Baroclinic Instability in the Generalized Phillips’ Model Part II: Three-layer Model

The nonlinear stability of the three-layer generalized Phillips model, for which the velocity in each layer is constant and the top and bottom surfaces are either rigid or free, is studied by employing Arnol’d’s variational principle and a prior estimate method. The nonlinear stability criteria are established. For com-parison, the linear instability criteria are also obtained by using normal mode method, and the influences of the free parameter, β parameter and curvature in vertical profile of the horizontal velocity on the linear in-stability are discussed by use of the growth rate curves.The comparison between the nonlinear stability criterion and the linear one is made. It is shown that in some cases the two criteria are exactly the same in form, but in other cases, they are different. This phenom-enon, which reveals the nonlinear property of the linear instability features, is explained by the explosive resonant interaction (ERI). When there exists the ERI, i.e., the nonlinear mechanisms play a leading role in the dynamical system, the nonlinear stability criterion is different from the linear one; on the other hand, when there does not exist the ERI, the nonlinear stability criterion is the same as the linear one in form.     

Baroclinic Instability in the Generalized Phillips’ Model Part I: Two-layer Model

By employing Arnol’d’s method (energy-Casimir), this paper has studied the nonlinear stability of the two-layer generalized Phillips’ model for which the top and bottom surfaces are either rigid or free, and obtained some nonlinear stability criteria. In addition, some linear stability criteria are obtained by normal mode method. The re-sults reveal the influences of the free surface parameter on the stability of atmospheric and oceanic motions     

Charney's Model—the Renowned Prototype of Baroclinic Instability—Is Barotropically Unstable As Well

The Charney model is reexamined using a new mathematical tool, the multiscale window transform(MWT), and the MWT-based localized multiscale energetics analysis developed by Liang and Robinson to deal with realistic geophysical fluid flow processes. Traditionally, though this model has been taken as a prototype of baroclinic instability, it actually undergoes a mixed one. While baroclinic instability explains the bottom-trapped feature of the perturbation, the second extreme center in the perturbation field can only be explained by a new barotropic instability when the Charney–Green number γ 1, which takes place throughout the fluid column, and is maximized at a height where its baroclinic counterpart stops functioning.The giving way of the baroclinic instability to a barotropic one at this height corresponds well to the rectification of the tilting found on the maps of perturbation velocity and pressure. Also established in this study is the relative importance of barotropic instability to baroclinic instability in terms of γ. When γ 1, barotropic instability is negligible and hence the system can be viewed as purely baroclinic; when γ 1, however, barotropic and baroclinic instabilities are of the same order;in fact, barotropic instability can be even stronger. The implication of these results has been discussed in linking them to real atmospheric processes.     

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.     

Study on Instability in Baroclinic Vortex Symmetric Disturbance under Effect of Nonuniform Environmental Parameters

With the aid of the baroclinicity parameter M2,inertial instability parameter F2 and the stratification instability paramter N2 as the slowly varying function both spatially and temporally,an energetic equation is derived of symmetric perturbation waves in baroclinic vortices in the framework of progressively changing wavetrain theory,or WKB,alongside the examination of effects of these parameters upon the vortex disturbance.     

Parameterization of Sheared Entrainment in a Well-developed CBL.Part Ⅱ:A Simple Model for Predicting the Growth Rate of the CBL

Following the parameterization of sheared entrainment obtained in the companion paper, Liu et al. (2016), the present study aims to further investigate the characteristics of entrainment, and develop a simple model for predicting the growth rate of a well-developed and sheared CBL. The relative stratification, defined as the ratio of the stratification in the free atmosphere to that in the entrainment zone, is found to be a function of entrainment flux ratio (A _e). This leads to a simple expression of the entrainment rate, in which A _e needs to be parameterized. According to the results in Liu et al. (2016), A _e can be simply expressed as the ratio of the convective velocity scale in the sheared CBL to that in the shear-free CBL. The parameterization of the convective velocity scale in the sheared CBL is obtained by analytically solving the bulk model with several assumptions and approximations. Results indicate that the entrainment process is influenced by the dynamic effect, the interaction between mean shear and environmental stratification, and one other term that includes the Coriolis effect. These three parameterizations constitute a simple model for predicting the growth rate of a well-developed and sheared CBL. This model is validated by outputs of LESs, and the results show that it performs satisfactorily. Compared with bulk models, this model does not need to solve a set of equations for the CBL. It is more convenient to apply in numerical models.     

Application of Radar Reflectivity Factor in Initializing Cloud-Resolving Mesoscale Model. Part Ⅱ: Numerical Simulation Experiments

Microphysics elements and vertical velocity retrieved were incorporated using the nudging method into the initial data assimilation of GRAPES (Global/Regional Assimilation and Prediction System) model.Simulation experiments indicated that nudging technique was effective in forcing the model forecast gradually consistent to the observations, yielding the thermodynamically and dynamically balanced analysis field. As viewed from the simulation results, water vapor is vital to precipitation, and it is a governing factor for the amount and duration of precipitation. The initial cloud water, rain water, and vertical velocity determine the strength distribution of convection and precipitation at the beginning time of forecast; the horizontal wind field steers the motion of the mesoscale weather system embedded in and impacts the position of precipitation zone to a large extent. The simulation experiments show that the influence of the initial retrieval data on prediction weakens with the increase of forecast time, and within the first hour of forecast, the retrieval data have an important impact on the evolution of the weather system, but its influence becomes trivial after the first three hours. Changing the nudging coefficient and the integral time-spacing of numerical model will bring some influences to the results. Herein only one radar reflectivity was used, the radar observations did not cover the whole model domain, and some empirical parameters were used in the retrieval method, therefore some differences still lie between simulation and observation to a certain extent, and further studies on several aspects are expected.     

An Online Model Correction Method Based on an Inverse Problem:PartⅡ——Systematic Model Error Correction

An online systematic error correction is presented and examined as a technique to improve the accuracy of real-time numerical weather prediction, based on the dataset of model errors(MEs) in past intervals. Given the analyses, the ME in each interval(6 h) between two analyses can be iteratively obtained by introducing an unknown tendency term into the prediction equation, shown in Part I of this two-paper series. In this part, after analyzing the 5-year(2001–2005) GRAPESGFS(Global Forecast System of the Global and Regional Assimilation and Prediction System) error patterns and evolution,a systematic model error correction is given based on the least-squares approach by firstly using the past MEs. To test the correction, we applied the approach in GRAPES-GFS for July 2009 and January 2010. The datasets associated with the initial condition and SST used in this study were based on NCEP(National Centers for Environmental Prediction) FNL(final) data.The results indicated that the Northern Hemispheric systematically underestimated equator-to-pole geopotential gradient and westerly wind of GRAPES-GFS were largely enhanced, and the biases of temperature and wind in the tropics were strongly reduced. Therefore, the correction results in a more skillful forecast with lower mean bias and root-mean-square error and higher anomaly correlation coefficient.     

Some Aspects of the Characteristics of Monsoon Disturbances Using a Combined Barotropic－Baroclinic Model

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The Role of Land-sea Distribution and Orography in the Asian Monsoon. Part Ⅱ:Orography

The role of various mountains in the Asian monsoon system is investigated by AGCM simulations with different mountains.The comparison of the simulation with Asian mountains(MAsia run)with the simulation without mountains(NM run)reveals that the presence of the Asian mountains results in a stronger South Asian summer monsoon(SASM),characterized by enhanced lower-tropospheric westerly winds,uppertropospheric easterly winds,and stronger water vapor convergence.In East Asia,the southerly winds and water vapor convergence are significantly strengthened in association with the intensified zonal pressure gradient between the East Asian continent and the Pacific Ocean.Both the dynamical and thermodynamic forcing of the Tibetan Plateau play important role in strengthening the Asian summer monsoon.In winter,the presence of Asian mountains significantly strengthens the continental high,which leads to a stronger Asian winter monsoon.The presence of African-Arabian mountains helps to intensify the exchange of mass between the Southern Hemisphere and Northern Hemisphere by strengthening the cross equatorial flows in the lower and upper troposphere over East Africa. Asian mountains also play a crucial role in the seasonal evolution of Asian monsoons.In comparison with the NM run,the earlier onset and later withdrawal of lower-tropospheric westerly winds can be found over South Asia in the MAsia run,indicating a longer SASM period.The African-Arabian mountains also moderately contribute to the seasonal variation of the South Asian monsoon.In East Asia,the clear southto-north march of the southerly winds and subtropical rainfall starts to occur in early summer when the effects of Asian mountains are considered.     

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.     

Application of Radar Reflectivity Factor in Initializing Cloud-Resolving Mesoscale Model. Part Ⅱ： Numerical Simulation Experiments

Microphysics elements and vertical velocity retrieved were incorporated using the nudging method into the initial data assimilation of GRAPES （Global/Regional Assimilation and Prediction System） model. Simulation experiments indicated that nudging technique was effective in forcing the model forecast gradually consistent to the observations, yielding the thermodynamically and dynamically balanced analysis field. As viewed from the simulation results, water vapor is vital to precipitation, and it is a governing factor for the amount and duration of precipitation. The initial cloud water, rain water, and vertical velocity determine the strength distribution of convection and precipitation at the beginning time of forecast; the horizontal wind field steers the motion of the mesoscale weather system embedded in and impacts the position of precipitation zone to a large extent. The simulation experiments show that the influence of the initial retrieval data on prediction weakens with the increase of forecast time, and within the first hour of forecast, the retrieval data have an important impact on the evolution of the weather system, but its influence becomes trivial after the first three hours. Changing the nudging coefficient and the integral time-spacing of numerical model will bring some influences to the results. Herein only one radar reflectivity was used, the radar observations did not cover the whole model domain, and some empirical parameters were used in the retrieval method, therefore some differences still lie between simulation and observation to a certain extent, and further studies on several aspects are expected.     

Application of Linear Thermodynamics to the Atmospheric System.Part Ⅱ: Exemplification of Linear Phenomenological Relations in the Atmospheric System

将边界层相似性理论同线性热力学理论结合，间接地以观测实验事实证明大气边界层内线性唯象关系是成立的，而且线性湍流输送系数同相应的线性唯象系数成正比关系。但实验事实表明，大涡对流的混合层线性唯象系数成正比关系。但实验事实表明，大涡对流的混合层线性唯象关系是不成立的，混合层内湍流输送过程是一种强的非线性过程。所以，对流边界层是一种远离平衡态非线性区的热力学状态。地转风和热成风是一种大气系统特有的动力过程和热力过程和交叉耦合现象，这是大气系统交叉耦合现象的一个实际例证。     

On the Unified Theory of Atmospheric Particle Systems Part Ⅱ:Self-affine Particles

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Planetary Stationary Waves in the Atmosphere Part II: Thermal Stationary Waves

The contribution of thermal forcing to the planetary stationary waves will be studied also by assuming that heat balance in stationary waves over zonally asymmetric thermal forcing must be maintained over a long time period. Using the same model of geostrophic waves introduced in Part I, we may explain successfully the observed and simulated responses to the thermal forcing in the atmosphere, such as the wave 1 structure at high levels of middle latitudes, the seasonal changes of the stationary waves in the Northern Hemisphere, the opposite phase distributions of stationary waves at high and low levels of the subtropical regions in both hemispheres and so on.     

The Role of the Halted Baroclinic Mode at the Central Equatorial Pacific in E1 Nifio Event

The role of halted “baroclinic modes” in the central equatorial Pacific is analyzed. It is found that dominant anomaly signals corresponding to “baroclinic modes” occur in the upper layer of the equatorial Pacific, in a two-and-a-half layer oceanic model, in assimilated results of a simple OGCM and in the ADCP observation of TAO. A second “baroclinic mode” is halted in the central equatorial Pacific corresponding to a positive SST anomaly while the first “baroclinic mode” propagates eastwards in the eastern equatorial Pacific. The role of the halted second “baroclinic mode” in the central equatorial Pacific is explained by a staged ocean-atmosphere interaction mechanism in the formation of El Ni?no: the westerly bursts in boreal winter over the western equatorial Pacific generate the halted second “baroclinic mode” in the central equatorial Pacific, leading to the increase of heat content and temperature in the upper layer of the central Pacific which induces the shift of convection from over the western equatorial Pacific to the central equatorial Pacific; another wider, westerly anomaly burst is induced over the western region of convection above the central equatorial Pacific and the westerly anomaly burst generates the first “baroclinic mode” propagating to the eastern equatorial Pacific, resulting in a warm event in the eastern equatorial Pacific. The mechanism presented in this paper reveals that the central equatorial Pacific is a key region in detecting the possibility of ENSO and, by analyzing TAO observation data of ocean currents and temperature in the central equatorial Pacific, in predicting the coming of an El Ni?no several months ahead.     

Planetary Stationary Waves in the Atmosphere Part I: Orographic Stationary Waves

It is proposed that the orographic stationary waves are required by long-term balance of momentum in the atmosphere with zonally asymmetric orographic forcing. This hypothesis may be confirmed successfully with the theoretical model of geostrophic waves. In the Part I, we will explain the observed phase distributions of orographic stationary waves at middle and high latitudes of the Northern Hemisphere, according to the long-term balance of zonal momentum over the stationary orographic forcing. It is revealed that the geographic distribution of stationary waves depends not only on local topgraphy but also on mean circulation fields and angular momentum flux in the atmosphere. So these waves cannot be simulated by the models in a restricted area.     

Topographically Forced Rossby Wave Instability and the Development of Blocking in the Atmosphere

In this paper, the linear stability of disturbance superimposed on basic state Rossby wave forced by topography is investigated, and pointed out that when a certain criterion is satisfied by the basic flow and the height of topography for the subresonance, the small disturbance may be unstable. Furthermore, we also compare the evolution of the instability disturbance with the development of blocking in the Pacific, and we suggested that the topographically forced Rossby wave instability may provide a possible mechanism for the development of blocking in the Pacific.