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Lightning is a destructive and highly visible product of severe storms, yetthere is still much to be learned about the conditions under which lightning ismost likely to occur. The GOES-16 and GOES-17 satellites, launched in 2016 and2018 by NOAA and NASA, collect a wealth of data regarding individual lightningstrike occurrence and potentially related atmospheric variables. The acutenature and inherent spatial correlation in lightning data renders standardregression analyses inappropriate. Further, computational considerations areforegrounded by the desire to analyze the immense and rapidly increasing volumeof lightning data. We present a new computationally feasible method thatcombines spectral and Laplace approximations in an EM algorithm, denoted SLEM,to fit the widely popular log-Gaussian Cox process model to large spatial pointpattern datasets. In simulations, we find SLEM is competitive with contemporarytechniques in terms of speed and accuracy. When applied to two lightningdatasets, SLEM provides better out-of-sample prediction scores and quickerruntimes, suggesting its particular usefulness for analyzing lightning data,which tend to have sparse signals.

Log-Gaussian Cox Process Modeling of Large Spatial Lightning Data using Spectral and Laplace Approximations