三维可压缩大气中的云尺度模式

我们设计了一个三维云尺度模式,它的控制方程由二部分组成:一是Euler式的可压缩运动方程,连续方程,压力变化方程及热力学方程;二是Lagrange式的云-降水微物理方程组。由于声波的存在对各个方程积分过程的影响程度不同,运用了时间分离方法。网格结构设计了二种:一般的和交叉的,并分别采用了松野积分方案和半隐式积分方案。模式经过严格的调试以后,进行了多个个例模拟研究,表明模式是稳定的,给出了合理的三维对流的发展图象,不仅模拟出垂直对流环流,而且模拟出对应的水平涡坏。利用该模式,研究了水平涡坏的形成和发展对云内下沉气流激发的影响和作用。     

The interaction of ellipsoidal vortices with background shear flows in a stratified fluid

We show that an arbitrarily oriented ellipsoid of uniform potential vorticity, embedded in a background flow described by a quadratic streamfunction, is an exact solution of the quasigeostrophic equations governing motion in a uniformly stratified, unbounded fluid. This type of flow includes plane horizontal shear and strain as well as uniform vertical shear of a unidirectional horizontal flow. We derive ordinary differential equations describing the motion of such a vortex and discuss some aspects of their solutions. We note the existence of steady states (solutions in which the vortex is in equilibrium with the background flow), of periodic solutions near these steady states, of non-periodic trajectories which nervertheless remain in the vicinity of the steady states, and of solutions which represent the shearing out of the vortex by the background flow. We try to use this information to propose partial answers to the question of when a given horizontal or vertical shear flow is likely to destroy a vortex and when a vortex might survive external shear and strain.     

正压大气中尺度半平衡和准平衡动力学模式

应用描写正压大气运动的基本方程组，分析了中尺度大气运动的物理特征，指出非平衡强迫运动是引起中尺度重要天气演变的根本原因。中尺度动力学方程组是中尺度动力学理论研究的基础，因此，结合中尺度大气运动的基本特征，依据严格的尺度分析理论和摄动理论，简化基于流体力学和热力学的大气动力学方程组使之能够恰当地描述出中尺度运动的基本特征，对于中尺度动力学的发展是极为必要的。基于非线性平衡方程所得到的半平衡和准平衡动力学模式分别与半地转和准地转模式极为相似，它们可以较精确地描述中尺度大气运动的基本特征，因而，可作为中尺度动力学研究的理论基础。将准平衡动力学模式应用于中尺度涡旋系统的研究，结论表明中尺度平衡涡旋系统主要是受梯度风控制，其流场和气压场的发展演变则由一个演化方程来描写，获得了较为理想的结果。     

高层冷涡对台风路径影响的数值模拟和动力分析

通过六层斜压干模式模拟了高层冷涡对台风运动的影响，并用涡度方程各动力项的诊断分析，证实了高层冷涡对台风运动的影响主要是通过改变台风中心周围的环流结构而达到的。分析还指出了总涡度倾向和台风运动的直接联系以及这种联系的持续稳定性。同时也发现总涡度倾向主要来自于涡度水平平流和散度场的贡献。说明台风运动主要由正压性动力因子控制。     

Dynamic and Numerical Study of Waves in the Tibetan Plateau Vortex简

In terms of its dynamics, The Tibetan Plateau Vortex （TPV） is assumed to be a vortex in the botmdary layer forced by diabatic heating and friction. In order to analyze the basic characteristics of waves in the vortex, the governing equations for the vortex were established in column coordinates with the balance of gradient wind. Based on this, the type of mixed waves and their dispersion characteristics were deduced by solving the linear model. Two numerical simulations with triple-nested domains--one idealized large-eddy simulation and one of a TPV that took place on 14 August 2006---were also carried out. The aim of the simulations was to validate the mixed wave deduced from the governing equations. The high-resolution model output data were analyzed and the results showed that the tangential flow field of the TPV in the form of center heating was cyclonic and convergent in the lower levels and anticyclonic and divergent in the upper levels. The simulations also showed that the vorticity of the vortex is uneven and might have shear flow along the radial direction. The changing vorticity causes the formation and spreading of vortex Rossby （VR） waves, and divergence will cause changes to the n~otion of the excitation and evolution of inertial gravity （IG） waves. Therefore, the vortex may contain what we call mixed ：inertial gravity-vortex Rossby （IG-VR） waves. It is suggested that some strongly developed TPVs should be studied in the future, because of their effects on weather in downstream areas.     

A new large-eddy simulation model for simulating air flow and warm clouds above highly complex terrain. Part I: The dry model

This paper presents the dry version of a new large-eddy simulation (LES) model, which is designed to simulate air flow and clouds above highly complex terrain. The model is three-dimensional and nonhydrostatic, and the governing equations are sound filtered by use of the anelastic approximation. A fractional step method is applied to solve the equations on a staggered Cartesian grid. Arbitrarily steep and complex orography can be accounted for through the method of viscous topography. The dynamical model core is validated by comparing the results for a spreading density current against a benchmark solution. The model accuracy is further assessed through the simulation of turbulent flow across a quasi two-dimensional ridge. The results are compared with wind-tunnel data. The method of viscous topography is not restricted to moderately sloped terrain. Compared to models using curvilinear grids, it allows this model to be applied to a much wider range of flows. This is illustrated through the simulation of an atmospheric boundary-layer flow over a surface mounted cube. The results show that the dry model version is able to accurately represent the complex flow in the vicinity of three-dimensional obstacles. It is concluded that the method of viscous topography was successfully implemented into a micrometeorological LES model. As will be shown in Part II, this allows the detailed study of clouds in highly complex terrain.     

热力强迫的非线性奇异惯性重力内波与高原低涡的联系

利用相平面分析法,由非绝热大气运动方程组导出了与非线性惯性重力内波有关的KdV方程,然后用直接积分法得到两类有天气意义的孤立波解,重点分析了与青藏高原暖性低涡有联系的一类具有间断点的奇异孤立波解的特征,进而讨论了高原非绝热加热对高原低涡生成、移动及高原低涡暖心结构的作用。     

台风移动规律的研究 Ⅰ.非绝热加热与水平温度分布的影响

根据大气运动原始方程组导出一个支配台风中心移动的基本方程。方程中包括了非绝热加热、温度场分布、地形与摩擦等各种可能影响台风移动的强迫因子。对非绝热加热与水平温度分布的作用所作分析表明,非轴对称的非绝热引导作用可使台风加速、减速或转向运动;温度场上的冷区对台风有吸引作用。      

A STUDY ON TYPHOON MOVEMENT PART Ⅰ:THE EFFECT OF DIABATIC HEATING AND HORIZONTAL TEMPERATURE DISTRIBUTION

A basic equation governing the movement of a typhoon has been derived based on the system of primitive equations of motion in the atmosphere. The role of several forcing factors which cause the deviation of the typhoon from the steering current have been discussed based on the governing equation. What is presented in Part Ⅰ is a theoretical analysis on the effects of diabatic heating and the horizontal temperature distribution. It is shown that the accelerations of a typhoon caused by diabatic heating and temperature advection coincide with the direction of the volume-averaged "diabatic steering velocity" QV and the "steering velocity of temperature advection" A_TV (V is the air velocity,Q the diabatic heating rate and A_T the temperature advection ), respectively. The precipitation (or condensation heating) on the right (left) side of a typhoon will accelerate (decelerate) the typhoon. The precipitation in the front (rear ) of the typhoon will turn it to the left (right) of its ordainal path. A typhoon will speed up (slow down) when it moves towards a region of cold (warm) air.     

GRAPES区域扰动预报模式动力框架设计及检验

设计了适用于四维变分同化系统的扰动预报模式GRAPES_PF。根据GRAPES的地形追随坐标非静力原始方程组,采用小扰动分离方法推导微分形式的线性扰动预报方程组,并利用与GRAPES非线性模式相似的数值求解方案求解线性扰动微分方程组。在设计扰动预报模式时采用了两个时间层半隐式半拉格朗日方案对动量方程、热力学方程、水汽方程和连续方程进行时间差分,空间差分方案的变量分布水平方向采用Arakawa C跳点网格,垂直方向采用Charney/Phillips跳层。利用代数消元法进一步推导得到只包含未来时刻扰动Exner气压的亥姆霍兹方程,进而通过广义共轭余差法（GCR）求解,在此基础上得到未来时刻扰动量的预报值。基于所开发的扰动模式开展了数值试验。首先在非线性模式中施加一个中尺度初始扰动高压,得到初始扰动在非线性模式中的后续演变,然后将相同的初始扰动作为扰动模式的初值进行时间积分,将扰动模式预报的结果与非线性模式的结果做了对比。结果表明,所开发的扰动模式GRAPES_PF较好地模拟了惯性重力内波的传播过程:初始高压扰动激发了一个迅速向外传播的惯性重力内波,在气压场向风场适应的过程中,水平风场、垂直运动、位温和湿度等变量均出现了扰动增量,与非线性模式得到的结果相当接近。GRAPES_PF作为GRAPES非线性模式的合理线性模式为建立基于线性扰动预报的区域四维变分同化系统奠定了科学基础。      

DESIGN OF A THREE-DIMENSIONAL GLOBAL ADIABATIC SPECTRAL PRIMITIVE EQUATION MODEL

A three-dimensional(3D)global adiabatic spectral primitive equation model has beendesigned.The main features are as follows.(1)Adoption of spherical harmonics and Tschebyscheff polynomials as the basis functions inthe horizontal and vertical respectively,but the unknowns in the spectral equations are two-dimensional;(2)Inclusion of the tropopause,which may vary with time and space;(3)Suggestion of a spectral method for representing the vertical structure of the atmosphereapplicable to the unsmoothed profile case;(4)In consideration of nonlinear vertical aliasing a technique is proposed to avoid it andnonlinear computational instability.Based on real data forecasts up to 48 hours have been performed.The results show that thestatistical verifications with the model are superior on the average to those with the T42L9 usedoperationally before 1995 at NMC of China at the same mean resolution.     

DESIGN OF A THREE-DIMENSIONAL GLOBAL ADIABATIC SPECTRAL PRIMITIVE EQUATION MODEL*

A three-dimensional(3D) global adiabatic spectral primitive equation model has been designed.The main features are as follows.(1) Adoption of spherical harmonics and Tschebyscheff polynomials as the basis functions in the horizontal and vertical respectively,but the unknowns in the spectral equations are two-dimensional;(2) Inclusion of the tropopause,which may vary with time and space;(3) Suggestion of a spectral method for representing the vertical structure of the atmosphere applicable to the unsmoothed profile case;(4) In consideration of nonlinear vertical aliasing a technique is proposed to avoid it and nonlinear computational instability.Based on real data forecasts up to 48 hours have been performed.The results show that the statistical verifications with the model are superior on the average to those with the T42L9 used operationally before 1995 at NMC of China at the same mean resolution.     

双三次数值模式与理想Lamb波、龙卷扰动对比模拟分析

通过"双三次曲面拟合—时间步长积分—双三次曲面拟合……",实现成为一种双三次曲面拟合新算法数值模式。它对模式大气作非线性(空间二阶可导)描述,是用数值分析(三次样条/双三次曲面)与计算方法近似求解大气运动非线性偏微分方程组。用Z坐标系高分辨率双三次数值模式,采用原始大气运动方程组和采用欧拉时间积分方案,设置理想扰动,对大气声波Lamb波做数值模拟;采用大气不可压假定,除去声波,对大气重力波龙卷扰动做数值模拟。对比模拟发现:理想Lamb波以声速在水平方向传播,扰动能量频散快,仅能在原地持续数秒钟;理想龙卷扰动则在原地可持续约1 min,且波动内圈(外圈)自下至上始终处于风场辐合(辐散)状态,具冷心结构和气压驻波特征,可因水汽进入扰动与借助凝结潜热释放而得到发展。     

基于螺旋度的中尺度平衡方程及非平衡流诊断方法

在回顾大尺度准地转平衡理论、各种平衡方程、平衡模式及非平衡流诊断工具的基础上,对平衡方程、非平衡方程给出了具体的定义.并在此基础上,进一步考虑中尺度强对流天气系统的特征,指出中尺度也有平衡运动的存在.但是由于中尺度对流系统中强烈的辐散风效应以及不可忽略的垂直运动的作用,以散度方程为基础的各种近似平衡方程不足以描述中尺度强对流天气系统的平衡运动,进而提出了从能够同时考虑旋转、辐散及垂直运动作用的螺旋度方程出发,寻找中尺度的平衡方程.在所得的平衡方程基础上,给出了相应的平衡模式和非平衡方程.并进一步将非平衡方程分解,用来诊断非平衡过程的平衡破坏和平衡恢复两个阶段,同时将它们与水平螺旋度和垂直螺旋度联系起来.     

A study on the motion characteristics and their impact on the wind measurement post-processing of the GPS dropwindsonde Part I: effects of the wind-finding equations

Since Global Positioning System dropwindsonde wind measurements are taken in neither a conventional Eulerian framework nor a perfect Lagrangian framework, proper post-processing is necessary to derive conventional Eulerian wind statistics from dropwindsonde measurements. In this study, the equations governing the dropwindsonde motions were first linearized and then analytically solved to explore the effects of the wind-finding equations introduced by Hock and Franklin (Bull Amer Meteor Soc 80:407–420, 1999) when retrieving horizontal winds from dropwindsonde measurements. It is found that the wind-finding equations are essential for calculating turbulence statistics from dropwindsonde measurements. To confirm, numerical simulations of dropwindsonde motions in a pseudo-stochastic wind field were further conducted based on the full nonlinear dropwindsonde motion-governing equations. Based on the simulation results, the present paper showed the effects of the wind-finding equations and the companion paper discussed the impacts of various post-processing/composition schemes on both the mean and turbulent wind statistics composited from pseudo-dropwindsonde measurements.     

半拉格朗日、半隐式欧拉方程组大气数值模式研究

介绍了一个具有较高时间积分效率的三维弹性大气数值模式。其中,控制方程为能够描述大气非静力及可压缩性的欧拉方程组,时间积分采用了高效率的“半拉格朗日、半隐式”方案。通过引用一个简化的“云物理过程”参数化方案,针对大气中深厚湿对流过程的若干问题进行了数值试验,结果表明,模式能够对该过程中的一些基本和复杂现象进行有效地模拟。试验结果还表明,动力学框架具有很好的稳定性,能够实现高效率的时间积分,它还具有较好的频散特性,保证了空间计算的精度,从而完好地描述了风暴的形态。     

关于不同尺度大气运动中的雷诺交换

本文从多尺度分解概念出发,建立了多尺度Reynolds方程组。证明了平均运动的Reynolds交换项应为各级子平均运动非线性项的平均和。文中将子尺度运动处理为描述质点个别运动的Langevin形式以避免Euler方式导致的高阶闭合困难,简单地得到了K闭合表示,给出了动量、热量、质点交换系数的表达式并阐明了它们之间差异的形成原因。此外本文还给出了表现无序脉动量在导向力(如浮力、科氏力)作用下建立有序平均量梯度的负K值及其存在条件,解释了大气中大尺度运动的一些负粘性现象。     

SYMMETRIC AND ASYMMETRIC MOTIONS IN THE BAROTROPIC FILTERED MODEL ATMOSPHERE

By expressing the stream function in terms of the symmetric and the antisymmetric components with respect to the equator,the barotropic vorticity equation can be separated into two equations,one describing the behaviours of the atmospheric symmetric motion,and the other those of the atmospheric antisymmetric motion.From them,for the entire global surface at the equivalent barotropic level,the conservations of several basic quantities,such as vorticity,angular momentum etc.in the symmetric and antisymmetric cases,have been discussed.In addition,the energy budget equations and the energy conservation expressions for the two kinds of motion are given.It can be seen from them that there are not only the conversion between the zonal mean kinetic energy and the disturbed kinetic energy in the atmosphere,but also the conversion between the kinetic energy generated by the symmetric and antisymmetric motions.In the case of including orography and horizontal diffusion into the vorticity equation,a mechanism of the generation of asymmetric behaviours of the atmosphere is proposed.The results show that the asymmetric distribution of orography and that of horizontal diffusion coefficients are likely the causes leading to the asymmetric motion.Finally,a theoretical comparison between the global model and the hemispheric one from the physical point of view is made.     

DEVELOPMENT OF MESOSCALE DISTURBANCE IN THREE-DIMENSIONAL INHOMOGENEOUS VORTEX

Starting from the anelastic equations describing deep convection in cylindrical coordinates, the WKBJ method is used to discuss the stability of asymmetric three-dimensional inhomogeneous vortex under the conditions of nonhydrostatic and non-equilibrium gradient wind. From the equation of wave action, the development of disturbance is qualitatively analyzed.     

非静力AREM模式设计及其数值模拟I:非静力框架设计

AREM（Advanced Regional Eta-coordinate Model）对中国暴雨、台风等中尺度天气系统的模拟、预报能力突出。但是伴随模式分辨率的提高,制约该模式发展的一个问题日渐突出,即"静力平衡近似"的约束。本文通过对原静力平衡系统进行修正,引入高阶订正参数定义第三运动方程来构建该模式的非静力动力框架。我们基于Euler原始方程组,有效结合原静力平衡模式的标准层结扣除及IAP（Institute of Atmospheric Physics）变换方法,推导出了球面余纬坐标下的非静力框架,并在E网格和η坐标下进行了时空离散。采用时间两部分离技术进行积分运算以提高计算效率,并通过"追赶法"结合迭代法计算声波。此框架可方便地继承静力平衡框架的特点,最大限度地保留静力平衡框架的优势。理论推导和数值试验表明,当非静力框架退化为静力平衡框架后,方程形式及其模拟结果一致。在文章第二部分将通过理想和实例试验检验非静力模式性能。