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.     

阴阳网格上质量守恒计算性能分析

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。     

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.     

基于球面阴阳网格数值计算研究进展

对球面阴阳网格的转换关系、优缺点及边界数据插值交换方法的相关知识进行了较为详细介绍。同时对应用球面阴阳网格的3种数值计算方法进行了回顾总结,包括优化的Schwarz方法、CIP-CSLR平流数值计算方法、多离散矩有限体积法。针对优化的Schwarz方法,从浅水方程组的离散入手,讨论了其在求解球面椭圆型问题的优势;而对CIP-CSLR平流数值计算方法和多离散矩有限体积法,主要从如何在网格单元内构造插值函数的角度对其进行分析。最后对开发全球非静力阴阳网格模式进行展望。     

一种区域格点三维变分分析方案--基本框架和初步试验

给出一种区域格点三维变分分析方案的基本框架.对方案中阶数巨大的背景场误差协方差矩阵加以处理,选用位势高度和风场非平衡部分的纬向风速、经向风速作为分析变量,减少矩阵阶数;进行变量变换,避免矩阵求逆;然后,采用与最优插值方案相似的水平和垂直方向可分离的理想相关模型,在水平方向上用递归滤波器代替矩阵运算,从而实现变分分析方案的求解.用单个和理想分布观测资料对方案测试,并进行实例试验,得到很好的计算结果.     

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.     

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.     

GRAPES_YY模式发展及其对梅雨锋降水模拟的性能检验

GRAPES_YY是在球面准均匀阴阳网格动力框架基础上发展起来的全球非静力模式，目前已耦合全套物理过程参数化方案，具备了中期天气预报能力。为了解模式对环流和降水的实际预报效果，检验模式对多尺度天气系统的预报能力和误差分布特征，以ERA-interim资料和逐时地面融合降水产品为参考，对1个月（2018年6月中旬—7月中旬）批量试验结果和一次长江流域梅雨个例（7月4—7日）模拟结果进行分析。结果表明:在改进上边界条件基础上，模式有较好的稳定性，短期预报时效内对全球环流和降水刻画准确，模式24 h累计降水纬向平均成功再现了低纬度和中纬度地区的两个降水峰值，但对低纬度对流性降水和中纬度格点尺度降水预报偏强。其次，模式成功模拟出7月4—6日中国东部梅雨雨带位置、走向及南北摆动，整体上能正确反映主要天气系统的移动演变，但受分辨率限制以及湿物理过程影响，暴雨以上量级降水还存在强度预报偏弱、位置偏北的问题。GRAPES_YY模式模拟结果基本合理可信，对中低纬度梅雨锋降水的预报能力较GRAPES_GFS略有改善。      

阴阳网格守恒算法的设计和改进

阴阳网格上的质量守恒算法对于阴阳网格在全球模式构建和应用具有重要意义,是模式长期稳定积分和保证计算效果的重要性能指标。本研究在已有的质量均匀分布假定下阴阳网格守恒强迫算法的基础上,构建网格内质量的双线性分布和边界通量线性分布的质量守恒强迫算法,以提高阴阳网格平流计算的精度和模式积分的稳定性。运用CIP-CSLR平流方案对通量形式平流方程数值求解,分别通过"余弦钟"平流试验、正弦波试验和变形流试验对质量双线性分布、边界通量线性分布的新方案与质量和通量均匀分布的原方案进行了对比,标准化误差和标量场分布均表明新方案可有效提高阴阳网格守恒算法的计算效果,且计算负担没有明显增加,具有较好的实用价值。     

同化多普勒雷达风资料的两种方法比较

以美国新近研发的天气研究预报模式(WRF)配置的三维变分同化系统WRF 3D-Var为平台,比较了两种不同的同化多普勒雷达径向风资料的方法。一种是WRF 3D-Var系统现有的径向风资料直接同化方法;另一种是首先用两步变分法由多普勒资料反演出水平风,再同化反演风场。针对2003年7月4~5日的一次淮河暴雨过程进行的同化试验结果表明,同化了雷达风资料后得到的水平风场包含了更多的中尺度特征;从降水预报评分和预报的雷达回波来看,两种方法都能够明显改进降水预报,这种正作用能维持6 h左右;相对而言,同化反演的水平风场的效果略优于直接同化雷达径向风的效果。     

三维变分和物理初始化方法相结合同化多普勒雷达资料的试验研究

以美国新近研发的天气研究预报模式(WRF)配置的三维变分(3D-Var)同化系统WRF 3D-Var为平台,结合物理初始化方法(Physical Initialization,简称PI)来同化多普勒雷达径向风和回波强度观测资料.其基本做法是首先用物理初始化方法由雷达回波资料估计出比湿、云水混合比和垂直速度,然后用估计的比湿和云水混合比对模式的相应变量进行调整,最后再将估计出的垂直速度作为一种新的观测类型添加到现有的WRF 3D-Var目标函数中,同时以WRF 3D-Var提供的方法直接同化径向风.针对2002年6月19日的一次强对流性降水过程和2003年7月5日的一次梅雨锋暴雨过程进行了一组同化多普勒雷达径向风和回波资料的试验研究.同化结果表明:分析变量的增量场和观测的雷达回波有很好的对应关系.在雷达回波区,有正的比湿增量、云水含量增量和垂直速度增量,并且水平风增量在此辐合;在没有雷达回波的地方有负的垂直速度增量.预报结果表明,调整云水含量对降水预报改善不明显,调整比湿对降水预报改进明显,直接用物理初始化估计出的垂直速度替代模式的初始垂直速度,对降水预报改进不明显,但以新的方案同化雷达资料能有效地缩短模式的起转时间(spin-up time),明显改进短时降水预报.     

Operational convective-scale data assimilation over Iran: A comparison between WRF and HARMONIE-AROME

The impact of applying three-dimensional variational data assimilation (3D-Var DA) on convective-scale forecasts is investigated by using two mesoscale models, the Weather Research and Forecasting model (WRF-ARW) and the Hirlam and Aladin Research Model On Non-hydrostatic-forecast Inside Europe (HARMONIE-AROME). One month (1 to 30 December 2013) of numerical experiments were conducted with these two models at 2.5 km horizontal resolution, in order to partly resolve convective phenomena, on the same domain over a mountainous area in Iran and neighboring areas. Furthermore, in order to estimate the domain specific background error statistics (BES) in convective scales, two months (1 November to 30 December 2017) of numerical experiments were carried out with both models by downscaling operational ECMWF forecasts. For setting the numerical experiments in an operational scenario, ECMWF operational forecast data were used as initial and lateral boundary conditions (ICs/LBCs). In order to examine the impact of data assimilation, the 3D-Var method in cycling mode was adopted and the forecasts were verified every 6 hours up to 36 hours for selected meteorological variables. In addition, 24 h accumulated precipitation forecasts were verified separately. Generally, the WRF and HARMONIE-AROME exhibit similar verification statistics for the selected forecast variables. The impact of DA on the numerical forecast shows some evidence of improvement in both models, and this effect decreases severely at longer lead times. Results from verifying the 24 h convective-scale precipitation forecasts from both models with and without DA suggest the superiority of the WRF model in forecasting more accurately the occurred precipitation over the simulation domain, even for the downscaling run.     

华南地区中尺度模式预报的初值影响分析

基于GRAPES 3D-Vat同化系统，介绍了根据静力平衡关系由高度场的增量来计算温度场的增量的方法，并结合常规探空资料同化，针对影响华南地区的一次冷空气过程的个例，分析了常规观测资料对初始场的影响。采用GRAPES区域中尺度模式进行了控制试验和同化试验，观测资料的检验表明，资料同化对GRAPES中尺度模式预报有正面影响，初始时刻预报敏感性较大并且变化较快，靠近地面的低层预报敏感性较为复杂，常规探空资料对高层大气预报能力的提高相对于中低层较小。     

Use of incremental analysis updates in 4D-Var data assimilation

The four-dimensional variational(4D-Var) data assimilation systems used in most operational and research centers use initial condition increments as control variables and adjust initial increments to find optimal analysis solutions. This approach may sometimes create discontinuities in analysis fields and produce undesirable spin ups and spin downs. This study explores using incremental analysis updates(IAU) in 4D-Var to reduce the analysis discontinuities. IAU-based 4D-Var has almost the same mathematical formula as conventional 4D-Var if the initial condition increments are replaced with time-integrated increments as control variables.The IAU technique was implemented in the NASA/GSFC 4D-Var prototype and compared against a control run without IAU. The results showed that the initial precipitation spikes were removed and that other discontinuities were also reduced,especially for the analysis of surface temperature.     

A New Infrared Atmospheric Sounding Interferometer Channel Selection and Assessment of Its Impact on Met Office NWP Forecasts

A new set of Infrared Atmospheric Sounding Interferometer(IASI) channels was re-selected from 314 EUMETSAT channels.In selecting channels,we calculated the impact of the individually added channel on the improvement in the analysis outputs from a one-dimensional variational analysis(1D-Var) for the Unified Model(UM) data assimilation system at the Met Office,using the channel score index(CSI) as a figure of merit.Then,200 channels were selected in order by counting each individual channel's CSI contribution.Compared with the operationally used 183 channels for the UM at the Met Office,the new set shares 149 channels,while the other 51 channels are new.Also examined is the selection from the entropy reduction method with the same 1D-Var approach.Results suggest that channel selection can be made in a more objective fashion using the proposed CSI method.This is because the most important channels can be selected across the whole IASI observation spectrum.In the experimental trial runs using the UM global assimilation system,the new channels had an overall neutral impact in terms of improvement in forecasts,as compared with results from the operational channels.However,upper-tropospheric moist biases shown in the control run with operational channels were significantly reduced in the experimental trial with the newly selected channels.The reduction of moist biases was mainly due to the additional water vapor channels,which are sensitive to the upper-tropospheric water vapor.     

任意正交曲线坐标系下的海洋模式动力框架的发展与评估

本文发展了一个可以适用于任意水平正交曲线坐标系的海洋模式动力框架,并将其应用于中国科学院大气物理研究所大气科学和地球流体力学数值模拟国家重点实验室发展的气候系统海洋模式LICOM2.0（LASG/IAP Climate system Ocean Model,version2.0）。在经纬网格坐标系下,新的动力框架与LICOM2.0原有的动力框架模拟结果完全一致。基于新的动力框架,海洋模式可采用能够准确描述北冰洋地形的三极网格,克服了LICOM2.0经纬网格版本必须将北极点处理为孤岛的缺陷,从而显著改进了模式对于北冰洋环流和北大西洋经圈翻转流函数（AMOC）的模拟能力。此外,引进三极网格还可以避免模式网格距随纬度增加而急剧减小带来的计算不稳定,在LICOM2.0的三极网格版本中,模式不需要采用任何空间滤波方案仍然能够保证计算的稳定性,从而与LICOM2.0的经纬网格版本相比,极大地提高了模式的并行效率,这一点在当水平分辨率提高到0.1度时表现得尤为明显,海洋模式的并行加速比可以从经纬网格版本的5.8左右提高到三极网格版本的15.0左右。     

GRAPES区域扰动预报模式动力框架设计及检验

设计了适用于四维变分同化系统的扰动预报模式GRAPES_PF。根据GRAPES的地形追随坐标非静力原始方程组,采用小扰动分离方法推导微分形式的线性扰动预报方程组,并利用与GRAPES非线性模式相似的数值求解方案求解线性扰动微分方程组。在设计扰动预报模式时采用了两个时间层半隐式半拉格朗日方案对动量方程、热力学方程、水汽方程和连续方程进行时间差分,空间差分方案的变量分布水平方向采用Arakawa C跳点网格,垂直方向采用Charney/Phillips跳层。利用代数消元法进一步推导得到只包含未来时刻扰动Exner气压的亥姆霍兹方程,进而通过广义共轭余差法（GCR）求解,在此基础上得到未来时刻扰动量的预报值。基于所开发的扰动模式开展了数值试验。首先在非线性模式中施加一个中尺度初始扰动高压,得到初始扰动在非线性模式中的后续演变,然后将相同的初始扰动作为扰动模式的初值进行时间积分,将扰动模式预报的结果与非线性模式的结果做了对比。结果表明,所开发的扰动模式GRAPES_PF较好地模拟了惯性重力内波的传播过程:初始高压扰动激发了一个迅速向外传播的惯性重力内波,在气压场向风场适应的过程中,水平风场、垂直运动、位温和湿度等变量均出现了扰动增量,与非线性模式得到的结果相当接近。GRAPES_PF作为GRAPES非线性模式的合理线性模式为建立基于线性扰动预报的区域四维变分同化系统奠定了科学基础。      

Conformal octagon: An attractive framework for global models offering quasi-uniform regional enhancement of resolution

Summary With the increasingly widespread adoption of massively parallel processing (MPP) computers for applications in computational fluid dynamics it becomes appropriate to reconsider the geometrical configuration of the computational grid that best suits the problem. In the case of global numerical weather prediction we have recently advocated a conformal spherical-cubic geometry. Among its merits, this grid lends itself naturally to simple domain-decomposition and obviates the need for polar filtering.Here we extend the same principles, but with an emphasis on the problem of regional forecasting. In this case we observe that it is possible to cover the global domain with a conformal grid geometry based on the mapping to the sphere of a back-to-back pair of octagonal regions. In the most symmetrical case, each octagon maps to a hemisphere. By compounding this mapping with a nonhomogeneous conformal mapping of the sphere to itself, one can also arrange to have quasi-uniform enhanced resolution of the resulting grid inside any chosen circle on the sphere, at the expense of relatively coarse resolution degrading gradually with distance outside the circle of interest.With appropriate grid dimensions, the new conformal octagon decomposes naturally into several identical square subdomains for efficient distribution over the nodes of an MPP computer.With 11 Figures     

Application of the Characteristic CIP Method to a Shallow Water Model on the Sphere

Semi-implicit algorithms are popularly used to deal with the gravitational term in numerical models. In this paper, we adopt the method of characteristics to compute the solutions for gravity waves on a sphere directly using a semi-Lagrangian advection scheme instead of the semi-implicit method in a shallow water model, to avoid expensive matrix inversions. Adoption of the semi-Lagrangian scheme renders the numerical model always stable for any Courant number, and which saves CPU time. To illustrate the efficiency of the characteristic constrained interpolation profile (CIP) method, some numerical results are shown for idealized test cases on a sphere in the Yin-Yang grid system.     

GRAPES Hybrid-3DVar对台风苏迪罗的数值试验

为了把反映天气形势变化的背景误差协方差引入到变分分析系统中来提高分析质量,本文在GRAPES区域三维变分框架的基础上通过扩展控制变量方法实现动态与静态背景误差协方差耦合,建立混合三维变分分析系统（GRAPES Hybrid-3DVar）。通过控制变量扰动产生的集合样本进行单点观测分析试验验证Hybrid-3DVar及其局地化方案的合理性,并针对台风苏迪罗进行实际观测资料同化和数值预报试验,结果表明:用集合样本描述的背景误差协方差是随着天气流型变化的,动力场和质量场的离散度在台风中心处最大,因而混合同化的分析增量包含更多细微结构和中小尺度信息;其分析和24 h内预报要素质量优于3DVar,24 h内降水强度和落区预报也更准确,混合同化分析改善了3DVar分析的降水空报问题;同时混合同化分析的24 h内台风路径预报也最接近实况,台风强度预报在48 h之内都比3DVar更接近观测。