COUPLING CHEMICAL TRANSPORT
MODEL SOURCE ATTRIBUTIONS WITH
POSITIVE MATRIX FACTORIZATION:
APPLICATION TO TWO IMPROVE SITES
IMPACTED BY WILDFIRES
Sturtz et. al. 2014
ATMS 790 seminar
Ashley Pierce
OUTLINE
Background
 Source Apportionment

Positive Matrix
Factorization (PMF)
 Chemical Transport
Model (CTM)
 Hybrid

The study
 Model comparison and
evaluation
 Implications

2
BACKGROUND
Particulate matter (PM2.5): mixture of small particles
and liquid drops
 Aerosol: PM suspended in a gas (e.g. air)
 Volatile Organic Compounds (VOCs): variety of
chemicals (benzene, isoprene)


Secondary Organic Aerosols (SOA)
Carbonaceous aerosols – major component of fine
particulate mass
 IMPROVE: Interagency Monitoring of Protected
Visual Environments (1985)
 National Ambient Air Quality Standards (NAAQS)

3
SOURCE APPORTIONMENT
Primary & secondary
pollutants
Transport, transformation,
& removal processes
Primary pollutants
Transport, transformation,
& removal processes
Primary & secondary
pollutants
Emission
Source
Receptor
(Anthropogenic combustion, biomass burning,
biogenic emissions from plants)
Affected site/organism or measurement area
Source-Receptor relationship: determining the role of meteorology and physical/chemical effects linking
source emissions to receptor concentrations
Source profiles: the experimentally determined unique proportion of species concentrations
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(or speciated PM or speciated aerosol) from a source
Ex. Biomass burning – OC, EC, levoglucosan
Feature: A factor profile (source factor) unique proportion of speciated aerosols determined by the PMF
analysis
PARTICULATE CARBON
Fossil carbon: coal, oil, gas fuels
 Biogenic carbon: biomass burning, meat cooking,
Secondary organic aerosols (SOAs)


Upper bound for biomass burning contribution
5
More volatile, lower light absorption
Higher light absorption
6
http://www.lucci.lu.se/wp1_projects.html
IMPORTANCE


Adversely affect health, contribute to haze, affect radiation
balance
Biogenic sources of carbonaceous aerosols
80-100% of fine particulate carbon in rural areas
 ~50% in some urban areas




Carbonaceous species often largest contributor to haze and
PM2.5
Smoke thought to be large contributor (W and SE U.S.)
Difficult to apportion smoke from other emissions or
between smoke types
>50% of smoke particulate mass can be secondary organic
aerosol (SOA)
 Similar to SOA composition formed from gases emitted by
plant respiration


Biomass burning emissions inventories likely overestimate
PM emissions, underestimate VOC emissions from biomass
combustion and biogenic release
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POSITIVE MATRIX FACTORIZATION (PMF)
Multivariate factor analysis
 Uses matrix of speciated sample data

Source contributions
 Source profiles



Inputs:

Species concentrations (𝑥𝑖𝑗 )

uncertainties (𝜎𝑖𝑗 )

number of sources (user−defined, 𝑝)
Interpret source types:
Source profile information
 Wind direction analysis
 Emission inventories

8
PMF DISADVANTAGES

True source profiles not known (no emission info)

Requires assumptions that are not always true
Can’t apportion secondary organic aerosols to
source types
 Factor profiles can have large errors and may
correspond to a mixture of source types
 Uncertainties in measurements are not always
known or well-defined

9
PMF ADVANTAGES

Each data point can be weighted individually

uncertainty value (𝜎𝑖𝑗 )
𝑛
𝑚
𝑄=
𝑖=1 𝑗=1
𝑥𝑖𝑗 −
2
𝑝
𝑔
𝑓
𝑘=1 𝑖𝑘 𝑘𝑗
𝜎𝑖𝑗
Data below detection limit
 Variability in solution estimated by bootstrapping
technique, “re-sampling” of data set
 Based on observations
 Don’t need source emissions
 Less uncertainty than CTM

10
CHEMICAL TRANSPORT MODEL (CTM)
CAPITA Monte Carlo Lagrangian CTM
 Direct simulation of atmospheric pollutants
 Each emitted quantum contains a fixed quantity of
mass for various pollutants based on the source
emission rate


Individual particles subjected to transport, transformation,
and removal processes
6-day back trajectories of air masses using
meteorological data from the Eta Data Assimilation
System (EDAS)
 Non-fire emissions: Western Regional Air Partnership
(WRAP) 2002 emissions inventory
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 Biomass burning: MODIS inventory


Source profiles compiled from burns
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CTM DISADVANTAGES
Large information requirements
 Chemical mechanisms are incomplete
 Large errors and biases


Particularly with wildfires
Driven by emissions inventory
 Overall higher root mean square error (RMSE)
than PMF and Hybrid

13
CTM ADVANTAGES
Identification and separation of different source
types based on emissions inventory
 Primary and secondary carbonaceous fine
particles can be identified from source types


biomass combustion, biogenic, mobile, area, oil, point,
other
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HYBRID

Source-oriented

Measured data used to constrain CTM
Direct incorporation of measured data into model
 Post-processing of model results


Receptor-oriented

CTM results constrain receptor model (PMF) using
Multilinear Engine-2 (ME-2)
15
MASS BALANCE

𝑥 – speciated sample data matrix with dimensions 𝑖 by 𝑗
𝑖 : number of samples
 𝑗 : chemical species measured







ε𝑖𝑗 - residual for each sample/species (model error)
Want to identify:
𝑔𝑖𝑘 – amount of mass contributed by each source to each
individual sample
𝑝
𝑓𝑘𝑗 – species profile of each source
𝑥 =
𝑔 𝑓 +ε
𝑝 – number of sources
𝑖𝑗
𝑖𝑘 𝑘𝑗
𝑘=1
No samples can have a negative source contribution

𝑔𝑖𝑘 and 𝑓𝑘𝑗 > 0
𝑖𝑗
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THE STUDY
Goal:
 Distinguish source contributions to total fine
particle carbon
Biogenic sources
 Biomass combustion due to wildfires


Using a receptor-oriented hybrid model
17
SITES
Speciated PM2.5 from Monture and Sula Peak
Montana
 Three year: 2006-2008

Monture
Sula
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SPECIES
Species with 0.2 ≤ S/N < 2.0 were down weighted by
factor of 3
 Removed species:

S/N ratio <0.2
 below detection limit
 missing > 50% samples
 Mass reconstruction outside IMPROVE limits

8% samples from Monture
 25% samples from Sula


Looked at 23 species
19
SOURCES
Smallest value of 𝑝 where a change in the ratio of
cross-validated 𝑄𝑚𝑖𝑛 to 𝑄𝑡ℎ𝑒𝑜𝑟𝑒𝑡𝑖𝑐𝑎𝑙 approaches
zero
 User judgment based on qualitative agreement
between the species profiles (𝑓𝑘𝑗 ) and prior
knowledge of source profiles from known source
types within the model region

20
Missoula paper
mill & mining
Gold, cobalt and
Molybdenum
mines
Dry soils,
Long-range
Transport,
Fires?
21
COMPARISON
22
SEASONS (CTM AND HYBRID)
23


Winter (Dec Jan Feb)
Spring (Mar Apr May)


Summer (Jun Jul Aug)
Autumn (Sep Oct Nov)
MODEL EVALUATION
Root mean square error (RMSE) – measure of the
differences between the value predicted by the model
and the observed values
 Sample standard deviation of the differences between
predicted and observed values
 Measure of accuracy

𝑅𝑀𝑆𝐸 =

𝑛
𝑡=1(𝑋𝑝
− 𝑋𝑜 )2
𝑛
Correlation coefficient (R) – measure of strength
and direction of linear relationship between two
variables
The covariance of two variables divided by the product
of their standard deviations

24
MODEL EVALUATION
25
MODEL EVALUATION
0.83
0.67
PMF γ = 0
 CTM γ = 1

Monture γ = 0.83
 Sula γ = 0.67

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HYBRID DISADVANTAGES

Still unable to distinguish between primary and
secondary biomass combustion impacts

CTM model predictions were highly correlated
Equation 2 should account for multiplicative bias
but does not work with high correlation and no
tracer species
 Requires experts to run model in current form

27
HYBRID ADVANTAGES
Complementary attributes from PMF and CTM
 Directly applying the CTM predictions to the PMF
model allows for resolution of sources not identified by
the PMF alone



Biogenic vs. biomass combustion
Theoretically primary and secondary features should
be distinguishable
28
IMPLICATIONS

Accurate identification of relevant sources and
impact on receptors will guide control policy
lower costs
 better results


Ability to better distinguish sources to prove
pollution events are due to exceptional events
such as wildfires
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REFERENCES









Norris, G., & Vedantham, R. (2008). EPA Positive Matrix Factorization (PMF) 3.0 Fundamentals & user
guide.
Paatero, P. (1999). The Multilinear Engine—A Table-Driven, Least Squares Program for Solving
Multilinear Problems, Including the n-Way Parallel Factor Analysis Model. Journal of Computational and
Graphical Statistics, 8(4), 854-888. doi: 10.1080/10618600.1999.10474853
Polissar, A. V., Hopke, P. K., Paatero, P., Malm, W. C., & Sisler, J. F. (1998). Atmospheric aerosol over
Alaska: 2. Elemental composition and sources. Journal of Geophysical Research: Atmospheres, 103(D15),
19045-19057. doi: 10.1029/98JD01212
Ramadan, Z., Eickhout, B., Song, X.-H., Buydens, L. M. C., & Hopke, P. K. (2003). Comparison of Positive
Matrix Factorization and Multilinear Engine for the source apportionment of particulate pollutants.
Chemometrics and Intelligent Laboratory Systems, 66(1), 15-28. doi: http://dx.doi.org/10.1016/S01697439(02)00160-0
Schichtel, B., Fox, D., Patterson, L., & Holden, A. Hybrid Source Apportionment Model: an operational tool
to distinguish wildfire emissions from prescribed fire emissions in measurements of PM2.5 for use in
visibility and PM regulatory programs.
Schichtel, B. A., & Husar, R. B. (1997). Regional Simulation of Atmospheric Pollutants with the CAPITA
Monte Carlo Model. Journal of the Air & Waste Management Association, 47(3), 301-333. doi:
10.1080/10473289.1997.10464449
Schichtel, B. A., & Husar, R. B. (1997). The Monte Carlo Model: PC-Implementation. Retrieved 02/16/15,
2015, from http://capita.wustl.edu/capita/CapitaReports/MonteCarloDescr/mc_pcim0.html
Schichtel, B. A., Malm, W. G., Collett, J. L., Sullivan, A. P., Holden, A. S., Patterson, L. A., . . . Barna, M. G.
(2008). Estimating the contribution of smoke to fine particulate matter using a hybrid-receptor model. Paper
presented at the Air and Waste Management aerosol and atmospheric optics.
Sturtz, T. M., Schichtel, B. A., & Larson, T. V. (2014). Coupling Chemical Transport Model Source
Attributions with Positive Matrix Factorization: Application to Two IMPROVE Sites Impacted by Wildfires.
Environmental Science & Technology, 48(19), 11389-11396. doi: 10.1021/es502749r
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EXTRA
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MULTILINEAR ENGINE-2 (ME-2)

performs iterations via a preconditioned conjugate
gradient algorithm until convergence to a minimum Q
value
𝑛
𝑚
𝑄=
𝑖=1 𝑗=1

𝑥𝑖𝑗 −
2
𝑝
𝑔
𝑓
𝑘=1 𝑖𝑘 𝑘𝑗
𝜎𝑖𝑗
Conjugate gradient algorithm: algorithm for the
numerical solution of particular systems of linear
equations, usually a symmetric, positive-definite
matrix
32
𝑛
𝑚
𝑄 = (1 − γ)
𝑖=1 𝑗=1
ε𝑖𝑗
𝜎𝑖𝑗
𝑛
2
𝑣
+ (γ)
𝑖=1 𝑡=1
ε𝑖𝑡
𝜔𝑖𝑡
2
ε𝑖𝑡
𝜔𝑖𝑡
𝑤
2
+
𝑏
𝑐
𝑢𝑠 +
𝑠=1
𝑢𝑙𝑟
𝑙=1 𝑟=1
𝜎𝑖𝑗 : species measurement uncertainty
𝜔𝑖𝑡 : CTM uncertainty
γ: user-defined weighting parameter for CTM predictions relative to mass
balance model
Residuals from Equations 1-2:

Equation 1: Standard PMF chemical mass balance
equation
𝑝
𝑥𝑖𝑗 =
𝑔𝑖𝑘 𝑓𝑘𝑗 + ε𝑖𝑗
𝑊ℎ𝑒𝑟𝑒 𝑔𝑖𝑘 , 𝑓𝑘𝑗 > 0
𝑘=1

Equation 2: 𝑡 th CTM constraint: 𝑡 = 1, 𝑣
contributions 𝑔𝑖𝑡 to total fine particulate carbon
predicted by the CTM model 𝑣 = 2 sources (total
biomass combustion and biogenic emissions)
33
𝑔′𝑖𝑡 = 𝑔𝑖𝑡 𝐼𝑡 + ε′𝑖𝑡
𝑊ℎ𝑒𝑟𝑒 𝑡 𝑖𝑠 𝑎 𝑠𝑢𝑏𝑠𝑒𝑡 𝑜𝑓 𝑘
𝑛
𝑚
𝑄 = (1 − γ)
𝑖=1 𝑗=1
ε𝑖𝑗
𝜎𝑖𝑗
𝑛
2
𝑣
+ (γ)
𝑖=1 𝑡=1
ε𝑖𝑡
𝜔𝑖𝑡
2
ε𝑖𝑡
𝜔𝑖𝑡
𝑤
2
+
𝑏
𝑐
𝑢𝑠 +
𝑠=1
𝑢𝑙𝑟
𝑙=1 𝑟=1
Prior source profile constraints:
 Equation 3: Normalized thermal fractions of carbon for each
source. Rescales 𝑓 such that 𝑔𝑖𝑘 in eq. 1 and 2 represents total
fine particle carbon and 𝑓𝑘𝑗 = mass fraction of species 𝑗 in source 𝑘
relative to total carbon
𝑤
𝑓𝑘𝑠 = 1 + 𝑢𝑠
𝑊ℎ𝑒𝑟𝑒 𝑠 𝑐𝑎𝑟𝑏𝑜𝑛 𝑓𝑟𝑎𝑐𝑡𝑖𝑜𝑛𝑠 𝑖𝑠 𝑎 𝑠𝑢𝑏𝑠𝑒𝑡 𝑜𝑓
𝑠=1
𝑗 𝑠𝑝𝑒𝑐𝑖𝑒𝑠 , 𝑢𝑠 = 0.001

Equation 4: Secondary feature profile constraint

Primary biogenic source consists only of VOCs


Sets all r=1 to c non-carbonaceous species near zero
Biomass source: carbon thermal fractions, potassium, nitrate, sulfate,
hydrogen
𝑓𝑙𝑟 = 0 + 𝑢𝑙𝑟
𝑊ℎ𝑒𝑟𝑒 𝑙 𝑖𝑠 𝑎 𝑠𝑢𝑏𝑠𝑒𝑡 𝑜𝑓 𝑘 𝑎𝑛𝑑 𝑟 𝑖𝑠 𝑎 𝑠𝑢𝑏𝑠𝑒𝑡 𝑜𝑓 𝑗 𝑠𝑝𝑒𝑐𝑖𝑒𝑠 ,
𝑢𝑙𝑟 = 1 ∗ 10−5
34