摘要
本文介绍了一个采用两时间层有限差分格式的、Boussinesq近似的、自由表面、模态分离的、采用地形坐标系的原始方程三维海洋环流数值模式(MASNUM)平台的建立。
本文从完整的地球流体力学控制方程组出发,在Boussinesq假定和静力学假定下,详细推导了地形坐标下雷诺平均的海水运动控制方程组,以此建立了模式的数学模型。数值算法上,内外模态的时间差分均采用了两时间层的欧拉前后差分格式(FB),空间采用Arakawa-C交错网格;为了抑制由于非线性作用产生的短波扰动的增长,构造了在任意海陆分布下保持计算区域内水体体积守恒的空间平滑算法。
斜压梯度力项的计算采用三次样条插值的密度雅克比式算法,并对原算法中的调和平均进行了修正,进一步减小了误差;对现有垂向速度的诊断算法中存在的问题进行了详细的检讨,证明在当前模式框架下难以找到一种完美的垂向速度计算方案。本文还对主要热力学变量如海水状态方程和静力稳定度的算法进行了讨论和更新;在前人工作基础上对常用的三大类共18种应用于环流模式的运动学开边界条件进行了归纳、对其构造算法进行了详细的推导,并将其作为子程序编入模式,供不同数值实验调用。
模式性能检验方面,首先对中国近海潮汐进行了模拟,MASNUM环流模式对迟角的模拟表现出一定的改善;其次,MASNUM环流模式能够模拟出典型斜压现象黄海冷水团的主要特征和季节演化规律,与观测有较好的一致性;第三,使用该模式对西北太平洋海域进行了进行了1/6度分辨率的计算,任意选取了30个计算点与相同条件下的POM模式的结果进行了3年时间序列的比较,参与比较的4个预报量无论在振幅还是相位上均表现出很好的一致性。这些实验和比较证实了本模式的可靠性。
A finite-difference, primitive equation, three-dimensional ocean circulation model (MASNUM circulation model) was established. This model is characterized by its Boussinesq approximation, free-surface, mode-splitting, terrain-following features, and temporally discretized with a two-level scheme.
The mathematical model of the oceanic motions is based on the terrain-following, Reynolds-averaged ocean governing equations, which are derived from the complete geophysical fluid dynamical equations under the hydrostatic and Boussinesq approximations. As the numerical techniques, a simplest two-level, single-step algorithm, Eulerian forward and backward difference method (FB), is adopted for the temporal difference. The staggered Arakawa-C stencil is used for spatial arrangements of the model variables. A volume-conserved spatial smoothing method is devised to surppress the growing of the short perturbations due to nonlinear terms.
The spline interpolated density Jacobian algorithm is cited in calculating the internal pressure gradient force. However, certain correction has to be made to the harmonic mean in the original algorithm to reduce the error. The error analysis and correction has been made to the diagnostic computation of the vertical velocity. The problem that the kinetic boundary conditions at the surface and the bottom cannot be strictly satisfied simultaneously in the original algorithm has been fixed.
The algorithms of some main thermodynamic variables, such as in-situ density and static stability have been reviewed and updated with up-to-date and stable computation methods. The detailed numerical forms are derived for three categories,18kinds of open boundary condtions for the kinetic variables prevelant in current ocean models. Most of these conditions have been included in the MASNUM circulation model, to be invoked in all kinds of numerical experiments.
To verify the performance of the MASNUM circulation model, the coastal tide of the China Seas is first simulated, and MASNUM circulation model appears improvements in the phase lag. Secondly, MASNUM circulation model could simulate the main features and seasonal evolutions of the Yellow-Sea Cold Water Mass, a typical baroclinic phenomenon. Thirdly, the MASNUM circulation model has been setup to compute the Northwest Pacific with horizontal resolution of1/6degrees and vertically16layers. The3-year time series of four prognostic variables has been compared with those of the POM model. The comparisons show farily good consistent in both amplitude and phase between the two models. These experiments and comparisons verified the reliablity and applicability of the newly-built circulation model to a large extent.
引文
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