Approximating dominant eigenvalues and eigenvectors of the local forecast error covariance matrix

Examining the dominant eigenvectors of a forecast error covariance matrix for Western Europe during a 607-day period, shows that these daily changing vectors remain in a low-dimensional space. The first few dominant eigenvectors of each day can almost completely be described by a fixed basis consisting of a relatively small number of elements. A simple method is presented that utilizes this property to determine the daily dominant eigenvectors and eigenvalues of the covariance matrix in an efficient manner. Results are given for a 2-day forecast period, but apply also for a forecast period of 3 days. Use of the method, instead of the Lanczos algorithm, in approximating the seven largest eigenvalues within a 1% accuracy level, resulted in a 30% reduction of the computational costs.