半拉格朗日模式风的半解析解及与差分解的比较试验

质点的轨迹计算是半拉格朗日模式的重要基础，传统的数值计算方法由于采用时间差分代替微分，只能得到质点运动轨迹终点的速度，因此质点的移动轨迹（位移）只能靠风速外推的方法计算，导致了模式计算不稳定等问题.借鉴精细积分法中使用半解析解的思路，利用正压原始方程研究了用运动方程的半解析解构建数值模式的可能性.求解了运动方程的一阶和二阶微分方程组的半解析解，通过时间积分半解析解计算质点运动轨迹.数值试验表明，一阶微分方程组的半解析解比差分解略有优势.二阶微分方程组的半解析解在时间步长增大时优势非常明显，而且在保证计算精度的前提下，节省计算时间，这对提高模式性能有重要作用.

The semi-analytical solutions of the wind for semi-Lagrangian model and the comparative experiments with the finite difference solutions

The algorithm for calculating parcel trajectory is very important in semi-Lagrangian weather prediction models, in which the traditional method is finite difference scheme. Since only the velocity at the end point of the parcel trajectory can be calculated, the displacement is obtained by wind speed extrapolation method. By referring to the semi-analytical solution (SAS) used in the precise integration method, the possibility of constructing a numerical weather prediction model by using the SAS method is raised. For this purpose, the SAS of the first and second order differential kinematics equations are obtained, then the displacement of air parcel can be obtained by integrating the SAS. The numerical experiments show that the result of the SAS of the first order kinematics equations is a little better than that of the finite difference scheme, and the SAS of the second order kinematics equations can get more accurate result and save the computing time by using a long integration time step.