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UNCLASSIFIED 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 ON ATMOSPHERIC TRANSMISSION AND RADIANCE MODELS 23 and 24 September 2003 The Museum of Our National Heritage Lexington, Massachusetts

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UNCLASSIFIED Acknowledgements Missile Defense Agency (MDA): Lt. Col. Gary Barmore Col. Kevin Greaney Dr. Harry Heckathorn James Kiessling AFRL/PRSA: Dr. Robert Lyons Tom Smith

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UNCLASSIFIED 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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UNCLASSIFIED 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)? Original code User specified variables Adifor processor Derivative code Basic Enhancement Process

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UNCLASSIFIED x y Exact derivative Finite Differences Automatic Differentiation (AD) vs. Finite Differences (FD) AD Derivatives are analytic (exact) Independent of step size Complete Jacobian with single execution AD is computationally more efficient FD Derivatives are approximate Depends on step size Multiple runs (one variable at a time) FD is times slower than AD Historically, AD-enhanced codes have been difficult to create

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UNCLASSIFIED OKSIs AD Implementation Process Original code User specified variables Setup files AD tools any conflicts? Derivative code Create new user interface Compile and link Validate AD results User-friendly, validated AD-enhanced code resolve yes 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 GUIs to make the operation of the AD-enhanced code more intuitive Any invalid results? no yes

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UNCLASSIFIED The 3 GUI programs are designed to work with all AD-enhanced codes Input GUI: handles case setup and independent variable (IV) selection Output 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 Uncertainty Analysis Real-time Simulations Inverse Problems AD-enhanced code Wrapper Input GUI Uncertainty GUI Output GUI Etc. Applications OKSI User Tools: Universal GUI Approach

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UNCLASSIFIED Demonstration of AD-MODTRAN

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UNCLASSIFIED X-Y Plots Surface Plots Sensitivity of target intensity (w/sr/ m) to atmospheric water vapor profile (g/m 3 ) 4 plot types available from Output GUI: 1)pie/bar charts3) surface plots (2D) 2)X-Y plots (1D)4) image cubes (3D) sensitivity Sample AD Output

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UNCLASSIFIED Applications of AD-enhanced Output Sensitivity/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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UNCLASSIFIED 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: choose projects; then AD-enhanced MODTRAN

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UNCLASSIFIED 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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UNCLASSIFIED Backup Slides

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UNCLASSIFIED List of IVs List of DVs This list accounts for about 60% of the IVs and 80% of the DVs # of possible sensitivities = 1.66 x in a single AD-MODTRAN execution! Parameters Currently Handled by AD-MODTRAN Code

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UNCLASSIFIED 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 T mean Li,jLi,j Steady-state (SPURC) Sensitivity (AD-SPURC) 4. Physics-based Simulations

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UNCLASSIFIED Error = (AD-FD)/AD x 100% Increasing Nonlinearity 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 accuracy Example case: IV – aspect angle (130°) DV – Total Intensity (178 kw/sr)

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UNCLASSIFIED 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)

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