Status of Ground Flash Fraction Retrieval Algorithm

Dr. William Koshak, NASA-MSFC

GLM Science MeetingHuntsville, AL

September 19, 2012

Space Shuttle Video (STS-48)

Algorithms Use Maximum Group Area (MGA)

to retrieve Ground Flash Fraction (α)

+ =1000 CGs 4000 ICs 5000 total

Three Basic Algorithms:

Simple:

Bayesian:

Perturbation Methods:

Retrieve characteristics about these. INVERT

(Observe)

GLM Observes a Mixture of CG and IC MGAs

(1 ) get (assume & )g c g cx x x x x

g( ; , , , ...) ( ; ,...) (1 ) ( ; ,...) get ( , , , ...)g c g c c g cp x p x p x

( ; ) ( ) (1 ) ( ) get { , ( ), ( )} !g c g cp x p x p x p x p x

The pathway to theAnalytic Perturbation Method

MIX

(1 ) m g c

gNG g cNC c

NM m M G C

/gN N

(1 ) m g c

(1 )r r m u v

(Actual)

(Dynamic Model)

Nm

( , , )r d e

(1 )[ ] (1 )[ ] (1 )r r r r

m g cm a d b e u v

Find that minimizes:

( , ) fixed climate( , ) perturbants (perturbation vectors)

a bd e

2( , , ) ( )rS d e m m

BASIC PERTURBATION METHOD(Vary both d and e)

m

So force m m( ) (1 )( ) .i r i i r i im a d b e

(1 )( ) 0.i r i ii i

r

m b ed a S

QUASI-ANALYTIC PERTURBATION METHOD

lives in (u, v) plane

(1 )r r m u v

(Vary just e; d obtained analytically)

ANALYTIC PERTURBATION METHOD(d and e obtained analytically)

2 2 2 2

1 1

( ; , , ) ( ) | | ( ) | | ( ) ( ) .n n

r r r r i r ii i

H H p q p d q e

m a b d e

2 2 .i i i i id Ae B e C

2

1

( ) .n

i i i ii

H pA q e pB e pC

2( ) 0 .k kk

dH pA q e pBde

2 2 22

2 2 2

2 ( ) 2( ) , ( , , , ) , ( , , , )

, 1( ) , ( ) .

r r i i i r i i r irr i i r i i r

r r r

i i r i r r

r r

a a aA A B B C C

m bp p q q

m a b m a b

Define:

But:

Hence:

Where:

Find e that minimizes H:

Substitute optimal e back into expression for H:

, 1,..., .2( )

kk

pBe k npA q

2 2

1

( ; , , ) .4( )

ni

r ii

p BH pCpA q

m a b

… Quick plot of H vs. provides the solution (i.e. value of than minimizes H) r r

Using OTD Data Using LIS Data

RETRIEVAL ERRORS

Sampling from population [to create climate (a, b)]:• Ng = 40,000 flashes• Nc = 120,000 flashes• Z = Nc/Ng = 3

Thank You(Questions?)