Appendix G

Revised IMPROVE Algorithm for Estimating

Light Extinction from Particle Speciation Data
Revised IMPROVE Algorithm for Estimating Light Extinction

from Particle Speciation Data

Section II. Overview of the Revised Algorithm

(IMPROVE technical subcommittee for algorithm review)

The recommended revised algorithm is shown in the equation below with revised terms

in bold font. The total sulfate, nitrate and organic carbon compound concentrations are

each split into two fractions, representing small and large size distributions of those

components. Though not explicitly shown in the equation, the organic mass

concentration used in this new algorithm is 1.8 times the organic carbon mass

concentration, changed from 1.4 times carbon mass concentration as used for input for

the current IMPROVE algorithm. New terms have been added for sea salt (important

for coastal locations) and for absorption by NO2 (only used where NO2 data are

available). Site-specific Rayleigh scattering is calculated for the elevation and annual

average temperature of each of the IMPROVE monitoring sites as shown in the Table A

at the end of the document.

The apportionment of the total concentration of sulfate compounds into the

concentrations of the small and large size fractions is accomplished using the following

equations.

The same equations are used to apportion total nitrate and total organic mass

concentrations into the small and large size fractions.

[ ] [ ]

[ ] [ ]

[ ] [ ]

[ ]

[ ]

[ ]

[ ]

+ × [ ]

+

+ ×

+ × ×

+ ×

+ ×

+ × + ×

+ × × + × ×

≈ × × + × ×

Coarse Mass

Fine Soil

Elemental Carbon

bext

0 .6

1

10

[ ] [ ] [ ]

3

Larg e Sultate = Total Sulfate , for Total Sulfate ≥ 20 μg / m

[ ]

[ ]

[ ] [ ]

3

3

, 20 /

20 /

arg Total Sulfate for Total Sulfate g m

g m

Total Sulfate

L e Sulfate μ

μ

= × <

[Small Sulfate] = [Total Sulfate]−[Large Sulfate]
Sea salt is calculated as 1.8 x [Chloride], or 1.8 x [Chlorine] if the chloride measurement

is below detection limits, missing or invalid. The algorithm uses three water growth

adjustment term as shown in the Figure 2 and Table 1. They are for use with the small

size distribution and the large size distribution sulfate and nitrate compounds and for

sea salt (fS(RH), fL(RH) and fSS(RH) respectively).

Water Growth Curves

0

1

2

3

4

5

6

7

8

9

10

0 10 20 30 40 50 60 70 80 90 100

Relative Humidity (%)

f(R

H)

fS(RH)

fL(RH)

Original

fSS(RH)

Figure 1. Water growth curves for small and large size distribution sulfate and nitrate, sea salt and

the original IMPROVE algorithm sulfate and nitrate.

Table 1. f(RH) for small and large size distribution sulfate and nitrate, an sea salt.

RH (%) fS(RH) fL(RH) fSS(RH) RH (%) fS(RH) fL(RH) fSS(RH) RH (%) fS(RH) fL(RH) fSS(RH)

0 to 36 1.00 1.00 1.00 56 1.78 1.61 2.58 76 2.60 2.18 3.35

37 1.38 1.31 1.00 57 1.81 1.63 2.59 77 2.67 2.22 3.42

38 1.40 1.32 1.00 58 1.83 1.65 2.62 78 2.75 2.27 3.52

39 1.42 1.34 1.00 59 1.86 1.67 2.66 79 2.84 2.33 3.57

40 1.44 1.35 1.00 60 1.89 1.69 2.69 80 2.93 2.39 3.63

41 1.46 1.36 1.00 61 1.92 1.71 2.73 81 3.03 2.45 3.69

42 1.48 1.38 1.00 62 1.95 1.73 2.78 82 3.15 2.52 3.81

43 1.49 1.39 1.00 63 1.99 1.75 2.83 83 3.27 2.60 3.95

44 1.51 1.41 1.00 64 2.02 1.78 2.83 84 3.42 2.69 4.04

45 1.53 1.42 1.00 65 2.06 1.80 2.86 85 3.58 2.79 4.11

46 1.55 1.44 1.00 66 2.09 1.83 2.89 86 3.76 2.90 4.28

47 1.57 1.45 2.36 67 2.13 1.86 2.91 87 3.98 3.02 4.49

48 1.59 1.47 2.38 68 2.17 1.89 2.95 88 4.23 3.16 4.61

49 1.62 1.49 2.42 69 2.22 1.92 3.01 89 4.53 3.33 4.86

50 1.64 1.50 2.45 70 2.26 1.95 3.05 90 4.90 3.53 5.12

51 1.66 1.52 2.48 71 2.31 1.98 3.13 91 5.35 3.77 5.38

52 1.68 1.54 2.50 72 2.36 2.01 3.17 92 5.93 4.06 5.75

53 1.71 1.55 2.51 73 2.41 2.05 3.21 93 6.71 4.43 6.17
54 1.73 1.57 2.53 74 2.47 2.09 3.25 94 7.78 4.92 6.72

55 1.76 1.59 2.56 75 2.54 2.13 3.27 95 9.34 5.57 7.35

Algorithm Performance Evaluation

Performance of the current and proposed new algorithm for estimating extinction can be

assessed in a number of ways each of which serves to answer different questions.

Reduction of the biases in light scattering estimates at the extremes (i.e.

underestimation of the high values and over estimation of the low values) when

compared to nephelometer measurements was one of the most compelling reasons for

development of a new algorithm, so comparisons of bias for the current and proposed

new algorithm are one way to evaluate performance.

The fractional bias for each sample period was calculated as the difference in light

scattering (i.e. estimated bsp minus the measured bsp) divided by the measured light

scattering. These biases were then averaged in each quintile to indicate the bias in

those five subsets of the data from the lowest to the highest light scattering values. Two

different approaches to this grouping by quintiles were performed, referred to as criteria

1 and 2.

Criterion 1 used the measured light scattering to determine which sample periods were

in each quintile. Since we think of the nephelometer as the better measure of light

scattering, bias by this criterion better addresses the question of algorithm performance

with regards to the haze conditions. Criterion 2 uses the algorithm-estimated light

extinction to determine which sample periods were in each quintile. The Regional Haze

Rule index is based on the highest and lowest haze levels as determined by the

algorithm, so criterion 2 better addresses the haze rule application of the algorithm.

Tables 2 through 5 show the bias results by both criteria for the current and new

algorithm for sites averaged by RPO.

Table 2. Averaged fractional bias by RPO for the current IMPROVE algorithm with quintiles based

on measured light scattering (criterion 1). Bold font highlights the bias values that are lower than

corresponding values in Table 3.

RPO Quintile 1 Quintile 2 Quintile 3 Quintile 4 Quintile 5 Average

CEN 0.67 0.18 0.10 0.02 -0.11 0.17

MANE 0.93 0.27 0.19 0.10 0.01 0.28

VISTAS 0.59 0.21 0.11 0.02 -0.13 0.16

WRAP 1.07 0.37 0.18 0.07 -0.08 0.32

Table 3. Averaged fractional bias by RPO for the current new proposed algorithm with quintiles

based on measured light scattering (criterion 1). Bold font highlights the bias values that are

lower than corresponding values in Table 2.

RPO Quintile 1 Quintile 2 Quintile 3 Quintile 4 Quintile 5 Average

CEN 0.51 0.08 0.02 -0.03 -0.08 0.10

MANE 0.74 0.14 0.06 0.01 -0.02 0.17

VISTAS 0.50 0.16 0.11 0.06 -0.01 0.16

WRAP 0.84 0.25 0.08 0.01 -0.10 0.21
Table 4. Averaged fractional bias by RPO for the current IMPROVE algorithm with quintiles based

on estimated light scattering (criterion 2). Bold font highlights the bias values that are lower than

corresponding values in Table 5.

RPO Quintile 1 Quintile 2 Quintile 3 Quintile 4 Quintile 5 Average

CEN 0.42 0.19 0.18 0.09 -0.01 0.17

MANE 0.35 0.27 0.30 0.33 0.15 0.28

VISTAS 0.38 0.19 0.14 0.08 0.01 0.16

WRAP 0.58 0.37 0.26 0.25 0.15 0.32

Table 5. Averaged fractional bias by RPO for the current new proposed algorithm with quintiles

based on estimated light scattering (criterion 2). Bold font highlights the bias values that are

lower than corresponding values in Table 4.

RPO Quintile 1 Quintile 2 Quintile 3 Quintile 4 Quintile 5 Average

CEN 0.23 0.11 0.08 0.06 0.02 0.10

MANE 0.15 0.14 0.15 0.19 0.21 0.17

VISTAS 0.25 0.14 0.08 0.13 0.21 0.16

WRAP 0.37 0.19 0.19 0.16 0.17 0.21

These tables show that the new algorithm has lower fractional bias than the current

IMPROVE algorithm in all but the haziest conditions (i.e. quintile 5) regardless of the

criterion used to sort the data into quintiles. By criterion 1, the two algorithms perform

about the same for haziest days except for the sites in the southeastern U.S. (i.e. the

VISTA RPO), where the new algorithm has much lower bias (1% compared to 13%).

Using criterion 2, the current algorithm has consistently lower bias compared with the

new algorithm for the haziest days (i.e. quintile 5) for each of the RPOs. This seeming

paradox is the result of the somewhat greater imprecision of the new algorithm

compared to the current algorithm, which results in somewhat larger errors in selecting

worst haze sample periods for the new algorithm compared with the current algorithm.

Scatter plots (Figures 1 and 3) of light scattering estimates from the current and new

proposed algorithms versus nephelometer data for all available data at 21 monitoring

sites are one way to view the overall performance differences between the two. These

figures show that the bias at the extremes is reduced using the new algorithm compared

to the original IMPROVE algorithm (i.e. the points tend to be better centered on the oneto-one line). They also show that the somewhat reduced precision of the new algorithm

compared to the original IMPROVE algorithm (i.e. points are more broadly scattered).
0

50

100

150

200

250

300

350

0 50 100 150 200 250 300 350

Measured Bsp

Split Component Method Bsp

Figure 2. Scatter plot of the recommended revised algorithm estimates of light scattering versus

measured light scattering.

Similar pairs of scatter plots were prepared for each individual monitoring site (available

in the appendix). Figures 4 and 5 are example plots for Shenandoah and Grand

Canyon National Parks. The logarithmic scales on these plots exaggerate the scatter

for low values compared to high values. The individual-site scatter plots have the 80

th

percentile values indicated on the graphs for the predicted and measured values by

horizontal and vertical lines respectively. Points that are to the right of the vertical line

have nephelometer values that are among the 20% worst light scattering for that

monitoring sites. Points that are above the horizontal line have algorithm determined

values that are among the 20% worst estimated light scattering for that monitoring site.

Scatter Plot for SHEN using IMPROVE Algorithm

1

10

100

1000

1 10 100 1000

Measured Bsp

Predicted Bsp

Scatter Plot for SHEN using New Algorithm

1

10

100

1000

1 10 100 1000

Measured Bsp

Predicted Bsp

Figure 4. Scatter plots of the current IMPROVE and new recommended algorithm estimates of

light scattering versus measured light scattering for Shenandoah National Park. Horizontal and

vertical lines are at the 80

th

percentile for estimated and measured light scattering.
Scatter Plot for GRCAusing IMPROVE Algorithm

1

10

100

1000

1 10 100 1000

Measured Bsp

Predicted Bsp

Scatter Plot for GRCAusing New Algorithm

1

10

100

1000

1 10 100 1000

Measured Bsp

Predicted Bsp

Figure 5. Scatter plots of the current IMPROVE and new recommended algorithm estimates of

light scattering versus measured light scattering for Grand Canyon National Park. Horizontal and

vertical lines are at the 80

th

percentile for estimated and measured light scattering.

The proposed new algorithm performs noticeably better with respect to having data

points more centered on the one-to-one line at the high and low haze level extremes

than the current IMPROVE algorithm for Shenandoah National Park, which is typical for

the high haze level locations in the southeast U.S. A large number of the measured

worst haze sample periods are correctly identified by both algorithms (these are the

points above and to the right of the two 80

th

percentile lines). The differences between

the two algorithms for Grand Canyon National Park and most of the other less hazy

locations are not apparent in these scatter plots.

The final approach for evaluating the relative performance of the two algorithms is to

compare the average composition of the best haze days and the worst haze days as

selected using each algorithm and using the measured light scattering. Table 6 and 7

contain the average composition by RPO for days selected as best and worst by these

three methods. Similar results for each of the 21 nephelometer monitoring locations are

shown in tables in the appendix.

Table 6. Mean light scattering and percent PM2.5 composition for the five major components for

20% best days as determined by measurement, the current IMPROVE algorithm and the proposed

new algorithm.

RPO

Mean

Bsp

(Mm-1)

Percent

Ammonium

Sulfate

Percent

Ammonium

Nitrate

Percent

OCM

Percent

Soil

Percent

Coarse

Percent

EC

Measured 6.8 19 2 15 8 54 2

CENRAP IMPROVE 9.1 20 2 15 7 53 2

NEW 8.1 21 3 16 7 51 2

Measured 6.1 22 3 22 4 47 3

MANEVU IMPROVE 8.4 21 3 22 4 47 3

NEW 7.4 22 4 22 4 45 3

Measured 13.8 25 7 21 4 40 3

VISTAS IMPROVE 18.4 25 7 21 4 40 3

NEW 17.0 25 8 21 4 39 3
Measured 3.4 13 3 18 8 55 3

WRAP IMPROVE 5.2 14 3 19 8 53 3

NEW 4.5 15 3 19 8 52 3

Table 7. Mean light scattering and percent PM2.5 composition for the five major components for

20% worst days as determined by measurement, the current IMPROVE algorithm and the

proposed new algorithm.

RPO

Mean

Bsp

(Mm-1)

Percent

Ammonium

Sulfate

Percent

Ammonium

Nitrate

Percent

OCM

Percent

Soil

Percent

Coarse

Percent

EC

Measured 76 34 6 19 5 34 2

CENRAP IMPROVE 67 34 6 19 5 33 2

NEW 72 34 6 19 6 34 2

Measured 61 36 6 23 3 30 3

MANEVU IMPROVE 61 36 6 22 3 30 3

NEW 63 35 6 23 3 31 3

Measured 120 46 5 21 3 22 2

VISTAS IMPROVE 106 47 4 21 3 23 2

NEW 127 47 3 22 3 22 2

Measured 36 15 6 27 7 42 3

WRAP IMPROVE 33 14 6 27 6 44 3

NEW 33 13 6 27 6 44 3

These tables demonstrate that the composition associated with the best and worst haze

days are not very sensitive to the method of identifying the sample periods that fit in

best and worst categories. Some of the individual sites (e.g. Grand Canyon) have

somewhat larger variations in the composition between measurement-selected days

compared to algorithm-selected days, though there’s little difference between the

average composition comparing the two algorithms on the best and worst days. The

contributions to light extinction by the various components were not explicitly calculated,

but are inherently somewhat different because of the explicit differences in the two

algorithms.

In summary, the proposed new algorithm for estimating haze reduces the biases

compared to measurements at the high and low extremes. This is most apparent for

the hazier eastern sites. The composition of days selected as best and worst by the

current and the new algorithm are very similar, and similar to days selected by

measurements. Most of the reduction of bias associated with the new algorithm is

attributed to the use of the split component extinction efficiency method for sulfate,

nitrate and organic components that permitted variable extinction efficiency depending

on the component mass concentration. Though not subject to explicit performance

testing, the proposed new algorithm also contains specific changes from the current

algorithm that reflect a better understanding of the atmosphere as reflected in the more

recent scientific literature (e.g. change to 1.8 from 1.4 for organic compound mass to

carbon mass ratio) and a more complete accounting for contributors to haze (e.g. sea

salt and NO2 terms), and use of site specific Rayleigh scattering terms to reduce

elevation-related bias.