Evaluation of Emission Control Strategies for Regional Scale Air Quality:

Performance of Direct and Surrogate Techniques

Presented at the 6th Annual CMAS Conference Friday Center, UNC-Chapel Hill

October 1-3, 2007

Computational Chemodynamics Laboratory (CCL)Environmental and Occupational Health Sciences Institute (EOHSI)

A Joint Institute of UMDNJ-RW Johnson Medical School and Rutgers University170 Frelinghuysen Road, Piscataway, NJ 08854

*Atmospheric Sciences Modeling Division, Air Resources Laboratory, NOAA in partnership with the USEPA

S. Isukapalli, S. Wang, S. Napalenok* T. Kindap, and P. Georgopoulos

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Acknowledgments

• Alper Unal, WRI• Talat Odman and Yongtao Hu, Georgia Institute of Technology• USEPA (Funding for Center for Exposure and Risk Modeling)• NJDEP (Base funding for the Ozone Research Center)

• OTC Modeling Group Centers (Emissions inventories, Meteorology, etc.)

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Overview

• Surrogate Modeling Techniques • HDMR• DDM• Automatic Differentiation• Response Surface Modeling

• Case Study• Emissions and Regions• Estimates vs Brute Force

• Results and Discussion

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Use of surrogate models for emission control analysis

• Emissions control analysis is a multi-dimensional problem• Geographic regions [states/counties, etc.]• Types of emissions [point, biogenic, area, mobile, etc.] • Primary emissions [NOx, VOC, etc.]

• Some times, multi-objective problems

• Ozone, PM2.5, etc.

• Direct model simulation is expensive• 2 hours/day for OTC-12 domain simulation (8 Opteron nodes)

• Surrogate models can provide significant speedups• Construction of surrogate models is often parallelizable

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Use of surrogate models for emission control analysis

• Can provide a “Fast Equivalent Operational Model” (FEOM)• Can also be used in Uncertainty Propagation

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Use of surrogate models for emission control analysis

Several techniques exist for surrogate modeling• Response Surface Methods (Deterministic and Stochastic)• High Dimensional Model Representations (HDMR)• Local Gradient-Based Methods

•Decoupled Direct Method (DDM)•Adjoint Sensitivity Analysis Method•Automatic Differentiation

Features• Black-box models (Response Surface; HDMR; etc.)• Some changes to code (Automatic Differentiation)• Extensive changes to model code/new modules (DDM; Adjoint

Sensitivity)

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High Dimensional Model Representation (HDMR)

• System (a mathematical model; e.g. CMAQ):- Input I:- Output O:

• HDMR expresses model outputs as expansions of correlated functions:

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•The expressions of HDMR component functions are optimal choices for the output f (x) over the desired domain of the input variable space such that the HDMR expansion converges very rapidly

•Cut-HDMR:

• In practice, the HDMR expansion functions are represented as a set of low dimensional look-up tables

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•Decomposition of variance:

•The total variance 2(g) attributable to all inputs can be decomposed into individual contributions

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Automatic Differentiation (www.autodiff.org)

y(1) = 1.0 y(2) = 1.0 do i = 1,n if (x(i) > 0.0) then y(1) = x(i) * y(1) * y(1) else y(2) = x(i) * y(2) * y(2) endif enddo

dy(1) = 0.0 y(1) = 1.0 dy(2) = 0.0 y(2) = 1.0 do i = 1,n if (x(i) > 0.0) then dtemp = y(1)*dx(i) + x(i)*dy(1) temp = x(i) * y(1) dy(1) = y(1)*dtemp + temp*dy(1) y(1) = temp * y(1) else dtemp = y(2)*dx(i) + x(i)*dy(2) temp = x(i) * y(2) dy(2) = y(2)*dtemp + temp*dy(2) y(2) = temp * y(2) endif enddo

Chain Rule on Computer Instructions

Problems:ADIFOR does not support

F90/F95Commercial tools unproven

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Decoupled Direct Method (DDM)

• CMAQ-DDM 4.5 with CB4, Aero4, AQ • Serial version from Talat Odman, Georgia Inst. of

Technology• Parallel version from Sergey Napalenok, USEPA

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Domain for the Case Study

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• Impact of reductions in NOx emissions from five states:

• DE, MD, NJ, NY, and PA• Base Case:

• OTC12 BaseB

Case Study

• Evaluate performance of HDMR and DDM as surrogate models• 10% overall• 25% overall• 75% overall except PA (zero

reduction)

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Base Case (08/01/2002; Hours 14-17)

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10% overall reduction; HDMR (08/01/2002; Hours 14-17)

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25% overall reduction; HDMR (08/01/2002; Hours 14-17)

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75% overall reduction [except PA]; HDMR (08/01/2002; Hours 14-17)

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10% overall reduction; DDM (08/01/2002; Hours 14-17)

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25% overall reduction; DDM (08/01/2002; Hours 14-17)

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75% overall reduction [except PA]; DDM (08/01/2002; Hours 14-17)

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Discussion

• Approximations appear to break at about 25% changes in emissions

• Can be used for screening purposes for small variations• Potential mix of “global” and “gradient-based” sensitivities