A climatology of cell mergers with supercells and their association with mesocyclone evolution

In this study, we present a climatology of observed cell mergers along the paths of 342 discrete, right-moving supercells and their association with temporal changes in low-level mesocyclone strength (measured using azimuthal shear). Nearly half of the examined supercells experience at least one cell merger. The frequency of cell merger occurrence varies somewhat by geographical region and the time of day. No general relationship exists between cell merger occurrence and temporal changes in low-level azimuthal shear; this corroborates prior studies in showing that the outcome of a merger is probably sensitive to storm-scale and environmental details not captured in this study. Interestingly, we find a significant inverse relationship between pre-merger azimuthal shear and the subsequent temporal evolution of azimuthal shear. In other words, stronger low-level mesocyclones are more likely to weaken after cell mergers, and weaker low-level mesocyclones are more likely to strengthen. We also show that shorter-duration cell merger “events” (comprised of multiple individual mergers) are more likely to be associated with a steady or weakening low-level mesocyclone, while longer-duration cell merger events (3–4 individual mergers) are more likely to be associated with a strengthening low-level mesocyclone. These findings suggest what physical processes may influence the outcome of a merger in different scenarios and that the impact of these processes on low-level mesocyclone strength may change depending on storm maturity. We establish a baseline understanding of the supercell-cell merger climatology and highlight areas for future research in how to better anticipate the outcomes of cell mergers.

Tornado Formation and Intensity Prediction Using Polarimetric Radar Estimates of Updraft Area

A sample of 198 supercells are investigated to determine if a radar proxy for the area of the storm midlevel updraft may be a skillful predictor of imminent tornado formation and/or peak tornado intensity. A novel algorithm, a modified version of the Thunderstorm Risk Estimation from Nowcasting Development via Size Sorting (TRENDSS) algorithm is used to estimate the area of the enhanced differential radar reflectivity factor (ZDR) column in Weather Surveillance Radar – 1988 Doppler data; the ZDR column area is used as a proxy for the area of the midlevel updraft. The areas of ZDR columns are compared for 154 tornadic supercells and 44 non-tornadic supercells, including 30+ supercells with tornadoes rated EF1, EF2, and EF3; nine supercells with EF4+ tornadoes also are analyzed. It is found that (i) at the time of their peak 0-1 km azimuthal shear, non-tornadic supercells have consistently small (< 20 km2) ZDR column areas while tornadic cases exhibit much greater variability in areas, and (ii) at the time of tornadogenesis, EF3+ tornadic cases have larger ZDR column areas than tornadic cases rated EF1/2. In addition, all nine violent tornadoes sampled have ZDR column areas > 30 km2 at the time of tornadogenesis. However, only weak positive correlation is found between ZDR column area and both radar-estimated peak tornado intensity and maximum tornado path width. Planned future work focused on mechanisms linking updraft size and tornado formation and intensity is summarized and the use of the modified TRENDSS algorithm, which is immune to ZDR bias and thus ideal for real-time operational use, is emphasized.

Evaluating the response of a modified Gent-Thomas strain energy function having limiting chain extensibility condition in torsion and azimuthal shear

The purpose of this paper is to investigate the torsion and azimuthal shear of an incompressible hyperelastic cylinder having a modified Gent-Thomas strain energy with limiting chain extensibility condition. First, the torsional response of the modified Gent-Thomas model is obtained analytically and compared with those of Gent-Gent, Gent-Thomas, and Carroll strain energy models where the former model incorporates the limiting chain extensibility condition while the latter two are phenomenological models. The results show the modified Gent-Thomas model to be in better agreement with the experimental data of Rivlin and Saunders on torsion than the other three models. To further evaluate the response of the modified Gent-Thomas model, azimuthal shear deformation of an incompressible hyperelastic cylinder with the modified Gent-Thomas, Gent-Thomas, Gent-Gent, and Carroll strain energies is considered, where the angular displacement in azimuthal shear is determined analytically for the first three models and numerically for the fourth model. It is shown that the strain hardening effect, predicted either by the limiting chain extensibility condition for the modified Gent-Thomas and Gent-Gent models or phenomenologically by the Carroll model, is quite significant in the azimuthal shear response of the incompressible cylinder.

Estimates of Gradients in Radar Moments Using a Linear Least Squares Derivative Technique

The local, linear, least squares derivative (LLSD) approach to radar analysis is a method of quantifying gradients in radar data by fitting a least squares plane to a neighborhood of range bins and finding its slope. When applied to radial velocity fields, for example, LLSD yields part of the azimuthal (rotational) and radial (divergent) components of horizontal shear, which, under certain geometric assumptions, estimate one-half of the two-dimensional vertical vorticity and horizontal divergence equations, respectively. Recent advances in computational capacity as well as increased usage of LLSD products by the meteorological community have motivated an overhaul of the LLSD methodology’s application to radar data. This paper documents the mathematical foundation of the updated LLSD approach, including a complete derivation of its equation set, discussion of its limitations, and considerations for other types of implementation. In addition, updated azimuthal shear calculations are validated against theoretical vorticity using simulated circulations. Applications to nontraditional radar data and new applications to nonvelocity radar data including reflectivity at horizontal polarization, spectrum width, and polarimetric moments are also explored. These LLSD gradient calculations may be leveraged to identify and interrogate a wide variety of severe weather phenomena, either directly by operational forecasters or indirectly as part of future automated algorithms.

Radar Network–Based Detection of Mesocyclones at the German Weather Service

The radar network of the German Weather Service [Deutscher Wetterdienst (DWD)] provides 3D Doppler data in high spatial and temporal resolution, supporting the identification and tracking of dynamic small-scale weather phenomena. The software framework Polarimetric Radar Algorithms (POLARA) has been developed at DWD to better exploit the capabilities of the existing remote sensing data. The data processing and quality assurance implemented in POLARA include a dual-PRF dealiasing algorithm with error correction. Azimuthal shear information is derived and processed in the mesocyclone detection algorithm (MCD). Low- and midlevel azimuthal shear and track products are available as composite (multiradar) products. Azimuthal shear may be considered as a proxy for rotation. The MCD results and azimuthal shear products are part of the severe weather detection algorithms of DWD and are provided to the forecaster on the NinJo meteorological workstation system. The forecaster analyzes potentially severe cells by combining near-storm environment data with the MCD product as well as with the instantaneous azimuthal shear products (mid- and low level) and their tracks. These products and tracks are used to diagnose threat potential by means of azimuthal shear intensity and track longevity. Feedback from forecasters has shown the utility of the algorithms to analyze and diagnose severe convective cells in Germany and in adjacent Europe. In this paper, the abovementioned algorithms and products are presented in detail and case studies illustrating usability and performance are shown.

Some boundary-value problems for uniform isotropic incompressible materials

This chapter outlines the formulation and explicit solution of a number of simple boundary-value problems. Analysis is facilitated by the constraint of incompressibility. Examples include expansionand contraction of cylinders, torsion, azimuthal shear, and cavitation under conditions of spherical symmetry Further examples involving anti-plane shear are discussed in the Problems.