Empirical Orthogonal Functions of the 500 mb Height Weighted with Respect to the Analysis Error

Abstract

When the height of the 500 mb surface is represented with the aid of empirical orthogonal functions, the residual should consist mainly of analysis error. However, unlike the analysis error, the residual is larger over continents than over oceans. The reason for this disagreement is thought to be in the different structure of the analysis error over oceans and over continents. To overcome the disagreement, new functions are required. In this study the problem is formulated and a method for finding an approximate solution to the problem is presented. The residual variance field of the derived functions resembles the estimated analysis error variance field. The new functions take in more details from over continents. A study using the new functions shows that a weak ridge over the United States is described satisfactorily, whereas the old functions failed to do this. The new representation is smoother over oceans. The usefulness of the new functions in practice depends on applications.