Kinematic vorticity number – a tool for estimating vortex sizes and circulations

Abstract

The influence of extratropical vortices on a global scale is mainly characterised by their size and by the magnitude of their circulation. However, the determination of these properties is still a great challenge since a vortex has no clear delimitations but is part of the flow field itself. In this work, we introduce a kinematic vortex size determination method based on the kinematic vorticity number <em>W</em>_<em>k</em> to atmospheric flows. <em>W</em>_<em>k</em> relates the local rate-of-rotation to the local rate-of-deformation at every point in the field and a vortex core is identified as a simply connected region where the rotation prevails over the deformation. Additionally, considering the sign of vorticity in the extended <em>W</em>_<em>k</em>-method allows to identify highs and lows in different vertical layers of the atmosphere and to study vertical as well as horizontal vortex interactions. We will test the <em>W</em>_<em>k</em>-method in different idealised 2-D (superposition of two lows/low and jet) and real 3-D flow situations (winter storm affecting Europe) and compare the results with traditional methods based on the pressure and the vorticity fields. In comparison to these traditional methods, the <em>W</em>_<em>k</em>-method is able to extract vortex core sizes even in shear-dominated regions that occur frequently in the upper troposphere. Furthermore, statistics of the size and circulation distributions of cyclones will be given. Since the <em>W</em>_<em>k</em>-method identifies vortex cores, the identified radii are subsynoptic with a broad peak around 300–500 km at the 1000 hPa level. However, the total circulating area is not only restricted to the core. In general, circulations are in the order of 10⁷ m²/s with only a few cyclones in the order of 10⁸ m²/s.