Dynamics of Short-Term Univariate Forecast Error Covariances
Dynamics of Short-Term Univariate Forecast Error Covariances
复制标题
短期单变量预测误差协方差的动态
DOI：
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发表时间：
1993
期刊：
影响因子：
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通讯作者：
S. Cohn
中科院分区：
文献类型：
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作者：
S. Cohn
摘要研究了一般标量非线性偏微分方程（PDE）控制的动力学系统基于二阶闭包的协方差方程。如果支配动态涉及n个空间维度，则协方差方程是2n个空间维度中的PDE。因此，对于n = 3求解该方程在计算上是不可行的。这是一个障碍，随机动态预测以及新的方法，数据同化的基础上卡尔曼滤波器。它示出的协方差方程可以近似地解决，以任何所需的精度，而不是解决一个辅助系统的偏微分方程在n维。第一个是方差场的动力学方程。连续的方程描述，越来越高阶，由小距离分开的点的协方差函数或相关函数的形状的动态。例如，二阶方程描述了相关长度（湍流微尺度）场的演化。
Abstract The covariance equation based on second-order closure for dynamics governed by a general scalar nonlinear partial differential equation (PDE) is studied. If the governing dynamics involve n space dimensions, then the covariance equation is a PDE in 2n space dimensions. Solving this equation for n = 3 is therefore computationally infeasible. This is a hindrance to stochastic-dynamic prediction as well as to novel methods of data assimilation based on the Kalman filter. It is shown that the covariance equation can be solved approximately, to any desired accuracy, by solving instead an auxiliary system of PDEs in just n dimensions. The first of these is a dynamical equation for the variance field. Successive equations describe, to increasingly high order, the dynamics of the shape of either the covariance function or the correlation function for points separated by small distances. The second-order equation, for instance, describes the evolution of the correlation length (turbulent microscale) field...