × 160 km with the same number of grid points of 131 × 131. Vertical resolutions of 25, 35 and 45 vertical sigma levels are tested. The error in the MOB are evaluated in terms of mean kinetic energy and velocity against various grids, vertical, horizontal resolution and distributions, and bottom topography smoothing. Simulations with various grids show that GGT can be used as another tool in reducing -coordinate errors in coastal ocean modeling besides increasing resolution and smoothing bottom topography. Topographical smoothing not only reduces topographic slope, but changes realistic topography. A CNO grid with a high grid density packed along steep slopes and Monterey Submarine Canyon reduces the errors by 40% compared to a rectangular grid with the same number of grid points. The CNO grid is more efficient than the rectangular grid, since it has most of its grids over water. The simulations show that the presented MOB -coordinate model can be used with a confidence regarding horizontal pressure gradient error.     

一种面向虚拟地球的海面动态可视化优化方法

现有的虚拟地球中的海面可视化方法主要采用投影网格的方式组织海面格网,这种特殊的网格组织方式,导致其在反映不同海域差异性特征时存在缺陷。基于全球离散格网的海面可视化方法由于能够与虚拟地球离散的空间剖分相匹配,有效弥补了投影网格法的缺陷,因此更符合虚拟地球海面仿真应用的需要。然而现有的离散格网法存在绘制效率差、场景加载慢、需要修补格网缝隙等问题,限制了其应用发展。对此,本文在现有离散格网法基础上进行优化:首先,在数据结构上对传统等经纬度离散格网进行扩展,设计了一种面向GPU绘制的多尺度海面网格模型来组织管理海面格网;其次,为了实现风场驱动下的海浪动态绘制,在多尺度海面网格模型的基础上提出了一种支持实时风场更新的海浪动态绘制方法;同时,考虑到格网缝隙修补对系统效率的影响,本文针对海面格网特点并结合GPU技术提出了一种高效的海面格网缝隙修补方法。最后通过对比试验验证了本文方法的可行性和有效性。试验结果表明,本文方法绘制效率稳定,加载速度快,且能弥补现有方法在功能上的缺失,因此应用范围更加广泛。     

双相介质瑞雷面波有限差分正演模拟

为了研究双相介质瑞雷面波的形成机制及传播规律,促进瑞雷面波资料处理方法的发展。文章根据弹性波动方程,采用交错网格有限差分算法,对二维各向同性弹性介质做解析解与数值解的对比,在此基础上,将PML吸收边界条件,改进的镜像法应用于双相介质波动方程中,并作了稳定性分析,对双相介质水平层状、起伏分界面等典型模型瑞雷面波及体波在内的全波场进行研究。结果表明:基于弹性介质解析解与数值解的对比,在误差接受范围内,研究双相介质是可行的;把稍作改进的镜像法应用于双相介质中,能够有效地处理瑞雷面波自由边界问题;通过详细分析双相介质瑞雷面波及体波在内的全波场的信息,对以双相介质为基础的地震波勘探有一定的指导作用。     

基于DEM和水箱理论识别流域河网方法研究

本文应用水箱原理处理流域DEM数据中存在的洼地问题,提出流域河网识别及编码的新方法。首先,确定洼地网格,搜索洼地区域,计算洼地容量,根据水箱原理确定洼地出口,判断洼地的流向;然后,逐层合并消减洼地,修正洼地水流方向;最后,计算网格集水面积,进行河网识别和编码。本文结合云南东川蒋家沟流域的DEM资料进行河网识别,得到了完整的流域河网,结果与实际勘测的河网完全吻合,这表明应用该方法提取流域河网是可行的,能够为进一步的分布式水文、泥石流、环境模型提供条件。