半隐式半拉格朗日非静力数值天气预报谱模式动力框架若干关键技术研究

发布时间：2018-06-30 02:33

本文选题：非静力模式 + 谱方法　；参考：《国防科学技术大学》2015年博士论文

【摘要】：数值天气预报在过去几十年的发展中一直采用一个重要的近似:静力近似。随着计算机集群计算能力不断提升,数值预报模式的分辨率也越来越高,能够为用户提供更加精确的预报服务。一般而言,当水平分辨率优于10km时,静力近似已经不适用了。因此开发非静力模式是未来数值预报系统发展的迫切需求。相比静力模式,一方面非静力模式要增加预报变量,方程的形式更加复杂;另一方面非静力模式水平网格尺度更细,为了能够准确地显示高分辨率下小尺度地形引起的局部气象要素,需要很多特定的数值处理技术。本文针对现有非静力模式缺乏高精度垂直离散格式、模式误差增长估计手段不足等问题,在已有的数值方法基础上,对全球非静力谱模式绝热动力框架若干关键问题进行深入研究,主要工作包括:1.实现有限差分二维X-Z平面谱模式。二维X-Z平面模式是数值预报模式的研究模式,其方程组和数值离散要点同三维有限区域预报模式保持一致。对垂直有限差分离散格式进行了精巧设计,使得其满足非静力模式的垂直约束。模式采用半隐式半拉格朗日时间平流离散格式,同时也对侧边界、上下边界条件分别进行了处理以保证计算结果的正确。在二维模式下,测试了四种山峰波测试样例以及重力波样例,验证了模式采用的数值离散格式的准确性和稳定性。2.实现垂直混合有限元有限差分二维X-Z平面模式。基于质量坐标的非静力模式垂直离散存在一系列的约束条件,应用有限元垂直离散被证明是难以实现的。本文提出了一个高精度混合离散格式,对半隐式格式的线性部分进行有限差分离散,对非线性部分进行有限元离散。同时为提高有限差分离散的精度,增加线性部分计算的分层数量。有限元采用四阶B-spline样条基函数。为方便处理垂直边界,先把垂直场投射到三阶样条插值函数空间形成多项式分段函数,在处理完边界后再投射到B-spline空间。如此避免了B-spline样条基函数直接处理边界,使得有限元计算更加简洁高效。对二维有限元模式也进行了多种测试样例,并同有限差分进行了定性和定量的对比,结果表明混合有限元格式在精度上要优于有限差分格式。3.实现三维全球非静力谱模式。三维球面模式和二维模式的动力框架基本一致,但采用的谱方法基函数有区别,球面谱模式采用球面谐波函数为基函数。球面模式水平网格采用精简高斯网格,模式方程的曲率项通过半拉格朗日插值时方向转换矩阵引入。科氏力项采用的是隐式处理形式。对三维模式进行了一系列的测试,包括稳定状态测试、斜压不稳定波测试、Rossby-Haurwitz波测试、山峰波测试等。测试结果验证了三维模式的准确性和稳定性。4.研究混沌模型的初始误差增长特性,发现混沌模型的平均相对误差饱和值同初始误差值之间存在一个简单的对数线性关系:二者的对数和为常数。利用该关系,提出平均绝对误差的概念,混沌系统的平均绝对误差饱和值为与初始误差无关的常数。利用这一特性,给出一个定量计算可预报期限的数学估计模型。研究了混沌系统模型误差增长特性,发现模型平均绝对误差增长在短期内呈指数增长,一段时间后达到饱和。可利用模型误差增长指数大小和达到饱和值的时间作为衡量模型优劣的评价手段。
[Abstract]:The numerical weather forecast has been using an important approximation in the development of the past several decades: the static approximation. With the increasing computing power of the computer cluster, the resolution of the numerical prediction model is also getting higher and higher, which can provide more accurate prediction service for the users. Generally, when the horizontal resolution is better than 10km, the static approximation has been approximated. It is not applicable. Therefore, the development of non static model is an urgent need for the development of the future numerical forecast system. Compared with the static model, the non hydrostatic model should increase the prediction variable and the form of the equation more complex. On the other hand, the scale of the non static model is finer, in order to accurately display the small scale terrain under high resolution. The local meteorological elements need a lot of specific numerical processing techniques. In this paper, in view of the lack of high precision vertical discrete schemes and the lack of model error growth estimation methods, the main problems of the key problems of the global non static spectral model thermal dynamic force framework are studied in this paper. The work includes: 1. to realize the finite difference two-dimensional X-Z plane spectrum pattern. The two-dimensional X-Z plane model is the model of the numerical prediction model. The equations and the numerical discrete points are consistent with the three-dimensional finite area prediction model. The vertical finite difference dispersion scheme is designed so that it satisfies the vertical constraint of the non static model. The semi implicit semi Lagrange time advection scheme is adopted in the formula, while the side boundary and the upper and lower boundary conditions are treated respectively to ensure the correctness of the calculation results. In the two-dimensional model, four peak wave samples and gravity wave examples are tested. The accuracy and stability of the numerical discrete scheme used in the model are verified.2. real. The vertical mixed finite difference two-dimensional X-Z plane model is presented. There is a series of constraints on the vertical discrete model of the non static mode based on the mass coordinates. The application of the finite element vertical dispersion is proved to be difficult to realize. A high precision mixed discrete scheme is proposed in this paper, and the finite difference dispersion is carried out for the linear part of the semi implicit scheme. In order to improve the precision of the finite difference separation and increase the accuracy of the finite difference separation dispersion and increase the number of layers calculated by the linear part, the finite element uses the four order B-spline spline basis function. In order to handle the vertical boundary, the vertical field is first projected to the three order spline interpolation function space to form a polynomial piecewise function, after the processing of the boundary. Then it is projected into the B-spline space, so that the B-spline spline basis function is avoided directly and the finite element calculation is more concise and efficient. A variety of test examples are also carried out for the two-dimensional finite element model, and the qualitative and quantitative comparison with the finite difference is made. The results show that the hybrid finite element scheme is better than the finite difference. The three-dimensional global non static spectral model is realized by format.3.. The three-dimensional spherical model is basically the same as the dynamic frame of the two-dimensional model, but the basis function of the spectral method is different. The spherical spectral model uses the spherical harmonic function as the base function. The spherical pattern horizontal grid uses the simplification of the Gauss grid, the curvature of the mode equation is interpolated by half Lagrange interpolation The time direction transformation matrix is introduced. The Coriolis force term is used in implicit treatment. A series of tests are carried out on the three-dimensional model, including stable state test, baroclinic unstable wave test, Rossby-Haurwitz wave test, peak wave test and so on. The test results verify the accuracy and stability of the three-dimensional model and the initial error of the chaotic model of the.4. model. It is found that there is a simple logarithmic linear relationship between the average relative error saturation value of the chaotic model and the initial error value: the logarithm and the constant of the two is a constant. Using this relation, the concept of the mean absolute error is proposed. The mean absolute error saturation value of the chaotic system is a constant independent of the initial error. A mathematical estimation model is given for the quantitative calculation of the predictable term. The error growth characteristic of the chaotic system model is studied. It is found that the average absolute error growth of the model increases exponentially in the short term and reaches the saturation after a period of time. The time of the model error growth index to the saturation value can be used as the evaluation of the model. Price means.
【学位授予单位】：国防科学技术大学
【学位级别】：博士
【学位授予年份】：2015
【分类号】：P456.7;O241.8

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