Air pollution variability is strongly dependent on meteorology. However,
quantifying the impacts of changes in regional climatology on pollution
extremes can be difficult due to the many non-linear and competing
meteorological influences on the production, transport, and removal of
pollutant species. Furthermore, observed pollutant levels at many sites show
sensitivities at the extremes that differ from those of the overall mean,
indicating relationships that would be poorly characterized by simple linear
regressions. To address this challenge, we apply quantile regression to
observed daily ozone (O

Poor air quality is projected to become the most important environmental
cause of premature human mortality by 2030 (WHO, 2014). Long-term exposure to
high levels of ozone (O

A changing climate may modulate air quality, with implications for human health. Pollutant formation, transport, lifetime, and even emissions all depend, to a certain degree, on local meteorological factors (Jacob and Winner, 2009; Tai et al., 2010), meaning that changes in the behaviors of these factors will often lead to changes in pollutant levels and exposure risks. Understanding the relationships between meteorological variability and observed pollutant levels will be critical to the development of robust pollution projections, as well as sound pollution control strategies. However, while straightforward sensitivity analyses using long-term averages and simple linear regressions provide valuable information on mean pollutant behavior, they are insufficient for analyses of extreme behaviors. Drivers and sensitivities characteristic of average pollutant responses will not necessarily be reflected throughout the entire pollutant distribution. To evaluate these relationships statistically, alternative methodologies must be used.

Previous studies examining the impact of meteorology on pollution levels have addressed the problem using a variety of tools. Modeling sensitivity studies offer a direct means of comparing the impacts of large-scale scenarios or individually adjusted parameters, allowing for a degree of comparison and replication that is impossible using only observations (e.g., Hogrefe et al., 2004; Mickley et al., 2004; Murazaki and Hess, 2006; Steiner et al., 2006; Heald et al., 2008). From such output, pollutant levels under multiple conditions or scenarios can be evaluated more or less in the same way that observed levels are, including the examination of global burdens, regional patterns, or even local exceedance frequencies as a function of meteorological changes. However, while these tools are powerful, it can be difficult to verify and understand projected changes due to the high degree of complexity of these models. On the other hand, observation-based examinations (e.g., Bloomer et al., 2009; Rasmussen et al., 2012) are tied closely to the actual underlying physical processes producing changes in pollutant levels, but are naturally limited in terms of identifying and quantifying the impacts of individual drivers – it is difficult to separate the impacts of different meteorological factors without the benefit of multiple sensitivity comparisons afforded by models.

Daily maximum 8 h O

Ordinary least-squares (OLS) regressions are effective tools for identifying
trends and sensitivities in the distribution of pollution levels as a whole,
especially for well-behaved data showing uniform sensitivities. Previous
studies have analyzed the impacts of changes in weather and climate on
O

This situation is one common example of a distribution that might be better characterized through the use of more advanced statistical tools, such as quantile regression (QR) (Koenker and Bassett Jr., 1978). A semi-parametric estimator, quantile regression seeks to minimize the sum of a linear (rather than quadratic) cost function, making it less sensitive to outliers than OLS regression. Unweighted, this simple change produces a conditional median (or 50th quantile regression), rather than the conditional mean of OLS regression. Applying appropriately chosen weights to the positive and negative residuals of this cost function then targets specific percentiles of the response, allowing for the quantification of sensitivity across nearly the entire response distribution. An example of this regression performed across a broad range of percentiles is shown in Fig. 1b, including the 5th quantile in black, the 50th quantile in yellow, and the 95th quantile in red.

Here, we apply multivariate QR to an analysis of meteorological drivers of
O

Location of AQS stations included in this study. The magnitude of each station's 95th percentile measurement is indicated by color.

We use O

Meteorological variables are taken from the National Centers for Environmental Prediction (NCEP) North American Regional Reanalysis (NARR) product (Mesinger et al., 2006). With a spatial resolution of 32 km and 8 output fields per day (representing 3-hourly averages), NARR output provides a reasonable spatial and temporal match for each of the AQS stations of interest. While the NARR product represents modeled output and includes its own errors and biases when compared to observations, it allows for the consistent use of many variables at high spatial and temporal resolution, most of which would not be available at all included AQS stations examined here. NARR reanalyses have been used in previous examinations of meteorological air pollution drivers with some success (e.g., Tai et al., 2010).

As an initial step towards understanding the impacts of meteorology on pollutant extremes, we construct a large set of possible meteorological covariates, including NARR meteorological variables for a range of time frames. By extending the initial scope of possible drivers, we attempt to capture the important factors and interactions, including not only effects that were important at all sites, but also those that stood out only in particular regions or types of locations. To this end, we begin by considering as many potential indicators as possible, gradually trimming the list down to a final set to be used in the multivariate quantile regressions. We use the 3-hourly NARR output to reconstruct hourly resolution diurnal cycles for each meteorological variable at each station through time series cubic splines and bilinear interpolation of the gridded fields to station latitudes and longitudes. In some cases regional means were included, primarily due to insufficient variability in individual cell values for that variable at some sites.

In addition to the raw variables available through NARR output, we calculate
several derived parameters. The synoptic recirculation of air has been
linked to elevated pollutant concentrations at many sites around the world,
especially in coastal regions where diurnal wind patterns are prone to
recirculation (Alper-Siman Tov et al., 1997; St. John and Chameides, 1997; Yimin and Lyons, 2003; Zhao
et al., 2009). When air masses are returned to a site with ongoing
emissions, the buildup of precursor concentrations may generate
exceptionally high pollutant levels. To measure this effect we calculate a
daily recirculation potential index (RPI) from surface wind speeds based on
the ratio between the vector sum magnitude (

Stagnation, or the relative stability of tropospheric air masses, is another
meteorological phenomenon previously cited as a driver of pollutant extremes (Banta
et al., 1998; Jacob and Winner, 2009; Valente et al., 1998). While some of
the raw meteorological fields (e.g., wind speed and precipitation) are
already themselves good indicators of local stagnation, lower-tropospheric stability (LTS), the difference between surface and 700 hPa potential
temperatures, is also calculated as a reflection of temperature inversion
strength in the lower troposphere (Klein and
Hartmann, 1993). Temperature inversions, in which the daytime pattern of air
being warmer near the Earth's surface is reversed, generally lead to stable,
stagnant conditions well-suited for the buildup of pollutants such as
O

From the selected set of raw and derived NARR meteorological fields (Table 1), we generate a range of temporal variables for each individual meteorological variable, including extrema and means for each 24 h day, as well as for 8 h daytime and previous 8 h nighttime ranges. To include possible long-term impacts of these meteorological variables, each of the 9 daily values are then extended into 3- and 6-day maxima, minima, and means, as well as a 1-day delta variable to show 24 h change, resulting in 63 total temporal options for each listed meteorological variable.

Meteorological fields used in variable selection procedure. Each
NARR field shown was included using nine different possible daily values
(24 h max/min/mean, 8 h daytime max/min/mean, previous 8 h
nighttime max/min/mean), as well as longer term (3- and 6-day) aggregates
and 1-day deltas of those daily values. Variables marked “9x9” represent
regional means, and were generated by averaging the 9

Biomass burning emissions can impact pollutant concentrations (e.g.,
Streets et al., 2003) with indirect correlations to daily meteorological
variability, making it a potentially confounding factor when performing
analyses using meteorological variables alone. To help examine and quantify
the likely impact of fires on observed pollutant levels, we create a simple
fire metric to represent the spatial and temporal proximity of each site to
satellite-observed burn locations. Using output from the Moderate Resolution Imaging Spectroradiometer (MODIS) Global Monthly Fire Location Product
(Giglio et al., 2003; Justice et al., 2002), we estimate the total fire proximity impact for each site by
applying spatial and temporal decays to burn detection confidence values,
and summing these values across all detected pixels through the equation

Combining the 63 described temporal options with all chosen raw and derived
meteorological variables results in over 1700 possible pollutant indicators,
making variable selection problematic. With driver identification an
important goal of this work, we initially keep the selection procedure as
open as possible, maximizing the first sweep of candidates and only
eliminating possible drivers after thorough evaluation (Fig. 3). However,
indiscriminate inclusion of additional variables opens the strong likelihood
of problems related to overfitting and multicollinearity. Furthermore, for
the sake of comparison between stations, we aim for a single set of indicator
variables for the entire set of observation sites included, making selection
on a station-by-station basis impractical. For these reasons we utilize a
stepwise multivariate approach based on combining covariate rankings at
individual stations into a single selection metric. To reduce the
computational cost of variable selection initially we use a testing subset of
stations, including 10 stations (with varying degrees of mean pollutant
levels) from each of the 10 EPA regions (shown in Figs. 4, 5, 7, and 8). We
then use observed pollutant levels (maximum 8 h average O

Flowchart of variable selection procedure described in Sect. 2.4.

We select meteorological indicators using 90th percentile quantile
regressions evaluated with the Bayesian information criterion (BIC) metric,
a statistical tool closely related to the Akaike information criterion (AIC)
and similarly based on the likelihood function (Schwarz, 1978; Lee et al., 2014). BIC evaluates the
likelihood of a given set of indicators representing the best set possible,
given a set of associated responses (in this case, daily pollutant levels),
with lower BIC values indicating a stronger statistical model (i.e., the set
of predictive meteorological indicators being evaluated). To perform
stepwise variable selection, we quantify the benefit (via BIC) of adding
each individual variable candidate to the list of selected variables in
turn. Large reductions in BIC indicate a more-important variable, while
small reductions (

We begin variable selection by using only time (measured in days elapsed) as
a predictor variable, accounting for any linear trend in pollutant behavior
over the course of the observed period (Fig. 3, step 3). From there, we
identify the most impactful temporal option (daily maximum, mean, minimum,
etc.) available for a single meteorological variable (e.g.,
surface temperature). We perform stepwise variable selection at each station
independently, selecting the candidate temporal option producing the
greatest reduction in BIC (and therefore greatest improvement in the
statistical model), and continuing until no further improvement is possible
(step 4). We then rank the final set of chosen variables at each station by
order of selection (step 5), invert those ranks, and sum these inverted
ranks over all 100 test stations (step 6). This sum represents an overall
importance metric, and will be large for variables that either appear
somewhat valuable at many stations, or that appear to be exceptionally
valuable at just a few stations. We then add the single temporal option with
the greatest summed total to the master list of selected variables. With a
new indicator chosen we filter the remaining candidates (step 8),
eliminating poor performers (those selected at too few sites in the previous
round) or those exhibiting collinearity with the current master list
(

Frequency at which normalized 95th percentile QR coefficients for
selected variables were in the top two out of all included variables (above)
for summer O

Same as Fig. 4, but for winter O

Through this routine, variables can stand out for selection by being either moderately important at many sites, or by being very important at fewer sites. By adjusting the threshold parameter for variable selection, the scope of variable inclusion can be tuned to a certain extent. Higher thresholds end the selection process sooner, as fewer and fewer new variables are ranked highly at enough stations to meet the summed value requirements, while lower values allow the process to continue adding less important variables. In this work we identify and compare both a concise “core” set of indicators (variables with summed inverse ranks of at least 2) and a “full” set of indicators (variables with summed inverse ranks of at least 1).

It should be noted that the NARR fields used to provide our input meteorological covariates likely exhibit intrinsic errors and biases which will certainly affect the predictive power of our models, as well as the strength of our variable selection process itself. Variables which are better represented (e.g., temperature) will have an advantage compared to other potentially important variables with greater uncertainties, such as precipitation.

The final sets of indicator variables represent those covariates most
broadly associated with changes in high pollutant levels due to
meteorological factors at the 100 chosen test sites. Using these selected
meteorological variables, we next perform linear multivariate quantile
regression to identify sensitivities for percentiles from 2 to 98 % at
each station in the full set of AQS sites. From these regressions we collect
summer (JJA) and winter (DJF) quantile sensitivities of O

To assess relative covariate importance across the USA we normalize quantile sensitivities to standard deviations of pollutant and indicator fluctuations and rank them in relation to each other at each site. Top-ranking covariates for any given station, then, are those whose variabilities (in normalized units of standard deviations) are most responsible for variability in the observed pollutant. Figures 4, 5, 7, and 8 show each variable's frequency of appearing as the first or second most important indicator by this metric, with similar variables grouped together into columns. We compare the covariates most associated with the 95th and 50th percentile of pollutant concentrations, finding similar, though not identical, frequencies between top performers for the two quantiles.

Selected covariates for O

In the summertime, covariates linked to high-percentile O

While maximum daily surface temperature stands out as the covariate with the
highest normalized impact on daily summer O

Spatial and frequency distributions for key covariates of summer
(top panels) and winter (bottom panels) O

Same as Fig. 4 but for summer PM

Same as for Fig. 4 but for winter PM

While the top covariate frequencies shown in Fig. 4 can help identify
dominant meteorological factors overall, they do not indicate spatial
distributions or sensitivity magnitudes. The bottom panel of Fig. 4 and top
panel of Fig. 6 address these aspects of selected top covariates, showing
where each tends to drive pollutant variability, as well as how the
sensitivity magnitudes are distributed overall. Spatially, the temperature
sensitivity of 95th percentile O

O

Same as Fig. 6 but for PM

Normalized pollutant concentration sensitivities to meteorological
covariates (0.0

Figure 7 shows that mean daily temperature is also a key player in predicting
summertime PM

In addition to temperature, 95th percentile PM

Unlike O

Compared to factors connected to median PM

The differences between typical 5th, 50th, and 95th percentile sensitivities
shown in Figs. 4, 5, 7 and 8, help to illustrate the ways in which
meteorological impacts on pollutants can vary in magnitude across the
response distribution. These differences can be more clearly quantified and
compared by measuring the slope of a QR regression itself as a function of
the percentile (Fig. 10). Using the full range of normalized QR output
gathered, from 2 to 98 %, we perform weighted least-squares regressions for
each selected variable at each station. The resulting slope for each
regression (in normalized units of standard deviations) can be interpreted as
a measure of change in sensitivity across the pollutant distribution, with
high values representing strong positive differences in sensitivity, and low
values representing strong negative differences. In other words, a zero slope
implies that the response of a pollutant to a given meteorological covariate
is relatively uniform regardless of the pollutant's concentration, while a
positive slope implies that responses at the high extremes tend to be greater
than those of lower percentiles. To put these changes in context, the overall
mean sensitivity for each variable is shown in color. Quantifying the extent
to which these differences in quantile sensitivities might impact the
response distributions themselves is beyond the scope of this work, but the
magnitudes of sensitivity differences relative to the mean sensitivities
themselves suggest large differences between mean and extreme behavior. For
example, the sensitivity change of summer O

Ordinary least-squares coefficient of determination (

For summertime O

The variables identified here were not selected based on their suitability
for ordinary least-squares regression, but they do show considerable skill at
predicting pollutant levels using this methodology, explaining over half of
the variability at most sites (Fig. 11). Predictive skill for summertime
O

PM

It is apparent that relatively simple meteorological processes, chosen for
their influence on high percentiles of O

Another important consideration in the analysis of these results is the
nonstationarity of both pollutant concentrations and sensitivities. As a
result of the implementation of widespread emissions controls,
concentrations of O

To a certain extent, these changes in pollution levels over time are
accounted for in our analysis through the inclusion of time (measured in
days since the start of the analyzed record) as an indicator variable.
However, changes in meteorological sensitivities themselves as a function of
decreasing emissions are not accounted for. To assess how these decreases in
emissions and overall pollution levels might have affected meteorological
sensitivities, the analyses above were repeated using 4-year subsets of the
full data record: 2004–2007 and 2008–2012, showing a widespread reduction in
sensitivities over time, presumably due to changes in precursor emissions.
For example, 95th percentile sensitivities of summertime O

This analysis demonstrates that air quality over the past decade was highly
sensitive to meteorology, and that this sensitivity varied across pollutant
type (O

We find that temperature is a dominant covariate at most stations in the
summer for both O

Climate change in coming decades is likely to induce a response in regional
air pollution. The sensitivities of O

This analysis framework offers new ways to investigate both the observed and simulated air-quality responses to climate. Through quantile regression, the selection and ranking of key predictors of pollutant variability can be evaluated robustly, focusing not on the mean behavior of a heavy-tailed pollutant distribution, but rather the sensitivities closer to the tail itself. Furthermore, the comparison of observed sensitivities to those simulated by regional or global air-quality models could identify key model biases relevant to the projection of future air quality, potentially providing insights on the underlying mechanistic reasons for those biases.

This work was supported by the EPA-STAR program. Although the research described in this article has been funded by the US EPA through grant/cooperative agreement (RD-83522801), it has not been subjected to the agency's required peer and policy review and therefore does not necessarily reflect the views of the agency, and no official endorsement should be inferred. The authors acknowledge Brian J. Reich for useful discussions. Edited by: S. Brown