Appendix A: Trajectory Analysis Methods Page A-1



# Appendix A: Application of Trajectory Analysis

Methods to Sulfate Source Attribution Studies in

the Northeast U.S.

Gary Kleiman, Iyad Kheirbek, and John Graham

Northeast States for Coordinated Air Use Management (NESCAUM) Boston, MA 02114.



### ABSTRACT
Back trajectories have been calculated (8 per day) for the five-year period including 2000 through 2004 using the HYSPLIT modeling system for 13 Eastern sites including 10 rural locations near Class 1 areas subject to EPA’s Regional Haze Rule and 7 urban location which have annual average PM 2.5 concentrations above or near the National Ambient Air Quality Standard (NAAQS). The back tr ajectories have been clustered based on 3-dimensional similarity to identify the p redominant meteorological pathways influencing each site. Trajectories have also been associated with the nearest temporal value of 24-hr average concentration of PM 2.5 and IMPROVE sulfate values measured at or near each site. Individual trajectories and clu stered probability fields are utilized in a variety of ways to apportion geographic contributio n to meteorological transport of sulfate. Results are compared with quantitative me thods of apportioning state-specific

contributions to observed sulfate and serve as an i ndependent check on contribution assessments developed through these alternative tec hniques.Appendix A: Trajectory Analysis Methods Page A-2



## Appendix A: Application of Trajectory Analysis Methods to

Sulfate Source Attribution Studies in the Northeast U.S.

A.1. Introduction

The 1999 Regional Haze Rule (RHR) contains requirem ents for a site-specific pollution apportionment as part of each mandatory F ederal Class I area’s long-term emissions management strategy. A variety of techni ques have been explored for conducting such pollution apportionments, but tagge d chemical transport modeling is one of the few techniques which provide quantitative as sessments of individual state or regional contributions to ambient concentrations. Given the importance of accurate pollution apportionment assessments, it is highly d esirable to have several independent techniques provide confirmation of transport model results.

Traditional trajectory analyses that associate an a mbient measurement of air quality with the geographical region upwind prior t o the observation are limited in that they demonstrate the relationship between ambient a ir quality and the integrated path along the length of a back trajectory. It is diffi cult to distinguish the contribution of a specific point along a single back trajectory from the contribution of other points along that path. Large numbers of back trajectories have been used in a variety of ways to try to “triangulate” by taking advantage of the variati on in meteorology and paths that an ensemble of back trajectories offers. 1-5 Combining results from multiple receptor sites offers a more robust method of triangulation and ca n yield very specific source regions associated with unique chemical signatures availabl e with source apportionment techniques. These methods – which include ensemble trajectory analysis and factor analysis methods – all select based on chemical sig natures. That is, they identify geographic regions on the basis of a unique chemica l characteristic, such as high levels of an observed pollutant or high levels of a specific combination of pollutants.

Moody et al., 6 following methods of Dorling, 7 have applied the Patterns in Atmospheric Transport History (PATH) clustering alg orithm, to large numbers of back trajectories in order to group trajectories by thre e-dimensional similarity. Calculation of average pollution levels corresponding to the membe rs of a cluster of back trajectories of similar three-dimensional structure provides a robu st technique of associating air pollutants with typical meteorological pathways, 8,9 but remains limited in its ability to distinguish individual points along an atmospheric pathway defined by a cluster of back trajectories. The cluster methods provide a way of identifying geographic regions based primarily on meteorological – rather than chemical – characteristics. The meteorologically selected regions can then be analy zed with respect to their chemical

associations.

The definition of an individual cluster of back tra jectories in PATH analysis is dependent on a subjective choice of the “Radius of Proximity.” This threshold defines the limiting difference between the three-dimension al coordinates of two back trajectories and determines if they are in the same cluster or d ifferent clusters. Selection of a smaller radius of proximity, in effect, will split clusters into component sub-clusters. Thus in the limiting case (radius of proximity = 0) the analysi s reverts to a traditional trajectoryAppendix A: Trajectory Analysis Methods Page A-3

analysis with each trajectory representing its own cluster. In this sense, PATH analysis offers a trade-off between uncertainty and fine sca le structure of a trajectory analysis. By defining a radius of proximity and back-trajectory length, 10,000+ back trajectories for each site over the 5 year period can be represented by approximately 10-20 clusters.

Using these trajectory and cluster data bases, as w ell as the associated receptorbased pollution data, we have carried out analyses using the incremental probability method, and two PATH-derived techniques method for attributing pollution transport to geographic areas.

These qualitative methods support and enhance the c onclusions derived through alternative methods (independent of back-trajectori es) of associating emissions with downwind air quality impacts (i.e. the use of chemi cal transport models, or source modeling, rather than the receptor based approaches used in trajectory analysis). He re we use our large database of back trajectories and corresponding air pollution measurements to develop multiple metrics related to Wishinski and Poirot’s “incremental probability” 10 which is reflective of the increase in probability – relative to the everyday probability – of a geographic region being associat ed with a predominant meteorological pathway for sulfate transport (as opposed to a sour ce region itself). The results are used to bolster the conceptual model of visibility impai rment at Class I sites presented in Chapter 2.



### A.2. Trajectory Approaches

The Hybrid Single Particle Lagrangian Integrated Tr ajectory (HYSPLIT)

model 11,12 was used to calculate back trajectories for 13 sit es in the Northeast and Eastern U.S. The locations correspond to Class I areas sub ject to the RHR as well as several sites where potential nonattainment issues with the PM 2.5 NAAQS warranted analysis. Results are presented primarily for three rural sites which geographically span the MANE-VU class I domain: Acadia National Park, Maine, Lye B rook Wilderness Area, Vermont, and Brigantine Wilderness Area, New Jersey.

Back trajectories were calculated eight times per d ay for starting heights of 200, 500 and 1000m above ground level using meteorologic al wind fields for the five year period 2000-2004. NOAA ARL archives analyzed meteor ological products for use with the HYSPLIT model including the Eta Data Assimilati on System (EDAS) wind fields, which cover North America with an 80 km spatial res olution and are based on 3-hourly variational analyses. 13 These back-trajectories -- and the underlying wind fields used to generate them -- provide the primary dataset used t o explore meteorological patterns in the Northeast. Figure A-1 shows a single EDAS back- trajectory representing the path that a particle of air has traveled prior to arriving at Acadia National Park.

The back trajectories with corresponding pollutant measurements and emissions data can be combined in a number of ways to yield v arious metrics which may help identify specific meteorological pathways that are more likely than others to contribute to sulfate transport to a specific receptor site.Appendix A: Trajectory Analysis Methods Page A-4

Figure A-1. Single HYSPLIT Calculated back-traject ory, Acadia National Park

A common method of analysis requires the calculatio n of residence-time probabilities, which are a measure of the time spen t in a specific grid cell relative to the total time spent in any grid cell. 14 When calculated for all trajectories considered in an analysis, this defines the everyday probability as shown in Equation 1.

Equation 1. Everyday Residence-time Probability

ies trajector all from cells grid all through passing endpoints total j i, cell grid through passing endpoints total

= =      

=

N n N n EP

ij ij

These residence time probabilities provide an indic ation of the fractional time spent in a specific grid cell relative to time spen t anywhere in the domain by air parcels that eventually pass over a given receptor. They c an be calculated for any subset of trajectories, including all the days within a time frame, yielding the “everyday” probability, or a subset corresponding to days with high measured concentrations of pollutants at a receptor site. Figure A-2 shows tr ajectories from the 10% of days with the highest sulfate concentrations during the 2000-2004 time period. The plot on the left shows the actual trajectories while on the plot on the right shows the resulting residencetime probability field for high sulfate days.

Figure A-2. Trajectories from the highest sulfate days at Acadia National Park. The highest 10% sulfate trajectories (left) and corresponding resid ence-time probability (right) are shown.Appendix A: Trajectory Analysis Methods Page A-5

When the residence-time probability field is calcul ated for the subset of days corresponding to high concentrations of pollutants (as shown in Figure A-2) the result is

called a high-day probability as shown in Equation 2.

Equation 2. High Day Residence-time Probability

tories day trajec high from cells grid all through passing endpoints day high total j i, cell grid through passing endpoints day high total

= =      

=

M m M m HP

ij ij

The difference between the everyday probability (Eq uation 1, all days during 2000-2004) and the high day probability (Equation 2 , high pollution days during 2000- 2004) has been referred to as the incremental probability and identifies areas where the probability of poor air quality is greater than the average probability associated with typical meteorological patterns (see Equation 3).

Equation 3. Incremental Probability

IP = EP HP

−

When calculated in this way for each trajectory wit h its individual pollutant concentration value, a standard incremental probabi lity analysis results and can serve as a basis for comparison to alternate metrics. Figure A-3 shows the 5-year incremental probability field for days corresponding to the top 10 percent of observed sulfate values at two sites: Acadia National Park in Maine and Lye Brook Wilderness in Vermont. These figures are based on available 500 meter star t height HYSPLIT-EDAS back trajectories and monitoring data for those sites. Incremental probabilities have been calculated for 7 sites in the MANE-VU region and 3 nearby sites in the VISTAS region. Plots for all sites (and several different percenti le groupings) are presented at the end of this Appendix.

Figure A-3. Incremental Probability (Top 10% obser ved sulfate days) at Acadia, ME and Lye Brook, VT during 2000-2004.



## Acadia Lye BrookAppendix A: Trajectory Analysis Methods Page A-6



### A.3. Cluster-Based Approaches

Trajectories can be used individually or grouped to create another dataset based on the PATH approach. 6 Trajectory clusters are based on the calculated Eu clidean

distance between three-dimensional normalized coord inates of the respective trajectories. These clusters are formed by finding the “central” trajectory which has the greatest number of neighboring trajectories within a subject ively selected “radius of proximity.”

There is a trade-off between the “resolution” of va rious modes of atmospheric transport identified by PATH and the number of clusters. Usi ng a narrow radius of proximity, more defined clusters that are easily associated wi th a specific class of meteorological transport result (e.g. fast flow from the Northwest , shallow coastal flow, etc.); however, it also results in a large number of clusters at each site.

In order to better define specific meteorological p athways that might be associated with pollutant transport, we used a radi us of proximity of 12 (this is a unit-less

value since the coordinates have all been normalize d prior to clustering) and a backtrajectory time of 120 hours. This typically resul ted in approximately 100-200 frequency based clusters at each site, but relatively few clu sters contain the majority of the trajectory population. Figure A-4 shows typical met eorological patterns among the most frequent clusters calculated for Brigantine Wildern ess Area, New Jersey. Results are plotted as a residence-time probability for each cl uster (see Equation 1). Clusters in the figure have been associated with specific atmospher ic “modes” or meteorological patterns that are commonly observed at multiple sit es. The modes pictured correspond to Northwest Fast flow (NWF), Southwest Interior (SWI) , Southwest Coastal (SWC), Southeast Maritime (SEM), Upper Midwest (UMW), and Northerly flow (N). Whereas each cluster is unique to a specific site and the s pecific group of trajectories clustered, the modes represent patterns which are often observed y ear after year, and from site to site. In this sense, the clusters provide a means of iden tifying modes of transport which can be used for identifying pollution transport mechanisms

.

Figure A-4. Residence-time probability for 6 frequ ency-based clusters observed at Brigantine Wilderness Area, New Jersey between 2000 and 2004.

NWF SWI SWC

SEM UMW N

Note: Codes reflect atmospheric “modes” or typical patterns of t ransport which consistently appear at multiple sites.Appendix A: Trajectory Analysis Methods Page A-7

While these frequency-based clusters are useful, a variant method of grouping these trajectories was developed to redistribute tr ajectories into the most common modes. This alternate method of clustering relies on the f requency-based cluster groups described in the preceding paragraphs, but forms trajectory g roups based on proximity rather than frequency. In the first step, the frequency-based approach is used to identify the central trajectories that represent the most populated freq uency-based clusters (approximately 10 clusters typically contain at least 98 percent of t he trajectories in the dataset using R=12 and 120 hour back-trajectory time). These 10 cent ral trajectories are then used to develop 10 proximity-based clusters by assigning ev ery trajectory in the dataset to its nearest central trajectories (calculated back to 72 hours). The main advantage of these proximity-based clusters is that they more uniforml y distribute the population of trajectories amongst the most frequently observed a tmospheric modes and result in more defined clusters than the frequency-based approach. Figure A-5 shows the proximitybased clusters resulting from the frequency-based c lusters shown in Figure A-1. In this proximity-based approach, trajectories are more eve nly distributed, as the entire trajectory dataset are assigned to only 10 modes.

Each trajectory, frequency-based cluster, and proxi mity-based cluster was associated with corresponding monitoring data (or a veraged monitoring data in the case of clusters) measured as close in time as possible to the “start” time of the back trajectory

calculation. Associations were made for PM 2.5 , sulfate ion, organic carbon, and aerosol extinction as PM components routinely measured as p art of the IMPROVE program, although results are presented here only for 24-hr integrated sulfate ion mass.



### A.3.1. Cluster-weighted Probability

Everyday probabilities can be calculated for any su bset of trajectories. When calculated for the trajectories within a given clus ter, that cluster’s everyday probability results. This is essentially a normalized version of the residence-time probabilities shown in Figure A-4 and Figure A-5. Everyday probabiliti es for clusters at 13 sites are Figure A-5. Residence-time probability for 6 proxi mity-based clusters observed at Brigantine Wilderness Area, New Jersey between 2000 and 2004.

NWF SWI SWC

SEM UMW

N

Note: Codes reflect atmospheric “modes” or typical patterns of t ransport which consistently appear at multiple sites.Appendix A: Trajectory Analysis Methods Page A-8

presented at the conclusion of this appendix. The everyday probabilities for clusters at an individual site and the associated average pollutio n information corresponding to each cluster is combined through a method identified her e as the cluster-weighted probability (CWP).

Each PATH-derived cluster’s residence-time probabil ity is weighted by the average sulfate value for any measurements correspo nding to a trajectory which is a member of that cluster. The weighted residence-tim e probability is summed over all clusters calculated for a site (as opposed to just the highest probability for a specific pollutant as was the case with the incremental prob ability metrics). The everyday probability is subtracted from the sum of cluster-w eighted probabilities to identify areas of increased (or in the case of negative values, de creased) probability of being associated with a meteorological pathway for pollutant transpo rt. Equation 5 presents the clusterweighted probability.

Equation 5. Cluster-weighted Probability

days) all on (based ion concentrat pollutant Average i) cluster with associated ns observatio on (based ion concentrat pollutant Average ) ( calculated

clusters of number total )

( 1

1

= = =      

⋅

− ⋅ = 

# ∑

=

C C L EP C RP C C CWP

i i

L

i i

Here, ( C ) i represents the average sulfate value for all traje ctories within cluster i

which had an associated SO 4 2- measurement (roughly 25-30 percent, given 1-in-3 d ay sampling schedules). By weighting the residence-t ime probability for cluster i by this quantity, we are implicitly assuming that similar t rajectories (i.e. traversing similar source regions under similar meteorological conditions) wi ll have similar resulting ambient
concentrations at the receptor. The quantity ( C ) represents the average value for sulfate measurements associated with trajectories in any of the clusters and acts to normalize the sum of the residence-time probabilities.

As we have examined two alternate methods for assig ning trajectories to clusters – frequency-based clustering and proximity-based cl ustering – two methods for calculating cluster weighted probabilities exist. The first uses the frequency-based clusters as the dataset, while the second uses the more distributed, proximity-based clusters as the dataset. Figure A-6 shows the CWP calculated for both methods at Brigantine Wilderness Area, New Jersey.

While calculated from the same underlying trajector y files and sulfate observations, this metric is calculated in a fundam entally different way than the incremental probability approach presented. The CW P uses trajectory clusters (as opposed individual trajectories) to develop a weigh ted probability field which is then compared to the everyday probability. The fact tha t the results are similar to those calculated for the IP technique provides reassuranc e that these approaches are reasonable for identifying areas that are associated with sulf ate transport.Appendix A: Trajectory Analysis Methods Page A-9



### A.4. Results

Regions of transport to different sites can be dete rmined using the trajectory (nonclustered) technique, incremental probability. In this method, pollution values are assigned to individual trajectories (as opposed to clusters) and regions associated with high sulfate transport are determined by looking at the difference of the high day trajectory probabilities from the everyday trajecto ry probabilities. Figure A-7 shows the top 10% sulfate incremental probability at three si tes, Acadia, Brigantine, and Lye Brook.

In these incremental probability plots, trajectorie s with higher pollution concentrations generally follow a path from the Mid west across the Northeast region prior to arriving at Acadia. Transport paths from t he Southeast and the Midwest are evident at Brigantine, and a combination of Midwest transport and transport from the Southeast along the industrial I-95 Corridor affect Lye Brook.

Incremental probability can also be used to look at the regions contributing to the best pollution days at a site. Figure A-8 shows the 10% lowest sulfate incremental probability. Best-day incremental probability show s that trajectories arriving to the sites Figure A-6. Cluster-weighted Probability methods a ssociated to sulfate transport using frequency based clusters on left and proximity-base d clusters on the right at Brigantine Wilderness Area, New Jersey.

Note: Areas of increased (yellow/red) or decreased (cyan/blue)

Figure A-7. Incremental Probability (Top 10% Sulfa te) at three sites,

Acadia, Brigantine and Lye Brook 2000-2004.

Acadia Brigantine 

### Lye BrookAppendix A: Trajectory Analysis Methods Page A-10

on days with low sulfate levels tend to follow a pa th from the north in Canada or off the Atlantic Ocean. This is an expected result as fewe r sources are located in this region.

By examining pollution levels associated with diffe rent clusters, we can gain insight into which atmospheric modes are associated with transport to sites in the MANEVU region. Figure A-9 compares the proximity-based cluster with the highest sulfate value at three sites, Lye Brook Wilderness Area, Br igantine Wilderness Area, and Acadia

National Park.

Figure A-9 demonstrates that the clusters showing t he highest pollution values show similar meteorological characteristics at diff erent sites. The three sites show that in the higher average pollution clusters, the air foll ows the path from the Midwest to the site in question. Lye Brook shows an east coast componen t contributing as an area of transport on the worst average sulfate days. Using this method, we have grouped trajectories purely based on meteorological charact eristics and can examine pollution levels within these groupings. Thus agreement betw een this method and the incremental probability results shown earlier suggest that whet her you select trajectories based on meteorology or chemistry, similar regions are ident ified as being associated with sulfate transport. Figures at the end of this appendix sho w the clusters and average pollution values for all the sites in the region analyzed.

Figure A-10 displays the proximity-based clusters w ith the lowest average sulfate concentrations. They show which meteorological mod e contributes to the best pollution days at three different sites, Acadia, Lye Brook, a nd Brigantine. This provides a method that is comparable to Figure A-8 where incremental probability for the lowest sulfate trajectories is shown. Again, the comparison is ma de between this clustering technique where trajectories are grouped solely on meteorolog ical characteristics and the incremental probability technique that looks at tra jectories with similar pollution

characteristics.

Much like the atmospheric modes that contribute to the highest sulfate levels at our three sites, very similar atmospheric patterns contribute to the best sulfate days across multiple sites in the region. Air masses moving in from the north and off the Atlantic Ocean contribute to the best days at Acadia, Brigan tine, and Lye Brook. Similar modes affect the best days at many other sites, seen in t he section following this appendix. Figure A-8. Incremental Probability (Bottom 10% Su lfate) at three sites, Acadia,

Brigantine and Lye Brook 2000-2004.

Acadia Brigantine Lye BrookAppendix A: Trajectory Analysis Methods Page A-11

Cluster weighted probabilities are used to combine cluster information with pollution information and the following CWP plots s how regions with greater probability of sulfate transport in red/yellow and regions of d ecreased probability of sulfate transport in blue. We have presented the CWP based on proxim ity-based clusters in Figure A-11, which shows results similar to Figure A-9 since the clusters weighted by the highest pollution values tend to enhance the regions they c over, consistent with a greater probability of contributing to sulfate transport. However, the CWP plots in Figure A-11 now contain information from all the clusters (and thus all the trajectories) in the dataset. Figure A-9. Pro ximity based cluster with the highest associated su lfate value for three sites in the MANE-VU region, Acadia (sulf=3.19 μ g/m 3 ), Brigantine (sulf=6.79 μ g/m 3 ), and Lye
Brook (sulf=4.56 μ g/m 3 ).



### Acadia 

### Brigantine

Figure A-10. Pr oximity based cluster with the lowest associated su lfate value for three sites in the MANE-VU region, Acadia (sulf=1.41 μ g/m 3 ), Brigantine (sulf=2.23 μ g/m 3 ), and Lye
Brook (sulf=1.16 μ g/m 3 ).



## Acadia 

## Brigantine Lye Brook

Figure A-11. Cluster Weighted Probability at three sites, Acadia, Brigantine and Lye Brook 2000-2004.

Acadia Brigantine Lye BrookAppendix A: Trajectory Analysis Methods Page A-12

By averaging the various probability fields across sites, we can gain insight into which regions are most likely to be associated with sulfate transport to multiple sites in the MANE-VU region. A region that is associated wi th transport to several sites in different locations is far more likely to be associ ated with large emission sources. Figure A-12 show a multi-site averages of incremental prob ability for the top 10 percent worst days at five northern sites, Acadia, Lye Brook, Cam p Dodge, Moosehorn, and Mohawk Mountain. Figure A-13 shows the multi-site average CWP which includes all proximitybased clusters for the same sites.

Figure A-12. Multi-site average probabilities show ing areas of increased (yellow/red) or decreased (cyan/blue) probability of being associat ed with sulfate transport to Acadia, Lye Brook, Camp Dodge, Moosehorn, and Mohawk Mountain o n the ten percent worst sulfate days.

Figure A-13. Multi-site average CWP s howing areas of increased (yellow/red) or decreased (cyan/blue) probability of being associated with su lfate transport to Acadia, Lye Brook,

Camp Dodge, Moosehorn, and Mohawk Mountain.Appendix A: Trajectory Analysis Methods Page A-13

From a qualitative perspective, the two metrics (IP and CWP) are quite similar showing significant sulfate transport (on an annual average basis) along the Eastern corridor from Virginia up through Maryland and East ern Pennsylvania. A second area of influence along the Ohio River valley between Ohio, Pennsylvania and West Virginia seems to play a significant role as well.

These averages can also be applied to different geo graphical regions as well. Figure A-14 shows the average IP while Figure A-15 shows the average CWP for four southern sites, Brigantine, Shenandoah, Dolly Sods, and Great Smokey Mountains. The figure highlights specific regions of higher probab ility of sulfate transport affecting a large area along the east coast.

Figure A-14. Multi-site average IP showing areas o f increased (yellow/red) or decreased (cyan/blue) probability of being associated with su lfate transport to Brigantine,

Shenandoah, Dolly Sods, and Great Smokey Mountains.

Figure A-15. Multi- site average CWP showing areas of increased (yellow /red) or decreased (cyan/blue) probability of being associated with su lfate transport to Brigantine,

Shenandoah, Dolly Sods, and Great Smokey Mountains.Appendix A: Trajectory Analysis Methods Page A-14



### A.5. Conclusions

A large database of back trajectories and correspon ding air pollution measurements have been used with trajectory cluster analysis techniques to apportion observed sulfate mass concentrations as an independ ent check on source modeling results. Clusters have been used here to develop m etrics related to Wishinski and Poirot’s “incremental probability” 10 which provides the relative increase in probabilit y of a geographic region being associated with a predomi nant meteorological pathway associated with pollutant transport.

Several techniques have identified state-specific c ontributions of SO 2 emission

sources to sulfate formation. Results indicate tha t cluster-based trajectory techniques can provide a semi-quantitative check on chemical trans port model results. This analysis demonstrates a potentially novel way of identifying regions that play a role in pollutant transport (and may host source emissions as well). Combined with meteorological information and source apportionment model results, the approach may yield a more comprehensive picture of source emissions and the c ircumstances under which they are transported to specific receptor sites.



### A.5.1. Acknowledgements

The U.S. EPA has made this work possible through th eir support of the MANEVU Regional Planning Organization. The HYSPLIT4 mo del was provided by NOAA. (HYbrid Single-Particle Lagrangian Integrated Traje ctory Model, 1997. Web address: http://www.arl.noaa.gov/ready/hysplit4.html, NOAA A ir Resources Laboratory, Silver Spring, MD). The authors would also like to thank Nicolas Hamel, who developed the “clustermaker” code which allowed us to perform the analysis in an efficient manner, Ingrid Ulbrich who set up and calculated the trajec tory database for many early years in the analysis and Jamie Lehner who assisted with man y early data analyses on which this

work has built.Appendix A: Trajectory Analysis Methods Page A-15



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