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 new cumulus parameterization scheme based on an explicit time-dependent tilting cloud model in ARPS model

A one-dimensional Explicit Time-dependent Tilting cloud Model (ETTM) that separates updraft and downdraft columns and takes into account the effect of cloud tilting on precipitation is introduced and incorporated into the Advanced Regional Prediction System (ARPS). Results of the stand-alone ETTM are compared with that of cloud resolving simulations using the ARPS mesoscale model. Inter-comparison is performed by qualitative examination of simulated parameters such as vertical distribution of fluxes of mass, heat, and moisture. Although there is a great degree of similarity between the vertical profiles, ETTM systematically underestimates magnitudes of all fluxes. Sensitivity tests carried with ETTM show that the effect of varying cloud radius and tilting angle is considerable on the simulated cloud behavior. Increasing the cloud radius, results in a corresponding increase in fluxes of mass, heat, and moisture, while increasing the cloud tilt angle has the opposite effect. Since ETTM showed promise as a suitable sub-grid cumulus parameterization scheme; it was incorporated into ARPS as an additional cumulus parameterization scheme (CPS) to be available for the wider community. Results of simulations using ETTM and other CPSs already available in ARPS were compared for 2, 4 and 10 km grid spacings to assess its utility. Simulation results of the 2 km grid showed that at this resolution, the simulated time series of updraft velocities using the new scheme (ETTM) compared well with the results of other schemes in the ARPS model. The simulations with horizontal resolution of 4 km that was compared with the convection resolving reference run (No-CPS-2KM) showed almost consistent results for all schemes except for one using KF scheme. The results of the simulation with the ETTM scheme and other schemes in the model with resolution of 10 km showed that at this resolution, there is not significant difference between the uses of these schemes.     

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

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.     

不同云降水方案对一次登陆台风的降水模拟

利用美国最新发展的新一代中尺度数值预报模式(WRF),研究了不同云降水方案对一次登陆台风的降水模拟问题,结果表明,在网格距适当小的情况下,同时采用积云对流参数化方案和云微物理方案(Kessler方案)时,其降水预报优于只使用积云对流参数化方案时的预报;在台风降水模拟的初期,Kain-Fritsch方案比Betts-Miller方案产生降水更快,更接近实况降水;在台风登陆后随时间的延长,对流降水重要性逐步下降,网格尺度降水逐渐增强。     

高阶精度有限差分方案下的非跳点网格试验:基于浅水波方程

非跳点网格在模式动力—物理过程的耦合方面具有独特的优势,但是由于二阶精度差分方案下非跳点网格频散误差较大而很少被使用于数值天气预报模式.随着近年来数值模式计算精度的不断提高,非跳点网格在频散关系方面的计算误差是否会发生变化还有待研究.本文在高阶精度差分格式下通过浅水波方程对跳点网格和非跳点网格的频散关系进行理论分析和数...     

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     

新一代天气雷达网资料的三维格点化及拼图方法研究

文中研究了几种把球坐标系下的雷达网反射率体扫资料插值到统一的笛卡尔坐标系下的经纬度网格上以及用多个雷达的反射率网格资料进行三维拼图的方法,并对多个雷达同步观测的反射率因子的空间一致性、系统误差以及雷达等距离线上回波的水平和垂直结构进行了分析。结果发现:在雷达资料格点化过程中,径向和方位上的最近邻居法和垂直方向的线性内插法的结合(NVI方法)是一种有效的雷达资料分析方法,它既能得到空间比较连续的反射率分析场,同时也较好地保留了体扫资料中原有的反射率结构特征;广州雷达和梅州雷达同步观测的空间一致性比较好;在多个雷达资料合成拼图的过程中,距离指数权重平均法能提供空间连续的三维反射率拼图数据,拼图也减轻了由雷达波束几何学引起的各种问题。     

Modelling the arctic convective boundary-layer with different turbulence parameterizations

Different parameterizations of subgrid-scale fluxes are utilized in a nonhydrostatic and anelastic mesoscale model to study their influence on simulated Arctic cold air outbreaks. A local closure, a profile closure and two nonlocal closure schemes are applied, including an improved scheme, which is based on other nonlocal closures. It accounts for continuous subgrid-scale fluxes at the top of the surface layer and a continuous Prandtl number with respect to stratification. In the limit of neutral stratification the improved scheme gives eddy diffusivities similar to other parameterizations, whereas for strong unstable stratifications they become much larger and thus turbulent transports are more efficient. It is shown by comparison of model results with observations that the application of simple nonlocal closure schemes results in a more realistic simulation of a convective boundary layer than that of a local or a profile closure scheme. Improvements are due to the nonlocal formulation of the eddy diffusivities and to the inclusion of heat transport, which is independent of local gradients (countergradient transport).     

Computing Streamfunction and Velocity Potential in a Limited Domain of Arbitrary Shape. Part II: Numerical Methods and Test Experiments

Built on the integral formulas in Part I,numerical methods are developed for computing velocity potential and streamfunction in a limited domain.When there is no inner boundary(around a data hole) inside the domain,the total solution is the sum of the internally and externally induced parts.For the internally induced part,three numerical schemes(grid-staggering,local-nesting and piecewise continuous integration) are designed to deal with the singularity of the Green’s function encountered in numerical calculations.For the externally induced part,by setting the velocity potential(or streamfunction) component to zero,the other component of the solution can be computed in two ways:(1) Solve for the density function from its boundary integral equation and then construct the solution from the boundary integral of the density function.(2) Use the Cauchy integral to construct the solution directly.The boundary integral can be discretized on a uniform grid along the boundary.By using local-nesting(or piecewise continuous integration),the scheme is refined to enhance the discretization accuracy of the boundary integral around each corner point(or along the entire boundary).When the domain is not free of data holes,the total solution contains a data-hole-induced part,and the Cauchy integral method is extended to construct the externally induced solution with irregular external and internal boundaries.An automated algorithm is designed to facilitate the integrations along the irregular external and internal boundaries.Numerical experiments are performed to evaluate the accuracy and efficiency of each scheme relative to others.     

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.     

Extreme precipitation in WRF during the Newcastle East Coast Low of 2007

In the context of regional downscaling, we study the representation of extreme precipitation in the Weather Research and Forecasting (WRF) model, focusing on a major event that occurred on the 8^th of June 2007 along the coast of eastern Australia (abbreviated “Newy”). This was one of the strongest extra-tropical low-pressure systems off eastern Australia in the last 30 years and was one of several storms comprising a test bed for the WRF ensemble that underpins the regional climate change projections for eastern Australia (New South Wales/Australian Capital Territory Regional Climate Modelling Project, NARCliM). Newy provides an informative case study for examining precipitation extremes as simulated by WRF set up for regional downscaling. Here, simulations from the NARCliM physics ensemble of Newy available at ～10 km grid spacing are used. Extremes and spatio-temporal characteristics are examined using land-based daily and hourly precipitation totals, with a particular focus on hourly accumulations. Of the different physics schemes assessed, the cumulus and the boundary layer schemes cause the largest differences. Although the Betts-Miller-Janjic cumulus scheme produces better rainfall totals over the entire storm, the Kain-Fritsch cumulus scheme promotes higher and more realistic hourly extreme precipitation totals. Analysis indicates the Kain-Fritsch runs are correlated with larger resolved grid-scale vertical moisture fluxes, which are produced through the influence of parameterized convection on the larger-scale circulation and the subsequent convergence and ascent of moisture. Results show that WRF qualitatively reproduces spatial precipitation patterns during the storm, albeit with some errors in timing. This case study indicates that whilst regional climate simulations of an extreme event such as Newy in WRF may be well represented at daily scales irrespective of the physics scheme used, the representation at hourly scales is likely to be physics scheme dependent.     

包含正定水汽输送算法改进的MM4中尺度模式与暴雨实例数值试验

暴雨预报是一个既重要又十分困难的问题。水汽条件是产生暴雨的关键，水汽的平流输送在模式的水汽方程中占有重要地位，模式对暴雨的预报能力必然涉及到水汽输送的计算精度问题；本文以著名的中尺度模式ＭＭ４为基础，理论测试和分析为依据，以引入新的正定高精度水汽输送算法作为消除模式水汽负值和改进中尺度模式预报能力的途径，研制了取名为改进的ＭＭ４中尺度模式，该模式除仍保留原ＭＭ４模式的所有功能外，增加了５种水汽输送算法的改进与选择，这５种算法是：１）Ｂ网格二阶守恒中心差（原ＭＭ４平流格式），２）上游差分，３）Ｂｏｔ（２阶），４）Ｂｏｔ（４阶），５）Ｐｒａｔｈｅｒ格式。多个暴雨、台风个例试验表明模式预报能力对水汽输送算法精度有显著的依赖性，采用高精度的水汽输送算法水汽保证正值并提高了模式对暴雨区、降水结构、雨团活动的预报能力。改进水汽输送算法的精度是提高中尺度模式对暴雨预报能力的重要途径。     

A comparison of boundary layer diffusion schemes in unstable conditions over land

We compare the results of a local and a nonlocal scheme for vertical diffusion in the atmospheric boundary layer with observations at the 200 m tower at Cabauw. This is done for a 12 h period during daytime on 31 May 1978, which is characterised by strong insolation, clear skies, moderately strong winds and weak advection. The local diffusion scheme uses an eddy diffusivity determined independently at each point along the vertical based on local vertical gradients of wind and virtual potential temperature, similar to the usual approach in atmospheric models. The nonlocal scheme determines an eddy diffusivity profile based on a diagnosed boundary-layer height and a turbulent velocity scale. It also incorporates nonlocal (vertical) transport effects for heat and moisture. The boundary-layer diffusion schemes are forced with the locally observed fluxes for heat and moisture. The outputs of the scheme are compared with the observed mean structure along the Cabauw tower, and the radiosonde profile at a nearby location (De Bilt). Overall, the nonlocal scheme transports moisture away from the surface more rapidly than the local scheme, and deposits the moisture at higher levels. The local scheme tends to saturate the lowest model levels unrealistically in comparison with the observations. We also compare the outputs of the two diffusion schemes with the results of a transilient model simulation. Subsequently, we study the impact on the model behaviour by varying important parameters in both diffusion schemes and we investigate the sensitivity to uncertainty in the environmental conditions. Finally, we study the interaction of the diffusion schemes with a simple surface flux scheme.     

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.     

辐射参数化的变化对模式中期和月预报的影响

在T106中期数值预报模式和T63气候模式中进行了两种辐射过程参数化的对比试验。目前在这两个模式中用作对照积分的辐射方案(OPE)是ECMWF的早期业务方案，而新的辐射方案(NEW)是ECMWF 1989年5月2日成为业务的版本。试验结果表明，OPE高估了短波水的吸收，导致太大的短波大气吸收和地表太小的向下短波辐射；OPE还低估了长波辐射冷却和大气顶的向外长波辐射(OLR)；NEW增加了地表有效辐射能量和对流层总的冷却，产生了较大的湍流热通量，对流活动加强，降水量明显增加；NEW还使平流层温度偏暖得到矫正。业务平行试验的统计检验表明，NEW对4～7天中期预报有较显著的改进。     

基于陆面模式Noah-MP的不同参数化方案在半干旱区的适用性

针对陆面模式Noah-MP对兰州大学半干旱气候与环境观测站（SACOL）2009年8月地表热通量模拟值偏差大的问题,通过分析相关物理过程和模拟试验来探究偏差的来源,并确定合适的参数化方案:采用Chen97方案计算感热输送系数可以改善感热通量的模拟;采用Jarvis气孔阻抗方案能增大植被蒸腾,改进模式对潜热通量的模拟效果,同时也使热通量在感热和潜热间的分配比例合理;采用LP92方案可减小土壤蒸发阻抗并有利于土壤蒸发,使得模式对潜热通量的模拟效果变好。不同参数化方案的组合试验表明:同时采用2组或3组新的参数化方案组合可以进一步减小模拟的地表感热和潜热通量的均方根误差,但是土壤湿度和温度的模拟效果并没有同步改善。     

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.     

高分辨区域输送模式中不同输送格式的对比试验

本文对两种输送格式在理论试验的基础上，引入19层高分辨区域输送模式EM3，由中尺度模式（MM4)提供实例输送风场，积分至13、18、30、50、70小时，作分析和对比数值试验。采用的两种格式是:二阶动量矩守恒的Prather格式（以下简称为SOM)及通量订正的Smolar格式。数值试验结果表明，高精度的SOM格式使数值扩散减小一个量级， 使输送物质（SO#-[2])中心浓度比Smolar格式增大3～4倍， 采用SOM格式还明显改进了浓度中心水平平均运动轨迹的模拟精度，选择高精度的平流格式是改进模拟结果的重要途径。     

水平气压梯度力差分格式误差的定量分析

通过分析发现地形坐标系中气压梯度力差分格式的计算误差应分为二类，其中，第二类误差在水平坐标面倾斜时出现。这种误差可理解为将水平坐标面上的气压(或位势高度)插回到等高面(或等压面)上的插值误差。 构造气压梯度力差分格式的目的正是为了减小这种第二类误差，而不是其他误差。 误差分析表明静力扣除法和Corby 格式的第二类误差都很小，比一般方法的误差小约一个量级。分析还表明第二类误差产生的主要原因是由于气压随高度非线性变化。依据这一分析思路，本文改进了#As(z)#a坐标系中的静力扣除法。 改进后的方法比改进前的误差小约一个量级。     

THE FORMULATION OF FIDELITY SCHEMES OF PHYSICAL CONSERVATION LAWS AND IMPROVEMENTS ON A TRADITIONAL SPECTRAL MODEL OF BAROCLINIC PRIMITIVE EQUATIONS FOR NUMERICAL PREDICTION*

In this paper,two formulation theorems of time-difference fidelity schemes for general quadratic and cubic physical conservation laws are respectively constructed and proved,with earlier major conserving time-discretized schemes given as special cases.These two theorems can provide new mathematical basis for solving basic formulation problems of more types of conservative time-discrete fidelity schemes,and even for formulating conservative temporal-spatial discrete fidelity schemes by combining existing instantly conserving space-discretized schemes.Besides.the two theorems can also solve two large categories of problems about linear and nonlinear computational instability.The traditional global spectral-vertical finite-difference semi-implicit model for baroclinic primitive equations is currently used in many countries in the world for operational weather forecast and numerical simulations of general circulation.The present work,however,based on Theorem 2 formulated in this paper,develops and realizes a high-order total energy conserving semi-implicit time-difference fidelity scheme for global spectral-vertical finite-difference model of baroclinic primitive equations.Prior to this,such a basic formulation problem remains unsolved for long,whether in terms of theory or practice.The total energy conserving semi-implicit scheme formulated here is applicable to real data long-term numerical integration.The experiment of thirteen FGGE data 30-day numerical integration indicates that the new type of total energy conserving semi-implicit fidelity scheme can surely modify the systematic deviation of energy and mass conserving of the traditional scheme.It should be particularly noted that,under the experiment conditions of the present work,the systematic errors induced by the violation of physical laws of conservation in the time-discretized process regarding the traditional scheme designs(called type Z errors for short) can contribute up to one-third of the total systematic root-mean-square(RMS) error at the end of second week of the integration and exceed one half of the total amount four weeks afterwards.In contrast,by realizing a total energy conserving semi-implicit fidelity scheme and thereby eliminating corresponding type Z errors,roughly an average of one-fourth of the RMS errors in the traditional forecast cases can be reduced at the end of second week of the integration,and averagely more than one-third reduced at integral time of four weeks afterwards.In addition,experiment results also reveal that,in a sense,the effects of type Z errors are no less great than that of the real topographic forcing of the model.The prospects of the new type of total energy conserving fidelity schemes are very encouraging.