The relationship between PM2.5 and anti-cyclone wave activity during summer over the United States

Abstract. To better understand the role of atmospheric dynamics in modulating surface concentrations of fine particulate matter (PM2.5), we relate the anti-cyclone wave activity (AWA) metric and PM2.5 data from the Interagency Monitoring of Protected Visual Environment (IMPROVE) data for the period of 1988–2014 over the US. The observational results are compared with hindcast simulations over the past two decades using the National Center for Atmospheric Research-Community Earth System Model (NCAR CESM). We find that PM2.5 is positively correlated (up to R = 0.65) with AWA changes close to the observing sites using regression analysis. The composite AWA for high aerosol days (all daily PM2.5 above the 90th percentile) shows a similarly strong correlation between PM2.5 and AWA. The most prominent correlation occurs in the Midwestern US. Furthermore, the higher quantiles of PM2.5 levels are more sensitive to the changes in AWA. For example, we find the averaged sensitivity of the 90th percentile PM2.5 to changes in AWA is approximately three times as strong as the sensitivity of 10th percentile PM2.5 at one site (Arendtsville, Pennsylvania; 39.92° N, 77.31° W). The higher values of the 90th percentile compared to the 50th percentile in quantile regression slopes are most prominent over the northeastern US. In addition, future changes in US PM2.5 based only on changes in climate are estimated to increase PM2.5 concentrations due to increased AWA in summer over areas where PM2.5 variations are dominated by meteorological changes, especially over the western US. Changes between current and future climates in AWA can explain up to 75 % of PM2.5 variability using a linear regression model. Our analysis indicates that higher PM2.5 concentrations occur when a positive AWA anomaly is prominent, which could be critical for understanding how pollutants respond to changing atmospheric circulation, as well as developing robust pollution projections.


. These two major revisions caused improvements in such aspects as the Madden-Julian oscillation and ENSO (Neale et al., 2008). The improved trend and magnitude of surface PM2.5 using this free-running model has been evaluated elsewhere (Tilmes et al., 2016).
The chemical emissions and forcing details for each of the model simulations are listed in Table 1. The simulation using specified dynamics (REFC1SD) for current levels of PM2.5 from 1991 to 2010 is driven by analyzed meteorological data 125 from Modern-Era Retrospective Analysis for Research and Applications (MERRA) (see Tilmes et al., 2016). This simulation follows the conventions of the CCMI (Eyring et al., 2013). For the AWA analysis for this case, we use the 500-hPa geo-potential height from MERRA, which should be very similar to that from ERA-Interim, since they use largely the same observations.
To compare the relationship between AWA and PM2.5 concentrations in online simulations, three simulations forced by trace gas projections and an interactively coupled ocean are employed. The GCM2000 and GCM2100 simulations are 25-year runs  (Eyring et al., 2013), which are repeated for all the simulated model years. Another future run (REFC2) is forced by future climate combined with future emissions following the REFC2 CCMI modeling protocol. In this run greenhouse gas forcing and emissions following the RCP6 scenario. The relationship between ozone and AWA has been examined in the GCM2000, GCM2100 and REFC2 simulations in Sun et al. (2019). Characteristics of the REFC1SD simulation are given in Phalitnonkiat et al (2018). Note that our REFC2 set-up covers volcanic eruptions in 140 the past, but possible volcanic eruptions in the future are not included (Eyring et al., 2013).

AWA calculation
Studies on finite amplitude wave activity (FAWA) have identified the link between the pattern of atmospheric circulation and large-scale wave dynamics (Nakamura and Solomon, 2011;Methven, 2013;Chen and Plumb, 2014;Lu et al., 2015). LWA adds the longitude dimension to the zonally average quantity FAWA and is calculated from the meridional displacement of 145 quasigeostrophic potential vorticity (PV) from zonal symmetry (Nakamura and Zhu, 2010). LWA helps differentiate longitudinally isolated events and describe extreme weather events at the local scales (Huang and Nakamura, 2016, Chen et al., 2015. Chen et al. (2015) used local finite-amplitude wave activity based on the 500-hPa geo-potential height for characterizing mid-latitude weather events. The total wave activity is composed of the cyclonic wave activity residing to the south of the equivalent latitude and the anticyclonic wave activity (AWA) to the north (see Fig. 1 in Sun et al, 2019). In this study, we focus 150 on AWA to characterize its connection with changes in PM2.5 concentrations. Over the US in summer LWA is dominated by its anticyclonic component (Sun et al., 2019). Sun et al. (2019) also used AWA to characterize ozone variability.

Quantile regression
Quantile regression is used to estimate the slopes for several conditional quantile functions (Koenker and Bassett, 1978). It characterizes the connection between a range of predictor variables and specified percentiles (or quantiles) of the response 155 variable. For example, Porter et al. (2015) analyzed the sensitivities of ozone and PM2.5 concentrations for response quantiles ranging from 2 to 98%. The parameters of quantile regression models evaluate the change in a specific quantile of the response variable caused by a one-unit change in the predictor variable. This permits us to measure how some percentiles of the PM2.5 may be more influenced by AWA than others, and this is indicated by changes in the regression coefficient. In order to illustrate the sensitivity of the PM2.5 concentration at different quantiles, we apply linear quantile regression for percentiles from 10 th to 160 90 th at the AREN1 site. And then we compare the 90 th percentile quantile regression coefficient with 50 th percentile quantile regression coefficient at each station.

The univariate linear regression model
To help explore and measure the likely relationship between AWA and PM2.5 levels, we use the univariate linear regression model, similar to a previous study focused on ozone (Sun et al., 2019). Here the slope of PM2.5 with respect to wave 165 activity (S i0,j0 (i, j)) on the daily time scale is used to show the linear association between changes (in time) of the normalized PM2.5 at a point (i 0 , j 0 ) and the normalized wave activity at another point. We use the projection of PM2.5 onto AWA to reveal how closely the AWA anomaly field resembles the spatial pattern that enhances PM2.5 on the daily time scale during the summer. The projection of AWA (p i0,j0 ) at all points in the domain onto S i0,j0 is defined according to the following equation: The similarity between AWA spatial pattern and the PM2.5-AWA regression coefficients' spatial structure is estimated by the projection value. The interannual change in PM2.5 due to changes in AWA is predicted based on a linear regression model as following equation (see Sun et al., 2019 for more discussion): The change of PM2.5 (denoted by ∆P M 2.5) in the future due to the change in AWA is calculated using the following equation, that is the climatological difference in future climate and the present climate (AW A f − AW A p ), project it onto S, and multiply it by the slope β: Here, S is calculated from the values for the present climate. The projected value can measure the similarity between the 180 AWA change and the PM2.5's trend with AWA by compressing the information of the AWA field into a single variable. This variable incorporates the non-local effect of AWA on PM2.5's variability.

The composite methodology
We use a composite methodology which is based around the most polluted (>90 th percentile) daily PM2.5 and the corresponding anomalies at every station. Composite 500-hPa geopotential height and AWA for daily values of PM2.5 larger than 90 th 185 percentile are produced by separately averaging all daily anomaly values of the corresponding 500-hPa geopotential height and AWA.

Results and discussion
The monthly mean PM2.5 surface concentrations with standard deviation for different scenarios at three representative sites are shown in Figure (Figure 3a; shading). The difference between two current climate simulations (REFC1SD minus GCM2000) for summertime AWA is shown in Figure 3b. The reduced AWA in the reanalysis forced simulation is found across most of the US, with the largest reduction in the Southwestern US as previously shown (Sun et al., 2019). In contrast, the AWA in summer is higher over the Northeastern US in the forced simulations. The corresponding changes in summertime PM2.5 205 concentration caused by a combination of different emissions and possibly changes in AWA is similar to changes in AWA, although the reduction is largely over South-central US. The difference between two future scenarios (GCM2100; REFC2) and current climate scenario (GCM2000) has a similar pattern (illustrated in Figure 3c and d), which shows a large increase in AWA in the Southwestern US, but there is a difference in the amplitude of these changes (contrast Figure 3c

Relationship between PM2.5 concentrations and AWA at specific stations
For the three observation sites highlighted here (AREN1, SIPS1 and LAVO1), the PM2.5 concentrations are positively correlated with AWA in the areas close to the sites where presumably at least some of emissions of PM2.5 are located ( Figure 4).

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The relationships between daily PM2.5 concentrations and AWA using CESM simulations presented here offer a test of the consistency between observational and model relationships in characterizing the response of PM2.5 to AWA. The highest regression coefficient occurs in the observational (Obs) and the reanalysis driven simulated cases (REFC1SD), as opposed to the case coupled metereology (GCM2000) (Figure 4a areas with the largest values of the composite AWA are located southward of the AREN1 and SIPSl sites. But at LAV01 the maximum is located to the northwest for the observational and reanalysis driven cases (Obs and REFC1SD), and eastward for the coupled model case (GCM2000). Overall, the composite AWA for PM2.5 also shows that the daily PM2.5 above its 90th 235 quantile correlates strongly with AWA during summer. Note that there is a spatial displacement between maximum of geopotential height and the maximum of AWA, since wave activity fundamentally measures the waviness of atmospheric general circulation, rather than the magnitude.

Relationship of AWA and PM2.5 regionally
Next we consider how the local relationship between PM2.5 and AWA changes in space. To simplify the visualization of the 240 spatial variability in the local relationship, we use the result from the previous section that the maximum regression coefficients between PM2.5 and AWA are usually close to the site where PM2.5 is measured ( Figure 5). The highest composite AWA anywhere in the domain and the highest regression coefficient with AWA are shown at each gridpoint in Figure 6. If we look at the relationship between the PM2.5 concentration and the wave activity at each location, it can be seen that PM2.5 concentrations are positively correlated with AWA throughout the US, but with varying strengths (Figure 6). A roughly similar 245 spatial distribution is obtained when either the composite AWA for high PM2.5 (left-hand side: Figure 6a, c, e, g and i) and for the regression coefficients between the PM2.5 and AWA (right-hand side: Figure 6b, The composite AWA is for PM2.5 that larger than the 90 th quantile, while the regression coefficient is for all PM2.5. The composite AWA and regression coefficient have similar spatial distributions suggesting the positive connection between daily PM2.5 and AWA is mainly produced by high PM2.5 concentration above its 90 th quantile. Overall, the relationship between 265 behavior of AWA and extreme PM2.5 concentration is generally consistent with the existing meteorological studies (Woolings et al., 2008;Coumou et al., 2015;Michel and Riviere, 2011;Ryoo et al., 2013).

The sensitivity of quantiles in PM2.5 concentrations to AWA
To examine the sensitivity of different levels of PM2.5 concentrations to AWA, we fit the linear regression and quantile regression for AWA and daily PM2.5 for summers between 1988 to 2014 from IMPROVE monitoring sites for different percentiles

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(10 th to 90 th percentiles) using an "impact region" of AWA at AREN1 site. Here the averaged AWA over the "impact region" is defined as an elliptic area bounded by the maximum and minimum longitude and latitude of the maximum composite AWA for PM2.5 larger than 90 th percentile minus the 0.05 contour line (blue elliptic circle in Figure 5a). One can clearly see that the higher percentiles of PM2.5 are more sensitive to the change in the averaged AWA over the impact region, e.g., the 90 th percentile of PM2.5 is approximately three times more sensitive to the averaged AWA over the impact region when compared 275 with the 10 th percentile of PM2.5 (Figure 7a).
In order to examine whether the relationship that high quantile of PM2.5 is more sensitive to the AWA than the low quantile of PM2.5 applies to the other sites, we calculate the difference of 90 th percentile quantile regression coefficient (slope) from PM2.5 increases more than the 50 th percentile of PM2.5 with the enhancement of the AWA. In the Northeast region (north and east of New York state with New York state included), this relationship is the most pronounced. This difference in response between the highest and median PM2.5 values indicates the different sensitivities within various percentiles of the PM2.5 levels.
These results are to some extent consistent with those from Porter et al. (2015), which addressed that averaged sensitivity of 95 th percentile summertime ozone to changes in highest daily temperature was larger than the sensitivity of 50 th percentile 285 summertime ozone.

Projected PM2.5 concentrations due to changes in future AWA
The strong association between PM2.5 concentrations and AWA in the current climate prompts us to investigate the extent to which we can utilize a linear regression model to predict changes in PM2.5 concentrations from AWA change in future climate.
Employing daily present-day summertime concentrations of PM2.5 and AWA for current climate from the coupled model Next we explore how much of the future change in PM2.5 concentrations can be predicted just on the basis of changes in 300 AWA. Using PM2.5-AWA relationships determined from current coupled model output (GCM2000), future PM2.5 changes can be estimated by using the linear relationship fitted with the current data and projected change of AWA in the future (as shown in equation (1)- (3)). Here we assume that the linear relationship between the predictors and PM2.5 do not change very much in the future compared to the present to extrapolate the current linear relationship between PM2.5 and AWA to the future.    Stippling indicates the regions that are statistically significant at the 95% confidence level. Unit: m for 500-hPa geopotential height and 10 8 m 2 for AWA. The blue outlined area in a) is the impact region, which is defined as the region of the maximum regression coefficient minus 0.05.