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A photochemical model based on a scaling analysis of ozone photochemistry Ainslie, Bruce 2004

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A Photochemical Model Based on a Scaling Analysis of Ozone Photochemistry by Bruce Ainslie B.Sc. (Eng), Queen's University, 1989 • M . S c , The University of British Columbia, 1991 ' A THESIS S U B M I T T E D IN P A R T I A L F U L F I L M E N T O F T H E R E Q U I R E M E N T S F O R T H E D E G R E E O F D O C T O R O F P H I L O S O P H Y in T H E F A C U L T Y O F G R A D U A T E STUDIES (Department of Earth and Ocean Sciences) We accept this thesis as conforming to the required standard T H E U N I V E R S I T Y OF BRITISH C O L U M B I A September 21, 2004 © Bruce Ainslie, 2004 Vitruvius says that small models are of no avail for ascertaining the effects of large ones; and I here propose to prove that this conclusion is a false one. L E O N A R D O D A V I N C I , Notebooks (about 1500 A.D.) Abstract iii Abstract A scaling-level model of a photochemical mechanism has been developed and integrated into an air quality model used to study ozone formation in an urban environment. A scaling analysis was used to capture the internal workings of a photochemical mechanism using the OZIPR trajectory model to simulate a smog chamber for a wide range of precursor con-centrations and a variety of environmental conditions. The Buckingham P i method of dimensional analysis was used to express the relevant variables in terms of dimensionless groups. These grouping show maximum ozone, initial N O x and initial V O C concentrations to be made non-dimensional by the average NO2 photolysis rate (jav) and the rate constant for the N O - O 3 titration reaction (k^o)', temperature by the NO-O3 activation energy (E/R) and time by the cumulative NO2 photolysis rate (J). The analysis shows dimensionless maximum ozone concentration can be described by a product of powers of dimensionless initial NOx concentration, dimensionless temperature (0(T)) and a similarity curve (/) directly dependent on the ratio of initial V O C to N O x concentration (R) and internally dependent on the cumulative NO2 photolysis rate: ' [ ° 3 k a * K ( [NOx]0 jav /k NO \jav/kNO When Weibull transformed, the dimensionless model output cluster onto two line segments. This is interpreted as-a break in ..the scaling and can be understood,in-terms of a change in governing feedback mechanisms separating low- and high'-NOx chemistry regimes. The similarity relationship can be modeled by two Weibull distributions using four parameters: two describing the slopes of the line segments (01,02) and two giving the location of their intersection (B, A): f(R;J) - l - e x p { - A ( ^ ) ° < f i ) } where a(B) = ° 2 ~ tanh(fl - 0( J)) + ° ' + ° 2 A fifth parameter (7) is used to normalize the model output. The most important parameter, B, the V O C to NOx ratio at the scaling break, defines a characteristic process scale for ozone photo-chemistry. The scaling analysis, similarity curve and parameterization appear to be independent of the details of the chemical mechanism, hold for a variety of V O C species and mixtures and are applicable over a wide range of V O C and NOx concentrations. The similarity relationship is used to 6(T)bf(R;J). Abstract iv generalize ozone-precursor relationships in terms of four rules governing ozone production (P(03)), to quantify NOx-inhibition and define isopleth slope. The scaling framework is used to study V O C reactivity, explore the scaling properties of a simple reaction mechanism and collapse a wide range of smog chamber measurements onto a single similarity curve. To complement the scaling analysis, a meteorological model and an emissions inventory were developed. These were incorporated into an air quality model used to explore the sensitivity of a regional ozone plume to environmental conditions, and precursor .concentrations. The air quality model consisted of a series of box models being advected by the mean wind, for a single day, where photochemistry of the precursors emissions was modeled using the similarity relationships developed from the scaling analysis. The chosen domain was the Lower Fraser Valley B . C . , a complex coastal region that experiences moderate ozone episodes during summertime fair-weather conditions. Emission fields were developed using published emission totals, four land-use categories and generic temporal emissions curves and were found to be comparable with fields based on more de-tailed inventories. Wind observations (speed and direction), from 53 stations, on a typical episode day, were interpolated to produce hourly wind fields. Mixing depths were determined using a simple slab model incorporating the interpolated wind fields and measured heat fluxes. The most prob-lematic aspect of the model was determining the effects of pollutant build up in the boundary layer, prior to the modeling day. This was handled by emitting precursors into the boundary layer and advecting them, without chemical reactions, until steady state concentrations were reached. These were dependent on the choice of background concentrations used to initialize the pre-conditioning scheme and were set so resulting boundary layer NOx and V O C concentrations were in agreement with the limited available data and peak ozone concentrations were typical of recent episodes. In departure from previous modeling studies, model validation was not through point by point analysis of model output and observations but through high level comparison of model sensitivity with a range of modeling techniques and observations. The model appears to capture ozone sen-sitivity to meteorological conditions and precursor concentrations; justifying its use as a screening tool. The model suggests: the region to be V O C limited; projected emissions reductions may not improve present episodic ozone concentrations; larger than anticipated reductions in NOx emis-sions, without equivalent additional V O C reductions, could increase episodic concentrations and future emissions reductions, stemming from T I E R 2 L D V standards, which target NOx emissions to a greater extent than V O C emissions, may not result in appreciable changes in episodic ozone concentrations. These conclusions are intended to guide comprehensive modeling studies. Contents v Contents Abstract i ii Contents v List of Tables xi i List of Figures xiv Acknowledgements xviii 1 Preface 1 1.1 A i m of thesis 1 1.2 Scope of thesis 2 1 Development of the W E X M o d e l 4 2 Introduction 5 2.1 Ground level ozone 5 2.1.1 Effects of ozone 6 2.1.2 Ai r quality standards and ozone 6 2.1.3 Meteorology and ozone 7 2.1.4 Emissions and ozone 7 2.2 Fundamentals of Ozone Photochemistry 7 2.2.1 Photochemical Cycle of NO, N02 and 0 3 8 2.2.2 Radicals .: . . . . . , . ' 8 2.2.3 Reaction Chains ' . . . . 10 2.2.4 Photochemical Ozone Production in the Presence of V O C s and NOx 10 2.2.5 Summary of Ozone photochemistry 11 2.2.6 Photochemistry and poetry 13 2.3 Approaches to Modeling Ground Level Ozone 13 2.3.1 Trends and Correlation Techniques 14 2.3.2 Eulerian Grid Based 15 2.3.3 Complementary Methods 16 2.4 Summary 18 3 Scaling Analysis of Ozone Photochemistry 19 3.1 Introduction 19 3.2 Scaling Analysis . 20 3.2.1 What is a scaling analysis? 20 Contents vi 3.2.2 Key Concepts 20 3.2.3 Scaling Analysis Methods 23 3.2.4 Scaling and Photochemical Modeling 25 3.3 Scaling Analysis of a NOx-only System 27 3.3.1 NOx-only Photochemical System 27 3.3.2 Relevant Variables 27 3.3.3 Variable Dimensions 28 3.3.4 Key Variables 28 3.3.5 Pi-Groups 29 3.3.6 Alternative Pi-Groups 29 3.3.7 OZIPR Model Output.. ..." . . V 30 3.3.8' Universal Curve. . . . . . . . . . ... ... . 33 3.3.9 Analytic Expression 34 3.4 Propene-NOx System 35 3.4.1 Ozone response surface • 36 3.4.2 Dimensional Considerations . = '. 37 3.4.3 Propene 40 3.4.4 O Z I P R Simulations 40 3.4.5 Similarity Relationship 41 3.4.6 Weibull Distribution 41 3.4.7 Scaling break and Lognormal Parameterization 43 3.4.8 Analogy with Richardson number and Surface Stability 44 3.4.9 W E X Model 46 3.4.10 Ozone-precursor relationships in the NOx Limited Region 48 3.5 Summary 51 4 Domain of Applicabil i ty for the Scaling Relationship 53 4.1 Introduction 53 4.2 Scaling Methodology 54 4.2.1 General simulation conditions 54 4.2.2 Determination of test matrix size 54 4.2.3 Selection of base concentrations and number of nodes 55 4.2.4 Determining W E X parameters 57 4.2.5 Statistical measures of agreement 58 4.3 Scenario I - R A D M 2 V O C Classes 58 4.3.1 Simulations with Methane, Ethane and Higher Alkanes 59 4.3.2 Simulations with Ethene and other Alkenes 61 4.3.3 Simulations with Aromatics 65 4.3.4 Simulations with Carbonyl compounds 65 4.3.5 Simulations with the Non-reactive class 67 4.3.6 Simulations with V O C Mixtures 67 4.3.7 Summary of R A D M 2 simulations 67 4.4 Scenario II - Other Mechanism 68 4.4.1 C B - I V Mechanism 68 4.4.2 SAPRC-90 Mechanism 69 4.4.3 Summary for Scenario II 70 4.5 Scenario III - Varying Temperature 70 Contents vii 4.5.1 Gross Influence of Temperature On Maximum Ozone Concentration 71 4.6 Scenario IV - Varying J . . . . ... 72 4.6.1 Parameterizing the similarity relationship 73 4.6.2 Translations and rotations of the similarity relationship 74 4.7 Scenario V - Effect of peak actinic flux 76 4.8 Scenario V I - Varying T and J 79 4.8.1 Variability of W E X parameters with J and T 80 4.8.2 'Universal' Similarity relationship 82 4.8.3 Universal Propene Curve 85 4.8.4 Scatter Plots 86 4.8.5 Summary 87 4.9 Scaling Limits 87 4.9.1 Precursor Scaling Limits 89 4.10 Conclusion 93 5 Scal ing B r e a k and Ozone Pho tochemis t r y 95 5.1 Introduction 95 5.2 The Temporal Variability of Ozone 95 5.2.1 Temporal variability of NO, NO2 and O3 for a single simulation 95 5.2.2 Reactive Odd Nitrogen (NOy) 97 5.2.3 Isopleth Plot and Stock Simulations 97 5.3 Ozone Production 100 5.3.1 Step function model for ozone production 103 5.3.2 Maximum ozone concentration 105 5.3.3 I E R and Step function model 106 5.3.4 P S P production 108 5.3.5 Quadratic Model for Ozone Production 110 5.3.6 Weibull Model I l l 5.3.7 Quadratic with Asymptotic Decay . 113 5.3.8 Production models with initial NOx dependence 115 5.3.9 Links between scaling break and regime change 117 5.3.10 W E X temporal ozone profile 118 5.4 Feedback Mechanisms and Ozone Photochemistry 119 5.4.1 Positive Feedback Loop 119 5.4.2 Negative Feedback Loops 121 5.5 Scaling Break and Low-NOx chemistry 123 5.5.1 Low-NOx chemistry 124 5.5.2 Low-NOx negative feedback loop 126 5.5.3 Scaling break and governing chemical processes 126 5.6 Feedback Loops and the similarity relationship 127 5.6.1 Acceleration Phase 128 5.6.2 Low-NOx Saturation Phase 128 5.7 Scaling Break and Ridgeline 128 5.7.1 Regulatory Basis for Ridgeline 129 5.7.2 Geometrical Basis for Ridgeline 130 5.7.3 Process Basis for Ridgeline 130 5.8 Relationship between Scaling break and other parameters 131 Contents ' viii 5.8.1 Scaling break Ridgeline and Chain Length (XOH) • • •* 131 5.8.2 Scaling break and fraction of HO' radicals that react with N O (fH02+No) • 132 5.8.3 Scaling break and OH' reactivity (koij) 133 5.8.4 Scaling Break and environmental conditions 134 5.9 Summary 134 6 Chemical Processes and the W E X Parameters 135 6.1 Introduction 135 6.2 W E X Scaling Parameter a 137 6.2.1 N O x Inefficiency 137 6.2.2 Range of a-values 138 6.2.3 Response surface sensitivity to a 139 6.2.4 Sensitivity of a to R A D M 2 modifications 139 6.3 W E X Scaling Parameter 7 141 6.3.1 NOz speciation and 7 141 6.3.2 Peak Ozone and P A N and HN03 Formation 142 6.3.3 Gamma and Isopleth shape 143 6.3.4 Variability of 7 144 6.3.5 7 R A D M 2 Experiments 144 6.4 Geometric Parameter A 145 6.4.1 Sensitivity of isopleth shape to A 146 6.4.2 Sensitivity of A to R A D M 2 modifications 146 6.5 Geometric Parameter ot\ 147 6.5.1 Sensitivity of the ozone response surface to ai 148 6.5.2 Ozone Isopleth Slope 148 6.5.3 NOx-inhibition and a i 149 6.5.4 W E X and NOx Inhibition 151 6.5.5 Range of a 1-values 152 6.5.6 Sensitivity of ax to R A D M 2 modifications 153 6.5.7 NOS scaling regime 154 6.6 Geometric Parameter 154 6.6.1 Sensitivity of ozone isopleths to ai 154 6.7 Conclusion 155 7 Evaluation of the W E X model using smog chamber data 157 7.1 Introduction 157 7.2 Smog chambers . : 158 7.2.1 Smog chamber design 158 7.2.2 Chamber limitations 159 7.3 Comparing the W E X model to smog chamber data 160 7.3.1 CSIRO Data set 162 7.3.2 I E R Analysis 162 7.3.3 W E X Analysis of temporal ozone concentrations 164 7.3.4 W E X analysis of maximum ozone concentration 166 7.4 Conclusion 168 Contents j x 8 VOC Reactivity - An Example of Scaling in Ozone Photochemistry 170 8.1 Introduction 170 8.2 V O C Reactivity 171 8.2.1 Incremental Reactivity 171 8.2.2 Maximum Incremental Reactivity 173 8.2.3 Relative Incremental Reactivity 174 8.2.4 R A D M 2 simulations of RIR 175 8.3 Concerns about V O C Reactivity Scales 177 8.4 GRS Mechanism - A n Example of an Ideal V O C Reactivity Scale 178 8.4.1 Ozone Isopleths and NOx-inhibition 178 8.4.2 Reaction Mechanism 179 8.4.3 Scaling and V O C reactivity 181 8.4.4 Radical Production and V O C reactivity 184 8.5 Conclusion 184 8.6 Summary for Part I 185 II Application of the W E X Model 186 9 Incorporating WEX into a Photochemical Model 187 9.1 Introduction 187 9.2 Modeling Domain 189 9.2.1 General Ai r Quality in the L F V 190 9.3 Meteorology of Ozone Episodes in the L F V 192 9.4 Previous Modeling 193 9.5 Interpolation of the Wind Fields 195 9.5.1 Interpolation 195 9.5.2 Divergence Reduction 196 9.6 Development of Back Trajectories 196 9.6.1 Limitations of the Trajectories 197 9.7 Parameterizing Mixed Height 198 9.7.1 Mixing Height Results . :. 200 9.8 Emissions • . . ' 202 9.8.1 Comparison with a Detailed Episode Specific Inventory 204 9.9 Speciation of V O C s 206 9.10 Boundary Layer Processes 207 9.10.1 Deposition 207 9.11 Initial Boundary Layer Concentrations 209 9.11.1 Residual Layer Concentrations 210 9.11.2 Initial Surface Concentrations 211 9.12 Developing W E X parameters 211 9.13 Predicted Ozone Concentrations 212 9.14 Temporal Behaviour 213 9.15 Conclusions 0 1 * Contents x 10 Model Results and Discussion 217 10.1 Sensitivity to Meteorological Parameters 217 10.1.1 Temperature 218 10.1.2 Residual layer concentrations 219 10.1.3 Actinic Flux 221 10.1.4 Wind Fields 222 10.1.5 Back Trajectories . . 223 10.1.6 Mixing Depths 223 10.2 Sensitivity to Emissions 225 10.2.1 Backcast emissions for 1985 226 10.2.2 Future scenario under Tier 2 automotive standards 226 10.2.3 Speciationv . - . v . : - . z\ . . . . . . . . . . H .. 227 10.3 L F V Ozone Isopleths . 228 10.4 Discussion 231 10.5 Conclusions . . .• 234 10.6 Summary for Part II • / 235 11 Conclusions 236 Bibliography 241 A Buckingham P i Method of Dimensional Analysis 257 A . l Buckingham P i Theorem 257 B O Z I P R Trajectory Model 260 B. l Overview 260 B. 2 Model Set-up 260 C RADM2 Chemical Mechanism 263 C. l Overview 263 C.2 Stable Inorganic Species • • 263 C.3 Stable Organic Species 263 C. 4 Organic and Inorganic Radicals Species 264 D Composite Weibull Models and the W E X Model 267 D. l Overview 267 D.2 Weibull Distribution and Failure Rates 267 D.2.1 Three Parameter Weibull 268 D.3 Multimodal Analysis 269 D.3.1 Sectional Model . 269 D.3.2 Mixed Model 270 D.3.3 Multiplicative Model 270 D.3.4 Competing Risk Model 270 D.4 W E X Model -271 Contents xi E Weibull and Isopleths Plots for Various VOC compounds . 273 E . l RADM2 Classes 273 E . l . l A'ikanes 273 E. l .2 Alkenes 275 E. l .3 Aromatics 276 E.1.4 Carbonyls 277 E . l . 5 Non-reactive 278 E. l .6 Mixtures 279 E.2 C B - I V Mechanism 280 E. 3 N R C Mechanisms 281 F Some Mathematical Definitions of the Ridgeline 282 F. l The ridgeline 282 F.2 Ridgeline based on ozone sensitivity to ratio of V O C to NOx 282 F.3 Ridgeline based minimum gradient along an ozone response surface 283 F.4 Ridgeline based minimum isopleth curvature 284 F. 5 Conclusion • • • 284 G Development of the Simple Emissions Inventory 285 G. l Spatial Emission Masks 286 G.2 Emission Sources 286 G.2.1 Mobile Source Emissions 286 G.2.2 Area Sources 288 G.2.3 Point Sources 289 H Physical Geography of the Modeling Domain 291 I CART Decision tree for the L F V 294 J Glossary of Acronyms and Abbreviations 296 List of Tables xii List of Tables 3.1 Units and dimensions for maximum ozone and its dimensional factors 28 3.2 Variable ranges and number of treatments for the OZIPR simulations of the NOx-only photochemical system 31 3.3 Initial conditions and maximum ozone concentration for three NOx-only OZIPR simulations have similar IT2 values 32 3.4 Physical quantities which affect ozone concentrations in a smog chamber 38 3.5 Ozone-precursor relationships in the NOx-limited region 50 4.1 A description of scenarios used to explore the universality of the similarity relationship. 54 4.2 Values of the six W E X parameters for each of the R A D M 2 classes and two urban mixtures 68 4.3 A comparison of W E X parameter values for the A R B mixture using the R A D M 2 and C B - I V chemical mechanisms 69 4.4 Date, average and total actinic fluxes, as measured by NO2 photolysis rates, for the five R A D M 2 simulations used to investigate the sensitivity of the similarity relation-ship on actinic flux 73 4.5 Test conditions for simulations with different latitudes but identical J-values 77 4.6 W E X parameter values for the Y V R and L A X simulations 79 4.7 W E X parameter values for the Y V R and L A X simulations 81 4.8 Scatter plot statistics 87 4.9 OLT precursor scaling domains 89 5.1 Scaling break and R-value of OH-chain maximum for seven R A D M 2 classes and two urban mixtures 131 5.2 Fraction of HO' that reacts with N O scaling break for various R A D M 2 classes and mixtures 132 6.1 Baseline and modified parameters for W E X generated isopleths 137 6.2 Comparison of O L T parameters for the original and modified R A D M 2 mechanism. . 140 6.3 Comparison of OLI parameters for the original and modified R A D M 2 mechanism. . 145 6.4 Comparison of X Y L E parameters for the original and modified R A D M 2 mechanism 7.147 6.5 R A D M 2 classes ranked by ai 153 6.6 Comparison of O L T parameters using the original and modified R A D M 2 mechanism. 153 7.1 Test conditions for the 20 CSIRO smog chamber experiments 163 7.2 Summary of statistics for the IER and W E X scatter plots 164 7.3 W E X parameters and power law exponents used to fit the CSIRO data 166 8.1 Various measures for V O C reactivity 171 List of Tables xiii 9.1 Occurrence of Episodes in the Lower Fraser Valley 192 9.2 Emissions categories in the simple emissions inventory. 204 9.3 Speciation of V O C s used in the L F V photochemical simulations 208 9.4 W E X parameters used in the L F V photochemical simulations 212 C . l R A D M 2 Chemical Species List for Inorganic Compounds 264 C.2 R A D M 2 Chemical Species List for Organic Compounds 265 C.3 R A D M 2 Chemical List for Radicals Species 266 G. l Spatial allocation of emissions in the simple emissions inventory 290 H . l Meteorological Stations within the modeling domain 292 H.2 Mapping of R P N Landuse classes to W E X landuse classes 293 H.3 Land use corrections for friction velocity and kinematic heatflux 293 List of Figures xiv List of Figures 2.1 Schematic of ozone photochemistry. 12 3.1 Schematic showing two separate approaches to performing a scaling analysis 25 3.2 Dimensionless maximum ozone concentration versus dimensionless initial NO con-centration for 5 different initial NO to NO2 ratios 32 3.3 Dimensionless steady-state ozone concentration scaled by the initial ratio of NO to NO2 as a function of dimensionless initial NO concentration. 33 3.4 Scatter plot showing n i / I l 3 using Eq . (3.6) versus Eq. (3.12) for five different II3 levels 35 3.5 Ozone response surface as a function of initial V O C and N O x concentration 37 3.6 Schematic of the fast NO-NO2-O2, cycle and the slower radical driven cycle 38 3.7 Dimensionless ozone scaled by dimensionless NOxa versus ratio of initial precursor concentrations (R) 42 3.8 Procedure used to prepare OZIPR model output before Weibull transforming 43 3.9 Scaled model output after Weibull transformation 44 3.10 Scaled O L T model output after Lognormal and Weibull transformation. . 45 3.11 Richardson number as a function of stability 46 3.12 Ozone isopleth plot for the NOx-OLT system. 48 4.1 Distribution of ln(R) when nodes = 41 and VOCbase = NOxi,ase 56 4.2 Schematic of steps used to find W E X parameters 58 4.3 Weibull and Isopleth plots for R A D M 2 class E T H . 61 4.4 Weibull transformed E T H model output versus \nR when NOx-scaling exponent (a) is -0.2 62 4.5 Weibull and Isopleth plots for R A D M 2 class OLI . 63 4.6 Weibull and Isopleth plots for R A D M 2 class OLI using 41 nodes 64 4.7 Ozone isopleths for OLI showing lines of constant etc 66 4.8 R A D M 2 simulations using O L T for four different temperatures 71 .4.9 Weibull transformed dimensionless model output after scaling by dimensionless tem-perature II4 72 4.10 Dimensionless model output for the five OLT simulations after scaling by dimension-less initial N O x concentration raised to-the 0.62 74 4.11 Dimensionless model output for the five OLT simulations after scaling by dimension-less initial N O x concentration and translating so scaling break is at origin 75 4.12 Dimensionless model output for the five OLT simulations after: scaling by dimen-sionless initial NOx concentration raised to the 0.62, shifting and rotating 76 4.13 Solar zenith angle as a function of local time for Vancouver and Los Angeles 78 4.14 NOx-scaled dimensionless maximum ozone concentration for O Z I P R simulations us-ing Los Angeles and Vancouver latitudes 78 List of Figures xv 4.15 Effects of horizontal translation by (5 on the 'Weibullized' arid .'scaled' data 79 4.16 Dependence of/5 on temperature and actinic flux . . . . : 81 4.17 Ridgeline as a function of J and T (from Johnson (1984)) 83 4.18 Weibull transformed model output for R A D M 2 simulations having five different levels of actinic flux and four different temperatures 84 4.19 Universal similarity relationship for O L T 85 4.20 Total actinic flux as a function of Julian day of the year for Vancouver in the summer 86 4.21 OLT scatter plots for four different actinic flux/temperature combinations. . . . . . 87 4.22 Schematic of O L T modeling domains 88 4.23 OLT similarity relationship in several scaling domains 90 4.24 Ozone isopleths for O L T over several scaling domains 91 4.25 Similarity relationship for different NOx-scaling exponents 92 4.26 The O L T NOx-scaling exponent as a function of initial O L T , NOx and R 93 5.1 Temporal evolution of ozone and other species during a simulation 96 5.2 Ozone isopleth diagram showing isomephitic line of 0.045 ppm 98 5.3 Temporal profiles for ozone and other species for eight simulations having initial NOx concentration of 0.045 ppm and various initial V O C concentrations 99 5.4 Weibull transformed dimensionless ozone concentrations for the isomephitic simula-tions 101 5.5 Simple step model function for ozone production 103 5.6 Three members of a family of step-model functions for ozone production 104 5.7 Ozone profiles for the three step function V O C concentrations 105 5.8 Ozone production, concentration and maximum concentration curves for a family of four different initial V O C concentration using a step-function model 107 5.9 Family of production curves for quadratic model 110 5.10 Ozone production, concentration and maximum ozone concentration for four initial V O C concentrations using the parabolic model of ozone production 112 5.11 Modified parabolic curve with hyperbolic tail 113 5.12 Ozone production, concentration and maximum ozone concentration for four initial V O C concentrations using the parabolic model with hyperbolic tail 114 5.13 Ozone concentration as a function of cumulative NO2 photolysis rate for nine different initial N O x and V O C conditions 116 5.14 Links between scaling break and regime change 118 5.15 Ozone concentration versus time for a series of nine smog chamber simulations. . . . 120 5.16 Ozone concentration versus time for S A P R C smog chamber simulation EC237. . . . 121 5.17 Positive Feedback loop for ozone production 122 5.18 The effects of HNO3 production on the reactivity of a photochemical system 123 5.19 Negative Feedback loop for ozone production 123 5.20 Loss of odd oxygen by various pathways 125 5.21 Second controlling or negative feedback loop for ozone production 126 5.22 Relationship between scaling break and underlying photochemical processes 127 5.23 Generalized ozone profile showing Lag, Acceleration and Low-NOx regimes 129 5.24 OH-chain length and / # o 2 for the Stock urban mixture 132 5.25 Scaling break as a function of OH-reactivity 133 6.1 Schematic representation of the four W E X geometric parameters 136 6.2 The effects of changing a on ozone response surface 140 List of Figures xvi 6.3 Scatter plot of 7 versus O^/NOz for six R A D M 2 classes and two urban mixtures. . . 142 6.4 Speciation of final NOz for seven R A D M 2 classes and two urban mixtures 143 6.5 The effects of changing 7 on ozone response surface 144 6.6 The effects of changing A on ozone response surface 147 6.7 The effects of changing a\ on ozone response surface. 148 6.8 The effects of changing o>\ on ozone isopleth slope 150 6.9 Relationship between isopleths tilting and packing 151 6.10 Dependence of NOx-inhibition on the three W E X parameters: a, A and ct\ 152 6.11 The effects of changing 02 on ozone response surface 155 7.1 Observed and modeled ozone concentrations for two different smog chamber experi-ments 161 7.2 Comparison of the I E R model and the CSIRO smog chamber data 165 7.3 Comparison of the W E X model and the CSIRO smog chamber data 167 7.4 Maximum ozone concentration from the CSIRO smog chamber experiments and the corresponding W E X model 168 8.1 IR for O L T calculated using the R A D M 2 mechanism and the W E X model 173 8.2 Relative incremental reactivities for the 12 R A D M 2 classes in the Stock mixture based on O Z I P R simulations and the W E X model 177 8.3 Weibull and isopleth plots for three different ROCs using the GRS mechanism. . . . 182 8.4 Weibullized plots of O L T and A L D with normal, twice and half the kon r a t e constants. 183 9.1 The Lower Fraser Valley 190 9.2 Modeling domain 191 9.3 Typical ozone plume in the L F V 192 9.4 500 hPa geopotential heights over the Northeastern Pacific Ocean on August 10th 2001.194 9.5 Sea-level pressure over the Northeastern Pacific Ocean on August 10th 2001 194 9.6 Four back trajectories derived from the interpolated wind fields and M C 2 model output. 199 9.7 Calculated mixing heights at four different hours 201 9.8 Calculated mixing heights at two different times along transect T l 202 9.9 Calculated mixing heights at two different times along S W - N E transect T2 203 9.10 Spatial pattern of V O C emissions at 1600 L S T based on simple inventory 205 9.11 Spatial pattern of N O x emissions at 1600 PST based on simple inventory 205 9.12 Comparison of V O C emissions between the simple inventory and the episode specific emissions inventory. 207 9.13 Comparison of N O x emissions between the simple inventory and the episode specific emissions inventory 208 9.14 Ozone plume based on simple model 213 9.15 Observed ozone plume at 1800 on August 10 t h 214 9.16 Predicted and observed ozone concentrations at various stations on August 10 t h 2001.215 10.1 Ozone plume after decreasing all temperatures 5°C 218 10.2 Ozone plume after increasing all temperatures 5°C 219 10.3 Ozone plume based using a clean residual layer 220 10.4 Modeled surface ozone concentrations at 1500 P S T July 19th using the M C 2 - C A L G R I D modeling system 221 10.5 Ozone plume using W E X parameters for a September 10th day 222 List of Figures xvii 10.6 Ozone plume resulting from a 1.5 x increasing in wind speed 223 10.7 Ozone concentrations using MC2-based trajectories 224 10.8 Ozone concentrations using MC2-based trajectories and mixing heights 225 10.9 Ozone concentrations based on 1985 emissions levels 227 lO.lOOzone concentrations based on projected future Tier 2 L D V emission standards. . . 228 lO.HOzone plume using W E X parameters based on S M O K E speciation 229 10.12Region wide ozone isopleths as a function of anthropogenic V O C and NOx emissions. 230 10.13Observed ozone concentrations in the L F V on June 21 s t , 2004 233 D . l A 'bathtub' curve showing changing failure rates with increasing use 268 D. 2 A comparison of four different methods of fitting model output with different 2-Weibull models 272 E. l Weibull and Isopleth plots for R A D M 2 class HC3 273 E.2 Weibull and Isopleth plots for R A D M 2 class HC5 274 E.3 Weibull and Isopleth plots for R A D M 2 class HC8 274 E.4 Weibull and Isopleth plots for R A D M 2 class OL2 275 E.5 Weibull and Isopleth plots for R A D M 2 class O L T 275 E.6 Weibull and Isopleth plots for R A D M 2 class X Y L E 276 E.7 Weibull and Isopleth plots for R A D M 2 class T O L U 276 E.8 Weibull and Isopleth plots for R A D M 2 class H C H O 277 E.9 Weibull and Isopleth plots for R A D M 2 class K E T 277 E.10 Weibull and Isopleth plots for R A D M 2 class A L D 278 E . l l Weibull and Isopleth plots for R A D M 2 class N R 278 E.12 Weibull and Isopleth plots the urban A R B mixture 279 E.13 Weibull and Isopleth plots the Stockwell urban mixture 279 E.14 Weibull and Isopleth plots for C B - I V classes P A R + O L E 280 E.15 Weibull and Isopleth plots for urban mixture using the C B - I V mechanism 280 E.16 Weibull and Isopleth plots for S A P R C class OLE1 281 E.17 Weibull and Isopleth plots for urban mixture using the S A P R C mechanism 281 I . l C A R T regression tree for Rocky Point Park (T9) * 295 Acknowledgements xviii Acknowledgements First and foremost, I would like to thank my supervisor, Dr. D. G . Steyn for his encouragement, guidance and intellectual support. I must also thank my examining committee, Drs. A . Bertram, I. G .McKendry and R. B . Stull who were always available for timely advice and"insight. A number of organizations provided funding for this research: the Sustainable Development Research Institute (SDRI) provided funding in the form of research assistantships, the University of British Columbia (UBC) through a University Graduate Fellowship, the department of Earth and Ocean Sciences (EOS) through teaching assistantships-in addition to funds for conference travel and finally Dr. Steyn provided support from his grants for both research and several conference visits. I would like to recognize Dr Gai l Tonnesen, at the University of California Riverside, for her help with the OZIPR model and her answers to all my inquiries concerning process analysis. I gratefully acknowledge the advice and model output provided by Dr. Marti l l i and the encouragement and support from Dr. Rucker, Pascal Hageli and Christian Reuten. I am indebted to Luca Delle Monache for his discussions and emissions data. This research was also advanced by valuable comments and discussions from all faculty and students in the Atmospheric Science Programme. I would like to thank everyone at SDRI, and especially Drs. Charmichael and Robinson, for the wonderful opportunity I had working on the Q U E S T integrated assessment model. Special thanks goes to Matt Wilkins for his help with C-programming and matters pertaining to the Linux operating system and to the EOS computer staff who were invaluable in keeping my computer going. I must acknowledge the patience of Jersey and Sheena, who must have found the long days in the office very trying. And lastly, my greatest debt of gratitude goes to my wife Margaret for her unwavering support over the last five years. Truly, greatest of them all. Chapter 1. Preface 1 C h a p t e r 1 Preface 1.1 Aim of thesis This thesis deals with ground level ozone, a relatively recent problem but now pervasive in many urban centres (United Nations Environmental Programme, 1992). Controlling this problem, like many environmental issues, has been slow, costly and difficult (National Research Council, 1991). As I will show, ozone forms as a results of complex interactions between emissions (both natural and anthropogenic), atmospheric processes and photochemical reactions. Each process is complex (with its own fields of expertise), incompletely characterized and central to ozone formation. Furthermore, improving ground level ozone requires linking knowledge about its formation (sci-ence) to choices society makes about present and future economic development and social behaviour (policy). But the future is unknown and can follow many courses. Thus, properly protecting future air quality is inherently inexact and unpredictable. Both this complexity and uncertainty present a tension for those trying to model ozone forma-tion: on the one hand, a model is required that is sensitive to the intricacies of weather, photo-chemistry and human actions (via emissions) while on the other hand, a model is required that can succinctly and quickly explore many possible futures. This tension leads two distinct classes of models: comprehensive 'black box' models, whose behaviours are difficult to understand, and due to their complexity and costs, preclude examining large numbers of possible futures; and less exact models, containing many approximations, which nonetheless succinctly describe ozone formation while elucidating important processes. Finally, while scientific inquiry should be objective, subjectivity inevitably creeps into every investigation, principally through the investigators values and beliefs (Meadows and Robinson, 1985). So, I state my personal bias here: I believe the air pollution meteorology community needs to make better use of 'simple, sophisticated' models in order to complement more comprehensive ones. With this in mind, the aim of this thesis is to develop a concise way of describing ozone formation, in polluted urban environments, that furthers understanding about the complex photochemical Chapter 1. Preface 2 processes. Specifically, this thesis distills the essential processes within a detailed photochemical mechanism in order to build a simple model of ozone formation. Concisely, it models a model to build a model. While this sounds academic, I will show the utility and importance of this work. That is, I develop more than just a meta-model - the methods produce a novel and powerful way of characterizing the behaviour of a photochemical system. This leads to the thesis' second, subtler and wider aim - to engage the air pollution modeling community in debate about the proper use and selection of models. In operational terms, this thesis addresses two simple questions: • How much detail is necessary to capture ozone sensitivity to V O C and NOx emissions in a particular region? • Given that a model is only as strong as its weakest link, what level of detail is justified in each modeling component? Answers to these questions, indirectly addressed throughout the thesis, come in focus in Chapter 10. 1.2 Scope of thesis The thesis is broken into two parts: Part I develops a model for ozone photochemistry while Part II makes use of the model. This division also has an heuristic/prognostic split: in Part I, I use my model to understand ozone formation while in Part II, I use the model to predict ozone concentrations. In the next Chapter, I introduce the problem of ground level ozone. Principally, I discuss the health and environmental impacts of ozone and the extent of the problem. I introduce the complex nature of ozone photochemistry and show its formation is further complicated by local emissions and by both large and small scale meteorological processes. I outline existing methods used to model ozone formation and show the importance of different modeling approaches. In Chapter 3, I introduce scaling methods, used to build my model, and present a limited set of results. In Chapter 4, I continue my scaling analysis and show its range of validity. The model is used to understand ozone formation in terms of feedback loops in Chapters 5 and 6. In Chapter 7, I compare my model with smog chamber results and discuss the difficulties associated with such comparisons. Chapter 8, the last of Part I, explores the concept of incremental reactivity and uses the model to show the limitations of a simple chemical mechanism. Chapter 1. Preface 3 In Part II, I couple my chemical model with a simple meteorological model to build a photo-chemical model of ozone formation (Chapter 9). I then model an ozone episode in the Lower Fraser Valley, British Columbia (Chapter 10). Final conclusions and ideas for future work are presented in Chapter 11. While my model has been tested using an episode in the L F V , and many of the examples used to illustrate ideas have also been drawn from this region, it is expected that techniques developed herein should be applicable to other regions. Finally, to make the presentation of ideas clearer, secondary and background material has been placed in appendices while acronyms and abbreviations are listed in the glossary (Appendix J). Part I Development of the W E X Model Chapter 2. Introduction 5 Chapter 2 Introduction 2.1 Ground level ozone Ozone, a triatomic form of oxygen, is found naturally in the stratosphere, a region of the atmosphere extending between 10 and 50 km above the surface of the earth, where it forms the ozone layer; absorbing ultraviolet radiation. It also occurs naturally in the troposphere as the result of exchange from the stratosphere (Lelieveld and Dentener, 2000) or through photochemical reactions involving naturally occurring oxides of nitrogen (NOx) and volatile organic compounds (VOCs) (Crutzen, 1995).1 Background tropospheric ozone concentrations are usually low - only a few tens of parts per billion (ppb) compared with stratospheric levels of about 10000 ppb. While there has been great concern about observed decrease in stratospheric ozone (World Meteorological Association, 1998), concentrations of tropospheric ozone appear to be increasing (Logan (1985), Volz and Kley (1988), Altshuller and Lefohn (1996)). Surface observations in remote European locations show an increase in background ozone concentrations of between 1 and 2% per year (Janach, 1989) largely due to increased anthropogenic emissions (Hough and Derwent, 1990). Additionally, increasing tropospheric ozone levels may affect the oxidizing capacity of the atmosphere and hence the chemical lifetimes of many species (Thompson, 1992) and also play a role in anthropogenic climate change (Mickley et al., 1999). Of interest in this thesis are high ozone concentrations, observed in densely populated urban and suburban areas, and often found in combination with other harmful pollutants such as: nitric acid (HNOs), carbon monoxide (CO), nitrogen dioxide (NO2), hydrogen peroxide (H2O2), per-oxyacetlynitrate (PAN) and fine particulate matter (PM2 .5). First identified in the Los Angeles region in the 1940s (National Research Council, 1991), high ozone and its related pollutants (called smog) are now found in virtually every large urban area - in 1998, 130 million people in the U.S. alone lived in areas violating federal ozone standards (Lin et al., 2001). Furthermore, ground level ozone has become a regional issue with elevated concentrations, from different urban areas, merging 1 More precisely, it is produced via photochemical reactions of oxides of nitrogen and radicals with V O C s acting as a radical source. Chapter 2. Introduction 6 into large scale plumes (Schere and Hidy, 2000). The main concern with ground-level ozone is its deleterious effects on human health and vegetation. 2.1.1 Effects of ozone Health Ozone is an oxidant of biological tissue. Exposure to elevated levels causes inflammation of the specialized cells which line the respiratory tract (Harte, 1991). Symptoms of exposure include: chest pain, lung and nasal congestion, and eye and nose irritation (Horvath and McKee, 1994). Numerous studies have linked exposure to high ozone levels with increased emergency room visits (Delfino et al., 1997), school absenteeism (Gilliland et al., 2001), reduced lung function (Brauer et al., 1996) and also as a trigger for asthmatics (Friedman et al., 2001). Furthermore, responsiveness is known to be sensitive to age: Petroeschevsky et al. (2001) report an increase in illness risk for individuals 65 years and older while Burnett et al. (2001) have shown negative health impacts for children less than two years of age. Finally, studies have shown that long-term exposure leads to diminished lung function and chronic respiratory symptoms (Galizia and Kinney, 1999). Environmental Ozone exposure also affects vegetation. Ozone uptake during respiration results in tissue damage and reduced plant growth (Runeckles, 2002). Most major North American agricultural crops show reduced yields after exposure to elevated ozone levels (Lesser et al., 1990). In fact, it is estimated that ozone, either alone or in combination with other pollutants, accounts for approximately 90% of crop losses from air pollution in the US (Heck et al., 1982). The estimated value of lost produce, due to ozone exposure, in the Lower Eraser Valley B .C . , was $ 9 million in 1986 (Runeckles, 2002). Plant response to ozone appears to depend more on the magnitude of the ambient concentration than exposure time (National Research Council, 1991), an important consideration when setting air quality standards (Heck and Cowling, 1997). 2.1.2 A i r quality standards and ozone To protect public health and welfare, ozone exposure standards have been set. In Canada, National Ambient Air Quality Objectives (NAAQOs) set a maximum one hour average acceptable ozone level at 82 ppb. A new, Canada wide standard (CWS), to be implemented by 2010, sets a goal of 65 ppb for the 4th highest 8-hour reading, averaged over three consecutive years (Canadian Council of Ministers of the Environment, 2000). In the US, the 1997 Clean Ai r Act Revision (CAAR97) Chapter 2. Introduction 7 sets a standard of 82 ppb averaged over 8 hours for the third highest reading averaged over 4 years (Environmental Protection Agency, 1997). The statistical nature of these standards reflects the natural variability of ozone to external influences - principally meteorological conditions - and accounts for rare or unusual events that might cause excessively high concentrations in otherwise acceptable areas (Ott, 1994). 2.1.3 Meteorology and ozone Elevated ozone levels are typically associated with slow moving high pressure systems producing clear skies, elevated temperatures and stagnant conditions (National Research Council, 1991). But local conditions also enhance ozone formation: mountains restrict horizontal circulation (Millan et al., 1997), weak thermal driven winds, produced in coastal locations, recirculate but do not vent pollutants (Steyn, 1996), high altitudes increase solar radiation (Fast and Zhong, 1998) and semi-permanent subsidence in subtropical latitudes limits vertical mixing (Lu and Turco, 1995). Thus, ozone formation is sensitive to both large and small scale meteorological processes2. 2.1.4 Emissions and ozone Ozone is not directly emitted but is a secondary pollutant formed via chemical reactions involving precursor pollutants. Both the biogenic (Guenther et al., 2000) and anthropogenic (Placet et al. (2000), Sawyer et al. (2000)) precursor sources show great spatial and temporal variability. Quanti-fying these emissions is difficult and presents a major source of uncertainty in understanding ozone formation (National Research Council, 1991). Furthermore^ future anthropogenic emissions are largely driven by both technological innovation and regulatory practices, both of which are difficult to predict (Intergovernmental Panel on Climate Change, 2001). 2.2 Fundamentals of Ozone Photochemistry The link between ozone production and the irradiation of mixtures of NOx and V O C s was first established in the 1950s (Haagen-Smit, 1952). Since that time, a great deal of effort has been directed at understanding the exact chemical processes involved. Complicating this research is the multitude of different V O C species typically found in a polluted environment, and the extremely large number of ways these species can react — it is estimated that an explicit treatment of ozone formation would 2 W h i l e meteorology can play an indirect role, by producing conditions conducive to ozone formation or by limiting dispersion, it can also play a direct role through the transport of ozone rich stratospheric air to the surface (Holton et al., 1995). Chapter 2. Introduction 8 contain more than 20,000 reactions involving several thousand reactants and products (Dodge, 2000). A brief description of ozone formation is given below. 2.2.1 Photochemical Cycle of NO, N02 and 0 3 To begin, ozone formation for the simplest photochemical system - one that involves only NOx and ozone - is discussed. The process begins with photolysis of NO2, at wavelengths < 424 nm, producing a single oxygen atom that combines with oxygen to produce ozone: N02 + hv -> NO + O (Rl ) O + O2 + M - • O3 + M (R2) where M represents a third molecule which stabilizes the formation of O 3 by absorbing excess energy. Reaction (R2) is the only reaction that produces ozone in the troposphere (Seinfeld and Pandis, 1998). The NO formed in (Rl) can react with ozone to regenerate N02: NO + 03 -» NO2 + O2 (R3) Although ozone is produced from the photolysis of nitrogen dioxide (Rl), the subsequent titra-tion of ozone by nitric oxide (R3) limits ozone formation resulting in a balance between ozone production and titration called the photostationary state3: .... j[N02}ss , . [ ° 3 U - kNO[NO]ss ( 2 1 ) where j — NO2 photolysis rate (1 /sec) and fcjvo — NO titration rate (cm3/'(molecules • sec)) Most anthropogenic N O x emissions occur as N O (Jacobson, 1999) and ozone concentrations based solely on Eq. (2.1) are lower than observed in urban atmospheres. To produce elevated ozone levels, another oxidation pathway is needed to convert NO to NO2 without consuming ozone. It is the oxidation of V O C s by radicals which provides such an alternate path. 2.2.2 Radicals In the atmosphere, temperatures, pressures and gas concentrations are so low that generally the only reactions which proceed at appreciable rates are those involving at least one radical species (Jacob, 1999). Radicals are ubiquitous compounds with an unpaired electron in their outer shell (Turco, implicit in this relationship is the assumption that the oxygen atom reacts so quickly that it is always in a steady state with [NO2] Chapter 2. Introduction 9 2002). Due to the unpaired electron, radicals are extremely reactive. The most important radicals in the photochemical production of ozone are the hydroxyl radical (OH')4 and the hydroperoxy radical (HO'). Special mention should also be made of atomic oxygen. In its excited state (0(lD)), it has all its electrons paired up (so technically it is not a radical) but is still very reactive while in its ground or triplet state, O (or more formally 0 ( 3 P ) ) is a radical with two unpaired electrons (and should technically be called a biradical). A complete understanding of the role radicals play in producing ozone requires an investigation into the radical life-cycle, namely: initiation, propagation and termination. Radical Initiation Radicals have high free energies and as a result, radical formation from non-radical sources requires energy. This production, called initiation, is typically a photolysis process (Jeffries, 1995). A n important source of new OH' radicals is the photolysis of ozone producing atomic oxygen in its excited state (01D) (Jeffries and Tonnesen, 1994). The excited oxygen atom can subsequently produce two hydroxyl radicals after reacting with a water molecule: 03 + hv -+ 02 + OlD (R4) OlD + H20 -» IOH' (R5) A n important source of hydroperoxy radicals is the photolysis of formaldehyde: HCHO + hv^ 2H0'2 + CO (R6) Radical Propagation Radicals are propagated when a reaction produces as many radicals as it consumes (Jeffries and Tonnesen, 1994). Propagation creates chains, allowing a single radicals to react many times (Seinfeld and Pandis, 1998). One of the most important propagation reactions involves the conversion of nitric oxide to nitrogen dioxide by the hydroperoxy radical: H0'2 + NO^ OH' + N02 (R7) Another important propagation reaction involves the oxidation of carbon monoxide by the hy-droxyl radical: 0 2 + OH' + CO^ HO'2 + C02 (R8) 4 Radica l species are denoted by a superscripted 'dot' unless otherwise noted Chapter 2. Introduction 10 R a d i c a l Te rmina t i on Reactions that incorporate radicals into stable products and stop the propagation chain are called termination reactions. The most important termination reaction is: OH' + N02 -» HN03 (R9) which consumes both nitrogen dioxide and the hydroxyl radical (Jeffries and Tonnesen, 1994). Another important class of termination reactions involves two radicals reacting together. A n ex-ample is the formation of hydrogen peroxide from two hydroperoxy radicals: HO'2 + HO'2 H202 (R10A) RO' + RO' -> higher peroxides (R10B) 2.2.3 Reaction Chains A reaction is said to be elementary if it occurs in a single step with no detectable reaction inter-mediates. In many instances, reactions that appear to be elementary occur in more than one step with radical reactions providing the intermediate steps (Pannetier and Souchay, 1967). A com-posite reaction involves more than one elementary reaction. If, in a composite reaction, certain intermediates are consumed in one step but regenerated in another, then the reaction is called a chain reaction or cycle. Chain reactions always involve initiation, termination and two or more propagation steps (Pannetier and Souchay, 1967). Ozone photochemistry is best viewed from the perspective of reaction chains. 2.2.4 Photochemical Ozone Production in the Presence of V O C s and NOx Ozone formation begins by hydroxyl attack on the. V O C . For simplicity, the V O C is often expressed using two components: as a generic grouping of hydrogen, carbon and oxygen atoms - which is called the root and identified as R, and a single extra hydrogen (H). The hydroxyl radical abstracts a hydrogen atom to produce a water molecule while the remnants of the V O C (the root) reacts with oxygen to produce a peroxy radical (RO'). These two reactions can be expressed in a single step: OH' + RH^ R0'2 + H20 (Rll) Next, the peroxy radical reacts with the nitric oxide to produce nitrogen dioxide and the oxy radical (RO*) in a propagation step: RO'2 + NO^ RO' + N02 (R12) Chapter 2. Introduction 11 The above reaction allows the conversion of NO to N02 without the loss of ozone while prop-agating the radical. The oxy radical then reacts with oxygen to produce a new V O C (R'CHO) called a carbonyl compound (where the R' represents a new root) and the hydroperoxy radical: RO- + 0 2 - * H0'2 + R'CHO (R13) The carbonyl may itself photolyze to produce more radicals (in what is called a branching reaction). Finally, the hydroperoxy radical can convert more NO to N02 while recreating the OH' radical: - H0'2 + NO -> OH' + N02 (P. 14) This last hydroxyl radical can then proceed to initiate another attack on a second V O C . The net effect of reactions (-R11) to (i?14) is two NO to N02 conversions through the loss and then recreation of the hydroxyl radical. As in the photostationary state, ozone is produced through the photolysis of N02 and the combining of atomic oxygen with molecular oxygen (R2). The nitric oxide formed in Rl is available for further conversion by peroxy radicals (reactions (R12) or (-R14)) and is called 'old N O ' to distinguish it from fresh emissions of NO. Without the loss (titration) of ozone with NO (R3), ozone concentrations can build to high levels 5. While the above reactions show the importance of radicals in producing elevated ozone concentrations, termination reactions (R9, R10A and R10B) slow ozone production by stopping radical propagation by incorporating them into stable products. Figure 2.1 shows a schematic of the reaction pathways in the photochemical production of ozone in a polluted urban environment. In the Figure, the rectangles highlight the role of radicals. The four rectangles form a box which reveals the radical's catalytic nature; participating in reactions without being consumed. The circles show the role of the NOx emissions; continuously cycling between NO and ./VO2. The two diamonds show the end products of the two termination sequences. Finally, the zig-zag lines show the photolysis reactions. 2.2.5 Summary of Ozone photochemistry Photochemical production can be viewed as two interconnected cycles: one involving NOx, the other V O C . In the first cycle, V O C s are consumed, producing secondary V O C s (for example carbonyl compounds) which rejoin the pool of available VOCs . In principle, repeated consumption of these secondary V O C s eventually leads to simpler and simpler compounds as hydrogen atoms are removed 5 Polluted environments'can record ozone concentrations as high as 200 to 400 ppb (National Research Council, 1991). This can be compared wi th typical background levels ranging between 30 to 50 ppb in rural areas of the United States and Europe (Logan, 1985). Chapter 2. Introduction 12 R02 +NO->RO +N0 2 N0 2 + hv-> O3 + NO 'Old NO', O3 ) RH + OH.->R02 ^ O i d N O ' 03 + hv ^ I RO +0 2~>H0 2 +R'CHO N0 2 + hv-> O3 + NO OH +N0 2->HN0 3 H0 2 +H0 2 ->H 2 0 2 F i gure 2.1: Schematic of ozone photochemistry showing the cycling of both NOx and radicals. to form water molecules and carbon atoms to form C02. In practice, not all V O C s are converted to water and COi\ some are removed by deposition, others remain unprocessed. The second cycle involves the interconversion of NOx between NO and N02 (reactions (Rl), (R3), (R12) and (-R14)) coupled with the gradual conversion of N O x to other nitrogen products (i.e. reaction R9) which eventually terminates photochemical activity. Wi th ozone production depending on both cycles, production is limited by whichever precursor is in greatest demand - intuitively a 'law of the minimum' (Sillman, 1993). Determining which precursor governs ozone production is Chapter 2. Introduction 13 the central challenge of this science. 2.2.6 Photochemistry and poetry To illustrate the cyclical nature of photochemical reaction chains, I have written a poem. It parodies a poem by Jonathan Swift - made famous by the physicist L . F . Richardson - who also parodied it to describe the nature of turbulence. So, Nat'ralists observe, a Flea Hath smaller Fleas that on him prey; And these have smaller still to bite 'em; And so proceed ad infinitum: J O N A T H A N S W I F T , On Poetry: A Rhapsody [1733] Big whorls have little whorls That feed on their velocity, And little whorls have lesser whorls And so on to viscosity. L E W I S F . R I C H A R D S O N , Weather Prediction by Numerical Process, (Cambridge, 1922) Big V O C s produce little V O C s In reactions radicals pursue, And little V O C s produce lesser V O C s And so on to cee-oh-two (CO<x)-B R U C E A l N S L I E Vancouver, 2003 2.3 Approaches to Modeling Ground Level Ozone Improvements to air quality have been largely driven by public pressure on governments to develop national standards and introduce air quality management plans. While in the last 25 years these strategies have reduced the number of episodes with extreme concentrations, they have been less successful at reducing the number of days when ozone levels exceed the standards (Schere and Hidy, 2000). Furthermore, with Canada and the US introducing new standards at levels closer to Chapter 2. Introduction 14 background concentrations, it is expected that the number of ozone exceedances will increase (Lin et al. (2001), Saylor et al. (1998)). Thus, there is a continuing need to study ground level ozone and different methods have been developed to satisfy different needs. For instance, while the question of ozone sensitivity to V O C or NOx has been largely driven by the need to inform public policy 6 , there is an increasing effort to study the problem from a purely scientific view (Sillman, 1999). Furthermore, the need to forecast short term ozone concentrations requires different approaches than predicting the future levels. I briefly discuss techniques used to forecast short term ozone levels (which I call trends and correlation techniques), to model ozone sensitivities to emissions (principally Eulerian grid based models) and various methods used to complement these models. I will show the limitations of each and highlight the need for proper model selection. 2.3.1 Trends and Correlation Techniques As public concern about air pollution increases, there is a growing need for air quality agencies to produce public health notifications in the form of one- or two-day ozone (or air quality) forecasts. These short term forecasts often need only predict ozone exceedances or general air quality indices (AQI). These are an overall measure of air quality achieved by comparing measured concentrations of various pollutants against their respective air quality objectives and then converting these relative concentrations to a number on an A Q I scale. This allows different pollutant levels to be compared on a common scale ranging from 0-25 or good with concentrations near background levels to 100+ or very poor with concentrations posing significant health risks. Perhaps the simplest way to produce these forecasts is with persistence - future ozone levels will be the same as today's. This method succeeds because many atmospheric variables (Wilks, 1995), including ozone (Robeson and Steyn, 1989), display serial correlation. For example, Robeson and Steyn (1989) have used persistence (along with Julian day of year) to develop a probability forecast for ozone concentration in the Lower Fraser Valley (LFV) B . C . . One draw back of this method is its inability to predict the beginning or end of an exceedance (Environmental Protection Agency, 1999). As an improvement, forecasts often relate future ozone levels to more easily forecast predictor variables. For example, Taylor (1992) has suggested that ozone levels will reach exceedance levels in the L F V if the summertime 850 mb temperatures are greater than 10°C. Forecasts using several predictors along with a set of rules to group ozone concentrations based on meteorological conditions lead to a more robust model. Such a Classification and Regression 6 I n the U.S. , to comply with the Clean A i r Act , states are required to demonstrate the effectiveness of proposed management plans through the use of models - effectively turning them into legal tools (Jeffries, 1995). Chapter 2. Introduction 15 Tree (CART) model has been used by Burrows et al. (1995) to predict ozone concentrations in the L F V . Related to C A R T models are artificial neural networks which use a complex set of weights and functions to relate predictor variables to ozone concentrations. The analysis allows for non-linear relationships; well suited to the underlying non-linear photochemical processes (Comrie, 1997). Finally, surface meteorological observations can be regressed against historic ozone concentrations to build statistical models for daily maximum ozone concentrations. Robeson and Steyn (1990) used this method to develop a regression model for maximum ozone concentration using daily maximum temperature and the previous days ozone concentration. While all of these simple models are adequate for forecasting next day ozone levels, all relate future ozone concentrations to meteoroldgicaf conditions - not emissions. As a result, these models might serve as a basis for short term policy decisions (i.e. restricting car use during poor air quality days) but cannot serve as a basis for improving air quality where knowledge of ozone sensitivity to emissions is required. 2.3.2 Eulerian Grid Based The best means of determining ozone sensitivity to precursor emissions is through the use of Eulerian grid based models (Russell and Dennis, 2000). These models use a fixed Cartesian grid over a domain of interest, to produce an array of discrete cells at which the relevant equations describing the motion and chemical evolution of the pollutants are numerically solved. They require spatially and temporally resolved meteorological and emissions fields as inputs. The models account for horizontal and vertical transport processes as well as spatial variability of emissions, land use and topography (Seinfeld, 1988). These models are typically not used to forecast short term ozone levels7 but rather to explore the consequences of economic development and policy decisions on future air quality. Unfortunately, the future is not fixed but largely free for our own creating (Robinson, 1988) and many futures can be envisioned, not all having similar air quality 8. Thus, there is a need for modeling a large set of future scenarios. Furthermore, since ozone levels are strongly influenced by meteorology (McKendry, 1994), there is a need to model a variety of synoptic conditions. However, in many instances, future air quality is explored only using meteorological conditions from a single 'design day'. A more appropriate modeling strategy is one that models many future scenarios using a Envi ronment Canada is developing an operational photochemical model for daily ozone forecasts (Pudykiewicz and Koziol , 1999). 8 T h i s marks a big difference between models that are sensitive to emissions and those that are sensitive to meteo-rology - in these, choice about future weather is not an option whereas choice about future emissions is. Chapter 2. Introduction 16 variety of meteorological conditions. Unfortunately, the sheer complexity and cost of these models often precludes performing large numbers of simulations. As a result, a variety of modeling methods have been developed to complement these models. 2.3.3 Complementary Methods Broadly speaking, there are three different techniques to compliment Eulerian grid models: observa-tionally based methods (OBM), process analysis and semi-empirical models (SEM). Generally, O B M corroborate Eulerian grid models, process analysis elucidates model behaviour and S E M screen for interesting scenarios requiring a more detailed analysis. Observat ional Based M e t h o d s O B M use ambient measurements to infer ozone sensitivities and production rates. OBMs can be subdivided into two classes: methods that make use of ambient V O C , N O x and CO and those based on secondary reaction products (Sillman, 1999). In the first class, the original idea was to use the morning ratio of V O C to N O x concentrations to infer ozone sensitivity. This method has since been shown to be unreliable (Wolffe and Korsog, 1992). Chameides et al. (1992) suggested using an OiJ*-reactivity weighted V O C to NOx ratio as an indicator of ozone sensitivity which has been used by Cardelino and Chameides (1995) to build a model for ozone sensitivity using ambient V O C , NOx and C O measurements. Another O B M determines ozone sensitivity using ambient ozone and N O x concentrations to calculate the extent that NOx emissions have reacted to from secondary products (Blanchard et al. (1994) and Chang et al. (1997)). Unfortunately, ozone concentrations at any location represent the cumulative effects of local production in an air mass over the course of several hours, while the above methods determine sensitivity of local ozone production rates (Sillman, 1999). The second class uses long-lived 'indicator' species, like nitric acid and hydrogen peroxide, to infer ozone sensitivity (Milford et al. (1994), Sillman (1995) and L u and Chang (1998)). In this approach, NOx-sensitive conditions coincide with high concentrations of certain 'indicator' species while VOC-sensitive conditions coincide with low values. Because these methods are based on concentrations of long lived species, it is expected that results are indicative of air mass sensitivity as opposed to local sensitivity. Chapter 2: Introduction 17 Process Analysis To understand the mechanisms responsible for modeled concentration changes, a diagnostic tool has been developed that tracks the chemical and mechanical processes that control ozone formation (Jeffries and Tonnesen, 1994). Ai r quality models calculate concentrations by solving the mass continuity equations for each species. The mass continuity equations relate the time rate of change of concentration to the various chemical and mechanical processes that bring about the chemical changes. Typically, only resulting concentrations are retained after the calculations and not the contribution of each process. Process analysis modifies the numerical solvers in order to integrate the rates of individual reactions and physical processes over time. These integrated rates, repre-senting the production and loss of each species by various reactions and processes, are then used to understand the behaviour of the Eulerian grid model. This method has also been used to determine indicator species which are sensitive to both local ozone production rates (Tonnesen and Dennis, 2000a) as well as ozone concentration (Tonnesen and Dennis, 2000b). Semi-Empir ical Mode l s In order to develop simple models of ozone formation which are sensitive to emissions, much research has been devoted to understanding the photochemical system in terms of a small set of variables. Typically, this research makes use of experimental data from reaction vessels or smog chambers, where possible confounding effects of meteorology and emissions are more easily controlled, to empirically fit ozone concentrations to initial precursor concentrations. Shen et al. (1977) used reaction vessel experiments to find a relationship for maximum ozone concentration as a function of initial NOx and a unknown function of the initial ratio of V O C to NOx. Subsequent computer simulations by Sakamaki et al. (1982) corroborated these findings. Chang and Rudy (1993) obtained a similar relationship and by finding a parameterization for the unknown function, were able to predict maximum ozone concentration as a function of initial precursor concentration. Their model, however, had only limited success in predicting ozone concentrations outside of regions where ozone is sensitive to NOx. Along a similar line, Johnson (1984) developed a set of functional relationships for ozone for-mation based on the analysis of smog chamber data. However these relationships, while providing an intuitive understanding of ozone photochemistry, predict a constant ozone production efficiency (number of ozone molecules produced for each NOx molecule consumed) in disagreement with field studies (Blanchard, 2000). Finally, Azzi et al. (1992) have used smog chamber data to develop a highly parameterized set Chapter 2. Introduction 18 of chemical reactions, involving only a few species, called the Generic Reaction Set (GRS). This scheme has been coupled with a meteorological model to produce a screening tool (Venkatram et al., 1994). However, the GRS has been shown to over predict ozone concentrations in situations where NOx is in short supply (called NOx-limited conditions) severely restricting its use in a screening tool (Tonnesen and Jeffries, 1994). The goal of this thesis is to develop a semi-empirical model for ozone formation in a NOx-V O C system, in terms of a small set of variables, which can be used as a screening tool as well as understand ozone photochemistry in both NOx and V O C limited conditions. 2.4 Summary Exposure to elevated ozone concentrations presents an ongoing threat to public health and welfare. The basic science behind ozone formation is complex and incompletely understood. Regulating the problem involves making predictions about the future which adds further uncertainty. This leads to a fundamental dilemma: while comprehensive grid models are the best means of studying this problem, they are costly to run, difficult to evaluate and by no means perfect. Finally, a thorough analysis requires examining a large set of future scenarios and meteorological conditions - a task for which Eulerian grid models are i l l suited. The best way around this dilemma is to use comprehensive grid models in conjunction with various other complementary models. In this thesis, I will first develop and then evaluate such a complementary model based on a scaling analysis of ozone precursor relationships. Chapter 3. Scaling Analysis of Ozone Photochemistry 19 C h a p t e r 3 Scaling Analysis of Ozone Photochemistry 3.1 Introduction In this chapter, Ipresent a scaling analysis of ozone photochemistry. Methods and results developed in this chapter are central to the whole thesis: the remaining chapters in PART I build on results introduced here while chapters in PART II use these results to build a simple model of ozone photochemistry which includes meteorological processes. I begin this chapter by introducing various concepts central to scaling: measurements systems, dimensional homogeneity, dimensionless groups and similarity. These concepts form the basis of a systematic method of performing a scaling analysis called the Buckingham P i theorem. I start by using this method to investigate the relationship between maximum ozone concentration and initial NOx concentration, actinic flux and temperature for the simplest photochemical system: one that has only initial NO and N02- I perform this preliminary analysis for two reasons: to introduce the important concepts using a simpler system and, as it will be shown, since this system.is amenable to an exact mathematical analysis, to show the strength and weakness of a scaling analysis. I then perform a scaling analysis of a photochemical system comprised of a single V O C and NOx. I use the Buckingham P i analysis to find a simple relationship which describes the dependence of maximum ozone concentration to initial V O C and NOx concentration. Parameterization of this relationship reveals a surprising behaviour of the photochemical system which is the study of Chapters 5 and 6. I conclude this chapter with a comparison of my parameterization, obtained via a scaling anal-ysis, with other parameterizations of ozone photochemistry. Chapter 3. Scaling Analysis of Ozone Photochemistry 20 3.2 Scaling Analysis 3.2.1 What is a scaling analysis? The central tenet of scaling is: within limited ranges, the dependence of a system (object(s) including physical properties and forces acting on it (them)) on absolute size are slight and the behaviour of a system at one size can be used to inform at another. A scaling analysis is a method of study based on this concept. Unfortunately, in many instances this concept does not hold. There are reasons why mice aren't the size of elephants or mountains 100 km high (Haldane (1985)). In these cases, there are important absolute sizes in nature which cannot be ignored. In many cases, 'size' does not have to be a length or weight but may turn out to be a simple combination of these or even a more complex combination of forces, sizes and other properties. As a result, the term scale is often used to describe this generalization of size. A central belief in the physical sciences is that physical laws should hold at all sizes (Schroeder, 1991): However, for complex systems, the relative importance of different forces may change with size. As a result, it often appears (to first order) that different laws hold at different scales. When-ever a complex system does not show different behaviour across different scales, a 'similarity rela-tionship' arises.1 In such instances, the complex system can be described using a simple statistical or geometrical framework where highly specific physical laws are not necessary. The identification of the appropriate scales (both the correct combination of forces, sizes, etc. which identifies the equivalence and the limits under which equivalence holds) is the first task of a scaling analysis. While similarity relationships often provide simple descriptions of complex phenomena, one of the most interesting and challenging aspects of a scaling analysis is understanding why complex systems can be described in simple terms when many entirely different physical processes are oc-curring. In many cases, such a posteriori analysis reveal the prime importance of a specific process. It is the intention of this thesis to describe the photochemical production of ground-level ozone in terms of similarity relationships without the need for specific chemical or atmospheric processes. Also, this analysis will identify specific processes which are of prime importance to ozone production in urban environments. 3.2.2 Key Concepts In this section, I outline key concepts related to scaling analysis. I distinguish between dimen-sional analysis (to be defined shortly) and scaling analysis; a general form of analysis which may 1 T h e term similarity is used to stress that, while systems may share similar behaviours, they are not identical. Chapter 3. Scaling Analysis of Ozone Photochemistry 21 include dimensional analysis. Many of the key concepts are related to the fundamental notion of measurement and how the physical world is described by quantitative means. Measurement Systems The act of measuring involves a comparison between an object (or phenomena) to be measured and a standard. Standards define measurement units which are further sub-divided into fundamental and derived units. Fundamental units are an arbitrary set of standards which form the 'building blocks' of a measurement system and derived units are obtained from the fundamental units based physical relationships (Barenblatt, 1996). For example, if length and time are chosen as fundamental units then a derived measurement unit for velocity could be defined by a uniform motion in which one unit of length is traversed in one unit of time. In the SI (Systeme International) system, there are seven fundamental units of measurement used to quantify all physical properties: mass, length, time, temperature, electric current, luminosity intensity and amount of substance. While this is the most common system, others exist, some having a different choice of fundamental units of measurement (i.e. the British Engineering System includes force as a fundamental unit). Regardless of choice of fundamental units, all measurement systems must be able to quantify all physical properties using some combination of their fundamental units. D imens ion A physical quantity measured in two different measuring systems may have different numerical values (i.e. speed of sound in SI and in the cgs measurement systems) and the change in its numerical value is determined by its dimensions. For example, if the unit of measurement for length is decreased by a factor of L (between measurement systems) and time by a factor of T, then the numerical values for velocity will be a factor of LT~l larger and the dimension of velocity is given by [ L T - 1 ] . A quantity whose numerical value is the same in all measurement systems is said to be dimensionless. A l l other quantities are called dimensional. Dimens iona l Homogene i ty One implicit assumption in any mathematical expression of a physical relationship is that separate terms represent physical quantities of the same kind. This requires every term to have the same dimensional formula and is called the principle of dimensional homogeneity (Bridgman, 1937). An implication of this principle is that physical laws must be independent of the measurement system used to describe them (Bridgman, 1937). This invariance to measurement system imposes con-Chapter 3. Scaling Analysis of Ozone Photochemistry 22 straints on the form that dimensional variables can take in an physical relationship when expressed as mathematical equations. Dimens iona l A n a l y s i s Dimensional analysis is a method of reasoning that uses the principle of dimensional homogeneity to simplify mathematical functions which express physical laws (Barenblatt, 1996). In this thesis, I will make use of dimensional analysis to derive a simple relationship for maximum ozone concentration and initial precursor concentrations. Dimensionless G r o u p s Any combination of physical quantities whose numerical value (i.e. measurement) is the same for every measurement system is called a dimensionless group. Such groups are of prime importance in scaling analysis and often given physical interpretations. For example, in fluid dynamics a commonly used dimensionless group is the Reynolds number: v where U is a typical velocity (in m/s say), L a typical length (in m) and v the dynamic viscosity (in m2/s). This group can be viewed as measuring the relative importance of inertial forces to viscous forces. In a scaling analysis, it is often these groups which determine the 'size' or scale of a phenomena; for instance a fluid flow is classified as turbulent or laminar based on the size of Re. Simi la r i ty Closely related to the concept of scaling is similarity. This is the equivalence of different phenomena based on the equality of a particular dimensionless group. For example, in a fluid flow, dynamic similarity of two different .flows implies the equivalence of their Reynolds numbers. Similarity justifies the use of results drawn from experiments with small scale physical models in the design of ships and aircraft. Self-s imilar i ty Associated with similarity is self-similarity. Some phenomena appear the same under magnification. The classic example is the branching nature of a fern leaf. The branching produces leaves that replicate of the entire plant. Furthermore, little leaves on each leaf can be viewed as smaller versions of the larger leaf. In nature, this kind of replication has limits (i.e. at the molecular level) whereas Chapter 3. Scaling Analysis of Ozone Photochemistry 23 mathematically, the pattern repeats ad infinitum. Wherever self-similarity holds, the phenomena has no preferred scale. Power Laws A power law is a relationship between two or more variables where one variable is expressed as a constant times the other raised to a fixed power. It is represented as a linear relationship on a log-log plot. Power laws have a special behaviour under scaling: If f(x) = axb then f(\x) = a(\x)b = A 6 / ( z ) i.e. scaling of the independent variable returns a scaled version of the dependent variable with the same scaling exponent. Such laws are self-similar and hence true on all scales. It is for this reason that power laws are often found in scaling analysis. 3.2.3 Scaling Analysis Methods There are different methods used to perform a scaling analysis. The selection of a particular method often depends on how well the system can be analytically described or how well it can be observed. Below is a description of two common methods used in a scaling analysis: Buckingham P i Theory and Scale Analysis. Both methods use similar concepts, often yield the same results, and in fact complement one another. B u c k i n g h a m P i T h e o r y This is a systematic method of dimensional analysis in which all the relevant physical variables of a phenomena are placed into dimensionless groups (Bridgman, 1937). Mathematically, the the-ory exploits the principle of dimensional homogeneity and the fact that the number of relevant dimensionless groups must equal the number of original variables less the number of fundamental dimensions (Bluman and Anco, 2002). As a result, the order of a problem can often be reduced. Scale Ana lys i s This method of analysis makes use of the governing equations relevant to the system to determine appropriate scales (Glickman, 2000). Each term in the governing equations is made dimensionless using typical values for all fundamental dimensions. The resulting dimensionless terms are then Chapter 3. Scaling Analysis of Ozone Photochemistry 24 compared. The smaller terms are ignored and the remaining terms are used to model the system. The remaining terms become the relevant dimensionless groups (or intrinsic scales) for the phenom-ena. Often different scales are necessary to account for different ranges of the physical quantities (for instance increasing fluid velocity may change a thermal system from a free convection to a forced convection regime). Examples of this method include: the development of Prandtl's equations for fluid flow in a boundary layer (Hmze, 1975), the development of the quasi-geostrophic equations in atmospheric physics (Dutton, 1976) or the analysis by Jackson and Steyn (1994) of gaps winds in a channel. Figure 3.1 shows a schematic of how both approaches fit into to an investigation of a complex phenomena. The Buckingham P i approach feeds off the observations and numerical analysis. Data obtained from these investigations are used to determine the relevant variables and design exper-iments. The arrows could in fact go both ways, as the Buckingham P i analysis can be used to determine data collection needs. The scale analysis makes use of the governing equations. Both methods establish a select set of dimensionless groups. The end result of both analyses is a de-scription of a simpler system in terms of dimensionless groups. While a mathematical analysis of the simpler system may still not be possible, the scaling analysis is still of value. By making use of the dimensionless groups, the number of independent experiments is reduced. Furthermore, observations or output from numerical models can be simplified by expressing results in terms of the dimensionless groups.2 The final stage of a scaling analysis involves fitting an empirical curve to the 'data' (observations or output from numerical models) in order to describe the relationship between groups. If the data fall on a single universal curve or a set of curves showing similar characteristics, then a similarity relationship is said to hold. The scaling analysis gives neither the relationship between the dimensionless groups nor the form of the equations (Stull, 1988). This must be found via trial and error or physical insight. For example, given a similarity relationship, one can often infer the relationship between variables or the dominant processes based on its mathematical form (i.e. inverse square law, exponential decay, etc..) and a few simple principles (conservation of energy, central limit theorem, etc.). This type of reasoning has been used by West et al. (1997) to explain the nature of allometric scaling laws in biology. 2 A classic example of how dimensionless groups simplify experimental results was given by von Karman who reduced a set of experimental results, giving the internal friction of various fluids under a set of different conditions, and presented as a set of curves and tables, to a single curve (Barenblatt, 1996). Chapter 3. Scaling Analysis of Ozone Photochemistry 25 Select relevant variable* and group into dimensionless quantites. / \ Buckingham Pi Theory Dimensionless groups can be used to guide \ experimental proceedures \^ Dimenstionless combination of several variables often with physical significance Data/numerical output plotted in terms of dimensionless groups and show common variability Dimensionless Groups Similarity Relationship Scale Analysis / y / Direct analytical approach it which represents an unlikey method. Figure 3.1: A schematic showing how different approaches to studying an intractable non-linear problem lead to formulation of relevant dimensionless groups. 3.2.4 Scaling and Photochemical Modeling A scaling analysis will be used to study the relationship between modeled maximum ozone con-centration and initial precursor concentrations. First, however, I would like to show how scaling methods are already extensively used in modeling episodes of elevated ground level ozone. In such models, scaling methods appear in each of the three major model components: emissions, meteo-rology and photochemistry. Chapter 3. Scaling Analysis of Ozone Photochemistry 26 Emissions The emissions component of an integrated photochemical model calculates the flux of pollutants for all major sources, throughout the simulation and across the domain of interest. Except for large industrial point sources, in-situ emissions rates are seldom measured. Instead they are inferred by relating laboratory measured emission rates to a surrogate whose spatial and temporal distribution is better characterized (National Research Council, 1991). For instance, in most urban centers, vehicle emissions are the dominant source of V O C and NOx emissions (National Research Council, 2000). Vehicle kilometers traveled (VKT) is used as the surrogate and laboratory measured emission rates (EFmMe) are used to determine emissions (^-mobile) i - e - : £mobiie(kg) = VKT (km) x EFmobiie(kg/km) Interestingly, while V K T might be easier to measure than in-situ emissions, it too, is seldom mea-sured. Instead, V K T is assumed to scale with road size, temporal traffic patterns and driving patterns (National Research Council, 2000). As emission inventories become more detailed, mobiles source emissions are further sub-divided based on: mean vehicle speed, vehicle age and vehicle type. Similar scaling methods are used for the other emission sources. In general, since emission inventories reflect the individual and collective actions of a society, and since there are no simple mathematical relationships describing these actions, emissions inventories consist almost entirely of scaling relationships based on more easily calculated surrogates. Meteorology In the meteorological component, local dispersion of pollutants by turbulent mixing is often not explicitly modeled but calculated using similarity relationships. These relationships scale turbulent mixing with: height, wind speed, surface heating and temperature structure of the atmospheric boundary layer (Arya, 1999). Chemistry Finally, scaling relationships are also used in the chemistry component. As mentioned before, modern photochemical mechanisms condense the complex chemical processes into a smaller set of reactions involving a limited number of species (Dodge, 2000). To achieve this condensation, organic compounds are grouped into manageable sets of V O C classes based on similarity of reactivity and emission rates (Stockwell et al., 1990). In essence, this thesis extends the scaling of VOCs, based on reactivity and emission rates, to a scaling of V O C - N O x reactivity based on initial concentrations, Chapter 3. Scaling Analysis of Ozone Photochemistry 27 temperature and actinic flux. I begin by studying a simpler NOx-only photochemical system before moving to more complex V O C - N O x mixtures. 3.3 Scaling Analysis of a NOx-only System In this section, I use the Buckingham P i method of dimensional analysis to study ozone production in a photochemical system having only NO and N02. A n overview of the Buckingham P i method is given in Appendix A . I use this simple system to develop my methods which I extend in the following section. The scaling analysis produces an expression for maximum ozone concentration as a function of initial N O x concentration and different environmental conditions (temperature and actinic flux). I compare it with an analytical model to show the success and limitations of the scaling analysis. 3.3.1 NOx-only Photochemical System Consider a chemical system involving the following two reactions3: N02 + hi/ NO + O3 (Rla) N O + O 3 —> N02 + 02 (-R3) where I assume that reaction R2 proceeds so quickly that Rl and R2 can be written as a composite reaction Rla. As mentioned in Chapter 2, the steady state concentration of N02, NO and O 3 is given by: [ n , _ j[NQ2}PSS M , [ ° 3 U " kNO[NO)PSS ( 3 1 ) Equation (3.1) describes the steady state ozone concentration in terms of the N02 photolysis rate and NO-titration rate and depends on the steady state NO and N02 concentrations. A scaling analysis will be used to relate maximum steady state ozone concentration to the initial NO and N02 concentrations. It will also examine the dependence of maximum ozone concentration on actinic flux and temperature. 3.3.2 Relevant Variables To start the scaling analysis, consider a smog chamber of volume V containing an initial amount (in moles) of NO (iV/vo) a n d N02 (NNO2) a t a temperature T irradiated by a time varying spectral 3 A more realistic description for a NOx-only photochemical system would .also include reactions driven by the ubiquitous radicals. For simplicity, I ignore these and treat (Rla) and (R3) as a complete description of the photo-chemistry. Chapter 3. Scaling Analysis of Ozone Photochemistry 28 Variable Description Units Dimension V Chamber volume cm 3 length3 No3 Maximum amount of ozone molecules number NNO Initial amount of NO molecules number NNO2 Initial amount of NO2 molecules number jpk Peak N02-photolysis rate constant s e c- 1 time-1 A NO-O3 collision frequency cm3(molecules • s)~1 length3(number • time)-1 E NO-O3 activation energy J • molecule-1 mass • length? • time-2 • number-1 kT average translational molecular energy J • molecule-1 mass • length2 • time-2 • number-1 Table 3.1: Units and dimensions for maximum ozone and its dimensional factors. actinic flux I(X, t) for duration At. It is expected that the maximum amount (in moles) of ozone (No3) will depend on N^o and N^o2- Guided by Eq. (3.1), I expect No3 to also depend the actinic flux via the NO2 photolysis rate. While, this rate is a complex function of wavelength, spectral intensity, absorption cross-section and quantum yield (Finlayson-Pitts and Pitts, 1999), I assume for a constant ozone column abundance and particulate loading, the rate is determined solely by the solar zenith angle. Furthermore, assuming that O 3 , NO2 and NO adjust their concentrations faster to changes in J(A, t) than I(X, t) changes with time, then the length of time the mixture is irradiated should be unimportant. These last two assumptions also suggest that maximum ozone formation should be dependent on the peak photolysis rate constant (jpk)- Finally, No3 is a function of the NO titration rate. This in turn depends on the reaction activation energy (E), the average molecular translational energy (kT where k is the Boltzmann constant) and the molecular collision rate (also called the frequency factor (^4)). In all, I expect No3 to be a function of seven factors: chamber volume (V), initial NNO and NNO2, peak NO2 photolysis rate (jpk), ozone-NO collision rate (A), activation energy (E) and molecular translational energy (kT). 3.3.3 Variable Dimensions The fundamental dimensions for maximum ozone and its seven independent factors are given in Table 3.1. In all, the problem contains four fundamental dimensions: length, time, mass and number of atoms or molecules. 3.3.4 Key Variables Because this system has four dimensions, four 'key variables' are required to non-dimensionalize the problem. These can be any of the variables from Table 3.1 subject to the following restrictions: Chapter 3. Scaling Analysis of Ozone Photochemistry 29 • There must be as many key variables as fundamental dimensions • A l l of the fundamental dimensions must be represented by the key variable • The key variables cannot be arranged into a single dimensionless group The chamber volume (V), peak photolysis rate constant (jpk), activation energy (E) and fre-quency factor (A) form an appropriate selection since they contain all dimensions and no single dimensionless group can be formed from them. 3.3.5 Pi-Groups Next, the remaining four variables (No3, NNO, NNO2 a n d T) are made dimensionless using the key variables. The resulting dimensionless variables, called Pi-groups after the engineering scientist Buckingham who developed the technique (Buckingham, 1914) are: No3 „ NNO , NNp2 , kT n i = VT]^jA> n 2 = V7]^A> n^V7]^jA> = U M 3.3.6 Alternative Pi-Groups The theorem allows new Pi-groups to be chosen from the original groups provided that the number of groups remains the same, all variables are represented and no Pi-groups can be formed from any other group (Stull, 1988). B y taking advantage of this option, I form the following Pi-groups: Np3 N N O NNQ2 ( E\ 1 T l = TT— :—77' ^2 = TT : TT) 7T3 = -n , ^4 = exp < — } (3.3) V • Jpk/A V • jpk/A NNO { kT J The relationship between maximum amount of ozone, for a simple photochemical system defined by (Rla) and (R3), and its relevant variables should now be expressible by four dimensionless groups; a reduction in the order of the problem by four i.e.: No3 = F (V,NNO,NNo2,jPk,kT,E,A) Dimensional 7Ti = / (7T2,7T3,774) Dimensionless While recasting the problem in terms of Pi-group has simplified the problem, the function relationship between Pi-groups must still be empirically determined using observations or numerical modeling. However, to aid in the search, a suitable form for the relationship can be guessed. To this end, I suggest the following functional relationship: TIi = 7ri/7r4 = / (7r2/7r4,7r3/7r4) (3.4) Chapter 3. Scaling Analysis of Ozone Photochemistry 30 By rewriting in this form, dimensionless number concentrations can be expressed in a simpler manner. For dimensionless ozone: U i = n = No, = j 0 3 j m a * ( 3 5 ) where [ 03 ] m a x ( = No3/V) is the maximum ozone concentration and k^o (= Aexp{—E/kT}) is the Arrhenius rate constant for reaction (RS) 4 . Similiar expressions for dimensionless NO and N02 are found using IT2 = 772/774 and IT3 = 773/774. To test this form, model output was generated. 3.3.7 O Z I P R Model Output Numerical simulation of a NOx-only photochemical system (defined exclusively by reactions R l a and R2) were carried out using a box model with a constant temperature, no dilution and the initial NO and N02 initially uniformly mixed before the start of irradiation. The initial ozone concentration was set to zero. The simulations used actinic flux levels appropriate to Vancouver B . C . (Latitude 49.25° N and Longitude 123.15° W) for a time interval beginning at 8:00 a.m. and ending at 7:00 p.m. (Pacific Standard Time). Parametrization of the NO2 photolysis rate with solar zenith was taken from the R A D M 2 (Stockwell et al., 1990) chemical mechanism. A matrix of simulations was run for 15 different NOx levels, five different [N02]0/[NO]0 ratios, four temperatures and five Julian dates for a total of 1500 simulations. The Julian dates, ranging between June 21 s t and September 15th, were chosen to provide a uniform spacing of jpfc-values while the temperature range was chosen to be representative of maximum summertime temperatures in the L F V , B.C.(Steyn et al., 1999). The simulated NOx concentrations range from values typical of remote locations to values found in urban and suburban boundary layers (National Research Council, 1991). Finally, the low end of the [N02]o/[NO]0 range corresponds to typical ambient conditions in the L F V (Jiang et al., 1997a) while the upper end represents ratios typical of raw vehicle exhaust (Lenner, 1987). Table 3.2 lists the ranges and number of treatments for each variable. I have recorded the NOx range using concentration units : (in ppm) for two 'reasons: this form is-the easiest to use based on the final II-groups and it is the conventional way of describing the relative amount of substance in air pollution meteorology. The numerical solver O Z I P R (Tonnesen, 2000) was used to simulate the reactions. OZIPR is a research-oriented version of EPA ' s OZIPP (Ozone Isopleth Plotting Package) computer modeling program. This is a simple trajectory model useful for relating ozone concentrations to different precursor concentrations and environmental conditions. A more complete description of the model 4 T h e Boltzmann constant (k) is not to be confused with the rate constant (fc^o) which wi l l always appear with a subscript. Chapter 3. Scaling Analysis of Ozone Photochemistry 31 Variable Range (units) Number of Treatments Temperature 293-308 (K) 4 Peak Photolysis 0.00738-0.00895 (1/sec) 5 Initial NOx concentration 0.00010-1.5000 (ppm) 15 Initial ratio of NO2 to NO 0.124-1.94 5 Table 3.2: Variable ranges and number of treatments for the OZIPR simulations of the NOx-only photochemical system. is given in Appendix B . Photochemistry was simulated using the R A D M 2 chemical mechanism (Stockwell et al., 1990). A complete description of this mechanism is given in Appendix C. From each simulation, maximum ozone concentration was recorded (which indeed coincided with peak NO2 photolysis rate). The relevant variables were made dimensionless using Eq. (3.4). In Figure 3.2, dimensionless maximum ozone concentration (I i i) has been plotted against di-mensionless initial NO (U2) for the various different initial [N02]0/[NO)0 ratios (II3). From this graph, the model output falls onto five distinct curves. Each tends to an asymptotic value as 1I2 becomes large. Furthermore, it appears that this asymptotic value corresponds to the n 3 -value. This suggests plotting I I i / n 3 versus II2 to obtain a single 'universal' curve. Figure 3.3 shows such a plot where the five curves have now almost collapsed onto a single curve. The collapse is best for the high and low II2 values but there is still some spread between the curves for 1I2 6 (5,20). A line of best fit has been drawn through the data which represents the empirically derived similarity relationship (discussed next). To understand the significance of this plot, consider three O Z I P R simulations, all for a latitude of 49.25°N having the following initial conditions: 1. A temperature of 35°C with an actinic flux appropriate for June 21 s t and starting with initial [NO]0 = 0.51 ppm and [N02]0 = 0.99 ppm. 2. A temperature of 20°C for August 10th with initial [N0]o = 0.63 ppm and [N02}0 = 0.63 ppm. 3. A temperature of 25°C for August 27th with initial [NO}0 = 0.56 ppm and p V 0 2 ] 0 = 0.19 ppm. The corresponding dimensionless NO concentrations (II2) are nearly identical: 29.6, 30.0 and 30.7. As a result, the analysis suggests that the corresponding ratios of n . i / n . 3 should be nearly identical and indeed they are: 0.91, 0:92 and 0.94- However, there are different "ways' to produce a constant n i / n . 3 ratio: and in this case, because of the large range in [N02]/[NO] ratios (1.94, 1.00, 0.33), Chapter 3. Scaling Analysis of Ozone Photochemistry 32 [N0]o [N02]o T Date jpk n 2 n 3 ill - rii/ris (ppm) (ppm) (K) (ppm/sec) - (1/s) (PPb) - - - -0.51 0.99 308 0.52 June 21 0.00895 30.4 29.6 1.94 1.77 0.91 0.63 0.63 293 0.41 August 10 0.0086 19.1 30.0 1.00 0.92 0.92 0.56 0.19 298 0.45 August 27 0.00819 5.7 30.7 0.33 0.31 0.94 Table 3.3: Initial conditions and maximum ozone concentration for three NOx-only OZIPR simulations have similar IJ.2 values. 2.0 1.5 1.0 II 0 .5 t" 0.0 I T + n3=0.124 n3=0.333 o n3=0.493 _ A n,= 1.000 _ • n 3 =i .941 -h-H+ ++ + ++ J I l_ 20 40 60 n 2 = [N0]o/(jpk/kN0) 80 100 Figure 3.2: Dimensionless maximum ozone concentration versus dimensionless initial NO concentration (n2) for 5 different initial NOa to N02 ratios. Values of U2 reflect different initial NO concentrations, kNO rates (via different temperatures) or j p k values (via different Julian dates). there is a large range in maximum ozone values: 30.4, 19.1 and 5.7 ppb. Table 3.3 summarizes these three simulations. Thus a wide range of ozone concentrations, arising from a wide range of simulations conditions, are nonetheless considered equivalent from a scaling perspective. Chapter 3. Scaling Analysis of Ozone Photochemistry 33 0 .75 h 0 .50 0 .25 0 .00 20 40 60 n 2 = [N0],/(v/kN 80 100 Figure 3.3: Dimensionless steady-state ozone concentration scaled by the initial ratio of NO to NO2 as a function of dimensionless initial NO concentration. Also plotted is the 'universal' similarity relationship rii/113 = o .5{(ni + 6n 2 + i ) 1 / 2 - ( n 2 + i)}. 3.3.8 Universal Curve By trial and error, a curve which fits the dimensionless model output has been found: 5i = 0 . 5 { ( n 2 + 6n 2 + 1 ) 1 / 2 - ( n 2 + 1 ) } (3.6) Equation 3.6 shows that as n 2 gets large, —> 1. This implies that for large enough initial NO concentration: ) n ] _ jPk[N02}o ,„ , [ ° 3 l m a x ~ kNO[NO}0 {6J> This expression is similar to Eq. (3.1) except now m a x i m u m ozone concentration is related to i n i -t i a l NOx concentrations. In essence, with enough initial NO (or high kj^o (via high temperatures) or small jpk (via little actinic flux)), the resulting maximum ozone concentration is achieved with very little change in the initial ratio of N02 to NO. Chapter 3. Scaling Analysis of Ozone Photochemistry 34 3.3.9 Analytic Expression It is possible, from this simple system, to derive an analytic expression for maximum ozone concen-tration as a function of the initial N O x concentrations (Seinfeld and Pandis, 1998). This is achieved by introducing two additional constraints to equation 3.1. The first is the conservation of nitrogen, namely: [NO](t) + [N02}(t) = [NO}0 + [N02}0 (3.8) and the second a stoichiometric balance of O 3 with NO : [NO}0 - [NO] (t) = [03]0 - [0 3] (£) (3.9) (i.e. both O 3 and NO are consumed and produced in a fixed proportion) Using these constraints, the steady state ozone concentration (when initial ozone concentration is set to zero ([03]o = 0)) is: { 2 "1 l / 2 (}N0]°+kL) +44[w02l°} (3l0) Maximum steady state ozone concentration (for fixed NO, N02 and temperature) occurs when j is a maximum i.e.: d [ ° * ] * " = 0 when f = 0 (3.11) dt dt K J Using Eq. (3.11) and rewriting Eq. (3.10) using dimensionless groups gives an exact relationship between Pi-groups: [OsW* = 1 / [NO}0 , A , 1 [f [NO]Q , ^ , 1 WO]o WO2I I'7' Jpk/kNO 2\3pk/kNO J 2\\jpk/kNO J jpk/kNO jpk/kNO J or n i = - ^ ( n 2 + i ) + ^ { ( n 2 + i ) 2 + 4 n 2 - n 3 } 1 / 2 (3.12) Equation 3.12 shows that it is not possible to express ITi/TI3 as a function of II2 only. Thus it is not possible to express the dependence of maximum ozone concentration on [NO]0, [N02]0, T and j by a single curve. Therefore, the 'universal' curve (Eq. 3.6) represents an approximation of the true relationship, obtained as an empirical fit to the OZIPR model output. However, while not exact, Eq. (3.6) provides a simple means of describing ozone formation in this systenvwhich is valid over a wide range of conditions. In Figure 3.4, I have plotted ni/Tl3, obtained via Eq. (3.12) versus ni/Tl3 from Eq. (3.6), for the same range of parameter values as given in Table 3.2. Also plotted is the 1 : 1 line, representing perfect agreement between the two equations. From the Figure, it • is apparent that the 'universal' curve over-predicts when II3 > 1, under-predicts when II3 < 1, however in these instances the discrepancy is less that 10%. Finally the two equations show perfect agreement when 17.3 = 1. Chapter 3. Scaling Analysis of Ozone Photochemistry 35 1:1 1.00 0.75 c o 1 0.50 Ld C \ c 0.25 0.00 0.00 0.25 0.50 0.75 1.00 n,/n 3 (Equation 3.5) Figure 3.4: Scatter plot showing iTi/113 using Eq. (3.6) versus Eq. (3.12) for five different II3 levels. Also shown is the 1 : 1 line. In most cases, an exact expression like Eq. (3.12) is not available and similarity methods provide the best means of describing the complex system in simpler terms. In the next section, I look at a more complex photochemical system where an exact relationship for ozone dependence on initial precursor concentration cannot be found and similarity methods must be used. 3.4 Propene-NOx System In this section, I use the Buckingham P i method of dimensional analysis to analyze a photochemical system involving a single V O C species and NOx. The analysis considers only the dependence of maximum ozone on initial precursor concentrations. A more detailed analysis, involving different VOCs, V O C mixtures and varying environmental conditions is postponed until the next chapter. I start the analysis with a qualitative description of an ozone response surface; highlighting the complex dependence of maximum ozone on initial precursor concentration. The analysis then pro-ceeds with a consideration of the important processes and variables which govern ozone formation in a V O C - N O x system. This is followed by the selection of appropriate Pi-groups, numerical simu-Chapter 3. Scaling Analysis of Ozone Photochemistry 36 lations and the eventual plotting of a similarity relationship. Parameterization of this relationship introduces results and methods which are central to much of this thesis. The section finishes with a comparison of ozone-precursor relationships. 3.4.1 Ozone response surface The dependence of ozone formation on initial amounts of V O C and NOx is most easily seen by plot-ting contours of maximum ozone against initial precursor concentrations. Such a response surface (plotted in Figure 3.5) is referred to as an ozone isopleth diagram and is generated by performing a larger number of photochemical simulations with varying initial V O C and NOx concentrations while keeping all other variables constant (Seinfeld and Pandis, 1998). Since isopleth diagrams are a concise way to depicting the effects of changing V O C or NOx concentrations on peak ozone concen-trations, they have also been used to quantitatively develop control strategies (National Research Council, 1991). The ozone response surface highlights the complex behaviour of maximum ozone on both the absolute and relative levels of V O C and NOx. For example, consider the two arrows in Figure 3.5. In the region marked by the lower arrow, maximum ozone levels initially increase as initial NOx concentrations increase. At a critical ratio of VOC-to NOx, the maximum ozone level reaches a peak and then starts to decrease as NOx concentrations are further increased (as indicated by the upper arrow). The location of peak maximum ozone forms a ridgeline, defined as the location where the sensitivity of maximum ozone to changing NOx concentrations is zero i.e.: d{Oz\max = 0 (3.13) d[NOx}0 This ridgeline definition is somewhat arbitrary; one could equally define the ridgeline as the lo-cation where maximum ozone shows equal sensitivity to changing NOx and V O C concentrations. The significance of different ridgeline definitions is investigated in chapter 4. The region below the ridgeline, called the NOx limited region (NLR), has ozone production limited by low NOx avail-ability. Above the ridgeline, maximum ozone increases with increasing V O C levels and is called the V O C limited region ( V L R ) . The objective of the scaling analysis is to find a simple mathematical description of this complex behaviour. While precursor concentrations are the most important factors in determining maximum ozone concentrations, other factors also influence the photochemistry. One group of factors, which I call environmental factors, includes temperature and actinic flux. In this chapter, I include these in the selection of the dimensionless groups but postpone an investigation of their influence until the next chapter. Another group, which I call mechanical factors, includes deposition, entrainment and Chapter 3. Scaling Analysis of Ozone Photochemistry 37 Initial VOC concentration - ppmC Figure 3.5: Ozone response surface as a function of initial VOC and NOx concentration. Isopleth show maximum ozone concentration in ppb. A ridgeline separates the surface into two regions: one shows an increase in ozone for an increase in initial NOx (marked by the lower arrow), the other a decrease (upper arrow). dilution. I do not include these in the scaling analysis but I examine their influence in Part II. In order to eliminate the possible confounding effects of both the mechanical and environmental factors, I simulate a smog chamber where dilution and entrainment are not present and deposition can be accounted for. Smog chambers are essentially large reaction vessels where emission, temper-ature, humidity and sunlight can be accurately controlled and the confounding effects of the real atmosphere can be removed (Finlayson-Pitts and Pitts, 1999). These chambers are not without their own complicating influences which I address in Chapter 7. 3.4.2 Dimensional Considerat ions For the V O C - N O x system, the presence of V O C s suggest radical driven chemistry, as outlined in Chapter 2, will be important. As mentioned before, the net effect of the radical driven chemistry is to slowly convert NO to N02 without consuming O 3 . This slower cycle is interconnected with the fast cycling of NOx between NO and N02. Figure 3.6 shows a schematic of the two cycles where the fast cycle is comprised of reactions (Rla) and (R3) and the slow cycle is characterized by NO-to-N02 conversion via the HO' radical; a product of OH' attack on VOCs . The presence of a fast and slow cycle suggest this problem will have several characteristic scales. Drawing on the results from the NOx-only scaling, I expect the maximum amount of ozone Chapter 3. Scaling Analysis of Ozone Photochemistry 38 _ _ _ _ _ ^ fflSf N0 2 ^ NO + 0V> VOC + OH* t NO HOV ^y-^-^siow F i glire 3.6: Schematic of the fast NO-NO2-O3 cycle and the slower radical driven cycle (adapted from Seinfeld and Pandis (1998)). Variable Description Units Dimensions V Chamber volume m 3 length3 No, Maximum amount of ozone moles number NNOX Initial amount of NOx moles number Jav Average NO2 photolysis rate constant sec"1 time-1 ANO NO-O3 collision frequency cm3 (molecules length3 (number time) 1 ENO Activation energy for O3 + NO titration J • molecule" -1 mass • length2 • time-2 • number-1 Nvoc Initial amount of V O C moles number At Length of test sec time AOH VOC — OH collision frequency cm3 (molecules length3 (number time)-1 EOH Activation energy for VOC + OH' reaction J • molecule -1 mass • length2 • time-2 • number-1 kT Average molecular translational energy J • molecule -1 mass • length2 • time-2 • number-1 Table 3.4: Smog chamber scaling parameters (No3) to be a function of the chamber volume (V) and molecular translational energy (kT) as well as the ozone titration activation energy (ENO) and molecular collision rate (A^o)- Because of the fast cycling between NO and NO2, it is likely that the total amount of the two (N^Ox) will be an important factor. The presence of the slower cycle suggests that maximum amount of ozone formed may not coincide with peak actinic flux. As a result, the average NO2 photolysis rate constant (jav) should be a better measure of the actinic flux than the peak'photolysis rate constant (jpk)-The slow cycle is characterized by the length of time the mixture is irradiated (At), the initial amount of V O C (Nvoc), the activation energy of the VOC-OH* attack (EOH) a n d the collision rate for this reaction (AOH)- Thus the problem has eleven different factors having four separate fundamental dimensions: length, time, mass and amount of substance. Table 3.4 summarizes the relevant variables and their dimensions. Four key variables (kT, V, jav and ANO), containing all the fundamental dimensions, have been Chapter 3. Scaling Analysis of Ozone Photochemistry 39 chosen to non-dimensionalize the remaining variables which yields the following seven (11 variables - 4 fundamental dimensions) dimensionless groups: NO3ANO I NVOCANO NNOXANO * = ~Vi—' *i = —vi . 7r2 = — ' (3-14) ' Jav Jav v Jav . A , EOH ENO ANO n3 = javAt, -4 = ^ - , ^5 = ^ r , «* = J ^ For Arrhenius type reactions, ANO and AOH are independent of temperature, their ratio becomes a constant and so TTQ will not influence the functional form of the similarity relationship and so can be ignored. Finally, I form a new pi-group (TVI) by dividing TT[ by TT2-Dimensionless analysis then suggests the relationship between maximum ozone and its governing variables can be expressed by: TT = /(7ri,7r2,7r 3,7r4,7r 5) (3.15) where / 5 is an unknown function of only five factors. This marks the end of the formal analysis. Further simplifications to the problem must be made through trial and error or by physical insight. Drawing on the results of the NOx-only scaling, I use TT^ to write II = 71-/715 and II2 = ^2/^5. I express the dimensionless activation energy (774) in an exponential form (II4 = exp[— ^ ^ ( ^ — Y~)]) ref where T r e / is a arbitrary reference temperature chosen to be 25° C. I further assume that 775 has only a temperature dependence that is captured by II4 and so the direct dependence of this group can be ignored. Finally, to be consistent in my notation, I set II3 = ^3. Thus, I hope to find a relationship between maximum ozone and its governing variables having the following form: n = / (n i ,n 2 ) i i3 , i i4 ) or (3.16) [OaW* _ , ( [NO]o [VOC]0 \ EOH fl J I • n. ' f A r n _ l ' Jav^l<, exp c r e / / J jav/kNO ^v/kMo' [NOx]0' ' I k \T To further simplify the functional form, a power law dependence for II2 is hypothesized. There is no a priori reason for such a selection; justification occurs when the data collapse onto a common 'universal' curve (Arya, 2001). However, the work of Chang and Rudy (1993), Blanchard et al. (1999), and Johnson (1984) all suggest that maximum ozone concentrations scales with a power of initial NOx concentration. Another consideration is that dimensional analysis only resolves power functions (Bridgman, 1937). With this in mind ,Eq . (3.17) can be rewritten: ^ = / (n 1 , n 3 ) n 4 ) (3.17) 5I use / (and later / ) as generic labels for the unknown function. These are different functions than those found in the NOx-only scaling analysis. Chapter 3. Scaling Analysis of Ozone Photochemistry 40 where a is an unknown exponent. The unknown function is now only dependant on three dimen-sionless groups. To keep the analysis simple, I will initially let only TIi vary. I examine the scaling behaviour for this simple case before extending the analysis to include varying actinic flux and temperature. Also, I examine only a single V O C , an alkene, in this section. In the next chapter, other VOCs are analyzed. 3.4.3 Propene I use propene as the sole V O C due to its relatively simple chemistry, its high reactivity and be-cause it is often used as a benchmark for comparing V O C reactivities (National Research Council, 1991). Unfortunately, in the R A D M 2 mechanism (Stockwell et al., 1990) propene is not specifically modeled. In this mechanism, alkenes are represented using 3 species: ethene (ETH), a surrogate for terminal alkenes (alkenes with a double bond attached to a carbon at the end of the molecule) called OLT and a third (OLI) used to represent internal alkenes, cyclic alkenes and dienes. The OLT surrogate generalizes the behaviour of terminal alkenes and reacts with OH' and O 3 with the same rate constants as propene (Stockwell et al., 1990). Therefore, it is expected that results obtained for OLT will be representative of propene. 3.4.4 OZIPR Simulations To generate model output, a matrix of simulations was run using the O Z I P R (Tonnesen, 2000) trajectory model. The test matrix consisted of 121 simulations created by independently varying initial OLT and NOx concentrations in 10% increments. The range of initial O L T concentrations was between 0.0 and 0.6 ppm while the NOx range was 0.0 to 0.15 ppm. The simulation conditions were similar to those outlined in Section 3.3.7, namely: start time was 7:00 a.m. (PDST) and end time was 6:00 p.m. (PDST), and there was neither dilution, entrainment nor deposition. However, these simulations were run with a constant temperature of 25°C, a 'total' dimensionless actinic flux of n3 = 347 (corresponding to Vancouver B . C . in mid-summer (August 3)) and an initial NO2 to NO ratio of 0.250. These simulations produced an overall maximum modeled ozone concentration of 348 ppb. Model output consisted of maximum ozone concentration along with initial V O C and NOx concentrations. However, before the model output was analyzed, some simulations were excluded. Whenever initial N O x concentration was zero ( and H i infinite), the R A D M 2 mechanism produced no ozone. These trivial simulations were removed. In addition, whenever the initial O L T concentra-tion were zero (Hi = 0), the R A D M 2 mechanism produced low ozone concentrations, independent Chapter 3. Scaling Analysis of Ozone Photochemistry 41 of OLT, representing ozone formation in a NOx-only system. Since the scaling analysis is con-cerned with V O C - N O x systems, these simulations were also excluded. After these removals, 100 simulations remained to determine /(TIi , I I2 , IT3). 3.4.5 Similarity Relationship Using Eq. (3.17), modeled maximum ozone concentration was made dimensionless and scaled by a power of dimensionless N O x i.e.: [ Q s W /([NOxiy ( 3 l 8 ) / k N O l \jav/k,NOj It was found that with a value of a — 0.6, model output, when plotted using Eq. (3.18) as a function of I i i (which is conventionally denoted by the variable R), collapsed onto a single common curve (Figure 3.7); suggesting success in the scaling analysis. The sigmoid shape of this curve suggests that it may be modeled by the cumulative distribution of a probability function. The idea for such parameterization was guided by Chang and Rudy (1993) who, after scaling ozone by NOx0-5 (and normalizing by a constant), found that the function: <f>(R) = 1 - e x p { - a i ? b } (3.19) fit their (scaled but not dimensionless) data well. This expression, chosen because of its simple functional form (Chang and Rudy, 1993), can be expressed as the cumulative distribution of a Weibull probability distribution after the transformation b = a and a = (3~a i.e.: 0(i2) = l-exp{-(#//?)<*} (3.20) That is, without realizing it, they found that a Weibull distribution was a suitable choice for modeling their results. 3.4.6 Weibull Distribution I have also chosen to use a Weibull distribution to parameterize my similarity relationship, not because I believe ozone formation is a Weibull process but rather because the Weibull distribution has a closed form inverse which provides an easy check for the suitability of the model. To check the suitability of the Weibull distribution, the NOx-scaled and dimensionless model output must first be normalized. This normalization represent the last of several manipulations of the model output that I perform in order to parameterize the similarity relationship. Figure 3.8 summarizes all these manipulations. I refer to the final scaled and normalized model output as simply the 'scaled data'. Chapter 3. Scaling Analysis of Ozone Photochemistry 42 7 10 8 4 0 + * + + T- - =1= - + -1 0 10 20 30 II, = [VOC] 0 / [NOx ] 0 = R 40 Figure 3.7: Dimensionless ozone scaled by dimensionless initial NOxa versus ratio of initial precursor concentration (R). Model output from RADM2 (Stockwell et al, 1990) simulations using OLT as the sole VOC, a constant temperature of 25° C and a total dimensionless actinic flux of J = 347. Once normalized, the Weibull transformation was applied to the 'scaled data': 1 W(f(R)) = In In (3.21) where 7 is the normalizing constant based on Eq. (3.18). I will refer to the Weibull transformed 'scaled data' and the 'Weibullized data'. To test the suitability of the Weibull model, W(f(R)) was plotted against In R, expecting that the 100 data points would cluster onto a single straight line. Figure 3.9 shows the plot of the 'Weibullized data' as a function of ln i? . From this figure, it is evident that the 'Weibullized data' collapses not onto one but two straight lines, which separates the similarity relationship into two.regions characterized by a change in slope at InR = 1.3 (R = 3.7). This shift hints at a change in governing chemical process; perhaps evidence of the change in ozone sensitivity to changing N O x concentration across the ridgeline. Included in the figure are two boundaries separating the figure into three regions: Region I, lies to the right of the break and regions Ha, l ib to the left. From the Figure, it appears that for small InR, that there is more scatter in the 'Weibullized data'. The scatter in these low InR values, associated with simulations having low initial OLT concentrations, suggests a different scaling, perhaps one similar to the scaling of the NOx-only systems. The transition is highlighted by the Chapter 3. Scaling Analysis of Ozone Photochemistry 43 OZIPR Simulations ^ \ ( No dilution,constant ]. V temperature, no deposition J 'Scaled Data' Data should collapse onto a single curve Model Output 121 data points /Scaled by\ \ NOx" Non-Trivial, Non-PSS Model Output 100 data points Figure 3.8: Procedure used to prepare OZIPR model output before Weibull transforming. boundary between regions H a and lib. It is difficult to objectively place this boundary and further investigation is required to better define it. 3.4.7 Scaling break and Lognormal Parameterization To show that the scaling break is not a by-product of the Weibull transformation, a lognormal distribution was used to fit the data. To test the effects of using the lognormal distribution to parameterize the similarity function, dimensionless OLT model output was transformed using the inverse error (ERFF) and inverse complementary error function (ERFCI). Such a transformation will take data drawn from a lognormal distribution and produce a straight line when plotted as a function of \n(R). Figure 3.10 shows the results of the OLT model output after this transformation. The transformed model output clusters around two lines segments with a break occurring at roughly ln(R) « 1.4. Also shown is the same model output after Weibull transforming. Both transformations show model output'cmstering onto two line segments.with^a break at roughly the same lnR-value. Chapter 3. Scaling Analysis of Ozone Photochemistry 44 0 c -4 - 6 Region lib Region lla; Region . + V -1 o 2 ln(R) Figure 3.9: Scaled model output after the Weibull transformation. Also shown are two vertical lines separating the plot into three regions. The dashed line at R = 3.7 indicates the shift in slopes and the second dashed lines marks the region of increased scatter. This suggests the scaling break is not an artifact of the Weibull model. For the remainder of this thesis, I use the Weibull model to parameterize all of my similarity relationships because of its simple form. 3.4.8 Analogy with Richardson number and Surface Stability The form of the 'Weibullized data' in Figure 3.9 suggests strong similarities with another figure also obtained via a scaling analysis. Based on micro-meteorological observations performed in Kansas in the summer of 1968, Businger et al. (1971) examined wind and temperature profiles using dimensional analysis. One of their results was a graph, shown in Figure 3.11, of dimensionless stability (Richardson number (Ri)) versus a dimensionless height (Q defined as: gdQ/dz kvgw'G'z z Ri = =—= versus C = =^— = -=• e(dU/dz)2 Qui L (3.22) Chapter 3. Scaling Analysis of Ozone Photochemistry 45 JL - i h 5 - 2 - 5 l _ - 2 Weibull Model Lognormal Model ln(R) - 4 ' i F i gure 3.10: Scaled model output after Lognormal and Weibull transformation. ERFI is the inverse error function and ERFCI is the inverse of the complementary error function. where 9 — local acceleration due to gravity e — mean temperature z — height above ground U — mean horizontal wind speed ky — von Karman constant w'O' — kinematic sensible surface heat flux u* — friction velocity L — Monin-Obukov dimensionless length scale In this graph, there are three striking similarities with Figure 3.9. First of all, the scaled data appears to collapse onto a single curve with a similar shape. The collapse of the data onto a common curve indicates a that Ri scales with (. Secondly, there appears to be a change in the slope of the curve. This can be attributed to a change in the sign of the turbulent kinematic sensible surface heat flux (w'@'). When w'O' is positive (and £ is negative), turbulence is generated by the surface heating. When the flux goes negative (and £ goes positive), the surface becomes a Chapter 3. Scaling Analysis of Ozone Photochemistry 46 05 | 1—nr~~r~"> -.2 . "I . .0 I 2 > . . 3 ' Figure 3.11: Richardson number as a function of stability (taken from Businger et al. (1971)). sink for heat and buoyant turbulent energy is consumed. Hence the change in the turbulent heat flux — from a source to a sink — represents a change in physical process and produces the two distinct line segments. Finally, there is more scatter in the data for the large negative ( values. The increased scatter corresponds to the transition from forced convection to free convection. In the free convection regime, the appropriate velocity scale becomes the convective velocity (to*) and not the friction velocity («*). This transition is not abrupt but gradual and hence the scaled points gradually become more scattered around the common fitted curve. The use of (, Ri and L as scaling parameters is a central idea in micro-meteorology (Arya, 2001). The utility and physical importance of these,parameters has been proven in many field studies: the 1968 Kansas Field Program (Businger et al., 1971) and various field campaigns in Australia (Garrat and Hicks, 1990) 3.4.9 W E X Model A parameterization for the similarity relationship, called the W E X model, has been developed to fit the 'Weibullized data' and is both continuous and differentiable at the break. W E X is a contraction of Weibull-Exponential because one of the line segments in the Weibull transformed similarity relationship (Weibull plane) has slope less than one. Such a Weibull generalizes the exponential distribution. I will discuss the physical significance of the magnitude of the slopes in chapter 5. Chapter 3. Scaling Analysis of Ozone Photochemistry 47 The W E X model is: <f>(R) = f(R)/7 = l-exp{-X(R/3)a{R)} (3.23) = WEX(R;aua2,3,\) (3.24) where the exponent a(R) is a function of R: ^ ) = ( ^ ) t a n h ( ^ - / 3 ) + ( ^ ) giving an expression for maximum ozone concentration: \^^=f\N^\a f { R ) ( 3 2 5 ) Jav I "'NO \3av/KNOj In this model (0:1,0:2) represent the slopes of the two line segments in the Weibull plane and R = 3 is the R-value at their matching point. The parameter A is related to the value of the 'Weibullized data' at R = 3. When a\ = a 2 and A = 1, the Weibull is recovered. There are other models used for fitting two Weibull functions to curves which show a break or 'dogleg'. Such curves arise frequently in the field of reliability engineering where failure rates often shows a characteristic change as a function of age. These models handle the 'dogleg' by several different means: matching two separate distributions at the break (Jiang et al., 1999), using the product of two Weibull curves (Jiang and Murthy, 1997) or using the weighted sum of different Weibulls (Jiang and Murthy, 1995b). While each of these models is capable of capturing the variability of the similarity relationship, the W E X model is a better choice in the present context because: • It explicitly identifies the location of the break point. • Regressing of model output to the W E X model is straight forward. • Its four parameters can be given a physical interpretation (see Chapters 5 and 6). A description of the various means of fitting two Weibulls is given in Appendix C. In Figure 3.12, I have plotted ozone isopleths using the O L T O Z I P R model output. Isopleths based on the W E X model (dotted lines), with'parameter values of: 7 = 9.5, a = 0.60, A = 0.92, 6 = 4.2, o>i — 2.2 and a2 = 0.72 have also been included along with a line of constant R = 4.2 (associated with the break). In addition, the ridgeline, as defined by Eq. (3.13) is also drawn. It has a value of R « 4.7 and from this figure; it appears that the scaling break seen in Figure 3.9 occurs above the ridgeline. The W E X model gives a good fit to the model output in the VOC-limited region (Ha), around the ridgeline and especially in the NOx-limited region (I). However, in Region l i b the model starts to noticeably diverge from the OZIPR model output. Chapter 3. Scaling Analysis of Ozone Photochemistry 48 Figure 3.12: Ozone isopleth plot for NOx-OLT system. All ozone concentrations in ppb. Solid lines are isopleths from OZIPR model. Dotted isopleths are from the WEX model. Also shown is the ridgeline (dashed line labeled Ridge,) and scaling break (dot-dashed line labeled R — (3). Regions I, Ha, lib have also been marked: Region I is below R = (3, Region Ila between R = (3 and dot-dashed line and Region lib above this second dot-dashed line. 3.4.10 Ozone-precursor relationships in the NOx Limited Region The W E X model captures the behaviour of the ozone response surface over a wide range of initial precursor concentrations including: parts of V L R , around the ridgeline and in the N L R . In this final section, I compare the W E X model to other models of ozone formation in the N L R . I begin by presenting a simplification to the model, valid only in the N L R , and then compare it with other models valid in this region. W E X model and NOx-only scaling The N L R lies below the ridgeline and the scaling break (Region I in Figure 3.12) where initial V O C concentrations are larger than initial NOx concentrations and their ratio (R = [VOC]0/[NOx]0) is greater than /3. From Figure 3.7 as R gets large, f(R) tends asymptotically to 7 as R —> 00 (where 7 is the normalizing constant). The similarity function (4>(R)) is now independent of R and Eq. Chapter 3. Scaling Analysis of Ozone Photochemistry 49 (3.17) can be rewritten as: I i i ~ 7II2 (Dimensionless) (3.26) i.e. the relationship between maximum ozone and initial precursor concentration is approximated by a simple power law. In terms of the original dimensional variables: [Oz)max « l{N0x]ao (Dimensional) (3.27) where 7 = j(jpk/kNo)1~a I call the region of an isopleth diagram where f(R) is independent of R and Equations (3.26 and 3.27) hold, the NOx-only Scaling region (NOS). This region is a sub-region of the N L R , away from the ridgeline, where isopleths are nearly parallel to the V O C axis. I now compare Eq. (3.27) with other ozone precursor models. I must point out that the other models do not make the distinction between N L R and NOS. In these models, [C^max refers not to the maximum ozone concentration for a particular simulation but rather the highest maximum ozone concentration (what I call peak ozone concentration) that can be formed for a given initial NOx concentration. I E R Model The first comparisons is with the IER model (Johnson, 1984) which expresses ozone formation in terms of Primary Smog Product (PSP) equal to the amount of ozone formed plus the amount of initial NO converted to N02-[PSP](t) = [03}(t) - [03}0 + [NO}0 - [NO](t) (3.28) where the t refers to concentration at time t and o refers to initial concentrations. Johnson (1984) argues that when P S P is a maximum (PSPmax), ozone is also at a maximum. With initial ozone concentration zero and final NO concentration negligible, Eq. (3.28) can be rewritten: PSPmax « [03]max + / [NOx(0)] (3.29) where / equals the initial ratio of NO to NOx. Based on extensive smog chamber studies performed at the Commonwealth Scientific and Industrial Research Organization (CISRO), "Johnson (1984) proposed an empirical relationship between maximum PSP and initial NOx: PSPmax = (3[NOx(0)} (3.30) where (3 was found to be 4.1 ± 0 . 4 (dimensionless). Using Eq. (3.29), equation 3.30 can be rewritten in terms of maximum ozone concentration: [03)max - ( / ? - / ) [NOx}0 (3.31) Chapter 3. Scaling Analysis of Ozone Photochemistry 50 Model/Reference Relationship Parameter Values P = 4.1 0 = 1.9 (when using ppm units) 7 = 1.03 (when using ppm units) 7 = 7 ' Oau/fc/vo)1-" = 1-93 (ppm units) and a = 0.6 (for a June 2 1 s t L F V simulation) Table 3.5: Ozone-precursor relationships in the NOx-limited region. This last expression gives a linear relationship between initial N O x concentration and peak ozone concentration whereas the W E X model (Eq. (3.27)) shows a power law dependence with an exponent of 0.6. The linear trend in Eq. (3.31) has generated concerns because it implies a constant ozone production efficiency (number of ozone molecules produced for each NOx molecule consumed) whereas field studies suggests that this increases as N O x decreases (Blanchard et a l , 1994). Modification to the IER Model The IER model has been modified by Blanchard et al. (1999) who used smog chamber data from the University of North Carolina (UNC), the Statewide Air Pollution Research Center (SAPRC) as well as photochemical box model simulations to suggest that Eq. (3.30) be replaced with: SPmax = B[NOx\a0 (3.32) where they refer to P S P as Smog Produced (SP). Or, in terms of maximum ozone concentration: [Oslma* = 6{NOx\a0 - f[NOx}0 (3.33) where B = 1.9 (when using ppm units) and a = 0.66. While Eq. (3.33) is similar to Eq. (3.27) -both having similar NOx-exponents - Eq. (3.27)-does not have the offset term (f[NOx]0). Chang and Suzio's Model Finally, Chang and Suzio (1995) have proposed the following relationship for maximum ozone in the N L R : [ 0 3 W x = liNOxW'2 (3.34) with 7 = 1.03 (ppm05). This expression is identical to Eq. (3.27) except for the magnitude of the exponent. However, it will be shown in Chapter 6 that the value of this exponent is sensitive to V O C species. Johnson (1984) [03]max = (P - f)[NOx]0 Blanchard et al. (1999) [ O 3 ] m o l = P[NOx}l/3 - f[NOx]a Chang and Rudy (1993) [03}max = y[NOx]l/2 W E X (for OLT) [03)max = i{NOx\« Chapter 3. Scaling Analysis of Ozone Photochemistry 51 To summarize, the W E X model predicts, in the NOS regime, maximum ozone concentration to be a function of initial N O x concentration only, consistent with Chang and Suzio (1995), Blanchard et al. (1999) and Johnson (1984). However, the W E X model gives different exponents and parameter values. Table 3.5 summarizes the ozone-precursor relationships in the N L R . 3.5 Summary In this chapter, I have introduced the concept of scaling and shown that scaling methods, in var-ious guises, already exist in Eulerian grid based photochemical models. In essence, this research represents an extension of these methods, where I have now parameterized the entire chemical mechanism. . I began my analysis with a NOx-only photochemical system and developed a simple relationship for maximum ozone concentration as a function of initial NO, N02 concentration, actinic flux (using the peak N02 photolysis rate) and temperature (via the temperature dependence of the NO-O3 titration rate). This relationship compares favourably with an exact mathematical representation. I then developed a simple parameterization (the W E X model) for maximum ozone concentra-tion as a function initial precursor concentration for a V O C - N O x system. The parameterization, when Weibull transformed, exhibits a striking feature (a 'dogleg') which suggests the photochemical system switches governing regimes. The switch coincides closely (but not exactly) with a change in ozone sensitivity to initial N O x concentration (the ridgeline on an isopleth diagram). The W E X model captures the complex dependence of ozone formation on initial precursor concentrations over a wide range: above, below and around the ridgeline. This represents an improvement over similar efforts by Johnson (1984), Chang and Rudy (1993) and Blanchard et al. (1999). These results suggest that over a wide range of initial precursor concentrations, and when viewed from the proper perspective (provided by the scaling analysis), the complex behaviour of an ozone response surface can be simply described. While this model is successful at predicting maximum ozone concentrations, it raises many interesting questions, namely: • Can the photochemistry of other V O C s and V O C mixtures be captured by a scaling relation-ships? • If so, do they all show a similar 'dogleg' in their similarity relationship? • How does varying temperature and actinic flux change the similarity relationship? Chapter 3. Scaling Analysis of Ozone Photochemistry 52 • Are these results a product of the R A D M 2 mechanism or are they universal to all chemical mechanisms? • Are these results consistent with observations? • What is the range of validity for the W E X parameterization? Through an investigation of these questions, I hope to build an heuristic understanding of the major factors controlling ozone photochemistry. The next chapter begins this investigation. Chapter 4. Domain of Applicability for the Scaling Relationship 53 C h a p t e r 4 Domain of Applicability for the Scaling Relationship 4.1 Introduction In this chapter, I explore ozone-precursor scaling relationships under a variety of conditions. I study the scaling behaviour for a variety of V O C s and V O C mixtures. In addition, to show the scaling behaviour is not an artifact of the R A D M 2 chemistry, two other photochemical mechanisms are used. I also examine-'the effects of two different environmental parameters - temperature and actinic flux - on the scaling. I vary the latter by modeling ozone formation for different days of year and different latitudes. To clarify my description of the numerical experiments, I propose the following terminology: • A scenario refers to design conditions common to a number of numerical runs. These include the type of V O C , temperature and chemical mechanism. • Test matrix refers to a set of numerical runs (usually 121 in total but may be more) having common design conditions (given by the scenario) but a range of initial V O C and NOx con-centrations. A scenario investigating temperature effects might have five test matrices each using a different temperature. • A simulation is a single numerical run with fixed initial V O C and N O x concentrations and whose actinic flux (J) and temperature (T) are given by the test matrix. Test matrices usually have 121 individual simulations. To explore the universality of the scaling relationship, six different scenarios were designed to isolate the influence of various factors on the similarity relationship. The first scenario examined the influence of different V O C s on the scaling analysis. A variety of V O C s and V O C mixtures were examined. The second scenario controlled for the influence of the chemical mechanisms. OZIPR simulations were run with two different mechanisms: C B - I V (Gery et al., 1989) and a modified version of the SAPRC90 (Carter, 1990) mechanism. The third scenario looked at the Chapter 4. Domain of Applicability for the Scaling Relationship 54 influence of temperature, the fourth Julian date, the fifth latitude while the last examined the effects of both temperature and Julian date. Table 4.1 gives a brief description of the scenarios. Before proceeding with the analysis, I must first clarify the various steps involved in performing the numerical experiments and analyzing the model output. 4.2 Scaling Methodology In this section I briefly outline the steps involved in producing the scaling analysis. Steps include the selection of the simulation conditions, the determination of test matrix size and procedures used to analyze the model output. 4.2.1 General s imulat ion conditions In order to standardize the analysis, all simulations started at 7:00 a.m. and ended at 6:00 p.m. (local daylight savings time). There was no dilution, no deposition and the temperature was held at a constant value (as set out in the scenario) throughout the simulation. The initial fraction of NO2 to NO (/) was always set at 0.25. No emissions where added; every simulation began with a well mixed charge of V O C and NOx. 4.2.2 De te rmina t ion of test mat r ix size As mentioned before, O Z I P R creates a test matrix of simulations through the process of indepen-dently varying the given (or what I call base) V O C and NOx concentrations. Careful selection of the base concentrations and the matrix size is essential to properly characterizing the scaling relationship. I begin by outlining how OZIPR develops the test matrix. Imagine a row matrix composed of V O C concentrations ranging from zero to the base value, in equal increments with the number of elements (called nodes) provided by the user. A higher value of nodes leads to smaller the increments and more elements.' A matrix of initial conditions is formed from the set of all possible combinations between such a V O C row matrix and an equivalent NOx Scenario .Name Environmental Conditions. Chemical Mechanism VOCs Varying Temperature and Actinic Flux R A D M 2 Classes and Mixtures Other Mechanisms Varying Temperature Varying Julian Date Varying Latitude Fixed Varying Vary T Fixed J Fixed Fixed T Varying J Fixed Fixed T Varying J Fixed Vary T Vary J Fixed Fixed • Fixed Varying Varying Fixed Fixed Fixed Fixed Table 4.1: A description of scenarios used to explore the universality of the similarity relationship. Chapter 4. Domain of Applicability for the Scaling Relationship 55 matrix i.e.: Matrix of initial VOC0 NOx0 [VOC] base nodes — 1 [NOx]base 0 [VOC)base 1 ' nodes — 1 ' _Q [NOx}base 1 [VOC] base ' nodes — 1 [NOx}base • (nodes — 1) lodes — 1) (4.1) nodes — 1 nodes — 1 ' ' nodes — 1 This matrix has nodes x nodes elements. As an example, setting nodes to 11, creates a matrix with 121 ( [VOC] 0 , [NOx]0) pairs with individual initial V O C and NOx concentrations ranging from 0 to the base concentration in 10% increments. Because of the importance of the ratio of initial V O C to NOx concentration (R) in the scaling analysis, the resulting set of R-values is also worth examining. By continuing to exclude simulations where initial NOx is zero (and hence R = oo) and those where initial V O C is zero (R = 0) the test matrix produces an ordered set of R-values having the following range: 1 \ nVOC]hnKP\ f[VOC]base nodes-1 ([VOC}base \ [NOx]base nodes ({ base V [NOx]base = {Rbase/(nodes - ! ) , - • • , Rbase, ' V [NOx}base (nodes - 1) • RbaSe} (4.2) This set has (nodes — 1) x (nodes — 1) elements. For example, with nodes set at 11, [VOC]base = 10 ppb and [NOx]base = 2 ppb, then Rbase = 5 and the range of R-values is (0.5, 50). Thus a larger value for nodes produces more simulations and, more importantly, a greater range of R-values. The distribution of R-values found in Eq. (4.2) is addressed in the next section. 4.2.3 Selection of base concentrations and number of nodes In the last section, I examined the range of R-values and initial V O C and NOx concentration in a test matrix for a given number of nodes and base concentrations. In this section, I examine how these must be chosen in order to best capture any scaling behaviour. Why is it important to control the range of initial conditions and R-values? As it will be shown, some VOCs have a low propensity to react with the OH* and high concentrations are required to produce a fixed amount of ozone. Similarly, some VOCs require a large relative abundance of V O C to NOx (R-value) in order to exhibit NOx-only scaling. To ensure that any analysis captures the full range of V O C oxidation behaviour, I propose the following objectives for node and base concentration selection: • The test matrix should have an equal number of simulations on either side of any observed scaling break. Chapter 4. Domain of Applicability for the Scaling Relationship 56 10 ~ 9 8 7 6 c Q. 4 3 2 1 0 - 4 - 3 - 2 - 1 0 1 2 3 4 ln(R) Figure 4.1: Distribution of\n(R) when nodes = 41 and V O C t , a S e = NOxi,ase. • To ensure that the model is not pushed outside of its calibrated range, the maximum modeled ozone concentration must represent realistic concentrations for a polluted urban environment. • Simulations must include a sufficiently large range of R-values to capture the asymptotic behaviour of the similarity function f(R). To meet the first objective, it is necessary to study the distribution of R-values found in Eq. (4.2). For convenience, I examine the distribution of ln(R) (since the scaling break is most evident in the Weibull plane which is plotted as a function of ln(i?)). Consider a scenario where both the base V O C and N O x concentrations are 1.0 ppb and the number of nodes is 41. In this case, the ratio of base V O C to base N O x (Rbase) is also 1.0. Figure 4.1 shows the fraction of all simulations whose value of ln(i?) lie within a range spanning ln(i?&ase/'nodes) to \n(Rbase • nodes). From the Figure, the distribution is centered around ln(i?) = 0.0 or R — 1.0; suggesting that the ratio of base V O C to NOx must equal the expected R-value for the break in order to have an equal numbers on simulations each side of the break. Since the R-value of any scaling break is not known a priori, a set of trial simulation must first be performed to provide an estimate of Rbreak- Meeting this objective places one constraint on the selection of [VOC]base and [NOx)base. Requiring peak maximum ozone concentration be in the range of 100-300 ppb gives a second constraint. This range is representative of elevated but not unrealistically high ozone concentra-tions for urban environments (National Research Council, 1991) and should not push the chemical Chapter 4. Domain of Applicability for the Scaling Relationship 57 mechanism outside of its intended regime. I use these first two constraints to determine base V O C and NOx levels. Finally, the third objective determines the number of nodes. In order to use the Weibull trans-formation, the modeled output must be normalized. The natural normalizing value, the asymptote of the similarity function, requires simulations with sufficiently large R-values. As Eq. (4.2) shows this is determined by nodes. Typically, nodes is set to 11 giving a maximum R-value of 10 x Rbase-If, however, a V O C does not show asymptotic behaviour in that range, a larger number of nodes is required. For example, with 41 nodes, OZIPR performs a total of 1681 simulations and allows R-values to be 40 times greater than Rbase- l n this thesis only nodes sizes of 11 and 41 are used. The above three constraints determine the selection procedure for [VOC}baSe, [NOx]baSe and nodes. Figure 4.2 outlines this procedure and shows the iterative nature of the selection process. In several instances (most notably for formaldehyde), R rvalues for asymptotic behaviour required more nodes than the O Z I P R maximum of 51. In these instances, nodes was set to 41 and base V O C and NOx concentrations were adjusted to provide reasonable peak ozone concentrations as well as a fair distribution of R-values. : .- ' •. 4.2.4 Determining W E X parameters To objectively determine optimal values for the six W E X parameters (7, a, a i , a2, 6, A) a computer program was used. The code required initial values for the parameters which was supplied, through visual inspection of the data, from a spreadsheet program. From this first guess, the code individ-ually varied only five of the parameters (a, ot\, a2, 0, A ), searching to minimize the R M S E between OZIPR model output and W E X values. The sixth parameter (7) was calculated using the selected NOx-scaling power (a). For each trial value of a, 7 was adjusted so that the maximum scaled model output was 0.99. This value was chosen because the Weibull transformation is quite sensitive to values very close to 1.0 (with 1.0 being mapped to an infinite value). Standardizing the maximum scaled ozone value also ensures a means of comparing the Weibull plots for different VOCs . To op-timize the fit, each of the five parameters was varied by ±10% around its first guess value. Due to scatter in some of data sets, it was decided that fitting around the ridgeline was to be a priority since this region present the most important area for identifying ozone sensitivity. To this end, for every trial /3-value, only R-values encompasses all but the lowest 10% and highest 10% of the R-values were used to fit the data. While only 80% of the OZIPR points were used for fitting, all points were used to quantify the ability of the W E X model to parameterize the similarity relationship. Chapter 4. Domain of Applicability for the Scaling Relationship 58 4.2.5 Statistical measures of agreement I use the correlation coefficient between the OZIPR and W E X ozone values as a measure of agree-ment between the two as well as the root mean square error between W E X - and OZIPR-calculated maximum ozone concentrations for each simulation: RMSE = ^ (nodes — l ) 2 4.3 Scenario I - RADM2 VOC Classes (nodes—l)2 (OZIPRi - WEXif i=l (4.3) To determine if the O L T scaling behaviour holds for other VOCs , a systematic analysis was per-formed using the R A D M 2 (Stockwell et al., 1990) mechanism. This mechanism does not explicitly Final OZIPR run > r Fit output using computer 1 Increase nodes Determine V O C ™ , NOx„„ nodes Y E S - * / A s y m p . o t e \ Y E S Found? First Guess Field Figure 4.2: Schematic of steps used to find WEX parameters. Chapter 4. Domain of Applicability for the Scaling Relationship 59 model every V O C since, as mentioned before, this could entail modeling over 20000 different species (Dodge, 2000). Instead, R A D M 2 has 14 classes of V O C s and assumes the oxidation behaviour of any V O C can be treated by one of these classes or by a linear combination of them (the 14 classes can be thought of as representing a set of basis vectors for the vector space of V O C compounds). These classes include methane, ethane, three classes for higher alkanes, ethene, terminal alkenes (alkenes with their double bonds at the end of the molecule), alkenes with internal double bonds, two classes for aromatics, aldehydes and ketones, isoprene and finally non-reactive VOCs . So, to explore the scaling behaviour of V O C s in general, a scaling analysis was performed on each of the R A D M 2 classes. As well, a scaling analysis was performed on two V O C mixtures considered to be representative of polluted urban environments. For each V O C class and the two mixtures, I present results using two figures. The first figure shows model output and corresponding W E X model after Weibull transforming and in the second, results are presented in the more conventional isopleth diagram. For brevity, only a sample of the figures, covering the range of agreement between model output and W E X model, is presented in this chapter with the remaining figures placed in Appendix E . 4.3.1 Simulations with Methane, Ethane and Higher Alkanes Alkanes are the most abundant V O C s found in urban environments (National Research Council, 1991). They are relatively unreactive, have low deposition rates and hence can be transported long distances (Stockwell et al., 1990). On average, methane comprises 13% of V O C emissions (moles C) while non-methane alkanes comprise 46% (Stockwell et al., 1990). To handle alkane reactions, R A D M 2 uses five categories. Methane (CH4) and ethane (ETH) are treated explicitly with the remaining higher alkanes sorted into three classes according to their OiJ*-reactivity. I did not perform a scaling analysis on methane due to its low OiJ'-reactivity. Its chemical lifetime is in the order of years - too long to be of importance at the urban or regional scale (Finlayson-Pitts and Pitts, 1999). It is worth mentioning however, that methane is of prime importance in the production of tropospheric ozone at the global scale. Alkanes with an CW-reactivi ty less than 5 x 1 0 3 p p m ~ 1 m i n ~ l are represented by HC3. This class includes propane, n-butane and alcohols like ethanol and methanol. The class HC5 represents alkanes with a reactivity between 5 x 103 p p m _ 1 m m _ 1 and 1 x 10 4 ppm~lmin~l and includes pentanes and hexanes while those with a reactivity greater than 1 x 1 0 4 p p r r C x m i r C l are represented using HC8. This last group includes long chained alkanes .like n-heptane. Due to their low reactivity, the alkanes were the hardest to scale. In Figure 4.3A, I plot the 'Weibullized' E T H model output (+) and corresponding W E X parameterization (solid line) as a Chapter 4. Domain of Applicability for the Scaling Relationship 60 function of ln(R). In Figure 4.3B, I replot the same results as an isopleth diagram where solid lines give OZIPR isopleths (in ppb) and the dotted lines give WEX-based isopleths (also in ppb). The two dashed lines in this Figure locate the respective ridgelines based on Eq. (3.13). Similar plots for HC3, HC5 and HC8 can be found in Appendix E . For both E T H and HC3, I had to set the number of nodes to 41 in order to capture the asymptotic behaviour and keep an equal number of simulations on both sides of the scaling break. For E T H , the scaling break appears to occur at ln(R) m 6.5 but it is not sharp. There appears to be more scatter in the 'Weibullized data' for simulations with \n(R) < 6. For E T H and HC3, the best choice for the NOx-exponent (a) appears to depend on the R-value. For E T H , when the exponent is chosen to be 0.7, the 'Weibullized data' scales for ln(R) > 7 (Figure 4.3A) but for ln(R) < 7 the correct choice appears to be -0.2 (Figure 4.4). However, choosing this lower value destroys any scaling at high R-values. The W E X parameterization for both E T H and HC3 produce isopleths that fit the OZIPR model output in the NOx-limited region (NLR) and up to the ridgeline (Figures 4.3B and E.1A). At the ridgeline and in the V L R , W E X isopleths diverge from OZIPR isopleths. For E T H and especially HC3 it is difficult to identify a sharp break in the Weibull plots. It appears that the Weibull plots for these V O C classes are composed of a family of curves each having a break at different R-values (this is especially evident in Figure 4.4). Furthermore, the OZIPR ridgelines for these classes are curved lines whereas the W E X model produces a straight ridgeline. HC3 has a more curved OZIPR ridgeline and also shows greater scatter in its 'Weibullized data'. Therefore, I suspected that scatter for these two classes occurs for two reasons: • The ridgeline cannot be characterized by a line of constant R (a straight-line). • The NOx-limited and VOC-limited regions have different NOx-scaling exponents (a). Neither HC5 nor HC8 appear to show scaling (Figures E.2A and E.3A). It is difficult to un-derstand why these classes do not show scaling while E T H and HC3 do. As well, the HC5 and HC8 classes produce progressively less ozone than E T H and HC3. Since that the major chemical loss for alkanes is through Oi7"-attack (Atkinson, 2000), and that the OH' radical abstracts the most weakly bound hydrogen atom (Seinfeld and Pandis, 1998), then one would expect that higher alkanes, with more secondary hydrogen atoms, would produce higher ozone levels. Yet the HC8 class produces no more than 10 ppb of ozone. It is likely that greater N O x and peroxy radical loss, through the formation of organic nitrates, accounts for this discrepancy. The E T H class is representative of VOCs that the W E X model cannot parameterize very well. The HC5 and HC8 classes the model cannot parameterize at all. Chapter 4. Domain of Applicability for the Scaling Relationship 61 WEX Ridgel ine i n ( R ) .. ETH Concentration - ppmC Figure 4.3: Weibull transformed OZIPR model output (+) for ETH as a function of \nR (figure A). Solid line is WEX model. In Figure B, the same results are plotted in the more conventional form of ozone isopleths (in ppb) with OZIPR model output in solid lines and WEX model in dotted lines. The two dashed lines refer to ridgelines for the OZIPR isopleths and the WEX model. Both were found by locating the region where ozone shows no sensitivity to changing NOx. 4.3.2 Simulations w i t h Ethene and other Alkenes Alkenes are hydrocarbons with a single double bond. They have higher OJy*-reactivities than alkanes and react readily with both ozone and the nitrate radical (NO' ) (Atkinson, 2000). Alkenes are constituents of gasoline and vehicle exhaust emissions (Seinfeld and Pandis, 1998). Isoprene, emitted naturally from vegetation provides another source of alkene emissions (Atkinson, 2000). Alkenes account for about 10% of nonmethane V O C concentrations in some US cities (Chameides et al., 1992). The simplest alkene, ethene (C2H4), is treated explicitly by R A D M 2 (as OL2) because it has the lowest alkene Oif*-reactivity and is typically found in higher concentrations than the other alkenes (Stockwell et al., 1990). As mentioned before, propene and other terminal alkenes are represented by the O L T class. Alkenes with an internal double bond are represented by OLI. Finally isoprene (ISO) is treated as a separate species whose reaction products are assumed to be the same as propene. Weibull transformed OZIPR model output as well as isopleth plots, for alkene classes OLI, OLT,OL2 , are shown in Figures E.4, E.5 and 4.5 respectively. Chapter 4. Domain of Applicability for the Scaling Relationship 62 2r l n (R) Figure 4.4: Weibull transformed ETH model output versus \nR when NOx-scaling exponent is (a)- 0.2. Changing the exponent to this lower value produces better scaling for ln R < 7 but destroys the scaling for ln R > 7. The hardest class to fit was 0 L 2 because of its lower CfiT'-reactivity. For OL2, nodes was set to 41 since its scaling break occurs at R = 4.9 while its asymptotic behaviour occurs at R 200. Its Weibull plot (Figure E.4A) showed a fair degree of scatter below the break but less above. The W E X parameterization fits the O Z I P R isopleths in the N L R and V L R but deviates around the ridgeline and for very low R-values (Figure E.4B). The 'Weibullized data' for both O L T (Figure E.5A) and OLI (Figure 4.5A) were well captured by the W E X model with OLI showing a slightly better fit. Both classes required only 11 nodes. As seen from the isopleth plots (Figures E.4B and 4.5B), the W E X model fits the two classes well in both the N L R and V L R . The fit along the ridgeline is best for OLI but both are better than OL2. Both classes seem to show a second break at high R-values. For OLI , it appears that the 'Weibullized data' shows another break with a downward trend at ln i? « 3 . I suspect this marks the beginning of a newregime where alkene+03. reactions are important. This new trend, impossible to see on an isopleth diagram because ozone' isopleths diagrams compress the response surface along the V O C axis at high R-values, warrants further study. Chapter 4. Domain of Applicability for the Scaling Relationship 63 - 1 0 1 2 3 4 0.0 0.1 0.2 0.3 0.4 0.5 0.6 in(R) OLI Concentration - ppmC Figure 4.5: Weibull transformed OZIPR model output (+) for OLI as a function of InR (figure A). Solid line is WEX model. In Figure B, the same results are plotted in the more conventional form of ozone isopleths (in ppb) with OZIPR model output in solid lines and WEX model in dotted lines. The dashed line represents the scaling break R = (3. Second Break To explore this second break, the OLI simulations were rerun using 41 instead of 11 nodes with the resulting range of R-values now extending from l / 4 0 t / l to 40 times the break (compared with l / 1 0 t h to 10 times in the original simulations). The Weibull plot for this larger data set is shown in Figure 4.6A where the W E X model (regressed against the original 11-node simulation) has been over plotted. The most important feature in this Figure is the more pronounced break in the 'Weibullized data' for InR > 3.0 and the upward curvature for InR < —1.0. Both trends suggest the appearance of new scaling regimes. Values of ln(jR) > 3.5 correspond to model output from simulations where the initial [OLI]Q to [NOx]0 ratio is greater than 33. At this ratio of OLI to NOx, maximum ozone concentration is strongly affected by the reaction O L I + O 3 . While this regime hints at the limits to the scaling analysis, it does not represent realistic conditions for a polluted urban environment and so no attempt will be made to better understand the variability in this region. While I was mainly interested in the second break at large R-values, increasing the number of nodes reveals a second trend, occurring at low R-values which also suggest a new scaling regime. This region represents a middle ground between NOx-only photochemistry (no V O C s and R = 0) and an urban environment with high V O C concentrations (and moderate to high R-values). This middle ground likely has a photochemical behaviour similar to the remote or background troposphere. While it is not the intention of this thesis to study ozone photochemistry in this Chapter 4. Domain of Applicability for the Scaling Relationship 64 - 3 - 2 - 1 0 1 2 3 4 5 6 0.0 0.1 0.2 0.3 0.4 0.5 0.6 in(R) OLI Concentration - ppmC Figure 4.6: Weibull transformed OZIPR model output (+) for OLI as a function of InR (figure A). The same initial conditions were used to produce these simulations as in Figure 1^.5 but with 41 nodes. The model output has been scaled by a larger 7 -value (8.25 versus 8.03) to accommodate slightly larger asymptotic values. The solid line is the WEX model. In Figure B, the OZIPR isopleths (solid lines and in ppb) based on the 41-node simulations whereas the WEX isopleths (dashed lines) are based on the 11 node regression. The dashed line represents the scaling break R = f3. region, the appearance of this trend (and the second break) raises important questions: • What is an appropriate range for V O C , NOx, R-values and O 3 (and environmental conditions as well) needed to capture the variability of maximum ozone concentration in a polluted urban environment? • Over what range of V O C , NOx, R-values and O 3 does the scaling analysis hold? In essence, these questions are similar to the objectives set out to characterize the Weibull plots. Namely, precursor and ozone ranges should be set so they represent physically reasonable situations. Furthermore, since the ridgeline represents the region of greatest interest to policy makers (due to different ozone abatement strategies on either side), characterization of the ridgeline and regions immediately above and below should be of prime importance in development of a control surface. This suggests the ridgeline should be centered as nearly as possible along the main diagonal (1 :1 line) of an isopleth diagram; requiring that ratio of maximum V O C to N O x equal the R-value of ridgeline. When the R-value of the break (0) is close to the R-value for the ridgeline, the above constraint is consistent with the selection criteria developed for nodes and Rbase-In Figure 4.6B, I have plotted ozone isopleths using the W E X model (dotted isopleths) and using Chapter 4. Domain of Applicability for the Scaling Relationship 65 OZIPR model output from the 41-node simulation where the six W E X parameters where found by a regression to the 11-node simulation. Again, the W E X model captures maximum ozone variability in the N L R , around the ridgeline and in parts of the V L R . Compare this to Figure 4.6A where the same W E X parameterization (based on the same model output) appears to show a much poorer fit. The difference is that in Figure 4.6A, extreme R-values are accentuated by the logarithmic axis, whereas in 4.6B, these regions of extreme R-values are compressed. This is best understood by examining Figure 4.7. In this Figure, OLI isopleths along with lines of constant R corresponding to: Rbreak, 10 Rbreak, and 1/10 Rbreak (range R-values for an 11-node simulations) and 40 Rbreak and 1/40 Rbreak (41-node range of R-values) have been plotted. Wi th 11 nodes, simulations with R-values occur in almost the entire quadrant - excluding only one part of the N L R with elevated ozone levels. From a geometrical point of view, moving to simulations with 41 nodes provides only a marginal increase in coverage and then, only in regions well removed from the ridgeline. This suggests, that in most instances, 11-node simulations are sufficient to characterize the dependence of maximum ozone on its precursors. Furthermore, since the region of interest is the ridge area, the bounds (l/10Rbreak, lORbreak) define limits where knowledge of the similarity relationships is most beneficial and where the W E X model should capture ozone variability. 4.3.3 Simulations with Aromatics Aromatic compounds are an important class of V O C s due to their high reactivity and abundance in solvents, gasoline and motor vehicle exhaust (Seinfeld and Pandis, 1998). Their chemistry is quite complex and not completely understood (National Research Council, 1991). The two R A D M 2 aromatic classes, X Y L E and T O L U , both show distinct breaks in their Weibull plots (Figure E.7A and E.6A). X Y L E shows more scatter above the ridgeline while T O L U below. Both W E X generated isopleths are in good agreement with the OZIPR results. The X Y L E isopleths (Figure E.6B) show more deviation around the ridgeline but produce a good fit for both high and low R-values. T O L U (Figure E.7B) shows better agreement along the ridgeline but has more difficulty at low R-values. 4.3.4 Simulations with Carbonyl compounds Carbonyl compounds have an oxygen atom joined to a carbon atom by a double bond. Two classes of carbonyls are aldehydes and ketones; aldehydes have one alkyl group joined to the carbon containing the oxygen double bond while ketones have two. Carbonyls emitted from both anthro-pogenic and biogenic sources, can also be formed as intermediates in the oxidation of hydrocarbons. Formaldehyde, the simplest aldehyde, a probable human carcinogen (EPA, 1988), is also a regu-lated emission for New Low Emission Vehicle (NLEV) in the United States (EPA, 2000). R A D M 2 Chapter 4. Domain of Applicability for the Scaling Relationship 66 0.0 0.1 0.2 0.3 0.4 0.5 0.6 OLI Concentration - ppmC Figure 4.7: Ozone isopleths for OLI versus initial OLI and NOx concentrations. Also shown is the line R = (3 and lines corresponding to: 10/3,1/10/3,40/3,1/40/3. uses three chemical classes to model carbonyls: formaldehyde (HCHO) is modeled explicitly, higher aldehydes by A L D and K E T for all ketones. Formaldehyde proved challenging to scale. Its break occurred at R = 4.4 but did not show asymptotic behaviour until an R-value around 600. While very reactive, this long gap between break and asymptote is similar to behaviour shown by less reactive E T H and OL2. Properly modeling this behaviour (as set out by the objectives in section 3.2.3) would require 136 (600/4.4) nodes or almost 20000 (1362) simulations - greater than the computational limits programmed into OZIPR. As a compromise, a base V O C to NOx ratio was chosen at 15 (well above B). With 41 nodes, this produced R-values up to 600, including 220 simulations (out of 1600) below the break. The Weibull plot (Figure E.8A) shows the 'Weibullized'data' clustering on.a common curve when the NOx-scaling exponent is 0.75. The W E X generated isopleths (Figure E;8B) have the correct shape but underestimate maximum ozone concentrations in the N L R and overestimate them in the V L R . Both A L D and K E T (Figures E.10 and E.9) were easier to characterize; each requiring only 11 nodes. A L D shows perhaps the best fit to the ozone isopleths of all R A D M 2 classes (Figure E.10B) Chapter 4. Domain of Applicability for the Scaling Relationship 67 with good agreement everywhere except at very low R-values. The K E T similarity relationship is also well described by the W E X model but produce isopleths which have a slightly poorer fit in the V L R (Figure E.9B). 4.3.5 Simulations with the Non-reactive class In the R A D M 2 mechanism, the non-reactive class (NR) does not react; its sole use is to account for non-reacting or slow reacting V O C s in an urban airshed. This class does not appear to scale by any power of NOxa (Figure E.11A) and is of no further concern. 4.3.6 Simulations with V O C Mixtures Two V O C mixtures, representative of polluted urban environments, were also modeled using R A D M 2 The first mixture was an Ai r Resources Board (ARB) modified version of the (Jeffries et al., 1986) analysis of the Lonneman (Lonneman, 1986) 29 city V O C canister study (Tonnesen, personal com-munication - hereafter referred to as the ' A R B ' mixture). The second was a mixture that was used by Stockwell et al. (1997) in his comparison of his R A D M 2 model and the Regional Atmospheric Chemistry Mechanism ( R A C M ) model and referred to as the ' S T O C K ' mixture 1 . Figures E.12 and E.13 show Weibull and isopleth plots for the ' A R B ' and 'Stock' mixtures. Both show the distinctive scaling break. Both similarity plots show an upward curvature for the very low R-values and a second break in the N L R . The W E X model (Figure E.12A) captures the A R B oxidation behaviour slightly better than the Stock behaviour (Figure E.13 A) which shows deviations at high R-values. 4.3.7 Summary of R A D M 2 simulations Table 4.2 gives the numerical values of each W E X parameter used to fit each of the 14 R A D M 2 classes and the two urban mixtures. The R A D M 2 classes (with the exception of the slow reacting alkanes (HC5 and HC8)) and the two urban mixtures, show scaling. That is, when model output is described using dimensionless maximum ozone (II = [03]max/(jav/k^o))-, dimensionless NOx (n2 = [NOx]0/(jav/kNO)) and the ratio of initial V O C to NOx (iii = [VOC]0/[NOx]0), model output over a wide range of conditions show a common variability. Furthermore, when the resulting similarity relationship is Weibull transformed, all of the reactive V O C classes and the two urban mixtures (which I define as the ' R A D M 2 scaling classes') show a distinct 'dogleg' at R-values 1 T h e speciation was supplied by Dr.Tonnesen (personal, communication), and is slightly different than the one suggested in Stockwell's paper. Chapter 4.- Domain of Applicability for the Scaling Relationship 68 Species 7 a a i Q 2 P A R M S E (ppb) Alkanes E T H 22.40 0.70 1.60 0.49 672.0 0.54 15.4 0.99 HC3 14.36 0.66 1.60 0.73 122.5 0.81 13.5 0.98 HC5 7.68 0.40 0.65 0.84 1638.0 1.36 18.3 0.77 HC8 0.45 0.43 0.00 0.00 1370.0 2.63 2.1 0.77 Alkenes OL2 22.20 0.70 1.80 0.53 4.9 0.40 8.2 0.94 OLI 8.03 0.57 1.90 0.81 4.5 1.29 2.6 1.00 OLT 9.53 0.60 2.22 0.72 4.2 0.92 4.2 1.00 Aromatics T O L U 7.77 0.48 3.10 0.69 10.1 1.29 7.0 1.00 X Y L E 7.57 0.56 1.92 0.44 5.3 1.61 6.5 1.00 Carbonyls H C H O 40.64 0.75 1.50 0.60 4.4 0.14 9.8 1.00 A L D 7.48 0.53 1.73 0.54 5.2 1.69 3.4 1.00 K E T 7.71 0.59 2.84 0.62 15.3 1.04 6.2 0.98 Unreactive N R 0.16 0.35 0.00 0.00 5.0 3.00 0.3 0.98 Mixtures A R B 8.16 0.58 2.34 0.63 8.5 1.40 3.6 1.00 S T O C K 8.15 0.57 2.68 0.59 9.4 1.40 4.5 1.00 Table 4.2: Values of the six WEX parameters for the RADM2 (Stockwell et ai, 1990) classes and two urban mixtures. near the ridgeline, suggesting that this kink is associated with a change in governing chemical process. A discussion about the significance of each parameter and its relationship to the underlying photochemical processes is postponed until the next chapter. The next section looks at ozone scaling relationships using different chemical mechanisms. 4.4 Scenario II — Other Mechanism To test whether the scaling is an artifact of the R A D M 2 mechanism, two different chemical mecha-nisms were used to simulate ozone formation: C B - I V and S A P R C . These two methods use entirely different approaches to condensing the photochemistry and so observation of ozone scaling from each will strengthen the premise that complex photochemical processes can be described using a small set of variables - at least to the extent that numerical models capture the chemical processes. 4.4.1 C B - I V Mechan i sm Grid based Eulerian photochemical models perform repeated chemical calculations at thousands of grid points at every time step. This requires a condensing of the chemistry into a compact form. There are two main methods to achieve this condensing: lumped molecule and lumped structure approach.2 The carbon bond mechanism, developed in 1976 by Systems Applications International, is an example of the lumped structure approach. In this approach, each V O C is broken into smaller reaction elements based on the type of carbon bonds it contains. For example, most single-bonded carbon atoms are treated using a carbon atom surrogate (PAR) and double-bonded carbon atoms 2 I n essence this thesis is a further condensing of these (condensed) mechanisms through a scaling analysis. Chapter 4. Domain of Applicability for the Scaling Relationship 69 Parameter R A D M 2 CB-IV 7 8.2 8.3 a 0.58 0.62 ct\ 2.3 2.4 « 2 0.63 0.52 P 8.5 9.6 A 1.4 1.2 Table 4.3: A comparison of WEX parameter values for the ARB mixture using the RADMS and CB-IV chemical mechanisms. using a two carbon surrogate called O L E . In this way, a simple alkane like n-butane would be represented by four P A R groups based on its four alkyl groups. Similarly, propene with one alkyl group and one double bond is represented by a single P A R and O L E group. This approach captures V O C oxidation behaviour with fewer surrogate species than with the lumped molecular approach, is more compact and more easily implemented in large grid-based Eulerian photochemical models (Gery et a l , 1989). The current version of the mechanism is called C B - I V (Gery et al., 1989). Two simulations were run using C B - I V . The first used a single P A R and single O L E (to represent propene) and the second simulated the A R B urban mixture used-in the R A D M 2 simulations with Dr. Tonnesen providing the speciation (personal communication). Figures E.14 and E.15 show the Weibull and isopleths plots for the P A R + O L E and A R B simulations. Both show the characteristic 'dogleg' in the Weibull plot and both have WEX-generated isopleths capturing the modeled ozone variability (Figures E.14B and E.15B). Table 4.3 lists W E X parameters used to fit the R A D M 2 and C B - I V model output for the A R B mixture. 4.4.2 SAPRC-90 Mechanism The lumped molecule approach uses particular organic compounds or generalized species to repre-sent organics of similar oxidation characteristics (Dodge, 2000). R A D M 2 is an example of a lumped molecule approach. Another is the Statewide Air Pollution Research Center (SAPRC-90) mecha-nism of (Carter, 1990). Unlike R A D M 2 , in this mechanism users can modify both the kinetic and mechanistic parameters of the organic chemistry. A condensed version of the SAPRC-90, called COND2243, which contains 54 chemical species and 129 reactions, was tuned for use in the Lower Fraser Valley, B . C . (LFV) by Jiang et al. (1996). This version - called CD2243V2 - was modified to reflect the region's urban V O C profile (Jiang et al., 1996). Simulations of propene, using the CD2243V2 surrogate O L E 1 , and a L F V urban V O C mixture, were performed. Both Weibull plots (Figures E.16A and E.17A) are characterized by a scaling break and both W E X models fit the OZIPR isopleths well (Figures E.16B and E.17B). Chapter 4. Domain of Applicability for the Scaling Relationship 70 4.4.3 Summary for Scenario II A scaling analysis has been used to study the oxidation behaviour of different VOCs . With the ex-ception of slow reacting alkanes and non-reacting species, all V O C s show scaling. Additionally, V O C mixtures are also amenable to this method of analysis. Furthermore, when analyzing photochem-istry using different chemical mechanisms, maximum ozone shows the same scaling relationships. The W E X model is able to parameterize the scaling relationships for these V O C s and their mix-tures. However, to conclude this exploration of the universality of ozone scaling, the influence of two key environmental conditions - temperature and actinic flux - must still be examined. 4.5 Scenario III — Varying Temperature To explore the sensitivity of the scaling analysis to temperature, four OZIPR simulations were performed. Each had a different test temperature but all had the same actinic flux. The simulations used the R A D M 2 mechanism with OLT as the sole V O C . The base O L T concentration was 0.6 ppm, the base NOx was 0.15 and 11 nodes were used. Each simulation used an actinic flux appropriate to Vancouver on June 21s*. The four test temperatures were 20, 25, 30 and 35°C which were held fixed throughout each simulation. To begin the analysis, maximum ozone and initial NOx concentrations were scaled by jav/^NO where, due to its temperature dependence, a different value of k^o was used for each simulation. This temperature dependence was determined using the R A D M 2 rate expression (Stockwell et al., 1990): kNO = 2490exp{-1400/T) (4.4) where kj^o has units of •p-pm~xmin~l and temperature (T) is in Kelvin. Next, a common NOx-scaling exponent (found by inspection using a spreadsheet program and subsequently refined using a computer program) was used to scale the model output and is plotted in Figure 4.8A. This figure shows a family .of four curves where each curve tends to a different asymptote with larger asymptotic values corresponding to the higher test temperatures. To plot these curves in the Weibull plane, the asymptotic value for the T = 35°C curve was used to normalize all four sets of 'scaled data'. These'were then Weibull transformed and plotted against ln J1? (Figure 4.8B). This Figure shows that each curve has its break at roughly the same location (lni? « 1.4) with similar slopes both before and after the break but each differentiated by a vertical shift. To collapse the four curves onto a single curve, a power law dependence for n 4 was tried where it was hoped that for some suitable exponent 6, the four sets of N O x and temperature scaled maximum Chapter 4. Domain of Applicability for the Scaling Relationship 71 Figure 4.8: RADM2 simulations using OLT for four different temperatures. Figure A shows NOx-scaled dimen-sionless maximum ozone concentration versus initial ratio of OLT to NOx concentration while Figure B shows the resulting curves after Weibull transforming. ozone values should be expressible by a single function of R i.e.: m = ^(E%kY\exp! W i M l " ' ( , 5 ) Jav/KNO \3av/kN0j { k \T Tref J J To test this hypothesis, the four family of curves shown in Figure 4.8A were further scaled by IT4. Initially a spreadsheet program was used to estimate the best value of b. This value was then used as a first guess in a computer program which sought to optimize the R M S E between the OZIPR model output and the W E X model. In all, five W E X parameters (a, a\, a2, (3, A) and the temperature scaling exponent b were systematically varied about their initial guess values until no new combinations could further reduce the R M S E . The method found the optimal NOx-scaling exponent to be 0.62 and the temperature exponent (6) to be 5.89. Figure 4.9A shows the resulting four Weibull curves after scaling by II2 and LY4. The curves have collapsed onto a common curve with some scatter for both small and large values of ln R. After mapping back to the similarity plane (Figure 4.9B), the family of curves has collapsed onto a single similarity relationship, with common asymptote although, again, there is some scatter in for the higher R-values. 4.5.1 Gross Influence of Temperature On Maximum Ozone Concentration In general, the system of photochemical reactions modeled by R A D M 2 comprises over 150 chemical reactions each with its own temperature sensitivity. These sensitivities can be either positive and Chapter 4. Domain of Applicability for the Scaling Relationship 72 CH 2 1 0 -1 i -2 C - 3 i f - 4 - 5 - 6 1 I 1 I I , 1 i i i i | i i , i , i i i | , i , , J o T=20°C : * A T=25°C fcP • T = 30°C : S X T=35°C : • . . . . i . . . . . . . , i , . . i . , , . i . , . . • - 2 12 G D I CN G ' i 1 1 1 1 1 1 1 1 1 1 1 1 ' ' i 1 B OT=20°C AT=25°C •T=30°C XT=35°C !(R) 0 5 10 15 20 25 30 35 40 45 R Figure 4.9: Weibull transformed dimensionless model output after scaling by dimensionless temperature I I4 . Figure A shows model output after Weibull transforming and Figure B shows the resulting similarity relation-ship. negative (i.e. show an increasing rate constant with increasing temperature or a decreasing rate constant with increasing temperature). While temperature alters each reaction rate differently, it appears that the gross influence of temperature on maximum ozone concentration can be expressed by a power law involving a single temperature scaling term with an Arrhenius form i.e.: n 4 - exp{-EOH/k(l/T-l/Tref)} (4.6) = exp {EOH/k/Tref} exp {-EOH Jk{l/T)} = Aexp{-EOH/k(l/T)} Thus, the gross temperature influence (II4) shows a positive temperature dependence implying that as temperature increases so does ozone concentrations consistent with statistical analysis of ozone trends (Robeson and Steyn (1990), Burrows et al. (1995)). 4.6 Scenario IV - Varying J This section investigates the effects of varying actinic flux on the similarity relationship. There are many different atmospheric compounds that absorb radiation and enter an excited state. These molecules may subsequently dissociate or return to a less excited state by other means (Seinfeld and Chapter 4. Domain of Applicability for the Scaling Relationship 73 Month Date jav (1/1000) s J September September August August June 12 2 20 3 22 5.152 5.758 6.490 7.247 8.056 204 228 257 287 319 Table 4.4: Date, average and total actinic fluxes, as measured by N02 photolysis rates, for the five RADM2 simu-lations used to investigate the sensitivity of the similarity relationship on actinic flux. Pandis, 1998). The dissociation products may react with other compounds or they may themselves undergo photolysis. While the consequences of such photochemical processes is complex, the purpose of this scenario is to quantify the gross influence of changing actinic flux on ozone formation. I accomplish this by performing five OZIPR simulations each at a constant test temperature (298 K) but varying the solar intensity. To measure the actinic flux (i.e. energy added to the system capable of driving photochemical reactions) the cumulative N02 photodisociation rate (JNO2) W A S used: The photodisociation rate coefficient has units s e c - 1 and so J is dimensionless. Implicit in this relationship is the dependence of JNO2 o n the solar zenith angle which in turn is a function of local time. A fourth order polynomial was used to express the R A D M 2 NO2 photolysis rate as a function of solar zenith angle. Next, expressions for solar zenith angle as a function of location (latitude and longitude) and date were used to express the photolysis rate as a function of local time (Stull, 2000). This allowed total actinic flux levels (J-values) to be calculated for any day of the year. Five summer dates, chosen to give an equally spaced range of J-values and encompassing the typical ozone season in Vancouver (Pryor and Steyn, 1995), are given in Table 4.4. Numerical simulations were run using the R A D M 2 mechanism (Stockwell et al., 1990) with the OLT class and a base concentration of 0.6 ppm. The base NOx concentration was 0.15 and 11 nodes were used. 4.6.1 Parameterizing the similarity relationship Dimensionless model output for each simulation was scaled by ([NOx]/(jav/k,No))a where a common value of a = 0.62 was found to produce the least amount of scatter between all of the five data sets. The resulting curves are plotted in Figure 4.10A. The five curves do not collapse onto a single curve but, again, appear to form a family of curves differentiated by their J-values. Next, the largest (4.7) Chapter 4. Domain of Applicability for the Scaling Relationship 74 Figure 4.10: Dimensionless model output for the five OLT simulations after scaling by dimensionless initial NOx concentration raised to the 0.62 (A) and after normalizing and Weibull transforming (B). value was used to calculate a common normalizing value (7 ) 3 . The 'scaled data' were then Weibull transformed and plotted against InR as shown in Figure 4.10B. From this figure, it is apparent that there is scatter for both large and small values of ln R and any parameterization (g) of this 'scaled data' must be a function of both R and J i.e.: 3av/kNO \ [NOx}0 J y y ' K ' 4.6.2 Translations and rotations of the similarity relationship Inspection of Figure 4.10B shows that for small InR values, the curve corresponding to the smallest actinic flux ( J = 204), lies below the others, while for the larger values of lni? , this curve lies above the others. It appears that changing actinic flux results in a rotation about \n~f3 of the 'Weibullized data'. To investigate this hypothesis, each curve was shifted so its scaling break occurred at the origin. In terms of the , W E X parameters, this amounts to a horizontal translation by ln/3 and a vertical translation related to lri'-\ (which I call 6( J)): If the Weibull transformed similarity function is: W(g(R;J)) = G(\nR;J) 3 A g a i n , the normalizing parameter was set at 1/0.99 times the largest value to avoid difficulties using the Weibull transformation. Chapter 4. Domain of Applicability for the Scaling Relationship 75 2 1 : A <><*><> 0 -\ - 1 -f o J = 2 0 4 ' l - 2 Jm A J = 2 2 8 -\ • J = 2 5 7 • - 3 Jim X J = 2 8 7 -+ J=319 ; c - 4 -- 5 - -- 6 . . . . i . . . . i . , , , i , , , , i T c - 3 - 2 - 1 0 1 l n ( R ) - In (0) 1 • B J O J = 2 0 4 : - <M A J = 2 2 8 -Jf • J = 2 5 7 : - o ST x J = 2 8 7 -f + J 3 1 9 : , , , , 1 , , i t i • i • 1 . i . i 1 i i • i I . i i . ' 3 - 2 - 1 0 1 2 ; ln(R)- In (,g) Figure 4.11: Dimensionless model output for the five OLT simulations after: A) scaling by dimensionless initial NOx concentration and shifting to scaling break is at origin and B) further rotating about scaling break. then the horizontal translation and vertical translations produce a new function (G'(lni2; J)): G'(lni2; J) = G(ln R - ln/3(J); J) - <5(J) Figure 4.11A shows the five curves after the horizontal and vertical translations where each now has its break at the origin. Although the curves are starting to collapse to a single universal curve, there is still evidence the curves have been rotated about their break point. The transformation necessary to rotate the curves involves multiplying each to a constant. It was found that each curve required a different amount of rotation; dependent on the J-value i.e.: G"(lnR; J) = k(J) • G'(\nR; J) (4.9) where G" represents the rotated similarity function. The J = 257 curve was used as a baseline and all of the others were rotated to match this one. Figure 4.11B, shows the effect of rotations on the five curves. Finally, these rotated and translated curves have been mapped back to the similarity plane and plotted against R/0 in Figure 4.12. There is now less variability between the curves and the resulting similarity function is a complex function of both R and J : g(R; J) = W~l (k(J) • (G(ln R - In B(J)) - <5(J))) In a subsequent section I will simplify this expression. Chapter 4. Domain of Applicability for the Scaling Relationship 76 J = 204 A J = 228 • J = 257 X J = 287 + J = 319 6 R / / S 12 Figure 4.12: Dimensionless model output for the five OLT simulations after: scaling by dimensionless initial NOx concentration raised to the 0.62, shifting and rotating. This analysis only gives a partial account of any actinic flux dependence. J-values are influ-enced by three factors: date, latitude and irradiation time. So far, I have varied J by keeping the irradiation time constant and varying the date. However, it is possible to produce actinic fluxes which have identical J-values but different peak values by changing simulation latitude and irradi-ation times. One question that comes to mind is: How does peak actinic flux affect the similarity relationship? If peak actinic flux has no direct influence, then OZIPR simulations with identical J-values but different jpk values should produce the identical scaled dimensionless maximum ozone concentrations. If, however, peak actinic flux has a direct influence on ozone formation, then such simulations will not show identical scaled values and a new scaling parameter would be needed to capture this jpk dependence. I explore these ideas in the next section. 4.7 Scenario V - Effect of peak actinic flux In this scenario, OZIPR simulations were performed for two different locations: Vancouver (49.15°N) and Los Angeles (34.0°N). Simulations had the same J-values but different jpk values. The longitude for both locations was adjusted to 120°W - the local prime meridian - so that both had the sun overhead at noon. Different Julian days of the year were chosen at each site so that resulting J -values were the same. Each simulation used the R A D M 2 mechanism (Stockwell et al., 1990) with Chapter 4. Domain of Applicability for the Scaling Relationship 77 the OLT was the sole V O C . Throughout each simulation, the temperature was held fixed at 298 K . Table 4.5 gives the test conditions. In Figure 4.13, Vancouver and Los Angeles solar zenith angle and the corresponding N02 photolysis rates are shown as a function of local time. Both N02 photolysis curves have the same area under their curves but have different peaks. The difference between the solar zenith curves is more pronounced than the difference between the photolysis rates because the N02 photolysis rate is not sensitive to solar zenith at small zenith angles. Figure 4.13 shows the Vancouver location to have initially higher photolysis rates while the Los Angeles location has more intense photolysis around noon. The question is: Will the higher initial actinic fluxes for the Vancouver location serve to stimulate early photochemical production (through increased radical production via inorganic sources (Jeffries and Tonnesen, 1994)) earlier and produce maximum ozone levels comparable to the Los Angeles location with its higher rates later in the day? If so then, maximum ozone concentrations will not be sensitive to jpk-Figure 4.14A shows NOx-scaled dimensionless maximum ozone versus R for both simulations (a common NOx-exponent of a — 0.607 was used). The curves show similar variability with the Vancouver curve (with maximum value of 10.16) lying slightly underneath the Los Angeles curve (maximum value of 10.24) suggesting the former has slightly more reactive conditions. Table 4.6 summarizes the W E X parameters used to fit each similarity relationship. The largest difference between parameter values is for 3; at the Vancouver location it is 4.86 versus 4.62 at the Los Angeles location. In order to examine the curves in the Weibull plane, both curves were normalized by the Los Angeles maximum value. Figure 4.14B shows the 'Weibullized data' for both curves -it appears that the two differ only by a horizontal translation. In Figure 4.15A, both curves have been translated so that their breaks occurred at \nR = 0. In Figure 4.15B these shifted curves have been transformed back to the similarity plane where the agreement between the two curves is better (although the initial difference was not great to start with). This analysis has shown that the dimensionless group J cannot account for all of the ozone Location Vancouver (YVR) Los Angeles (LAX) Month Date Latitude (°) Test Length (hours) Temperature (K) jav (1/s) J 0.006490 0.006490 August September 257 257 0.0085 0.0089 20 6 49.15 34 11 11 298 298 jpk Table 4.5: Test conditions for simulations with different latitudes but identical J-values. Chapter 4. Domain of Applicability for the Scaling Relationship 78 90 75 I 60 45 30 15 '••.\ I/' V il \ V. ii * v A w J l I I I I l L . 9.0 o 6.0 8 3.0 o Q. 0.0 7 8 9 10 11 12 13 14 15 16 17 1£ Local Time F i g u r e 4 . 1 3 : Solar zenith angle (in degrees) as a function of local time for Vancouver (dotted line) on August 20th and Los Angeles (dashed line) on September 6 t h . In addition, NO2 photolysis rate (1000/sec) as a function of local time for both Vancouver (single 'dot') and Los Angeles (three 'dots') are plotted. F i g u r e 4 . 1 4 : ' NOx-scaled dimensionless maximum ozone, concentration for OZIPR simulations using Los Angeles and Vancouver latitudes (A). Figure B shows the corresponding curves after normalizing by a common value and Weibull transforming. Chapter 4. Domain of Applicability for the Scaling Relationship 79 F i gure 4.15: Effects of horizontal translation by j3 on the 'Weibullized' (A) and 'scaled' (B) data. dependence on actinic flux; it does not distinguish between J-values with different peak actinic fluxes. In essence, a new scaling parameter would be needed to account for this: n 5 = ^ (4.10) Jav Since the effects caused by jpk appear to be small, and do not alter the general nature of the similarity relationship, this approach will not be pursued, and the remaining simulations will use actinic flux values using a Vancouver latitude. 4.8 Scenario VI - Varying T and J In this last section, a scaling analysis of ozone formation is performed using model output for 20 test matrices having four different temperatures and five different levels of actinic flux. The analysis starts by individually fitting the W E X model to each simulation and noting the variability of each Parameter Y V R L A X 7 10.16 10.24 a 0.607 0.607 ai 2.39 2.31 OC2 0.78 0.74 0 4.86 4.62 A 0.95 0.95 R M S E 12.1 11.8 Table 4.6: WEX parameter values for the YVR and LAX simulations. Chapter 4. Domain of Applicability for the Scaling Relationship 80 parameters value with temperature and actinic flux. Then, the dependence of 8 on J and T is parameterized and compared with results drawn from smog chamber simulations. Next a similarity relationship for maximum ozone concentration which accounts for varying initial O L T and NOx concentration, varying temperature and actinic flux is developed. Finally, scatter plots are used to show the level of agreement between this parameterization and the original model output. 4.8.1 Variability of W E X parameters with J and T To examine the combined effects of varying both temperature and actinic flux on the scaling analysis, OZIPR simulations were performed at five different actinic fluxes and at four different temperatures. A l l used the R A D M 2 mechanism Stockwell et al. (1990) with O L T as the sole V O C . A l l simulations started at 7:00 a.m. and ended 11 hours later at 6:00 p.m. Again, there was neither dilution nor deposition. Each simulation had base OLT concentration of 0.6 ppm and base NOx concentration of 0.15 ppm using 11 nodes. Actinic flux levels were the same as described in Section 4.6 while temperatures corresponded to those used in Section 4.5. Table 4.7 shows W E X parameter values for each of the twenty test matrices. From this Table a few important observations are: • The NOx-scaling exponent (a) shows the least variability of all of the parameters. • The normalizing parameter (7 ) and A show a much stronger dependence on temperature than actinic flux. • Both W E X slopes (a i and a2) increase with increasing temperature and increasing J-values. Additionally, a2 shows more sensitivity than a\ to both J and T. • The scaling break (8) is almost equally dependent on temperature and actinic flux. The behaviour of the scaling break is of special importance. As I will shortly show, it will be used to capture the J-dependence in the 'universal' similarity relationship. It also defines a natural scale for the ratio of initial V O C to NOx. Characterizing how this scale responds to changing environmental conditions provides valuable insight into the nature of ozone-precursor relationships. In Figure 4.16, /3-values from Table 4.7 have been plotted as a function of J . Four separate trends, each associated with a different temperature, are apparent. A power law has been used to model each trend. Each power law uses the same exponent but a different pre-exponential factor i.e.: 8(T, J) = c0J~cl where cQ = c0(T) (4.11) Each curve fits the /3-values with a correlation coefficient greater than 0.99. From this Figure, the following conclusions can be drawn: Chapter 4. Domain of Applicability for the Scaling Relationship 81 7 a J T293 T298 T303 T308 J T293 T298 T303 T308 319 8.38 9.54 11.56 13.98 319 0.63 0.61 0.60 0.64 287 8.64 9.78 11.87 14.28 287 0.63 0.61 0.60 0.63 257 8.96 10.14 12.19 14.61 257 0.64 0.61 0.60 0.62 228 9.30 10.44 12.51 14.92 228 0.64 0.62 0.60 0.61 204 9.60 10.67 12.68 15.09 204 0.66 0.62 0.61 0.61 Oil Ct2 J T293 T298 T303 T308 J T293 T298 T303 T308 319 2.14 2.21 2.33 2.46 319 0.65 0.73 0.80 0.85 287 2.20 2.27 2.33 2.49 287 0.66 0.74 0.79 0.88 257 2.28 2.37 2.41 2.51 257 0.71 0.77 0.82 0.87 228 2.30 2.42 2.51 2.61 228 0.73 0.83 0.86 0.89 204 2.33 2.46 2.59 2.69 204 0.78 0.90 0.93 0.95 P A J T293 T298 T303 T308 J T293 T298 T303 T308 319 4.46 4.12 3.74 3.36 319 0.94 0.89 0.76 0.58 287 4.87 4.55 4.20 3.72 287 0.97 0.95 0.82 0.63 257 5.25 4.92 4.57 4.19 257 0.96 0.96 0.84 0.70 228 5.89 5.36 4.95 4.57 228 0.99 0.94 0.86 0.73 204 6.50 5.82 5.31 4.92 204 0.98 0.93 0.82 0.73 Table 4.7: WEX parameter values for the YVR and LAX simulations. \0 \ T 25°C T 30°C 2 5 0 J F i gure 4.16: Dependence of WEX parameter fi (scaling break) on J for four different temperatures. Also shown are power-law fits to the model output where each power law is constructed to have the same exponent. • At any J-value, increasing temperature will always decrease 3. v • As J —> oo,3 —> 0. Physically, this implies that as more energy is provided to the OLT-NOx system, the ridgeline on an isopleth diagram shifts upwards. Simulations initially in the VOC Chapter 4. Domain of Applicability for the Scaling Relationship 82 limited region become NOx-limited. And given enough irradiation, the whole response surface becomes NOx-limited. • As J —> 0, 0 —> oo. This is just the corollary to the above, namely, as the actinic flux is reduced, the 0 moves towards the V O C axis and NOx-limited simulations become VOC-limited. In this way, the V L R can also be considered a light-limited region (Johnson (1984)). • The power law relationship for 8 implies there is no characteristic scale for the scaling break. Finally, it is interesting to compare Figure 4.16 with a similar figure produced by Graham Johnson for his IER model (Johnson, 1984). This figure, reproduced here as Figure 4.17, shows emission reduction control options as a function of cumulative sunlight. He defines cumulative sunlight in the same manner as J (but bases his calculations on a latitude of 34°S ). For a given actinic flux and initial V O C to N O x ratio (R-value), the plot determines if ozone production is controlled V O C or NOx emissions. To do this, one locates the point on the Figure corresponding to the expected J-and .R-values. Next, using the temperature of interest, one determines if this point lies on the V O C controlled or N O x controlled side of the expected temperature's dividing line. The dividing line is in essence the ridgeline. In this way, the diagram can also be used to show the ridgeline behaviour of the as a function of J and T. This behaviour is consistent with 0, the scaling break. I do not know how Johnson produced his plot - whether is was based on his smog chamber data, modeling or intuition. It is worth mentioning that 0 could be thought of as simply one of several regression parameters, determined by a computer, used to parameterize the behaviour of a numerical model. However, the fact that this regression parameter shows such a regular dependence on both temperature and actinic flux, consistent with observations drawn from smog chamber studies, suggests that this high level analysis captures the essence of ozone photochemistry. 4.8.2 'Universal' Similarity relationship To find a 'universal' similarity relationship for the T and J simulations, maximum ozone and initial NOx concentrations were first made dimensionless by k^o and jav using Eq. (4.4) and (4.7). Next, dimensionless maximum ozone was scaled by and Il\ where initial values for a and b were estimated using a spreadsheet program and the largest value was used to determine the normalizing constant (7). Next, it was assumed that these scaled.and normalized points were now only a function of R and J . Furthermore, it was assumed that the J-dependence could be modeled by a horizontal shift of the Weibull-transformed data. Next, the normalized points were Weibull transformed and translated along the horizontal axis. The amount of translation was equal to \n(0av) where 0av represents the average /3-value for each J-level. (No temperature dependence Chapter 4. Domain of Applicability for the Scaling Relationship 83 -.Cumulative sunlight ( -MJ^-o ' t \ — • •' 'precursor emissions' • • ' " < . - • ' j I , i i ! u lummer 0600 0800 1000 . I2O0 H00 1600 1800 2000 Solstice k • • ,•> -I-'- ' - • — " l • ' •"••• I • ; 1 ->. Frjuinnx 0700 0800 1000 1200 1100 1600 18/2000 * OJ0O 1000 - 1200 . iltOO vl6/1800:S^r-So l s l l^v ,<• . . . . . . . . . t(|3 e»«nt Time ol day (hrs Std-time] for given / k ^ - d i (3t°Lot., deor sky) •precursor ! • emissions-Figure 4.17: Ridgeline as a function of J and T (from Johnson (1984))-was allowed for (3 since it was assumed that all temperature dependence was explained by IT4 ). In this way, all scenarios having a common actinic flux were shifted by the same amount - regardless of temperature. The amount of each translation was parameterized by: Pav = CoJ~Cl (4.12) where cQ and c\ were found by regressing the temperature averaged 8-values against J . No rotations were used to capture the J-dependence; these transformations did not appear to reduce the scatter. Figure 4.18A shows all the data sets in the 'Weibullized data' after translating by \n0av . The Figure shows scatter for both \n(R/@) < —1.0 and ln(i?/6) > 1.0. One simulation in particular appeared to deviate from the others. This simulation had the lowest J-value and lowest temperature. This low flux/low temperature simulation suggests a limit to the scaling regime and is the subject of the next section. Figure 4.18B shows the same plot as 4.18A but with this simulation removed. There is a little less scatter in the m(R/3) > 1.0 region now. Also plotted on this Figure, is the W E X Chapter 4. Domain of Applicability for the Scaling Relationship 84 ; A . 1 ^ o M O J-204 T20°C • J-257 T30"C M A J-204 T25°C * J-257 T35°C S • J-204 T30"C • J-287 T20°C <M X J-204 T35"C X J=287 T25"C - I W O J-228 T20"C • J-287 T30°C -1 86 J-228 T25"C X J-287 T35'C 1 <S J-228 T30"C * J-319 T20°C O J-228 T35'C C J-319 T25'C • ir J-257 T20'C * J-319 T30"C ' ' . , . . i . . , O J-257 T25°C N I I I I M I I I I I • J-319 T35'C -T '.... 1 .... 1 i 1 • 1 1 i 1 • 1 1 1 . 1 1 M WEX Curve • J-257 T30*C M A J-204 T25°C * J-257 T35'C S • J-204 T30°C • J-287 T20"C iM X J-204 T35'C X J-287 T25°C - J • O J-228 I20X • J-287 T30"C " i 88 J-228 T25"C X J-287 T35*C J-228 T30"C • J-319 T20'C G J-228 T35°C C J-319 T25"C 1> J-257 T20"C * J-319 I30'C ' ' O J-257 I25'C 1 , . . , 1 , . . , 1 . , . • J-319 T35°C -, I , , , , 1 . . , . ' -2 - 1 0 1 l n (R / /3 ) - 3 - 2 0 1 ln (R / jS ) Figure 4.18: Weibull transformed model output for RADM2 simulations having five different levels of actinic flux and four different temperatures after horizontal translation by ln /3 a „ (A). Figure B is the same as (A) but the simulation with J = 204 and T = 20° C removed curve which has been fitted to these remaining 19 test matrices. The regression was performed using a computer to calculate the scaling powers (a and b) as well as the W E X parameters (a 1,0:2,A). The program required a first guess which was supplied by a spreadsheet program. The model was forced to fit more closely around the ridgeline area. To do this, the regression found W E X parameters which minimize the R M S E (between the W E X model and OZIPR model output) around an area defined by R/0 6 [0.2,5.0] . Again, the normalizing value (7 ) was determined to be 1/0.99 times the largest scaled value. Finally, /3-values were not calculated in the regression since they were already imposed on the similarity relationship through the horizontal translations. Finally, the 'Weibullized' and transformed 'data' has been mapped back to the similarity plane to give a 'universal' curve for O L T . Figure 4.19A shows that the 'universal' curve captures ozone variability for R-values less than R — 0 but shows more variability for higher R-values. In Figure 4.19B the J204, T20°C scenario has been removed and the 'universal' W E X curve added. Chapter 4. Domain of Applicability for the Scaling Relationship 85 Figure 4.19: Universal similarity relationship for OLT. Figure A shows the model output after scaling and translating and Figure B replots (A) without the J = 204 and T = 20° C simulation and with the 'universal' WEX parameterization. 4.8.3 Universal Propene Curve Based on the above analysis, the 'universal' curve OLT has the form: and 0(J) = c0J~Cl 7 = 11.5, A = 0.62, ai = 2.5, a2 = 0.69 a = 0.65,6 = 6.1 c0 = 413, ci =-0 .81 This 'universal' curve captures the variability of maximum ozone concentration over a wide range of NOx and O L T concentrations, as well as a range of actinic fluxes and temperatures typical of the 'ozone season' in Vancouver B . C . A total of 8 parameters are needed to fully characterize this variability. The importance of each parameter is discussed in the next two chapters. To make use of Eq . (4.13), one first calculates the expected environmental conditions: T and J. J can be easily calculated based on the expected total irradiation time, the station location and the day of the year. Figure 4.20 shows a contour plot of clear sky J-values for different latitudes Chapter 4. Domain of Applicability for the Scaling Relationship 86 90 751--60 TS •'1 45 ra 30 o is y ° At 15, 0 170. ?70 2SU 190 21.0 . 230 Julian Day of Year -270 1 250 270 Jo!. Figure 4.20: Total actinic fiux (as measured by the integrated NO2 photolysis rate) as a function of Julian day of the year and latitude. The plot assumes a fixed irradiation interval starting at 7:00 a.m. (local time) and ending at 6:00 p.m. (local time). (in the Northern Hemisphere) and days of the year (based on an irradiation time starting at 8:00 a.m. and ending at 7:00 p.m. (LST)). This plot allows J and jav. Next, the expected temperature determines k^o a n d n^. Finally, initial NOx and OLT concentrations give R. Equation (4.13) can then be evaluated to predict maximum ozone concentration. The next subsection compares results predicted by Eq. (4.13) directly with OZIPR model output. 4.8.4 S c a t t e r P l o t s To test the ability of the 'universal' W E X curve (Eq. (4.13)) to predict maximum ozone concentra-tions, it was compared with model output at 4 different temperatures/actinic fluxes combinations. Figure 4.21 shows four scatter plots of WEX-predicted ozone versus OZIPR model output. In gen-eral, the plots show most points lying-close to the y.= x line. The correlation coefficient for each plot is above 0.99. For each plot a line of best fit was calculated. Finally, the scatter of the data about this line was also determined. Table 4.8„ outlines these statistics. The W E X model consistently under predicts maximum'ozone (by 16%) for the low actinic flux case (A). As J increases, the model tends to over predict ozone and the R M S E increases. There does not appear to be more scatter at large ozone concentrations than low ones. This is in contrast Chapter 4. Domain of Applicability for the Scaling Relationship 87 Plot A B C D Temperature (C) 25 30 30 35 Actinic Flux (J) 204 257 287 319 Slope 1.1571 1.0314 0.9749 0.9749 Intercept (ppm) 0.0007 0.0077 0.0101 0.0101 R M S E (ppm) 0.00790 0.01125 0.01131 0.02060 Table 4.8: Statistics for four scatter plots comparing maximum ozone concentrations predicted by the 'universal' WEX model (Eq. (4-13)) and OZIPR model output using the RADM2 mechanism (Stockwell et ai, 1990) using OLT as the sole VOC. 0.00 0.15 0.30 0.45 0.00 0.15 0.30 0.45 WEX WEX Figure 4.21: Scatter plots showing modeled maximum ozone concentrations (in ppm) based on OZIPR model output and WEX 'universal' curve (Eq. (4-13)) for four different actinic flux/temperature combinations: (A) J204/T25, (B) J257/T30 (C) J287/T30 (D) J319/T35. to the shape of the 'universal' similarity curve which shows large scatter for large R-values. 4.8.5 Summary A scaling analysis for maximum ozone concentration, produced from an O L T - N O x system, has been performed which captures variability due to initial OLT and NOx concentrations as well as a range of temperatures and actinic fluxes typical of ozone episodes in the Vancouver, B . C . region. The Chapter 4. Domain of Applicability for the Scaling Relationship 88 similarity relationship displays a characteristic 'break' whemnormalized and Weibull^transformed. I find that the temperature dependence can be described by a power law. The dependence on actinic flux, captured through the J-dependence of 6, can be viewed as a horizontal translation of the 'Weibullized data'. The similarity relationship shows a lot of scatter for R-values greater than Q but scatter plots of maximum ozone concentration based on the 'universal' W E X curve and OZIPR model output show good agreement over the entire range of ozone concentrations. The next section investigates the range of validity of the parameterization. 4.9 Scaling Limits By parameterizing the behaviour of the chemical mechanism, I fix the relative importance of com-peting chemical processes and (implicitly) assume that this importance does not change over a range of [VOC] 0 , [NOx]0, .R-values, temperatures or actinic fluxes. The extent of this range, not directly determined by the scaling analysis, should be included as part of the parameterization. Outside of this scaling range, it is possible that different photochemical processes might control ozone formation, leading to a new scaling regime and a breakdown of the original parameterization. In this section, I consider the range of applicability (in terms of [ V O C ] 0 , [NOx]Q, R-values) for the W E X parameterization using O L T as an example. For the W E X model to be useful, its range of applicability must overlap the range of environmental conditions typically found in polluted urban environments. From Section 4.8, it appears that the temperature range for the O L T parameterization lies above 20°C while the actinic flux range should be such that the cumulative NO2 photolysis rates are greater than 200 (corresponding to summer dates between early March and early September for a latitude of 49°N). Therefore, it is likely that at temperatures below 20°C or J-values below 200 the W E X model (at least with its present parameter values) cannot be used to describe the relationship between maximum ozone concentration and initial precursor concentration. I will not attempt to determine an upper limit on ambient temperature since values higher than 35°C are not common in the L F V (Oke and Hay, 1998) - the region in which I model ozone formation in Part II. Furthermore, since the analysis captures ozone variability at the L F V ' s maximum J-value, no upper bound on this range is needed. Therefore, using the W E X parameterization in conditions with significantly higher temperatures and J-values (i.e. lower latitudes) will require further investigation. Chapter 4. Domain of Applicability for the Scaling Relationship 89 0 0.6 1.2 [VOC] 0 - ppm Figure 4.22: Schematic of OLT modeling domains. The shaded region gives to the original VOC and NOx range, used for the WEX parameterization, and is labeled 'C. The large box gives the larger modeling domain. The lines R— 2(3 and R = 4/3 produce three additional regions 'A', 'B' and 'D'. Region 'A ' identifies simulations have low R-values, region. 'D' encompasses simulations having high R-values and region 'B' identifies those simulations having R-values in the range 1/3/2,4/3] but lying outside of the original domain. For completeness, the line R = j3 has been included. 4.9.1 Precursor Scaling Limits I determined the scaling limits by developing a parameterization of O L T over a limited range of initial V O C and N O x concentrations and then calculate maximum ozone concentrations for higher precursor concentrations. I compare the extrapolated values with additional model output (simulating these higher concentrations) to establish the limits of applicability. Based on the W E X model, maximum ozone concentration depends on its precursors in two ways: as a function of [NOx]a and R. However, since R is a function of [ V O C ] 0 and [NOx}0, maximum ozone concentration is a function of three variables, each of which may have its own scaling limits. A first guess for the R-range can be made by looking at the O L T model output in the Weibull plane (cf. Figure 3.9). The increased scatter in the similarity relationship for InR > 3 (R > 20) and InR < 0.75 (R < 2) suggests that 0/2 < R < A0 (0 = 4.2) defines an appropriate range. One would expect that a comparison of W E X generated ozone isopleths with OZIPR isopleths (cf. Figure 3.12) would similarly give an estimate of the V O C and N O x range. However, this Figure does not show any consistent discrepancies at high V O C or NOx concentrations (it does, however, show the discrepancies at low R-values). Thus, in order to determine the V O C and NOx Chapter 4. Domain of Applicability for the Scaling Relationship 90 Label Range Description A R<f3/2 Low R-values B (3/2 <R< 4/3 and [VOC]0 > 0.6 ppm, [NOx]0 > 0.15 ppm Higher [ V O C ] 0 and [NOx]0 with only R-values around j3 C 13/2 < R< 4/3 and [ V O C j o < 0.6 ppm, [NOx]0 < 0.15 ppm Original domain without high and low R-values D R> 4f3 High R-values Table 4.9: OLT precursor scaling domains. ranges and improve the estimate of the R-range, OZIPR simulations were run over a much larger precursor range. Specifically, simulations were run with [VOC}base = 1.2 ppm and [NOx}baSe — 0-3 ppm - a doubling of the original V O C and NOx ranges. As well, 41 nodes were used in the simulations, extending the original (non-trivial) R-range from [0.4,40] to [0.1,160]. Figure 4.22 shows the [VOC],, and [NOx]Q ranges for the original and modified runs. The original V O C and NOx range is highlighted by the shaded region and is labeled ' C . Lines R = 2(3 and R = 4/3 have also been drawn forming three additional regions ' A ' , ' B ' and ' D ' . Region ' A ' identifies simulations have low R-values, region ' D ' encompasses simulations having high R-values and region ' B ' identifies those simulations having R-values in the range [,3/2,4/3] but outside of the shaded region. These regions are described in Table 4.9. In order to compare the model output on the larger domain with the original W E X parameteri-zation, the model output was first put into dimensionless form, scaled by [NOx]^ and normalized by 7 (where values from the 11-node regression were used for a and 7). To highlight the discrepancies in each of the four domains, separate comparisons are shown in Figures 4.22A,B,C and D (where the letters refer to one of the domains labeled in Figure 4.22). Figure 4.23A shows that, for low .R-values, the model output does not collapse onto a single common curve and the W E X parameterization overestimates for R > 0.5. In Figure 4.23B, the model output clusters around a common curve but shows more variability for R > 8. Figure 4.23C plots the model output in the original domain where the W E X model provides an excellent parameterization. Finally, in Figure 4.22D, model output and the W E X parameterization are compared at high R-values. Scaled model output in this domain shows great variability, with the W E X parameterization consistently overestimating. I have also made comparisons using the more conventional isopleth diagram (Figure 4.24). There, isopleths found using the W E X parameterization (established on the smaller domain, but now extrapolated over the entire domain (dotted isopleths)) are plotted along with isopleths (solid lines) found from the O Z I P R simulations. Superimposed are the boundaries of regions A , B , C and D. As was the case for the original domain (cf Figure 3.12), for low R-values (region A) , W E X isopleths have too steep a slope and overestimate the model output. In region B , the W E X model Chapter 4. Domain of Applicability for the Scaling Relationship 91 F i gure 4.23: OLT similarity relationship in several scaling domains. Figures A, B, C and D refer to the different regions discussed in Table 4-9. In each Figure, the WEX parameterization is given by the solid line and model output by the diamonds shows good agreement with the model output. However, for R > 8, the W E X mode overestimates maximum ozone concentrations. This discrepancy, not noticeable at lower V O C concentrations, suggests the similarity relationship breaks down at higher V O C concentrations. In region D, the model continues to overestimate. It appears that the OZIPR isopleths are not parallel to the V O C axis but instead gently slope upwards; a feature not captured by the asymptotic behaviour of the Weibull function. To reduce the variability in regions A , B and D, different NOx scaling exponents were tried. In region A , when the exponent o is set to zero (i.e. making maximum ozone concentration as a function of R only) the scatter is almost completely removed (Figure 4.25A). Also shown in the Figure is the original W E X parametrization. The model output now clusters along a common curve indicating for low R-values, maximum ozone scales with R only. In Figure 4.25B, a lower value for the exponent has been tried (0.55 versus 0.60) again, reducing the scatter. Finally, it appears that an exponent value of 0.5 is the best choice for the NOx dependence for large R-values (4.25D). Chapter 4. Domain of Applicability for the Scaling Relationship 92 R=p/2 0.0 0.3 0.6 0.9 1.2 OLT Concentration - ppmC F i gure 4.24: Ozone isopleths (in ppb) for OLT over several scaling domains. Dotted lines show isopleths based on the WEX model and solid lines using the model output. The shaded region represents the domain used to determine the WEX model. Regions A, B, C and D are explained in the text and in Table 4-9. However, with this choice of exponent, there is still a large amount of scatter. Finally, Figure 4.26 is a schematic showing the dependence of the N O x scaling exponent as a function of initial OLT, N O x and R-values. It appears that the NOx scaling exponent takes on three values based on the i?-value: 0.0 at low R, « 0.6 for 0/2 < R < 40 and 0.5 for high R. Furthermore, in the ridge area, it appears that as [OLT]Q and [NOx]0 increase, the NOx scaling exponent decreases. I have marked this transition with an arc extending between the lines R = 0/2 and R = 40. While I have shown it to be an abrupt transition, I expect that it slowly decreases from one to the other. Further analysis is required to see if this decrease continues at higher precursor concentrations. To summarize, the scaling analysis provides a means of capturing the behaviour of a chemical mechanism over a moderate range of initial V O C and NOx concentrations. However, the resulting parameterization breaks down when the ratio of initial O L T to NOx (R-value) is either very large or small. In addition, the parameterization is influenced by initial V O C concentration. Furthermore, the relationship between maximum ozone and initial NOx concentration depends on R. Despite this, the W E X parameterization, over the original limited domain, is able to predict maximum ozone concentration around the ridgeline and for a wide range of initial V O C and NOx concentrations. While this analysis has been for a single V O C species, I expect similar trends to hold for the other V O C and V O C mixtures. Ideally, the parameterization range should be guided by R/0-values and Chapter 4. Domain of Applicability for the Scaling Relationship 93 0 5 10 15 20 0 50 100 150 200 Figure 4.25: Similarity relationship for different NOx-scaling exponents. Figures A, B, C and D refer to the regions discussed in Table 4-9. In each Figure, the original WEX .parameterization is given by the solid line and model output scaled by different powers of initial NOx concentration by the diamonds. [ C l i m a x found in urban environments. Unfortunately, it is difficult to determine B from ambient measurements, so instead, I have chosen a parameterization range centered around the scaling break that keeps the maximum ozone concentration below 300 ppb. For OLT, the maximum error produced by the W E X model in this region is 3.8 ppb or 4.0%. 4.10 Conclusion In this chapter I have taken a novel approach of describing the ozone formation and shown it to be applicable for a wide range of V O C species and V O C mixtures. Furthermore the techniques prove to be independent of chemical mechanism. These techniques are also capable of capturing the variability of maximum ozone concentration on temperature and actinic flux. The analysis shows 7 and the NOx-scaling exponent (a) vary with V O C species a point not considered by Blanchard et al. (1999), Chang and Rudy (1993) or Johnson (1984). Furthermore, 7 appears to depend on Chapter 4. Domain of Applicability for the Scaling Relationship 94 0.30 R=p/2 E Q-Q. 0:15 x O 0.55 NOx 0.0 / M / / 0 6 / NOx N O x 0 5 R=4f3 0 0.6 1-2 [VOC]0-ppm Figure 4.26: The OLT NOx-scaling for OLT as a function of initial OLT, NOx and R. The shaded region represents the domain used to determine the WEX model. Regions A, B, C and D are explained in the text and in Table 4-9. The arc between R = f3/2 and R — 4/3 is intended to reflect a change in exponent values from 0.60 to 0.55 and not an abrupt jump. actinic flux which, again, has not been previously accounted for. This chapter has also shown the ranges of V O C , NOx, temperature and actinic flux for which of the scaling analysis is valid. In general the scaling analysis can be used in a two ways: to calculate maximum ozone con-centrations (using the similarity relationships) or to succinctly present data (by making use of the scaling techniques). In the next two chapters, I will outline a third application: to understand the general behaviour of a photochemical system through the interpretation of W E X parameters. A subsequent chapter will compare W E X modeled ozone concentrations with smog chamber data. Chapter 5. Scaling Break and Ozone Photochemistry 95 C h a p t e r 5 Scaling Break and Ozone P hot o chemist r y 5.1 Introduction This is the first of two chapters which explores the physical significance of the W E X parameters. This chapter deals with the 0 - the R-value which characterizes the change in chemical regime and hence scale break in the W E X model - while the next examines the remaining five parameters. I start by examining the relationship between ozone production, ozone concentration, maximum ozone concentration and 0. I begin with the temporal evolution of ozone concentration; showing that as the photochemistry proceeds, a fundamental shift in chemistry causes a change in the way ozone is produced. I then demonstrate that the scaling break is a manifestation of this shift. Next, I study the chemistry causing shift from a systems point of view; explaining the shift in terms of positive and negative feedback loops. Finally, I examine the relationship between the scaling break and the ridgeline, OiJ'-reactivity and chain length. 5.2 The Temporal Variability of Ozone I begin by examining how ozone concentration varies during a single O Z I P R simulation. Then, I study a sequence of simulations and show how. the temporal variability of ozone, NOx and various other species is affected by the initial V O C to NOx ratio. 5.2.1 Temporal variability of NO, NO? and 0 3 for a single simulation Figure 5.1 shows the temporal evolution of ozone and various other species for a simulation using the stock urban mixture. The initial concentration of NOx was 0.045 ppm and for the V O C mixture it was 1.35 ppm (for an R-value of 30), which puts the simulation in the NOx-only scaling regime. Note that the highest ozone concentration occurs at the simulation end. It is this ozone value that would be plotted on an isopleth diagram and used to find the W E X parameters. Chapter 5. Scaling Break and Ozone Photochemistry 96 6 9 12 15 18 time Figure 5.1: Temporal evolution of 03, N02, NO, HNO3, PAN, ONIT and other peroxides for an OZIPR simu-lation using the Stock urban mixture. The initial NOx concentration was 0.045 ppm and initial VOC concentration was 1.35 ppm for an R-value of 30. The temporal variability of the various species reveals important processes, namely: • For NO, its concentration almost immediately begins to drop. This represents the conversion of NO to NO2 by peroxy or hydroperoxy radicals (R7). • Initially, the NO2 concentration rises (at the expense of NO) then reaches a peak before falling. The drop in concentration coincides with the production of HNO3 (R9) and P A N . • The ozone curve is flat until about 8:00 a.m. after which it starts to rise. This coincides with the increase in NO2 and drop in NO concentration. Ozone growth continues throughout the day but at a slower rate by late morning (t « 11 : 00). • The P A N concentration increases rapidly around 8:00 am and reaches a maximum around 11:00 a.m. and then decreases throughout the remainder of the simulation. This drop may be explained as follows: P A N forms as the result of a reaction between nitrogen dioxide and . the acetylperoxy radical (modeled as ACO' in R A D M 2 ) : N02 + ACO\ -» PAN (R15) P A N also readily decomposes back into these products: PAN - • N02 + ACO' (R16) Chapter 5. Scaling Break and Ozone Photochemistry 97 Both reactions occur simultaneously and are highly temperature dependent (Finlayson-Pitts and Pitts, 1999). When both N02 and ACO* are abundant, P A N readily forms. However, as N02 becomes scarce, the balance between 7215 and 7216 shifts with more decomposition than production (low N02 slows 7215) resulting in a P A N reduction. • Nitric acid (HNO3) concentration rises rapidly before slowing around 11:00 a.m. The final concentration of PAN+HN03, roughly equal to the initial N O x concentration, represents the conversion of NOx to other nitrogen compounds. NOx, P A N and nitric acid represents three major components of an important class of atmospheric species called reactive odd nitrogen. 5.2.2 Reactive Odd Nitrogen (NOy) Reactive odd nitrogen (NOy) represents the sum of NOx and all compounds that are the products of the atmospheric oxidation of NOx. In the R A D M 2 mechanism, these include: nitric oxide (NO), nitrogen dioxide (NO2), nitric acid (HNO3), peroxyacyl nitrates ( P A N and T P A N ) , alkyl nitrates (ONIT), the nitrate radical (NO3), nitrous acid (HONO) and dinitrogen pentoxide (N205). The first five represent the most important components of NOy. In the absence of deposition and dilution, [NOy] is conserved under photochemical reactions. Based on the simple description of ozone photochemistry given in the introduction, it is important to note that without termination reactions, NOx acts as a catalyst; cycling between NO and N02 (whereas the V O C s are gradually consumed). However, with termination reactions, the continuous cycling of N O x between NO and N02 is broken and ozone photochemistry ceases when all N O x has been converted to other forms of NOy (Jeffries and Tonnesen, 1994). Another class of nitrogen compounds is called total reacted nitrogen (NOz) and is defined as the difference between NOx and N O y NOz = NOx - NOy When [NOz] « [NOx]0, a photochemical system stops reacting. In the next chapter, I will show that partitioning of NOz between the HNO3, P A N and ONIT determines several W E X parameters. 5.2.3 Isopleth Plot and Stock Simulations To extend the analysis to include the effects of initial V O C and NOx concentrations, I now examine a sequence of eight simulations. To keep the analysis simple, all eight simulations start with the same initial NOx concentration but with varying initial V O C concentrations in order to provide a range of R-values above, below and along the ridgeline. I have marked the initial V O C and NOx Chapter 5. Scaling Break and Ozone Photochemistry 98 R=3 6 9 VOC Concentration - ppmC Figure 5.2: Ozone isopleth plot using the Stock urban mixture showing an isomephitic line of [NOx]0 = 0.045 ppm. Also drawn are rays of constant R-values. The intersection of these rays with the isomephitic line, indicated by stars, gives the initial VOC concentrations for the eight simulations. concentrations, for these simulations, on an isopleth diagram (Figure 5.2) along with an isomephitic1 (constant NOx) line at [NOx]0 = 0.045 ppm. Also drawn are rays of constant R at values: 3, 6, 9, 12 , 15, 18, 24 and 30. The intersection of these rays and the isomephitic path, indicated by stars, marks the initial conditions for the eight simulations. The isopleth diagram shows simulations R = 3 and 6 are above the ridgeline, R = 9 is close to the scaling break (3 = 9.4) and the remainder are in the NOx limited region. For each simulation, 0 3 , NO, N02, PANs ( R A D M 2 classes P A N + T P A N ) , HN03, ONIT ( R A D M 2 class for organic nitrate) and peroxides ( R A D M 2 classes H202 + OP1 + OP2 and P A A ) are plotted as a function of time. On each figure, ozone concentrations are given on the right-hand axis and the remaining on the left axis. The plots reveal several features which merit discussion. To start, inspection of the N02 concentration curve shows that increasing R (i.e. increasing initial V O C concentration) speeds up the early NO to NQ2 conversion. For example, the NO2 peak occurs at 12:00 for R — 6 and t = 9 : 00 for R = 24. In all cases, the rise in ozone follows the NO2 rise; occurring earlier in the simulation for higher R-values. Also, in each simulation, NO concentrations decrease, more quickly with increasing i?.' For all but the R = 3 simulation, NO2 *I have coined this word based on the term 'mephitic air' used by Rutherford after his discovery of nitrogen in 1772 Chapter 5. Scaling Break and Ozone Photochemistry 99 Figure 5.3: Temporal evolution of 03, N02, NO, HNO3, PAN, ONIT, and peroxides concentrations for eight different OZIPR simulations each starting with initial NOx concentration of 0.045 ppm but varying initial VOC concentration. levels peak and then fall. For simulations below the scaling break (R > 9), N02 concentrations level off at a value around 2 ppb. The drop in NO and N02 is matched by an increase in HNO3 for simulations with R > 9 and by an increase in HN03) PANs and O N I T for the higher R-values. Finally, at the higher R-values, production of peroxides becomes noticeable. Secondly, in all simulations, ozone concentration increases. monotonically and the maximum Chapter 5. Scaling Break and Ozone Photochemistry 100 value increases with increasing R-value until R ss 24 where it remains roughly constant. This represents the NOS regime where maximum ozone concentration is now a largely a function of initial NOx concentration only. For simulations below the scaling break, the ozone temporal variability shows a marked decrease in growth rate towards early afternoon. Close inspection shows this slowing down coincides with the leveling off of N02 at its low value. Thus it appears that once [./VO2] ~ 0 (nitrogen dioxide concentrations do not go exactly to zero due to a steady state that is reached with P A N and the nitrate radical), ozone growth slows but does not cease. Inspection also shows that this change in growth rate occurs earlier with increasing ( V O C ] 0 . Finally, for simulations with R > /?, the ozone versus time profile is 's-shaped'; with low con-centrations for the first few hours, followed by a rapid increase and then a gradual slowing down. This pattern, which resembles the similarity profile (except there N O x - s c a l e d dimensionless m a x i m u m ozone was plotted as a function of R ) , suggests a Weibull transformation may reveal something about the temporal dynamics of ozone formation. In order to use this transformation, all concentrations were first normalized by a common value: [ 0 3 ] m a x = 230 ppb (= j[NOx]^ where 7 and a are the W E X parameters for this example). Next, each normalized profile (/(i)/7) was Weibull transformed and plotted against ln(t — t0) (Figure 5.4). The Figure indicates for R > 12, simulations produce a marked 'dogleg' around ln(i —10) = 2.0, with the bend more pronounced and occurring sooner for greater R-values. This bend marks a change in the rate of increase of ozone concentration with time and coincides with the low ./VO2 condition (see Figure 5.3). There is also another bend in the time series at ln(t — t0) RS 0. This break is related to conditions which are radical limited and needs more explanation. I propose that the 'dogleg' arises from a change in the way ozone is produced; reflecting a change in governing chemical process. I also propose that this change causes the observed scaling break. To prove these assertions, I use the concept of ozone production. 5.3 Ozone Production Following Tonnesen and Dennis (2000b), ozone concentration can be expressed as the cumulative production of ozone over a given time period i.e.: where P(Oz) represents the instantaneous production of ozone. This production represents the net effect of reactions which produced ozone to those that consume it i.e.: (5.1) d[03] = Ozone Produced — Ozone Consumed (5.2) dt Chapter 5. Scaling Break and Ozone Photochemistry 101 Fi gure 5.4: Weibull transformed dimensionless ozone concentrations (for the eight isomephitic simulations given in Figure 5.3) plotted against \n(t — t0). Determining an expression for P(03), given a chemical reactions set, is a straight-forward pro-cess. For example, for the NOx-only system, ozone is produced in R l (with rate JNO2[N02}) and consumed in R2 (with rate kNo[NO}[03]) resulting in the following expression for ozone production: P(Oz) = JNO2[N02} - kNO[NO}[03] (5.3) Chapter 5. Scaling Break and Ozone Photochemistry 102 While expressions like Eq. (5.3) are easy to develop, even for systems involving many VOCs and radicals, evaluating them directly is usually not possible. However, expressions for P(03), based on simplified photochemical systems, while not amenable to analytic evaluation, do provide useful insight into the governing chemical processes. For instance, Sillman et al. (1990), have found that when the instantaneous N O x concentration exceeds instantaneous V O C concentration: kOH[VOC}(A[03} + B[VOC}) 1 3 j kHN03[N02}-C[VOC} { • } where A, B, C are constants which measure the rate of radical production from ozone, aldehydes and carbonyl compounds respectively. This expression shows that ozone production increases with increasing V O C concentration and decreases with increasing N02 concentration. When instanta-neous V O C concentration exceeds NOx, they find a different approximation holds: P ( 0 3 ) ~ [NO] (A[03\ - B[VOC}fl2 (5.5) where production now shows only a slight dependence on V O C concentration and is proportional to NO concentration. Thus Sillman et al. (1990) classify ozone production into two different regimes based on the ratio of instantaneous V O C to NOx concentrations; This division is also supported by Kleinman (1994) who further suggests that this separation reflects a fundamental change in photochemistry: .. the two types of photochemistry apparent at low and high NOx concentrations are not merely continuous differences, as NOx is varied, but instead reflects a structural change in reaction mechanism.' It is the intent of this chapter to prove that the scaling break arises as a result of such a structural change. There are several steps involved in the proof. To start, I propose that as the photochemical reactions proceed and NOx is removed more quickly than the VOCs , the resulting low NOx environment triggers a shift in ozone production. This shift in production affects the resulting ozone concentration (via Eq. (5.1)), gives rise to the 'dog-leg' in the ozone concentration versus time curve and ultimately alters the maximum or final ozone concentration. Next, I propose that the initial relative abundance of V O C to NOx (R-value) determines whether a switch to low-NOx conditions will occur. I will then show that these two assertions imply that a switch in ozone production causes a scaling break in maximum ozone concentration (when plotted as a function of R) if the initial R-value is greater than a fixed value (/?). I prove these assertions by constructing several simple models for ozone production, each showing two distinct production regimes. I use these models to explore how the change in production affects ozone concentration as a function of both time and initial precursor concentration. Chapter 5. Scaling Break and Ozone Photochemistry 103 P(03) time r Figure 5.5: Simple step model function for ozone production. 5.3.1 Step function model for ozone production I begin by constructing a simple model for ozone production (P(03)) which shows a regime change - a step function. I use this model to show the connection between a production regime shift and the corresponding relationship for maximum ozone concentration as a function of initial V O C concentration. While this model may seem contrived, I will show that it captures interesting properties of ozone photochemistry and, in fact, represents the basis for the I E R model (Johnson, 1984). In subsequent sections, I modify the model to make it more realistic. The model, shown in Figure 5.5, has a constant P(03) level until time t* at which point pro-duction drops to zero. The initial high production reflects the initially VOC-limited chemistry (analogous to the low-VOC regime in Eq.(5.4)). The drop to zero production at t* reflects a switch to NOx-limited conditions, where all initial NOx has been converted to stable nitrogen products and production ceases (analogous to the low-NOx regime in Eq. (5.5)). To this model, I add several features. I want to include a P(Os)-dependence on initial precursor concentrations, and to start, I include only a V O C dependence - later a N O x dependence will be added. From Eq. (5.4), Sillman et al. (1990) show P(03) increases with increasing V O C concentration. To give the step function model such a V O C dependence, I construct a family of production curves with the following three properties (which, for now, I only partially justify but later generalize and discuss): P r o p e r t y I: Motivated by Eq. (5.4), a larger initial V O C concentration produces a greater initial P ( 0 3 ) level. P r o p e r t y II: For a greater initial V O C concentration, regime shift occurs earlier. P r o p e r t y III : The switchover time (£*) is such that the area under the P ( 0 3 )-time curve is Chapter 5. Scaling Break and Ozone Photochemistry 104 P(03) [VOC]=high [VOC]=medium [VOCHow I I f * f * n m time Figure 5.6: Three members of a family of step-rnodel functions for ozone production. The high VOC switches regimes at t*h, the medium at t^ while the low VOC never switches regimes. constant. The area under a P((93)-time curve represents an ozone concentration (see Eq. (5.1)) and so this rule implies production ceases when the corresponding ozone concentrations reach a fixed value, independent of V O C . This property, the hardest to justify, is explained as follows: I want the model to have the greatest maximum (peak) ozone concentration as a function of initial NOx only. With production zero after the switchover, maximum ozone concentration becomes a constant (independent of V O C ) . In Figure 5.6 I have sketched three members of a family of production curves, identified by initial V O C concentration, based on the above properties. From this Figure, the higher V O C concentration has a larger initial production but regime shift occurs sooner. The area under both the high and medium curves is constant. For the low V O C concentration, initial production rate is so low that switchover never occurs. From a model for ozone production, ozone concentrations can be determined using Eq. (5.1). For the simple step-model function, this produces temporal profiles which increase linearly with time. If initial production is great enough and switchover occurs, then ozone concentrations reach a plateau where they remain. Figure 5.7 is a schematic of ozone concentration versus time curves for the production family given in Figure 5.6. From this Figure, higher production associated with the highest initial V O C concentration results in ozone concentrations rising quickest. However, both the medium and high V O C curves achieve the same final ozone concentration. The low V O C curve rises the slowest and never reaches the plateau. Chapter 5. Scaling Break and Ozone Photochemistry 105 [VOC]=high / .*"'[V0Q=medium ____ " ^ - "[VOC]=low time t * m Figure 5.7: Ozone concentration curves for the three VOC given in Figure 5.6. The highest VOC reaches the plateau at t*h, the medium at while the lowest never reaches a plateau. 5.3.2 Maximum ozone concentration To finish the analysis, I now plot maximum ozone concentration as a function of initial V O C . How-ever, instead of sketching curves, I numerically calculated a set of production, concentration and maximum ozone concentration curves using the step function model and typical production values. These results are not based on O Z I P R model output. In Figure 5.8A, I start with typical production rates which I use to calculate concentrations (B) and maximum ozone concentration (C) for four initial V O C concentrations. In Figure 5.8A ozone production for the lowest initial V O C concen-tration ([KOC],, = 1.0 ppm) never shifts regimes, while the next highest shifts and the largest two switch progressively sooner. Integration of the production curves gives resulting ozone concentra-tions. Finally, in Figure 5.8C, the relationship between maximum ozone concentrations and initial V O C concentration has been plotted with two linear line segments passing through the data. The arrow running between Figures 5.8B and 5.8C indicates how the final ozone concentration along any curve in Figure 5.8B becomes the maximum concentration for that initial V O C concentration2. Thus, the step function model produces a maximum ozone/initial V O C curve which is piecewise -unlike the curved or 's-shaped' curves produced from OZIPR model output. A second shortcoming of the step function model is that maximum ozone/initial V O C curve attains its maximum value rather than approaching it asymptotically. It is worthwhile noting that the [C>3](i) versus t curve for [V0C]o = 4.0 ppb (Figure 5.8B), is geometrically similar to the [ 0 3 ] m a x versus [ V O C ] 0 profile (Figure 5.8C). This trend is also 2 W h i l e only four curves are shown in Figures 5.8A and B , Figure 5.8C has been plotted using an additional 6 initial V O C concentrations. To avoid clutter, these extra members were not plotted in the first two graphs. Chapter 5. Scaling Break and Ozone Photochemistry 106 evident in the OZIPR simulations where dimensionless and scaled curves, for NOx-limited conditions, show an 's-shaped' profile, similar to the shape of the W E X similarity relationship (for example, compare the R = 30 plot in Figure 5.3 with the similarity function in Figure 3.7). For the step function model, this similarity arises because P(03) increases linearly with [70C]„ . The corresponding parameterization for ozone as a function of time and initial V O C concentration ([0 3](i; [VOC] 0 )) is linear in both time and [ V O C ] c . Had I chosen a P(03) production with quadratic dependence on [VOCJo , each [03](£; [^OC]„) curve would still be piecewise linear in time, but the parameterization of maximum ozone as a function of initial V O C ([03] m Q X([V*OC] 0)) would be quadratic for V O C concentrations that do not have a regime change and linear (constant) for those that do. Since O Z I P R model output produces [Oa](£; [VOC] 0 ) curves which are geometrically similar to [ 0 3 ] m a x ( [ ^ O C ] 0 ) curves, I suggest that any parameterization for the [0 3 ] (£ ; [VOC] 0 ) should have initial V O C and time to the same power. This implies initial V O C concentration and time have the same effect on ozone concentration; increasing initial V O C concentration is equivalent to 'speeding up the clock'. I include this as a fourth property to be satisfied by a family of ozone production curves in Section 5.3.5. So far, I have introduced a simple parameterization for ozone production and a set of rules to create a family of curves based on initial V O C concentration. I have shown that starting from the production curves, the [ 0 3 ] m a x versus [ V O C ] 0 relationship follows from Eq. (5.1). For the step function model, the [OsjmaxQ^OC],,) relationship differs from similar relationships obtained from model output: it is not 's-shaped' and it does not asymptotically approach its limiting value. While I will improve these shortcomings later, my main intention in this section is to provide the simplest basis (or essence) of ozone photochemistry. I believe that this step function model, with the properties for developing a family of curves based on initial V O C concentration, is a beginning to this end. In fact, in the next subsection, I show how the step model function generalizes the IER model. 5.3.3 IER and Step function model While the step function model may seem a bit contrived, I now show that it can be used to develop the IER model (Johnson, 1984). Development of this model was guided by results for an extensive set of outdoor smog chamber experiments3 and was intended' to provide a simple set of formulae which quantitatively describe ozone formation (Johnson, 1984). The model predicts that initially, 3 I n essence my ozone model is being developed along a.similar line but I am being guided by model output not smog chamber data. I wi l l show that each is not without its own difficulties." Chapter 5. Scaling Break arid Ozone Photochemistry 107 A 50 20 [VOC]„=4.0 ppm [V0C] o=3.0 ppm [VOC]„ -2 .0 ppm [ V O C ] a o l . O ppm 2 4 6 8 10 t - t„ .„ (hr) F i gure 5.8: Ozone production (A), concentration (B) and maximum concentration (C) for a step function model. The arrow between Figures B and C highlights the relationship between final ozone concentration and maximum ozone concentration. smog potential (PSP) (the sum of ozone produced and initial NO converted to NO2): [PSP}(t) = [03}(t) - [03]0 + [NO}0 - [NO](t) (5.6) increases linearly with cumulative N02 photolysis rate: [PSP](t)=p{T)[VOC}0 f jNo2dt (5.7) Jstart where p(T) is a temperature dependent measure of the V O C reactivity. 4 While the independent variable in this equation is time, the cumulative photolysis of NO2 (f JN02 dt)- a measure of. the energy added to the photochemical system - could also be used as the independent variable. By setting j(t) = JJN02dt, Equation 5.7 describes a linear dependence between smog potential and j(t) i.e.: [PSP](j(t)) = p(T)[VOC]0j(t) I have slightly modified the original notation to avoid confusion with my notation. Chapter 5. Scaling Break and Ozone Photochemistry 108 Differentiation of Eq. (5.7) with respect to j(t) gives PSP production rate (P(PSP)): . P(PSP)(j(t)) = ^^y^ = P(T)[V0C}0 c< [VOC)0 (5.8) Thus production is initially constant (and proportional to initial V O C concentration). Furthermore, the model does not have smog potential growing indefinitely with j(t). The model limits smog potential to a maximum value, independent of initial V O C concentration: [PSP]max = P[NOx]0 which implies that at some time (tcease), smog production ceases: P(PSP)(j(tcease)) = 0 (5.9) Together, Equations 5.8 and 5.9 describe a step function model for P S P production (when considered as a function of Furthermore, PSP production also satisfies my properties I, II, III for a family of production curves, namely: Property I: This property is satisfied by Eq. (5.8) which shows initial production is greater for larger initial V O C concentration. Property II: The I E R model has PSP reaching a maximum value (0[NOx]o) when: p(T)[VOC]0j(t) > 3[NOx)0 (5.10) Again, this implies P(PSP) goes to zero, with switchover (j*) occurring when: 7* - u n - m ° x ] o (5 I D 3 ~ J [ t } ~ p(T)[V0C]o [5-U> which decreases with increasing [ V O C ] 0 . Property III: The left hand side of the inequality in Eq. (5.10) represents the area under a PSP production-jjvo2 curve (when this is given by a step function), indicating that switchover occurs when a fixed area (in this case B[NOx)0) is reached. Thus we can think of the I E R model as parameterizing P S P production using a step function model which satisfies properties I, II, III of Section 4.3.1. While the I E R model has been criticized for its linear dependence of maximum ozone concentration on initial NOx (Blanchard, 2000), the basis for this model (Eq. 5.7 and 5.10) is supported by environmental chamber data and current understanding of atmospheric chemistry (Blanchard et al., 1994). 5.3.4 PSP production In this section, I justify the step-function nature of the IER model, and propose improvements, by examining PSP production using a simple reaction set. Consider a photochemical system which Chapter 5. Scaling Break and Ozone Photochemistry 109 includes the two NOx-only reactions ( R l a and R3) along with the conversion of NO to N02 by peroxy radicals (R12): N02 + hu^ NO + 03 (Rla) NO + 03^ NO2 + O2 (R3) NO + R0'2 -» N02 + RO* (R12) Based on these three reactions ozone production remains unchanged from the NOx-only.system P(03) = ^ 1 = j[No2] - kNO[NO}[03] (5.12) at The rate of change of NO is given by: d[NO] i.e.: dt j[N02} - kNO[NO}[03} - kR02[RO'2}[NO} (5.13) Subtracting Eq. (5.12) from Eq. (5.13) gives a relationship for P S P production: P(PSP) = ^ - ^ = kR02[RO'2}[NO] (5.14) Equation 5.14 can be used as a physical basis for the IER model and to propose improvements. Based on Eq. (5.14) P(PSP) is non-zero so long as there is initial NO and RO' radicals. As NOx is converted to NOz, N O concentrations drop (for example, see Figure 5.3) suggesting that P(PSP) should also decrease. This explanation does not take into account peroxy radical influences on PSP production but it does suggest that P(PSP) should show a drop from an initial state to a lower one. Equation 5.14 can be used to justify Property I: assuming the main source of peroxy radicals arises from photolysis of V O C s and OH* attack on VOCs, then higher initial V O C concentrations should lead to higher RO' concentrations and higher P(PSP). I cannot justify Property II and III using Eq. (5.14) but I can use it to suggest improvements to the step function model. Namely, as the sun reaches its zenith, both V O C photolysis and OH' attack should increase with time (since the main source of OH' is the photolysis of ozone) before reaching a peak around midday (when the sun is at its zenith), and then declining throughout the afternoon. This suggests replacing the initial constant production with a production which starts at zero, increases to a maximum and then decreases. I use these ideas to improve the step-function model (and indirectly the IER model) in the next section. However, I modify my model to use j(t) as the independent variable instead of t. Chapter 5. Scaling Break and Ozone Photochemistry 110 prop [VOC]=high \ [VOC]=medium \ \ [VOC]=low t l j(t) Jn Figure 5.9: Family of production curves for three initial VOC concentrations using the quadratic model. With the high initial VOC concentration, production peaks before falling to zero at t*h. Production from the medium VOC concentration ceases at t*m while production from the lowest VOC never falls to zero. 5.3 .5 Quadratic Model for Ozone Production To include the effects of ozone production on changing solar zenith, I replaced the linear step function model with a quadratic version. In this configuration, production increases with j(t) until reaching a maximum after which time it decreases until reaching zero where it remains fixed (representing a switch to low production after most NOx is converted to NOz). I developed a parameterization for a family of such curves, based on my three properties: Property I: Higher [ 7 0 C ] o leads to higher peak production. Property II: Higher [ F O C ] 0 leads to a quicker switch to zero production. Property III: The area under each production-j(£) curve is constant. Property IV: [ V 0 C ] o and j(t) are both of order two in the parameterization of [0 3](£; [VOC] 0 ) . Figure 5.9 shows a schematic of three production curves based on this model. As before, integra-tion of the production curves yields ozone concentrations and the maximum from each concentration curve then gives a single point on the [ 0 3 ] m a x versus [ V O C ] 0 curve. These steps have been carried in Figure 5.10: Figure (A) shows production based on typical values, (B) concentrations after in-tegration, (C) maximum ozone versus initial V O C concentration (where, again, addition [ V O C ] 0 levels have been included to highlight features) and (D) gives the corresponding 'Weibullized data' modeled by two line segments. Again, these plots are not based on O Z I P R model output but simply the quadratic production model using typical production rates to quantify the various curves. Is the quadratic model an improvement over the step-function model? To start, both the concen-tration curves (Figure 5.10B) and the maximum ozone curve (Figure 5.10C) are now more 's-shaped', Chapter 5. Scaling Break and Ozone Photochemistry 111 in closer agreement with Figure 5.3 and Figure 3.7 respectively.5 However, to be consistent with the model output, the concentration curves for [ V O C ] 0 = 4.0 (Figure 5.10B) should approach its limiting value in an asymptotic manner. Furthermore, while the Weibull plot shows two distinct linear segments, the zero slope of second curve is unrealistic (based on the results of Chapter 4). To eliminate both flaws will require production to asymptotically approach zero after peaking. I examine the consequences of such a parameterization in section 5.4.7. Finally, note that the Weibull plot produces a scaling break not because of the local maximum in ozone production but instead because production is fixed at zero after most of the NOx conversion to NOz. For instance, the [ V 0 C ] o = 2.4 ppb production curve does not reach zero production and, consequently, its ozone maximum lies to the left of the scaling break in the Weibull plot (In2.4 = 0.88). However, this production curve reaches a maximum at j « 180. This suggests that the local maximum in the ozone production curve does not produce the scaling break. I explore this premise in the next section. 5.3.6 Weibull Model In this section, I present a model for ozone production which shows asymptotic decay after reaching a maximum. M y intention with this model is not to see how well it reproduces the OZIPR features but rather to prove that a change in curvature or a maximum in production are not associated with the scaling break. To do this, I created a model for production which peaks and then shows asymptotic decay. While any bounded curve, which is non-zero for all j(t), will serve for the parameterization, I have chosen the Weibull distribution. Let the family of production curves be given by: [VOC)0 (\voc)0pa-1 P ( 0 3 ) ( j ; [VOC]0) = ^—^ [^f^) e x P [- {^P21 (5.15) with corresponding ozone concentrations: [03]{j{t)\\yOC]0)=(l-exp and maximum ozone concentration: [03}max = ( 1 - exp ([VOC]0j V P' f[VQC}0J V P' (5.16) where J = j(tend) is a constant. Letting J/0' = 1/6, the single Weibull model from Chapter 3 (Eq.(3.9) but now as a function of V O C instead of R)) is recovered. Wi th maximum ozone concentration parameterized by a 5 I n Figure 3.7 I have plotted NOx-scaled dimensionless maximum ozone versus R. For now, I am ignoring the effects of initial N O x by assuming a constant value. As a result, the two curves plot equivalent variables. Chapter 5. Scaling Break and Ozone Photochemistry 112 Figure 5.10: Ozone production (A), concentration (B), and maximum ozone concentration (C) {or four initial VOC concentrations using a parabolic model of ozone production. Also plotted is Weibull transformed nor-malized maximum ozone concentration versus natural logarithm of initial VOC concentration (D). single Weibull (Eq. (5.16)), there cannot be a break in the 'Weibullized data' - a single Weibull produces a single straight line upon Weibull transformation. However, such a parameterization shows both a local maximum and a change in curvature (where slope of the production-time curve switches from positive to negative). I conclude, that the scaling break is neither associated with a production maximum nor a change in production curvature - it must be associated with something Chapter 5. Scaling Break and Ozone Photochemistry 113 quadratic P(03) F i gure 5.11: Modified quadratic curve with hyperbolic tail. Transition occurs at j*. fundamentally different. That a parameterization like Eq. (5.16) shows no scaling break but produces a 'ridgeline' on a isopleth diagram (see for example Figure 2 in Chang and Rudy (1993)) is also of interest and is discussed in the next chapter. 5.3.7 Quadratic with Asymptotic Decay I now create a model for ozone production which shows a scaling break and has 'Weibullized data' showing a non-zero slope after the scaling break. In order to produce the break, the quadratic model is fitted with a hyperbolic tail. This tail represents the shift in production that occurs once most NOx is converted to NOz. I make use of the quadratic model but stress that any family of curves which has the desired properties (to be outlined next) will capture the key features of the OZIPR curves - there does not appear to be any physical link between the Weibull distribution and ozone formation. The model makes a transition to hyperbolic behaviour once the area under the production curve reaches a constant. In addition, the total area under the production curve is bounded. This now places two integral constraints on the model; one for total area under the production curve and the other for transition to the hyperbolic regime. Figure 5.11 sketches the model. To create a family of production curves, I make the peak value increase with increasing initial V O C concentration and require this peak to occur sooner. Figure 5.12 shows a family of production, concentration and the corresponding maximum value and Weibull plots based on this model. Both the concentration (Figure 5.12B) and maximum value profiles (Figure 5.12C) show asymptotic behaviour. The Weibull plot (Figure 5.12D) shows results clustering onto two line segments with Chapter 5. Scaling Break and Ozone Photochemistry 114 Figure 5.12: Ozone production (A), concentration (B), and maximum ozone concentration (C) for four initial VOC concentrations using the parabolic model with hyperbolic tail. Also shown is the Weibull transformed maximum ozone concentration fit by two line segments (D). the second segment having a positive, non-zero slope. Thus, even for a quadratic parameterization for production, a Weibull distribution produces a good fit to the corresponding maximum ozone curves. ' Let me summarize what-1 have accomplished so far.' I have found that the best starting point Chapter 5. Scaling Break and Ozone Photochemistry 115 for developing a simple model of ozone photochemistry begins with ozone production. I find that any model for ozone production should initially increase, reach a maximum and then asymptoti-cally decrease. Furthermore, the parameterization should have a transition to a second functional relationship in order to produce a scaling break. In addition, production should increase with in-creasing initial V O C concentration. Any production parameterization which has these properties will reproduce the key traits of the O Z I P R model output namely: • Ozone concentration and maximum ozone concentration curves will have an 's-shape'. • A scaling break will be observed when maximum ozone versus initial V O C concentration is Weibull transformed. • Maximum ozone versus initial V O C concentration curves which are well modeled by a com-posite of two Weibull distribution. To complete my characterization of ozone formation, I must still include a NOx dependence. 5.3.8 Production models with initial NOx dependence In this section I make explicit any NOx (and hence R) dependence on ozone production and gen-eralize the four properties outlined in Section 5.3.5. I start by examining ozone concentrations from a set of nine O Z I P R smog chamber simulations using the Stock urban speciation. Figure 5.13 shows the nine ozone curves plotted as a function of j(t). A l l simulations have R-values greater than 8. Along the first row, all simulations have initial an N O x concentration of 0.015 ppm, along the second 0.045 ppm and along the third 0.075 ppm. The first column of plots have a common R-value of 12, the second column 24 and the third 30. In each plot, I have also included a dashed vertical line at the approximate j-value where the concentration curve shows a slowing of growth. From these plots, a number of observations can be made: • A switch to a slowing of ozone concentration occurs at the same j-value for simulations with identical R-values; independent of both initial NOx and V O C concentration. In addition, increasing R causes the transition to occur sooner. • Ozone concentration at the time of switch is roughly constant for simulations with identical initial NOx concentrations; independent of initial V O C or R-values. In terms of production, this implies that for a given initial NOx concentration, switchover occurs for a fixed area under the production curve, independent of V O C or R. In addition, as initial NOx increases, ozone concentration at the switch increases. Chapter 5. Scaling Break and Ozone Photochemistry 116 R=12 V0C=D.1i NOx = 0.0\5 VOC = 0.36 = 0.015 R=12 VOC = 0.54 NOx = 0.045 150 225 R=12 VOC=0.90 NOx = 0 .075 360 300 R = 3Q V0C=0 .45 NOx = 0.015 I 150 225 R = 30 VOC=1.35 NOx1 = 0.045 R = 30 V0C = 2.25 NOx = 0.075 Figure 5.13: Ozone concentration as a function of cumulative NO2 photolysis rate for nine different initial NOx and VOC conditions. Dashed lines roughly indicate the slowing of the increase in ozone concentration. • For simulations with identical R-values, increasing initial N O x concentration increases final ozone concentration. In terms of ozone production, it now appears that P(03) should increase with both increasing R and NOx and that the timing of the regime shift is determined by initial R-value only. These suggests the following modifications to my original parameterization properties: Chapter 5. Scaling Break and Ozone Photochemistry 117 P r o p e r t y Ia: Larger R-values lead to greater peak P(03) levels. P r o p e r t y l b : Larger initial N O x concentrations lead to greater peak P(Os) levels. P r o p e r t y II: Larger R-values cause the transition (j*) to occur sooner. P r o p e r t y I l i a The total area under the P(03)-j(t) curve is a function of initial NOx only. P r o p e r t y I l l b : The area under the P(03)-j(t) curve at the transition time is a function of initial NOx only. P r o p e r t y I V : The resulting parameterization for ozone concentration must have R and j(t) to the same order. At first glance, the I E R model does not appear to satisfy these properties. For example, PSP production (Eq. (5.8)) shows neither an R nor an [NOx}0 dependence but only a V O C dependence. However, closer inspection shows the model does satisfy the above rules but, as a consequence of the way it scales maximum ozone with initial NOx and the way production depends on R, both the NOx and R dependence cancel - leaving what appears to be only a V O C dependence. This can be seen by rewriting the PSP production rate (Eq. (5.8), (5.9)) using R = [VOC)0/[NOx}0 as: Equation (5.17) now includes an initial NOx dependence as well as an R dependence. Production now increases with R (Ia) and [NOx]0 (lb), transition occurs sooner for higher R (II) and area under the production curve (both at the total (Ilia) and transition (Illb)) is a function of [NOx}0 (— p[NOx]0). Finally, integration of Eq. (5.17) shows PSP is a linear function of j and R (IV). 5.3.9 Links between scaling break and regime change So far in this chapter, I have set out to understand the scaling break in terms of the underlying chemistry. Along the way, I have developed two different but related ideas: the link between ozone production and the scaling break and the essential properties of ozone production. I summarize the latter first. The fundamental basis for describing ozone formation is in terms of ozone production. A realistic parameterization for production should show -P(Os) initially increasing, reaching a peak value and then decreasing. Corresponding ozone concentration curves will then show 's-shaped' behaviour. The parameterization should have two distinct regimes so that the corresponding Weibull plot has a scaling break. However, the scaling break corresponds to neither a local maximum in production nor a change in curvature - instead it stems from a change in regime. Regime change appears to occur once the cumulative production (i.e. ozone concentration) reaches a critical level. Ozone (5.17) Chapter 5. Scaling Break and Ozone Photochemistry 118 Regime ^ Change in ^ Shift in temporal ^ Shift in maximum Scaling Change 0 3 production 0 3 curve 0 3 profile Break Figure 5.14: Links between scaling break and regime change. production in the second regime should show a non-zero and asymptotically decreasing trend to generate a non-zero slope of the 'Weibullized data' after the scaling break. The link between scaling break and regime shift runs like this: A change in photochemical regime causes a fundamental shift in ozone production which alters the temporal variability of the ozone concentration curve. This affects the maximum concentrations which are used to produce the [C^maa; versus [ V O C ] 0 (or more generally [ 0 3 ] m a x versus R) curve which, when Weibull trans-formed, produces the scaling break. A schematic of this logic is given in Figure 5.14. This analysis gives rise to a new question: What is the physical basis for the regime change? For a given [NOx]0! why does regime shift occur at a fixed ozone level? I address this questions in the next sections. The second major finding of this chapter has been the development of a set of properties which characterizes ozone production. I have shown that the IER model (Johnson, 1984) can be thought of as a step function parameterization for smog production (P(PSP)) satisfying these properties. I have also used these properties to propose improvements to the I E R model. 5.3.10 W E X temporal ozone profile Before moving on, I present a parameterization for ozone concentration as a function of j(t) based on the W E X model. Based on the four properties for ozone production, the parameterization for maximum ozone concentration (Eq. (3.25)) can be extended, by adding a j-dependence whenever an independence occurs (Property IV): J ^ 0 ( W o , W - 7 ( I ^ Jav/KNO \3av/KNO 1 — exp -A R[ 0' (5.18) where J/0' = \j0. The corresponding ozone production relationship is: / [NOx] N a n /0-'N a~l P{Oz) Jav/kNO \jav/kNoJ "0' \ 0' Figure 5.15 shows 9 plots of ozone concentration versus j(t). Each plot has model output from the RADM2 mechanism using the Stock urban speciation, along with curves based on Eq. (5.18). I must mention that new W E X parameter values were not found specifically for Eq. (5.18) - the same values found during the regression of maximum ozone to initial V O C and NOx were used. The R = 12 and R = 24 plots correspond to those in Figure 5.13 but in order to get a wider exp -A R[ (5.19) Chapter 5. Scaling Break and Ozone Photochemistry 119 variety of initial conditions, I have replaced the R = 30 plots with three simulations below the ridgeline with R = 6. Except for the low j?/low NOx plots (R = 6 and [NOx]0 = 0.015,0.045 ppm), Eq. (5.18) shows good agreement with the model output. In many cases, Eq. (5.18) does not match the transition time exactly but does manage to be within ±10% j*. Notice that the final ozone concentrations are in close agreement with the model output - this is to be expected since these maximum values were the ones used in the regression of the W E X parameters. Figure 5.15 can be compared with smog chamber experiments used to validate the R A D M 2 mechanism. Figure 5.16 shows ozone concentrations during a smog chamber study experiment conducted at the State Wide Air Pollution Research Centre (SAPRC) in Riverside, California. Also included is the simulated ozone concentration using a version of R A D M 2 model which has been modified to include expected chamber effects. The simulation started with 0.476 ppm of NOx and 17.79 ppm of a complex mixture of reactive organic species (Carter and Lurman, 1991). From the Figure, the level of agreement between R A D M 2 and the data appears to be of the same order as Eq. (5.18) and R A D M 2 . 5.4 Feedback Mechanisms and Ozone Photochemistry In this section I explain the chemistry behind the regime change. While ozone production results from the integrated effect of a complex set of photochemical processes, Jeffries and Tonnesen (1994) suggest that it should be viewed as the interaction of two competing cycles each driven by sunlight: a radical driven organic cycle and an inorganic NO-cycle. It is the interaction of these cycles that leads to ozone production. I will describe these cycles from a slightly different perspective - using positive and negative feedback loops - and show that it is the interaction of the feedback loops that leads to the scaling break. 5.4.1 Positive Feedback Loop In section 5.3.4, I showed that for a simplified set of reactions, PSP production was proportional to the product of peroxy radical concentration times NO concentration (Eq. 5.14). In a similar vein, Sillman et al. (1990) argue that ozone production is proportional to the rate of OH' attack on VOCs: P(03) ~koH[OH'}[VOC} (5.20) Equation (5.20) implies production increases when OH' concentration increases. However, as mentioned in the introduction, a major source of OH' radicals is the photolysis of ozone (i?4 and i?5). Hence P(03) increases when ozone concentration increases. Thus we can say that ozone is an Chapter 5. Scaling Break and Ozone Photochemistry 120 R=6 VOC = 0.09 NOx = 0 .015 R = 6 V0C = 0.27 NOx = 0 .045 R = 6 VOC = 0 .45 NOx = 0 .075 3 5 0 3 0 0 R=12 VOC = 0.18 NOx = 0 .015 R = 1 2 VOC=0.54 NOx = 0 .045 R=12 VOC=0.90 NOx = 0 .075 R = 24 V0C = 0.36 NOx - 0 .015 1 5 0 KO-JJNM'H R = 24 V 0 C = 1 . 0 8 NOx = 0 .045 Figure 5.15: Ozone concentration versus time for a series of nine smog chamber simulations. Solid lines represent model output using the RADM2 mechanism (Stockwell et al., 1990) and circles represent results based on Eq. 5.18. autocatalyst in its own production i.e. ozone production increases as ozone concentration increases. This is analogous to saying: It takes money to make money. Figure 5.17 depicts ozone production as a positive feedback mechanism. In this schematic, ozone Chapter 5. Scaling Break and Ozone Photochemistry 121 •. Tirot,Mla : Figure 5.16: Ozone concentration versus time for SAPRC smog chamber simulation ECS37. Dots are smog chamber observations and the solid line is model output using the RADMS mechanism (Stockwell et ai, 1990). Taken from Carter and Lurman (1991). photolyzes to produce OH* radicals which attack V O C s to produce peroxy radicals. These convert NO to NO2 which then photolyzes to produce ozone. Note that each ozone photolysis can produce two OH' (reaction i?5) and each OH' can initiate two NO-to-N02 conversions. Furthermore, since the second NO-to-N02 conversion (not shown in Figure 5.17), reproduces the OH', the original OH' can attack even more VOCs , leading to further ozone production. 5.4.2 Negative Feedback Loops Positive feedback loops cannot continue indefinitely. At some point, these amplifying processes uncover stabilizing mechanisms that limit growth. For ozone production this happens with the production of NOz. A n interesting aspect of ozone production is that initial NO must first be converted to NO2 before ozone levels rise since surplus NO quickly titrates ozone (R2). Thus ozone concentrations rise in response to elevated NO2 concentrations. Furthermore, high ozone levels lead to elevated OH' levels (R4 and R5). However, high OH' and NO2 concentrations favour the formation of nitric acid (R9) - on average OH' reacts with NO2 5.5 times faster than with V O C s (Seinfeld and Pandis, 1998) - leading to increased HN03 production (P(HN03)). To see the effects of P(HN03) on the system reactivity, I have plotted in Figure 5.18 instantaneous NO2 and HN03 concentration as Chapter 5. Scaling Break and Ozone Photochemistry 122 P ( 0 3 ) [ 0 3 ] [OH*] [N0 2] > [H0 2M Figure 5.17: Ozone production builds ozone concentration. Photolysis of ozone gives rise to elevated hydroxyl con-centrations resulting in increased attack on VOCs and enhanced peroxy concentrations. These radicals convert more NO to NO2 which leads to greater ozone production. Because each ozone photolysis can produce two hydroxyl radicals and each OH' can oxidize many NO molecules, a small initial amount of ozone can lead to a large final concentration. well as the fraction of OH* that react with V O C (denoted as foH+voc) as a function of. j using the R A D M 2 (Stockwell et al., 1990) mechanism and the Stock urban speciation with [ V O C ] 0 = 1.08 ppm and [N0x]o = 0.045 ppm . Initially, both the N02 concentration and foH+voc increase as the system reacts. However, NO to NO2 conversions increase NO2 concentration to a point where N02 competes with the V O C s for the OH' radical causing a decrease in foH+voc and an increase in HNO3 concentration - effectively lowering the reactivity of the system. Finally, the continued removal of N02 via HNO3 production results in sufficiently low NOx concentrations that NO2 no longer competes effectively for OH'. This is marked by an increase in foH+voc and by a slowing of the increase in [HNO3]. The dynamics of the system at the resulting low NOx concentrations (discussed in the next section) is paramount to understanding the regime change (and hence the scaling break). To summarize, as ozone production begins to show rapid growth, it produces conditions favourable for nitric acid production. This production removes N02 and ultimately slows ozone production. This negative feedback loop is schematically sketched in Figure 5.19. Chapter 5. Scaling Break and Ozone Photochemistry 123 / '.[NO.) [HNOj] 0 l_i „...-• I 10.80 0 60 120 180 240 300 i Figure 5.18: The effects of HNO3 production on the reactivity of a photochemical system. [NO2], [HNO3] and foH+voc versus cumulative NO2 photolysis rate j for an OZIPR simulation using the RADM2 mech-anism (Stockwell et al., 1990) and the stock urban mixture. P(OJ [03] [N02] [OH'] > [HNOJ Figure 5.19: Negative Feedback loop for ozone production. As ozone levels rise, more OH' is produced via ozone photolysis. High OH' concentration coupled with high NO2 concentration favours HNO3 formation which removes N02; lowering ozone production. 5.5 Scaling Break and Low-NOx chemistry The main objective of this chapter is to show that the observed scaling break represents a change in chemical process. To this end, I have shown that the scaling break stems from a change in the temporal variability of ozone production. To understand this variability, I have presented ozone Chapter 5. Scaling Break and Ozone Photochemistry 124 photochemistry as a dynamical system which is initially controlled by a strong positive feedback mechanism. I have then shown that as a result of this positive feedback, conditions are created which awaken a self-regulating negative feedback loop. I am now in a position to show that this negative feedback loop creates conditions favourable to a second negative feedback loop and that the switch to this new loop represents the fundamental change in chemical process that causes the scaling break. 5.5.1 Low-NOx chemistry In Figure 5.18, I showed that as N02 and OH' concentrations rise, HNO3 production follows suit which slows ozone production by removing NOx from the system, and, in the absence of fresh NOx emissions, N O x concentrations become very low. This sets up conditions similar to those found in the remote troposphere where N O x is the rate limiting precursor to ozone production (Seinfeld and Pandis, 1998). For clean background conditions over the Pacific ocean, L iu et al. (1992) have shown that NO concentrations play a critical role in determining if ozone is produced via: HO\ + NO -> N02 + OH' (R7) RO\ + NO -* N02 + RO' (R12) (followed by N02 photolysis (Rla) and ozone formation (i?3)) or if it is consumed via: 0 3 + hu - 0(lD) + 02 (R4) 0(lD) + H20 -> 20H' + 02 (R5) H0'2 + 0 3 -» OH' + 202 (R17) Now, I have been modeling ozone formation in a smog chamber, with elevated V O C levels. While such elevated levels are not found in the remote troposphere, I believe that in a low-NOx environment, both the smog chamber and remote troposphere are controlled by the same processes. To prove this assertion, I examine the NOx limiting behaviour using Oi / ' - cha in length. In essence, when NO is low, the OH '-chain length is low because radicals are not propagated efficiently via R7 and R12, so that ozone photolysis can be a net loss for ozone production. For example, while ozone photolysis can produce as many as two OH' radicals, and even if most of these react with VOCs to produce HO' and RO' radicals, without sufficient NO to propagate the radicals and produce N02, peroxide producing reactions (R8A&B) take place and terminate the oxidation chain. In addition, as HO' concentrations build up (via OH' + VOC reactions), reaction 7217 becomes important and presents a new sink for ozone. Chapter 5. Scaling Break and Ozone Photochemistry 125 0 60 120 180 240 300 0 60 120 180 240 30C j j Figure 5.20: Loss of odd oxygen by various pathways for a RADM& (Stockwell et al., 1990) using the Stock urban speciation (A) with the corresponding OH'-chain length (B). In Figure 5.20A, I have plotted the percent of odd oxygen loss (LOx) versus j for the R A D M 2 (Stockwell et al., 1990) simulation of the previous section. I consider the loss of odd-oxygen (Ox = 0 3 + N02 + 2NOI +QQ-D) + 0(3P) + HNOA + 3N205 + PAN) in this circumstance because R5, R17 as well as R9 (formation of nitric acid) are all losses of odd-oxygen. I have partitioned LOx into five categories: i?5, R17, R9, various reactions involving the nitrate radical and other miscellaneous reactions. From this Figure, initially the principle loss of odd oxygen is via nitric acid formation (while the 'other' loss is high at the simulation start, in absolute terms it is quite small and does not represent a significant process). As the system reacts, a point is reached where all of the five categories provide significant avenues for loss. After which, losses via O 3 + HO' and O 3 -f hu dominate. To show that the loss of ozone via R3 and R13 does not lead to significant ozone production (via the feedback loop discussed in section 5.4.1), in Figure 5.20B, I have plotted the Oif ' -chain length as a function of j. From this Figure, it can be seen that the chain length is very close to 1.0 for j > 150, suggesting that few OH' radicals are recreated and RA and R17 do indeed represent losses. This supports the assertion that, like the remote troposphere, under low-NOx conditions, ozone loss via photolysis and HO' emerge as important processes. These new processes define a funda-mentally different regime that I now show gives rise to the scaling break. Chapter 5. Scaling Break and Ozone Photochemistry 126 P(03) [ O J [OH*] [OJ - A > [HO'] Figure 5.21: Second controlling or negative feedback loop for ozone production. Ozone photolysis leads to new OH' radicals which, after VOC attack, produce HO' radicals. These react with ozone; lowering ozone production. 5.5.2 Low-NOx negative feedback loop The loss of ozone at low-NOx to R17 represents another controlling or negative feedback loop for the photochemical system. I describe this loop as follows: initial ozone production leads to increased ozone concentrations. High ozone levels lead to high OH' concentrations which in turn lead to an abundance of RO' and HO' radicals. This HO' then titrates some of the abundant ozone; slowing ozone production. The cycle is schematically drawn in Figure 5.21. 5.5.3 Scaling break and governing chemical processes To summarize, a shift in processes governing ozone production, brought on by low NOx conditions, leads to a marked reduction in ozone production. This change in production manifests itself in the temporal variability of ozone concentration and is most evident in the maximum values. But what determines whether low NOx environment will occur? Property 2 suggests a mixture's R-value does. A n aside on the significance of R R, is the ratio of two quantities: n=[voc\o [N0x)o and to understand its significance consider the denominator: in order to reach the low NOx envi-ronment, (almost) all the initial N O x must be converted to NOz. Larger [NOx}0 implies more NOx to process. However, for the numerator, increasing [ Y O C ] 0 leads to ozone levels rising sooner and a Chapter 5. Scaling Break and Ozone Photochemistry 127 Shift in temporal profile of ozone > curve Change in regulating Low NOx feedback mechanism * concentration Figure 5.22: Relationship between scaling break and underlying photochemical processes, (arrows imply 'caused by') quicker conversion of N O x to NOz (see Figure 5.3). Thus the ratio of [ V O C ] 0 to [NOx]0 measures the processing rate for N O x to the amount of NOx to process - a quantity that varies inversely with time. Thus, I suggest that R can be thought of as a surrogate for time; a finding consistent with ozone production Property IV which indicates that R and j always appear to the same order in the parameterization of ozone concentration. And finally, j3 can be thought of as a characteristic size for this time scale. And now, I can finish drawing the link between the scaling break and the governing chemical processes. The ratio R, a measure of the time necessary to process a fixed amount of NOx, deter-mines whether a mixture of V O C and N O x wil l produce a low N O x environment before the end of irradiation. As I have already pointed out, in the low-NOx environment, ozone production slows; reducing maximum ozone concentrations. As a result, when maximum ozone concentrations are plotted as a function of R and Weibull transformed, a scaling break is observed. Figure 5.22 gives a schematic of the links between scaling break and regime shift. I must point out that the scaling break is also observed when [03,}max/[NOx}g versus R is Weibull transformed. In the next chapter, I explain the significance of ratio. 5.6 Feedback Loops and the similarity relationship I finish the analysis of ozone formation based on feedback processes by qualitatively describing the shape of the similarity curve. At the origin, where R & 0, the similarity relationship has low maximum ozone concentrations.6 As mentioned in Section 5.2.1, ozone is formed only after significant NO has been converted to N02. As a result, for a V O C / N O x mixture with excess NOx (low R-values), a large amount of NO must first be converted to N02 • B y the time all the NO has been converted, N02 photolysis rate may be well past its maximum and only a small amount of 6 A c t u a l similarity relationship relates [Oz}max/[NOx]1 to R which is equal to (within a constant) [Oz\max/{Oz]uu where [Os] u;t is the ultimate ozone that can be formed for a given amount of N O x . - .. . . Change in way Scaling break JL. > maximum ozone p increases with R Chapter 5. Scaling Break and Ozone Photochemistry 128 ozone may be produced. Low ozone production leads to little radical initiation and photochemical process cannot tap into the positive feedback (autocatalytic) mechanism. So, at low R-values, maximum ozone concentrations are low. Furthermore, there is little increase in maximum ozone concentrations as R-values increase until ozone is produced early enough in the simulation. I call this slow increase a lag phase. ~ ' • 5.6.1 Acceleration Phase Closely following the lag phase, is an acceleration phase, where the positive feedback mechanism accelerates ozone production. In this phase, a greater relative abundance of V O C to NOx means relatively less NO to convert and OH' + N02 termination reactions (i?9) are less likely to occur (because VOC + OH' reactions are now more likely). This allows NO-to-N02 conversions to occur sooner leading to greater N02 photolysis and greater ozone production. This in turn triggers more radical initiation, accelerating V O C attack and ozone production. The acceleration phase is seen as a sharp rise in maximum ozone over a small change in R-values. 5.6.2 Low-NOx Saturation Phase Finally, for simulations that have sufficiently high initial V O C to N O x ratios, the positive feedback mechanisms occur so soon that HNO% production removes enough N O x to push the system into a low-NOx regime. This results in a slowing of ozone production which in turn affects ozone concentration. I call this the low-NOx saturation phase. In Figure 5.23, I have sketched a similarity relationship and labeled the lag, acceleration and low-NOx saturation phases. I finish the analysis by comparing the scaling break with: the ridgeline, two processed based variables (OH'-chain length and fraction of HO' that reacts with N O (fH02+No)), a physical quantity (OH' reactivity (fc/vo)) and two environmental variables (temperature and cumulative N02 photolysis rate). I start with the most obvious link: the ridgeline and 0. 5.7 Scaling Break and Ridgeline Before exploring the relationship between the scaling break and ridgeline, the concept of ridgeline must be more carefully defined. As it will be shown below, while the ridgeline is a familiar concept, unfortunately it can be defined in more than one way. Definitions can be made from three points of view: a regulatory (or sensitivity), a geometric (or mathematical) and a process based (or physical). Other definitions exist (Sillman, 1999) and since each has a specific objective, each produces a Chapter 5. Scaling Break and Ozone Photochemistry 129 Figure 5.23: Generalized ozone profile showing. Lag, Acceleration and Low-NOx regimes. Also shown is the shape of the similarity relationship in the absence of a regime shift (dotted line). different 'ridgeline'. I will show that the scaling break is most closely aligned with the process based point of view. 5.7.1 R e g u l a t o r y B a s i s f o r R i d g e l i n e Because of the importance of NOx-inhibition, a ridgeline based on ozone sensitivity to NOx is of paramount importance to regulators. Such a ridgeline should divide an ozone response surface into two regions: one where high N O x levels limit radical propagation to such an extent that increasing NOx concentrations decreases ozone levels and the other where ozone is insensitive to changing V O C concentrations but decreases with decreasing NOx. Mathematically, this requires finding the location on the response surface where ozone shows no change to changing N O x 7 i.e.: ^[03] max n Woxjo = 0 (5-21) Using the W E X model, the location where ozone sensitivity to changing N O x concentration vanishes is given by: d[NOx\0 \Jav/kNOj which requires: [af(R) - Rf'(R)} = 0 (5.23) Since the solution to 5.23 is a function of R only, it defines a straight line on an isopleth diagram. But R = 0 is not a solution to Eq. (5.23), indicating that the line R = 0 does not coincide with a 7 W h i l e a similar definition could be made using V O C sensitivity, this definition is more broadly applicable to the remote troposphere where ozone is N O x sensitive (Sillman, 1999). Chapter 5. Scaling Break and Ozone Photochemistry 130 NOx-sensitivity based ridgeline. Rather, results from Chapter 4 suggest that the scaling break lies above the ridgeline on an isopleth diagram. 5.7.2 Geometrical Basis for Ridgeline The advantage of a ridgeline definition based on ozone sensitivity to initial NOx concentration is ease of identification on an isopleth diagram. However, from a purely geometric point of view, this definition does not put the ridgeline in the right spot. That is, a hiker would not locate the ridgeline in this manner, but instead would set the ridgeline along the uphill path (gradient) showing the smallest slope. However, even by this definition, the ridgeline may not be correctly placed for some geometric figures. A better definition is one that sees the ridgeline as the location where contours show the maximum curvature. It turns out that these two geometric definitions put the ridgeline in different locations and both prove difficult to evaluate mathematically (see Appendix F). Finally, I would like to mention that a parameterization for the similarity relationship using only a single Weibull function, will clearly not produce a scale break but still produces a 'ridgeline' when used to produce an isopleth diagram. This further suggests that the 'ridgeline' is mainly a geometric property of a set of curves and does not necessarily reflect any change in chemical process. 5.7.3 Process Basis for Ridgeline Finally, one can also formulate a definition based on the photochemical processes (Seinfeld and Pandis, 1998): That combination of initial V O C and NOx at which all the N O x is converted into nitrogen-containing products by the end of the simulation so that there is no NO left to participate in NO-to- iV02 conversions nor any N02 left to photolyze. This definition, while chemically precise, makes ridge identification difficult on an isopleth di-agram. However, this definition corresponds closely with the concepts used to explain the scaling break. There, however, the scaling break defines the combination of initial V O C and NOx at which most of the N O x gets converted to NOz with little free NOx available for NO-to-N02 conversions or photolysis. Thus the scaling break coincides most closely with a process based ridgeline. However, Sillman (1999) points out that the actual split between V O C and NOx-sensitive is a broad transition region rather than a sharp line. Following this reasoning, I propose that the most natural division of an ozone response surface is into three regions: V O C sensitive (or NOx-saturated) region, ridge or transition region and NOx-only scaling region. I suggest that 0 marks. the boundaries the VOC-sensitive/ridge regions. The NOx-only scaling region identifies that part Chapter 5. Scaling Break and Ozone Photochemistry 131 Species P R//3 at O-f/'-chain Maximum A L D K E T OLI OLT X Y L E T O L U HCHO Stock Arb 5.2 15.3 4.5 4.2 5.3 10.1 4.2 9.4 8.5 1.06 0.98 1.11 0.96 1.26 0.99 1.19 1.06 0.94 Table 5.1: Scaling break and R-value of OH-chain maximum for seven RADM2 classes and two urban mixtures. of the response surface where maximum ozone concentration is independent of [ V O C ] 0 . In the next chapter, I propose a means of determining the boundary of this region using the slope of ozone isopleths. 5.8 Relationship between Scaling break and other parameters To end this chapter, the scaling break is compared with the OiJ ' -chain length; the fraction of HO' that reacts with NO; the OH '-reactivity; temperature and cumulative N02 photolysis rate. 5.8.1 Scaling break Ridgeline and Chain Length (XOH) Both Seinfeld and Pandis (1998) and Tonnesen and Jeffries (1994) suggest that the OH'-chain length is a maximum slightly above the (sensitivity based) ridgeline - in roughly the same location as the scaling break. To examine any possible connection between chain length and the scaling break, OZIPR simulations were rerun using process analysis (Tonnesen, 2000). For each simulation, average OH'-ch&in length (XOH) w a s calculated. It was found to depend only on R as evident in Figure 5.24A. For each R A D M 2 scaling class, the R-value at maximum XOH (ROH) w a s determined and the ratio of ROH to (3 is given in Table 5.1. From this table we see that there is a close correlation between the location of OiJ*-chain maximum and the scaling break, with most values within ±10% of unity. The biggest exceptions are X Y L E and H C H O , which show OH'-ch&'m maximum well below the scaling break (it must be noted that while both /HO2+NO a n d OH'-chain length appear to be functions of R only, there is still some scatter in the model output leading to small uncertainty in actual location of both the scaling break and O-ff'-chain maximum). The deviation of both X Y L E and H C H O suggests that while the scaling break and maximum OH'-ch&in length are related, they do not occur at the same .R-value. Chapter 5. Scaling Break and Ozone Photochemistry 132 0.0 12 12 R//8 Figure 5.24: OH-chain length (A) and }HO2 (B) for the Stock urban mixture as a function of R//3. Species 0 IHQ2+NO SX R = P ALD 5^ 2 096 KET 15.3 0.97 OLI 4.5 0.95 OLT 4.2 0.97 XYLE 5.3 0.89 TOLU 10.1 0.95 HCHO 4.2 0.92 Stock 9.4 0.96 Arb 8.5 0.94 Table 5.2: Fraction of HO* that reacts with NO scaling break for various RADM2 classes and mixtures. 5.8.2 Scaling break and fraction of HO' radicals that react with NO {JHO^+NO) The fraction of HO' radicals that react with NO (fH02+No) measures the extent to which HO* radicals react with NO (in potential ozone producing reactions) or with themselves (in radical termination reactions). A value of JHOI+NO below 1.0 implies an over-abundance of HO* relative to available NO; suggesting that JH02+NO can be used to infer when production is governed by low-NOx chemistry. Process analysis was used to calculated average /HO2+NO for each of the 7 scaling R A D M 2 classes and the two urban mixtures. Again, it was found that /HO2+NO scaled with R (Figure 5.24B) and the f-values, for the R A D M 2 scaling classes, at R — 0 are given in Table 5.2. The Table shows that over a wide range of [3 values, there is a narrow range of /H02+NO values at the scaling break (with the exception of X Y L E ) indicating that the scaling break coincides with a fixed ratio of !H02+NO (~ 0.95) largely independent of V O C species. Chapter 5. Scaling Break and Ozone Photochemistry 133 16TKET Ol , , , I , , • i . . . i 0 4 . 0 X 1 0 4 8 . 0 X 1 0 4 1 . 2 X 1 0 5 k0H - pprrrV F i gure 5.25: Scaling break as a function of OH-reactivity for eight RADM2 classes and non-linear line of best fit. 5 . 8 . 3 Scaling break and OH' reactivity (kern) One might expect that V O C s with higher OiJ'-reactivities would show lower 0 values i.e. with a higher OiT'-reactivity, more peroxy radicals can be produced (through OH* attack), for a given [V0C]o, leading to low-NOx conditions (via NO-to-N02 conversions and HN03 production) at lower R-values. However, many V O C s photolyze to produce their own (organic) source of radicals that can also initiate ozone formation. Such V O C s should have a lower 0 value than would be expected based on their OiJ'-reactivity alone. Figure 5.25 shows OiJ'-reactivity versus 0 for the seven scaling R A D M 2 classes. In addition, a trend line through the results has been drawn. A non-linear model was chosen to reflect the underlying non-linear feedback mechanisms involved in ozone formation. This line has 0 decreasing as reactivity increases. From the Figure, both H C H O and OL2 have 0 values lower than can be explained by their Cff'-reactivity. Since formaldehyde readily photolyzes to produce hydroperoxy radicals, this photolytic source of radicals supplements its low OiJ'-reactivity. OL2 produces 1.6 H C H O molecules every time its peroxy radical reacts with NO (in addition to 0.2 A L D and 1.0 HO*) which appears to be more than the other alkenes Both T O L and OLI have higher values than would be expected from their reactivities. Neither one directly photolyzes and their peroxy radicals ( T O L P and OLIP respectively) produce few carbonyl compounds when converting NO to N02. Chapter 5. Scaling Break and Ozone Photochemistry- ISA 5.8.4 Scaling Break and environmental conditions In the previous chapter, I showed that the 0 dependence on total actinic flux (J) and temperature was negative i.e. 0 decreased when either J or T increased (see Figure 4.16). I now explain this dependence. Increasing total actinic flux results in more N02 photolysis and enhanced ozone production. Higher ozone levels and increased photolysis lead to greater radical production. This leads to more NO-to-N02 conversions, a quicker increase in N02 followed by NOz formation. Therefore an initial mixture of V O C s and NOx, with R < 0, might reach low-NOx conditions when J is increased. Thus an increase in J leads to a decrease in 0. Similarly, since most reaction rates increase with temperature (Levine, 1978), the net effect of increased temperature is to speed up the oxidation process and allow V O C sensitive conditions to become NOx-sensitive. 5.9 Summary This chapter has provided a mechanistic understanding for the observed scaling break. I started by describing ozone formation in terms of ozone production and showed that the break stems from a regime shift in ozone production. This shift can be interpreted as a change in negative (or controlling) feedback loops associated with low-NOx conditions. Along the way, I outlined four properties that govern ozone production for V O C / N O x mixtures. Both the W E X and IER (Johnson, 1984) are examples of models which parameterize these properties. I also used the properties to parameterize the temporal variability of ozone concentration with the W E X model. The scaling break coincides closely with a process based definition of ridgeline and, in fact, could be used to define a new 'ridgeline'. The magnitude of the scaling break appears to be a complex function of the Oi7"-reactivity and the ability of the V O C to produce radicals (either directly or through the photolysis of secondary carbonyl compounds). The scaling break is also closely related to a maximum in Oi l ' - cha in length and a specific value of /H02+NO- The next chapter examines the remaining W E X parameters from a similar mechanistic approach. Chapter 6. Chemical Processes and the WEX Parameters 135 C h a p t e r 6 Chemical Processes and the WEX Parameters 6.1 Introduction In this chapter, I explore the relationship between the remaining W E X parameters (7,0,0:1,0:2,A) and photochemical processes. As a reminder, the W E X model is: [ ° 3 W = (WOxlA* jav fk.NO \jav/kNO ) f(R) = l - «p{-A(^) where a(R) = " 2 ~ a i tanh(fl - 0) + a i + °"2 (6.1) While it is tempting to speculate that each parameter is controlled by a specific chemical reac-tion, I will show that groups of reactions, which form sub-processes within the larger photochemical system, determine parameter size. As a result, it is best to view W E X parameters as represent-ing the integrated effects of various reaction groups. I begin by describing how each parameter arises in the model; grouping them into two classes: scaling and geometric. The scaling parameters are a and 7. By scaling, I mean that these parameters are used in the scaling analysis to derive the similarity relationship (and define a power-law relationship) whereas the others are used in its parameterization. Scaling parameters One way to view the similarity relationship is as a family of curves where each simulation belongs to one member of a family. Each curve is distinguished by its initial N O x concentration. In other words, each curve relates [ 0 3 ] m a x to R along an isomephitic path. The parameter a is used to scale [ 0 3 ] m a a ; , along each curve, so that the resulting family of maximum ozone concentrations produces a common variability (the similarity relationship) independent of initial NOx concentration. Thus a measures the dependence of maximum ozone concentration on initial NOx at any given R-value. Chapter 6. Chemical Processes and the WEX Parameters 136 The other scaling parameter, 7, used to normalize the similarity relationship, relates peak maximum ozone concentration (the greatest value of maximum ozone for any given combination of initial V O C and NOx) to initial NOx concentration - a global 'NOx-efRciency'. Geomet r ic Parameters The four geometric parameters (ai,a2,/?,A), schematically shown in Figure 6.1, characterize two line segments in the Weibull plane; o.\ and a2 give the two slopes while 0 and A locate the intersection of the two line segments. Sensi t iv i ty A n a l y s i s To examine the link between chemistry and W E X parameter values, two types of sensitivity anal-ysis were performed. The first is a straightforward comparison between two isopleth diagrams; one produced using a set of 'baseline' W E X parameters, the other produced with one 'baseline' parameter altered (to produce a 'modified' parameter set). While Chapter 4 shows a wide range of parameter values for the different V O C classes and V O C mixtures, I have chosen the OLT (the R A D M 2 propene surrogate) parameter values as a standard (or baseline). From these baseline values, I individually perturb the parameter values (with perturbation size guided by the parameter range found in Chapter 4) and then compare isopleth plots. Table 6.1 summarizes the baseline and altered parameters values. In all, five analyses where made, one for each parameter. Chapter 6. Chemical Processes and the WEX Parameters 137 Parameter Baseline Modified Value 7 10.0 5.0 a 0.6 0.45 ai 2.0 4.0 0.75 0.33 P 4.0 8.0 A 1.0 2.0 Table 6.1: Baseline and Modified parameters for WEX generated isopleths. The second investigation involves a sensitivity analysis of the R A D M 2 chemical mechanism in order to reveal possible relationships between specific reaction rates or reaction products and corresponding W E X parameters (after regression to the similarity relationship). This analysis is problematic; a single change to the mechanism (say a change to a specific reaction rate or reaction product) often produces changes to several W E X parameters. The resulting modified mechanism may not accurately represent ozone formation, however the intention is to explore W E X parameter sensitivity to R A D M 2 reaction rates and reaction products. 6.2 WEX Scaling Parameter a The first W E X parameter to study is the scaling parameter a. It has the property of collapsing maximum ozone concentrations, taken along different isomephitic paths (when plotted as a function of R), onto a common curve. In the extreme, when a = 0, maximum ozone along each isomephitic path is independent of initial NOx concentration and ozone isopleths become lines of constant R. However, such an situation is unrealistic - the range of a-values, found in Chapter 4, appears to lie between 0.48 and 0.75. Finally, Eq. (6.1) shows as a increases, maximum ozone concentration, along each path, becomes more dependent on underlying.NOx concentration. 6.2.1 NOx Inefficiency For all of the V O C and V O C mixtures analyzed in Chapter 4, the value of a was less than 1.0; implying that a doubling of initial NOx concentration does not lead to a doubling of maximum ozone concentration. Thus a quantifies the extent to which an increase in N O x is not matched by an equal increase in maximum ozone (at similar R-values) - a 'NOx-inefficiency' To understand this inefficiency, consider a simulation using the R A D M 2 (Stockwell et al., 1990) aldehyde surrogate A L D where, in the N L R , the following maximum ozone concentrations are Chapter 6. Chemical Processes and the WEX Parameters 138 observed: [Oslmax = 200 ppb when [NOx]D = 40 ppb (03)max = 402 ppb when [NOx}0 = 160 ppb (6.2) Thus a four fold increase in initial NOx, results in only a doubling of maximum ozone. This 'inefficiency' is related to an increase in importance of NOx reactions that do not lead to ozone production (Jeffries, 1995). Consider, for example, the following reactions, important in the N L R : 03 + N02 -> NO' + 02 (R18) NO' + hu -* NO + O2 (R19) NO' + aldehydes -» HN03 + ACO' (R20) where NO', ACO' are the nitrate and acetylperoxy radicals. Wi th higher initial N O x concentra-tions, reactions R18, R19 and R20 are more likely to occur. Reaction R18 provides a sink for both ozone and N02 while reactions i?19 and i?20 are a sink for NO2 only. A l l three side reactions cause ozone efficiency (ozone produced for each NOx consumed) to decrease as N O x increases, a process consistent with field studies (Liu et al., 1987). I find that increasing N O x changes the reaction pathways in such a way that the resulting 'NOx-inefficiency' not the same for all R-values (remem-ber, I have chosen a value for a, the 'NOx-inefficiency', which fits the model output best around the scaling break). A t low R, a better fit to the 'scaled data' often has a « 0.2, indicating that for simulations with low R-values, doubling initial NOx results in little if any increase in ozone. It must be remembered that at low R-values, with the photochemical system radical limited, substantial NOx remains unprocessed at simulation end. Therefore, it is not surprising that maximum ozone shows little response to increased initial NOx. For very large R-values, I have found that maximum ozone often scales with an exponent closer to 0.5; suggesting that the system becomes less efficient as reactions like R18, R19 and R20 become important. The scatter in the similarity relationship, observed in region lib (Figure 3.9), likely stems from a change in the 'NOx-inefficiency'. 6.2.2 Range of a-values The correct value for a has been debated ever since Johnson first proposed that SP = A.l[NOx]0 in his IER model (Johnson, 1984).1 This linear relationship implies a constant 'NOx-inefficiency' and has been questioned by Blanchard et al. (1999) who suggest, based on numerical simulations using 1 Again, SP refers to smog potential which-includes ozone produced as well as NO converted to other forms of NOy. Thus SP is closely associated with odd-oxygen (Ox). Chapter 6. Chemical Processes and the WEX Parameters * 139 a typical urban mixture of VOCs , it be replaced by a non-linear relationship with an exponent of 2/3 i.e.: SP = [NOxfJ3. Chang and Rudy (1993) have determined that for maximum ozone, the NOx-scaling exponent should be 1/2 i.e.: [ 0 3 ] m a x = j[NOx]0^2. While they arrive at their results using model simulations they also fit their model to smog chamber data. Finally, both Akimoto et al. (1979) (based on propene-NOx experiments) and Shen et al. (1977) (using cyclohexane experiments) also suggest a NOx-scaling exponent of 1/2. I find a shows the least variability among the W E X parameters suggesting that specific V O C chemistry plays only a minor role in its determination - a possible reason why Johnson (1984), Blanchard et al. (1999) and Chang and Rudy (1993) assumed it to be constant. I have found a ranges from a low of 0.48 (TOLU) to a high of 0.75 (HCHO). Both urban mixtures give a common value of 0.58 - midway between values found by Blanchard et al. (1999) and Chang and Rudy (1993). 6.2.3 Response surface sensitivity to a Ozone isopleths, using the baseline W E X parameter values, have been plotted in Figure 6.2A while Figure 6.2B shows ozone isopleths after reducing a from 0.6 to 0.45. The main difference lies in the transition region between V L R and N L R ; lowering a makes the transition more gradual. In addition, reducing a appears to slightly reduce maximum ozone concentrations (although mainly in the higher ozone regime). 6.2.4 Sensitivity of a to R A D M 2 modifications To investigate the relationship between the R A D M 2 mechanism and a, R A D M 2 was modified in an attempt to cause the greatest change in 'NOx-inefficiency' (while avoiding changes to the other parameters). The O L T class was used as the sole V O C in a set of smog chamber simulations using a modified mechanism. When O L T reacts with the OH' radical, R A D M 2 produces the O L T P peroxy radical. When this radical reacts with NO, the products include carbonyl compounds A L D and H C H O : OLTP + NO^ ALD + HCHO + HO\ + N02 (R21) When A L D reacts with the OH' radical, ACO* is formed: ALD + OH' -> ACO' (R22) which is the sole P A N precursor in R A D M 2 i.e.: ACOl + N°2 PAN (R15) Chapter 6. Chemical Processes and the WEX Parameters 140 F i gure 6.2: The effects of changing a on ozone response surface. Figure A shows maximum ozone concentration (in ppb) as a function of initial VOC and NOx concentration calculated using the WEX model and baseline parameter values. Figure B shows the resulting ozone isopleths (in ppb) after a reduction in a from 0.6 to 0.45 (while all other WEX parameters have been held constant). Parameter Original Modified 7 9.5 10.8 a 0.6 0.65 cu 2.2 2.2 C*2 0.72 0.82 P 4.2 4.7 A 0.92 0.7 Table 6.2: Comparison of OLT parameters for the original and modified RADM2 mechanism. Reaction (JR15) is a side reaction which consumes NO2 (and thereby preventing ozone formation (via Rla)) and increases 'NOx-inefficiency'. By making this reaction less likely, 'NOx-inefficiency' should decrease and hence a should increase. To test this hypothesis, R A D M 2 was modified so that only half an A L D molecule is formed from the O L T P + N O conversion (R21). OZIPR simulations were run with this modified mechanism and regressed to the W E X model. Table 6.2 shows the W E X parameters for O L T using the original and modified R A D M 2 mechanism. From the table we see a 10% increase in a. Wi th less A L D and ACO' produced, less mass runs through R15, the system is more efficient and the NOx scaling exponent is closer to 1.0. Notice, Chapter 6. Chemical Processes and the WEX Parameters 141 however, that there has been as large a change to both 7 (increasing) and A (decreasing) and a slight increase in 0. These multiple changes suggest that W E X parameters are sensitive to many aspects of the photochemical system and no single reaction controls an individual W E X parameter. For this reason, W E X parameter should be viewed at best as describing processes within the larger reaction system. 6.3 WEX Scaling Parameter 7 The W E X parameter 7 relates peak maximum ozone to initial NOx. i.e.: where [0 3 ] p e afc is the greatest maximum ozone concentration value for any combination of initial V O C and NOx. A higher 7-value means V O C s produce higher ozone maximum ozone concentrations for a given amount NOx. 6.3.1 NOz speciation and 7 For a mixture of V O C and NOx which becomes NOx-limited, most of the initial NOx is converted to NOz before simulation end so that [NOx]a [NOz]finai. Furthermore, peak maximum ozone concentration occurs for NOx-limited conditions so [ 0 3 ] m a x ~ [03\peak- Thus one might expect a relationship between 7, [ 0 3 J p e a f c and [NOz)finai similar to Eq. (6.3) to hold for simulations with R S> 0. Figure 6.3 compares 7 to [03}finai/[NOz}finai for 8 NOx-limited smog chamber simulations: the six R A D M 2 scaling classes and the two urban mixtures. In each case, there is a strong correlation between 7 and [03]max/'[NOz\finai as seen by the clustering of values along a common line above the 1 : 1 line. I use the link between ozone, NOz and 7 to describe the physical significance of 7. I will show that the magnitude of a V O C s peak ozone concentrations is determined by the way final NOz is partitioned. For example, V O C s which facilitate the conversion of NOx to P A N have lower 7-values than those that facilitate HNO3 production. Specifically, the largest 7-value is 40.6 (HCHO) while the smallest is 7.5 (ALD) . The products of the Otf'-attack on H C H O are HO' and C O , neither or which is a P A N precursor, while the product of 0i7*-attack on A L D is the acetylperoxy radical (ACO') - RADM2 ' s only P A N precursor. Furthermore, the relatively unreactive alkene OL2 has the second highest 7-value. In the R A D M 2 mechanism OL2 produces a large amount of H C H O upon oxidation i.e. every time the OL2P peroxy radical converts an NO to NO2, it produces 1.6 H C H O and only 0.2 A L D molecules. This can be compared with the alkene OLI ( 7 = 8.0), whose peroxy radical produces only 0.28 H C H O molecules but 1.45 A L D molecules 7 oc [^3Jpeafc [NOx]° (6.3) Chapter 6. Chemical Processes and the WEX Parameters 142 8 h 7 Ll i I , I i I _ , I , i I •7 8 9 10 1 1 12 7 Figure 6.3: Scatter plot of 7 versus Oz/NOz for six RADM2 classes and two urban mixtures. Also shown is the 1 : 1 line. Due to the large values for HCHO (-f = 39.1 and 03inax/NOzfi„ai) they have not been plotted. for every conversion. Figure 6.4 shows the speciation of final NOz for the 8 R A D M 2 classes and two mixtures in terms of HN03, P A N + T P A N , and ONIT. 6.3.2 Peak Ozone and P A N and HN03 Formation As noted in the previous section, V O C s which create conditions favourable for P A N formation have lower peak maximum ozone levels than those that favour nitric acid formation. Why? The answer lies in how these two nitrogen products form: ACO'3 + N02 -> PAN (R15) OH' + N02 -> HN03 (R9) While both reactions consume nitrogen dioxide, P A N production requires ACO* (produced from VOCs oxidation) while HN03 production requires OH' radicals whose production is relatively independent of V O C (and hence R-value). Since the main source of OH' radicals is the photolysis of ozone, HN03 production requires high ozone levels to produce sufficient OH' radicals necessary to consume all of the NOx. Thus, V O C s which do not produce P A N precursors (like HCHO) , must convert all NOz to HN03 and ONIT. This is consistent with Bowman and Seinfeld (1994) who, Chapter 6. Chemical Processes and-the WEX Parameters 143 ONIT (white) PAN (grey) H N 0 3 (block) OLT OLI TOLU X Y L E H C H O ALD KET Arb S t o c k RADM2 C l a s s F i gure 6.4: Speciation of final NOz (organic nitrate (outline), PAN (shade) and nitric acid (dark)) for seven RADM2 classes and two urban mixtures. using the SAPRC90 mechanism with an urban V O C mixture, find that P A N formation depends directly on a V O C s ability to produce, either directly or indirectly, the peroxyacetyl radical. In the N L R , with N02 in short supply, ozone concentrations must rise to high levels, in order to supply the necessary OH' radicals, before nitric acid will be produced. Low P A N production also explains why the R A D M 2 classes with two highest 7-values (HCHO and E T H E ) required 41 nodes - production of NOz and final consumption of NOx (through HNO3) is largely insensitive to V O C concentration and hence there is a large change in R-values between the scaling break and when maximum ozone scales with N O x only. 6.3.3 Gamma and Isopleth shape Figure 6.5A shows ozone isopleths based on the baseline W E X parameters and 6.5B shows those with 7 reduced by 50%. Both sets of isopleths have the same shape but those with the lower 7-value are not as tightly spaced. (I have changed the contouring interval from 50 to 25 ppb between figures to highlight the pure scaling nature of 7). In essence, changing 7 has the same effect as changing the isopleth labels. Chapter 6. Chemical Processes and the WEX Parameters 144 >v I i 1 1 1 1 1 1 1 1 1 1 I i i i I U . V J U ' . . . ' . . . I . . . I , , , I 0.00 0.15 0.30 0.45 0.60 0.00 0.15 0.30 0.45 0.60 VOC Concentration - ppmC VOC Concentration - ppmC Figure 6.5: The effects of changing 7 on ozone response surface. Figure A shows maximum ozone concentration (in ppb) as a function of initial VOC and NOx concentration calculated using the WEX model and baseline parameter values. Figure B shows the resulting ozone isopleths (in ppb) after a reduction in 7 from 1.0 to 2.0 (while all other WEX parameters have been held constant) 6.3.4 Var i ab i l i t y of 7 As mentioned above, 7 determines the highest possible ozone concentrations in the NOS regime. Johnson (1984) suggests that this value is independent of V O C species. In addition, both Blanchard et al. (1999) and Chang and Rudy (1993) do not suggest how this factor might depend on V O C species. I have found that 7 shows a great range of variability (from a high of 39.1 for H C H O to a low of 7.5 for A L D ) but is essentially constant for the two urban mixtures (7-values of 8.15 and 8.16). 6.3.5 7 R A D M 2 Exper iments The link between R A D M 2 chemistry and 7 is evident from the modified R A D M 2 mechanism used in Section 6.2. In this mechanism, reducing A L D production (and hence ACO* and P A N production) for every N O + O L T P reaction, increases 7. By reducing the propensity for P A N production, NOz must be created by means which require higher ozone concentrations. It must be mentioned that both P A N and HNO3 production do not appear to be the sole determinants of 7. The reaction Chapter 6. Chemical Processes and the WEX Parameters 145 VOC + O 3 , specific to alkenes, consumes ozone at high R-values. Since this reaction does not involve NOx, this ozone titration should not affect the 'NOx-inefficiency' (and hence a). To see how this reaction might affect 7, O L T simulations were run with a modified OLT + O3 reaction rate. Specifically, the R A D M 2 mechanism was modified so that the original reaction rate of 0.0166 ppm m m - 1 (at 25°C) was increased to 0.236 ppm min"1 (identical to the OLI rate). Table 6.3 shows the resulting W E X parameters for the original and modified mechanism. The biggest change is for 7 and A which have moved in opposite directions. As more mass runs through the OLT + O3 reaction, less net ozone is produced. The value of a is almost unchanged (0.60 versus 0.58) confirming that the OLT + O 3 reaction is not a strong determinant of a. 6.4 Geometric Parameter A The next parameter to study is A - the vertical coordinate of the scaling break in the Weibull plane. It measures the ratio of maximum ozone concentration when R equals 0 to the maximum in the NOS regime. This can be explained by making reference to the W E X model (Eq. (6.1)). In the NOx-only scaling region, f(R) ~ 1 and maximum ozone concentration is at its ultimate value: Since maximum ozone concentration in the NOS regime represents the highest ozone concentra-tion that can be achieved from a given initial NOx (subject to environmental conditions), A then quantifies the extent to which V O C s can continue to produce ozone once low-NOx conditions have been reached. V O C s (or V O C mixtures) with low A-values are not able to produce much additional and at the scaling break R — 0 So the ratio of maximum ozone at the break to maximum possible (or ultimate value) is: (6.4) Parameter Original Modified 7 9.5 7.8 a 0.6 0.58 a i 2.2 2.0 a 2 0.72 0.88 P 4.2 3.9 A 0.92 1.3 Table 6.3: Comparison of OLI parameters for the original and modified RADM2 mechanism. Chapter 6. Chemical Processes and the WEX Parameters 146 ozone when [ V O C ] 0 is increased past the level needed to produce R = Q. Interestingly, the largest A-value is for A L D (1.7) while the lowest is for H C H O (0.14) - an exact reversal from the 7-values. Using Eq. (6.4), this gives a ratio of 0.82 for A L D ([03] m a x is 82% of peak value at B ) and 0.13 for H C H O ([03] m a x is only 13% of its peak value at the scaling break). Further investigation shows that for the six scaling R A D M 2 classes and two urban mixtures, A and 7 are the most strongly correlated pair of W E X parameters with a correlation coefficient of -0.87. This suggests A is related to the way initial N O x is converted to final NOz; V O C s which do not produce P A N precursors, continue to produce substantial ozone after NOx depletion, and have a low A-value. 6.4.1 Sensitivity of isopleth shape to A The effects of doubling A on isopleth shape are examined in Figures 6.6. The most striking feature is the quick transition made by the isopleths from the V L R to the N L R . If the ridge area is defined as the location where isopleths show the greatest curvature, then increasing A narrows this area. Increasing A also increases isopleth packing in the V L R but does not greatly affect isopleth slope in this region. 6.4.2 Sensitivity of A to R A D M 2 modifications Parameter A measures the ability of a V O C to produce ozone after low-NOx conditions are reached. This appears to be largely determined by final NOz speciation.2 To explore this connection, the reaction mechanism for the aromatic class X Y L E , was modified in an attempt to reduce P A N formation. After Off'-attack, X Y L E produces 0.17 molecules of cresol (CSL). Cresol's main reaction path-way is with the hydroxyl radical; producing 0.9 molecules of the T P A N precursor T C 0 3 for every re-action. I modified the R A D M 2 mechanism to eliminate X Y L E ' s C S L production after OiJ*-attack, with the expectation that this will allow more ozone to be produced after the scaling break. The resulting W E X parameters, regression against model output using this modified reaction scheme, are given in Table 6.4. It shows C S L elimination has reduced A by 41% (while increasing 7, a, a2 and decreasing ct\) and allowed more ozone production. 2However, the results of the second R A D M 2 experiment (section 6.3) suggest that final N O z speciation is not the sole determinant of A. For alkenes, at least, increasing ozone titration by V O C s increases A. Chapter. 6. Chemical Processes and the WEX Parameters 147 * w ' — 1 ' ' ' 1 1 1 1 1 J 1 1 ' 1 1 1 U . U U I i i i I i i . I i i i | i , , 1 0.00 0.15 0.30 0.45 0.60 0.00 0.15 0.30 0.45 0.60 VOC Concentration - ppmC VOC Concentration - ppmC Figure 6.6: The effects of changing X on ozone response surface. Figure A shows maximum ozone concentration (in ppb) as a function of initial VOC and NOx concentration calculated using the WEX model and baseline parameter values. Figure B shows the resulting ozone isopleths (in ppb) after a doubling of X (while all other WEX parameters have been held constant). Parameter Original Modified 7 7.6 8.5 a 0.56 0.64 Ql 1.9 1.7 « 2 0.44 0.71 P 5.3 5.4 X 1.6 0.95 Table 6.4: Comparison of XYLE WEX parameters for the original and modified RADMS mechanism after the elimination of CSL production. 6.5 Geometric Parameter a\ The analysis continues with a\ - the slope of the lower Weibull line segment. First, I begin by examining the sensitivity of an ozone response surface to ct\. This leads to an investigation of isopleth slope, which I define as the angle ozone isopleths make with the V O C axis. The relationship between isopleth slope and NOx-inhibition is then considered. I finish by looking at the variability of a i , among the R A D M 2 classes, and its sensitivity to R A D M 2 modifications. Chapter 6. Chemical Processes and the WEX Parameters 148 Figure 6.7: The effects of changing a\ on ozone response surface. Figure A shows maximum ozone concentration (in ppb) as a function of initial VOC and NOx concentration calculated using the WEX model and baseline parameter values. Figure B shows the resulting ozone isopleths (in ppb) after a doubling of ai (while all other WEX parameters have been held constant). 6.5.1 Sensitivity of the ozone response surface to a\ Figure 6.7A and B show the effects of doubling a\ from 2.0 to 4.0 (approximately going from the 2.1 of OLT to the 3.4 of T O L U ) on an ozone response surface. The greatest effect is on the V L R ; isopleths become more tightly packed and have a shallower slope (with respect to the V O C axis). Ozone concentrations are roughly the same everywhere and the isopleths have a similar shape around the ridge and in the N L R . I now use the W E X model to develop an expression for isopleth slope and to show its dependence on ot\. 6.5.2 Ozone Isopleth Slope At any location on an isopleth diagram, the angle an isopleth makes with the horizontal (VOC) axis can be defined. This isopleth slope is readily evaluated using the W E X model: Consider a unit normal u = (cos9, sin8) parallel to an isopleth at some point ( [VOC] 0 , [NOx]a) on an isopleth Chapter 6. Chemical Processes and the WEX Parameters 149 diagram. By definition, u is at right angles to the gradient i.e.: Letting: 0 = u-\7[03}max 0 = ( c o s g , s i n g ) - P j ° 3 U x a [ 0 3 U x \ V ' ' \d[VOC]0' d[NOx]0J { } Woxi ~ 7 V ) [ a f { R ) ~ R f { R ) ] V = a-l | ! ^ = 7 ( J ^ ) m ( 6 . 6 ) 0[VOC\0 \3av/kN0j then solving Eq. (6.5) for 6 gives: 6? = tan" v The last expression is a function of R only, and it shows that for every line of constant R, isopleths are crossed at the same angle. In Figure 6.8A, I have used Eq. (6.7) to plot slope against R (using the baseline W E X parameters). When R « 0 (approaching the NOx-axis), the isopleths have a slope of 90 degrees; parallel to the NOx-axis. The ridgeline is highlighted by the change in 0's sign - going from +90 to -90. As a reminder, the scaling break (0) is 4.0 which lies to the left of the ridge in this plot (but above on an isopleth diagram). In the NOx-limited region, isopleth start to swing around and become parallel to the VOC-axis; with slope close to 0 degrees. A n interesting feature of the Figure is the local minimum in the VOC-limited region. In Figure 6.8A, the minimum is 28° at R « 3.5. In Figure 6.8B, I have replotted 6 using the same W E X parameters but with a doubling of a\. In this case, the minimum occurs at roughly the same R-value but #m, n drops to 20°. This suggests increasing ot\ decreases isopleth tilt in the V L R . Since, isopleths which make a shallower angle with the V O C axis show a greater change in maximum ozone concentration for a fixed decrease in initial N O x (holding initial V O C concentration constant), one would expect a\ to be a measure of a V O C s NOx-inhibition, a point I address next. 6.5.3 NOx-inhibition and ot\ NOx-inhibition is the phenomena by which maximum ozone concentration decreases when initial NOx concentration increases. On an isopleth diagram, this phenomena is evident in the V L R where ozone isopleths slope away from NOx axis. There are three reasons why maximum ozone concentration decreases for an increase in initial NOx concentration: Chapter 6. Chemical Processes and the WEX Parameters 150 NOx . Limited 5 R 10 Figure 6.8: The effects of changing a.\ on of ozone isopleth slope. Figure A shows slopes using baseline WEX parameters while modified values where used to construct the slopes in Figure B. 1. As initial NOx increases, there is more NO available for ozone titration (RS). 2. Secondly, by titrating ozone, radical initiation (via RA) is also reduced, further slowing ozone formation. This has a compounding effect on production: ozone will now form later, when actinic flux starts to decline. 3. Finally, with higher N02 concentrations, more HNO3 forms resulting in a loss of both radicals and NOx. The above processes present another way of describing the positive feedback mechanism mentioned in Chapter 5 (although, now from the opposite point of view). While isopleth slope is one factor in determining NOx-inhibition, it does not fully determine the phenomena. For instance, a V O C which shows a small Qmin (large tilting of isopleths in the V L R ) but does not have very tight isopleth packing may not show the same sensitivity to changing NOx concentrations as one that has a high packing and less shallow slope. These ideas are schematically presented in Figure 6.9. Clearly both factors play a role in determining NOx-inhibition and their relative importance can be analytically quantified using the W E X model. Chapter 6. Chemical Processes and the WEX Parameters 151 [NOx]o [NOx]D [VOC] 0 [VOC] o Figure 6.9: Isopleths with large tilting but low packing (A) and high packing with low tilting (B). By inspection, it is not possible to tell which shows greater NOx-inhibition. 6.5.4 W E X and NOx I n h i b i t i o n To investigate the effects of both isopleth slope and packing on NOx-inhibition, I used the W E X model to evaluate the derivative of maximum ozone with respect to NOx. This is a complex function of NOx and all the W E X parameters: NOx-inhibition (77) depends directly on 7, which, as mentioned before, is related to isopleth packing. It also depends on the 6 W E X parameters in a complex way. However, since NOx-inhibition is only of concern above the ridgeline, I will ignore any dependence on a2 and treat a = a\ independent of R. In Figure 6.10, I have plotted: versus R//3 under three different scenarios. The plot shows the variability of Eq. (6.9) to changes in any of the three parameters (A, a i , a) when these are altered by 33% from a set of baseline conditions with a\ = 2.0, A = 1.2, a — 0.66. When a\ is increased to 2.67, Eq. (6.9) (and NOx-inhibition) increases for R/0 > 0.45 (i.e Eq. (6.9) becomes more negative). Reducing A to 0.9 reduces the NOx-inhibition up to R/0 «s 0.8 and slightly increases it afterwards. Reducing a to 0.5, leads to a slight increase in NOx-inhibition for all R/0. While this analysis has only looked at the sensitivity of Eq. (6.9) using a single baseline set of conditions, it suggests that NOx-inhibition is more sensitive to a\ than A or a. It is important to note that Eq. (6.9) scales with R/0 which is not the case with the derivative of maximum ozone with respect to [VOC]„ (Eq. (6.6)). It has a (6.8) af(R) - Rf'(R) = a (1 - exp [-\{R/0)a>]) - Xa^R/0)^ exp [-A(i?//5)Q 1] (6.9) Chapter 6. Chemical Processes and the WEX Parameters 152 0.2 1.2 o . 2 - 0 . 4 . Baseline _ X=1.2 . 0^=2.0 - ' G = 0,5 . a2=0.8 - a=0.66 . . . . / a , = 2.67 - 0 . 6 - 0 . 8 L Figure 6.10: Dependence of NOx-inhibition on the three WEX parameters: a, X and a\. Each curve shows the variability of Eq. (6.9) as a function of R/j3 for a range of parameter values listed in the text. direct /3-dependence which leads to important differences between n and v (a matter addressed in Chapter 7). While this is by no means a comprehensive sensitivity analysis, it shows, as expected, both 7 and ot\ are important determinants of NOx-inhibition. Furthermore, since NOx-inhibition is closely related to the positive feedback mechanism (Section 5.4), a\ is also a measure of the strength of the positive feedback mechanism; large ai-values produce more 's-shaped' similarity curves. 6.5.5 Range of OL\-values I have listed the R A D M 2 classes by increasing ot\ in Table 6.5. The table shows formaldehyde having the smallest value (1.5) while T O L U has the largest (3.1). To understand the range of values and the relative ordering, recall that any V O C which has its own photolytic source of radicals can initiate radical attack without having to rely on ozone-produced OH*. Such V O C are less dependent on the autocatalytic nature of the positive feedback loop. So, I expect V O C s which readily photolyze, or those which produce more carbonyl compounds upon oxidation, will have lower a i values. Table 6.5 shows that the two lowest values are both aldehydes compounds (HCHO and A L D ) which readily photolyze to produce radicals. Strangely, the carbonyl class K E T , also a photolytic source of radicals, has one of the highest values for which I have no immediate explanation. T O L U , has the highest value while the other aromatic class X Y L E has an intermediate value. Chapter 6. Chemical Processes and the WEX Parameters 153 R A D M 2 class en HCHO L 5 A L D 1.7 OL2 1.8 OLI 1.9 X Y L E 1.9 OLT 2.2 K E T 2.8 T O L U 3.1 Table 6.5: RADM2 classes ranked by a\. Parameter Original Modified Mechanism 7 9.5 9.5 a 0.6 0.58 a i 2.2 2.7 Q2 0.72 0.52 p 4.2 10.6 A 0.92 1.3 Table 6.6: Comparison of OLI parameters using the original and modified RADM2 mechanism. Neither directly photolyzes but both form peroxy radicals ( T O L P and X Y L P respectively) that pro-duce carbonyl compounds after reacting with N O . Every X Y L P conversion produces 0.45 M G L Y (methylgloxal) and 0.806 D C B (an unsaturated dicarbonyl) both of which produce radicals upon photolysis. Every conversion of T O L P produces only 0.17 M G L Y and 0.7 D C B along with 0.16 G L Y (glyoxal), which results in fewer carbonyl compounds per reaction. While a more thorough comparison would calculate the fraction of total radical production coming from secondary alde-hydes, this initial analysis suggests that X Y L E deserves its higher ranking because of i