Theory and Observations of Controls on Lightning Flash Size Spectra

Previous analyses of very high frequency (VHF) Lightning Mapping Array (LMA) observations relative to the location of deep convective updrafts have noted a systematic pattern in flash characteristics. In and near strong updrafts, flashes tend to be smaller and more frequent, while flashes far from strong vertical drafts exhibit the opposite tendency. This study quantitatively tests these past anecdotal observations using LMA data for two supercell storms that occurred in Oklahoma in 2004. The data support a prediction from electrostatics that frequent breakdown and large flash extents are opposed. An energetic scaling that combines flash rate and flash area exhibits a 5/3 power-law scaling regime on scales of a few kilometers and a maximum in flash energy at about 10 km. The spectral shape is surprisingly consistent across a range of moderate to large flash rates. The shape of this lightning flash energy spectrum is similar to that expected of turbulent kinetic energy spectra in thunderstorms. In line with the hypothesized role of convective motions as the generator of thunderstorm electrical energy, the correspondence between kinematic and electrical energy spectra suggests that advection of charge-bearing precipitation by the storm's flow, including in turbulent eddies, couples the electrical and kinematic properties of a thunderstorm.