Modeling the flash rate of thunderstorms. Part I: Framework

In this study a straightforward theoretical approach to determining the flash rate in thunderstorms is presented. A two-plate capacitor represents the basic dipole charge structure of a thunderstorm, which is charged by the generator current and discharged by lightning. If the geometry of the capacitor plates, the generator-current density, and the lightning charge are known, and if charging and discharging are in equilibrium, then the flash rate is uniquely determined. To diagnose the flash rate of real-world thunderstorms using this framework, estimates of the required relationships between the predictor variables and observable cloud properties are provided. With these estimates, the flash rate can be parameterized. In previous approaches, the lightning rate has been set linearly proportional to the electrification rate (such as the storm's generator power or generator current), which implies a constant amount of neutralization by lightning discharges (such as lightning energy or lightning charge). This leads to inconsistencies between these approaches. Within the new framework proposed here, the discharge strength is allowed to vary with storm geometry, which remedies the physical inconsistencies of the previous approaches. The new parameterization is compared with observations using polarimetric radar data and measurements fromthe lightning detection network, LINET. The flash rates of a broad spectrumof discrete thunderstormcells are accurately diagnosed by the new approach, while the flash rates of mesoscale convective systems are overestimated.