Review of numerical methods for nonhydrostatic weather prediction models

Summary ?Currently available computer power allows to run operational numerical weather prediction models at resolutions higher than 10 km. The aim of such high resolution modeling is the prediction of local weather, including orographically induced winds and local precipitation patterns. In this range the hydrostatic approximation is no longer valid and nonhydrostatic models have to be used instead. For several decades these models have been developed for research purposes only, but operational application is now reality. In this paper, the numerical methods used in current nonhydrostatic forecast models will be reviewed and some promising techniques in this field will be discussed. Special attention is given to aspects such as the choice of the vertical coordinate, the efficiency of algebraic solvers for semi-implicit time discretizations, and accurate and non-oscillatory advection schemes. Received July 6, 2001; revision October 12, 2001     

Formulation and verification of a land surface parameterization for atmospheric models

The need for a well-defined lower boundary condition for atmospheric numerical models is well documented. This paper describes the formulation of a land surface parameterization, which will be used in atmospheric boundary-layer and mesoscale numerical models. The land surface model has three soil layers for the prediction of soil moisture and soil temperature. Model soil properties depend on soil texture and moisture content. A homogeneous distribution of vegetation is also included, so that transpiration may be included, as well as the interception of precipitation by vegetation elements. The simulated vegetation also affects the mean surface albedo and roughness characteristics.First ISLSCP Field Experiment (FIFE) data are used to verify the model. Three cases during the growing season were chosen, each case having different amounts of vegetation cover. Stand alone simulations, where observations of atmospheric and radiation variables are input to the land surface model, were performed. These simulations show that the model is able to reproduce observed surface energy budgets and surface temperatures reasonably well. The RMS differences between modeled and obsered turbulent fluxes of heat and moisture are quite comparable to those reported by more detailed land surface models.     

检验全球数值预报模式的相似度等指标

本文依照泛函形式并考虑了球面经纬网格的特点,定义了用于全球数值模式效果检验的指标:距离、距平相似度和倾向相似度,给出了相应的计算方法,并以全球WRF模式为例,检验了该模式的中期预报效果。所得结论如下:指标距离、距平相似度和倾向相似度物理意义明确,易于理论分析,考虑了球面经纬网格的特点,检验准确度高,具有普适性,能方便应用于球面经纬网格输出的数值模式检验。指标距离、距平相似度的检验结果分别与传统检验指标均方根误差、距平相关系数相一致,该指标还可直接用于向量场(如风场)的整体检验。本文的全球WRF模式所做的检验表明,对本文个例,该模式的全球500 hPa中期天气形势预报在第7 d及之内皆可用,5 d及之内预报效果更佳。     

Long-range weather forecasts through numerical and empirical methods

There has been much improvement in numerical weather prediction since L.F. Richardson (1922, Weather Prediction by Numerical Process, Cambridge University Press, Cambridge, p. 236) wrote his famous book. NWP has primarily been successful in improving day-by-day forecasts starting from an observed detailed Initial Condition (IC) out to about a week. The purpose of this paper is to discuss first the state of the art in long-range NWP by presenting results of a new large numerical experiment (named DERF90; from Dynamical Extended Range Forecasting in 1990 out to 90 days) conducted at the National Meteorological Center (NMC) during the summer and autumn of 1990 (Section 2). One hundred and twenty eight 90-day global forecasts were made from successive daily initial conditions (IC), thus giving us ample opportunity to assess skill of forecasts at lead times beyond 1 week.We then move on to define the notion of a limit of predictability (LOP), and following a procedure by Lorenz (1982), give a numerical estimate of the LOP using the DERF90 data set. We then produce a list of reasons, as to why this estimate (LOP = 18 days) should not be taken too literally. In particular, we argue that the LOP varies as a function of the flow itself, and it would be (much) larger if we had, as we will ultimately, a coupled ocean-atmosphere model for making long-lead forecasts. Last, but not least, we present results of empirical forecasts that point to modest but significant skill well beyond the traditional LOP (a few weeks).A specific recent example of empirical forecasting is discussed. Through Canonical Correlation Analysis (CCA), experimental forecasts are being made for the United States surface temperatures at lead times of several seasons. While modest, the skill is significant in that it defies the existence or a 3-week LOP, and so demonstrates the potential for model improvements.     

智能网格SCMOC及多模式降水预报对比

以三源融合网格实况降水分析资料CMPAS为参照,基于二分法经典检验、预报评分综合图和面向对象MODE检验等方法,对比分析2021年智能网格预报SCMOC以及ECMWF全球、CMA-Meso中尺度模式在秦岭及周边地区的降水预报表现,主要结论如下：1)ECMWF能够很好地刻画日平均降水量、日降水量标准差以及地形影响下降水量、降水频次的空间分布特征,但对于0.1 mm以上量级的降水预报频次远高于观测,暴雨预报频次低于观测,SCMOC、CMA-Meso日降水量大于等于0.1 mm的降水频次和暴雨频次预报更好;SCMOC不足在于降水的空间精细分布特征描述能力相对较弱。2)ECMWF预报的大于等于0.1 mm降水频次日峰值出现时间整体较观测偏早3 h左右,CMA-Meso、SCMOC与观测总体吻合较好。3)三种产品24 h降水量大于等于0.1 mm的TS(Threat Score)评分数值上基本一致,但降水预报表现的特征显著不同,SCMOC成功率高、命中率低,漏报多、空报少,ECMWF、CMA-Meso则相反;24 h、3 h大雨以上量级降水SCMOC的TS评分、成功率、命中率一致优于其他两种产品...     

On the applicability of numerical mass-consistent wind field models

A three-dimensional nonhydrostatic model is used to calculate the complex wind field in a coastal and a hilly region. These results are used to test the applicability of a mass-consistent wind model for different numbers of input wind data. While for the coastal area the mass consistent model calculates reasonable results even for a small number of input wind data, this number increases significantly in complex terrain.     

Incorporation of planetary boundary-layer processes into numerical forecasting models

A study has been made of the evolution of the planetary boundary layer height (PBLH), the heat flux, and momentum flux using Clarke's Wangara data for a period of two days and two nights, 33/34–34/35. The observed Wangara data are considered as being an output of the first two internal levels of a general circulation model, at 1000 and 2000 m height. A time-dependent equation has been used to forecast, explicitly, the PBLH for both convectively unstable and stable periods. A comparison is made between observed and computed values whenever possible. In the unstable case, the Deardorff model (1974) has been used for the prediction of the unstable PBLH. Part of the stable case study involved a formulation of a time-dependent model for the prediction of the stable PBLH. The solution obtained from the model compared favourably with the results of a model suggested by Khakimov. Contribution number 382.     

Dynamics between order and chaos in conceptual models of glacial cycles

The dynamics of glacial cycles is studied in terms of the dynamical systems theory. We explore the dependence of the climate state on the phase of the astronomical forcing by examining five conceptual models of glacial cycles proposed in the literature. The models can be expressed as quasiperiodically forced dynamical systems. It is shown that four of them exhibit a strange nonchaotic attractor (SNA), which is an intermediate regime between quasiperiodicity and chaos. Then, the dependence of the climate state on the phase of the astronomical forcing is not given by smooth relations, but constitutes a geometrically strange set. Our result suggests that SNA is a candidate for representing the dynamics of glacial cycles, in addition to well-known quasiperiodicity and chaos.     

WRF ARW and CHIMERE models for numerical forecasting of surface ozone concentration

Results of joint calculations with meteorological WRF ARW model and chemistry transport CHIMERE model are considered as a basis of the modern system of the air quality assessment and forecasting. The system was designed in the Russian Hydrometeorological Center and Institute of Applied Physics of the Russian Academy of Sciences. Detailed prognostic information about the atmosphere state provided by the WRF ARW was used in the CHIMERE model for describing the air mass transport processes, chemical transformation, and pollution deposition. Results of retrieval and forecast of surface ozone concentration as one of main air quality indicators are under consideration. Calculations of ozone concentrations for different configurations of a prognostic system differ in resolution of model grid and in the way the boundary conditions are prescribed.     

On the bogussing of tropical cyclones in numerical models: A comparison of vortex profiles

Summary At the resolutions currently in use, and with the sparse oceanic data coverage, numerical analyses cannot adequately represent tropical cyclone circulations for use in numerical weather prediction models. In many cases there is no circulation present at all. Most numerical weather prediction centers therefore employ a bogussing scheme to force a tropical cyclone vortex into the numerical analysis. The standard procedure is to define a synthetic data distribution based on an analytically prescribed vortex, which is passed to the analysis scheme as a set of high quality observations.In this study, four commonly used bogus vortices are examined by comparing resultant forecast tracks in an environment at rest, and in a background flow that simulates a typical monsoon trough-subtropical ridge structure. There are three main findings, each of which has significance for operational tropical cyclone track prediction. First, great care is needed in the choice of the characteristics of the bogus vortex, such as the radius and magnitude of the maximum wind. Second, the tropical cyclone trajectories can be very sensitive to their initial position in the idealised environment. Third, the bogus vortex can substantially influence the environment, especially over longer time periods and for vortices of larger size.With 9 Figures     

On the bogusing of tropical cyclones in numerical models: The influence of vertical structure

Summary In this study, idealised conditions are used to study the influence of vertical structure of the bogus vortex on its motion in numerical models by comparing the resultant forecast tracks. Two vortices were used: one has a cyclonic circulation throughout the troposphere and the other has an upper tropospheric anticyclone. Both vortices have the same structure in the middle and lower troposphere. The two vortices were inserted into four different environmental flows on a beta-plane: (a) a resting atmosphere; (b) a uniform flow; (c) a horozontal shear flow and (d) a vertical shear flow. The results show that the forecast tracks are very sensitive to the vertical structure of the bogus vortex, especially when the environmental flow is very weak, or is westerly and has a cyclonic horizontal shear. However, this sensitivity is reduced in moderate vertical shear. This motion sensitivity is found to arise from the vertical coupling mechanism by which the upper-and lower-level circulations interact with each other when a horizontal displacement occurs between them.The vertical structure of the bogus vortex can also affect the intensity of the model cyclone, depending on the configuration of the environmental flow. In general, the bogus vortex without an upper-level anticyclone will intensify quicker and will develop more intense than the one with an upper-level anticyclone. The vertical coupling mechanism can result in different asymmetric rainfall pattern in cyclone core region depending on the vertical structure of the bogus vortex. The asymmetric divergent flow associated with these convective asymmetries may in turn further influence the vortex motion. It is suggested that care needs to be taken in determining the vertical structure of the bogus vortex in numerical models.With 14 Figures     

下一代大气模式中的数值方法综述

数值预报是逐日天气预报、气候预测和气象防灾减灾的核心科技支撑。为进一步提高预报预测的准确度和延长预见期,甚高分辨率、多圈层耦合、多尺度嵌套、多尺度集合、数值地球系统模拟技术等是下一代数值预报的重要发展方向。异构众核高性能计算机和E级计算的高速发展为这一发展提供了契机,但也对现有业务数值预报中采用的数值方法提出了挑战。此文仅对国内外下一代大气模式涉及到的数值方法进行综述,着重于数值算法、准均匀球面网格和时间积分方案等3个方面,期望为相关研究者提供参考。     

论过去资料在数值天气预报中使用的理论和方法

对中国气象学家在数值天气预报中使用过去实况演变资料的理论和方法作卫概要性总结,其中不仅讨论了近期实况演变资料的应用,还了积累数十年的历史资料的应用问题。文中强调要改变对数值预报问题的提法,回顾了由初值问题改为演变问题,再改为反问题的历史。     

Parametrization and influence of subgridscale orography in general circulation and numerical weather prediction models

Summary The problem of representing the drag due to subgridscale orography is examined. Results from model simulations are used to illustrate clear deficiencies in the global angular momentum budgets and possible ways of correcting for these deficiencies are considered. It is argued that a formulation for the stress due to subgridscale gravity waves is required, as was first recognized by Boer et al. (1984a, b), and the impact of a scheme based on Palmer et al. (1986) is presented. The scheme is improved by using directionally-dependent subgridscale orographic variances. Results from 90-day integrations using the ECMWF and UKMO models with similar resolutions are very much in accord both with and without a wave drag parametrization scheme; showing much improved wintertime circulations.The relationship between the wave drag and the model orography is examined with the use of idealized stress profiles whereby the wave drag is limited to either near the surface or in the stratosphere. A combination of parametrized wave drag with an envelope orography performs best at this stage of development.Results are presented from a substantial series of ten-day forecast experiments with the ECMWF operational model using mean and (1 ) envelope orographies, these show significant improvements in forecast skill.With 26 Figures     

Key issues in developing numerical models for artificial weather modification

The scientific foundation of artificial weather modification is meso- and small-scale dynamics and cloud–precipitation microphysics. Artificial weather modification requires the realistic coupling of weather patterns, dynamical processes, and microphysical processes. Now that numerical models with weather dynamical characteristics have been widely applied to artificial weather modification, several key points that should not be neglected when developing numerical models for artificial weather modification are proposed in this paper, including the dynamical equations, model resolution, cloud–precipitation microphysical processes, numerical computation method, and initial and boundary conditions. Based on several examples, approaches are offered to deal with the problems that exist in these areas.     

地形跟随坐标下的中尺度模式气压梯度力计算误差分析及其改进方案

GRAPES_Meso模式预报存在南风偏大、虚假降水偏多等问题,且在大地形下游地区异常明显。平缓-混合坐标可以有效减小气压梯度力计算误差以及平流输送误差,而这两种误差与风场和水汽场预报密切相关。基于GRAPES_Meso模式选择四种平缓-混合坐标对一次典型的高原东部准静止锋降水过程进行模拟分析。模拟结果表明,较弱的天气形势演变下,平缓-混合坐标的改进效果比较明显,可以有效缓解风场预报偏差、虚假降水、虚假天气系统等问题,个例模拟的结果与实况更接近。

     

The verification of numerical models with multivariate randomized block permutation procedures

Summary Multivariate randomized block permutation procedures (MRBP) can be used effectively to verify numerical models. Compared to other statistical methods, MRBP shows several distinct advantages. First of all, MRBP operates in the same Euclidean analysis space as its input data. The root mean square error (RMSE) is discussed, since it is a natural choice as a distance measure between two data sets and is closely related to the distance measure on which MRBP is based. The RMSE by itself provides no basis for inferential comparisons, whereas MRBP is well suited for such deductions. Since MRBP is computationally economical and requires only a few case studies for meaningful comparisons, it is also useful for model development.With 3 Figures     

数值模式中的大气边界层参数化方案综述

大气边界层对下垫面和自由大气之间的热量、动量和物质交换以及全球辐射的收支平衡有着非常重要的作用,数值模式中对边界层的模拟需要通过参数化方案表现出来。综述了数值模式中常用的边界层参数化方案,从闭合框架以及边界层内的重要物理过程这两个方面对各类方案进行了总结,并讨论了边界层参数化方案的发展方向。     

Eddy exchange coefficients in numerical models of the planetary boundary layer

Specification of the eddy exchange coefficients is perhaps one of the most difficult problems in the numerical modeling of the planetary boundary layer. These coefficients have been computed from finite-difference analogs to analytical expressions associated with surface boundary-layer similarity theory, which is based on observations in an equilibrium surface layer. This procedure leads to erroneous results in the region above the surface layer and in a non-equilibrium surface layer. In addition, differencing problems arise in regions of small vertical wind shear. A new turbulence transport model has been obtained through the closure procedures for the transport equations of the Reynolds stress and the turbulent length scale. The new approach could be used to calculate Reynolds stresses and eddy exchange coefficients throughout a non-neutral planetary boundary layer under non-equilibrium conditions.