Orthogonal Rotation of Spatial Patterns Derived from Singular Value Decomposition Analysis

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  • 1 Northwest Research Associates, Bellevue, Washington
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Abstract

Singular value decomposition (SYD) analysis is frequently used to identify pairs of spatial patterns whose time series are characterized by maximum temporal covariance. It tends to compress complicated temporal covariance between two fields into a relatively few pairs of spatial patterns by maximizing temporal covariance explained by each pair of spatial patterns while constraining them to be spatially orthogonal to the preceding ones of the same field. The resulting singular vectors are sometimes complicated and difficult to interpret physically. This paper introduces a method, an extension of SVD analysis, which linearly transforms a subset of total singular vectors into a set of alternative solutions using a varimax rotation. The linear transformation (known as “rotation"), weighting singular vectors by the square roots of the corresponding singular values, emphasizes geographical regions characterized by the strongest relationships between two fields, so that spatial patterns corresponding to rotated singular vectors are more spatially localized. Several examples are shown to illustrate the effectiveness of the rotation in isolating coupled modes of variability inherent in meteorological datasets.

Abstract

Singular value decomposition (SYD) analysis is frequently used to identify pairs of spatial patterns whose time series are characterized by maximum temporal covariance. It tends to compress complicated temporal covariance between two fields into a relatively few pairs of spatial patterns by maximizing temporal covariance explained by each pair of spatial patterns while constraining them to be spatially orthogonal to the preceding ones of the same field. The resulting singular vectors are sometimes complicated and difficult to interpret physically. This paper introduces a method, an extension of SVD analysis, which linearly transforms a subset of total singular vectors into a set of alternative solutions using a varimax rotation. The linear transformation (known as “rotation"), weighting singular vectors by the square roots of the corresponding singular values, emphasizes geographical regions characterized by the strongest relationships between two fields, so that spatial patterns corresponding to rotated singular vectors are more spatially localized. Several examples are shown to illustrate the effectiveness of the rotation in isolating coupled modes of variability inherent in meteorological datasets.

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