Introduction of an atmospheric moment combining Eulerian and Lagrangian aspects of vortices: Application to tornadoes

Various definitions of the intensity of atmospheric vortices exist. These definitions are often based on local parameters in a field. Otherwise, atmospheric vortices are analyzed concerning their geometric properties. A combination of both is rarely used.The aim of this publication is an expansion from a local, mass-specific view to a mass-related strength parameter, called atmospheric moment. The atmospheric moment is characterized by a combination of Eulerian parameters of intensity and Lagrangian aspects like track length and area of atmospheric vortices. The atmospheric moment is designed analogous to the seismic moment that describes the strength of earthquakes. Probability density distributions of tornadoes concerning their atmospheric moment show power law behavior. Compared with earthquakes, the scaling exponent is slightly smaller but of comparable order. In principle, this theoretical concept can also be applied to other atmospheric vortices like cyclones and hurricanes.