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UNITED STATES ENVIRONMENTAL PROTECTION AGENCY

Office of Air Quality Planning and Standards (OAQPS)

Research Triangle Park, North Carolina 27711

December 14, 2012

MEMORANDUM

SUBJECT: Re-analysis of the relationship between 24-hour and 4-hour visibility index levels.

FROM: Neil Frank and Mark Schmidt, Air Quality Analysis Group, OAQPS/OAR /s/

TO: PM NAAQS Review Docket (EPA-HQ-OAR-2007-0492)

This memorandum presents an update to the analysis of the relationship between 24-hour 

and 4-hour estimated light extinction levels presented in Appendix G of the Policy Assessment

(PA) for the review of the particulate matter (PM) national ambient air quality standards

(NAAQS) (US EPA, 2011a). This update includes (1) a revision to the estimates of 24-hour and

4-hour visibility index levels using a consistent approach to estimate organic mass and (2) a 

better accounting for the uncertainties in 24-hour and 4-hour estimates of the visibility index 

values via the use of an alternative statistical approach. The updated analysis reveals that the 24-

hour and 4-hour light extinction values are even more closely related than presented previously 

in the PA or the proposed rule for the PM NAAQS (77 FR 38890, June 29, 2012).

Background

In Appendix G of the PA, EPA explored various approaches for calculating adjusted 

candidate protection levels (CPLs) for a 24-hour average PM2.5 light-extinction indicator that are 

generally equivalent to CPLs of 20, 25, and 30 deciviews (dv) for a daily maximum daylight 4-

hour average PM2.5 light extinction indicator, on an aggregate or central tendency basis. In 

developing these adjusted CPLs, EPA compared, for 15 study areas, (i) values of 24-hour 

average PM2.5 light extinction calculated using the original IMPROVE algorithm combined with 

site-specific daily data on PM2.5 mass and composition and site-specific long-term relative 

humidity conditions with (ii) values of daily maximum daylight 4-hour average PM2.5 light 

extinction calculated from the hourly results of the Urban-Focused Visibility Assessment 

(UFVA) (U.S. EPA, 2010b) modeling of hourly PM2.5 light extinction. The Appendix G 

approach for estimating 24-hour light extinction involved estimating organic mass (OM) for each 

Chemical Speciation Network (CSN) sampling day by subtracting a sampler-dependent estimate 

of the organic carbon (OC) artifact from the OC measurement to estimate PM2.5 OC and

multiplying the result by 1.4 (i.e., OM = PM2.5 OC *1.4). This was distinctly different than the 

approach followed in the UFVA, which entailed numerous and complex data processing steps to 
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generate hourly PM2.5 composition information from less time resolved data, including 

application of the SANDWICH approach (Frank, 2006) for estimating OM via material balance.

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Some of the approaches described in Appendix G to determine generally equivalent 24-

hour adjusted CPLs focused on comparing 24-hour and 4-hour light extinction values in each of 

the 15 urban areas assessed in the UFVA, whereas other approaches focused on comparisons of 

aggregated data across the urban areas. Two of these city-specific approaches (regressions of 

annual 90th percentile light extinction values and regressions of 3-year average light extinction 

design values) gave nearly identical results and were determined in Appendix G to be most 

appropriate for identifying generally equivalent 24-hour adjusted CPLs. These approaches 

identified as A and B (as depicted in Figures G-7 and G-8, Appendix G of the PA) had high Rsquared values of the regressions and used data from days with PM2.5 light extinction conditions 

in the range of 20 to 40 dv. In contrast, other approaches were highly influenced by PM2.5 light 

extinction conditions well below this range. Based on these analyses and staff conclusions, 

including a preference for Approach B, presented in Appendix G of the PA, the EPA identified 

adjusted 24-hour CPLs of 21, 25, and 28 dv as being generally equivalent to 4-hour CPLs of 20, 

25, and 30 dv, as shown below in Table 1.

Other approaches, including Approaches C, D, and E, also shown in Table 1, provided 

information about how city-specific or pooled 24-hour values compared to 4-hour values. While 

these approaches had lower R-squared values than Approaches A and B, they illustrated that 

there is a significant range in values among different cities, suggesting that average or 90th

percentile values might not accurately represent all locations. Notably, Approaches C and E 

generated a range of city-specific estimates of generally equivalent 24-hour levels that 

encompassed the range of levels considered appropriate for 4-hour CPLs, including the CPL of 

30 dv at the upper end of that range.2

 1 In Appendix F of the Policy Assessment, the EPA specifically evaluated which multiplier would produce 24-hour 

results most similar to the SANDWICH approach using 24-hour PM2.5 organic carbon derived from the new 

Chemical Speciation Network (CSN) carbon monitoring protocol established in 2007, and concluded that a 

multiplier of 1.6 is most appropriate for purposes of comparing the hourly PM2.5 light extinction with calculated 24-

hour extinction (see Appendix F, section F.6 for a full explanation).

2 As discussed in more detail in Appendix G of the PA, some days have higher values for 24-hour average light 

extinction than for daily maximum 4-hour daylight light extinction, and consequently an adjusted "equivalent" 24-

hour CPL can be greater than the original 4-hour CPL. This can happen for two reasons. First, the use of monthly 

average historical RH data will lead to cases in which the f(RH) values used for the calculation of 24-hour average 

light extinction are higher than all or some of the four hourly values of f(RH) used to determine daily maximum 4-

hour daylight light extinction on the same day. Second, PM2.5 concentrations may be greater during non-daylight 

periods than during daylight hours.
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Table 1. Relationships between 24-hour and 4-hour levels from Policy Assessment 

(Corrected Table G-6)

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Approach Description

24-hour level equivalent 

to 20dv for 4 hour 

(range among 15 cities)

24-hour level equivalent 

to 25dv for 4 hour 

(range among 15 cities)

24-hour level equivalent 

to 30dv for 4 hour 

(range among 15 cities)

A 3-year 90th percentile 

design values regression 22 dv 25 dv 28 dv

B Annual 90th percentile 

values regression 21 dv 25 dv 28 dv

C All-days city-specific 

regressions, then averaged

19 dv 

(17 - 21)

23 dv 

(21 - 25)

27 dv 

(24 - 30)

D All days pooled regression 19 dv 23 dv 27 dv

E Median ratios, then 

averaged

19 dv 

(17 - 21)

24 dv 

(21 - 26)

29 dv 

(25 - 31)

Estimating 24-hour and 4-hour light extinction levels using a more consistent approach

The first step in this reanalysis of urban speciation data is to consistently estimate OM 

with a multiplier of 1.6. As noted above, EPA previously derived 4-hour and 24-hour light 

extinction levels using different approaches. The 4-hour levels were derived with the UFVA 

approach which entailed numerous and complex data processing steps to generate hourly PM2.5 

composition information from less time resolved data, including an estimate of OM using the 

SANDWICH material balance, while the 24-hour levels were based on the original IMPROVE 

algorithm and using a 1.4 multiplier applied to PM2.5 OC. Based on the results of the analysis 

presented in Appendix F of the PA, a 1.6 multiplier was found to provide a suitable estimate of 

OM from PM2.5 OC measured by the new CSN monitoring protocol. This produced estimates 

comparable to OM estimated using the SANDWICH approach. 

Revising the statistical model

The relationships between 24-hour light extinction levels and 4-hour light extinction

levels derived in the PA were all based on a simple linear regression which utilizes an ordinary 

least squares (OLS) approach. The OLS approach determines a fitted line that makes the sum of 

squared vertical distances between the points of the data set and the fitted line as small as 

possible. This results in an equation of the form Y = b0 + b1X, where Y is the predicted variable

(i.e., 24-hour light extinction levels), and X is the explanatory variable (i.e., 4-hour levels). This 

approach does not account for any error in X, and as a result may overestimate the intercept “a”

and underestimate the slope “b” when there are errors associated with X. When the error in X is 

large, the biases in the estimated parameters of the regression line can also be large.

 3 Note that the city-specific ranges shown in Table G-6, Appendix G of the Policy Assessment are incorrectly stated 

for Approaches C and E. Drawing from the more detailed and correct results for Approaches C and E presented in 

Tables G-7 and G-8, respectively, the city-specific ranges in Table G-6 for Approach C should be 17 – 21 dv for the 

CPL of 20 dv; 21 – 25 dv for the CPL of 25 dv; and 24 – 30 dv for the CPL of 30 dv; the city-specific ranges in 

Table G-6 for Approach E should be 17 – 21 dv for the CPL of 20 dv; 21 – 26 dv for the CPL of 25 dv; and 25 – 31 

dv for the CPL of 30 dv.
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There is an alternative “errors-in-variables” regression model designed to determine the 

line of best fit by accounting for errors in observations for both X and Y. This model is known as 

a Deming regression. A special case of the Deming model is an orthogonal regression which 

assumes that the uncertainties in the observations of X and of Y are approximately equal and 

determines the line of best fit by minimizing the sum of squared perpendicular distances from the 

data points to the regression line. The orthogonal regression results in an equation Y = c0 + c1 X. 

A Deming regression in general and an orthogonal regression in particular will more 

appropriately result in a lower intercept and a higher slope than those derived using an OLS 

regression, and accordingly, provide more accurate values of the predicted variable (Y) for each 

chosen value of the explanatory variable (X). Another property of orthogonal regression is its 

symmetry. Unlike OLS, where the regression of Y on X does not produce the same equation as 

the regression of X on Y, that is not true with orthogonal regression. Using the notation above 

for orthogonal regression, the relationship between X and Y can be derived directly from the 

relationship of Y on X. Specifically, this orthogonal regression equation will be X = (Y - c0) / c1.

Estimating the relationship between 24-hour and 4-hour light extinction levels using a 

multiplier of 1.6 for OM and alternative regression models

Accordingly, in the tables presented below, we have updated the analyses presented in 

Appendix G of the PA using a multiplier of 1.6 for OM for organic carbon measured with the 

new CSN monitoring protocol and using two regression models, including the original OLS 

regression approach and the orthogonal approach described above. The formulas are:

Y = b0 + b1X, (based on OLS regression); and 

Y = c0 + c1X, (based on orthogonal regression).

For each model, comparisons between 24-hour and 4-hour values were made based on the 

following approaches,4 consistent with Appendix G of the PA:

• Approach A: 3-year 90th percentile design values

• Approach B: Annual 90th percentile values

• Approach C: All-days city-specific values

• Approach D: All-days pooled values for all cities

The results of these revised analyses are shown below in Table 2 for the updated OLS 

regressions and in Table 3 for the orthogonal regressions, which we consider more appropriate 

for the reasons discussed above. For Approach B (annual 90th percentile values), Table 3 shows 

that the 24-hour CPLs of 19, 24, and 29 dv are estimated to be generally equivalent to 4-hour 

CPLs of 20, 25, and 30 dv. This is in contrast to the values for Approach B of 21, 25, 28 dv 

presented as comparable to these same 4-hour CPLs in the PA. Thus, compared to the findings in

the PA (Appendix G, Table G-6) as corrected and presented above as Table 1, the 24-hour and 4-

hour light extinction values are more closely related for the highest CPL based on this improved 

 4 Approach E presented in Appendix G of the PA is based on the median values per city and is not affected by the 

regression analyses. Therefore, the results from Approach E do not change with the reanalysis and are not included 

in Tables 2 and 3.
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re-analysis, which incorporated a more consistent approach to estimating OM in the calculations

of 4-hour and 24-hour light extinction values. Moreover, the low and high end of the range of 

city-specific levels from Approach C using the orthogonal regression method bracket the average 

levels derived from all approaches. In particular, we note that the high end of the range of cityspecific values from Approach C is 30 dv with OLS regression but is 36 dv with orthogonal 

regression. The updated city-specific results are shown in Table 4. The information from Tables 

2-4, along with the parameter estimates of the two regression models, is combined into Table 5.

The revised analysis more clearly indicates that city-specific 24-hour light extinction can 

be both higher (for the highest CPL) and lower (for the lowest CPL) than 4-hour values (see 

Table 3, Approach C and Table 4); and that the average values are generally more closely related 

(Table 3, Approaches A – D) than presented previously in Appendix G of the PA.

Table 2. “Equivalent” Levels for Calculated 24-Hour PM2.5 Light Extinction Using Four 

Approaches, based on Ordinary Least Squares Regression (analogous to Table G-6 from the PA,

with update to 1.6 multiplier for 24-hour speciation sampling days with new carbon protocol)

Approach Description

24-hour level equivalent 

to 20dv for 4 hour 

(range among 15 cities)

24-hour level equivalent 

to 25dv for 4 hour 

(range among 15 cities)

24-hour level equivalent 

to 30dv for 4 hour 

(range among 15 cities)

A 3-year 90th percentile design 

values regression 22 dv 25 dv 28 dv

B Annual 90th percentile values 

regression 21 dv 25 dv 28 dv

C All-days city-specific 

regressions, then averaged

20 dv

(17-21)

23 dv

(21-26)

27 dv

(24-30)

D All days pooled regression 19 dv 23 dv 27 dv

Table 3. “Equivalent” Levels for Calculated 24-Hour PM2.5 Light Extinction Using Four 

Approaches, based on Orthogonal Regression (analogous to Table G-6 from the PA, with update to 1.6 

multiplier for 24-hour speciation sampling days with new carbon protocol)

Approach Description

24-hour level equivalent 

to 20dv for 4 hour 

(range among 15 cities)

24-hour level equivalent 

to 25dv for 4 hour 

(range among 15 cities)

24-hour level equivalent 

to 30dv for 4 hour 

(range among 15 cities)

A 3-year 90th percentile design 

values regression 22 dv 25 dv 28 dv

B Annual 90th percentile values 

regression 19 dv 24 dv 29 dv

C All-days city-specific 

regressions, then averaged

20 dv

(17-22)

24 dv

(22-29)

29 dv

(25-36)

D All days pooled regression 19 dv 24 dv 28 dv
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Table 4. Comparison of City Specific Results using OLS and Orthogonal Regressions

20 dv 25 dv 30 dv 20 dv 25 dv 30 dv

Tacoma 21 26 30 22 29 36

Fresno 19 23 28 18 24 29

Los Angeles 18 22 26 18 22 26

Phoenix 20 24 28 21 27 32

Salt Lake City 17 22 27 18 23 28

Dallas 18 21 24 18 22 25

Houston 20 23 25 20 23 27

St. Louis 20 23 26 20 24 28

Birmingham 21 24 28 21 25 29

Atlanta 20 23 27 19 24 28

Detroit 20 24 28 20 24 28

Pittsburgh 21 25 29 21 25 30

Baltimore 21 24 28 21 25 29

Philadelphia 18 22 26 17 22 27

New York City 21 24 27 20 24 28

Average 20 23 27 20 24 29

Minimum 17 21 24 17 22 25

Maxium 21 26 30 22 29 36

OLS Regression

Approach C: City Specific Results 

24-hour levels (in dv) equivalent to 4-hour levels of 20, 25 and 30 dv

(by regression model )

City

Orthogonal Regression
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Table 5. Revised Relationships between 24-Hour and 4-Hour Levels Using Multiplier of 1.6 

for OM and Two Regression Models (OLS and Orthogonal Regressions)
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References

U.S. EPA (2010b). Particulate Matter Urban-Focused Visibility Assessment – Final Report. 

Office of Air Quality Planning and Standards, U.S. Environmental Protection Agency, 

Research Triangle Park, NC. EPA-452/R-10-004. July 2010. Available: 

http://www.epa.gov/ttn/naaqs/standards/pm/s_pm_2007_risk.html.

U.S. EPA (2011a). Policy Assessment for the Review of the Particulate Matter National Ambient 

Air Quality Standards. Office of Air Quality Planning and Standards, U.S. Environmental 

Protection Agency, Research Triangle Park, NC. EPA 452/R-11-003. April 2011. 

Available: http://www.epa.gov/ttn/naaqs/standards/pm/s_pm_2007_pa.html.