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Optical Characteristics and Ground Flash Fraction Retrieval Analysis

This paper explores the optical characteristics of OTD flashes and the implications for flash-type discrimination, along with a model for retrieving the ground flash fraction from satellite lightning imager data. Detailed results from the research are presented, highlighting the use of mean optical data for flash discrimination and the mixed exponential distribution model. The paper also discusses the Bayesian inversion method and the sensitivity of retrieval errors to different sample sizes. The analysis includes simulated tests and a preliminary global retrieval of ground flash fraction using extensive data.

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Optical Characteristics and Ground Flash Fraction Retrieval Analysis

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  1. Flash-Type Discrimination GOES-AWG/R3 GLM Science Meeting September 29-30, 2009 Huntsville, AL Dr. William Koshak; NASA-MSFC

  2. Very Brief Summary of Results From … Koshak, W. J., Optical Characteristics of OTD Flashes and the Implications for Flash-Type Discrimination, to be submitted to JTECH, 2009. Koshak, W. J., R. J. Solakiewicz, Retrieving the Fraction of Ground Flashes from Satellite Lightning Imager Data Using CONUS-Based Optical Statistics, to be submitted to JTECH, 2009. Koshak, W. J., A Mixed Exponential Distribution Model for Retrieving Ground Flash Fraction from Satellite Lightning Imager Data, to be submitted to JTECH, 2009.

  3. Paper #1 Highlights

  4. IDL FlashMovie.pro Analysis Typical Ground Flash: Typical Cloud Flash: “Return Stroke Detector” … large group areas seem to indicate presence of a return stroke

  5. Distributions of MGA Cloud Flashes: Ground Flashes:

  6. Use of Mean Data Example of CLT: • Mean optical data could be used to discriminate • flash type since Central Limit Theorem removes • distributional overlap. • Using mean data implies examining • several (say N )flashes. • Examining N flashes implies you are looking • for the fraction of the N flashes that are • ground flashes.

  7. Paper #2 Highlights

  8. Paper #2 Highlights Mean of kth optical charactertistic: “Poor Man” Retrievals (Ground Flash Fraction) Multiple optical characteristics: One optical characteristic:

  9. Paper #3 Highlights

  10. Mixed Exponential Distribution Model Ground MGAs Cloud MGAs Results from Paper #1 Distribution of MGA modeled as a Mixed Exponential Distribution: Population Means of MGA: Require that:

  11. 1st International Interactive Workshop on Inverse Methods 1976

  12. Bayesian Inversion Bayes’ Law: Find parameters that maximize the probability on LHS. Invoking ignorance prior, means you just maximize the following : Formally : Practically :

  13. Initialization for Numerical Search Population mean and variance of the mixture: Using 1st equation to solve for gives an equation quadratic in , hence: where initialization as follows results in an initialization of :

  14. Retrieval Errors: Effect of Finite Sampling • Simulated tests • 4000 known “mixtures” of CGs/ICs. • Retrieval errors of ground flash fraction shown • for different values of N (# flashes analyzed)

  15. Retrieval Errors: Sensitivity to Alpha N = 2000 N = 5000 • Simulated tests • 100 known “mixtures” of CGs/ICs for each ground flash fraction (alpha) bin • Mean ground flash fraction retrieval errors shown for 2 values of N • Errors largest for alpha near 0 or 1 due to well-known “label switching” ambiguity

  16. “Label Switching” Problem p(y) is invariant under the following transformation: Specifically:

  17. Global Retrieval of Ground Flash Fraction (Preliminary) • 5 yrs OTD data • 4,365,395 flashes • 4o resolution bins • 563 bins • >= 2000 flashes/bin • Mean Alpha = 0.158 • Min Alpha = 0.009 • Max Alpha = 0.95 Ground flash fraction (alpha)

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