Model studies of blocking predictability using the adjoint sensitivity formalism

Abstract

Adjoint sensitivity calculations of a blocking index to the sets of normal modes, adjoint modes and singular vectors growing on instantaneous basic state flows that precede the onset of blocks are performed. A two-layer isentropic primitive aquation model on the hemisphere is used. The blocking index is a normalized L2 dot oroduct of the dailyl flow anomalies with a "mean blocking patten". Two case studies are performed. The first case study features a block contained in the control run, while the second features a block excited by supperposing a perturbation onto the control run during a period of time free of blocks. A convenient method of evaluating the sensitivities is presented. The method is based on expandind the initial condition in terms of the structures of each set, whereby the concept of projectability of the normal modes is naturally incorporated. It is founf that the mechanism of initial growth, which is distinct from that of the usuall exponential growth, has to be taken into taken into account in theories of error growth based on normal modes. The singular vectors are found to form the best set of precursors for the transition to blocks in a 3 to 4 day ensemble forecast. Extensions of the range of predictability to 6 days require proper account of nonlinearities in any optimization scheme designed o provide the perturbations of the ensemble. It is proposed that the blocks presented in both case studies develop in a two-step man-ner. The first step features the thorncroft-hoskins-McIntyre LC1-type developing troughs, and the second step consists of a repid intensification of the blocking ridge by exponential growth of the leading normal modes