变步长显式完全平方守恒差分格式

综合隐式完全平方守恒差分格式和显式瞬时平方守恒差分格式的优点，针对一类非线性发展方程构造了一种通过自动调节时间步长来保持平方守恒性的显式差分格式。它基于加小耗散的思想，但又与小耗散法有所不同。本文取的耗散项不是一般的人工耗散，而是取能够弥补由于时间离散所产生的截断误差的所谓（时间）协调耗散。因此，该格式具有较高的时间精度。在数值试验中，该类格式可取得满意的效果。     

强迫耗散非线性发展方程准完全平方守恒格式的构造

从描述大气和海洋运动的强迫耗散非线性发展方程出发，对强迫耗散非线性大气和海洋方程组显式差分格式的计算稳定性进行了分析，构造了一类强迫耗散性发展方程的显式准完全平方守恒差分格式，理论分析和数值试验证明，这类显式准完全平方守恒差分格式是计算稳定的．值得推广应用。     

An Economical Consistent Dissipation Operator and Its Applications to the Improvement of AGCM

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An economical consistent dissipation operator and its applications to the improvement of AGCM

This paper introduces a new consistent dissipation operator. It is based on the explicit square conservation scheme and the theory of consistent dissipation. The operator makes full use of the advantages of the Leap-frog scheme, i.e., its second order time precision and its explicit solution manner. Meanwhile, it overcomes the fatal disad-vantage, the absolute instability in computations, of the scheme. When it is applied to the explicit square conservation scheme, the time precision of the scheme reaches to third order. Especially, the computational stability of this scheme is as good as the third order explicit Runge-Kutta scheme. The CPU time required in computations by the scheme is less than that required by the explicit square conservation scheme with the consistent dissipation operator constructed from the Runge-Kutta method. Therefore, the new operator is an economical one. The application of the operator to the improvement of the dynamical model of the L2IAP AGCM shows its time-saving property and its good effects     

强迫耗散非线性发展方程显式差分格式的计算稳定性

基于计算准稳定的概念来分析强迫耗散非线性方程显式差分格式的计算稳定性，给出强迫耗散非线性大气方程组显示差分格式计算准稳定的判据，为设计强迫耗散非线性大气方程组计算稳定的显式差分格式提供了新的思路和理论依据。     

高精度迎风偏斜格式的比较与分析

利用一种具有任意阶精度的一般显式有限差分公式构造出高精度迎风偏斜格式，并利用 Fourier分析法评估了这些迎风偏斜格式的耗散误差与频散误差。结果表明，偶阶精度格式的数值相速度快于实际相速度，而奇阶精度格式的数值相速度慢于实际相速度。并且，偶阶精度格式的耗散误差与频散误差低于相邻的奇阶精度格式。为了检验这些格式的计算性能，在一维问题上进行了应用。首先，考虑恒定风场条件下的一维平流试验。主要选择两种不同的初始条件来评价数值格式的精度，这两种试验问题分别是高斯函数、方波函数。试验结果表明，随着数值格式精度的提高，数值格式的误差逐渐减小。而对于高于六阶精度的格式来说，改进的程度并不是很大。其次，应用各阶格式到具有两种不同初始条件的无粘Burgers方程。数值结果表明，随着数值格式阶数的增加，数值结果也得到了明显改进。而对于高于六阶精度的格式来说，进一步的变化并不明显。总之，在兼顾效率与精度条件下六阶迎风偏斜格式是最好的。     

A Two-Step Shape-Preserving Advection Scheme

This paper proposes a new two-step non-oscillatory shape-preserving positive definite finite difference advection transport scheme, which merges the advantages of small dispersion error in the simple first-order upstream scheme and small dissipation error in the simple second-order Lax-Wendroff scheme and is completely different from most of present positive definite advection schemes which are based on revising the upstream scheme results. The proposed scheme is much less time consuming than present shape-preserving or non-oscillatory advection transport schemes and produces results which are comparable to the results obtained from the present more complicated schemes. Elementary tests are also presented to examine the behavior of the scheme.     

再论发展方程差分格式的构造和应用

【摘　要】本文把一大类大气、海洋方程归结为一种发展方程,具体构造了若干定时间步长的显式完全平方守恒差分格式。并证明在一定条件下,这类格式也具有能量守恒、“广义能量”守恒和“平均尺度”守恒的特性,它表明这类格式具有较好的计算稳定性和省时性。文中还探讨了显式平方守恒格式与隐式平方守恒格式之间的密切联系。最后给出了令人满意的用四波的R-H波作数值检验的结果。     

不同模式扰动方案在风暴尺度集合预报中的对比试验研究

由于适用于中长期集合预报的模式扰动技术在风暴尺度集合预报系统中的影响并不明确,为探究不同模式扰动方案在风暴尺度集合预报中的效果,基于WRF模式设计了3组模式扰动方案:多物理扰动（MP）方案、随机物理倾向扰动（Stochastically Perturbed Parameterization Tendencies,SPPT）方案以及由MP方案与SPPT方案组合构建的一种新混合扰动（SPMP）方案。对2013年7月5—6日发生在江淮流域的一次强对流天气过程进行了数值模拟。结果表明:MP方案在积分前期的降水概率评分较高,对高层大气的扰动效果更为合理;SPPT方案主要作用于积分中后期,对大气低层及近地面的扰动效果最为理想,尤其是对于地面水汽场的模拟;SPMP方案能显著提高大气中高层各预报变量的离散度,降低均方根误差,提升集合成员的可信度,有效弥补降水预报评分在单独使用MP方案和SPPT方案不同积分时段的不足。在扰动水平传播方向上,SPMP方案的扰动形态主要受MP方案主导;垂直方向上,SPMP方案在低层的扰动形态与SPPT方案一致,在高层受MP方案控制。波谱能量分析表明3组方案的扰动能量随积分时间均有向大尺度传播的趋势,SPMP方案能有效补偿两种方案能量在各尺度的耗散。      

An improved two-time-level split-explicit integration scheme for non-hydrostatic compressible models

Summary A new two-time-level split-explicit time integration scheme for the use in non-hydrostatic compressible modelling is presented. It is demonstrated that the scheme is numerically stable and has a smaller splitting error than other comparable split-explicit schemes. This error is due to the combination of advection and fast-wave terms in the numerical scheme.To outline where the splitting error occurs and how it acts within the splitting mechanism, a short review of existing split-explicit time integration methods is given. An in-depth analysis of the eigenvalues of several two-time-level schemes is performed showing that instabilities are associated with the splitting error term. The term has different signs for forward moving and backward moving waves, causing exponential growing or decaying. This unwanted characteristic is not prevented by a diffusive term in general, but might be counteracted by schemes using an estimate of the fast waves at the midpoint of the time increment.The importance of this fast-waves midpoint estimate leads to the formulation of a class of split-explicit two-time-level schemes. Within this framework any forward-in-time and stable advection scheme might be combined with the fast-waves terms in the splitting algorithm.The new method is implemented in the non-hydrostatic model LM of DWD. Some test cases are presented, indicating that the new scheme has the potential to be used in an operational environment.     

Constructions and Applied Examinations of a Kind of Square-Conservative Schemes in High Precision in the Time Direction

In order to meet the needs of work in numerical weather forecast and in numerical simulations for climate change and ocean current, a kind of difference scheme in high precision in the time direction developed from the completely square-conservative difference scheme in explicit way is built by means of the Taylor expansion. A numerical test with 4-wave Rossby-Haurwitz waves on them and an application of them on the monthly mean current the of South China Sea are carried out, from which, it is found that not only do the new schemes have high harmony and approximate precision but also can the time step of the schemes be lengthened and can much computational time be saved. Therefore, they are worth generalizing and applying.     

HLAFS显式云降水方案及其对暴雨和云的模拟(II)暴雨和云的模拟

在HLAFS业务数值预报模式的动力框架下,利用文章(I)所述的显式云降水方案,对一次暴雨过程和伴随着的云物蓝砸淮伪?雨过程和伴随着的云物泪果表明,显式方案对降水落区和强降水中心位置的预报较原HLAFS的大尺度饱和凝结方案有明显改进.模式能合理地揭示出暴雨发生、发展过程中的云系演变规律和云物理过程.冰相过程对降水、中尺度热力和动力场有明显影响,特别是冰相过程有利于降水的早期的形成速率.与卫星TBB资料的对比分析表明,引进显式方案后,模式能较合理地模拟出云系的轮廓、位置、范围、强度、生消和移向,模式模拟出的云顶温度与卫星测量出的云顶温度较为一致.     

两种变时间步长的显式差分算法

针对一类大气、海洋问题，从算子方程出发，在显式完全平方守恒差分格式的基础上提出两种变时间步长的差分算法，使数值计算更加有效。在人工调节时间步长法中，通过人为控制方程中算子能量变化的办法调整时间步长；在自动调节时间步长法中，通过数值试验自动比较出所构造差分格式稳定性的好坏，将它与泰勒展开法及分解算法进行混合应用，验明了自动调节时间步长法具有综合判断差分格式好坏的功能，并得出一些有意义的结论。     

考虑气压的晴空大气下行长波辐射参数化方案及其适用性分析

基于Prata晴空大气下行长波辐射参数化方案,针对其在高原地区及可降水量较小地区理论精度较差的缺点,考虑不同高度的大气柱发射的长波辐射量不同,提出了三种考虑气压的大气下行长波辐射参数化方案,通过全球ERA-5再分析数据进行最小二乘拟合确定经验常数并在全球不同区域对其适用性进行了分析.模拟结果表明,考虑气压的参数化方案有...     

An explicit approach to microphysics in MC2

Abstract

An explicit microphysics scheme, including warm rain and ice‐phase processes, has been incorporated into the Canadian Mesoscale Compressible Community Model (MC2). Three equations for cloud water mixing ratio, rain water mixing ratio, and ice or snow mixing ratio are solved explicitly. The hydrometeor mass loading term is also included. For the single ice category, a generalized gamma size distribution is assumed and a new formulation by Meyers et al. (1992) is used to predict the ice concentration.

A numerical simulation of the ERICA IOP2 cyclone shows that the scheme is efficient. Despite running at a relatively large time step, the scheme succeeded in capturing the deepening rates and the mesoscale features of the cyclone. The distribution of cloud and precipitation is in good agreement with satellite observations. Comparison with other implicit schemes available in MC2 show comparable performance in terms of deepening rate and precipitation rate. However, the explicit scheme generates mesoscale features in better agreement with observations.     

藉物理耗散技术改进强降水数值模拟的初步研究

利用PSU/NCAR非静力中尺度模式MM5V3,对影响我国北方一次非汛期突发性强降水过程实例,进行了三重嵌套模式区域采用若干不同降水方案(特别是采用显式微物理方案与积云对流参数化方案若干组合)的对比试验,在揭示物理耗散技术正是通过将模式水平扩散方案纠正到符合热力学第二定律的约束而使该中尺度模式的模拟精度和模拟质量获得明显提高的物理实质的同时,从一个侧面证实了数值模式引入第二定律对提高数值天气预报准确率的重要性。     

A Numerical Study of Sensitivity of the Physical Dissipative Technique to Precipitation Parameterization in a Mesoscale Model

1. IntroductionRecently, the improvement of accuracy in the out-puts of a numerical mesoscale model by the physi-cal dissipative technique is reached (Liu et al., 2002;Liu and Liu, 2003). The effect of improvement ofthis technique differs not only from model to model,but from scheme to scheme of parameterization em-ployed in the same model. The rapid developmentof the computer technology makes possible the com-plicated numerical experiments by a model with highresolution and multiple domains …     

A high-order compact scheme with square-conservativity

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GRAPES区域模式水汽平流方案的比较与改进

与欧拉显式时间差分方法相比,GRAPES区域模式采用半隐半拉格朗日时间差分方案可增加时间步长且不影响稳定性,而且模式积分可有较高的计算效率和准确性。半拉格朗日法需要用到内插算法来预测下一时刻的值,对于水汽场的内插值来说,常常会造成预报值的过饱和或者是负值,需要进行特殊处理。比较GRAPES模式的准单调半拉格朗日方案(QMSL)和高精度正定保形方案(PRM),分析模式的降水预报、形势预报,同时初步总结了两方案的优缺点。在参考LCSL(Linear Constraint Semi-Lagarangain)方案的基础上,改进QMSL方案,通过连续试验运行,表明新方案基本稳定可靠,对于降水预报、形势预报有一定的改进,在台风预报试验中也有良好的表现。