![Page 1: Photo by Chuck Doswell Ground Flash Fraction Retrieval Algorithm GLM Science Meeting December 1-3, 2010, Huntsville, AL Dr. William Koshak, NASA/MSFC/VP61](https://reader034.vdocuments.us/reader034/viewer/2022052606/5a4d1b1d7f8b9ab05999431c/html5/thumbnails/1.jpg)
photo by Chuck Doswell
Ground Flash Fraction Retrieval AlgorithmGLM Science Meeting
December 1-3, 2010, Huntsville, ALDr. William Koshak, NASA/MSFC/VP61
![Page 2: Photo by Chuck Doswell Ground Flash Fraction Retrieval Algorithm GLM Science Meeting December 1-3, 2010, Huntsville, AL Dr. William Koshak, NASA/MSFC/VP61](https://reader034.vdocuments.us/reader034/viewer/2022052606/5a4d1b1d7f8b9ab05999431c/html5/thumbnails/2.jpg)
# GLMFlashes
Ground Flash FractionRetrieval Algorithm
(today’s talk)
# GLMGroundFlashes
# GLMCloudFlashes
MSFC LNOM(lightning NOx)
Air Quality Models (e.g. CMAQ)
Global Chemistry/Climate Models (e.g. GISS Model E, Geos Chem)
Desired Future Application
![Page 3: Photo by Chuck Doswell Ground Flash Fraction Retrieval Algorithm GLM Science Meeting December 1-3, 2010, Huntsville, AL Dr. William Koshak, NASA/MSFC/VP61](https://reader034.vdocuments.us/reader034/viewer/2022052606/5a4d1b1d7f8b9ab05999431c/html5/thumbnails/3.jpg)
Algorithm is used to solve an Algorithm is used to solve an Inversion ProblemInversion Problem
f
UnknownMeasurements g
K(Kernel)
(Footprints) (Dragon)
![Page 4: Photo by Chuck Doswell Ground Flash Fraction Retrieval Algorithm GLM Science Meeting December 1-3, 2010, Huntsville, AL Dr. William Koshak, NASA/MSFC/VP61](https://reader034.vdocuments.us/reader034/viewer/2022052606/5a4d1b1d7f8b9ab05999431c/html5/thumbnails/4.jpg)
What % Strike Ground?
![Page 5: Photo by Chuck Doswell Ground Flash Fraction Retrieval Algorithm GLM Science Meeting December 1-3, 2010, Huntsville, AL Dr. William Koshak, NASA/MSFC/VP61](https://reader034.vdocuments.us/reader034/viewer/2022052606/5a4d1b1d7f8b9ab05999431c/html5/thumbnails/5.jpg)
Consider a (linear) Optics Analog Mueller Matrix: A matrix which can be used to reproduce the effect of a given optical element when applied to a Stokes vector.
Optical Element Mueller Matrix (Singular)1 1 0 01 1 0 010 0 0 020 0 0 0
1 0 0 10 0 0 010 0 0 021 0 0 1
Linear horizontal polarizer
Right-handed circular polarizer
Optical Elements
Kfobserver
g Source
![Page 6: Photo by Chuck Doswell Ground Flash Fraction Retrieval Algorithm GLM Science Meeting December 1-3, 2010, Huntsville, AL Dr. William Koshak, NASA/MSFC/VP61](https://reader034.vdocuments.us/reader034/viewer/2022052606/5a4d1b1d7f8b9ab05999431c/html5/thumbnails/6.jpg)
In Reality:
MultipleScatteringMedium
![Page 7: Photo by Chuck Doswell Ground Flash Fraction Retrieval Algorithm GLM Science Meeting December 1-3, 2010, Huntsville, AL Dr. William Koshak, NASA/MSFC/VP61](https://reader034.vdocuments.us/reader034/viewer/2022052606/5a4d1b1d7f8b9ab05999431c/html5/thumbnails/7.jpg)
ActualForwardMultipleScatteringProblem
![Page 8: Photo by Chuck Doswell Ground Flash Fraction Retrieval Algorithm GLM Science Meeting December 1-3, 2010, Huntsville, AL Dr. William Koshak, NASA/MSFC/VP61](https://reader034.vdocuments.us/reader034/viewer/2022052606/5a4d1b1d7f8b9ab05999431c/html5/thumbnails/8.jpg)
Eqs. (21)is the ForwardProblem… it’s ugly.
InverseProblemis uglier.
![Page 9: Photo by Chuck Doswell Ground Flash Fraction Retrieval Algorithm GLM Science Meeting December 1-3, 2010, Huntsville, AL Dr. William Koshak, NASA/MSFC/VP61](https://reader034.vdocuments.us/reader034/viewer/2022052606/5a4d1b1d7f8b9ab05999431c/html5/thumbnails/9.jpg)
Is there achannelto ground?
Formal Inverse Problem:Reconstruct Channel from Intensity
![Page 10: Photo by Chuck Doswell Ground Flash Fraction Retrieval Algorithm GLM Science Meeting December 1-3, 2010, Huntsville, AL Dr. William Koshak, NASA/MSFC/VP61](https://reader034.vdocuments.us/reader034/viewer/2022052606/5a4d1b1d7f8b9ab05999431c/html5/thumbnails/10.jpg)
Historical Recap• Several studied the forward problem
Thomason & Krider 1982 (Monte Carlo)Koshak et al. 1994 (Boltzmann Diffusion)Suszcynsky et al. 2000 (optical & vhf data, not theory)Light et al. 2001 (Monte Carlo)Davis & Marshak 2002 (Green’s functions)
• Nobody published the inverse problem for channel reconstruction; flash-by-flash-discrimination (FBFD)
• Neural Net (Boccippio … unknown status); probabilistic FBFD
• Bayesian Inversion (Koshak); ground flash fraction retrieval
![Page 11: Photo by Chuck Doswell Ground Flash Fraction Retrieval Algorithm GLM Science Meeting December 1-3, 2010, Huntsville, AL Dr. William Koshak, NASA/MSFC/VP61](https://reader034.vdocuments.us/reader034/viewer/2022052606/5a4d1b1d7f8b9ab05999431c/html5/thumbnails/11.jpg)
Bayesian Inversion
![Page 12: Photo by Chuck Doswell Ground Flash Fraction Retrieval Algorithm GLM Science Meeting December 1-3, 2010, Huntsville, AL Dr. William Koshak, NASA/MSFC/VP61](https://reader034.vdocuments.us/reader034/viewer/2022052606/5a4d1b1d7f8b9ab05999431c/html5/thumbnails/12.jpg)
Find & examine the “group” in the flash having the Maximum Area.
Use just 1 physical parameter
![Page 13: Photo by Chuck Doswell Ground Flash Fraction Retrieval Algorithm GLM Science Meeting December 1-3, 2010, Huntsville, AL Dr. William Koshak, NASA/MSFC/VP61](https://reader034.vdocuments.us/reader034/viewer/2022052606/5a4d1b1d7f8b9ab05999431c/html5/thumbnails/13.jpg)
Distributions of the Maximum Group Area (MGA)
Ground Flashes Cloud Flashes
![Page 14: Photo by Chuck Doswell Ground Flash Fraction Retrieval Algorithm GLM Science Meeting December 1-3, 2010, Huntsville, AL Dr. William Koshak, NASA/MSFC/VP61](https://reader034.vdocuments.us/reader034/viewer/2022052606/5a4d1b1d7f8b9ab05999431c/html5/thumbnails/14.jpg)
Shifted MGA y = MGA – 64 km2
![Page 15: Photo by Chuck Doswell Ground Flash Fraction Retrieval Algorithm GLM Science Meeting December 1-3, 2010, Huntsville, AL Dr. William Koshak, NASA/MSFC/VP61](https://reader034.vdocuments.us/reader034/viewer/2022052606/5a4d1b1d7f8b9ab05999431c/html5/thumbnails/15.jpg)
![Page 16: Photo by Chuck Doswell Ground Flash Fraction Retrieval Algorithm GLM Science Meeting December 1-3, 2010, Huntsville, AL Dr. William Koshak, NASA/MSFC/VP61](https://reader034.vdocuments.us/reader034/viewer/2022052606/5a4d1b1d7f8b9ab05999431c/html5/thumbnails/16.jpg)
![Page 17: Photo by Chuck Doswell Ground Flash Fraction Retrieval Algorithm GLM Science Meeting December 1-3, 2010, Huntsville, AL Dr. William Koshak, NASA/MSFC/VP61](https://reader034.vdocuments.us/reader034/viewer/2022052606/5a4d1b1d7f8b9ab05999431c/html5/thumbnails/17.jpg)
![Page 18: Photo by Chuck Doswell Ground Flash Fraction Retrieval Algorithm GLM Science Meeting December 1-3, 2010, Huntsville, AL Dr. William Koshak, NASA/MSFC/VP61](https://reader034.vdocuments.us/reader034/viewer/2022052606/5a4d1b1d7f8b9ab05999431c/html5/thumbnails/18.jpg)
Retrieval Errors with Increasing N (N = # flashes observed)
![Page 19: Photo by Chuck Doswell Ground Flash Fraction Retrieval Algorithm GLM Science Meeting December 1-3, 2010, Huntsville, AL Dr. William Koshak, NASA/MSFC/VP61](https://reader034.vdocuments.us/reader034/viewer/2022052606/5a4d1b1d7f8b9ab05999431c/html5/thumbnails/19.jpg)
Improvements using Normal Priors
Priors P(µg) and P(µc) areUniformly Distributed
Priors P(µg) and P(µc) areNormally Distributed
P(α, µg , µc) = P(α) P(µg) P(µc) = 1· P(µg) P(µc)
![Page 20: Photo by Chuck Doswell Ground Flash Fraction Retrieval Algorithm GLM Science Meeting December 1-3, 2010, Huntsville, AL Dr. William Koshak, NASA/MSFC/VP61](https://reader034.vdocuments.us/reader034/viewer/2022052606/5a4d1b1d7f8b9ab05999431c/html5/thumbnails/20.jpg)
Retrieved Ground Flash Fraction
![Page 21: Photo by Chuck Doswell Ground Flash Fraction Retrieval Algorithm GLM Science Meeting December 1-3, 2010, Huntsville, AL Dr. William Koshak, NASA/MSFC/VP61](https://reader034.vdocuments.us/reader034/viewer/2022052606/5a4d1b1d7f8b9ab05999431c/html5/thumbnails/21.jpg)
Koshak, W. J., Optical Characteristics of OTD Flashes and the Implications for Flash-Type Discrimination, J. Atmos. Oceanic Technol., 27, 1822-1838, 2010. (November issue)
Koshak, W. J., R. J. Solakiewicz, Retrieving the Fraction of Ground Flashes from Satellite Lightning Imager Data Using CONUS-Based Optical Statistics, accepted in J. Atmos. Oceanic Technol., August 30, 2010.
Koshak, W. J., A Mixed Exponential Distribution Model for Retrieving Ground Flash Fraction from Satellite Lightning Imager Data, accepted in J. Atmos. Oceanic Technol., August 30, 2010.
For More Details …