PROBLEMS EXISTING IN THE VERTICAL DISCRETIZATION OF THE HYDROSTATIC EQUATION AND IMPROVEMENT TESTS

Through analysis and numerical computation of ECMWF's discrete scheme of hydrostatic equation(Baede et al.1979),it has been found that in the case of equal △σ there exist systematic errors in the scheme.The error E_Φ caused by taking the arithmetic mean of the geopotential heights of two adjacent half σ-levels as the geopotential height of the corresponding integer σ-level,increases with height and has an unacceptable maximum in the vicinity of the top of the atmosphere;however,the errors caused by the temperature treatment are generally small.On the other hand,if an uneven △σ-scheme in which the levels in the upper and lower atmosphere are denser than those in the middle atmosphere,is adopted,then E_Φ can be much reduced.However,if the resolution of the original equal Art-scheme doubles,then E_Φ can only be found to be much reduced in the troposphere and that in the vicinity of the atmospheric top is still unacceptable.Two numerical schemes for improvement have been presented. Of them one is the same as the ECMWF's scheme,but with equal △lnσ,and the other is to integrate the equation by the use of Tschebyscheff polynomials T_n and to adopt the zeros of T_N as the atmospheric levels where N is the total number of levels.The results show that with both schemes the computational errors can be much reduced,especially the latter,due to the fact that the errors of three statistical types are generally less than the root mean square error of the geopotential heights reported in TEMP.     

A STUDY ON DEFORMATIONS OF RAY AND ITS RELEVANT FACTORS*

In this paper,the effects of first and second meridional derivative(i.e.h_s^u,d²f/dy²,u″)of the Coriolis parameter,Westerly profile and topography structure on ray routes are qualitatively analysed by use of a simplified mathematical model.The analysis indicates that the second derivatives of the above relevant factors play an important role in the formation of great circle route.A profile of west wind similar to the real atmosphere may result in a "sine wave pattern" of ray.The effects of west wind shear,β factor and the slope of topography on the scale of radius of great circle,critical latitude of rays ard the amplitude of wave train of teleconnection are also discussed.Additionally,the characters of critical velocity profile for meridionally trapped wave are mentioned.     

HⅢ(2n)中元素的一种标准化表示

给出HⅢ(2n)中元素的一种标准化表示,HⅢ(2n)={Z∈C^2n×2n|1/2(Z+Z'')>0,ZJ=JZ''},J=0 I_n-I_n 0,1/2(Z+Z)>0表示矩阵1/2(Z+z'')是正定的。     

NUMERICAL EXPERIMENTS OF THE INFLUENCE OF DIABATIC HEATING ON TROPICAL CYCLONE ASYMMETRIC STRUCTURE

Using the barotropic volticity equation that contains forcing from diabatic heating with appropriate parameterization. a number of numerical experiments are conducted for the tropical cyclone that is initially symmetric The result shows that the diabatic heating has important effects on the asymmetric structure in addition to the roll of the β term and nonlinear advection term in its formation. It again confirms the conclusion that the diabatic heating is a possible mechanism responsible for such structures in the tropical cyclone.     

DYNAMICAL STUDY OF DIABATIC HEATING INFLUENCE ON RADIAL INHOMOGENEOUS STRUCTURE OF TROPICAL CYCLONE*

Based on the tropical cyclone (TC) asymmetric disturbance as the superposition of the symmetric environmental circulation,the analytical solution of travelling wave is given by using the barotropical nondivergent model with diabatic heating forcing and non-friction in a plane polar coordinate.Then,the TC radial inhomogeneous structure is analyzed on radial/tangential velocity and geopotential height.It is found that the different kinds of structures are influenced by the Coriolis parameter (f),TC intensity (Ω),disturbance circular frequency (ω),and TC angular wavenumber (m).And,the diabatic heating (Q₁) has significant impacts on the radial/tangential velocity distribution shaped like the inner-tight and outer-relaxed.     

An Analysis of the Low Moving Speed of Landfalling Typhoon In-Fa in 2021

The movement speed of Typhoon In-Fa (2021) was notably slow, at 10 km h?1 or less, for over 20 hoursfollowing its landfall in Zhejiang, China, in contrast to other typhoons that have made landfall. This study examines thefactors contributing to the slow movement of Typhoon In-Fa, including the steering flow, diabatic heating, vertical windshear (VWS), and surface synoptic situation, by comparing it with Typhoons Yagi (2018) and Rumbia (2018) whichfollowed similar tracks. The findings reveal that the movement speed of Typhoons Yagi and Rumbia is most closelyassociated with their respective 500 hPa environmental winds, with a steering flow of 10–12 m s ?1. In contrast, Typhoon In Fa’s movement speed is most strongly correlated with the 850 hPa environmental wind field, with a steering flow speed ofonly 2 m s ?1. Furthermore, as Typhoon In-Fa moves northwest after landfall, its intensity is slightly greater than that ofTyphoons Yagi and Rumbia, and the pressure gradient in front of Typhoon In-Fa is notably smaller, leading to its slowmovement. Additionally, the precipitation distribution of Typhoon In-Fa differs from that of the other two typhoons,resulting in a weak asymmetry of wavenumber-1 diabatic heating, which indirectly affects its movement speed. Furtheranalysis indicates that VWS can alter the typhoon’s structure, weaken its intensity, and ultimately impact its movement.     

A STUDY ON TYPHOON MOVEMENT PARTⅡ:DYNAMICAL ROLE OF SMALL TOPOGRAPHY AND THE PLANETARY BOUNDARY LAYER

The dynamic effects of small topography (in the sense of the characteristic height of the topography as compared with the vertical thickness of the system of motion) and the Ekman pumping caused by the frictional convergence in the bounary layer on the motion of a typhoon have been qualitatively discussed in this part based on the governing equation of typhoon motion derived in part I of this paper. The results show that a topographical ridge tends to attract the typhoon approaching it and this explains at least partially the phenomenon that the typhoon over the western Pacific tends to accelerate just before their making land fall over the coastal areas. It is also shown that the Ekman pumping at the top of the boundary layer favors the typhoon acceleration along the local steering current.     

Tropical cyclones and polar lows: Velocity,size, and energy scales,and relation to the 26°C cyclone origin criteria

The goal of this paper is to quantitatively formulate some necessary conditions for the development of intense atmospheric vortices. Specifically, these criteria are discussed for tropical cyclones (TC) and polar lows (PL) by using bulk formulas for fluxes of momentum, sensible heating, and latent heating between the ocean and the atmosphere. The velocity scale is used in two forms: (1) as expressed through the buoyancy flux b and the Coriolis parameter l_c for rotating fluids convection, and (2) as expressed with the cube of velocity times the drag coefficient through the formula for total kinetic energy dissipation in the atmospheric boundary layer. In the quasistationary case the dissipation equals the generation of the energy. In both cases the velocity scale can be expressed through temperature and humidity differences between the ocean and the atmosphere in terms of the reduced gravity, and both forms produce quite comparable velocity scales. Using parameters b and l_c, we can form scales of the area and, by adding the mass of a unit air column, a scale of the total kinetic energy as well. These scales nicely explain the much smaller size of a PL, as compared to a TC, and the total kinetic energy of a TC is of the order 10¹⁸-10¹⁹ J. It will be shown that wind of 33 m s^-1 is produced when the total enthalpy fluxes between the ocean and the atmosphere are about 700 W m^-2 for a TC and 1700 W m^-2 for a PL, in association with the much larger role of the latent heat in the first case and the stricter geostrophic constraints and larger static stability in the second case. This replaces the mystical role of 26^oC as a criterion for TC origin. The buoyancy flux, a product of the reduced gravity and the wind speed, together with the atmospheric static stability, determines the rate of the penetrating convection. It is known from the observations that the formation time for a PL reaching an altitude of 5--6 km can be only a few hours, and a day, or even half a day, for a TC reaching 15--18 km. These two facts allow us to construct curves on the plane of T^s and ΔT=T_s-T_a to determine possibilities for forming an intense vortex. Here, T_a is the atmospheric temperature at the height z=10 m. A PL should have ΔT>20^oC in accordance with the observations and numerical simulations. The conditions for a TC are not so straightforward but our diagram shows that the temperature difference of a few degrees, or possibly even a fraction of a degree, might be sufficient for TC development for a range of static stabilities and development times.     

A CLOUD-RESOLVING MODELING STUDY OF SURFACE RAINFALL PROCESSES ASSOCIATED WITH LANDFALLING TYPHOON KAEMI(2006)

The detailed surface rainfall processes associated with landfalling typhoon Kaemi(2006) are investigated based on hourly data from a two-dimensional cloud-resolving model simulation. The model is integrated for 6 days with imposed large-scale vertical velocity, zonal wind, horizontal temperature and vapor advection from National Center for Environmental Prediction (NCEP) / Global Data Assimilation System (GDAS) data. The simulation data are validated with observations in terms of surface rain rate. The Root-Mean-Squared (RMS) difference in surface rain rate between the simulation and the gauge observations is 0.660 mm h^-1, which is smaller than the standard deviations of both the simulated rain rate (0.753 mm h^-1) and the observed rain rate (0.833 mm h^-1). The simulation data are then used to study the physical causes associated with the detailed surface rainfall processes during the landfall. The results show that time averaged and model domain-mean P_s mainly comes from large-scale convergence (Q_WVF) and local vapor loss (positive Q_WVT). Large underestimation (about 15%) of P_s will occur if Q_WVT and Q_CM (cloud source/sink) are not considered as contributors to P_s. Q_WVF accounts for the variation of P_s during most of the integration time, while it is not always a contributor to P_s. Sometimes surface rainfall could occur when divergence is dominant with local vapor loss to be a contributor to P_s. Surface rainfall is a result of multi-timescale interactions. Q_WVE possesses the longest time scale and the lowest frequency of variation with time and may exert impact on P_s in longer time scales. Q_WVF possesses the second longest time scale and lowest frequency and can explain most of the variation of P_s. Q_WVT and Q_CM possess shorter time scales and higher frequencies, which can explain more detailed variations in P_s. Partitioning analysis shows that stratiform rainfall is dominant from the morning of 26 July till the late night of 27 July. After that, convective rainfall dominates till about 1000 LST 28 July. Before 28 July, the variations of in rainfall-free regions contribute less to that of the domain-mean Q_WVT while after that they contribute much, which is consistent to the corresponding variations in their fractional coverage. The variations of Q_WVF in rainfall regions are the main contributors to that of the domain-mean Q_WVF, then the main contributors to the surface rain rate before the afternoon of 28 July.     

RADIATIVE COOLING AND BROADBAND PHENOMENON IN LOW-FREQUENCY WAVES

In this paper, we analyze the effects of radiative cooling on the pure baroclinic low-frequency waves under the approximation of equatorial β-plane and semi-geostrophic condition. The results show that radiative cooling does not, exclusively, provide the damping effects on the development of low-frequency waves.Under the delicate radiative-convective equilibrium, radiative effects will alter the phase speed and wave period,and bring about the broadband of phase velocity and wave period by adjusting the vertical profiles of diabaticheating. When the intensity of diabatic heating is moderate and appropriate, it is conductive to the development and sustaining of the low-frequency waves and their broadband phenomena, not the larger, the better. The radiative cooling cannot be neglected in order to reach the moderate and appropriate intensity of diabatic heating.     

A QUANTITATIVE STUDY FOR ABNORMAL FREEZING RAINS AND SNOWSTORMS IN SOUTHERN CHINA IN EARLY 2008

A quantitative diagnosis is carried out for the upward branch of a local meridional circulation over southern China(SC) during the abnormal snowstorms with severe freezing rain from 10 January to 3 February 2008.The diagnostic study shows that the upward branch is mainly associated with the zonal advection of westerly momentum and meridional temperature advection instead of the latent heating(which is commonly the dominant factor in many other storm cases).The corresponding weather analyses indicate that(1) the zonal advection of westerly momentum represents the effect of the upper-level divergence on the anticyclone-shear side in the entrance of a 200 hPa westerly jet with a westward deviation from its climatological location over southwestern Japan;(2) the meridional temperature advection represents the interaction between the mid-lower layer(850 to 400 hPa) warm advection over SC(ahead of temperature and pressure troughs with the latter trough deeper than the former in the Bay of Bengal) and cold advection over north China(steered by an underlying flow at 500 hPa);(3) the relatively weak vapor transport(compared to that of spring,summer and autumn) from the Bay of Bengal and the South China Sea to SC and the existence of a temperature inversion layer in the lower troposphere over SC diminish the effect of latent heating.With the significant increase of vapor transport after 24 January,the role of latent heating is upgraded to become the third positive contributor to the upward branch over SC.     

TURBULENCE CHARACTERISTICS OF THE ATMOSPHERIC SURFACE LAYER OVER AN OPEN GRASSLAND*

Described in this paper is an experiment on atmosphere-surface turbulent exchange and boundary layer turbulence properties conducted in July 1994 over the Kerqin Grassland,Jilin,China.The characteristics of the turbulent spectrum,and the relationships of the standard deviation of the turbulent velocity components and sensible heat flux with the atmospheric stability are studied using data from a sonic anemometer and a fast-response platinum resistance thermometer mounted on a 100 m tower.The results show that in the surface layer over a flat,uniform and open grassland,for a broad stability range(-22.12≤Z_iL≤17.98),the velocity spectra obey the-2/3 power law in the inertial subrange,and 1 power law at low frequencies.Under near neutral stratification,σ_u/u_*=1.20,σ_v/u_*=1.23 and σ_w/u_*=1.02.For Z_i/L≤-0.2,the standard deviations of the turbulent velocity components follow a 1/3 power law.For Z_i/L≤-0.1,the standard deviation of the temperature fluctuations follows a-1/3 power law,and as Z_i/L≤-0.08,it exhibits nonlinear behavior.Sensible heat flux is well correlated to the stability parameter.     

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.     

Seasonal Variations of the East Asian Subtropical Westerly Jet and the Thermal Mechanism

The seasonal variations of the intensity and location of the East Asian subtropical westerly jet (EAWJ) and the thermal mechanism are analyzed by using NCEP/NCAR monthly reanalysis data from 1961 to 2000. It is found that the seasonal variation of the EAWJ center not only has significant meridional migration, but also shows the rapid zonal displacements during June-July. Moreover, there exists zonal inconsistency in the northward shift process of the EAWJ axis. Analysis on the thermal mechanism of the EAWJ seasonal variations indicates that the annual cycle of the EAWJ seasonal variation matches very well with the structure of the meridional difference of air temperature, suggesting that the EAWJ seasonal variation is closely related to the inhomogeneous heating due to the solar radiation and the land-sea thermal contrast. Through investigating the relation between the EAWJ and the heat transport, it is revealed that the EAWJ weakens and shifts northward during the warming period from wintertime to summertime, whereas the EAWJ intensifies and shifts southward during the cooling period from summertime to wintertime. The meridional difference of the horizontal heat advection transport is the main factor determining the meridional temperature difference. The meridional shift of the EAWJ follows the location of the maximum meridional gradient of the horizontal heat advection transport. During the period from April to October, the diabatic heating plays the leading role in the zonal displacement of the EAWJ center. The diabatic heating of the Tibetan Plateau to the mid-upper troposphere leads to the rapid zonal displacement of the EAWJ center during June-July.     

USE OF A NEW STEERING FLOW METHOD TO PREDICT TROPICAL CYCLONE MOTION

A tropical cyclone is a kind of violent weather system that takes place in warmer tropical oceans and spins rapidly around its center and at the same time moves along surrounding flows. It is generally recognized that the large-scale circulation plays a major role in determining the movement of tropical cyclones and the effects of steering flows are the highest priority in the forecasting of tropical cyclone motion and track. This article adopts a new method to derive the steering flow and select a typical swerving track case (typhoon Dan, coded 9914) to illustrate the validity of the method. The general approach is to modify the vorticity, geostropical vorticity and divergence, investigate the change in the non-divergent stream function, geoptential and velocity potential, respectively, and compute a modified velocity field to determine the steering flow. Unlike other methods in regular use such as weighted average of wind fields or geopoential height, this method has the least adverse effects on the environmental field and could derive a proper steering flow which fits well with storm motion. Combined with other internal and external forcings, this method could have wide application in the prediction of tropical cyclone track.     

Diagnosis of a Moist Thermodynamic Advection Parameter in Heavy-Rainfall Events

A moist thermodynamic advection parameter, defined as an absolute value of the dot product of hori- zontal gradients of three-dimensional potential temperature advection and general potential temperature, is introduced to diagnose frontal heavy rainfall events in the north of China. It is shown that the parameter is closely related to observed 6-h accumulative surface rainfall and simulated cloud hydrometeors. Since the parameter is capable of describing the typical vertical structural characteristics of dynamic, thermodynamic and water vapor fields above a strong precipitation region near the front surface, it may serve as a physical tracker to detect precipitable weather systems near to a front. A tendency equation of the parameter was derived in Cartesian coordinates and calculated with the simulation output data of a heavy rainfall event. Results revealed that the advection of the parameter by the three-dimensional velocity vector, the covariance of potential temperature advection by local change of the velocity vector and general potential temperature, and the interaction between potential temperature advection and the source or sink of general potential temperature, accounted for local change in the parameter. This indicated that the parameter was determined by a combination of dynamic processes and cloud microphysical processes.     

Simulations of the East Asian subtropical westerly jet by LASG/IAP AGCMs

Performances of two LASG/IAP(State Key Laboratory of Numerical Modeling for Atmospheric Sci- ences and Geophysical Fluid Dynamics/Institute of Atmospheric Physics)Atmospheric General Circulation Models(AGCMs),namely GAMIL and SAMIL,in simulating the major characteristics of the East Asian subtropical westerly jet(EASWJ)in the upper troposphere are examined in this paper.The mean vertical and horizontal structures and the correspondence of the EASWJ location to the meridional temperature gradient in the upper troposphere are well simulated by two models.However,both models underestimate the EASWJ intensity in winter and summer,and are unable to simulate the bimodal distribution of the ma- jor EASWJ centers in mid-summer,relative to the observation,especially for the SAMIL model.The biases in the simulated EASWJ intensity are found to be associated with the biases of the meridional temperature gradients in the troposphere,and furthermore with the surface sensible heat flux and condensation latent heating.The models capture the major characteristics of the seasonal evolution of the diabatic heating rate averaged between 30°-45°N,and its association with the westerly jet.However,the simulated maximum diabatic heating rate in summer is located westward in comparison with the observed position,with a rela- tively strong diabatic heating intensity,especially in GAMIL.The biases in simulating the diabatic heating fields lead to the biases in simulating the temperature distribution in the upper troposphere,which may further affect the EASWJ simulations.Therefore,it is necessary to improve the simulation of the meridional temperature gradient as well as the diabatic heating field in the troposphere for the improvement of the EASWJ simulation by GAMIL and SAMIL models.     

ON DIAGNOSTIC ANALYSIS OF ENERGY FIELDS OF EXPLOSIVE ENHANCEMENT OF TYPHOON OFFSHORE

The energetics process of offehore typhoon in three kinds of explosive enhancement (T_EE) are ana lyzed using ECMWF data. The results are as follows: (a) During the explosive development process,the enhancement of the rotational kinetic enersy (K_W) is mainly in the lower troposphere while that ofthe potential energy (PE) is in the upper troposphere. The magnitude of rotational kinetic energy islargely bigger than that of divergent enersy (K_Χ). (b) The environmental energy advected into the typhoon was about 30% of the internal increment of typhoon energy. The magnitude of energy was an order larger than increment of typhoon energy. (c) Among those three kinds of explosively developed typhoon, the enersy transformation mechanisms are different. (d) The influence of environment fields onabrupt intensification of typhoons couldn't be overestimated.     

THE HEATING FIELD IN AN ASYMMETRIC HURRICANE PART II:RESULTS OF COMPUTATIONS

This is the second part of a paper on the distribution of heating fields in a hurricane. The first part dealt with the mathematical framework. The second part, i. e. the present paper deals with numerical calculations for an actual hurricane.The following sequence of calculations has been performed after the analysis and tabulation of an initial field of the tangential velocity V (r, θ, p): (1) the radial equation of motion is used to determine the geopotential heights; (2) the hydrostatic equation is used to determine the temperature field; (3) the tangential equation and the mass continuity equation are combined to obtain an omega equation whose solution determines the vertical velocity; (4) the radial velocity is next determined from the mass continuity equation; and (5) the heating function is finally determined from the first law of thermodynamics.The results of this study show an asymmetric banded structure (eye wall and rainband) of the vertical motion field as well as the heating field; these s     

FEATURES OF ENERGY BUDGET AND CONVERSION OF DEVELOPED AND UNDEVELOPED TROPICAL CYCLONE

With two cases of local tropical disturbances in both developed and undeveloped phases, contributions to the genesis and development by kinetic formation and transfer from divergent and nondivergent winds are studied using energy budget equations. Computations are done of conversion kinetic energy between the two types of winds. The result indicates that the subgrid scale effect is the principal source of kinetic energy for a tropical cyclone to grow into a typhoon; the cumulus convection plays a dominant role, in company of relatively weaker contributions on vdrious phases of the life cycle by convergence of fluxes of divergent and nondivergent winds as well as the formation of kinetic energy by the former wind. It is also suggested that the conversion of kinetic energy between the divergent and nondivergent winds C(K_x, K_ψ)is increasing with the development of disturbance mainly due to the contribution by C₁=f^▽Χ^▽ψ. The disturbance is shown in the distribution of C(K_x, K_ψ) to increase in a favorable anticyclonic outflow corresponding to the upper level where the conversion becomes negative in developing and mature phases while the wind velocity increases with enhanced conversion fr0m K_x to K_ψ the lower level in association with the growth of the disturbance. In addition,geopotential energy P converts to kinetic energy of the divergent wind in every stage from formation to mature of the disturbance by means of C(P, K_x), the maximum appearing on the middle and upper layers of the troposphere.The intensity of C(P, K_x) is consistently in phase with variation of C(K_x, K_ψ).