Singular Vectors, Finite-Time Normal Modes, and Error Growth during Blocking

Abstract The evolution of finite-time singular vectors growing on four-dimensional space–time basic states is studied for cases of block development over the Gulf of Alaska and over the North Atlantic, using a two-level tangent linear model. The initial singular vectors depend quite sensitively on the choice of norm with the streamfunction norm characterized by small-scale baroclinic disturbances, the kinetic energy norm giving intermediate-scale baroclinic disturbances, and the enstophy norm typified by large-scale disturbances with large zonal flow contributions. In all cases, the final evolved singular vectors consist of large-scale equivalent barotropic wave trains across the respective blocking regions. There are close similarities between the evolved singular vectors in each of the norms, particularly for the longer time periods considered, and with corresponding evolved finite-time adjoint modes and evolved maximum sensitivity perturbations. For the longer time periods considered, each of these evo...

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