四阶矩准正态分布和三阶矩剪切近似验证？

本文利用近地面层大气湍流量的观察资料对四阶矩的准正态分布假定和三阶矩的剪切近似进行了实验验证。结果表明，四阶矩能够较好地符合准正态分布假定；三阶矩不仅完全满足剪切近似，甚至还可以对剪切程度进一步加强，并且得到了一系列剪切近似的加强修正系数。     

具有对数正态分布几何过程的统计推断

在假定几何过程的初始分布为对数正态分布的前提下 ,研究了几何过程的统计推断问题。对其中的参数分别用极大似然法和改进的矩法进行了估计。然后 ,在理论推导、模拟试验和实际数据分析的基础上提出了一些建议。     

高阶正定守恒的中心约束多矩有限体积平流模式

采用新的均匀三点中心约束多矩有限体积方法（3-point Multi-moment Constrained finite-Volume scheme for Uniform Points with Center Constraints, MCV3_UPCC）,发展了一个三阶正定守恒的平流模式。三点多矩有限体积方法在单网格内定义等距的3个自由度,采用多矩约束条件并通过控制方程获得时间演变方程。新的三点中心约束多矩方法能在单网格内采用等距的3个点值及中心一阶、二阶导数作为约束条件进行空间4次多项式数值重构,获得3个自由度的时间演变方程;所构建的新数值方案具有三阶精度,边界通量连续性保证了其数值严格守恒。为了抑制该方法的非物理数值振荡,引入了边界保型限制器技术,它能够把数值解控制在既定物理场最小值（最小值为0时则保持数值正定）与最大值之间。数值试验表明新发展的三阶平流模式具有良好的计算精度,能够严格保持数值解的正定性和守恒性,同其他高精度平流模式相当,在实际大气模式水汽等平流输送应用中具备良好的发展潜力。      

准地转理论基本问题回顾与讨论

准地转理论是大气动力学的中心问题之一,它提供了从大气动力学基本原理入手分析大尺度天气系统演变的方法。准地转理论有助于预报员理解中高纬度大尺度天气系统的三维结构,分析、预报天气系统的发展和移动,因此被称为短期天气预报的理论基础。准地转理论具有完整的理论体系,它包含了较多的基本假定,故容易导致对其中的一些基本问题的理解有混淆。本文从基础的动力学知识出发,对准地转理论的基本概念、基本近似、核心理论及其在实际天气预报过程中的应用作了回顾和讨论。内容包括:准地转运动与准地转近似定义、准地转运动理论的范畴、天气图上的大尺度运动、准地转运动理论与短期天气预报的关系、由斜压二层模式下的准地转理论对高空槽脊和地面气旋发展与移动的判断等。     

基于灰度共生矩阵与AdaBoost判别法的冰雹预测

选取新疆地区雹云与非雹云雷达反射率图像进行降雹与无雹天气分析。用中值滤波与九阶拉普拉斯算子处理图像得到图像的纹理信息。用灰度共生矩阵方法提取图像的能量、熵、惯性矩、相关性、逆差矩并提取图像的一、二、三阶颜色矩,将这8个变量进行标准化作为特征数据,利用AdaBoost判别法建立判别分类器,对雹云图像进行分析判别。结果显示该文采用的方法能够明显的区分降雹与无雹云层,判别误差较小,具有参考价值。     

海气耦合非线性随机模式求解探讨

本文首先对一个假定随机强迫为高斯白噪声的四次方非线性海气耦合随机模式进行了ε一阶近似的摄动处理，将非线性随机模式化为显含随机项的线性系统和隐含随机项的非线性系统，通过对输出响应的分析表明:该模式结构和随机项的特性使得随机强迫输出的响应只能通过模式的线性区；非线性项仅对气候系统的方差及其对应的频谱有一定量的偏差作用，而对一般输出特性没有贡献。在这基础上，求出了模式输出谱，并给出了计算。     

旋转扰动流体中壁面湍流不稳定及其拟序结构研究Ⅱ：数值模式

对第一部分的实验结果进行了讨论,指出局地最大、最小涡度的存在与所谓的正压不稳定和大气中经常观测到的滚动涡有关。速度廓线中的拐点和涡度极大值点对应不稳定发展的位置。另外,为了改进湍流的模拟,根据“准正则”近似,发展了一个三阶闭合模式。这个模型已被证明可以描述与湍流过程有关的流体动力学变量的趋势。     

不同扰动场对大气重力波参数结果影响的初步探讨

如何获取大气重力波参数是大气动力学理论研究的重点和难点。本文以2013年8月6—8日晋西北地区出现的一次雷阵雨天气过程为例,利用常用的二阶、三阶、四阶曲线拟合和带通滤波方法获取垂直高分辨率探空资料的扰动场,对这些扰动场提取的大气重力波参数进行对比分析。结果表明:不同扰动场(二阶、三阶、四阶曲线拟合以及带通滤波)对所获取重力波参数的大小及变化趋势存在影响,但对不同重力波参数的影响程度不一样。其中,对波固有周期、水平和垂直波长的大小及变化趋势影响很大,而对波传播方向、对地水平群速及固有相速的影响程度则较弱。结合6—8日天气现象的大气动力特征,发现由二阶曲线拟合、带通滤波对应扰动场得到的重力波参数的大小及变化趋势与此吻合,其结果可信度最高;而由四阶曲线拟合扰动场得到重力波参数值的可信度最低。     

台湾海峡桃源地区低能见度统计特征分析

根据1974～1990年台湾海峡东岸桃源地区逐日地面观测信息化资料分析，揭示了该地区低能见度变化特征；利用韦布尔（Weibull）分布对能见度的概率分布特征加以描述，进一步证实了能见度的概率分布特性，说明能见度并不服从正态分布，而在实际中应用最广泛的是正态分布，因此要对能见度进行正态化转换，在资料正态的假定下，便可利用统计回归方法得出单站能见度的预报方程。     

基于卡尔曼滤波递减平均算法的集合预报综合偏差订正

针对集合预报存在的偏差和集合离散度通常偏小的问题,在卡尔曼滤波递减平均的一阶矩和二阶矩偏差订正方案的基础上发展了综合偏差订正方案,并利用B08RDP WWRP(The WWRP Beijing 2008 Olympics Research and Development Project)项目中日本气象厅(JMA)区域集合预报的850 hPa温度资料,将敏感性试验得到的一阶矩和二阶矩订正的最优权重系数应用于综合偏差订正方案,并对其订正效果进行多方面检验分析。试验结果表明,一阶矩订正可以有效减小集合平均偏差,集合平均预报质量得到了明显改善;二阶矩订正对集合离散度具有较强的调整能力,订正后的集合预报可靠性、区分不同天气事件的能力总体上得到了提高;综合偏差订正方案有效融合了一阶矩和二阶矩订正的优势,其各自的最优权重系数适用于综合偏差订正方案,对集合平均偏差和离散度具有良好的订正效果,能够改善集合预报的整体质量。但一阶矩与二阶矩订正对综合偏差订正的贡献程度随评分指标而异,一阶矩订正对等级概率(RPS)评分和异常值百分比评分的贡献分别为83.75%和18.83%,可信度的改善约83.98%源于二阶矩订正,而相对作用特征(ROC)评分中二者的贡献基本相当。     

On the influence of non-Gaussianity on turbulent transport

Non-Gaussianity effects, first of all the influence of the third and fourth moments of the velocity probability density function, have to be assessed for higher-order closure models of turbulence and Lagrangian modelling of turbulent dispersion in complex flows. Whereas the role and the effects of the third moments are relatively well understood as essential for the explanation of specific observed features of the fully developed convective boundary layer, there are indications that the fourth moments may also be important, but little is known about these moments. Therefore, the effects of non-Gaussianity are considered for the turbulent motion of particles in non-neutral flows without fully developed convection, where the influence of the fourth moments may be expected to be particularly essential. The transport properties of these flows can be characterized by a diffusion coefficient which reflects these effects. It is shown, for different vertical velocity distributions, that the intensity of turbulent transport may be enhanced remarkably by non-Gaussianity. The diffusion coefficient is given as a modification of the Gaussian diffusivity, and this modifying factor is found to be determined to a very good approximation by the normalized fourth moment of the vertical velocity distribution function. This provides better insight into the effect of fourth moments and explains the varying importance of third and fourth moments in different flows.     

用非线性近似方法反演单多普勒雷达风场(英)

回顾了近年来由单多普勒雷达观测反演风场的各种方法。这些方法大部分基于线性假设,因此风场的非线性变化经常影响反演结果,使得反演的风场误差增大。我们提出一种以非线性近似理论为基础的反演方法,该方法主要考虑了风场分片光滑的特点并充分利用了雷达的径向风场数据。我们把该方法应用到1998年淮河能量与水循环实验的两个个例中。通过同双多普勒雷达观测的结果比较,发现该方法能反演较高分辨率和准确性的水平风场,反演的垂直风场也比较合理。     

Third- and fourth-order mixed moments of turbulent velocity and temperature fluctuations in the atmospheric surface layer

Fourth-order mixed moments of velocity and temperature fluctuations, measured within the atmospheric surface layer, are compared with results obtained by assuming the quasi-Gaussian approximation. Standard deviations of the products uw, u and w(u and w are the longitudinal and vertical velocity fluctuations; is the temperature fluctuation) are in good agreement with those obtained using the quasi-Gaussian assumption. Good agreement is also obtained between measured and Gaussian estimates of fourth-order moments including all three fluctuations u, w, Schwarz inequalities, commonly used in the clipping approximation in turbulence modelling, are found to provide bounds for third-order moments of w, that are too conservative. More reasonable, tighter, bounds for these moments are given by inequalities obtained by Lumley.     

Dynamics of Absolute Vorticity in the Boussinesq Fluid

1.IntroductionDensityoffluidsisaveryimportantquantitytodeterminenuidpropertiessuchascompressibilityandbaroclinicity.Becauseofcomplexityofdensityvariationinrealfluids,variousassumptionshavebeenmadetoreducethedegreeofthecomplexity.TheBoussinesqapproximation(Boussinesq,1903;SpiegelandVeronis,1960;Turner,1973;DrazinandReid,1981)isoneoftheseassumptions,whichiswidelyusedinthestudiesofatmosphericsciencessuchasfrontogenesis(Hoskins,1972;Thorpe,1990),convectionandclouddynamics(OguraandPhillips,1962…     

COMPARISON AMONG EMPIRICAL PROBABILITY DENSITY FUNCTIONS OF THE VERTICAL VELOCITY IN THE SURFACE LAYER BASED ON HIGHER ORDER CORRELATIONS

Vertical velocity fluctuations were measured in theatmospheric surface layer by means of an ultrasonic anemometer andhigher order correlations were calculated on two time series, recordedin unstable and neutral conditions, and selected for the wholemeasurement period on the basis of the inversion test (stationaritytest). Comparisons have been made between observed and predictedcorrelations by considering Gaussian joint-PDF and Gram-Charlierseries expansions truncated to the fourth and sixth order as doneearlier by Frenkiel and Klebanoff. A bi-Gaussian PDF, given by amixture of two Gaussian PDFs, has also been considered. This lasthas been constructed assuming that either the first three or the firstfour moments are given, and the relationships between correlationfunctions of different order are derived. The departure from Gaussianbehaviour in both stability conditions is derived. Though Gram-Charlier series expansions show a good correspondence toexperimental reality, their use as non-Gaussian probabilitydistributions cannot be suggested in theoretical approaches andshould be considered with care in practical applications, due topossible occurrences of small negative probabilities. The resultsshown in this paper support the applicability of the bi-Gaussian PDFcreated using up to the fourth moment.     

The Distribution and Uncertainty Quantification of Wind Profile in the Stochastic General Ekman Momentum Approximation Model

The general Ekman momentum approximation boundary-layer model(GEM) can be effectively used to describe the physical processes of the boundary layer. However, eddy viscosity, which is an approximated value, can lead to uncertainty in the solutions. In this paper, stochastic eddy viscosity is taken into consideration in the GEM, and generalized polynomial chaos is used to quantify the uncertainty. The goal of uncertainty quantification is to investigate the effects of uncertainty in the eddy viscosity on the model and to subsequently provide reliable distribution of simulation results. The performances of the stochastic eddy viscosity and generalized polynomial chaos method are validated based on three different types of eddy viscosities, and the results are compared based on the Monte Carlo method. The results indicate that the generalized polynomial chaos method can be accurately and efficiently used in uncertainty quantification for the GEM with stochastic eddy viscosity.     

Third-Order Moment Closure Through A Mass-Flux Approach

The parameterization of the third moments, the flux of the heat flux and the flux of the potential temperature variance, is considered. It is shown that present parameterizations of these moments using the mass-flux approach with a `top-hat' profile assumption lead to a significant underestimation, resulting in an inaccurate representation of second moments in the convective boundary layer. It is also shown that the underestimation is a result of the `top-hat' profileassumption in which the sub-plume contributions to the total fluxes are ignored. By including these contributions a new parameterization is proposed, whichsatisfies the physical requirements of symmetry andrealizability, and gives results that are in fair agreement with thelarge-eddy simulation data.     

多层四流球谐函数算法的构建及在大气辐射传输模式中的应用

为了在不大幅度增加计算成本的情况下提高大气辐射传输计算的精度,利用单层四流球谐函数结合多层二流累加法,构造了可用于多层大气的四流球谐函数算法。为了比较与其他辐射传输算法的差异,引入48流离散纵坐标算法作为比较标准,Eddington 近似、四流离散纵坐标算法作为比较对象。在真实大气廓线条件下,计算了晴空和有云大气顶向上辐射通量、地表向下辐射通量以及加热率廓线。得出以下结论：在晴空情况下,与作为标准的48流离散纵坐标法相比,Eddington 近似、四流离散纵坐标法和新构造的四流球谐函数方法加热率绝对误差都小于0?3 K／d;向上、向下辐射通量的相对误差分别小于1％和0?6％。这表明在晴空情况下,3种算法对加热率的计算精度差别不大;对辐射通量的计算精度,两种四流近似算法比传统的 Eddington 近似更为精确。在有云情况下,与48流离散纵坐标法相比,四流球谐函数和四流离散纵坐标法计算的云顶加热率相对误差小于1％,而 Eddington 近似计算的云顶加热率相对误差大于5％。结果表明：新构造的四流球谐函数算法可用于大气辐射传输模式,在不大幅度增加计算成本的同时,提高了晴空大气的整体辐射计算精度和有云大气辐射加热率的计算精度。     

An Investigation of Higher-Order Closure Models for a Forested Canopy

Simultaneous triaxial sonic anemometer velocity measurements vertically arrayed at six levels within and above a uniform pine forest were used to examine two parameterization schemes for the triple-velocity correlation tensor employed in higher-order closure models. These parameterizations are the gradient-diffusion approximation typically used in second-order closure models, and the full budget for the triple-velocity correlation tensor typically employed in third-order closure models. Both second- and third-order closure models failed to reproduce the measured profiles of the triple-velocity correlation within and above the canopy. However, the Reynolds stress tensor profiles (including velocity variances) deviated greatly from the measurements only within the lower levels of the canopy. It is shown that the Reynolds stresses are most sensitive to the parameterization of the triple-velocity correlation in these lower canopy regions where local turbulent production is negligible and turbulence is mainly sustained by the flux transport term. The failure of the third-order closure model to reproduce the measured third moments in the upper layers of the canopy-top contradicts conclusions from a previous study over shorter vegetation but agrees with another study for a deciduous forest. Whether the third-order closure model failure is due to the zero-fourth-cumulant closure approximation is therefore considered. Comparisons between measured and predicted quadruple velocity correlations suggest that the zero-fourth-cumulant approximation is valid close to the canopy-atmosphere in agreement with recent experiments.     

Optimal Perturbations Triggering Weather Regime Transitions: Onset of Blocking and Strong Zonal Flow

In this paper, the approach proposed by Mu and Jiang (2008) to obtain the optimal perturbations for triggering blocking (BL) onset is generalized to seek the optimal perturbations triggering onset of the strong zonal flow (SZF) regime. The BL and SZF regimes are characterized by the same dipole-like anomaly pattern superposed on the climatological flow, but with opposite sign. The results show that this method is also superior at finding the initial optimal perturbations triggering onset of the SZF regime, especially in the medium range. Furthermore, by comparing the two kinds of conditional nonlinear optimal perturbations (CNOPs) trig-gering onset of BL and SZF regimes, we find that in the linear approximation, there is symmetry in the sensitivities for BL and SZF onset, and the perturbations that optimally trigger onset of BL and SZF regimes at times when linear approximation is valid are also characterized by the same spatial pattern but with opposite sign. Whereas when the optimization time is extended to 6 days, the two kinds of CNOPs lose their out-of-phase behavior. The nonlinearity results in an asymmetry between the sensitivity for BL and SZF onset. Additionally, we find that the optimal perturbations have one common property, which is that the second baroclinic mode contributes more to the initial perturbations while the barotropic mode dominates the final structures.