An Adaptive Nonhydrostatic Atmospheric Dynamical Core Using a Multi-Moment Constrained Finite Volume Method

An adaptive 2 D nonhydrostatic dynamical core is proposed by using the multi-moment constrained finite-volume(MCV) scheme and the Berger-Oliger adaptive mesh refinement(AMR) algorithm. The MCV scheme takes several pointwise values within each computational cell as the predicted variables to build high-order schemes based on single-cell reconstruction. Two types of moments, such as the volume-integrated average(VIA) and point value(PV), are defined as constraint conditions to derive the updating formulations of the unknowns, and the constraint condition on VIA guarantees the rigorous conservation of the proposed model. In this study, the MCV scheme is implemented on a height-based, terrainfollowing grid with variable resolution to solve the nonhydrostatic governing equations of atmospheric dynamics. The AMR grid of Berger-Oliger consists of several groups of blocks with different resolutions, where the MCV model developed on a fixed structured mesh can be used directly. Numerical formulations are designed to implement the coarsefine interpolation and the flux correction for properly exchanging the solution information among different blocks. Widely used benchmark tests are carried out to evaluate the proposed model. The numerical experiments on uniform and AMR grids indicate that the adaptive model has promising potential for improving computational efficiency without losing accuracy.     

The Development of a Nonhydrostatic Global Spectral Model

With the development of numerical weather prediction technology,the traditional global hydrostatic models used in many countries of the world for operational weather forecasting and numerical simulations of general circulation have become more and more unfit for high-impact weather prediction.To address this,it is important to invest in the development of global nonhydrostatic models.Few existing nonhydrostatic global models use consistently the grid finite difference scheme for the primitive equations of dynamical cores,which can subsequently degrade the accuracy of the calculations.A new nonhydrostatic global spectral model,which utilizes the Eulerian spectral method,is developed here from NCAR Community Atmosphere Model 3.0(CAM3.0).Using Janjic's hydrostatic/nonhydrostatic method,a global nonhydrostatic spectral method for the primitive equations has been formulated and developed.In order to retain the integrity of the nonhydrostatic equations,the atmospheric curvature correction and eccentricity correction are considered. In this paper,the Held-Suarez idealized test and an idealized baroclinic wave test are first carried out,which shows that the nonhydrostatic global spectral model has similar climate states to the results of many other global models for long-term idealized integration,as well as better simulation ability for short-term idealized integration.Then,a real case experiment is conducted using the new dynamical core with the full physical parameterizations of subgrid-scale physical processes.The 10-day numerical integration indicates a decrease in systematic error and a better simulation of zonal wind,temperature,and 500-hPa height.     

全球大气数值模式动力框架研究进展

随着数值计算方法和高性能计算机技术的发展以及大气科学理论的完善,国外研制出了许多全球高分辨率非静力大气数值模式,为了让国内的模式开发者对当前全球大气数值模式的现状有一个清晰的了解,归纳总结2012年8月在美国大气研究中心参与评估测试的全世界17个非静力全球大气数值模式,主要从基本方程组、球面网格、离散方法、守恒性质、参数化物理过程与动力框架的耦合和全球大气模式的评估等进行回顾、归纳和讨论,对国内的模式研发者有一定的参考意义。     

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.     

GRAPES模式中三维科氏力计算及其效果评估

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。      

A study of nonhydrostatic effects in idealized sea breeze systems

Nonhydrostatic effects in two-dimensional mesoscale sea breeze systems are investigated by numerical simulations. It is shown that nonhydrostatic effects are directly contributed by the vertical gradients of the vertical velocity variance as well as by the vertical accelerations. It is also shown that a K-type turbulence closure is not suitable in a nonhydrostatic primitive equation model, and a higher-order closure scheme should therefore be used. Results from hydrostatic and fully-nonhydrostatic models are compared for various surface and atmospheric background conditions, such as scale and strength of surface heating, geostrophic wind, stability, surface roughness contrast, Coriolis effect, etc. It is found that for strongly developed sea breeze cases, vertical gradients of vertical velocity variance contribute most to nonhydrostatic forcing in the lower layers, and that the resultant nonhydrostatic pressure gradient acts against the hydrostatic pressure gradient, so that nonhydrostatic simulations produce weaker systems than hydrostatic ones. For weak sea breeze systems, the difference between the two models tends to be small.     

国家自然科学基金大气科学学科二级申请代码下设研究方向与关键词解读:D0511大气数值模式发展

为响应国家自然科学基金委员会“优化学科布局”改革,大气科学学科于2020年完成了申请代码调整,明确了“分支学科”“支撑技术”“发展领域”三大板块的新布局。调整后大气数值模式发展被设置为“支撑技术”板块中的独立代码（D0511）。大气数值模式本质是基于物理或化学过程,应用数值算法求解偏微分方程组的数值解。大气数值模式发展应以攻克关键核心技术为导向,提升我国在该领域综合国际竞争力。为了服务大气数值模式发展领域的基金项目申请和评审,推动学科进一步发展,本文对国家自然科学基金大气科学学科二级申请代码D0511大气数值模式发展下设的研究方向和关键词进行了解读。系统介绍了D0511的设置背景、下设研究方向及关键词的总体框架。在对关键词进行解读的同时,基于文献计量方法和Web of Science数据库对该代码下不同方向的词频和研究热点进行了分析和讨论。结合近两年申请情况分析了关键词的使用情况,并就关键词的选择和优化提出了建议。后续还将在关键词设置基本指导思想不变的前提下,根据实际需求不断完善其具体内容。本文有助于申请人更好地理解及选择D0511下设的研究方向与关键词,亦可作为D0511研究方向和关...     

对流层中层中尺度对流涡旋在台风榴莲(2001)生成中的作用——模拟诊断分析

本文基于PSU/NCAR MM5中尺度模式对台风榴莲 (2001) 生成过程成功的数值模拟, 利用模式输出的较高时空分辨率资料, 对台风榴莲生成过程中对流层中层中尺度对流涡旋 (MCV) 的作用进行了诊断分析。结果表明, 中层MCV在台风榴莲生成中的作用有三个重要方面: 第一, 中尺度组织化作用: 伴随中层MCV的垂直次级环流圈, 使得区域内的积云对流热塔趋向于逐步在中心区域集中, 热塔相互之间容易发生相互作用, 通过合并过程有些热塔得到加强, 而有些趋于消亡。同时, 热塔聚集后的群体效应反馈作用又使得中层MCV加强或维持, 进一步促进热塔的合并以及向轴对称化发展; 第二, 存贮效应: 因为中层MCV的生命史比积云对流热塔长, 能够将消亡对流热塔所携带的热量、 水汽、 涡度加以存贮和保留, 使得中层MCV区域向有利于TC生成的方向发展, 最终成为TC环流的 “胚胎”; 第三, 中层MCV与对流层低层的槽 (涡旋) 以及对流热塔之间通过相互作用, 共同实现中低层系统的垂直耦合。     

基于并行可扩展科学计算工具集求解GRAPES全球非静力模式亥姆霍兹问题

亥姆霍兹方程是非静力平衡大气模式动力内核的主要计算瓶颈之一,其离散矩阵性态差,采用常见预条件Krylov迭代往往收敛很慢。随着全球非静力平衡大气模式时空分辨率的不断提高,亥姆霍兹方程求解面临求解精度和计算时间的双重困难。在高分辨率情况下,迭代计算步数和计算量剧增,而且很多传统的预条件迭代求解方法不收敛,迫切需要研究收敛性和并行可扩展性兼备的预条件迭代方法。为此,在安腾机群上建立了基于并行可扩展科学计算工具集(PETSc)的GRAPES全球非静力平衡模式亥姆霍兹问题并行解法器对比研究平台,结合高性能预条件库(hypre),完成了对GRAPES在用解法器、代数多重网格、并行不完全LU分解(EUCLID)及加性Schwarz区域分解等一系列克雷洛夫预条件迭代的分析对比。结果显示PETSc结合高性能预条件库的并行方案是解决GRAPES模式三维亥姆霍兹方程高效并行计算的一个有效途径,其中以代数多重网格预条件迭代的性能最突出;并行加速比分析显示,代数多重网格预条件迭代的并行可扩展性明显优于GRAPES现有解法器,更适用于更高精度和较大规模并行计算。     

An improved dynamic core for a non-hydrostatic model system on the Yin-Yang grid

A 3D dynamic core of the non-hydrostatic model GRAPES(Global/Regional Assimilation and Prediction System) is developed on the Yin-Yang grid to address the polar problem and to enhance the computational efficiency. Three-dimensional Coriolis forcing is introduced to the new core, and full representation of the Coriolis forcing makes it straightforward to share code between the Yin and Yang subdomains. Similar to that in the original GRAPES model, a semi-implicit semi-Lagrangian scheme is adopted for temporal integration and advection with additional arrangement for cross-boundary transport. Under a non-centered second-order temporal and spatial discretization, the dry nonhydrostatic frame is summarized as the solution of an elliptical problem. The resulting Helmholtz equation is solved with the Generalized Conjugate Residual solver in cooperation with the classic Schwarz method. Even though the coefficients of the equation are quite different from those in the original model, the computational procedure of the new core is just the same. The bi-cubic Lagrangian interpolation serves to provide Dirichlet-type boundary conditions with data transfer between the subdomains. The dry core is evaluated with several benchmark test cases, and all the tests display reasonable numerical stability and computing performance. Persistency of the balanced flow and development of both the mountain-induced Rossby wave and Rossby–Haurwitz wave confirms the appropriate installation of the 3D Coriolis terms in the semi-implicit semi-Lagrangian dynamic core on the Yin-Yang grid.     

非静力AREM模式设计及其数值模拟II:数值模拟试验

在程锐等（2018）中,我们完成了非静力AREM（Advanced Regional Eta-coordinate Model）模式动力框架设计。本文将通过理想和实例试验检验其模拟能力。设计理想试验并通过与国际成熟的中尺度非静力框架比较,直接检验非静力AREM三维动力框架在细致分辨率（约1 km）下的模拟性能。可以看出,非静力AREM与ARPS（Advanced Regional Prediction System）、WRF（Weather Research and Forecasting Model）模拟出类似的积云对流结构及演变特征,从而基本确证了本文发展的非静力框架的正确性。结合原静力平衡模式的初始化和物理参数化过程,形成非静力AREM模式系统。台风实例模拟表明,粗分辨率下静力、非静力AREM模式性能接近;但在高分辨率下,非静力明显优于静力模式。我们还开展了批量降水试验检验,对非静力AREM模式性能进行了进一步的验证。     

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。      

对流层中层中尺度涡旋在台风榴莲(2001)生成中的作用—数值模拟及验证

西太平洋热带气旋（TC）的生成和季风槽及中尺度对流系统（MCS）的活动有密切关系,但以往这方面的实例数值模拟很少。为了进一步探讨由MCS对流强迫产生的对流层中层中尺度涡旋（MCV）在TC生成中的作用,作者利用非静力平衡的中尺度模式PSU/NCAR MM5对台风榴莲（2001）的生成过程进行了高分辨率（6 km）数值模拟和比较验证。结果表明:模式成功地模拟出榴莲的生成地点,其与MCS的相对位置关系与以往的观测研究结果一致;模拟的TC移动路径、强度变化与最优观测报告比较接近,准确反映了TC未来登陆地点,以及中心气压缓慢下降和迅速下降两个阶段;对云系演变的模拟,成功模拟出了TC初生时的涡旋云系和季风槽中MCS云系的分离现象,以及在TC登陆前达到成熟阶段时出现的台风眼和螺旋云带。此外,模式还成功模拟出中层MCV,它的水平尺度约200 km,位于800~400 hPa之间,具有暖心结构等,均与已有观测结果相近。模式初始场中包含有充分的MCS信息,是模拟取得成功的关键因素之一。     

An accurate multimoment constrained finite volume transport model on Yin-Yang grids

A global transport model is proposed in which a multimoment constrained finite volume (MCV) scheme is applied to a Yin-Yang overset grid. The MCV scheme defines 16 degrees of freedom (DOFs) within each element to build a 2D cubic reconstruction polynomial. The time evolution equations for DOFs are derived from constraint conditions on moments of line-integrated averages (LIA), point values (PV), and values of first-order derivatives (DV). The Yin-Yang grid eliminates polar singularities and results in a quasi-uniform mesh. A limiting projection is designed to remove nonphysical oscillations around discontinuities. Our model was tested against widely used benchmarks; the competitive results reveal that the model is accurate and promising for developing general circulation models.     

Simulation of orographically generated waves in a nonhydrostatic model of an adiabatic atmosphere

Results of numerical experiments on the simulation of a flow moving around an isolated mountain are presented. The influence of the sizes of a barrier and of the flow velocity on characteristics of wave oscillations is discussed. All calculations are carried out with the authors’ two-dimensional (in the vertical plane) version of a nonhydrostatic dynamic scheme, in which equations of the dry quasi-incompressible atmosphere are solved with a semi-implicit semi-Lagrangian method. This method uses large time steps as compared to explicit-implicit Eurlerian methods. The results of calculations agree with results obtained by other authors, which gives hope for finding physically correct solutions in the simulation of nonhydrostatic processes in the atmosphere.     

一个基于Eta垂直坐标的新WRF动力框架及其数值试验

针对我国陡峭地形数值预报难题,本文在国际先进WRF(Weather Research and Forecasting)模式动力框架中引入阶梯地形垂直坐标,以期为改进复杂地形区域数值天气预报提供模式发展可选方案.设计气柱质量变换方法,实现阶梯地形和追随地形两种垂直坐标下动力方程组的形式一致,从而简化方程组离散及程序实现的...     

Application of a quasi-nonhydrostatic parameterization for numerically modeling neutral flow over an isolated hill

A parameterization of the nonhydrostatic pressure was modified and adapted to a nonlinear numerical model of the neutral atmospheric boundary layer. A hydrostatic model and the quasinonhydrostatic version were used to simulate neutral flow over a symmetrical hill of uniform roughness. Mean-flow quantities and some turbulence characteristics of the flow from both models are presented. These results were compared with observations, analytic theory, and other numerical models.The quasi-nonhydrostatic method produced qualitative features commonly observed in such flows that the hydrostatic model could not simulate. For instance, the observed velocity reduction at the hill base and the speedup at the summit both were simulated by the quasi-nonhydrostatic model. However, computation of vertical velocities from the incompressible continuity equation is inadequate above regions of recirculation and presents a limitation to the method.Journal Paper No. J-12741 of the Iowa Agriculture and Home Economics Experiment Station, Ames, Iowa. Project No. 2779.     

Evaluation of an alternative method for numerically modeling nonhydrostatic flows over irregular terrain

Modeling nonhydrostatic atmospheric flow requires the solution of the vertical equation of motion and a prognostic or diagnostic equation for pressure. If the nonhydrostatic components of the flow are relatively small, they can be approximated and incorporated into a purely hydrostatic model, which usually is conceptually simpler and computationally more efficient. A method to do this for a linear model of local thermally-induced circulations is further developed and adapted to a non-linear numerical model of the neutral atmospheric boundary layer. A hydrostatic model and the quasi-nonhydrostatic version were used to simulate neutral flow over simple terrain features. One set of observations taken over a simple change in roughness and another set taken over a change in both roughness and terrain were simulated by both models to assess the capabilities of the quasi-nonhydrostatic technique.It is found that (as expected) the pressure deviation from the hydrostatic state is negligible for the roughness change, but it is an important aspect of neutral flow over terrain. Thus, for flow encountering a simple roughness change, the hydrostatic approximation is good, even for small horizontal scales. However, the quasi-nonhydrostatic model qualitatively produces the features in the observations for flow over a terrain change that the hydrostatic model cannot produce.Journal Paper No. J-12737 of the Iowa Agriculture and Home Economics Experiment Station, Ames, Iowa. Project No. 2779.     

A nonhydrostatic model based on a new approach

Summary ?The nonhydrostatic Meso model developed at NCEP (Janjic et al, 2001) is based on a new approach. Namely, a hydrostatic NWP model using mass based vertical coordinate has been extended to include the nonhydrostatic motions. In this way favorable features of the hydrostatic formulation have been preserved. This procedure did not require any linearization or approximation. The nonhydrostatic dynamics has been introduced through an add-on module. The nonhydrostatic module can be turned on and off, so that easy comparison can be made of hydrostatic and nonhydrostatic solutions. Here, the basic philosophy behind the discretization methods applied in the model, and not covered by Janjic et al (2001), is discussed, and the latest developments are reviewed. The forecast examples shown indicate that significant differences between hydrostatic and nonhydrostatic forecasts may develop even at relatively coarse resolution of 8 km. Possible future developments are considered. Received May 7, 2001; revised October 15, 2001