2.1 Ozone design values analyzed

This work considers ODVs reported from the beginning of US ozone monitoring in the mid-1970s through 2017 in 17 northern US states. An ODV, the statistic upon which the US NAAQS is based, is calculated every year for each ozone monitoring station in the US if the measurements achieve the specified completeness criteria. Each year all recorded ODVs are added to EPA's Air Quality System data archive (https://www.epa.gov/aqs, last access: 23 June 2019). All ODVs reported for the northern states were downloaded from this archive; only the ODVs marked as valid were retained for analysis. Exceptional events that have concurrence from the US EPA were excluded. Table S1 summarizes these archived ODVs for each state, including the number of monitoring sites, the years spanned by the reported ODVs, and their maximum and minimum values. The reported ODVs span the range from 169 to 41 ppb. Yellowstone National Park (NP) in another state (Wyoming) is also included because its measurement record has been examined in previous analyses of long-term trends of US background ozone concentrations (e.g., Lin et al., 2017). It should be noted that very few sites have continuous measurements over the indicated time spans and that many sites operated for only short periods. All reported ODVs are included in this analysis even if only a single ODV was reported for a particular site. It is implicitly assumed that the temporal discontinuities associated with initiation or termination of individual sites do not prevent an accurate quantification of temporal trends of ODVs within the regions selected for analysis.

2.2 Exponential ODV trend analysis

A well-established conceptual model (e.g., Parrish et al., 1986) guides our analysis. Ambient ozone concentrations at US surface sites are composed of two contributions: (1) background ozone and (2) enhancements resulting from ozone produced from photochemical processing of US anthropogenic emissions of ozone precursors. The first contribution is the ozone that would be present in the absence of US emissions of ozone precursors from anthropogenic sources; this ozone is transported into the US or produced over the US from naturally emitted precursors. The US EPA has defined this contribution as US background ozone (e.g., Dolwick et al., 2015). The first contribution has remained relatively constant, while the second contribution has greatly decreased over the past 2 to 4 decades in response to reductions in anthropogenic emissions of ozone precursors.

In this work we focus on the time period of decreasing ODVs. Fitting observational data to a simple functional form is a common tool utilized for quantitative observational analysis; linear trend analysis (i.e., fitting observational data to a linear function) is one example. Here we choose to fit observed ODVs to Eq. (1),

with three undetermined parameters. This equation is the simplest possible functional form consistent with the guiding conceptual model of a background contribution and a consistently decreasing anthropogenic contribution. (A linear fit with only two undetermined parameters – slope and intercept – is simpler but cannot fit a positive background contribution, as a decreasing linear fit will eventually go negative.) We identify the first term of Eq. (1), y₀, as an estimate of the ODV that would result from US background ozone alone (i.e., consistently called US background ODV) and the second term as an estimate of the enhancement of observed ODVs above y₀ (i.e., consistently called US anthropogenic ODV enhancement) due to contributions from photochemical processing of US anthropogenic precursor emissions. This second term decreases exponentially with a time constant of τ and equals A in the reference year, which we choose as 2000.

A simple intuitive argument suggests that an exponential decrease in the anthropogenic ozone contribution is expected to be a reasonable approximation for the response of maximum ozone concentrations to implementation of emission controls. When controls are initiated, early progress can be rapid, since large existing emission sources evolved without planning for their control. With time, reducing emissions will become progressively more difficult, since the most easily controlled emissions will likely be addressed first, and the smaller, remaining emissions will be more difficult and/or expensive to control. This expected increasing difficulty in reducing emissions may well lead to an approximately constant fractional decrease in anthropogenic ozone enhancements, which corresponds to an approximately exponential decrease in these enhancements.

A previous analysis (Parrish et al., 2017a) quantified the temporal evolution of the maximum ODVs in seven southern-California air basins over the 1980–2015 period (shorter periods beginning later and ending in 2015 in two basins). That work utilized fits to Eq. (1) (with the reference year 1980 instead of 2000) and showed that a single value of $\mathit{\tau }=\mathrm{21.9}\pm \mathrm{1.2}$ years, a single value of $y_{\mathrm{0}}=\mathrm{62.0}\pm \mathrm{1.9}$ ppb, and a different value of A in each air basin provided an excellent fit (r²=0.984) to the ODVs in all of those air basins.

As we will see in the following analysis, in the northeastern states the period of consistently decreasing ODVs (generally 2000 and later, hence the choice of 2000 as the reference year in Eq. 1) is too short to allow precise determinations of all three parameters of Eq. (1) from fits to individual ODV time series. In the face of this difficulty, our primary analysis approach is to assume that the τ value (21.9 years) derived for southern California is also appropriate for the northeastern states. Uncertainty in the value of τ is then the greatest source of uncertainty in the analysis results; the impact of this uncertainty will be addressed in Sect. 3.3.2.

Equation (1) assumes that decreasing US anthropogenic ODV enhancements is the only cause of ODV variability at a particular location. Other factors (e.g., rising anthropogenic emissions in Asia, variable occurrences of wild fires, interannual meteorological and climate variability, etc.) can also potentially affect observed ODVs. The approach taken here is to interpret the observed ODVs initially on the basis of Eq. (1) and to examine the fraction of the ODV variance captured by that interpretation. The remaining fraction of the variance is then attributed to other factors, including those listed above. We use three statistics to quantify the variance in the total data set and the fraction not captured by Eq. (1). The total variance in a data set is the square of the standard deviation of those data (in units of ppb²). The root-mean-square deviation (RMSD) between the derived fit and the observed ODVs gives an absolute measure (in ppb) of the ODV variability about the fit; the square of the RMSD (in units of ppb²) gives an estimate of the variance not captured by the fit. The square of the correlation coefficient (r²) between the observed ODVs and the values derived from the fit to Eq. (1) gives a measure of the fraction of the total variance that is captured by that fit; the difference between unity and the r² value is then a relative measure (as a fraction) of the ODV variance not captured by Eq. (1). In the southern-California air basins (Parrish et al., 2017a), the derived r²=0.984 and RMSD ≈4 ppb indicate that all factors not included in Eq. (1) account for no more than 1.6 % of the total variance in the basin maximum ODVs analyzed in that work and contribute a RMSD to those ODVs of no more than ∼4 ppb.

A potential complication in the interpretation of the two terms of Eq. (1) arises if there is a significant fraction of US anthropogenic ozone precursor emissions that have not been reduced by emission controls. Ozone produced from such emissions will not have decreased in the same manner as that produced from most US anthropogenic emissions, which could raise the derived value of y₀ above the actual US background ODV. Parrish et al. (2017a) have discussed this issue with regard to the emissions associated with the intense agricultural activity in the Imperial Valley of the Salton Sea air basin, where the derived y₀ is higher than in other southern-California air basins. The final section of this paper briefly considers the possible impact of this complication in the northeastern US states. One difference between the application here and that of Parrish et al. (2017a) should be noted. The former work chose 1980 as the reference year, while here we choose the year 2000. The curves derived from the fits to Eq. (1) and the values derived for the y₀ parameter do not depend on the choice of reference year, while the values derived for the A parameter do. Consequently, comparing the A parameters derived here with those given for California by Parrish et al. (2017a) requires adjustments for this difference, which can be provided through the second term of Eq. (1).

2.3 Additional observation-based analyses of ODV time series

Acknowledging the uncertainty introduced by the assumptions required to implement the exponential analysis described in Sect. 2.2, we derive y₀ through three additional, somewhat different approaches that also provide two estimates of τ appropriate for the northeastern states.

An independent analysis approach discussed in Sect. 2.3 of Parrish et al. (2017a) can estimate US background ODVs without assuming any specific functional form for the time dependence of the ODV enhancements. Different assumptions underlie this analysis – namely that all of the ODV time series under consideration follow the same functional form, but not necessarily an exponential decrease, and that all time series are approaching a common US background ODV (i.e., y₀ value). These assumptions imply that all of the time series will converge to a common ODV as anthropogenic precursor emissions are reduced to zero; this common ODV is necessarily the regional US background ODV. In practice this analysis uses correlations between time series of ODVs with US anthropogenic ODV enhancements that differ as much as possible. One time series is selected as a reference; in the examples discussed here the time series with the largest US anthropogenic ODV enhancements is selected. Other time series are then linearly correlated with this reference. The intercept of each linear correlation with the 1:1 line then provides an estimate of the US background ODV; at that point the ODVs from the two time series are equal. Parrish et al. (2017a) show that the results of this approach for seven southern-California air basins are nearly identical to the results from fits to Eq. (1). We apply this approach to estimate US background ODV in the northeastern US and compare the results to those from the exponential analysis.

Two additional approaches can approximately quantify the value of τ in the northeastern states; both of these approaches assume that constant values of y₀ and τ are appropriate for all ODV time series included in each analysis. First, a linear fit to the initial period of decreasing ODVs provides direct information regarding the magnitude of τ and y₀. The absolute value and the time derivative of Eq. (1) when evaluated at year 2000 are y₀+A and $-A/\mathit{\tau }$, respectively. Fits to two ODV time series provide four parameters ($\mathit{\tau },y_{\mathrm{0}},A_{\mathrm{1}}$, and A₂) if the τ and y₀ values are the same for the two time series. Algebraic manipulation gives $\mathit{\tau }=-{\mathrm{\Delta }}_{\mathrm{year}\mathrm{2000}\mathrm{value}}/{\mathrm{\Delta }}_{\mathrm{slope}}$, where Δ indicates the difference in the subscripted parameter between the two linear fits, and y₀= (${\mathrm{\Sigma }}_{\mathrm{year}\mathrm{2000}\mathrm{value}}+\mathit{\tau }\cdot {\mathrm{\Sigma }}_{\mathrm{slope}})/\mathrm{2}$, where Σ indicates the sum of the subscripted parameter from the two fits. A complication with this approach is that the linear fits to time periods of significant length give biased measures of the derivative and year-2000 value of Eq. (1); however, this bias can be corrected to first order through numerical comparison of a linear fit to the selected period of the exponential fit. The second approach is described in Sect. 2.4 of Parrish et al. (2017a) and is adapted here to the northeastern-US ODV time series. It uses an iterative, nonlinear regression analysis that simultaneously derives values for τ and y₀, plus the A parameter for each ODV time series included in the analysis. This analysis will be adapted to the northeastern-US ODV time series. These two additional approaches help to constrain the uncertainty of the assumed value of τ (21.9 years).

2.4 Confidence limits and uncertainties

In this work we consistently give 95 % confidence limits for derived parameters, unless indicated otherwise. Most of the analysis in this work is based on nonlinear, least-squares regression fits of the archived ODVs to Eq. (1), and interpretation of the derived values for y₀ and A. In this interpretation it is important to properly consider the uncertainty of these values. We begin with the 95 % confidence limits given by the least-squares fitting routines, which are then adjusted to account for the known covariance between the recorded ODVs. Each ODV is a 3-year running mean; therefore only every third ODV is independent of the others determined at a given site. Consequently, the number of independent ODVs in each fit is smaller than the number of reported ODVs by approximately a factor of 3. Thus, all confidence limits derived from the fitting routines have been increased by a factor of 3^1∕2 to account for this covariance. Note that the confidence limits are typically one to a few parts per billion; thus results and their confidence limits are often given to 0.1 ppb precision even though the last significant figure is likely not justified.

There are additional sources of covariance between the ODVs included in any particular fit. The ODVs from different sites within a region can covary due to regionally coherent interannual variability, and interannual variability may lead to covariance between ozone concentrations measured in successive years. We are not able to account for the effect of this additional covariance; the derived confidence limits are thus lower limits for the true confidence limits of the derived parameters. However, as discussed in the next section, we can find no indication that additional regional or temporal covariance of the ODVs makes significant contributions to the uncertainties of the results. The influence of often-cited major drivers of temporal variation in ozone, which could possibly cause such covariance, is discussed in Sect. 4 and found to be small.

3.1 ODVs in rural western states

The sparsely populated, three-state, rural western region generally lies on the northern US Great Plains downwind of more mountainous terrain to the west. Figure 1 shows a topographical map of the region, with the locations of the ozone monitoring sites indicated. This area gradually slopes to the east and north. All of the monitoring sites lie below 1.55 km elevation, with the exception of Yellowstone NP at 2.43 km.

The histories of the ODVs recorded in the region are illustrated in Figs. 3 and 4, and averages with standard deviations and variances are given in Table 1. The gaps in the Montana and South Dakota records were caused by extended periods when no valid ODVs were recorded at any site within the respective states. Throughout the ODV record there is little variability due to any cause. The 283 tabulated ODVs recorded over 39 years at 35 sites in the three states average at 59.3 ppb, with a standard deviation of 3.7 ppb (corresponding to a variance of 13.4 ppb²) – strong evidence that the ODVs correspond to an approximately constant US background ODV within this region with no evidence for significant US anthropogenic ODV enhancements. At the individual sites and within each state the entire measurement records are all well described by averages with small standard deviations (Table 1): < 3 ppb in Montana and North Dakota and < 4 ppb in South Dakota, the state whose sampling sites span the largest elevation range (0.34 to 1.55 km). US background ODVs generally increase with the elevation of the sampling site (e.g., see discussion in Jaffe et al., 2018), so larger variability is expected when the monitoring sites within a state span a larger range of elevations. The state averages in Table 1 lie within a range of ∼6 ppb, but there are some significant differences: a maximum in South Dakota (61.5 ppb) and a minimum in Montana (55.4 ppb), with North Dakota being intermediate (59.3 ppb). Consistent with the site elevation differences, the average ODV at Yellowstone NP is significantly larger than that at Glacier NP: 64.0 ppb at 2.43 km and 54.5 ppb at 0.96 km, respectively. The variances in the data sets vary from 2 to 15 ppb²; these values indicate that only small variance in long-term ODV records can arise from variation in US background ozone alone, at least in this particular region of the country.

Figure 4Time series of all ODVs (grey symbols) reported from all monitoring sites in three rural western states plus Yellowstone NP, located in Wyoming. The two sets of colored symbols are results from two long-term sites in national parks.

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Table 1ODV statistics from the rural western states.

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3.2 Exponential fits to ODVs in northeastern states

A topographical map showing the networks of ozone monitoring sites in the eight northeastern US states is given in Fig. 2. All of the ODVs recorded in four of the eight states are plotted in Figs. 5 and 6 along with curves showing fits of Eq. (1) to the ODVs from selected groups of sites over selected time periods. These ODV time series are in striking contrast to those in the rural western states (compare Figs. 5 and 6 with Fig. 4), with much larger concentrations showing strong decreases over the past 2 to 3 decades and much greater variability in ODVs. We attribute this contrast to the much greater influence of US anthropogenic ODV enhancements in the northeastern states. The greater variability is quantitatively reflected in the ODV variance in this region (252 ppb²), which is nearly a factor of 20 larger than that seen in the rural western states; this comparison shows the dominant influence of the US anthropogenic ODV enhancements in the northeastern states.

Figure 5Time series of all ODVs (grey symbols) reported from all monitoring sites in New York and Connecticut. The three sets of colored symbols indicate the results from groups of sites that are discussed in detail. The curves are fits of Eq. (1) to respective colored symbols and to all data points for Connecticut.

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Figure 6Time series of all ODVs (grey symbols) reported from all monitoring sites in Massachusetts and Maine. The four sets of colored symbols indicate the results from groups of sites that are discussed in detail. The curves are fits of Eq. (1) to respective colored symbols.

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The four states included in Figs. 5 and 6 are shown for illustrative purposes, with Figs. S3–S10 of the Supplement showing detailed ODV temporal plots and fitted curves to the selected groups of sites in all eight states. These groups of sites were selected to represent different environments within each state, with the expectation that similar temporal ODV trends will be found at all sites within each group. The strategy adopted is to fit the ODVs recorded at all sites within each group over the time period beginning when a clear, consistent decrease in ODVs is first established and continuing through 2017, the most recent year for which ODVs are available. This strategy is required since Eq. (1) is designed to provide fits to ODVs only during such periods of consistent decreases. In all cases these fits begin by 2000, with some beginning earlier – either at the start of measurement record, in 1990, or in 1995, determined by the best, consistent fit to the functional form of Eq. (1). Figures S3–S10 include maps indicating the locations of all selected groups of sites. In all, 17 groups within the eight states were selected; they are listed in Table 2 along with the parameters derived from the fits of Eq. (1).

Table 2Results of least-squares fits to Eq. (1) illustrated in Figs. 5–7 and S3–S10; RMSD indicates the root-mean-square deviation between the observed ODVs and the derived fit.

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Figure 7Comparison of fits of the ODVs from 17 groups of sites in eight northeastern US states shown in Figs. 5, 6, and S3–S10 to Eq. (1). The parameters of these fits are included in Table 2.

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There are some consistent general features of the ODV time series and the corresponding fits that inform the following analysis.

Throughout the measurement record, the largest ODVs are found in the states that contain the New York City metropolitan area (New York, New Jersey, and southwestern Connecticut) or that lie directly downwind (coastal Connecticut and Long Island, New York). Such sites compose two of the selected groups of sites in New York and Connecticut (see highlighted points in that area in the map of Fig. 2), whose ODVs and fits of Eq. (1) are highlighted in Fig. 5.

In several states, the largest ODVs are recorded at coastal sites (i.e., Connecticut, Massachusetts, New Hampshire, and Maine in Figs. 5, 6, S5, S7, S8, and S10). The large ODVs at coastal sites emphasize the important, widely discussed (e.g., Wolff and Lioy, 1980; Wilcox, 1996) role of transport in bringing high ozone concentrations from the major East Coast urban areas far downwind, particularly when that transport occurs over the waters of the Long Island Sound and the coastal Atlantic Ocean. Two relatively isolated Massachusetts coastal sites on the offshore island of Martha's Vineyard and near the tip of Cape Cod record some of the highest ODVs within that state (see Fig. S7). Dukes County, which includes only Martha's Vineyard, with a total population of ∼17 000, was once designated as a marginal non-attainment area for ozone.

In the past, ODVs at rural, generally upwind sites on the western border of New York (green symbols in on the left in Fig. 2) were significantly smaller than in the northeastern US urban areas, although in recent years that difference has diminished (Fig. 5). These upwind rural areas in New York, and similar sites in Vermont (Fig. S9), experienced ozone concentrations exceeding 80 ppb throughout the measurement record until about 2005. These high concentrations caused Chautauqua County, New York, with a population of ∼95 000, to also once be designated as a marginal non-attainment area, again emphasizing the importance of ozone transport in the northeastern US, although in this case the source of the transported ozone is not as clearly established.

Additional systematic features of the ODV time series in the northeastern US are discussed in Sect. S1 of the Supplement.

All of the curves derived from the fits of Eq. (1) to the long-term trends of the ODVs shown in Figs. 5, 6, and S3–S10 are compared in Fig. 7, with the corresponding parameters included in Table 2. Except for the four fits denoted by the colored dotted and dashed curves, all fits are similar in the sense that they exhibit the same relative long-term decrease and are asymptotically approaching approximately the same value of y₀. The same relative long-term decrease is necessarily forced by the use of the same value of τ=21.9 years in all fits. However, the derived A and y₀ values do provide information regarding the spatial and temporal variation in ODVs over the past 2 to 3 decades. Three of the four curves with noticeably different behavior are from fits to the groups of sites with the highest recently reported ODVs (Connecticut, especially the coastal sites, and the New York sites highlighted in Figs. 2 and 5); these are discussed further in Sect. S1 of the Supplement. The fourth exception is the one high-elevation site (Mt. Washington in New Hampshire at an elevation of 1.9 km), which is also discussed separately in Sect. S1. The parameters in Table 2 provide the basis for quantitatively comparing the fits throughout the northeastern US in the next two sections.

3.2.2 Estimation of US anthropogenic ODV enhancements in northeastern states from exponential fits

The fits to Eq. (1) with τ=21.9 years provide estimates of A, the US ODV enhancement in the reference year 2000; Table 2 lists these values for the 17 selected groups of sites from two-parameter fits, i.e., fits with y₀ and A as independent parameters determined from the least-squares fits themselves. However, the results above show that a constant value of $y_{\mathrm{0}}=\mathrm{45.8}\pm \mathrm{1.7}$ ppb is characteristic of the entire northeastern US region. Using this result allows fits of Eq. (1) to all groups of sites without the larger uncertainty in the y₀ derived from the individual fits. Consequently, results of one-parameter fits of Eq. (1) (i.e., with y₀ held constant at the value of 45.8 ppb) are included in Table 1 as the A^* values. (Such a fit is not included for the Mt. Washington results, since US background ODV is evidently greater than 45.8 ppb, as discussed in Sect. S1 of the Supplement.) The A^* values generally agree with the A values from the two-parameter fits within their confidence limits, which are smaller, since only one parameter needs to be derived. The exceptions to the agreement between A and A^* are the fits to the exceptions discussed earlier – the two groups of Connecticut sites and the New York maximum ozone sites, which are the upper three colored curves in Fig. 7. In Table 2 the A values for these three groups of sites are anomalously small compared to the results from neighboring groups of sites (i.e., New Jersey, Rhode Island, and Massachusetts/coastal); the A^* values for all of these neighboring groups of sites agree more closely. In the following discussion we take these A^* values as the best estimate for the US anthropogenic ODV enhancements in the northeastern states.

Figure 8Approximate contour plot of the US anthropogenic ODV enhancement due to photochemical production from precursor emissions in the year 2000, estimated from the A^* values given in Table 2.

A contour plot (Fig. 8) derived from the A^* values in Table 2 provides an overview of the spatial variation in the US anthropogenic ODV enhancements across the northeastern US. The groups of selected sites fit to Eq. (1) give only coarse spatial resolution across the region, so the contour plot has uncertainties not apparent from the smooth spatial variability in this figure. This uncertainty has been mitigated in deriving the contour plot by including duplicate A^* values at the site locations in each selected group of sites; these additions ensure that the contouring program reproduces a more nearly constant value over the sometimes-large regions covered by the selected groups of sites. Despite the uncertainties, the contour plot does give a useful, semi-quantitative representation of the magnitude and regional variation in the US anthropogenic ODV enhancements in the region. Note that the contour plot and the A and A^* values of Table 2 describe the ODV enhancements in the year 2000. As is apparent from Eq. (1) and the illustrated temporal trends in the figures, the ODVs have decreased throughout the last 2 to 3 decades. The e-folding time of τ=21.9 years implies that between the reference year of 2000 and 2017, the ODV enhancements decreased by a factor of 2.2. Hence, dividing the year-2000 ODVs in the contour plot by that factor gives an approximation of the 2017 US anthropogenic ODV enhancements.

Figure 9Comparison of observed ODVs color-coded by year with those calculated from Eq. (1) for (a) all monitoring sites and (b) for the maximum observed in each state. The dashed lines indicate the 1:1 relationships, with y₀ near the origin indicated by the larger circle. The dotted lines indicate the NAAQS. The number of data points, square of the correlation coefficient, and the root-mean-square difference between the observed and calculated ODVs for 2000–2017 are annotated.

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The ability of Eq. (1) to accurately reproduce observed ODVs can be judged by comparing the observed ODVs with the values predicted from the fits derived with y₀=45.8 ppb and τ=21.9 years. Figure 9a shows this comparison as a correlation plot. The fits for ODVs recorded at all sites in the eight northeastern states over the entire measurement period are calculated from the A^* values at each site interpolated from the contour plot of Fig. 8. The correlation is high (r²=0.71) for the 1719 separate ODVs recorded at the 148 sites over the 2000–2017 period but significantly lower for earlier years as expected from the figures, illustrating the derived fits. A general decrease in ODVs throughout the region did not begin until 2000, which is about the time that the US EPA “NO_x SIP Call” began reducing power-plant NO_x emissions across much of the eastern US (Aleksic et al., 2013). There is significant scatter about the 1:1 line in the comparison in Fig. 9a; the RMSD between observed and calculated ODVs is 5.6 ppb for the 2000–2017 period. Much of this scatter is due to variability in ODVs recorded at different sites within a given region, which arises from differences in local photochemical ozone production and transport patterns. This variability can be reduced by comparing state maximum ODVs (Fig. 9b) rather than individual site ODVs. Figure 10 plots the time series of these state maximum ODVs recorded in each year with respective fits over the 2000–2017 period. The derived A^* values (given in Table 3) are somewhat larger than would be expected from the contour plot in Fig. 8, consistent with consideration of only the maximum ODVs recorded in each state. Stronger correlation (r²=0.89) is found for the fits to the state maximum ODVs as expected, since considering only the largest of the state's ODVs in a given year removes much of the regional variability across the state.

Figure 10Time series of maximum ODVs reported from any site within each of the eight northeastern states. The solid curves are fits of Eq. (1) to the respective colored symbols for the 2000–2017 period. The derived A^* values from these fits are given in Table 3. The dashed lines are projections of the solid curves.

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Table 3Results of least-squares fits of Eq. (1) to the state maximum ODVs illustrated Fig. 10; y₀ and τ were held constant at 45.8 ppb and 21.9 years, respectively. The absolute root-mean-square deviations between the observed ODVs and the derived fits are indicated. Year_NAAQS indicates the projected year that the fit to the state maximum ODV drops to the NAAQS of 70 ppb.

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3.3 Evaluation of uncertainty of the exponential fits to ODVs in northeastern states

Here the methods described in Sect. 2.3 are applied to investigate the uncertainty of the results from the exponential fits presented in Sect. 3.2. Section 3.3.4 provides an overall assessment of this uncertainty.

Figure 11Comparison of maximum observed ODVs in the New York City and Los Angeles urban areas. (a) Temporal trend of observations (symbols) and fit to Eq. (1), including extrapolation to infinite time; annotations indicate year that extrapolations decrease to 70 ppb. The New York City results are the maxima from either the states of New York or New Jersey, and the Los Angeles results are those for the South Coast Air Basin (Fig. 8 of Parrish et al., 2017a). (b) Bar graph indicating maximum ODVs in 2000 and 2015 (hatched bars) and the estimated US background (bkgd) ODV (solid bars); the maximum ODVs are derived from the fits to Eq. (1) included in (a).

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3.3.1 Alternative approach for estimating US background ODVs in the northeastern US states

The independent analysis approach introduced in Sect. 2.3 can estimate US background ODVs through correlations between separate ODV time series. The ODVs from each of the 13 groups of sites that give the black lines in Fig. 7 are included in this analysis. The reference ODV time series chosen is the maximum observed ODVs in the New York City urban area (NYC urban maximum), which is equated to the maximum ODV observed each year in either New York or New Jersey. These maxima (plotted in Fig. 11a) are all recorded near the New York urban area. This reference is selected because these are among the largest ODVs recorded in the northeastern US, and after 2000 this time series closely follows an exponential decrease with little interannual variability. Figure 12 shows three example linear correlations (the ODVs recorded at the three sets of Massachusetts sites) with that reference. Figs. S12–S18 of the Supplement show all of the linear regressions for the 13 regional data sets, Fig. S19 compares all of the fits, and Table S2 collects the results. These results are quite variable (25 to 62 ppb) due to the relatively short 2000–2017 data records and because the slopes are not widely different from unity, preventing a precise determination of the intercepts of the correlations with the 1:1 line. However, the average of the derived background ODVs (49.2±3.9 ppb for ordinary linear regressions and 42.5±5.7 ppb for reduced major axis regressions, where 95 % confidence limits of the averages are indicated) bracket the result derived from the exponential fits, and neither average is statistically significantly different from that earlier result. The agreement between these two approaches for estimating US background ODVs shows that the assumption of an exponential decrease in the ODV enhancements is not essential for estimating the background ODV (although that approach does give more precise results) and increases our confidence in the results of each approach.

Figure 12Correlation between the ODVs from three sets of Massachusetts sites and the maximum ODVs recorded in the New York city urban area. Lines of corresponding color show ordinary linear regression (solid) and reduced major axis regression with equal weighting (dashed) fits of the correlated data sets for the ODVs recorded in 2000–2017. The black symbol shows the mean US background ODV derived from the exponential fits to the ODV time series, and the dotted line indicates the 1:1 relationship.

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3.3.2 Estimate of τ and y₀ from linear fits to ODV trends in the northeastern US states

Linear fits to the period of decreasing ODVs for three ODV time series are shown in Fig. 13. These three series were chosen so that one (NYC urban maximum introduced in the previous section) includes the largest ODVs, and two have some of the smaller ODVs in the northeastern US; this choice gives the largest contrast in the absolute year-2000 values and fitted slopes in order to provide the most precise τ and y₀ determinations. Table S3 gives the year-2000 values and slopes of those fits, which give zero-order estimates of $\mathit{\tau }=-{\mathrm{\Delta }}_{\mathrm{year}\mathrm{2000}\mathrm{value}}/{\mathrm{\Delta }}_{\mathrm{slope}}$ and y₀= (${\mathrm{\Sigma }}_{\mathrm{year}\mathrm{2000}\mathrm{value}}+\mathit{\tau }\cdot {\mathrm{\Sigma }}_{\mathrm{slope}})/\mathrm{2}$. However, as is apparent in Fig. 13, the year-2000 value and slope derived from each linear fit over the 18-year or 26-year period are biased with respect to the instantaneous value and slope of Eq. (1) in year 2000. This bias can be estimated from linear fits over those same time periods to the exponential curves defined by the zero-order estimates of τ and y₀. Table S3 gives year-2000 values and slopes corrected to first order for this bias. These corrected values give $\mathit{\tau }=\mathrm{21.1}\pm \mathrm{5.9}$ and 21.7±5.0 years and y₀=48.7 and 47.0 ppb for the fit parameters from the upper and lower Fig. 13 panels, respectively. These τ values compare favorably with the assumed California value (21.9 years), while the y₀ values are larger than derived in the analysis using exponential fits to Eq. (1) (45.8±1.7 ppb).

Figure 13Comparison of linear and exponential fits to three ODV data sets. The black line segments are linear fits to 2000–2017 for two data sets and 1991–2017 for one data set. The colored curves are the exponential fits to these time series, also shown in Figs. 11, S9, and S10.

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