Accuracy of multi-parameter response surfaces generated from sensitivity coefficients Daniel Cohan and Antara Digar CMAS Conference 2009 October 19, 2009

Incorporating Uncertainty Analysis into Integrated Air Quality Planning U.S. EPA – Science To Achieve Results (STAR) Program Grant # R DANIEL COHAN (PI) DENNIS COX ANTARA DIGAR MICHELLE BELL MENG JI ROBYN WILSON JAMES BOYLAN MICHELLE BERGIN BYEONG-UK KIM

Project Objectives Quantify uncertainty in the modeling that informs state-level air quality attainment plans –Control costs and emissions reductions –Pollutant responses to emission reductions –Health impacts Explore how uncertainty can be communicated and incorporated in the decision-making process

Multi-pollutant, multi-objective air quality planning How can we objectively evaluate disparate control options, impacting different precursors, sectors, and locations? NO x SO 2 PM 2.5 Ozone Acid deposition N deposition Human health Visibility Ecosystems and crops PM VOC NH 3 Source Emission Ambient Impact Societal Impact Attainment

Air Quality Modeling  Pollutant sensitivities to emissions reductions Cost Assessment  Control costs and emissions reductions Health Assessment  Health benefits Integrated Evaluation of Control Options Attainment Evaluation  Improvement at monitors Cohan et al., Environmental Management 2007 $, Tons ppb/ton ppb, Impacts

Causes of Uncertainty in Modeled Concentrations and Sensitivities Parametric Uncertainty: Caused by uncertainty in model input parameters –Emission inventory, reaction rates, boundary conditions, etc. –Focus of this study Structural Uncertainty: Caused by imperfections in the model’s numerical representations of atmospheric chemistry and dynamics Model/User Error

How parametric uncertainty affects sensitivity to ΔEmissions ΔEi*ΔEi* Digar and Cohan, manuscript in preparation

Probability distribution of pollutant response (ΔC) to emission control (ΔE) Dwd NOx Dwd Anth VOC Dwd Bio VOC RJs R(NO2+OH) R(NO+O3) BC (O3) BC (NOy) Impact of Emission Control Under Parametric Uncertainty Monte Carlo CMAQ impractical – Need more efficient approach ΔEΔE ΔCΔC

Efficient characterization of parametric uncertainty by response surface equations 1. Compute high-order sensitivities relating  (Inputs) to  (Pollutant Response) -- E.g.: (∂ 2 Ozone/∂E NOx ∂E BioVOC ) shows how biogenic VOC inventory affects sensitivity of ozone to NO x emissions 2. Create “surrogate model” of pollutant response to ΔEmissions as function of uncertain inputs -- ΔC actual = F(ΔEmissions, ΔInput i,j,k,… )(Taylor series) 3. Apply Monte Carlo sampled inputs in surrogate model to generate probability distribution for ΔC ΔCΔC ΔEΔE

Emissions Conc. C base How to compute sensitivities: Brute Force or Decoupled Direct Method C E-10% -10% C E+10% +10% E base CMAQ-HDDM (in base case) Brute Force (3 runs; finite difference)

Computing concentration response to emission reduction under uncertainty (2 nd -order Taylor expansion) Impact of ΔE if no uncertainty in inputs: ΔE j = -ε j E j ΔC = ε j S j (1) - 0.5ε j 2 S j (2) + … Impact if Φ k error in each input parameter P k : P k * = (1+Φ k )P k P j * = (1+Φ j )P j ΔE j * = -ε j (1+Φ j )E j ΔC* = (1+Φ j )ε j S j (1) - 0.5(1+Φ j ) 2 ε j 2 S j (2) + (1+Φ j )ε j Σ (Φ k S j,k (2) ) Previously shown accurate for ozone response to +/- 50% emissions ??? How accurate for big changes in multiple inputs ??? We’ve assumed: (1) Accurate sensitivity coefficients; (2) 2nd-order sensitivities sufficient; (3) Additive impacts of input uncertainties

??? Does it Work ??? Accuracy Testing of Surrogate Model 3-day air pollution episode from Georgia SIP –CMAQ v. 4.5 with CB-IV chemistry, 12-km grid –Year 2002 meteorology with Year 2009 emissions Evaluate surrogate model up to 50%  E and  Inputs Pollutant Impact Emission Controlled Uncertain Inputs Sensitivity Method Ozone (8-hr) Atlanta NO x E_NOx; E_VOC; R_photolysis CMAQ-HDDM PM Sulfate (24-hour) Atlanta SO 2 E_SO 2 ; E_NH 3 ; R_photolysis Brute Force

Highly accurate predictions of impact under extreme uncertainty

8-hour Ozone Performance Actual impact of -50% Atlanta NO x, if +50% E_NO x, E_VOC and R_photolysis Prediction Neglecting Uncertainty Surrogate Model Prediction

24-hour PM Sulfate Performance Actual impact of -50% Atlanta SO 2, if +50% E_SO2, E_NH3, and R_photolysis Surrogate Model Prediction Prediction Neglecting Uncertainty

Special Case: Discrete control options at coal-fired power plants Largest point sources of NO x and SO 2 Major focus of Georgia control efforts Discrete control options –SCR  ~85% NO x reduction –Scrubber  ~95% SO 2 reduction –Replace w/natural gas  85% NO x, 99.8% SO 2 cut Amount of emission reduction independent of domain-wide inventory

“Discrete Model” to predict impact of known emission reduction Compute ΔC impact of power plant control under: –Base case conditions –P k reduced by 10% Response coefficient: F k = 10(ΔC base -ΔC -10% ) Predict impact when multiple P k are uncertain: ΔC* = ΔC base + ΣΦ k F k Power Plant Emis Input P k P k,-10% 4 runs to determine each F k Targeted Reduction Base Case

Accuracy of Discrete Model Pollutant Impact Emission Controlled Uncertain Inputs Bias (NMB) Error (NME) R2R2 Ozone (8-hr) -85% McDonough NO x +50% all other E_NO x, E_VOC, and R_photolysis 3.3%13.1%0.993 PM Sulfate (24-hour) -99.8% McDonough SO 2 +50% all other E_SO 2, E_NH 3, and R_photolysis -0.7%3.9%0.998 Impact of Plant McDonough  natural gas, if input parameters +50% Even more accurate than continuum model, because targeted at predetermined emission reduction

Discrete model performance for +50% change in input parameters Actual PM_SO4 Impact of -99.8% McDonough SO 2 Predicted PM_SO4 Impact of -99.8% McDonough SO 2

Conclusions New methods efficiently characterize impact of emission reductions under parametric uncertainty –Can use HDDM or brute force –Continuum model well suited to flexible % controls –Discrete model applicable when % control is known High confidence that both methods accurately represent relationships in underlying model –Caveat: Methods only as good as underlying model Next talk: Applying surrogate model to estimate likelihood of attainment for SIP strategy