非静力滞弹性模式中水平分辨率与垂直分辨率的协调性初探

为了理论上研究非静力滞弹性模式中水平分辨率与垂直分辨率之间的搭配问题，以线性斜压滞弹性方程组为出发方程，导出解析的频散方程、水平群速方程和垂直群速方程，同时在最优三维网格C／CP下进行离散，也导出频散方程、水平群速方程和垂直群速方程，然后用图示的方法，比较了在不同的水平和垂直格距下模拟解析解所产生的误差。结果表明：当垂直格距和水平格距相当时，在C／CP网格上对惯性重力波的频率、水平群速和垂直群速都能较好地模拟，产生的相对误差均在5％以下。     

非均匀网格下的高阶精度中央差分格式:理论推导和理想试验

传统的高阶精度有限差分格式通常是在均匀网格的基础上推导得到的,在非均匀网格的情况下它会出现精度退化的问题。基于泰勒展开方法构造了一种适用于非均匀网格的2阶、4阶和6阶精度中央有限差分方案,利用Burgers方程和一维平流方程对新方案的性能进行测试,着重分析新方案对其误差大小及分布形态的改进效果。数值模拟结果表明:在非均匀网格下,提高差分方案的精度可明显减小数值解误差(降低了70%~88%),特别是当差分精度从2阶提高到4阶的时候。同时,高阶精度方案在梯度变化较大或者网格距较粗区域的模拟结果更有优势,4阶和6阶精度方案在以上区域的误差远小于2阶精度方案。方案可用于提高数值天气预报模式中非均匀分层模式的垂直差分计算精度。      

一个在球面半规则网格上的求解Helmholtz方程的多重网格法

该文就球面上求解Ｈｅｌｍｈｏｌｔｚ方程的问题提出了一个多重网格有限差分法，有限差分风格的分辨率在纬度方向（即经向）不变而在经度方向（即纬向）可变，以使球面上网格点的实际间隔大致保持均匀，在每个网格点，把其残差减小到给定量所需要的ＣＰＵ时间与网格分产率无关，由于可变网络距的结果，其离散误差要比二阶误差稍糟些，该解算方法适用于球面上的一般椭圆型方程，对不宜做均匀网格距求解的一些问题也是有用的。     

垂直网格计算频散性的研究

在线性斜压原始方程组的基础上, 从频率和群速方面讨论了几种垂直跳点网格和时间—垂直跳点网格的计算频散性, 并指出了出现错误群速的垂直尺度范围。以便为原始方程大气模式选取垂直网格提供指导。     

三维变量配置对惯性重力波频散性模拟的影响

在线性斜压原始方程组的基础上，从频率和群速方面讨论了由水平网格 (C、Z网格) 和垂直网格 (L、CP、LZ、LY网格) 组合而成的几种三维网格 (C/L、C/CP、Z/LZ、Z/LY) 的计算频散性并分析了各种网格出现偏差的原因，结果表明三维网格C/CP (水平网格为C网格垂直网格为Charney-Phillips网格) 与Z/LZ（水平网格为Z网格垂直网格为LZ网格）计算频散性能较好。从而为原始方程大气模式选取三维网格提供指导。     

应用于双向套网格模式的一种变格距差分解法

本文提出了一种用于双向套网格模式的变格距差分计算方案。该方案在不同格距的网格区采用不同精度的差分格式，它自然地连接粗细网格，避免了一般套网格方案在粗细网格相重合点上进行的重复计算。用解析法和数值试验证明了:它与其它一些变格距差分格式相比，对短波的穿透能力有明显改进，虚假的反射也较小。应用该方案建立了正压原始方程双向套网格模式，并采用空间分解和时间分解计算方法。这不仅使二维问题转化为二个一维问题，而且二维套网格也可简化为一维均匀网格和一维套网格两部分，从而使计算和程序简化。用理想场为初值所做的一系列数值试验表明，该模式中的波可以自由进出粗细网格区，计算稳定。最后，还用该模式做了台风路径预报试验，给出了一些试验结果。     

一个有限区域中尺度模式的设计及预报试验

以一个６层原始方程模式的基本动力学框架为基础，设计了一个对物理过程考虑得较全面的中尺度原始方程模式。该模式采用（ｘ，ｙ，σ）坐标系；大气上界取为１０ｈＰａ，提供多种水平边界条件；水平和垂直分辨率均可调；降水方案包括大尺度降水和深厚积云对流降水；地面温度的计算采用地面热量收支方程；考虑了地气和海气交换作用；垂直交换系数的计算采用Ｌｉｏｕｉｓ格式；水平扩散采用二阶形式和四阶形式相结合的方案，扩散系数是网格点位置和风场的函数；积分方案采用经济的中央差格式。在水平格距取８０ｋｍ，垂直方向不等距地分为１６层的分辨率条件下，利用该模式进行逐个个例预报试验。结果表明，模式计算稳定，能较好地报出主要的天气形势，预报的降水也较接近实际。文中给出了一些检验指标的统计结果。还在预报能力及模式特性方面与原６层模式进行了对比。     

垂直变量配置对静力适应过程的影响

为了研究垂直变量配置对静力适应过程的影响,本文从描写静力适应过程的方程组出发,分别在将所有变量置于整层上的非跳点N网格;将垂直速度和温度放置在整层,水平速度、气压和密度等变量放置在半层的Charney Phillips跳点网格(CP网格);将水平速度、气压和温度放置在整层,将垂直速度和密度放置在半层的Lorenz跳点网格(L网格);将密度变量放置在整层的Charney Phillips跳点网格(CP_N网格);将密度放置在整层的Lorenz跳点网格(L_N网格)上进行离散,垂直格距分1 km、0.5 km、0.2 km和0.01 km,研究了在这5种网格上产生的频率和垂直群速的相对误差。结果表明:(1)L_N网格和CP网格是完全等效的两种网格。(2)不论垂直格距为多少,CP网格和L网格的误差都是最小,N网格次之,CP_N网格的误差最大。(3)随着垂直格距的减少,在这几种网格上产生的误差都在减小。对于CP网格、L网格和N网格,在水平长波和垂直短波处产生的误差较大。而CP_N网格对水平波长变化不敏感,垂直波长越短,误差越大。(4)当垂直格距为0.01 km时,这几种网格都对水平波长的变化不敏感了,仅对垂直波长敏感。(5)CP网格、L_N网格和L网格在描写静力适应过程和斜压地转适应过程都是误差最小的垂直变量配置方案,因此在非静力完全可压缩深层大气数值预报模式中应优先选择这3种方案。     

用多重网格法解赫姆霍兹型欧拉方程

讨论了用多重网格方法（ＭＧＭ）求解赫姆霍兹型欧拉方程第一边值的五个定解问题，并与变系数超松弛迭代法作了比较。结果表明，在相同的精度条件下，前者所需的计算时间要比后者少，时间效率比随着网格数的增加而明显提高，反映了用多重网格方法求解大型差分方程组数值解的优越性。     

“雅安天漏”研究II．数值预报试验

本文建立了一个用于研究“雅安天漏”的有限区域数值预报模式，并用该模式对１０个“雅安天漏”个例进行了数值预报试验，取得了较满意的结果。该模式动力框架的主要特点是：（１）模式的基本方程组便于构造出完全能量守恒的差分格式；（２）采用了静力扣除；（３）模式的垂直坐标选用了η坐标；（４）选用Ｅ网格作为变量的水平分布形式；（５）位势高度与其他预报量在垂直方向交错分布；（６）对Ｅ网格的波解分离问题采取了特殊的处理技巧；（７）首次采用“半格距”差分解决了矩形Ｅ网格及球坐标Ｅ网格沿对角线的差分计算；（８）采用显示分解的时间积分方案；（９）尽量保留初始场信息。模式的物理过程主要包括：（１）大尺度凝结降水；（２）对流调整及对流降水；（３）水平扩散和垂直通量输送；（４）地面辐射收支和边界层参数化。试报降水的主要降水中心及降水范围与观测分析比较相似。大于１０ｍｍ和２５ｍｎ降水的ＴＳ平均评分分别为０．４１和０．３２。     

A Variable Mesh Spacing for Large-Eddy Simulation Models in the Convective Boundary Layer

A variable vertical mesh spacing for large-eddy simulation (LES) models in a convective boundary layer (CBL) is proposed. The argument is based on the fact that in the vertical direction the turbulence near the surface in a CBL is inhomogeneous and therefore the subfilter-scale effects depend on the relative location between the spectral peak of the vertical velocity and the filter cut-off wavelength. From the physical point of view, this lack of homogeneity makes the vertical mesh spacing the principal length scale and, as a consequence, the LES filter cut-off wavenumber is expressed in terms of this characteristic length scale. Assuming that the inertial subrange initial frequency is equal to the LES filter cut-off frequency and employing fitting expressions that describe the observed convective turbulent energy one-dimensional spectra, it is feasible to derive a relation to calculate the variable vertical mesh spacing. The incorporation of this variable vertical grid within a LES model shows that both the mean quantities (and their gradients) and the turbulent statistics quantities are well described near to the ground level, where the LES predictions are known to be a challenging task.     

几种垂直跳点网格计算频散性的比较研究

为证明两种新的垂直跳点网格--LZ网格和LY网格的有效性,从频率、群速和出现错误群速的垂直尺度范围等方面与现有的几种垂直跳点网格和时间--垂直跳点网格进行了比较.结果表明:LZ网格计算频散性与目前使用的最广泛的并且计算频散性也是最佳的CP网格相当,而LY网格次之,从而为模式设计者选取垂直网格提供了又一种选择.     

基于变分原理的自适应网格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格技术。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格;对照解析解,发现提出的自适应网格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。     

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。     

两种垂直分层方法对GPS水汽层析结果的影响

利用北京房山地区9个全球定位系统测站组成的实验站网,研究GPS水汽层析网格的划分方法,采取垂直均匀和垂直非均匀两种分层方法,分析GPS层析网格垂直分层对水汽层析结果的影响。结果表明：均匀和非均匀垂直分层方法得到的GPS水汽层析结果是可靠的,均可以与探空水汽结果进行比较。但垂直非均匀分层更符合大气水汽的实际分布特征,层析解算精度更高,尤其对测站高度差较小的GPS站网,尽量选择垂直非均匀分层方法。垂直均匀和垂直非均匀分层方法均可以为北京地区GPS层析网格垂直划分提供参考。     

A Length Scale Defining Partially-Resolved Boundary-Layer Turbulence Simulations

Numerical weather prediction (NWP) model forecasts at horizontal grid lengths in the range of 100 m to 1 km are now possible. Within this range of grid lengths, the convective boundary layer (CBL) is partially resolved and thus in the so-called ‘grey zone’. For simulations in the grey zone, numerical dissipation sources from both the advection scheme and the subgrid model are likely to be significant. Until now, these effects have not been incorporated fully into our understanding of the grey zone. In order to quantify these effects, a dissipation length scale is defined based on the second moment of the turbulent kinetic energy (TKE) spectrum. An ensemble of simulations of a CBL are performed using a large-eddy model across the grey-zone resolutions and for a range of subgrid model, advection scheme and vertical grid configurations. The dissipation length scale distinguishes the effects of the different model configurations in the grey zone. In the middle of the boundary layer, the resolved TKE is strongly controlled by the numerical dissipation. This leads to a similarity law for the resolved TKE in the grey zone using the dissipation length scale. A new definition of the grey zone emerges where the inversion depth and dissipation length scale are the same size. This contrasts with the typical definition using the horizontal grid length. At the inversion, however, the variation of the dissipation length scale with grid length is less predictable, reflecting significant challenges for modelling entrainment in the grey zone. The dissipation length scale is thus a simple diagnostic to aid both NWP and large-eddy modellers in understanding the grey zone.     

Improved Tropical Cyclone Forecasts with Increased Vertical Resolution in the TRAMS Model

The numerical simulation of typhoons has been found to be very sensitive to the vertical resolution of the model. During the updating of the TRAMS model from version 1.0 to 3.0, the horizontal resolution has been increased from 36 km to 9 km, while the vertical layer number only increased from 55 to 65 layers. The lack of high vertical resolution limits the performance of the TRAMS model in typhoon forecasting to a certain extent. In order to study the potential improvement of typhoon forecasting by increasing the vertical resolution, this paper increases the vertical resolution of the TRAMS model from 65 to 125 layers for the first time for a comparative simulation test. The results of the case study with Typhoon Hato (2017) show that the model with high vertical resolution can significantly enhance the warm structure caused by water vapor flux convergence and vertical transport, thus accurately simulating the rapid strengthening process of the typhoon. Meanwhile, the model with 125-layer vertical resolution can simulate the asymmetric structural characteristics of the wind field, which are closer to the observations and can help to reduce the bias in typhoon track forecasting. The improvement of vertical resolution is also trialed by using the batch test results of several landfalling typhoons in 2016-2017. The experimental results show that the typhoon forecast of the model becomes consistent with the observations only when the number of vertical layers of the model increases to about 125 layers, which in turn causes a large computational burden. In the next step, we will try to solve the computational burden problem caused by ultra-high vertical resolution with the top boundary nesting technique, and realize the application of high vertical resolution in the actual operation of the TRAMS model.     

A comparative study of some mathematical models of the mean wind structure and aerodynamic drag of plant canopies

A semi-analytical method for describing the mean wind profile and shear stress within plant canopies and for estimating the roughness length and the displacement height is presented. This method incorporates density and vertical structure of the canopy and includes simple parameterizations of the roughness sublayer and shelter factor. Some of the wind profiles examined are consistent with first-order closure techniques while others are consistent with second-order closure techniques. Some profiles show a shearless region near the base of the canopy; however, none displays a secondary maximum there. Comparing several different analytical expressions for the canopy wind profile against observations suggests that one particular type of profile (an Airy function which is associated with the triangular foliage surface area density distribution) is superior to the others. Because of the numerical simplicity of the methods outlined, it is suggested that they may be profitably used in large-scale models of plant-atmosphere exchanges.