半拉格朗日平方守恒计算格式的研究

作者研究了一种新的显式平方守恒的半拉格朗日计算格式.该格式是欧拉空间平方守恒格式在半拉格朗日空间的推广和发展,并采用了守恒插值方法.此外,还给出这种格式在一维原始方程上的应用.     

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.     

半隐式半拉格朗日平方守恒计算格式的构造

在显式半拉格朗日完全平方守恒格式基础上, 构造出半隐式半拉格朗日完全平方守恒计算格式, 它继承了显式半拉格朗日完全平方守恒格式的优点, 并突破计算不稳定柯朗条件对时间步长的约束, 使时间步长大为增长.此外, 还给出这种新的计算格式在一维原始方程上的应用.     

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.     

The Application of Flux-Form Semi-Lagrangian Transport Scheme in a Spectral Atmosphere Model

A flux-form semi-Lagrangian transport scheme(FFSL) was implemented in a spectral atmospheric GCM developed and used at IAP/LASG.Idealized numerical experiments show that the scheme is good at shape preserving with less dissipation and dispersion,in comparison with other conventional schemes.Importantly,FFSL can automatically maintain the positive definition of the transported tracers,which was an underlying problem in the previous spectral composite method(SCM).To comprehensively investigate the impact of FFSL on GCM results,we conducted sensitive experiments.Three main improvements resulted:first,rainfall simulation in both distribution and intensity was notably improved,which led to an improvement in precipitation frequency.Second,the dry bias in the lower troposphere was significantly reduced compared with SCM simulations.Third,according to the Taylor diagram,the FFSL scheme yields simulations that are superior to those using the SCM:a higher correlation between model output and observation data was achieved with the FFSL scheme,especially for humidity in lower troposphere.However,the moist bias in the middle and upper troposphere was more pronounced with the FFSL scheme.This bias led to an over-simulation of precipitable water in comparison with reanalysis data.Possible explanations,as well as solutions,are discussed herein.     

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。     

完全非内插半拉格朗日格式在一维 Burgers方程及二维浅水波方程上的应用

在作者过去提出的完全非内插半拉格朗日格式的基础上,针对半拉格朗日格式由于内插带来预报场人为的光滑性问题,进一步发展了这种计算格式,证明了此格式的计算稳定性。为检验这种新的计算格式的性能,在一维和二维问题上进行了应用。在一维问题中采用了一维无粘Burgers方程（方程中有突变点）;二维问题采用了浅水波方程,同时将这些计算结果与Ritchie方案及欧拉方案或一般半拉格朗日内插方案的计算结果进行了比较,发现新格式消除了内插和预报场的人为光滑,并且计算精度有一定程度的提高,这为以后将此格式推广到全球谱模式打下了基础。     

两步保形平流方案在高分辨率球面经纬网格下的跳点差分试验

尝试用一个基于有限差分的两步保形平流方案（TSPAS）替代美国国家大气研究中心第5版公用大气模式（NCAR-CAM5）欧拉-谱动力框架中的半拉格朗日传输（SLT）平流方案,并针对不同分辨率版本,计算水汽等物质的传输过程。通过设计保证守恒性的跳点差分法,解决了基于经纬网格的模式在高分辨率下由于极区纬向格距过小而造成的差分方案积分时间步长过短的问题,使得TSPAS在高分辨率下仍然可以使用较大的时间步长。理想试验表明：（1）跳点TSPAS在守恒性、数值精度（量级上）、保形性等方面均较好地保持了原TSPAS的特点,而积分步长可增大到与CAM5-SLT相同,比原TSPAS提高超过一个数量级;（2）较半拉格朗日传输方案,尽管TSPAS的耗散更大,但是在相同时间步长下更省时,且改进了半拉格朗日传输求解平流方程造成的不守恒问题。CAM5的比较试验表明：（1）采用跳点TSPAS的模式结果与非跳点计算结果相当,在高纬度跳点区域也并未出现模拟异常;（2）在高分辨率下,采用跳点TSPAS方案的CAM5模拟结果与原模式结果相近,并初步显示对东亚青藏高原南侧的虚假降水有所抑制。该工作确保了基于欧拉通量差分型的TSPAS在高分辨率模式下的大时间步长稳定积分,为解决有限差分方法在高分辨率模式发展中的相关计算问题提供了启示,为后续针对东亚地区的模式性能改进奠定了基础。     

Implementation of a Conservative Two-step Shape-Preserving Advection Scheme on a Spherical Icosahedral Hexagonal Geodesic Grid

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.     

一种新的大气稳定度分类方法

提出了一种运用灰色聚类理论对大气稳定度进行分类的新方法,用该方法及上海江湾站1993年1、4、7、10四个月的逐时常规观测资料对当时当地的大气稳定度进行了分类,最后与国标分类法所得结果进行了比较,得到了更优、更合理的类分布,说明该方法是大气稳定度分类中一种简单、实用而且效果更好的新方法。     

JFNK方法在求解全隐式一维非线性平流方程中的应用

JFNK(Jacobian-free Newton-Krylov)方法是由Newton迭代方法和Krylov子空间迭代方法构成的嵌套迭代方法。作者以全隐式差分的一维非线性平流方程（亦称无粘Burgers方程）探讨采用全隐式格式计算的必要性和JFNK方法的有效性。模拟结果表明, 隐式结果比显式和半隐式结果在稳定度和精度方面较大的优越性, 特别是模拟气流强的系统以及要素空间分布具有较大梯度的系统。     

A Positivity-preserving Conservative Semi-Lagrangian Multi-moment Global Transport Model on the Cubed Sphere

A positivity-preserving conservative semi-Lagrangian transport model by multi-moment finite volume method has been developed on the cubed-sphere grid. Two kinds of moments(i.e., point values(PV moment) at cell interfaces and volume integrated average(VIA moment) value) are defined within a single cell. The PV moment is updated by a conventional semi-Lagrangian method, while the VIA moment is cast by the flux form formulation to assure the exact numerical conservation. Different from the spatial approximation used in the CSL2(conservative semi-Lagrangian scheme with second order polynomial function) scheme, a monotonic rational function which can effectively remove non-physical oscillations is reconstructed within a single cell by the PV moments and VIA moment. To achieve exactly positive-definite preserving, two kinds of corrections are made on the original conservative semi-Lagrangian with rational function(CSLR)scheme. The resulting scheme is inherently conservative, non-negative, and allows a Courant number larger than one.Moreover, the spatial reconstruction can be performed within a single cell, which is very efficient and economical for practical implementation. In addition, a dimension-splitting approach coupled with multi-moment finite volume scheme is adopted on cubed-sphere geometry, which benefitsthe implementation of the 1 D CSLR solver with large Courant number.The proposed model is evaluated by several widely used benchmark tests on cubed-sphere geometry. Numerical results show that the proposed transport model can effectively remove nonphysical oscillations and preserve the numerical nonnegativity, and it has the potential to transport the tracers accurately in a real atmospheric model.     

关于半拉格朗日半隐式大气模式的时步问题

讨论半拉格朗日半隐式大气模式中时步的限制,展示时步过大时用一般的首尾两点平均方案计算非线性源汇项的严重误差,提出精确的源汇项计算格式并作了特例计算和比较,讨论了被模拟的大气过程和波动的特征对时步的要求,指出柯朗数NC=C·△t/△X是大气模式时空步长匹配的重要参数.指出云降水和大气化学过程特征时间对相应的正定变量的计算时步的限制.     

一种利用积分球原理的日照计新方案

该文提出了一种利用积分球原理设计的新型日照传感器。该传感器由限角挡环、积分球体和光电探测器组成。积分球为一有5个针孔的空心正球体。针孔可阻挡散射光进入球内,而射入球内的直射光,经内壁多次漫反射后,其亮度呈均匀分布。与日照阈值下相应的亮度相比较可确定日照之有无。该日照传感器具有无转动部件、结构简单、无需调整及便于操作等优点。     

冷平流强迫背景下攀枝花市一次雷暴过程综合分析

基于欧洲中心ERA5再分析资料、NCEP再分析资料、卫星和雷达资料以及MICAPS气象资料,运用天气学方法对2020年4月13日四川省攀枝花市发生的冷平流强迫类雷暴天气过程进行综合分析。结果表明：本次雷暴过程混合了冰雹、短时强降水、雷暴大风等多种天气,其主要影响系统为200 hPa高空急流、500 hPa高原槽、700 hPa切变线和西南急流以及地面辐合线。200~500 hPa西北干冷空气顺高原槽南下对本次过程起主导作用,弱的700 hPa西南急流为本地输送了水汽和不稳定能量,中低层切变线和地面辐合线促进了暖湿气流的辐合抬升。此外,“上冷下暖”的气层结构、中低层较强的垂直风切变、气流的低层辐合与高层辐散、适宜的0℃和-20℃层高度、较强的CAPE和K指数、较大的700~500 hPa温度垂直递减率等因素也是本次雷暴天气过程发生发展的关键。     

A 3D Nonhydrostatic Compressible Atmospheric Dynamic Core by Multi-moment Constrained Finite Volume Method

A 3D compressible nonhydrostatic dynamic core based on a three-point multi-moment constrained finite-volume (MCV) method is developed by extending the previous 2D nonhydrostatic atmospheric dynamics to 3D on a terrain-following grid. The MCV algorithm defines two types of moments: the point-wise value (PV) and the volume-integrated average (VIA). The unknowns (PV values) are defined at the solution points within each cell and are updated through the time evolution formulations derived from the governing equations. Rigorous numerical conservation is ensured by a constraint on the VIA moment through the flux form formulation. The 3D atmospheric dynamic core reported in this paper is based on a three-point MCV method and has some advantages in comparison with other existing methods, such as uniform third-order accuracy, a compact stencil, and algorithmic simplicity. To check the performance of the 3D nonhydrostatic dynamic core, various benchmark test cases are performed. All the numerical results show that the present dynamic core is very competitive when compared to other existing advanced models, and thus lays the foundation for further developing global atmospheric models in the near future.     

守恒型有理函数插值半拉格朗日平流方案及性能分析

通过多种理想试验对正定、保形守恒型有理函数插值半拉格朗日平流方案分别在平面直角坐标以及阴阳网格球面坐标中进行了计算性能分析,并采用多种误差模对守恒型有理函数插值半拉格朗日平流方案的网格收敛性进行评估。结果表明,采用分段有理函数插值的守恒型半拉格朗日平流方案可以有效消除不连续分布处的数值振荡、保证正定性,物理场平滑分布时维持1-2阶收敛速度;而在不连续点或大梯度区域以及应用分维技术的多维算法都会通过有理函数的降阶特性,影响平流计算的收敛阶数,并且,在球面坐标中受球面曲率的影响,守恒型有理函数插值半拉格朗日平流算法的网格收敛速度有所降低。     

地气通量中存贮和平流项计算方案的探讨

从物质收支方程出发,推导了一个包含物质存贮、水平平流输送、垂直对流输送以及传统的涡度相关项的地气通量计算方程。平流项本质上是地表非均匀性的结果,不同下垫面的感热和潜热通量也不同,将会产生中尺度环流,使得辐合辐散过程得以维持,从而将体元内的物质输送到体元以外,因此可以通过计算水汽和感热的存贮,间接求出物质的水平平流输送。量纲分析和实际的资料应用都表明,存贮和平流的通量贡献是非常小的。尤其是在均匀下垫面下,方程中的存贮和平流项的通量贡献可以忽略,因此估算地气通量时仅需考虑涡度相关项和Webb修正项即可。而在非均匀下垫面下,在1 d以上的时间尺度上,为方便计算,可以忽略存贮和平流的通量贡献;而在小时这样的时间尺度上,从物质能量收支守恒的角度考虑,估算地气通量需要包括存贮和平流的通量贡献。     

一次平流雾的形成和传播特征研究

2013年3月18-19日,江苏出现了一次罕见的平流雾过程,雾区先在长江北岸形成,继而向苏北传播。本文对这次平流雾的形成机理及特征进行了分析,并对雾区的传播机制进行了研究。结果表明:此次平流雾的形成主要受冷空气控制后暖湿平流的影响,冷锋过境后的影响是平流雾形成的基础,东海变性冷高压北抬是其形成的必要条件;地面东南风和低空东南水汽输送共同推动雾区向北传播;长江、洪泽湖、高邮湖等水域对平流雾增强起着重要作用;强浓雾呈渐进式发展,爆发性增强不明显以及云雾共存结构等是本次平流雾的主要特征。本论文的研究结果对平流雾的预报具有重要的实用价值。