Lightning Distance Estimation Using LF Lightning Radio Signals via Analytical and Machine-Learned Models

Lightning geolocation is useful in a variety of applications, ranging from weather nowcasting to a better understanding of thunderstorm evolution processes and remote sensing of the ionosphere. Lightning-generated radio signals can be used in range estimation of lightning return strokes, for which the most commonly employed technique is the time difference of arrival in lightning detection networks. Though these instrument networks provide the most reliability and best accuracy, users without access to them can instead benefit from lightning geolocation using a standalone instrument. In this article, we present the framework for training fast models capable of estimating negative cloud-to-ground lightning location from single-instrument observations of very low frequency/low frequency (VLF/LF, 3-300 kHz) radio pulses or "sferics," without knowledge of the ionosphere's D-region state. The models are generated using an analytical method, based on the delay between ground and skywave, and a machine learning method. The training framework is applied to three different data sets to assess model accuracy. Validation of the machine-learned models for these data sets, which include both simulated and observed sferics, confirms this technique as a promising solution for lightning distance estimation using a single receiver. Distance estimates using a machine-learned model for observed sferics in Kansas yield an RMSE of 53 km with 68% of them being within 9.8 km. Estimates using the analytical method are found to have an RMSE of 54 km with 68% of them being within 32 km. Limitations of our methodology and potential improvements to be investigated are also discussed.