Empirical Development of Ozone Isopleths: Applications to Los Angeles

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Empirical Development of Ozone Isopleths: Applications to Los Angeles Yu Qian, Lucas R. F. Henneman, James A Mulholland, and Armistead G. Russell Environ. Sci. Technol. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.estlett.9b00160 • Publication Date (Web): 11 Apr 2019 Downloaded from http://pubs.acs.org on April 15, 2019

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Environmental Science & Technology Letters

Empirical Development of Ozone Isopleths: Applications to Los Angeles

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1Yu

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Qian, 2Lucas R.F. Henneman, 1James A. Mulholland, and 1*Armistead G. Russell School of Civil and Environmental Engineering, Georgia Institute of Technology, GA 30332, United States

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Department of Biostatistics, Harvard T.H. Chan School of Public Health, Harvard University, Boston, Massachusetts 02115, United States

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*Corresponding Author. Phone: 404-894-3079; Email: [email protected]

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Abstract: Understanding quantitative relationships between ambient ozone concentrations and precursor emissions are important to policymakers and stakeholders. Such relationships are often captured as ozone isopleth diagrams developed using air quality models. Model-based approaches have limitations, including errors stemming from uncertainties in inputs and modeled processes, and can be computationally burdensome. We develop and apply an empirical method based on ozone design values calculated in the South Coast Air Basin, California, for 1975-2016 to construct ozone isopleths. The study domain is the area with the highest ozone levels in the US that has experienced high levels of emissions controls. Quadratic and log-quadratic models were constructed, and both capture the actual observations very well (R2 is about 0.98) and recreate the general characteristics of traditional air quality model-generated isopleths. The empirical approach benefits from being based on observations which have high accuracy (but low spatial coverage). Analysis shows that uncertainties are under 30% near likely future control levels. Furthermore, the method shows that the NOx-VOC-ozone system in the 1970’s was in the region where VOC controls were most effective and then more recently moved to the region where both VOC and NOx controls are effective.

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1. Introduction

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The response of ozone to changes in emissions of volatile organic compounds (VOCs) and nitrogen oxides (NOx) has been derived using air quality models of varying complexity, including box models to fully three-dimensional chemical transport models (CTMs)1–8. While box models tend to focus on the chemistry driving the system, CTMs are developed to capture all of the major processes impacting ozone and related pollutants, including chemistry, emissions, transport, and deposition. Both provide information on the response of ozone to varying levels of NOx and VOC.

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A convenient representation of the relationship of ozone to VOC and NOx levels (emissions or initial conditions) is the ozone isopleth (Fig. 2) (or “EKMA” diagram3. Such depictions are typically developed by running a model many times with varying levels of VOC and NOx inputs and then fitting a surface to the simulated ozone levels. This is relatively straightforward when using a box model1–4, but it becomes computationally intensive when using a CTM because of the much greater computational requirements, though CTMs have been used to develop isopleths for different regions5–8. Another less computationally intensive approach to develop isopleths uses sensitivity analyses to construct a reduced form model9,10, using a Taylor series approximation:

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(1) C(x0 + Δε1, y0 + Δε2) = C(x0, y0) + Δε1S(1) ε1 (x0, y0) + Δε2Sε2 (x0, y0) +

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𝑆(2) 𝜀1𝜀2(x0, y0) +

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+

(Δ𝜀2) 2

2

𝑆(2) 𝜀2𝜀2(x0, y0) +

(Δ𝜀1) 6

3

𝑆(3) 𝜀1𝜀1𝜀1(x0, y0) +

2

𝑆(2) 𝜀1𝜀1(x0, y0) + (Δε1)(Δε2)

(Δ𝜀1) Δε2)

(Δε1)(Δ𝜀2)2

2

2

2(

𝑆(3) 𝜀1𝜀1𝜀2(x0, y0) +

(Δ𝜀2)3 6

(Δ𝜀1)2

𝑆(3) 𝜀2𝜀2𝜀2(x0, y0) +…

(EQN. 1) 1 ACS Paragon Plus Environment

𝑆(3) 𝜀1𝜀2𝜀2(x0, y0)


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where x0 and y0 are the initial emissions of the precursors (tons/day), Δε1 and Δε2 are changes around x0 and y0 respectively, C is the response concentration (ppb), and S(i) is the ith order sensitivity (ppb/(tons/day))10. In this case, the CTM, with a higher order sensitivity analysis tool (e.g., HDDM10), is used to calculate the sensitivities to VOC and NOx emissions. Hakami et al.10 found that the third order terms were typically small, such that a reduced model based using first and second order sensitivities compared well to using the multiple applications of the full CTM at varying emissions levels. An important finding from early studies was that the isopleths at different locations could vary dramatically6, effectively showing that not only do the peak ozone levels vary spatially and temporally, but the sensitivities do as well. These results indicate that different emission control strategies will vary in efficacy regionally. In some regions, reducing NOx emissions was more effective at reducing ozone than lowering VOC emissions a comparable amount (e.g., downwind of urban areas). At other locations, controlling NOx led to increases of ozone (e.g., in denser, urban areas).

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A challenge with developing isopleths using models is that they rely on the integrity of the underlying model and its ability to capture the processes impacting ozone (e.g., chemistry, deposition, dispersion) and the inputs (e.g., particularly meteorological and emissions, but also land use, vegetation, and other inputs). Such inputs and process descriptions are known to be uncertain, as is evident in the model’s ability to accurately simulate ozone levels. Simon et al.11 found that CTM-ozone concentration have mean fraction errors on the order of 25% and a correlation R2 of 0.5 when compared to observations. Furthermore, models tend to be biased low for simulating peak ozone levels11. The latter point is particularly concerning when considering that compliance with the US National Ambient Air Quality Standard (NAAQS) for ozone is based upon the fourth highest eight-hour average ozone in a year (averaged over three years)12.

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Given the potential issues with relying on model-derived approaches to developing ozone isopleths, it is of interest to explore empirical approaches. The long record of ozone monitoring, along with significant changes in emissions, allows for the development of observation-based ozone isopleths. Previous empirical studies13–17 used observational data for both ozone and its precursors (NOx and VOC) to investigate the relationship between ozone and those precursors. Pollack et al.15, Kim et al.16, and Fujita et al.17 explored ozone-precursor sensitivity variations by evaluating the ozone weekend-weekday effect. Such information provides information on how ozone may respond to NOx emissions changes, though there are significant differences between the response to a weekend reduction in NOx emissions vs. reductions in NOx emissions during the entire week17, as well as how the reductions are spatially distributed. Here, we develop a method that utilizes estimated emissions and the ozone design values (ODV) in the Los Angeles area, CA, USA to define numerical relationships between estimated emissions of VOC and NOx, and ODV. Using estimated emissions of both VOC and NOx, over a long observational period allows developing quantitative sensitivity relationships, embodies as ozone isopleth diagrams, which are readily compared to air quality model results and can be used intuitively by stakeholders. Further, the approach allows for estimating uncertainties in future projects and expected ODV variability.

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2. Methods a. Data Sources

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Data used in this study includes: (1) observationally-based, yearly ozone design values (ODVs) data for South Coast Air Basin (SoCAB) and (2) estimated yearly anthropogenic emission data for NOx and VOC. The study period is from 1975 to 2016. Monitoring sites map is shown in Fig. S1.

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The ODV is a statistic used in relationship to the NAAQS12. The eight-hour ozone design value is the average of the fourth highest annual maximum daily average eight-hour ozone concentration (ppb) of three consecutive years. ODV data were obtained from the California Air Resources Board database18.

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NOx and VOC emission data (tons/day, annual average) were obtained from the California Almanac of Emissions and Air Quality 2009 Edition19,20 [Historically, CARB used ‘ROG’ (reactive organic gas), which is defined similarly to VOC, the more globally used term. The two estimates are very similar: see SI, particularly Fig. S2]. Emission data were reported on a five-year basis and annual values were linearly interpolated between years.

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b. Empirical Isopleth Development Using Regression Modeling

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Regression modeling approaches21 were used to fit a multivariable function between the ODV and the VOC and NOx emissions. Prior study10 found that a quadratic relationship could fit the simulated ozone within a broad range of emission levels (+/- 50%), and produced an ozone isopleth that matched the one developed by application of the full CTM5,6. Here we explored using both a quadratic and a log-quadratic model using least squares fitting:

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ODV (ENOx, EVOC) or Log10(ODV (ENOx, EVOC)) = β + αNOx ∗ ENOx + αVOC ∗ EVOC + αNOx ― VOC ∗ (ENOx ∗ EVOC) + αNO2x ∗ E2NOx + αVOC2 ∗ E2VOC

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(EQN. 2)

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where ODV is the observed ozone design value (e.g., ppb), Evoc and ENOx are estimated annual average emission rates (e.g., tons/day) of VOC and NOx respectively, and the αi’s are regression coefficients (e.g., ppb ozone/(tons/day) or ppb ozone/(tons/day)2). Other non-linear forms could also be used, though the two shown in EQN. 2 lead to results that have the typical form of ozone isopleths, and utilize relatively fewer parameters, limiting overfitting. Higher order terms grow particularly fast when extrapolating beyond the original data.

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c. Uncertainty Analysis: While an empirical approach may have potential utility versus CTM approaches, it does not eliminate uncertainties. First, observations suggest that the relative year-to-year change are captured16,22–25, as does our own analysis (Fig. S3, Table S8, see SI), though some studies suggest that the absolute estimated emissions levels may be biased (e.g., McDonald et al.26). Second, as any approach based on regression, the coefficients are uncertain, and the relationship(s) will not capture the full complexity of the physicochemical system. A formal uncertainty analysis was conducted following the approach outlined in Helwig27 (See SI). In addition, a novel analysis of uncertainties in the independent variables (emissions) was also conducted by simulating that the relative reduction from year to year is uncertain such that the relative uncertainty in the emissions continually increases with time using 1000 emission reduction pathways (See SI). 3. Results a. Ozone Design Value and NOx and VOC Emission Trends 3 ACS Paragon Plus Environment


Emissions of NOx and VOC, and the associated ODV, have decreased significantly between 1975 and 2016 (a 67% decrease in NOx emissions, 81% decrease in VOC emissions and a 61% decrease in the ODV; Fig. 1). Before 1997, estimated VOC emissions and their reductions since 1975 were higher than those for NOx. Since 1997, VOC reductions have slightly exceeded NOx emissions reductions. The emissions trends shown here are consistent with observations from other trend studies16,24,25. The ODV reduction has followed. We found high linear correlations between ODV and NOx and VOC emissions: R2= 0.97 (VOC) and 0.82 (NOx) (Fig. 1). The correlation between NOx emissions and ODV was lower at higher ODVs, reflecting the greater VOC emissions reductions and the non-linearity of the relationship. 3000

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2500

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2000

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1500

150 NOX

1000

VOC

500 0 1970

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1990

2000

2010

ODV

150 100 50

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ODV 1980

200 ODV (ppbv)

Emission (tons/day)

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ODV v.s N ODV v.s VO

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Fig. 1 Left: The Trend of ODV, NOx emissions and VOC emissions in South Coast Air Basin from 1975 to 2016; Right: Relationships between ODV and estimated NOx emissions/VOC emissions from 1975 to 2016 with linear fits.

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b. Empirically-derived Nonlinear Ozone Relationships

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Base-Quadratic Regression Function:

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ODV (ENOx, EVOC) = 1.03 + 0.13*ENOx + 0.11*EVOC + 3.5*10-5 *(ENOx*EVOC) – 1*10-4 *(ENOx2) – 1*10-5 *(EVOC2)

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(EQN. 6)

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Log-quadratic Regression Function:

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Log10 (ODV (ENOx, EVOC)) = 1.72 + 4.5*10-4 *ENOx + 2.4**10-4 *EVOC + 1.8*10-7 *(ENOx*EVOC)

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– 3.5*10-7 *(ENOx2) – 7*10-8 *(EVOC2)


(EQN. 7)

1000 Emission

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R2‘s are >0.99 (adjusted R2‘s are >0.98), suggesting that, at least near the observational values, the



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models capture how ozone responds to emissions. The good performance and the prediction ability of


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both models were also strengthened by the result of a 10% cross-validation test (see SI), which gives consistently high R2’s (0.98 average) and low RMSE (6 ppb in average) (Fig. S3). The first order sensitivities to emissions of NOx are positive, while the second order sensitivities are negative, showing that as emissions of NOx increase, the sensitivity of ozone to NOx emissions decreases, and ultimately becomes negative. The second order sensitivities to VOC emissions are small, such that ozone usually tends to increase as VOC emissions increase, except at high levels of VOC emissions. The mixed second order derivative is positive, showing that as both emissions of VOC and NOx increase, ozone increases.

Fig. 2 ODV-Emissions Isopleths developed by empirically-derived non linear regression model. And the uncertainty related to the models. Axes define the emissions space with varying levels of estimated NOx and VOC and corresponding modeled ODV indicated by color. Historical observations are noted with red spots. Left column shows the result of full base-quadratic model (a, c, e). Right column shows the result of full logquadratic model (b, d, f). Top Row: emission space and Isopleths constructed based on different regression models(a, b). White lines are the zero-NOx sensitivity ridge lines (upper part with negative ODV to NOx sensitivity). Red lines are the equal NOx-VOC sensitivity ridge lines (upper part with higher ODV to VOC sensitivity). Middle Row: Prediction uncertainty of regression models at different emissions levels (c, d). Bottom Row: Relative Prediction uncertainty of regression models at different emissions levels (e, f).



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An issue with the non-log quadratic fit is that the predicted ozone can go negative, e.g., at conditions representing low VOC emissions and high NOx emissions, where the atmosphere would become very NOx-rich/radical limited28. The log-quadratic model leads to positive ozone levels for all levels of VOC and NOx emissions and reduces dispersion, which motivates the use of this model.

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The relationships can be used to develop ozone isopleths, which show the similar characteristic form of isopleths developed using atmospheric chemical mechanisms and chemical transport models (Fig. 2ab).

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We also used AIC model selection to generate reduced models (Fig. S4, see SI), which does not capture the typical isopleth form well, supporting the use of the full models.

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c. Uncertainty Analysis Formal uncertainty analysis based upon both dependent (ODVs) and independent (emissions) variables found a small uncertainty near the observations, growing as one moves away from the historical observations (Fig. 2, Fig. S7, Table S1). The average result of 1000 emission uncertainty simulations is similar to the original model (Table S2, See SI). Comparison between the two models also find similar result (Fig. S5). For cases of zero emissions, the estimated values were 1 ± 68 ppb and 52 ± 17 ppb, for the non-log model and log model respectively. Relative uncertainties with the log model tend to be less than with the base approach (Fig. S6). (While it is unphysical, the regression model without the log transformation, and the related uncertainties, can lead to values below zero.) 4. Discussion The empirical approach has additional applications beyond providing a straightforward approach to developing isopleths. Having a relatively simple, observationally-founded approach to quantifying ozone-emissions relationships in an air basin can be used to provide quantitative responses (sensitivities) of ozone to emissions. Sensitivities to both NOx and VOC emissions are found by taking the derivatives of the regression models with respect to NOx and VOC emissions, respectively (for the base model): ∂ODV ∂𝐸NOx ∂ODV ∂𝐸𝑉𝑂𝐶

= αNOx + αNOx ― VOCΕVOC +2αNO2xΕNOx

(ΕQN. 8)

= αVOC + αNOx ― VOCΕNOx +2α𝑉𝑂𝐶2ΕVOC

(ΕQN. 9)

The case where the sensitivity to NOx emissions is of particular interest as this represents where ozone will increase in response to NOx controls, and may be interpreted as a “ridgeline”. The zero-NOx sensitivities are found to have the same form for both models: 𝛼𝑁𝑂𝑥

(ΕQN. 10)

𝐸𝑁𝑂𝑥 = 567 + 0.15ΕVOC

(ΕQN. 11)

2αNO2 x

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αNOx ― VOC

ΕVOC

𝐸𝑁𝑂𝑥 = ―

―

2αNO2 x

For the quadratic model, the zero-NOx sensitivity is (Fig. 2a):

And for the Log- Quadratic model, the zero-NOx sensitivity is (Fig. 2b): 𝐸𝑁𝑂𝑥 = 636 + 0.26ΕVOC 8 ACS Paragon Plus Environment

(ΕQN. 12)

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A second characteristic of the ozone isopleth is where the sensitivities to NOx and VOC emissions are the same leading to the equal NOx-VOC sensitivity (a second type of ridgeline):

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𝐸𝑁𝑂𝑥 =

αVOC ― αNOx 2αNO2 ― αNOx x

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2αVOC2 ― αNOx ― VOC

2αNO2 ― αNOx ― VOC ΕVOC

(EQN. 13)

x

For the two models, this leads to the equal sensitivity relationships (Fig. 2ab):

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+ ― VOC

𝐵𝑎𝑠𝑒 𝑚𝑜𝑑𝑒𝑙: 𝐸𝑁𝑂𝑥 = 90 + 0.21ΕVOC

(EQN. 14)

𝐿𝑜𝑔 𝑀𝑜𝑑𝑒𝑙: 𝐸𝑁𝑂𝑥 = 239 + 0.36 ΕVOC

(EQN. 15)

and

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Given that the underlying relationships are based on quadratic fits, both the zero NOx sensitivity and the equal NOx-VOC sensitivities lead to linear relationships (Fig. 2ab), which would suggest a level of simplification as isopleths developed using CTMs appear more complex. However, it is difficult to quantify such relationships without a very large number of simulations, or a high-order direct technique10. Using a reduced form approach from a CTM based on first and second derivatives would also lead to linear forms.

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One potential advantage of this approach is that it integrates how the locations used in determining the design value move both in time and space in response to emissions changes, which is more straightforward than other concentration-based methods, though only within the range of observations. This is not possible to capture using a box model; it is computationally expensive when using a CTM (one would have to identify where the ODV moves each year, using three-year averages), and would be subject to considerable uncertainty.

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It is possible to use the predicted ozone value for zero anthropogenic emissions (both NOx and VOC) as the background value, but that entails considerable uncertainty and additional assumptions. First, extrapolation is subject to increased uncertainty. Second, there is little reason to think that the times or locations that are used to determine the design values in past years would be the same as would have the fourth highest ozone level when anthropogenic emissions approach zero. Estimated background levels for ozone along the Pacific Coast tend to peak in spring, not summer. In addition, with no anthropogenic emissions, ozone advected into the basin (e.g., from transpacific transport) would deposit out as the air parcels moved eastward, which would lower ozone levels, so the highest levels might be expected along the coast. Thus, using such a regression approach would assume that the summertime ODV concentrations, which are clearly linked to emissions, are informative about nonsummertime levels and that the approach captures how the location where the peak occurs (which is also strongly influenced by emissions) will move with time.

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One particularly insightful application of the method is that it can provide estimates of how the sensitivity of the ODV has varied through time, and likely will respond in the future given emissions changes. Such estimates can be compared to model-derived estimates and, potentially with further analysis, to estimate ozone production efficiencies29. Looking at the trajectory of the observed ozone through “emissions space” (i.e., how the two axes in Fig. 2 define varying levels of estimated NOx and VOC emissions), it would appear that through the first approximately 20 years, the trajectory was in the region where small NOx emission controls, alone would have led to slight increases in the ODV. The 9 ACS Paragon Plus Environment


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more recent reductions are moving the trajectory to where further NOx emissions are beneficial (in the region below the zero-NOx and the equal NOx-VOC sensitivity lines). This finding is consistent with other observation-based empirical studies13,14,29. The regression modeling approach shows that the ODV would increase if one solely reduced NOx emissions, which is consistent with the weekend-weekday analysis studies (e.g.,30,17), though it is important to note that the ODV values used here include both weekend and weekday values and that there are dynamic differences between reducing NOx emissions over the weekend and a reduction in NOx emissions over all day.17

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The approach can also be used to forecast future ODV levels in response to emissions changes. Predicted ODVs for 2017 and 2018 are, respectively 102±10 and 101±11, which are consistent with the observations (112 ppb and 111 ppb), though indicate those two recent years are near the top of the predicted range. For 2030, the projected decreases in NOx and VOC emissions are 50% and 24%, respectively, leading to a predicted ODV of 82±19 ppb, similar to the estimate of Collet et al.31. Reducing only NOx to the 2030 levels leads to an ODV of 88±27. We also evaluated the zero VOC emission scenario (keeping current NOx emissions), leading to an ODV of 72±13 ppb. Such forecasts assume that the VOC reactivity of the emissions reductions remains similar (e.g., using a measure like the Maximum Ozone Incremental Reactivity scale32 the incremental reactivity does not change significantly). The method could also be used to estimate population exposure isopleths.

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While the empirical approach developed is particularly attractive in that it is relatively straightforward to apply, uses limited computational resources, and is driven by observations, it has limitations. First, it requires a long record of ozone observations along with estimated emissions, and those need to have changed substantially over the period studied. Second, regression approaches are subject to uncertainties when extrapolating that grow with distance from observations. Third, the accuracy of this approach is dependent upon the accuracy of the estimated emissions of NOx and VOC, particularly how well they capture the actual emission trends and assumes that other factors, e.g., meteorological drivers, biogenic emissions (which will change due to both meteorological changes and land use changes) and the reactivity of the VOC emissions reductions do not change markedly from historical trends. Formal uncertainty analysis provides some assessment of such uncertainties, though it assumes that the emissions levels were estimated accurately, that the quadratic model form is reasonable, and that the coefficients capture most of the important processes driving the ODV. This is supported by comprehensive chemical transport modeling. More detailed comparisons of chemical transport models and such empirical approaches should be conducted to identify and quantify the uncertainties in both approaches.

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Acknowledgements

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This publication was supported, in part, by grants from the US EPA (Agreement No. EPA 83588001) and the National Science Foundation (grants 1444745, 1743753). It has not been formally reviewed by EPA or NSF. The views expressed in this document are solely those of the authors and do not necessarily reflect those of the funding agencies, nor do they endorse any products or commercial services mentioned in this publication.

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Note


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The authors declare that they have no actual or potential competing financial interests.

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Supporting Information

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The Supporting Information is available.

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The SI includes the following sections: study domain and monitoring sites map (Fig. S1), Emission data source description (including Fig. S2), cross-validation result (including Fig. S3), detailed derivation of empirical model uncertainty calculation, results of reduced model (including Fig. S4), the comparison between base and log models (Fig. S5), models uncertainty distributions (Fig. S6), assessment of emissions uncertainties (including Fig. S7, Table S1, Table S2), comparison between the trends of CARB estimated emissions inventory with observed concentrations for CO, NOx, and ROG (including Fig. S8, Table S3).

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Empirical Development of Ozone Isopleths: Applications to Los Angeles

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Qian, 2Lucas R.F. Henneman, 1James A. Mulholland, and 1*Armistead G. Russell School of Civil and Environmental Engineering, Georgia Institute of Technology, GA 30332, United States

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Department of Biostatistics, Harvard T.H. Chan School of Public Health, Harvard University, Boston, Massachusetts 02115, United States

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*Corresponding Author. Phone: 404-894-3079; Email: [email protected]

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