非线性气候系统扰动发展线性估计的局限性

采用Lorenz方程组研究了非线性系统扰动发展的线性估计和非线性估计,基于扰动的非线性发展计算了系统扰动线性发展的相对误差和绝对误差。结果表明,非线性系统扰动发展的线性估计只适用于小扰动短时间的发展;对于较长的时间跨度,Lorenz系统扰动的线性发展和非线性发展有较大差别,线性化方程组不能刻划非线性对扰动发展的影响。因此,在研究大气和海洋非线性系统扰动的发展时,应采用非线性模式。

Limitation of linear estimation of perturbation development in nonlinear climate system

The linear and nonlinear evolutions of initial perturbations in Lorenz system are investigated. According to the nonlinear evolution of initial perturbations, the relative and absolute errors of the perturbation development are computed. It is shown that the linear estimation of the perturbation development holds only for the sufficiently small initial perturbations and short time intervals. For the long time interval, there is notable difference between the linear and nonlinear evolutions of initial perturbations. In this case, the linearized equations cannot disclose the effect of nonlinearity on perturbation development. Therefore, in the studies of the atmospheric and oceanic sciences, the nonlinear model should be adopted.