共查询到20条相似文献，搜索用时 468 毫秒
1.
AN IMPROVED SEMI-IMPLICIT TIME DIFFERENCE SCHEME OF SPECTRAL MODEL AND NUMERICAL APPLICATIONS* 
下载免费PDF全文
下载免费PDF全文 In fact,the popular semi-implicit time difference scheme of spectral model still includes some important linear terms using time explicit difference scheme,and the major terms are directly related to fast internal-and external-gravity waves in the atmospheric forecasting equation.Additionally,due to using time difference on two terms at different time.the popular schemear tificially introduces unbalance between pressure gradient force and Coriolis force terms while numerically computing their small difference between large quantities.According to the computational stability analysis conducted to the linear term time difference scheme in simple harmonic motion equation,one improved semi-implicit time difference scheme is also designed in our study.By adopting a kind of revised time-explicit-difference scheme to these linear terms that still included in spectral model governing equations,the defect of spectral model which only partlyusing semi-implicit integrating scheme can be overcome effectively.Moreover,besides all spectral coefficients of prognostic equations,especially of Helmholtz divergence equation,can be worked out without any numerical iteration,the time-step (computation stability) can also be enlarged (enhanced) by properly introducing an adjustable coefficient. 相似文献
2.
3.
Hann-Ming H. Juang 《Meteorology and Atmospheric Physics》1992,50(1-3):75-88
Summary The set of fully compressible nonhydrostatic equations governing a broad spectrum of atmospheric motion was transformed fromz coordinates to sigma coordinates under a hydrostatic base state. The hydrostatic base state may be either time-independent, such as a hydrostatic balance with-out motion or with motion such as a thermal wind balance, or time-dependent such as might be obtained from the result of integrating a hydrostatic model. The transformed set of equations can be used to predict and study all scales of at mospheric phenomena.The set of perturbation equations was also derived under the same condition. The computational sensitivity in computation of pressure gradient force in sigma coordinate can be improved by computing the pressure gradient interms of perturbations under a certain hydrostatic state.The hydrostatic regional spectral model developed by Juang and Kanamitsu (1991) was modified to be a nonhydrostatic spectral model based on the nonhydrostatic equations in sigma coordinates with time-dependent hydrostatic base states. A semi-implicit time integration scheme was used. Two experiments were performed to test this nonhydrostatic spectral model with acceptable results.With 7 Figures 相似文献
4.
一类计算性系统误差消除与斜压原始方程天气气候模式改进 总被引：1，自引：0，他引：1
斜压原始方程半隐式全能量守恒格式的构造问题长期没有解决。本研究在成功地构造实现其全能量完全守恒的半隐式方案基础上，进行了此守恒方案与欧洲中期天气预报中心（ECMWF）的σ－坐标原始方程全球谱模式半隐式方案间的实际资料对比实验。实验表明，850hPa平均预报高度场RMS误差在积分一周以后得到明显改进，到第30天其预报误差降低达到了50％，进一步的对比实验表明，对流层中部和下部的月预报平均高度场RMS误差也显降低，而且一些明显的系统性误差也得到大幅度改进。更加详细的分析显示，这些收益的很大一部分是从超长波成分的改进中得到的。这说明，通过构造守恒性时间差分方案消除了响应的计算性系统误差源汇，进而能够使模式气候漂移得到显改进，而这种误差源汇存在于传统的，现仍被普遍采用的斜压原始方程天气气候模式中。 相似文献
5.
THE FORMULATION OF FIDELITY SCHEMES OF PHYSICAL CONSERVATION LAWS AND IMPROVEMENTS ON A TRADITIONAL SPECTRAL MODEL OF BAROCLINIC PRIMITIVE EQUATIONS FOR NUMERICAL PREDICTION* 下载免费PDF全文
下载免费PDF全文 Zhong Qing 《Acta Meteorologica Sinica》1999,13(2):226-248
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. 相似文献
6.
钟青 《Acta Meteorologica Sinica》1999,(2)
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. 相似文献
7.
8.
9.
本文给出了一种求解非线性平衡方程的新的有效的方法及有关的数值试验结果。和以往的求解方法相比，本方法的优点是:收敛速度快，不需要冗长的迭代计算，也不需要对初始高度场的某些记录作修改，并能节省大量的计算时间。文中利用北半球七层原始方程谱模式，使用了1982年的客观分析资料，进行中期数值天气预报试验。试验结果表明，用非线性平衡方程初值化方法制作中期数值预报比其他的如线性平衡方程初值化方程的更佳。后者因去掉了非线性项的作用，天气系统的强度预报结果偏弱且偏平滑。 相似文献
10.
Three-Step Difference Scheme for Solving Nonlinear Time-Evolution Partial Differential Equations 下载免费PDF全文
下载免费PDF全文 In this paper, a special three-step difference scheme is applied to the solution of nonlinear time-evolution equations, whose coefficients are determined according to accuracy constraints, necessary conditions of square conservation, and historical observation information under the linear supposition. As in the linear case, the schemes also have obvious superiority in overall performance in the nonlinear case compared with traditional finite difference schemes, e.g., the leapfrog（LF） scheme and the complete square conservation difference（CSCD） scheme that do not use historical observations in determining their coefficients, and the retrospective time integration（RTI） scheme that does not consider compatibility and square conservation. Ideal numerical experiments using the one-dimensional nonlinear advection equation with an exact solution show that this three-step scheme minimizes its root mean square error（RMSE） during the first 2500 integration steps when no shock waves occur in the exact solution, while the RTI scheme outperforms the LF scheme and CSCD scheme only in the first 1000 steps and then becomes the worst in terms of RMSE up to the 2500th step. It is concluded that reasonable consideration of accuracy, square conservation, and historical observations is also critical for good performance of a finite difference scheme for solving nonlinear equations. 相似文献
11.
证明了模式在预报时段的纬向平均环流误差，是由于在预报时段内模式大气和真实大气中西风加速过程的不同造成的。又由于原始方程的无加速定理中各强迫因子具有良好的线性迭加性，因此能够清楚地将造成模式系统误差的动力因子分解开来。通过对Ｔ４２Ｌ９模式的分析，说明原始方程的无加速定理可以作为分析模式系统误差的良好手段。动力诊断分析结果表明，模式对纬向平均环流分布具有较好的预报能力，但在各缔带也存在明显的误差。通过无加速定理的分解分析，本文研究了这些误差的成因及改善模式的可能途径。 相似文献
12.
13.
14.
将两时间层稳定外插方案(Stable Extrapolation Two-Time-Level Scheme,SETTLS)引入GRAPES区域模式,并将其用于上游点和非线性项的时间外插计算。对线性项采用二阶精度的非中央权重时间平均,并取等温参考大气的温度大于实际大气平均温度,以保证半隐式积分方案的稳定性。原GRAPES时间积分方案对线性项做一阶非中央权重时间平均,对参考大气的选择并无限制,而为保证稳定性,须取较大的非中央权重系数,但非中央权重系数会对低波数波动产生较强的衰减作用。理想试验结果表明,相比原GRAPES半隐式半拉格朗日(SISL)时间积分方案,新SISL时间积分方案计算稳定且对波动的衰减作用较弱。 相似文献
15.
A. J. Simmons D. M. Burridge M. Jarraud C. Girard W. Wergen 《Meteorology and Atmospheric Physics》1989,40(1-3):28-60
Summary An outline is given of the numerical formulations that have been utilized for medium-range prediction at the European Centre for Medium-Range Weather Forecasts. The sigma-coordinate grid-point model adopted for the first phase of operational forecasting, and the hybrid-coordinate spectral model which replaced it, are described. Particular emphasis is placed on aspects of the time-stepping employed in the spectral model. It is shown how a semi-implicit treatment of the zonal advection of vorticity and specific humidity, and selective use of enhanced horizontal diffusion, enables time-steps to be used which are well over 50% longer than would otherwise be possible in a spectral model with a classical semi-implicit treatment of gravity-wave terms, with negligible computational cost and negligible impact on forecast accuracy, at T 106 resolution at least. Some discussion of the stability of the semi-implicit gravity-wave scheme is also included.The experimental evidence which led to the operational change from the grid-point to the spectral model is summarized, and the sensitivity of forecasts to the horizontal resolution of the spectral model is illustrated. Both the change in method and increases in resolution result in systematic improvements in the details of cyclone development, and they occasionally have major beneficial impact on the evolution of the forecast in the medium range. Conventional objective verification indicates a much smaller mean improvement of T 106 resolution over T 63 than of T 63 over T 42, although the advantage of T 106 is nevertheless clear-cut. This advantage is more than confirmed by synoptic assessment. Scope for further improvement is indicated by first results from global forecasts with a resolution of T 159. Indications of sensitivity to the magnitude of horizontal diffusion and the resolution of the model orography are also given.The spectral model was initially used operationally with a 16-level vertical resolution, and the uppermost level at which prognostic variables were held was 25 mb. The results which justified a subsequent change to 19 levels, with increased stratospheric resolution and a 10 mb top level, are presented. In this case the principal medium-range forecast improvement came about because better initial analyses could be produced when the 19-level model was used in data assimilation.With 24 Figures 相似文献
16.
蛙跳格式的替代方案及其在大气环流模式中的应用 总被引：3，自引：0，他引：3
蛙跳（Leapfrog）时间差分格式采用AsselinRobert时间滤波方案去除计算解能够降低原始方程组的时间差分格式的计算精度,采用二阶Runge-Kutta格式构造欧拉前差方案可弥补蛙跳格式的不足。即在不存在计算解的条件下去除滤波影响,更大程度保持方程组的计算准确性。作者基于NCAR CAM3.0(Community Atmosphere Model 3.0)完善的软件平台,将原模式的三时间层蛙跳时间差分方案修改为两时间层二阶Runge-Kutta时间差分格式,对与重力波有关项使用中央差隐式处理,以此构建半隐式大气环流谱模式。通过斜压波实验比较不同格式在保持初值稳定性上的表现,从而发现,二阶Runge-Kutta方案能够更好的保证方案的初值稳定性。同时在纬向对称平衡场中加入扰动的情况下,二阶Runge-Kutta方案模拟的斜压波动发展演变的特征具有良好的收敛性,对波动发展的描述能力更强。存在这种优势的可能原因可归结为格式自身的优势和摆脱了时间滤波的负面影响,通过加入不同滤波系数的比较实验可以看到,滤波的平滑作用对模式结果的影响显著,但格式自身的优势也是改进模拟结果的主要因素。通过非绝热条件下20 年（1980～1999年）气候态全模式模拟考察模式在气候模拟中的表现,结果表明,此方案在长期的气候模拟中同样可降低预报变量及诊断变量的模拟误差,具有更好的模拟能力。 相似文献
17.
Suk-Jin Choi 《Asia-Pacific Journal of Atmospheric Sciences》2018,54(1):293-301
To fundamentally understand discretized equations and differential operators, this study investigates the eigenvalues of the spherical gradient matrix and spherical Laplacian matrix discretized by the spectral element method (SEM) on the cubed-sphere grid (CS) for solid-body rotation. The gradient matrix with prescribed wind for the solid-body rotation has small positive real numbers in the eigenvalues, which implies that the solutions of the advection equation for solid-body rotation can be unstable and distorted. However, the unstable model can be effectively controlled by the Laplacian matrix, and all eigenvalues of the Laplacian matrix are aligned along the negative part of the real axis. The maximum eigenvalues of the gradient matrix and Laplacian matrix exhibit the characteristic of a linear function of the resolution, which is important to determine the upper limit of the time-step size for stable time integration. This study suggests suitable e-folding time scale of the diffusion using the 6th order for applications of the advection-diffusion equation. Regarding the characteristics of the eigenvalues, the setting of the stable time step is discussed. A method to implement the diffusion operators in the third-order Runge-Kutta time integration scheme in the advection-diffusion model is also discussed. 相似文献
18.
GRAPES模式中三维科氏力计算及其效果评估 总被引：1，自引：0，他引：1
作为一种连续可压缩流体,大气具有分层流体特性,其状态变化可由牛顿第二定律、热力学第一定律、连续方程和理想大气状态方程组成的偏微分方程组描述。为了更加精细地描述GRAPES全球模式的动力过程,使模式大气更接近真实大气,在全球非静力模式GRAPES中考虑三维科氏力作用,通过重新构建半隐式半拉格朗日求解大气动力方程组的亥姆霍兹方程系数,在不改变求解方案的前提下实现对GRAPES模式动力过程的更新。然后采用在静力平衡基础上建立的三维大气理想试验对新的动力过程进行数值试验,检验其计算效果和数值稳定性。结果显示,考虑三维科氏力的模式动力框架计算稳定,提高了三维标量和矢量场的计算精度,在水平1°×1°分辨率模式中,平衡流试验第15天计算结果标量场Π'的l1和l2误差分别为0.00023和0.0004,而三维矢量场 V 的l1和l2误差分别为0.002和0.003,均较原模式误差小一个数量级。在罗斯贝-豪威兹波、地形罗斯贝波和斜压波试验中,新框架均表现出很高的计算稳定性和良好的计算效果。 相似文献
19.
蛙跳(leapfrog)时间差分格式采用Asselin-Robert时间滤波方案去除计算解能够降低原始方程组的时间差分格式的计算精度,采用二阶Adams-Bashforth格式构造的欧拉前差方案可弥补蛙跳格式的不足,即:在不存在计算解的条件下去除滤波的影响,更大程度的保持方程组的计算准确性。本文基于NCAR CAM3.0(Community Atmosphere Model 3.0)完善的软件平台,将原模式的三时间层蛙跳时间差分方案修改为两时间层二阶Adams-Bashforth时间差分格式,对与重力波有关项使用中央差隐式处理,以此构建半隐式大气环流谱模式。利用动力检验的方法探讨模式对垂直分辨率的敏感性,从而寻找模式在较小计算代价下提高计算效果的可能。通过斜压波实验发现,提高垂直分辨率使模式具有更强的斜压波模拟能力,其模拟效果甚至已经与提高水平分辨率的效果相当,可以作为一种弥补模式运算效率不足的可行方案。 相似文献
20.
A THREE-DIMENSIONAL CLOUD-SCALE MODEL SUITABLE FOR COMPRESSIBLE ATMOSPHERE 总被引：2，自引：0，他引：2 下载免费PDF全文
下载免费PDF全文 A three-dimensional cloud-scale model has been designed.The governing equations of the model arecomposed of two groups of equations:one group includes compressible motion equations,continuity equation,pressure equation and thermodynamic equation,which are of Eulerian type,and the other consists of cloud-precipitation microphysics equations which are of Lagrangian type.Since the degree of influence of sound waveon the air motion is quite different from that on the temperature or hydrometeors,the time splitting procedureis used in solving governing equations.Both unstaggered and staggered meshes have been utilized.Integra-tion schemes adopted are the Eulerian backward difference method for the unstaggered mesh and semi-implicitmethod for staggered mesh.Several experiments of modelling have been conducted and a reasonable three-dimensional image of deep convection is obtained.With this model the horizontal and vertical vortex circula-tions are simulated.Furthermore,the effects of horizontal vortex on the formation and development ofdowndraft within cloud have also been studied. 相似文献