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     

THE HEATING FIELD IN AN ASYMMETRIC HURRICANE -PART I:SCALE ANALYSIS

A closed system of equations describing an asymmetric disturbance in cylindrical geometry is expanded about a small parameter. The small parameter describes the ratio of the magnitude of divergence in the boundary layer to that above that layer. A low order system describes a gradient wind balance in the radial direction and is quasi-symmetric with respect to the pressure and temperature fields. This system can be solved as an inverse problem for a mature steady state hurricane. The procedure entails asking the questions what structure and heating distributions are required to maintain a given asymmetric distribution of the tangential velocity (i. e. the angular momentum) in steady state. The method of characteristics enables us to solve for the vertical motion. That in turn determines the radial motion from the mass continuity equation. Application of the hydrostatics to the cylindrical thermal wind equation determines the pressure and the thermal fields and finally the required heating fields are dedu     

Three-Dimensional Wind Field Retrieved from Dual-Doppler Radar Based on a Variational Method: Refinement of Vertical Velocity Estimates

In this paper,a scheme of dual-Doppler radar wind analysis based on a three-dimensional variational method is proposed and performed in two steps.First,the horizontal wind field is simultaneously recovered through minimizing a cost function defined as a radial observation term with the standard conjugate gradient method,avoiding a weighting parameter specification step.Compared with conventional dual-Doppler wind synthesis approaches,this variational method minimizes errors caused by interpolation from radar observation to analysis grid in the iterative solution process,which is one of the main sources of errors.Then,through the accelerated Liebmann method,the vertical velocity is further reestimated as an extra step by solving the Poisson equation with impermeable conditions imposed at the ground and near the tropopause.The Poisson equation defined by the second derivative of the vertical velocity is derived from the mass continuity equation.Compared with the method proposed by O’Brien,this method is less sensitive to the uncertainty of the boundary conditions and has better stability and reliability.Furthermore,the method proposed in this paper is applied to Doppler radar observation of a squall line process.It is shown that the retrieved vertical wind profile agrees well with the vertical profile obtained with the velocity–azimuth display(VAD)method,and the retrieved radial velocity as well as the analyzed positive and negative velocity centers and horizontal wind shear of the squall line are in accord with radar observations.There is a good correspondence between the divergence field of the derived wind field and the vertical velocity.And,the horizontal and vertical circulations within and around the squall line,as well as strong updrafts,the associated downdrafts,and associated rear inflow of the bow echo,are analyzed well.It is worth mentioning that the variational method in this paper can be applied to simultaneously synthesize the three-dimensional wind field from multiple-Doppler radar observations.     

STUDY ON THE GENESIS OF ASYMMETRICAL DISTRIBUTION CHARACTERISTICS OF PRECIPITATION ASSOCIATED WITH THE TYPHOON HAITANG (2005) FROM THE VIEW OF ATMOSPHERIC FACTOR

The distribution of precipitation field from the typhoon Haitang (2005) during its landing on Fujian province shows obvious asymmetric feature. Based on the NCEP/NCAR FNL (Final Analysis) data, this study reveals the contributions of atmospheric factor to the asymmetrical distribution characteristics of precipitation associated with the typhoon, through the analysis of water vapor condition, vertical ascending motion condition, the calculation of the dry Q vector and its decomposition, and adiabatic heating in the air column of 1000hPa -600hPa (lower atmosphere) and 500hPa-100hPa (upper atmosphere). The results are as follows: (1) In the lower atmosphere, the humidity on both sides of typhoon path can be equivalent, while it is more wet on the right side than left in the upper atmosphere, which obviously presents asymmetric distribution characteristics. (2) Both range and intensity of the vertical motion on the right side are wider and stronger than counterparts on the left side no matter in the lower or upper atmosphere. (3) In the upper atmosphere, forcing role of atmosphere in vertical upward motion on the right side of typhoon path is the same as that on the left, while it is significantly different in the lower atmosphere, which is significantly broader in scope and stronger in the intensity, along with obvious asymmetric distribution characteristics. In addition, the further analysis of the Q vector decomposition indicates that the forcing effect of mesoscale weather systems on vertical upward motion is stronger than that of large scale weather systems in the lower atmosphere. (4) The adiabatic heating always exists on both lower and upper atmosphere, and the range and intensity of the adiabatic heating forcing showed asymmetric distribution on both lower and upper atmosphere. (5) In a summary, the upper atmosphere humidity conditions, the forcing role of lower atmosphere in vertical upward motion, especially, to mesoscale weather system, and adiabatic heating in the lower atmosphere, all show similar asymmetric distribution characteristics to that of precipitation field from the typhoon Haitang (2005), that is to say, the atmospheric factors as mentioned above are all contributed to genesis of the asymmetric distribution characteristics of precipitation.     

QUALITY CONTROL OF SINGLE DOPPLER RADAR DATA AND RETRIEVAL OF HORIZONTAL WIND FOR A LANDING TYPHOON

The removal of noise and velocity ambiguity and retrieval and verification of horizontal wind field is a prerequisite to make the best and fullest use of Doppler radar measurements. This approach was applied to the Doppler radar data collected during August 2005 for a landing typhoon Matsa (0509) in Yantai, Shangdong Province, and the verified result shows that the quality control for this dataset was successful. The horizontal wind field was retrieved and then verified by studying the characteristics of the radar radial velocity and large-scale wind field and the vertical cross section of the radial velocity determined with the typhoon center as the circle center and comparing it with satellite imagery. The results show that the meso- and small-scale systems in Matsa and its horizontal and vertical structure could be clearly retrieved using the dataset collected by single Doppler radar, and a shear or a convergence was corresponding with a band of severe storm around Matsa. At the same time, the retrieved wind field from single Doppler radar is proved to be a reliable and high-resolution dataset in analyzing the inner meso-scale structure of Matsa. It is also proved that the method for removing the velocity ambiguity could be an effective approach for preliminary quality control of the Doppler radar data, and the VAP method could also be a reasonable solution for the analysis of mesoscale wind field.     

THE LOW-PRESSURE SYSTEM IN THE VERTICAL VELOCITY OMEGA ON THE SCALE OF SYSTEM SENSITIVITY

In this study, the relationship between scale and vertical velocity in a low-pressure system is explored using the wave characteristics of atmospheric disturbances and the structural characteristics of low-pressure systems. The ω differential equation, as determined by the transient geopotential height field Φ, is solved to obtain an analytical solution composed only of wavelength, horizontal speed, and atmospheric stability, i.e., the ω diagnostic equation of a low-pressure system. This equation also shows that vertical velocity in the low-pressure system is very sensitive to the horizontal scale, i.e., a smaller horizontal scale means a larger vertical velocity.     

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.     

EFFECTS OF THREE-DIMENSIONAL STRUCTURE OF HEATING FIELD ON THE SUMMER MONSOON CIRCULATION IN ASIA

In this paper,a primitive equation linear wave model is used to examine the effects of three-dimen-sional structure of heating field on the behavior of stationary planetary waves in summer and to comparethe roles of different heating functions for the formation and maintenance of summer monsoon circulationin Asia.It is shown that the aloft heating connected with the latent heating,especially the deep condensationheating associated with the cumulus convection in low latitudes,plays a crucial part in the Asian summer mon-soon and the structures of planetary wave responses are quite sensitive to the vertical distribution of heating.     

ON THE PARAMETERIZATION OF THE VERTICAL VELOCITY AT THE TOP OF PLANETARY BOUNDARY LAYER

In this paper, an equation of the vertical velocity at the top of PBL is derived by use of a PBL model which is based on an analytic and actual form of K. Results show that the vertical velocity is a function of geostrophic vorticity, geostrophic wind speed, Coriolis parameter and the roughness of the ground, thus improving Charney-Eliassen's formula. The order of magnitude of the vertical velocity computed from our equation is in agreement with that from the latter, but more factors affecting the vertical velocity are included.     

On the parameterization of the vertical velocity at the top of planetary boundary layer

In this paper, an equation of the vertical velocity at the top of PBL is derived by use of a PBL model which is based on an analytic and actual form of K. Results show that the vertical velocity is a function of geostrophic vorticity, geostrophic wind speed, Coriolis parameter and the roughness of the ground, thus improving Charney-Eliassen’s formula. The order of magnitude of the vertical velocity computed from our equation is in agreement with that from the latter, but more factors affecting the vertical velocity are included.     

Diagnosis of the forcing of inertial-gravity waves in a severe convection system

The non-hydrostatic wave equation set in Cartesian coordinates is rearranged to gain insight into wave generation in a mesoscale severe convection system. The wave equation is characterized by a wave operator on the lhs, and forcing involving three terms—linear and nonlinear terms, and diabatic heating—on the rhs. The equation was applied to a case of severe convection that occurred in East China. The calculation with simulation data showed that the diabatic forcing and linear and nonlinear forcing presented large magnitude at different altitudes in the severe convection region. Further analysis revealed the diabatic forcing due to condensational latent heating had an important influence on the generation of gravity waves in the middle and lower levels. The linear forcing resulting from the Laplacian of potential-temperature linear forcing was dominant in the middle and upper levels. The nonlinear forcing was determined by the Laplacian of potential-temperature nonlinear forcing. Therefore, the forcing of gravity waves was closely associated with the thermodynamic processes in the severe convection case. The reason may be that, besides the vertical component of pressure gradient force, the vertical oscillation of atmospheric particles was dominated by the buoyancy for inertial gravity waves. The latent heating and potential-temperature linear and nonlinear forcing played an important role in the buoyancy tendency. Consequently, these thermodynamic elements influenced the evolution of inertial-gravity waves.     

A NOVEL METHOD FOR CALCULATING VERTICAL VELOCITY: A RELATIONSHIP BETWEEN HORIZONTAL VORTICITY AND VERTICAL MOVEMENT

The present work provides a novel method for calculating vertical velocity based on continuity equations in a pressure coordinate system.The method overcomes the disadvantage of accumulation of calculating errors of horizontal divergence in current kinematics methods during the integration for calculating vertical velocity,and consequently avoids its subsequent correction.In addition,through modifications of the continuity equations,it shows that the vorticity of the vertical shear vector(VVSV) is proportional to-ω,the vertical velocity in p coordinates.Furthermore,if the change of ω in the horizontal direction is neglected,the vorticity of the horizontal vorticity vector is proportional to-ω.When ω is under a fluctuating state in the vertical direction,the updraft occurs when the vector of horizontal vorticity rotates counterclockwise;the downdraft occurs when rotating clockwise.The validation result indicates that the present method is generally better than the vertical velocity calculated by the ω equation using the wet Q-vector divergence as a forcing term,and the vertical velocity calculated by utilizing the kinematics method is followed by the O'Brien method for correction.The plus-minus sign of the vertical velocity obtained with this method is not correlated with the intensity of d BZ,but the absolute error increases when d BZ is =40.This method demonstrates that it is a good reflection of the direction of the vertical velocity.     

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.     

THE POSITION VARIATION OF THE WEST PACIFIC SUBTROPICAL HIGH AND ITS POSSIBLE MECHANISM

Using NCEP/NCAR daily reanalysis data and SCSMEX data, an investigation is carried out of the relationship between the position variation of the west Pacific subtropical high (WPSH) and the apparent heating in June 1998 based on the complete vertical vorticity equation. It is found that the non-adiabatic heating plays an important role in the position variation of WPSH. In comparison with climatic mean status, the vertical change of non-adiabatic heating is stronger in the north side of WPSH in June 1998, but weaker in the south side of WPSH. The anomalous non-uniform heating induces anomalous cyclonic vorticity in South China, areas to the south of the Yangtze and its mid-lower valleys, but anomalous anticyclonic vorticity in the Indo-China Peninsula and South China Sea areas lead to the more southward position of WPSH than the mean.     

THE SEMI-GEOSTROPHIC ADAPTATION PROCESS WITH TWO-LAYER BAROCLINIC MODEL IN LOW LATITUDE ATMOSPHERE

In this paper, the adaptation process in low latitude atmosphere is discussed by means of a two-layer baroclinic model on the equator β plane, showing that the adaptation process in low latitude is mainly dominated by the internal inertial gravity waves. The initial ageostrophic energy is dispersed by the internal inertial gravity waves, and as a result, the geostrophic motion is obtained in zonal direction while the ageostro-phic motion maintains in meridional direction, which can be called semi-geostrophic balance in barotropic model as well as semi-thermal-wind balance in baroclinic model. The vertical motion is determined both by the distribution of the initial vertical motion and that of the initial vertical motion tendency, but it is unrelated to the initial potential vorticity. Finally, the motion tends to be horizontal. The discussion of the physical mechanism of the semi-thermal-wind balance in low latitude atmosphere shows that the achievement of the semi-thermal-wind balance is due to the adjustment between the stream field and the temperature field through the horizontal convergence and divergence which is related to the vertical motion excited by the internal inertial gravity waves. The terminal adaptation state obtained shows that the adaptation direction between the mean temperature field and the shear flow field is determined by the ratio of the scale of the initial ageostrophic disturbance to the scale of one character scale related to the baroclinic Rossby radius of deformation. The shear stream field adapts to the mean temperature field when the ratio is greater than 1, and the mean temperature field adapts to the shear stream field when the ratio is smaller than 1.     

RETRIEVAL OF HORIZONTAL WIND PERTURBATION FIELDS FROM SIMULATED SINGLE DOPPLER RADAR OBSERVATIONS

The application of the single Doppler radar dataset analysis is usually confined to the assumption that the actualwind is linearly distributed or uniform locally.Following some dynamic features of convective weather,a conceptualmodel of moderate complexity is constructed,wherewith a horizontal wind perturbation field is retrieved directly fromthe single Doppler radar measurements.The numerical experiments are based on a 3-D cloud model-generatedconvective cell,whose radial velocity component is taken as the radar observations that are put into the closed equationsbased on the conceptual model to retrieve the horizontal wind perturbation field.After the initial field is properlytreated,the retrieval equation is solved in terms of the 2-D FFT technique and the sensitivity to noise is examined.Finally,contrast analysis is done of the retrieved and the cloud model output wind fields,indicating the usefulness of theapproach proposed in this paper.     

Shearing wind helicity and thermal wind helicity

Helicity is defined as H ： V ω, where V and ω are the velocity and vorticity vectors, respectively. Many works have pointed out that the larger the helicity is, the longer the life cycle of the weather system is. However, the direct relationship of the helicity to the evolution of the weather system is not quite clear. In this paper, the concept of helicity is generalized as shearing wind helicity （SWH）. Dynamically, it is found that the average SWH is directly related to the increase of the average cyclonic rotation of the weather system. Physically, it is also pointed out that the SWH, as a matter of fact, is the sum of the torsion terms and the divergence term in the vorticity equation. Thermal wind helicity （TWH）, as a derivative of SWH, is also discussed here because it links the temperature field and the vertical wind field. These two quantities may be effective for diagnosing a weather system. This paper applies these two quantities in cylindrical coordinates to study the development of Hurricane Andrew to validate their practical use. Through analyzing the hurricane, it is found that TWH can well describe the characteristics of the hurricane such as the strong convection and release of latent heat. SWH is not only a good quantity for diagnosing the weather system, but also an effective one for diagnosing the development of the hurricane.     

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 thesymmetric environmental circulation,the analytical solution of travelling wave is given by usingthe barotropical nondivergent model with diabatic heating forcing and non-friction in a plane polarcoordinate.Then,the TC radial inhomogeneous structure is analyzed on radial/tangential velocityand geopotential height.It is found that the different kinds of structures are influenced by theCoriolis parameter(f),TC intensity(Ω),disturbance circular frequency(ω),and TC angularwavenumber(m).And,the diabatic heating(Q_1)has significant impacts on the radial/tangentialvelocity distribution shaped like the inner-tight and outer-relaxed.     

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.     

THE RELATIONSHIP BETWEEN HORIZONTAL VORTICITY INDUCED BY VERTICAL SHEAR AND VERTICAL MOTION DURING A SQUALL LINE PROCESS

The horizontal vorticity equation used in this study was obtained using the equations of motion in the pressure coordinate system without considering friction, to reveal its relationship with vertical shear. By diagnostically analyzing each term in the horizontal vorticity equation during a squall line process that occurred on 19 June 2010, we found that the non-thermal wind term had a negative contribution to the local change of upward movement in the low-level atmosphere, and that its impact changed gradually from negative to positive with altitude, which could influence upward movement in the mid- and upper-level atmosphere greatly. The contribution of upward vertical transport to vertical movement was the largest in the low-level atmosphere, but had negative contribution to the upper-level atmosphere. These features were most evident in the development stage of the squall line. Based on analysis of convection cells along a squall line, we found that in the process of cell development diabatic heating caused the subsidence of constant potential temperature surface and non- geostrophic motion, which then triggered strong convergence of horizontal acceleration in the mid-level atmosphere and divergence of horizontal acceleration in the upper-level atmosphere. These changes of horizontal wind field could cause a counterclockwise increment of the horizontal vorticity around the warm cell, which then generated an increase of upward movement. This was the main reason why the non-thermal wind term had the largest contribution to the strengthening of upward movement in the mid- and upper-level atmosphere. The vertical transport of large value of horizontal vorticity was the key to trigger convection in this squall line process.