基于变分原理的自适应网络技术及其权函数问题研究

利用两个具有解析解的算例研究基于变分原理的自适应网络技术。结果表明，对运动激波算例，权函数考虑二阶导数项比考虑梯度项更能有效地减小误差；对气旋锋生算例，仅以梯度作为权函数亦不能提高精度，考虑速度场、锋生函数分布的权函数能更合理地安排网络；对照解析解，发现提出的自适应网络技术能明显提高计算精度，在节省内存等方面显示了突出的优点。     

自适应网格技术在数值模式中的应用研究 I.一维问题

利用变分原理的自适应网格技术被应用到三个有解析解的问题上,它能根据问题 的求解、在解的大梯度区自动加密网格,从而非常成功地算出了激波。通过分析发现自适应 网格技术在提高精度、减少运行时间方面显示了优良的性能。     

自适应网格技术在数值模式中的应用研究Ⅰ.一维问题

利用变分原理的自适应网格技术被应用到三个有解析解的问题上,它能根据问题的求解,在解的大梯度区自动加密网格,从而非常成功地算出了激波.通过分析发现自适应网格技术在提高精度、减少运行时间方面显示了优良的性能.     

自适应网格技术在数值模式中的应用研究 II.二维问题

用一个具有解析解的二维动力锋生成过程算例,对比自适应网格方案和固定网格方案的优劣,结果表明:同等误差要求下,固定网格方案的网格点数为自适应网格方案的3倍。从时间演化上看,自适应网格对温带气旋的预报,在同等误差要求下,可比固定网格的预报延长10小时以上。文章对加权系数选取及对解的影响进行了分析,从几个切面的计算结果展示了自适应网格对网格的优良安排并能抓住锋面特征结构。文章分析了光滑性、正交性对结果的影响。结果表明:网格的光滑性影响有一个优化值;在网格适当安排情况下,要适度考虑正交性。     

自适应网格模式在暴雨数值模拟中的应用

基于变分原理，自适应网格技术能根据数值模式的特点，在模式解梯度大的地区自动加密网格，提高模式的分辨率。将其应用于MM4模式中，采用多重网格法以加速自适应网格的生成。对1996年8月4日至5日发生在华北的特大台风暴雨过程，用自适应网格模式和均匀网格模式进行了数值模拟和动力诊断分析，以研究自适应网格模式在天气预报和模拟应用中的特点。试验表明，采用自适应网格后计算稳定，对所关心的天气系统及其降水的模拟精度均高于均匀网格模式，对形势场、风场的模拟精度也有明显改善。     

中尺度的自适应模式在降雪数值模拟中的应用

在中尺度模式的基础上引进了自适应网格设计的方法，它可以任意加密局地网格，从而达到以较小的计算量获得较高的计算精度的目的。自适应网格技术基于变分原理，能根据数值模式的特点，在物理量梯度大的地方，自动加密网格，提高模式的分辨率。文章将自适应网格技术应用于MM4中，用来模拟2002年3月2～4日华北地区的一场中一大雪过程。结果表踢，采用自适应网格技术后，结果稳定，对所关心的天气系统及其降水的模拟精度与采用均匀网格相比得到踢显改善，温度场和风场预报也有不同程度的提高。     

非均匀网格下的高阶精度中央差分格式:理论推导和理想试验

传统的高阶精度有限差分格式通常是在均匀网格的基础上推导得到的,在非均匀网格的情况下它会出现精度退化的问题。基于泰勒展开方法构造了一种适用于非均匀网格的2阶、4阶和6阶精度中央有限差分方案,利用Burgers方程和一维平流方程对新方案的性能进行测试,着重分析新方案对其误差大小及分布形态的改进效果。数值模拟结果表明:在非均匀网格下,提高差分方案的精度可明显减小数值解误差(降低了70%~88%),特别是当差分精度从2阶提高到4阶的时候。同时,高阶精度方案在梯度变化较大或者网格距较粗区域的模拟结果更有优势,4阶和6阶精度方案在以上区域的误差远小于2阶精度方案。方案可用于提高数值天气预报模式中非均匀分层模式的垂直差分计算精度。      

急流对锋面次级环流的影响

通过一个考虑非绝热加热项和摩擦项的原始方程组,取沿锋面方向地转近似,寻出一个描述定常锋面次级环流的方程,研究高低空急流对锋面次级环流和锋生过程的作用。结果表明:高低空急流能改变锋面环流位置、强度,使锋生过程加强。     

中尺度数值模式的自适应网格设计

引进了自适应网格设计的方法。自适应网要生成行技术基础变分原理,所生成的网格具有光滑性、一定程度的正交性和机调节网格疏密程度的优点,这种新技术可任意加密局地网格,从而达到以较小的计算量获得较高的计算精度的目的。将自适应网格技术应用于ＭＭ４中,并用来模拟１９２年６月１４日这次大范围暴雨过程。结果表明,采用自适应网格后计算稳定,２４ｈ降水预报得到明显改善。     

Petterssen锋生函数的推广及其与垂直运动强迫项的关系

Petterssen 的锋生方程,建立了水平位温梯度大小的拉格朗日变率(称为锋生函数)与水平速度场中运动学不变属性间的关系式。根据标量锋生函数的空间分布推断锋区中垂直环流的存在,在天气业务中是不罕见的。另一方面,Hoskins 及其同事引入了一种准地转ω方程,其中动力强迫项与 Q 矢量的水平散度成正比。所谓 Q 矢量,定义为矢量水平位温梯度沿地转气流的拉格朗日变率。Q 矢量的形式,启发我们把 Petterssen 锋生函数推广成适用于矢量水平位温梯度的情况。这种推广后的锋生函数称为矢量锋生函数,包括新引入的水平位温梯度方向的拉格朗日变率表达式。     

Turbulence frontogenesis

Summary The frontogenesis function in terms of the time derivative of the gradient of any relevant airborne quantity comprises all processes contributing to frontogenesis. Thus the various terms of this function are able to reveal processes of frontal development and their structure. Therefore the evaluation of these terms from measurements or in the frame of model simulations offers the chance of gaining more insight in frontal processes. If frontogenesis is evaluated from average basic data representative for a certain time-or space-scale, the result will be a kind of average frontogenesis, which naturally contains turbulence terms in the form of covariances. The processes described by these terms are called turbulence frontogenesis.This paper describes the basic formalisms of turbulence frontogenesis, offers cross-sections of these terms gained in experiments flown in sea-breeze fronts and gives some hints about their general behaviour.With 4 Figures     

Investigation of the mei-yu front using a new deformation frontogenesis function

A new frontogenesis function is developed and analyzed on the basis of a local change rate of the absolute horizontal gradient of the resultant deformation. Different from the traditional frontogenesis function, the newly defined deformation frontogenesis is derived from the viewpoint of dynamics rather than thermodynamics. Thus, it is more intuitive for the study of frontogenesis because the compaction of isolines of both temperature and moisture can be directly induced by the change of a flow field. This new frontogenesis function is particularly useful for studying the mei-yu front in China because mei-yu rainbands typically consist of a much stronger moisture gradient than temperature gradient, and involve large deformation flow. An analysis of real mei-yu frontal rainfall events indicates that the deformation frontogenesis function works remarkably well, producing a clearer mei-yu front than the traditional frontogenesis function based on a measure of the potential temperature gradient. More importantly, the deformation frontogenesis shows close correlation with the subsequent(6 h later) precipitation pattern and covers the rainband well, bearing significance for the prognosis or even prediction of future precipitation.     

A generalized frontogenesis function and its application

With the definition of generalized potential temperature, a new generalized frontogenesis function, which is expressed as the Lagrangian change rate of the magnitude of the horizontal generalized potential temperature gradient, is derived. Such a frontogenesis function is more appropriate for a real moist atmosphere because it can reflect frontogenesis processes, in which the atmosphere in a frontal zone is typically characterized by neither completely dry nor uniform saturation. Furthermore, by derivation, the expression of generalized frontogenesis function includes both temperature and humidity gradients, which is different from and superior to the traditional frontogenesis function in moist processes, which also uses equivalent potential temperature. Diagnostic studies of real cases are performed and show that the generalized frontogenesis function in non- uniformly saturated moist atmosphere indeed provides a useful tool for frontogenesis, compared to using the traditional frontogenesis function. The new frontogenesis function can be used in situations involving either a strong temperature or moisture gradient and is closely correlated with precipitation.     

The Adaptive Wavelet Collocation Method and Its Application in Front Simulation

The adaptive wavelet collocation method(AWCM)is a variable grid technology for solving partial differential equations(PDEs)with high singularities.Based on interpolating wavelets,the AWCM adapts the grid so that a higher resolution is automatically attributed to domain regions with high singularities. Accuracy problems with the AWCM have been reported in the literature,and in this paper problems of effciency with the AWCM are discussed in detail through a simple one-dimensional(1D)nonlinear advection equation whose analytic solution is easily obtained.A simple and effcient implementation of the AWCM is investigated.Through studying the maximum errors at the moment of frontogenesis of the 1D nonlinear advection equation with different initial values and a comparison with the finite difference method(FDM) on a uniform grid,the AWCM shows good potential for modeling the front effciently.The AWCM is also applied to a two-dimensional(2D)unbalanced frontogenesis model in its first attempt at numerical simulation of a meteorological front.Some important characteristics about the model are revealed by the new scheme.     

Gerris数值方案及其在海洋数值模拟中的应用

基于动态自适应网格的开源软件Gerris受到越来越多海洋和水文研究者的关注.概述了Gerris开发背景、研究现状和特点,详细阐述了Gerris数值方案,包括动态自适应网格、动态负载平衡技术原理、广义正交曲线坐标系、内嵌复杂固体边界和地形数据的处理方法,并探讨了Gerris在海洋数值模拟中的初步应用.结果表明,Gerris动态自适应网格在多尺度问题模拟中的优势独特,在海洋数值模拟应用中可通过自适应网格提高地理特征的精度,通过GTS(或KDT)格式的数据来处理地形和网格,达到同时兼顾精确性和易用性的目的,使得Gerris与其他海洋模式进行有机结合成为重要发展方向.     

Present-day concepts of atmospheric frontogenesis. Part 1. Theoretical ideas

Presented is a review of quantitative characteristics of atmospheric frontogenesis that describe it as the process of variations of the vector of the horizontal temperature gradient (both in value and in direction) in an individual particle. The frontogenesis that strives for recovering the thermal wind balance disturbed in the case of inhomogeneous advection, generates vertical circulation which is both thermally direct (warm air ascends relative to cold air) and thermally opposite (upward motions in the cold air). Given are the expressions for computing frontogenesis using the data on temperature, pressure, and wind. Used is the resolution of the frontogenetic vector function into components along the isoline of potential temperature both on and across the constant-pressure surface. The first component describes the change in the temperature gradient vector due to the rotation of isotherms (rotational frontogenesis), and the second component, the variations of the absolute value of the gradient (scalar frontogenesis). Quantitative characteristics of frontogenesis are efficient diagnostic parameters both for understanding weather processes and weather forecast specification and for the verification and enhancement of numerical models.     

Semigeostrophic Frontal Boundary Layer

The viscous semigeostrophic solutions obtained for the baroclinic Eady wave fronts are analyzed for the generation of the cross-frontal temperature gradient in the boundary layer. In the case of free-slip boundaries, the cross-frontal gradient is maximally generated at the surface by meridional temperature advection. In the case of no-slip boundaries, surface friction reduces the meridional temperature advection in the boundary layer: The maximum generation occurs above the surface layer and the temperature gradient at the surface is maintained by vertical diffusion. The no-slip solution is compared with the Ekman-layer model solution. Errors are quantified for the use of the Ekman-layer model in the mature state of frontogenesis.The surface frontogenesis is found to be affected by diffusivity both directly and indirectly. The direct effect of diffusivity is represented explicitly by the diffusion term in the potential temperature equation. The indirect effect of diffusivity is related implicitly to the temperature advection caused by the viscous part of the ageostrophic motion whose horizontal velocity component is defined by the frictional wind deflection (away from the geostrophy). The direct effect of diffusivity is frontolytical, whilst theindirect effect of diffusivity is frontogenetic in the mesoscale vicinity of the front. The indirect effect of diffusivity contributes dominantly to the mesoscale surface frontogenesis for the free-slip case, but it is offset by the divergence of the dynamic part of the ageostrophic motion at the surface level for the non-slip case.