水汽方程积分计算格式的数值试验

该文把Easter(1993)的水汽方程积分方案应用到球坐标的有限区模式（LAFS）中，并作了两组比较性试验。Easter的方案是把水汽的通量方程和连续方程联立求解。在计算中不会出现水汽负值。而且稳定性好。本文所做的两组试验表明。Easter的方案比LAFS的原方案所产生的计算性扩散小。因而降水预报更接近实况。但CPU时间增加了16%。     

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.     

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。     

GRAPES模式中高精度正定保形物质平流方案的研究Ⅰ:理论方案设计与理想试验

平流计算的精度对数值模式的结果有着重要影响.如何在半拉格朗日模式中发展高阶精度的标量平流计算方案是提高半拉格朗日数值模式精度的重要问题.文中采用计算流体力学中一个新的高精度正定保形的物质平流方案,通过映射单元格方法将其与半拉格朗日模式结合起来,既保留了半拉格朗日时间积分方案中积分时间步长大、计算效率高的特点,又发挥新方...     

相变修正方案在GRAPES模式标量平流中的应用

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.     

云凝结物平流输送对降水云系发展影响的数值模拟研究

大气动力学中"平流输送"是非常重要的宏观动力学过程,云凝结物的平流输送与降水云系的发展演变密切相关,它把宏观动力过程与各种云凝结物粒子的时空演变联系起来,云凝结物的平流输送可以增加或减少局地大气中云凝结物的含量,改变云凝结物的空间分布状况,影响云凝结物的微观物理过程,进而促进或抑制降水云系的发展演变.本文在数值模拟研究中.通过改变云凝结物平流输送的状况来研究宏观动力过程对云微观物理过程的影响,因而利用ARPS模式开展3个分别排除云凝结物水平平流输送、垂直平流输送和三维平流输送的敏感试验,进行关于云凝结物平流输送对降水云系发展演变影响的敏感性数值模拟研究.结果表明,云凝结物的平流输送对水汽比湿的影响很小.云凝结物的三维平流输送有利于增加降水云系中雪和霰的混合比含量,抑制云水、雨水和云冰混合比含量的增长.云凝结物的水平平流输送可以降低降水云系中云水和雨水的混合比含量,增加云冰和雪的混合比含量;云凝结物垂直平流输送的作用是增加降水云系中雨水、雪和霰的混合比含量,减少云与冰混合比含量.云凝结物三维平流输送效应的分析表明,云凝结物的三维平流输送主要通过调整云凝结物的微物理过程源汇项以及降水粒子(雨水、雪和霰)的下落末速项来改变降水云系中云凝结物的垂直结构;另外,雪的三维平流输送对雪本身的分布也有一定影响.     

水汽输送的算法精度与模式暴雨预报能力的对比分析

利用中尺度模式ＭＭ４，研究了中尺度模式的暴雨模拟对于不同不汽输送方案的敏感性。采用５种平流差分格式来计算水汽的水平输送，用该模式对３次暴雨过程作了数值试验。并把不同方案的降水模拟结果与实况进行了对比。结果表明，中尺度模式的暴雨模拟对水汽输送方案十分敏感，正定高精度的Ｐｒａｔｈｅｒ格式的模拟结果最接近实况。     

高阶正定守恒的中心约束多矩有限体积平流模式

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。      

The influence of numerical advection schemes on the results of ocean general circulation models

The dependence of results from coarse-resolution models of the North Atlantic circulation on the numerical advection algorithm is studied. In particular, the sensitivity of parameters relevant for climate simulations as e.g., meridional transport of mass and heat and main thermocline thickness is investigated. Three algorithms were considered: (a) a central difference scheme with constant values for horizontal and vertical diffusion, (b) an upstream scheme with no explicit diffusion, and (c) a flux-corrected transport (FCT) scheme with constant and strictly isopycnal diffusion. The temporal evolution of the three models on time scales of centuries is markedly different, the upstream scheme resulting in much shorter adjustment time whereas the central difference scheme is slower and controlled by vertical diffusion rather than advection. In the steady state, the main thermocline structure is much less diffusive in the FCT calculation which also has much lower heat transport. Both horizontal circulation and overturning in the meridional-vertical plane are strongest in the upstream-model. The results are discussed in terms of the effective vertical (diapycnal) mixing in the different models. A significant increase in vertical resolution would be required to eliminate the high sensitivity due to the numerical algorithms, and allow physically motivated mixing formulations to become effective.This paper was presented at the International Conference on Modelling of Global Climate Change and Variability, held in Hamburg 11–15 September 1989 under the auspices of the Meteorological Institute of the University of Hamburg and the Max Planck Institute for Meteorology. Guest Editor for these papers is Dr. L. Dümenil     

PRM标量平流方案在GRAPES全球预报系统中的应用

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。     

Improvement of the semi-Lagrangian advection scheme in the GRAPES model: Theoretical analysis and idealized tests

ABSTRACT The Global/Regional Assimilation and PrEdiction System （GRAPES） is the newgeneration numerical weather predic- tion （NWP） system developed by the China Meteorological Administration. It is a fully compressible non-hydrostatical global/regional unified model that uses a traditional semi-Lagrangian advection scheme with cubic Lagrangian interpola tion （referred to as the SL_CL scheme）. The SL_CL scheme has been used in many operational NWP models, but there are still some deficiencies, such as the damping effects due to the interpolation and the relatively low accuracy. Based on Reich＇s semi-Lagrangian advection scheme （referred to as the R2007 scheme）, the Re_R2007 scheme that uses the low- and high-order B-spline function for interpolation at the departure point, is developed in this paper. One- and two-dimensional idealized tests in the rectangular coordinate system with uniform grid cells were conducted to compare the Re..R2007 scheme and the SL_CL scheme. The numerical results showed that： （1） the damping effects were remarkably reduced with the Re_R2007 scheme; and （2） the normalized errors of the Re_R2007 scheme were about 7.5 and 3 times smaller than those of the SL_CL scheme in one- and two-dimensional tests, respectively, indicating the higher accuracy of the Re..R2007 scheme. Furthermore, two solid-body rotation tests were conducted in the latitude-longitude spherical coordinate system with non uniform grid cells, which also verified the Re_R2007 scheme＇s advantages. Finally, in comparison with other global advection schemes, the Re_R2007 scheme was competitive in terms of accuracy and flow independence. An encouraging possibility for the application of the Re_R2007 scheme to the GRAPES model is provided.     

高空急流对青藏高原切变线影响的数值试验与动力诊断

利用NCEP 1°×1° FNL分析资料和中尺度数值模式WRF对一次青藏高原（简称高原）切变线过程进行了数值试验,主要研究高空急流强度对高原切变线的影响,并结合ω方程分析了影响高原切变线上垂直上升运动的若干因子。研究得出高空急流的强度对低层风场有重要影响,急流增强会使高原切变线上的风切变增大,切变线变长,同时高空急流强度的增强也有利于高原切变线上水汽的辐合。高空急流可通过影响高层辐散、低层辐合的散度场垂直配置对高原切变线上的正涡度柱与辐合上升运动产生作用。ω方程的诊断分析表明,温度平流的拉普拉斯项对高原切变线上的垂直上升运动起主导作用,低层暖平流有利于切变线上产生上升运动。高空急流强度的变化对差动涡度平流项的影响要大于温度平流拉普拉斯项,高空急流强度的增强会放大差动涡度平流项和温度平流项的正贡献,从而更加有利于上升运动及高原切变线的维持。      

Numerical analysis and case experiment for forecasting capability by using high accuracy moisture advectional algorithm

Summary The paper concerns the sensitivity of the regional mesoscale model (MM4) to a moisture transport algorithm with different accuracies, and the effective improvement of the capability to simulate meso-scale synoptical event by using the revised version of the algorithm. The two advective schemes of second-order moment conservational Prather scheme (PRS hereinafter) and the polynomial-fitted fourth-order Bott scheme and the upstream scheme (UPS) are introduced into the MM4 to calculate moisture transport in order to provide other types of the algorithm with different accuracies for choice in addition to the original B grid second-order central scheme. Of the three schemes, the first two ensure the positive definite character with high accuracy (almost no numerical disspation and computational dispersion); and the last one also keeps the positive definite feature, but possesses stronger capability of numerical dissipation. Case studies have been undertaken of several rainstorm and typhoon events by virtue of the different-accuracy moisture transport algorithm, other things being the same. Results reveal great differences between them. An significant improvement is found in determining meso-scale synoptic system structure, rain cluster activity, rainstorm belt and its center, severity and its persistence, and the false alarm of or failure to report subrainstorm center when the PRS scheme is employed. Obviously, these differences and improvement are only due to moisture re-distribution for different schemes of moisture transport and the related variation of latent heat. The paper investigates the influences of different numerical schemes. The high accuracy and positive solution PRS application which produces a significant improvement in the model result, demonstrating the sensitivity of the model to moisture distribution in the model represents an important measure to improve the simulation by means of revising the numerically calculating method.With 11 Figures     

通量和平流形式预报方程的数值预报试验

本文利用1982年5月8日和1979年6月28日两个实例,进行了四种方案的48小时数值预报试验,比较了它们的预报质量及彼此间的差异。四种方案是:经典通量、通量修正、经典平流和平流修正。试验表明,在有地形的数值预报模式中,采用平流形式的预报方程组比采用通量形式的为好,既可有较高的计算精度,又可节省计算时间。     

Application of a Shape-Preserving Advection Scheme to the Moisture Equation in an E-grid Regional Forecast Model

This paper presents a methodology which is very useful to design shape-preserving advection finite difference scheme on general E-grid horizontal arrangement of variables through introducing a two-step shape-preserving positive definite advection scheme in the moisture equation of the LASG-REM (LASG regional E-grid eta-coordinate forecast model). By trial-forecasting six local heavy raincases, the efficiency of the shape-preserving advection scheme in practical application has been examined. The LASG-REM with the shape-preserving advection scheme has a good forecasting ability for local precipitation.     

An advection scheme based on the combination of particle mesh method and pure Lagrangian approach

Possibility of using pure Lagrangian approach in modeling transport phenomena is described in this paper. The application of pure Lagrangian approach in real atmospheric field induces highly irregular spatial distribution of grid points, after only a few time steps. In order to avoid problems caused by that irregularity, a quasi interpolation procedure is proposed. Proposed interpolation procedure is similar to the radial basis functions interpolation and does not impose any demands about spatial distribution of the grid points or about continuity and differentiability of the field that needs to be interpolated. Besides that, proposed procedure is explicitly mass conserving. Combination of particle mesh method and pure Lagrangian approach creates efficient transport scheme that does not produce any new local maxima and minima in advected field. In proposed advection scheme motion of points are performed in Lagrangian manner while spatial derivatives are evaluated on the basis of values interpolated onto regular grid. Applicability of proposed advection scheme in an unambiguous way is proved by performing “standard” numerical tests with (i) the slotted cylinder under solid body rotation, (ii) the test with Doswell’s idealized cyclogenesis as well as (iii) integration of shallow water equations.     

基于新型LE水平跳点网格的阴阳网格平流方案设计

为了模拟球面平流传输过程,本文基于球面阴阳重叠网格设计了一种两时间层半拉格朗日平流方案.该方案在球面坐标下采用新型的LE水平跳点网格,同时针对阴阳网格重叠区,采用了不同插值方法进行比较分析,且进行了相关的理想数值试验对方案设计效果进行评估.数值试验表明方案设计是成功的,阴阳网格重叠区平流对插值方案比较敏感;半拉格朗日方案能较好地模拟球面刚体平流和变形涡旋的结构、位置及演变过程,并具有较好的数值稳定性和较高的数值精度.     

Implementation of the semi-Lagrangian advection scheme on a quasi-uniform overset grid on a sphere

The semi-Lagrangian advection scheme is implemented on a new quasi-uniform overset （Yin-Yang） grid on the sphere. The Yin-Yang grid is a newly developed grid system in spherical geometry with two perpendicularly-oriented latitude-longitude grid components （called Yin and Yang respectively） that overlapp each other, and this effectively avoids the coordinate singularity and the grid convergence near the poles. In this overset grid, the way of transferring data between the Yin and Yang components is the key to maintaining the accuracy and robustness in numerical solutions. A numerical interpolation for boundary data exchange, which maintains the accuracy of the original advection scheme and is computationally efficient, is given in this paper. A standard test of the solid-body advection proposed by Williamson is carried out on the Yin-Yang grid. Numerical results show that the quasi-uniform Yin-Yang grid can get around the problems near the poles, and the numerical accuracy in the original semi-Lagrangian scheme is effectively maintained in the Yin-Yang grid.     

江门地区一次暴雨天气分析及数值预报的应用

本文探讨了江门地区前汛期一次暴雨天气发生发展的物理机制和数值预报产品的特点,结果表明：槽前的正涡度平流导致强烈辐合上升运动,触发边界层不稳定能量的释放,是暴雨产生的触发机制;时、空分辨率较细的数值预报产品对暴雨落点、落区预报提供了较好的参考依据。