Aimé Fournier

The atmospheric state is describable by spatial point values or by harmonic coefficients. Spatially localized structures have slowly-decaying; harmonic coefficients; coefficients define global scales but individually specify no location. These representations are dual in the sense of Heisenberg uncertainty, or of 'wave-particle duality' according to Charney. Actual atmospheric structures fall between these abstractions, being partly localized in both representations. This thesis applies orthonormal wavelet analysis (WA), a generalized representation, to such structures, and seeks to determine what added value WA provides in our attempt to characterize and analyze weather features. The major goal of this work is a new simultaneous description of the space and scale dependence of nonlinear (NL) interactions during atmospheric blocking. This is the first application of WA to global meteorological data.

Blocking is part of low-frequency variability of the general circulation, associated with high-amplitude quasi-steady wave disturbances. The generation and persistence of blocking; patterns are ill-understood processes. Such disturbances are strongly localized spatially, rendering traditional zonal Fourier series-based scale analysis of their kinetic energy (KE) budget problematical, because truncated Fourier series poorly describe localized coherent structures and strong gradients. A more suitable mathematical description is necessary, so in this thesis I investigate the suitability and preferability of the wavelet description.

Energetics is the study of the transfer of energy of different forms (or other conserved quantities) between fields which comprise the atmospheric state. These statistics may be decomposed in any orthogonal basis. Winter atmospheric blocking is studied by WA and by a new, WA-based energetics scheme. Just the largest scale WA components are found to mostly describe blocking. New forms of the KE transfer functions with the mean and eddy parts of the circulation are introduced. These quantify the spatially localized conversion of KE between scales. Careful accounting of wavelet-indexed transfers allows the introduction of a physically meaningful localized scale flux function. New support is found for the hypothesis that blocking is partially maintained by up-scale cascades. Specifically, in both Atlantic and Pacific blocking cases there is a down-scale cascade upstream of the block, and an up-scale cascade at or downstream of the block, consistent with the heuristic idea that blocking is maintained by transfers from eastward propagating eddies being zonally contracted upon entering the blocking strain field, and dilated upon leaving.