Lightning Scaling Laws Revisited

Abstract

Scaling laws relating storm electrical generator power (and hence lightning flash rate) to charge transport velocity and storm geometry were originally posed by Vonnegut (1963). These laws were later simplified to yield simple parameterizations for lightning based upon cloud top height, with separate parameterizations derived over land and ocean. It is demonstrated that the most recent ocean parameterization: (1) yields predictions of storm updraft velocity which appear inconsistent with observation, and (2) is formally inconsistent with the theory from which it purports to derive. Revised formulations consistent with Vonnegut's original framework are presented. These demonstrate that Vonnegut's theory is, to first order, consistent with observation. The implications of assuming that flash rate is set by the electrical generator power, rather than the electrical generator current, are examined. The two approaches yield significantly different predictions about the dependence of charge transfer per flash on storm dimensions, which should be empirically testable. The two approaches also differ significantly in their explanation of regional variability in lightning observations.