Dynamic Multi-scale Modes of Severe Storm Structure Detected in Mobile Doppler Radar Data by Entropy Field Decomposition

The mechanisms by which tornadoes are formed within supercell thunderstorms (tornadogenesis) remain a significant scientific mystery. This is a problem of both great scientific interest and social impact, as the ability to understand tornado formation is critical in reducing the time between issuing of tornado warnings to potentially affected populations and tornado formation.  However, the interplay of spatio-temporally varying processes within the highly dynamic supercell environment and tornadoes is much too complex to lend itself to analytical modeling, leaving es sentially two methods as viable approaches to addressing this problem: numerical simulation (e.g., Klemp and Rotunno (1983); Rotunno and Klemp (1985); Wicker and Wilhelmson (1995); Adler-man et al. (1999); Markowski et al. (2003); Markowski and Richardson (2014)) and observational methods, such as Doppler radar and in situ observations (e.g., Brandes (1978, 1984); Dowell and Bluestein (1997); Wakimoto and Cai (2000); Wakimoto et al. (2011, 2012); Trapp (1999); Dowell and Bluestein (2002a,b); M. et al. (2002); Beck et al. (2006); Wurman et al. (2007b,a,c); Grzychet al. (2007); Marquis et al. (2008); Wurman et al. (2010); Atkins et al. (2012); Marquis et al. (2012); Markowski et al. (2012a,b); Kosiba et al. (2013); Kosiba and Wurman (2013); Wurman and Kosiba (2013); Wurman et al. (2014)).  But while numerical simulations have the advantage of well-controlled initial conditions and explicitly described dynamics, they are computationally intensive and still can only approximate the physical conditions under which tornadogenesis occurs. Observational methods have their own drawbacks, not the least of which is the difficulty of deploying instruments in advantageous positions in rapidly evolving and hazardous environments and problematic terrain and the difficulty observing critical quantitites such as temperature and humidity aloft. Nevertheless, advances in observational technologies, in particular mobile Doppler radar and occasional in-situ observations, have facilitated the acquisition of increasingly accurate spatio-temporal volumetric data in tornadic storms. As the data integrity and complexity has increased, the role of data analysis has become increasingly critical. However, to date the primary method of analysis in Doppler radar studies of tornadogenesis has been confined to essentially qualitative analyses based on traditional visualization methods such as contour diagrams, isosurfaces, and streamline generation (e.g. Markowski et al. (2012a,b); Kosiba et al. (2013)). While these methods are straightforward (though burdensome) to implement, they are limited in their ability to capture and quantify spatio- temporal correlations patterns, or “modes”, that typically characterize such complex systems. This is a difficult task in a wide range of disciplines employing imaging of spatio-temporal data, such as functional magnetic resonance imaging (FMRI).

To address this problem, we have developed a general approach to the analysis of space-time volumetric data called the entropy field decomposition (EFD) (Frank and Galinsky (2016b,a)) which is based upon the reformulation of probability in terms of field theory, called Information Field Theory (Ensslin et al. (2009)), with the addition that prior coupling information is used to construct optimal (in the sense of maximum entropy) pathways or patterns in parameters space using our recently developed theory of Entropy Spectrum Pathways (ESP) (Frank and Galinsky (2014)). In addition to the detection of spatio-temporal modes, EFD can estimate optimal long- range connections simultaneously with local parameter estimates through the incorporation of the recently developed geometrical optics tractography method guided by ESP (GO-ESP; (Galinsky and Frank (2015))).

In this paper we apply EFD to dual-Doppler radar data collected by a Doppler On Wheels mobile radar system (DOW (Wurman et al. (1997); Wurman (2001))) during the genesis and intensification of a tornado observed in the 2nd Verification of the Origins of Tornadoes Experiment (VORTEX2 (Wurman et al. (2012))). We demonstrate the ability to extract spatio-temporal features hypothesized to be associated with tornadogenesis observed by more traditional, but laborious and primarily qualitative, analysis methods (Markowski et al. (2012a,b); Kosiba et al. (2013)). In addition, we demonstrate the ability to reconstruct long-term correlations (tracts) of the underlying fields (e.g., vorticity), revealing how such long- range coherences are related to estimated local parameters (e.g. vorticity stretching) and detect spatio-temporal modes of measured quantities (e.g.,radar reflectivity), providing a quantitative picture of the dynamics of tornadogenesis. In particular, we investigate the role of the descending reflectivity core (DRC) that has been implicated as a possible triggering/focusing mechanism in tornadogenesis (Markowski et al. (2012a); Kosibaet al. (2013)) and demonstrate results that support this hypothesis quantitatively.  Our method is both automated and quantitative and provides an analysis approach of increased sensitivity to kinematic features possibly related to tornadogenesis, and thus may provide an analysis method suitable for use with operational weather radar networks deployed in the service of protecting the public.