THE MODELING IMPROVEMENT OF HURRICANE ANDREW BY THE TECHNIQUE OF IRREVERSIBLE THERMODYNAMIC OPERATORS*

Although incorporating the horizontal diffusion into the atmospheric governing equations is a part of the dynamics of a model,it is based on the computational consideration originally,which is to overcome the nonlinear aliasing or computational instability and smooth the physical fields at the same time.The generally used forms of the fourth-order diffusion,either linear or nonlinear,however,can not properly describe the real physical diffusion processes and thus affect the accuracy of forecasting and modeling.In this paper,based on the nature of the physical diffusion.the scheme of horizontal diffusion of the MM5 Version 3 is improved according to the second law of thermodynamics which controls the irreversable evolutionary direction of a many-body system and the potential ability of the improvement of the new scheme in modeling accuracy is revealed by introducing the technique suggested in this paper,via a theoretical case and the computational case of the hurricane Andrew that landed on Florida in 1992.     

MM5模式水平扩散项的改进及其对陕西“8.28”暴雨模拟的影响

在数值预报发展的过程中,我们通常把水平扩散项当作滤波器用来光滑或是过滤掉模式积分过程中所产生的毫无天气意义的并会引起非线性计算不稳定的所谓计算噪音或“超短波”,从而达到阻尼虚假短波以及抑制非线性计算不稳定的目的,但这仅仅只是从计算数学或计算物理的角度来考虑,并不能真正反映扩散的物理本质。本文尝试运用热力学第二定律的思想对MM5模式中的水平扩散项进行改造,以便更好地消除原模式中的扩散项所导致的Gibbs振荡现象。通过对陕西2003年8月28日暴雨的数值模拟表明,改进后的MM5模式的输出量（如相对湿度、温度、速度）的相关系数以及均方根误差均有明显的改进。     

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。     

北半球七层原始方程谱模式（三）及其五天中期数值预报试验

北半球七层原始方程谱模式ff考虑了较完整的物理过程:（1）地形作用（采用了σ坐标系）和地面摩擦；（2）动量、热量，水汽的水平扩散过程和垂直扩散过程（其中包括了下垫面感热和水汽作用）；（3）水汽凝结潜热作用；（4）云和辐射作用；（5）积云对流过程等。上述模式采用了非线性平衡方程初值化方法。并利用逐日客观分析资料，制作5天中期数值预报试验。本文给出了1982年冬季和夏季的20个例子的五天数值预报验证结果和一个例子的中期数值预报图和对应的实况图。预报效果比较好。在数值预报试验中，虽然纬向波数只取15个波，但所取得的短期、中期的预报效果能和一些较高分辨率模式的预报效果相比较。     

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、     

LONG VALID TIME ENERGY PERFECT CONSERVATIVE FIDELITY SPECTRAL SCHEMES OF BAROTROPIC PRIMITIVE EQUATIONS*

In accordance with a new compensation principle of discrete computations,the traditional meteorological global (pseudo-) spectral schemes of barotropic primitive equation (s) are transformed into perfect energy conservative fidelity schemes,thus resolving the problems of both nonlinear computational instability and incomplete energy conservation,and raising the computational efficiency of the traditional schemes.As the numerical tests of the new schemes demonstrate,in solving the problem of energy conservation in operational computations,the new schemes can eliminate the (nonlinear) computational instability and,to some extent even the (nonlinear) computational diverging as found in the traditional schemes,Further contrasts between new and traditional schemes also indicate that,in discrete operational computations,the new scheme in the case of nondivergence is capable of prolonging the valid in-tegral time of the corresponding traditional scheme,and eliminating certain kind of systematical computational "climate drift",meanwhile increasing its computational accuracy and reducing its amount of computation.The working principle of this paper is also applicable to the problem concerning baroclinic primitive equations.     

基于单多普勒雷达的光流法改进技术

本文对基于径向速度的光流法在实际应用中存在的误差进行了分析,并提出了有效的改进方案。合成数据试验结果表明:基于径向速度的光流法在反演低仰角(小于2.5°)数据和包含非线性变化的实际风场时存在较大的误差。在低仰角情况下,由于径向速度在垂直方向的分量非常小,导致垂直速度的反演包含较大的计算误差并影响水平速度的反演精度。而当实际风场存在较大非线性变化时(如锋面、切变线等),算法中的局部约束条件被破坏,导致切变区域反演精度降低或出现奇异值。针对这两种情况,本文提出了有效的改进算法。在低仰角情况下引入了简化的约束方程,并加入了径向速度一致性的约束条件来克服实际风场非线性带来的误差。通过理想数据试验和实际个例的检验发现,改进后的算法可以有效地提高风场反演的精度和应用范围。     

一种新的正定平流方案及其在水汽预报方程中的应用

本文在Smolarkiewicz(1983)方案的基础上,提出了一种新的正定平流方案。它是无条件计算稳定的,形式简单、物理意义清楚且阻尼小,能够很容易地应用到多维模式中。文中通过一简单的平流试验,与其它几种有名的正定平流方案进行了比较;最后将这种方案应用到国家气象中心细网格有限区域业务预报模式水汽预报方程中,避免了原水汽计算方案产生严重负水汽的问题,并对24h降水预报场进行分析。     

有地形模式中气压梯度力误差扣除法

：在现有有地形的数值模式中，陡峭地形区气压梯度力的计算存在一个普遍问题，即计算精度较高的格式比较繁琐而费时，简单省时的格式又不精确和不稳定。为解决这个问题，作者等在最近提出了一种方法，称为气压梯度力的误差扣除法。该方法假定：气压梯度力的计算误差主要来自地形而与气压形势关系较小。用理想场对该方法进行检验后表明，这一方法是成功的。本文则用气候模式对作者提出的有地形数值模式中气压梯度力的误差扣除法进行了模拟检验。所用模式是作者等使用多年的Ｐ－混合坐标系５层模式，选用了四种气压梯度力的计算格式，即ＤＤＤ格式、Ｃｏｒｂｙ格式、平均温度格式和经典中央差格式。比较了这四种格式在有无误差扣除时的模拟结果，发现：对于计算精度较高的格式，如ＤＤＤ格式、Ｃｏｒｂｙ格式及平均温度格式，有无误差扣除的结果相差不大，但误差扣除法仍可在一定程度上改善模拟效果。对于计算精度差的格式，如经典中央差格式，在无误差扣除时计算不稳定，得不到模拟结果，进行误差扣除后，从根本上提高了其计算精度，因而也提高了计算的稳定性，达到了较满意的模拟效果。而且与其它格式的模拟结果相当接近。本文提出的误差扣除法可同时用于格点模式和谱模式。     

Application and numerical experiments with a highly-accurate advection scheme in a regional transfer model

Summary This paper examines a 19-level regional transfer model, EM3. The sensitivity of the results to different transfer schemes and effectiveness of using a high-precision scheme in raising modeling accuracy is examined. The use of a good scheme to improve the ability to simulate horizontal diffusion close to reality is also explored. EM3 was run with different precision schemes, i.e., a high-precision second-order moment conservation prather scheme (SOM for short) and an anti-diffusion Smolarkiewicz scheme (Smolar for short). The model was run 70 hrs. Results indicate that EM3 is much more sensitive to the precision of the schemes. SOM and Smolar, were compared, the former showing very weak numerical diffusion and computational dispersion so that positive solutions were kept. It is shown that i) numerical diffusion in SOM is one order of magnitude less compared to the latter; ii) the central intensity of transferred SO₂ increases by 4–5 times and the average motion trajectory of the concentration center is much improved in SOM; iii) SOM allows EM3 to precisely reflect the real horizontal diffusion. Therefore, choice of a high-precision advection scheme for EM3 will contribute greatly to an increase in its simulation accuracy.With 4 Figures     

采用隐式立方样条计算平流过程的数值模式及理想实验

本文介绍了一种用隐式立方样条求解平流方程的数值方法,并从理论上对其无条件稳定性进行了证明,在此基础上建立了一个在地形坐标系下的两维原始方程模式,模式在行星边界层参数化中引入了湍流动能方程,在模式顶部引入了吸收层.数值实验表明:模式有较好的计算稳定性,对较高的模式水平分辨率和复杂地形均有较强的适应能力;对复杂地形和下垫面非均匀热源条件下中尺度系统的模拟能获得合理的结果,并具有较高的精确度.     

模式垂直分辨率对梅雨锋暴雨数值模拟的影响

利用中尺度数值模式MM5(V3),对2003年7月7日~8日发生在武汉地区的一次梅雨锋暴雨过程进行了数值模拟。采用经过简化处理的基于矢量模的双参数最优化处理方法,对模式大气进行了垂直分层。在水平分辨率不变的情况下,数值模式的垂直分层分别采用25层和36层进行了对比模拟试验。模拟结果表明,水平分辨率达到较高的精度后,粗的垂直分辨率会放大模式中地形的作用,造成数值模拟雨带落区的偏差;要得到比较好的模拟结果,需要相应的提高数值模式的垂直分辨率。水平分辨率与垂直分辨率的不协调,会在水平方向上产生虚假的重力波,影响数值模式的模拟结果。     

准地转动量近似下风速切变线上的波动

利用准地转动量近似下的斜压两层大气的非线性方程组及非线性边界条件，研究了切变线上波动的稳定性，导出了切变线上孤立波解。较好地解释了切变线上易产生低涡等天气系统现象。     

非静力平衡大气非线性层结对称运动的稳定性和突变

在假定了环境地转风具有水平和垂直的线性切变的情况下,考虑大气层结的线性和非线性切变的作用,建立了一个非线性常微分方程组,然后构造了一个Hamilton函数,通过讨论Hamilton函数的凸凹性,得到了非线性层结对称运动的不稳定判据,同时讨论了非线性层结对称运动产生突变的条件。     

THE INITIAL WIND SCHEME OF THE HEMISPHERIC SPECTRAL MODEL AND ITS EFFECT ON THE DATA ASSIMILATION

A series of data assimilation and forecast test have been carried out with a hemispheric spectralmodel(T42L9H).It is found that the numerical scheme for determining hemispheric initial wind isimportant to data assimilation and forecast.An inappropriate scheme may cause computationalsources of divergence near the equator,which are responsible for the spurious strong precipitationand corresponding latent heat release.Obviously,this problem differs from either thehemispheric/global domain effect or the tropical data effect pointed by Dalley et al.(1981).Basedon the previous studies,the new scheme of divergence and vorticity correction is presented,andthe difference with other schemes and its effects on the data assimilation are discussed against thecontrol test.Preliminary tests have shown that the new divergence correction scheme proposed in thispaper may be a preferable choice to overcome the initial computational errors in the hemisphericdata assimilation.     

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.     

半球谱模式的风场初值及其对资料同化的影响

利用半球谱模式（Ｔ４２Ｌ９）进行了大量的资料同化和预报试验。结果表明，半球风场初值方案对资料同化和预报有重要的影响。不恰当的初值处理会导致虚假散度源，在非绝热模式中可能进一步诱发虚假的强降水与相应的潜热释放。很明显，这个问题既不同于Ｄａｌｌｅｙ［１］所分析的半球／全球范围效应，也不同于所谓的赤道资料效应。文章在前人研究的基础上，提出了散度和涡度修正方案，进而用对比试验方法讨论了该方案与其他方案的差异以及对同化的影响。初步试验表明，散度修正方案是半球资料同化中克服初值计算误差的一个较好的选择。     

EXPERIMENT ON THE FORECAST OF CHARACTERISTIC QUANTITIES OF ATMOSPHERIC TURBULENCE BY MESOSCALE MODEL MM5

In nested nonhydrostatic mesoscale model MM5,the characteristic quantities of atmosphericturbulence,i.e.,the standard deviations of the turbulent fluctuated speeds for three directions inPBL are computed by Mellor-Yamada's level 2.5 closure scheme.The magnitudes and the verticalprofiles of these quantities computed from the model are closely connected with temperature andwind speed profiles as well as the type of the ground with a significant diurnal variation,and are inagreement with known magnitudes and regularities in different stratification conditions.Hence themethod in this paper is reasonable and convincible.Their horizontal distribution depends on thehorizontal distribution of the stratification.The method of predicted characteristic quantities ofturbulence from mesoscale model in this paper can be used in the problem of atmospheric diffusionand atmospheric environment.     

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.     

预估-校正的半隐式半拉格朗日时间积分方案及其在CMA-GFS模式中的应用

CMA-GFS采用的是传统的二时间层半隐式半拉格朗日时间积分方案(SISL).拉格朗日平流速度和非线性项需要采用时间外插进行计算,在急流轴附近等梯度大值区会造成计算不稳定,甚至积分中断现象.文中通过构造预估-校正半隐式半拉格朗日时间积分方案(SISL/P-C),以减少时间外插的影响;半隐式系数由原来的0.72减小到0....