1 UNITED STATES ENVIRONMENTAL PROTECTION AGENCY Office of Air Quality Planning and Standards (OAQPS) Research Triangle Park, North Carolina 27711

December 1 4 , 2012

MEMORANDUM

SUBJECT: Re

- analysis of the relationship between 24

- hour and 4

- hour visibilit y index levels

.
FROM: Neil Frank and Mark Schmidt , Air Quality Analysis Group , O A Q P S / O A R / s /

TO: PM NAAQS Review Docket ( EPA

- HQ

- OAR

- 2007

- 0492 )
This memorandum presents a n update to the analysis of the relationship between 24

- hour and 4

- hour estimated light extinction levels presented in Appendix G of the P olicy A ssessment ( 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 ap proach to estimate organic mass and (2) a better account ing for the uncertainties in 24

- hour and 4

- hour estimates of the visibility index values via the use of an alternative statistical approach

. The up dated analysis reveal s 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 exp lored various approaches for calculating adjusted candidate protection levels ( CPLs ) for a 24

- hour average PM 2.5 light

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

- hour average PM 2.5 light extinction indicator, on an aggregate or central tendency basis

. In developing these adjusted CPLs, EPA compar ed , for 15 study areas, (i) values of 24

- hour average PM 2.5 light extinction calculated using the original IMPROVE algorithm combine d with site

- specific daily data on PM 2.5 mass and composition and site

- specific long

- term relative humidity conditions with (ii) values of daily maximum daylight 4

- hour average PM 2.5 light extinction calculated from the hourly results of the U rban

- F ocused Visibility Assessment ( UFVA ) ( U.S. EPA, 2010b ) modeling of hourly PM 2.5 light extinction

. The Appendix G approach for estimat ing 24

- hour light extinction involved estimat ing organic mass ( OM ) for each Chemical Speciation Network ( CSN ) sampling day by subtr act ing a sampler

- dependent estimate of the organic carbon ( OC ) artifact from the OC measurement to estimate PM 2.5 OC and multiply ing the result by 1.4 ( i

. e. , OM = PM 2.5 OC *1.4 )

. This was distinctly different than t he approach followed in the UFVA, which e ntailed numerous and complex data processing steps to2 generate hourly PM 2.5 composition information from less time resolved data, including application of the SANDWICH approach (Frank, 2006) for estimating OM via material balance

. 1

Some of the approache s 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 aggrega ted 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 App endix 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 R

squared values of the regressions and used data from day s with PM 2.5 light extinction conditions in the range of 20 to 40 dv. In contrast , other approaches were highly influenced by PM 2.5 light extinction conditions well below this range. Based on these analyses and staff conclusions , including a preference fo r 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 val ues among different cities, suggesting that average or 90 th 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 I n Appendix F of the Policy Ass essment , the EPA specifically evaluated which multiplier would produce 24

- hour results most similar to the SANDWICH approach using 24

- hour PM 2.5 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 PM 2.5 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 dai ly maximum 4

- hour daylight light extinction on the same day. Second, PM 2.5 concentrations may be greater during non

- daylight periods than during daylight hours.3 Table 1. R elationships between 24

- hour and 4

- hour levels from Policy Assessment ( Corrected Table G

- 6 ) 3

Approach Description 24

- hour leve l 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 90 th percentile design values regressi on 22 dv 25 dv 28 dv

B Annual 90 th 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 d ays pooled regression 19 dv 23 dv 27 dv

E Median ratios, then averaged 19 dv (1 7

- 2 1 ) 24 dv (21

- 26) 29 dv (25

- 31)

Estimating 24

- hour and 4

- hour light extinction levels using a more con sistent approach

T he 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 PM 2.5 composition information from less time resolved data, including an estimate of OM using the SANDWICH material balance, while the 2 4

- hour levels were based on the original IMPROVE algorithm and using a 1.4 multiplier applied to PM 2.5 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 PM 2.5 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 der ived in the PA were all based on a simple linear regression which utilizes an ordinary least squares (OLS) approach. Th e OLS approach determines a fitted line that makes the sum of squared vertical distances between the points of the data set and the fitte d line as small as possible. This results in an equation of the form Y = b 0 + b 1 X , where Y is the predicted variable (i.e., 24

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

- hour levels )

. T his approach does not account for any er ror 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 ar e 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 2 0 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.4 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 th e Deming model is an orthogonal regr ession which assumes that the uncertainties in the observations of X and of Y are approximately equal and determines the line of best fit by minimiz ing the sum of squared perpendicular distances from the data points to the regression line. The orthogonal r egression results in an equation Y = c 0 + c 1 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, p rovide 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 th e 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 equa tion will be X = ( Y

- c 0 ) / c 1 . 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 t he analyses pres ented 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 descri b ed above . The formulas are :

Y = b 0 + b 1 X , ( based on OLS regression ) ; and

Y = c 0 + c 1 X , ( 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 :

• A pproach A: 3

- year 90 th percentile design values

• Approach B: A nnual 90th percentile value s

• Approach C : All

- days city

- specific values

• Approach D: All

- days p ooled values for all cities

The results of th e s e revised analyses are shown below in Table 2 for th e 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 90 th percentile value s ) , Table 3 shows that the 24

- hour CPLs of 19 , 24 , and 29 dv are estim ated 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 p resented 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 3.5 re

- analysis, which incorporated a more consistent approach to estimating OM in the calcula tions 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 city

specific 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 e stimates of the two regression models , is combined into Table 5.
The revised analysis more clearly indicates th a t 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.

T able 2 . “Equivalent” Levels for Calculated 24

- Hour PM 2.5 Light Extinction Using Fo ur 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 90 th percentile design values regression 22 dv 25 dv 28 dv

B Annual 90 th pe rcentile values regression 2 1 dv 25 dv 2 8 dv

C All

- days city

- specific regressions, then averaged 20 dv (1 7

- 2 1 ) 2 3 dv (2

1

- 2 6

) 2 7 dv (2

4

- 3

0

) D All days pooled regression 19 dv 2 3 dv 2 7 dv

Table 3 . “Equivalent” Levels for Calculated 24

- Hour PM 2.5 Light E xtinction 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 ho ur (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 90 th percentile design values regression 22 dv 25 dv 28 dv

B Ann ual 90 th percentile values regression 19 dv 2 4 dv 29 dv

C All

- days city

- specific regressions, then averaged 20 dv (1 7

- 22 ) 24 dv (22

- 2

9

) 2 9 dv (25

- 36) D All days pooled regression 19 dv 2 4 dv 28 dv6 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 Regression7 Table 5. Revised Relationships b etween 24

- Hour a nd 4

- Hour Levels Using Multiplier o f 1.6 f

or OM a nd Two Regression Models (OLS a nd Orthogonal Regressions )8 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

.