An Improved Method for Evaluating the non-Linear Terms in the Nlmsfd Model

The non-linear terms in the non-linear mixed spectral finite difference (NLMSFD) model are evaluated by a simple yet more efficient method. The explicit expressions for the non-linear terms, which can number O(100), are no longer required. The improved algorithm results in source code of smaller size, faster execution time, and provides a more reliable way to evaluate the non-linear terms. Results from numerical experiments have shown that this approach is particularly useful in higher-order turbulence closure schemes.     

Development of a non-linear mixed spectral finite difference model for turbulent boundary-layer flow over topography

Further development of the non-linear mixed spectral finite difference (NLMSFD) model of turbulent boundary-layer flow over topography is documented. This includes modifications and refinements to the solution procedure, the incorporation of second-order turbulence closures to the model and the three-dimensional extension of the model. Based on these higher order closures, linear limitations, boundary-layer approximation and non-linear effects are discussed. The impact of different turbulence closures on the prediction of the NLMSFD model is also demonstrated. Furthermore, sample results for 3D idealized topography (sinusoidal) are presented. The parameterization of drag over small-scale topography is also addressed.     

正压原始方程有限区域谱模式的预报试验

本文包括四方面内容; (1)给出一个单向嵌套的有限区域浅水波方程谱模式的具体方案及其预报试验结果。这个模式基于文献。其特点是:基本展开函数为“修正的双傅氏级数”,它由两部分组成:正交双博氏级数及非正交的线性函数,这两部分之间互不正交。 (2)对同一实例,比较了谱方法,差分法,假谱法24h,48h预报结果。甚至同格距缩小一半的差分法相比,谱方法预报效果仍优于差分法预报效果。 (3)试验了谱模式的固定边界、刚体边界、侧边界条件随时间变化但不加松弛处理,以及侧边界条件随时间变化加松弛处理四种方案。结果表明,合理的边界条件及有效的边界处理方法对谱模式来说是至关重要的。 (4)提出并试验了谱模式的一种地形区计算方案,有助于谱模式中对陡峭地形的处理。     

AN IMPROVED SEMI-IMPLICIT TIME DIFFERENCE SCHEME OF SPECTRAL MODEL AND NUMERICAL APPLICATIONS

In fact,the popular semi-implicit time difference scheme of spectral model still includes someimportant linear terms using time explicit difference scheme,and the major terms are directlyrelated to fast internal-and external-gravity waves in the atmospheric forecasting equation.Additionally,due to using time difference on two terms at different time.the popular schemeartificially introduces unbalance between pressure gradient force and Coriolis force terms whilenumerically computing their small difference between large quantities.According to thecomputational stability analysis conducted to the linear term time difference scheme in simpleharmonic motion equation,one improved semi-implicit time difference scheme is also designed inour study.By adopting a kind of revised time-explicit-difference scheme to these linear terms thatstill included in spectral model governing equations,the defect of spectral model which only partlyusing semi-implicit integrating scheme can be overcome effectively.Moreover,besides all spectralcoefficients of prognostic equations,especially of Helmholtz divergence equation,can be workedout without any numerical iteration,the time-step (computation stability) can also be enlarged(enhanced) by properly introducing an adjustable coefficient.     

AN IMPROVED SEMI-IMPLICIT TIME DIFFERENCE SCHEME OF SPECTRAL MODEL AND NUMERICAL APPLICATIONS*

In fact,the popular semi-implicit time difference scheme of spectral model still includes some important linear terms using time explicit difference scheme,and the major terms are directly related to fast internal-and external-gravity waves in the atmospheric forecasting equation.Additionally,due to using time difference on two terms at different time.the popular schemear tificially introduces unbalance between pressure gradient force and Coriolis force terms while numerically computing their small difference between large quantities.According to the computational stability analysis conducted to the linear term time difference scheme in simple harmonic motion equation,one improved semi-implicit time difference scheme is also designed in our study.By adopting a kind of revised time-explicit-difference scheme to these linear terms that still included in spectral model governing equations,the defect of spectral model which only partlyusing semi-implicit integrating scheme can be overcome effectively.Moreover,besides all spectral coefficients of prognostic equations,especially of Helmholtz divergence equation,can be worked out without any numerical iteration,the time-step (computation stability) can also be enlarged (enhanced) by properly introducing an adjustable coefficient.     

Impact of a Saturation-Dependent Dissipation Source Function on Operational Hindcasts of Wind-Waves in the Australian Region

The impact of a modified parametric form of the dissipation source function S ds on the skill of an operational spectral wind-wave model is investigated. Numerical experiments are made with a version of the WAM model presently used operationally by the Australian Bureau of Meteorology to produce sea-state forecasts within the Australian region. Performances of wave hindcasts obtained using several alternative forms of this newly proposed dissipation source function are compared to those produced with forms of S ds commonly used operationally. A new ad hoc technique to compare modelled and observed wave spectra is introduced to assess the quality of calculated one-dimensional frequency spectra.

Our results indicate that wave model performance in terms of integral spectral parameters, such as the significant wave height H s , may benefit from improved parameterisations of the dissipation source term S ds . On the other hand, we also found that model performance was relatively poor in terms of predictions of the one-dimensional frequency spectrum, regardless of the chosen form of S ds . These results suggest that further refinements of the dissipation source term are strongly dependent on improved parametrisations of the nonlinear interactions source term S nl .     

大气位势场对海表温度异常线性定常响应的数值试验

利用具有月、季长期天气过程数值天气预报能力的滤波距平模式(FAM)、运用谱方法研究了大气位势场对海表温度异常(SSTA)的线性定常响应,分析了SSTA强迫作用所产生的定常行星波波型、大气中遥相关型以及大气位势场响应对SSTA位置和基本气流的敏感性,得到一些有意义的结果。     

非线性正规模初值化及其对资料同化和预报的影响

文章介绍了国家气象中心中期数值预报谱模式（T42L9）的非线性正规模初值化方案（NNMI）。讨论了该方案对资料同化和预报的影响。试验表明，应用前5个垂直模，经2次迭代能够得到一个对分析资料修正较小的平衡初始场。它成功地消除了预报中虚假的高频重力波振荡，对改进资料同化和模式预报起了重要作用。     

Short‐term forecasting with a multi‐level spectral primitive equation model part I ‐ model formulation

A global baroclinic primitive equation model using the spectral technique has been constructed for short‐ and medium‐range numerical weather prediction. The spectral technique, which is a special case of the Galerkin method, employs spherical harmonic basis functions in the evaluation of all horizontal derivatives. The use of a transform technique allows all the horizontal operations to be performed efficiently and allows physical processes to be evaluated in real space. The model employs a semi‐implicit algorithm for time integration and finite differencing in the vertical. Physical processes include orography, moist convection, large scale precipitation and boundary layer processes.     

Relaxation Factor Effects in the Non-Linear Mixed Spectral Finite Difference Model of Flow Over Topographic Features

The nonlinear version of the mixed spectral finite difference model of atmospheric boundary-layer flow over topography is reviewed. The relations between the stability of the iteration scheme and its relaxation parameter are discussed. Suitable choice of the relaxation factor improves the computational stability on terrain with maximum slope up to 0.5 or 0.6 in certain circumstances. Examples of relatively high slope terrain are used to test the stability. A two-dimensional version of the model is considered. More detailed simulations are studied and analyzed for a comparison with wind-tunnel flow over periodic sinusoidal surfaces. An application on real topography is given for Bolund hill in Roskilde, Denmark.     

Meso-scale perturbations and thermohaline fronts in the south atlantic ocean

A linear quasi-geostrophic model and a non-linear balanced model are used to study the properties of the oceanic baroclinic waves. From a linear point of view, the oceanic meso-scale (200–400 km) disturbances found near the Brazil and Falkland currents confluence zone seem to be generated by baroclinic instability. Non-geostrophic and non-linear effects due to a single original wave are superimposed on the linear fields associated with the most unstable wave. Characteristics very similar to observations are obtained in the evolution to finite amplitude. The evolution of oceanic thermal rings is very well reproduced by the non-linear model. However, the stage of saturation is not reached in the model results since the feedback to the thermal basic state is not included.     

A numerical study of the mechanism for the effect of northern winter arctic ice cover on the global short-range climate evolution

By using a nine-layer global spectral model involving fuller parameterization of physical processes, with a rhomboidal truncation at wavenumber 15, experiments are performed in terms of two numerical schemes, one with long-term mean coverage of Arctic ice (Exp.1), the other without the ice (Exp.2). Results indicate that the Arctic re-gion is a heat source in Exp.2 relative to the case in Exp.1. Under the influence of the polar heat source simulated, there still exist stationary wavetrains that produce WA-EUP and weak PNA patterns in Northern winter. That either the Arctic or the tropical heat source can cause identical climatic effects is due to the fact that the anomaly of the Arc-tic ice cover will directly induce a south-propagating wavetrain, and bring about the redistribution of the tropical heat source/ sink. The redistribution is responsible for new wavetrains that will exert impact on the global climate. The simulation results bear out further that the polar region in Exp.2 as a heat source, can produce, by local forcing, a pair of positive and negative difference centers, which circle the Arctic moving eastwards. Observed in the Northern Hemisphere extratropics is a 40-50 day oscillation in relation to the moving pair, both having the same period.     

Comments on the Synergism Between the Analytic Planetary Boundary-Layer Model and Remote Sensing Data

This paper is adapted from a presentation at the session of the European Geophysical Society meeting in 2002 honouring Joost Businger. It documents the interaction of the non-linear planetary boundary-layer (PBL) model (UW-PBL) and satellite remote sensing of marine surface winds from verification and calibration studies for the sensor model function to the current state of verification of the model by satellite data. It is also a personal history where Joost Businger had seminal input to this research at several critical junctures. The first scatterometer in space was on SeaSat in 1978, while currently in orbit there are the QuikSCAT and ERS-2 scatterometers and the WindSat radiometer. The volume and detail of data from the scatterometers during the past decade are unprecedented, though the value of these data depends on a careful interpretation of the PBL dynamics. The model functions (algorithms) that relate surface wind to sensor signal have evolved from straight empirical correlation with simple surface-layer 10-m winds to satellite sensor model functions for surface pressure fields. A surface stress model function is also available. The validation data for the satellite model functions depended crucially on the PBL solution. The non-linear solution for the flow of fluid in the boundary layer of a rotating coordinate system was completed in 1969. The implications for traditional ways of measuring and modelling the PBL were huge and continue to this day. Unfortunately, this solution replaced an elegant one by Ekman with a stability/finite perturbation equilibrium solution. Consequently, there has been great reluctance to accept this solution. The verification of model predictions has been obtained from the satellite data.     

Non-linear climate feedback analysis in an atmospheric general circulation model

 A method is described for evaluating the ‘partial derivatives’ of globally averaged top-of-atmosphere (TOA) radiation changes with respect to basic climate model physical parameters. This method is used to analyse feedbacks in the Australian Bureau of Meteorology Research Centre general circulation model. The parameters considered are surface temperature, water vapour, lapse rate and cloud cover. The climate forcing which produces the changes is a globally uniform sea surface temperature (SST) perturbation. The first and second order differentials of model parameters with respect to the forcing (i.e. SST changes) are estimated from quadratic least square fitting. Except for total cloud cover, variables are found to be strong functions of global SST. Strongly non-linear variations of lapse rate and high cloud amount and height appear to relate to the non-linear response in penetrative convection. Globally averaged TOA radiation differentials with respect to model parameters are also evaluated. With the exception of total cloud contributions, a high correlation is generally found to exist, on the global mean level, between TOA radiation and the respective parameter perturbations. The largest non-linear terms contributing to radiative changes are those due to lapse rate and high cloud. The contributions of linear and non-linear terms to the overall radiative response from a 4 K SST perturbation are assessed. Significant non-linear responses are found to be associated with lapse rate, water vapour and cloud changes. Although the exact magnitude of these responses is likely to be a function of the particular model as well as the imposed SST perturbation pattern, the present experiments flag these as processes which cannot properly be understood from linear theory in the evaluation of climate change sensitivity. Received: 16 January 1997/Accepted: 9 May 1997     

A regional spectral nested shallow water equation model

A method to expand meteorological elements in terms of finite double Fourier series in a limited-region and a spectral nested shallow water equation model based upon the method with conformal map projection in rectangular coordinates, have been proposed, and computational stability and efficiency of time integration have been discussed.     

Comparison and Analysis of Two Different Calculation Schemes of SLEVE- Hybrid Coordinate in GRAPES_MESO Model

The calculation scheme of the smoothed-level and hybrid (SLEVE-hybrid for short) coordinates in numerical forecasting model is not limited to one. It is divided into the semi-analytical scheme and the finite differential scheme in terms of the various differential methods of the coordinate deformation variables. Comparing the dynamic equation and the long-time batch simulation results of the two schemes, the present study draws the following conclusions. The first- order finite difference accuracy of the coordinate deformation variables in the finite differential scheme is theoretically lower than that in the semi-analytical scheme. The larger the vertical gradient of the layer thickness is, the larger the relative errors of the finite differential scheme are. The long-time batch simulation test in the GRAPES model dynamic core demonstrates that the bias of the temperature and the geopotential height in the semi-analytical scheme is smaller under the default layering, while the simulation difference of the two schemes is greatly reduced when the layering is more uniform.     

Comparison and Analysis of Two Different Calculation Schemes of SLEVE-Hybrid Coordinate in the GRAPES＿MESO Model

The calculation scheme of the smoothed-level and hybrid(SLEVE-hybrid for short) coordinates in numerical forecasting model is not limited in number. It is divided into the semi-analytical scheme and the finite differential scheme in terms of the various differential methods of the coordinate deformation variables. Having compared the dynamic equation and the long-time batch simulation results of the two schemes, the present study draws the following conclusions. The first-order finite difference accuracy of the coordinate deformation variables in the finite differential scheme is theoretically lower than that in the semi-analytical scheme. The larger the vertical gradient of the layer thickness is, the larger the relative errors of the finite differential scheme are. The long-time batch simulation test in the GRAPES model dynamic core demonstrates that the bias of the temperature and the geopotential height in the semianalytical scheme is smaller under the default layering, while the simulation difference of the two schemes is greatly reduced when the layering is more uniform.     

有限区分析预报系统及其业务应用

中国国家气象中心在新开发的有限区多元最优插值分析技术及１５层球面网格原始方程模式的基础上建立了一个新的有限区分析预报系统。１９９１年投入业务使用，主要用于２４－４８ｈ降水预报。这个系统是依附于全球同化预报系统的一个分支系统。亦即使用全球谱模式６ｈ预报作为初估值进行有限区细网格分析及使用其１２—６０ｈ预报作为侧边界值进行非同步嵌套预报。作为一个升级模式系统，它的进步表现在：较充分使用了卫星测湿资料及地面资料的细网格多元最优插值分析；同时使用同场及质量场初值，成功地实现了有限区非线性正规模初始化处理；采用位涡拟能守恒差分格式，包含较真实地形的球面坐标原始方程模式；实现了具有不同模式地形的差分模式与谱模式的嵌套及设计了分级降水客观检验系统。     

A NUMERICAL STUDY FOR MECHANISM OF THE EFFECT OF NORTHERN SUMMER ARCTIC ICE COVER ON THE GLOBAL SHORTRANGE CLIMATE CHANGE

In terms of nine-layer global spectral model involving fuller parameterization of physical process,with arhomboidal truncation at wavenumber 15,experiments are conducted by virtue of two numerical schemes,one withlong-range mean coverage of Arctic ice,and the other with supercooled water at the same temperature as the ice,fol-lowed by an analysis of the difference field simulated by the two schemes.Results show that(1)the impact of Arctic iceon the northern short-range climate is realized through the change in polar ice coverage to cause local temperaturechange in the polar region to set up gradient difference in temperature from north to south,thus affecting the atmospher-ic circulations and,on the other hand,two trains of two-dimensional Rossby waves excited by the atmospheric heatsource anomaly have impacts on the Northern Hemisphere(NH)extratropical region,one of which is similar to the JPteleconnection pattern first presented by Nitta(1987);(2)The significant impact of Arctic ice anomaly on the southernshort-range climate change is accomplished with the aid of the anomaly of the equatorial heat source that excites a two-dimensional Rossby wavetrain propagating along a great circle route into the Southern Hemisphere(SH)extratropics,and the cross-equatorial propagation of the NH wavetrain also has effects on the SH atmosphere.Simulation indicatesthat with the 15-day integration the Arctic ice exerts an influence mainly on the NH and when the model atmosphere isgetting stabilized,the effect is dominantly on the SH short-range climate change.     

最优差分方案

在数值预报和数值模拟中,描述空间微分项的最主要的方法是有限差分法,但使用差分方法会引入截断误差.伍荣生1979年指出,通过在原物理场的基础上构造一个新的物理场,替代原物理场进行差分计算,可以达到减小误差的目的.该文是伍荣生1979年工作的继续,目的在于解释伍荣生1979年所构造的差分格式并得到更为一般化的差分格式.文中给出新的差分格式结合了经典有限差分方法的快速计算和谱方法的高精度的优点.如果在一个给定的网格上对气象要素场进行离散傅里叶级数展开,则基函数(正弦或余弦)的频谱是事免已知的.作者将伍荣生1979年构造物理场的方法视为对物理场的一次平滑,探讨了获取二次平滑场、多次平滑的一般化方法.获取平滑场的基奉原理是使得在固定频谱上的差分逼近程度达到最优.通过对频谱上的累计误差的下降速度分析表明,平滑次数的上限为3次.数值分析的结果表明,二次平滑的最大误差是未作任何平滑的最大误差的0.04倍,在使用相同计算代价的情况下,二次平滑的最大误差是经典的差分格式的0.3倍.平流试验的结果也表明,新的差分格式即一次平滑、二次平滑方案的结果远远优于经典的差分格式.新的差分格式意义在于,在不加密网格的情况下提供了一条提高数值计算精度的途径.