用样条Galerkin方法近似解正压原始方程组

用双三次B-样条作为基函数,对矩形域上的正压原始方程组构造了一种较高精度的Ga-lerkin近似;给出了相应的数值解法,并在TQ-6机上得到实现。初步的数值试验表明,计算过程是非常稳定的,对旋转适应过程的模拟是成功的。对一个实例所做的48小时预报可与较高分辨率的差分模式相比。     

球面上斜压原始方程组保持总有效能量守恒的差分格式

本文从标准层结近似下球面上的斜压原始方程组出发,针对两类常用的网格系统——C-网格和B-网格,分别设计出可以保持总动能、总有效位能和总有效表面位能之和守恒的差分格式.同时,讨论了定义在交错网格上的差分和平均算子的一些很有用的性质.     

长时效的正压原始方程能量完全守恒(拟)谱模式

遵循误差反演补偿新计算原理,对正压原始方程传统气象全球拟谱模式方案进行了改造,构造了正压原始方程能量完全守恒全球拟增模式新计算方案,解决了正压原始方程的(非线性)计算稳定性问题和能量守恒整体性质保持问题,改进了相应正压原始方程传统气象全球拟谱模式方案的计算效能。新方案的数值试验表明:在计算实践上,新方案在解决能量守恒问题的同时,可解决(非线性)计算稳定性问题,并在一定条件下可解决非线性计算收敛性问题。进一步的比较数值试验还表明:在计算实践上,新方案具有在提高相应传统气象方案的计算精度,减少其计算量的同时,延长其计算时效,解决其中一类特定“气候漂移”问题方面的效用。本工作原理也适用于斜压原始方程情形。     

有效的正压原始方程拟能守恒保真（拟）谱模式

本工作遵循保真计算原理与方法,对正压原始方程气象传统全球（拟）谱模式方案进行改造,构造了正压原始方程拟能完全守恒（拟）谱模式新型保真计算方案,解决了正压原始方程的（非线性）计算稳定性问题和拟能守恒整体性质保持问题,改进了相应正压原始方程气象传统全球（拟）谱模式方案的计算效能。新型保真方案的数值实验表明,计算实践中,新方案在解决拟能守恒问题的同时,可解决（非线性）计算稳定问题,并在一定条件下可解决非线性计算收敛性问题。进一步的比较数值实验还表明,计算实践中,新型保真计算方案在提高相应气象传统方案的计算精度、     

正压原始方程的差分格式

本文把[1—3]中的数值方法应用于正压原始方程组,并给出了差分格式的严格的误差估计。特别分析了边界误差的影响,并构造了一些新的算法。     

试论正压原始方程的计算稳定性

本文讨论了正压原始方程的差分方程的计算稳定性问题,指出该方程具有两类不同的计算稳定性条件,它们分别与重力波的强度和速度有关。本文还分析了引起非线性计算不稳定的原因,并认为抑制非线性计算不稳定问题可归结为抑制重力波强度不随积分步次的增长而不断增大的问题。     

正压原始方程的一个数值试验

本文为应用正压原始方程作数值预报的初步试验。采用时间空间中央差分进行数值求解。通过试验确定了一种简单可用的边界条件及初始条件。 应用此方案对四个天气实例进行了24小时预报。计算结果尚好。对这四个实例中所包括的正压天气过程一般能较好的反映出来。     

湿大气方程组解的渐近性质

研究无穷维Ｈｉｌｂｅｒｔ空间中,湿大气运动系统解的长期行为,在导得了湿大气运动方程是Ｈｉｌｂｅｒｔ空间中一个非常特殊的算子方程之后,利用算子的性质讨论了全局吸收集和全局吸引子的存在性,揭示出系统解的渐近行为表现在吸引子的结构上及系统向非绝热加热的非线性适应过程。最后指出了几个简化方程组与原方程组在解的长期行为上的根本不同,从而给出长期天气或气候研究中简化方程组必须遵循的原则。     

正压原始方程有限区域谱模式的预报试验

本文包括四方面内容; (1)给出一个单向嵌套的有限区域浅水波方程谱模式的具体方案及其预报试验结果。这个模式基于文献。其特点是:基本展开函数为“修正的双傅氏级数”,它由两部分组成:正交双博氏级数及非正交的线性函数,这两部分之间互不正交。 (2)对同一实例,比较了谱方法,差分法,假谱法24h,48h预报结果。甚至同格距缩小一半的差分法相比,谱方法预报效果仍优于差分法预报效果。 (3)试验了谱模式的固定边界、刚体边界、侧边界条件随时间变化但不加松弛处理,以及侧边界条件随时间变化加松弛处理四种方案。结果表明,合理的边界条件及有效的边界处理方法对谱模式来说是至关重要的。 (4)提出并试验了谱模式的一种地形区计算方案,有助于谱模式中对陡峭地形的处理。     

正压原始方程模式显式积分方案的试验

本文用正压原始方程模式试验了显式积分方案的稳定性和精确性,并考察了时间平滑和空间平滑对这些特性的影响。试验所得的结果对于选取合适的中、短期数值天气预报模式的显式积分方案将有参考作用。     

正压初始方程的交替格式数值解法

本文用线性理论分析和实例计算验证计算波移速偏慢问题,提出使用L.C—L格式交替使用方案,以改进预报系统移速偏慢。文中还应用偏微分方程的特征流型理论,分析边界条件的适当提法,小范围矩形区域预报实例表明,对边界值作特征锥处理,对边界误差向内部传播有一定程度的抑制作用。     

The second order approximation to the nonlinear wave in barotropic atmosphere

A kind of technique of computer extension of perturbation series is presented and used in seeking for the second-order approximation to a large-scale travelling wave solution of the barotropic primitive equations. Numerical experiments show that the second-order approximation keeps major characters of the travelling wave solution and is indeed more exact than the zero-order and the first order approximations.     

Analysis—Prediction experiments over Indian region using primitive equation barotropic model

The impact of initial guess and grid resolutions on the analysis and prediction has been investigated over the In-dian region. For this purpose, an univariate objective analysis scheme and a primitive equation barotropic model have been used. The impact of initial guess and the resolutions on analysis and prediction is discussed.     

Split-explicit integration of primitive equation barotropic model for the prediction of movement of monsoon depression

The split-explicit version of a limited area primitive equation barotropic model is formulated and tested for the prediction of movement of monsoon depressions. The model is integrated upto 48 hours with split-explicit time inte-gration scheme (Gadd, 1978a) using input of four synoptic cases. The model is also integrated explicitly. The forecast results obtained from both the versions are compared and discussed. The computational time in former version is less than half of the computational time needed in explicit version.     

Planetary geostrophic equations for the atmosphere with evolution of the barotropic flow

Atmospheric phenomena such as the quasi-stationary Rossby waves, teleconnection patterns, ultralong persistent blockings and the polar/subtropical jet are characterized by planetary spatial scales, i.e. scales of the order of the earth’s radius. This motivates our interest in the relevant physical processes acting on the planetary scales. Using an asymptotic approach, we systematically derive reduced model equations valid for atmospheric motions with planetary spatial scales and a temporal scale of the order of about 1 week. We assume variations of the background potential temperature comparable in magnitude with those adopted in the classical quasi-geostrophic theory. At leading order, the resulting equations include the planetary geostrophic balance. In order to apply these equations to the atmosphere, one has to prescribe a closure for the vertically averaged pressure. We present an evolution equation for this component of the pressure which was derived in a systematic way from the asymptotic analysis. Relative to the prognostic closures adopted in existing reduced-complexity planetary models, this new dynamical closure may provide for more realistic increased large-scale, long-time variability in future implementations.     

A barotropic model of the Ekman planetary boundary layer based on the geostrophic momentum approximation

A model of a stationary planetary boundary layer is proposed based on the equation of motion with the advective term retained. The latter is modeled by means of the so-called geostrophic momentum approximation in two versions — original and modified. New expressions for the vertical velocity W at the top of the boundary layer are derived and analyzed. They underestimate W compared to the classical expression.     

The pseudospectral approximation applied to the shallow water equations on a sphere

Abstract

The Radar data Analysis, Processing and Interactive Display (RAPID) system, developed by McGill University researchers, synthesizes spherical coordinate radar data onto Cartesian maps displaying Constant Altitude Plan Position Indicator (CAPPI) reflectivity, Vertically Integrated Liquid water content (VIL), and other radar‐based parameters. In this study, Carvel radar (53.34°N, 114.09°W) data from July 2000 were processed using McGill's RAPID software. Specifically, we compared observations of severe convection, as identified by selected radar‐based reflectivity parameters, with surface severe weather reports and atmospheric sounding data. July 2000 was characterized by frequent severe thunderstorm activity over central Alberta; there were seven days with golfball‐sized hail, and two days with confirmed tornadoes. The VIL, upper level VIL (UVIL), and the maximum reflectivity at 7 km (Z7) were employed to quantify the strength and frequency of storms within a 120‐km radial distance of Carvel. For each day, the intensity of the convection was quantified by counting the total number of 1‐km² pixels in the study area that exceeded the severe thresholds for VIL, UVIL and Z7. The severe thunderstorm algorithms were found to be very effective at correctly identifying the observed severe thunderstorm events. All three radar parameters indicated a diurnal cycle, with severe convection starting after noon and peaking between 16:00 and 18:00 Local Daylight Time. A positive correlation was evident between the observed storm severity and the daily UVIL and Z7 pixel counts. The daily UVIL and Z7 pixel counts were also positively correlated with the Convective Available Potential Energy (CAPE) calculated from proximity soundings.