The Stochastic Lagrangian Apportionment Method (SLAM)

Article pubs.acs.org/est

A Method to Quantitatively Apportion Pollutants at High Spatial and Temporal Resolution: The Stochastic Lagrangian Apportionment Method (SLAM) John C. Lin*,† and Deyong Wen‡ †

Department of Atmospheric Sciences, University of Utah, Salt Lake City, Utah 84112-0102, United States Department of Earth and Environmental Sciences, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada

‡

S Supporting Information *

ABSTRACT: We introduce a method to quantify upwind contributions to concentrations of atmospheric pollutants. The Stochastic Lagrangian Apportionment Method (SLAM) carries out the following: (1) account for chemical transformations and depositional losses; (2) incorporate the effects of turbulent dispersion; (3) simulate the locations of the sources with high spatial and temporal resolution; and (4) minimize the impact from numerical diffusion. SLAM accomplishes these four features by using a time-reversed Lagrangian particle dispersion model and then simulating chemical changes forward in time, while tagging and keeping track of different sources. As an example of SLAM’s application, we show its use in apportioning sources contributing to ammonia (NH3) and ammonium particulates (p-NH4+) at a site in southern Ontario, Canada. Agricultural emissions are seen to dominate contributions to NH3 and p-NH4+ at the site. The source region of NH3 was significantly smaller than that of p-NH4+, which covered numerous states of the American Midwest. The source apportionment results from SLAM were compared against those from zeroing-out individual sources (“brute force method”; BFM). The comparisons show SLAM to produce almost identical results as BFM for NH3, but higher concentrations of p-NH4+, likely due to indirect effects that affect BFM. Finally, uncertainties in the SLAM approach and ways to address such shortcomings by combining SLAM with inverse methods are discussed.

■

INTRODUCTION

The objective of this paper is to introduce a method to apportion emissions influencing air quality. The “Stochastic Lagrangian Apportionment Method” (SLAM) can yield quantitative information about sources contributing to chemically active species that can undergo transformations in the atmosphere at high spatiotemporal resolution while maintaining computational efficiency. We first review established techniques for source apportionment, pointing out similarities and differences with the SLAM method. Then we introduce and describe SLAM in detail. To illustrate its application to a specific air quality problem, the method is used to examine the sources affecting ammonia and ammonium particulates. Results from SLAM, as applied to apportionment of ammonia/ammonium particulates, are shown; we also quantitatively compare SLAM against an alternative apportionment method. Finally, we discuss remaining uncertainties within SLAM and the possibilities for

Deteriorating air quality is a pressing issue in many regions around the world due to rising populations, industrialization, and increased migration from rural to urban areas, in which populations are living in close proximity to strong pollutant emissions.1,2 As cities and societies grapple with ways to improve air quality, understanding where, how much, and which kinds of emissions affect pollutant concentrations is of critical importance. This has long been a subject studied by air quality researchers, under the umbrella term of “source apportionment”.3−5 Numerous applications of source apportionment are associated with managing and improving air quality. For example, a knowledge of pollutant transport across state and national borders is necessary to develop “State Implementation Plans” to bring air quality in compliance with the Clean Air Act.6 Quantifying pollutant emissions from natural sources is also necessary to demonstrate “exceptional events” that cause pollutant levels to be elevated above regulatory limits. A knowledge of sources contributing to observed pollutant concentrations is also critical for devising regulations in order to improve air quality. © 2014 American Chemical Society

Received: Revised: Accepted: Published: 351

January 29, 2014 November 25, 2014 December 1, 2014 December 1, 2014 dx.doi.org/10.1021/es505603v | Environ. Sci. Technol. 2015, 49, 351−360

Environmental Science & Technology

Article

Table 1. Comparisons Between SLAM and Several Commonly Adopted Source Apportionment Methods. Y, N, and N/A Refer to “Yes”, “No”, and “Not Available”, Respectivelya positive matrix factorization

chemical mass balance requires prior guess of sources retrieves locations of sources simulates atmospheric transport backward in time includes turbulence effects on atmospheric transport incorporates chemical production and loss processes a

Y (chemical signatures, not strengths) N N (no consideration of transport) N/A (no consideration of transport) N

potential source contribution function

tagged species approaches

stochastic lagrangian apportionment method (SLAM)

N

N

Y

Y

N N (no consideration of transport) N/A (no consideration of transport) N

Y Y (mean-wind trajectories) N

Y N

Y Y (Lagrangian particles)

Y

Y

N

Y

Y

Note that sensitivity analysis methods that are not strictly source apportionment methods are not included here.

combining it with other source apportionment methods to overcome its weaknesses.

The simplest of these methods traces out a single backtrajectory from the receptor to represent air arriving at the receptor.18,19 This “mean-wind” trajectory approach neglects turbulent dispersion but has been widely adopted in source apportionment studies.20−22 Another related technique that attempts to elucidate locations of source regions whose emissions affect receptor concentrations is the potential source contribution function (PSCF) method.23 While the PSCF may indicate potential source regions, the resulting source apportionment is not quantitative. In other words, PSCF does not provide quantitative information about the amount of pollution at the receptor originating from a specific gridcell.13 Numerous authors have combined mean-wind trajectories with chemical transformation calculations for source apportionment purposes.24−26 However, these methods are subject to difficulties in assigning a spatial scale to the source region. Researchers often have to associate arbitrary box sizes to the mean trajectories,24,26 introducing arbitrariness in the spatial extent of apportioned sources. Furthermore, for receptors in the lower atmosphere, adopting the aforementioned mean-wind trajectory approaches is highly problematic, due to neglect of the strong turbulence that controls dispersion in the planetary boundary layer (PBL).17,27,28 In contrast to mean trajectories, Lagrangian particle dispersion models (LPDM) attempt to incorporate the effects of turbulent dispersion by simulating a three-dimensional ensemble of air parcels that are advected with stochastic velocities that simulate the effects of turbulent eddies.29,30 The air parcels are represented by numerous computational “particles” that disperse due to the model’s stochasticity, and the fact that each particle occupies an infinitesimal volume in the atmosphere means that the entire particle ensemble characterizes the pollutant dispersion, directly analogous to the way different molecules originally found in a small volume disperse in the atmosphere. Recently, running an LPDM backward rather than forward in time has been shown to be an effective way to study atmospheric species, since the air parcel trajectories moving backward in time from the receptor elucidates the linkage between the receptor and upwind sources.29,31−33 From the time-reversed LPDM simulations, one can construct the “footprint” of a receptor34 or, similarly, the “source-receptor matrix”.32 Despite the efficacy of the time-reversed LPDM approach for source apportionment, it has mainly been applied to passive atmospheric species that do not undergo chemical trans-

■

PREVIOUS SOURCE APPORTIONMENT METHODS This section reviews previous source apportionment methods, whose similarities and differences are summarized in Table 1. Statistical Methods. Also known as “receptor methods”,5−7 statistical methods are among the first source apportionment methods developed. These methods attempt to match observed pollutant concentrations to sources, each of which has a distinct chemical signature that can be fitted against observed concentrations and different chemicals.8 Examples of statistical methods include “chemical mass balance” (CMB)9 or “factor analysis” methods such as positive matrix factorization (PMF)10 and Unmix.11 Despite the widespread application of statistical methods, they are subject to major weaknesses. CMB depends upon numerous assumptions that are often not satisfied: constant emissions, nonreactive species, known a priori source types and chemical signatures, and linearly independent source signatures.3 For factor analysis methods, relying upon observations solely to quantify sources is an ill-posed problem, requiring introduction of additional assumptions or information.7 PMF is known to yield nonunique solutions,5,12 and some retrieved sources from PMF and Unmix are not always mapped to realworld sources in a straightforward manner or are even realistic.6,13 As such, comparisons between different statistical methods often show retrieved sources that differ depending on the exact method adopted.6,13,14 Statistical methods are subject to two additional major shortcomings. First, these methods do not explicitly take into account chemical transformations or losses, in general. Second, statistical methods lack consideration of atmospheric flows, which act to transport and disperse the pollutants. The consequence of this deficiency is that no information exists regarding source locations.3 When the chemical signatures of two source profiles are not distinct enough, then the statistical methods cannot distinguish their contributions, even if they are located in different upwind source regions. To incorporate information regarding atmospheric transport, statistical methods have been enhanced by wind sector information13 and atmospheric trajectories15,16 (next section). Trajectory-Based Methods. In order to incorporate more atmospheric transport information into source apportionment analyses, researchers have adopted various trajectory-based methods, in which pathways of air parcels arriving at the receptor are elucidated by integrating velocity vectors backward in time.17 352

dx.doi.org/10.1021/es505603v | Environ. Sci. Technol. 2015, 49, 351−360


Article

formations or those that undergo first-order losses.32,35,36 Only in the past few years has the time-reversed LPDM approach incorporated nonlinear chemistry. As a first illustration of this approach, Wen et al.37 describe a “backward-time stochastic” air quality modeling system that enables nonlinear chemical simulations to be carried out in two steps: (1) running the time-reversed LPDM, thus elucidating the air parcel trajectories arriving at the receptor by simulating particles backward in time, and then (2) carrying out nonlinear chemical transformations forward in time and modifying pollutant concentrations as they are tracked along trajectories marked out by the particles. The source apportionment method described in this paper is a natural extension of this approach. Eulerian Tagged Species Approaches. In contrast to the Lagrangian methods using back-trajectories, another class of source apportionment method adopts an Eulerian perspective, covering the model domain with multiple fixed gridboxes. Pollutants are transported in and out of the gridboxes, and each box also serves as a “reaction chamber” in which chemical species react with one another. A whole class of source apportionment methods takes such Eulerian chemical transport models (CTM) and uses “tagged species” to label each separate process or source location.38−40 For instance, emissions from mobile sources can be tagged separately from forest fire emissions, and the tagging can be further differentiated between different locations, for example, fire emissions from Idaho versus Colorado. For chemically reactive species that form from precursors (e.g., secondary particulates, ozone), implementation of the tagged species method is more complicated, because each precursor and the associated chemical reaction need to be tagged appropriately. While the tagged species approach as implemented within Eulerian models is powerful and potentially yields source apportionment information throughout the model domain, it is not without disadvantages. First, since each separate emission contribution needs to be tagged, the method necessitates considerable computational effort (no. gridcells × no. source types × no. species). Thus, to reduce the computational cost, source regions are often coarsely resolved, typically spanning length-scales of hundreds of km.6,39 Second, the lack of trajectories means that it is difficult to analyze the transport history and the influences on the air parcel before arriving at the receptor. Eulerian Adjoint Methods. To date, one of the most sophisticated methods for sensitivity analyses is the use of adjoint methods.41−43 In these methods, the sensitivity of a pollutant field (e.g., ozone concentration44) is calculated relative to numerous inputs (emissions, meteorology, boundary conditions). The adjoint methods solve the computational cost problem associated with the tagged species approach, since the adjoint isolates the sensitivity and retrieves the emission contribution to the receptor at the gridscale.42,45 However, despite being a powerful method, the adjoint method is not without issues. First, construction of the adjoint requires nonlinearities in the CTM to be linearized,46 limiting the size of the perturbation to the pollutant field that can be diagnosed.44 Second, construction of the adjoint version of the CTM and updating the adjoint as the CTM evolves is a nontrivial task, requiring significant human resources for testing and debugging.47,48 Third, the adjoint method is a sensitivity method, and not a source apportionment method (see “Brute Force Method” section).49 Fourth, due to the numerical artifacts associated with advection schemes in gridded

models,50 Eulerian CTMs are subject to considerable “effective numerical diffusion” smearing out pollution plumes in the resulting simulations.51,52 Such diffusion is a fundamental consequence of the advection scheme, present in all Eulerian models, and not easily mitigated by finer grid spacing.51 More extensive discussion regarding numerical diffusion and the implications for source apportionment can be found in the SI. Brute Force Method. The “brute force method” (BFM) is a conceptually straightforward but powerful method that simply apportions sources by modifying the source strengths, and then rerunning the CTM and quantifying concentration changes at the receptor(s). Due to changes to the source strengths, the BFM is, strictly speaking, a “sensitivity analysis” like the adjoint approach rather than a source apportionment method. While source apportionment methods seek to attribute the observed pollutant concentration to upwind sources, sensitivity analyses examine the changes in pollutant concentration that would result from modifying upwind emissions. Although related, the differences between the sensitivity yielded by BFM and source apportionment are accentuated in cases where nonlinear responses are involved.3−5 Furthermore, the BFM may be infeasible as a source apportionment method if large numbers of source locations and types need to be resolved, since a separate model run is necessary for each separate source. A comparison between source apportionment results from BFM versus the new SLAM method will be shown in the Results.

■

METHODOLOGY: SLAM The source apportionment described in this paper draws upon elements of past approaches outlined in the previous section. The Stochastic Lagrangian Apportionment Method (SLAM) is a receptor-oriented method that combines the trajectory-based method and the tagged species approach in a model that simulates nonlinear chemical transformations. To elucidate the atmospheric transport of air arriving at the receptor, the SLAM approach adopts a backward-time Lagrangian particle dispersion model, a more sophisticated approach than mean-wind trajectory approaches (see “Trajectory-Based Methods”). While SLAM makes use of tagged species in apportioning sources, the key difference from previous tagged species approaches is its Lagrangian formulation, in contrast to the Eulerian approach of stationary grid boxes. A similar methodology has already been applied to apportion the sources of water,53−55 but not to air qualityrelevant pollutants and their precursors. The Lagrangian approach is associated with several key advantages over its Eulerian counterpart. Lagrangian advection of pollutants is subject to minimal numerical diffusion56,57 found in Eulerian advection schemes, which can artificially smear out plumes and gradients50,58,51 (SI). Similarly, the air parcels can be tracked backward in time starting from a point where the receptor is found, while the Eulerian approach is limited to representing the receptor with a gridbox, in effect introducing a dilution when compared against point-like measurements by sensors.32,34 Other unphysical artifacts that may be present in Eulerian advection schemes that are avoided by Lagrangian methods include lack of mass conservation59 and the presence of negative mixing ratios.60 Furthermore, the computational cost of advecting additional species with Lagrangian methods is minimal, while the cost increases approximately linearly with the number of species in the case of Eulerian advection.61,62 This advantage is nontrivial when one considers the numerous species involved in chemical 353



Article

Here i represents different locations and times upwind of the receptor, with the time and location linked through the Lagrangian formulation. At a particular time step i, the concentration change (ΔCi) can originate from numerous processesemissions (E), chemical source (S), chemical loss (L), and depositional loss (D):

reactions affecting the concentration of a species like PM2.5, or air quality in general.5 Finally, the Lagrangian approach yields the back trajectories that enable researchers to track air parcels arriving at the receptor.29

■

ALGORITHM DESCRIPTION Here we describe the SLAM algorithm, which is also represented schematically in Figure 1. For simplicity’s sake we will first examine the case with a single air parcel. The generalization to multiple parcels can be found in the SI.

ΔCi = Ei + Si − Li − Di

(2)

where D is the sum of both dry and wet deposition. The goal of source apportionment is to partition contributions to receptor concentration C from different sources, for example, different emission types, locations, or chemical reactions giving rise to C. Source apportionment would then represent the receptor concentration as the sum of different χ’s, with each χ indicating the source contribution from a particular time step or source type: T

C = χ0 +

∑ (χE

i

+ χS )

i=1

fj = 1 −

The concentration C at a receptor is a function of initial concentration C0 and the changes ΔC along the air parcel history. For a single parcel whose transport history includes T timesteps since initialization at the boundary condition, C is given by

i=1

(Lj + Dj) Cj − 1

(4)

The assumption here is that each loss process could affect any pollutant molecule equally within air parcel, regardless of source. Thus, for an emission at time step i, the contribution is reduced by a factor f j at each subsequent time step, ranging from i+1 to time step T:

T

∑ ΔCi

(3)

χEi is the emission contribution from the location where the parcel is found at time step i; similarly, χSi is the chemical source contribution from time step i. χ0 is the contribution from the boundary condition, which also serves as initial concentration for a Lagrangian air parcel. The distinction is made here between χ versus C: χ represents the net contribution, accounting for the fact that a chemical species originating from an upwind location could have decayed by the time the parcel arrives at the receptor. This includes the net contribution from the boundary condition (χ0), which may have been altered from the original value C0 during its transport to the receptor. χ can be subdivided further into different kinds of E and S. For instance, emissions from stationary versus mobile sources can be differentiated, or chemical sources from different precursors can be distinguished. The model simply needs to track them separately. In this regard, SLAM is similar to the tagged species approaches mentioned earlier. In the sample problem below involving source apportionment of ammonia and ammonium particulates, we will specifically apply SLAM to examine the contributions from agricultural versus nonagricultural sources. In order to calculate χ, the fraction of the original source lost to chemical reactions or deposition is quantified. For instance, to determine χEi, the original contribution Ei is reduced by a fraction at every time step, as the parcel moves toward the receptor from i+1 to time step T. The fractional loss during time step j is given by (Lj + Dj)/Cj‑1, which is the fraction of the concentration from the previous time step that is lost to chemistry and deposition. Thus, the fraction that is retained at time step j, accounting for loss processes, is given by

Figure 1. Schematic of the Stochastic Lagrangian Apportionment Method (SLAM) for a single parcel. For the general case of multiple air parcels, mixing between parcels needs to be taken into account (see SI). C (orange line) represents the time evolution of the air parcel’s concentration (arbitrary unit) as it travels over the landscape. In this simple example, the time step is set to 6 h. At each time step i, the concentration is increased or decreased by an increment ΔCi due to emissions, deposition, or chemical transformation. χ represents the source contribution from a particular time step or process. χEi is the emission contribution from where the parcel is found at time step i. The blue and yellow lines represent the time evolution of the source contribution from industrial and agricultural emissions at i = 2 and i = 4, respectively. For multiple air parcels, the situation is more complicated, and mixing/averaging between parcels needs to also be accounted for (see SI). The single parcel considered here is initialized with C0 = 1 (arbitrary concentration unit). It then decays to 0 in the first time step due to chemical loss. In i = 2 the concentration is increased to 4 by industrial emissions, represented with the blue color. During the third time step, the parcel experiences depositional loss, reducing C to 1. Here the original contribution from industrial emission of 4 units is reduced by a factor (given by eq 4) of (1−3/4) = 1/4, to χE2 = 1. During i = 4, the parcel concentration is enhanced by 2 units, due to emissions from agricultural emissions (yellow). The parcel is now a mixture of contributions from industrial (blue) and agricultural (yellow) emissions, resulting in the color of the parcel being green. The enhancement from agricultural emissions in i=4 does not affect the industrial emissions in i = 2, so the final χE2 = 1.

C = C0 +

i

(1) 354


Environmental Science & Technology χE = Ei i

⎡ (L + Dj) ⎤ ⎢1 − j ⎥ = Ei Cj − 1 ⎥⎦ ⎢ j=i+1 ⎣

Article

T

T

∏

∏

fj

j=i+1

source affecting ozone levels in southern Ontario by Wen et al.37 and Yap et al.20 Setup of STILT-Chem Model. STILT-Chem was used to simulate hourly concentrations of NH3 and p-NH4+ at the Longwoods site in southern Ontario (Figure 2) for half a year,

(5a)

Similarly, the contribution to the receptor by a chemical source at time step i is given by χS = Si i

⎡ (L + Dj) ⎤ ⎢1 − j ⎥ = Si Cj − 1 ⎥⎦ ⎢ j=i+1 ⎣ T

T

∏

∏ j=i+1

fj

(5b)

We can show that the definition of source contribution in eq 5 leads to the source apportionment equation (eq 3) to yield a value of C that is identical to that in eq 1. The interested reader can turn to the SI for a demonstration of the equivalence between eqs 1 and 3, given the definition of χEi in eq 5. STILT-Chem Model. We implemented SLAM within a recently developed Lagrangian air quality model, STILTChem.37,63 STILT-Chem was built on top of the Stochastic Time-Inverted Lagrangian Transport model (STILT),34 a LPDM that has been designed for time-reversibility and critically evaluated against tracer release data.64 STILT-Chem incorporated chemical transformations along with dry/wet depositions37 as well as aqueous and multiphase reactions related to transformation of ammonia into particulate ammonium.

■

EXAMPLE: APPLICATION TO AMMONIA/AMMONIUM As an example to illustrate SLAM, we show its application in apportioning sources contributing to ammonia (NH3) and its reaction product, ammonium (NH4+) particulates. NH3 is the most abundant basic gas in the atmosphere,65 and through its neutralization of acids, forms particulate NH4+.66 Ammonium particulates (p-NH4+) are an important component of particulate matter (PM).67 With PM’s well-established adverse health effects,68−70 it has been classified as a criterion pollutant, particularly the smaller particulates (PM2.5).71 Reductions in NH3 emissions have been suggested as an effective way to reduce total PM.72 Thus, from an air quality perspective, it is important to understand the sources of NH3 contributing to their concentrations at a receptor. Major sources of NH3 over land include animal and human excreta, fertilizers, fossil fuel combustion, and biomass burning.73 Primary sinks of NH3 are deposition and transformation to p-NH4+.65 p-NH4+ is lost primarily via depositional processes.63 Agricultural activity contributes greatly to NH3 emissions and indirectly to p-NH4+, from fertilizer application to livestocks’ excreta.74 For instance, it has been suggested that increased livestock farming increases infant mortality rate nearby.75 The southern part of Ontario is an agricultural hotspot, accounting for over half of corn and winter wheat production in Canada.76 Thus, it is important to quantify and understand how much NH3 and p-NH4+ at a receptor located in southern Ontario derive from agricultural versus nonagricultural emissionsan example of a source apportionment problem. In addition, it is helpful to know where the NH3 and p-NH4+ originate. Due to the proximity of southern Ontario to the U.S.Canada border, it is also critical to quantify exactly how much NH3 and the resulting p-NH4+ derive from emissions outside of Canada that are then transported across the border. Crossborder transport has already been suggested to be an important

Figure 2. Inventory-based emissions of NH3 [mol/s] from agricultural (a, b) and nonagricultural (c, d) sources, averaged from June 1st to Nov 30th, 2006. (b) and (d) zoom into the area marked by the red box, in the vicinity of the Longwoods site in southern Ontario, Canada.

from 1 June to 30 November 2006. Longwoods is a measurement site located within an enclosed agricultural field77 that is ∼190 km southwest of Toronto and ∼140 km northeast of Detroit (Figure 2). p-NH4+ was measured over 24h periods using a filter-pack system.78,79 NH3 measurements were carried out at Longwoods and numerous other sites as one-week averages from 2006 to 2007, during the Southern Ontario Ammonia Passive Sampler Survey (SOAPSS).80 The setup of STILT-Chem was identical to that in Wen et al.,81 with ensembles of 500 particles released every hour from the Longwoods site, at a height of 5m above ground. Details can also be found in the SI. In order to investigate the different source contributions to the site, NH3 emissions were split into agricultural sources (fertilizer + livestock) and nonagricultural sources: i.e., on-road mobile, off-road mobile, nonagricultural areal, and point sources. Figure 2 shows the maps for agricultural versus nonagricultural emissions of NH3, averaged over the simulation period. Agricultural NH3 emissions are enhanced in the farmlands, for example, the California Central Valley, the American Midwest, and southern Ontario. The nonagricultural emissions are smaller over the U.S./Canada and are focused in major urban and industrial areas, where fossil fuel combustion is concentrated. These emissions were input into the STILT-Chem model to examine the source apportionment at the Longwoods site, using the SLAM method. 355



■

Article

RESULTS Comparisons Against p-NH4+ Observations. While this paper focuses on source apportionment rather than a detailed evaluation of the STILT-Chem model, we first show comparisons between the simulated and observed time series of p-NH4+ (Figure 3). For brevity’s sake the observed vs

Values of model evaluation statistics recommended by the U.S. EPA82 are as follows: mean fractional bias (MFB) = 34%, mean fractional error (MFE) = 63%, and ratio of means (ROM) = 1.14. Regardless of these errors, the simulations exhibited performance comparable to other models. For a comprehensive evaluation and discussion of STILT-Chem-simulated p-NH4+ at multiple sites in Southern Ontario, see Wen et al.63 Source Apportionment of NH3 and p-NH4+ using SLAM. The SLAM method was adopted to carry out source apportionment for each simulated hourly value of NH3 and pNH4+, generating a time series of contributions from agricultural versus nonagricultural emissions of NH3, as well as the boundary condition. The source apportionment time series are shown for NH3 and p-NH4+ in SI Figure S1 and Figure 3, respectively. The simulated NH3 consists almost entirely of contributions from agricultural emissions throughout the entire June ∼ November period, as indicated by the overlap between the lines in red (simulated) and blue (agriculture), with minimal contributions from the boundary condition or nonagricultural sources. Agricultural emissions of NH3 were also the dominant contributor that gave rise to p-NH4+ concentrations at Longwoods (Figure 3). The relative contribution from nonagricultural emissions to p-NH4+ was seen to increase in November, as agricultural emissions decreased in autumn and winds transported urban and industrial emissions to Longwoods (see SI Figure S4c). The SLAM method also yields detailed spatial information regarding where the sources contributing to the receptor concentrations are. This is a key advantage over statistical source apportionment methods such as CMB and PMF, which do not provide information about source locations. The source locations impacting the receptor concentration are controlled by atmospheric transport, for example, factors such as wind direction/speed, wind shear, and turbulence strength. These factors combine to determine the trajectories of air parcels arriving at the receptor, which are precisely what are

Figure 3. Time series of the observed and simulated p-NH4+ concentrations at Longwoods, as well as the SLAM-apportioned contributions from agricultural emission sources, nonagricultural emission sources, and boundary conditions. The green arrows indicate the times of elevated concentrations whose footprints are shown in SI Figure S4.

simulated NH3 are shown in the SI (Figure S1). The hourly simulations were averaged to correspond with the measurement frequency of NH3 (weekly) and p-NH4+ (daily), respectively. As an additional test of the model, we also simulated nitrate and sulfate concentrations and compared them against observed values at the same site (SI). The timing of p-NH4+ enhancements is captured well by the model (Figure 3), albeit the enhancement levels exhibit errors.

Figure 4. Map of net NH3 emission contributions to NH3 concentration at the receptor (Longwoods), averaged over the entire simulation period from June first to November 30th, 2006 for (a) agricultural and (b) nonagricultural sources. A similar map of net NH3 emission contributions to pNH4+ concentration at the receptor (Longwoods) is also available for (a) agricultural and (b) nonagricultural sources. 356



Article

Figure 5. Comparison between agricultural contributions to concentrations of a) NH3 and b) p-NH4+ at the Longwoods site, predicted by SLAM versus the brute force method (BFM). The BFM was carried out by setting agricultural emissions to zero and quantifying the decreases in NH3 and p-NH4+. NH3 is averaged over a week and p-NH4+ over 24 h, to correspond with the observations. The 1:1 line is shown in dashed green, while the blue line is the regression line, fitted using the major axis method.

apportionment results from SLAM, we compared SLAM against results from an alternative techniquethe brute force method (BFM), which zeroes out the agricultural emissions of NH3 and calculates the resulting reductions in concentrations of NH3 and p-NH4+. Note that this is a test of the model’s internal consistency between source apportionment methods; it does not necessarily test the veracity of either the SLAM- or BFM-apportioned sources, which would require independent data sets. Figure 5 shows the source contributions as suggested by SLAM and BFM. The calculated contribution to NH3 from agricultural NH3 emissions were close to identical between SLAM and BFM. For p-NH4+ SLAM’s predictions were strongly correlated with values from BFM (r = 0.961), albeit SLAM predicted higher contributions than BFM, in general. Similar discrepancy in p-NH4+ between BFM and another tagged species apportionment method (PSAT) was also observed by Koo et al.4 The discrepancy can be traced to indirect effects associated with the impact of perturbations in species other than the one that is decreased.4,38 The reduction in NH3 from zeroing out agricultural NH3 emissions within BFM results in changes in species other than NH3, which leads to a smaller decrease in pNH4+. Thus, this is a difference between SLAM, which is a source apportionment method, versus BFM, which strictly speaking is a sensitivity method, implying that the discrepancy between SLAM and BFM does not necessarily imply errors in SLAM.

simulated by a backward-time Lagrangian particle dispersion simulation that lies at the heart of the SLAM method. For a discussion of the transport information generated by STILTChem, as encapsulated in “footprint” maps, please refer to the SI (Figure S4). Maps of NH3 emissions contribution to the NH3 and p-NH4+ concentrations at Longwoods are shown in Figure 4. The contrast in the spatial extent of emission contributions to NH3 versus p-NH4+ is striking. NH3 concentrations were primarily contributed by emissions in relatively local, nearby locations, while p-NH4+ concentrations can be affected by emissions that are hundreds of km upwind. Thus, while NH3 at Longwoods is primarily derived from emissions in southern Ontario, Michigan, and Ohio, p-NH4+ can be formed from NH3 emitted not only in the vicinity of southern Ontario, but also the entire American Midwest. p-NH4+ can originate even from nonagricultural NH3 emissions in faraway urban areas such as Chicago and Minneapolis, albeit the contribution is greatly diminished as one moves further upwind from Longwoods (note logarithmic colorscale). The relatively near-field contributions to NH3 concentrations reflects the fact that NH3 in the atmosphere is quickly converted or lost.65,83 Wen et al.63 have already found that most of the contributions to NH3 at Longwoods were found within 60 km of the site. NH3 emitted from sources further upwind have already deposited to the surface or converted to p-NH4+, which can then be transported for hundreds of km before being removed through depositional processes. In general, rates of dry deposition for p-NH4+ are much smaller than that of NH3.65 The regional impact of NH3 emissions on p-NH4+ has also been pointed to by Makar et al.,67 who pointed to the fact that reductions in ammonia emissions “have trans-boundary consequences”, a point also suggested in our results by the significant contributions of p-NH4+ from U.S. emissions (Figure 4). Comparison of Source Apportionment from SLAM Versus the Brute Force Method. As a test of the source

■

DISCUSSION

Strengths of SLAM. The Stochastic Lagrangian Apportionment Method (SLAM) yields source apportionment for chemically active pollutants at both high temporal and spatial resolution. For instance, the source apportionment for p-NH4+ is generated for each simulated time point (hourly, averaged to daily in Figure 3). SLAM also provides highly resolved spatial information regarding the source apportionment (Figure 4), at the native resolution of the emission grids. 357



■

The reason SLAM can provide such detailed spatiotemporal information for source apportionment can be traced to the time-reversed LPDM formulation at the core of the SLAM method. In other words, the air parcels arriving at the receptor are isolated by the time-reversed LPDM. Thus, SLAM isolates and quantifies the influences on the receptor, without incurring the computational cost of tracking sources that affect areas other than the receptor37 while reducing the impact of numerical diffusion in smearing out the source region and limiting the ability to resolve it (SI). Weaknesses of SLAM. While the SLAM method possesses numerous strengths that have been highlighted in this paper, the method does have shortcomings as it is currently implemented. First, due to its receptor-oriented nature, each SLAM calculation yields source apportionment for a single receptor, rather than for multiple gridcells covering a wide geographical area, such as provided by Eulerian methods. Second, the mixing between air parcels within STILT-Chem at the meteorological gridscale is simple and induces numerical diffusion of its own, but it is not inherent to the SLAM approach and can be greatly improved in the future.37,57 Third, a consequence of its strength in the use of Lagrangian trajectories to elucidate the upwind sources affecting the receptor actually results in potential uncertainties. Trajectories are known to be subject to errors,84,85 and these errors grow as their duration increases.86 However, the impact of uncertainties in atmospheric transport is found in all source apportionment approaches using simulated transport, including Eulerian approaches, and not unique to SLAM. Finally, SLAM requires prior estimates of source strengths (e.g., Figure 2) so the method is obviously subject to errors in emission inventories, which can be large.87−91 Toward a Hybrid SLAM + Inverse Analysis Apportionment Method. To address potential uncertainties in the source strengths and in the source/sink calculations, we envision SLAM may be used in conjunction with inverse modeling, as part of a “hybrid” source apportionment method. Pioneered by Schichtel et al.,92 the hybrid method applies an inverse calculation to initial source apportionment, in order to correct for potential biases in the emission inventory and modeling errors in chemical sources/sinks. While these studies adopted the computationally inefficient brute force method for source apportionment, we suggest that SLAM could be used instead. Thus, through this hybrid source apportionment approach, systematic errors in the air quality modeling system, which the SLAM method is subject to, can be minimized.

■

Article

AUTHOR INFORMATION

Corresponding Author

*Phone: (801)581-7530; fax: (801)585-3681; e-mail: John. [email protected]. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS We gratefully acknowledge Q. Zheng and M. Moran at Environment Canada’s Air Quality Research Division for providing the ammonia emission inventory. D.W. was supported by both Environment Canada and the University of Waterloo. The support and resources from the Center for High performance Computing at the University of Utah are gratefully acknowledged.

■

REFERENCES

(1) Molina, M. J.; Molina, L. T. Megacities and atmospheric pollution. J. Air Waste Manage. Assoc. 2004, 54, 644−680. (2) WMO. WMO/IGAC Impacts of Megacities on Air Pollution and Climate; World Meteorological Organization: 2012; p 299. (3) Blanchard, C. L. Methods for attributing ambient air pollutants to emssions sources. Ann. Rev. Energy Environ. 1999, 24, 329−365. (4) Koo, B.; Wilson, G. M.; Morris, R. E.; Dunker, A. M.; Yarwood, G. Comparison of source apportionment and sensitivity analysis in a particulate matter air quality model. Environ. Sci. Technol. 2009, 43, 6669−6675. (5) Seinfeld, J. H.; Pandis, S. N. Atmospheric Chemistry and Physics, 2nd ed.; Wiley: Hoboken, NJ, 2006; p 1203. (6) Lowenthal, D. H.; Watson, J. G.; Koracin, D.; Chen, L.-W. A.; Dubois, D.; Vellore, R.; Kumar, N.; Knipping, E. M.; Wheeler, N.; Craig, K.; Reid, S. Evaluation of regional-scale receptor modeling. J. Air Waste Manage. Assoc. 2010, 60, 26−42. (7) Henry, R. C. Multivariate receptor modelscurrent practice and future trends. Chemom. Intell. Lab. Syst. 2002, 60, 43−48. (8) Hopke, P. K.; Ito, K.; Mar, T.; Christensen, W. F.; Eatough, D. J.; Henry, R. C.; Kim, E.; Laden, F.; Lall, R.; Larson, T. V. PM source apportionment and health effects: 1. Intercomparison of source apportionment results. J. Exposure Sci. Environ. Epidemiol. 2006, 16, 275−286. (9) Watson, J. G.; Cooper, J. A.; Huntzicker, J. J. The effective variance weighting for least squares calculations applied to the mass balance receptor model. Atmos. Environ. 1984, 18 (7), 1347−1355. (10) Paatero, P.; Tapper, U. Positive matrix factorization: A nonnegative factor model with optimal utilization of error estimates of data values. Environmetrics 1994, 5, 111−126. (11) Henry, R. C. Multivariate receptor modeling by N-dimensional edge detection. Chemom. Intell. Lab. Syst. 2003, 65, 179−189. (12) Brown, S. G.; Lee, T.; Norris, G. A.; Roberts, P. T.; Collett, J. L., Jr.; Paatero, P.; Worsnop, D. R. Receptor modeling of near-roadway aerosol mass spectrometer data in Las Vegas, Nevada, with EPA PMF. Atmos. Chem. Phys. 2012, 12, 309−325. (13) Watson, J. G.; Chen, L.-W. A.; Chow, J. C.; Doraiswamy, P.; Lowenthal, D. H. Source apportionment: Findings from the U.S. Supersites program. J. Air Waste Manage. Assoc. 2008, 58, 265−288. (14) Kelly, K. E.; Kotchenruther, R.; Kuprov, R.; Silcox, G. D. Receptor model source attributions for Utah’s Salt Lake City airshed and the impacts of wintertime secondary ammonium nitrate and ammonium chloride aerosol. J. Air Waste Manage. Assoc. 2013, 63 (5), 575−590. (15) Pekney, N. J.; Davidson, C. I.; Zhou, L.; Hopke, P. K. Application of PSCF and CPF to PMF-modeled sources of PM2.5 in Pittsburgh. Aerosol Sci. Technol. 2006, 40, 952−961. (16) Heo, J.-B.; Hopke, P. K.; Yi, S.-M. Source apportionment of PM2.5 in Seoul, Korea. Atmos. Chem. Phys. 2009, 9, 4957−4971. (17) Lin, J. C., Lagrangian modeling of the atmosphere: An introduction. In Lagrangian Modeling of the Atmosphere, Lin, J. C.;

ASSOCIATED CONTENT

S Supporting Information *

(1) Source apportionment equations, (2) Generalization of source apportionment equations to multiple air parcels, (3) Setup of STILT-Chem model for simulating NH3 and p-NH4+, (4) Comparisons against NH3 observations, (5) Comparisons against nitrate and sulfate observations, (6) Transport information from STILT-Chem (“footprint”), (7) Impacts of excessive numerical diffusion are available. This material is available free of charge via the Internet at http://pubs.acs.org. This material is available free of charge via the Internet at http://pubs.acs.org/. 358



Article

Brunner, D.; Gerbig, C.; Stohl, A.; Luhar, A.; Webley, P., Eds. American Geophysical Union: 2012; Vol. 200, pp 1−11. (18) Wiin-Nielsen, A. On the application of trajectory methods in numerical forecasting. Tellus 1959, 11, 180−196. (19) Danielsen, E. F. Trajectories: Isobaric, isentropic and actual. J. Meteorol. 1961, 18, 479−486. (20) Yap, D.; Ning, D. T.; Dong, W. An assessment of source contributions to the ozone concentrations in southern Ontario, 1979− 1985. Atmos. Environ. 1988, 22 (6), 1161−1168. (21) Dorling, S. R.; Davies, T. D.; Pierce, C. E. Cluster analysis: A technique for estimating the synoptic meteorological controls on air and precipitation chemistryMethod and applications. Atmos. Environ. 1992, 26A (14), 2575−2581. (22) Moody, J. L.; Galloway, J. N. Quantifying the relationship between atmospheric transport and the chemical composition of precipitation on Bermuda. Tellus 1988, 40B, 463−479. (23) Ashbaugh, L. L.; Malm, W. C.; Sadeh, W. Z. A residence time probability analysis of sulfur concentrations at Grand Canyon National Park. Atmos. Environ. 1985, 19 (8), 1263−1270. (24) Kleeman, M. J.; Hughes, L. S.; Allen, J. O.; Cass, G. R. Source contributions to the size and composition distribution of atmospheric particles: Southern California in September 1996. Environ. Sci. Technol. 1999, 33, 4331−4341. (25) Mysliwiec, M. J.; Kleeman, M. J. Source apportionment of secondary airborne particulate matter in a polluted atmosphere. Environ. Sci. Technol. 2002, 36 (24), 5376−5384. (26) Strong, J.; Whyatt, J. D.; Hewitt, C. N.; Derwent, R. G. Development and application of a Lagrangian model to determine the origins of ozone episodes in the UK. Atmos. Environ. 2010, 44, 631− 641. (27) Stohl, A.; Wotawa, G. A method for computing single trajectories representing boundary layer transport. Atmos. Environ. 1993, 29, 3235−3238. (28) Koracin, D.; Vellore, R.; Lowenthal, D. H.; Watson, J. G.; Koracin, J.; McCord, T.; DuBois, D. W.; Chen, L.-W. A.; Kumar, N.; Knipping, E. M.; Wheeler, N. J. M.; Craig, K.; Reid, S. Regional source identification using lagrangian stochastic particle dispersion and HYSPLIT backward-trajectory models. J. Air Waste Manage. Assoc. 2011, 61, 660−672. (29) Lin, J. C.; Brunner, D.; Gerbig, C.; Stohl, A.; Luhar, A. K.; Webley, P. W. Lagrangian Modeling of the Atmosphere; American Geophysical Union, 2012; Vol. 200, p 349. (30) Rodean, H. C. Stochastic Lagrangian Models of Turbulent Diffusion; American Meteorological Society: Boston, 1996; Vol. 26. (31) Lin, J. C.; Brunner, D.; Gerbig, C. Studying atmospheric transport through Lagrangian models. EOS 2011, 92 (21), 177−178. (32) Seibert, P.; Frank, A. Source-receptor matrix calculation with a Lagrangian particle dispersion model in backward mode. Atmos. Chem. Phys. 2004, 4, 51−63. (33) Flesch, T. K.; Wilson, J. D.; Yee, E. Backward-time Lagrangian stochastic dispersion models and their application to estimate gaseous emissions. J. Appl. Meteorol. 1995, 34, 1320−1332. (34) Lin, J. C.; Gerbig, C.; Wofsy, S. C.; Andrews, A. E.; Daube, B. C.; Davis, K. J.; Grainger, C. A., A near-field tool for simulating the upstream influence of atmospheric observations: The Stochastic TimeInverted Lagrangian Transport (STILT) model. J. Geophys. Res. 2003, 108, (4493), DOI: 10.1029/2002JD003161. (35) Miller, S. M.; Matross, D. M.; Andrews, A. E.; Millet, D. B.; Longo, M.; Gottlieb, E. W.; Hirsch, A. I.; Gerbig, C.; Lin, J. C.; Daube, B. C.; Hudman, R. C.; Dias, P. L. S.; Chow, V. Y.; Wofsy, S. C. Sources of carbon monoxide and formaldehyde in North America determined from high-resolution atmospheric data. Atmos. Chem. Phys. 2008, 8, 7673−7696. (36) Benmergui, J.; Sharma, S.; Wen, D.; Lin, J. C., Quantitative attribution of processes affecting atmospheric chemical concentrations by combining a time-reversed Lagrangian particle dispersion model and a regression approach. In Lagrangian Modeling of the Atmosphere; Lin, J. C., Brunner, D., Gerbig, C.; Stohl, A., Luhar, A., Webley, P., Eds.; American Geophysical Union, 2013; Vol. 200, pp 251−264.

(37) Wen, D.; Lin, J. C.; Millet, D.; Stein, A.; Draxler, R. A backwardtime stochastic Lagrangian air quality model. Atmos. Environ. 2012, 54, 373−386. (38) Wagstrom, K. M.; Pandis, S. N.; Yarwood, G.; Wilson, G. M.; Morris, R. E. Development and application of a computationally efficient particulate matter apportionment algorithm in a threedimensional chemical transport model. Atmos. Environ. 2008, 42, 5650−5659. (39) Dunker, A. M.; Yarwood, G.; Ortmann, J. P.; Wilson, G. M. Comparison of source apportionment and source sensitivity of ozone in a three-dimensional air quality. Environ. Sci. Technol. 2002, 36, 2953−2964. (40) Kleeman, M. J.; Cass, G. R.; Eldering, A. Modeling the airborne particle complex as a source-oriented external mixture. J. Geophys. Res. 1997, 102 (D17), 21355−21372. (41) Elbern, H.; Schmidt, H.; Talagrand, O.; Ebel, A. 4D-variational data assimilation with an adjoint air quality model for emission analysis. Environ. Modell. Software 2000, 15, 539−548. (42) Henze, D. K.; Hakami, A.; Seinfeld, J. H. Development of the adjoint of GEOS-Chem. Atmos. Chem. Phys. 2007, 7, 2413−2433. (43) Hakami, A.; Henze, D. K.; Seinfeld, J. H.; Singh, K.; Sandu, A.; Kim, S.; Byun, D. W.; Li, Q. The adjoint of CMAQ. Environ. Sci. Technol. 2007, 41, 7807−7817. (44) Menut, L. Adjoint modeling for atmospheric pollution process sensitivity at regional scale. J. Geophys. Res. 2003, 108 (D17), 8562. (45) Kopacz, M.; Jacob, D. J.; Henze, D. K.; Heald, C. L.; Streets, D. G.; Zhang, Q., Comparison of adjoint and analytical Bayesian inversion methods for constraining Asian sources of carbon monoxide using satellite (MOPITT) measurements of CO columns. J. Geophys. Res. 2009, 114, (D04305), DOI: 10.1029/2007JD009264. (46) Errico, R. M. What is an adjoint model? Bull. Am. Meteorol. Soc. 1997, 78, 2577−2591. (47) Anderson, J.; Hoar, T.; Raeder, K.; Liu, H.; Collins, N.; Torn, R.; Avellano, A. The data assimilation research testbed: A community facility. Bull. Am. Meteoro. Soc. 2009, 1283−1296. (48) Rabier, F.; Jarvinen, H.; Klinker, E.; Mahfouf, J. F.; Simmons, A. The ECMWF operational implementation of four-dimensional variational assimilation. I: Experimental results with simplified physics. Q. J. R. Meteorol. Soc. 2000, 126, 1143−1170. (49) Henze, D. K.; Seinfeld, J. H.; Shindell, D. T. Inverse modeling and mapping US air quality influences of inorganic PM2.5 precursor emissions using the adjoint of GEOS-Chem. Atmos. Chem. Phys. 2009, 9, 5877−5903. (50) Smolarkiewicz, P.; Pudykiewicz, J. A. A class of semi-Lagrangian approximations for fluids. J. Atmos. Sci. 1992, 49, 2082−2096. (51) Rastigejev, Y.; Park, R. J.; Brenner, M. P.; Jacob, D. J., Resolving intercontinental pollution plumes in global models of atmospheric transport. J. Geophys. Res. 2010, 115, (D02302), DOI: 10.1029/ 2009JD012568. (52) Santillana, M., Quantifying the loss of information in source attribution problems using the adjoint method in global models of atmospheric chemical transport. arXiv 2013, 1311.6315. (53) Schicker, I.; Radanovics, S.; Seibert, P. Origin and transport of Mediterranean moisture and air. Atmos. Chem. Phys. 2010, 10, 5089− 5105. (54) Stohl, A.; James, P.; Lagrangian, A. Analysis of the atmospheric branch of the global water cycle. Part II: Moisture transports between Earth’s ocean basins and river catchments. J. Hydrometeorol. 2005, 6, 961−984. (55) Sodemann, H.; Masson-Delmotte, V.; Schwierz, C.; Vinther, B. M.; Wernli, H., Interannual variability of Greenland winter precipitation sources: 2. Effects of North Atlantic Oscillation variability on stable isotopes in precipitation. J. Geophys. Res. 2008, 113, (D12111), DOI: 10.1029/2007JD009416. (56) McKenna, D. S.; Konopka, P.; GrooB, J.-U.; Gunther, G.; Muller, R., A new chemical Lagrangian model of the stratosphere (CLaMS) 1. Formulation of advection and mixing. J. Geophys. Res. 2002, 107, (D16). 359



Article

(57) Konopka, P.; Ploeger, F.; Muller, R., Entropy-based and static stability-based Lagrangian model grids In Lagrangian Modeling of the Atmosphere; Lin, J. C., Brunner, D., Gerbig, C., Stohl, A., Luhar, A., Webley, P., Eds.; American Geophysical Union, 2012; Vol. 200, pp 99−109. (58) Shin, S.; Reich, S. Hamiltonian particle-mesh simulations for a non-hydrostatic vertical slice model. Atmos. Sci. Lett. 2009, 10, 233− 240. (59) Brasseur, G. P.; Khattatov, B.; Walters, S., Modeling. In Atmospheric Chemistry and Global Change; Brasseur, G. P., Orlando, J. J., Tyndall, G. S., Eds. ; Oxford University Press: New York, 1999; pp 423−462. (60) Rood, R. B. Numerical advection algorithms and their role in atmospheric transport and chemistry models. Rev. Geophys. 1987, 25, 71−100. (61) Brunner, D., Atmospheric chemistry in Lagrangian models-overview. In Lagrangian Modeling of the Atmosphere; Lin, J. C., Brunner, D., Gerbig, C., Stohl, A., Luhar, A., Webley, P., Eds.; American Geophysical Union, 2013; Vol. 200, pp 225−233. (62) Colella, P.; Woodward, P. R. The piecewise parabolic method (PPM) for gas-dynamical simulations. J. Comput. Phys. 1984, 54, 174− 201. (63) Wen, D.; Lin, J. C.; Zhang, L.; Vet, R.; Moran, M. D. Modeling atmospheric ammonia and ammonium using a stochastic Lagrangian air quality model (STILT-Chem v0.7). Geosci. Model Dev. 2013, 6, 327−344. (64) Hegarty, J.; Draxler, R. R.; Stein, A.; Brioude, J.; Mountain, M.; Eluszkiewicz, J.; Nehrkorn, T.; Ngan, F.; Andrews, A. evaluation of lagrangian Particle Dispersion Models with Measurements from Controlled Tracer Releases. J. Appl. Meteorol. Climatol. 2013, 52, 2623−2637. (65) Asman, W. A. H.; Sutton, M. A.; Schjorring, J. K. Ammonia: Emission, atmospheric transport and deposition. New Phytol. 1998, 139, 27−48. (66) Wu, S.-Y.; Krishnan, S.; Zhang, Y.; Aneja, V. Modeling atmospheric transport and fate of ammonia in North CarolinaPart I: Evaluation of meteorological and chemical predictions. Atmos. Environ. 2008, 42, 3419−3436. (67) Makar, P. A.; Moran, M. D.; Zheng, Q.; Cousineau, S.; Sassi, M.; Duhamel, A.; Besner, M.; Davignon, D.; Crevier, L.-P.; Bouchet, V. S. Modelling the impacts of ammonia emissions reductions on North American air quality. Atmos. Chem. Phys. 2009, 9, 7183−7212. (68) Kaiser, J.; Granmar, M. Mounting evidence indicts fine-particle pollution. Science 2005, 307 (5717), 1858−1861. (69) Pope, C. A. Epidemiology of fine particulate air pollution and human health: Biologic mechanisms and who’s at risk? Environ. Health Perspect. 2000, 108 (suppl. 4), 713−723. (70) Schwarze, P. E.; Orevik, J.; Lag, M.; Refsnes, M.; Nafstad, P.; Hetland, R. B.; Dybing, E. Particulate matter properties and health effects: Consistency of epidemiological and toxicological studies. Hum. Exp. Toxicol. 2006, 25, 559−579. (71) EPA. Integrated Science Assessment for Particulate Matter; U.S. Environmental Protection Agency: Research Triangle Park, NC, 2009. (72) Ansari, A. S.; Pandis, S. N. Response of inorganic PM to precursor concentrations. Environ. Sci. Technol. 1998, 32, 2706−2714. (73) Bouwman, A. F.; Lee, D. S.; Asman, W. A. H.; Dentener, F. J.; van der Hoek, K. W.; Olivier, J. G. J. A global high-resolution emission inventory for ammonia. Global Biogeochem. Cycles 1997, 11, 561−587. (74) Schlesinger, W. H. Biogeochemistry: An Analysis of Global Change; Academic Press: San Diego, 1997. (75) Sneeringer, S. Does animal feeding operation pollution hurt public health? A national longitudinal study of health externalities identified by geographic shifts in livestock production. Am. J. Agric. Econ. 2009, 91 (1), 124−137. (76) Statistics Canada 2006 Census of Agriculture: Farm Data and Farm Operator Data: Tables. http://www.statcan.gc.ca/pub/95-629x/2007000/4123856-eng.htm.

(77) Zbieranowski, A. L.; Aherne, J. Spatial and temporal concentration of ambient atmospheric ammonia in southern Ontario, Canada. Atmos. Environ. 2012, 62, 441−450. (78) Sirois, A. Temporal variation of oxides of sulphur and nitrogen in ambient air in eastern Canada: 1979−1994. Tellus 1997, 49B, 270− 291. (79) Zhang, L.; Vet, R.; Wiebe, A.; Mihele, C.; Sukloff, B.; Chan, E.; Moran, M. D.; Iqbal, S. Characterization of the size-segregated watersoluble inorganic ions at eight Canadian rural sites. Atmos. Chem. Phys. 2008, 8, 7133−7151. (80) Vet, R.; Li, S.-M.; Beaney, G.; Belzer, W.; Chan, E.; Dann, T.; Friesen, K.; Hayden, K.; Hou, A. Y.; Iqbal, S. Characterization of ambient ammonia, PM and regional deposition across Canada. In 2008 Canadian Atmospheric Assessment of Agricultural Ammonia, Chapter 6; Environment Canada: Gatineau, QC, Canada, 2008. (81) Wen, D.; Zhang, L.; Lin, J. C.; Vet, R.; Moran, M. D. An evaluation of ambient ammonia concentrations over southern Ontario simulated with different dry deposition schemes within the STILTChem model. Geosci. Model Dev. Discuss. 2013, 6, 6075−6115. (82) Guidance on the Use of Models and Other Analysis for Demonstrating Attainment of Air Quality Goals for Ozone, PM2.5, and regional haze; U. S. EPA: Research Triangle Park, NC, 2007. (83) Pinder, R. W.; Gilliland, A. B.; Dennis, R. L., Environmental impact of atmospheric NH3 emissions under present and future conditions in the eastern United States. Geophys. Res. Lett. 2008, 35, (L12808), DOI: 10.1029/2008GL033732. (84) Lin, J. C.; Gerbig, C., Accounting for the effect of transport errors on tracer inversions. Geophys. Res. Lett. 2005, 32, DOI: 10.1029/ 2004GL021127. (85) Gebhart, K. A.; Schichtel, B. A.; Barna, M. G. Directional biases in back trajectories caused by model and input data. J. Air Waste Manage. Assoc. 2005, 55, 1649−1662. (86) Stohl, A. Computation, accuracy and applications of trajectoriesA review and bibliography. Atmos. Environ. 1998, 32, 947−966. (87) Smith, S. J.; van Aardenne, J.; Klimont, Z.; Andres, R. J.; Volke, A.; Arias, S. D. Anthropogenic sulfur dioxide emissions: 1850−2005. Atmos. Chem. Phys. 2011, 11, 1101−1116. (88) Zhao, Y.; Nielsen, C. P.; Lei, Y.; McElroy, M. B.; Hao, J. Quantifying the uncertainties of a bottom-up emission inventory of anthropogenic atmospheric pollutants in China. Atmos. Chem. Phys. 2011, 11, 2295−2308. (89) Simon, H.; Allen, D. T.; Wittig, A. E. Fine particulate matter emissions inventories: Comparisons of emissions estimates with observations from recent field programs. J. Air Waste Manage. Assoc. 2008, 58, 320−343. (90) Miller, C. A.; Hidy, G.; Hales, J.; Kolb, C. E.; Werner, A. S.; Haneke, B.; Parrish, D.; Frey, H. C.; Rojas-Bracho, L.; Deslauriers, M.; Pennell, B.; Mobley, J. D. Air emission inventories in North America: A critical assessment. J. Air Waste Manage. Assoc. 2006, 56, 1115− 1129. (91) Cohan, D. S.; Hakami, A.; Hu, Y.; Russell, A. G. Nonlinear response of ozone to emissions: Source apportionment and sensitivity analysis. Environ. Sci. Technol. 2005, 39, 6739−6748. (92) Schichtel, B. A.; Malm, W. C.; Gebhart, K. A.; Barna, M. G.; Knipping, E. M., A hybrid source apportionment model integrating measured data and air quality model results. J. Geophys. Res. 2006, 111, (D07301), DOI: 10.1029/2005JD006238.

360


The Stochastic Lagrangian Apportionment Method (SLAM)

Recommend Documents