正压半地转模式中的非频散周期解

本文求得正压半地转模式中非线性正压Rossby波的非频散周期解的存在条件与解。论证了Taylor展开的可能性，并给出了相应的无量纲a判据。最后给出了非线性特征波动的波速公式及波参数间的一些诊断关系。     

正压大气中非线性重力惯性波的非频散周期解——论Taylor展开的可能性

本文论证了正压大气中非线性重力惯性波的非频散周期解存在性及找到了该波解存在条件。通常来说要得到解析解是困难的,故利用Taylor展开来得到近似解。本文给出了Taylor展开的可能性。然后在Taylor展开允许的情况下,我们得到了近似解的表达式及波速公式,给出了该波动流场与位势高度场的配置结构,并揭示了非线性效应使得波动结构变得不对称。     

Wave-CISK的一个斜压半地转模式和低频振荡

本文建立了一个描写低纬大气运动的斜压半地转的wave-CISK模式,其中引入了一个反映CISK机制的无量纲的凝结潜热参数η(z),并求得了η=0和η≠0条件下wave-CISK模式的解析解,理论研究进一步说明wave-CISK机制对于大气低频振荡起重要的作用。     

A BAROCLINIC SEMI-GEOSTROPHIC MODEL USING THE WAVE-CISK THEORY AND LOW-FREQUENCY OSCILLATION*

A baroclinic semi-geostrophic model describing the atmospheric motion in low latitudes and using the wave-CISK theory is established and the analytic solution is obtained. It is shown that the effect of nondimensional latent heat parameter which is assumed to depend only on height and used to state the wave-CISK mechanism is very important to the low-frequency oscillation.     

INFLUENCES OF TOPOGRAPHY ON BAROCLINIC SOLITARY ROSSBY WAVES IN A MULTILEVEL MODEL

The KdV equation with topography included in an N-level model is derived. It is shown that if the topography ex-ists. the KdV equation may describe the solitary Rossby waves in the case of basic current without vertical shear, and itis no necessary to introduce the MKdV equation. The results of calculations show that the change of horizontal shearpattern of basic flow may cause an important change of the streamline pattern of the solitary waves with the oddmeridional wavenumber m, and has no effect for the even meridional wavenumber m. The vertical shear increases thesteepness of the barotropic solitary modes, and it has a complicated effect on the baroclinic modes. The influences oftopographic slope on the solitary waves are very great. The southern and northern slopes of topography may cause dif-ferent solitary wave patterns, with the effect of northern slope greater. The effect of Froude number on the solitarywaves is generally to steepen the solitary waves, however, the effect also depends on the meridional wavenumber m andthe modes of solitary wave.     

年周期气候态对气候模式的修正

文中从两个独立的假定导出了距平模式,即:假定年周期气候态为控制实际气候系统演化方程组的解或假定反映年周期气候态的基态量远大于反映气候扰动态的扰动量。第一个假定放宽了导出距平模式的条件,而在第二个假定下距平模式在一定的近似程度下是成立的。另外笔者注意到:距平模式通过引入实际观测到的年周期态,相当于在非距平模中引入了年周期气候态的修正项。     

THE FORMULATION OF FIDELITY SCHEMES OF PHYSICAL CONSERVATION LAWS AND IMPROVEMENTS ON A TRADITIONAL SPECTRAL MODEL OF BAROCLINIC PRIMITIVE EQUATIONS FOR NUMERICAL PREDICTION

In this paper,two formulation theorems of time-difference fidelity schemes for generalquadratic and cubic physical conservation laws are respectively constructed and proved,with earliermajor conserving time-discretized schemes given as special cases.These two theorems can providenew mathematical basis for solving basic formulation problems of more types of conservative time-discrete fidelity schemes,and even for formulating conservative temporal-spatial discrete fidelityschemes by combining existing instantly conserving space-discretized schemes.Besides.the twotheorems can also solve two large categories of problems about linear and nonlinear computationalinstability.The traditional global spectral-vertical finite-difference semi-implicit model for baroclinicprimitive equations is currently used in many countries in the world for operational weatherforecast and numerical simulations of general circulation.The present work,however,based onTheorem 2 formulated in this paper,develops and realizes a high-order total energy conservingsemi-implicit time-difference fidelity scheme for global spectral-vertical finite-difference model ofbaroclinic primitive equations.Prior to this,such a basic formulation problem remains unsolved forlong,whether in terms of theory or practice.The total energy conserving semi-implicit schemeformulated here is applicable to real data long-term numerical integration.The experiment of thirteen FGGE data 30-day numerical integration indicates that the newtype of total energy conserving semi-implicit fidelity scheme can surely modify the systematicdeviation of energy and mass conserving of the traditional scheme.It should be particularly notedthat,under the experiment conditions of the present work,the systematic errors induced by theviolation of physical laws of conservation in the time-discretized process regarding the traditionalscheme designs(called type Z errors for short)can contribute up to one-third of the totalsystematic root-mean-square(RMS)error at the end of second week of the integration and exceedone half of the total amount four weeks afterwards.In contrast,by realizing a total energyconserving semi-implicit fidelity scheme and thereby eliminating corresponding type Z errors,roughly an average of one-fourth of the RMS errors in the traditional forecast cases can be reducedat the end of second week of the integration,and averagely more than one-third reduced at integraltime of four weeks afterwards.In addition,experiment results also reveal that,in a sense,theeffects of type Z errors are no less great than that of the real topographic forcing of the model.The prospects of the new type of total energy conserving fidelity schemes are very encouraging.     

热带对流活动对热带内外地区环流季内遥相关变化的作用

基于ＥＣＭＷＦ客观分析资料，本文采用诊断分析的方法研究了１９８３／１９８４和１９８６／１９８７两年冬季季内３０—６０ｄ低频域中热带对流与热带外环流以及低频扰动动能频散之间的关系。结果表明，热带对流强度上的差异可以造成热带内外地区季内遥相关波列以及低频波能频散上的差别。热带对流作用可以是联系热带内外地区季内遥相关作用的一个重要的衔接因子。     

冬季北半球大气低频环流型的年际变化特征

采用NCEP/NCAR逐日再分析资料,利用31点数字滤波器提取了58个冬季(1951/1952-2008/2009年)的500 hPa高度场低频分量,通过经验正交函数分析方法定义了6种低频环流型.从逐年低频环流型的差异和低频环流型系数两个角度分析低频环流型的年际变化特征;给出了58个冬季的主要低频环流型并分析了逐年低频...     

THE FORMULATION OF FIDELITY SCHEMES OF PHYSICAL CONSERVATION LAWS AND IMPROVEMENTS ON A TRADITIONAL SPECTRAL MODEL OF BAROCLINIC PRIMITIVE EQUATIONS FOR NUMERICAL PREDICTION*

In this paper,two formulation theorems of time-difference fidelity schemes for general quadratic and cubic physical conservation laws are respectively constructed and proved,with earlier major conserving time-discretized schemes given as special cases.These two theorems can provide new mathematical basis for solving basic formulation problems of more types of conservative time-discrete fidelity schemes,and even for formulating conservative temporal-spatial discrete fidelity schemes by combining existing instantly conserving space-discretized schemes.Besides.the two theorems can also solve two large categories of problems about linear and nonlinear computational instability.The traditional global spectral-vertical finite-difference semi-implicit model for baroclinic primitive equations is currently used in many countries in the world for operational weather forecast and numerical simulations of general circulation.The present work,however,based on Theorem 2 formulated in this paper,develops and realizes a high-order total energy conserving semi-implicit time-difference fidelity scheme for global spectral-vertical finite-difference model of baroclinic primitive equations.Prior to this,such a basic formulation problem remains unsolved for long,whether in terms of theory or practice.The total energy conserving semi-implicit scheme formulated here is applicable to real data long-term numerical integration.The experiment of thirteen FGGE data 30-day numerical integration indicates that the new type of total energy conserving semi-implicit fidelity scheme can surely modify the systematic deviation of energy and mass conserving of the traditional scheme.It should be particularly noted that,under the experiment conditions of the present work,the systematic errors induced by the violation of physical laws of conservation in the time-discretized process regarding the traditional scheme designs(called type Z errors for short) can contribute up to one-third of the total systematic root-mean-square(RMS) error at the end of second week of the integration and exceed one half of the total amount four weeks afterwards.In contrast,by realizing a total energy conserving semi-implicit fidelity scheme and thereby eliminating corresponding type Z errors,roughly an average of one-fourth of the RMS errors in the traditional forecast cases can be reduced at the end of second week of the integration,and averagely more than one-third reduced at integral time of four weeks afterwards.In addition,experiment results also reveal that,in a sense,the effects of type Z errors are no less great than that of the real topographic forcing of the model.The prospects of the new type of total energy conserving fidelity schemes are very encouraging.     

A STATISTICAL MODEL FOR PREDICTION OF INTENSITY AND FREQUENCY OF TROPICAL CYCLONES MAKING LANDFALL ON CHINA

Based on NCEP/NCAR reanalysis data and Yearbook of China landfalling tropical cyclones(hereafter CLTC) from 1949 to 2008,correlation between CLTC frequency/intensity and 500 hPa height field and sea surface temperature(SST) fields are investigated and employed for TC statistical prediction.A prediction model for yearly and monthly intensity and frequency of CLTC is established with binomial curve fitting by choosing the gridpoints with high correlation coefficients as composite factors.Good performance of the model in experiments shows that the model could be used in routine forecast.     

物理守恒律保真格式构造与数值预报斜压原始方程传统谱模式改进研究

文中构造并证明了一般二次和三次物理守恒律时间差分保真格式两个构造定理,以往一些主要时间离散守恒格式构造方案可作为两个定理特例给出。它们不仅可为解决更加广泛类别的时间离散保真格式构造基本问题提供适用数学基础,而且也为结合已有瞬时空间离散守恒格式,解决更加广泛类别的时-空离散意义下保真格式构造基本问题提供适用的数学基础。此外,文中两个定理还可解决两大类问题的线性和非线性计算不稳定性问题。斜压原始方程传统半隐式全球谱-垂直有限差分模式目前是世界上许多国家的业务预报和大气环流模式。本工作利用文中新构定理,构造并且实现了斜压原始方程全球谱-垂直有限差分模式半隐式高阶全能量守恒方案。以往该项基本问题无论在理论还是实践上长期以来一直都未能得到解决。