基于螺旋度的中尺度平衡方程及非平衡流诊断方法

在回顾大尺度准地转平衡理论、各种平衡方程、平衡模式及非平衡流诊断工具的基础上,对平衡方程、非平衡方程给出了具体的定义.并在此基础上,进一步考虑中尺度强对流天气系统的特征,指出中尺度也有平衡运动的存在.但是由于中尺度对流系统中强烈的辐散风效应以及不可忽略的垂直运动的作用,以散度方程为基础的各种近似平衡方程不足以描述中尺度强对流天气系统的平衡运动,进而提出了从能够同时考虑旋转、辐散及垂直运动作用的螺旋度方程出发,寻找中尺度的平衡方程.在所得的平衡方程基础上,给出了相应的平衡模式和非平衡方程.并进一步将非平衡方程分解,用来诊断非平衡过程的平衡破坏和平衡恢复两个阶段,同时将它们与水平螺旋度和垂直螺旋度联系起来.     

湖北省潜在蒸散估算模型对比

利用湖北省74个气象站1961~2011年逐日气象资料,通过与FAO56-Penman-Monteith(FAO-PM)模型潜在蒸散估算结果对比,从月、季、年际变化及不同干湿状况条件比较了PriestleyTaylor、Hargreaves及Thornthwaite 3种简化的经验模型在湖北省的适用性。结果表明:3种简化模型与FAO-PM模型计算的逐月潜在蒸散均存在一定偏差,Thornthwaite模型偏差最大且冬夏季偏差反位相,Priestley-Taylor模型偏差最小,Hargreaves模型各月间的偏差最为稳定。3种简化模型与FAOPM模型估算结果具有良好的线性关系,且在各区域间相对稳定,但不同季节和干湿状况下各有差异,其中Hargreaves模型各季节间和不同干湿状况下与FAO-PM模型的关系均最为稳定。在年际变化上,Priestley-Taylor和Hargreaves模型与FAO-PM模型计算结果年际波动基本一致,Thornthwaite模型与FAO-PM模型计算结果尽管在量值上较为接近,但年际波动偏小;Priestley-Taylor和FAOPM模型年潜在蒸散趋势变化基本一致,Hargreaves模型年潜在蒸散趋势变化微弱,而Thornthwaite模型年潜在蒸散趋势变化与FAO-PM模型相反。建议在湖北省气象资料匮乏或不便应用的情况下,作物模拟模型及气候变化等研究中采用Priestley-Taylor估算模型,日常干旱监测及水资源规划中采用Hargreaves模型,干湿气候区划等工作中可采用Thornthwaite模型。同时,使用中应基于FAO-PM模型对经验模型进行适当订正,模型订正应建立在季节或月尺度。     

条件数在区域日降水量预报中的应用研究

针对前汛期广西北部暴雨洪涝灾害频发的问题，利用T213模式和日本细网格降水预报等数值预报产品，采用条件数计算选取回归因子的方法建立广西北部区域平均降水量的预报方程。进行了2004、2005年两年5-6月的前汛期业务预报应用试验。采用条件数方法建立的预报方程和传统的逐步回归预报方程的平均预报误差分别为6．3569mm和7．0096mm，同期T213模式的预报误差为7．9456mm。试验表明新方法比传统的逐步回归方程和T213模式具有更高的预报精度，有较好的业务应用前景。计算对比可知，采用条件数计算选择的预报因子间的复共线性较微弱，而逐步回归方法选择的因子间的复共线性很严重，影响了回归方程的预报效果。     

水汽方程古典解的适定性研究

对于球坐标系下的水汽方程,当考虑水汽的凝结或凝华过程时,利用水汽方程的特点得到了关于水汽方程的弱极值原理的较强形式。利用该弱极大值原理,证明了对于第一类、第二类和第三类边值问题,水汽方程解的唯一性和稳定性。利用Schauder方法,证明了对于第一类、第二类和第三类边值问题,C2空间连续的水汽方程解的存在性。此外,还严格证明了水汽方程古典解的非负性。       

包含超梯度力作用的台风次级环流诊断方程

次级环流在台风的发展和维持中起着重要作用,基于梯度风平衡的Sawyer Eliassen（SE）方程常用于台风次级环流的诊断。然而梯度风平衡关系在台风边界层及边界附近有较大误差,这导致SE方程求解出的次级环流在边界层也会有较大误差。本文在梯度风平衡方程中保留包含径向摩擦力项在内的超梯度力项,得到包含超梯度力作用的SE方程,从方程形式上看超梯度力主要是通过调节与斜压性相关的系数来影响次级环流的。对“森拉克”（2008）台风次级环流的诊断结果显示,在不人为改变边界层流场结构的情况下,新的SE方程能显著改善次级环流的求解效果,避免眼墙外侧边界层附近的虚假对流并且减小虚假入流。     

垂直切变基流中东西向地形对惯性重力波稳定性的影响

利用分层浅水波方程和小参数(WKB)方法，考虑具有垂直切变的基流和地形的作用，求得惯性重力波的局地频率方程，并根据此方程分析讨论了在多种环境条件下波动的稳定性情况。     

A Homogeneous Langevin Equation Model, Part i: Simulation of Particle Trajectories in Turbulence with a Skewed Velocity Distribution

A Lagrangian stochastic model for the time evolution of the velocity of a fluid particle is presented. This model is based on a one-dimensional generalized Langevin equation, and assumes the velocity probability distribution of the turbulent fluid is skewed and spatially homogeneous. This has been shown to be an effective approach to simulating vertical dispersion in the convective boundary layer. We use a form of the Langevin equation that has a linear (in velocity) deterministic acceleration and a random acceleration that is a non-Gaussian, skewed process. For the case of homogeneous fluid velocity statistics, this 'linear-skewed' Langevin equation can be integrated explicitly, resulting in an efficient numerical simulation method. Model simulations were tested using cases for which exact, analytic statistical properties of particle velocity are known. Results of these tests show that, for homogeneous turbulence, a linear-skewed Langevin equation model can overcome the difficulties encountered in applying a Langevin equation with a skewed random acceleration. The linear-skewed Langevin equation model results are compared to results of a 'nonlinear-Gaussian' Langevin equation model, and show that the linear-skewed model is significantly more efficient.     

边界微分方程及其应用

本文讨论二维Helmholtz方程外边值问题的求解,以较为严格的方式建立了更精准的新的边界微分方程.在贴体坐标系下,Helmholtz方程可转化为非齐次Bessel方程.将Bessel方程的一般解代入Sommerfeld辐射条件可以得到等价于原Helmholtz方程的积分-微分方程,再利用分部积分消去其中积分,即可建立高频问题的边界微分方程.文中通过若干算例对新得到的边界微分方程进行了数值验证.     

Sensitivity of lidar equation solution to boundary values and determination of the values

An analytical dependence of the optical depth solution to lidar equation on boundary values was con-firmed. According to the dependence this paper analyzed the sensitivity of lidar equation solutions obtained by forward and backward integration algorithms to the boundary values and quantitatively expounded an error limit to the boundary values under a given inversion accuracy. Furthermore, this paper presented a method for determination of the far-end boundary value in the case of inhomogeneous atmosphere, improving the accuracy of lidar equation solution.     

自忆预报模式中记忆特性的探讨

运用有限振幅斜压波的截谱方程对自忆模式中的的记忆性进行了理论探讨。推导了相应的自忆性方程,在给定记忆函数呈线性和指数衰减型时求出了它的解析解,并讨论了这些解的物理意义和预报含意;证明了零解自忆性方程与记忆函数形式无关。通过计算遗忘因子,对动力可预报性和回溯阶等问题进行了讨论,并指出可将其统一纳入大气记忆理论的框架中。     

球面正压粘性大气的运动特征

通过对球面正压粘性大气非线性扰动的研究表明:由于波动之间的弱非线性相互作用，球面小扰动的波包演变是由一种较为简单的方程形式控制，当此粘性力消失时，该方程为非线性Schr?dinger方程。研究结果还表明:非线性Schr?dinger孤立波的形成，有两个因子非常重要，一是运动的球面性，另一个则是基本风场的经向切变。前者反映了球面运动的特殊性。本文还从另一个角度证明了粘性力的作用对波动起着加强能量的耗散作用，不利于这种几率波（Schr?dinger 孤立波）的形成。     

Rossby波的能量、能量通量与Lagrange函数

利用正压涡度方程计算波动能量通量时,它的形式将不同于直接利用运动方程所求得的通量,这是一个于六十年代初所提出的问题。在本文中,对此问题进行再次分析与研究。结果表明,如果将运动方程进行改写,使其包含了与涡度方程相等的条件,对于波动而言,就整个波动范围求平均且假定波动振幅为常数,则可得到相同的表示式。于文中,还利用此改写的运动方程,导得了波动位能的表示式,这为进一步研究非线性Rossby波提供了一个物理基础。     

Discussion on the complete-form vorticity equation and slantwise vorticity development

The complete form of the vertical vorticity tendency equation (the complete-form vorticity equation) is derived from the Ertel potential vorticity equation to contain thermodynamic factors. In this study, a new complete-form vorticity equation, which has the same form as the original complete-form vorticity equation, is deduced from the absolute vorticity vector equation combined with the continuity equation and the expression of three-dimensional (3D) entropy gradient. By comparing the complete-form vorticity equation with the classical vertical vorticity equation, it is found that regardless of whether or not the isentropic surface is tilting, the two vorticity equations are in essence the same. The “baroclinic term” of the complete-form vorticity equation is exactly equal to the solenoidal term of the classical one, and there is a significant amount of cancellation between the two baroclinic items (the “slantwise term” and the horizontal vorticity change term) in the complete-form vorticity equation. In operational weather analysis, the tilt of the isentropic surface can be diagnosed according to the density of the isotherm on the upper-level isobaric map. For synoptic-scale motion, the vertical vorticity produced by the tilt of the isentropic surface is due to the contribution of atmospheric baroclinicity, which is measured by the solenoid. The 3D solenoid is parallel to the isentropic surface, so the more tilted the isentropic surface, the bigger the projection of the 3D solenoid in the vertical direction. The baroclinic contribution can be interpreted based on the PV thinking theory, but the relationship between the vorticity field and the potential vorticity field is not immediate.     

On the Significance and Use of the Generalized Moist Potential Vorticity Equation

In this paper,the continuity and thermodynamic equations including moisture forcings were derived.Using these two equations and the basic momentum equation of local Cartesian coordinates,the budget equation of generalized moist potential vorticity(GMPV) was derived.The GMPV equation is a good generalization of the Ertel potential vorticity(PV) and moist potential vorticity(MPV) equations.The GMPV equation is conserved under adiabatic,frictionless,barotropic,or saturated atmospheric conditions,and it is closely associated with the horizontal frontogenesis and stability of the real atmosphere.A real case study indicates that term diabatic heating could be a useful diagnostic tool for heavy rainfall events.     

客观预报方程中因子的选取及应用效果分析

利用因子选取及方程建立人机交互平台,建立了云南省125个气象站的降水、温度客观要素预报方程.对比试验表明,绝大多数组合因子都优于单因子,组合因子预报方程的质量普遍比单因子预报方程好.预报检验结果显示,干季的降水预报尚未达到可用程度,雨季小雨及中雨、大雨的预报有一定业务指导意义,对于反映中小尺度系统的暴雨天气预报效果较差,在因子的选择上还需要做大量细致的工作.温度预报具有一定的参考价值,但还有待进一步改进.     

最优化方法在天气预报中的应用

本文根据最优化方法原理,提出了选择非线性最优预报因子和建立非线性预报方程的办法。试验表明:用此方法选出来的非线性预报因子和建立的方程比线性的好。最后还指出了此方法可推广到预报量离散的情况,建立非线性的判别方程,同时可用于长、中、短期天气预报。     

A Homogeneous Langevin Equation Model, Part ii: Simulation of Dispersion in the Convective Boundary Layer

We present a Lagrangian stochastic model of vertical dispersion in the convective boundary layer (CBL). This model is based on a generalized Langevin equation that uses the simplifying assumption that the skewed vertical velocity probability distribution is spatially homogeneous. This approach has been shown to account for two key properties of CBL turbulence associated with large-scale coherent turbulent structures: skewed vertical velocity distributions and long velocity correlation time. A 'linear-skewed' form of the generalized Langevin equation is used, which has a linear (in velocity) deterministic acceleration and a skewed random acceleration. 'Reflection' boundary conditions for selecting a new velocity for a particle that encounters a boundary were investigated, including alternatives to the standard assumption that the magnitudes of the particle incident and reflected velocities are positively correlated. Model simulations were tested using cases for which exact, analytic statistical properties of particle velocity and position are known, i.e., well-mixed spatial and velocity distributions. Simulations of laboratory experiments of CBL dispersion show that (1) the homogeneous linear-skewed Langevin equation model (as well as an alternative 'nonlinear-Gaussian' Langevin equation model) can simulate the important aspects of dispersion in the CBL, and (2) a negatively-correlated-speed reflection boundary condition simulates the observed dispersion of material near the surface in the CBL significantly better than alternative reflection boundary conditions. The homogeneous linear-skewed Langevin equation model has the advantage that it is computationally more efficient than the homogeneous nonlinear-Gaussian Langevin equation model, and considerably more efficient than inhomogeneous Langevin equation models.     

ENERGY,ENERGY FLUX AND LAGRANGIAN OF ROSSBY WAVE

The energy flux derived from the barotropic vorticity equation differs from that obtained directly from the momentum equation.We re-study this problem raised in the early 1960s.The results show that if the momentum equation is rewritten in such a way that it contains the same conditions as that for the barotropic vorticity equation,then the same form of average energy flux can be obtained for the waves with constant amplitudes.With this new momentum equation,the potential energy of Rossby wave is derived and Lagrangian of nonlinear barotropic vorticity equation can be approximately found with this potential energy.This provides a physical basis for studying the dynamics of nonlinear Rossby wave with the approach of calculus of variation.     

Dynamical Implications of Block Averaging

We show that traditional Reynolds (block) averaging produces turbulence statistics whose time evolution is incompatible with the Navier–Stokes equation. Specifically, the zero integral scale that block averaging always produces leads to a trivial (zero-equals-zero) solution of the Navier–Stokes equation for autocovariances. We suggest alternative methods for analyzing turbulence time series that do not always generate a zero integral scale and, as a result, yield autocovariances whose time evolutions are compatible with the Navier–Stokes equation.     

东营市相对湿度集成预报系统

运用多元回归法和多因子权重回归法分别建立预报模型，并在此基础上建立了相对湿度集成预报系统。