Testing of the Simplified Light Extinction Estimates at the 

SEARCH Site in Birmingham Alabama

Ivar Tombach

2 November 2010

Introduction

Comments I provided to the EPA on 30 August 2010, concerning EPA’s second draft 

Policy Assessment Document (PAD) for the PM2.5 NAAQS,1 included results of a 

comparison of fine particle light extinction (bext,fp) estimates using both the “simplified 

method” in the PAD and values derived from hourly measurements of particulate matter

chemical composition that were made by the SEARCH program. 

The Southeastern Aerosol Research and Characterization Study (SEARCH) network has 

been analyzing 24-hr filter samples and operating semi-continuous analyzers at multiple 

locations in the Southeast. The semi-continuous analyzers provide measurements of the 

concentrations of PM2.5 mass and of sulfates, nitrates, ammonium, total carbon, and 

elemental carbon with one-hour resolution. Such data allow application of the IMPROVE 

algorithm on an hourly basis2 without recourse to the various scaling steps required to 

estimate light extinction applying EPA’s simplified Speciated PM2.5 Mass-calculated 

Light Extinction (SPMLE) method to daily speciated PM concentration measurements,

following the method described in the draft PAD.

As EPA strives to simplify its method for estimating hourly light extinction in urban 

areas, one needs to be concerned whether those simplifications produce erroneous 

estimates of light extinction or smooth out relevant actual diurnal or day-to-day variations

 1 Comments Concerning the Visibility-Related Portion of the Second External Review Draft of the 

Policy Assessment for the Review of the PM NAAQS, by Ivar Tombach, 30 August 2010.

2

 Except that concentrations of the elements that make up fine soil are not measured hourly. 

Rather, concentrations from 24-hr filter samples serve as estimates for every hour of the day.
2

in that extinction. Analyses carried out with SEARCH data, as described in this memo,

explore some of these questions. 

To evaluate the simplified method, the hourly PM2.5 light extinction results obtained by 

using EPA’s SPMLE calculation method were compared with hourly light extinction 

calculated from hourly speciated concentration measurements, using EPA’s variant of the 

original IMPROVE algorithm in both cases. For this analysis, I originally used both 24-hr 

and 1-hr measurements made at the Jefferson Street (JST), Atlanta, SEARCH site, during 

2005-2007 (the same years as those analyzed by EPA in the PAD). 

The analysis contained in my August comments compared the two methods for a metric 

based on hourly values of bext,fp over all daylight hours with RH ≤ 90%. That analysis, as 

extracted from my August comments, is Attachment 1 to this memo. That attachment 

also provides more information about the data sources.

Subsequently, in response to a request from EPA staff, I carried out a second, similar 

analysis that addressed an alternative metric of daily maximum hourly values of bext,fp, for 

the same SEARCH JST data set under the same constraints. The results of that second 

analysis were submitted to the EPA on 27 September 2010.3 That document is 

Attachment 2 to this memo.

These analyses showed reasonable agreement between estimates of hourly light 

extinction by EPA’s simplified method and those derived by applying the same modified 

IMPROVE algorithm using hourly PM2.5 component measurements in Atlanta by the

SEARCH program. There wasn’t sufficient time during the formal comment period to 

carry out analysis for other locations, both urban and rural, but EPA staff expressed an 

interest in seeing such results if they became available. In response, this memo provides 

results of analyses using data from the SEARCH site at Birmingham, Alabama (BHM). 

The analyses herein are identical to the two sets of analyses carried out for JST and

described in the two attachments.

Summary of Approach

In the PAD, the EPA elected to use a modified version of the traditional IMPROVE 

algorithm to estimate light extinction from the concentrations of various chemical 

components in particulate matter. In my original comments, I expressed reservations 

about the choice of the traditional algorithm and about the modifications EPA made to it. 

However, for the sake of consistency, all of my analyses of SEARCH data use EPA’s 

modified IMPROVE algorithm.

To review, the 10 steps of EPA’s new approach, as summarized on pages 4-34 and 4-35 

of the PAD, are reproduced here. My comments in italics describe adjustments I made to 

be able to apply the SEARCH data.

 3 Comparison of Daylight Maximum Hour Calculations, by Ivar Tombach, 27 September 2010.
3

• Step i. Estimate 24-hour organic carbonaceous mass from the CSN organic carbon 

measurement, via a multiplier, rather than by the SANDWICH method. For CSN, 

substitute SEARCH. Although I remain skeptical about EPA’s choice of a 

multiplier of 1.7, I have used it here for my calculations with the SEARCH data.

• Step ii. Calculate 24-hour fine soil/crustal from the CSN measurements of the 

related PM2.5 crustal elements. In lieu of CSN 24-hr speciated concentration 

measurements, I used the similar 24-hr sulfate, nitrate, OC, EC, and fine soil 

constituent measurements made by the SEARCH Particle Composition Monitor 

(PCM). As I’ve noted previously, the fine soil formula in the PAD differs slightly 

from the IMPROVE soil formula. My calculations use the IMPROVE formula for 

soil, but this choice should have negligible impact on the results of my 

evaluations.

• Step iii. Calculate 24-hour neutralized, dry sulfate and nitrate in the same manner as 

in the IMPROVE network and Regional Haze program, by multiplication by 

factors of 1.375 and 1.29 respectively. This step implies that the CSN sulfates and 

nitrates are in the forms of ammonium sulfate and ammonium nitrate, which is 

consistent with the assumed forms in the IMPROVE algorithm but will overstate 

the sulfate concentration at times when the sulfate is not fully neutralized, as is 

often the case in the Southeast in summer. For my analyses I used sulfate and 

nitrate concentrations determined from sampling by the SEARCH PCM and,

consistent with the EPA, also assumed that the sulfate is fully neutralized.

• Step iv. Sum the five components, for each day. The result is a version of the PM2.5

mass concentration, sans fine sea salt, i.e., [PM2.5] = [AmSulfate] + [AmNitrate] 

+ [OCM] + [EC] + [Soil].

• Step v. Calculate the five component fractions (i.e., percentages) of the sum-of-five, 

for each day.

• Step vi. Looking across all CSN sampling days in a given calendar month, average 

the daily component fractions for sulfate, for nitrate, etc. These monthly-average 

component fractions will be applied on every day in that month. For CSN, 

substitute SEARCH PCM.

• Step vii. For each day, determine a scaling factor to reconcile [the 24-hr average 

of] hourly PM2.5 mass measurements from a continuous instrument with the 24-

hour PM2.5 mass determined by FRM sampling. The continuous PM2.5 instrument 

in SEARCH is a Torsion-Element Optical Microbalance (TEOM), operated at a 

temperature of 30° C. The FRM PM2.5 concentrations were determined using a 

Rupprecht & Patashnick Model 2025 FRM sampler.

• Step viii. For each day, apply this scaling factor to the 1-hour measurements of 

PM2.5 mass from the continuous instrument.
4

• Step ix. For each day and daylight hour in the month, multiply the scaled value of 

hourly PM2.5 mass by the component fractions from Step vi.

• Step x. These hourly speciated PM2.5 concentrations are then combined with 

collocated hourly averaged relative humidity as input to the IMPROVE algorithm 

to calculate the speciated PM2.5 mass-calculated light extinction. As with many of 

EPA’s calculations, this analysis excluded hours with values of RH > 90%.

Note that my calculations are not a validation of the ability of the simplified method, or 

of any of the other methods considered by the EPA, to accurately portray hour-by-hour 

actual light extinction. Rather, they should be considered as initial exploration of whether 

the simplifications in EPA’s method bias or alter the structure of the extinction estimates.

Results for BHM

The component mass fractions for BHM that result from Step (v) of the SPMLE approach 

are summarized in Table 1. A lack of valid 24-hr nitrate measurements from mid May to 

the end of September 2005 means that averages could not be calculated for June through 

September, and the average for May 2005 is not based on a complete month of data. 

Table 1. Monthly averages of filter sample 24-hr fractional contributions of

chemical components in the PM2.5 mass concentration at BHM.

AmSulf 

Fraction

AmNitr 

Fraction

OCM 

Fraction

EC 

Fraction

Soil 

Fraction

Jan 0.281 0.123 0.420 0.097 0.081

Feb 0.256 0.144 0.415 0.112 0.073

Mar 0.326 0.101 0.384 0.112 0.077

Apr 0.312 0.055 0.427 0.115 0.091

May 0.379 0.055 0.404 0.099 0.064

June 0.400 0.029* 0.393 0.100 0.078

July 0.435 0.034* 0.360 0.059 0.113

Aug 0.467 0.026* 0.326 0.076 0.105

Sept 0.429 0.025* 0.358 0.095 0.093

Oct 0.338 0.058 0.393 0.107 0.104

Nov 0.276 0.075 0.450 0.115 0.085

Dec 0.252 0.110 0.444 0.125 0.069

3-yr Avg. 0.336 0.073 0.402 0.103 0.085

2005 Avg 0.302 0.092 0.422 0.112 0.072

2006 Avg 0.347 0.067 0.395 0.102 0.090

2007 Avg 0.349 0.067 0.395 0.099 0.090

* 2-year (2006 & 2007) averages
5

Although the day-to-day values of the component mass fractions are highly variable, note 

in Table 1 that, on average, ammonium sulfate and OCM combined account for about 

80% of the fine mass. With the 1.7 multiplier, OCM accounts on average for slightly 

more of the mass than does ammonium sulfate, which is also the case for JST. Annually, 

ammonium nitrate accounts for 7 to 9%, EC for 10 to 11% (vs. 8 to 9% at JST), and the 

fine soil for 7 to 9% of the mass (vs. 4 to 5% at JST). These fractions vary with month, 

sometimes with large changes, although the year-to-year fractions are relatively stable. 

The monthly averages in Table 1 hide the day-to-day and hour-to-hour variation, of 

course. 

The SEARCH hourly speciated measurements provide concentration results that are

analogous to the products of Step (ix) in EPA’s method, except that the values are not 

constrained by monthly-average factors required by the EPA procedure, but rather reflect

the actual hour-by-hour and day-by-day variation of the composition of the fine PM. The 

only exception is fine soil, for which hourly measurements were not made and therefore 

the daily average concentration of soil was used for every hour of the day. At JST soil is 

typically a minor fraction of the PM2.5, as noted in the attachments; its contribution at 

BHM is a bit larger, but using the 24-hr average will generally not affect the quality of 

the hourly estimates. Brief episodic dust events would be an exception. 

In particular, some areas of Birmingham have occasional episodes of high concentrations 

of industrial “dust” that contains substantial amounts of metals, such as zinc. Such metals 

are not accounted for in the soil term of IMPROVE formula, and hence are not reflected 

in Table 1, but yet have been observed for short periods of time with concentrations of 

such metals that are many tens of micrograms per cubic meter.

The SEARCH hourly speciated concentrations were then inserted into the modified 

traditional IMPROVE algorithm, as described in Step (x). Two metrics were evaluated 

for BHM – (1) light extinction during all daylight hours and (2) the maximum hourly 

light extinction on each day. The results for these analyses are described below in a 

format patterned after the presentation of the results of the JST analyses. The analogous 

results for JST are described in Attachments 1 and 2, respectively.
6

Results – All Daylight Hours

Figure 1 shows every valid hourly value of bext,fp (PM2.5 light extinction) at BHM during 

2005-07, as produced by the two methods –the SPMLE of the PAD in the top panel and

as calculated directly from hourly component measurements in the bottom panel. Only 

hours designated as daylight hours are shown and conditions with RH>90% have been 

excluded from the analysis.

Figure 1. Time series plots of all hourly daylight values of bext,fp at BHM generated 

by the PAD method (top panel) and the direct calculation method (lower panel). RH 

≤ 90%.
7

Figure 1 illustrates several points:

• Both methods can be plagued by data gaps. In the top panel of Figure 1, the 

4-month absence of 24-hr nitrate measurements on filters derails the calculation 

of monthly fine PM2.5 mass concentration in step (iv) of SPMLE method that was 

summarized above, and hence prevents calculation of component fractions in Step 

(v), speciated concentrations in Step (ix) and light extinction in Step (x). Hence, if 

the filter samplers for any component are out of commission for a month, then the 

PAD method cannot be used. There are also small breaks in the data because filter 

samples were only taken on every 3rd day in 2005 at BHM; daily sampling 

resumed in 2006. Generally, however, the monthly averages of the component 

fractions are quite robust, since only a valid hourly PM2.5 concentration and the 

RH are needed for each hourly point in the PAD method (top panel). In contrast, 

the direct calculation method (the bottom panel) has more short gaps in the data, a 

consequence of needing five valid hourly concentration measurements and a value 

of RH for each hour. 

• Both plots show similar patterns in the main body of the data, but “spikes” in one 

plot are not always present in the other. A notable discrepancy of this type is 

associated with the very large spikes, up to above 800 Mm-1, in the latter part of 

May 2007 in the PAD plot; there is no corresponding pattern in the direct 

calculation plot because missing concentration data precluded the calculation of 

light extinction then.

The same data sets are compared in a scatter plot in Figure 2. The only points plotted are 

those for hours for which both methods produced a value. Consequently, the high PAD 

bext,fp values produced by the spike in May 2007 do not appear because there were no 

corresponding hourly values from the direct calculation. The correlation between the two 

data sets is respectable (R2 = 0.80) and just slightly weaker than the corresponding 

comparison at JST. The black line is the ordinary least squares (OLS) regression line and 

the red line is the OLS line forced through the origin. The red line has a slope of 1.00, 

which suggests that one data set is not biased relative to the other; JST also showed a 

slope of 1.00. The dashed green lines denote a factor of 2 around the 1:1 line (which just 

happens to be the OLS line through the origin). The dense data “cloud” spills outside the 

two green lines when bext,fp is less than about 150 Mm-1, which indicates that the hourly 

bext,fp values produced by the two methods can readily differ by more than a factor of two. 

This scatter is greater than what was observed at JST. Relative agreement improves at 

higher values of extinction. 
8

Figure 2. Comparison of hourly daylight values of PAD bext,fp with directly 

calculated values for BHM during 2005-2007, for RH ≤ 90%. A few points lie 

outside the plot area but were used in the calculations. Ordinary least squares 

regression lines and formulas are shown in black and red. The dashed green lines 

delineate a factor of two around the 1:1 line.

We can gain insight into the significance of any differences between the results of the 

two methods by looking at their distributions. Table 2 summarizes some statistics about 

the two data sets for each of the three years. In particular, the 98th percentile of all the 

valid hourly values of bext,fp is a metric that appears in the draft PAD for consideration.
9

Table 2. Statistical comparison of the two bext,fp data sets for all daylight hours for 

BHM.

2005 2006 2007

PAD Direct PAD Direct PAD Direct

# of daylight hours 4107 4107 4107 4107 4107 4107

# of daylight hours

(RH≤90%) w/ valid 

data

1101 794 2942 2103 3101 2181

Maximum bext,fp

(Mm-1)

673 533 780 738 823 626

98th %-ile bext,fp 

(Mm-1)

362 387 264 261 331 239

Note the following in Table 2:

• Although the number of possible daylight hours (as defined by the UFVA) per 

year is 4107, that number was reduced appreciably by the RH ≤ 90% cutoff and 

by the need for valid values for all needed calculations for that hour. The onceevery-third-day sampling also took its toll in 2005. The PAD method produced 

more hourly estimates of bext,fp than the direct method.

• For 2006, both methods calculated very similar highest extinction values. 

Although they did not occur on the same day, they did occur two days apart, 

during the same episode in December. In the other two years, the maximum 

estimated values of extinction differed to a greater degree and occurred several 

months apart, which demonstrates that the SPMLE method can miss the mark by 

a wide margin at times. 

• The 98th percentile values of bext,fp are expected to be less sensitive to the 

extremes reflected by the maximum values, and indeed this is the case. The bext,fp

values calculated by the two methods agreed closely in 2006, although those 

values occurred on different days. 

Table 2 shows that both methods give design values (i.e., 3-year average 98th-percentile 

values of bext,fp with RH≤90%) that exceed the upper end of the SPMLE range of 64 to 

191 Mm-1 recommended by EPA staff on page 4-50 of the draft PAD. The annual 98th

percentile values that make up these design values are in the range of 239 to 387 Mm-1 

(depending on method).
10

Results – Daily Maximum Daylight Hours

The above analysis compared the two methods for a metric that was based on hourly 

values of bext,fp over all daylight hours with RH ≤ 90%. A new analysis that addresses, 

similarly, the alternative metric of daily maximum hourly values of bext,fp, for the same 

data set under the same constraints, follows below. 

The scatter plot in Figure 3 displays the relationship for 2005–2007 between values of 

daily maximum hourly bext,fp derived using the method in the PAD and the values 

calculated directly from the chemical measurements using the modified traditional 

IMPROVE algorithm. Figure 3 is the counterpart of Figure 2 in the previous section.

In Figure 3, as in Figure 2, the black line is the ordinary least squares (OLS) linear 

regression line and the red line is the OLS line forced through the origin. Since there is 

only one point per day, there are fewer points on Figure 3 than in its all-hours 

counterpart. The coefficient of determination (R2) between the data sets is rather poor –

R2 = 0.39 for the line through the origin. (It was a more respectable 0.72 for JST.) Unlike 

the wedge-shaped data “cloud” in the earlier figure, here the bounds on the data scatter 

appear to be ill defined. The scatter does not appear to be in the form of a systematic 

pattern of offsets from the central line. As a reference for the eye, two green lines are 

drawn at a distance of ± 50 Mm-1 horizontally or vertically from a 1:1 line (essentially the 

red line). Disagreements between the two methods are still relatively common outside 

that range, though, and a range of more than ± 100 Mm-1 is needed to contain 90 to 95% 

of the data.

Table 3 summarizes some statistics about the two data sets that were plotted in Figure 3, 

for each of the three years 2005 through 2007. The table displays both the 98th and 90th

percentiles of all the daily maximum hourly values of bext,fp during each year, metrics that 

were considered in the second draft PAD. Although there is some variability in these 

percentiles from year to year, the 3-year averages of various percentiles of light 

extinction are consistently greater for the PAD SPMLE method than for the direct 

method, a systematic bias that was not apparent in the JST analysis. Note though, the 90th

percentiles in 2006 are identical, although they occurred three months apart!

Table 3 shows that both methods considered here give design values (i.e., 3-year average 

98th-percentile values of daily maximum hourly bext,fp whenever RH≤90%) that greatly 

exceed the upper end of the SPMLE range of 64 to 191 Mm-1 recommended by EPA 

staff. The annual 98th percentile values that make up these design values are in the range 

of 300 to 540 Mm-1 (depending on method and year), and are considerably greater than 

the roughly 250 to 350 Mm-1 values for all daylight hours that appeared in Table 2.
11

Figure 3. Comparison of daily maximum hourly daylight values of PAD bext,fp with 

directly calculated values for BHM during 2005-2007, for RH ≤ 90%. A few points 

lie outside the plot area, but are included in the regression calculations. Ordinary 

least squares regression lines and formulas are shown in black and red. The dashed 

green lines delineate deviations of ± 50 Mm-1 from the 1:1 line.

Table 3. Statistical comparison of the two daily maximum hour bext,fp data sets for 

BHM.

2005 2006 2007

PAD Direct PAD Direct PAD Direct

# of days considered, 

(RH<90% and valid data)

322 342 335

# of valid max hour 

extinction values

238 183 290 251 308 242

Maximum bext,fp (Mm-1) 673 487 676 738 823 626

98th %-ile of daily max 

bext,fp values (Mm-1)

475 314 484 540 550 399

90th %-ile of daily max 

bext,fp values (Mm-1)

229 188 272 272 305 249
12

A comparison of Tables 2 and 3 shows that the observation made in EPA’s documents, 

that the extinction at the 98th percentile of all hourly values is approximately the same as 

that at the 90th percentile of maximum daily values, is reasonably correct for 2006, a 

little less so for 2007, but totally misses the mark for 2005. Lower data completeness in 

2005, relative to 2006 and 2007, could be a contributing factor, though.

Conclusions

In summary, these new analyses at BHM show greater differences between the two 

methods than were observed at JST. Birmingham is a more industrial city than Atlanta, so 

it has greater haze and that haze is more likely to be less uniform spatially and 

temporally, and hence to vary more with meteorological conditions. There is often 

reasonable agreement between extinction estimates made by the two methods considered 

here, but substantial and consistent differences were also observed. Setting aside the 2005 

comparison because of less complete data than in 2006 and 2007, note that PAD 98th

percentile extinction values in 2007 for both metrics were greater by 30-35% (roughly 

100 to 140 Mm-1) than those of the direct analyses. As one goes farther from the highest 

values, down to the 90th percentile for the maximum daily value metric, agreement 

between the methods improves, both in absolute and relative senses, but the maximum 

daily hour metric is generally more inconsistent, even at 90th percentile, than the all hours 

metric

One aspect that is more troublesome for BHM than JST is limited temporal agreement 

between the estimates of haziness by the two methods, especially when using the daily 

max extinction metric. As an example, according to the SPMLE method, the 8th highest 

(roughly 98th percentile) daily max extinction at BHM in 2007 was 531 Mm-1 on March 

13th, while the direct calculation method arrived at a very different 8th highest extinction 

of 372 Mm-1 on August 15th, 5 months later. On March 13th both methods estimated 

relatively similar extinction, but on August 15th, the SPMLE calculated an extinction of 

190 Mm-1, which doesn’t compare well with the 372 Mm-1 estimate of the direct method.

Therefore, the conclusion of the JST analyses has to be tempered somewhat for BHM to 

reflect the consistent bias of one method relative to the other, the non-robust nature of the 

daily max hour metric (especially at 98th percentile), and the greater lack of temporal 

agreement as to when during the year the greatest haziness occurs. Although individual 

hourly estimates of bext,fp may differ considerably, the agreement between the two 

methods improves when more stable percentile levels are chosen, i.e, ones farther down 

from the 99th percentile, and the all hours metric is used instead of the daily maximum 

hour. It is likely that a multi-year index, such as the average of 90th percentiles over 3 

years, will also be more stable and consistent, but that hypothesis was not tested here.

One approach that does not improve matters is that of using a range of percentiles – e.g., 

the average of all values between the 92nd and the 90th percentiles. The biases between 

the methods tend to be consistent over a range of extinction values, so nothing is gained 

by adding this complexity. 
13

If some of these concepts are followed, the EPA’s simplified method of estimating hourly 

light extinction may still provide usable estimates of bext,fp, as compared to estimates 

made with actual on-site hourly PM2.5 component concentration data.

An important caveat: These conclusions are based on analyses of data from two Southern 

cities. The results may not be applicable to other cities, especially in other areas of the 

country, to other city sizes, and to other pollutant mixes. Also, all of the comparisons 

here have been between two calculation methods for estimating light extinction, neither 

of which has been tested against actual visibility measurement. It is important that 

research be carried out to link these extinction estimates to actual optical measurements 

of haze, so that the haze management program will aim at goals that are meaningful for 

society.
ATTACHMENT 1

Comparison of All Daylight Hour Calculations at JST

The following text and figure are extracted, with some minor editing, from pages 21 to 20 

of Comments Concerning the Visibility-Related Portion of the Second External Review 

Draft of the Policy Assessment for the Review of the PM NAAQS, by Ivar Tombach, 30 

August 2010:

I have compared the hourly PM2.5 light extinction results obtained by using EPA’s 

simplified SPMLE [Speciated PM2.5 Mass-calculated Light Extinction] calculation 

method with the results of the hourly light extinction calculated from hourly speciated 

concentration measurements, using the same variant of the IMPROVE algorithm in both 

cases. For this analysis, I used the every-day measurements made at the Jefferson Street 

(JST), Atlanta, SEARCH site, during 2005-2007 (the same years as those analyzed by 

EPA in the PAD [Policy Assessment Document]). 

Note that my calculations are not a validation of the ability of the simplified method, or 

of any of the other methods considered by the EPA, to accurately portray hour-by-hour 

actual light extinction. Rather, they should be considered as initial exploration of whether 

the simplifications in EPA’s latest method alter the fine structure of the extinction 

estimates to such a degree that they cannot be considered usable.

The same data sets are compared in a scatter plot in Figure 5. The only points plotted are 

those for hours for which both methods produced a value. Consequently, the high PAD 

bext,fp values produced by the spike in May 2007 do not appear because there were no 

corresponding hourly values from the direct calculation [because of a carbon analyzer 

malfunction]. The correlation between the two data sets is respectable (R2 = 0.85). The 

black line is the ordinary least squares (OLS) regression line and the red line is the OLS 

line forced through the origin. The red line has a slope of 1.00, which suggests that one 

data set is not biased relative to the other. The dashed green lines denote a factor of 2 

around the 1:1 line (which just happens to be the OLS line through the origin). The dense 

data “cloud” just barely fits between the two green lines when bext,fp is less than about 

150 Mm-1, which indicates that the hourly bext,fp values produced by the two methods can 

readily differ by up to a factor of two. Relative agreement improves at higher values of 

extinction. Even above 300 Mm-1 there are occasional values that differ by a factor of two 

from their counterparts, though. 
2

Figure 5. Comparison of hourly daylight values of PAD bext,fp with directly 

calculated values for JST during 2005-2007, for RH ≤ 90%. Ordinary least squares 

regression lines and formulas are shown in black and red. The dashed green lines 

delineate a factor of two around the 1:1 line.

We can gain insight into the significance of any differences between the results of the 

two methods by looking at their distributions. Table 2 summarizes some statistics about 

the two data sets for each of the three years. In particular, the 98th percentile of all the 

valid hourly values of bext,fp is a metric that appears in the draft PAD for consideration.

y = 0.93x + 9.33

R2 = 0.85

y = 1.00x

R2 = 0.84

0

100

200

300

400

500

600

0 100 200 300 400 500 600

bextfp (Mm-1)

PAD bextfp (Mm-1)
3

Table 1. Statistical comparison of the two bext,fp data sets for JST.

2005 2006 2007

PAD Direct PAD Direct PAD Direct

# of daylight hours 4107 4107 4107 4107 4107 4107

# of daylight hours 

(RH≤90%) w/ valid 

data

2614 2106 3023 2589 2952 2564

Maximum bext,fp

(Mm-1)

494 533 444 453 910 452

98th %-ile bext,fp 

(Mm-1)

255 255 229 235 236 207

 Note the following in Table 2:

• Although the number of possible daylight hours (as defined by the UFVA) per 

year is 4107, that number was reduced appreciably by the RH ≤ 90% cutoff and 

by the need for valid values for all needed calculations for that hour. As we 

discussed earlier, the PAD method produced more hourly estimates of bext,fp than 

the direct method.

• For 2006, both methods calculated very similar highest extinction values and 

determined them to occur at the very same hour of the year. In the other two 

years, the maximum estimated values of extinction differed to a greater degree 

and did not occur on the same day. The very large discrepancy in 2007 is due to 

missing total carbon data during a high PM episode in May 2007, which caused 

the direct method to miss the episode, as was discussed above in connection with 

Figure 4.

• The 98th percentile values of bext,fp are expected to be less sensitive to the 

extremes reflected by the maximum values, and indeed this is the case. The bext,fp

values calculated by the two methods agreed exactly in 2005, although those 

identical values occurred on different days. Agreement was also very good in 

2006 but less so in 2007, again a consequence of the missing total carbon data 

during the high PM episode in May 2007.

Table 2 shows that both methods give design values (i.e., 3-year average 98th-percentile 

values of bext,fp with RH≤90%) that exceed the upper end of the SPMLE range of 64 to 

191 Mm-1 recommended by EPA staff on page 4-50 of the draft PAD. The annual 98th

percentile values that make up these design values are in the range of 207 to 255 Mm-1 

(depending on method).
4

Although this analysis suggests that, at least at the SEARCH JST site, the EPA’s 

simplified method of estimating hourly light extinction does not1 appear to materially 

degrade the quality of the estimates relative to those made with actual on-site hourly 

PM2.5 component concentration data, this exercise does not demonstrate any of the 

following:

• Equivalency between the simplified method (Method F) and the method the EPA 

has used previously (Method A);

• The ability of EPA’s variant of the original IMPROVE algorithm to produce 

reliable estimates of hourly light extinction from PM2.5 component concentrations 

in urban areas;

• Equivalency between the simplified method (or, for that matter, of any of the 

methods considered by the EPA) and actual hourly light extinction. That veryessential evaluation requires comparison with on-site hourly measurements of 

light extinction.

 1

 [This “not” was inadvertently left out of my August comments, although this conclusion was 

stated correctly elsewhere in that document.]
ATTACHMENT 2

Comparison of Daylight Maximum Hour Calculations

Ivar Tombach

27 September 2010

The comments I submitted to the EPA on 30 August 2010, concerning EPA’s second 

draft Policy Assessment Document (PAD) for the PM2.5 NAAQS,2 included results of a 

comparison of fine particle light extinction (bext,fp) estimates using both the “simplified 

method” in the PAD and values derived from hourly measurements of the principal 

chemical components in the original IMPROVE algorithm, using daily aerosol 

measurements made at the Jefferson Street (JST), Atlanta, SEARCH monitoring site 

during 2005-2007.

The analysis in that report compared the two methods for a metric that was based on 

hourly values of bext,fp over all daylight hours with RH ≤ 90%. (That analysis, as extracted 

from my August comments, is attached to this memo.) This memo provides a new 

analysis that addresses, similarly, the alternative metric of daily maximum hourly values 

of bext,fp, for the same data set under the same constraints. Information about the data 

sources is contained in the Attachment.

The scatter plot in Figure 1 displays the relationship for 2005 – 2007 between values of 

daily maximum hourly of bext,fp derived using the method in the PAD and the values 

calculated directly from the chemical measurements using the traditional IMPROVE 

algorithm. Figure 1 is the counterpart of Figure 5 in my earlier report, which is included 

in the Attachment. 

In Figure 1, the black line is the ordinary least squares (OLS) linear regression line and 

the red line is the OLS line forced through the origin. Since there is only one point per 

day, there are fewer points on Figure 1 than in its all-hours counterpart. Unlike the 

wedge-shaped data “cloud” in the earlier figure, here the bounds on the data scatter 

appear to be parallel to the central line, i.e., the scatter appears to be in the form of offsets 

from the central line that don’t depend on the magnitude of the light extinction, rather 

than the multiplicative form in the figure in my earlier report. As a reference for the eye, 

the two green lines are at a distance of ± 50 Mm-1 horizontally or vertically from a 1:1 

line (essentially the red line). Disagreements between the two methods are still relatively 

common outside that range, though, and a range of ± 100 Mm-1 is needed to contain 90 to 

95% of the data.

 2 Comments Concerning the Visibility-Related Portion of the Second External Review Draft of the 

Policy Assessment for the Review of the PM NAAQS, by Ivar Tombach, 30 August 2010.
2

Figure 1. Comparison of daily maximum hourly daylight values of PAD bext,fp with 

directly calculated values for BHM during 2005-2007, for RH ≤ 90%. Ordinary least 

squares regression lines and formulas are shown in black and red. The dashed green 

lines delineate deviations of ± 50 Mm-1 from the 1:1 line.

Table 1 summarizes some statistics about the two data sets that were displayed in Figure 

1, for each of the three years 2005 through 2007. (This new table is analogous to Table 2 

in my earlier report, attached.) Table 1 displays both the 98th and 90th percentiles of all 

the daily maximum hourly values of bext,fp during each year, which are metrics that were 

considered in the second draft PAD. Although there is some variability in these 

percentiles from year to year, the 3-year averages for the two methods are within about 

5% of each other, with neither method showing obvious bias relative to the other.

y = 0.70x + 54.99

R2 = 0.49

y = 0.95x

R2 = 0.39

0

100

200

300

400

500

600

0 100 200 300 400 500 600

Daily Max Hour bextfp (Mm-1)

PAD Daily Max Hr bextfp (Mm-1)
3

Table 2. Statistical comparison of the two daily maximum hour bext,fp data sets for 

BHM.

2005 2006 2007

PAD Direct PAD Direct PAD Direct

# of days considered, 

(RH<90% and valid data)

322 342 335

# of valid max hour 

extinction values

238 183 290 251 308 242

Maximum bext,fp (Mm-1) 673 487 676 738 823 626

98th %-ile of daily max 

bext,fp values (Mm-1)

475 314 484 540 541 399

90th %-ile of daily max 

bext,fp values (Mm-1)

229 188 272 272 305 267

Table 1 shows that both methods considered here give design values (i.e., 3-year average 

98th-percentile values of daily maximum hourly bext,fp whenever RH≤90%) that greatly 

exceed the upper end of the SPMLE range of 64 to 191 Mm-1 recommended by EPA 

staff. The annual 98th percentile values that make up these design values are in the range 

of 300 to 400 Mm-1 (depending on method and year), which are also considerably greater 

than the roughly 200 to 250 Mm-1 values for all daylight hours that appeared in Table 2 in 

my earlier report.

The PAD included the observation that the 98th percentile of all hours is about the same 

as the 90th percentile of the daily maximum hours. When one compares Table 1 above 

with Table 2 in the Attachment, that relationship also seems to apply to the SEARCH JST 

data analyzed here.

In summary, these new analyses with daily maximum hour extinction lead to conclusions 

similar to those of the earlier analyses with extinction during all daylight hours, with RH 

≤ 90% in both cases. Specifically, at least at the SEARCH JST site, although individual 

hourly estimates of bext,fp may differ considerably, when data are aggregated over time the 

EPA’s simplified method of estimating hourly light extinction appears not to materially 

degrade the quality of estimates of various percentile levels bext,fp, as compared to 

estimates made with actual on-site hourly PM2.5 component concentration data.

It is worth repeating that this exercise does not demonstrate any of the following, 

however:

• Equivalency between the simplified method used here (Method F) and the method 

the EPA has used previously (Method A);
4

• The ability of EPA’s variant of the original IMPROVE algorithm to produce 

reliable estimates of hourly light extinction from PM2.5 component concentrations 

in urban areas;

Equivalency between the simplified method (or, for that matter, of any of the methods 

considered by the EPA) and actual hourly light extinction. That very-essential evaluation 

requires comparison with on-site hourly measurements of light extinction.