Lightning channel length and flash energy determined from moments of the flash area distribution

A widely used approach in observational and modeling studies of NO_x produced by lightning is to relate NO_x production to the number of flashes, without regard for the distribution of lightning flash sizes. Recent studies have begun to consider channel length and flash size, which is now observable with VHF Lightning Mapping Array data. This study uses a capacitor model for flash energy based on the flash coverage area, which defines a size scale. This flash area is then filled with channel using a fractal method and compared to other methods that estimate length directly from the VHF source locations. In the presence of instrument measurement errors, area- and fractal-based estimates are shown to be more stable estimators of flash length than connect-the-dots approaches and therefore are better suited for comparison to NO_x production. A geometric interpretation of using vertical profiles of VHF source density to weight the altitude distribution of total channel length is developed. An example of the time series of moments of the lightning flash size distribution is shown for an example case, and some meteorological interpretation is given.