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1.
把用半拉格朗日方法处理水平平流与用半隐式方法处理重力波动结合起来可以取比半隐式欧拉方法允许的更长的时间步长。这样,时间步长就受对垂直平流作显式处理的稳定性的限制。为了消除这种稳定性约束,我们提出既用于水平平流又用于垂直平流的半拉格朗日平流方案。这方面工作已在加拿大区域有限元天气预报模式中进行,此模式包含了对大多数有关的次网格尺度过程的参数化。模式结果表明,即使取远超过欧拉模式稳定性限制的时间步长,三维半拉格朗日方案仍然可以作出稳定、精确的积分。 相似文献
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大气环流模式降水的模拟对水汽方程差分方案的敏感性试验 总被引：4，自引：0，他引：4
分别采用3种应用比较广泛的水汽方程差分方案:多维正定平流传输方案(MPDATA)、通量修正传输方案(FCT)和两步保形平流方案(TSPAS),对大气物理所9层大气环流模式(IAP 9L AGCM)的降水模拟作敏感性试验,分析比较3种方案下模式降水气候平均场的差异,从而揭示模式降水对水汽方程差分方案的敏感性.试验结果显示,不同的水汽方程差分方案对大气环流模式降水的气候模拟有较大影响,并由此从3种差分方案中为IAP 9L AGCM寻找出一种较好的水汽计算方案. 相似文献
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本文提出一种将浅水波方程分裂为半拉格朗日平流项处理和适应项作隐式欧拉跳点差分格式(Eulerianalternating direction implicit)处理的积分方法。这种方法比半隐式方法简单,只需要给出线性三角方程(lineartridiagonal systems of equations)的解而不是赫姆霍尔兹方程的解就可以了。此方案理论上的性质已在E型格点上得到检验,对平流和简单罗斯贝(Rossby)渡是无条件稳定的,且有可以容忍的重力惯性设的稳定判据。通过采用两个时间层次积分方法给出了这两种波型二阶精度的解,并且不产生由分裂法引起的误差。将此方法用于有限区域正压模式,进行24小时的实例预报,其结果比Bates和McDonald以前提出的半拉格朗日方法更有效。 相似文献
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全球（Z）双三次数值模式的设计与个例模拟（Ⅰ）：模式动力框架设计 总被引：3，自引：2，他引：1
引入双三次数值模式：双三次数值模式是通过作三次样条与双三次曲面拟合,实现各个大气要素量场的二阶可导,从而可对各个预报方程作时间积分。双三次数值模式适合采用大气运动原始方程组和采用水平方向准拉格朗日／垂直方向欧拉时间积分方案。且本文的全球（Z）双三次数值模式与个例模拟实际采用Navier—Stokes“浅薄大气”原始方程组,建立球面Z坐标系上的非静力、全可压、干／湿绝热大气运动动力框架。其离散化气压、气温预报方程与个例模拟揭示出大气运动中凝结降水,其天气学原因不仅是湿空气作Z坐标垂直上升运动。而且是湿空气被“减压／减温”,即湿空气作P坐标“垂直上升运动”,后者可由大气平流运动（如Rossby波）引起。 相似文献
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半拉格朗日平流内在耗散的定量分析 总被引：1，自引：0，他引：1
因在估计每一空气微团的出发点上的流场值时运用了插值方法,所以,半拉格朗日平流方案是耗散的。本文用一、二、三、四次精度的拉格朗日插值方案的放大因子计算了耗散衰减的时间尺度,以及产生的有效涡动粘滞系数(为波长和Courant余数的函数)。然后把半拉格朗日平流方案的内在耗散同许多传统的耗散形式(如拉普拉斯或双谐涡动粘滞)作了比较。着重说明了半拉格朗日平流和许多传统的欧拉技术的一致性。还利用所选择的严谨参数是符合守恒规则的观点,讨论了耗散对时间步长和格距的依赖关系。 相似文献
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《高原气象》2017,(4)
三次样条函数(样条格式)为二阶可导非线性格式,但样条格式线性部分是二阶导数中央差。本文在简谐波真解条件下,推导证明二阶导数中央差比一阶导数中央差的空间截断误差以及相速和群速误差均减少一倍。借鉴谱模式动力框架核心思想,高斯网格二维谱变换半隐式-半拉格朗日积分方案,研究准均匀经纬网格样条格式变换显式-准拉格朗日积分方案。引入原始大气运动方程,推导样条格式二阶时空离散准拉格朗日预报方程通式,得出静力守恒气压、气温预报方程,在经纬网格基础上,设计两种基本准均匀经纬网格,通过对压、温、湿、风及广义牛顿力(加速度)场做"经纬网格-准均匀经纬网格"三次样条函数变换,求得"水平双三次曲面+垂直三次样条"拟合上游点三次运动路径,用"匀加速"变率预报风场,进而求得一个时间步长平均"静力平流"三维位移散度场,并用它预报气压场增压和气温场绝热增温,从而实现全球静力质量守恒经纬网格三次样条函数变换显式-准拉格朗日积分方案,经初步积分试验,证明上述动力框架是可行的。 相似文献
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从大气运动原始方程和欧拉算符出发,用泰勒级数展开,给出二阶时空微商余项预报方程。进而讨论用三次插值函数——双三次曲面拟合求上游点的准拉格朗日时间积分方案与相应的二阶时空余差数值模式——“双三次模式”。则双三次模式是通过实现各个大气物理量场的二阶可导,从而可对预报方程做空间非线性(“三次”)时间离散积分,成为“双三次曲面拟合——时间步积分——双三次曲面拟合——……”一种新算法数值模式。讨论双三次数值模式的数学基础:三次插值函数及其数值分析极性定律用于数值模式。指出:双三次模式和谱模式都具有数学“收敛性”;而Coons双三次曲面具有对变量场拟合二阶可导“最优性”;和Hermite双三次曲面片具有对网格变量场二阶可导运算“等价性”。又指出:有限差分模式的中央差近似斜率和曲率,分别是三次样条斜率和曲率作“三点平滑”。双三次模式适合采用原始大气运动方程,适合采用准拉格朗日时间积分方案,并给出一个理想全球模拟个例。因大气运动本质上是非线性的,理论上可按变量场双三次曲面曲率判断,以采用符合物理诠释的局域或单点平滑,以保持模式时间积分稳定性。且未来容易实现全球多重/时变套网格双三次数值模式。 相似文献
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IAP AGCM-4动力框架的积分方案及模式检验 总被引：7，自引：3，他引：4
以灵活性跳点格式和时间分解算法为重点, 介绍了IAP (中国科学院大气物理研究所) AGCM-4的动力框架, 并用R-H (Rossby-Haurwitz) 波和Held-Suarez方案对框架进行了检验。结果表明: 高纬灵活性跳点格式很好地保持了普通跳点格式的各种性质, 未产生计算紊乱现象, 可在一定程度上增大时间步长, 在未采用滤波处理时增大时间步长的效果更为显著; 时间分解算法, 即将平流过程与适应过程分开计算, 二者都采用3次非线性迭代积分方案, 在N=5和N=10 (N为平流过程时间步长与适应过程时间步长的比值) 的情况下, 可分别节省CPU时间10.7%和19.9%; R－H波检验表明, 在积分的前80天, 框架较好地保持了R－H 4波的波形, 总有效能量仅衰减0.1%, 从第80天开始, 风场波形开始变形和破碎, 对应的动能和总能量也开始急剧衰减, 至第365天, 总有效能量衰减约8%, 此时, 风场和高度场亦变得较平直。经分析, 第80天R－H波破碎的主要原因是平流项的计算误差使R－H波失稳, 而其后的高度场和风场的变平直是典型的旋转适应机制; Held－Suarez方案检验也证明该框架是可靠的。 相似文献
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相变修正方案在GRAPES模式标量平流中的应用 总被引：2，自引：1，他引：1
如何更好地模拟水物质的空间分布和小尺度变化,对于数值天气预报效果的改进,特别是对于更好地模拟降水过程,具有重要的意义.计算机的飞速发展使数值模式的分辨率不断提高,云的显式计算成为可能,这样就要求水物质在平流的过程中必须要做到高精度、守恒、保形.水物质场是正定标量的场,具有空间和时间变化幅度大、存在强梯度甚至不连续的特点,水物质场的合理模拟一直是数值预报中的一个难题.GRAPES模式中的标量平流方案采用PRM分段有理函数方法,比较好地解决了该半拉格朗日模式中水物质平流的高精度、守恒、保形问题,但是当有凝结潜热发生时,由于半拉格朗日平流方案求解上游点时的插值,在云边缘区域会造成虚假的云水,进而导致不合理的相变过程.为了解决以上问题,本研究在GRAPES模式中PRM平流方案的案础上,加入了非线性半拉格朗日相变潜热的修正方案,旨在改进GRAPES模式对水物质平流问题的模拟,提高降水的预报效果.该研究通过理想试验,验证了非线性半拉格朗口相变修正方案可以有效地限制云边缘由于半拉格朗日平流方案插值产生的虚假柑变;然后将该方案加入GRAPES模式的PRM水物质平流方案中,通过实际个例模拟验证了加入非线性半拉格朗日方案以后,模式可以更好地模拟水物质的平流过程,且对云中热力场及水物质分布地模拟更加合理,同时预报出的雨带中心区与实况更加符合. 相似文献
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An Eulerian flux-form advection scheme, called the Two-step Shape-Preserving Advection Scheme(TSPAS), was generalized and implemented on a spherical icosahedral hexagonal grid(also referred to as a geodesic grid) to solve the transport equation. The C grid discretization was used for the spatial discretization. To implement TSPAS on an unstructured grid,the original finite-difference scheme was further generalized. The two-step integration utilizes a combination of two separate schemes(a low-order monotone scheme and a high-order scheme that typically cannot ensure monotonicity) to calculate the fluxes at the cell walls(one scheme corresponds to one cell wall). The choice between these two schemes for each edge depends on a pre-updated scalar value using slightly increased fluxes. After the determination of an appropriate scheme, the final integration at a target cell is achieved by summing the fluxes that are computed by the different schemes. The conservative and shape-preserving properties of the generalized scheme are demonstrated. Numerical experiments are conducted at several horizontal resolutions. TSPAS is compared with the Flux Corrected Transport(FCT) approach to demonstrate the differences between the two methods, and several transport tests are performed to examine the accuracy, efficiency and robustness of the two schemes. 相似文献
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PRM标量平流方案在GRAPES全球预报系统中的应用 总被引：4，自引：0，他引：4
如何更好地模拟水物质的分布,对于数值天气预报效果的改进,特别是对于更好地模拟降水过程,具有重要的意义。半拉格朗日模式中的标量平流计算要求做到高精度、守恒、正定和保形,但GRAPES_GFS (Global-Regional Assimilation and PrEdiction System, Global Forecast System) 中采用的QMSL(Quasi-Monotone Semi-Lagrangian)平流方案在水汽的强梯度、不连续区域计算精度较低,且不能做到严格守恒。本研究借鉴计算流体力学领域的研究进展,将一个基于分段有理函数的物质平流方案PRM(Piecewise Rational Method)引入GRAPES_GFS中,按照通量形式求解水汽方程,并对极区进行了混合等技术处理。通过一系列理想试验对两种平流方案进行了对比,证明了PRM方案精度较高,特别是在水汽梯度大的区域优势明显,频散、耗散误差较小,守恒、保形性也要好于QMSL方案。通过对GRAPES_GFS中批量预报试验效果的检验,验证了PRM方案可以有效地改进模式对水物质分布的模拟,提高了降水的预报效果,对模式综合预报性能的提升也有明显作用。 相似文献
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Lagrangian transport of water vapor and cloud water in the ECHAM4 GCM and its impact on the cold bias 总被引：1，自引：0，他引：1
The Lagrangian advection scheme ATTILA has been applied for the transport of water vapor and cloud water in the general circulation
model (GCM) ECHAM4.L39(DLR) (E39) instead of the operational semi-Lagrangian transport scheme (SLT). ATTILA is a purely Lagrangian
scheme that is numerically non-diffusive, while the operational semi-Lagrangian scheme exhibits a considerable numerical diffusion
in the presence of sharp gradients. The model version E39/SLT significantly overestimates the water vapor mixing ratio in
the extratropical lowermost stratosphere (wet bias) by a factor of 3–5 compared to HALOE observations. Compared to E39/SLT,
E39/ATTILA shows substantially reduced water vapor mixing ratios in the extratropical lowermost stratosphere up to 70%, and
a steeper meridional water vapor gradient in the subtropics which is in better agreement with observations. Furthermore, the
temperature distribution as simulated with E39/SLT is characterized by a pronounced cold temperature bias in the extratropical
lowermost stratosphere (cold bias) and in the polar stratosphere above 50 hPa in winter (cold pole). The improvements concerning
the water vapor distribution in E39/ATTILA lead to a substantial reduction of the simulated cold bias by approximately 5–7 K
which also results in a better representation of the modeled tropopause, especially in the extratropics. Sensitivity studies
indicate that the warming of the extratropical lowermost stratosphere in E39/ATTILA is directly related to the reduced wet
bias resulting in a less infrared radiative cooling. Additionally, the cold pole problem is also slightly reduced in E39/ATTILA
by approximately 2–5 K. 相似文献
15.
The Dynamical and Climate Tests of an Atmospheric General Circulation Model Using the Second-Order
Adams-Bashforth Method 
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下载免费PDF全文 The Asselin-Robert time filter used in the leapfrog scheme can degrade the accuracy of calculations. The second-order Adams-Bashforth method with the same accuracy as the leapfrog scheme is not subject to time splitting instability. A new semi-implicit atmospheric general circulation spectral model is developed on the basis of NCAR (National Center for Atmospheric Research) CAM3.0 (Community Atmosphere Model3.0). In this new model, the second-order Adams-Bashforth method is used as an alternative to the leapfrog scheme, and a Crank-Nicholson scheme is incorporated for the treatment of fast gravity modes. In this paper, the new model is tested by the Held-Suarez test and an idealized baroclinic wave test. Results of the Held-Suarez test show that the second-order Adams-Bashforth model has similar climate states to those of many other global models and it converges with resolutions. Based on the idealized baroclinic wave test, the capability of di?erent time di?erencing methods for keeping the initial steady-state are compared.This convinces a better ability of the second-order Adams-Bashforth method in maintaining the stability of the initial state. Furthermore, after the baroclinic wave is triggered through overlaying the steady-state initial conditions with the zonal perturbation, the second-order Adams-Bashforth method has an excellent property of convergence, and can represent the process of the baroclinic wave development much better than
the original scheme in CAM3.0. A long-term integration of the new model during the period of 1980-1999 is also carried out and compared with that of CAM3.0. It is found that due to the reduction of simulation errors of prognostic variables, the second-order Adams-Bashforth method also has a better simulation ability for the diagnostic variables, such as precipitation. 相似文献
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Recently, a new atmospheric general circulation model （GAMIL： Grid-point Atmospheric Model of IAP LASG） has been developed at the Institute of Atmospheric Physics （IAP）, Chinese Academy of Sciences （CAS）, which is based on the Community Atmospheric Model Version 2 （CAM2） of the National Center for Atmospheric Research （NCAR）. Since the two models have the same physical processes but different dynamical cores, the interannual variability simulation performances of the two models are compared. The ensemble approach is used to reduce model internal variability. In general, the simulation performances of the two models are similar. Both models have good per- formance in simulating total space-time variability and the Southern Oscillation Index. GAMIL performs better in the Eastern Asian winter circulation simulation than CAM2, and the model internal variability of GAMIL has a better response to external forcing than that of CAM2. These indicate that the improvement of the dynamic core is very important. It is also verified that there is less predictability in the middle and high latitudes than in the low latitudes. 相似文献
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采用新的均匀三点中心约束多矩有限体积方法（3-point Multi-moment Constrained finite-Volume scheme for Uniform Points with Center Constraints, MCV3_UPCC）,发展了一个三阶正定守恒的平流模式。三点多矩有限体积方法在单网格内定义等距的3个自由度,采用多矩约束条件并通过控制方程获得时间演变方程。新的三点中心约束多矩方法能在单网格内采用等距的3个点值及中心一阶、二阶导数作为约束条件进行空间4次多项式数值重构,获得3个自由度的时间演变方程;所构建的新数值方案具有三阶精度,边界通量连续性保证了其数值严格守恒。为了抑制该方法的非物理数值振荡,引入了边界保型限制器技术,它能够把数值解控制在既定物理场最小值（最小值为0时则保持数值正定）与最大值之间。数值试验表明新发展的三阶平流模式具有良好的计算精度,能够严格保持数值解的正定性和守恒性,同其他高精度平流模式相当,在实际大气模式水汽等平流输送应用中具备良好的发展潜力。 相似文献
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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
19.
阴阳网格上质量守恒计算性能分析 总被引：3，自引：1，他引：2
质量守恒数值计算是球面准均匀阴阳网格构造全球大气环流模式的重要条件,也是提高阴阳网格应用质量的重要技术手段。本文针对通量形式平流方程,在球面坐标上采用多种理想数值试验对阴阳网格上的三种守恒计算方案和边界插值非守恒计算方案进行了比较检验。发现,质量守恒方案不仅对全球数值积分重要,还影响数值计算精度,满足局地守恒条件的全球强迫守恒方法可以获得较高的精度;网格内质量均匀分布的阴阳网格边界通量一致性守恒强迫计算方案,实现了在不增加计算误差条件下保证局地和全球守恒的目的,且具有很小的计算负担,可以作为阴阳网格上全球质量强迫守恒的有效计算方案;而网格质量的线性分布可以有效提高阴阳网格的数值积分计算精度,但在一定程度上会增加计算负担。 相似文献