A Wavelet Representation of Synoptic-Scale Coherent Structures

Midlatitude cyclogenesis as interpreted in the framework of either baroclinic development or potential vorticity thinking heavily relies on the concept of synoptic-scale anomaly. Given the existence of potential vorticity inversion and attribution, what is at stake to provide a mathematical definition for this concept is a complete finite-amplitude alternative to the linear-based theory of cyclogenesis. The existence of a reasonably objective way to represent anomalies in both real and idealized flows would not only help understanding cyclogenesis, it would also have many other applications for both theory and in practical forecasts. Inspired by the recent theory of wavelet representation of coherent structures in two-dimensional fluid mechanics, a wavelet representation of three-dimensional potential vorticity anomalies is built. This algorithm relies on the selection of the appropriate two-dimensional wavelet coefficients from the stationary wavelet transform in order to guarantee the critical translation-invariance property. The sensitivity of the algorithm to the position, size, and shape of the structures is assessed. The wavelet extraction is then applied to the upper-level precursor of a real-case storm of December 1999 and is compared to a basic monopolar extraction. Using potential vorticity inversion and forecasts with a primitive-equation model, it is found that both anomalies have similar implications on the development of the surface cyclone. However, the coherence in time of the extracted wavelet structure in the forecast and analysis sequence is more satisfactory than the extracted monopole: this suggests that the underlying mathematical description of an anomaly proposed here does, indeed, point toward the direction of an actual physical reality of the concept.