The capability to detect air quality signals – be they meteorological, chemical, or of some other type – is a fundamental component of modern climate science and atmospheric chemistry. The debate over the existence or length of a global warming hiatus (Lewandowsky et al., 2015; Roberts et al., 2015; Medhaug et al., 2017) and research examining the time of emergence of climatological (Weatherhead et al., 2002; Deser et al., 2012; Hawkins and Sutton, 2012; de Elía et al., 2013; Schurer et al., 2013), meteorological (Giorgi and Bi, 2009; King et al., 2015), chemical (Camalier et al., 2007; Strode and Pawson, 2013; Barnes et al., 2016; Garcia-Menendez et al., 2017), and other sectoral signals (e.g., Monier et al., 2016) embody an accumulation of techniques and strategies for filtering noise (due to natural variability) and maximizing the capability to detect statistically significant signals and trends in noisy data. It is well established that temporal averaging (e.g., Lewandowsky et al., 2015) and spatial averaging (e.g., Frost et al., 2006; Hawkins and Sutton, 2012; Barnes et al., 2016) can enhance signal detection capabilities in atmospheric data. Here we extend this research by quantifying the impact of both spatial and temporal averaging – individually and in combination – of surface ozone on the magnitude of the calculated variability, which is largely driven by the influence of meteorological variability on atmospheric chemistry (e.g., Jacob and Winner, 2009). We offer recommendations for strategically averaging in space and time to maximize signal detection capabilities. In particular, we examine estimates of mean ozone and of the ozone variability that results from meteorology, although our approach can be generalized to other air quality applications.

For observed ozone data, strategies for reducing spatial and temporal noise are limited: a longer time series is needed, more observations need to be made, or the spatial region over which the ozone observations are being averaged needs to be enlarged. For surface ozone estimates using models, however, there exist a variety of strategies for reducing the noise (due to chemical and meteorological variability) relative to the strength of the signal, although they cluster into three main types. The first strategy is to average or combine multiple runs of structurally different models under the assumption that errors, biases, and uncertainties within the individual models are reduced and the multi-model or multi-dataset mean is a best estimate of the actual, aggregated ozone field. This is most notably done with multi-model ensembles within the Atmospheric Chemistry and Climate Model Intercomparison Project (ACCMIP) framework (Lamarque et al., 2013; Young et al., 2013; Stevenson et al., 2013), and this approach tends to assume that all members in the ensemble are independent and equally skillful. This assumption, however, may result in a loss of some valuable information (Knutti, 2010). Another form of this strategy is to run multiple model runs within a single model, but under different initial conditions or sets of parametric assumptions (e.g., Deser et al., 2012; Monier et al., 2013, 2015; Kay et al., 2015; Garcia-Menendez et al., 2015, 2017). This approach cannot address structural uncertainties and internal (unforced) variability between models, but is capable of identifying parametric uncertainties within a single model.

The second strategy to reduce ozone variability is to expand the temporal averaging window, which can influence the interpretation of the determined ozone value (e.g., Brown-Steiner et al., 2015). The Environmental Protection Agency (EPA) National Ambient Air Quality Standard (NAAQS) for ozone (US EPA, 2015) explicitly takes this into account, both in the length of the averaging period (daily maximum 8 h average) and the selection criteria for the standard (fourth highest over the previous 3 years). The calculated ozone variability can be further reduced by utilizing even longer averaging periods, such as monthly (e.g., Rasmussen et al., 2012), seasonal (e.g., Fiore et al., 2014; Barnes et al., 2016), annual, or decadal mean values (e.g., Garcia-Menendez et al., 2017). This strategy is analogous to the averaging of meteorological data to derive a climate signal, and, just as Lewandowsky et al. (2015) recommend averaging 17 or more years in order to achieve climatological estimates of temperature trends, there is a growing body of literature recommending averaging short-timescale chemical variability (what could be called chemical weather, see Lawrence et al., 2005) for 15 or more years (e.g., Garcia-Menendez et al., 2017) in order to achieve an estimate of what could be called the chemical climate (see Möller, 2010).

The third strategy to reduce ozone variability is to average surface ozone values over larger spatial regions, and, while there is a significant body of literature discussing the capability and interpretation of coarse-resolution model representations of the sub-grid-scale heterogeneity (Pyle and Zavody, 1990; Searle et al., 1998; Wild and Prather, 2006), there are few that strategically expand the spatial scale over which averaging is applied in order to maximize signal detection capabilities. This strategy has been applied in other fields of the atmospheric sciences as well as for general gridded datasets (e.g., Pogson and Smith, 2015), and spatial averaging has been suggested as a means of reducing temperature variability and smoothing biases at the smallest spatial scales within a single model run (Räisänen and Ylhäsi, 2011). This “scale problem” has also been noted as an important consideration when analyzing aerosol indirect effects (McComiskey and Feingold, 2012) and for the detection and attribution of extreme weather events (Angélil et al., 2017).

Our objective in this study is to provide a framework for selecting spatial and temporal averaging scales that reduces the uncertainty in analyzing ozone signals and limits the likelihood of overconfidence in an estimate of surface ozone that arises from meteorological variability. This type of framework can be useful from two different research perspectives. The first research perspective has a priori an ozone estimate (either observed or modeled) at a certain spatial and temporal scale (e.g., a 3-year simulation of surface ozone over the northeastern US) and aims to quantify the likelihood that this estimate is representative of the long-term ozone behavior (rather than overly sensitive to meteorological variability of that particular 3-year period). Since ozone is strongly influenced by natural fluctuations in meteorology (Jacob and Winner, 2009; Jhun et al., 2015) and since extremes in surface ozone and temperature tend to co-occur (Schnell and Prather, 2017), atypically hot or cold periods can strongly influence ozone behavior over short timescales.

The second research perspective is to identify an ozone signal of a certain magnitude (or threshold) and decide what spatial and temporal averaging scales are needed to best identify that signal. The ozone signal could be large (e.g., determining the effectiveness or compliance with a 5 ppbv incremental reduction of the EPA NAAQS for ozone; US EPA, 2015) or small (e.g., identifying annual ozone trends within the US, which Cooper et al., 2012, show can be on the order of 0.10–0.45 ppbv) and can be highly sensitive to spatial and temporal heterogeneity and meteorological variability. Barnes et al. (2016) found that surface ozone trends over 20-year periods can vary by ±2 ppbv due solely to climate variability, while interannual variability can be on the order of ±15 ppbv (Fiore et al., 2003; Tilmes et al., 2012; Lin et al., 2014) and day-to-day variability can be even larger, extending regularly from near-background levels of 40–50 ppbv up to 100 ppbv during the summertime (Fiore et al., 2014).

In this study, we quantify the impact of both temporal and spatial averaging on the calculated ozone variability – due solely to meteorological variability – in order to maximize the capability to detect signals. We use simulated ozone (with the Community Atmosphere Model with Chemistry, CAM-chem) and observational data (with the EPA's Clean Air Status and Trends Network, CASTNET) within the United States in order to answer the following four questions. (1) Within a given dataset (model or observations), with both spatial and temporal coverage, what is the magnitude of the ozone variability due to meteorology at the smallest scale, and how does spatial and temporal averaging reduce this variability? (2) Are there combinations of temporal and spatial averaging scales that maximize the signal detection capability for surface ozone data? (3) How sensitive are the above strategies to different configurations (i.e., emissions, meteorology, and climate) of the CAM-chem modeling framework? And (4) how could they be applied to other datasets (chemical, meteorological, or climatological)? We limit our focus to spatial scales within the United States as it has high spatial and temporal variability and numerous observations, and since averaging over larger regions (e.g., the Northern Hemisphere, or the globe) would produce a smaller calculated variability.

In Sect. 2, we describe the CAM-chem model and our simulations, as well as the CASTNET observational database and the regional definitions used throughout this paper. In Sect. 3 we quantify the temporal and spatial variability of surface ozone, show how temporal and spatial averaging reduces the calculated ozone variability, and demonstrate the spatial heterogeneity of the calculated ozone variability. In Sect. 4, we discuss the potential strategies that could be used to maximize ozone signal detection due to meteorological variability, explore uncertainties, and make recommendations for future research.

We examine both present-day (one simulation and one observed dataset) and future (two simulations) surface ozone in this study. For present-day analysis, we simulate surface ozone using CAM-chem, a component of the Community Earth System Model (CESM) and available observations within the US from the EPA CASTNET database. For future analysis, and in order to examine the potential for patterns of variability to change in the future, we utilize two existing simulations of CAM-chem conducted by Garcia-Menendez et al. (2017). Much of this analysis is conducted using the R language (R Project, https://www.r-project.org/, last access: 7 June 2018). Here we summarize each of the three datasets and our approach to our analysis in Sect. 3.

Here we examine the spatial and temporal behavior of MOZ_2000, MOZ_2050, and MOZ_2100 and compare MOZ_2000 to present-day CASTNET observations. We introduce the moving temporal averaging windows, explore possible thresholds of acceptable error or signal strength, and examine the influence of expanding spatial averaging regions. Finally, we combine these temporal and spatial averaging techniques into a single framework.

We now return to the original four research questions posed in Section 1. First, what is the magnitude of ozone variability due to meteorology alone at the smallest scale and what is the impact of increasing the scale of temporal and spatial averaging? In both observed and modeled MDA8 O3 surface data, the small-scale variability driven solely by the meteorological variability impact on atmospheric chemistry (expressed as the standard deviation as a percentage of the mean) can exceed 20 % (Table 1, Fig. 2d). The chemical variability examined here is the result of fluctuations in meteorology, which itself results from larger-scale climatological drivers. While variability in emissions also influences atmospheric chemistry, our analysis has removed the influence of emissions variability and isolated the variability due to meteorology. A more comprehensive analysis of chemical variability will need to account for both meteorological and emission variability, which is complicated by temporal trends in both the emissions of ozone precursor species and the climate.

There is high temporal and spatial heterogeneity of surface ozone variability (Fig. 2d), with the lowest values found in the western US (< 10%), higher values found in the eastern US (up to 20 %), and the highest values found over coastal or heavily populated regions (up to 30 %). Averaging over longer temporal scales (by increasing the averaging window) and over larger spatial scales (by expanding the averaging region) can reduce the magnitude of the calculated variability, with temporal averaging proving to be more effective than spatial averaging in most cases (Fig. 8). In this study, we performed simple spatial averaging, but there are other methodologies for smoothing two-dimensional signals (e.g., Räisänen and Ylhäisi, 2011; Pogson and Smith, 2015) that could potentially increase signal detection capabilities.

Second, are there combinations of temporal and spatial averaging that maximize the filtration of calculated ozone variability and thus maximize the potential for signal detection? Figure 8 (and Fig. S4) demonstrates clearly that there are cases in which the combined usage of temporal and spatial averaging can reduce the calculated variability better than either strategy alone (see Fig. 8b), although there are many regions within the eastern US in which spatial averaging has little to no impact on reducing the calculated variability (Fig. 8c) or even results in an increase in the calculated variability (Fig. 8d). There are no such cases (see Fig. S4) in which expanding the temporal averaging scale increases the calculated ozone variability. This could potentially enable region-specific averaging strategies that help decision-makers identify and meet regional air quality objectives.

Third, are these results dependent on the particular parameterizations of the CESM CAM-chem model and are they consistent with the available CASTNET observations? The three CESM CAM-chem simulations exhibited consistent representations of ozone variability, consistent with our understanding of future changes to the climate (and meteorology) and the resulting impact on atmospheric chemistry (Table 1, Figs. 4, S1, and S2). Compared to the CASTNET observations (which we detrended to remove the influence of changing precursor emissions), the present-day simulation (MOZ_2000) exhibited a high ozone bias in the eastern US, while the representation of the ozone variability is comparable (Table 1).

Fourth, how may these strategies be applied to other datasets, be they chemical, meteorological, or climatological? Much of this analysis could be applied to any dataset that has spatial and temporal coverage, as long as some set of acceptable thresholds is provided. While our time step in this analysis is daily (given the MDA8 O3 metric), and applied only to summertime (JJA) days, any time step (i.e., hourly, monthly, annual, decadal) could be utilized as long as cyclical trends (e.g., diurnal or seasonal cycles) are removed. Indeed, the sliding-scale presentation in Figs. 8 and S4 can specifically be utilized to identify particular spatial and temporal scales that are sufficient to identify signals at particular thresholds and to identify particular geographic regions that are best suited to identify a given signal. For example, Sofen et al. (2016) identified regions across the globe where additional observations would be particularly suited to improve our understanding of surface ozone behavior, and our analysis could potentially be used to identify particular temporal and spatial averaging scales that could further maximize the capability for trend detection. In particular, Sofen et al. (2016) noted that the peak in the power spectrum of the El Niño–Southern Oscillation (ENSO) on surface ozone is at the 3.8-year timescale, and that, within some regions within the US, the amplitude of the ENSO influence on surface ozone approached 0.5 ppbv (and up to 1.1 ppbv globally). Our analysis shows that there are no grid cells within the continental US where a 0.5 ppbv signal can be identified at the 5-year (or shorter) temporal averaging scale (Fig. S4), but that there are many regions – especially within the western US – in which even a modest amount of spatial averaging can identify surface ozone signals below the 1 ppbv level with a 5-year or shorter averaging window. The type of sliding-scale analysis – in which spatial and temporal averaging are utilized individually and in combination – as presented in Figs. 8 and S4 could readily be applied to a wide range of atmospheric (and other) topics to aid in the capability to identify signals that exist both in space and in time. In particular, low-frequency oscillations (e.g., ENSO, and others) and other forms of internally or externally forced trends (e.g., anthropogenic and natural changes in emissions) are readily adaptable to this type of analysis, which could address signals pertaining to precipitation, biogenic emissions, boundary layer variables, cloud properties, and many others.

We did not quantify statistical significance (as in Lewandowsky et al., 2015) as our goals were to understand the general nature of ozone variability at all scales and for all signal strengths. Statistical significance testing (and other statistical techniques) can certainly provide additional information as to the strengths of ozone signals within the underlying variability and can be used to extend these results in a case-by-case manner, but we leave this testing to future studies that can focus on particular air quality objectives at particular temporal and spatial scales. Furthermore, future research examining the impact of spatial and temporal averaging using regional-scale models, models with different resolutions, and the inclusion of urban observations could provide additional insight into understanding chemical variability and averaging techniques.

Smaller signals require longer temporal averaging periods to identify. Figure 4 shows that a 0.5 ppb MDA8 O3 signal will emerge after 15–20 years of temporal averaging. The range here reflects different spatial averaging domains, with larger domains requiring shorter temporal averaging windows than smaller domains (i.e., 15 years for averaging over the continental US and 20 years for averaging over the northeastern US). This would mean that an average trend of 0.25–0.33 ppb year-1 would require a time series of at least 15 years to identify. Similarly, a 1.0 ppb MDA8 O3 signal emerges after 7–15 years, which indicates an average trend of 0.14–0.67 ppb year-1 would take at least 7 years to identify. Finally, a 5 ppb signal can be identified in less than 3 years, which indicates that an average trend of 1.67 ppb year-1 or greater would only require a 3-year time series. This presents particular difficulties if the ozone signal of interest is a trend spanning a time period on the same order. The 10–15 year averaging timescale we propose translates into a length of time beyond which you are likely to not see spurious trends above 0.5 ppb, but there are many cases in which the identification of a small trend is desired with less than 10–15 years of available data.  For instance, Jiang et al. (2018) have found that NOx emissions reductions since 2005 are not as strong as previously expected, showing a significant slowdown beginning in 2011. This has large implications for ozone and for short-term decisions for air quality managers within the United States, who have to promulgate policies on short-term scales without the luxury of postponing action until longer and more complete datasets become available. As we have shown, spatial and temporal variability due to meteorology is high, and the identification and quantification of trends over 5, 10, or 15 years is difficult, particularly at small spatial scales.

However, as we have shown, a consideration of the impact on variability – and how variability changes over time – is often pivotal to understanding the nature of the signals being examined. In this paper, we have provided methods for quantifying the spatial and temporal variability and strategies for determining which types of signals are likely detectable at particular temporal and spatial scales. Some signals, especially small signals at small scales, are simply not large enough to emerge from the variability and thus may not be detectable without additional data or expanding the temporal and spatial averaging scales used for analysis. Quantifying the signal-to-noise ratio at a variety of spatial scales, and determining an acceptable threshold of a particular signal, could be one accessible method for providing this context. The risk in neglecting the quantification and contextualization of the magnitude of the ozone signal relative to the magnitude of the variability induced by the internal meteorology – and the impact of temporal and spatial averaging – is primarily the risk of drawing conclusions that are more sensitive to a particular peculiarity in the underlying variability rather than the signal itself.

We quantified the impact of spatial and temporal averaging at different scales – both individually and combined – on estimates of summertime surface ozone variability and the resulting likelihood of overconfidence in estimates of chemical signals over the United States using CASTNET observations and the CESM CAM-chem model. We simulate three multi-decadal time periods, each with constant surface emissions, and find that this analysis is consistent across our simulated time periods and that our results are not sensitive to particular configurations and parametric choices within the CESM CAM-chem (i.e., emissions, meteorology, and climate). We also provide a conceptual framework for gaining understanding of the influence of spatial and temporal averaging that may be adapted to a wide range of atmospheric and surface phenomena, provided sufficient spatial and temporal coverage. Here we focus on summertime surface ozone, a highly variable (in both space and time) atmospheric constituent with severe human health impacts and implications for planetary climate, which is the focus of many local, regional, and national policies. However, these ozone signals (e.g., temporal trends or regional averages) are frequently small when compared to the magnitude of the day-to-day ozone variability, and thus detecting these signals can be challenging. In particular, it would be impractical to delay interpreting observations for 10–15 years or alternatively to expand the spatial averaging such that small-scale features are smoothed away. Nonetheless, it is unwise to over-interpret trends and signals based on observations from a limited spatial area and over a short temporal period. Our analysis and conceptual framework presented here cannot solve this tension, but it does demonstrate some strategies which can allow for a selection of spatial and temporal averaging scales, and a consideration of the error threshold, that can aid in this signal detection on a case-by-case basis. Taking into account the complex interactions involving trends and variability between emissions, chemistry, meteorology, and climatology necessitates a variety of strategies. This work quantifies the impact of spatial and temporal averaging in signal detection, which can be used in conjunction with ensembles of simulations, statistical techniques, and other strategies to further our understanding of the chemical variability in our atmosphere.

In order to quantify the impact of spatial and temporal averaging on summertime ozone variability, we start by selecting four telescoping spatial regions (the continental US, the eastern US, the northeastern US, and a single grid cell within the northeastern US) and examine all possible choices for averaging windows (ranging from daily to multi-decadal windows), although we focused primarily on averaging windows of 1, 5, 10, and 20 years. We find that – consistent with previous studies – summertime MDA8 O3 variability is largest at the smallest spatial and temporal scales and is frequently on the order of ±10–20 ppbv or which is roughly 15–20 % of the mean ozone signal. In order to minimize the chemical noise that results from meteorological variability – and thus enhance the signal – we find averaging windows of 10–15 years (and sometimes longer at the smaller spatial scales) combined with modest (nearest-neighbor) spatial averaging substantially improve the capability for signal detection. For signals that are large compared to the underlying meteorological variability (e.g., strong emissions reductions), shorter averaging windows and smaller spatial regions may be used. We recognize that achieving a 10–15 year temporal averaging window is difficult, but this recommendation is consistent with recent literature (e.g., Barnes et al., 2016; Garcia-Menendez et al., 2017). For studies where 10–15 years of averaging is impractical, we recommend that some spatial and temporal context is provided that demonstrates that the signals being examined are robust and not the result of internal variability or noise. We also recognize that our analysis is just one strategy for enhancing signal detection capabilities and will ideally be used alongside others, such as perturbed initial condition ensembles, running simulations with either internal or forced meteorology, and examining a region or time period with different models or parameterizations.

We show that the largest summertime ozone variability is found in the eastern US (Figs. 5 and S4), and subsequently there are many regions within the eastern US where even a 20-year averaging window has a non-negligible likelihood of estimating ozone variability that is dependent (with possible error in the 1–3 ppbv range) on the particular years selected. In addition, over much of the eastern US, simulations of 5 years or less have a substantial likelihood (40–90 %, Figs. S1 and S2) of reflecting the influence of meteorological variability on chemistry rather than the mean state of surface ozone, with the possibility of 5–10 ppbv error (Fig. S4). While we have detrended the CASTNET observations to compare to the constant year-2000 cycled emissions in the simulations, the CASTNET time series inherently includes the compounded variability of both meteorological and emission sources. Future studies will need to expand this analysis to include trends and variability in the emissions, as well as in the meteorology.

Finally, we demonstrate a conceptual framework that allows for a sliding-scale view of surface ozone variability, in which both temporal and spatial averaging is examined at every grid cell within the continental US. We show that the magnitude of estimates of ozone variability can be reduced with both temporal and spatial averaging, although temporal averaging tends to be more effective. While there are many regions in which both temporal and spatial averaging used in conjunction substantially reduce the estimate of ozone variability, there are some regions where spatial averaging is ineffective or even counter-effective. In contrast, this is not the case for temporal averaging, which consistently reduces the magnitude of estimated ozone variability. Our analysis could be combined with other studies (e.g., Sofen et al., 2016) to guide observational and modeling strategies and identify regions and scales at which particular signals are most likely to be identified.