大气环流模式中云系的超级参数化方案及其特征线方法之研究

就大气环流模式中如何有效处理云系,我们的目标:建立能考虑各种尺度和各种过程之间相互作用的多重尺度云系动力学(下称:云系超级参数化),并应同时考虑如下云的几何学与辐射传输两个问题:1)云的几何学,考虑如何描写云内结构的三维不均匀性和表面特征的几何不光滑性;2)云的辐射,考虑复杂云结构的辐射计算问题,并最终在大气环流模式中具体实现.本研究是理论部分,主要论述云系超级参数化框架和计算方法问题,主要结论如下:1)阐明了从多重尺度角度研究大气模式中云系的超级参数化方案是完全必要的.2)本云系超级参数化方案是3维完全Euler流体方程组,保留了全Coriolis力,Ertel全PV守恒,考虑声波等对云和降水微物理过程的影响.该云系超级参数化方案需要与大气大尺度动力学方程组进行耦合.3)关键问题为确定云系局部解的存在时间长度,不必考虑整体解.因为在实际大气中各物理量的不光滑,甚至不连续和间断,是有充分的物理意义的.大气中的间断除粘性和热传导等不可逆过程外,同时伴随着成云致雨的相变过程.4)在可积性和连续性条件下,证明了特征线的存在性;在Lipshitz条件下,证明了特征线的存在性和唯一性.5)给出了特征线积分的Picard方法的具体计算步骤,并同时给出了特征线积分稳定步长的具体条件.6)沿着特征线,初始场随着时间的推移,将发生平移、旋转与纯变形三种位移的几何和,这就是球面上平流方程的保形问题.

Study on Cloud System Superparameterization and the Method of Characteristic Lines in the Atmospheric General Circulation Model

About cloud treatment in the Atmospheric General Circulation Model(hereafter,AGCM),our ultimate objective is to build multi-scale cloud system dynamics(hereafter,superparameterization)concerning with interaction among various scales and various processes and to consider the cloud geometry,in which the 3-dimensional inhomogeneous of cloud interior and the non-smoothness of cloud outer boundary are described,and cloud radiation,in which the calculation method of the complex cloud radiation is designed.Then,the above schemes will be realized in the AGCM.This paper focuses on the frame of cloud system superparameterization and the problem of computational method.The conclusions is as follows.1) It is expounded that research on cloud system superparameterization from the multi-scales is very necessary.2) In the cloud system superparameterization,3-dimensional full Euler equations(the compressible nonhydrostatic) are used,including full Coriolis force,full conservative of Ertel potential vorticity,the effect of sound wave on microphysical processes about cloud and precipitation.The superparameterization should be nested the atmospheric hydrostatic model in large scale.3) It is the key problem to decide the life time about the local solution of cloud system superparameterization equations,not to consider its global solution.The reason is that the non-smooth of solution in the real atmosphere is fully reasonable from the view of physics,concerning with the irreversible processes such as viscosity and thermal conduction and the phase change processes about cloud and precipitation.4)If the integrable and continuoes conditions are satisfied,the existence of characteristic lines is proven.Moreover,If Lipshitz continuous condition is satisfied,the existence and uniqueness of characteristic lines is proven.5) With Picard's method,the detailed method to obtain the characteristic line is posed and the computational time step which guarantees stability is found.6) As time changes,the initial field along the characteristic lines will evolve with three kinds of motion,a translational motion,a rotation and pure deformation.This is the shape preserving problem of pure advection on the sphere.