The moist atmosphere with occurring precipitation is considered to be a multiphase fluid composed of dry air, water vapor and hydrometeors. These compositions move with different velocities： they take a macroscopic motion with a reference velocity and a relative motion with a velocity deviated from the reference velocity. The reference velocity can be chosen as the velocities of dry air, a gas mixture and the total air mixture. The budget equations of continuity and momentum are formulated in the three reference-velocity frames. It is shown that the resulting equations are dependent on the chosen reference velocity. The diffusive flux due to compositions moving with velocities deviated from the reference velocity and the internal sources due to the phase transitions of water substances result in additional source terms in continuity and momentum equations. A continuity equation of the total mass is conserved and free of diffusive flux divergence if the reference velocity is referred to the velocity of the total air mixture. However, continuity equations in the dry-air and gas- mixture frames are not conserved due to the mass diffusive flux divergence. The diffusive flux introduces additional source terms in the momentum equation. In the dry-air frame, the diffusive flux of water substances and the phase transitions of water substances contribute to the change of the total momentum. The additional sources of total momentum in the frame of a gas mixture are associated with the diffusive flux of hydrometeors, the phase transitions of hydrometeors and the gas- mixture diffusive flux. In the frame of total air mixture, the contribution to the total momentum comes from the diffusive flux of all atmospheric compositions instead of the phase transitions. The continuity and momentum equations derived here are more complicated than the traditional model equations. With increasing computing power, it becomes possible to simulate atmospheric processes with these sophisticated equations. It is helpful to the improvement of
A new invariant called the generalized Ertel Rossby invariant （GER） was developed in this study. The new invariant is given by the dot product of the generalized vorticity and the generalized velocity. The generalized vortieity is the absolute vorticity minus the cross product of the gradient of Lagrangian--time integrated temperature and the gradient of entropy. The generalized velocity is the absolute velocity minus the sum of the gradient of Lagrangian-time integrated kinetic potential and the Lagrangian time integrated temperature multiplied by the gradient of entropy. In addition to the traditional potential vorticity, the GER invariant may provide another useful tool to study the atmospheric dynamic processes for weather phenomena ranging from large scales to small scales.
The effects of sea surface temperature（SST）,cloud radiative and microphysical processes,and diurnal variations on rainfall statistics are documented with grid data from the two-dimensional equilibrium cloud-resolving model simulations.For a rain rate of higher than 3 mm.h 1,water vapor convergence prevails.The rainfall amount decreases with the decrease of SST from 29℃ to 27℃,the inclusion of diurnal variation of SST,or the exclusion of microphysical effects of ice clouds and radiative effects of water clouds,which are primarily associated with the decreases in water vapor convergence.However,the amount of rainfall increases with the increase of SST from 29℃ to 31℃,the exclusion of diurnal variation of solar zenith angle,and the exclusion of the radiative effects of ice clouds,which are primarily related to increases in water vapor convergence.For a rain rate of less than 3 mm.h 1,water vapor divergence prevails.Unlike rainfall statistics for rain rates of higher than 3 mm.h 1,the decrease of SST from 29℃ to 27℃ and the exclusion of radiative effects of water clouds in the presence of radiative effects of ice clouds increase the rainfall amount,which corresponds to the suppression in water vapor divergence.The exclusion of microphysical effects of ice clouds decreases the amount of rainfall,which corresponds to the enhancement in water vapor divergence.The amount of rainfall is less sensitive to the increase of SST from 29℃ to 31℃ and to the radiative effects of water clouds in the absence of the radiative effects of ice clouds.
针对2008年初发生在贵州地区的严重冻雨过程,分别从环流背景、低空急流和水汽输送条件等方面分析了准静止锋维持的原因,并选取本次灾害最严重的第3次过程为典型个例,利用WRF模式针对准静止锋影响下的贵州冻雨进行数值模拟来研究冻雨的发生机制。模拟结果较好地反映出高低空环流形势场特征,强雨雪降水带的走向、落区,以及地面温度的分布,均与观测基本吻合。通过分析高分辨率模式的模拟结果,揭示了准静止锋上贵州地区冻雨的层结结构特征及云物质在冻雨区的分布特征。研究结果表明,贵州中部的冻雨区除一般的三层结构(包含冰晶层、暖层和冷层)外,还具有典型的两层结构特征,即:高空的固体降水粒子稀少,900~600 h Pa深厚的逆温层和0℃以上的暖层使中低空存在大量液态粒子,下落的液滴经过近地面的浅薄冷层,形成大量过冷却雨滴,而后降落至地面迅速冻结。
The non-uniqueness of solution and compatibility between the coupled boundary conditions in computing velocity potential and streamfunction from horizontal velocity in a limited domain of arbitrary shape are revisited theoretically with rigorous mathematic treatments.Classic integral formulas and their variants are used to formulate solutions for the coupled problems.In the absence of data holes,the total solution is the sum of two integral solutions.One is the internally induced solution produced purely and uniquely by the domain internal divergence and vorticity,and its two components（velocity potential and streamfunction） can be constructed by applying Green＇s function for Poisson equation in unbounded domain to the divergence and vorticity inside the domain.The other is the externally induced solution produced purely but non-uniquely by the domain external divergence and vorticity,and the non-uniqueness is caused by the harmonic nature of the solution and the unknown divergence and vorticity distributions outside the domain.By setting either the velocity potential（or streamfunction） component to zero,the other component of the externally induced solution can be expressed by the imaginary（or real） part of the Cauchy integral constructed using the coupled boundary conditions and solvability conditions that exclude the internally induced solution.The streamfunction（or velocity potential） for the externally induced solution can also be expressed by the boundary integral of a double-layer（or singlelayer） density function.In the presence of data holes,the total solution includes a data-hole-induced solution in addition to the above internally and externally induced solutions.
The energetics of the third stage of a snowstorm over China was analyzed using ECWMF data.The analysis of the energy budget for the Middle East trough and the western Pacific trough that developed toward China on 25-28 January 2008 showed the advection of the geopotential by the ageostrophic wind to be both a crucial source and the primary sink of the eddy kinetic energy centers associated with the troughs.The magnitudes of the energy conversion terms,interaction kinetic energy conversion and baroclinic conversion,were too small to explain the development of the energy centers and the jet streaks.The energy centers gained energy at their entrance regions via the convergence of the ageostrophic geopotential fluxes,and then lost energy at their exit regions by the same fluxes.At the entrance regions,the fluxes converged,increasing the geopotential gradient,which generated a stronger geostrophic wind and higher kinetic energy,resulting in an ascending motion in this area.When the troughs moved to China,the ascending motion caused by the convergence of the fluxes at entrance region intensified the snowstorms over central and southern China.
ABSTRACT The third precipitation episode of China＇s great snowstorms of 2008 was analyzed using station observations and ECMWF six-hourly data. The variation of the shape of the upper-level subtropical jet played an important role in the rainfall over south- ern China. With the eastward movement of the trough, the jet shape changed from two straight jets to a tilting jet over China and then it moved southward. With these variations, the south-north movement of ascending flow and precipitation area over southern China occurred.
Built on the integral formulas in Part I,numerical methods are developed for computing velocity potential and streamfunction in a limited domain.When there is no inner boundary（around a data hole） inside the domain,the total solution is the sum of the internally and externally induced parts.For the internally induced part,three numerical schemes（grid-staggering,local-nesting and piecewise continuous integration） are designed to deal with the singularity of the Green＇s function encountered in numerical calculations.For the externally induced part,by setting the velocity potential（or streamfunction） component to zero,the other component of the solution can be computed in two ways：（1） Solve for the density function from its boundary integral equation and then construct the solution from the boundary integral of the density function.（2） Use the Cauchy integral to construct the solution directly.The boundary integral can be discretized on a uniform grid along the boundary.By using local-nesting（or piecewise continuous integration）,the scheme is refined to enhance the discretization accuracy of the boundary integral around each corner point（or along the entire boundary）.When the domain is not free of data holes,the total solution contains a data-hole-induced part,and the Cauchy integral method is extended to construct the externally induced solution with irregular external and internal boundaries.An automated algorithm is designed to facilitate the integrations along the irregular external and internal boundaries.Numerical experiments are performed to evaluate the accuracy and efficiency of each scheme relative to others.
