664
Figure 4. HERM fitting performance examined by species-specific residual (χi2) and correlation 665
coefficient (ri2) for the BSP 2008-2009 dataset (hybrid 7-source model, see Table 6). Species 666
noted in blue show relatively extreme χi2 and/or ri2. 667
0.001 0.01 0.1 1 10 100 1000
0 0.5 1
Reduced Chi2 (χi2) by Species
Correlation Coefficient (ri
2) by Species HERM Fitting Performace (BSP Samples)
Ni
NO3 -EC Mn Cu
Sr Zn K Br Se
Pb
Rb
Table 1. Source apportionment of simulated PM2.5 speciation dataset (Scenario A) by CAS HERM and EPA CMB, compared with the 668
actual source contributions.
669
Samples Mean Contribution* (µg m-3)
Correlation (r2) R/U Ratio† (<0.5/0.5-1.5/1.5-2.5/>2.5) Source Eliminated‡
Noncon-vergence Source(s) # Actual
(x)
HERM (y)
CMB (z)
x vs y x vs z y vs z x vs y x vs z y vs z HERM CMB HERM CMB
AMSUL 50 2.591 2.599 2.599 0.983 0.983 1.000 19 21 7 3 24 20 4 2 50 0 0 0 0 0 0 0 AMNIT 50 4.817 4.757 4.757 0.988 0.988 1.000 12 20 11 7 19 23 7 1 50 0 0 0 0 0 0 0 BB 50 4.866 4.777 4.777 0.963 0.963 1.000 17 19 12 2 16 16 10 8 50 0 0 0 0 0 0 0 MV 50 2.423 2.459 2.460 0.979 0.980 1.000 23 22 4 1 17 18 6 9 50 0 0 0 0 0 0 0 U-Dust 50 2.330 2.313 2.314 0.983 0.983 1.000 12 17 11 10 21 25 3 1 50 0 0 0 0 0 0 0
Sum 17.026 16.906 16.906 HERM: x2 = 0.182
*Actual source contribution (Sjk) and those derived by HERM and EPA CMB models are noted as x, y, and z, respectively. Mean values take into 670
account all available data.
671
†Residue-Uncertainty (R/U) ratio of x and y is calculated by |y-x|/σy where σy is the source contribution uncertainty estimated by HERM. The 672
ratios are then categorized into 4 ranges: <0.5, 0.5-1.5, 1.5-2.5, and >2.5 with numbers in each range shown in the table. Similarly, R/U ratio of x 673
and z is calculated by |z-x|/σz where σz is the source contribution uncertainty estimated by EPA CMB. R/U ratio of y and z is calculated by |y-674
z|/(σy 2+ σz
2)½. 675
‡Number of source eliminated due to negative source contribution. When occurring, no uncertainty estimate is provided by EPA CMB.
676
⁑Number of non-convergence due to collinearity. When occurring, no uncertainty estimate is provided by HERM or EPA CMB.
677 678
Table 2. Source apportionment of simulated PM2.5 speciation dataset (Scenario B) by CAS HERM and EPA CMB, compared with the 679
actual source contributions.
680
Samples Mean Contribution* (µg m-3)
Correlation (r2) R/U Ratio† (<0.5/0.5-1.5/1.5-2.5/>2.5) Source Eliminated‡
Noncon-vergence Source(s) # Actual
(x)
HERM (y)
CMB (z)
x vs y x vs z y vs z x vs y x vs z y vs z HERM CMB HERM CMB
Low collinearity between U-Dust and R-Dust (α = 0.9)
AMSUL 50 2.404 2.418 2.418 0.992 0.992 1.000 24 19 7 0 44 6 0 0 50 0 0 0 0 0 0 0 BB 50 4.758 4.831 4.831 0.985 0.985 1.000 26 21 3 0 45 5 0 0 50 0 0 0 0 0 0 0 MV 50 4.899 4.887 4.887 0.993 0.993 1.000 25 19 6 0 44 6 0 0 50 0 0 0 0 0 0 0 U-Dust 50 2.479 2.256 2.257 0.738 0.738 1.000 8 14 15 13 19 26 2 0 47 0 0 0 0 3 0 0 R-Dust 50 2.488 2.597 2.597 0.892 0.892 1.000 11 18 12 9 26 21 2 1 50 0 0 0 0 0 0 0
Sum 17.029 16.990 16.990 HERM: x2 = 0.151
Median collinearity between U-Dust and R-Dust (α = 0.99)
AMSUL 50 2.404 2.418 2.418 0.990 0.990 1.000 16 25 9 0 42 8 0 0 50 0 0 0 0 0 0 0 BB 50 4.758 4.900 4.900 0.979 0.979 1.000 19 27 4 0 48 1 1 0 50 0 0 0 0 0 0 0 MV 50 4.899 4.820 4.820 0.989 0.989 1.000 26 18 6 0 45 4 1 0 50 0 0 0 0 0 0 0 U-Dust 50 2.479 2.589 2.588 0.179 0.179 1.000 15 26 8 1 22 4 4 8 38 0 0 0 0 12 0 0 R-Dust 50 2.488 2.337 2.338 0.276 0.277 1.000 13 28 8 1 23 3 1 9 36 0 0 0 0 14 0 0
Sum 17.029 17.063 17.063 HERM: x2 = 0.171
High collinearity between U-Dust and R-Dust (α = 0.998)
AMSUL 50 2.404 2.401 2.444 0.985 0.985 1.000 24 18 5 3 39 9 1 0 49 0 0 0 0 0 0 1 BB 50 4.758 4.769 4.699 0.987 0.987 1.000 26 21 3 0 45 4 0 0 49 0 0 0 0 0 0 1 MV 50 4.899 4.896 4.864 0.996 0.996 1.000 30 18 2 0 46 3 0 0 49 0 0 0 0 0 0 1 U-Dust 50 2.479 1.739 1.656 0.029 0.017 0.997 47 3 0 0 7 1 2 10 20 0 0 0 0 29 0 1 R-Dust 50 2.488 3.165 3.208 0.051 0.055 0.997 48 2 0 0 8 3 1 24 36 0 0 0 0 13 0 1
Sum 17.029 16.970 16.871 HERM: x2 = 0.158
*†‡⁑See footnotes in Table 1.
681 682
Table 3. Source apportionment of ambient PM2.5 speciation dataset (BSP 2008-2009) by CAS HERM and EPA CMB.
683
Samples Mean Contribution* (µg m-3) Correlation (r2)
R/U Ratio† (<0.5/0.5-1.5/1.5-2.5/>2.5)
Source Eliminated‡
Noncon-vergence Source(s) # Actual HERM (y) CMB (z) y vs z y vs z HERM CMB HERM CMB
AMSUL 226 0.555 0.553 1.000 213 1 0 0 0 0 0 12
AMNIT 226 0.161 0.158 1.000 210 0 0 0 0 4 0 12
RDust1 226 0.005 0.005 0.998 109 0 0 0 0 105 0 12
RDust2 226 0.123 0.122 0.991 134 3 0 0 0 77 0 12
ADust 226 0.506 0.514 0.999 195 0 0 0 0 19 0 12
BBh 226 0.105 0.107 1.000 174 0 0 0 0 40 0 12
BBl 226 1.358 1.363 1.000 188 0 0 0 0 26 0 12
MV 226 0.419 0.422 0.996 212 1 0 0 0 1 0 12
Coal 226 0.029 0.025 0.427 195 1 0 0 0 18 0 12
Sum 3.760 3.261 3.269 HERM: x2 = 1.81
*Source contribution (Sjk) derived by HERM and EPA CMB models are noted as y and z, respectively. Mean values take into account all available 684
data. The 9 sources include ammonium sulfate (AMSUL), ammonium nitrate (AMNIT), two road dusts (RDust1, RDust2), Asian dust (ADust), 685
wood burning with both low and high combustion efficiencies (BBh and BBl), traffic (MV), and miscellaneous coal combustion (Coal).
686
†Residue-Uncertainty (R/U) ratio of y and z is calculated by |y-z|/(σy 2+ σz
2)½, where σy and σz is the source contribution uncertainty estimated by 687
HERM and EPA CMB, respectively. The ratios are then categorized into 4 ranges: <0.5, 0.5-1.5, 1.5-2.5, and >2.5 with numbers in each range 688
shown in the table.
689
‡Number of source eliminated due to negative source contribution. When occurring, no uncertainty estimate is provided by EPA CMB.
690
⁑Number of non-convergence due to collinearity. When occurring, no uncertainty estimate is provided by HERM or EPA CMB.
691 692
Table 4. Source apportionment of simulated PM2.5 speciation dataset (Scenario A) by CAS HERM and EPA PMF 5.0, compared with 693
the actual source contributions.
694
Samples Mean Contribution* (µg m-3)
Correlation (r2) R/U Ratio† (<0.5/0.5-1.5/1.5-2.5/>2.5) Noncon-vergence⁑⁑⁑⁑
Source(s) # Actual (x)
HERM4+1 (y)
HERM3+2 (z)
x vs y x vs z y vs z x vs y x vs z y vs z HERM4+1 HERM3+2
AMSUL 50 2.591 2.610 2.808 0.982 0.975 0.993 19 22 7 2 5 14 9 22 10 23 14 3 0 0 AMNIT 50 4.817 4.748 4.828 0.986 0.986 1.000 13 24 10 3 5 18 17 10 33 11 4 2 0 0 BB 50 4.866 4.750 4.701 0.987 0.994 0.992 20 15 6 9 19 25 5 1 33 17 0 0 0 0 MV 50 2.423 2.513 3.393 0.977 0.996 0.968 8 17 10 15 3 4 12 31 4 8 10 28 0 0 U-Dust 50 2.330 2.213 1.124 0.982 0.543 0.552 11 24 10 5 0 0 2 48 3 2 6 39 0 0 Sum 17.026 16.834 16.854 HERM4+1: x2 = 0.121; HERM3+2: x2= 0.093
Source(s) # Actual (x)
HERM0+5 (y)
PMF (z)
x vs y x vs z y vs z x vs y x vs z y vs z HERM0+5 PMF
AMSUL 50 2.591 2.474 3.368 0.976 0.937 0.976 10 18 7 15 2 3 5 40 1 2 6 41 0 0 AMNIT 50 4.817 6.765 5.989 0.976 0.955 0.973 4 5 2 39 3 3 4 40 7 16 4 23 0 0 BB 50 4.866 2.366 2.705 0.570 0.557 0.981 1 1 3 45 3 3 4 40 10 19 15 6 0 0 MV 50 2.423 3.963 3.186 0.995 0.958 0.962 4 5 3 38 3 4 2 41 7 10 5 28 0 0 U-Dust 50 2.330 1.310 1.594 0.098 0.207 0.915 0 4 2 44 0 6 6 38 13 13 15 9 0 0
Sum 17.026 16.878 16.842 HERM0+5: χ2 = 0.152; PMF: x2 = 0.161
*Actual source contribution (Sjk) and those derived by HERM or EPA PMF models are noted as x, y, or z, respectively. Mean values take into 695
account all available data. HERM4+1 specifies 4 source profiles (AMSUL, AMNIT, MV, and U-Dust) while calculating 1 source profile (BB).
696
HERM3+2 specifies 3 source profiles (AMSUL, AMNIT, and U-Dust) while calculating 2 source profiles (BB and MV). HERM0+5 and PMF 697
calculate all 5 profiles (non-specified). Calculated source profiles are matched to the known sources by ranking the correlation coefficients across 698
source contributions.
699
†⁑
See footnotes in Table 1.
700 701
Table 5. Source apportionment of simulated PM2.5 speciation dataset (Scenario A) by CAS HERM, compared with the actual source 702
contributions.
703
Samples Mean Contribution* (µg m-3)
Correlation (r2)
R/U Ratio†
(<0.5/0.5-1.5/1.5-2.5/>2.5) Source(s) # Actual
(x)
HERM3+2’
(y)
x vs y x vs y
AMSUL 50 2.591 2.806 0.975 5 14 10 21
AMNIT 50 4.817 4.825 0.986 8 20 13 9
BB 50 4.866 4.460 0.989 7 25 12 6
MV 50 2.423 2.294 0.996 16 33 1 0
U-Dust 50 2.330 2.470 0.987 7 9 14 20
Sum 17.026 16.855 HERM3+2’: x2 = 0.124
*Actual source contribution (Sjk) and those derived by HERM are noted as x and y, respectively. Mean values take into account all available data.
704
HERM3+2’ specifies 3 source profiles (AMSUL, AMNIT, and U-Dust) while also specifying the silicon (Si) and calcium (Ca) contents in one of the 705
two unknown source profiles to be zero. Other profile elements are calculated by the model. Derived source profiles are matched to BB or MV 706
according to correlation coefficients across source contributions.
707
†See footnotes in Table 1.
708 709
Table 6. Source apportionment of ambient PM2.5 speciation dataset (BSP 2008-2009) by CAS HERM models.
710
Samples Mean Source Contribution* (µg m-3) Correlation (r2) R/U Ratio†
(<0.5/0.5-1.5/1.5-2.5/>2.5)
# EV-CMB Sources (x)
HERM4+2 Sources (y)
HERM5+2 Sources (z)
x vs y x vs z y vs z x vs y x vs z y vs z
226 AMSUL 0.555 AMSUL 0.488 AMSUL 0.481 0.986 0.987 0.999 56 160 10 0 27 98 58 43 221 5 0 0 226 AMNIT 0.161 AMNIT 0.174 AMNIT 0.172 0.991 0.992 1.000 204 22 0 0 177 49 0 0 226 0 0 0 226 RDust1 0.005
226 RDust2 0.123 RDust2 0.096 RDust2 0.092 0.254 0.435 0.844 158 62 6 0 121 86 19 0 219 7 0 0 226 ADust 0.506 ADust 0.515 ADust 0.510 0.966 0.973 0.995 169 54 3 0 123 88 14 1 218 8 0 0
226 BBh 0.105
226 BBl 1.358 BB~ 2.217 BB~ 2.256 0.966 0.972 0.999 38 85 79 24 11 34 39 142 204 22 0 0 226 MV 0.419 MV + Ind.~ 0.204 Ind.~ 0.124 0.803 0.759 0.936 11 146 62 7 0 1 3 222 7 40 67 112
226 Coal 0.029 MV 0.076 0.017 88 107 27 4
Sum 3.261 3.694 3.712 χ2 = 1.81 (EV-CMB), 1.53 (HERM4+2), and 1.23 (HERM5+2)
*Source contribution (Sjk) derived by three HERM models are noted as x, y and z, respectively. EV-CMB is accomplished by HERM using 9 full 711
source profiles (same as Table 3), HERM4+2 specifies 4 source profiles while calculating 2 source profiles, and HERM5+2 specifies 5 source profiles 712
while calculating 2 source profiles. The last two use the HERM hybrid mode. Mean values take into account all available data.
713
~Source (profiles) calculated by HERM. “Ind.” stands for mixed industrial emissions.
714
†Residue-Uncertainty (R/U) ratio of x and y is calculated by |y-x|/(σx 2+ σy
2)½ where σx and σy are the source contribution uncertainty estimated by 715
HERM. The ratios are then categorized into 4 ranges: <0.5, 0.5-1.5, 1.5-2.5, and >2.5 with numbers in each range shown in the table. Similarly, 716
R/U ratio of x and z is calculated by |z-x|/(σx2
+ σz2
)½ and R/U ratio of y and z is calculated by |y-z|/(σy2
+ σz2
)½. 717
718
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