发展方程的非线性计算不稳定问题

进一步讨论了有关非线性不稳定的一些问题,其主要内容有： １．考察了有代表性的三类发展方程,指出其对应的差分格式是否出现非线性计算不稳定,与原微分方程解的性质密切相关。 ２．进一步讨论了带周期边条件的守恒型差分格式的非线性计算稳定性问题,总结了克服非线性不稳定的有效措施。 ３．以非线性平流方程为例,着重分析了带非周期边条件的非守恒差分格式的非线性计算稳定性问题,给出了判别其计算稳定性的“综合分析判别法”。     

一次梅雨锋暴雨过程中多尺度能量相互作用的研究I.理论分析

本文是讨论梅雨锋暴雨过程中多尺度能量相互作用问题的开始部分。为了分析梅雨锋暴雨过程中的多尺度能量相互作用,从z坐标系中的运动方程和热力学方程出发,把基本物理量分成大尺度背景场（>2000 km）、α中尺度（200~2000 km）和β中小尺度系统（< 200 km）分量,利用滞弹性近似,推导了大尺度背景场、α中尺度和β中小尺度系统三个尺度的动能方程和位能方程。能量方程中包含了各尺度动能之间的转换、位能之间的转换以及动能和位能之间的转换。动能方程主要包括各尺度动能之间转换项、动能输送项、水平气压梯度力做功项、垂直方向扰动气压梯度力做功项、浮力做功项、地转偏向力分量做功项以及摩擦力做功项。位能方程主要包括各尺度位能之间转换项、位能输送项、浮力做功项以及非绝热加热做功项。其中浮力做功项为位能和动能之间的能量转换项,是暴雨发生发展过程中比较关键的能量转换项。关于将能量方程用于梅雨锋暴雨过程中并且诊断能量相互作用影响暴雨发展和消亡过程的物理机制等问题,将在以后的研究中给出。     

General forms of dynamic equations for atmosphere in numerical models with topography

The atmospheric dynamic equations have been transformed from the z-coordinate system into a generalized vertical coordinate system by using a so-called DDD transformation method. Then the general-ized system is assumed being pressure, sigma or incorporated pressure-sigma coordinate system and corre-sponding equations are obtained with the second-order accuracy. It is pointed out that the usual equations are only of the first-order accuracy when their space-differential terms are approximated by central finite differences. Therefore the usual forms of the equations may result in quite large errors on steep slopes of mountains included in a model.     

一种快速预处理算法及其在浅水波方程中的应用

为了提高数值求解大气方程的计算速度,我们研究了稀疏逼近逆预处理方法及其在数值求解浅水波方程中的应用,这是一种求解大型线性方程组的快速算法,该算法的核心内容是稀疏逼近逆非零元模式的选取。首先导出了一种稀疏逼近逆的非零元模式及其确定方法,然后以浅水方程的差分格式为例,借助于GMRES迭代算法,对这种预处理快速算法应用前后的计算速度进行了比较,发现该快速算法能大幅度提高运算速度。另外,该预处理快速算法简单、易于并行,是一种值得在大气方程中推广应用的方法。     

利用T106资料制作降水概率和相对湿度预报

利用T10 6模式产品 ,采用MOS预报方法 ,建立了甘肃省 15个站降水概率和相对湿度的预报方程。通过相对湿度的绝对误差评分、降水概率的B评分和Bs 评分对预报方程的预报结果进行评估 ,认为预报方程有一定的预报能力。     

Consistent balanced models in bounded and periodic domains

An analysis is made of a family of balanced models which are intermediate in physical content and complexity between the primitive equations and quasigeostrophy. The family is based on the linear balance equations and balance equations, and is characterized by truncations of the full vorticity and divergence equations that retain a global energy invariant. Consistent initial boundary value problems for this family of models are derived, and various aspects of numerical balanced model design are discussed.     

移极旋转坐标系中的大气动力学方程

本文仅研究无粘、无地形和绝热运动假定下的大气动力学问题，用分析力学的方法求得了固定在地球上的移极旋转坐标系， 如直角坐标系， 球坐标系和柱坐标系中的第二类 Lagrange方程。从而求得普遍的大气动力学方程。所谓的视示力 —— Coriolis力和离心力 —— 与其它各种力统一处理。当地球自转轴不为坐标系的z轴时，不存在大气运动的对称和反对称性。特别值得提出的是以往很多学者利用柱坐标系来数值模拟台风(飓风)的轴对称和非轴对称性时所使用的基本方程是含糊的， 本文给出了准确的基本方程。     

T42模式产品在南昌地区大—暴雨中的统计学解释应用

使用1990—1991年5—6月的T_(42)模式产品,采用样本正态化消空剔除手段,分别建立了中雨、大雨的消空方程y_1、y_2及大-暴雨判别方程y_3。y_1、y_2减少空报,y_3减少漏报。3个方程配套使用比用单个方程的效果好,成功界限指数有明显的提高,1992年试用效果较好。     

Mathematical Derivation of Spatially-Averaged Momentum Equations for an Urban Canopy Model Using Underlying Concepts of the Immersed Boundary Method

We propose a new approach to derive spatially-averaged momentum equations for an urban canopy model that resolves buildings vertically and not horizontally. First, in order to mathematically describe the actual momentum field as a completely continuous field, the underling concepts of the immersed boundary method are employed, where we assume that (i) the entire simulation space, including that occupied by buildings, is filled with a fluid, and (ii) an external body force field exists that reduces the wind speed to zero at all positions coinciding with the space occupied by the buildings. Then, in order to obtain the required spatially-averaged momentum equations in a self-consistent manner, a spatial-averaging operation is applied to the Navier–Stokes equations that include a term representing the external force field. The applied spatial-averaging operation is equivalent to the conventional spatial filtering operation used in large-eddy simulations. To examine the significance of the subgrid-scale (SGS) stresses of the spatially-averaged momentum equations, a numerical simulation is performed for a flow around a regular array of cubical blocks with a grid resolution that is sufficient to resolve the blocks. By estimating the individual terms in the spatially-averaged momentum equations using the simulation results, we show that the SGS stresses contribute significantly to the spatially-averaged momentum budget, and therefore they should not be neglected in urban canopy modelling.     

分数阶混合随机泛函微分方程的能控性

主要研究了分数阶混合随机泛函微分方程的能控性.在无限维空间下,假设所考虑方程线性部分生成半群不是紧的,使用非紧性测度技术和Mönch不动点定理,给出了方程能控性充分条件,并通过一个例子说明了结论的有效性.     

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.     

分解算法中的两个问题

文中指出了分解算法中的两个问题:(1)为了使算法获得最佳效果,除按快、慢过程分解方程外,进一步的分解应按什么原则?(2)时间离散是否可以任意,如果不然,应采取什么形式?针对这两个问题得到的研究结果是:和一般设计简化模式一样,分解后的方程应保持原方程的重要物理性质,特别是其整体性质(如能量守恒和质量守恒等),而且,其分解后方程的解还应和原方程的解一致,至少对其中重要的解应一致.至于时间离散,在差分的情况则应采用二时间层格式;如采用三时间层格式,则会导致差分方程(或差分微分方程)和偏微分方程的不相容.     

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.     

Evaluating the generalizability of GEP models for estimating reference evapotranspiration in distant humid and arid locations

Evapotranspiration estimation is of crucial importance in arid and hyper-arid regions, which suffer from water shortage, increasing dryness and heat. A modeling study is reported here to cross-station assessment between hyper-arid and humid conditions. The derived equations estimate ET₀ values based on temperature-, radiation-, and mass transfer-based configurations. Using data from two meteorological stations in a hyper-arid region of Iran and two meteorological stations in a humid region of Spain, different local and cross-station approaches are applied for developing and validating the derived equations. The comparison of the gene expression programming (GEP)-based-derived equations with corresponding empirical-semi empirical ET₀ estimation equations reveals the superiority of new formulas in comparison with the corresponding empirical equations. Therefore, the derived models can be successfully applied in these hyper-arid and humid regions as well as similar climatic contexts especially in data-lack situations. The results also show that when relying on proper input configurations, cross-station might be a promising alternative for locally trained models for the stations with data scarcity.

     

一类扰动时滞微分方程的多重周期解

讨论了一类扰动时滞微分方程的多重周期解的存在性问题,运用凸Hamilton系统理论和Morse指标理论得到了这类方程多重周期解的存在性。     

建立η坐标系下的假不压模式及其数值试验

滤除声波的大气运动方程中不包含声波,基于滤除声波方程建立的数值模式可以用较大的时间步长进行数值积分。Durran在1989年提出了一种新的滤除声波的方法,命名为“假不可压”方程,该方程考虑了温度扰动引起的密度变化,忽略了气压扰动引起的密度变化。本文根据Durran提出的假不可压理论,推导出了一组地形追随坐标下的通量形式的假不可压方程。该方程在形式上与WRF（Weather Research and Forecasting）模式中ARW（Advanced Research WRF）动力框架的控制方程非常接近。我们进一步将推导出的假不可压控制方程改写到了WRF模式中,建立了基于WRF模式框架的假不可压模式。用构建的假不可压模式和WRF模式做了两组对比试验:湿热泡对流试验和重力流试验。比较两种模式的模拟结果,可以看出假不可压模式的模拟结果与WRF模式的模拟结果非常接近,说明在WRF模式框架下建立的假不可压模式是合理可信的。     

An invariant theory of the linearized shallow water equations with rotation and its application to a sphere and a plane

The system of linearized shallow water equations is formulated in this paper on any rotating and smooth surface M in terms of differential geometry. The system decouples into two separate equations: a scalar one for the height deviation and a vector one for the velocity field. For low and high frequencies these equations yield asymptotic equations whose solutions are the generalizations of the Poincare and Rossby waves to smooth surface. The application of these equations to the β-plane yields both new and previously known equations for the height deviation and for the velocity components. The application of the equations to the rotating spherical Earth shows that the meridional amplitudes of Poincare and Rossby waves are both described by the prolate angular spheroidal wave functions. The asymptotic and the power series expansions of the eigenvalues of these functions yield new approximations for the dispersion relations of these waves on a sphere. The new dispersion relations are very accurate in the physically relevant range of the single nondimensional model parameter – the square of the nondimensional gravity waves’ phase speed. The invariant formulation can also be applied to other surfaces that are of geophysical interest such as an oblate ellipsoid of revolution.     

上海浦西地区雾持续时间的统计释用预报

丰海浦西地区雾持续时间释用预报（PPM）的结果分析和中尺度数值预报资料基础上，应用模式输出统计（MOS）方法，构造了与上海地区成雾条件和雾的维持有一定关系的数值预报要素组成的预报因子，并进行逐步回归分析，建立了雾持续时间的统计释用预报方程，同时，提出了在小样本情况下应用交互验证分析法时克服因子不稳定的一种方法，研制了雾时业务预报的统计释用集成方案，并进行了对比分析，结果表明，统计释用预报集成方案较完全预报（PPM）的结果有明显改进。可供业务试用。     

滞弹性系统中对称扰动的涡度方程的特征分析

采用滞弹性近似下的三维中尺度大气动力学方程组,得到了滞弹性系统中对称扰动的涡度方程,并对涡度方程中各物理量进行分析。研究结果表明,相对于浅对流的情况而言,深对流情况下对称扰动的涡度方程较为复杂,滞弹性近似对于研究深对流运动是有效的。     

湿空气动热力学理论及应用研究进展

回顾了湿空气热动力学的研究进展,对未饱和湿大气、饱和湿大气及非均匀饱和湿大气的动热力方程、能量方程、连续方程等进行了梳理,指出饱和湿空气动量方程与非均匀饱和湿空气动量方程的最大区别在于对凝结过程的处理不同。饱和湿大气中,由于大气均是饱和的,由饱和造成的水凝物可处处出现,不能区分真正发生水汽凝结的区域。而非均匀饱和湿空气中,凝结发生与相对湿度的幂次方有关(即与凝结概率函数的分布有关),在相对湿度较小的区域不会出现水汽凝结,凝结区与非凝结区可自动区别,其描述的凝结过程与实际大气更接近。同时,总结了湿大气水汽凝结饱和非均匀分布的动热力物理量在高影响天气分析中的应用,最后讨论了未来推进湿空气动力学研究需重点考虑的一个内容。