Environmental Protection Planning and Standards April 1988
EPA-450/4-88-005 Agency Research Triangle Park NC 27711
Air
Chemical Mass Balance
Receptor Model
Diagnostics
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EPA-450/4-88-00
April 1988
Chemical Mass Balance Receptor Model
Diagnostics
By
Dr. Ronald C. Henry
Mr. Bong Mann Kim
University of Southern California
Environmental Engineering Program
Civil Engineering Department
University Park
Los Angeles, CA 90089-0231
EPA Project Officer: Thompson G. Pace
U.S. ENVIRONMENTAL PROTECTION AGENCY
Office of Air and Radiation
Office of Air Quality Planning and Standards
Research Triangle Park, North Carolina 2771 1
U.S. Environmental Protection
Region 5, Library
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This report has been reviewed by the Office of Air Quality Planning and Standards, U.S. Environmental
Protection Agency, and approved for publication. Any mention of trade names or commercial products is not
intended to constitute endorsement or recommendation for use.
EPA 450/4-88-005
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Executive Summary
The purpose of this study is to develop, test, and recommend
means for identification of influential species in a Chemical
Mass Balance (CMB) model. Influential species are defined as
those which have a large effect on the estimated source
contributions or its errors. Knowledge of the influential species
aids the interpretation of CMB results and can suggest schemes to
improve a CMB model. The degree of influence of a species can be
defined in two ways. One way is to calculate the effects of
deleting it from the model; many standard regression diagnostics
are based on this approach. The other way uses diagnostics based
on a different approach: CMB estimates of source contributions
can be interpreted as a weighted sum of the species
concentrations at the receptors. Thus, the influence of each
species on a particular source is determined by the amount of
weight given to it by the CMB least squares fit. These new
measures are called nondeletion diagnostics to distinguish them
from the deletion diagnostics.
Extensive testing was carried out on two deletion and two
nondeletion diagnostics in order to build an experience base with
which to compare them. The testing used sets of artificial data
generated by two different source composition matrices. One set
had four sources and little multicollinearity, while the second
had eight sources and substantial collinearity. The measurement
error in the species was taken as 10%; the error in the source
matrix was 10, 30, or 50 %. Three simulation runs were carried
out for each level of error. The means and standard deviations of
the diagnostics were determined for each error scenario and
served as a convenient way to summarize the results of the
simulations. These results agreed with theoretical arguments
which showed that a single influence diagnostic based on a
modification of the pseudo-inverse matrix (MPIN) was the best
choice. Experience gained in the tests on simulated data showed
that the MPIN contains virtually all the information present in
both deletion and non-deletion diagnostics. The test results
support the following recommendations for interpretation of the
MPIN diagnostic. MPIN is normalized such that it takes on values
from minus one to one. Species with MPIN absolute values of 1 to
0.5 are associated with influential species. Noninfluential
species have MPIN absolute values of 0.3 or less. Species with
absolute values between 0.3 and 0.5 are ambiguous, but should
generally be considered noninfluential.
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Table of contents
1. Introduction 1
2. Theoretical background 2
2.1 Basic Approach 3
2.1.1 Deletion diagnostics 5
2.1.1.1 SDFBETA 6
2.1.1.2 SDFSBETA 7
2.1.2 Nondeletion diagnostics 7
2.1.2.1 SPINBETA 8
2.1.2.2 SPINSBETA 9
2.2 Modified PIN matrix (MPIN) 9
2.2.1 Comparisons of MPIN with other diagnostics . 10
3. Generation of simulated data sets 12
3.1 Background 12
3.2 Approach 13
3 .3 Procedure 19
4. Effective variance weighted least squares method .... 20
5. Results 21
6. Conclusions and recommendations 25
REFERENCES 26
APPENDIX
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1. Introduction
Receptor modeling is being used increasingly as a method
to identify the sources and to apportion ambient
concentrations of particulate pollutants and to determine the
best control strategies. These models estimate the source
impacts at a receptor site from the measurements of aerosol
properties made at the receptor or sampling site. Receptor
models and their application have been reviewed by Cooper and
Watson (1980), Gordon (1980), and Hopke (1985). Henry et al
(1984) has presented a review of receptor model fundamentals.
Usually.a least squares fitting approach is applied to
Chemical Mass Balance (CMB) models calculations of the source
contributions of particulates (Axetell and Watson, 1987; Pace
and Watson, 1987). Written in matrix form, the CMB equation
is,
C = AS, ( 1 )
where C is the nxl vector of ambient chemical species
concentrations, A is the nxp source composition matrix, and S
is the pxl vector of source contributions. When estimating
the contributions of sources whose chemical compositions are
similar, the least squares solution is mathematically
unstable, the so called collinearity problem. Henry (1982)
presented some rules that can be used to determine which
sources in a CMB model can be estimated to a given accuracy
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and which cannot be so estimated. The same, work also gives a
method that allows one to find estimable linear combinations
of sources which by themselves cannot be accurately
estimated.
In the previous year's work (Henry and Kim, 1986),
collinearity indicators were studied. Eigenvectors
corresponding to the smallest eigenvalues were found to be
the best indicators of the collinearity. Also, guidelines
were prepared for users on how to use eigenvectors to detect
the sources contributing to the collinearity. The objective
of the current project is to examine several regression
diagnostics to identify the influential fitting species and
provide the best diagnostic and a guideline for its use.
2. Theoretical background
There are several uses for diagnostic tests which
identify the most influential species in a CMB calculation. A
CMB result that is found to be very heavily dependent upon
species which have very uncertain source composition data
will obviously be more suspect than one which is known to
depend most heavily upon well known species. If possible,
steps should be taken to improve the source composition data
for the influential species. Perhaps additional source
sampling is needed, or reanalysis of existing source samples
by a more sensitive analytical technique.
The best application of these diagnostics is in a
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proactive manner by assembling and analyzing a tentative
source composition matrix before the study, thereby
determining where best to apply the available resources.
Perhaps additional sampling of one source to better
characterize an influential species is not necessary, but the
diagnostics may indicate another species in another source
for which it is vital to have improved source composition
information.
The diagnostics often confirm our intuition in
identifying tracer species as influential species. However,
because of the interactions among the sources in a least
squares fit, at times our intuition may be fooled and the CMB
source contribution estimate may depend crucially on some
minor species. These cases are not rare and can only be dealt
with properly by diagnostics of the type investigated in this
study.
2.1 Basic Approach
There are several established diagnostic tools for
identifying influential data points. Specifically, DFBETA,
DFBETAS, DFFIT, DFFITS, RSTUDENT, and COVRATIO have been most
commonly used as diagnostic tools. These are discussed in
detail by Belsley et al (1980) and have been applied to the
CMB model by DeCesar et al (1985;1986). All the above
diagnostics are single row deletion diagnostics. In other
words, they examine how the deletion of a single row
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(species) affects the estimated regression coefficients
(source contribution estimates), the predicted values
(species concentrations), the residuals or the estimated
covariance structure of the regression coefficients. A
species is judged to be influential by these diagnostics if
its removal from the CMB leads to a large relative change in
one of the aspects of the model listed above.
In addition to single row deletion diagnostics, several
nondeletion diagnostics were studied. These diagnostics give
the contribution of a species to the source contribution
estimate or its error variance in the full model without
deletion.
The original plan of this study was to introduce a
composite diagnostic tool which incorporates both modified
single row deletion diagnostics and nondeletion diagnostics
to give a reliable indicator of those species of special
importance to the CMB. Nondeletion diagnostics were developed
to supplement single row deletion diagnostics under the
assumption that species which are influential when deleted
from the model are not necessarily those species that have
the most influence on the full model results.
The remainder of this report takes the following form.
Two selected deletion diagnostics, with minor modifications
to increase their interpretability, are described. Next, two
nondeletion diagnostics based on the weighted pseudo-inverse
(PIN) matrix are introduced. These four diagnostics are then
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shown to be similar to a single diagnostic, the modified PI'N
matrix (MPIN).
The last sections of the report describe the Monte-
Carlo simulation studies carried out to test the new
diagnostic. Finally, specific numerical recommendations for
interpretation of the diagnostic are given.
2.1.1 Deletion diagnostics
The basis of this diagnostic technique is an analysis of
the response of various regression model outputs to
controlled perturbations of the model inputs. The deletion of
a single species from the CMB is usually taken as the
perturbation. In this study, changes in the source
contribution estimates (SCEs) and the estimated variance of
the SCEs in response to the perturbed regression model are
the basis for two new deletion diagnostics closely related to
the standard DFBETA diagnostic.
The first deletion diagnostic, SDFBETA, is the
fractional change in the SCE if a row (species) is deleted
from the CMB source composition matrix. The second
diagnostic, SDFSBETA, is the fractional change in the
variance of the SCE if a row is removed from the source
composition matrix. Because of their normalization, both
diagnostics are less than or equal to one in absolute value.
The closer the absolute value of the diagnostic is to one,
the more influential the species.
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2.1.1.1 SDFBETA
The change in the SCEs when the ith row is deleted is
expressed as DFBETA.
(A*A) -^i^i
DFBETAi = S - S(i) = , ( 2 )
1 - hi
where S(i) is the SCE estimated with the ith row deleted, a^
is a row vector of A, e^ is a ith residual and
ni = ai (ATA)-1aJ_T (note that the A in this equation is the
full matrix, including a-jj . DFBETA is usually normalized to
the standard deviation of the SCE to form DFBETAS (Belsley et
al, 1980). Experience gained in the previous year's work
showed DFBETAS is unstable to errors. In other words, keeping
all else constant, even modest random changes in the errors
lead to large changes in DFBETAS. For this reason, this study
adopted a different normalization. DFBETA is normalized to
the SCE itself,
DFBETA
S DFBETA i
-H
Sj -
With this normalization SDFBETA is more easily interpreted
than DFBETAS. However, SDFBETA is also unstable to errors,
like DFBETAS, even if little or no collinearity is present.
This instability is caused by the presence of the residual,
e^, in Eq.2. Table A2 - Table A7 in appendix demonstrates
this point. Therefore, SDFBETA is not recommended as a
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diagnostic tool.
2.1.1.2 SDFSBETA •
The change of the estimated variance of the SCE when the
ith row is deleted is also of interest to users. This change
is calculated in Silvey (1969) and normalized to the variance
of the SCEs to form SDFSBETA:
Var (Sj(i)) - Var (Sj)
SDFSBETAij
Var (Sj)
where
Var (S) = a2(ATA)~1 , and ( 5 )
.Var (S(i)) = a2(ATA - a-j^i11)-1 ( 6 )
(ATAJ-laiTaKATA)-!
= a2 ( (ATA) -1 + ) . ( 7 )
1 - ai(ATA)-laiT
Note that a in a properly defined CMB is 1.
2.1.2 Nondeletion diagnostics
The basis of the nondeletion diagnostic technique is an
analysis of the degree of influence of the species on the
predicted SCE and the variance of the SCE for the full model,
i.e., without any deleted species.
Henry (1985) presented a complete error analysis of the
CMB receptor model and showed the central role played by the
weighted pseudo-inverse (PIN) of the source composition
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matrix. Two diagnostic tools are developed based on the PIN.
The first diagnostic, SPINBETA, is the fraction of the
predicted SCE contributed by the given species as shown by
the PIN matrix. The second diagnostic is the fraction of the
variance in the SCE contributed by a given species as
indicated by the square of the PIN. Both diagnostics are
normalized to be less than or equal to one in absolute value.
As before, the closer the diagnostic is to one, the more
influential the species.
2.1.2.1 SPINBETA
The weighted pseudo-inverse matrix (PIN) of source
composition matrix is defined by
PA = (ATWA)
where A is the source composition matrix and W is matrix of
weights for CMB. The matrix product of the PIN matrix and
ambient .concentrations column vector, C, gives the estimated
SCEs,
Sj = | Pij Cif j = l,2,...,p ( 9 )
where p^j is the ij species of the PIN and C^ is the
concentration of the ith species. From this, it is clear that
the fraction of the predicted SCE for source j contributed by
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species i is,
SPINBETA-j
(10)
This defines the first nondeletion diagnostic.
2.1.2.2 SPINSBETA
It is also of interest to find the influential species
based on the variance of SCE. Henry (1985) derived the
equation for the variance of the SCEs using the PIN matrix..
The variance of the SCEs is the product of terms involving
the squared species of the PIN matrix and the effective
variances. Therefore, the contribution to the variance of the
SCE of each species for each source is given by the matrix
formed from the product of the squared species of the PIN
matrix and the effective variances. This matrix is normalized
to the variance of SCE to give the second nondeletion
diagnostics:
SPINSBETA^
p. .2
P13
Var (Sj)
(11)
2.2 Modified PIN matrix (MPIN)
In the previous section, four diagnostic tools were
developed including both deletion diagnostics and nondeletion
diagnostics. However, careful examination of the defining
equations shows that each of these four diagnostics is either
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exactly or approximately proportional to the modified PIN
matrix (MPIN) as defined by:
MPIN =
Note that the MPIN only differs from the PIN by a factor of
W1/2. This difference, however, is critical.
2.2.1 Comparisons of MPIN with other diagnostics
The equations for diagnostics are more easily compared
with the MPIN if the weighted matrix, W, is incorporated as a
factor of W1/2 in the source matrix and ambient data vector.
For example, equation 11 then becomes,
SPINSBETA-j
. .2
Var (Sj)
(13)
where P-H is the- MPIN. Therefore, the species of SPINSBETA
are exactly the squared species of MPIN. Similarly, there are
only slight differences, between the mathematical equations
for the three other diagnostics and MPIN. In SPINBETA, the
weighted C vector is the additional term to MPIN. In SDFBETA,
standardized residual [e-;/(l-h^) ] is the extra part to MPIN.
Finally, the inverse of variance of the residual [l/(l-h-[)]
in SDFSBETA is the only extra term to MPIN.
Table A2 - Table A7 in appendix compares the four
diagnostics and the MPIN diagnostic. Each diagnostic is
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normalized to the largest value for each source. All
diagnostics, therefore, are always less than or equal to one
and closer it is to one, the greater the influence of that
species on a given source.
As shown in Table A2 - Table A7, SDFBETA is unstable to
errors even if little or no collinearity between source
profiles is present. This instability is caused by the extra
residual part in SDFBETA. Therefore, SDFBETA is not
recommended as a diagnostic tool.
SPINBETA gives almost the same information as MPIN does
because the only different term in SPINBETA, ambient data
vector C, is weighted. As explained before, the species of
SPINSBETA is exactly the square of the species of MPIN.
However, as can be seen in Table A2 - Table A7, SPINSBETA and
MPIN do not always give exactly the same number because they
are normalized to the largest value for each source.
Experience has shown that the extra term to MPIN in
SDFSBETA, variance of the residual, does not provide extra
information. As a result, SPINBETA, SPINSBETA and SDFSBETA
are redundant in the sense that they provide little
additional information and require much extra computation
time. Therefore, this study simply adopted MPIN as a new
diagnostic tool for detecting influential species for CMB
receptor model.
Since the MPIN represents the above three diagnostics
inherently, influential species detected by MPIN are
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important species in terms of deletion and nondeletion
diagnostics. MPIN is especially well suited to the CMB
receptor model because it does not require extra calculation
time, but can be obtained automatically during the SCE
calculation.
A series of Monte Carlo simulations were performed to
verify the above results and to determine a suitable cut-off
value for MPIN at which a species is considered to be
influential. The simulations are described below, followed by
final conclusions and specific recommendations on the
interpretation of MPIN.
3. Generation of simulated data sets
The purpose of the simulated data sets is to produce an
experience base of results for known levels of error in the
model. Although the simulation runs are called Monte Carlo
simulations, their results are not intended to estimate any
parameter with any accuracy. Thus, the results are to be
evaluated in a qualitative and comparative fashion.
3.1 Background
Simulated data were generated as the same way as the
previous study using the matrix equation,
C = ( A + eA ) S° + ec (14)
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where C is the vector of . ambient chemical species
concentrations, A is the matrix of source compositions, and
S° is the vector of the true SCE. Lognormal random errors
(e^) were introduced to the source matrix and normally
distributed measurement errors (e^) were introduced to the
ambient concentrations.
The source compositions were taken from the Portland
Aerosol Characterization Study (PACS). Two groups of sources
were used for this study, PACS 1 and PACS 3. As shown in
Table 1 and 2, the sources in PACS 1 are Marine, Urban
dust(Udust), Auto, Residual oil (Rdoil), Kraft, Aluminum
production (Alpro), Steel, and Ferromanganese (FeMn). The
PACS 3 set consists of Marine, Urban dust (Udust) , Auto and
Residual oil (Rdoil) sources. Each source vector has 21
species with concentrations representative of fine particle
aerosol. PACS 1 and PACS 3 source composition matrices are
presented in Table 1 and Table 2 respectively. Typical values
assumed for true SCE are given in Table 3.
3.2 Approach
Three sets of source composition matrix were created
from the original composition matrix with uncertainties of
10%, 30%, and 50%. Similarly, three corresponding ambient
data sets were produced with uncertainties of 10%. This means
that the standard deviation of the errors was taken to be 10%
of the mean value of the chemical species concentrations, C^.
Page 13
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Table 2. Fractional Fine Particle Compositions
of Four Source Types* (PACS 3)
SPECIES
oc
EC
NO 3
S04
Na
Mg
Al
Si
Cl
K
Ca
Ti
V
Cr
Mn
Fe
Ni
Cu
Zn
Br
Pb
MARINE
0.000000
0.000000
0.000000
0.100000
0.400000
0.048000
0.000000
0.000000
0.400000
0.014000
0.014000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.002000
0.000000
UDUST
0.118000
0.018500
0.000000
0.004200
0.012500
0.013000
0.088400
0.223000
0.000000
0.010300
0.024400
0.006400
0.000230
0.000450
0.001230
0.060000
0.000093
0.000300
0.001100
0.000200
0.003700
AUTO
0.500000
0.038000
0.009100
0.013000
0.000000
0.000000
0.011000
0.008200
0^030000
0.000720
0.012500
0.000000
0.000000
0.000000
0.000000
0.021000
0.000180
0.000730
0.003500
0.050000
0.200000
RDOIL
0.070000
0.031000
0.006500
0.481000
0.035000
0.000000
0.005300
0.009600
0.000000
0.002800
0.015800
0.001100
0.034400
0.000470
0.000460
0.029700
0.053600
0.000750
0.004000
0.000130
0.001100
Page 15
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Table 3. Source Contributions Chosen as the True Value
PACS 1 MARINE = 2
UDUST =35
AUTO =10
RDOIL = 5
KRAFT = 5
ALPRO = 5
STEEL =10
FeMn = 5
PACS 3 MARINE = 2
UDUST =35
AUTO =10
RDOIL = 5
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Unlike the normal distribution, the lognormal distribution,
used to generate errors in the source matrix, is skew
symmetric and the meaning of 10%, 30%, and 50% error is not
obvious. If gm is the geometric mean and ag is the geometric
standard deviation, then an uncertainty (or error) of e% is
defined by the equation,
) x 100 = e% (15)
9m
With this definition, an error of 50% implies that the 2
sigma point of the error of the error distribution is 50%
above the mean.
The geometric standard deviation,
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Page 18
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sufficient for this purpose. As a practical matter, carrying
out 400 repetitions, say, would have made it impossible to
test as many different cases as we did.
3.3 Procedure
The simulated data sets are created as follows.
In the following, the superscript ° denotes the "true"
or unperturbed value.
1). Simulate the errors in source matrix using random numbers
drawn from a lognormal distribution of geometric mean
and geometric standard deviation aa = J 1 + e/100 .
where e refers to the percent errors in source matrix as
defined in equation 15.
2). Generate true concentrations using a model which
represents the situation under study using,
ci° = * aij°sj° / i = 1, ,N (17)
3). Simulate the measurement process to obtain measured
value of C^ using random numbers drawn from a normal
distribution of mean 0 and standard deviation of 0.1Cj_°:
Ci = Ci° + ec (18)
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4). Obtain weights to be used in the effective variance
weighted least squares method.
wi2 = °ci + * fflij sj2
where CTC^ = O.IC^0 and
-------
5. Results
For each data set, results are summarized in the
Appendices. The following observations can be made from the
results.
Tables 5 and 6 are examples of the analysis applied to
the results in the Appendices. Table 5 gives the influential
species as determined by the five diagnostics under
consideration for the data set 3 simulations, i.e., eight
sources, large collinearity, 50% error in the source matrix
and 10% error in the observations. The Table also gives the
coefficient of variation of the diagnostics, this is a good,
rough measure of the stability of the diagnostic to errors.
SDFBETA is seen by this measure to be rather unstable, while
the other measures are quite stabile. Comparison of the
influential elements according to the various diagnostics
shows a comfortingly high degree of agreement between them.
Only SDFBETA has consistently different results, and this is
undoubtedly caused by its instability.
Table 6 is the same as Table 5 but for simulation set 6,
i.e., four sources, little collinearity, 50% error in the
source matrix and 10% error in the measurements. The results
as shown in this Table are the same as in Table 5. As a
whole, the results in the Appendices also give the same
results as enumerated below.
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Table 5'. Influential elements and their coefficient of
variation by different diagnostics for data
set 3.
MARINE
UDUST
AUTO
RDOIL
KRAFT
ALPRO
STEEL
FeMn
SDFBETA
Cl (.000)*
OC (.360)
N03(.592)
Br (.087)
OC (.395)
V (.309)
Ni (.988)
S04(.000)
Al (.000)
Cr (.751)
N03(.000)
SDFSBETA
Cl (.000)
Si (.007)
Ti (.086)
Br (.000)
Pb (.065)
V (.000)
Ni (.167)
S04(.000)
Al (.000)
Cr (.000)
N03(.000)
SPINBETA
Cl (.000)
Ti (.002)
Si (.050)
Pb (.027)
Br (.123)
Ni (.000)
V (.047)
S04(.000)
Al (.000)
Cr (.182)
. NO3(.000)
SPINS BETA
Cl (.000)
Si (.004)
Ti (.060)
Br (.000)
Pb (.038)
V (.000)
Ni (.088)
S04(.000)
Al (.000)
Cr (.000)
N03(.000)
NMPIN
Cl (.000)
Si (.002)
Ti (.030)
Br (.000)
Pb (.019)
V (.000)
Ni (.045)
S04( .000)
Al (.000)
Cr (.000)
N03(.000)
* coefficient of variation = standard deviation/mean of three
simulation runs
Page 22
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Table 6. Influential elements and their coefficient of
variation by different diagnostics for data
set 6.
SDFBETA
SDFSBETA
SPINBETA
SPINSBETA
NMPIN
MARINE
UDUST
AUTO
RDOIL
Cl (
Na (
Mn (
Cr (
Mg (
Br (
N03(
Pb (
Ni (
V (
.000)*
.404)
.454)
.176)
.584)
.108)
.648)
.709)
.000)
.643)
Cl i
Na i
Si i
Ti i
Al i
Br i
Pb i
N03I
Ni I
V •(
(.000)
(.102)
(.003)
(.056)
(.036)
(.095)
(.187)
(.151)
(.000)
(.131)
Na
Cl
Cr
K
Ti
Pb
N03
Br
V
S04
(
(
(
(
(
(
(
(
(
(
.000)
.027)
.215)
.032)
.104)
.063)
.236)
.224)
.009)
.028)
Cl
Na
Si
Ti
Al
Br
Pb
N03
Ni
V
(
(
(
(
(
(
(
(
(
(
.000)
.057)
.002)
.050)
.032)
.070)
.139)
.131)
.000)
.086)
Cl
Na
Si
Ti i
Al i
Br i
Pb i
N03i
Ni i
V i
( .000)
(.029)
( .001)
(.025)
(.017)
(.035)
(..068)
(.066)
(.000)
(.042)
* coefficient of variation = standard deviation/mean of three
simulation runs
Page 23
-------
1) As was expected, SDFBETA is unstable to errors (Table A2-
Table A7). Therefore, SDFBETA is not recommended as a
diagnostic tool.
2) SDFSBETA, SPINBETA, and SPINSBETA give almost the same
information as MPIN does (Table A2 - Table A7).
Therefore, MPIN can be used as a new diagnostic tool
representing above three diagnostics implicitly.
3) Influential species detected by MPIN are, therefore,
important species in determining SCE and their variances
in CMB receptor model.
4) In general, influential species are not specific to
certain type of sources but are dependent on the
mix of sources chosen in the CMB.
5) Number of influential species for certain type of source
is often only one or two, but sometimes can be more than
this.
6) When there are several influential species, deletion of
some (but not all) of these species may not drastically
affect the SCE or their variance. However, deletion of all
of the influential species detected has drastic effects on
the SCE and its variance (Table A8).
7) As was expected, deletion of some or all the
noninfluential species identified by MPIN has little
affect on the SCE and their variances (Table A8).
Page 24
-------
6. Conclusions and recommendations
A new diagnostic tool, MPIN, was developed and tested
for its ability to detect influential species for CMB
applications. The MPIN diagnostic gives the relative
importance of the species for each source both in determining
the SCE and their variances. Unfortunately, there, can be no
universal rule for cutoff value to detect which species are
influential and which species are not. The definition of
"influential" is somewhat arbitrary and subjective and
dependent on the specific application. The following
guidelines for use of the MPIN diagnostic are based on
experience gained in this project and are recommended as
guidelines for interpreting the normalized MPIN.
1) Species having normalized MPIN number of greater than 0.5
are considered to be influential,
2) Species having normalized MPIN number of between 0.3 and
0.5 are considered to be intermediate, and
3) Species having normalized MPIN number of less than 0.3
are considered to be noninfluential.
Page 25
-------
REFERENCES
Axetell K., Watson J.G., and Pace T.G., 1987, "Receptor model
technical series volume III (revised): CMB user's manual
(version 6.0)", EPA-450/4-83-014R.
Belsley D. A., Kuh E., and Welsch R. E., 1980, "Regression
diagnostics: Identifying influential data and sources of
collinearity," John Wiley & Sons, New York.
Cooper J.A. and Watson J.G., 1980, "Receptor oriented methods
of air particulate source apportionment," J. Air Pollut.
Control Ass.. 30. 1116-1125.
DeCesar R.T., Edgerton S.A., Khalil M.A.K., and Rasmussen
R.A., 1985, "Sensitivity analysis of mass balance receptor
modeling: Methychloride as an indicator of wood smoke,"
Chemosphere. 14. 1495.
DeCesar R.T., Edgerton S.A., Khalil M.A.K., and Rasmussen
R.A., 1986, "A tool for designing receptor model studies to
apportion source impacts with specified precisions," in
Receptor methods: Real world issues and applications, Air
Pollution Control Association, Pittsburgh, PA.
Gordon G. E. , 1980, "Receptor Models," Envir.. Sci.. Tech..
14, 792-800.
Henry R. C., 1982, "Stability analysis of receptor models
that use least squares fitting," in Receptor Models Applied
to Contemporary Air Pollution Problems, Air Pollution Control
Association, Pittsburg, PA.
Henry R. C., Lewis C. W., Hopke P. K., and Williamson H. J.,
1984, "Review of receptor model fundamentals," Atmos.,
Environ.. 18. 1507-1515.
Henry R. C., 1985, "The effects of errors and bias on
chemical mass balance receptor models as shown by the
pseudoinverse matrix," Presented at the 78th Annual Meeting
of the Air Pollution Control Association, Detroit, Michigan.
Henry R.C., and Kim B. , 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 & Sons, New York.
Page 26
-------
Pace T.G., and Watson J.G., 1987, "Protocol for applying and
validating the CMB model," EPA-450/4-87-010, Research
Triangle Park, NC.
Silvey S. D. , 1969, "Multicollinearity and imprecise
estimation," J. Royal Statist. Soc.. Series B, 31. 539-552.
Page 27
-------
Appendix
Results of each data set are summarized in Tables as
shown below:
PACS I
PACS 1
PACS 3
PACS 3
Set
Set
Set
Set
Set
Set
Set
Set
3*
1
2
3
4
5
6
6
Table
Table
Table
Table
Table
Table
Table
Table
Al
A2
A3
A4
A5
A6
A7
AS
: Listing of whole output
•
*
: Comparisons of MPIN
: other diagnostics
•
•
: Comparisons of MPIN
: other diagnostics
Effects of deletion
: influential and
with
with
of
noninfluential elements
* Characteristics of data set is given in Table 4.
In Table Al - Table A7, NMPIN is the normalized MPIN. MEAN-
and STD- represent the mean and standard deviation of three
simulation runs. For example, MEANNMPIN is the mean value of
NMPIN for three runs.
A - 1
-------
Table Al. Complete listing of three simulation runs
for data set 3
EIGENVALUES
2.564 2.084 1.213 ' .680 .562 .194 .129 ".036
INVERSE SINGULAR VALUE
.625 .693 .908 1.213 1.334 2.273 2.779 5.238
EIGENVECTORS
MARINE .701 ~.669 '.168 ~.050 ".054 ~.164 ~.019 .020
UDUST .041 .005 .072 .065 .107 .077 .454 .875
AUTO .106 -.010 .246 .951 ".127 .003 ~.081 ".039
RDOIL .618 .741 ".207 ".019 ".087 ~.135 ~.005 .010
KRAFT .205 '.004 -.007 ~.044 ".023 .953 . ".217 .026
ALPRO .091 ".008 .045 .038 .055 .190 .850 ~.476
STEEL -182 .043 .342 ".001 .908 ".042 ".129 -.077
FeMn .176 .033 .863 ".293 ".367 ".057 ".015 .000
VARIANCE AND COVARIANCE MATRIX
MARINE .591 .330 ".070 .090 ".695 -.533 ".087 .025
UDUST .330 22.645 "1.128 .155 .229 '8.342 "2.114 '.124
AUTO -.070 "1.128 1.505 '.036 .073 .027 .032 '.136
RDOIL .090 .155 '.036 .560 '.597 -.302 ".127 .013
KRAFT ".695 .229 .073 ".597 5.091 ".821 ".068 ".214
ALPRO ".533 "8.342 .027 ".302 ".821 11.993 .219 ".163
STEEL '.087 "2.114 .032 ".127 ".068 .219 1.875 ".308
FeMn .025 ".124 ".136 .013 '.214 '.163 -.308 1.011
STANDARD ERROR OF REGRESSION COEFFICIENT
MARINE UDUST AUTO RDOIL KRAFT ALPRO STEEL FeMn
.768 4..7S9 1.227 .748 2.256 3.463 1.369 1.005
SOURCE STRENGTH
MARINE UDUST AUTO RDOIL KRAFT ALPRO STEEL FeMn
3.426 33.570 7.899 4.188 6.419 8.211 10.277 5.530
A -
-------
Table Al. Continued
SDFBETA
MARINE UDUST AUTO RDOIL KRAFT ALPRO STEEL FeMn
OC .015 .898 1.000 .016 .014 .176 .230 .000
EC .025 .438 .260 .044 .026 .161 .169 .011
N03 .017 .730 .277 .070 .137 .349 .432 1.000
S04 .356 .176 .063 .050 1.000 .027 .130 .077
Na .431 .169 .265 .120 .343 .079 .195 .007
Mg .048 .252 .205 .104 .055 .567 .707 .139
Al .109 .174 .158 .074 .062 1.000 .130 .041
Si .006 .295 .047 .003 .001 .069 .040 .003
Cl 1.000 .154 .195 .099 .317 .130 .008 .006
K .016 1.000 .421 .046 .113 .318 .356 .645
Ca .024 .616 .052 .013 .018 .167 .163 .021
Ti .007 .375 .065 .006 .001 .084 .047 .003
V .125 .118 .148 1.000 .322 .087 .193 .014
Cr .080 .508 .014 .105 .096 .016 1.000 .126
Mn .010 .386 .157 .032 .045 .025 .403 .397
Fe .006 .142 .021 .009 .003 .057 .183 .026
Ni .030 .173 .039 .414 .119 .034 .096 .022
Cu .074 .352 .264 .030 .006 .188 .790 .093
Zn .042 .165 .342 .019 .008 .138 .921 .052
Br .017 .189 .855 .014 .014 .004 .003 .024
Pb .004 .032 .199 .002 .002 .003 .004 .007
SDFSBETA
MARINE UDUST AUTO RDOIL KRAFT ALPRO STEEL FeMn
OC .000 .152 .185 .000 .000 .005 .053 .000
EC .001 .086 .030 .005 .001 .010 .068 .000
N03 .000 .064 .009 .003 .005 .013 .119 1.000
S04 .178 .014 .002 .006 1.000 .000 .040 .022
Na .075 .004 .009 .010 .034 .001 .025 .000
Mg .001 .008 .005 ,.008 .001 .036 .338 .020
Al .043 .034 .028 .034 .010. 1.000 .101 .016
Si .001 1.000 .025 .001 .000 .049 .097 .001
Cl 1.000 .007 .012 .017 .072 .005 .000 .000
K .000 .123 .021 .001 .004 .011 .083 .425
Ca .001 .180 .001 .000 .000 .012 .067 .002
Ti .001 .904 .026 .001 .000 .040 .077 .001
V . .009 .003 .004 1.000 .043 .001 .036 .000
Cr .004 .048 .000 .012 .004 .000 1.000 .025
Mn .000 .041 .007 .002 .001 .000 .241 .365
Fe .000 .042 .001 .001 .000 .006 .368 .011
Ni .002 .016 .001 .522 .018 .001 .027 .002
CU .003 .019 .011 .001 .000 .005 .508 .011
Zn .000 .002 .007 .000 .000 .001 .286 .001
Br .001 .050 1.000 .002 .001 .000 .000 .007
Pb .001 .022 .808 .001 .000 .000 .002 .010
-------
Table Al. Continued
SPINBETA
MARINE UDUST AUTO RDOIL KRAFT ALPRO STEEL FeMn
OC -019 .473 .611 .025 .016 .124 .224 .001
EC -064 .482 .332 .137 .062 .237 .344 .031
NO-s -016 .286 .126 .078 .115 .182 .314 1.000
SQ .394 .082 .034 .067 1.000 .017 .113 .093
Na -564 .093 .171 .190 .406 .059 .200 .010
Mg .056 .123 .117 .145 .058 .370 .642 .173
Al -194 .131 .138 .158 .099 1.000 .180 .079
Si .047 .993 .184 .032 .010 .311 .249 .022
Cl 1.000 .065 .096 .120 .287 .073 .006 .006
K .015 .397 .194 .052 .096 .168 .263 .654
Ca «061 .674 .066 .041 .042 .243 .330 .059
Ti .046 1.000 .201 .043 .004 .299 .234 .023
V .091 .037 .053 .883 .213 .036 .111 .011
Cr -072 .195 .006 .115 .079 .008 .714 .124
-014 .232 .109 .055 .058 .020 .449 .608
.026 .270 .047 .051 .013 .145 .645 .124
Ni .060 .147 .038 1.000 .215 .039 .151 .048
Cu «119 -240 .209 .058 .008 .171 1.000 .162
Zn -043 .072 .172 .024 .008 .080 .741 .058
Br -041 .190 1.000 .041 .031 .005 .005 .061
Pb .041 .139 .988 .030 .014 .017 .035 .082
SPINSBETA
MARINE UDUST AUTO RDOIL KRAFT ALPRO STEEL FeMn
OC .000 .181 .253 .000 .000 .018 .058 .000
EC .003 .108 .043 .009 .003 .038 .079 .001
N03 .000 .049 .008 .004 .015 .029 .084 1.000
S04 .123 .004 .001 .002 1.000 .000 .010 .008
Na .181 .003 .009 .014 .118 .002 .021 .000
Mg .003 .009 .007 .013 .004 .123 .364 .031
Al .039 .012 .011 .017 .013 1.000 .032 .007
Si .003 1.000 .029 .001 .000 .142 .090 .001
Cl 1.000 .003 .005 .010 .104 .005 .000 .000
K .000 .125 .025 .002 .014 .033 .078 .571
Ca .003 .233 .002 .001 .002 .044 .080 .003
Ti .003 .933 .031 .002 .000 .121 .073 .001
V .016 .002 .003 1.000 .110 .002 .022 .000
Cr .011 .052 .000 .019 .016 .000 1.000 .035
Mn .000 .041 .008 .002 .005 .000 .222 .478
Fe .001 .052 .001 .002 .000 .022 .424 .018
Ni .004 .015 .001 .689 .060 .001 .022 .003
Cu .009 .023 .015 .001 .000 .017 .580 .018
Zn .001 .002 .011 .000 .000 .004 .351 .003
Br .003 .043 1.000 .002 .002 .000 .000 .007
Pb .003 .021 .880 .001 .000 .000 .002 .012
A - 4
-------
Table Al. Continued
NMPIN
. MARINE UDUST
AUTO RDOIL KRAFT ALPRO STEEL
FeMn
oc
EC
NO 3
S04
Na
Mg
Al
Si
Cl
K
Ca
Ti
V
Cr
Mn
Fe
Ni
Cu
Zn
Br
Pb
.021
.054
.015
.351
.425
.054
.198
.059
1.000
.017
.054
.054
.127
.104
.015
.027
.060
.094
.036
.055
.053
.425
.328
.220
.059
.057
.097
.108
1.000
.053
.354
.483
.966
.041
.228
.203
.228
.121
.153
.048
.208
.144
.503
.207
.089
.023
.095
.084
.104
.170
.071
.158
.043
.177
.054
.007
.087
.036
.029
.122
.105
1.000
.938
.022
.094
.061
.049
.117
.115
.13.2
.032
.098
.047
.030
.042
1.000
.136
.049
.043
.830
.037
.016
.046
.032
.020
.059
.123
1.000
.344
.063
.114
.014
.322
.118
.042
.006
.332
.128
.071
.016
.246
.007
.007
.047
.020
.134
.194
.169
.015
.043
.350
1.000
.377
.072
.181
.210
.348
.049
.012
.022
.148
.039
.131
.064
.007
.021
.242
.281
.290
.098
.147
.604
.179
.300
.006
.280
.283
.271
.149
1.000
.471
.651
.149
.761
.593
.007
.044
.001
.028
1.000
.087
.008
.177
.085
.029
.007
.755
.055
.029
.016
.187
.692
.135
.052
.133
.050
.087
.110
A - 5
-------
Table Al. Continued
EIGENVALUES
3.248 1.543 1.141 - .587 .531 .188 .136 .029
INVERSE SINGULAR VALUE
.555 .805 .936 1.305 1.373 2.309 2.714 5.869
EIGENVECTORS
MARINE .957 ~.241 ~.003 ~.055 ~.016 ".153 ".009 .018
UDUST .026 .058 .033 .121 .021 .105 .393 .902
AUTO .076 .143 .136 .334 .912 .029 ".094 ~.044
RDOIL .132 .714 ".629 ".129 .029 ".245 .021 .009
KRAFT .179 .162 ".133 ".069 ".052 .915 ".280 .015
ALPRO .078 .070 .009 .063 .019 .250 .863 ".421
STEEL .107 .285 .166 .837 ".399 ".040 ".113 ".077
FeMn .108 .545 .735 ".381 ".065 ".049 ".017 .001
VARIANCE AND COVARIANCE MATRIX
.025
".083
".184
".007
~. 175
-.201
-.261
.939
STANDARD ERROR OF REGRESSION COEFFICIENT
MARINE UDUST AUTO RDOIL KRAFT ALPRO STEEL FeMn
.679 5.410 1.388 1.019 2.260 3.455 1.371 .969
SOURCE STRENGTH
MARINE UDUST AUTO RDOIL KRAFT ALPRO STEEL FeMn
2.540 39.583 9.261 6.060 3.085 2.689 10.185 5.209
MARINE
UDUST
AUTO
RDOIL
KRAFT
ALPRO
STEEL
FeMn
.461
.420
".104
.145
-.685
-.511
".085
.025
.420
29.270
"1.521
.188
.152
"10.432
"2.561
".083
".104
"1.521
1.927
".096
.187
.162
.029
".184
.145
.188
".096
1.039
"1.068
".309
".150
".007
".685
.152
.187
"1.068
5.108
".770
".044
-.175
-.511
"10.432
.162
".309
-.770
11.939
.434
-.201
-.085
"2.561
.029
".150
-.044
.434
1.879
".261
A - 6
-------
Table Al. Continued
SDFBETA
oc
EC
NO 3
S04
Na
Mg
Al
Si
Cl
K
Ca
Ti
V
Cr
Mn
Fe
Ni
Cu
Zn
Br
Pb
MARINE
.031
.014
.009
.403
.225
.000
.082
.010
1.000
.004
.026
.043
.033
.005
.003
.013
.046
.008
.003
.063
.027
UDUST
1.000
.236
.234
.154
.076
.001
.063
.226
.115
.212
.365
.952
.011
.017
.057
.349
.066
.021
.007
.266
.088
AUTO
.964
.119
.079
.071
.088
.001
.049
.033
.115
.077
.033
.150
.022
.000
.025
.053
.032
.015
.017
1.000
.444
RDOIL
.051
.154
.119
.333
.304
.003
.114
.010
.390
.072
.059
.071
.547
.017
.028
.065
1.000
.001
.014
.153
.055
KRAFT
.036
.032
.075
1.000
.248
.001
.047
.001
.371
.040
.021
.002
.084
.006
.010
.009
.145
.000
.002
.053
.016
ALPRO
.581
.126
.261
.027
.064
.008
1.000
.146
.160
.178
.261
.596
.020
.002
.005
.331
.034
.028
.017
.053
.001
STEEL
.748
.240
.302
.201
.191
.013
.134
.096
.058
.177
.197
.383
.053
.093
.181
1.000
.084
.132
.140
.009
.024
FeMn
.063
.002
1.000
.166
.016
.003
.072
.004
.023
.389
.031
.019
.003
.012
.197
.154
.037
.018
.010
.146
.079
SDFSBETA
MARINE UDUST AUTO RDOIL KRAFT ALPRO STEEL FeMn
.054 .000
.057 .000
.098 1.000
.023 .015
.026 .000
.299 .013
.081 .022
.097 .000
.002 .000
.069 .309
.031 .001
.073 .000
.020 .000
1.000 .016
.196 .215
.278 .006
.010 .002
.397 .007
.318 .001
.000 .008
.001 .011
A - 7
OC
EC
NO 3
S04
Na
Mg
Al
Si
Cl
K
Ca
Ti
V
Cr
Mn
Fe
Ni
Cu
Zn
Br
Pb
.000
.000
.000
.166
.063
.000
.054
.002
1.000
.000
.001
.002
.014
.005
.000
.000
.005
.002
.000
.003
.002
.179
.103
.109
.025
.008
.006
.033
1.000
.014
.183
.201
.843
.002
.065
.035
.063
.011
.018
.002
.052
.027
.224
.035
.017
.007
.014
.006
.026
.029
.019
.032
.002
.028
.009
.000
.009
.002
.004
.013
.011
1.000
.919
.000
.011
.007
.030
.030
.006
.027
.001
.040
.005
.001
.001
1.000
.016
.002
.001
.661
.000
.002
.004
.003
.000
.002
.011
1.000
.076
.001
.017
.000
.135
.006
.001
.000
.087
.007
.001
.000
.052
.000
.000
.002
.001
.007
.004
.016
.000
.001
.029
1.000
.050
.003
.016
.012
.040
.001
.000
.000
.007
.000
.004
.001
.000
.000
-------
Table Al. Continued
SPINBETA '
MARINE UDUST AUTO RDOIL KRAFT ALPRO STEEL FeMn
OC .021 .448 .513 .014 .024 .162 .246 .023
EC .046 .487 .291 .194 .098 .162 .364 .003
N03 .017 .293 .118 .091 .139 .203 .278 1.000
SO4 -417 .104 .057 .138 1.000 .011 .100 .090
Na .481 .107 .146 .260 .513 .056 .197 .017
Mg .033 .107 .111 .131 .068 .420 .753 .179
Al .202 .101 .093 .112 .112 1.000 .158 .093
Si .064 .914 .159 .026 .006 .368 .285 .014
Cl 1.000 .075 .090 .156 .359 .065 .028 .012
K .016 .543 .234 .113 .151 .285 .334 .796
Ca .073 .660 .071 .065 .056 .294 .262 .045
Ti .070 1.000 .188 .046 .003 .390 .296 .016
V .145 .030 .074 .953 ..352 .036 .111 .007
Cr .111 .256 .007 .156 .127 .015 1.000 .144
Mn .016 .219 .115 .066 .055 .011 .515 .607
Fe .017 .293 .053 .033 .011 .173 .617 .103
Ni .116 .108 .062 1.000 .35.0 .035 .101 .049
Cu .111 .197 .171 .004 .006 .168 .924 .137
Zn .046 .060 .168 .074 .029 .092 .878 .067
Br .081 .223 1.000 .079 .066 .028 .005 .098
Pb .074 .15.9 .951 .060 .042 .002 .031 .114
SPINSBETA
MARINE UDUST AUTO RDOIL KRAFT ALPRO STEEL FeMn
OC .001 .205 .287 .000 .001 .028 .061 .001
EC .001 .127 .048 .019 .007 .015 .070 .000
N03 .000 .069 .012 .006 .022 .035 .061 1.000
S04 .141 .008 .002 .012 1.000 .000 .007 .007
Na .145 .006 .012 ,.034 .203 .002 .021 .000
Mg .001 .007 .008 .010 .004 .113 .339 .024
Al .044 .010 .009 .011 .017 1.000 .023 .010
Si .006 1.000 .032 .001 .000 .171 .096 .000
Cl 1.000 .005 .007 .020 .159 .004 .001 .000
K .000 .182 .036 .007 .020 .053 .068 .486
Ca .004 .257 .003 .002 .003 .054 .040 .002
Ti .005 .888 .033 .002 .000 .143 .076 .000
V .029 .001 .007 1.000 .210 .002 .014 .000
Cr .014 .066 .000 .023 .023 .000 1.000 .026
Mn .000 .037 .011 .003 .003 .000 .203 .357
Fe .000 .076 .003 .001 .000 .028 .333 .012
Ni .013 .010 .003 .786 .148 .001 .008 .003
CU .008 .022 .018 .000 .000 .017 .480 .013
Zn .001 .002 .016 .003 .001 .005 .391 .003
Br .007 .047 1.000 .005 .006 .001 .000 .011
pb .006 .025 .949 .003 .002 .000 .001 .016
A - S
-------
Table Al. Continued
NMPIN
oc
EC
NO 3
SO4
Na
Mg
Al
Si
Cl
K
Ca
Ti
V
Cr
Mn
Fe
Ni
Cu
Zn
Br
Pb
MARINE
.023
.036
.017
.375
.380
.028
.211
.075
1.000
.014
.060
.070
.170
.120
.015
.017
.115
.090
.035
.084
.079
UDUST
.452
.357
.263
.087
.078
.084
.098
1.000
.070
.426
.507
.942
.033
.258
.193
.276
.099
.149
.043
.216
.157
AUTO
.536
.220
.109
.050
.111
.089
.093
.180
.086
.189
.056
.183
.084
.007
.105
.051
.059
.133
.125
1.000
.974
RDOIL
.013
.137
.079
.111
.184
.098
.105
.027
.140
.085
.048
.042
1.000
.151
.056
.030
.886
.003
.051
.073
.058
KRAFT
.028
.086
.149
1.000
.451
.063
.130
.008
.399
.141
.052
.004
.458
.153
.058
.013
.385
.005
.025
.077
.050
ALPRO
.168
.122
.187
.010
.042
.336
1.000
.414
.063
.229
.232
.378
.040
.015
.010
.168
.033
.130
.068
'.028
.002
STEEL
.247
.264
.247
.083
.144
.582
.153
.310
.026
.260
.199
.276
.120
1.000
.451
.577
.092
.693
.625
.005
.031
FeMn
.025
.002
1.000
.084
.014
.156
.101
.018
.012
.697
.039
.017
.009
.162
.598
.109
.050
.115
.054
.106
.127
A - 9
-------
Table Al. Continued
EIGENVALUES
3.586 2.189 1.254 .562 .508 .224 .181
INVERSE SINGULAR VALUE
.528 .676 .893 1.334 1.403 2.115 2.353
EIGENVECTORS
MARINE .953 ".234 ~.102 ".059 .015 ".144 .039
UDUST .025 .031 .070 .129 ".065 .208 .323
AUTO .076 .049 . .178 .816 .527 ~.022 ~.117
RDOIL .175 .937 ".240 ~.063 .073 ~.146 .052
KRAFT .168 .119 .002 ~.083 .007 .811 ".540
ALPRO .076 .048 .049 .098 ".033 .495 .755
STEEL .103 .146 .303 .420 ".819 ".076 ".127
FeMn .099 .160 .895 ".343 .200 ".071 .019
VARIANCE AND COVARIANCE MATRIX
MARINE .403 .373 ".105
UDUST .373 23.538 "1.321
AUTO ".105 "1.321 1.904
RDOIL .085 .203 ".060
KRAFT ".592 .023 .151
ALPRO -.362 -8.302 .126
STEEL -.103 -2.261 .015
FeMn .026 ".205 ".157
.085
.203
.060
.587
.613
.228
.167
.020
-.592
.023
.151
-.613
4.591
-.581
.016
-.248
•
"8.
*
*
«
8.
•
•
362
302
126
228
581
798
421
054
".103
"2.261
.015
".167
.016
.421
2.044
".327
036
5.248
.018
.908
'. 049
.011
. 010
\405
'.087
'.005
.026
'.205
M57
.020
'.248
'.054
'.327
.967
STANDARD ERROR OF REGRESSION COEFFICIENT
MARINE UDUST AUTO RDOIL KRAFT
.635 4.852 1.380 .766 2.143
SOURCE STRENGTH
MARINE UDUST AUTO RDOIL KRAFT
2.341 33.610 9.408 4.393 6.100
ALPRO STEEL FeMn
2.966 1.430 .984
ALPRO STEEL FeMn
.976 10.652 5.397
A - 10
-------
Table Al. Continued
SDFBETA
oc
EC
NO 3
S04
Na
Mg
Al
Si
Cl
K
Ca
Ti
V
Cr
Mn
Fe
Ni
Cu
Zn
Br
Pb
MARINE
.008
.004
.010
.361
.245
.002
.039
.005
1.000
.009
.009
.007
.020
.078
.014
.002
.001
.038
.001
.035
.012
UDUST
.466
.180
1.000
.323
.184
.027
.082
.234
.229
.747
.369
.341
.032
.602
.503
.059
.003
.235
.005
.317
.089
AUTO
.435
.091
.320
.133
.206
.0.18
.058
.027
.215
.236
.023
.043
.027
.002
.144
.007
.001
.134
.006
1.000
.366
RDOIL
.041
.110
.552
.458
.668
.064
.169
.017
.730
.154
.032
.032
1.000
.713
.240
.028
.045
.129
.000
.158
.049
KRAFT
.008
.008
.148
1.000
.303
.003
.028
.000
.370
.056
.008
.001
.052
.092
.044
.002
.002
.009
.000
.025
.006
ALPRO
.222
.057
.816
.035
.113
.101
1.000
.117
.202
.463
.204
.16,5
.030
.077
.062
.045
.001
.204
.004
.044
.001
STEEL
.108
.056
.463
.086
.139
.080
.048
.027
.012
.231
.089
.037
.039
1.000
.428
.070
.002
.453
.019
.002
.007
FeMn
.006
.003
1.000
.099
.002
.013
.014
.003
.008
.391
.014
.004
.004
.124
.359
.010
.000
.052
.001
.035
.016
SDFSBETA
MARINE UDUST
OC
EC
NO 3
S04
Na
Mg
Al
Si
Cl
K
Ca
Ti
V
Cr
Mn
Fe
Ni
Cu
Zn
Br
Pb
.000
.000
.000
.142
.049
.000
.045
.002
1.000
.000
.001
.002
.008
.003
.000
.000
.002
.003
.001
.003
.002
.133
.104
.079
.023
.006
.006
.041
.988
.011
.156
.180
1.000
.004
.040
.053
.039
.016
.020
.004
.049
.025
.240
.055
.017
.008
.015
.006
.042
.028
.020
.032
.001
.033
.007
.000
.009
.001
.003
.014
.012
1.000
.876
.000
.009
.006
.011
.017
.008
.041
.001
.025
.002
.000
.002
1.000
.013
.003
.002
.732
.001
.000
.003
.002
AUTO RDOIL KRAFT ALPRO STEEL FeMn
.000 .005 .064 .000
.001 .002 .089 .000
.008 .009 .151 1.000
1.000 .000 .015 .028
.068 ..000 .029 .000
.000 .014 .493 .020
.021 1.000 .126 .015
.000 .040 .120 .002
.126 .001 .000 .000
.004 .010 .134 .540
.000 .009 .093 .003
.000 .038 .105 .002
.053 .001 .060 .001
.004 .000 1.000 .022
.002 .000 .343 .343
.000 .004 .491 .015
.031 .001 .032 .002
.000 .002 .675 .013
.000 .000 .497 .001
.001 .000 .000 .007
.001 .000 .001 .011
A - 11
-------
Table Al. Continued
SPINBETA
MARINE UDUST AUTO RDOIL KRAFT ALPRO STEEL FeMn
OC .036 .574 .786 .027 .028 .223 .284 .019
EC -039 .458 .340 .146 .059 .119 .301 .023
N03 -012 .371 .174 .107 .162 .247 .366 1.000
S04 -419 .109 .066 .081 1.000 .010 .062 .091
Na -537 .118 .193 .223 .571 .059 .190 .003
Mg .032 .106 .100 .129 .036 .319 .660 .140
Al .162 .101 .104 .108 .100 1.000 .125 .046
Si .068 1.000 .171 .037 .001 .408 .248 .030
Cl 1.000 .067 .092 .111 .319 .048 .007 .006
K .020 .461 .213 .049 .102 .234 .303 .650
Ca .059 .683 .062 .031 .044 .308 .349 .069
Ti .067 .996 .185 .049 .005 .394 .229 .030
V .127 .058 .074 .964 .285 .046 .155 .018
Cr .126 .283 .001 .175 .127 .030 1.000 .158
Mn .022 .237 .100 .059 .061 .024 .430 .457
Fe .038 .281 .052 .070 .023 .174 .713 .131
Ni .080 .138 .056 1.000 .264 .050 .137 .035
CU .098 .177 .148 .051 .019 .125 .725 .106
Zn .069 .097 .176 .001 .001 .059 .793 .030
Br .065 .173 .801 .045 .041 .020 .002 .051
Pb .080 .167 1.000 .048 .033 .002 .026 .083
SPINSBETA
MARINE UDUST AUTO RDOIL KRAFT ALPRO STEEL FeMn
oc .001 .156 .311 .000 .001 .026 .066 .000
Ec .001 .128 .075 .015 .003 .009 .096 .001
.000 .061 .014 .006 .019 .029 .102 1.000
-141 .007 .003 .005 1.000 .000 .004 .011
Na .131 .005 .014 ,.020 .185 .001 .022 .000
Mg .001 .008 .007 .013 .001 .076 .513 .030
Al .031 .009 .010 .013 .015 1.000 .025 .004
Si .006 .994 .031 .002 .000 .180 .105 .002
Cl 1.000 .003 .007 .011 .127 .002 .000 .000
K .000 .146 .033 .002 .012 .041 .109 .658
Ca .002 .230 .002 .001 .002 .051 .104 .005
Ti .006 1.000 .037 . .003 .000 .171 .091 .002
V .019 .003 .005 1.000 .120 .002 .038 .001
Cr .012 .046 .000 .021 .015 .001 1.000 .033
Mn .001 .053 .010 .004 .006 .001 .299 .445
Fe .001 .047 .002 .003 .000 .020 .525 .023
Ni .006 .013 .002 .818 .078 .002 .022 .002
Cu .010 .025 .018 .002 .000 .014 .718 .020
Zn .003 .005 .017 .000 .000 .002 .546 .001
Br .008 .044 1.000 .004 .004 .001 .000 .009
Pb .007 .024 .921 .002 .002 .000 .001 .014
A - 12
-------
Table Al. Continued
NMPIN
MARINE UDUST
AUTO RDOIL KRAFT ALPRO STEEL FeMn
oc
EC
NO 3
S04
Na
Mg
Al
Si
Cl
K
Ca
Ti
V
Cr
Mn
Fe
Ni
Cu
Zn
Br
Pb
.028
.035
.009
.376
.362
.030
.177
.077
1.000
.019
.047
.077
.139
.109
.024
.033
.076
.100
.056
-.089
.084
.395
.358
.246
.086
.070
.088
.096
.997
.059
.381
.480
1.000
.056
.215
.230
.217
.115
.157
.069
.210
.155
.557
.274
.119
.053
.118
.086
.102
.176
.083
.182
.045
.192
.073
.001
.099
.042
.048
.136
.129
1.000
.960
.020
.124
.077
.069
.143
.116
.112
.040
.106
.044
.024
..053
1.000
.144
.062
.059
.904
.049
.001
.059
.043
.025
.059
.137
1.000
.430
.037
.122
.001
.356
.108
.039
.007
.347
.123
.075
.022
.280
.022
.001
.063
.039
.161
.097
.171
.008
.037
.276
1.000
.424
.044
.202
.226
.413
.046
.024
.024
.141
.044
.116
.044
.025
.002
.256
.309
.319
.064
.147
.716
.157
.325
.008
.330
.322
.302
.195
1.000
.546
.725
.150
.847
.739
.004
.032
.019
.028
1.000
.107
.003
.174
.067
.045
.008
.811
.073
.046
.026
.181
.667
.152
.044
.142
.032
.093
.116
A - 13
-------
Table Al. Continued
MEANS DFBETA
OC
EC
NO 3
SO4
Na
Mg
Al
Si
Cl
K
Ca
Ti
V
Cr
Mn
Fe
Ni
Cu
Zn
Br
Pb
MARINE
.018
.015
.012
.374
.301
.017
.077
.007
1.000
.010
.020
.019
.059
.054
.009
.007
.026
.040
.016
.038
.014
UDUST
.788
.285
.655
.217
.143
.094
.106
.251
.166
.653
.450
.556
.054
.376
.315
.183
.081
.203
.059
.257
.070
AUTO.
.800
.156
.225
.089
.186
.075
.088
.036
.175
.245
.036
.086
.066
.006
.109
.027
.024
.138
.121
.952
.336
RDOIL
.036
.102
.247
.281
.364
.057
.119
.010
.406
.091
.035
.036
.849
.279
.100
.034
.487
.053
.011
.109
.035
KRAFT
.019
.022
.120
1.000
.298
.020
.046
.001
.353
.070
.016
.001
.153
.065
.033
.005
.089
.005
.004
.031
.008
ALPRO
.327
.115
.475
.030
.086
.226
1.000
.111
.164
.320
.211
.282
.046
.032
.031
.144
.023
.140
.053
.034
.002
STEEL
.362
.155
.399
.139
.175
.267
.104
.054
.026
.255
.149
.156
.095
.698
.337
.418
.060
.458
.360
.005
.012
FeMn
.023
.005
1.000
.114
.008
.052
.043
.003
.012
.475
.022
.009
.007
.087
.318
.063
.020
.054
.021
.068
.034
STDSDFBETA
MARINE UDUST AUTO RDOIL KRAFT ALPRO. STEEL FeMn
OC
EC
NO 3
S04
Na
Mg
Al
Si
Cl
K
Ca
Ti
V
Cr
Mn
Fe
Ni
Cu
Zn
Br
Pb
.012
.010
.005
.026
.113
.027
.036
.003
.000
.006
.009
.021
.057
.043
.006
.006
.023
.033
.023
.023
.012
.284
.136
.388
.092
.058
.138
.060
.038
.058
.402
.144
.343
.057
.314
.231
.150
.086
.168
.092
.065
.033
.316
.091
. .129
.038
.090
.113
.061
.010
.053
.173
.015
.057
.071
.008
.073
.023
.020
.125
.191
.083
.125
.018
.055
.265
.209
.279
.051
.048
.007
.316
.056
.023
.033
.262
.379
.121
.028
.481
.067
.010
.082
.029
.015
.013
.039
.000
.048
.031
.017
.001
.031
.038
.007
.001
.148
.051
.020
.004
.076
.004
.004
.020
.007
.222
.053
.298
.005
.025
.299
.000
.039
.036
.143
.047
.275
.036
.040
.029
.162
.019
.097
.074
.026
.001
.340
.093
.085
.058
.031
.383
.048
.037
.028
.092
.055
.197
.085
.524
.136
.507
.051
.329
.490
.004
.010
.035
.005
.000
.046
.007
.076
.029
.001
.009
.147
.009
.009
.006
.065
.106
.079
.019
.037
.028
.068
.039
A - 14
-------
Table Al. Continued
MEANSDFSBETA
oc
EC
NO 3
S04
Na
Mg
Al
si
Cl
K
Ca
Ti
V
cr
Mn
Fe
Ni
Cu
Zn
Br
Pb
MARINE
.000
.001
.000
.162
.062
.000
.047
.002
1.000
.000
.001
.002
.011
.004
.000
.000
.003
.003
.001
.002
.002
UDUST
.155
.097
.084
.021
.006
.007
.036
.996
.011
.154
.187
.916
.003
.051
.043
.048
.015
.019
.002
.050
.025
AUTO
.217
.040
.014
.006
.012
.006
.032
.027
.017
.029
.002
.029
.006
.000
.008
.001
.002
.012
.010
1.000
.868
RDOIL
.000
.008
.005
.016
.019
.007
.034
.001
.028
.003
.001
.001
1.000
.014
.002
.001
.639
.001
.001
.003
.002
KRAFT
.000
.001
.008
1.000
.059
.001
.016
.000
.111
.005
.000
.000
.061
.005
.001
.000
.033
.000
.000
.001
.000
ALPRO
.006
.005
.013
.000
.001
.026
1.000
.046
.003
.012
.011
.039
.001
.000
.000
.005
.000
.004
.001
.000
.000
STEEL
.057
.071
.123
.026
.027
.377
.102
.105
.001
.095
.064
.085
.039
1.000
.260
.379
.023
.527
.367
.000
.001
FeMn
.000
.000
1.000
.021
.000
.018
.018
.001
.000
.425
.002
.001
.000
.021
.307
.011
.002
.010
.001
.007
.011
STDSDFSBETA
MARINE UDUST AUTO RDOIL KRAFT ALPRO STEEL FeMn
OC
EC
NO 3
S04
Na
Mg
Al
Si
Cl
K
Ca
Ti
V
Cr
Mn
Fe
Ni
Cu
Zn
Br
Pb
.000
.000
.000
.018
.013
.000
.006
.000
.000
.000
.000
.000
.003
.001
.000
.000
.002
.000
.000
.001
.001
.023
.010
.023
.006
.002
.001
.004
.007
.003
.030
.012
.079
.001
.013
.009
.013
.003
.001
.001
.002
.003
.028
.013
.004
.004
.003
.000
.009
.002
.004
.006
.001
.004
.002
.000
.001
.001
.001
.002
.003
.000
.056
.000
.003
.002
.012
.010
.001
.007
.000
.012
.002
.001
.001
.000
.002
.001
.001
.107
.001
.001
.001
.001
.000
.001
.003
.000
.022
.000
.006
.000
.034
.001
.000
.000
.023
.002
.000
.000
.017
.000
.000
.001
.000
.001
.005
.004
.000
.000
.011
.000
.005
.002
.003
.002
.001
.000
.000
.000
.002
.000
.001
.000
.000
.000
.006
.016
.027
.013
.002
.103
.023
.013
.001
.034
.031
.017
.020
.000
.075
.107
.011
.140
.114
.000
.001
.000
.000
.000
.006
.000
.004
.004
.001
.000
.116
.001
.001
.000
.004
.081
.004
.000
.003
.000
.001
.001
A - 15
-------
Table Al. Continued
MEANSPINBETA
MARINE UDUST AUTO RDOIL KRAFT ALPRO STEEL FeMn
oc
EC
NO 3
S04
Na
Mg
Al
Si
Cl
K
Ca
Ti
V
Cr
Mn
Fe
Ni
Cu
Zn
Br
Pb
.025
.050
.015
.410
.527
.040
.186
.060
1.000
.017
.064
.061
.121
.103
.017
.027
.085
.109
.053
.062
.065
.498
.476
.317
.099
.106
.112
.111
.969
.069
.467
.673
.999
.042
.245
.229
.281
.131
.205
.076
.196
.155
.637
.321
.139
,053
.170
.109
.111
.172
.093
.214
.067
.191
.067
.005
.108
.051
.052
.176
.172
.934
.980
.022
.159
.092
.095
.224
.135
.126
.032
.129
.071
.046
.046
.933
.149
.060
.051
1.000
.037
.033
.055
.046
.023
.073
.139
1.000
.497
.054
' .103
.006
.321
.116
.047
.004
.283
.111
.058
.016
.276
.011
.013
.046
.030
..170
.173
.211
.013
.058
.370
1.000
.362
.062
.229
.282
.361
.039
.018
.018
.164
.041
.155
.077
.017
.007
.251
.337
.319
.092
.196
.685
.154
.261
.014
.300
.314
.253
.126
.905
.464
.658
.129
.883
.804
.004
.031
.014
.019
1.000
.091
.010
.164
.073
.022
.008
.700
.058
.023
.012
.142
.557
.119
.044
.135
.052
.070
.093
STDSPINBETA
MARINE UDUST AUTO RDOIL KRAFT ALPRO STEEL FeMn
OC
EC
NO 3
S04
Na
Mg
Al
Si
Cl
K
Ca
Ti
V
Cr
Mn
Fe
Ni
Cu
Zn
Br
Pb
.009
.013
.003
.014
.042
.013
.021
.011
.000
.002
.007
.013
.027
.028
.004
.010
.029
.011
.014
.020
.021
.067
.015
.047
.014
.012
.010
.017
.048
.005
.073
.011
.002
.015
.045
.010
.011
.020
.033
.019
.025
.014
.138
.026
.031
.016
.024
.008
.024
.013
.003
.020
.004
.008
.012
.003
.008
.003
.012
.031
.004
.115
.026
.007
.031
.014
.037
.035
.009
.028
.006
.024
.036
.018
.003
.044
.030
.005
.018
.000
.029
.038
.021
.015
.006
.022
.024
.000
.083
.017
.007
.004
.036
.030
.008
.001
.069
.028
.003
.006
.068
.007
.015
.018
.014
.050 .
.060
.033
.004
.002
.050
.000
.049
.013
.058
.034
.054
.006
.011
.007
.016
.008
.026
.017
.012
.009
.030
.032
.044
.026
.005
.059
.028
.021
.012
.036
.046
.037
.026
.165
.044
.050
.026
.142
.069
.002
.005
.012
.015
.000
.002
.007
.021
.024
.008
.003
.083
.012
.007
.006
.017
.087
.014
.008
.028
.019
.025
.019
A - 16
-------
Table Al. Continued
MEANSPINSBETA
MARINE UDUST AUTO RDOIL KRAFT ALPRO STEEL • FeMn
oc
EC
NO 3
S04
Na
Mg
Al
Si
Cl
K
Ca
Ti
V
Cr
Mn
Fe
Ni
Cu
Zn
Br
Pb
.001
.002
.000
.135
.152
.002
.038
.005
1.000
.000
.003
.005
.021
.012
.000
.001
.008
.009
.002
.006
.005
.181
.121
.059
.006
.005
.008
.010
.998
.004
.151
.240
.940
.002
.055
.044
.058
.013
.023
.003
.045
.023
.284
.055
.011
.002
.012
.007
.010
.031
.006
.031
.002
.034
.005
.000
.010
.002
.002
.017
.014
1.000
.916
.000
.014
.005
.006
.023
.012
.014
.001
.013
.004
.001
.002
1.000
.021
.003
.002
.764
.001
.001
.004
.002
.001
.005
.019
1.000
.169
.003
.015
.000
.130
.015
.002
.000
.147
.018
.005
.000
.096
.000
.000
.004
.001
.024
.021
.031
.000
.002
.104
1.000
.165
.004
.042
.050
.145
.002
.000
.000
.023
.001
.016
.004
.000
.000
.062
.081
.082
.007
.021
.406
.027
.097
.000
.085
.075
.080
.025
1.000
.241
.428
.018
.592
.429
.000
.001
.000
.001
1.000
.009
.000
.029
.007
.001
.000
.571
.003
.001
.000
.031
.427
.018
.002
.017
.002
.009
.014
STDSPINSBETA
MARINE UDUST AUTO RDOIL" KRAFT ALPRO STEEL FeMn
OC
EC
NO 3
S04
Na
Mg
Al
Si
Cl
K
Ca
Ti
V
Cr
Mn
Fe
Ni
Cu
Zn
Br
Pb
.000
.001
.000
.010
.026
.001
.007
.001
.000
.000
.001
.001
.007
.002
.000
.000
.005
.001
.001
.003
.002
.024
.012
.010
.002
.001
.001
.001
.004
.001
.029
.015
.056
.001
.010
.008
.016
.002
.001
.002
.002
.002
.029
.017
.003
.001
.002
.000
.001
.002
.001
.006
.001
.003
.002
.000
.002
.001
.001
.002
.003
.000
.035
.000
.005
.001
.005
, .010
.002
.003
.000
.005
.003
.001
.001
.000
.002
.001
.001
.067
.001
.001
.002
.001
.000
.002
.004
.000
.045
.001
.002
.000
.028
.004
.001
.000
.055
.004
.001
.000
.046
.000
.000
.002
.001
.005
.015
.003
.000
.000
.025
.000
.020
.002
.010
.005
.025
.000
.000
.000
.004
.000
.002
.001
.000
.000
.004
.013
.020
.003
.001
.094
.005
.008
.000
.021
.032
.010
.012
.000
.051
.096
.008
.119
.103
.000
.001
.000
.000
.000
.002
.000
.004
.003
.001
.000
.086
.002
.001
.000
.005
.063
.006
.000
.004
.001
.002
.002
A - 17
-------
Table Al. Continued
MEANNMPIN
MARINE UDUST AUTO RDOIL KRAFT ALPRO STEEL FeMn
oc
EC
NO 3
S04
Na
Mg
Al
Si
Cl
K
Ca
Ti
V
Cr
Mn
Fe
Ni
Cu
Zn
Br
Pb
.024
.042
.014
.367
.389
.037
.195
.070
1.000
.016
.054
.067
.145
.111
.018
.026
.084
.094
.042
.076
.072
.424
.348
.243
.078
.068
.089
.ioi
.999
.060
.387
.490
.969
.043
.234
.208
.240
.111
.153
.053
.212
.152
.532
.233
.106
.042
.108
.086
.100
.175
.080
.176
.048
.184
.070
.005
.097
.043
.045
.130
.120
1.000
.957
.019
.118
.072
.076
.148
.110
.117
.033
.115
.059
.034
.046
1.000
.144
.056
.044
.874
.029
.023
.059
.046
.025
.068
.136
1.000
.408
.055
.122
.008
.359
.122
.044
.005
.379
.135
.068
.017
.303
.011
.011
.062
.036
.154
.138
.176
.011
.041
.321
1.000
.405
.059
.204
.223
.380
.045
.017
.018
.152
.038
.126
.059
.020
.008
.248
.285
.285
.082
.146
.634
.163
.311
.013
.290
.268
.283
.155
1.000
.489
.651
.130
.767
.652
.005
.036
.015
.019
1.000
.093
.008
.169
.084
.031
.009
.755
.056
.031
.017
.177
.652
.132
.049
.130
.045
.095
.118
STDNMPIN
MARINE • UDUST AUTO RDOIL KRAFT ALPRO STEEL FeMn
OC
EC
NO 3
S04
Na
Mg
Al
Si
Cl
K
Ca
Ti
V
Cr
Mn •
Fe
Ni
Cu
Zn
Br
Pb
.004
.011
.004
.014
.032
.015
.017
.010
.000
.002
.006
.012
.022
.008
.006
.008
.028
.005
.012
.019
.017
.029
.017
.021
.016
.011
.007
.007
.002
.009
.037
.015
.029
.011
.022
.019
.032
.011
.004
.014
.004
.007
.027
.036
.016
.017
.012
.003
.006
.005
.008
.016
.007
.007
.015
.004
.009
.007
.015
.007
.013
.000
.018
.005
.022
.010
.032
.034
.010
.014
.007
.022
.023
.013
.006
.000
.008
.006
.014
.039
.024
.026
.014
.013
.004
.016
.013
.000
.057
.015
.008
.006
.038
.017
.007
.001
.069
.016
.009
.005
.073
.009
.013
.015
.015
.018
.051
.010
.004
.004
.040
.000
.025
.014
.024
.011
.033
.004
.006
.008
.014
.005
.008
.013
.011
.011
.007
.023
.036
.017
.002
.072
.014
.013
.011
.036
.063
.017
.038
.000
.050
.074
.033
.077
.077
.002
.007
.013
.015
.000
.013
.006
.012
.017
.014
.003
.057
.017
.015
.009
.013
.049
.022
.004
.014
.012
.010
.008
A - 1!
-------
Table A2. Mean and standard deviation of three simulation
runs for MPIN and other diagnostics for data set 1
MEANSDFBETA
MARINE UDUST AUTO RDOIL KRAFT ALPRO STEEL FeMn
oc
EC
NO 3
S04
Na
Mg
Al
Si
Cl
K
Ca
Ti
V
Cr
Mn
Fe
Ni
Cu
Zn
Br
Pb
.105
.076
.009
.201
.178
.051
.260
.055
1.000
.006
.029
.033
.118
.109
.005
.023
.070
.029
.055
.203
.091
.527
.243
.159
.061
.063
.055
.059
.740
.100
.264
.170
.637
.055
.275
.172
.151
.134
.055
.016
.231
.077
.421
.104
.048
.023
.071
.034
.036
.062
.078
.077
.003
.057
.058
.003
.066
.010
.028
.036
.038
.910
.500
.033
.101
.032
.042
.072
.104
.108
.016
.085
.033
.014
.017
.818
.103
.037
.024
.712
.004
.028
.076
.026
.089
.087
.117
.836
.468
.119
.212
.005
.590
.186
.041
.004
.550
.187
.105
.003
.415
.003
.030
.181
.053
.209
.213
.258
.056
.138
.371
1.000
.484
.279
.240
.109
.448
.149
.001
.060
.123
.098
.123
.032
.006
.031
.274
.154
.169
.078
.108
.422
.086
.172
.044
.182
.097
.117
.137
.891
.348
.440
.141
.237
.374
.020
.017
.035
.013
.838
.074
.006
.224
.130
.010
.015
.639
.024
.009
.004
.234
.741
.124
.080
.056
.051
.234
.133
STDSDFBETA
MARINE UDUST AUTO RDOIL KRAFT ALPRO STEEL FeMn
oc
EC
NO 3
S04
Na
Mg
Al
Si
Cl
K
Ca
Ti
V
Cr
Mn
Fe
Ni
Cu
Zn
Br
Pb
.159
.121
.005
.122
.036
.083
.358
.044
.000
.005
.036
.018
.064
.071
.005
.024
.047
.015
.088
.265
.088
.410
.209
.110
.074
.061
.046
.032
.254
.109
.197
.043
.373
.045
.186
.103
.102
.066
.036
.020
.079
.057
.273
.087
.028
.026
.060
.027
.017
.035
.075
.073
.000
.034
.045
.003
.031
.008
.015
.025
.046
.155
.448
.048
.149
.008
.025
.025
.154
.141
.011
.041
.021
.016
.004
.315
.040
.024
.024
.268
.001
.046
.089
.024
.119
.128
.041
.284
.181
.176
.240
.004
.191
.157
.040
.002
.398
.066
.055
.005
.221
.001
.047
.186
.044
.063
.209
.255
.080
.168
.282
.000
.288
.367
.191
.048
.404
.156
.001
.060
.095
.079
.109
.032
.005
.027
.287
.178
.061
.062
.067
.505
.075
.091
.030
.171
.054
.046
.095
.188
.020
.345
.,056
.145
.518
.010
.014
.051
.017
.142
.063
.004
.302
.147
.003
.008
.388
.021
.004
.003
.038
.271
.103
.006
.018
.079
.219
.101
A - 19
-------
Table A2. Continued
MEANSDFSBETA
MARINE UDUST AUTO RDOIL KRAFT ALPRO STEEL FeMn
oc
EC
NO 3
S04
Na
Mg
Al
Si
Cl
K
Ca
Ti
V
Cr
Mn
Fe
Ni
Cu
Zn
Br
Pb
.000
.000
.000
.099
.030
.000
.040
.002
1.000
.000
.000
.001
.007
.005
.000
.000
.001
.001
.000
.002
.002
.078
.046
.044
.008
.003
.003
.022
1.000
.007
.088
.112
.776
.001
.055
.023
.027
.010
.008
.001
.022
.009
.148
.030
.011
.004
.011
.004
.023
.016
.012
.016
.000
.016
.004
.000
.010
.000
.001
.008
.007
.973
.839
.000
.004
.004
.011
.014
.004
.035
.001
.019
.002
.000
.001
1.000
.015
.002
.000
.468
.000
.000
.002
.001
.000
.001
.008
1.000
.094
.001
.024
.000
.159
.007
.001
.000
.061
.008
.002
.000
.023
.000
.000
.002
.000
.002
.005
.008
.000
.001
.021
1.000
.042
.003
.008
.006
.029
.001
.000
.000
.003
.000
.003
.001
.000
.000
.019
.021
.085
.032
.019
.170
.040
.063
.003
.040
.040
.041
.016
1.000
.155
.194
.016
.220
.159
.000
.000
.000
.000
1.000
.011
.000
.013
.031
.000
.000
.303
.001
.000
.000
.032
.287
.007
.002
.007
.001
.008
.011
STDSDFSBETA
MARINE UDUST AUTO RDOIL KRAFT ALPRO STEEL FeMn
OC
EC
NO 3
SO4
Na
Mg
Al
Si
Cl
K
Ca
Ti
V
Cr
Mn
Fe
Ni
Cu
Zn
Br
Pb
.000
.000
.000
.010
.005
.000
.003
.000
.000
.000
.000
.000
.001
.000
.000
.000
.000
.000
.000
.000
.000
.001
.001
.004
.000
.000
.000
.002
.000
.000
.002
.003
.075
.000
.000
.002
.001
.000
.001
.000
.004
.000
.012
.002
.001
.000
.001
.000
.001
.001
.001
.002
.000
.001
.000
.000
.001
.000
.000
.001
.001
.046
.160
.000
.000
.000
.001
.001
.000
.002
.000
.002
.000
.000
.000
.000
.002
.000
.000
.062
.000
.000
.000
.000
.000
.000
.001
.000
.007
.000
.002
.000
.009
.001
.000
.000
.003
.000
.000
.000
.003
.000
.000
.000
.000
.000
.001
.001
.000
.000
.001
.000
.002
.000
.001
.000
.001
.000
.000
.000
.000
.000
.000
.000
.000
.000
.001
.001
.012
.003
.001
.003
.002
.003
.001
.003
.004
.003
.001
.000
.012
.012
.000
.016
.004
.000
.000
.000
.000
.000
.001
.000
.001
.002
.000
.000
.004
.000
.000
.000
.005
.047
.001
.000
.002
.000
.002
.001
A - 20
-------
Table A2. Continued
MEANSPINBETA
oc
EC
NO 3
S04
Na
Mg
Al
Si
Cl
K
Ca
Ti
V
Cr
Mn
Fe
Ni
Cu
Zn
Br
Pb
MARINE
.032
.046
.014
.350
.283
.027
.194
.065
1.000
.006
.044
.052
.112
.121
.004
.017
.056
.078
.031
.074
.078
UDUST
.359
.268
.192
.062
.057
.070
.088
1.000
.051
.336
.409
. .821
.032
.256
.159
.183
.101
.112
.028
.133
.099
. AUTO
.509
.222
.100
.043
.106
.079
.092
.132
.069
.147
.014
.121
.053
.004
.107
.019
.034
.121
.107
.906
1.000
RDOIL
.018
.092
.067
.087
.140
.101
.133
.029
.100
.059
.032
.036
1.000
.160
.050
.030
.849
.017
.027
.043
.036
KRAFT
.025
.048
.122
1.000
.453
.067
.137
.004
.359
.137
.051
.004
.306
.147
.075
.003
.230
.005
.016
.056
.033
ALPRO
.101
.148
.143
.024
.049
.306
1.000
.345
.057
.168
.153
.269
.035
.001
.025
.096
.035
.114
.047
.002
.024
STEEL
.161
.167
.244
.111
.127
.478
.109
.230
.031
.207
.223
.173
.095
1.000
.376
.448
.117
.555
.445
.012
.018
FeMn
.010
.010
1.000
.079
.008
.157
.114
.012
.010
.685
.039
.011
.002
.213
.612
.098
.055
.117
.040
.090
.123
STDSPINBETA
MARINE UDUST AUTO RDOIL KRAFT ALPRO STEEL FeMn
OC
EC
NO 3
S04
Na
Mg
Al
Si
Cl
K
Ca
Ti
V
Cr
Mn
Fe
Ni
Cu
Zn
Br
Pb
.007
.005
.001
.033
.027
.008
.009
.001
.000
.001
.000
.003
.011
.003
.001
.aoi
.009
.010
.002
.016
.009
.062
.016
.022
.005
.004
.006
.003
.000
.002
.019
.007
.054
.004
.002
.023
.015
.016
.013
.004
.026
.012
.075
.019
.008
.005
.006
.007
.002
.009
.001
.015
.004
.001
.002
.003
.014
.004
.006
.012
.005
.103
.000
.003
.008
.005
.012
.005
.009
.008
.001
.002
.007
.002
.002
.000
.005
.006
.002
.159
.002
.002
.007
.003
.007
.002
.017
.000
.044
.015
.018
.000
.037
.004
.005
.001
.049
.015
.018
.002
.056
.001
.002
.014
.007
.015
.027
.009
.006
.006
.019
.000
.015
.004
.019
.005
.011
.002
.002
.003
.006
.005
.015
.004
.003
.003
.025
.014
.015
.013
.005
.065
.007
.005
.002
'.020
.005
.008
.007
.000
.055
.028
.020
.061
.022
.000
.003
.005
.004
.000
.012
.007
.022
.002
.005
.003
.102
.006
.003
.001
.030
.114
.007
.005
.029
.006
.022
.016
A - 21
-------
Table A2. Continued
MEANSPINSBETA
MARINE UDUST AUTO RDOIL KRAFT ALPRO STEEL FeMn
oc
EC
NO 3
S04
Na
Mg
Al
Si
Cl
K
Ca
Ti
V
Cr
Mn
Fe
Ni
Cu
Zn
Br
Pb
.001
.002
.000
.130
.093
.001
.038
.005
1.000
.000
.002
.004
.016
.015
.000
.000
.004
.006
.001
.008
.006
.108
.067
.033
.003
.003
.004
.006
1.000
.002
.103
.163
.850
.001
.055
.025
.038
.010
.011
.001
.021
.009
.220
.046
.009
.002
.011
.005
.007
.018
.004
.020
.000
.019
.003
.000
.012
.000
.001
.013
.011
.985
.898
.000
.007
.004
.006
.018
.008
.014
.001
.008
.003
.001
.002
1.000
.020
.002
.001
.654
.000
.001
-.002
.001
.001
.002
.015
1.000
.225
.004
.017
.000
.121
.019
.003
.000
.108
.020
.006
.000
.056
.000
.000
.004
.001
.010
.024
.022
.001
.003
.096
1.000
.143
.003
.031
.028
.110
.002
.000
.001
.013
.001
.013
.003
.000
.001
.026
.031
.064
.013
.019
.231
.012
.064
.001
.047
.059
.046
.011
1.000
.171
.274
.016
.315
.234
.000
.000
.000
.000
1.000
.006
.000
.023
.012
.000
.000
.471
.002
.000
.000
.042
.420
.012
.003
.013
.002
.010
.015
STDSPINSBETA
MARINE UDUST AUTO RDOIL KRAFT ALPRO STEEL. FeMn
OC
EC
NO 3
S04
Na
Mg
Al
Si
Cl
K
Ca
Ti
V
Cr
Mn
Fe
Ni
Cu
Zn
Br
Pb
.000
.000
.000
.006
.008
.000
.001
.000
.000
.000
.000
.000
.001
.000
.000
.000
.001
.000
.000
.001
.000
.002
.001
.003
.000
.000
.000
.001
.000
.000
.003
.002
.053
.000
.001
.001
.002
.000
.001
.000
.002
.000
.017
.004
.001
.000
.001
.000
.000
.001
.001
.001
.000
.001
.000
.000
.001
.000
.000
.001
.001
.027
.103
.000
.000
.000
.000
.001
.000
.000
.000
.001
.000
.000
.000
.000
.001
.000
.000
.045
.000
.000
.000
.000
.000
.000
.001
.000
.007
.000
.001
.000
.009
.001
.000
.000
.003
.001
.000
.000
.006
.000
.000
.000
.000
.001
.004
.001
.000
.000.
.003
.000
.006
.000
.002
.001
.007
.000
.000
.000
.000
.000
.001
.000
.000
.000
.001
.002
.010
.001
.000
.004
.000
.002
.000
.004
.004
.002
.001
.000
.005
.013
.000
.017
.005
.000
.000
.000
.000
.000
.001
.000
.002
. .001
.000
.000
.005
.000
.000
.000
.006
.041
.002
.000
.002
.001
.001
.001
A - 22
-------
Table A2. Continued
MEANNMPIN
oc
EC
NO 3
S04
Na
Mg
Al
Si
Cl
K
Ca
Ti
V
Cr
Mn
Fe
Ni
Cu
Zn
Br
Pb
MARINE
.032
.048
.014
.360
.305
.026
.194
.071
1.000
.007
.047
.064
.125
.121
.005
.020
.059
.079
.034
.087
.080
UDUST
.328
.258
.181
.058
.056
.064
.080
1.000
.046
.321
.404
.921
.032
.234
.160
.195
.098
.103
.027
.144
.093
AUTO
.469
.214
.095
.041
.104
.073
.084
.132
.063
.140
.014
.136
.054
.004
.108
.021
.033
.112
.106
.992
.947
RDOIL
.016
.087
.062
.080
.136
.091
.119
.029
.090
.055
.031
.040
1.000
.143
.049
.031
.808
.015
.026
.046
.033
KRAFT
.024
.049
.122
1.000
.474
.065
.132
.005
.348
.139
.053
.005
.329
.142
.080
.003
.236
.005
.017
.064
.033
ALPRO
.102
.155
.148
.024
.053
.309
1.000
.379
.057
.175
.167
.332
.040
.001
.028
.113
.038
.115
.051
.003
.025
STEEL
.162
.176
.253
.114
.137
.480
.108
.252
.031
.216
.242
.213
.106
1.000
.414
.523
.125
.561
.484
.014
.018
FeMn
.010
.010
1.000
.078
.008
.152
.110
.013
.010
.687
.041
.013
.002
.205
.647
.111
.057
.113
.042
.102
.121
STDNMPIN
MARINE UDUST AUTO RDOIL KRAFT ALPRO STEEL FeMn
OC
EC
NO 3
S04
Na
Mg
Al
Si
Cl
K
Ca
Ti
V
Cr
Mn
Fe
Ni
Cu
Zn
Br
Pb
.003
.002
.000
.009
.014
.004
.003
.001
.000
.001
.001
.001
.003
.001
.001
.000
.005
.002
.001
.004
.002
.003
.001
.008
.001
.002
.003
.004
.000
.002
.005
.003
.029
.002
.002
.002
.004
.002
.005
.003
.008
.002
.018
.009
.006
.002
.004
.001
.003
.002
.005
.005
.003
.004
.002
.002
.006
.002
.003
.007
.006
.014
.054
.001
.002
.003
.002
.004
.001
.001
.002
.005
.003
.001
.002
.000
.005
.002
.001
.028
.001
.001
.003
.002
.001
.003
.004
.000
.008
.001
.006
.001
.013
.004
.002
.000
.005
.002
.000
.002
.013
.002
.002
.002
.001
.003
.012
.003
.003
.003
.005
.000
.009
.001
.005
.003
.010
.001
.002
.002
.002
.000
.004
.001
.003
.002
.003
.005
.019
.005
.001
.004
.002
.005
.003
.009
.009
.004
.003
.000
.006
.012
.002
.015
.005
.002
.001
.003
.003
.000
.004
.006
.006
.005
.006
.002
.004
.003
.005
.001
.016
.032
.009
.002
.011
.008
.007
.003
A - 23
-------
Table A3. Mean and standard deviation of three simulation
runs for MPIN and other diagnostics for data set 2
MEANSDFBETA
MARINE UDUST AUTO RDOIL KRAFT ALPRO STEEL FeMn
OC -031 .345 .301 .009 .022 .112 .131 .014
EC -029 .311 .093 .062 .064 .089 .162 .014
N03 -009 .179 .030 .021 .085 .037 .137 .529
S04 .248 .068 .022 .045 .775 .011 .046 .066
Na .170 .050 .037 .045 .249 .013 .066 .007
Mg .030 .159 .087 .108 .112 .469 .792 .329
Al .398 .241 .103 .102 .303 .679 .232 .203
Si .074 .605 .072 .012 .006 .288 .127 .020
Cl .800 .095 .043 .093 .517 .046 .035 .013
K .018 .277 .075 .017 .073 .071 .128 .543
Ca .060 .439 .020 .017 .039 .152 .166 .052
Ti .089 .875 .098 .020 .002 .240 .167 .023
V .419 .093 .104 1.000' .764 .053 .202 .011
Cr .146 .214 .002 .050 .104 .004 .650 .202
Mn .014 .298 .064 .042 .090 .006 .503 .797
Fe .023 .285 .024 .025 .013 .134 .530 .158
Ni .146 .160 .044 .493 .384 .031 .143 .090
Cu .102 .133 .074 .014 .002 .147 .498 .153
Zn .053 .060 .085 .024 .020 .071 .609 .074
Br .071. .220 .485 .031 .080 .004 .013 .092
Pb .149 .266 1.000 .052 .097 .015 .037 .244
STDSDFBETA
MARINE UDUST AUTO RDOIL KRAFT ALPRO STEEL FeMn
OC
EC
NO 3
S04
Na
Mg
Al
Si
Cl
K
Ca
Ti
V
Cr
Mn
Fe
Ni
Cu
Zn
Br
Pb
.034
.007
.008
.099
.174
.014
.423
.071
.346
.024
.059
.097
.503
.202
.005
.010
.192
.080
.032
.046
.038
.078
.213
.239
.045
.055
.071
.289
.455
.106
.189
.033
.217
.047
.148
.261
.062
.119
.116
.041
.283
.180
.255
.029
.023
.004
.029
.043
.093
.065
.029
.078
.016
.091
.108
.002
.011
.013
.050
.055
.037
.357
.000
.009
.055
.026
.029
.047
.073
.122
.013
.082
.009
.008
.005
.000
.023
.030
.016
.295
.017
.025
.038
.034
.008
.044
.105
.374
.240
.030
.343
.005
.472
.038
.009
.003
.246
.069
.055
.006
.268
.002
.019
.100
.068
.113
.098
.017
.008
.006
.464
.556
.344
.041
.037
.132
.173
.029
.003
.004
.130
.029
.209
.088
.004
.004
.031
.111
.176
.023
.071
.262
.282
.097
.041
.081
.029
.039
.089
.457
.443
.184
.107
.435
.330
.019
.022
.017
.021
.447
.018
.005
.123
.175
.017
.008
.419
.028
.009
.009
.230
.290
.057
.097
.143
.060
.075
.051
A - 24
-------
Table A3. Continued
MEANSDFSBETA
MARINE UDUST AUTO RDOIL KRAFT ALPRO STEEL FeMn
oc
EC
NO 3
S04
Na
Mg
Al
Si
Cl
K
Ca
Ti
V
cr
Mn
Fe
Ni
Cu
Zn
Br
Pb
.000
.001
.000
.122
.039
.000
.048
.002
1.000
.000
.001
.002
.010
.005
.000
.000
.002
.002
.000
.003
.003
.115
.081
.072
.017
.006
.005
.032
1.000
.011
.133
.161
.853
.002
.059
.034
.041
.012
.011
.001
.032
.015
.153
.035
.013
.008
.014
.005
.022
.019
.017
.021
.001
.020
.006
.000
.009
.001
.002
.009
.009
.916
.917
.000
.006
.004
.018
.021
.006
.029
.001
.028
.002
.001
.001
1.000
.014
.002
.001
.515
.000
.000
.002
.001
.000
.001
.010
1.000
.093
.001
.028
.000
.158
.005
.000
.000
.079
.007
.002
.000
.035
.000
.000
.002
.001
.004
.005
.012
.001
.001
.026
1.000
.048
.004
.012
.009
.038
.001
.000
.000
.004
.001
.003
.001
.000
.000
.031
.041
.093
.017
.023
.256
.056
.080
.003
.057
.043
.059
.023
1.000
.186
.253
.017
.292
.247
.000
.001
.000
.000
1.000
.014
.000
.015
.024
.000
.000
.353
.001
.000
.000
.025
.272
.008
.002
.007
.001
.007
.012
STDSDFSBETA
MARINE UDUST ' AUTO RDOIL KRAFT ALPRO STEEL FeMn
OC
EC
NO 3
SO4
Na
Mg
Al
Si
Cl
K
Ca
Ti
V
Cr
Mn
Fe
Ni
Cu
Zn
Br
Pb
.000
.000
.000
.017
.009
.000
.003
.000
.000
.000
.000
.000
.002
.000
.000
.000
.001
.000
.000
.000
.001
.024
.012
.009
.003
.001
.001
.006
.000
.002
.'027
.034
.039
.001
.005
.005
.009
.002
.001
.001
.010
.001
.008
.005
.004
.003
.002
.001
.003
.002
.003
.002
.000
.002
.001
.000
.002
.000
.001
.002
.001
.145
.109
.000
.002
.001
.008
.009
.002
.003
.000
.011
.001
.000
.001
.000
.003
.000
.000
.181
.000
.000
.000
.001
.000
.001
.003
.000
.021
.000
.006
.000
.029
.000
.000
.000
.007
.001
.000
.000
.014
.000
.000
.000
.001
.001
.003
.002
.000
.001
.005
.000
.002
.001
.002
.002
.002
.000
.000
.000
.000
.000
.001
.000
.000
.000
.004
.002
.006
.004
.001
.034
.007
.008
.001
.008
.010
.003
.001
.000
.008
.057
.001
.019
.021
.000
.000
.000
.000
.000
.001
.000
.002
.002
.000
.000
.015
.000
.000
.000
.007
.057
.001
.000
.002
.000
.002
.001
A - 25
-------
Table A3. Continued
MEANS PINBETA
MARINE
OC
EC
NO 3
S04
Na
Mg
Al
si
Cl
K
Ca
Ti
V
Cr
Mn
Fe
Ni
Cu
Zn
Br
Pb
.028
.054
.018
.363
.353
.020
.194
.070
1.000
.019
.053
.065
.125
.099
.014
.021
.075
.093
.044
.085
.071
UDUST
.479
.430
.250
.091
.095
.103
.105
.985
.071
.459
.590
.943
.040
.234
.219
.267
.119
.150
.046
.179
.108
AUTO
.573
.293
.108
.062
.146
.102
.090
.141
.090
.186
.038
.148
.064
.003
.114
.037
.045
.137
.138
1.000
.871
RDOIL
.021
.138
.072
.110
.205
.128
.120
.032
.131
.067
.042
.044
.984
.138
.060
.040
.922
.024
.032
.057
.039
KRAFT
.026
.081
.132
1.000
.523
.071
.142
.006
.379
.124
.047
.003
.334
.115
.068
.011
.285
.002
.013
.065
.037
ALPRO
.159
.175
.175
.024
.065
.390
1.000
.373
.066
.235
.244
.346
.037
.010
.014
.151
.045
.136
.068
.012
.014
STEEL
.257
.320
.296
.093
.188
.756
.145
.289
.038
.313
.314
.257
.130
1.000
.538
.679
.149
.799
.737
.010
.021
FeMn
.015
.013
1.000
.089
.015
.188
.098
.022
.012
.800
.055
.022
.004
.163
.665
.124
.052
.127
.053
.092
.102
STDSPINBETA
MARINE UDUST AUTO RDOIL KRAFT ALPRO STEEL FeMn
OC
EC
NO 3
S04
Na
Mg
Al
Si
Cl
K
Ca
Ti
V
Cr
Mn
Fe
Ni
Cu
Zn
Br
Pb
.007
.017
.006
.007
.019
.007
.041
.013
.000
.006
.007
.009
.028
.014
.004
.006
.013
.008
.008
.015
.011
.086
.023
.024
.012
.008
.020
.013
.026
.014
.098
.114
.055
.006
.024
.008
.061
.025
.005
.016
.024
.012
.039
.033
.012
.010
.008
.023
.015
'.010
.008
.018
.010
.021
.011
.001
.010
.006
.008
.008
.020
.000
.070
.007
.014
.002
.002
.008
.018
.012
.002
.006
.006
.006
.003
.027
.021
.002
.003
.083
.002
.009
.003
.001
.004
.026
.025
.000
.074
.020
.040
.002
.017
.005
.003
.004
.077
.016
.003
.004
.040
.001
.005
.015
.012
.046
.033
.015
.006
.012
.051
.000
.046
.003
.043
.045
.075
.002
.011
.011
.029
.012
.015
.013
.013
.007
.032
.044
.041
.017
.018
.169
.027
.029
.013
.065
.053
.004
.026
.000
.087
.071
.035
.062
.051
.007
.006
.011
.016
.000
.005
.005
.024
.018
.007
.003
.071
.007
.007
.000
.031
.018
.016
.008
.017
.018
.011
.001
A - 26
-------
Table A3. Continued
MEANSPINSBETA
MARINE UDUST AUTO RDOIL KRAFT ALPRO STEEL FeMn
oc
EC
NO 3
S04
Na
Mg
Al
Si
Cl
K
Ca
Ti
V
Cr
Mn
Fe
Ni
Cu
Zn
Br
Pb
,001
.002
.000
.137
.108
.000
.045
.007
1.000
.000
.003
.006
.022
.015
.000
.000
.006
.008
.002
.009
.009
.146
.105
.051
.006
.005
.006
.010
1.000
.004
.139
.215
.899
.002
.059
.036
.053
.011
.015
.001
.029
.014
.220
.051
.010
.003
.014
.006
.007
.022
.006
.024
.001
.023
.004
.000
.010
.001
.002
.013
.013
.948
.948
.000
.011
.004
.009
.026
.010
.012
.001
.012
.003
.001
.002
1.000
.020
.003
.001
.678
.000
.001
.003
.002
.001
.005
.019
1.000
.224
.004
.023
.000
.138
.014
.002
.000
.153
.019
.005
.000
.089
.000
.000
.005
.002
.018
.021
.029
.001
.003
.105
1.000
.163
.004
.041
.042
.136
.002
.000
.000
.019
.002
.014
.003
.000
.000
.039
.053
.065
.006
.019
.308
.016
.078
.001
.059
.056
.061
.016
1.000
.193
.320
.016
.380
.324
.000
.001
.000
.000
1.000
.007
.000
.026
.010
.001
.000
.519
.002
.001
.000
.035
.402
.014
.003
.013
.002
.009
.015
STDSPINSBETA
MARINE UDUST AUTO RDOIL KRAFT ALPRO STEEL FeMn
OC
EC
N03
S04
Na
Mg
Al
Si
Cl
K
Ca
Ti
V
Cr
Mn
Fe
Ni
Cu
Zn
Br
Pb
.000
.001
.000
.003
.020
.000
.007
.001
.000
.000
.000
.001
.003
.001
.000
.000
.002
.001
.000
.001
.002
.027
.013
.005
.001
.000
.001
.001
.000
.001
.026
.038
.026
.000
.003
.003
.011
.002
.001
.001
.007
.002
.011
.008
.003
.001
.002
.001
.002
.003
.001
.002
.001
.002
.001
.000
.002
.000
.001
.003
.002
.090
.069
.000
.003
.001
.004
.007
• .002
.001
.000
.003
.001
.000
.001
.000
.003
.000
.001
.128
.000
.000
.000
.001
.000
.002
.004
.000
.034
.001
.006
.000
.009
.000
.000
.000
.014
.001
.001
.000
.025
.000
.000
.001
.001
.005
.009
.003
.000
.002
.010
.000
.015
.001
.005
.009
.015
.000
.000
.000
.003
.000
.002
.001
.000
.000
.005
.001
.006
.001
.001
.034
.001
.005
.000
.010
.012
.002
.002
.000
.010
.061
.002
.023
.021
.000
.000
.000
.000
.000
.001
.000
.002
.002
.000
.000
.017
.000
.000
.000
.008
.056
.002
.000
.004
.001
.002
.002
A - 27
-------
Table A3. Continued
MEANNMPIN
MARINE UDUST . AUTO RDOIL KRAFT ALPRO STEEL FeMn
oc
EC
NO 3
S04
Na
Mg
Al
Si
Cl
K
Ca
Ti
V
Cr
Mn
Fe
Ni
Cu
Zn
Br
Pb
.026
.047
.019
.371
.327
.018
.213
.084
1.000
.019
.050
.078
.149
.122
.015
.022
.079
.089
.042
.095
.092
.381
.324
.226
.078
.074
.079
.097
1.000
.059
.372
.463
.948
.041
.244
.189
.229
.105
.121
.037
.170
.118
.469
.226
.101
.055
.117
.080
.085
.147
.077
.156
.031
.152
.066
.003
.101
.032
.041
.113
.113
.973
.973
.017
.104
.066
.095
.160
.099
.111
.033
.110
.055
.033
.044
1.000
.143
.051
.035
.821
.020
.025
.054
.043
.025
.070
.138
1.000
.472
.063
.152
.007
.371
.119
.043
.003
.390
.139
.069
.011
.297
.002
.012
.071
.047
.133
.142
.169
.023
.055
.324
1.000
.403
.060
.203
.205
.368
.040
.010
.013
.139
.042
.117
.058
.011
.017
.196
.229
.255
.076
.139
.554
.128
.280
.030
.242
.236
.247
.125
1.000
.439
.564
.125
.616
.569
.008
.023
.014
.011
1.000
.084
.013
.161
.100
.025
.011
.721
.047
.025
.004
.187
.633
.118
.051
.113
.047
.096
.123
STDNMPIN
MARINE UDUST AUTO RDOIL KRAFT ALPRO STEEL FeMn
OC
EC
NO3
S04
Na
Mg
Al
Si
Cl
K
Ca
Ti
V
Cr
Mn
Fe
Ni
Cu
Zn
Br
Pb
.006
.011
.006
.003
.030
.005
.016
.008
.000
.005
.005
.007
.008
.005
.004
.007
.015
.007
.004
.007
.013
.036
.020
.010
.004
.003
.009
.006
.000
.007
.035
.042
.014
.004
.006
.009
.025
.009
.003
.013
.021
.007
.011
.017
.014
.012
.008
.008
.010
.009
.008
.007
.009
.008
.005
.001
.011
.004
.009
.013
.009
.047
.036
.005
.014
.007
.018
.023
.010
.005
.005
.012
.007
.000
.006
.000
.011
.004
.008
.079
.004
.002
.004
.008
.003
.013
.014
.000
.036
.007
.020
.003
.013
.002
.002
.004
.018
.004
.006
.004
.041
.002
.003
.008
.014
.021
.032
.010
.010
.015
.016
.000
.019
.008
.012
.022
,020
.002
.010
.010
.009
.006
.010
.007
.012
.011
.012
.003
.012
.010
.003
.031
.004
.009
.007
.021
.026
.003
.008
.000
.011
.055
.008
.018
.018
.006
.008
.010
.013
.000
.006
.005
.007
.012
.007
.003
.012
.003
.006
.000
.022
.045
.007
.003
.017
.010
.010
.007
A - 28
-------
Table A4. Mean and standard deviation of three simulation
runs for MPIN and other diagnostics for data set 3
MEANSDFBETA
MARINE UDUST AUTO RDOIL KRAFT ALPRO STEEL FeMn
oc
EC
NO 3
S04
Na
Mg
Al
Si
Cl
K
Ca
Ti
V
Cr
Mn
Fe
Ni
Cu
Zn
Br
Pb
.018
.015
.012
.374
.301
.017
.077
.007
1.000
.010
.020
.019
.059
.054
.009
.007
.026
.040
.016
.038
.014
.788
.285
.655
.217
.143
.094
.106
.251
.166
.653
.450
.556
.054
.376
.315
.183
.081
.203
.059
.257
.070
.800
.156
.225
.089
.186
.075
.088
.036
.175
.245
.036
.086
.066
.006
.109
.027
.024
.138
.121
.952
.336
.036
.102
.247
.281
.364
.057
.119
.010
.406
.091
.035
.036
.849
.279
.100
.034
.487
.053
.011
.109
.035
.019
.022
.120
1.000
.298
.020
.046
.001
.353
.070
.016
.001
.153
.065
.033
.005
.089
.005
.004
.031
.008
.327
.115
.475
.030
.086
.226
1.000
.111
.164
.320
.211
.282
.046
.032
.031
.144
.023
.140
.053
.034
.002
.362
.155
.399
.139
.175
.267
.104
.054
.026
.255.
.149
.156
.095
.698
.337
.418
.060
.458
.360
.005
.012
.023
.005
1.000
.114
.008
.052
.043
.003
.012
.475
.022
.009
.007
.087
.318
.063
.020
.054
.021
.068
.034
STDSDFBETA
MARINE UDUST AUTO RDOIL KRAFT ALPRO STEEL FeMn
OC
EC
NO 3
S04
Na
Mg
Al
Si
Cl
K
Ca
Ti
V
Cr
Mn
Fe
Ni
Cu
Zn
Br
Pb
.012
.010
.005
.026
.113
.027
.036
.003
.000
.006
.009
.021
.057
.043
.006
.006
.023
.033
.023
.023,
.012
.284
.136
.388
.092
.058
.138
.060
.038
.058
.402
.144
.343
.057
.314
.231
.150
.086
.168
.092
.065
.033
.316
.091
.129
.038
.090
.113
.061
.010
.053
.173
.015
.057
.071
.008
.073
.023
.020
.125
.191
.083
.125
.018
.055
.265
.209
.279
.051
.048
.007
.316
.056
.023
.033
.262
.379
.121
.028
.481
.067
.010
.082
.029
.015
.013
.039
.000
.048
.031
.017
.001
.031
.038
.007
.001
.148
.051
.020
.004
.076
.004
.004
.020
.007
.222
.053
.298
.005
.025
.299
.000
.039
.036
.143
.047
.275
.036
.040
.029
.162
.019
.097
.074
.026
.001
.340
.093
.085
.058
.031
.383
.048
.037
.028
.092
.055
.197
.085
.524
.136
.507
.051
.329
.490
.004
.010
.035
.005
.000
.046
.007
.076
.029
.001
.009
.147
.009
.009
.006
.065
.106
.079
.019
.037
.028
.068
.039
A - 29
-------
Table A4. Continued
MEANSDPSBETA
MARINE UDUST AUTO RDOIL KRAFT ALPRO STEEL FeMn
oc
EC
NO 3
S04
Na
Mg
Al
Si
Cl
K
Ca
Ti
V
Cr
Mn
Fe
Ni
Cu
Zn
Br
Pb
.000
.001
.000
.162
.062
.000
.047
.002
1.000
.000
.001
.002
.011
.004
.000
.000
.003
.003
.001
.002
.002
.155
.097
.084
.021
.006
.007
.036
.996
.011
.154
.187
.916
.003
.051
.043
.048
.015
.019
.002
.050
.025
.217
.040
.014
.006
.012
.006
.032
.027
.017
.029
.002
.029
.006
.000
.008
.001
.002
.012
.010
1.000
.868
.000
.008
.005
.016
.019
.007
.034
.001
.028
.003
.001
.001
1.000
.014
.002
.001
.639
.001
.001
.003
.002
.000
.001
.008
1.000
.059
.001
.016
.000
.111
.005
.000
..000
.061
.005
.001
.000
.033
.000
.000
.001
.000
.006
.005
.013
.000
.001
.026
1.000
.046
.003
.012
.011
.039
.001
.000
.000
.005
.000
.004
.001
.000
.000
.057
.071
.123
.026
.027
.377
.102
.105
.001
.095
.064
.085
.039
1.000
.260
.379
.023
.527
.367
.000
.001
.000
.000
1.000
.021
.000
.018
.018
.001
.000
.425
.002
.001
.000
.021
.307
.011
.002
.010
.001
.007
.011
STDSDFSBETA
MARINE
OC .000
EC .000
N03 -000
SO4 .018
Na .013
Mg .000
Al .006
Si .000
Cl .000
K .000
Ca .000
Ti .000
V .003
Cr .001
Mn .000
Fe .000
Ni .002
Cu .000
Zn .000
Br .001
Pb .001
DUST
.023
.010
.023
.006
.002
.001
.004
.007
.003
.030
.012
.079
.001
.013
.009
.013
.003
.001
.001
.002
.003
AUTO
.028
.013
.004
.004
.003
.000
.009
.002
.004
.006
.001
.004.
.002
.000
.001
.001
.001
.002
.003
.000
.056
RDOIL
.000
.003
.002
.012
.010
.001
.007
.000
.012
.002
.001
.001
.000
.002
.001
.001
.107
.001
.001
.001
.001
KRAFT.
.000
.001
.003
.000
.022
.000
.006
.000
.034
.001
.000
.000
.023
.002
.000
.000
.017
.000
.000
.001
.000
ALPRO
.001
.005
.004
.000
.000
.011
.000
.005
.002
.003
.002
.001
.000
.000
.000
.002
.000
.001
.000
.000
.000
STEEL
.006
.016
.027
.013
.002
.103
.023
.013
.001
.034
.031
.017
.020
.000
.075
.107
.011 ,
.140
.1-14
.000
.001
FeMn
.000
.000
.000
.006
.000
.004
.004
.001
.000
.116
.001
.001
.000
.004
.081
.004
.000
.003
.000
.001
.001
A - 30
-------
Table A4. Continued
MEANSPINBETA
MARINE UDUST AUTO RDOIL KRAFT ALPRO STEEL FeMn
oc
EC
NO 3
S04
Na
Mg
Al
Si
Cl
K
Ca
Ti
v •
Cr
Mn
Fe
Ni
Cu
Zn
Br
Pb
.025
.050
.015
.410
.527
.040
.186
.060
1.000
.017
.064
.061
.121
.103
.017
.027
.085
.109
.053
.062
.065
.498
.476
.317
.099
.106
.112
.111
.969
.069
.467
.673
.999
.042
.245
.229
.281
.131
.205
.076
.196
.155
.637
.321
.139
.053
.170
.109
.111
.172
.093
.214
.067
.191
.067
.005
.108
.051
.052
.176
.172
.934
.980
.022
.159
.092
.095
.224
.135
.126
.032
.129
.071
.046
.046
.933
.149
.060
.051
1.000
.037
.033
.055
.046
.023
.073
.139
1.000
.497
.054
.103
.006
.321
.116
.047
.004
.283
.111
.058
.016
.276
.011
.013
.046
.030
.170
.173
.211
.013
.058
.370
1.000
.362
.062
.229
.282
.361
.039
.018
.018
.164
.041
.155
.077
.017
.007
.251
.337
.319
.092
.196
.685
.154
.261
.014
.300
.314
.253
.126
.905
.464
.658
.129
.883
.804
.004
.031
.014
.019
1.000
.091
.010
.164
.073
.022
.008
.700
.058
.023
.012
.142
.557
.119
.044
.135
.052
.070
.093
STDSPINBETA
MARINE UDUST AUTO RDOIL KRAFT ALPRO STEEL FeMn
OC
EC
N03
S04
Na
Mg
Al
Si
Cl
K
Ca
Ti
V
Cr
Mn
Fe
Ni
CU
Zn
Br
Pb
.009
.013
.003
.014
.042
.013
.021
.011
.000
.002
.007
.013
.027
.028
.004
.010
.029
.011
.014
.020
.021
.067
.015
.047
.014
.012
.010
.017
.048
.005
.073
.011
.002
.015
.045
.010
.011
.020
.033
.019
.025
.014
.138
.026
.031
.016
.024
.008
.024
.013
.003
.020
.004
.008
.012
.003
.008
.003
.012
.031
.004
.115
.026
.007
.031
.014
.037
.035
.009
.028
.006
.024
.036
.018
.003
.044
.030
.005
.018
.000
.029
.038
.021
.015
.006
.022
.024
.000
.083
.017
.007
.004
.036
.030
.008
.001
.069
.028
.003
.006
.068
.007
.015
.018
.014
.050
.060
.033
.004
.002
.050
.000
.049
.013
.058
.034
.054
.006
.011
.007
.016
.008
.026
.017
.012
.009
.030
.032
.044
.026
.005
.059
.028
.021
.012
.036
.046
.037
.026
.165
.044
.050
.026
.142
.069
.002
.005
.012
.015
.000
.002
.007
.021
.024
.008
.003
.083
.012
.007
.006
.017
.087
.014
.008
.028
.019
.025
.019
A - 31
-------
Table A4 *, Continued
MEANSPINSBETA
MARINE UDUST AUTO RDOIL KRAFT ALPRO STEEL FeMn
oc
EC
NO 3
S04
Na
Mg
Al
Si
Cl
K
Ca
Ti
V
Cr
Mn
Fe
Ni
Cu
Zn
Br
Pb
.001
.002
.000
.135
.152
.002
.038
.005
1.000
.000
.003
.005
.021
.012
.000
.001
.008
.009
.002
.006
.005
.181
.121
.059
.006
.005
.008
.010
.998
.004
.151
.240
.940
.002
.055
.044
.058
.013
.023
.003
.045
.023
.284
.055
.011
.002
.012
.007
.010
.031
.006
.031
.002
.034
.005
.000
.010
.002
.002
.017
.014
1.000
.916
.000
.014
.005
.006
.023
.012
.014
.001
.013
.004
.001
.002
1.000
.021
.003
.002
.764
.001
.001
.004
.002
.001
.005
.019
1.000
.169
.003
.015
.000
.130
.015
.002
.000
.147
.018
.005
.000
.096
.000
.000
.004
.001
.024
.021
.031
.000
.002
.104
1.000
.165
.004
.042
.050
.145
.002
.000
.000
.023
.001
.016
.004
.000
.000
.062
.081
.082
.007
.021
.406
.027
.097
.000
.085
.075
.080
.025
1.000
.241
.428
.018
.592
.429
.000
.001
.000
.001
1.000
.009
.000
.029
.007
.001
.000
.571
.003
.001
.000
.031
.427
.018
.002
.017
.002
.009
.014
STDSPINSBETA
MARINE UDUST AUTO RDOIL KRAFT ALPRO STEEL FeMn
OC
EC
NO 3
S04
Na
Mg
Al
Si
Cl
K
Ca
Ti
V
Cr
Mn
Fe
Ni
Cu
Zn
Br
Pb
.000
.001
.000
.010
.026
.001
.007
.001
.000
.000
.001
.001
.007
.002
.000
.000
.005
.001
.001
.003
.002
.024
.012
.010
.002
.001
.001
.001
.004
.001
.029
.015
.056
.001
.010
.008
.016
.002
.001
.002
.002
.002
.029
.017
.003
.001
.002
.000
.001
.002
.001
.006
.001
.003
.002
.000
.002
.001
.001
.002
.003
.000
.035
.000
.005
.001
.005
.010
.002
.003
.000
.005
.003
.001
.001
.000
.002
.001
.001
.067
.001
.001
.002
.001
.000
.002
.004
.000
.045
.001
.002
.000
.028
.004
.001
.000
.055
.004
.001
.000
.046
.000
.000
.002
.001
.005
.015
.003
.000
.000
.025
.000
.020
.002
.010
.005
.025
.000
.000
.000
.004
.000
.002
.001
.000
.000
.004
.013
.020
.003
.001
.094
.005
.008
.000
.021
.032
.010
.012
.000
.051
.096
.008
.119
.103
.000
.001
.000
.000
.000
.002
.000
.004
.003
.001
.000
.086
.002
.001
.000
.005
.063
.006
.000
.004
.001
.002
.002
A - 32
-------
Table A4. Continued
MEANNMPIN
oc
EC
NO 3
S04
Na
Mg
Al
Si
Cl
K
Ca
Ti
V
Cr
Mn
Fe
Ni
Cu
Zn
Br
Pb
MARINE
.024
.042
.014
.367
.389
.037
.195
.070
1.000
.016
.054
.067
.145
.111
.018
.026
.084
.094
.042
.076
.072
UDUST
.424
.348
.243
.078
.068
.089
.101
.999
.060
.387
.490
.969
.043
.234
.208
.240
.111
.153
.053
.212
.152
AUTO
.532
.233
.106
.042
.108
.086
.100
.175
.080
.176
.048
.184
.070
.005
.097
.043
.045
.130
.120
1.000
.957
RDOIL
.019
.118
.072
.076
.148
.110
.117
.033
.115
.059
.034
.046
1.000
.144
.056
.044
.874
.029
.023
.059
.046
KRAFT
.025
.068
.136
1.000
.408
.055
.122
.008
.359
.122
.044
.005
.379
.135
.068
.017
.303
.011
.011
.062
.036
ALPRO
.154
.138
.176
.011
.041
.321
1.000
.405
.059
.204
.223
.380
.045
.017
.018
.152
.038
.126
.059
.020
.008
STEEL
.248
.285
.285
.082
.146
.634
.163
.311
.013
.290
.268
.283
.155
1.000
.489
.651
.130
.767
.652
.005
.036
FeMn
.015
.019
1.000
.093
.008
.169
.084
.031
.009
.755
.056
.031
.017
.177
.652
.132
.049
.130
.045
.095
.118
STDNMPIN
MARINE UDUST
AUTO RDOIL KRAFT ALPRO STEEL
FeMn
OC
EC
NO 3
so4
Na
Mg
Al
Si
Cl
K
Ca
Ti
V
Cr
Mn
Fe
Ni
Cu
Zn
Br
Pb
.004
.011
.004
.014
.032
.015
.017
.010
.000
.002
.006
.012
.022
.008
.006
.008
.028
.005
.012
.019
.017
.029
.017
.021
.016
.011
.007
.007
.002
.009
.037
.015
.029
.011
.022
.019
.032
.011
.004
.014
.004
.007
.027
.036
.016
.017
.012
.003
.006
.005
.008
.016
.007
.007
.015
.004
.009
.007
.015
.007
.013
.000
.018
.005
.022
.010
.032
.034
.010
.014
.007
.022
.023
.013
.006
.000
.008
.006
.014
.039
.024
.026
.014
.013
.004
.016
.013
.000
.057
.015
.008
.006
.038
.017
.007
.001
.069
.016
.009
.005
.073
.009
.013
.015
.015
.018
.051
.010
.004
.004
.040
.000
.025
.014
.024
.011
.033
.004
.006
.008
.014
.005
.008
.013
.011
.011
.007
.023
.036
.017
.002
.072
.014
.013
.011
.036
.063
.017
.038
.000
.050
.074
.033
.077
.077
.002
.007
.013
.015
.000
.013
.006
.012
.017
.014
.003
.057
.017
.015
.009
.013
.049
.022
.004
.014
.012
.010
.008
A - 33
-------
Table A5. Mean and standard deviation of three
simulation runs for MPIN and other
diagnostics for data set 4
MEANSDFBETA
MARINE UDUST AUTO RDOIL
oc
EC
NO 3
S04
Na
Mg
Al
Si
Cl
K
Ca
Ti
V
Cr
Mn
Fe
Ni
Cu
Zn
Br
Pb
.117
.055
.077
.057
.642
.271
.022
.151
1.000
.055
.034
.085
.073
.192
.064
.090
.089
.021
.115
.047
.057
.079
.168
.087
.095
.040
.368
.282
.489
.220
.694
.320
.628
.068
.430
.380
.449
.165
.069
.208
.069
.068
.365
.243
.683
.102
.158
.182
.036
.134
.257
.192
.017
.196
.195
.163
.128
.025
.316
.085
.558
.688
.624
.029
.022
.080
.446
.022
.041
.015
.051
.056
.026
.000
.030
.527
.061
.008
.007
.877
.017
.115
.039
.041
STDSDFBETA
MARINE UDUST AUTO - RDOIL
OC
EC
NO 3
S04
Na
Mg
Al
Si
Cl
K
Ca
Ti
V
Cr
Mn
Fe
Ni
Cu
Zn
Br
Pb
.193
.043
.099
.054
.307
.312
.025
.228
.000
.015
.044
.068
.102
.315
.065
.092
.083
.019
.094
.048
.045
.108
.063
.039
.112
.027
.342
.387
.309
.163
.482
.205
.341
.058
.495
.196
.122
.075
.102
.089
.001
.067
.552
.141
.446
.083
.103
.194
.038
.108
.257
.159
.013
.163
.184
.209
.103
.016
.250
.108
.157
.269
.344
.046
.004
.070
.481
.006
.031
.019
.059
.029
.011
.000
.010
.488
.090
.004
.003
.213
.020
.031
.021
.029
A -
-------
Table A5. Continued
MEANSDFSBETA
MARINE UDUST AUTO RDOIL
oc
EC
NO 3
S04
Na
Mg
Al
Si
Cl
K
Ca
Ti
V
Cr
Mn
Fe
Ni
Cu
Zn
Br
Pb
.002
.001
.002
.002
.363
.017
.001
.001
1.000
.001
.000
.001
.001
.001
.001
.001
.001
.001
.002
.002
.002
.089
.198
.084
.033 .
.011
.634
.905
.988
.279
.736
.540
.952
.035
.727
.895
.700
.050
.139
.079
.101
.049
.173
.044
.434
.007
.023
.011
.004
.007
.039
.006
.000
.008
.020
.009
.009
.000
.016
.051
.070
1.000
.764
.003
.002
.027
.611
.003
.004
.003
.003
.016
.001
.000
.002
.945
.003
.000
.000.
.910
.007
.016
.015
.012
STDSDFSBETA
MARINE UDUST AUTO RDOIL
OC
EC
NO 3
SO4
Na
Mg
Al
Si
Cl
K
Ca
Ti
V
Cr
Mn
Fe
Ni
Cu
Zn
Br
Pb
.000
.000
.000
.000
.111
.003
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.012
.015
.011
.006
.003
.099
.090
.021
.046
.105
.082
.072
.006
.061
.094
.037
.008
.017
.013
.006
.005
.005
.005
.047
.001
.001
.001
.000
.001
.002
.000
.000
.001
.003
.001
.000
.000
.001
.002
.002
.000
.059
.000
.000
.003
.025
.001
.001
.000
.000
.001
.000
.000
.000
.095
.000
.000
.000
.084
.001
.003
.001
.001
A - 35
-------
Table A5. Continued
MEANSPINBETA
MARINE UDUST AUTO RDOIL
oc
EC
NO 3
S04
Na
Mg
Al
Si
Cl
K
Ca
Ti
V
Cr
Mn
Fe
Ni
Cu
Zn
Br
Pb
.068
.063
.065
.051
.769
.183
.052
.056
1.000
.045
.018
.054
.037
.057
.051
.057
.040
.063
.062
.059
.062
.291
.441
.257
.135
.082
.686
.832
.927
.317
.871
.633
.884
.133
.832
.826
.776
.181
.369
.269
.250
.170
.519
.262
.739
.081
.150
.114
.066
.099
.151
.103
.013
.106
.128
.119
.102
.016
.131
.285
.322
1.000
.853
.065
.058
.187
.753
.055
.071
.061
.067
.099
.041
.000
.045
.894
.072
.016
.011
.989
.109
.152
.125
.108
STDSPINBETA
MARINE UDUST AUTO RDOIL
OC
EC
NO 3
S04
Na
Mg
Al
Si
Cl
K
ca
Ti
V
Cr
Mn
Fe
Ni
Cu
Zn
Br
Pb
.003
.005
.005
.003
.117
.004
.005
.011
.OTOO
.005
.004
.011
.001
.016
.002
.009
.007
.003
.001
.009
.004
.009
.066
.022
.011
.019
.082
.104
.126
.026
.182
.042
.106
.014
.113
.154
.081
.004
.033
.034
.019
.005
.045
.025
.034
.011
.015
.007
.001
.018
.006
.015
.002
.012
.011
.027
.010
.003
.008
.013
.027
.000
.072
.002
.003
.004
.060
.001
.001
.004
.009
.002
.007
.000
.008
.113
.013
.001
.002
.018
.002
.003
.010
.009
A - 36
-------
Table A5. Continued
MEANSPINSBETA
MARINE UDUST AUTO RDOIL
oc
EC
NO 3
S04
Na
Mg
Al
Si
Cl
K
Ca
Ti
V
Cr
Mn
Fe
Ni
Cu
Zn
Br
Pb
.004
.004
.004
.003
.593
.038
.003
.003
1.000
.002
.000
.003
.002
.003
.003
.003
.002
.004
.004
.004
.005
.091
.212
.076
.027
.008
.641
.915
.989
.120
.756
.569
.957
.026
.747
.906
.725
.038 . .
.149
.084
.076
.041
.233
.062
.520
.008
.022
.014
.005
.009
.022
.009
.000
.011
.019
.012
.012
.000
.016
.072
.098
1.000
.828
.004
.003
.034
.708
.003
.006
.004
.004
.010
.001
.000
.002
.963
.005
.000
.000
.940
.011
.023
.016
.014
STDSPINSBETA
MARINE UDUST AUTO RDOIL
OC
EC
NO 3
S04
Na
Mg
Al
Si
Cl
K
Ca
Ti
V
Cr
Mn
Fe
Ni
Cu
Zn
Br
Pb
.000
.000
.001
.000
.089
.003
.000
.001
.000
.000
.000
.001
.000
.001
.000
.000
.000
.000
.000
.001
.001
.011
.014
.009
.005
.003
.090
.081
.018
.015
.096
.078
.064
.004
.056
.084
.033
.006
.017
.013
.004
.003
.007
.006
.046
.001
.002
.001
.000
.001
.001
.000
.000
.001
.002
.001
.000
.000
.001
.003
.002
.000
.046
.000
.000
.004
.021
.001
.001
.000
.000
.001
.000
.000
.000
.064
.001
.000
.000
.057
.001
.004
.001
.001
A - 37
-------
Table A5. Continued
MEANNMPIN
MARINE UDUST AUTO RDOIL
oc
EC
NO 3
S04
Na
Mg
Al
Si
Cl
K
Ca
Ti
V
Cr
Mn
Fe
Ni
Cu
Zn
Br
Pb
.064
.060
.064
.057
.769
.196
.055
.055
1.000
.042
.019
.054
.041
.054
.054
.057
.039
.060
.061
.059
.067
.301
.460
.276
.165
.089
.799
.956
.995
.346
.868
.753
.978
.160
.864
.951
.851
.194
.385
.290
.276
.201
.483
.248
.721
.089
.148
.120
.069
.095
.149
.094
.014
.106
.139
.111
.107
.016
.127
.269
.313
1.000
.910
.061
.056
.185
.841
.055
.076
.064
.066
.099
.037
.000
.046
.981
.069
.017
.011
.969
.105
.151
.126
.117
STDNMPIN
MARINE UDUST AUTO RDOIL
OC
EC
NO 3
S04
Na
Mg
Al
Si
Cl
K
Ca
Ti
V
Cr
Mn
Fe
Ni
Cu
Zn
Br
Pb
.002
.000
.007
.003
.057
.008
.002
.005
.000
.004
.003
.006
.004
.007
.004
.004
.006
.001
.003
.009
.005
.019
.015
.015
.015
.016
.055
.043
.009
.021
.054
.052
.033
.012
.033
.044
.020
.015
.021
.022
.007
.008
.007
.012
.032
.007
.008
.004
.001
.005
.004
.002
.002
.004
.008
.005
.002
.003
.004
.006
.004
.000
.025
.002
.003
.010
.013
.005
.005
.001
.003
.003
.002
.000
.004
.033
.004
.001
.001
.029
.006
.013
.005
.006
A - 38
-------
Table A6. Mean and standard deviation of three
simulation runs for MPIN and other
diagnostics for data set 5
MEANSDFBETA
MARINE UDUST AUTO RDOIL
oc
EC
NO 3
S04
Na
Mg
Al
Si
Cl
K
Ca
Ti
V
Cr
Mn
Fe
Ni
Cu
Zn
Br
Pb
.018
.016
.084
.093
.730
.139
.039
.039
.760
.013
.027
.027
.032
.035
.025
.065
. .025
.060
.023
.012
.098
.059
.092
.229
.249
.088
.431
.359
.413
.217
.238
.656
.283
.082
.527
.245
.540
.081
.265
.098
.070
.269
.097
.042
.570
.152
.111
.062
.046
.048
.100
.031
.011
.045
.065
.074
.046
.035
.056
.167
.092
.176
.963
.040
.031
.123
.785
.137
.074
.029
.023
.247
.042
.006
.023
.345
.152
.010
.019
.523
.193
.252
.114
.390
STDSDFBETA
MARINE UDUST AUTO RDOIL
OC
EC
NO 3
S04
Na
Mg
Al
Si
Cl
K
Ca
Ti
V
Cr
Mn
Fe
Ni
Cu
Zn
Br
Pb
.008
.006
.072
.092
.271
.175
.036
.047
.415
.004
.017
.020
.040
.013
.027
.070
.019
.026
.012
.010
.024
.020
.037
.181
.277
.026
.445
.290
.513
.196
.167
.220
.138
.101
.430
.199
.403
.045
.087
.107
.069
.090
.036
.002
.490
.143
.007
.061
.048
.050
.067
.015
.004
.034
.072
.043
.053
.038
.028
.028
.072
.166
.065
.051
.043
.058
.373
.191
.088
.023
.008
.369
.062
.004
.014
.140
.238
.007
.013
.408
.250
.404
.186
.528
A - 39
-------
Table A6. Continued
MEANS DFS BETA
OC
EC
NO 3
S04
Na
Mg
Al
Si
Cl
K
Ca
Ti
V
Cr
Mn
Fe
Ni
Cu
Zn
Br
Pb
MARINE
.002
.002
.002
.001
.318
.012
.001
.001
1.000
.001
.000
.001
.001
.001
.001
.001
.001
.002
.002
.002
.002
UDUST
.119
.268
.128
.064
.027
.703
.975
.940
.316
.771
.645
.953
.045
.704
.897
.684
.066
.209
.099
.138
.089
AUTO
.221
.046
.410
.016
.030
.015
.007
.010
.053
.010
.000
.012
.022
.013
.013
.001
.021
.062
.080
.900
.866
RDOIL
.006
.003
.038
.930
.006
.006
.005
.004
.024
.002
.000
.002
.855
.003
.000
.000
.926
.014
.028
.021
.020
STDSDFSBETA
MARINE UDUST AUTO RDOIL
OC
EC
NO 3
S04
Na
Mg
Al
Si
Cl
K
Ca
Ti
V
Cr
Mn
Fe
Ni
CU
Zn
Br
Pb
.001
.000
.000
.000
.079
.003
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.001
.001
.014
.017
.004
.011
.011
.087
.040
.060
.005
.070
.075
.061
.007
.145
.023
.028
.010
.037
.003
.025
.021
.070
.014
.087
.004
.011
.003
.002
.003
.017
.002
.000
.003
.002
.005
.003
.000
.001
.018
.029
.088
.233
.001
.001
.010
.086
.002
.001
.000
.000
.002
.000
.000
.000
.146
.000
.000
.000
.128
.003
.006
.007
.002
A - 40
-------
Table A6. Continued
MEANSPINBETA
MARINE UDUST AUTO RDOIL
oc
EC
NO 3
S04
Na
Mg
Al
Si
Cl
K
Ca
Ti
V
Cr
Mn
Fe
Ni
Cu
Zn
Br
Pb
.077
.074
.071
.039
.892
.162
.043
.038
1.000
.034
.022
.043
.036
.051
.042
.055
.036
.073
.077
.050
.063
.379
.619
.389
.192
.165
.792
.861
.795
.363
.844
.912
.892
.183
.938
.854
.949
.221
.501
.367
.294
.247
.636
.311
.866
.117
.219
.140
.088
.100
.184
.118
.016
.124
.159
.157
.124
.052
.153
.336
.410
.931
.941
.100
.082
.253
.872
.093
.088
.072
.065
.122
.046
.006
.053
.958
.078
.023
.022
.984
.157
.233
.137
.142
STDSPINBETA
MARINE UDUST AUTO RDOIL
OC
EC
NO 3
S04
Na
Mg
Al
Si
Cl
K
Ca
Ti
V
Cr
Mn
Fe
Ni
Cu
Zn
Br
Pb
.011
.001
.009
.010
.015
.021
.004
.004
.000
.004
.005
.005
.005
.001
.006
.006
.002
.006
.012
.009
.016
.030
.074
.035
.047
.022
.087
.122
.114
.032
.020
.084
.123
.022
.055
.126
.046
.033
.082
.018
.028
.033
.114
.037
.180
.016
.031
.011
.003
.019
.042
.016
.004
.008
.013
.017
.011
.007
.002
.063
.109
.060
.052
.008
.011
.031
. .115
.008
.004
.008
.008
.019
.002
.003
.006
.060
.004
.003
.003
.027
.024
.012
.017
.020
A - 41
-------
Table A6. Continued
MEANSPINSBETA
MARINE UDUST AUTO RDOIL
oc
EC
NO 3
S04
Na
Mg
Al
Si
Cl
K
Ca
Ti
V
Cr
Mn
Fe
Ni
CU
Zn
Br
Pb
.005
.004
.004
.002
.557
.030
.002
.002
1.000
.001
.000
.002
.001
.002
.002
.002
.001
.005
.005
.003
.005
.118
.280
.117
.049
.019
.707
.978
.946
.129
.788
.668
.958
.035
.722
.907
.708
.051
.215
.102
.107
.071
.284
.062
.489
.016
.028
.019
.009
.013
.028
.013
.000
.016
.023
.018
.017
.002
.021
.084
.108
.928
.900
.008
.005
.046
.948
.006
.008
.006
.006
.013
.002
.000
.003
.898
.005
.001
.000
.950
.020
.038
.022
.021
STDSPINSBETA
MARINE UDUST AUTO RDOIL
OC
EC
NO 3
S04
Na
Mg
Al
si
Cl
K
Ca
Ti
V
Cr
Mn
Fe
Ni
Cu
Zn
Br
Pb
.001
.001
.001
.000
.075
.005
.001
.000
.000
.000
.000
.000
.000
.001
.000
.000
.000
.001
.001
.001
.001
.015
.018
.003
.007
.008
.076
.036
.054
.012
.065
.071
.055
.005
.135
.020
.027
.007
.036
.0,04
.011
.015
.071
.016
.078
.003
.008
.004
.002
.003
.009
.002
.000
.003
.001
.005
.003
.000
.000
.020
.033
.065
.173
.001
.001
.012
.062
.002
.001
.000
.000
.002
.000
.000
.000
.104
.000
.000
.000
.087
.004
.007
.006
.002
A - 42
-------
Table A6. Continued
MEANNMPIN
MARINE UDUST AUTO RDOIL
oc
EC
NO 3
S04
Na
Mg
Al
Si
Cl
K
Ca
Ti
V
Cr
Mn
Fe
Ni
Cu
Zn
Br
Pb
.070
.064
.063
.045
.745
.174
.050
.047
1.000
.036
.019
.047
.038
.047
.048
.050
.038
.069
.067
.056
.067
.342
.529
.342
.220
.137
.840
.989
.972
.358
.887
.817
.978
.188
.847
.952
.841
.226
.463
.320
.327
.266
.530
.248
.698
.126
.167
.139
.095
.114
.167
.115
.014
.127
.151
.132
.129
.042
.146
.288
.326
.963
.945
.087
.067
.214
.973
.074
.090
.079
.076
.115
.047
.005
.056
.946
.068
.025
.018
.974
.140
.195
.147
.146
STDNMPIN
MARINE UDUST AUTO RDOIL
OC
EC
N03
S04
Na
Mg
Al
Si
Cl
K
Ca
Ti
V
Cr
Mn
Fe
Ni
Cu
Zn
Br
Pb
.008
.004
.006
.001
.051
.014
.005
.005
.000
.004
.003
.004
.006
.007
.005
.004
.005
.006
.005
.010
.007
.022
.017
.005
.015
.027
.045
.018
.028
.017
.036
.043
.028
.013
.079
.011
.016
.015
.038
.007
.017
.028
.065
.032
.056
.011
.023
.013
.009
.013
.028
.008
.004
.011
.003
.020
.011
.001
.002
.035
.048
.033
.094
.005
.008
.028
.032
.011
.006
.003
.002
.008
- .003
.002
.004
.056
.002
.001
.000
.045
.015
.019
.019
.007
A - 42
-------
Table A7. Mean and standard deviation of three
simulation runs for MPIN and other
diagnostics for data set 6
MEANSDFBETA
MARINE UDUST AUTO RDOIL
oc
EC
NO 3
S04
Na
Mg
Al
si
Cl
K
Ca
Ti
V
cr
Mn
Fe
Ni
Cu
Zn
Br
Pb
.013
.045
.062
.015
.708
.123
.012
.026
1.000
.008 .
.012
.022
.021
.050
.050
.030
.040
.061
.029
.053
.042
.050
.282
.443
.090
.094
.603
.234
.410
.385
.231
.383
.372
.066
.737
.760
.497
.210
.356
.135
.357
.165
.094
.196
.616
.042
.137
.100
.021
.072
.194
.043
.004
.051
.076
.135
.134
.023
.142
.264
.130
.902
.612
.018
.029
.262
.370
.080
.070
.020
.034
.129
.013
.003
.022
.468
.063
.021
.010
1.000
.115
.105
.180
.090
STDSDFBETA
MARINE- UDUST AUTO RDOIL
OC
EC
NO 3
S04
Na
Mg
Al
Si
Cl
K
Ca
Ti
V
Cr
Mn
Fe
Ni
Cu
Zn
Br
Pb
.002
.052
.049
.003
.286
.056
.007
.035
.000
.010
.012
.017
.015
.017
.031
.022
.009
.050
.027
.012
.027
.015
.311
.492
.092
.022
.352
.184
.512
.104
.270
.326
.223
.018
.130
.345
.463
.081
.265
.141
.165
.084
.028
.246
.399
.025
.035
.066
.012
.107
.057
.061
.004
.039
.053
.075
.093
.018
.022
.269
.107
.097
.434
.005
.027
.319
.247
.071
.042
.016
.042
.028
.016
.003
.013
.301
.010
.011
.008
.000
.087
.129
.111
.038
A - 44
-------
Table A7. Continued
MEANSDPSBETA
MARINE UDUST AUTO RDOIL
oc
EC
NO 3
S04
Na
Mg
Al
Si
Cl
K
Ca
Ti
V
Cr
Mn
Fe
Ni
Cu
Zn
Br
Pb
.003
.003
.002
.001
.501
.015
.001
.001
1.000
.001
.000
.001
.001
.001
.001
.002
.001
.002
.002
.002
.002
.100
.309
.182
.053
.031
..752
.919
.998
.340
.818
.734
.930
.046
.826
.893
.809
.076
.173
.091
.147
.090
.310
.078
.629
.017
.045
.020
.009
.014
.077
.013
.000
.016
.032
.020
.017
.002
.034
.079
.116
.948
.824
.007
.003
.034
.705
.007
.006
.004
.004
.021
.001
.000
.002
.818
.004
.000
.000
1.000
.011
.023
.019
.019
STDSDFSBETA
MARINE UDUST AUTO RDOIL
OC
EC
NO 3
S04
Na
Mg
Al
si
Cl
K
Ca
Ti
V
Cr
Mn
Fe
Ni
Cu
Zn
Br
Pb
.000
.000
.000
.001
.051
.004
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.001
.001
.000
.015
.048
.012
.020
.024
.067
.033
.003
.037
'.103
.034
.052
.030
.139
.139
.029
.025
.018
.032
.037
.004
.014
.013
.095
.009
.009
.003
.002
.003
.011
.002
.000
.002
.013
.002
.004
.001
.011
.011
.037
.090
.154
.004
.003
.028
.059
.007
.003
.002
.002
.003
.000
.000
.001
.107
.004
.000
.000
.000
.010
.014
.009
.015
A - 4!
-------
Table A7. Continued
MEANSPINBETA
MARINE UDUST AUTO RDOIL
oc
EC
NO 3
S04
Na
Mg
Al
Si
Cl
K
Ca
Ti
V
Cr
Mn
Fe
Ni
Cu
Zn
Br
Pb
.076
.075
.061
.042
1.000
.158
.044
.038
.860
.030
.023
.045
.038
.053
.046
.048
.029
.091
.086
.037
.056
.333
.581
.380
.200
.164
.811
.811
.724
.359
.882
.Til
.864
.172
.890
.851
.757
.165
.568
.373
.267
.271
.679
.337
.827
.130
.248
.155
.090
.097
.199
.132
.013
.131
.170
.161
.132
.044
.127
.444
.491
.798
.944
.119
.076
.200
.971
.106
.090
.069
.061
.119
.048
.008
.051
.995
.080
.022
.017
.793
.181
.246
.134
.154
STDSPINBETA
MARINE UDUST AUTO RDOIL
OC
EC
NO 3
S04
Na
Mg
Al
Si
Cl
K
Ca
Ti
V
Cr
Mn
Fe
Ni
Cu
Zn
Br
Pb
.002
.008
.013
.010
.000
.014
.003
.009
.023
.007
.003
.005
.006
.011
.013
.004
.004
.009
.012
.004
.007
.054
.078
.052
.057
.066
.120
.087
.186
.006
.028
.099
.090
.057
.191
.241
.049
.048
.065
.065
.055
.027
.023
.030
.195
.037
.022
.042
.008
.016
.017
.018
.007
.024
.020
.034
.032
.008
.027
.051
.091
.179
.059
.030
.046
.048
.027
.051
.007
.019
.025
.005
.004
.005
.009
.009
.042
.006
.003
.041
.073
.073
.067
.032
A - 46
-------
Table A7. Continued
MEANSPINSBETA
MARINE UDUST AUTO RDOIL
oc
EC
NO 3
S04
Na
Mg
Al
Si
Cl
K
Ca
Ti
V
Cr
Mn
Fe
Ni
Cu
Zn
Br
Pb
.006
.006
.004
.002
.707
.033
.003
.003
1.000
.001
.001
.003
.002
.003
.003
.004
.002
.005
.005
.003
.004
.096
.315
.158
.043
.020
.751
.927
.999
.158
.831
.751
.937
.036
.835
.902
.823
.056
.179
.093
.120
.077
.373
.098
.678
.018
.036
.024
.011
.017
.045
.017
.000
.020
.031
~ .025
.021
.003
.031
.101
.147
.961
.864
.010
.004
.039
.782
.006
.008
.005
.005
.014
.002
.000
.003
.873
.006
.000
.000
1.000
.016
.032
.021
.021
STDSPINSBETA
MARINE UDUST AUTO RDOIL
OC
EC
NO 3
S04
Na
Mg
Al
Si
Cl-
K
Ca
Ti
V
Cr
Mn
Fe
Ni
Cu
Zn
Br
Pb
.001
.001
.001
.001 •
.040
.009
.000
.000
.000
.001
.000
.000
.000
.001
.000
.000
.001
.001
.001
.001
.000
.014
.047
.008
.017
.015
' .059
.030
.002
.017
.094
.031
.047
.023
.126
.128
.028
.020
.018
.032
.028
.007
.015
.014
.089
.010
.006
.004
.003
.004
.007
.002
.000
.002
.012
.002
.005
.001
.011
.014
.044
.067
.120
.005
.004
.030
.045
.006
.003
.002
.003
.002
.001
.000
.001
.075
.005
.000
.000
.000
.013
.018
.010
.014
A - 47
-------
Table A7. Continued
MEANNMPIN
MARINE UDUST AUTO RDOIL
oc
EC
NO 3
S04
Na
Mg
Al
Si
Cl
K
Ca
Ti
V
Cr
Mn
Fe
Ni
CU
Zn
Br
Pb
.075
.077
.066
.046
.840
.179
.055
.055
1.000
.033
.027
.053
.042
.057
.054
.060
.044
.071
.073
.051
.060
.310
.560
.397
.204
.133
.866
.963
.999
.397
.911
.867
.968
.183
.912
.948
.907
.233
.423
.301
.344
.276
.611
.313
.822
.130
.190
.156
.103
.131
.211
.130
.013
.140
.175
.158
.144
.050
. .175
.318
.380
.980
.928
.097
.062
.190
.884
.074
.087
.071
.072
.116
.044
.008
.050
.934
.072
.021
.018
1.000
.120
.174
.144
.141
STDNMPIN
MARINE UDUST AUTO RDOIL
OC
EC
NO 3
S04
Na
Mg
Al
Si
Cl
K
Ca
Ti
V
Cr
Mn
Fe
Ni
Cu
Zn
Br
Pb
.004
.005
.005
.013
.024
.024
.001
.000
.000
.008
.004
.002
.005
.005
.004
.000
.006
.004
.009
.010
.003
.022
.042
.010
.041
.060
.034
.016
.001
.022
.051
.018
.024
.059
.068
.069
.015
.043
.021
.054
.042
.012
.012
.023
.054
.036
.016
.012
.014
.014
.016
.009
.006
.008
.033
.007
.016
.009
.031
.022
.061
.034
.063
.022
.029
.073
.025
.036
.019
.016
.017
.007
.007
.005
.011
.039
.032
.002
.002
.000
.049
.048
.031
.046
A - 48
-------
Table AS. Effects of deletion of influential and
nonifluential elements to source apportionments
and their variance for data set 6
Deleted elements
None
Na
Cl
Na,Cl
Si,Ti,Cr,Mn
Zn
EC,Cu,Zn
OC,EC,Cu,Zn
Cl,Mn,Ni,Br
Source apportionment
Marine
2.10
1.68
2.61
^92
2.15
2.10
2.09
2.08
2.73
Udust
36.62
36.41
35.99
36.83
34.16
36.63
36.80
36.94
32.67
Auto
11.00
11.22
11.25
11.16
11.27
11.01
11.07
11.25
12.86
Rdoil
4.85
4.81
4.78
4.84
4.93
4.85
4.85
4.85
5.29
Standard error of
source apportionment
Marine
.41
.53
.63
2.29
.41
.41
.41
.41
.63
Udust
2.76
2.77
2.83
3.03
3.56
2.78
2.88
2.92
3.01
Auto
1.31
1.32
1.33
1.34
1.34
1.34
1.40
1.52
1.62
Rdoil
.65
.65
.66
.66
.65
.66
.66
.66
.84
A - 49
-------
TECHNICAL REPORT DATA
(Please read Instructions on the reverse before completing)
1. REPORT NO.
EPA 450/4-88-005
3. RECIPIENT'S ACCESSION NO.
4. TITLE AND SUBTITLE
Chemical Mass Balance Receptor Model Diagnostics
5. REPORT DATE
April 1988
6. PERFORMING ORGANIZATION CODE
7. AUTHOR(S)
8. PERFORMING ORGANIZATION REPORT NO.
Dr. Ronald C. Henry and Mr. Bong Mann Kim
ATION NAME AND ADDRESS
Southern California
9. PERFORMING ORGANI
University of
Civil Engineering Department
University Park
Los Angeles, CA 90089-0231
10. PROGRAM ELEMENT NO.
11. CONTRACT/GRANT NO.
12. SPONSORING AGENCY NAME AND ADDRESS
U.S. Environmental Protection Agency
OAQPS, SRAB, MD-14
Research Triangle Park, N.C. 27711
13. TYPE OF REPORT AND PERIOD COVERED
14. SPONSORING AGENCY CODE
15. SUPPLEMENTARY NOTES
EPA Project Officer: Thompson G. Pace
16. ABSTRACT
This document (1) describes diagnostics which will assist the CMB user
in identifying the most influential species in CMB calculations; (2) 'demon-
strates testing done on diagnostics by using sets of artificial data and
intercomparisons among diagnostics; and (3) recommends a modification of
the pseudo-inverse matrix (MPIN) diagnostic to be used in identifying
influential species. Influential species are those which have large effect
on the estimated source contributions or its error.
17.
KEY WORDS AND DOCUMENT ANALYSIS
DESCRIPTORS
b.IDENTIFIERS/OPEN ENDED TERMS C. COSATI Field/Group
Diagnostics
Chemical Mass Balance
Influential species
MPIN Diagnostic
18. DISTRIBUTION STATEMENT
19. SECURITY CLASS (This Report)
21. NO. OF PAGES
82
20. SECURITY CLASS (This page)
22. PRICE
EPA Form 2220-1 (Rev. 4-77) PREVIOUS EDITION is OBSOLETE
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U.S. Environmental Protection Agency
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