变分连续同化中优化步长的推导方法及数值试验

The Method of Calculating the Optimal Step Size in Variational Continual Assimilation and the Numerical Experiments

一个好的变分同化方法 ,必须考虑到预报模式具有误差 ,并对模式误差进行纠正。变分连续同化 (VCA)通过在模式方程中引进一个修正项 ,连续地调整模式变量 ,从而达到以上目的。在变分连续同化的迭代过程中 ,优化步长的选取方法对于同化迭代是否收敛、收敛速度快慢与否都至关重要 ,文中推导了一种有效利用观测资料计算优化步长的新方法 ,并以大气运动方程中一维非线性平流波和二维惯性波为例 ,进行了四维变分资料同化数值试验。数值结果表明 ,VCA方法和计算优化步长的公式都是有效的。

A good variational assimilation method must consider the errors of numerical forecast model and correct them By introducing a forcing term into the model forecast equation, the variational continual assimilation method can continually adjust the model variables and achieve the above objective Because the optimal step size is very important to the iterative convergent rate, a new method of calculating the optimal step size is introduced in this paper The nonlinear one dimensional advective equation and the two dimensional inertial wave equations are used in the numerical experiments The numerical results verify that the VCA and the new method of calculating the step size are both available