Adjoint Sensitivity and Finite-Time Normal Mode Disturbances during Blocking

Abstract

The finite-time normal mode instability of four-dimensional space?time basic states has been studied for cases of block development over the Gulf of Alaska, over the North Atlantic, and over southern Greenland using a two-level tangent linear model. The authors find three generic types of finite-time normal modes, denoted as ?recurring,? ?traveling,? and ?flip? modes. The dominant finite-time normal modes associated with block development have large-scale structures in the respective blocking regions; they tend to closely reflect the structures of the developing blocks. The time evolution in the tangent linear model of finite-time adjoint modes has been examined for each of the three cases of block development. These adjoint modes have faster than normal mode exponential growth. The initial structures of the dominant adjoint modes are characterized by small-scale baroclinic wave trains located primarily upstream of the blocking region. As the disturbances grow explosively, they increase their scale and propagate eastward into the blocking region where, within a few days, they take up large-scale structures similar to the respective fastest growing finite-time normal modes. The structures and time evolution of maximum sensitivity perturbations during blocking have been analyzed. Dominant normal mode structures focused in the blocking regions have been chosen as weight functions in response functions measuring forecast sensitivity. The maximum sensitivity perturbations are found to be very similar to respective finite-time adjoint modes in their structures and time developments. It is suggested that, during periods of rapid regime transition, the error structure at the end of a 2?4-day period of weather prediction is likely to resemble the dominant finite-time normal modes for the period in question.