We thank Drs. George Craig and Christian Keil for their support during the course of the work. Helpful discussions about cloud electrification and lightning with Drs. Ted Mansell, Dennis Boccippio, Axel Seifert, Kersten Schmidt, Earle Williams, and Rohan Jayaratne are gratefully acknowledged. Professor H. D. Betz kindly provided the LINET data. Our thanks are extended to the Convective Storms Group at NCSU and to the anonymous reviewers for their careful comments on the manuscript. This study was funded by the DLR project “Wetter und Fliegen.”
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Introducing this quantity was motivated by Boccippio (2002), who used a so-called charge-removal efficiency.
Note, however, that the approach by Blyth et al. (2001) is dimensionally inconsistent [see their Eq. (1)]. They stipulate that fΔQ ∝ j. While the left-hand side of this equation has the dimension of an electric current ([fΔQ] = A), the right-hand side has the dimension of a current density ([j] = A m−2). Indirectly, this implies that there is a characteristic cross-sectional area of the updrafts that is identical for all storms.
Their reasoning suggests that they erroneously used energy instead of power, as did Price and Rind (1992). Setting f ∝ W, while the lightning energy
From a mathematical perspective, this pattern of behavior is reflected in the quadratic equation for ΔQ that may be obtained from Eq. (19). Assuming an ideal capacitor where W = Q2/(2C), and in addition that W > 0 and ΔW < 0, the root of the quadratic equation becomes complex if |ΔW| > W.
Using, e.g., the electrostatic field, Ψ = E results in a somewhat complicated equation for the flash rate, which after some manipulations reduces to Eq. (26).
This corresponds to the balance Ic − IL − Ileak = 0.
Note that lightning rates of several hundred flashes per minute are reported to have accompanied intense supercells, as inferred from VHF sources using the Lightning Mapping Array (LMA) (e.g., Kuhlman et al. 2006). However, the LMA detects different properties of a discharge than LINET does, rendering the inferred flash rates not directly comparable. Moreover, grouping of VHF signals detected by the LMA into flashes is not straightforward and leads to uncertainties in the inferred flash rate especially in high-flash-rate storms, as discussed in Wiens et al. (2005, p. 4157).
A mouse-over function of the software used to display the radar data resulted in a higher accuracy in retrieving the data than is implied by the images in Fig. 5.
If charge is removed from altitudes of order 10 km, this corresponds to about 150 C of lightning charge.