Three-dimensional potential vorticity structures for extreme precipitation events on the convective scale

Abstract

Three-dimensional potential vorticity (PV) structures on the convective scale during extreme precipitation events are investigated. Using the high resolution COSMO-REA2 data set, 3D composites of the PV, with and without Coriolis parameter and related variables, are evaluated for different classes of precipitation intensity. The development of a significant horizontal dipole structure in the immediate vicinity of the precipitation maximum and the updraft can be explained by the twisting term in the vorticity equation. This is because the vorticity equation is proportional to the PV equation for strong convective processes. This theoretical is important on the convective scale without the consideration of the Coriolis effect, which is a typical characteristic on the synoptic scale. In accordance to previous studies, the horizontal PV dipole is statistically confirmed by 3D composites of the PV and corresponding variables. We show that the dipole structures are especially distinct for the relative PV without Coriolis parameter and the relative vorticity. On the convective scale, the thermodynamical sources and sinks of the potential vorticity indicate the diabatic processes that are related to conservative vortex dynamics via the proportionality of the diabatic heating and the vertical velocity. This work confirms that the PV equation is an important tool in atmospheric dynamics that unifies the thermodynamical processes as well as the dynamical processes into one scalar.

Keywords:

• potential vorticity
• twisting term
• vorticity equation, extreme precipitation

Acknowledgments

The authors thank the unknown reviewer for helpful comments and suggestions. We also thank Tracy Kiszler for careful reading the manuscript and Martin Rudolph for reproducing Fig. 2. The authors thank the University of Bonn and the German Weather Service (DWD) for providing the COSMO-REA 2 data set and the Deutsche Forschungsgemeinschaft for their support within the framework of CRC 1114 ‘Scaling Cascades in Complex Systems’, project A01. The authors acknowledge support by the Open Access Publication Fund of the Freie Universität Berlin.

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Notes

Notes

1 Recall the notation for the wind vector components $\mathbf{v}=(u,v,w),$ and the Coriolis parameter vector $(0,\mathcal{\ell },f)$ with $\mathcal{\ell }=2\Omega \hspace{0.17em}\text{cos}\hspace{0.17em}(\phi )$ and $f=2\Omega \hspace{0.17em}\text{sin}\hspace{0.17em}(\phi ).$

2 Chagnon and Gray (2009) assume a Gaussian heating profile of the form $B=c\hspace{0.17em}\text{exp}\hspace{0.17em}\left[-\left(\frac{x-x_0}{2{\sigma }_x^2}+\frac{z-z_0}{2{\sigma }_z^2}\right)\right]$ with the location of the centre of the heating (x₀, y₀), the heating length-scales in the cross-frontal and vertical directions σ_x and σ_z, and c denotes the constant maximum amplitude of the heating rate B.