Bayesian Analysis of Lightning Data Sets

As lightning locating systems improve in quality and quantity, applications of lightning data have increased across a variety of meteorological disciplines. Because of this, it is critical to understand how the performance of each system compares to the others. One metric used to compare lightning locating systems is the detection efficiency. This can be used to select a system for a particular application. As more lightning locating systems become operational, there is an opportunity to combine data from various systems to provide a more robust estimate of lightning activity. Hence, there is a growing need to quantitatively decide how to best assimilate data between systems in order to fully exploit applications of lightning data.

Typically, the detection efficiency of one system is found by comparing the data from one system to another, assuming the latter provides a truth data set. This represents a frequentist approach of comparing systems. Strictly speaking, this method provides a conditional probability, i.e., the probability one system detects a lightning discharge given another system has. However, there is more information to be gleaned when comparing lightning locating systems. The “reverse” conditional probability can also be found. These two quantities can be combined with Bayes' Theorem to provide a relative detection efficiency, a more robust metric when comparing lightning locating systems. In this manner, the full information provided by both systems can be used. Further, this Bayesian methodology can be extended to more than just two lightning data sets.

We present results comparing three different ground based lightning locating systems: the Global Lightning Dataset 360 (GLD360), the Earth Networks Total Lightning Network (ENTLN), and the World Wide Lightning Location Network (WWLLN). The base measurement of each corresponds to a similar process in the lightning discharge and is used for the comparison. The conditional probabilities that lightning is detected by one system is found relative to each other system. These are exploited using Bayes' Theorem to determine the relative detection efficiency for each system. These results are explored across different domains to assess system attributes. In addition, probability laws are used to derive the quantitative benefit in assimilating each lightning locating system into a combined data set. This application of Bayesian methods to relatively new meteorological data sets provides a clear and quantitative way to compare lightning data.