Lightning Scaling Relations Revisited

Abstract

Scaling relations connecting storm electrical generator power (and hence lightning flash rate) to charge transport velocity and storm geometry were originally posed by Vonnegut in the 1960s. These 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 Vonnegut's original theory. Revised formulations consistent with Vonnegut's original framework are presented. These demonstrate that Vonnegut's theory is, to first order, consistent with recent satellite observations. 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 and numerically testable. The two approaches also differ significantly in their physical explanations of regional variability in lightning observations.