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AD-MODTRAN: An Enhanced MODTRAN Version for Sensitivity and Uncertainty Analysis

G. Scriven, N. Gat, J. Kriesel (OKSI)J. Barhen, D. Reister, Oak Ridge National Laboratory

M. Fagan, Rice University

26 th ANNUAL REVIEW CONFERENCE ONATMOSPHERIC TRANSMISSION AND RADIANCE MODELS

23 and 24 September 2003The Museum of Our National Heritage

Lexington, Massachusetts

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Acknowledgements

Missile Defense Agency (MDA):Lt. Col. Gary BarmoreCol. Kevin GreaneyDr. Harry HeckathornJames Kiessling

AFRL/PRSA:Dr. Robert LyonsTom Smith

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Outline• What is Automatic Differentiation (AD)?

• Creation of user friendly interface (GUI)

• Demonstration of AD-MODTRAN

• Application of AD-enhanced codes

• Status of AD-MODTRAN

• Recommendations

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How it works•AD computes analytic derivatives via symbolic differentiation

•Applies the chain rule to compute derivatives of outputs w.r.t. inputs

•Follows loops, conditional statements, subroutines, common blocks, etc.

•Can create the entire sensitivity matrix (Jacobian) in a single run of the code

What is Automatic Differentiation (AD)?

))(()(

)())((

T

LTTL

TT

L

TLTLo

o

o

Original code

User specifiedvariables

Adiforprocessor

Derivativecode

Basic Enhancement Process

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x

y Exact

der

ivativ

eFinite Differences

Automatic Differentiation (AD) vs. Finite Differences (FD)

AD Derivatives are analytic (exact)Independent of step sizeComplete Jacobian with single executionAD is computationally more efficient

FDDerivatives are approximateDepends on step size Multiple runs (one variable at a time)FD is 15-30 times slower than AD

• Historically, AD-enhanced codes have been difficult to create

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OKSI’s AD Implementation ProcessOriginal

code

User specifiedvariables

Setupfiles

ADtools

anyconflicts?

Derivativecode

Createnew user interface

Compileand link

ValidateAD results

User-friendly,validated

AD-enhancedcode

resolveyes

no

Final product

•Only the differentiation is automatic, other steps require significant developer efforts (yellow)•OKSI created supplemental tools to further automate the process•These tools include GUI’s to make the operation of the AD-enhanced code more intuitive

Any invalid

results?

no

yes

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• The 3 GUI programs are designed to work with all AD-enhanced codesInput GUI: handles case setup and independent variable (IV) selectionOutput GUI: handles output data selection for visualization/application Uncertainty GUI: handles bookkeeping of IV uncertainties

• GUIs have been tested on AD-MODTRAN and AD-SPURC

UncertaintyAnalysis

Real-timeSimulations

InverseProblems

AD-enhanced code

Wrapper

InputGUI

UncertaintyGUI

OutputGUI

Etc.

Applications

OKSI User Tools: Universal GUI Approach

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Demonstration of AD-MODTRAN

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0 5 10 15 20Altitude, km

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50

100

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400

450

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Se

nsi

tivity

tow

ate

rva

po

rd

en

sity

5 m4 m3 m2 m

X-Y Plots Surface Plots

Sensitivity of target intensity (w/sr/m) to atmospheric water vapor profile (g/m3)

4 plot types available from Output GUI:1) pie/bar charts 3) surface plots (2D)2) X-Y plots (1D) 4) image cubes (3D)

sensitivity

Sample AD Output

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2 3 4 5Wavelength, m

0

50

100

150

200

250

Inte

nsi

ty,k

w/s

r/m

0 0.05 0.1 0.15 0.2 0.25 0.3

Flowfield Temperature

Flowfield CO2 mole fraction

CO2 Bandmodel Parameters

Flowfield CO mole fraction

Aspect angle

Atmospheric temperature (h=2 km)

Atmospheric temperature (h=3 km)

Range

Missile altitude

Atmospheric temperature (h=4 km)

Inpu

t Par

amet

er

Fraction of Total Uncertainty

Pressure, mbar Temperature, K H2O, g/m3

200

220

240

260

280

300

320

0 2 4 6 8 10 12Altitude, km

TRUE

Retrieved

0

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0 2 4 6 8 10 12

Altitude, km

TRUE

Retrieved

0

2

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0 2 4 6 8 10 12

Altitude, km

TRUE

Retrieved

Applications of AD-enhanced OutputSensitivity/Uncertainty Analysis

Real-time, Physics-based Simulations(ex: turbulent fluctuations)

Inverse Problem Solutions(ex: atmospheric retrieval)

Error Propagation

20%

10%

5%

Movie

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Status of AD-MODTRAN

• Handles about 70% of ALL inputs and 90% of all outputs

• AD-MODTRAN should compile on any machine

• GUIs run only on Windows based platforms

• Minimal validation testing has been done

• Currently available as an alpha release

• Request form may obtained at:

www.oksi.com; choose “projects”; then “AD-enhanced MODTRAN”

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Recommendations

• Get user input!

• Address ALL inputs and outputs in AD-MODTRAN

• Create automated validation tools (using finite differences)

• Apply AD to latest version of MODTRAN

• Implement AD-MODTRAN in existing projects (atm. comp., simulations, …)

• Apply AD to SAMM2

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Backup Slides

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List of IVs List of DVs

Independent Variables (IVs) count

User input file (TAPE5) 48sensor specificationsviewing geometry

Band model parameters 1,152,000s/d &1/d all species, temps, wavenumbers

Atmospheric profiles 600temperature, pressure, densityspecie concentrations

TOTAL 1,152,648

Dependent Variables (DVs) Count

Spectral Transmittance 104,000

Spectral Radiance 40,000

Average Transmittance 1

Integrated Radiance 1

TOTAL 144,002

This list accounts for about 60% of the IVs and 80% of the DVs

# of possible sensitivities = 1.66 x 1011

in a single AD-MODTRAN execution!

Parameters Currently Handled by AD-MODTRAN Code

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Example: fluctuating plume temperatures due to turbulent mixing/chemistry

A) Assume temperatures fluctuate randomly with a Gaussian distribution

B) Compute resulting pixel radiances using AD derivatives

2

Tmean

Li,j

Steady-state(SPURC)

Sensitivity(AD-SPURC)

4. Physics-based Simulations

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10-5 10-4 10-3 10-2 10-1

Step Size, degrees

-0.909

-0.908

-0.907

-0.906

-0.905

-0.904

-0.903

-0.902

-0.901

No

rma

lize

dD

eri

vativ

e,

DV

/IV

*IV

/DV

FDAD

10-6 10-5 10-4 10-3 10-2 10-1 100 101

step size

10-4

10-3

10-2

10-1

100

101

Err

or,

%

Error = (AD-FD)/AD x 100%

IncreasingNonlinearity error

Increasing Truncation &

round off error

• Ideal FD step size is not known apriori• Multiple FD runs (per IV) required to determine appropriate step size• Optimal step may still have residual error

AD vs. FD: computational accuracyExample case: IV – aspect angle (130°)

DV – Total Intensity (178 kw/sr)

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0 5 10 15 20

Number of Independent Variables (IVs)

0

5

10

15

20

25N

orm

aliz

ed

Exe

cutio

nT

ime Automatic Differentiation (AD)

Finite Difference (FD)

AD vs. FD: computational efficiency

•AD is about 5 times faster than FD (when ideal step size is known apriori)•In reality AD will be about 15 to 30 times faster (for unknown ideal step size)