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R-Square is mathematically related to the reduced Chi-Square as shown
in Appendix A. It will generally approach a value of 1,0 when the reduced
Chi-Square indicates a good fit. Generally speaking, the Chi-Square statistic
is more revealing because it indicates how well the model has explained the
receptor concentrations relative to the source and receptor measurement
uncertainties. R-Square does not contain this relationship to measurement
uncertainty. [Target 0.8 to 1.0].
3.3.3 t-Statistic
The standard error of the source contribution estimates is an important
indicator of the precision, or certainty in the model estimates. The "t"
statistic is used to interpret the standard error. Botn statistics are
found on the source contribution display. A "t" value of less than 2.0
is generally used to identify model estimates that are not significantly
different from zero. -Source estimates with small "t" values may indicate
that the source is not contributing a quantity which exceeds the detection
limts of the modeled system. A low t-Statistic also implies that the
standard error estimates themselves are uncertain representations of the
true standard error.
The presence of low t values for several sources within a run may also
result from collinearities among the source profiles or imprecision in
either the source profiles or the ambient data. Section 3.3.4 discusses a
more definitive indicator of collinearity that is provided on the source
uncertainty clusters display. The preliminary analyses are useful in
corroborating whether a suspected source is a likely contributor at the
monitoring site. Corroborative use of the results of preliminary analyses
is described in Section 3.6. [Target t > 2.0].
3.3.4 Uncertainty/Similarity Clusters
The interaction of certain source profiles may lead to high standard
errors (and low t-Statistics) for one or more of the sources. High standard
errors associated with a particular source contribution estimate may be
attributable to the profiles of other sources as well as to the uncertainty
of its own profile. The uncertainty/similarity display helps to identify
clusters (U/S clusters), consisting of other possible sources whose profiles
may be interacting to cause high standard errors on one or more of the
sources in the cluster. It also contains an estimate of the SUM of the
SCE's (and the uncertainty of the SUM) for the sources in each cluster.
The uncertainty/similarity display identifies sources which may be
collinear or whose source profile uncertainties are large, making it
difficult for the model to distinguish between those particular sources.
These difficult-to-distinguish sources are the "clusters" and the sources
in the cluster are identified by number. Only tnose clusters which con-
tain a source whose SCE is uncertain (i.e., a t-Statistic < 2.0) are dis-
played; other clusters may be present but they are not displayed because
16
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the SCE's for their sources are acceptable as is. A Singular Value
Decomposition (SVD) analysis is performed to determine these clusters and
the results are summarized in this display. The clusters are listed in
rank order such that the cluster which causes the largest overall uncertainty/
similarity problem is listed first. The criteria for screening the SVD to
identify clusters is discussed in the user's manual. The inherent uncertainty
is used to make this ranking (after Henry, 1982).
Reducing the values of the standard errors of the SCE's is the ultimate
goal once the correct sources have been included in the model run. The U/S
clusters display identifies those sources whose profiles, if improved, would
most substantially affect the model's ability to estimate SCE's with reduced
standard errors. The sources in these clusters are candidates for improve-
ment to the source profiles, either by more precise measurement of the
profiles or by adding additional species to make the profiles less similar
(less collinear). Further discussion of collinearity and source profile
uncertainty can be found in Appendix A and Section C.3 of Appendix C. The
calculations are documented in an Appendix -to the CMB Version 6 User's
Manual.
SCE's of sources within groups which are near the top of the list will
have the highest standard errors or uncertainties. However, the estimate
of the "SUM" of the SCE's of all of the sources in a group is known with
more relative certainty than are the individual SCE's. The program computes
this sum and a revised uncertainty for the sum and presents this information
on the right side of the display. This sum may prove useful for a particlar
application because of the reduction in uncertainty. The sum is equivalent
to combining the source types in the uncertainty grouping into a single
source type. Source type resolution is lost, but greater confidence in the
sum of the source contributions is gained. [Target - no clusters],
3.3.5 Ratios and Residuals of Fitting Species
The RATIO C/M of the calculated (CALC) species mass to measured (MEAS)
species mass is a convenient indicator of the magnitude of the residual.
Ideally, it is equal to 1.0. A ratio » 1.0 means that more mass for a
given species was accounted for by the model than was measured on the
ambient sample. This statistic is found on the species contribution display.
[Target - 0.5 to 2.0].
The RATIO R/U statistic, also found on the species contribution display,
is useful for interpreting the significance of the ratio of calculated to
measured receptor species concentration. The residuals (R) are the signed
difference between the CALC and the MEAS values for each species at the
receptor location. The uncertainty (U) is the uncertainty in the estimate
of the residual. If the absolute value of the residuals statistic exceeds
2.0, the residual is high enough to be of concern. [Target |< 2.0|].
17
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A RATIO R/U » 2.0 or « -2.0 for a species could be caused by the
following:
1) incorrect ambient measurement of that species;*
2) incorrect source profiles for that species;*
3) inclusion of noncontributing source in the fit ("high positive" residual
(> 2.0) only); or
4) absence of a contributing source from th"^ fit ("nigh negative" residual
(< -2.0) only).
*This would include underestimating the uncertainty of that species in
either the ambient data or one of the source profiles.
Both the RATIOS C/M and R/IJ provide insight into the magnitude of
the difference between the measured a'nd calculated mass-(the residual) for
each species. The RATIO R/U is generally a more revealing indicator since
it combines both the magnitude of the residual and the uncertainty in the
estimate of the residual into a single measure.
3.3.6 Source-Species Contributions
. The SSCONT command shows the percent contribution of each source to
each species included in the fit. This information is used to identify
potentially incorrect profiles or an incorrect source list which might be
responsible for large species residuals (RATIO R/U). For example, if a
species has a large residual and the SSCONT indicates that a particular
source "accounts for" almost all of that species CALCULATED value, tne
profile value for that species should be carefully reviewed along with the
ambient data for that species to determine which is in error.
3.4 Deviations from Model Assumptions
The CMB diagnostics and statistics discussed in Sections 3.3.1 through
3.3.6 indicate when deviations from model assumptions may have occurred.
These deviations do not necessarily invalidate the CMB results-they merely
indicate the potential for invalidity. This is why a separate step is
necessary in the applications and validation protocol which evaluates the
effects of these deviations from assumptions and determines whether or not
these effects can be tolerated.
The CMB model is based on several assumptions and the model should be
applied in a manner that is as consistent as possible with those assumptions.
These assumptions are explicitly listed below and are further discussed in
Appendix C to this document. Deviations from these assumptions may result
in unacceptably large errors in the source contribution estimates. Therefore,
these assumptions should be reviewed when the model is applied to ensure
that expected deviations from them will not significantly bias the source
contribution estimates. The assumptions of the CMB with an effective variance
solution are:
18
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1. Compositions of source emissions are constant over the period of
ambient and source sampling.
2. Chemical species do not react with each other, i.e., they add
linearly.
3. All sources with a potential for significantly contributing to the
receptor have been identified and have had their emissions characterized,
4. The number of sources or source categories is less than the number
of species.
5. The source compositions are linearly independent of each other.
6. Measurement uncertainties are random, uncorrelated, and normally
distributed.
3.5 Identifying and Correcting Problems by Changing the Model Inputs
There are four main categories of problems which, once they have been
identified, can be addressed to improve the performance of the model. The
problem categories are: 1) incorrect ambient data; 2) incorrect source
profiles; 3) incorrect source list; and 4) profile uncertainty/similarity.
These are discussed briefly below and with a Quick Guide and examples in
Appendix B. The following subsections discuss ways in which the model's
diagnostics and statistics discussed in Section 3.3 may indicate possible
problems with the model input, their possible causes and corrective action.
Note that in some cases, not all "indications" must persist for a problem
to be present. The more "indications" that persist, the more evidence of
a problem. Because of the complex interactions of all of the data in a
least squares estimate, the statistics or diagnostics may not always be
adequate to conclusively isolate a problem with model input. Additional
physical evidence is also very helpful. A flowchart is presented in Section
3.5.5 to provide a systematic approach to identifying and correcting
problems.
3.5.1 Correcting the Ambient Data - Gross Errors
There may be inaccuracies in the ambient species that have not been
uncovered in the routine data validation. If the data are "suspect" and
there are no apparent data entry or analytical errors, the next step would
be to eliminate the suspect species from the fit and rerun the model.
Examine the changes in the estimates for each source. If the estimate
changes by more than one standard error, and if the receptor concentration
or a source profile value for the removed species is suspect, then either
remeasure the species or use the SCE calculated without that species in the
fit. Example B.I in Appendix B illustrates the identification of incorrect
ambient data.
19
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INDICATION:
o RATIO R/U « -2.0 for a species suggests either the ambient
data are high or the profile data are low for that species;*
o RATIO R/U » 2.0 for a species would imply that the ambient
data are low or the profile data for that species are high. If
profile data are suspect, see Section 3.5.2 and problem B.2.*
ACTION: 1. Review the uncertainty assigned to the species with the high
residuals. Make any justifiable and appropriate changes and
rerun the CMB. If this improves the RATIO R/U, Step 2 is not
necessary.
2. Delete the suspect species from the list of fitting species
and rerun. If the SCE changes by at least one standard
error, do not use this species in the fit until it has been
remeasured.
* (NOTE: RATIO R/U can also indicate an incorrect source list -
see Section 3.5.3; also, it can be due to an under-
estimated uncertainty for that species in either
the ambient data or one of the source profiles.
3.5.2 Correcting Source Profiles - Gross Errors
A gross error in the value of one or more species in a profile might
result in a high standard error in the SCE and a high residual for those
species. Therefore, one or more high residual values su-ggests that the uncer-
tain source profile (and the associated species in particular) be checked
and remeasured if necessary. The high residual is a likely species to check
for errors. Appendix B contains Example B.2 which illustrates the problem
of gross errors in a profile. Indications of the problem are given below.
INDICATION:
o SCE that is inconsistent with preliminary analyses or physical
evidence;
o one or more species has a "high (pos. or neg.)" residual which
cannot be attributed to incorrect ambient data; further evidence
of species error if the SSCONT reveals that one source contribution
dominates that species.
ACTION: Review profile data for the suspect species carefully. Correct
or remeasure profile if necessary.
20
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3.5.3 Changing the Source List
3.5.3.1 Missing Sources
Missing source types are identified by a low percent mass explained
(e.g., less than 80%) and/or a RATIO R/U « -2.0 for chemical species which
are in the missing source. A "high negative" residual for one or more
species and a high Chi-Square are also indicative of missing sources. The
key to identifying these sources resides in the calculated to measured
chemical concentrations listed in the SPECIES CONCENTRATION display. "Hign
negative" residuals imply that a source is needed which will supply a
larger quantity of that species. The PHATRIX command lists all of the
source profiles in the model's input data file. These profiles can be
examined to determine which ones would would supply sufficient quantities
of the missing concentrations if they were added to the set of fitting
sources. The CMS can be reapplied as many times as is necessary to deterni:
which source types and source profiles best account for the underestimated
receptor concentrations. A source should not be included in the final fU
just because it "explains" the data; however, there must be a physical
justification for the source's contribution at a receptor if it is to be
included in the fit.
The source list can be changed by adding or deleting sources. Example
B.3 illustrates the identification of a missing source. Indication of a
missing source is given by the following conditions.
INDICATION:
o High Chi-Square;
o Low percent mass explained;
o RATIO R/U « -2.0 (a "high negative" residual) for one or more
species that are known to be present in the suspect source.
ACTION: Add source profiles to the fit and reevaluate.
3.5.3.2 Noncontributing Sources
Noncontributing source types, or better stated, source types with
contributions lower than detection limits, are identified by T-STAT values
below 2. Such source types may be eliminated from the fit if tne source
contribution is indeed small.
Noncontributing source situation is illustrated in Appendix B in
Example 8.5 and Indications are summarized below.
INDICATION:
o T-STAT between -2.0 and 2.0
o RATIO R/U » 2.0 ("high positive") residual for a species which
is attributed to the suspect source by the SSCONT diagnostic
21
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o Negative SCE
o Physical basis for the source's contribution is weak.
ACTION: Delete source from fit.* However, if the source's contribution
(SCE) is large and there is a strong physical basis for us
presence, the profile should be remeasured to reduce its uncertainty.
*NOTE: If the source is present but a very small contribution to
total mass, it should only be removed from the fit if the SSCONT
shows that none of the species in the source account for more than
5 to 10% of the ambient concentration for those species.
3.5.4 Improving Source ProfilesUncertainty/Similarity
As discussed in Appendix C.3, there are two reasons (other tnan yross
errors) to improve the source profiles: (1) high profile uncertainty;
(2) collinearity with low profile uncertainty. This section disc-sses
methods of identifying col linear sources and ways to reduce the i, certainty
in SCEs.
The uncertainty/similarity display identifies those source !:;es v/h->c''i
interact sufficiently to contribute to large standard errors in tie source
contribution estimates in'that group. An indication that the interaction
may be significant can be seen by noting the sources on the ll/S cijster
display.
A simple test is proposed to determine if the uncertainty in the SCE is
due to high profile uncertainty: reduce the uncertainties in the profile to
levels that might be reasonable to achieve if the source profiles were measured
more precisely; then, rerun the CMB - if the clusters containing those
sources are no longer listed, it is likely that collinearity per se is not
significant. Remeasurement of the profile will probably improve the unce^-
tainties of the source contribution estimates. It is possible that reducing
the uncertainty will not eliminate the clusters but the SCE uncertainty v i ~ 1
likely be improved somewhat. This would suggest that collinearity is also
present. Appropriate action is discussed below. Example B.4 illustrates
this problem.
INDICATION:
o Two or more sources listed in a U/S cluster
o T-statistic < 2.0 for one or more sources in that cluster
if the T-STAT becomes > 2.0 when species uncertainties for profile
for that source is arbitrarily reduced to a potentially achievable
level, this indicates that the uncertainty in the source profile
is at least partially responsible for the "apparent" collinearity.
ACTION: Remedies for unacceptably high uncertainties due to collinearity
can take five forms ranked from most to least desirable.
22
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(1) the profile of one or more of the cluster sources could be improved by
measuring additional species.
(2) Reduce the uncertainties in the source profiles of the cluster sources.
If the T-STAT becomes > 2.0, and if these profile uncertainties are realistically
achievable by remeasurement, then the "apparent" collinearity can be improved
in large part by improving the uncertainty in the profiles. Ideally, t'ne
U/S cluster tor that group of sources would disappear. Remeasure and r^rjn
the CMB with the improved measurements. More precise source profile
measurements must be obtained before re-applying the model.
(3) The estimate of the SUM of the source categories in the U/S cluster can
be used. Obtain independent estimates of the contributions of the individual
source categories-and use them to apportion the SUM into the source categories.
(4) combine the profiles of the collinear source profiles into a single
signature of a "composite source category" that chemically represents the
source categories identified by the U/S cluster. For example, resuspended
road dust and windblown soil dust are chemically similar, and some modelers
include a single term to represent "crustal material" instead of the two
individual source types. This would result in improved source estimates of
t:ie crustal component, which can then serve as an estimate of the combined
impact of the two sources. This aggregated estimate might then be partitioned
into its components by another method (e.g., dispersion modeling, microscopy,
or wind trajectory analysis).
(5) Species which are causing the similarity in source profiles might be
deleted from the fit. These species can often tie determined from the display
produced by the SSCONT command. Often one of the cluster sources will be
» 100% for that species and the other will be negative. Unfortunately,
eliminating too many species from the fit may cause the model to fail the
applicability requirements in Section 3.1. Also, the results should
acknowledge that the deleted source may be present.
3.5.5 Problem Identification and Correction Strategy
Figure 1 shows the order in which the above actions should be taken.
Generally, it is best to make only one change at a time to the model setup
before rerunning. An exception is that data errors should all be corrected
when they are identified. This stepwise procedure may necessitate cycling
through the steps several times. Each time a change is made, it may "clarify"
the need to make a change that was not evident on a previous iteration (e.g.,
you may address a collinearity problem and reveal a data problem previously
unidentified because of the collinearity). The cycling process is repeated
until no changes are justified by the criteria in Section 3.5.1 through
3.5.4. Example 8.6 in Appendix 8 illustrates a solution where multiple
problems are present after the initial run. The use of this flowchart will
greatly increase the consistency of CMB application among users. However,
some operator judgments are necessary regarding data validity and corrective
action(s) to address collinearity.
23
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TEMPORARY "FIX-
DELETE SOURCE FROM
TOP U/S CLUSTER
W/ SMALLEST SCE
PERMANENT SOLUTION
REFER TO
SECTION 3 51
RE-INCLUDE DELETED
SOURCES » RERUN
Figure 1. Flowchart for Problem Identification And Correction
24
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3.6 Consistency/Stability of the Model Results
The CMB source contributions should be compared to the results of
other receptor methods to provide corroboration of results. In addition to
providing corroboration of CMB estimates, qualitative receptor analyses can
provide clues to the causes of unresolved issues in the sensitivity and
summary statistics reviews. For instance, meteorological data and spatial
emissions inventories could be used to identify potential missing sources
of a particular fitting element, as could microscopy or factor analysis.
In the event that significant inconsistencies are observed, all results
should be reviewed, focusing on those particular sources that appear to be
inconsistent among the different methods. If there is compel liny evidence
that the CMB model inputs be changed, the deviations from model assumptions,
model sensitivity and summary statistics (Sections 3.3, 3.4 and 3.5)
should be reevaluated in addition to rerunning the CMB model.
The CMB estimates should be tested to see how sensitive they are to
the various input data. Unstable estimates (source contribution estimates
that change by more than one standard error estimate) are an indication
that the model may not be providing stable results. For CMB validation,
model stability tests are usually taken to mean the evaluation of model
estimates to changes in input parameters, such as the selected 'sources and
their profiles, as well as selection of fitting species used to reach a
solution with the CMB model. The following is a discussion of three types
of parameter changes that should be included in a model stability (sensitivity)
test, and a discussion of ways to make the model less sensitive (more
stable).
3.6.1 Source Profile Sensitivity
The CMB model's effective variance fitting procedure uses estimates
of the source profile and receptor concentration uncertainties to "weight"
their effect in arriving at source contribution estimates. It is helpful
to explore how sensitive the source contribution estimates are to changes
in the source profiles and these uncertainties. This can be done by intro-
ducing changes into the source profiles and rerunning the model for each
change.
The model user can select several species from a source(s) of
particular regulatory interest and assign worst case values to those species
in the profile. The model can then be rerun with the worst case profile(s).
A practical way to accomplish this sensitivity analysis is to include a
"worst case" source profile along with the "best estimate" profile in the
"FS" or "CS" data file. The resulting source estimate(s) can be considered
"brackets" to the source contribution estimates and can be compared to the
uncertainty intervals calculated for each run. If the bracketing interval
is greater than the calculated uncertainty interval, then the model may be
sensitive to changes in the source profiles.
25
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3.6.2 Receptor Concentration Sensitivity
The stability of source contribution estimates with respect to receptor
concentrations is best tested with collocated chemical measurements from
one of the sampling sites. These collocated measurements are usually
included as part of the quality assurance plan for a subset of all samples.
If nearly equivalent source contribution estimates are derived from these
two independent measurements of the same ambient air, then the receptor
data are not likely causing instabilities in the CMB results.
Lacking these collocated data, portions of the input data may be
perturbed randomly or systematically in proportion to their uncertainty
(e.y., Javitz and Watson, 1986; Watson and Robinson, 1984). The source
contribution estimates for the sources of regulatory interest should not
change by more than one standard error in response to small perturbations
if the results are stable. (A "small" perturbation is defined as one std.
error of the ambient species concentrations.) If the results are not stable,
the validity of the CMB result for that particular data are questionable.
3.6.3 Fitting Species Sensitivity
The stability of CMB model results to the fitting species can be evaluated
by identifying a species which SSCONT attributes in large part to a single
source. Eliminate this species from the fit and examine how much the cor-
responding source contribution changes. If this change is greater than the
STDERR, then that species must be greatly influencing the "fit." Review the
quality of both the source and ambient measurements for that species carefully
because of its influence on the model estimates.
3.7 Evaluating Results of the CMB Analyses
If (a) the CMB model is determined to be applicable (Section 3.1),
(b) the summary statistics and diagnostics are generally within target
ranges (Section 3.3), (c) there are.no significant deviations from model
assumptions (Section 3.5), and (d) the sensitivity tests in Section 3.6
uncovered no unacceptable instability or consistency problems, the CMB
analysis is considered valid. If uncertainties associated source estimates
are too high for decision-making purposes even after taking the steps recom-
mended in this protocol, then the source compositions being used are not
representative of the sources in the airshed, or they contain too much
uncertainty associated with the influential species.
It is recommended that both a dispersion model and receptor model be
used in a collaborative manner to perform an apportionment, provided that
the dispersion model is applicable and the receptor model is valid for the
particular application (U.S. EPA 1987C).
26
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4.0 ACKNOWLEDGMENTS
The primary authors of this document were Thompson G. Pace, P.E., of
the U.S. EPA and Dr. John G. Watson of the Desert Research Institute.
However, the experience, talent and ideas of the co-authors played a
large role in its development. The co-authors participated in a workshop
to review and revise the document in May 1986 in San Francisco. The co-
authors are: Dr. Kit Wagner, Mr. Bart Croes, Mr. Duane Ono, Dr. Hal
Javitz, Mr. Mike Naylor, Dr. Judith C. Chow, Dr. David Maughan, Dr. Edwin
Meyer, Mr. Luke Wijnberg, Mr. Ken Axetell, Mr. Mike Anderson, Mr. John
Core, Mr. Pat Hanrahan, Dr. Ron Henry, Mr. Bong Mann Kim, Mr. Chung Liu,
and Dr. Andy Gray.
Several others provided review and comment outside of the workshop.
The reviews by Dr. Glen Gordon, Mr. William Cox, Mr. Chuck Lewis,
Dr. Thomas D. Dzubay, Mr. Robert K. Stevens, Mr. Johnnie Pearson,
Dr. Richard DeCesar, Dr. Sylvia Edgerton, and Ms. Bridget Landry are
greatly appreciated. The typing and revisions by Ms. Cathy Coats,
Ms. Jo Harris, and Ms. Linda Ferrell are much appreciated.
27
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5.0 References
Blumenthal, D., Watson, J. 6., Richards, L. W., Itering, S. V., and
Chow, J. C. (1986), "Southern California Air Quality Study: Suggested
Program Plan," Sonoma Technology, Santa Rosa, CA.
Chow, .;. C., 1985, "A Composite Modeling Approach to Assess Air Pollution
Source'Receptor Relationships," Doctor of Science Dissertation, Harvard
'Jni vanity, Boston, MA, July 1985.
Chow, J. C., Watson, J. G., Egami, R. T., Wright. B., Ralph, C., Naylor,
M., Smith, J., and Serdoz, R. (1986), "Program Plan for State of Nevada
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Chow, J. C., Watson, J. G., and Frazier, C. A. (1986A), "A Survey of Existing
Fugii~ /e/Area Source Characterization Methods for Receptor Modeling" to be .
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Compa-ison of Source Apportionment Procedures: Results for Simulated Data
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Dattner, S. L., DeCesar, R. T., Gordon, G. E., Heisler, S. L., Hopke, P. K.,
Shah, J. J., Thurston, G. D., and Williamson, H. J. (1984), "Interlaboratory
Comparison of Source Apportionment Procedures: Results for Simulated Data
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DeCesar, R. T., and Cooper, J. A. (1982), "Evaluation of Multivariate and
Chemical Mass Balance Approaches to Aerosol Source Apportionment, Using
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Dzubay, T. G., Stevens, R. K. et al. (1982A), "Intercomparison of Results
of Several Receptor Models for Apportioning Houston Aerosol", Proceedings,
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Receptor Model Results for Houston Aerosol," Atm. Env., _18 (8): 1555-1566.
Friedldnder, S. V. (1981), "New Developments in Receptor Modeling Theory,"
Atmospheric Aerosol: Source/Air Quality Relationships, ed. by E. S. Marias
and P. K. Hopke, CS Symposium Series 167, American Chemical Society,
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Gerlach, R. W., Currie, L. A. and Lewis, C. D. (1982), "Review of the Quail
Roost II Receptor Model Simulation Exercise," Proceedings, Receptor Models
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Gordon, G. E. (1984), "Atmospheric Tracers of Opportunity from Important
Classes of Air Pollution Sources," DOE Workshop on Atmospheric Tracers,
Santa Fe, NM.
Gordon, G. E., Pierson, W. R., Daisey, J. M., Lioy, P. J., Cooper, J. A.,
Watson, J. G., and Cass, G. R. (1984), "Consideration for Design of Source
Apportionment Studies," Atm. Env., 18:1567-1582.
Gordon, G. E. and Ann Sheffield, University of Maryland, Chemistry Building,
College Park, Maryland, 20742, Personal communication to Tom Pace, April
1987.
Henry, R. C. (1982), "Stability Analysis of Receptor Models That Use Lowest
Squares Fitting" in Receptor Models Applied to Contemporary Pollution Problems,
edited by S. L. Dattner and P. K. Hopke, Air Pollution Control Association,
Pittsburgh, PA, p. 141.
Henry, R. C. and Kim, B. M. (1986), "Evaluation of Receptor Model Performance,"
Report to U.S. Environmental Protection Agency, Technology Development
Section, Air Management Technology Branch, Monitoring and Data Analysis
Division, Office of Air Quality Planning and Standards, Research Triangle
Park, NC.
Hopke, P. K. (1985), Receptor Modeling in Environmental Chemistry,
John Wiley and Sons, New York, 1985.
davitz, H. S. and Watson, J. G. (1986) "Feasibility Study of Receptor
Modeling for Apportioning Utility Contributions to Air Constituents,
Deposition Quality and Light Extinction," Draft Report for Electric Power
Research Institute, prepared by SRI International, Menlo Park, CA.
Lewis, C. W. and Stevens, R. U. (1985) "Hybrid Receptor Model for Secondary
Sulfate from an S02 Point Source," Atmospheric Environment, _T9, 917-924.
Liu, C. S., Gray, H. A., Grisinger, J. E., and Davidson, A. (1986), "Draft
1987 AQMP Revision Working Paper No. 2: PM^Q Modeling Approach," prepared
by the South Coast Air Quality Management District, El Monte, CA.
Mueller, P. K. and Hidy, G. M. et al. (1983), "The Sulfate Regional
Experiment: Report of Findings," Electric Power Research Institute Report
#EA-1901, Palo Alto, CA.
Scheff, P. and Wadden, R. A. (1986), "Predicting Unidentified and Secondary
Sources With Chemical Mass Balance Receptor Modeling," Receptor Methods
for Source Apportionment Real World Issues and Applications, Edited by
T. G. Pace, APCA, Pittsburgh, PA, 1986.
Stafford, M. A. and Liljestrand, H. M. (1984), "On the Distinction of Secondary
Species in Acid Deposition," presented at the 77th Annual Meeting of the
Air Pollution Control Association, San Francisco, CA.
29
-------
Stevens, R. K. and Thompson G. Pace (1984), "Review of the Mathematical and
Empirical Receptor Models Workshop (Quail Roost II)." Atm. Env. 18, 1499-1506.
Trijonis, J., "Model Reconciliation," Special Report prepared for U.S. EPA
and TRC Environmental Consultants under Contract 68-02-3886, Work Asignment
No. 13, Research Triangle Park, NC 27711, September 1985.
U.S. EPA, 1978, Digest of Ambient Particulate Analysis and Assessment
Methods, EPA-450/3-78-013, U.S. EPA, Research Triangle Park, NC 27711,
September 1978.
U.S. EPA, 1980, Interim Guidelines and Specifications for Preparing Quality
Assurance Project Plans, QAMS-005/80, U.S. EPA, Office of Research and
Development, Research Triangle Park, NC 27711, December 1980.
U.S. EPA, 1981A, Receptor Model Technical Series, Volume I: Introduction
to Receptor Models, EPA-450/4-81-016a, U.S. EPA, Research Triangle Park, NC
27711, July 1981.
U.S. EPA, 19818, Receptor Model Technical Series, Volume II: Chemical Mass
Balance, EPA-450/4-81-016b, U.S. EPA, Research Triangle Park, NC 27711,
July 1981.
U.S. EPA, 1981C, "SOP for Technicon Determination of Sulfate in Suspended
Particulate Matter Collected on Glass Fiber Filters," EMSL/RTP SOP-EMD-005,
U.S. EPA, Research Triangle Park, NC 27711, November 1987.
U.S. EPA, 1981D, "SOP for the Extraction of Sulfate and Nitrate and for the
Technicon Determination of Sulfate or Suspended Particulate Matter Collected
on Dichotomous Filters," EMSL/RTP SOP-EMD-006, U.S. EPA, Research Triangle
Park, NC 27711, November 1981.
U.S. EPA, 1983A, Receptor Model Technical Series, Volume IV: Summary of
Particle Identification Techniques, EPA-450/4-83-018, U.S. EPA, Research
Triangle Park, NC 27711, June 1983.
U.S. EPA, 1984A, Receptor Model Technical Series, Volume V: Source
Apportionment Techniques and Considerations in Combining Their Use, EPA-
450/4-84-020, U.S. EPA, Research Triangle Park, NC 27711, July 1984.
U:S. EPA, 19848, Interim Procedures for Evaluating Air Quality Models, EPA-
450/4-85-023, U.S. EPA, Research Triangle Park, NC 27711, September 1984.
U.S. EPA, 1985A, Technical Support Document for Residential Wood Combustion
EPA-450/4-85-XXX, U.S. EPA, Research Triangle Park, NC 27711, June 1985, Draft.
U.S. EPA, 1985B, Receptor Model Technical Series, Volume VI: Multivariate
Methods, EPA-450/4-85-007, U.S. EPA, Research Triangle Park, NC 27711,
July 1985.
U.S. EPA, 1985C, Receptor Model Source Composition Library, EPA 450/4-85-
002, U.S. EPA, Research Triangle Park, NC 27711, November 1984.
30
-------
U.S. EPA, 1986A, Guideline on Air Quality Models (Revised) U.S. EPA, Research
Triangle Park, NC 27711, revision in preparation.
U.S. EPA, 1986B, Procedures for Estimating Probability of Nonattainment of
a P.MIQ NAAQS Using Total Suspended Particulate or PM]^ Data, EPA-450/4-86-
017, U.S. EPA, Research Triangle Park, NC 27711, December 1986.
U.S. EPA, 1986C, Guideline on the Identification and Use of Air Quality Data
Affected by Exceptional Events, EPA-450/4-86-007, U.S. EPA, Research Triangl^
Park, NC 27711, July 1986.
U.S. EPA, 1987B, Receptor Model Technical Series, Vol. Ill (Revised), Chemical
Mass Balance Receptor Model User's Manual, EPA-450/x-xx-xxx, U.S. EPA,
Research Triangle Park, NC 27711, May 1987.
U.S. EPA, 1987C, PM10 SIP Development Guideline, U.S. EPA, EPA 450/2-87-
001, 'Research Triangle Park, NC 27711, January 1987.
U.S. EPA, 1987D, Procedures for Reconciling Differences in Receptor and
Dispersion Models, U.S. EPA, EPA 450/4-87-008, Research Triangle Parx, NC
27711, May 1987.
Watson, J. G. (1979), "Chemical Element Balance Receptor Model Metnodology
for Assessing the Sources of Fine and Total Suspended Particulate Matter in
Portland, Oregon," Ph.D. dissertation, Oregon Graduate Center, Beaverton, Oregon,
Watson, J. G., Lioy, P. J. and Mueller, P. U. (1983), "The Measurement
Process: Precision, Accuracy and Validity," in Air Sampling Instruments for
Evaluation of Atmospheric Contaminants. Sixth Edition, American Conference of
Governmental Industrial Hygienists, Cincinnati, OH.
Watson, J. G. and Robinson, N. F. (1984), "A Method to Determine Accuracy
and Precision Required of Receptor Model Measurements," APCA/ASQC Specialty
Conference on: Quality Assurance in Air Pollution Measurements. Boulder, CO.
Watson, J. G. and Robinson, J. F. (1984), "A Method to Specify Measurements
for Receptor Models," Proceedings of the National Symposium on Recent Advances
in Pollutant Monitoring of Ambient Air and Stationary Sources, U.S. EPA,
Research Triangle Park, NC, April, 1984.
Watson, J. G., Cooper, J, A., and Huntzicker, J. J. (1984), "The Effective
Variance Weighting for Least Squares Calculations Applied to the Mass
Balance Receptor Model," Atm. Env., JUS:1347-1335.
Watson, J. G. and Chow, J. C. (1986), "Volume 4 - An Evaluation of Ambient
Aerosol Chemistry in the Western United States," Draft Report of Western
States and Deposition Project, Phase I of SYSAPP-86-129, prepared for
Western Governor's Association, Denver, Colorado.
31
-------
APPENDIX A
Determining Source Profiles and Their Uncertainties
Source profile variability needs to be assessed on a case-by-case
basis by reviewing the nature of the fuels and raw materials used by the
sources. Also, values and uncertainties of those species which are the
most influential in the "fit" should be carefully examined to ensure that
both the ambient data and source profiles are accurate, valid and precise.
The SSCONT command (see Section 3.3.6) shows the percent contribution of
each source to each species in the fit. This provides some indication of
.each species' influence on the fit.
Most combustion processes use fuels with variable chemical compositions.
Coal and fuel oil combustion source profiles may change substantially when
the origin of the fuel changes (e.g., South American vs. Middle East Crude).
Process upsets and control device malfunctions also affect source profiles,
but usually not as much as they affect the mass emission rates. Manufactjring
process emissions may be stable over time, but the use of different raw
materials or changing product specifications could cause source profiles to
vary.
The most accurate and reasonably "certain" information about sources
in an airshed is derived from samples of the effluents from those sources,
preferably at the same time that the receptor measurements are being
taken. This may only be possible during a comprehensive (Level III) CMB
application. The alternatives are to measure the source profiles from
representative sources at representative times in the airshed under study,
or to use profiles measured on similar sources in other airsheds and compiled
in a source composition library (U.S. EPA, 1985C).
Source sampling to obtain source profile information is not as
complicated as sampling to determine the mass emission rate. This is
because source profiles require only that species be characterized as % of
total mass of sample collected. (Not in terms of their absolute emission
rate.) Hot exhaust sampling, diluted (cooled) exhaust sampling, airborne
plume sampling, ground-based plume sampling, and grab sampling methods have
been developed and are applicable to different source types (Chow .et al.,
1986A).
"Grab sampling" is an especially useful and inexpensive method of
characterizing soil dust or storage piles. The procedure is so named
because samples of the effluent or raw material are "grabbed" in bulk
instead of sampled from an exhaust stream. These sources can be sampled
in bulk and resuspended onto filters in the laboratory so that chemical
analysis can be performed. In some cases, it can be determined that the
effluent captured by the source's control device is chemically representative
of the emissions. In these cases, a bulk sample of the captured effluent
may be likewise resuspended. The "grab sample" procedure is generally much
less expensive than stack sampling and can yield acceptable profiles for
some types of sources.
A-l
-------
Any source profile contains both measurement and analytical uncertainty.
Use of any profile data which are not representative of the source at the
time the ambient sample was collected introduces additional (location and/or
time) uncertainty in the source profiles. The combination of these (the over-
all uncertainty) is assigned to each species in a source profile and the CMB
model uses these uncertainties to weight a species' influence on the solution.
The uncertainty estimates for each species in the source profile are just
as important as the source profile values themselves. Uncertainty estimates
can be based on the judgment of an engineer or scientist knowledgeable
about each particular source and its operating characteristics. This
judgment takes advantage of natural lower and upper limits to the possible
uncertainty. The analytical uncertainty derived from error propagation
provides a lower limit of the uncertainty estimate in a source profile. An
upper limit is imposed by the constraint that the sum of all the fractional
chemical compositions in a source profile cannot exceed unity, and random
uncertainties cannot be so large that this might occur. A value between
these extremes is often appropriate for CMB analysis. Repeated source
tests over a range of operating variables provides a better estimate of the
average profile of a source type and the standard deviation of that average
is a good estimate of its uncertainty.
The EPA Source Composition Library presents typical compositions and
uncertainties for the most common source types. These uncertainties may be
understated when the profile is used to represent conditions at another
location. Uncertainties of magnitude similar or even greater than those in
the Library should be assigned when source composition data without uncer-
tainties has been obtained. The value of the CMB performance diagnostics
is substantially reduced without accurate estimates of source profile
uncertainty.
Previous applications of the CMB model suggest that typical uncertainties
in both receptor and source measurements of up to +-30% in each of the species
is tolerable; large uncertainties of +-50 to 100% or more for some species
may also be tolerable (Watson 1979). As noted, the effective variance
weighted least squares algorithm incorporated in the CMB model considers
both ambient and source data uncertainties. This fitting procedure gives
less emphasis to those highly variable elements in the fitting process. If
most elements in a source are highly variable, the source contribution
estimate for that source is likely to have a high uncertainty.
A-2
-------
UNCERTAINTY/SIMILARITY CLUSTERS
SUM OF COMB. SOURCES
SPECIES COI
SAMPLE OUR;
R S(
CHI S(
SPECIES-I-*
1 TOT
9 F *
11 NA *
12 MG
13 AL *
14 SI *
16 S
17 CL *
19 K *
20 CA *
22 TI *
23 V *
24 CR
25 MN *
26 FE *
28 NI *
29 CU
30 ZN
35 BR *
82 PB *
91 OC *
92 EC *
93 S04 *
94 N03 *
YCENTRATIONS
VTION
3UARE
3UARE 1.
ii MFAS-
73.30000+-
.03600+-
.97000+-
.85000+-
4.80000+-
14.50000+-
.56000+-
.33000+-
.54000+-
2.00000+-
.40000+-
.02600+-
.02600+-
.08300+-
3.50000+-
.02200+-
.05200+-
.11000+-
.22000+-
.62000+-
13.10000+-
1.70000+-
1.70000+-
1.60000+-
- SITE:PACS2 DATE:0124 78 SIZf
24 START HOUR 0
99 PERCENT MASS 101.3
76 DF 9
PAI r nft-rm
1.10000
.01700
.14000
.12000
.16000
.50000
.14000
.05000
.03000
.07000
.02000
.00200
.00200
.00400
.13200
.00300
.00400
.01000
.02000
.07000
4.30000
.90000
.50000
.30000
74.59217+-
.09646+-
1.05442+-
.90611+-
4.40322+-
15.46888+-
.52574+-
.32922+-
.60618+-
1.75155+-
.55770+-
.02551+-
.02529+-
.08149+-
3.23851+-
.02248+-
.02541+-
.07245+-
.15044+-
.76834+-
13.10000+-
1.14293+-
1.70000+-
1.60000+-
4.83016
.05719
.05228
.07983
.40123
.82643
.04939
.06526
.03237
.12300
.09907
.00349
.00937
.00779
.16125
.00403
.00689
.02069
.04846
.11825
1.04393
.45013
.15074
.17316
---rtrt i lu
1.02+-
2.68+-
1.09+-
1.07+-
.92+-
1.07+-
.94+-
1.00+-
1.12+-
.88+-
1.39+-
.98+-
.97+-
.98+-
.93+-
1.02+-
.49+-
.66+-
.68+-
1.24+-
1.00+-
.67+-
1.00+-
1.00+-
::COARSE
C/n RATIO R/U
.07 TOT
2.03 F
.17 NA
.18 MG
.09 AL
.07 SI
.25 S
.25 CL
.09 K
.07 CM
.26 TI
.15 V
.37 CR
.11 MN
.06 FE
.23 NI
.14 CU
.20 ZN
.23 BR
.24 PB
.34 OC
.44 LC
.31 S04
.22 N03
.26
1.01
.56
.39
-.92
1.00
-.23
-.01
1 . 50
-1.76
l.5b
-.12
-.07
-.17
-1.25
.09
-3.3
-1.63
-1.33
1.08
.00
-.55
.00
.00
B-2
-------
APPENDIX 8
Examples and Quick Guide for Identifying Problems
and Corrective Action
There are four situations which, once they have been identified, can
be addressed to improve the performance of the CMB. If they are not
satisfactorily addressed, the model cannot be considered valid for a par-
ticular application or the source contribution estimates will nave to be
used with unacceptable uncertainties. The situations are: 1) incorrect
ambient data; 2) incorrect source profiles; 3) missing source in the
solution; 4) profile uncertainty/col linearity; and 5) noncontribating source
in the solution.
The following provides a Quick Guide and examples to illustrate the
process of using the model's statistics and diagnostics to help identify
these situations. The indicators proposed in these examples are derived
from a consensus of experienced model users and should be considered as
"guides" " not as "rules". They are not a "cure-all". They are only
included to assist the discovery of errors in the input data which may
cause the model to provide incorrect Source Contribution Estimates and they
may be modified and improved in future revisions to this Protocol as a wide
range of experience is gained in practical applications.
Example B is assumed to be the "correct" solution for the data set
used in this example. Examples B.I - B.5 show how the results would appear
if the data were modified to include (one at a time) the situations identified
above. Example B.6 shows a composite of several of these situations.
EXAMPLE B: THE "CORRECT" SOLUTION
SOURCE CONTRIBUTION ESTIMATES - SITE:PACS2 DATE:0124 78 SIZE:COARSE
SAMPLE DURATION 24 START HOUR 0
R SQUARE .99 PERCENT MASS 101.8
CHI SQUARE 1.76 OF 9
SOURCE
* TYPE
3 UDUST
4 AUTPB
5 RDOIL
6 VBRN1
11 ALPRO
13 FERMN
17 S04
18 N03
19 OC
SCE(UG/M3)
55.0169
2.8220
.2834
3.9257
2.1796
.1251
1.3812
1.3541
7.5042
STD ERR
1.8952
.5755
.0811
1.5100
.9945
.0531
.5240
.3545
4.5103
TSTAT
29.0298
4.9033
3.4932
2.5998
2.1917
2.3535
2.6357
3.8194
1.6638
MEASURED CONCENTRATION FIIME/COARSE/TOTAL:
42.60000+- .6007 . 73.30000+- 1.100/ 115.90000+- 1.253
B-l
-------
PROBLEM B.I: INCORRECT AMBIENT DATA
INDICATION:
o RATIO R/U « -2.0 for a species suggests either the ambient
data are high or the profile data are low for the flagged species;
o RATIO R/U » 2.0 for a species would imply that the ambient
data are low or the profile data for that species are high. If
profile data are suspect, see Section 3.5.2 and problem 8.2.
ACTION: 1. Review the uncertainty assigned to the species with the high
residuals. Make any justifiable and appropriate changes and
rerun the CMB. If this reduces the RATIO R/U, Step 2 is not
necessary.
2. Delete the suspect species from the list of fitting species
and rerun. If the SCE changes by one standard error, do not
use this species in the fit until it has been remeasured.
EXAMPLE B.I: IDENTIFYING INCORRECT AMBIENT DATA
SUMMARY: A CHI SQUARE » 4 and a % MASS of -120% suggest that the fit
is not satisfactory. The RATIO R/U for Si was « -2.0 implying high ambient
data for that species (also, low profile data for the major source of that
species or absence of a source of Si in the source list). The profile data
were checked and were believed to be correct. The ambient data was then
reviewed and it was found that the Si ambient data was erroneously entered
as 29 ug/m3 for this example when the correct value was 14.5. Notice that
the SCE's for UDUST and ALPRO are significantly changed with respect to
Example B. The high ambient Si data raised the UDUST SCE to 69.6 ug/m3 and
the ALPRO SCE is lowered.
SOURCE CONTRIBUTION ESTIMATES - SITE:PACS2
SAMPLE DURATION 24 START HOUR 0
R SQUARE .93 PERCENT MASS 118.4
CHI SQUARE 11.54 DF 9
DATE.-0124 73 SIZE:COARSE
SOURCE
* TYPE
3 UDUST
4 AUTPB
5 RDOIL
6 VBRN1
11 ALPRO
13 FERMN
17 S04
18 N03
19 OC
SCE(UG/M3)
69.5898
2.6964
.2797
3.4292
.5877
.0257
1.4130
1.3834
7.3824
STD ERR
2.1824
.6017
.0801
1.4281
.8251
.0580
.5244
.3490
4.5131
TSTAT
31.8870
4.4809
3.4912
2.4012
.7123
.4433
2.6947
3.9634
1.6358
B-4
-------
ENTER COMMAND
SSCONT
CALC SP£CIES(PER SOURCE)
1INU
SPECtSOURCE
1 TOTAL
9 =
11 NA
12 MG
13 AL
14 SI
16 S
17 CL
19 K
20 CA
22 TI
?3 V
24 CR
25 MN
26 FE
28 NI
29 CU
30 ZN
35 BR
82 PB
91 OC
92 EC
93 S04
94 N03
1 V 1UUML
3
.751
.122
.993
.997
.756
1.062
.000
.000
1.049
.825
1.389
.571
.952
.663
.901
.100
.317
.550
.020
.328
.140
.502
.024
.007
KM 1 i\J -
4
.038
.000
.000
.000
.006
.002
.020
.257
.004
.018
.000
.000
.000
.000
.017
.023
.040
.090
.641
.910
.108
.063
.022
.016
MEAS
5
.004
.004
.010
.000
.000
.000
.067
.000
.001
.002
.001
.375
.005
.002
.002
.690
.004
.010
.000
.001
.002
.005
.080
.001
SPECIES(ALL SOURCES)
6
.054
.000
.026
.000
.012
.002
.034
.660
.044
.021
.000
.000
.000
.057
.002
.000
.068
.000
.009
.000
.177
.081
.037
.125
11
.030
2.543
.054
.069
.142
.000
.000
.079
.000
.009
.004
.034
.013
.QUO
.002
.208
.059
.002
.012
.000
.000
.021
.022
.000
13
.002
.010
.004
.000
.000
.000
.004
.002
.024
.001
.000
.001
.002
.261
.001
.000
.001
.007
.001
.000
.001
.001
.003
.004
17
.019
.000
.000
.000
.000
.000
.814
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.812
.000
18
.013
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.846
19
.102
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.573
.000
.000
.000
B-3
-------
MEASURED CONCENTRATION FINE/COARSE/TOTAL:
42.60000+- .600/ 73.30000+- 1.100/ 115.90000+- 1.253
UNCERTAINTY/SIMILARITY CLUSTERS
SUM OF COMB. SOURCES
SPECIES CONCENTRATIONS - SITE:PACS2
SAMPLE DURATION 24 START HOUR
R SQUARE .93 PERCENT MASS
CHI SQUARE 11.54 DF
DATE:0124 78
0
118.4
9
SIZErCOARSE
ortoito-l -:!--- ----;! C.MO- ---
1 TOT
9 F
11 NA
12 MG
13 AL
14 SI
16 S
17 CL
19 K
20 CA
22 TI
23 V
24 CR
25 MN
26 FE
28 NI
29 CU
30 ZN
35 BR
82 PB
91 OC
92 EC
93 S04
94 N03
*
*
*
*
*
*
*
*
*
*
*
*
*
it
*
*
*
*
73.30000+-
.03600+-
.97000+-
.85000+-
4.80000+-
29.00000+-
.56000+-
.33000+-
.54000+-
2.00000+-
.40000+-
.02600+-
.02600+-
.08300+-
3.50000+-
.02200+-
.05200+-
.11000+-
.22000+-
.62000+-
13.10000+-
1.70000+-
1.70000+-
1.60000+-
1.10000
.01700
.14000
.12000
.16000
.50000
.14000
.05000
.03000
.07000
.02000
.00200
.00200
.00400
.13200
.00300
.00400
.01000
.02000
.07000
4.30000
.90000
.50000
.30000
86
1
1
4
19
2
4
13
1
1
1
----U,~M_O-
.78726+- '
.03048+-
.26480+-
.08755+-
.85758+-
.54129+-
.53117+-
.27837+-
.74277+-
.16760+-
.70362+-
.02865+-
.03155+-
.07828+-
.06171+-
.01949+-
.02697+-
.08731+-
.14299+-
.79707+-
.10000+-
.31958+-
.70000+-
.60000+-
._ .
4.94793
.03639
.06380
.09877
.48899
1.04456
.05034
.05884
.04039
.15426
.12529
.00407
.01183
.00871
.20300
^0400
.00851
.02599
.04630
.13206
1.09582
.55518
.15206
.16353
* "
1
1
1
1
1
1
1
1
1
1
1
1
1
1
r\n i lu
.18+-
.85+-
.30+-
.28+-
.01+-
.67+-
.95+-
.84+-
.38+-
.08+-
.76+-
.10+-
.21+-
.94+-
.16+-
.89+-
.52+-
.79+-
.65+-
.29+-
.00+-
.78+-
.00+-
.00+-
\j/ n----r\rt i iu f\/ u
.07
1.09
.20
.21
.11
.04
.25
.22
.11
.09
.33
.18
.46
.11
.07
.22
.17
.25
.22
.26
.34
.52
.31
.21
TOT
F
NA
MG
AL
SI
S
CL
K
CA
TI
V
CR
MN
FE
NI
CU
ZN
BR
PB
OC
EC
S04
N03
2.66
-.14
1.92
1.53
.11
-8.17
-.19
-.67
4.03
.99
2.39
.58
.46
-.49
2.32
-.50
-2.66
-.81
-1.53
1.18
.00
-.36
.00
.00"
8-5
-------
ENTER COMMAND
SSCONT
CALC SPECIES(PER SOURCE)
SPECtSOURCE
1 TOTAL
9 F
11 NA
12 MG
13 AL
14 SI
16 S
17 CL
19 K
20 CA
22 TI
23 V
24 OR
25 MN
26 FE
28 NI
29 CU
30 ZN
35 BR
82 PB
91 OC
92 EC
93 S04
94 N03
V lUUttL.
3
.949
.155
1.255
1.261
.957
.672
.000
.000
1.327
1.044
1.757
.723
1.204
.838
1.139
.127
.401
.696
.025
.415
.177
.634
.030
.009
l\rt 1 1U -
4
.037
.000
.000
.000
.006
.001
.019
.245
.004
.017
.000
.000
.000
.000
.016
.022
.038
.086
.613
.870
.103
.060
.021
.015
ME AS
5
.004
.004
.010
.000
.000
.000
.066
.000
.001
.002
.001
.370
.005
.002
.002
.681
.004
.010
.000
.000
.001
.005
.079
.001
SPECIES(ALL SOURCES)
6
.047
.000
.023
.000
.010
.001
.029
.577
.038
.018
.000
.000
.000
.050
.002
.000
.059
.000
.008
.000
.154
.071
.032
.109
11
.008
.686
.015
.019
.038
.000
.000
.021
.000
.002
.001
.009
.004
.000
.001
.056
.016
.000
.003
.000
.000
.006
.006
.000
13
.000
.002
.001
.000
.000
.000
.001
.000
.005
.000
.000
.000
.000
.054
.000
.000
.000
.001
.000
.000
.000
.000
.001
.001
17
.019
.000
.000
.000
.000
.000
.833
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.831
.000
18
.019
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.865
19
.101
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.564
.000
.000
.000
B-6
-------
PROBLEM B.2: GROSS ERROR IN A SOURCE PROFILE
INDICATION:
o SCE that is inconsistent with preliminary analyses or physical
evidence;
o one or more species has a "high (pos. or neg.)" residual which
cannot be attributed to incorrect ambient data; further evidence
if the SSCUNT reveals that one source dominates that species.
Review profile data for the suspect species carefully. Correct
or remeasure profile if necessary.
ACTION:
EXAMPLE 8.2: GROSS ERROR IN A SOURCE PROFILE
SUMMARY: The Ca RATIO R/U is « -2.0 implying high ambient data or low profile
data for Ca and several other species. In SSCONT, the Ca is dominated by
UOUST. tkith the ambient and profile data were checked and no problem was
found with Ca. The RATIO R/U for Fe was » 2.0 implying low ambient data
or high profile c.ata for Fe. The ambient data were reviewed and Fe was
found to be high in the UDUST profile (.114 instead of .057). This example
points out that the diagnostics can only suggest possible sources of error.
One real data errur (in Fe) caused other species (Ca) to "appear" to be
incorrect.
SOURCE CONTRIBUTION ESTIMATES - SITE:PACS2
SAMPLE DURATION 24 START HOUR
R SQUARE .94 PERCENT MASS
CHI SQUARE 11.51 DF
OATE:0124 78 SIZE:COARSE
0
86.8
9
SOURCE
* TYPE
3 UDUST
4 AUTPB
5 RDOIL
6 VBRN1
11 ALPRO
13 FERMN
17 S04
18 N03
19 OC
SCE(UG/M3)
38.868B
2.7047
- .2403
7.1187
5.7457
.2239
1.2995
1.1902
6.2125
STD ERR
1.2080
.5265
.0878
2.1008
1,2366
.0638
.5278
.4004
4.5956
TSTAT
32.1758
5.1368
2.7354
3.3886
4.6463
3.5111
2.4620
2.9723
1.3518
MEASURED CONCENTRATION FINE/COARSE/TOTAL:
42.60000+- .600/ 73.30000+- 1.100/ 115.90000+-
1.253
8-7
-------
UNCERTAINTY/SIMILARITY CLUSTERS
SUM OF COMB. SOURCES
SPECIES CONCENTRATIONS - SITE:PACS2
SAMPLE DURATION 24 START HOUR
K SQUARE .94 PERCENT MASS
CHI SQUARE 11.51 OF
DATE:0124 78
0
86.8
9
SIZE .-COARSE
1 TOT
9 F
11 HA
12 MG
13 Au
14 Si
16 S
17 CL
19 K
20 CA
22 TI
23 V
24 CR
25 MN
26 FE
28 NI
29 CU
30 ZN
35 BR
82 PB
91 OC
92 EC
93 S04
94 N03
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
73
4
14
2
3
13
1
1
1
.30000+-
.03600+-
.97000+-
.85000+-
.80000+-
.50000+-
.56000+-
.33000+-
.54000+-
.00000+-
.40000+-
.02600+-
.02600+-
.08300+-
.50000+-
.02200+-
.05200+-
.11000+-
.22000+-
.62000+-
.10000+-
.70000+-
.70000+-
.60000+-
1.10000
.01700
.14000
.12000
.16000
.50000
.14000
.05000
.03000
.07000
.02000
.00200
.00200
.00400
.13200
.00300
.00400
.01000
.02000
.07000
4.30000
.90000
.50000
.30000
63
4
10
1
4
13
1
1
1
.60400+-
.24521+-
.87972+-
.75371+-
.49870+-
.97881+-
.50959+-
.54612+-
.46919+-
.32928+-
.39731+-
.02111+-
.01862+-
.08626+-
.53500+-
.02699+-
.02835+-
.05500+-
.14940+-
.68511+-
.10000+-
.05713+-
.70000+-
.60000+-
4.72030
.13036
.05058
.06538
.39619
.58834
.05195
.10871
.02488
.09279
.07006
.00273
.00669
.00988
.11542
.00466
.00598
.01482
.04763
.10008
1.06037
.39077
.16139
.24324
.87+-
6.81+-
.91+-
.89+-
.94+-
.76+-
.91+-
1.65+-
.87+-
.66+-
.99+-
.81+-
.72+-
1.04+-
1.30+-
1.23+-
.55+-
.50+-
.68+-
1.11+-
1.00+-
.62+-
1.00+-
1.00+-
O/ 1 1 -r\,T 1 1 \.J r\/ U
.07
4.84
.14
.15
.09
.05
.25
.41
.07
.05
.18
.12
.26
.13
.06
.27
.12
.14
.23
.20
.34
.40
.31
.24
TOT
F
NA
MG
AL
SI
S
CL
K
CA
TI
V
CR
MM
FE
NI
CU
ZN
BR
P8
OC
EC
S04
N03
-2.00
1.59
-.61
-.70
-.71
-4.56
-.34
1.81
-1.32
-5.77
-.04
-1.44
-1.06
.31
5.90
.90
-3.29
-3.08
-1.37
.53
.00
-.66
.00
.00
B-8
-------
ENTER COMMAND
SSCONT
CALC SPECIES(P£R SOURCE)
SPECtSOURCE
1 TOTAL
9 F
11 NA
12 MG
13 AL
14 SI
16 S
17 CL
19 K
20 CA
22 TI
23 V
24 CR
25 MN
26 FE
28 NI
29 CU
30 ZN
35 8R
82 PB
91 OC
92 EC
93 S04
94 N03
V iUUttL
3
.530
.036
.701
.704
.534
.751
.000
.000
.741
.583
.981
.404
.673
.468
1.266
.071
.224
.389
.014
.232
.099
.354
.017
.005
r\rt t j.u -
4
.037
.000
.000
.000
.006
.002
.019
.246
.004
.017
.000
.000
.000
.000
.016
.022
.038
.086 '
.615
.872
.103
.060
.021
.015
MEAS
5
.003
.304
.009
.000
.000
.000
.057
.000
.001
.002
.001
.318
.004
.001
.002
.585
.003
.009
.000
.000
.001
.004
.068
.001
SPECIES(A,_L SOURCES)
6
.097
.000
.048
.000
.021
.004
.061
1.197
.079
.038
.000
.000
.000
.103
.004
.000
.123
.000
.017
.000
.321
.147
.067
.227
11
.J78
6.703
.142
.183
.375
.000
/}00
.209
.000
.023
.011
.088
.035
,UOO
.006
.548
.155
.(105
.031
.000
.000
.054
.057
.000
13
.003
.018
.007
.000
.000
.000
.007
.003
.044
.001
.000
.002
.004
.467
.001
.000
.002
.012
.002
.000
.002
.002
.006
.008
17
.018
.000
.000
.000
.000
.000
.7^6
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.764
.000
18
.016
.000
.000
.000
.000
.000
.000
. 000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.744
19
.085
.000
.000
.000
.QUO
.000
.000
.oou
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.474
.000
.000
.000
B-9
-------
PROBLEM B.3: MISSING SOURCE
INDICATION:
o High Chi -Square;
o Low percent mass explained;
o RATIO K/U « -2.0 (a "nigh negative" residual) for one or more
species%that are known to be present in the suspect source.
ACTION: Add sources to the fit and reevaluate.
EXAMPLE B.3: IDENTIFYING A MISSING SOURCE
SUMMARY: The Chi -Square is hig
« -2.0. Using the flowchart p
and no problems were found. Th
for missing sources. These low
motor vehicle exhaust source.
high, in fact), suggesting that
The absence of motor vehicle ex
butions to be different from th
has few species in common with
h and two species, Br and
rocedure in Figure 1, all
Pb have RATIO R/U
data was rechecked
us, the source list was reviewed to check
ratios for 3r and Pb suggest a missing
~he percent mass explained is not low (a bit
a missing source may be a minor contributor.
haust does not cause the other source contri-
e "correct" ones because its source profile
cue other sources.
SOURCE CONTRIBUTION ESTIMATES - SITE:PACS2
SAMPLE DURATION 24 START HOUR
R SQUARE .91 PERCENT MASS
CHI SQUARE 12.16 DF
DATE:0124 78 SIZErCOARSE
0
102.5
10
SOURCE
* TYPE
3 UDUST
5 RDOIL
6 VBRN1
11 ALPRO
13 FERMN
17 S04
18 N03
19 OC
SCE(U6/M3)
55.4251
.2620
5.7480
3.0749
.1072
1.3842
1.2880
7.8295
STD ERR
1.9200
.08.31
1.7679
1.1644
.0610
.5259
.3729
4.5613
TSTAT
28.8676
3.1540
3.2513
2.6408
1.7588
2.6322
3.4536
1.7165
MEASURED CONCENTRATION FINE/COARSE/TOTAL:
42.60000+- .600/ 73.30000+- 1.100/ 115.90000+- 1.253
B-10
-------
UNCERTAINTY/SIMILARITY CLUSTERS
SUM OF COMB. SOURCES
SPECIES CONCENTRATIONS - SITE:PACS2 D
SAMPLE DURATION 24 START HOUR
R SQUARE .91 PERCENT MASS
CHI SQUARE 12.16 DF
SPECIES-I-M MEAS CALC-
1 TOT
9 F
11 NA
12 MG
13 AL
14 SI
16 S
17 CL
19 K
20 CA
22 TI
23 V
24 CR
25 MN
26 FE
28 NI
29 CU
30 ZN
35 BR
82 PB
91 OC
92 EC
93 S04
94 N03
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
73.
4.
14.
2.
3.
13.
1.
1.
1.
30000+-
03600+-
97000+-
85000+-
80000+-
50000+-
56000+-
33000+-
54000+-
00000+-
400UO+-
02600+-
02600+-
08300+-
50000+-
02200+-
05200+-
11000+-
22000+-
62000+-
10000+-
70000+-
70000+-
60000+-
1.10000
.01700
.14000
.12000
.16000
.50000
.14000
.05000
.03000
.07000
.02000
.00200
.00200
.00400
.13200
.00300
.00400
.01000
.02000
.07000
4.30000
.90000
.50000
.30000
75.
1.
4.
15.
1.
3.
13.
1.
1.
1.
11888+-
13403+-
09359+-
93657+-
70535+-
57675+-
52105+-
35636+-
61736+-
75470+-
56247+-
02523+-
02560+-
08100+-
20850+-
02271+-
02634+-
06291+-
01138+-
2Q541+-
10000+-
11920+-
70000+-
60000+-
ATE:0124 78 SIZE
0
102.5
10
DflTTll
4.86535
.08205
.05449
.07992
.41893
.83378
.05130
.08534
.03257
.12433
.09977
.00341
.00944
.00929
.16094
.00403
.00714
.02051
.00832
.08319
1.11467
.47212
.15639
.20264
«\ n i i. *_*
1.02+-
3.72+-
1.13+-
1.10+-
.98+-
1.07+-
.93+-
1.08+-
1.14+-
.88+-
1.41+-
.97+-
.98+-
.98+-
.92+-
1.03+-
.51+-
.57+-
.05+-
.33+-
1.00+-
.66+-
1.00+-
1.00+-
I: COARSE
*
C/M RATIO R/U
.07
2.88
.17
.18
.09
.07
.25
.31
.09
.07
.26
.15
.37
.12
.06
.23
.14
.19
.04
.14
.34
.45
.31
.23
TOT
F
NA
MG
AL
SI
S
CL
K
CA
TI
V
CR
MN
FE
NI
CU
ZN
BR
PB
OC
EC
S04
NO 3
.36
1.17
.82
.60
-.21
1.11
-.26
.27
1.75
-1.72
1.60
-.19
-.04
-.20
-1.40
.14
-3.13
-2.06
-9.63
-3.81
.00
-.57
.00
.00
B-ll
-------
ENTER COMMAND
SSCONT
CALC SPECIES(PER SOURCE)
iNU
SPECtSOURCE
1 TOTAL
9 F
11 NA
12 MG
13 AL
14 SI
16 S
17 CL
19 K
20 CA
22 TI
23 V
24 CR
25 MN
26 FE
28 MI
29 CU
30 ZN
35 8R
82 PB
91 OC
92 EC
93 S04
94 N03
1Y1UUML r
3
.756
.123
1.000
1.004
.762
1.070
.000
.000
1.057
.831
1.399
.576
.959 '
.668
.907
.101
.320
.554
.020
.331
.141
.505
.024
.007
^M 1 1U -
5
.004
.004
.009
.000
.000
.000
.062
.000
.001
.002
.001
.347
.005
.001
.002
.638
.004
.010
.000
.000
.001
.005
.074
.001
ME AS
6
.078
.000
.039
.000
.017
.004
.049
.967
.064
.031
.000
.000
.000
.083
.003
.000
.099
.000
.014
.000
.259
.118
.054
.183
SPECIES(ALL SOURCES)
11
.042
3.587
.076
.098
.201
.000
.000
.112
.000
.012
.006
.047
.019
.000
.003
.294
.083
.003
.017
.000
.000
.029
.031
.000
13
.001
.009
.003
.000
.000
.000
.003
.001
.021-
.001
.000
.001
.002
.224
.001
.000
.001
.006
.001
.000
.001
.001
.003
.004
17
.019
.00*
.000
.000
.000
.000
.816
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.814
.000
18
.018
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.805
19
.107
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.598
.000
.000
.000
B-12
-------
PROBLEM B.4: COLLINEARITY
INDICATION:
o Two or more sources listed in a U/S cluster
o T-statistic < 2.0 for one or more sources in that cluster
if the T-STAT becomes > 2.0 when species uncertainties for profile
for that source is arbitrarily reduced to a potentially achievable
level, this indicates that the uncertainty in the source profile
is at least partially responsible for the "apparent" collinearity.
ACTION: Remedies for unacceptably high uncertainties due to collinearity
can take four forms ranked from most to least desirable. There is an
additional remedy if the collinearity is associated with high
uncertainties as discussed above.
EXAMPLE B.4: COLLINEARITY
SUMMARY: VBRN2 is a source that was added to the source list to introduce
collinearity. In this case, VBRN2 was actually not contributing but it
illustrates the possibility that two potentially legitimate sources may
have similar signatures causing collinearity. Following the Figure 1
flowchart, all source profile and species data have been checked and no
missing sources are apparent at this time. The only indications of a
problem are the negative SCE for VBRN2 and the fact that VBRN1, VBRN2 and
OC sources were all flagged in U/S clusters, indicating collinearity.
The SSCONT screen suggests that removing Cl from the fit might reduce the
collinearity. Other approaches would include deleting one or two of the
sources from the fit. The uncertainty/similarity display suggests that
the combined contribution of sources 6 & 19 is 13.9 +- 5.1 and the sum of
6,7, and 19 is only 12.1 +- 4.7. This suggests that VBRN2 (source #7) may
be an insignificant contributing source and could be deleted. Other
options for dealing with collinearity are discussed in Section 3.5.4.
Only VBRNl's SCE is significantly affected by the addition of VBRN2, but
its STD. ERROR nearly triples with respect to the "true" solution (Example
B). Notice that the "true" VBRN1 still falls within one uncertainty
interval of the VRRN1 contribution in this example. This example graphically
illustrates the effects of col Linearity on source contribution estimates
and their uncertainties.
B-13
-------
SOURCE CONTRIBUTION ESTIMATES - SITE:PACS2
SAMPLE DURATION 24 START HOUR
R SQUARE .99 PERCENT MASS
CHI SQUARE 1.45 DF
DATE:0124 78 SIZE:COARSE
0
103.9
8
SOURCE
* TYPE
3 UDUST
4 AUTPB
5 RDOIL
6 VBRN1
7 VBRN2
11 ALPRO
13 FERMN
17 S04
18 N03
19 OC
SCE(UG/M3)
55.9124
2.7711
.2748
8.0754
-1.7924
2.3581
.1061
1.4063
1.1798
5.8962
STD ERR
2.1142
.5742
.0838
4.3667
1.6701
1.2212
.0758
.5395
.4333
4.9430
TSTAT
26.4464
4.8263
3.2791
1.8493
-1.0733
1.9310
1.4003
2.6067
2.7226
1.1928
MEASURED CONCENTRATION FINE/COARSE/TOTAL:
42.60000+- .600/ 73.30000+- 1.100/ 115.90000+- 1.253
UNCERTAINTY/SIMILARITY CLUSTERS
SUM OF COMB. SOURCES
6
6
7
6
19
7 19
11
7 11
13
12
8
.972+-
.179+-
.566+-
.641+-
5.144
4.700
2.172
3.305
SPECIES CONCENTRATIONS - SITE:PACS2
SAMPLE DURATION 24 START HOUR
R SQUARE .99 PERCENT MASS
CHI-SQUARE 1.45 DF
DATE:0124 78
0
103.9
8
SIZErCOARSE
1
9
11
12
13
14
16
17
19
20
22
23
TOT
F *
NA *
MG
AL *
SI *
S
CL *
K *
CA *
TI *
V *
73.
.
.
,
4.
14.
.
.
,
2.
,
.
30000+r
03600+-
97000+-
85000+-
80000+-
50000+-
56000+-
33000+-
54000+-
00000+-
40000+-
02600+-
1.10000
.01700
.14000
.12000
.16000
.50000
.14000
.05000
.03000
.07000
.02000
.00200
76.
#
1.
*
4.
15.
.
.
,
1.
B
.
18761+-
09823+-
09454+-
92472+-
56913+-
74725+-
52360+-
38261+-
52175+-
80675+-
56560+-
02552+-
5.01175
.09247
-.05457
.08303
.41389
.84354
.06079
.15282
.08708
.12900
.10069
.00349
1.04+-
2.73+-
1.13+-'
1.09+-
.95+-
1.09+-
.93+-
1.16+-
.97+-
.90+-
1.41+-
.98+-
u./ n----r\« i iu r\/ u
.07
2.87
.17
.18
.09
.07
.26
.50
.17
.07
.26
.15
TOT
F
NA
MG
AL
SI
S
CL
K
CA
TI
V
.56
.66
.83
.51
-.52
1.27
-.24
.33
-.20
-1.32
1.61
-.12
B-14
-------
PROBLEM B.5: NONCONTRIBUTING SOURCE IN FIT CAUSING COLLINEARITY
INDICATION:
o T-STAT between -2.0 and 2.0
o RATIO R/U » 2.0 ("high positive" residual) for a species
which is attributed to the suspect source by the SSCONT
diagnostic
o Negative SCE
o Physical basis for the source's contribution is */eak.
o SCE's, statistics and diagnostics do not change if the suspect
source is deleted
ACTION: Delete source from fit
EXAMPLE R.5: REMOVING NONCONTRIBUTING SOURCES FROM THE FIT
SUMMARY: All source profile and species data were reviewed and found to
be correct. At this point, no justification can be made that a missing
source must be added. The SCE for the GLASS source is negative and has
the lowest T-STAT of any SCE. The organic carbon (OC) source has a
T-STAT < 2.0 and the magnitude of the STDERR is high (4.5), so it may
well be a minor or noncontributor. The uncertainty/similarity display
shows that there is significant collinearity involving the GLASS source.
There is no "high positive" RATIO R/U to indicate that GLASS is a noncon-
tributor. In this case, the fact that deletion of the GLASS source did
not affect the SCE's, statistics and diagnostics coupled with its negative
SCE and low T-STAT were used to conclude that the GLASS was noncontributing.
SOURCE CONTRIBUTION ESTIMATES - SITE:PACS2
SAMPLE DURATION 24 START HOUR
R SOUARE .99 PERCENT MASS-
CHI SQUARE 1.73 OF
DATE:0124 78 SIZE:COARSE
0
102.2
8
SOURCE
* TYPE
3 UDUST
4 AUTPB
5 RDOIL
6 VBRN1
11 ALPRO
13 FERMN
15 GLASS
17 S04
18 N03
19 OC
SCE(UG/M3)
55.9343
2.8157
.2801
4.0938
2.2675
.1217
-2.0215
2.6921
1.3582
7.3781
STD ERR
2.0525
.5775
.0814
1.5473
1.0213
.0542
1.6002
1.2022
.3565
4.5155
TSTAT
27.2514
4.8755
3.4399
2.6458
2.2202
2.2429
-1.2633
2.2394
3.8095
1.6340
MEASURED CONCENTRATION FINE/COARSE/TOTAL:
42.60000+- .600/ 73.30000+- 1.100/ 115.90000+- 1.253
B-16
-------
24 CR
25 MN
26 FE
28 NI
29 CU
30 ZN
35 8R
82 P8
91 OC
92 EC
93 S04
94 N03
*
*
*
*
*
*
*
*
*
3
13
1
1
1
.02600+-
.08300+-
.50000+-
.02200+-
.05200+-
.11000+-
.22000+-
.62000+-
.10000+-
.70000+-
.70000+-
.60000+-
.00200
.00400
.13200
.00300
.00400
.01000
.02000
.07000
4.30000
.90000
.50000
.30000
3
13
1
1
1
.02550+-
.08324+-
.29570+-
.02242+-
.02864+-
.07313+-
.14953+-
.76144+-
.10000+-
.22355+-
.70000+-
.60000+-
.00952
.01157
.16395
.00399
.00763
.02101
.04775
.11811
1.34876
.53045
.19156
.24294
.98+-
1.00+-
.94+-
1.02+-
.55+-
.66+-
.68+-
1.23+-
1.00+-
.72+-
1.00+-
1.00+-
.37
.15
.06
.23
.15
.20
.23
.24
.34
.49
.31
.24
CR
MN
FE
NI
CU
ZN
BR
PB
OC
EC
S04
N03
-.05
.02
-.97
.08
-2.71
-1.58
-1.36
1.03
.00
-.46
.00
.00
ENTER COMMAND
SSCONT
CALC SPECIES(PER SOURCE)
1HU
SPECtSOURCE
1 TOTAL
9 F
11 MA
12 MG
13 AL
14 SI
16 S
17 CL
19 K
20 CA
22 TI
23 V
24 CR
25 MN
26 FE
28 NI
29 CU
30 ZN
35 BR
82 PB
91 OC
92 EC
93 S04
94 N03
1 V 1UUML.
3
.763
.124
1.009
1.013
.769
1.080
.000
.000
1.066
.839
1.412
.581'
.968
.674
.915
.102
.323
.559
.020
.334
.143
.510
.024
.007
H rt 1 1 U -
4
.038
.000
.000
.000
.006
.002
.020
.252
.004
.017
.000
.000
.000
.000
.017
.023
.039
.088
.630
.894
.106
.062
.021
.016
MEAS
5
.004
.004
.010
.000
.000
.000
.065
.000
.001
.002
.001
.364
.005
.002
.002
.669
.004
.010
.000
.000
.001
.005
.078
.001
SPECIES(ALL SOURCES)
6
.110
.000
.054
.000
.024
.005
.069
1.358
.090
.043
.000
.000
.000
.117
.004
.000
.140
.000
.019
.000
.364
.166
.076
.257
7
-.024
-.159
-.006
.000
-.002
-.001
-.051
-.538
-.216
-.008
-.003
.000
-.008
-.010
.000
.000
-.019
.000
-.004
.000
-.064
-.046
-.053
-.022
11
.032
2.751
.058
.075
.154
.000
.000
.086
.000
.010
.004
.036
.015
.000
.003
.225
.063
.002
.013
.000
.000
.022
.024
.000
13
.001
.009
.003
.000
.000
.000
.003
.001
.021
.001
.000
.001
.002
.221
.001
.000
.001
.006
.001
.000
.001
.001
.003
.004
17
.019
.000
.000
.000
.000
.000
.829
.000
.000
.000
.000
.000
.000
.000
,000
.000
.000
.000
.000
.000
.000
.000
.827
.000
18
.016
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.737
19
.080
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
. .000
.000
.000
.000
.000
.000
.000
.000
.000
.450
.000
.000
.000
8-15
-------
UNCERTAINTY/SIMILARITY CLUSTERS
SUM OF COMB. SOURCES
3 15
3 6
3 6
15 17
17
15
11
17
15
56.
60.
60.
605+-
699+-
274+-
671+-
2.026
2.431
2.384
.3?7
SPECIES CONCENTRATIONS - SITE:PACS2
SAMPLE DURATION 24 START HOUR
R SQUARE .99 PERCENT MASS
CHI SQUARE 1.73 DF
OATE:0124 78
0
102.2
SIZE:CJARSE
orm.
1
9
11
12
13
14
16
17
19
20
22
23
24
25
26
28
29
30
35
82
91
92
93
94
, ICO-
TOT
F
NA
MG
AL
SI
S
CL
K
CA
TI
V
CR
MN
FE
NI
CU
ZN
BR
PB
OC
EC
S04
N03
i -:
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
73.30000+-
.03600+-
.97000+-
.85000+-
4.80000+-
14.50000+-
.56000+-
.33000+-
.54000+-
2.00000+-
.40000+-
.02600+-
.02600+-
.08300+-
3.50000+-
.02200+-
.05200+-
.11000+-
.22000+-
.62000+-
13.10000+-
1.70000+-
1.70000+-
1.60000+-
1.10000
-.01700
.14000
.12000
.16000
.50000
.14000
.05000
.03000
.07000
.02000
.00200
.00200
.00400
.13200
.00300
.00400
.01000
.02000
.07000
4.30000
.90000
.50000
.30000
74.
4.
15.
»
1.
*
3.
.
»
13.
1.
1.
1.
91993+-
09912+-
88748+-
92261+-
48975+-
72217+-
73020+-
33818+-
58858+-
77534+-
56702+-
02558+-
02188+-
08198+-
29103+-
02252+-
02585+-
07319+-
15025+-
76278+-
10000+-
16405+-
70000+-
60000+-
4.35608
.05956
.05694
.08360
.40866
.84027
.10215
.06746
.03336
.12508
.10073
.00351
.00955
.00799
.16388
.00403
.00702
.02103
.04838
.11909
1.04598
.45855
.34105
.17648
1.02+-
2.75+-
.91+-
1.09+-
.94+-
1.08+-
1.30+-
1.02+-
1.09+-
.89+-
1.42+-
.98+-
.84+-
.99+-
.94+-
1.02+-
.50+-
.67+-
.68+-
1.23+-
1.00+-
.68+-
1.00+-
1.00+-
i^/ n
.07
2.10
.14
.1R
.09
.07
.37
.26
.09
.07
.26
.15
.37
.11
.06
.23
.14
.20
.23
.24
.34
.45
.36
.22
- - -^.-\
TOT
F
MA
MG
AL
SI
S
CL
K
CA
TI
V
CR
MN
FE
NI
CU
ZN
BR
PB
OC
EC
S04
N03
1 LIJ r\ / J
.33
1.02
-.55
.50
-.71
1.25
.98
.10
1.08
-1.57
1.63
-.10
-.42
-.11
-.99
.10
-3.24
-1.58
-1.33
1.03
.00
-.53
.00
.00
8-17
-------
ENTER COMMAND
SSCONT
CALC SPECIES(PER SOURCE)
SPECtSOURCE
1 TOTAL
9 F
11 NA
12 MG
13 AL
14 SI
16 S
17 CL
19 K
?n CA
22 TI
23 V
24 CR
25 MN
26 FE
28 NI
29 CU
30 ZN
35 3R
82 PB
91 OC
92 EC
93 S04
94 N03
₯ i uunu
3
.763
.124
1.009
1.013
.769
1.080
.000
.000
1.0-67
.839
1.412
.581"
.968
.674
.916
.102
.323
.559
.020
.334
.143
.510
.024
.007
r\rv i iu -
4
.038
.000
.000
.000
.006
.002
.020
.256
.004
.018
,000
.000
.000
.000
.017
.023
.040
.090
.640
.908
.107
.063
.022
.016
MEAS
5
.004
.004
.010
.000
.000
.000
.067
.000
.001
.002
.001
.371
.005
,.002
.002
.682
.004
.010
.000
.000
.001
.005
.079
.001
SPECIES(ALL SOURCES)
6
.056
.000
.027
.000
.012
.003
.035
.689
.045
.022
.000
.000
.000
.059
.002
.000
.071
.000
.010
.000
.184
.084
.039
.130
11
.031
2.645
.056
.072
.148
.000
.000
.082
. .000
.009
.004
.035
.014
.000
.002
.216
.061
.002
.012
.000
.000
.021
.023
.000
13
.002
.010
.004
.000
.000
.000
.004
.002
.024
.001
.000
.001
.002
.254
.001
.000
.001
.006
.001
.000
.001
.001
.003
.004
15
-.028
-.030
-.192
.000
-.001
.000
-.408
-.004
-.051
-.003
.000
-.004
-.143
-.001
.000
.000
-.002
-.002
-.001
-.012
.000
.000
-.773
-.008
17
.037
.QUO
.000
.000
.000
.000
1.586
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.oou
.000
.000
.000
.000
1.584
.000
18
.019
.000
,000
.Ouu
.000
.000
.000
.000
.000
.000
.000
.000
.000
.oou
.000
.000
.000
.000
.000
.000
.000
.000
.000
.849
19
.101
.uoo
.oou
.QUO
.uoo
.000
.000
. oou
.000
.000
.000
.OUU
.000
.000
.000
.000
.uoo
.000
.000
.000
.b63
.000
.000
.000
B-18
-------
EXAMPLE B.6: COMPOSITE - PROBLEMS B.I, B.2, B.3, B.4, B.5
SOURCE CONTRIBUTION ESTIMATES - SITE:PACS2
SAMPLE DURATION 24 START HOUR
R SQUARE .73 PERCENT MASS
CHI SQUARE 44.78 DF
DATE:0124 78 SIZE:COARSE
0
106.8
8
SOURCE
* TYPE
3 UOUST
5 RDOIL
6 VBRN1
7 VBRN2
11 ALPRO
13 FERMN
15 GLASS
17 S04
18 N03
19 OC
SCE(UG/M3)
41.9295
.2729
63.8163
-6.8923
3.3383
-.2333
-1.6067
1.8586
-1.5037
-22.7108
STD ERR
1.5526
.1488
18.1976
5.5143
2.1902
.4555
2.1410
1.6012
1.8503
12.6036
TSTAT
27.0065
1.8343
3.5069
-1.2499
1.5242
-.5122
-.7504
1.1608
-.8127
-1.8019
INDICATIONS:
o Chi-Square is » 4, indicating that the fit of the data is not
satisfactory.
o RATIO R/U « -2.0 for silicon (Si) suggesting that either:
1) the ambient Si data are high; 2) profile(s) containing Si are low, or
3) tnere is a missing source which is dominated by Si.
o RATIO R/U « -2.0 for Pb and Br suggesting bad ambient data, bad
profile data, or a missing source, as above.
o RATIO R/U » 2.0 for Fe suggesting that either: 1) ambient Fe data
are low or profiles containing Fe are high.
o Minor R/U problems for Cl, In.
o Evidence of col linearity involving sources 6, 7, and 19.
o Evidence of an undetermined problem with source 15.
ACTION: Using the flowchart in Figure 1, the data problems would be
first addressed: Si would be resolved as in problem B.I, and Fe would be
resolved as in problem B.2. Then, the Pb-Br problem is resolved as a
missing source as in problem B.3. Following this, the col linearity
problems would be addressed as in 8.4 and B.5.
B-19
-------
MEASURED CONCENTRATION FINE/COARSE/TOTAL:
42.60000+- .600/ 73.30000+- 1.100/ 115.90000+-
1.253
UNCERTAINTY/SIMILARITY CLUSTERS
SUM OF COMB. SOURCES
6 19
6 7 19
6 7
11 15 17
3 11 15 17
3 11
15 17
41.106+-
34.213+-
56.924+-
3.590+-
45.520+-
45.268+-
.252+-
12.539
10.441
15.480
2.510
2.895
2.595
1.226
SPECIES CONCENTRATIONS - SITE:PACS2
SAMPLE DURATION 24 START HOUR
R SQUARE .73 PERCENT MASS
CHI SQUARE 44.78 DF
UATE:0124 78
0
106.8
SIZErCOARSE
SPECIES-I-M MEAS-
1 TOT
9 F
11 NA
12 MG
13 AL
14 SI
16 S
17 CL
19 K
20 CA
22 TI
23 V
24 CR
25 MN
26 FE
28 NI
29 CU
30 ZN
35 8R
82 PB
91 OC
92 EC
93 S04
94 N03
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
73
4
29
2
3
13
1
1
1
.30000+-
.03600+-
.97000+-
.85000+-
.80000+-
.00000+-
.56000+-
.33000+-
.54000+-
.00000+-
.40000+-
.02600+-
.02600+-
.08300+-
.50000+-
.02200+-
.052005
.11000+-
.22000+-
.62000+-
.10000+-
.70000+-
.70000+-
.60000+-
1.10000
.01700
.14000
.12000
.16000
.50000
.14000
.05000
.03000
.07000
.02000
.00200
.00200
.00400
.13200
.00300
.00400
.01000
.02000
.07000
4.30000
.90000
.50000
.30000
78.
*
1.
9
4.
12.
,
2.
*
1.
*
*
*
,
4.
.
CALC-
26896+-
12011+-
06045+-
73585+-
69 7 08+-
27399+-
66017+-
89758+-
32103+-
90081+-
42139+-
02191+-
01555+-
07500+-
91307+-
02331+-
.07101+-
.
.
.
13.
2.
1.
1.
04598+-
03764+-
14923+-
10001+-
63859+-
70000+-
60000+-
RATIO C/M RATIO R/U
9.61944
.64140
.10329
.09458
.62825
.94406
.22953
1.00184
.31140
.26835
.07564
.00296
.00720
.07681
.14060
.00407
.02638
.01553
.02928
.06299
7.24982
2.14457
.71868
1.61313
1.07+-
3.34+-17
1.09+-
.87+-
.98+-
.42+-
1.18+-
8.78+- 3
.59+-
.95+-
1.05+-
.84+-
.60+-
.90+-
1.40+-
1.06+-
1.37+- .
.42+-
.17+-
.24+-
1.00+-
1.55+- 1
1.00+-
1.00+- 1
.13
.89
.19
.17
.13
.03
.50
.31
.58
.14
.20
.13
.28
.93
.07
.23
52
.15
.13
.11
.64
.51
.52
.03
TOT
F
NA
MG
AL
SI
S
CL
K
CA
TI
V
CR
MN
FE
NI
CU
ZN
BR
PB
OC
EC
S04
N03
.51
.13
.52
-.75
-.16
-15.66
.37
2.56
-.70
-.36
.27
-1.14
-1.40
-.10
7.33
.26
.71
-3.46
-5.14
-5.00
.00
.40
.00
.00
8-20
-------
ENTER COMMAND
SSCONT
CALC SPECIES(PER SOURCE)
UHUlVlUUttU KAM 1VJ -
MEAS SPECIES(ALL SOURCES)
SPECtSOURCE
1 TOTAL
9 F
11 MA
12 MG
13 AL
14 SI
16 S
17 CL
19 K
20 CA
22 TI 1
23 \l
24 CR
25 MN
26 FE 1
28 NI
29 CU
30 ZN
35 BR
82 PB
91 OC
92 EC
93 S04
94 N03
3
.572
.093
.756
.760
.577
.405
.000
.000
.800
.629
.059
.435
.726
.505
.366
.076
.242
.419
.015
.250
.107
.382
.018
.005
5
.004
.004
.010
.000
.000
.000
.065
.000
.001
.002
.001
.36.1
.005
.002
.002
..665
.004
.010
.000
.000
.001
.005
.077
.001
6
.871
.000
.428
.000
.191
.020
.547
10.733
.709
.341
.000
.000
.000
.923
.035
.000
1.105
.000
.154
.000
2.874
1.314
.601
2.034
7
-.094
-.613
-.023
.000
-.006
-.001
-.197
-2.068
-.830
-.032
-.012
.000
-.032
-.039
-.001
.000
-.072
.000
-.014
.000
-.247
-.178
-.203
-.086
11
.046
3.895
.083
.106
.218
.000
.000
.121
.000
.014
.006
.051
.021
.000
.004
.319
.090
.003
.018
.000
.000
.031
.033
.000
13
-.003
-.019
-.007
.000
.000
.000
-.007
-.003
-.045
-.002
.000
-.002
-.004
-.486
-.001
.000
-.002
-.012
-.002
.000
-.002
-.002
-.006
-.008
15
-.022
-.024
-.152
.000
-.001
.000
-.324
-.003
-.041
-.002
.000
-.003
-.117
.000
.000
.000
-.1)01
-.002
.000
-.010
.000
.000
-.614
-.006
17
.025
.000
.000
.000
.000
.000
1.095
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
1.093
.uoo
18
-.021
.000
.000
.000
.000
.000
.000
.000
.000
.000
- .000
.000
.000
.000
.000
.000
.001)
.000
.000
.000
.000
.000
.000
-.940
19
-.310
.000
.000
.000
.000
.oon
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.QUO
.000
.000
-1.734
.000
.000
.000
B-21
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APPENDIX C
CMB Model Assumptions
C.I Constant Composition of Source Emissions
The chemical profile of particulate emissions must remain constant
during transport between source and receptor. There are two types of changes
which may occur. First, if the chemical composition of emitted particles
differs substantially with particle size, deposition (settling or removal)
of the larger particles could alter the source profile as perceived at the
receptor. For instance, a particular element might be much more prevalent
in the fine particles (< 2.5um) than in the coarse ones (> 2.Bum) because
of the nature of the source's operation. If the source profiles were avail-
able for the fine and coarse particles separately, there would be little
cause for concern; however, if only a "total" profile (fine and coarse
together) were available, deposition, which primarily, affects the coarse
particles, would effectively alter the profile between source and receptor.
Remedial actions could include re-measurement of the profile in the
separate size fractions, or deletion from the profile of species that are
affected by the selective deposition of large particles.
Second, gases that react and transform into particles during transport
between source and receptor are often not represented in the source profiles.
One such gas that requires careful consideration is $03, because of its
potential for conversion to sulfate. This is discussed further in
Section 3.2.1. It may be possible to construct a model that fits on both
particulate and gaseous sulfur (e.g., Chow, 1985, Sheff and Wadden, 1985).
C.2 Proper Source Identification and Characterization
Incorrect source identification takes one of three forms:
o Contributing source types are missing.
o Non-contributing source types have been included.
o Several sets of source profiles provide equally precise but
significantly different source composition estimates.
C.2.1 Missing Source Types
The most common source types are those of secondary compounds of
sulfate, nitrate, and organic carbon. These substances are emitted as
gases which later turn into particles which are measured at the receptor.
Most source profiles apply only to primary species. Several methods have
been proposed for dealing with secondary species, none of which are
completely satisfactory or proven.
C-l
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The most common, and easiest method, is the single constituent
source type proposed by Watson (1979). This source profile contains only
one entry for the constituent (i.e., sulfate, nitrate, or organic carbon)
which is the result of secondary aerosol formation. This "source" will
account for the secondary contributors to these species, but it cannot
identify the individual source types contributing the secondary components.
The sulfate, nitrate and organic carbon which is primary (i.e., emitted
as that species as opposed to being formed in the atmosphere) will be
accounted for by the source profile measured at the emission point. Tnese
individual contributors can be identified by using the PSCONT command.
Another .nethod, proposed by Chow (198b) and Scheff and Wadden (198b)
is the combination of gaseous and particulate compounds containing the
secondary species. Very few source profiles and ambient data which are
currently available contain adequate measurements of gaseous and particulate
phases, and this method would only be applicable in a Level III study (e.g.,
Blumenthal and Watson, 1986; Chow et al., 1986; Liu et al., 1986).
A final method for dealing with the missing secondary source types
involves modifying the source profiles by a fractionation coefficient cal-
culated froiM transport times and depositio-n and transformation rates.
These fractionation factors might also be determined from emissions-aging
experiments in enclosed environments such as smog chambers (Liu et al.,
1986). Research on such fractionation coefficients is in progress (e.g.,
Friedlander, 1981; Stafford and Liljestrand, 1984; Lewis and Stevens, 1985;
Chow, 1985) which might be applicable in certain situations. These
fractionation coefficients are unvalidated, however, and may add more
uncertainty than they eliminate.
C.2.2 Non (or Low) - Contributing Source Types
Low contributing sources generally do not affect the SCE for other
sources if their profiles are not similar to them. Therefore, they need
not be eliminated from the fit unless they are shown to be truly very minor
contributors (see 3.5.3.2) and their profiles are collinear with other sources,
C.2.3 Conflicting Results
In the process of applying the CMB to different sets of chemical
species and source types for a given receptor sample, it is common to find
more than one "fit" which possesses a low Chi-Square, has a nigh R-Square,
and which accounts for most of the chemical concentrations measured in the
receptor samples. This was demonstrated in an example by Watson (197y)
from which he concluded that "the receptor model tells what could be the
contributors, not necessarily what are the contributors." It is important
to try all suspected source types in the fit to help identify if this
situation exists. In such case, additional physical information is then
needed to determine which of them is likely to be true. This may be derived
from wind direction analysis, microscopic examination of the ambient sample,
operating schedules, dispersion modeling, etc.
C-2
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C.3 Linear Independence of Profiles
The source profiles must be linearly independent or as nearly so as
possible. Collinear, or chemically similar source profiles can interact
to introduce large uncertainties into the SCE. There is always some
similarity among source profiles, because there are a finite number of
elements or species that are readily measurable, and a much larger number
of sources. High source profile uncertainty can exacerbate collinearity
caused by similar profiles or can result in large standard errors.
As explained in Section 3.3.4, inherent uncertainty is a measure of
this collinearity and high uncertainty in source profiles and, thus, the
capability of the model to distinguish among the sources included in the
model run. The sources within each U/S cluster are those which are
largely responsible for the inherent uncertainty of the cluster through
their interaction with each other and the uncert,^ :ity associated with
their individual species (after Henry, 1982).
Inherent uncertainty is not a concept which the CMB user inust understand
in detail. The user must, however, appreciate that a high inherent uncer-
tainty is caused by groups of sources that have somewhat similar profiles
and/or by profile uncertainties which are sufficiently large such that the
model cannot distinguish among them with acceptable standard errors. This
ultimately results in higher standard errors for the SCE's. If source
profiles were known exactly (profile uncertainty equal to zero), the
model would tolerate a fairly high collinearity and still provide stable
and acceptable SCE's. However, source profiles generally are not known
exactly and this imprecision can both reduce the amount of collinearity the
model can tolerate and increase the standard error of the SCE's for the
sources in the uncertainty cluster.
There are two possible means to reduce the standard errors of their
SCE's, which are listed within U/S clusters. The first is to measure
additional species (at both the source and the receptor) which will allow
these sources to be differentiated from each othe-- by the CMB. The
second is to reduce the uncertainties in the source profiles in the cluster
by making more precise source profile measurements.
In order to identify the appropriate means to improve the source
contribution estimate (i.e., reduce uncertainty in the profile or measure
additional species to reduce collinearity) one must determine whether the
high inherent uncertainty of the cluster must be attributed to collinearity
or to source profile uncertainties.. A simple test is proposed in section
3.5.4.
C.4 Additional CMB Assumptions
In addition to the above four assumptions, tne number of source
categories must be less than the number of species included in the fit. Also,
measurement errors must be random, uncorrelated and normally distributed.
C-3
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TECHNICAL REPORT DATA
(Please read Instructions on the reverse before completing)
1. REPORT NO.
2.
3. RECIPIENT'S ACCESSION NO.
4. TITLE AND SUBTITLE
5. REPORT DATE
Protocol for Applying and Validating the CMB Model
May 1987
6. PERFORMING ORGANIZATION CODE
7. AUTHOR(S)
Thompson G. Pace and Dr. John G. Watson
8. PERFORMING ORGANIZATION REPORT NO.
9. PERFORMING ORGANIZATION NAME AND ADDRESS
10. PROGRAM ELEMENT NO.
Air Management Technology Branch Desert Research
Monitoring and Data Analysis Division Institute
U.S. Environmental Protection Agency Reno, NV 89506
Research Triangle Park, NC 27711
11. CONTRACT/GRANT NO
CX-813087-01-1
12. SPONSORING AGENCY NAME AND ADDRESS
U.S. Environmental Protection Agency
OAQPS, MDAD, MD-14
Research Triangle Park, NC 27711
13. TYPE OF REPORT AND PERIOD COVERED
14 SPONSORING AGENCY CODE
15. SUPPLEMENTARY NOTES
16. ABSTRACT
This protocol is intended to supplement the User's Manual for the CMB model by pro-
viding technical guidance on: (a) the selection of model input data, (b) determina-
tion of validity and uncertainty of a specific model application, and (c) reduction of
the uncertainty associated with the results of a specific application. The objective
of a CMB application is to use information about the chemical composition of sources
in an airshed (source profiles) along with data on the chemical composition of the
ambient air to estimate the source contributions which would best "explain" the chemica
properties of measured ambient data (species).
The guidance provided by this document consists of a seven-step process:
1. assessing the general applicability of the CMB model to the situation under study;
2. configuring the model with appropriate sources, source profiles, and chemical
species concentrations at receptor sites;
3. examining model statistics and diagnostics;
4. determining agreement with model assumptions;
5. identifying problems, changing the model configuration and rerunning;
6. testing the consistency and stability of model results; and
7. evaluating the validity of model results.
17.
KEY WORDS AND DOCUMENT ANALYSIS
DESCRIPTORS
b.IDENTIFIERS/OPEN ENDED TERMS
c. COSATI Field/Group
* Receptor Models
« Chemical Mass Balance
Source Apportionment
Least Squares
Multiple Linear Regression
18. DISTRIBUTION STATEMENT
19. SECURITY CLASS (This Report I
Unlimited
21. NO. OF PAGES
70
20. SECURITY CLASS (This page I
Unlimited
22. PRICE
EPA Form 2220-1 (R«v. 4-77) PREVIOUS EDITION is OBSOLETE
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