Abstract
An analytic perturbation method is introduced for retrieving the lightning ground flash fraction in a set of N lightning flashes observed by a satellite lightning mapper. The value of N must be large, typically in the thousands, and the satellite lightning optical observations consist of the maximum group area (MGA) produced by each flash. Moreover, the method subsequently determines the flash type (ground or cloud) of each of the N flashes. Performance tests of the method were conducted using simulated observations that were based on Optical Transient Detector (OTD) and Lightning Imaging Sensor (LIS) data. It is found that the mean ground flash fraction retrieval errors are below 0.04 across the full range 0–1 under the nominal conditions defined. In general, it is demonstrated that the retrieval errors depend on many factors (i.e., the number N of satellite observations, the magnitude of random and systematic instrument measurement errors, the ground flash fraction itself, and the number of samples used to form certain climate distributions employed in the method). The fraction of flashes accurately flash typed by the method averaged better than 78%. Overall, the accuracy of ground flash fraction and flash-typing retrievals degrade as the simulated population ground and cloud flash MGA distributions become more identical. Finally, because the analytic perturbation method was found to be quite robust (i.e., it performed well for several arbitrary underlying MGA distributions), it is not restricted to the lightning problem studied here but can be applied to any inverse problem having a similar problem statement.
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