AN ADJOINT SENSITIVITY STUDY OF THE EFFICACY OF MODAL AND NONMODAL PERTURBATIONS IN CAUSING MODEL BLOCK ONSET

With a blocking index as the response function, the adjoint sensitivit y formalism is used to assess the impact of normal modes, adjoint mode s, and regional singular vectors on prediction of block onset in a two -layer model. The authors focus on three blocks excited by perturbing the model's state vector at times preselected using the maximal pertur bation that defines the direction in phase space associated with the l argest possible change in the response function. The sets of normal mo des, adjoint modes, and regional singular vectors (using the total ene rgy or the L-2 norm) are computed on instantaneous basic-state flows f or the preselected times and sensitivity results are presented for a t ime window of 3 days. When ordered by decreasing values of the growth rates of the normal modes, the authors find that some distant normal m odes and adjoint modes can produce larger changes in the response func tion than some of their leading counterparts. In contrast. the sets of regional singular vectors contain easily identifiable subsets of stru ctures associated with relatively large changes in the response functi on. The largest changes are produced by less than the first 20 regiona l singular vectors. Some of these individual regional singular vectors capture the onset of the block when used as perturbations to the init ial condition in a nonlinear model integration, a result of the import ance for ensemble forecasting. It is found that the first five most ex plosive regional singular vectors of the energy (L-2) norm explain ove r:10% (60%) of the norm contained in the maximal perturbation at initi al time. Despite the failure of all individual normal modes to excite the block, as opposed to adjoint modes and regional singular vectors, the authors argue that, paradoxically, the normal mode concept remains a viable tool to explain the dynamics of block onset.