Adjoint sensitivity study on idealized explosive cyclogenesis

The adjoint sensitivity related to explosive cyclogenesis in a conditionally unstable atmosphere is investigated in this study.The PSU/NCAR limited-area,nonhydrostatic primitive equation numerical model MM5 and its adjoint system are employed for numerical simulation and adjoint computation,respectively.To ensure the explosive development of a baroclinic wave,the forecast model is initialized with an idealized condition including an idealized two-dimensional baroclinic jet with a balanced three-dimensional moderateamplitude disturbance,derived from a potential vorticity inversion technique.Firstly,the validity period of the tangent linear model for this idealized baroclinic wave case is discussed,considering different initial moisture distributions and a dry condition.Secondly,the 48-h forecast surface pressure center and the vertical component of the relative vorticity of the cyclone are selected as the response functions for adjoint computation in a dry and moist environment,respectively.The preliminary results show that the validity of the tangent linear assumption for this idealized baroclinic wave case can extend to 48 h with intense moist convection,and the validity period can last even longer in the dry adjoint integration.Adjoint sensitivity analysis indicates that the rapid development of the idealized baroclinic wave is sensitive to the initial wind and temperature perturbations around the steering level in the upstream.Moreover,the moist adjoint sensitivity can capture a secondary high sensitivity center in the upper troposphere,which cannot be depicted in the dry adjoint run.     

登陆台风莫拉克(2009)的涡度拟能收支分析

利用涡度拟能、散度平方项(简记为散度能量)和总变形平方项(简记为变形能量)来表征涡度、散度和变形的强度,并推导这3个物理量的倾向方程。这些方程中既包含代表这些物理量相互转化的符号相反项,也含有代表共同强迫的符号相同项,其中,涡度拟能局地变化主要由涡度拟能与变形能量的共同强迫项、涡度拟能与变形能量的转化项以及涡度拟能与散度能量的转化项组成。针对2009年第8号台风莫拉克,利用美国全球预报系统分析场资料计算这些方程中的强迫项,分析涡度拟能及其收支特征,以此来探讨影响台风莫拉克涡度拟能局地变化的主要物理因素。结果表明,在莫拉克发展和衰减阶段,涡度拟能与变形能量的共同强迫项(涡-形相同项)和涡度拟能与散度能量的转化项(涡-散转化项)是影响涡度拟能局地变化的重要强迫项。涡度拟能与变形能量转化项(涡-形转化项)的贡献相对来说弱一些。影响位涡拟能局地变化的重要物理因素是涡-形相同项和涡-形转化项中的平流输送项和散度耦合项,以及涡-散转化项中散度耦合项。变形能量一方面通过涡-形转化项向涡度拟能转化,直接促进涡度拟能增长;另一方面通过散-形转化项向散度能量转化,再通过涡-散转化项散度能量向涡度拟能转化,间接促进涡度拟能增长。     

Adjoint Sensitivity Experiments of a Meso-β-scale Vortex in the Middle Reaches of the Yangtze River

A relatively independent and small-scale heavy rainfall event occurred to the south of a slow eastwardmoving meso-α-scale vortex. The analysis shows that a meso-β-scale system is heavily responsible for the intense precipitation. An attempt to simulate it met with some failures. In view of its small scale, short lifetime and relatively sparse observations at the initial time, an adjoint model was used to examine the sensitivity of the meso-β-scale vortex simulation with respect to initial conditions. The adjoint sensitivity indicates how small perturbations of initial model variables anywhere in the model domain can influence the central vorticity of the vortex. The largest sensitivity for both the wind and temperature perturbation is located below 700 hPa, especially at the low level. The largest sensitivity for the water vapor perturbation is located below 500 hPa, especially at the middle and low levels. The horizontal adjoint sensitivity for all variables is mainly located toward the upper reaches of the Yangtze River with respect to the simulated meso-β-scale system in Hunan and Jiangxi provinces with strong locality. The sensitivity shows that warm cyclonic perturbations in the upper reaches can have a great effect on the development of the meso-β-scale vortex. Based on adjoint sensitivity, forward sensitivity experiments were conducted to identify factors influencing the development of the meso-β-scale vortex and to explore ways of improving the prediction. A realistic prediction was achieved by using adjoint sensitivity to modify the initial conditions and implanting a warm cyclone at the initial time in the upper reaches of the river with respect to the meso-β-scale vortex, as is commonly done in tropical cyclone prediction.     

Sources of CAM3 vorticity bias during northern winter from diagnostic study of the vorticity equation

CAM3 (Community Atmosphere Model version 3) simulation bias is diagnosed using the vorticity equation. The study compares CAM3 output with ECMWF (European Centre for Medium-Range Weather Forecasts) 40?year reanalysis (ERA-40) data. A time mean vorticity bias equation is also formulated and the terms are grouped into categories: linear terms, nonlinear terms, transient contributions, and friction (calculated as a residual). Frontal cyclone storms have much weaker band passed kinetic energy and enstrophy in CAM3. The downstream end of the North Atlantic storm track (NAST) has large location error. While the vorticity equation terms have similar amplitude ranking in CAM3 and ERA-40 at upper levels, the ranking differs notably in the lower troposphere. The linear and friction terms dominate the vorticity bias equation. The transient terms contribute along the storm track, but the nonlinear terms are generally much smaller, with the primary exception being over the Iberian peninsula. Friction is much stronger in CAM3. As evidence, nearly all wavelengths (including the longest planetary waves) have smaller amplitude in CAM3 than in ERA-40 vorticity data. Negative near surface vorticity tendency bias on the European side of the Arctic is linked to the NAST track error (evident in the divergence term). CAM3 misses the Beaufort high in sea level pressure (SLP) due to low level warm temperature bias, too little vortex compression, and to too little horizontal advection of negative vorticity compared with ERA-40. Generally lower SLP values in CAM3 over the entire Arctic follow from lower level warm bias in CAM3.     

东北低压爆发性发展过程的诊断分析

本文对一次东北低压的快速强烈发展过程做了扰动动能、扰动有效位能及涡度收支平衡分析。结果表明:1.气旋爆发性发展前后,扰动动能的产生项变化剧烈,是主要的扰动动能源。气旋爆发性发展前期,以斜压过程为主,而在爆发期,由正压过程制造的扰动动能也有大量增加,同样是不可忽视的,且这时扰动动能通过系统边界与外界的交换很小。2.扰动有效位能在气旋强烈发展前有大幅度增长,由潜热释放造成的扰动有效位能的产生数值很小,平均有效位能向扰动有效位能的转换是扰动有效位能的主要来源。3.在气旋的爆发期,对流层中层及上层的涡度变化最为显著,涡度平衡中,散度项对对流层中下层正涡度的增长贡献最大,而网格尺度及次网格尺度的垂直输送项和涡度平流项对中上层正涡度的迅速增加有着重要意义。     

EFFECT OF THE NONLINEAR TERM ON MOVEMENT AND DEVELOPMENT OF TROPICAL CYCLONE

The dynamics of tropical cyclone is investigated in a nondivergent barotropic model with nobasic flow. The effect of nonlinear term on the movement and development of tropical cyclone isemphatically demonstrated. The advection of asymmetric vorticity by the symmetric flow (AAVS)produces the small-scale gyres (SSGs). The SSGs counterclockwise rotate around the tropicalcyclone center. The interaction of SSGs with the large-scale beta gyres (LSBGs) leads to theoscillation in translation speed and vacillation in translation direction for tropical cyclone. Theadvection of symmetric vorticity by the asymmetric flow (ASVA) steers the symmetric circulationof tropical cyclone. The ventilation flow vector determined by the asymmetric flow is closecorrelated with the motion vector of tropical cyclone. The nonlinear advection of relative vorticityis an order of magnitude greater than the linear advection of planetary vorticity, However, theasymmetric circulation created by the planetary vorticity advection provides a background conditionfor anomalous motions of the tropical cyclone. The combination of the linear and nonlinear effectsresults in accelerated, decelerated, changing direction and/or counterclockwise looping motions ofthe tropical cyclone.     

非绝热加热对热带气旋非对称结构影响的数值试验

利用含非绝热加热强迫的正压涡度方程。将非绝热加热作适当的参数化处理。对初始对称 热带气旋作了一系列数值试验,结果表明：不仅β项、平流项在热带气旋非对称结构的形成中有重要作用,而且非绝热加热对热带气旋的非对称结构亦有重要影响,从而验证了非绝热加热是热带气旋非对称结构形成的一种可能机制的结论。     

POTENTIAL VORTICITY STRUCTURE OF SUMMER CYCLONES OVER THE CHANGJIANG-HUAIHE VALLEY

Based on the theory of Ertel potential vorticity,the isentropic potential vorticity maps and vertical pro-files of potential vorticity for two summer cyclones over the Changjiang-Huaihe Valley are analysed.Afterdiscussing a possible mechanism for the genesis and development of such systems and their differences fromtypical extratropical cyclones,a conceptual model for their activities is proposed:A weak disturbance in the mid-level of troposphere originated from around the Qinghai-Xizang Plateau may cause heavy precipitation underfavourable conditions and latent heat release in the mid-troposphere leads to downward extension of cycloniccirculation and a wave on the quasi-stationary front.This weak cyclone can develop substantially and becomea typical extratropical cyclone only when air from the lower stratosphere flows downslope along isentropic sur-faces into the region of interest.     

一般多层准地转基本流的扰动发展 与非线性稳定性

考察了一般多层准地转模式中初值与参数共同扰动的情形。在初始扰动场仅依赖于初始扰动位势涡度、初始扰动边界速度环量与扰动参数的条件下,给出了扰动能量、扰动位涡拟能发展上（下）界精细的显式估计。进而在Lyapunov意义下广义非线性稳定性概念的基础上,得到了对应于Arnold 第二定理的非线性稳定性判据。本文工作推广了仅考虑模式中初值扰动情形所得到的相应结果。     

EFFECT OF THE NONLINEAR TERM ON MOVEMENT AND DEVELOPMENT OF TROPICAL CYCLONE*

The dynamics of tropical cyclone is investigated in a nondivergent barotropic model with no basic flow. The effect of nonlinear term on the movement and development of tropical cyclone is emphatically demonstrated. The advection of asymmetric vorticity by the symmetric flow(AAVS) produces the small-scale gyres(SSGs). The SSGs counterclockwise rotate around the tropical cyclone center. The interaction of SSGs with the large-scale beta gyres(LSBGs) leads to the oscillation in translation speed and vacillation in translation direction for tropical cyclone. The advection of symmetric vorticity by the asymmetric flow(ASVA) steers the symmetric circulation of tropical cyclone. The ventilation flow vector determined by the asymmetric flow is close correlated with the motion vector of tropical cyclone. The nonlinear advection of relative vorticity is an order of magnitude greater than the linear advection of planetary vorticity, However, the asymmetric circulation created by the planetary vorticity advection provides a background condition for anomalous motions of the tropical cyclone. The combination of the linear and nonlinear effects results in accelerated, decelerated, changing direction and/or counterclockwise looping motions of the tropical cyclone.     

NONLINEAR BAROTROPIC INSTABILITY INCLUDING FRICTION DISSIPATION,THERMAL DRIVING AND LARGE TOPOGRAPHY*

From a nonlinear quasi-geostrophic barotropic vorticity equation including frictional dissipation,thermal driving and large topography used by Charney in investigation of the multiple flow equilibria and blocking,using the Serrin-Joseph energy method and the variational principle,we found the nonlinear barotropic stability criteria of the zonal basic flow with the total energy,total enstrophy and their linear combination respectively,and compared the criteria with Charney's results.     

鄂霍茨克海阻高发展过程的正斜压涡度和涡度拟能的演变特征

用正斜压分解法，对1998年发生在鄂霍茨克海的阻高进行涡度和涡度拟以分析，结果发现：在阻高的不同阶段，正压涡度和正压涡度拟能远大于斜压涡度和斜压涡度拟能且在不同的阶段有着不同的演变过程；在阻塞的酝酿阶段正压和斜压涡度和涡度拟能不稳定增长，且向西南传播；在维持阶段，正压和斜压涡度和涡度拟能的增长达到最大值，阻塞形势建立并维持在阻塞区域内；在消亡阶段，正压涡度和涡度拟能与斜压涡度拟能则呈现出不稳定减少，向东南传播，阻塞崩溃，然后又增长。     

Sensitivity of tropical cyclone intensification to inner-core structure

In this study, the dependence of tropical cyclone (TC) development on the inner-core structure of the parent vortex is examined using a pair of idealized numerical simulations. It is found that the radial profile of inner-core relative vorticity may have a great impact on its subsequent development. For a system with a larger inner-core relative vorticity/inertial stability, the conversion ratio of the diabatic heating to kinetic energy is greater. Furthermore, the behavior of the convective vorticity eddies is likely modulated by the system-scale circulation. For a parent vortex with a relatively higher inner-core vorticity and larger negative radial vorticity gradient, convective eddy formation and radially inward propagation is promoted through vorticity segregation. This provides a greater potential for these small-scale convective cells to self-organize into a mesoscale inner-core structure in the TC. In turn, convectively induced diabatic heating that is close to the center, along with higher inertial stability, efficiently enhances system-scale secondary circulation. This study provides a solid basis for further research into how the initial structure of a TC influences storm dynamics and thermodynamics.     

广义涡度与位势涡度守恒定律及其应用

在文中推得了广义涡度守恒定律,并利用此定律在一般情况下求得了广义位势涡度定律。它放宽了最初Ertel的位势涡度定律的限制条件。并对涡度拟能、螺旋性守恒定律的物理意义作了讨论,这些定律能够描述大气运动的重要动力学性质。     

一次引发强沙尘天气的快速发展蒙古气旋的诊断分析

利用NCEP分析资料和常规气象观测资料对造成2006年3月9-10日华北大范围强沙尘天气,产生大风的蒙古气旋快速发展过程进行了分析。结果表明：气旋发展前期,高层反气旋性流场对波能量发展有正的贡献,有利于气旋的爆发性发展。在气旋发展过程中,温度平流和涡度平流均为气旋发展的主要因子,但涡度平流在气旋发展初期相对温度平流较弱。斜压作用出现在低层,并随着气旋后部的锋消作用以及前部的锋生而显著增强,这对于有效位能的释放、动能的产生以及气旋的发展有重要作用,同时,斜压强迫能够诱发出强烈的非地转风。此外,位涡分析表明,气旋的发展与冷空气活动的关系比较密切,并且存在明显的高低空系统之间的相互作用,而水汽和潜热释放产生的作用不明显。同时揭示出该气旋发生发展机制不但与挪威学派的温带气旋模型有较大差别,而且与Petterssen总结的A、B类气旋、引起我国夏半年降水的江淮气旋和西南涡等低压系统亦不相同。     

Study of initial vorticity forcing for block onset by a 4-dimensional variational approach

With the aid of a global barotropic model, the role of the interaction of the synoptic-scale disturbance and the planetary flow in block onset is examined by a 4-dimensional variational approach. A cost function is defined to measure the squared errors of the forecasted stream functions during block onset period (day 4 and day 5 in this study) over a selected blocking domain. The sensitivity of block onset with respect to the initial synoptic-scale disturbance is studied by examining the gradient of the defined cost function with respect to the initial (during the first 24 hours) vorticity forcing, which is evaluated by the adjoint integration. Furthermore, the calculated cost function and gradient are connected with the limited-memory quasi-Newton optimization algorithm for solving the optimal initial vorticity forcing for block onset. For two studied cases of block onset (northern Atlantic and northern Pacific) introducing the optimal initial vorticity forcing, the nonlinear barotropic advection process mostly reconstructs these blocking onset processes. The results show that the formation of blocking can be correctly described by a barotropic nonlinear advection process, in which the wave- (synoptic-scale) flow (planetary-scale) interaction plays a very important role. On an appropriate planetary-scale flow, a certain synoptic-scale disturbance can cause the blocking onset by the interaction between the synoptic scale perturbations and the planetary scale basic flows. The extended forecasts show that the introduction of the optimal initial vorticity forcing can predict the blocking process up to the 7th or 8th day in this simple model case. The experimental results in this study show that the 4-dimensional variational approach has a good potential to be applied to study the dynamics of the medium-range weather processes. This simple model case study is only an initial trial. Applying the framework in this study to a complex model will further our understanding of the mechanism of the atmospheric/oceanic processes and improve their prediction.     

云迹风资料在热带气旋移向预报中的应用

利用云迹风并结合实测风,从涡度方程出发,对１９９８年南海和西太平洋的几个热带气候进行诊断计算。结果反映,涡度局地变率ｅ↓ζ／ｅｔ对热带气旋移动有指示意义,它既可批示热带气旋正常路径,在引导气流不明显的情况下,也能对气旋的转折路径有较明显的反映,气旋常朝涡度局地变率最在的方向移动。当热带气旋周围有数个ｅ↓ζ／ｅｔ中心时写和提交 矢量合成法确定了气旋的最大可能移动方向。此外,玷如引导气流一样,热带气旋     

Hurricanes Ivan, Jeanne, Karl (2004) and mid-latitude trough interactions

Summary Singular vectors (SVs) constructed from the adjoint model of the U.S. Naval Operational Global Atmosphere Prediction System (NOGAPS) for three Atlantic hurricanes in 2004, Ivan, Jeanne and Karl, are examined to understand interactions between them and a mid-latitude trough system. By optimizing the perturbation energy localized in a small region centered at the 48-hour projected position of a tropical cyclone, the initial time singular vector represents the sensitive region to the final state within the specified region for a specified optimization period. For hurricane Ivan, the SV analysis reveals the merging of a shortwave mid-latitude trough and Ivan to form a new trough system. This new trough system impacted the evolution of hurricane Jeanne in subsequent time through the upstream flow of the trough that moved toward Jeanne. This is consistent with previous studies on the sensitivity of tropical cyclone prediction using SV diagnostics. The SV associated with Jeanne at later stage shows that Jeanne influenced the third hurricane Karl through the trough system as Karl went through extratropical transition and became part of the trough. This effect is magnified when the SV is computed using the moist adjoint system containing large scale precipitation. Detailed diagnostics of the SVs for individual components at different levels show that the sensitivity associated with the trough is very similar for those optimized for Jeanne and Karl, respectively, thus providing evidence that the mid-latitude trough impacted Jeanne and Karl at the same time. This study demonstrates the capability of singular vector in diagnosing complicated interactions among a mid-latitude trough and three co-existing tropical cyclones.     

大气中的位涡守恒和Rossby波的能量、波作用与拟能守恒

推导得到普遍形式的位涡度守恒方程，其条件是外源Ｇ和摩擦Ｆ组成的矢量散度为零，放松了位涡守恒的绝热无摩擦限制，对准地转位涡方程，利用ＷＫＢ近似，得到了层结可变情况下的ＲＯｓｓｂｙ波的能量、波作用和拟能守恒的条件，对于空间缓变的基本气流，它们分别是基本气流与空间坐标无关，基本气流与ｘ无关和基本气流是空间坐标的函数。最后还给出了地形存在情况下的Ｒｏｃｓｂｙ波的能量、波作用和拟能守恒的条件。     

Statistical distributions of singular vectors for tropical cyclones affecting Korea over a 10-year period

To investigate the statistical sensitivity distributions of tropical cyclone (TC) forecasts over the Korean Peninsula, total energy (TE) singular vectors (SVs) were calculated and evaluated over a 10-year period. TESVs were calculated using the fifth-generation Pennsylvania State University/National Center for Atmospheric Research Mesoscale Model (MM5) and its tangent linear and adjoint models with a Lanczos algorithm over a 48-h period. Chosen cases were 21 TCs that affected the Korean Peninsula among 230 TCs that were generated in the western North Pacific from 2001 to 2010. Sensitive regions indicated by TESVs were mainly located near mid-latitude troughs and TC centers but varied depending on TC track and environmental conditions such as subtropical high and mid-latitude trough. The cases were classified into three groups by clustering TC tracks based on the finite mixture model. The two groups that passed through the western and southern sea of the Korean Peninsula had maximally sensitive regions in the mid-latitude trough and largely sensitive regions around the TC center, while the other group that passed straight through the eastern sea of the Korean Peninsula had maximally sensitive regions near the northeastern region of the TC center. Vertically, the former two clustered groups had the westerly tilted TESVs and potential vorticity structures under the mid-latitude troughs at the initial time, indicating the TCs were in a baroclinic environment. Conversely, the straight-moving TCs were not in a baroclinic environment. Based on the results in the present study, the TCs moving toward a fixed verification region over the Korean Peninsula have different sensitivity regions and structures according to their moving tracks and characteristic environmental conditions, which may provide guidance for targeted observations of TCs affecting the Korean Peninsula.