2 

The UFVA approach to estimation of hourly PM2.5 light extinction has the following complex 

aspects: 

1. The SANDWICH mass balance model is used to estimate 24-hour average PM2.5 sulfate, 

nitrate, and organic carbonaceous material (OCM) mass loading on the FRM filter for 

each Chemical Speciation Network (CSN) sample day.2

 This requires information on 

daily temperature and relative humidity. The sulfate and nitrate components are initially 

derived from the relevant CSN filters, with adjustments to represent FRM mass. FRM 

sulfate includes estimated particle bound water while the FRM nitrate loading may underrepresent the ambient concentration of nitrate. These are re-adjusted in a subsequent step 

to represent ambient conditions prior to calculation of extinction. 

2. The estimates of 24-hour average PM2.5 elemental carbon and fine soil component 

concentrations are determined from the analysis of the relevant CSN filter. 

3. Monthly mean diurnal variations of each of the major PM2.5 components from CMAQ air 

quality simulation modeling results for the location of each monitoring site are applied to 

sample day-specific CSN 24-hour samples to create preliminary estimates of hourly 

component concentrations. For the UFVA, available output from a 2004 CMAQ 

modeling platform was used. This step can result, for example, in preliminary estimates 

of concentrations of sulfate that are fairly uniform throughout a day while concentrations 

of nitrate may show much more variation because of temperature effects on the 

gas/particle partitioning of nitrate. 

4. Estimates of hourly PM2.5 mass are developed by normalizing continuous PM2.5

measurements to the 24-hour FRM filter mass. 3

5. The preliminary estimates of hourly components from step 3 above are scaled up or down 

in equal proportion to reconcile their sum to the estimate of hourly PM2.5 mass.

6. The resulting hourly PM2.5 sulfate and nitrate component concentrations are adjusted to 

reflect actual atmospheric concentration, which is assumed to be represented by the CSN 

filter sulfate and nitrate measurements. (This step in effect un-does the estimated FRM 

sulfate mass enhancement due to particle bound water and the FRM nitrate loss 

introduced by the SANDWICH mass balance model.) 

7. The original IMPROVE algorithm is used to estimate hourly PM2.5 light extinction from 

hourly PM2.5 component and hourly relative humidity values. 

Analytical Approach in this Memo 

This analysis examines the difference between calculated hourly PM2.5 light extinction values 

used in the UFVA and values generated using simpler approaches, explored in a step-wise 

fashion. In each step, one of the steps described above is omitted or simplified. All of the simpler 

 

2 Frank, N., Retained Nitrate, Hydrated Sulfates, and Carbonaceous Mass in Federal Reference Method Fine 

Particulate Matter for Six Eastern U.S. Cities, J. Air Waste Manage. Assoc., 56, 500-511, 2006. 3 This memo is based on 2005-2007 data. The continuous PM2.5 instruments operating in this period were not EPAapproved as Federal Equivalent Methods (FEMs). EPA-approved FEMs were first used in state networks in 2009. 

EPA staff envisions that in any future monitoring of hourly PM2.5 mass to implement a visibility-based secondary 

PM NAAQS, EPA-approved continuous FEMs will be required. For both the UFVA and this memo, therefore, 

hourly PM2.5 mass values from continuous instruments were adjusted day-by-day to match the 24-hour average 

PM2.5 mass reported by the collocated filter-based sampler.
3 

approaches (designated by letter of the alphabet and described below) use the original 

IMPROVE algorithm without the Rayleigh and PM10-2.5 terms. 4 

Approach A. This designates the UFVA approach, but without the PM10-2.5 term in the 

IMPROVE algorithm. 

Approach B. This approach uses a simpler approach to estimating organic carbonaceous mass 

and nitrate than in the UFVA approach briefly described in the steps listed above. 

Table 1 contrasts in detail the steps in this simpler approach B (and approach F, 

below) to the steps of approach A. The key distinguishing features of approach B 

are (i) a multiplier of 1.7 is applied to the CSN measurement of organic carbon 

(after a correction for blank filter artifact) rather than estimating organic 

carbonaceous material by the mass-balance SANDWICH approach, and (ii) the 

hourly PM2.5 mass (still normalized to match the FRM value for the 24-hour 

PM2.5 mass as in the UFVA approach) is speciated using that day’s CSNmeasured component mix directly, with no correction for possible nitrate loss by 

the continuous instrument or the FRM. 

Approach D. This approach is the same as B except that the time-varying diurnal component 

profile from CMAQ is replaced by a flat profile for each sample day. This has the 

effect of giving each hour of the day the same percentage mix of components, but 

each CSN day is treated separately. 

Approach E. In this approach, step 3 above was modified. The preliminary estimates of hourly 

component concentrations for every day were calculated by applying the CMAQ 

diurnal profile to the monthly-average 24-hour concentration of that component 

(in μg/m3). This results in an estimate of the mass concentration of each 

component for each hour of “an average day.” Then these values were adjusted by 

a common factor to match the hour-specific PM2.5 mass concentrations in each 

day. Thus, this method suppresses the information from the CSN data on how the 

24-hour component mix varies day-to-day, but hours still vary in component mix 

due to the application of the CMAQ profiles. 

Approach F. This approach is the same as B except both flat diurnal PM2.5 component 

variation are assumed and monthly averaged PM2.5 component percentages are 

used in place of sample period-specific values from CSN data (i.e., the approach 

combines aspects of approaches D and E). The net effect is that every hour of a 

month is assumed to have the same percentage mix of components. For greatest 

clarity, the data sources and calculation steps used in this approach are listed in 

Table 2. 

Approach I. This approach simply uses the PM2.5 mass concentration times a single constant. 

This approach was included to show the performance of using PM2.5 mass 

 

4

 Note that the letter designations for the approaches are not contiguous. This is because EPA staff tested additional 

approaches that are not included in this technical memo. Note also that all of the figures include approach 

designators, as plan designators. The 1.7 multiplier for OC was selected for this memo after a brief assessment of 

what multiplier value would reproduce SANDWICH results on average. After the completion of this work, a more 

thorough analysis based on 2007-2009 CSN data only from sites that had converted to the IMPROVE carbon 

methods indicated that a multiplier of 1.6 is more appropriate when using OC data collected with the newer CSN 

carbon methods. The 1.6 value is used in the final version of the Policy Assessment Document.
4 

without adjusting for particle composition and humidity effects on hygroscopic 

particles. The constant used for this approach was 4.35 m2/g.5

As the results below show, approaches B, D, E, and F produce hourly PM2.5 light extinction 

values that are quite comparable to the hourly PM2.5 light extinction values in the original UFVA 

(i.e., approach A). Approach F is of particular interest because it is the most simplified of the 

methods tested that make use of CSN measurements, and its use of monthly-averaged PM2.5 

component concentrations means that it can be applied every day, not just on days with CSN 

monitoring data (i.e., 1-day-in-3 or 1-day-in-6).6 

Appendix 4B of the final Policy Assessment Document considers two approaches that are slight 

variations of approaches D and F, using 2007-2009 data instead of 2005-2007 data as used in this 

memo.

 

5 The value of 4.35 m2

/g has no derivation of particular importance. If this approach were to be pursued further, 

more careful analysis would be appropriate, including analysis of the possibility of site-specific or region-specific 

constants.

6 Note that Approach F as applied for this memo required the availability of filter-based FRM/FEM data for 24-hour 

concentration, and that most filter-based PM2.5 monitoring sites do not operate every day. However, see the related 

comment at step (xi) of Table 2.
5 

1 Table 1. Detailed Comparative Description of Approaches A, B, and F for Estimating 1-hour PM2.5 Light 2 

UFVA Step7 Aspect of Approach Approach A Approach B 

1 Estimation of 24-hour organic 

carbonaceous mass 

The SANDWICH method is used to subdivide the 24-hour PM2.5 mass reported by the 

FRM for each day and site into hydrated ammonium sulfate, ammonium nitrate, elemental carbon, organic carbonaceous material (OCM), and fine soil. This is done using information from the CSN measurements, physical models, and dayspecific temperatures and relative humidity. OCM is estimated as the residual needed to achieve mass balance after estimation of the other components. 

Organic carbonaceous mass is assumed to equal the organic carbon value reported from CSN sampling, minus a blank filter correction that depends on sampler model and laboratory method for carbon but not on monitoring site, times 1.7. 

Sa

1, continued Estimation of 24-hour elemental 

carbon mass 

CSN elemental carbon concentration 

Same as A Sa

1, continued Estimation of 24-hour 

ammonium sulfate mass 

CSN sulfate concentration, with day-specific SANDWICH estimates of associated ammonium and water. 

Sulfate ion measurement from the CSN filter is multiplied by 1.375 to represent dry ammonium sulfate. 

Sa

1, continued Estimation of 24-hour 

ammonium nitrate mass 

Nitrate ion on the FRM Teflon filter is estimated by SANDWICH, with dayspecific estimates of associated ammonium and water. 

Nitrate ion measurement from the CSN filter is multiplied by 1.29 to represent dry ammonium nitrate. 

Sa

7 The numbering of steps follows that used to describe the UFVA approach in section 3.3.1 of the UFVA.
6 

UFVA Step7 Aspect of Approach Approach A Approach B 

1, continued Estimation of 24-hour fine 

soil/crustal mass 

Calculated from CSN elements, but without Al (a difference from the IMPROVE approach) 

Same as A Sa

2 Diurnal pattern of PM2.5

components 

The CMAQ-derived monthly normalized diurnal profiles for the sulfate, nitrate, elemental carbon, organic carbon and fine soil/crustal components (each of which averages to 1.0 across 24 hours) were multiplied by the day-specific SANDWICH-based estimates of the 24-hour average concentrations of the five PM2.5 components, to get 

intermediate day-specific hourly estimates of the five components (including ammonium and water associated with sulfate and nitrate ion). 

CMAQ-derived profiles were applied to the mass concentration of each of the five components in same way as in Approach A. However, as described above, in Approach B the sulfate, nitrate, and organic carbonaceous material components are defined and estimated differently than in Approach A. 

No 

3 Sum the 5 components The hourly concentrations of 

these five components (including day-specific ammonium and water associated with sulfate and nitrate ion when the FRM Teflon filter is weighed) were added together, to get a sumof-components estimate of hourly PM2.5 mass for the day 

of the FRM/CSN sampling. 

The hourly concentrations of the five components were added together, to get a sumof-components estimate of hourly PM2.5 for the day of 

FRM/CSN sampling. Note that water is not included. 

Caavthe 

folFoCS(drthe eacthe cosam
7 

UFVA Step7 Aspect of Approach Approach A Approach B 

4 Hourly PM2.5 concentration, 

consistent with 24-hour FRM concentration. 

The hourly data from the continuous PM2.5 instrument 

on the day of the FRM sampling were normalized by their 24-hour average, to get a normalized diurnal profile. This profile was applied to the 24-hour PM2.5 mass reported 

by the FRM sampler, to get a preliminary, FRM-consistent estimate of hourly PM2.5 mass 

for the day of the FRM sampling. This keeps the average of the valid 1-hour PM2.5 values equal to the 24-

hour value from the FRM sampler. 

Same as A Sa

coTa

5, 6 Adjust preliminary estimates of 

hourly PM2.5 component 

concentrations (reflecting CMAQ diurnal profiles and 24-hour measurements) to be consistent with estimate of hourly PM2.5 mass. 

The two estimates of hourly PM2.5 mass from steps 3 and 4 

were compared, hour-by-hour. Within each hour, the estimates of all five components from step 2 were increased or decreased by a common factor so that the sum of the five components after this adjustment was equal to the estimate of the hourly PM2.5 mass from step 4. The adjustment percentage varied from hour-to-hour. 

Same as A No

Momi

dirspeho
8 

UFVA Step7 Aspect of Approach Approach A Approach B 

7 Adjust the FRM-consistent 

estimate of sulfate to the CSN/IMPROVE-consistent basis expected by the IMPROVE algorithm. 

Each hourly estimate of sulfate concentration on the FRM filter from step 6 (which includes estimates of associated ammonium and particle bound water) was adjusted so that it excludes water and reflects full neutralization and therefore is consistent with the reporting practices of the IMPROVE program and the IMPROVE algorithm. 

No adjustment is needed, given that the factors of 1.375 and 1.29 already assume full neutralization and no water. 

Sa

8 Adjust the FRM-consistent 

estimate of nitrate to the CSN/IMPROVE-consistent basis expected by the IMPROVE algorithm. 

A similar adjustment as in step 7 (for sulfate) was made to each hour’s nitrate concentration from step 6, so that the estimate of hourly nitrate would reflect actual atmospheric conditions and be consistent with the IMPROVE algorithm. This can result in the estimate of nitrate used in the IMPROVE algorithm being higher than the FRMconsistent estimate, for days on which the SANDWICH method predicts a loss of nitrate from the FRM filter. 

No adjustment is made. Implication: On warm days when the FRM filter has lost nitrate mass, the estimates of hourly PM2.5 will 

be lower than actual atmospheric mass. All hourly PM2.5 components will be 

reduced, by the fraction that the lost nitrate is of total PM2.5

mass. 

Sa

Not numbered in UFVA Estimation of PM2.5 light 

extinction from estimates of hourly concentrations of PM2.5

components. 

Original IMPROVE algorithm, including f(RH) determined from hourly RH. Hours with RH >90% were excluded from design values and from most graphical displays of results. 

Same as A Sa
9 

Table 2. Calculation Steps for Approach F. 

Calculation Step Comments 

(i) For each CSN sampling day, subtract OC artifact from OC measurement, and multiply by 1.7 to estimate organic carbonaceous material (OCM). 

The values for the OC artifact ranged from 0

depending on sampler model. The artifact adURG 3000N sampler is of most interest prosis the single sampler now in use for carbon sURG 3000N was used only at about one-haland only in the second half of 2007. For thoorganic carbon artifact of 0.4 μg/m3 was assof the UFVA and this document, based on ethis sampler. EPA staff are currently exploribetter way to adjust for organic carbon artifarecent, larger field blank and back-up filter d

(ii) For each CSN sampling day, calculate fine soil/crustal PM2.5(FS) from CSN measurements of crustal elements Si, Ca, Fe, and Ti, using the formula Fine soil PM2.5 = 3.73 × [Si] + 1.63 × [Ca] + 2.42 × [Fe] + 1.94 × [Ti] 

This 4-element approach to estimation of finused in the SANDWICH method. It is a modelement approach used in the Regional Haze originally selected for the SANDWICH metconcern over the uncertainty of the [Al ]meaIMPROVE sites. [Al ]measurements using Cconsidered less uncertain than IMPROVE mAppendix 4B of the final Policy Assessment staff intends to revert to the 5-element approRegional Haze program. 

(iii) For each CSN sampling day, multiply CSN measurement of sulfate ion (S) by 1.375, and multiply CSN measurement of nitrate ion (N) by 1.29, to reflect associated ammonium under an assumption of full neutralization. (iv) Sum the above estimates of the 5 components of PM2.5: Sum = 1.375*S + 1.29*N + OCM + EC + FS 

Here, S means sulfate ion and N means nitra

(v) For each CSN sampling day, calculate the 5 component factions: 
10 

sulfate fraction = 1.375*S/Sum Nitrate fraction = 1.29*N/Sum OCM fraction = OCM/Sum EC fraction = EC/Sum FS fraction = FS/Sum (vi) Average the fraction for sulfate from step (v) across the CSN sampling days of that calendar month of that calendar year. Repeat for the other 4 components. Call these the monthlyaverage component fractions. 

In the analysis reported in this memo, no mi

CSN samples was applied when calculating component fractions. It may be more appropminimum requirement of four samples per musually 80% of the samples scheduled per mone-in-six-days sampling. 

(vii) For each CSN sampling day, average the 24 values of 1-hour PM2.5 mass from the continuous instrument. Divide the 24-hour FRM value for PM2.5 mass by this average. Call this the “instrument scaling factor”. (viii) For each CSN sampling day, multiply each 1-hour PM2.5mass value from the continuous instrument by the instrument scaling factor. 

As explained in footnote 2, hourly PM2.5 ma

from continuous instruments were adjusted to match the 24-hour concentration reported FRM/FEM filter-based sampler only for the analysis. Prospectively, if only continuous inas federal equivalent methods (FEM) were apurposes of measuring hourly PM2.5 mass co

purposes of estimating hourly PM2.5 light exadjustment presumably would not be neededstep were omitted, then FRM measurements required data source for this approach. 

(ix) For each daylight hour of each day of that month (including days without CSN sampling) multiply the value of hourly PM2.5mass from step (viii) by the monthly-average component fractions from step (vi). (x) Insert the results from step (ix) into the original IMPROVE algorithm, along with f(RH) calculated based on same-hour RH. Omit the Rayleigh scattering term and the contribution from PM10-2.5. Estimates of PM2.5 light extinction in hours with RH greater than 90% are not used in design value calculations and graphics presented in this memo. 

The exclusion of hours with RH>90% originthat a direct instrumental measurement of PM might results in high values of light extinctioconditions of fog or precipitation. While appemploy a light extinction instrument, the accmass and RH measurements at such high vaconcern. 
11 

Comparative Performance of Simplified PM2.5 Light Extinction Approaches 

The performance assessment of simplified approaches for calculated PM2.5 light extinction was 

accomplished by comparing hourly values of PM2.5 light extinction generated by each approach 

to their corresponding paired values generated using the original UFVA method, which is labeled 

above as approach A. Annual box and whisker plots of the percentage differences between the 

paired values, as well as annual and monthly scatter plots and regression analysis of these paired 

data, were generated. Selected graphs and summary tables of regression statistics are included 

below to show the degree of comparability between the various approaches to the original 

estimates of PM2.5 light extinction. 

The box and whisker plots of the differences between calculated hourly PM2.5 light extinction by 

approaches B, D, E, and F are shown in Figures 1 and 2. In the box and whisker plots of 

percentage difference, the percentage difference is calculated as follows: 

Percentage difference = [(simpler approach estimate) – (“A” estimate)] / (“A” estimate) * 100% 

Note that a few points in the box and whisker plots have extreme values for the percentage 

difference. These instances have been traced to the effect of rounding differences for very low 

values of PM2.5 light extinction. 

The patterns of relatively small bias for the 15 urban areas are notably similar in each of the 

plots. Keeping in mind that the differences in the approach are iterative with approach B 

differing from approach A only by not using the SANDWICH model to estimate organic 

component mass concentration and to adjust nitrate concentrations, while the three other 

approaches (i.e., D, E, and F) add additional simplifications, it is perhaps surprising that the cityto-city pattern of the box positions and sizes are remarkably similar for these four approaches. 

This suggests that the simplification between approaches A and B (i.e., replacing the 

SANDWICH model) is responsible for the greatest amount of differences in calculated hourly 

PM2.5 light extinction between approach A and D, E, and F, or in other words, the additional 

changes introduced in the remaining three approaches did not much affect the resulting hourly 

values.8

 

The degree of comparability for paired hourly PM2.5 light extinction between approach F and A, 

and between approach F and B values by month and urban area is evident in regression statistics 

(Tables 3 and 4). In both tables, the regression lines have slopes and R2 values near 1.0, with 

small intercepts for most urban areas and months implying that the values are highly comparable. 

The western urban areas (e.g., Fresno, Houston, Los Angeles, Phoenix, Salt Lake City and 

Tacoma) have slopes and R2 values for some months that imply a bias and/or noisier relationship 

between values calculated by approaches F and A.9 As expected the regression relationships 

show that values calculated by approach F are more similar to those of approach B (Table 4) 

 

8 In the box and whisker plots, some extreme values of the percentage change are due to rounding effects when the 

values involved were very small.

9 One can speculate that the bias and/or noisier relationship for some months are in Fresno, Los Angeles, and Salt 

Lake City due to nitrate episodes, in Houston due to episodes of Saharan dust transport, and in Tacoma due to 

biomass burning episodes.
12 

since neither uses the SANDWICH model, than to those of approach A (Table 3) which included 

the SANDWICH model estimates. Four scatter plots of calculated hourly PM2.5 light extinction 

for all months that compare approach F to approach A and approach F to approach B for 

Baltimore and Fresno are show in Figure 3 as examples of the degree of comparability for 

eastern and western urban areas. 

 

The analysis documented in this memo is not a comprehensive assessment of why there are 

greater differences between approaches A and B than between approaches B and any of D, E, 

and F. However, some explanations are suggested by the results themselves. The fact that hourto-hour and day-to-day variations in the dry PM2.5 composition can be replaced by monthly 

averaged values without much loss of precision in calculated hourly PM2.5 light extinction 

suggests that these shorter term variations within a single month at a single monitoring site are 

usually not very influential. If day-to-day variations in the component mix are not very 

influential, this may imply that the different estimates of component percentage mix caused by 

use of the UFVA approach versus the simpler approach B may also not be very influential. By 

process of elimination, this suggests that the greater differences between approaches A and B 

may be due to the adjustment in the UFVA method to account for negative sampling artifact for 

ammonium nitrate. The UFVA method (approach A) can result in hourly sum-of-fivecomponent-concentrations that average over 24 hours to a value greater than the FRM-reported 

PM2.5 mass, while approach B does not. This is consistent with the behavior for sites that have 

high ammonium nitrate (e.g., Fresno and Los Angeles). Another approach that properly accounts 

for nitrate loss effects but otherwise has the simplifications of approach F might be an even 

better method to calculate PM2.5 light extinction. In particular, if hourly data from continuous 

FEM reflect actual ambient nitrate concentrations during each hour, direct use of such data 

without normalization to match the 24-hour average reported by the FRM may produce better 

estimates of actual hourly PM2.5 light extinction during hours when light extinction is highest. 

Another assessment has looked more closely at why the use of monthly averaged composition to 

estimate PM2.5 light extinction produces comparable results to the use of daily values.10 In that 

assessment the terms of the IMPROVE algorithm were rearranged to show that light extinction 

equals PM2.5 mass times the sum of a dry extinction efficiency term and a moist extinction 

efficiency term. Both extinction efficiencies terms depend on composition and the moist term 

also depends on relative humidity. The dry term can vary in theory from 1 m2

/g to 10 m2/g, but is 

commonly in a range from about 3 m2

/g to 4 m2/g for typical urban PM2.5 composition, which is 

dominated by sulfate, nitrate, and/or organic PM2.5. The moist extinction efficiency term depends 

on the hygroscopic fraction of the PM2.5 mass (i.e., composed of sulfate and nitrate) so if ranges 

from 0 to 1.0, which varies regionally and seasonally, as well as day to day and hourly. The 

moist extinction efficiency term is the product of the hygroscopic fraction and a non-linear 

function of relative humidity that varies from 0 m2/g (for relative humidity <40%) to 9.5 m2/g 

(for relative humidity at 90%). It seems that most of the variations in light extinction associated 

with variations in the moist extinction efficiency are due to the relative humidity variability 

compared PM2.5 composition variability. Overall, this other assessment supports the conclusions 

from this analysis (i.e., that use of monthly mean PM2.5 composition values in the IMPROVE 

 

10 Memo: “Assessment of the Use of Speciated PM2.5 Mass-Calculated Light Extinction as a Secondary PM NAAQS 

Indicator of Visibility”, Marc Pitchford, NOAA, November 17, 2010.
13 

algorithm does not greatly degrade the estimation of PM2.5 light extinction compared to use of 

sample period specific PM2.5 composition). 

A final caveat is appropriate. In an attempt to capture diurnal variations in the component mix of 

PM2.5 as best as possible, the UFVA approach (approach A) made use of 2004 monthly-average 

diurnal profiles for each component. Individual hours in 2005-2007 could have a quite different 

component mix than predicted by the UFVA approach, even though the UFVA approach as best 

as possible reconciles the hourly component concentrations to the 24-hour average 

concentrations on the corresponding day as revealed by the CSN sample. Thus, using approach A 

as “truth” for comparison to another approach may not fully reveal the differences that could 

exist between that approach and a direct measurement of PM2.5 light extinction. Such a 

comparison does, however, give an indication of the additional variability caused by dropping 

complex calculation steps that are part of the UFVA approach. 
14 

Figure 1. Box and whisker plot of the percent difference in calculated hourly PM2.5 light extinction between 

approaches B and A (top plot), and between D and A (bottom plot) by urban area. 

(Approach B takes a simple approach to 24-hour-average component mix for each separate day and omits the UFVA correction for nitrate loss. 

Approach D adds the further simplification of the component mix being the same across all hours.)
15 

Figure 2. Box and whisker plot of the percent difference in calculated hourly PM2.5 light extinction between 

approaches E and A (top plot), and between F and A (bottom plot) by urban area. 

(Approach A is the original UFVA approach. Approach B takes a simple approach to 24-hour-average component mix for each separate day and 

omits the UFVA correction for nitrate loss. Approach D adds the further simplification of the component mix being the same across all hours.)
16 

Figure 3. Scatter plots of calculated PM2.5 light extinction by approach F versus approach A (“original”, left) 

and versus approach B (right) for Baltimore (top) and Fresno (bottom). 

(Approach A is the original UFVA approach. Approach B takes a simple approach to 24-hour-average component mix for each separate day and 

omits the UFVA correction for nitrate loss. Approach F adds the further simplifications of the component mix being the same across all hours of 

the month.) 
17 

Table 3. Linear regression equation and R2 values for relating hourly PM2.5 light extinction values calculat(x in the equation) to those using approach A (y in the equation) by month for 15 urban areas. 11

Month 1 2 3 4 5 6 7 8 9 10 Atlanta, GA

y=1.09*x+‐0.73;Rsq=0.98

y=1.03*x+1.92;Rsq=0.98

y=1.01*x+‐1.52;Rsq=0.97

y=1.06*x+‐4.65;Rsq=0.98

y=1.02*x+‐4.41;Rsq=0.97

y=0.99*x+‐3.52;Rsq=0.97

y=0.96*x+‐1.38;Rsq=0.96

y=0.98*x+‐4.01;Rsq=0.98

y=0.98*x+‐2.8;Rsq=0.98

y=0.97*x+0.42;Rsq=0.99

Baltimore, MD

y=0.99*x+1.25;Rsq=0.99

y=1.06*x+‐3.6;Rsq=1

y=0.97*x+3.27;Rsq=0.99

y=1.02*x+0.41;Rsq=0.96

y=0.99*x+0.83;Rsq=0.9

y=0.98*x+‐3.78;Rsq=0.96

y=0.94*x+‐2.59;Rsq=0.98

y=0.88*x+2.1;Rsq=0.99

y=0.96*x+‐3.25;Rsq=0.98

y=1.05*x+‐2.77;Rsq=0.98

Birmingham,AL

y=1.09*x+‐2.17;Rsq=0.97

y=1.04*x+0.7;Rsq=0.97

y=1.06*x+‐2.82;Rsq=0.97

y=1.06*x+‐3.91;Rsq=0.97

y=0.94*x+2.05;Rsq=0.97

y=0.98*x+‐4.9;Rsq=0.98

y=1.02*x+‐6.87;Rsq=0.97

y=0.9*x+2.31;Rsq=0.93

y=1*x+‐6.31;Rsq=0.98

y=1.06*x+‐3.87;Rsq=0.97

Dallas,TX

y=1.17*x+‐0.86;Rsq=0.97

y=1.1*x+0.43;Rsq=0.98

y=1.14*x+‐3.9;Rsq=0.96

y=1.04*x+‐2.66;Rsq=0.97

y=1.03*x+‐3.1;Rsq=0.96

y=0.93*x+0.75;Rsq=0.95

y=0.96*x+‐0.01;Rsq=0.96

y=0.98*x+‐0.63;Rsq=0.91

y=1.01*x+‐3.02;Rsq=0.93

y=1.06*x+‐2.35;Rsq=0.97

Detroit,MI

y=1.02*x+2.24;Rsq=0.97

y=0.95*x+3.79;Rsq=0.99

y=0.99*x+2.13;Rsq=0.99

y=1.1*x+‐0.5;Rsq=0.96

y=0.92*x+5.42;Rsq=0.96

y=0.96*x+2.14;Rsq=0.96

y=0.99*x+0.17;Rsq=0.93

y=1.29*x+‐18.07;Rsq=0.9

y=1.12*x+‐8.63;Rsq=0.97

y=1.18*x+‐3.36;Rsq=0.95

Fresno,CA

y=1.05*x+‐0.76;Rsq=0.98

y=1.05*x+2.04;Rsq=0.99

y=1.15*x+4.9;Rsq=0.96

y=1.31*x+‐4.13;Rsq=0.87

y=1.27*x+‐2.92;Rsq=0.83

y=1.24*x+‐5.26;Rsq=0.87

y=1.06*x+‐0.97;Rsq=0.97

y=1.3*x+‐6.59;Rsq=0.86

y=1.39*x+‐6.67;Rsq=0.89

y=1.48*x+‐7.51;Rsq=0.94

Houston, TX

y=0.83*x+4.6;Rsq=0.96

y=0.97*x+‐1.12;Rsq=0.99

y=0.9*x+0.8;Rsq=0.99

y=1.02*x+‐3.72;Rsq=0.98

y=0.97*x+‐2.87;Rsq=0.97

y=0.84*x+7.59;Rsq=0.92

y=0.76*x+11.38;Rsq=0.85

y=0.88*x+5.36;Rsq=0.93

y=0.99*x+‐2.92;Rsq=0.98

y=1.06*x+‐3.39;Rsq=0.99

LosAngeles, CA

y=1.18*x+‐0.57;Rsq=0.98

y=1.1*x+2.01;Rsq=0.98

y=1.08*x+7.64;Rsq=0.96

y=1.14*x+2.11;Rsq=0.96

y=1.04*x+12.59;Rsq=0.96

y=1.33*x+‐3.58;Rsq=0.86

y=1.26*x+‐2.89;Rsq=0.92

y=1.38*x+‐12.8;Rsq=0.84

y=1.4*x+‐9.14;Rsq=0.91

y=1.25*x+‐0.9;Rsq=0.96

11 After completion of the second draft PAD, an error related to SANDWICH processing of 2005-2007 PM2.5 speciation data was disc

affected the UFVA method (also designated in this memo as approach A) predictions of hourly PM2.5 light extinction to a small degreeusing the approaches designated in this memo as B, D, etc. The comparisons between the latter approaches and approach A were also v

the reader may notice by careful comparison of results in this table and Tables 4 and 5 to similar results in the second draft PAD.
18 

Month 1 2 3 4 5 6 7 8 9 10 NewYork,NY

y=1.03*x+2.14;Rsq=0.98

y=1.03*x+‐1.36;Rsq=1

y=1.01*x+3.61;Rsq=0.99

y=1.1*x+‐0.68;Rsq=0.98

y=1.06*x+‐1.45;Rsq=0.97

y=1.1*x+‐6.27;Rsq=0.96

y=1.02*x+‐7.94;Rsq=0.96

y=0.98*x+‐1.24;Rsq=0.97

y=1.03*x+0.25;Rsq=0.96

y=1.22*x+‐7.93;Rsq=0.97

Philadelphia,PA

y=0.95*x+3.2;Rsq=0.99

y=1.01*x+‐1.74;Rsq=0.99

y=1*x+1.45;Rsq=0.99

y=0.96*x+2.39;Rsq=0.94

y=0.9*x+1.44;Rsq=0.98

y=0.92*x+‐0.44;Rsq=0.98

y=0.91*x+1.75;Rsq=0.98

y=0.85*x+5.59;Rsq=0.98

y=0.89*x+1.3;Rsq=0.96

y=0.95*x+3.85;Rsq=0.97

Phoenix, AZ

y=1.21*x+‐2.37;Rsq=0.89

y=1.13*x+‐1.38;Rsq=0.97

y=0.88*x+1.25;Rsq=0.96

y=0.85*x+1.94;Rsq=0.94

y=0.93*x+0.87;Rsq=0.9

y=0.88*x+1.65;Rsq=0.97

y=0.77*x+4.02;Rsq=0.69

y=0.92*x+0.62;Rsq=0.99

y=0.86*x+0.48;Rsq=0.97

y=0.92*x+1.18;Rsq=0.72

Pittsburgh, PA

y=1.1*x+‐3.63;Rsq=0.95

y=0.99*x+1.91;Rsq=0.97

y=0.98*x+0.09;Rsq=0.99

y=1.09*x+‐2.39;Rsq=0.97

y=1.07*x+‐5.49;Rsq=0.92

y=0.95*x+‐1.28;Rsq=0.97

y=1.03*x+‐9.91;Rsq=0.96

y=0.94*x+‐1.93;Rsq=0.97

y=1.04*x+‐7.42;Rsq=0.94

y=1.02*x+‐1.66;Rsq=0.97

SaltLakeCity, UT

y=0.91*x+8.62;Rsq=1

y=0.97*x+4.95;Rsq=0.99

y=1.12*x+1.95;Rsq=0.97

y=1.14*x+‐1.2;Rsq=0.88

y=0.98*x+0.92;Rsq=0.83

y=1.02*x+0.98;Rsq=0.87

y=1*x+0;Rsq=0.99

y=0.98*x+‐0.43;Rsq=0.97

y=0.88*x+5.49;Rsq=0.87

y=1.08*x+0.17;Rsq=0.93

StLouis,MO

y=1.01*x+1.72;Rsq=0.99

y=1.03*x+‐0.14;Rsq=1

y=1.06*x+‐0.01;Rsq=0.98

y=1.14*x+‐3.92;Rsq=0.94

y=1.08*x+‐3.27;Rsq=0.93

y=0.92*x+0.97;Rsq=0.95

y=0.98*x+‐2.77;Rsq=0.97

y=1*x+‐7.97;Rsq=0.98

y=0.94*x+‐0.89;Rsq=0.97

y=1.19*x+‐3.77;Rsq=0.95

Tacoma, WA

y=1.02*x+0.02;Rsq=1

y=0.99*x+0.65;Rsq=0.94

y=1.07*x+‐0.1;Rsq=0.97

y=1.22*x+‐3.78;Rsq=0.96

y=1.18*x+‐4.43;Rsq=0.92

y=1.09*x+‐0.14;Rsq=0.9

y=1.1*x+‐1.28;Rsq=0.94

y=1.22*x+‐4.35;Rsq=0.95

y=1.06*x+0.02;Rsq=0.96

y=0.99*x+0.69;Rsq=0.98
19 

Table 4. Linear regression equation and R2 values for relating hourly PM2.5 light extinction values calculat

(x in the equation) to those using approach B (y in the equation) by month for15 urban ar

Month 1 2 3 4 5 6 7 8 9 10 Atlanta,GA

y=1.01*x+0.4;Rsq=0.98

y=1.06*x+0.26;

Rsq=0.96

y=1.02*x+‐0.15;Rsq=0.99

y=1.02*x+‐0.72;Rsq=0.99

y=1.02*x+‐0.83;Rsq=0.99

y=1.02*x+‐1.06;Rsq=0.99

y=1.02*x+‐0.38;Rsq=0.95

y=1.04*x+‐3.54;

Rsq=0.98

y=1.02*x+‐0.74;Rsq=0.99

y=1*x+111;Rsq=0.9

Baltimore, MD

y=0.96*x+1.84;Rsq=0.99

y=1.09*x+‐5.5;

Rsq=0.99

y=1.04*x+‐1.21;Rsq=1

y=1.01*x+1.15;Rsq=0.98

y=1.02*x+‐1.15;

Rsq=1

y=0.99*x+0.73;Rsq=0.99

y=1.01*x+‐0.36;Rsq=0.98

y=1*x+0.25;Rsq=1

y=1.02*x+‐1;

Rsq=1

y=0.97*+2.23;Rsq=0.9

Birmingham, AL

y=1.08*x+‐2.37;Rsq=0.98

y=0.98*x+3.39;

Rsq=0.96

y=1.01*x+0.05;Rsq=0.99

y=1.07*x+‐2.22;

Rsq=0.98

y=1*x+1.38;Rsq=0.99

y=1.01*x+‐0.71;Rsq=0.99

y=1.06*x+‐4.76;Rsq=0.98

y=0.98*x+2.12;Rsq=0.95

y=1.02*x+‐2.17;

Rsq=0.98

y=1*x+146;Rsq=0.9

Dallas, TX y=1.08*x +‐1.32;

Rsq=0.99

y=1.05*x+‐1.39;

Rsq=0.99

y=1.06*x+‐1.42;Rsq=0.99

y=1.08*x+‐2.68;Rsq=0.98

y=1.04*x+‐1.58;Rsq=0.99

y=0.98*x+1.45;Rsq=0.95

y=0.99*x+0.46;Rsq=0.96

y=0.94*x+2.44;Rsq=0.91

y=1*x+‐0.52;Rsq=0.99

y=1.02*+‐0.48;Rsq=0.9

Detroit,MI

y=1.06*x+‐4.02;

Rsq=0.98

y=1.05*x+‐2.66;Rsq=1

y=1.03*x+‐1.35;

Rsq=0.99

y=1.01*x+0.23;Rsq=0.99

y=0.99*x+‐0.13;

Rsq=1

y=0.98*x+0.79;Rsq=0.99

y=1.02*x+‐0.65;Rsq=0.99

y=1.09*x+‐5.76;

Rsq=0.97

y=1.02*x+‐0.88;

Rsq=0.99

y=1.05*+‐1.29;

Rsq=0.9

Fresno,CA

y=1.06*x+‐5.57;Rsq=0.99

y=1.05*x+‐4.18;

Rsq=0.99

y=1.03*x+‐0.85;Rsq=1

y=1.02*x+‐0.57;Rsq=0.99

y=1.02*x+‐0.24;Rsq=0.98

y=1.03*x+‐0.55;Rsq=0.99

y=1*x+‐0.76;Rsq=1

y=1.02*x+‐0.58;

Rsq=0.99

y=1.04*x+‐1.01;

Rsq=0.99

y=1.1*x‐3.18;Rsq=0.9

Houston,TX

y=0.97*x+2.57;Rsq=0.99

y=1.08*x+‐1.78;

Rsq=0.97

y=1.01*x+0.8;Rsq=0.99

y=1.04*x+‐0.93;Rsq=0.99

y=1.02*x+‐0.48;Rsq=0.98

y=0.9*x+8.05;

Rsq=0.93

y=0.77*x+13.92;Rsq=0.81

y=0.92*x+7.13;Rsq=0.93

y=1.01*x+‐0.91;

Rsq=0.99

y=1.05*+‐1.77;

Rsq=0.9

LosAngeles,CA

y=1.08*x+‐3.01;Rsq=0.99

y=1.04*x+‐1.62;

Rsq=1

y=1.02*x+0.31;

Rsq=0.99

y=1.05*x+‐3;Rsq=0.99

y=1*x+0.89;Rsq=1

y=1.05*x+‐2.16;Rsq=0.99

y=1.03*x+‐0.3;

Rsq=0.99

y=1.03*x+‐0.34;

Rsq=0.99

y=1.06*x+‐1.65;

Rsq=0.99

y=1.08*+‐3.22;

Rsq=0.9

NewYork, NY

y=1*x+‐0.52;Rsq=1

y=1.01*x+‐0.82;Rsq=1

y=0.99*x+0.86;

Rsq=1

y=1.03*x+‐0.26;Rsq=1

y=1*x+0.17;Rsq=0.99

y=1.07*x+‐3.4;Rsq=0.99

y=1.03*x+‐4.03;Rsq=0.99

y=1.02*x+‐2.4;

Rsq=0.99

y=1.01*x+‐0.93;Rsq=1

y=1.06*+‐3.4;

Rsq=0.9
20 

Month 1 2 3 4 5 6 7 8 9 10 Philadelphia, PA

y=1.03*x+‐1.63;Rsq=0.99

y=1.02*x+‐2.07;

Rsq=0.99

y=1.02*x+‐0.65;Rsq=1

y=1.05*x+‐1.63;

Rsq=0.98

y=0.99*x+0.1;Rsq=1

y=0.99*x+0.42;

Rsq=1

y=1.02*x+0.32;Rsq=0.98

y=0.99*x+2.35;Rsq=0.99

y=0.96*x+1.39;Rsq=0.99

y=1.01*+0.84;Rsq=1

Phoenix,AZ

y=1.17*x+‐3.94;Rsq=0.93

y=0.95*x+1.15;Rsq=0.99

y=0.84*x+1.91;Rsq=0.97

y=0.9*x+1.35;Rsq=0.94

y=0.98*x+0.6;Rsq=0.96

y=0.98*x+0.63;Rsq=0.98

y=0.88*x+3.02;Rsq=0.81

y=0.94*x+1.07;Rsq=0.99

y=0.97*x+0.28;Rsq=0.98

y=0.98*+1.01;Rsq=0.8

Pittsburgh, PA

y=1.04*x+‐0.57;Rsq=0.97

y=1*x+0.78;Rsq=0.99

y=1.01*x+0.29;

Rsq=1

y=1.05*x+‐0.59;

Rsq=0.99

y=1.01*x+‐0.88;

Rsq=0.99

y=1*x+0.02;Rsq=0.99

y=1.02*x+‐3.12;Rsq=0.99

y=1.04*x+‐3.96;

Rsq=0.99

y=1.02*x+‐1.58;

Rsq=0.99

y=0.98*+2.1;Rsq=0.9

Salt Lake

City, UT y=1*x+1;

Rsq=1

y=1.02*x+‐0.82;

Rsq=1

y=1.07*x+‐0.81;

Rsq=0.99

y=1.05*x+‐0.51;

Rsq=0.95

y=0.98*x+0.79;Rsq=0.96

y=1.02*x+‐0.44;Rsq=0.99

y=0.97*x+0.77;Rsq=0.99

y=0.96*x+0.74;Rsq=0.96

y=0.75*x+8.1;Rsq=0.8

y=0.97*+1.37;Rsq=0.9

St Louis,

MO

y=1.04*x+‐0.73;

Rsq=0.99

y=1.03*x+‐0.62;Rsq=1

y=1.08*x+‐4.01;

Rsq=0.99

y=1.08*x+‐2.89;Rsq=0.98

y=1.04*x+‐1.27;Rsq=0.97

y=0.99*x+0.5;Rsq=0.99

y=1.03*x+‐1.96;Rsq=0.99

y=1.02*x+‐3.12;

Rsq=0.99

y=1*x+‐0.23;Rsq=0.99

y=1*x+102;Rsq=0.9

Tacoma,WA

y=0.97*x+1.51;Rsq=1

y=1.08*x+3.92;

Rsq=0.73

y=1.02*x+0.31;Rsq=0.97

y=1.03*x+‐0.72;Rsq=0.99

y=1.02*x+‐0.71;Rsq=0.98

y=1.02*x+‐0.21;Rsq=0.99

y=1.04*x+‐0.37;Rsq=0.98

y=1.03*x+‐0.58;

Rsq=0.99

y=0.98*x+1.41;Rsq=0.98

y=0.97*+0.92;Rsq=0.9
21 

PM2.5 Mass Concentration Used Alone to Calculate PM2.5 Light Extinction 

Approach I predicts PM2.5 light extinction by merely multiplying the same hourly PM2.5 values 

as used in approach A (continuous PM2.5 instrument normalized to match the FRM 24-hour 

concentration) by a constant, 4.35 m2

/g.12 As shown in Figures 4 and 5, the results are not nearly 

as comparable as those calculated using approach F (or any of the methods that include 

composition and hourly relative humidity data). 

The variations in the relationships are even more evident in the monthly regression equations as 

shown in Table 5. The slopes range from about one half to nearly two with R2 values that are 

often below 0.9 and as low as 0.4. 

 

Figure 4. Box and whisker plot of the percent difference in calculated hourly PM2.5 light extinction between 

approaches I and A by urban area. 

 

12 The value of 4.35 m2

/g has no derivation of particular importance. If this approach were to be pursued further, 

more careful analysis would be appropriate, including analysis of the possibility of site-specific or region-specific 

constants. Selection of the best possible constant for a given monitoring site might remove the bias of approach I 

relative to approach A for that site, but would not reduce the spread of the errors.
22 

Figure 5. Scatter plots of hourly calculated PM2.5 light extinction for approach I versus approach A 

(“original”) for four selected urban areas. 
23 

Table 5. Linear regression equation and R2 values for relating hourly PM2.5 light extinction values calculated using approach 

those using approach A (y in the equation) by month for 15 urban areas.

Month 1 2 3 4 5 6 7 8 9 10 

Atlanta,GA

y=1.49*x+

‐6.01;

Rsq=0.91

y=1.45*x

+‐6.61;

Rsq=0.85

y=1.25*x

+‐8.03;

Rsq=0.85

y=1.33*x

+‐11.91;

Rsq=0.85

y=1.2*x+‐

7.04;

Rsq=0.77

y=1.06*x+

5.99;

Rsq=0.65

y=0.87*x+

25.82;

Rsq=0.55

y=1.06*x+

8.1;

Rsq=0.62

y=1.21*x

+‐2.64;

Rsq=0.75

y=1.22*x

+‐2.26;

Rsq=0.89

Baltimore, MD

y=1.28*x+

‐8.13;

Rsq=0.88

y=1.65*x

+‐31.12;

Rsq=0.84

y=1.47*x

+‐17.18;

Rsq=0.79

y=1.03*x

+0.1;

Rsq=0.79

y=1.05*x

+6.54;

Rsq=0.62

y=1.23*x+

‐6.26;

Rsq=0.7

y=1.1*x+‐

1.47;

Rsq=0.74

y=1.09*x+

7.77;

Rsq=0.85

y=1.33*x

+‐8.8;

Rsq=0.81

y=1.49*x

+‐7.7;

Rsq=0.72

Birmingham, AL

y=1.29*x+

‐5.76;

Rsq=0.8

y=1.31*x

+‐7.25;

Rsq=0.85

y=1.11*x

+‐5.05;

Rsq=0.89

y=1.05*x

+‐2.93;

Rsq=0.85

y=1.06*x

+‐6.34;

Rsq=0.9

y=1*x+‐

2.72;

Rsq=0.82

y=1.09*x+

‐0.42;

Rsq=0.77

y=0.95*x+

2.44;

Rsq=0.77

y=1.16*x

+‐13.85;

Rsq=0.8

y=1.24*x

+‐7.38;

Rsq=0.87

Dallas,TX

y=1.68*x+

‐8.85;

Rsq=0.84

y=1.93*x

+‐21.66;

Rsq=0.88

y=1.53*x

+‐12.91;

Rsq=0.79

y=1.34*x

+‐10.87;

Rsq=0.75

y=1.16*x

+‐2.83;

Rsq=0.69

y=0.86*x+

3.04;

Rsq=0.74

y=0.86*x+

3.72;

Rsq=0.75

y=0.96*x+

‐2.36;

Rsq=0.7

y=1.04*x

+‐2.03;

Rsq=0.71

y=1.19*x

+‐2.94;

Rsq=0.81

Detroit,MI

y=1.19*x+

11.68;

Rsq=0.72

y=1.26*x

+5.08;

Rsq=0.85

y=1.12*x

+7.21;

Rsq=0.67

y=1.16*x

+‐5.67;

Rsq=0.86

y=0.79*x

+11.4;

Rsq=0.82

y=0.78*x+

14.2;

Rsq=0.84

y=0.99*x+

8.98;

Rsq=0.73

y=1.22*x+

1.21;

Rsq=0.55

y=1.22*x

+‐11.05;

Rsq=0.72

y=1.42*x

+‐6.23;

Rsq=0.79

Fresno,CA

y=1.2*x+2

.32;

Rsq=0.83

y=1.26*x

+1.71;

Rsq=0.84

y=1.43*x

+0.17;

Rsq=0.83

y=1.29*x

+‐2.1;

Rsq=0.67

y=0.98*x

+4.24;

Rsq=0.54

y=1.01*x+

‐1.51;

Rsq=0.68

y=0.94*x+

‐1.1;

Rsq=0.93

y=1.13*x+

‐5.1;

Rsq=0.73

y=1.24*x

+‐4.61;

Rsq=0.73

y=1.6*x+‐

7.84;

Rsq=0.71

Houston, TX

y=1.29*x+

‐2.32;

Rsq=0.87

y=1.35*x

+‐6.35;

Rsq=0.81

y=1.23*x

+‐7.63;

Rsq=0.85

y=1.38*x

+‐18.36;

Rsq=0.82

y=1.33*x

+‐19.81;

Rsq=0.76

y=1.07*x+

‐2.13;

Rsq=0.77

y=0.54*x+

20.69;

Rsq=0.57

y=0.75*x+

11.34;

Rsq=0.43

y=1.21*x

+‐12.05;

Rsq=0.82

y=1.3*x+‐

10.7;

Rsq=0.95

LosAngeles, CA

y=1.41*x+

‐5.87;

Rsq=0.87

y=1.19*x

+3.9;

Rsq=0.85

y=1.24*x

+6.92;

Rsq=0.8

y=1.41*x

+‐5.96;

Rsq=0.78

y=1.4*x+‐

3.52;

Rsq=0.78

y=1.7*x+‐

25.06;

Rsq=0.57

y=1.22*x+

5.35;

Rsq=0.59

y=1.57*x+

‐21.03;

Rsq=0.5

y=1.38*x

+‐6.02;

Rsq=0.71

y=1.43*x

+‐13.45;

Rsq=0.81

NewYork,NY

y=1.49*x+

‐13.85;

Rsq=0.9

y=1.17*x

+‐5.14;

Rsq=0.92

y=1.39*x

+‐5.93;

Rsq=0.87

y=1.21*x

+‐1.68;

Rsq=0.89

y=1.2*x+‐

2.33;

Rsq=0.8

y=1.35*x+

‐9.03;

Rsq=0.78

y=1.17*x+

0.72;

Rsq=0.65

y=1.29*x+

‐12.79;

Rsq=0.79

y=1.37*x

+‐5.7;

Rsq=0.89

y=1.89*x

+‐21.25;

Rsq=0.83
24 

Month 1 2 3 4 5 6 7 8 9 10 Philadelphia, PA

y=1.36*x+

‐8.52;

Rsq=0.77

y=1.1*x+

2.02;

Rsq=0.79

y=1.03*x

+1.75;

Rsq=0.83

y=0.81*x

+7.79;

Rsq=0.68

y=0.88*x

+4.55;

Rsq=0.85

y=0.97*x+

3.07;

Rsq=0.78

y=1.03*x+

1.63;

Rsq=0.82

y=0.79*x+

34.86;

Rsq=0.69

y=0.8*x+

10.76;

Rsq=0.64

y=1.01*x

+8;

Rsq=0.86

Phoenix, AZ

y=0.83*x+

‐2.5;

Rsq=0.89

y=0.76*x

+‐1.53;

Rsq=0.97

y=0.65*x

+1.46;

Rsq=0.96

y=0.56*x

+2.12;

Rsq=0.92

y=0.6*x+

1.7;

Rsq=0.88

y=0.62*x+

1.11;

Rsq=0.96

y=0.5*x+5

.73;

Rsq=0.61

y=0.69*x+

0.51;

Rsq=0.97

y=0.6*x+

0.85;

Rsq=0.95

y=0.6*x+

2.35;

Rsq=0.58

Pittsburgh, PA

y=1.6*x+‐

7.37;

Rsq=0.75

y=1.22*x

+0.01;

Rsq=0.77

y=1.18*x

+‐1.9;

Rsq=0.76

y=1.06*x

+0.12;

Rsq=0.74

y=1.06*x

+0.38;

Rsq=0.56

y=0.97*x+

11.89;

Rsq=0.67

y=1.06*x+

10.46;

Rsq=0.51

y=1.28*x+

‐9.71;

Rsq=0.74

y=1.18*x

+‐2.72;

Rsq=0.62

y=1.16*x

+2.65;

Rsq=0.72

SaltLakeCity, UT

y=1.38*x+

‐4.77;

Rsq=0.93

y=1.25*x

+‐0.91;

Rsq=0.92

y=1.23*x

+‐0.88;

Rsq=0.87

y=0.92*x

+2.08;

Rsq=0.75

y=0.73*x

+4.3;

Rsq=0.69

y=0.83*x+

2.88;

Rsq=0.79

y=0.9*x+0

.11;

Rsq=0.98

y=0.88*x+

‐0.16;

Rsq=0.96

y=0.79*x

+5.83;

Rsq=0.87

y=1.1*x+

2.25;

Rsq=0.82

StLouis,,MO

y=1.5*x+‐

0.32;

Rsq=0.91

y=1.69*x

+‐23.16;

Rsq=0.87

y=1.78*x

+‐23.32;

Rsq=0.83

y=1.29*x

+‐5.92;

Rsq=0.69

y=1.24*x

+‐7.67;

Rsq=0.73

y=0.88*x+

8.95;

Rsq=0.74

y=1.12*x+

‐5.02;

Rsq=0.75

y=1.07*x+

‐2.69;

Rsq=0.72

y=1.03*x

+2.61;

Rsq=0.74

y=1.7*x+‐

15.07;

Rsq=0.79

Tacoma, WA

y=1.1*x+2

.32;

Rsq=0.98

y=1.52*x

+‐2.25;

Rsq=0.94

y=1.28*x

+0.12;

Rsq=0.92

y=1.37*x

+‐3.6;

Rsq=0.86

y=1.15*x

+‐1.92;

Rsq=0.71

y=1.1*x+2

.17;

Rsq=0.63

y=1.03*x+

2.64;

Rsq=0.81

y=1.3*x+‐

2.74;

Rsq=0.68

y=1.07*x

+2.74;

Rsq=0.84

y=1.36*x

+‐0.96;

Rsq=0.91