Vortex Rossby waves on smooth circular vortices: Part II. Idealized numerical experiments for tropical cyclone and polar vortex interiors

Idealized linear and nonlinear numerical experiments are carried out to test the predictions of the theory developed in Brunet and Montgomery [Vortex Rossby Waves on Smooth Circular Vortices Part I: Theory (pages 153–177, this issue)]. For a monopolar tropical cyclone-like vortex whose strength lies between a tropical depression and tropical storm, linear theory remains uniformly valid in time in the vortex core for all azimuthal wavenumbers. Examples elucidate aspects of the vortex Rossby wave/merger spin up mechanism proposed previously. For the case of the polar vortex, however, wavenumber 1 disturbances in the continuous spectrum are predicted to develop a nonlinear evolution for realistic polar-night stratospheric-jet configurations and wave breaking is demonstrated to occur within the dynamics of the continuous spectrum.     

Effect of Baroclinicity on Vortex Axisymmetrization.Part Ⅱ：Baroclinic Basic Vortex

The effect of baroclinicity on vortex axisymmetrization is examined within a two-layer dynamical model.Three basic state vortices are constructed with varying degrees of baroclinicity：（i） barotropic,（ii） weak baroclinic,and （iii） strong baroclinic.The linear and nonlinear evolution of wavenumber-2 baroclinic disturbances are examined in each of the three basic state vortices.The results show that the radial propagating speed of the vortex Rossby wave at the lower level is larger with the stronger baroclinicity,resulting in a faster linear axisymmetrization process in the stronger baroclinic vortex.It is found that the nonlinear axisymmetrization process takes the longest time in the strongest baroclinic vortex among the three different basic vortices due to the weaker kinetic energy transfer from asymmetric to symmetric circulations at the lower level.A major finding in this study is that the same initial asymmetric perturbation can have different effects on symmetric vortices depending on the initial vortex baroclinicity.In numerical weather prediction models,this implies that there exists a sensitivity of the subsequent structural and intensity change solely due to the specification of the initial vertical shear of the tropical cyclone vortex.     

Effect of Baroclinicity on Vortex Axisymmetrization.Part Ⅰ：Barotropic Basic Vortex

The barotropic and baroclinic disturbances axisymmetrized by the barotropic basic vortex are examined in an idealized modeling framework consisting of two layers.Using a Wentzel-Kramers-Brillouin approach,the radial propagation of a baroclinic disturbance is shown to be slower than a barotropic disturbance,resulting in a slower linear axisymmetrization for baroclinic disturbances.The slower-propagating baroclinic waves also cause more baroclinic asymmetric kinetic energy to be transferred directly to the barotropic symmetric vortex than from barotropic disturbances,resulting in a faster axisymmetrization process in the nonlinear baroclinic wave case than in the nonlinear barotropic wave case.     

Vortex Rossby waves on smooth circular vortices: Part I. Theory

A complete theory of the linear initial-value problem for Rossby waves on a class of smooth circular vortices in both f-plane and polar-region geometries is presented in the limit of small and large Rossby deformation radius. Although restricted to the interior region of barotropically stable circular vortices possessing a single extrema in tangential wind, the theory covers all azimuthal wavenumbers. The non-dimensional evolution equation for perturbation potential vorticity is shown to depend on only one parameter, G, involving the azimuthal wavenumber, the basic state radial potential vorticity gradient, the interior deformation radius, and the interior Rossby number.In Hankel transform space the problem admits a Schrödinger’s equation formulation which permits a qualitative and quantitative discussion of the interaction between vortex Rossby wave disturbances and the mean vortex. New conservation laws are developed which give exact time-evolving bounds for disturbance kinetic energy. Using results from the theory of Lie groups a nontrivial separation of variables can be achieved to obtain an exact solution for asymmetric balanced disturbances covering a wide range of geophysical vortex applications including tropical cyclone, polar vortex, and cyclone/anticyclone interiors in barotropic dynamics. The expansion for square summable potential vorticity comprises a discrete basis of radially propagating sheared vortex Rossby wave packets with nontrivial transient behavior. The solution representation is new, and for this class of swirling flows gives deeper physical insight into the dynamics of perturbed vortex interiors than the more traditional approach of Laplace transform or continuous-spectrum normal-mode representations. In general, initial disturbances are shown to excite two regions of wave activity. At the extrema of these barotropically stable vortices and for a certain range of wavenumbers, the Rossby wave dynamics are shown to become nonlinear for all initial conditions. Extensions of the theory are proposed.     

Surface pressure profiles, vortex structure and initialization for hurricane prediction. Part II: numerical simulations of track, structure and intensity

In part 1 of this study, an assessment of commonly used surface pressure profiles to represent TC structures was made. Using the Australian tropical cyclone model, the profiles are tested in case studies of high-resolution prediction of track, structure and intensity. We demonstrate that: (1) track forecasts are mostly insensitive to the imposed structure; (2) in some cases [here Katrina (2005)], specification of vortex structure can have a large impact on prediction of structure and intensity; (3) the forecast model mostly preserves the characteristics of the initial structure and so correct structure at t?=?0 is a requirement for improved structure forecasting; and (4) skilful prediction of intensity does not guarantee skilful prediction of structure. It is shown that for Ivan (2004) the initial structure from each profile is preserved during the simulations, and that markedly different structures can have similar intensities. Evidence presented suggests that different initial profiles can sometimes change the timing of intensification. Thus, correct initial vortex structure is an essential ingredient for more accurate intensity and structure prediction.     

Monthly Extended Predicting Experiments with Nonlinear Regional Prediction. Part II: Improvement of Wave Component Prediction

Based on Chen et al. (2006), the scheme of the combination of the pentad-mean zonal height departure nonlinear prediction with the T42L9 model prediction was designed, in which the pentad zonal heights at all the 12-initial-value-input isobar levels from 50 hPa to 1000 hPa except 200, 300, 500, and 700 hPa were derived from nonlinear forecasts of the four levels by means of a good correlation between neighboring levels.Then the above pentad zonal heights at 12 isobar-levels were transformed to the spectrum coefficients of the temperature at each integration step of T42L9 model. At last,the nudging was made. On account of a variety of error accumulation, the pentad zonal components of the monthly height at isobar levels output by T42L9 model were replaced by the corresponding nonlinear results once more when integration was over. Multiple case experiments showed that such combination of two kinds of prediction made an improvement in the wave component as a result of wave-flow nonlinear interaction while reducing the systematical forecast errors. Namely the monthly-mean height anomaly correlation coe cients over the high- and mid-latitudes of the Northern Hemisphere, over the Southern Hemisphere and over the globe increased respectively from 0.249 to 0.347, from 0.286 to 0.387, and from 0.343 to 0.414 (relative changes of 31.5%, 41.0%, and 18.3%).The monthly-mean root-mean-square error (RMSE) of T42L9 model over the three areas was considerably decreased, the relative change over the globe reached 44.2%. The monthly-mean anomaly correlation coefficients of wave 4-9 over the areas were up to 0.392, 0.200, and 0.295, with the relative change of 53.8%, 94.1%,and 61.2%, and correspondingly their RMSEs were decreased respectively with the rate of 8.5%, 6.3%, and 8.1%. At the same time the monthly-mean pattern of parts of cases were presented better.     

Dynamical and Thermal Problems in Vortex Development and Movement. Part I: A PV–Q View

Based on the Lagrangian change equation of vertical vorticity deduced from the equation of threedimensional Ertel potential vorticity(PV e),the development and movement of vortex are investigated from the view of potential vorticity and diabatic heating(PV-Q).It is demonstrated that the asymmetric distribution in the vortex of the non-uniform diabatic heating in both vertical and horizontal can lead to the vortex’s development and movement.The theoretical results are used to analyze the development and movement of a Tibetan Plateau(TP) vortex(TPV),which appeared over the TP,then slid down and moved eastward in late July 2008,resulting in heavy rainfall in Sichuan Province and along the middle and lower reaches of the Yangtze River.The relative contributions to the vertical vorticity development of the TPV are decomposed into three parts:the diabatic heating,the change in horizontal component of PV e(defined as PV 2),and the change in static stability θ z.The results show that in most cases,diabatic heating plays a leading role,followed by the change in PV 2,while the change of θ z usually has a negative impact in a stable atmosphere when the atmosphere becomes more stable,and has a positive contribution when the atmosphere approaches neutral stratification.The intensification of the TPV from 0600 to 1200 UTC 22 July 2008 is mainly due to the diabatic heating associated with the precipitation on the eastern side of the TPV when it uplifted on the up-slope of the northeastern edge of the Sichuan basin.The vertical gradient of diabatic heating makes positive(negative) PV e generation below(above) the maximum of diabatic heating;the positive PV e generation not only intensifies the low-level vortex but also enhances the vertical extent of the vortex as it uplifts.The change in PV e due to the horizontal gradient of diabatic heating depends on the vertical shear of horizontal wind that passes through the center of diabatic heating.The horizontal gradient of diabatic heating makes positive(negative) PV e generation on the right(left) side of the vertical shear of horizontal wind.The positive PV e generation on the right side of the vertical shear of horizontal wind not only intensifies the local vertical vorticity but also affects direction of movement of the TPV.These diagnostic results are in good agreement with the theoretic results developed from the PV-Q view.     

风暴尺度天气下利用集合卡尔曼滤波模拟多普勒雷达资料同化试验 II. 考虑模式误差的情形

文章的第I部分(兰伟仁等, 2010), 利用模拟雷达资料在假定模式无误差的情况下进行了一系列的集合卡尔曼滤波(EnKF)敏感性试验, 验证了EnKF方法在风暴尺度天气资料同化中的作用。本文继续探讨EnKF在有显著模式误差的情况下同化模拟多普勒雷达资料的效果问题。试验中假定模式误差主要来源于微物理过程参数化的不确定性。结果表明: 模式误差在不同程度上影响了EnKF分析的效果, 对微物理量的影响尤其明显; 在EnKF分析中, 利用微物理过程参数化集合的方法来考虑模式误差, 对速度场、 位温场以及比湿场有较明显的正作用, 但对于微物理量场分析效果较差; 若包含控制试验的微物理过程参数化方案, 则EnKF对所有变量都有正效果, 随着同化循环次数的增加, 分析结果更加合理; 只考虑冰相过程的微物理过程参数化方案的集合, 分析效果进一步提高。     

Surface pressure profiles, vortex structure and initialization for hurricane prediction. Part I: analysis of observed and synthetic structures

Without detailed reconnaissance, consistent representation of hurricane-like vortices in initial conditions for operational prediction and research simulations still remains elusive. It is thus often necessary, particularly for high-resolution intensity forecasting, to use synthetic tropical cyclone circulations to initialize forecast models. Variants on three commonly used surface pressure profiles are evaluated for possible use. Enhancements to the original profiles are proposed that allows definition of both the inner-core and outer circulation. The latter improvement creates a vortex more consistent with the estimated outer structure which sometimes appears to be crucial to the evolving intensity of the storm. It also allows smoother merging of the synthetic vortex with the environment. Comparisons of the profiles against (a) structure estimates, (b) each other, (c) structures obtained via conservation of angular momentum, and (d) observed vorticity structures, suggest that a new enhanced Fujita profile best represents real TC structures. Student-t tests indicate that improved fitting to the observations is statistically significant.     

GRAPES集合卡尔曼滤波资料同化系统Ⅰ:系统设计及初步试验

集合卡尔曼滤波资料同化方法,可以用集合样本统计出随天气形势变化的误差协方差,是当前资料同化领域的研究热点。主要介绍了GRAPES集合卡尔曼滤波资料同化系统的设计以及初步的试验结果。针对集合卡尔曼滤波同化实际观测资料难以实施的问题,采用成批观测同化的顺序同化方法进行多变量的集合卡尔曼滤波同化;为了滤除有限集合数造成的误差相关噪音和缓解求逆矩阵不满秩的问题,在水平和垂直方向都采用了Schur滤波;建立了与GRAPES预报模式的垂直坐标和预报变量一致的模式面集合卡尔曼滤波系统;集合样本的生成考虑了模式变量的空间相关和模式变量之间的相关,通过利用三维变分分析中的控制变量变换得到模式变量扰动场。通过比较GRAPES集合卡尔曼滤波资料同化系统和GRAPES区域三维变分资料同化系统的单点观测资料同化分析结果,对比背景误差相关系数的分布,验证了GRAPES集合卡尔曼滤波系统的正确性。此外,同化区域探空观测资料试验结果表明,GRAPES集合卡尔曼滤波资料同化系统能够得到合理的分析,并且具有实际运行能力。对分析结果进行12h预报表明,GRAPES集合卡尔曼滤波资料同化系统的分析协调性不如三维变分资料同化系统。     

涡旋发展和移动的动力和热力问题Ⅰ:PV-Q观点

基于从三维埃尔特尔位涡（PV_e）方程推导出的垂直涡度的拉格朗日变化方程,从位涡和非绝热加热（PV-Q）的观点研究涡旋的发展和移动,阐明了涡旋中非均匀的非绝热加热在垂直和水平方向的非对称分布对涡旋发展和移动的影响。应用得到的理论结果分析了2008年7月下旬一次青藏高原低涡的发展和移动过程,该低涡形成于青藏高原中西部,东移滑山青藏高原然后继续东移,给四川盆地和长江中下游带来强降水。低涡的垂直涡度发展可分解成由非绝热加热、位涡水平分量（PV₂）和静力稳定度（θ_z）变化引起的3个部分。结果表明,在大多数情形下,非绝热加热对垂直涡度发展起着主导作用;其次是位涡水平分量（PV₂）变化的作用;当稳定大气变得更稳定时θ_z变化起负作用,当大气趋向中性层结时θ_z变化则起正作用。2008年7月22日06—12时（世界时）,当青藏高原低涡沿着四川盆地东北边的斜坡爬升时,低涡加强主要是由位于涡旋东边的强降水凝结潜热加热引起的。非绝热加热的垂直梯度在非绝热加热的最大中心的下（上）层产生正（负）PV_c制造,正的PV_e制造不仅加强低层涡旋的发展,而且,增强涡旋的垂直范围。非绝热加热的水平梯度对位涡变化的影响取决于加热中心处的水平风的垂直切变,其在该水平风的垂直切变的右（左）边产生了正（负）的PV_e制造。水平风的垂直切变的右边的正PV_e制造不仅加强了该处的垂直涡度,而且,影响着低涡的移动方向。这些诊断结果证实了PV-Q观点的理论结果。     

Atmospheric radiative equilibria. Part II: bimodal solutions for atmospheric optical properties

 A simple theoretical model of atmospheric radiative equilibrium is solved analytically to help understand the energetics of maintaining Earth's tropical and subtropical climate. The model climate is constrained by energy balance between shortwave (SW) and longwave (LW) radiative fluxes. Given a complete set of SW and LW optical properties in each atmospheric layer, the model yields a unique equilibrium-temperature profile. In contrast, if the atmospheric temperature profile and SW properties are prescribed, the model yields essentially two distinct LW transmissivity profiles. This bimodality is due to a nonlinear competition between the ascending and descending energy fluxes, as well as to their local conversion to sensible heat in the atmosphere. Idealized slab models that are often used to describe the greenhouse effect are shown to be a special case of our model when this nonlinearity is suppressed. In this special case, only one solution for LW transmissivity is possible. Our model's bimodality in LW transmissivity for given SW fluxes and temperature profile may help explain certain features of Earth's climate: at low latitudes the temperature profiles are fairly homogeneous, while the humidity profiles exhibit a bimodal distribution; one mode is associated with regions of moist-and-ascending, the other with dry-and-subsiding air. The model's analytical results show good agreement with the European Centre for Medium-Range Weather Forecasts' reanalysis data. Sensitivity analysis of the temperature profile with respect to LW transmissivity changes leads to an assessment of the low-latitude climate's sensitivity to the “runaway greenhouse” effect. Received: 7 December 1999 / Accepted: 19 February 2001     

Scientific uncertainty and climate change: Part II. Uncertainty and mitigation

In public debate surrounding climate change, scientific uncertainty is often cited in connection with arguments against mitigative action. This article examines the role of uncertainty about future climate change in determining the likely success or failure of mitigative action. We show by Monte Carlo simulation that greater uncertainty translates into a greater likelihood that mitigation efforts will fail to limit global warming to a target (e.g., 2 °C). The effect of uncertainty can be reduced by limiting greenhouse gas emissions. Taken together with the fact that greater uncertainty also increases the potential damages arising from unabated emissions (Lewandowsky et al. 2014), any appeal to uncertainty implies a stronger, rather than weaker, need to cut greenhouse gas emissions than in the absence of uncertainty.     

North African climate variability. Part 2: Tropical circulation systems

Summary Tropical North African climate variability is investigated using a Sahel rainfall index and streamflow of the Nile River in the 20^th century. The mechanisms that govern tropical North Africa climate are diagnosed from NCEP reanalysis data in the period 1958–1998: spatially – using composite and correlation analysis, and temporally – using wavelet co-spectral analysis. The Sahelian climate is characterised by a decadal rhythm, whilst the mountainous eastern and equatorial regions exhibit interannual cycles. ENSO-modulated zonal circulations over the Atlantic/Pacific sector are important for decadal variations, and create a climatic polarity between South America and tropical North Africa as revealed through upper-level velocity potential and convection patterns. A more localised N–S shift in convection between the Sahel and Guinea coast is associated with the African Easterly Jet.     

辅助模型辨识方法(1):自回归输出误差系统

研究了自回归输出误差(AR-OE)系统的辅助模型随机梯度算法、辅助模型多新息随机梯度算法、辅助模型递推最小二乘算法,自回归输出误差自回归滑动平均(AR-OEARMA)系统(即AR-Box-Jenkins系统)的辅助模型广义增广随机梯度算法、辅助模型多新息广义增广随机梯度算法、辅助模型递推广义增广最小二乘算法,以及AR-Box-Jenkins系统的基于滤波的辅助模型广义增广随机梯度算法、基于滤波的辅助模型多新息广义增广随机梯度算法、基于滤波的辅助模型递推广义增广最小二乘算法等.     

“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10 mm和２５ mm降水的TS平均评分分别为0.41和0.32。     

An Updated Coupled Model for Land-Atmosphere Interaction. Part II： Simulations of Biological Processes

In Part I, the authors succeeded in coupling the spectral atmospheric model （SAMIL_R42L9） developed at the State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics, Institute of Atmospheric Physics, Chinese Academy of Sciences （LASG/IAP/CAS） with the land surface model, Atmosphere-Vegetation-Interaction-Model （AVIM） and analyzed the climate basic state and land surface physical fluxes simulated by R42_AVIM. In this Part Ⅱ, we further evaluate the simulated results of the biological processes, including leaf area index （LAI）, biomass and net primary productivity （NPP） etc. Results indicate that R42_AVIM can simulate the global distribution of LAI and has good consistency with the monthly mean LAI provided by Max Planck Institute for Meteorology. The simulated biomass corresponds reasonably to the vegetation classifications. In addition, the simulated annual mean NPP has a consistent distribution with the data provided by IGBP and MODIS, and compares well with the work in literature. This land-atmosphere coupled model will offer a new experiment tool for the research on the two-way interaction between climate and biosphere, and the global terrestrial ecosystem carbon cycle.     

Monthly Extended Predicting Experiments with Nonlinear Regional Prediction. Part I: Prediction of Zonal Mean Flow

Systematic errors have recently been founded to be distinct in the zonal mean component forecasts,which account for a large portion of the total monthly-mean forecast errors. To overcome the difficulty of numerical model, the monthly pentad-mean nonlinear dynamic regional prediction models of the zonal mean geopotential height at 200, 300, 500, and 700 hPa based on a large number of historical data (NCEP/NCAR reanalysis data) were constituted by employing the local approximation of the phase space reconstruction theory and nonlinear spatio-temporal series prediction method. The 12-month forecast experiments of 1996 indicated that the results of the nonlinear model are better than those of the persistent, climatic prediction,and T42L9 model either over the high- and mid-latitude areas of the Northern and Southern Hemispheres or the tropical area. The root-mean-square of the monthly-mean height of T42L9 model was considerably decreased with a change of 30.4%, 26.6%, 82.6%, and 39.4%, respectively, over the high- and mid-latitudes of the Northern Hemisphere, over the high- and mid-latitudes of the Southern Hemisphere, over the tropics and over the globe, and also the corresponding anomaly correlation coe cients over the four areas were respectively increased by 0.306-0.312, 0.304-0.429, 0.739-0.746, and 0.360-0.400 (averagely a relative change of 11.0% over the globe) by nonlinear correction after integration, implying that the forecasts given by nonlinear model include more useful information than those of T42L9 model.     

辅助模型辨识方法(2):输入非线性输出误差系统

针对具有已知基的输入非线性输出误差系统,提出了基于过参数化模型的辅助模型递推辨识方法和辅助模型递阶辨识方法,提出了基于关键项分离的辅助模型递推辨识方法、基于关键项分离的辅助模型两阶段辨识方法和辅助模型三阶段辨识方法,提出了基于双线性参数模型分解的辅助模型随机梯度算法和基于双线性参数模型分解的辅助模型递推最小二乘算法,并给出了几个典型辨识算法的计算量、计算步骤.这些算法的收敛性分析都是需要研究的辨识课题.