A Multilevel Perturbation Method-Hydrostatic Deduction and Its Applicability to Designing the Nonhydrostatic Model

在尺度分析的基础上,利用大气垂直运动方程中各项量级的分布特点,提出了多级扰动法.通过它可以使该方程中量级最大的垂直气压梯度力项(VPGF)和重力项(G)的相应扰动项的量级随级次n的增加明显减小,而其他项的量级不变;而且,方程中最大的垂直截断误差的量级也随n的增加而减小,直到高级扰动项不再是扰动方程中仅有的最大项时为止.另外,因截断误差的量级和被离散项的量级成正比,在方程中VPGF的截断误差就是该方程中最大的垂直截断误差,可以表示该方程的总的垂直截断误差.故垂直气压梯度力扰动项的量级的减小还可以使该方程中最大的垂直截断误差减小,用多级扰动法可以使最大垂直截断误差控制在可容许的范围内,使垂直气压梯度力扰动项和重力扰动项计算准确,可以较好地描写对流活动.这样,最大垂直截断误差对倾向的影响就不致歪曲或掩盖垂直柯氏力项和曲率项对倾向的贡献.还可以证明:扰动平衡方程的解是静力扰动.多级扰动法实质上是多次利用扰动平衡方程的解,从低级扰动中扣除其所含和解大小相同的静力扰动部分,使高一级扰动项的量级减小,达到其与其他项量级接近,以减小方程中的最大量级差的一种方法.而且,n的变化不影响方程的性质.可以说,多级扰动法使大气基本态垂直廓线有较大的改善,使其与大气实际垂直廓线很接近,通过静力平衡,使基本模式大气不包含垂直声波.     

地形坐标系数值模式中气压梯度力的计算

本文详细地讨论了σ坐标模式引入地形时气压梯度力的截断误差。通过理论分析和数值计算看到,对于不同的σ定义和模式变量的垂直分布,Corby格式的精度可以有很大差别。为了减小梯度力的计算误差,对于模式的垂直离散化和梯度力的差分格式提出了一些改进意见。     

复杂地形强降雪过程中垂直运动诊断分析

利用WRF模式对2018年11月30日伊犁河谷和天山北坡强降雪过程进行数值模拟,并分析复杂地形强降雪过程垂直速度和垂直动能变化机制。研究表明,冷锋过境造成地表气压升高,干空气气柱质量增大,从而导致垂直气压梯度力和干空气气柱浮力发生变化,进而引起垂直运动发生发展。垂直速度局地时间变化主要取决于扰动垂直气压梯度力、水物质拖曳力和扰动干空气浮力。在天山北坡,气流过山时,迎风坡的扰动垂直气压梯度力较大,扰动干空气浮力较小,二者合力促进上升运动;在背风坡,扰动垂直气压梯度力和扰动空气浮力形成向下的合力,产生下沉加速度,导致背风坡下沉大风。扰动垂直气压梯度力做功和扰动干空气浮力做功情况基本相反,背风坡扰动垂直气压梯度力和综合强迫做功项抑制垂直动能,扰动干空气浮力和水物质拖曳力做功项增强垂直动能。此外,扰动垂直气压梯度力和扰动干空气浮力做功项主要出现在中低层,水物质拖曳力做功项主要位于低层,平缓地形处的综合强迫做功明显小于地形复杂处。     

多级扰动法——静力扣除及其在非静力模式设计中的可应用性

在尺度分析的基础上,利用大气垂直运动方程中各项量级的分布特点,提出了多级扰动法.通过它可以使该方程中量级最大的垂直气压梯度力项(VPGF)和重力项(G)的相应扰动项的量级随级次n的增加明显减小,而其他项的量级不变;而且,方程中最大的垂直截断误差的量级也随n的增加而减小,直到高级扰动项不再是扰动方程中仅有的最大项时为止....     

高度场垂直插值方法的数值预报试验

本文假设温度场与气压对数成逐段线性分布。在有地形时,气压梯度力项采用在P坐标系计算的方法,即回插法。分别用理想地形和温压场分布及两个实例检验了高度场垂直插值不同方法的误差。结果表明,假设高度场随气压对数平方成逐段线性分布的方法,可以简化计算,节省机时,计算精度也较高。     

有地形模式中气压梯度力误差和扣除法的模拟试验

在现有有地形的数值模式中，陡峭地形区气压梯度力的计算存在一个普遍问题，即计算精度较高的格式比较繁琐而费时，简单省时的格式又精确和不稳定，为解决这个问题，作者等在最近提出了一种方法，称为气压梯度力的误差扣除法，该方法假定：气压梯度力的计算误差主要来自地形而与气压形势关系较小，用理想场对该方法进行检验后表明，这一方法是成功的。     

温度初值确定之合理性与气压梯度力项的计算

本文讨论数值试验中两个基本问题:温度初值确定和气压梯度力的计算。首先比较几种利用静力方程差分解求温度初值方案所引起的误差,提出一种把等压面高度场插值与静力方程微分解结合起来求取等σ面温度初值的方法,结果表明用这种方法确定的温度初值及其水平分布和垂直递减率接近实测值。文章又讨论山脉地区气压梯度力计算问题,表明气压梯度力的计算精度不仅与计算方案有关,而且与温度初值有很大的关系。利用本文提出的方案得到的温度初值来计算气压梯度力,误差达到比较满意的精度。     

Investigating the initiation and propagation processes of convection in heavy precipitation over the western Sichuan Basin

青藏高原大地形和四川盆地西侧的陡峭地形过渡带,夏季暴雨频发,易带来泥石流等次生地质灾害。本文选定该地区2010年8月的一次暴雨过程,研究了伴随对流尺度降水的强对流的激发和传播。具体借助于垂直动量方程,并将扰动气压分离为动力和浮力分量,通过动力扰动气压梯度、浮力扰动气压梯度、以及浮力等几种强迫作用的不平衡,探索对流激发和传播的主导因子。经分析发现,在本次暴雨过程中,较之动力过程,热力作用对对流的激发和传播发挥着更为重要的作用,垂直运动及倾向指向未来雨区     

Characteristics of pressure gradient force errors in a terrain-following coordinate

"地形追随坐标系中气压梯度力误差的特征分析"一文通过几何分析和理想实验,对比了地形追随坐标系两种方案(经典方案和协变方案)中气压梯度力(PGF)误差的特征。结果表明:(1)经典方案的PGF误差受"垂直气压梯度","气压梯度的方向(α)","垂直层的坡度(φ)"三者影响,垂直气压梯度越大,气压梯度与水平方向的夹角越大,垂直层坡度越大,误差越大;(2)协变方案的PGF误差不受上述三因子影响。此外,通过定义参数TT(TT=tanφ·tanα)能定量分析经典方案的PGF误差。     

1979—2013年ERA-Interim资料的青藏高原低涡活动特征分析

为了更好地了解青藏高原多尺度地形的动力作用,并为改良数值模式中地形的表示方法奠定基础,通过采用2010年青藏高原西南部6个地面台站的观测资料以及4种不同分辨率的分析(再分析)资料,分别估算了冈底斯山及整个青藏高原主体范围内的地表气压拖曳,得出了青藏高原可能存在的拖曳类型,并且分析了青藏高原气压拖曳的一些特征。得出如下主要结论:由罗斯贝波产生的波动拖曳作为行星尺度的拖曳对青藏高原地区总拖曳的贡献最大;同时,青藏高原范围内存在着大量与天气过程密切相关的天气尺度的拖曳;对于冈底斯山对气流的中尺度动力作用的进一步分析可知,夏季基本全为气流分离,冬季500 hPa以下为气流分离,500—200 hPa为气流分离和波动破碎的混合区,而200 hPa以上的平流层则为重力波的产生及其破碎区域;冈底斯山地区的地表气压拖曳主要集中在3000—5000 m高度,并且,冈底斯山总拖曳的方向近乎与山脊垂直;地表气压和地形高度资料的分辨率越高,所能分辨出的更小波长的气压拖曳也越多,估算出的高原主体范围内的拖曳值也越大;变压梯度和地形梯度是影响气压拖曳的基本因子,但地形梯度对拖曳的影响最终是通过气压梯度来实现的。     

初论双三次数值模式

讨论在数学Rn空间里,存在孔斯双三次曲面拟合的可能数值模式(以下称双三次数值模式)。双三次数值模式特点是,在诊断上对天气系统中的由各个物理定律表述的(离散点)大气物理量场,可通过数学三次样条函数做双三次曲面拟合,则模式大气(包括天气系统)的各个物理量场均达到二阶可导,即是大气运动方程中的各个物理量场都存在各自的一、二阶空间微商,从而可以对模式大气与天气系统做时间积分。与有限差分模式和谱模式存在所谓的空间截断误差和波数截断误差相比较,双三次数值模式存在所谓的空间拟合误差,恰是现行有限差分模式空间截断误差的高阶小量。而双三次数值模式具有谱模式准确计算空间微商的优点,且双三次数值模式的数学构架能够较好地适应大气运动动力框架,是可与有限差分模式和谱模式相比较的另一数值分析新算法的气象数值模式。     

Spectral distributions of the pressure gradient force errors in σ-coordinate spectral and grid-point models in an idealized case

Summary The spectral distributions of the pressure gradient force errors of the spectral and the finite-difference techniques used in combination with the vertical coordinate were examined in an idealized case of an atmosphere at rest and in hydrostatic equilibrium. The vertical temperature profile was piece-wise linear in lnp, with an inversion at the bottom. Trapezoidal mountains of different widths were used. The same amounts of input information were given to both the spectral and the finite-difference methods. In the rms sense, the spectral errors were generally much larger than those of the finite-difference method. However, on the larger and medium scales, a remarkable similarity of the error spectra of the two methods was found. The build up of the error of the spectral method occurs at the smallest scales. This may explain difficulties in documenting the error in higher resolution spectral models where the contribution to the total error in this part of the spectrum may be removed as the small-scale noise by the horizontal smoothing and/or filtering. In order to reduce the small-scale noise generation, the finite-difference pressure gradient force may be used in spectral models.With 6 Figures     

一个直接用观测资料计算大范围散度、涡度和垂直速度的方案

提出了一个直接用观测资料,便于用电子计算机计算大范围散度、涡度和垂直速度的方案。还提出了计算某些物理量的梯度、平流和通量的方法。对于在垂直方向不均匀分层的计算,垂直边界条件个数和连续方程不协调的问题,以及在地形起伏的山地如何计算垂直速度等问题,也作了初步讨论。最后,用一次华南大范围降水的例子进行了计算,结果和预报员经验还比较一致。     

数值积分过程中截断误差和舍入误差的分离方法及其效果检验

本文讨论数值积分过程中截断误差和舍入误差的分离方法和理论,解析地给出某些数值计算方法的理论截断误差,并以此来分离计算结果中的误差.然后引入参考解的办法,用来分离更为一般的微分方程求解过程中的截断误差和舍入误差.以参考解算法为基础,对一个偏微分方程的数值解进行计算,所得结果与采用理论截断误差得到的结果进行了对比,发现:(...     

A three-dimensional satellite retrieval method for atmospheric temperature and moisture profiles

A three-dimensional variational method is proposed to simultaneously retrieve the 3-D atmospheric temperature and moisture profiles from satellite radiance measurements. To include both vertical structure and the horizontal patterns of the atmospheric temperature and moisture, an EOF technique is used to decompose the temperature and moisture field in a 3-D space. A number of numerical simulations are conducted and they demonstrate that the 3-D method is less sensitive to the observation errors compared to the 1-D method. When the observation error is more than 2.0 K, to get the best results, the truncation number for the EOF＇s expansion have to be restricted to 2 in the 1-D method, while it can be set as large as 40 in a 3-D method. This results in the truncation error being reduced and the retrieval accuracy being improved in the 3-D method. Compared to the 1-D method, the rms errors of the 3-D method are reduced by 48% and 36% for the temperature and moisture retrievals, respectively. Using the real satellite measured brightness temperatures at 0557 UTC 31 July 2002, the temperature and moisture profiles are retrieved over a region （20°-45°N, 100°- 125°E） and compared with 37 collocated radiosonde observations. The results show that the retrieval accuracy with a 3-D method is significantly higher than those with the 1-D method.     

基于变分原理的自适应网络技术及其权函数问题研究

利用两个具有解析解的算例研究基于变分原理的自适应网络技术。结果表明，对运动激波算例，权函数考虑二阶导数项比考虑梯度项更能有效地减小误差；对气旋锋生算例，仅以梯度作为权函数亦不能提高精度，考虑速度场、锋生函数分布的权函数能更合理地安排网络；对照解析解，发现提出的自适应网络技术能明显提高计算精度，在节省内存等方面显示了突出的优点。     

Accurate pressure gradient calculations in hydrostatic atmospheric models

Most models of atmospheric flow which use the primitive equations require a diagnostic equation to determine local total pressure. In hydrostatic models, this equation is the vertically integrated hydrostatic equation. A frequently used approximation to this integration is to hold the temperature constant within model layers yielding a linear proportionality between p or (Exner's function) and z. This procedure yields static pressures with errors on the order of 10^–3mb.If terrain following coordinates are used, terms arise in the horizontal momentum equations involving the gradient of total pressure along the coordinate surface, less a correction for the variation of the hydrostatic pressure along a sloped surface. Erroneous horizontal accelerations are common in these models which result from spurious pressure gradients that are due to inaccurate computation of the static pressure. This error may be amplified if the computation of the slope correction term of the horizontal pressure gradient is not consistent with the method of calculating the total pressure.We derive a methodology to be used in the vertical pressure integrations that is exact if the potential temperature lapse rate is constant between integration limits. The method is applied to both the integration of the hydrostatic equation and the computation of the slope correction term in the horizontal pressure gradient. The method employs a fixed vertical grid and a dynamic one defined by the significant levels in the vertical temperature distribution. With this methodology, the error in calculation of the horizontal pressure gradient acceleration is greatly reduced, especially in situations where the isothermal surfaces are not parallel to the vertical coordinate surfaces. The problem of aliasing and the treatment of significant temperature levels is described.     

The use of successive dynamic initialization by nudging to simulate cyclogenesis during GALE IOP 1

Summary Synoptic/diagnostic case studies have increasingly come to rely on numerical simulations started from some initial state after which the model generated fields receive no further information from observed data. The purpose of this paper is to demonstrate the use of a dynamic data assimilation technique based on nudging to create a dynamically consistent high-resolution four-dimensional data set that can be used for synoptic diagnostic studies. The nudging technique is applied in the Goddard Mesoscale Atmospheric Simulation System (GMASS) using the 3-h radiosonde data collected during GALE IOP 1. A unique aspect of this application is nudging toward data analyses for which the areal coverage shifts with time. One of the two nudging simulations assimilates surface pressure in addition to the temperature, mixing ratio, and wind components. The nudging values are determined by linear interpolation between 3-h observation times. Assuming a linear variation of the assimilated value in time leads to estimates of the nudging coefficients which take into account the accuracy of the observations.Both nudging simulations are more accurate in terms of S hand root-mean-square error (RMSE) scores than a control sunulation without successive initialization. The nudging simulation with surface pressure is more accurate than the nudging simulation without surface pressure assimilation for this case. The simulation with surface pressure nudging captures the surface cyclogenesis and the associated strong rise-fall couplet in the 500 hPa height field. It also exhibits the strongest ageostrophic flow and exit region vertical circulation associated with a jet streak on the western side of the intensifying upper-level trough.The data sets made possible by the dynamic assimilation/ simulation cycles are dynamically consistent, have high spatial and temporal resolution and are ideally suited for diagnostic studies. Examples presented include the evolution of the ageostrophic flow associated with the exit region of an upper-level jet propagating toward the base of an intensifying trough with increasing cyclonic curvature of the flow. The nudging simulation with surface pressure provides the resolution and accuracy required to depict the rapid transformation (within a 12-h period) of the exit region ageostrophic flow from predominantly cross contour to along contour as the jet streak approaches the base of the trough.With 19 Figures