用有限区域风速场准确求解流函数和速度势场的方法

流函数和速度势是气象业务和研究中常用于表述风速的一组变量。用有限区域风速场, 使用有限差分方法求解得到的流函数和速度势场重建初始风速场, 由于受区域边界的限制往往有明显的偏差。虽然有许多求解方法的研究, 但是, 至今仍尚未见到一种真正准确的求解计算方案。首先, 介绍用Arakawa A网格和D网格分布的有限区域风速场求解流函数和速度势场的一般有限差分计算方法, 探讨用它们的解重建风速场产生误差的原因。然后, 针对这些原因, 对给定的有限区域, 通过线性外推初始风速场, 扩展求解计算区域, 使用协调、一致的有限差分格式方案, 准确计算求解区域的边界有旋风速、散度风速和速度势的定解边界条件, 以及恰当选择流函数、速度势、涡度和散度等变量的分布网格, 设计了用上述两种网格分布的风速场准确求解流函数、速度势场的方案, 并对其正确性加以证明, 它们可以推广应用于其他Arakawa网格。用实际资料试验同样显示, 方案避免了重建风速场误差的出现, 与初始风速场相比, 全场风速最大偏差精度达到10-12m/s或以上, 在计算机精度造成的计算误差影响范围内。本文的研究很好解决了长期以来用有限区域风速场、 使用有限差分方法无法准确求解流函数和速度势场的问题。     

有限区域流函数和速度势的计算及其在台风中应用

在Endlich提出求解旋转风和辐散风基础上,本文给出了直接利用风场迭代计算流函数和速度势的方法,该方法不但能求解流函数和速度势,还可将原始风场直接分解为旋转风和辐散风。此方法在有限区域中,能大大降低边界条件对计算结果的影响,不仅能计算准确的涡度和散度,还能很好的重建原始风场。采用此方法,对"0808"号台风"凤凰"进行了诊断分析,得到了台风不同时期的流函数和速度势、旋转风和辐散风。结果发现在台风的不同时期,流函数与高度场相似,可用其低值中心来分析台风移动路径和强度的变化,速度势存在高值区,其中心与高度场低值中心不吻合;旋转风的涡旋中心也可用来反映台风中心,台风南侧辐散风较大,故可用来反映南方水汽供应对台风发展、成熟、衰退的影响。     

近70年有限区域流函数速度势算法研究的回顾和新进展

流函数和速度势能很好反映流体的涡度和散度特征,一直广泛应用于全球和区域大气和海洋环流分析、污染物扩散和资料同化等研究领域。近年发现,有限区域流函数速度势常用算法计算中小尺度系统复杂流场和复杂下垫面驱动的边界层流场时,精度显著下降。本文全面回顾上世纪五十年代以来的五类常用算法,从数学原理和物理意义两方面简述优缺点,总结其适用范围;指出常用的调和—余弦法在可解性条件方面的科学问题,并设计订正方案,以提高其在求解复杂流场问题中的适用性和计算精度;通过理想函数和实际天气过程复杂流场的多组数值试验,直观定量显示并归纳总结适于不同分辨率资料的算法。本文旨在为流函数速度势及其相关变量在极端天气气候事件机理分析和数值预报等领域的有效应用,提供科学依据。     

基于Endlich迭代调整的全球流函数和速度势计算及风场分解与重建

本文将有限区域求解流函数和速度势的Endlich迭代调整方法(E-T方法)推广至全球区域,并与常用Guass-Seidel迭代求解Poisson方程方法(G-P方法)进行了比较。结果表明:E-T方法适应于全球流函数和速度势的计算,其由内向外调整,不需严格考虑边界条件,可消除边界对计算结果的影响;E-T方法能准确分解和重建原始风场,而由于极地边界和差分格式影响,G-P方法求得的旋转风和辐散风之和不能准确重建原始风场,尤其是经向为固定边界时,两极地附近重建风场误差非常明显;E-T方法与G-P方法另一重要差异是前者利用流函数和速度势与风场偏微分关系直接进行迭代求解,不需计算涡度和散度,不但保证了重建风场的准确性,还防止了涡度和散度计算误差带来的二次污染。     

计算有限区域内的流函数和势函数的新方法

本文给出了一种在有限区域上计算流函数和函数的新方法,实验结果表明这种方法不仅可以使计算结果具有物理意义,收敛快,而且可以使误差减小到任意给定的精度。     

有限区域流函数和速度势的3种求解方法在分析台风Bilis暴雨增幅中的比较研究

将有限区域流函数、速度势求解中常用的两种张驰法(即理查逊法和加速利布曼法)与调和—余弦谱展开法(H-C法)进行了比较,理论研究表明:H-C法单独考虑边界影响分量,物理意义明确,且不会丢失边界上的天气系统;从计算上看,H-C法重建的风场能精确还原原始风场,且计算效率明显高于两种张驰法,即收敛更快。通过在台风Bilis(0604)暴雨增幅过程诊断中的应用发现,常用的两种张驰迭代方法在求解有限区域流函数和速度势的问题上效果都不是很好,即:用理查逊法和加速利布曼法计算的流函数和速度势重建的风场与原始风场差别较大,不能准确还原原始风场;用H-C法不仅计算效率高,还原的风场与原始风场差异极小,且不受南边界较强的西南季风涌影响,在暴雨增幅前期能较好地反映与暴雨增幅相关的强辐合信号。因此,可用H-C法计算得到的无辐散风和无旋风对有限区域的天气系统进行更深入的动力结构分析。     

Computing Streamfunction and Velocity Potential in a Limited Domain of Arbitrary Shape. Part II: Numerical Methods and Test Experiments

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.     

Computing Streamfunction and Velocity Potential in a Limited Domain of Arbitrary Shape. Part I: Theory and Integral Formulae

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.     

Hybrid Methods for Computing the Streamfunction and Velocity Potential for Complex Flow Fields over Mesoscale Domains

Three types of previously used numerical methods are revisited for computing the streamfunction ψ and velocity potential χ from the horizontal velocity v in limited domains. The first type, called the SOR-based method, uses a classical successive over-relaxation(SOR) scheme to compute ψ(or χ) first with an arbitrary boundary condition(BC) and then χ(orψ) with the BC derived from v. The second type, called the spectral method, uses spectral formulations to construct the inner part of(ψ, χ)—the in...     

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.     

济南章丘大气边界层风温场特征研究

基于章丘气象站2004—2009年实测资料,研究了当地大气边界层风向、风速、气温的时空分布特征,并利用SPSS 17.0数据统计软件的曲线参数估计法,探讨了符合章丘实际的风速随高度变化的拟合曲线及其数学函数关系。结果显示:研究地区大气边界层盛行风向为SSW,且呈现随高度增加沿顺时针方向偏转的特征;风速变化特征在10—300 m和350—1500 m不同高度层存在显著差异,春、夏、秋季和年平均风速随高度变化的指数曲线拟合结果总体好于幂函数曲线,而冬季则相反;气温变化特征四季基本一致,近地面层存在逆温现象,冬季逆温日数最多;逆温强度冬半年的大于夏半年的。