SOURCE ORIENTED vs RECEPTOR ORIENTED MODELS

1
SOURCE ORIENTED vs RECEPTOR ORIENTED MODELS

• Source oriented given source characteristics and
  meteorological data, estimate pollutant
  concentrations at receptor site(s)
• Receptor oriented given measured pollutant
  concentration at receptor site, estimate the
  contributions of different sources, source
  apportionment

2
Receptor models

• CMB Chemical Mass Balance
• Factor Analysis (Multivariate methods)
• PCA Principal Component Analysis
• PMF Positive Matrix Factorization

3
Chemical Mass Balance Receptor Modelling
Source 1xi1 i1,n
3
Receptoryi i1,n
1
Source 3xi3 i1,n
2
Source 2xi2 i1,n
4
Components

• PM
• metals
• ions
• PAH
• OC/EC
• etc.
• Gas phase
• various organic cpds
• VOCs
• etc.

5
Chemical Mass Balance Receptor Modelling

6
Chemical Mass Balance Receptor Modelling

7
Chemical Mass Balance Receptor Modelling Simple
Spreadsheet Implementation

• Electronic spreadsheets like Excel make it easy
  to implement the model in the above form.
• The Solver function in Excel enables the
  minimization operation.
• Graphical tools in Excel enable qualitative
  assessment of model fit and the inputs.

8
(No Transcript)
9
(No Transcript)
10
(No Transcript)
11
(No Transcript)
12
U.S. EPAs CMB8

• The CMB model incorporates the statistics to
  improve our estimate of the source contributions
  by weighting the source and receptor profiles
  according to the uncertainties associated with
  them.
• It also reports the uncertainties associated with
  the source contribution estimates and goodness
  of fit parameters.
• Version 8 is windows based, more user friendly.
• Example Source apportionment for motor vehicle
  related VOCs in micro-environments

13
Chemical Mass Balance Receptor Modelling U.S.
EPAs CMB Model

• There are uncertainties associated with both the
  receptor and source profiles. The measured
  quantities are thus
• The model results then also have uncertainties
  associated with them

14
U.S. EPAs CMB Model The effective variance
method

• The CMB model uses an effective variance which
  looks at variances in both the receptor and
  source profiles, the latter weighted by the
  source contributions. The inverse of these are
  then used to weight the discrepancies for each
  element, I.e. the contribution of a component
  with smaller effective variance will be weighted
  more in the iterative procedure.

15
CMB Effective Variance Iterative
procedure(simplified)

• Start with all source contributions 0
• Find the elements of the effective variance
  matrix
• Estimate new source contribution estimates that
  will reduce the sum of the square of the errors
  weighted by the elements of the effective
  variance matrix.
• Check the new source estimates against previous
  ones
• Go to 5 if all are within 1 of old values
• Otherwise replace them with new values and go
  to 2.
• 5. Assign the last source contribution
  estimates, calculate statistical performance
  indicators and report

16
Sources
17
Species
18
(No Transcript)
19
(No Transcript)
20
(No Transcript)
21
Fitting sources and species

• The receptor data may contain concentrations of
  many species, some of which may not be
  particularly interesting for our source
  apportionment.
• We may also have data on many source types, only
  some of which have practical significance for a
  particular receptor.
• We may therefore choose the relevant species and
  sources as fitting, I.e. those that will be
  included in the iterative refinement procedure.
  The remaining sources will not be considered at
  all. The mass balances on the remaining species
  will be calculated and reported but will not
  affect the source apportionment.

22
Receptors

• The last two columns are x-y coordinates of
  receptors for graphical display of results

23
Source contribution estimates SCE
24
STD ERR

• The standard errors reflect the precision of the
  ambient data, the source profiles, and the amount
  of collinearity among different profiles.
• There is about a 66 probability that the true
  source contribution is within one standard error
  and about a 95 probability that the true
  contribution is within two standard errors of the
  source contribution estimate.

25
TSTAT

• The T-statistic (TSTAT) is the ratio of the
  source contribution estimate to the standard
  error.
• A TSTAT value less than 2.0 indicates that the
  source contribution estimate is at or below a
  detection limit.

26
Performance measures

• R SQUARE
• PERCENT MASS
• CHI SQUARE
• DF

27
CHI SQUARE

• The chi-square is the weighted sum of squares of
  the differences between the calculated and
  measured fitting species concentrations.
• The weighting is inversely proportional to the
  squares of the precision in the source profiles
  and ambient data for each species. Ideally, there
  would be no difference between calculated and
  measured species concentrations and chi-square
  would equal zero.
• A value less than 1 indicates a very good fit to
  the data, while values between 1 and 2 are
  acceptable. Chi-square values greater than 4
  indicate that one or more species concentrations
  are not well explained by the source contribution
  estimates.

28
DF

• The degrees of freedom equal the number of
  fitting species minus the number of fitting
  sources. The degrees of freedom is needed when
  statistical significance tests are applied to the
  chi-square value.

29
R SQUARE

• The R-square is the fraction of the variance in
  the measured concentrations that is explained by
  the variance in the calculated species
  concentrations.
• It is determined by a linear regression of
  measured versus model-calculated values for the
  fitting species.
• R-square ranges from 0 to 1.0. The closer the
  value is to 1.0, the better the source
  contribution estimates explain the measured
  concentrations.
• When R-square is less than 0.8, the source
  contribution estimates do not explain the
  observations very well with the fitting source
  profiles and/or species.

30
PERCENT MASS

• Percent mass is the percent ratio of the sum of
  the model-calculated source contribution
  estimates to the measured mass concentration.
  This ratio should equal 100, although values
  ranging from 80 to 120 are acceptable. If the
  measured mass is very low (lt 5 to 10 ?g/m3),
  percent mass may be outside of this range because
  the precision of the mass measurement is on the
  order of 1 to 2 ?g/m3.

31
Combined Performance Measure

• The Fit Measure is calculated using the
  algorithm
• Fit_measure Wt_chisqr ( 2 / chisqr )
• Wt_R-square R-square
• Wt_pcmass pcmass / 100 (for pcmass lt 100) or
  
• Wt_pcmass 100 / pcmass ( for pcmass gt 100)
• Wt_fracest Frac_Est
• where chisqr, rsquare, and pcmass are the
  performance measures for reduced chi-square, R-
  square, and per cent mass, respectively, and
  where Frac_Est is the ratio of the number of
  estimable fitting sources to the total number of
  fitting sources.
• The weights accorded to each of these variables
  (Wt_chisqr, Wt_R-square, Wt_pcmass , and
  Wt_fracest) are set to 1.0 by default. These
  weights may be changed in the Options window.

32
Source contributions to species

• Recall that the basis of the CMB model is that
  species are transported equally effectively from
  the source to the receptor (i.e. conservative
  species)
• However, because each component is present in
  different relative abundances in the various
  sources, the contribution of different sources to
  the receptor load for a particular component
  will be different for each component.
• Furthermore, the mass balance closure for each
  component will be different.

33
(No Transcript)
34

• This display shows how well the individual
  ambient concentrations are reproduced by the
  source contribution estimates. It offers clues
  concerning which sources might be missing or
  which ones do not belong in the calculation.
• Fitting species are marked with an asterisk in
  the column labeled ' I '.
• Note that the symbol lt flags values less than the
  uncertainty.
• The asterisks indicate numerical overflow,
  meaning that the number is too large to be
  displayed in the allocated field.

35

• The column labeled RATIO R/U contains the ratio
  of the signed difference between the calculated
  and measured concentrations (the residual)
  divided by the uncertainty of that residual
  (square root of the sum of the squares of the
  uncertainty in the calculated and measured
  concentrations).
• The R/U ratio specifies the number of uncertainty
  intervals by which the calculated and measured
  concentrations differ.
• When the absolute value of the R/U ratio exceeds
  2, the residual is significant. If it is
  positive, then one or more of the profiles is
  contributing too much to that species. If it is
  negative, then there is an insufficient
  contribution to that species and a source may be
  missing.
• The sum of the squared R/U for fitting species
  divided by the degrees of freedom yields the chi
  square. The highest R/U values for fitting
  species are the cause of high chi square values.

36
(No Transcript)
37
MPIN

• The Modified Psuedo Inverse (MPIN) matrix shows
  which species have the largest influence on the
  source contribution estimates from each profile.
• MPIN is normalized such that it takes on values
  from -1 to 1. Species with MPIN absolute values
  of 1 to 0.5 are considered 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.

38
MPIN matrix
39
VOC's Associated with Motor Vehicles
Exhaust EmissionsEvaporative Emissions
C1 - C10 RangeAlkanesAlkenesAlkynesCycloalkane
sAromatics
40
Chemical Mass Balance Receptor Modelling
Source profile characterization
Fuel
Whole gasoline
Headspace vapor
Individual vehicles
Exhaust emissions - UDDS
Evaporative emissions - SHED
Fleet emission characteristics
Tunnel studies Roadside measurements
41
Source Profiles
42
ERMD Source Profiles with 17 species
0.45
0.4
0.35
0.3
0.25
Fraction of total
0.2
0.15
0.1
6 GA
0.05
5 LPG
4 CNG
0
3 HOTST
2 COLDST
1 FUEL
Ethylene
Ethane
Propane
n-butane
n-pentane
benzene
3m-pentane
e-benzene
o-xylene
43
1994 Fleet Average Emissions with two fuels
44
Ozone forming potential of exhaust from 1994
Fleet
45
Modelled Species Profile
3m-pentane m-cyclopentanebenzene
cyclohexane iso-octanen-heptane toluene
n-octane e-benzenemp-xylenen-nonane1,2,4-t
m-benzene
ethylene acetylene ethane propane
isobutane isobutylenen-butane 2m-butane
n-pentane 2,3-dm-butane 2m-pentane
Fitting species
46
Nose-level Ambient Sampling Schedules
Slater Street Curbside 20 Weekdays in
August-September
2 Stations, 3 Sampling Sessions Morning
730-930Noon 1130-1330Afternoon
1530-1730 (Evening 2200 - 2400)

• 3 Underground Garages
• 12 Weekdays in December-January
• 2 Stations, 2 Sampling sessions in each garage
• A.M. 730 - 930
• P.M. 1500 - 1700

47
(No Transcript)
48
(No Transcript)
49
(No Transcript)
50

• Watson, J.D., E. Fujita, J.C. Chow, and B.
  Zielinska. 1998. Northern Front Range Air Quality
  Study Final Report., Desert Research Institute.

51
Other receptor models

• CMB applies the mass balance principles to known
  receptor and source compositions to arrive at the
  source contribution estimates.
• Another type of source apportionment analyzes
  multiple measurements at the receptor (I.e. many
  hours of hourly average data) without prior
  knowledge of the sources but attempts to identify
  factors that explain the variation in the
  composition. The factors are then interpreted as
  types of sources.

52
Positive Matrix Factorization, PMF
53
Positive Matrix Factorization, PMF

• The rows of the F matrix then are interpreted to
  be the profiles of factors (sources), and the
  rows of the G matrix are the contributions of
  each source for that observation period.

54
CMB PMF Comparison

• Even a single receptor observation can be
  analyzed by CMB, assuming we have characterized
  the potential sources.
• PMF does not require that we characterize the
  potential sources but it does require sufficient
  observations to identify the potential sources.

55
The SPECIATE database

• Source profiles for PM and VOC samples are
  compiled in a database (SPECIATE) which reports
  measurements from different studiES.
• The profiles in this database can be extracted
  for use with CMB.