广东省统一深度基准项目的设计研究

根据对广东省现有长期验潮站数量、分布以及水位数据情况的分析,确立了在已有长期验潮站的基础上,采用适当布设短期验潮站的方式,对长期验潮站进行加密补充;建立海区调和常数变化模型,并结合水深数据、卫星测高数据,构建海洋潮汐模型;最终建立深度基准模型的总体设计思路。广东省统一深度基准的建立,可实现深度基准面1985高程模型的构建,相邻测区间水深成果的无缝拼接,沿海水深成果与陆地地形成果的相互转换,GNSS技术下的水深测量(无验潮模式)以及对沿海范围内海岸线和海岛岸线的精确推算。     

附有限制条件的间接平差秩亏时解法初探

在附有限制条件的间接平差的应用中,若所列观测方程中实际用到的未知参数的个数少于所选参数的总数u时,就会出现法方程系数阵秩亏的问题。为了解决此问题,在理论公式推导的基础上,给出了一种新的解决方法,并结合算例进行了验证。     

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。     

利用GPU实现基于物理模型的流体运动仿真

纳维-斯托克斯方程是描述流体运动的基础物理模型。首先简要介绍了在计算机上实现该模型的数值解算方法。在流体运动的计算机视觉仿真中,密度渲染才是最终结果,因此,又阐述了流体的密度场与速度场的关系,并且给出了流体仿真的基本流程。由于可编程图形处理器(GPU)具有并行性和速度快等特点,流体模拟的解算和渲染在图形处理器上运行更加高效,但是利用GPU编程实现流体仿真必须要实现3个核心转换,最后以支持3维纹理的Direct3D10为例,给出了利用GPU实现流体运动仿真两个简单实例。     

高程基面问题浅议

介绍国内现存的几种高程基面,分析工程中使用高程基面时存在的问题,提出测量系统规范化、标准化的紧迫性和必要性。     

Parameter estimation for basin-scale ecosystem-linked population models of large pelagic predators: Application to skipjack tuna

A Spatial Ecosystem and Population Dynamic Model (SEAPODYM) is used in a data assimilation study aiming to estimate model parameters that describe dynamics of Pacific skipjack tuna population on ocean-based scale. The model based on advection–diffusion–reaction equations explicitly predicts spatial dynamics of large pelagic predators, while taking into account data on several mid-trophic level components, oceanic primary productivity and physical environment. In order to improve its quantitative ability, the model was parameterized through assimilation with commercial fisheries data, and optimization was carried out using maximum likelihood estimation approach. To address the optimization task we implemented an adjoint technique to obtain an exact, analytical evaluation of the likelihood gradient. We conducted a series of computer experiments in order to (i) determine model sensitivity with respect to variable parameters and, hence, investigate their observability; (ii) estimate observable parameters and their errors; and (iii) justify the reliability of the computed solution. Parameters describing recruitment, movement, habitat preferences, natural and fishing mortality of skipjack population were analysed and estimated. Results of the study suggest that SEAPODYM with achieved parameterization scheme can help to investigate the impact of fishing under various management scenarios, and also conduct forecasts of a given species stock and spatial dynamics in a context of environmental and climate changes.     

A two-dimensional finite volume hydrodynamic model for coastal areas: Model development and validation

A two dimensional implicit finite volume scheme for solving the shallow-water equations is developed. The effects of the Coriolis force, surface wind stress, and waves are included. A non-uniform rectilinear forward staggered grid is used with Cartesian coordinates. The time integration is performed using the Euler implicit technique. The convective flux is treated using the deferred correction method. The viscous terms are discretized using a second order central difference approximation. The SIMPLE (Semi-Implicit Method for Pressure-Linked Equations) algorithm is used for coupling the velocity components and the water elevation gradient for the water level correction. The system of equations is solved sequentially using the Strongly Implicit Procedure (SIP). To simulate wave driven current, a phase averaged wave model is used first to simulate wave transformation and calculate radiation stresses. The performance of the developed model is validated for different sources of external forces and different combinations of boundary conditions. The validation cases include tidal circulation in a harbor and wave induced currents behind a breakwater parallel to the coastline. The model is finally applied to simulate the flow pattern in a closed artificial lagoon and along the coastline near Damietta Port located along the Northern coast of Egypt. Results of the developed model agree well with the published results for the considered cases.     

Simulation of nonlinear wave run-up with a high-order Boussinesq model

This paper considers the numerical simulation of nonlinear wave run-up within a highly accurate Boussinesq-type model. Moving wet–dry boundary algorithms based on so-called extrapolating boundary techniques are utilized, and a new variant of this approach is proposed in two horizontal dimensions. As validation, computed results involving the nonlinear run-up of periodic as well as transient waves on a sloping beach are considered in a single horizontal dimension, demonstrating excellent agreement with analytical solutions for both the free surface and horizontal velocity. In two horizontal dimensions cases involving long wave resonance in a parabolic basin, solitary wave evolution in a triangular channel, and solitary wave run-up on a circular conical island are considered. In each case the computed results compare well against available analytical solutions or experimental measurements. The ability to accurately simulate a moving wet–dry boundary is of considerable practical importance within coastal engineering, and the extension described in this work significantly improves the nearshore versatility of the present high-order Boussinesq approach.     

Velocity potential formulations of highly accurate Boussinesq-type models

The highly accurate Boussinesq-type equations of Madsen et al. (Madsen, P.A., Bingham, H.B., Schäffer, H.A., 2003. Boussinesq-type formulations for fully nonlinear and extremely dispersive water waves: Derivation and analysis. Proc. R. Soc. Lond. A 459, 1075–1104; Madsen, P.A., Fuhrman, D.R., Wang, B., 2006. A Boussinesq-type method for fully nonlinear waves interacting with a rapidly varying bathymetry. Coast. Eng. 53, 487–504); Jamois et al. (Jamois, E., Fuhrman, D.R., Bingham, H.B., Molin, B., 2006. Wave-structure interactions and nonlinear wave processes on the weather side of reflective structures. Coast. Eng. 53, 929–945) are re-derived in a more general framework which establishes the correct relationship between the model in a velocity formulation and a velocity potential formulation. Although most work with this model has used the velocity formulation, the potential formulation is of interest because it reduces the computational effort by approximately a factor of two and facilitates a coupling to other potential flow solvers. A new shoaling enhancement operator is introduced to derive new models (in both formulations) with a velocity profile which is always consistent with the kinematic bottom boundary condition. The true behaviour of the velocity potential formulation with respect to linear shoaling is given for the first time, correcting errors made by Jamois et al. (Jamois, E., Fuhrman, D.R., Bingham, H.B., Molin, B., 2006. Wave-structure interactions and nonlinear wave processes on the weather side of reflective structures. Coast. Eng. 53, 929–945). An exact infinite series solution for the potential is obtained via a Taylor expansion about an arbitrary vertical position z = zˆ. For practical implementation however, the solution is expanded based on a slow variation of zˆ and terms are retained to first-order. With shoaling enhancement, the new models obtain a comparable accuracy in linear shoaling to the original velocity formulation. General consistency relations are also derived which are convenient for verifying that the differential operators satisfy a potential flow and/or conserve mass up to the order of truncation of the model. The performance of the new formulation is validated using computations of linear and nonlinear shoaling problems. The behaviour on a rapidly varying bathymetry is also checked using linear wave reflection from a shelf and Bragg scattering from an undulating bottom. Although the new models perform equally well for Bragg scattering they fail earlier than the existing model for reflection/transmission problems in very deep water.     

Tsunami generation,propagation, and run-up with a high-order Boussinesq model

In this work we extend a high-order Boussinesq-type (finite difference) model, capable of simulating waves out to wavenumber times depth kh < 25, to include a moving sea-bed, for the simulation of earthquake- and landslide-induced tsunamis. The extension is straight forward, requiring only an additional term within the kinematic bottom condition. As first test cases we simulate linear and nonlinear surface waves generated from both positive and negative impulsive bottom movements. The computed results compare well against earlier theoretical, numerical, and experimental values. Additionally, we show that the long-time (fully nonlinear) evolution of waves resulting from an upthrusted bottom can eventually result in true solitary waves, consistent with theoretical predictions. It is stressed, however, that the nonlinearity used far exceeds that typical of geophysical tsunamis in the open ocean. The Boussinesq-type model is then used to simulate numerous tsunami-type events generated from submerged landslides, in both one and two horizontal dimensions. The results again compare well against previous experiments and/or numerical simulations. The new extension compliments recently developed run-up capabilities within this approach, and as demonstrated, the model can therefore treat tsunami events from their initial generation, through their later propagation, and final run-up phases. The developed model is shown to maintain reasonable computational efficiency, and is therefore attractive for the simulation of such events, especially in cases where dispersion is important.