非静力中尺度高分辨率模式模拟中的垂直坐标影响研究

近几年来,随着高性能计算机技术的高速发展,甚高分辨率的中尺度数值预报模式业务应用已成为可能,与之相关的一系列模式技术的新问题也随之提了出来,垂直坐标系的影响就是其中之一。文中借助于美国新一代数值预报模式WRF(WeatherReseachandForecast),比较了非静力中尺度模式高分辨率模拟应用的垂直坐标影响问题。研究表明,当选用几何高度(z)和气压(p)来构造地形追随坐标时,低层两坐标引起的误差基本一样,中高层高度地形追随坐标引起的误差小于气压地形追随坐标;而且分辨率越高差异愈大。高分辨率模拟结果也表明,这种差异趋势是存在的;此外,本文对天气过程的预报要素场进行了相关的分析。     

IMPACT STUDY ON THE CALCULATION OF VERTICAL VELOCITY IN DIFFERENT VERTICAL COORDINATE SYSTEMS

1 INTRODUCTION First, let’s have a review of various vertical coordinate systems used in numerical weather prediction (NWP). Richardson[1] (1922) first attempted to use the geometrical height z as the vertical coordinate system. Though geometrical height is easy to understand as a concept, it had not been applied in NWP until Kasahara and Washington (1967) rewrote his predictive equations and used state-of-the-art high-speed computers to conduct NWP in height coordinates. Eliassen[2]…     

不同垂直坐标系对垂直速度计算的影响

近年来,随着高精度中尺度数值预报模式和多尺度统一模式的发展,与之相关的一些非静力中尺度模式技术也随之提了出来,垂直坐标系的影响问题就是其中之一。本文借助于高精度美国新一代数值预报模式WRF(Weather Reseach and Forecast),模拟分析了两种不同的坐标系对模式大气中垂直速度计算的影响。试验结果表明,不同的坐标系对大气垂直速度大小计算存在着差异,特别是当分辨率提高时,不同垂直坐标系对大气垂直结构的刻画的差别更加明显。由于垂直速度与降雨过程密切相关,垂直速度的计算差异必然影响模式对降雨过程的描述。理想试验结果表明,在气压地形追随坐标中气压梯度力的计算对地表气压计算很敏感。     

Effects of terrain-following vertical coordinates on high-resolution NWP simulations

With increasing resolution in numerical weather prediction(NWP)models,the model topography can be described with finer resolution and includes steeper slopes.Consequently,negative effects of the traditional terrain-following vertical coordinate on high-resolution numerical simulations become more distinct due to larger errors in the pressure gradient force(PGF)calculation and associated distortions of the gravity wave along the coordinate surface.A series of numerical experiments have been conducted in this study,including idealized test cases of gravity wave simulation over a complex mountain,error analysis of the PGP estimation over a real topography,and a suite of real-data test cases.The GRAPES-Meso model is utilized with four different coordinates,i.e.,the traditional terrain-following vertical coordinate proposed by Gal-Chen and Somerville(hereinafter referred to as the Gal.C.S coordinate),the one-scale smoothed level(SLEVE1),the two-scale smoothed level(SLEVE2),and the COSINE(COS)coordinates.The results of the gravity wave simulation indicate that the GRAPES-Meso model generally can reproduce the mountain-induced gravity waves,which are consistent with the analytic solution.However,the shapes,vertical structures,and intensities of the waves are better simulated with the SLEVE2 coordinate than with the other three coordinates.The model with the COS coordinate also performs well,except at lower levels where it is not as effective as the SLEVE2 coordinate in suppressing the PGF errors.In contrast,the gravity waves simulated in both the Gal.C.S and SLEVE1 coordinates are relatively distorted.The estimated PGF errors in a rest atmosphere over the real complex topography are much smaller(even disappear at the middle and upper levels)in the GRAPES-Meso model using the SLEVE2 and COS coordinates than those using the Gal.C.S and SLEVE1 coordinates.The results of the real-data test cases conducted over a one-month period suggest that the three modified vertical coordinates(SLEVE1,SLEVE2,and COS coordinates)give better results than the traditional Gal.C.S coordinate in terms of forecasting bias and root mean square error,and forecasting anomaly correlation coefficients.In conclusion,the SLEVE2 coordinate is proved to be the best option for the GRAPES-Meso model.     

Kinetic Energy Budget Equations of Rotational and Divergent Flow in Terrain-following Coordinates

In this study, kinetic energy budget equations of rotational and divergent flow in pressure coordinates are derived on terrain-following coordinates. The new formulation explicitly shows the terrain effects and can be applied directly to model-simulated dynamic and thermodynamic fields on the model’s original vertical grid. Such application eliminates interpolation error and avoids errors in virtual weather systems in mountainous areas. These advantages and their significance are demonstrated by a numerical study in terrain-following coordinates of a developing vortex after it moves over the Tibetan Plateau in China.     

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。      

地形追随坐标系下埃特尔位涡的计算

随着数值天气预报模式的日益普及以及位涡在不同天气、气候时、空尺度上的广泛应用,对采用模式输出资料计算的埃特尔（Ertel）位涡的精度提出了更高要求。将气象要素从中尺度模式普遍采用的地形追随坐标系向定义位涡的z或p坐标系的插值过程（插值法）,是导致埃特尔位涡计算误差的主要原因。文中利用地形追随坐标系与z（p）坐标系的变换关系,导出了z坐标系定义的埃特尔位涡在地形追随坐标系中的表达形式,实现了直接在模式格点上计算埃特尔位涡（直接法）,在提高计算精度的同时,保留了其在z坐标系中的物理意义,方便了分析与应用。为了进一步分析直接法在减少计算误差方面的作用,使用WRF模式对2016年7月发生在华北地区复杂地形背景下的一次黄淮气旋爆发过程进行了模拟,利用模式输出资料对此次天气过程中强降水时段插值法计算误差的分布进行了分析。结果表明,利用直接法计算位涡可有效减少插值法引入的计算误差,中低层均方根误差可达0.5 PVU,中高层可达0.3 PVU。将其应用到中小尺度对流性天气精细化结构的分析及气候统计研究中,可以有效减少插值法误差对结果产生的不良影响,提高计算和分析准确度。      

逐层平滑地形的平缓地形追随坐标在高分辨率GRAPES模式中的应用研究

高分辨率GRAPES模式如3 km模式对地形的识别程度更高,模式中各高度坐标面可识别的地形坡度也更大,地形作用带来的气压梯度力计算误差和平流输送误差更突出。平缓地形追随坐标可以通过多种方式衰减坐标面上的地形影响进而减小这些计算误差。选择一种逐层平滑地形的平缓地形追随坐标,基于GRAPES-3km模式进行理想试验和批量模拟试验。试验结果显示:逐层平滑地形的平缓地形追随坐标相对其他平缓地形追随坐标对地形重力波模拟更接近解析值;24 h滚动预报月连续模拟试验中逐层平滑地形的平缓地形追随坐标一定程度上能降低高层月平均的温度场、风场的模拟误差,月平均的降水评分也有所提高。逐层平滑地形的平缓地形追随坐标应用于GRAPES-3km模式有较好的模拟效果。      

Model evaluation experiments in the North Atlantic Basin: simulations in nonlinear terrain-following coordinates

A primitive equation ocean circulation model in nonlinear terrain-following coordinates is applied to a decadal-length simulation of the circulation in the North Atlantic Ocean. In addition to the stretched sigma coordinate, novel features of the model include the utilization of a weakly dissipative, third-order scheme for tracer advection, and a conservative and constancy-preserving time-stepping algorithm. The objectives of the study are to assess the quality of the new terrain-following model in the limit of realistic basin-scale simulations, and to compare the results obtained with it against those of other North Atlantic models used in recent multi-model comparison studies.The new model is able to reproduce many features of both the wind-driven and thermohaline circulation, and to do so within error bounds comparable with prior model simulations (e.g., CME and DYNAMO). Quantitative comparison with comparable results obtained with the Miami Isopycnic Coordinate Model (MICOM) show our terrain-following solutions are of similar overall quality when viewed against known measures of merit including meridional overturning and heat flux, Florida Straits and Gulf Stream transport, seasonal cycling of temperature and salinity, and upper ocean currents and tracer fields in the eastern North Atlantic Basin. Sensitivity studies confirm that the nonlinear vertical coordinate contributes significantly to model fidelity, and that the global inventories and spatial structure of the tracer fields are affected in important ways by the choice of lateral advection scheme.     

多尺度非静力通用模式框架的设计策略

针对目前国际上数值预报模式的最新发展趋势,综述了新形势下多尺度非静力通用数值预报模式框架的设计策略。目前世界上开发通用模式主要有两个途经,一是建立一个离散化方案和源程序代码共享的、全球和有限区通用的模式,二是建立一个单一的全球可变分辨率的模式。还从通用模式方程组的选取策略、模式网格属性的构造,时间积分方案、空间离散方案,垂直坐标的选取等方面进行了分析。     

不同平缓-混合坐标对一次高原准静止锋降水过程模拟影响对比分析

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。     

JFNK方法概述及其在大气全隐式非静力模式中的应用方案

首先介绍了近年来新发展的非线性方程全隐式数值求解的JFNK方法,及其在地球流体力学方面应用计算实例.可看到,无论在计算精度还是计算效率方面,全隐式数值求解远远超过常规的半隐式计算格式.其次,还讨论了JFNK方法在气象非静力模式中应用方案,并提出了用静力假定和半隐式差分格式来构造预条件处理器,变三维求解为二维求解,简化了方程组求解难度.该方案不仅可用于差分模式,也为用譜方法求解非静力模式提供可能.     

天津市中尺度数值预报业务系统的设计与实现

为适应省级中尺度数值预报业务的需要,设计实现了天津市中尺度数值预报业务系统。该系统由高性能计算机系统、中尺度数值预报模式以及业务运行流程组成的,其设计与实现涉及到高性能计算机系统的建设、中尺度数值预报模式的业务数据流转以及系统运行监控流程的设计等多个方面。高性能计算机系统的建设包括系统选型、功能设计和安装调试等部分,中尺度数值预报模式的业务数据流转以及系统运行监控流程的设计是整个系统业务化的关键。天津市中尺度数值预报业务系统通过工程建设和技术开发完成了奥运期间的气象预报服务任务,已投入业务化运行。     

Three-dimensional variational data assimilation of WindSat ocean surface winds for the genesis and forecasting of tropical storm Henri

With available high-resolution ocean surface wind vectors retrieved from the U.S. Naval Research Laboratorys WindSat on Coriolis, the impact of these data on genesis and forecasting of tropical storm Henri is examined using the non-hydrostatic, fifth-generation mesoscale model (MM5) of Pennsylvania State University-National Center for Atmospheric Research plus its newly released three-dimensional variational data assimilation (3DVAR) system. It is shown that the assimilation of the WindSat-retrieved ocean surface wind vectors in the 3DVAR system improves the model initialization fields by introducing a stronger vortex in the lower troposphere. As a result, the model reproduces the storm formation and track reasonably close to the observations. Compared to the experiment without the WindSat surface winds, the WindSat assimilation reduced an error between the model simulated track and observations of more than 80 km and also improved the storm intensity by nearly 2 hPa. It suggests that these data could provide early detection and prediction of tropical storms or hurricanes.     

EXPERIMENTAL STUDY OF THE ROLE OF INITIAL AND BOUNDARY CONDITIONS IN MESOSCALE NUMERICAL WEATHER PREDICTION

~~EXPERIMENTAL STUDY OF THE ROLE OF INITIAL AND BOUNDARY CONDITIONS IN MESOSCALE NUMERICAL WEATHER PREDICTION@闫敬华$Guangzhou Institute of Tropical & Marine Meteorology, CMA, Guangzhou 510080 China @Detlev Majewski$Duetscher Wetterdinst, Offenbach, Germany~~National Project "973" (Research on Heavy Rain in China) and BMBF of Germany (WTZ- Project CHN01/106)…     

A nonhydrostatic model for simulation of airflow over mesoscale bell-shaped ridges

This paper describes a nonhydrostatic and incompressible mesoscale model formulation using a terrain-following coordinate system. A tensor transformation procedure is used to derive a diagnostic equation for the nonhydrostatic pressure field. The model features a simplified second-order turbulence closure scheme. The two-dimensional version of the nonhydrostatic model, as well as the corresponding hydrostatic model, are applied to simulate stably stratified airflow over mesoscale bell-shaped mountain ridges. The results show that the nonhydrostatic model is capable of simulating nonhydrostatic dynamics of mesoscale lee wave systems such as the trapped wave phenomenon.     

一种改进的平缓-混合地形追随坐标在GRAPES中尺度模式中的应用研究

平缓-混合地形追随坐标（T-F坐标）可以减小坐标面上的地形影响带来的各种计算误差。以余弦三角函数为基函数的平缓-混合坐标（COS坐标）高层坐标面水平,计算误差较小,但是低层坐标面之间的厚度较薄,增大了计算误差,给模式稳定性及模拟效果带来较大的影响。设计一种改进的COS坐标,使低层坐标面垂直分布更加均匀,应用于GRAPES-Meso模式进行理想试验和实际模拟试验。结果表明,改进的COS坐标相对COS坐标,中高层计算误差相当,低层地形作用衰减的垂直变化更加均匀,减小了计算误差,提高了计算稳定性;地形重力波试验结果显示,改进的COS坐标重力波破碎相对COS坐标有一定缓解,更接近解析值;批量模拟试验结果显示,改进的COS坐标各个层次上的月平均模拟偏差比单尺度双曲函数平缓-混合坐标（简称SLEVE1坐标）更小,均方根误差减小,距平相关系数增大。改进的COS坐标有效地解决了COS坐标的计算问题,提高了模式预报效果。      

Impact of 4DVAR Assimilation of AIRS Total Column Ozone Observations on the Simulation of Hurricane Earl

The Atmospheric Infrared Sounder(AIRS) provides twice-daily global observations of brightness temperature, which can be used to retrieve the total column ozone with high spatial and temporal resolution.In order to apply the AIRS ozone data to numerical prediction of tropical cyclones, a four-dimensional variational(4DVAR) assimilation scheme on selected model levels is adopted and implemented in the mesoscale non-hydrostatic model MM5. Based on the correlation between total column ozone and potential vorticity(PV), the observation operator of each level is established and five levels with highest correlation coefficients are selected for the 4DVAR assimilation of the AIRS total column ozone observations. The results from the numerical experiments using the proposed assimilation scheme for Hurricane Earl show that the ozone data assimilation affects the PV distributions with more mesoscale information at high levels first and then influences those at middle and low levels through the so-called asymmetric penetration of PV anomalies.With the AIRS ozone data being assimilated, the warm core of Hurricane Earl is intensified, resulting in the improvement of other fields near the hurricane center. The track prediction is improved mainly due to adjustment of the steering flows in the assimilation experiment.