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





                             Page  1

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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





                             Page 2

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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





                             Page 3

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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





                              Page  4

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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.





                             Page 5

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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

                              Page 6

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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


                             Page 7

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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






                             Page 8

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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

                              Page  9

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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



                             Page 10

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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





                             Page  11

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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)










                             Page 12

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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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 C
 O
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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
                         Page 16

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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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U
0)
i

0) 0)
A U
e ^
3 3
2 0
CO


C
a) a)
U (0
^j O
3 43
o a
CO
X

3 M
^ -P
EH (C
2



0 O O O 0 0
H  &> &> &>  &>
O O O O O O
H n If) H O If)





CM rg 04 n CM CM








CO CO CO T T T










H H H o n n

CO CO CO CO CO CO
O U O O O CJ
rfj *4j rij i4j i4j rtj
CU CU CU &4 Ou CU




Simulated
data Sets
H
EH
W
CO
OJ
EH
W
CO
n
EH
W
CO
EH
W
CO
If)
EH
W
CO
V>
W
CO
Page 18

-------
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  =  * aijsj /             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)





                             Page 19

-------
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.
                             Page 21

-------
       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

-------
       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

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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

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                                    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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