# 2 The UFVA approach to estimation of hourly PM 2.5 

# light extinction has the following complex

aspects:

1. The SANDWICH mass balance model is used to estimate 24-hour average PM 2.5 

# 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 su lfate and nitrate com ponents are initially

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

sulfate includes estimated particle bound wa ter while the FRM nitr ate loading may underrepresent the ambient concentra tion of nitrate. These are re-a djusted in a subsequent step

to represent ambient conditions pr ior to calculation of extinction.

2. The estimates of 24-hour average PM 2.5 

# elemental carbon and fine soil component

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

3. Monthly mean diurnal variati ons of each of the major PM 2.5 

# components from CMAQ air

quality simulation modeling results for the loca tion 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 re sult, 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 PM 2.5 

# mass are developed by normalizing continuous PM 2.5



# 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 th eir sum to the estimate of hourly PM 2.5 

# mass.

6. The resulting hourly PM 2.5 

# sulfate and nitrate component concentratio ns are adjusted to

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

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

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

introduced by the SANDWICH mass balance model.)

7. The original IMPROVE algorithm is used to estimate hourly PM 2.5 

# light extinction from

hourly PM 2.5 

# component and hourly relative humidity values.

Analytical Approach in this Memo

This analysis examines the difference between calculated hourly PM 2.5 

# 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 Nitr ate, 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 co ntinuous 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 al phabet and described below) use the original

IMPROVE algorithm without the Rayleigh and PM 10-2.5 

# terms. 4



# Approach A. This designates the UFVA approach, but without the PM 10-2.5 

# 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 br iefly described in th e 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-balan ce 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 possi ble 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 wa s modified. The preliminary estimates of hourly

component concentrations for every da y were calculated by applying the CMAQ

diurnal profile to the mont hly-average 24-hour concentr ation of that component

(in μg/m3). This results in an estimat e 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 step s 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 completi on 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 PM 2.5 

# light extinction

values that are quite comparable to the hourly PM 2.5 

# 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 measur ements, and its use of monthly-averaged PM 2.5 

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

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



# Appendix 4B of the final Policy Assessment Docume nt considers two approaches that are slight

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

memo.

5 

# The value of 4.35 m 2 

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

more careful analysis would be appropriate, including anal ysis 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 PM 2.5 

# monitoring sites do not operate every day. However, see the related

comment at step (xi) of Table 2.5Table 1. Detailed Comparative Description ofApproaches A, B, and F for Estimating 1-hour PM2.5Light Extinction.12UFVA Step7Aspect of Approach Approach AApproach B Approach F1 Estimation of 24-hour organiccarbonaceous massThe SANDWICH method isused to subdivide the 24-hourPM2.5mass reported by theFRM for each day and siteinto hydrated ammoniumsulfate, ammonium nitrate,elemental carbon, organiccarbonaceous material(OCM), and fine soil. This isdone using information fromthe CSN measurements,physical models, and dayspecific temperatures andrelative humidity. OCM isestimated as the residualneeded to achieve massbalance after estimation of theother components.Organic carbonaceous mass isassumed to equal the organiccarbon value reported fromCSN sampling, minus a blankfilter correction that dependson sampler model andlaboratory method for carbonbut not on monitoring site,times 1.7.Same as B1, continued Estimation of 24-hour elementalcarbon massCSN elemental carbonconcentrationSame as A Same as A1, continued Estimation of 24-hourammonium sulfate massCSN sulfate concentration,with day-specificSANDWICH estimates ofassociated ammonium andwater.Sulfate ion measurement fromthe CSN filter is multiplied by1.375 to represent dryammonium sulfate.Same as B1, continued Estimation of 24-hourammonium nitrate massNitrate ion on the FRM Teflonfilter is estimated bySANDWICH, with dayspecific estimates ofassociated ammonium andwater.Nitrate ion measurement fromthe CSN filter is multiplied by1.29 to represent dryammonium nitrate.Same as B7The numbering of steps follows that used to describe the UFVA approach in section 3.3.1 of the UFVA.6UFVA Step7Aspect of Approach Approach AApproach B Approach F1, continued Estimation of 24-hour finesoil/crustal massCalculated from CSNelements, but without Al (adifference from theIMPROVE approach)Same as A Same as A2 Diurnal pattern of PM2.5componentsThe CMAQ-derived monthlynormalized diurnal profiles forthe sulfate, nitrate, elementalcarbon, organic carbon andfine soil/crustal components(each of which averages to 1.0across 24 hours) weremultiplied by the day-specificSANDWICH-based estimatesof the 24-hour averageconcentrations of the fivePM2.5components, to getintermediate day-specifichourly estimates of the fivecomponents (includingammonium and waterassociated with sulfate andnitrate ion).CMAQ-derived profiles wereapplied to the massconcentration of each of thefive components in same wayas in Approach A. However,as described above, inApproach B the sulfate,nitrate, and organiccarbonaceous materialcomponents are defined andestimated differently than inApproach A.No diurnal profiles are used.3 Sum the 5 components The hourly concentrations ofthese five components(including day-specificammonium and waterassociated with sulfate andnitrate ion when the FRMTeflon filter is weighed) wereadded together, to get a sumof-components estimate ofhourly PM2.5mass for the dayof the FRM/CSN sampling.The hourly concentrations ofthe five components wereadded together, to get a sumof-components estimate ofhourly PM2.5for the day ofFRM/CSN sampling. Notethat water is not included.Calculate the monthlyaverage percentage mix ofthe 5 PM2.5components, asfollows:For each day of 24-hourCSN sampling, sum the five(dry) components. Calculatethe fraction of sum-of-5 foreach component. Averagethe fraction for eachcomponent across the CSNsampling days in the month.7UFVA Step7Aspect of Approach Approach AApproach B Approach F4 Hourly PM2.5concentration,consistent with 24-hour FRMconcentration.The hourly data from thecontinuous PM2.5instrumenton the day of the FRMsampling were normalized bytheir 24-hour average, to get anormalized diurnal profile.This profile was applied to the24-hour PM2.5mass reportedby the FRM sampler, to get apreliminary, FRM-consistentestimate of hourly PM2.5massfor the day of the FRMsampling. This keeps theaverage of the valid 1-hourPM2.5values equal to the 24-hour value from the FRMsampler.Same as A Same as A, but see thecomment on this topic inTable 2.5, 6 Adjust preliminary estimates ofhourly PM2.5componentconcentrations (reflectingCMAQ diurnal profiles and 24-hour measurements) to beconsistent with estimate ofhourly PM2.5mass.The two estimates of hourlyPM2.5mass from steps 3 and 4were compared, hour-by-hour.Within each hour, theestimates of all fivecomponents from step 2 wereincreased or decreased by acommon factor so that the sumof the five components afterthis adjustment was equal tothe estimate of the hourlyPM2.5mass from step 4. Theadjustment percentage variedfrom hour-to-hour.Same as A Not applicableMonthly-average percentagemix of PM2.5components isdirectly applied to the dayspecific FRM-consistenthourly PM2.5mass.8UFVA Step7Aspect of Approach Approach AApproach B Approach F7 Adjust the FRM-consistentestimate of sulfate to theCSN/IMPROVE-consistentbasis expected by theIMPROVE algorithm.Each hourly estimate ofsulfate concentration on theFRM filter from step 6 (whichincludes estimates ofassociated ammonium andparticle bound water) wasadjusted so that it excludeswater and reflects fullneutralization and therefore isconsistent with the reportingpractices of the IMPROVEprogram and the IMPROVEalgorithm.No adjustment is needed,given that the factors of 1.375and 1.29 already assume fullneutralization and no water.Same as B8 Adjust the FRM-consistentestimate of nitrate to theCSN/IMPROVE-consistentbasis expected by theIMPROVE algorithm.A similar adjustment as in step7 (for sulfate) was made toeach hour’s nitrateconcentration from step 6, sothat the estimate of hourlynitrate would reflect actualatmospheric conditions and beconsistent with the IMPROVEalgorithm.This can result in the estimateof nitrate used in theIMPROVE algorithm beinghigher than the FRMconsistent estimate, for dayson which the SANDWICHmethod predicts a loss ofnitrate from the FRM filter.No adjustment is made.Implication:On warm days when the FRMfilter has lost nitrate mass, theestimates of hourly PM2.5willbe lower than actualatmospheric mass. All hourlyPM2.5components will bereduced, by the fraction thatthe lost nitrate is of total PM2.5mass.Same as BNot numbered in UFVA Estimation of PM2.5lightextinction from estimates ofhourly concentrations of PM2.5components.Original IMPROVEalgorithm, including f(RH)determined from hourly RH.Hours with RH >90% wereexcluded from design valuesand from most graphicaldisplays of results.Same as A Same as A9Table 2. Calculation Steps for Approach F.Calculation Step Comments(i) For each CSN sampling day, subtract OC artifact from OCmeasurement, and multiply by 1.7 to estimate organiccarbonaceous material (OCM).The values for the OC artifact ranged from 0.32 to 1.53 μg/m3,depending on sampler model. Theartifact adjustment for theURG 3000N sampler is of most interest prospectively, because itis the single sampler now in use for carbon sampling in CSN. TheURG 3000N was used only at about one-half of the 15 study sitesand only in the second half of2007. For those sites and days, anorganic carbon artifact of 0.4 μg/m3was assumed for the purposesof the UFVA and this document,based on early experience withthis sampler. EPA staff are currently exploring whether there is abetter way to adjust for organiccarbon artifact based on a morerecent, larger field blank and back-up filter data set.(ii) For each CSN sampling day,calculate fine soil/crustal PM2.5(FS) from CSN measurements ofcrustal elements Si, Ca, Fe, andTi, using the formulaFine soil PM2.5= 3.73 × [Si] + 1.63 ×[Ca] + 2.42 × [Fe] + 1.94× [Ti]This 4-element approach to estimation of fine soil is the approachused in the SANDWICH method. Itis a modification of the 5-element approach used in the Regional Haze program. It wasoriginally selectedfor the SANDWICH method because ofconcern over the uncertainty ofthe [Al ]measurements atIMPROVE sites. [Al ]measurements using CSN methods areconsidered less uncertain thanIMPROVE measurements. ForAppendix 4B of the final Policy Assessment Document, EPAstaff intends to revert to the5-element approach used in theRegional Haze program.(iii) For each CSN sampling day, multiply CSN measurement ofsulfate ion (S) by 1.375, and multiply CSN measurement ofnitrate ion (N) by 1.29, to reflectassociated ammonium under anassumption of full neutralization.(iv) Sum the above estimates of the 5 components of PM2.5:Sum = 1.375*S + 1.29*N + OCM + EC + FSHere, S means sulfate ionand N means nitrate ion.(v) For each CSN sampling day, calculate the 5 componentfactions:10sulfate fraction = 1.375*S/SumNitrate fraction = 1.29*N/SumOCM fraction = OCM/SumEC fraction = EC/SumFS fraction = FS/Sum(vi) Average the fraction for sulfate from step (v) across the CSNsampling 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 minimum number ofCSN samples was applied when calculating monthly-averagecomponent fractions. It may bemore appropriate to apply aminimum requirement of four samples per month, which isusually 80% of the samples scheduled per month at a site usingone-in-six-days sampling.(vii) For each CSN sampling day, average the 24 values of 1-hourPM2.5mass from the continuous instrument. Divide the 24-hourFRM value for PM2.5mass 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 instrumentscaling factor.As explained in footnote 2, hourly PM2.5mass concentrationsfrom continuous instruments wereadjusted on a day-by-day basisto match the 24-hour concentration reported by a collocatedFRM/FEM filter-based sampler only for the purpose of thisanalysis. Prospectively, if onlycontinuous instruments approvedas federal equivalent methods (FEM) were allowed to be used forpurposes of measuring hourly PM2.5mass concentrations forpurposes of estimating hourly PM2.5light extinction, thisadjustment presumably would not be needed. If the adjustmentstep were omitted, then FRM measurements would not be arequired data source for this approach.(ix) For each daylight hour ofeach day of that month (includingdays without CSN sampling) multiply the value of hourly PM2.5mass from step (viii) by the monthly-average component fractionsfrom step (vi).(x) Insert the results from step (ix) into the original IMPROVEalgorithm, along with f(RH) calculated based on same-hour RH.Omit the Rayleigh scattering term and the contribution fromPM10-2.5. Estimates of PM2.5light extinction in hours with RHgreater than 90% are not used indesign value calculations andgraphics presented in this memo.The exclusion of hours with RH>90% originated out of concernthat a direct instrumental measurement of PM light extinctionmight results in high values oflight extinction due to naturalconditions of fog or precipitation. While approach F does notemploy a light extinction instrument, the accuracy of hourly PM2.5mass and RH measurements at suchhigh values of RH is still aconcern.

# 11 Comparative Performance of Simplified PM 2.5 

# Light Extinction Approaches

The performance assessment of simp lified approaches for calculated PM 2.5 

# light extinction was

accomplished by comparing hourly values of PM 2.5 

# light extinction generated by each approach

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

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

paired values, as well as annual and monthly scatter plot s and regression analys is of these paired

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

below to show the degree of comparability be tween the various approaches to the original

estimates of PM 2.5 

# light extinction.

The box and whisker plots of the diffe rences between calculated hourly PM 2.5 

# light extinction by

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

percentage difference, the percentage difference is calculated as follows:

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

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

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

values of PM 2.5 

# light extinction.

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

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

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

component mass concentration and to adjust ni trate 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 di fferences in calculated hourly

PM 2.5 

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

changes introduced in the remain ing three approaches did not mu ch affect the resulting hourly

values. 8



# The degree of comparability for paired hourly PM 2.5 

# light extinction between approach F and A,

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

(Tables 3 and 4). In both tables, the regression lines have slopes and R 2 

# 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., Fr esno, Houston, Los Angeles, P hoenix, Salt Lake City and

Tacoma) have slopes and R 2 

# values for some months that imply a bias and/or noi sier 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 th e 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 epis odes 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 PM 2.5 

# light extinction

for all months that compare approach F to a pproach 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 va riations in the dry PM 2.5 

# composition can be replaced by monthly

averaged values without much loss of precision in calculated hourly PM 2.5 

# 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 appr oach 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 fo r negative sampling artifact for

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

PM 2.5 

# mass, while approach B does not. This is consis tent with the behavior for sites that have

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

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

better method to calculate PM 2.5 

# light extinction. In particular, if hourly data from continuous

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

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

estimates of actual hourly PM 2.5 

# 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 PM 2.5 

# light extinction produces comparable results to the use of daily values. 10 

# In that

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

equals PM 2.5 

# 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 dr y term can vary in theory from 1 m 2 

# /g to 10 m 2 

# /g, but is

commonly in a range from about 3 m 2 

# /g to 4 m 2 

# /g for typical urban PM 2.5 

# composition, which is

dominated by sulfate, n itrate, and/or organic PM 2.5 

# . The moist extinction efficiency term depends

on the hygroscopic fraction of the PM 2.5 

# mass (i.e., composed of sulfate and nitrate) so if ranges

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

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

function of relative humidity that varies from 0 m 2 

# /g (for relative humidity <40%) to 9.5 m 2 

# /g

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

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

compared PM 2.5 

# composition variability. Overall, this other assessment supports the conclusions

from this analysis (i.e., that use of monthly mean PM 2.5 

# composition values in the IMPROVE

10 

# Memo: “Assessment of the Use of Speciated PM 2.5 

# 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 PM 2.5 

# light extinction compared to use of

sample period specific PM 2.5 

# composition).

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

PM 2.5 

# as best as possible, the UFVA approach (a pproach A) made use of 2004 monthly-average

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

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

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

concentrations on the correspondi ng day as revealed by the CSN sa mple. Thus, using approach A

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

exist between that approach a nd a direct measurement of PM 2.5 

# 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 PM 2.5 

# light extinction between

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

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

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

# 15 Figure 2. Box and whisker plot of the pe rcent difference in calculated hourly PM 2.5 

# light extinction between

approaches E and A (top plot), and betwee n 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 separat e day and

omits the UFVA correction for nitr ate loss. Approach D adds the further simplifi cation of the component mix being the same acro ss all hours.)

# 16 Figure 3. Scatter plots of calculated PM 2.5 

# light extinction by approach F versus approach A (“original”, left)

and versus approach B (right) for Ba ltimore (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 separat e day and

omits the UFVA correction for nitrat e loss. Approach F adds the further simplifica tions of the component mix being the same acr oss all hours of

the month.)17Table 3. Linear regression equation and R2values for relating hourly PM2.5light extinction values calculated using approach F(x in the equation) to those using approach A (yin the equation) by month for 15 urban areas.11Month123456789101112Atlanta,GAy=1.09*x+‐0.73;Rsq=0.98y=1.03*x+1.92;Rsq=0.98y=1.01*x+‐1.52;Rsq=0.97y=1.06*x+‐4.65;Rsq=0.98y=1.02*x+‐4.41;Rsq=0.97y=0.99*x+‐3.52;Rsq=0.97y=0.96*x+‐1.38;Rsq=0.96y=0.98*x+‐4.01;Rsq=0.98y=0.98*x+‐2.8;Rsq=0.98y=0.97*x+0.42;Rsq=0.99y=1.04*x+0.12;Rsq=0.96y=1.04*x+0.63;Rsq=0.98Baltimore,MDy=0.99*x+1.25;Rsq=0.99y=1.06*x+‐3.6;Rsq=1y=0.97*x+3.27;Rsq=0.99y=1.02*x+0.41;Rsq=0.96y=0.99*x+0.83;Rsq=0.9y=0.98*x+‐3.78;Rsq=0.96y=0.94*x+‐2.59;Rsq=0.98y=0.88*x+2.1;Rsq=0.99y=0.96*x+‐3.25;Rsq=0.98y=1.05*x+‐2.77;Rsq=0.98y=0.99*x+6.6;Rsq=0.99y=1.02*x+0.14;Rsq=0.97Birmingham,ALy=1.09*x+‐2.17;Rsq=0.97y=1.04*x+0.7;Rsq=0.97y=1.06*x+‐2.82;Rsq=0.97y=1.06*x+‐3.91;Rsq=0.97y=0.94*x+2.05;Rsq=0.97y=0.98*x+‐4.9;Rsq=0.98y=1.02*x+‐6.87;Rsq=0.97y=0.9*x+2.31;Rsq=0.93y=1*x+‐6.31;Rsq=0.98y=1.06*x+‐3.87;Rsq=0.97y=1.05*x+‐2.19;Rsq=0.98y=1.02*x+0.36;Rsq=0.99Dallas,TXy=1.17*x+‐0.86;Rsq=0.97y=1.1*x+0.43;Rsq=0.98y=1.14*x+‐3.9;Rsq=0.96y=1.04*x+‐2.66;Rsq=0.97y=1.03*x+‐3.1;Rsq=0.96y=0.93*x+0.75;Rsq=0.95y=0.96*x+‐0.01;Rsq=0.96y=0.98*x+‐0.63;Rsq=0.91y=1.01*x+‐3.02;Rsq=0.93y=1.06*x+‐2.35;Rsq=0.97y=1.04*x+‐1.16;Rsq=0.96y=1.03*x+2.16;Rsq=0.99Detroit,MIy=1.02*x+2.24;Rsq=0.97y=0.95*x+3.79;Rsq=0.99y=0.99*x+2.13;Rsq=0.99y=1.1*x+‐0.5;Rsq=0.96y=0.92*x+5.42;Rsq=0.96y=0.96*x+2.14;Rsq=0.96y=0.99*x+0.17;Rsq=0.93y=1.29*x+‐18.07;Rsq=0.9y=1.12*x+‐8.63;Rsq=0.97y=1.18*x+‐3.36;Rsq=0.95y=1.04*x+5.56;Rsq=1y=0.94*x+4.14;Rsq=0.99Fresno,CAy=1.05*x+‐0.76;Rsq=0.98y=1.05*x+2.04;Rsq=0.99y=1.15*x+4.9;Rsq=0.96y=1.31*x+‐4.13;Rsq=0.87y=1.27*x+‐2.92;Rsq=0.83y=1.24*x+‐5.26;Rsq=0.87y=1.06*x+‐0.97;Rsq=0.97y=1.3*x+‐6.59;Rsq=0.86y=1.39*x+‐6.67;Rsq=0.89y=1.48*x+‐7.51;Rsq=0.94y=1.07*x+5.44;Rsq=0.98y=0.97*x+5.71;Rsq=0.99Houston,TXy=0.83*x+4.6;Rsq=0.96y=0.97*x+‐1.12;Rsq=0.99y=0.9*x+0.8;Rsq=0.99y=1.02*x+‐3.72;Rsq=0.98y=0.97*x+‐2.87;Rsq=0.97y=0.84*x+7.59;Rsq=0.92y=0.76*x+11.38;Rsq=0.85y=0.88*x+5.36;Rsq=0.93y=0.99*x+‐2.92;Rsq=0.98y=1.06*x+‐3.39;Rsq=0.99y=1.07*x+‐3.64;Rsq=0.95y=1.06*x+‐2.09;Rsq=0.98LosAngeles,CAy=1.18*x+‐0.57;Rsq=0.98y=1.1*x+2.01;Rsq=0.98y=1.08*x+7.64;Rsq=0.96y=1.14*x+2.11;Rsq=0.96y=1.04*x+12.59;Rsq=0.96y=1.33*x+‐3.58;Rsq=0.86y=1.26*x+‐2.89;Rsq=0.92y=1.38*x+‐12.8;Rsq=0.84y=1.4*x+‐9.14;Rsq=0.91y=1.25*x+‐0.9;Rsq=0.96y=1.08*x+7.75;Rsq=0.98y=1.09*x+5.38;Rsq=0.9711After completion of the second draft PAD, an error related to SANDWICH processing of 2005-2007 PM2.5 speciation data was discovered and corrected. Thisaffected the UFVA method (also designated in this memo as approach A) predictions of hourly PM2.5 light extinction to a small degree, but not the predictionsusing the approaches designated in this memo as B, D, etc. The comparisons between the latter approaches and approach A were also very slightly affected, asthe reader may notice by careful comparison ofresults in this table and Tables 4 and 5 to similar results in the second draftPAD.18Month123456789101112NewYork,NYy=1.03*x+2.14;Rsq=0.98y=1.03*x+‐1.36;Rsq=1y=1.01*x+3.61;Rsq=0.99y=1.1*x+‐0.68;Rsq=0.98y=1.06*x+‐1.45;Rsq=0.97y=1.1*x+‐6.27;Rsq=0.96y=1.02*x+‐7.94;Rsq=0.96y=0.98*x+‐1.24;Rsq=0.97y=1.03*x+0.25;Rsq=0.96y=1.22*x+‐7.93;Rsq=0.97y=1.07*x+0.64;Rsq=0.99y=1.05*x+1.63;Rsq=0.98Philadelphia,PAy=0.95*x+3.2;Rsq=0.99y=1.01*x+‐1.74;Rsq=0.99y=1*x+1.45;Rsq=0.99y=0.96*x+2.39;Rsq=0.94y=0.9*x+1.44;Rsq=0.98y=0.92*x+‐0.44;Rsq=0.98y=0.91*x+1.75;Rsq=0.98y=0.85*x+5.59;Rsq=0.98y=0.89*x+1.3;Rsq=0.96y=0.95*x+3.85;Rsq=0.97y=1.05*x+1.94;Rsq=0.99y=0.96*x+3.08;Rsq=0.99Phoenix,AZy=1.21*x+‐2.37;Rsq=0.89y=1.13*x+‐1.38;Rsq=0.97y=0.88*x+1.25;Rsq=0.96y=0.85*x+1.94;Rsq=0.94y=0.93*x+0.87;Rsq=0.9y=0.88*x+1.65;Rsq=0.97y=0.77*x+4.02;Rsq=0.69y=0.92*x+0.62;Rsq=0.99y=0.86*x+0.48;Rsq=0.97y=0.92*x+1.18;Rsq=0.72y=1.05*x+‐1.68;Rsq=0.92y=1.16*x+‐2.69;Rsq=0.94Pittsburgh,PAy=1.1*x+‐3.63;Rsq=0.95y=0.99*x+1.91;Rsq=0.97y=0.98*x+0.09;Rsq=0.99y=1.09*x+‐2.39;Rsq=0.97y=1.07*x+‐5.49;Rsq=0.92y=0.95*x+‐1.28;Rsq=0.97y=1.03*x+‐9.91;Rsq=0.96y=0.94*x+‐1.93;Rsq=0.97y=1.04*x+‐7.42;Rsq=0.94y=1.02*x+‐1.66;Rsq=0.97y=1.06*x+‐1.21;Rsq=0.99y=0.99*x+2.34;Rsq=0.98SaltLakeCity,UTy=0.91*x+8.62;Rsq=1y=0.97*x+4.95;Rsq=0.99y=1.12*x+1.95;Rsq=0.97y=1.14*x+‐1.2;Rsq=0.88y=0.98*x+0.92;Rsq=0.83y=1.02*x+0.98;Rsq=0.87y=1*x+0;Rsq=0.99y=0.98*x+‐0.43;Rsq=0.97y=0.88*x+5.49;Rsq=0.87y=1.08*x+0.17;Rsq=0.93y=1.06*x+0.81;Rsq=0.97y=0.91*x+5.89;Rsq=0.99StLouis,MOy=1.01*x+1.72;Rsq=0.99y=1.03*x+‐0.14;Rsq=1y=1.06*x+‐0.01;Rsq=0.98y=1.14*x+‐3.92;Rsq=0.94y=1.08*x+‐3.27;Rsq=0.93y=0.92*x+0.97;Rsq=0.95y=0.98*x+‐2.77;Rsq=0.97y=1*x+‐7.97;Rsq=0.98y=0.94*x+‐0.89;Rsq=0.97y=1.19*x+‐3.77;Rsq=0.95y=0.98*x+5.24;Rsq=0.97y=1*x+2.3;Rsq=0.99Tacoma,WAy=1.02*x+0.02;Rsq=1y=0.99*x+0.65;Rsq=0.94y=1.07*x+‐0.1;Rsq=0.97y=1.22*x+‐3.78;Rsq=0.96y=1.18*x+‐4.43;Rsq=0.92y=1.09*x+‐0.14;Rsq=0.9y=1.1*x+‐1.28;Rsq=0.94y=1.22*x+‐4.35;Rsq=0.95y=1.06*x+0.02;Rsq=0.96y=0.99*x+0.69;Rsq=0.98y=1.03*x+1.52;Rsq=1y=1.02*x+2.46;Rsq=0.9819Table 4. Linear regression equation and R2values for relating hourly PM2.5light extinction values calculated using approach F(x in the equation) to those using approach B (yin the equation) by month for15 urban areas.Month123456789101112Atlanta,GAy=1.01*x+0.4;Rsq=0.98y=1.06*x+0.26;Rsq=0.96y=1.02*x+‐0.15;Rsq=0.99y=1.02*x+‐0.72;Rsq=0.99y=1.02*x+‐0.83;Rsq=0.99y=1.02*x+‐1.06;Rsq=0.99y=1.02*x+‐0.38;Rsq=0.95y=1.04*x+‐3.54;Rsq=0.98y=1.02*x+‐0.74;Rsq=0.99y=1*x+1.11;Rsq=0.99y=1*x+1.2;Rsq=0.98y=0.99*x+0.81;Rsq=0.99Baltimore,MDy=0.96*x+1.84;Rsq=0.99y=1.09*x+‐5.5;Rsq=0.99y=1.04*x+‐1.21;Rsq=1y=1.01*x+1.15;Rsq=0.98y=1.02*x+‐1.15;Rsq=1y=0.99*x+0.73;Rsq=0.99y=1.01*x+‐0.36;Rsq=0.98y=1*x+0.25;Rsq=1y=1.02*x+‐1;Rsq=1y=0.97*x+2.23;Rsq=0.98y=0.99*x+2.99;Rsq=0.99y=1.02*x+‐0.17;Rsq=0.98Birmingham,ALy=1.08*x+‐2.37;Rsq=0.98y=0.98*x+3.39;Rsq=0.96y=1.01*x+0.05;Rsq=0.99y=1.07*x+‐2.22;Rsq=0.98y=1*x+1.38;Rsq=0.99y=1.01*x+‐0.71;Rsq=0.99y=1.06*x+‐4.76;Rsq=0.98y=0.98*x+2.12;Rsq=0.95y=1.02*x+‐2.17;Rsq=0.98y=1*x+1.46;Rsq=0.98y=1.02*x+0.76;Rsq=0.99y=1*x+1.59;Rsq=0.99Dallas,TXy=1.08*x+‐1.32;Rsq=0.99y=1.05*x+‐1.39;Rsq=0.99y=1.06*x+‐1.42;Rsq=0.99y=1.08*x+‐2.68;Rsq=0.98y=1.04*x+‐1.58;Rsq=0.99y=0.98*x+1.45;Rsq=0.95y=0.99*x+0.46;Rsq=0.96y=0.94*x+2.44;Rsq=0.91y=1*x+‐0.52;Rsq=0.99y=1.02*x+‐0.48;Rsq=0.99y=1.03*x+‐0.71;Rsq=0.99y=1.13*x+‐3.74;Rsq=0.99Detroit,MIy=1.06*x+‐4.02;Rsq=0.98y=1.05*x+‐2.66;Rsq=1y=1.03*x+‐1.35;Rsq=0.99y=1.01*x+0.23;Rsq=0.99y=0.99*x+‐0.13;Rsq=1y=0.98*x+0.79;Rsq=0.99y=1.02*x+‐0.65;Rsq=0.99y=1.09*x+‐5.76;Rsq=0.97y=1.02*x+‐0.88;Rsq=0.99y=1.05*x+‐1.29;Rsq=0.99y=0.99*x+4.66;Rsq=1y=1.09*x+‐5.4;Rsq=0.95Fresno,CAy=1.06*x+‐5.57;Rsq=0.99y=1.05*x+‐4.18;Rsq=0.99y=1.03*x+‐0.85;Rsq=1y=1.02*x+‐0.57;Rsq=0.99y=1.02*x+‐0.24;Rsq=0.98y=1.03*x+‐0.55;Rsq=0.99y=1*x+‐0.76;Rsq=1y=1.02*x+‐0.58;Rsq=0.99y=1.04*x+‐1.01;Rsq=0.99y=1.1*x+‐3.18;Rsq=0.99y=1.05*x+‐4.61;Rsq=0.99y=1.04*x+‐4.37;Rsq=0.99Houston,TXy=0.97*x+2.57;Rsq=0.99y=1.08*x+‐1.78;Rsq=0.97y=1.01*x+0.8;Rsq=0.99y=1.04*x+‐0.93;Rsq=0.99y=1.02*x+‐0.48;Rsq=0.98y=0.9*x+8.05;Rsq=0.93y=0.77*x+13.92;Rsq=0.81y=0.92*x+7.13;Rsq=0.93y=1.01*x+‐0.91;Rsq=0.99y=1.05*x+‐1.77;Rsq=0.99y=1.12*x+‐3.15;Rsq=0.99y=1.14*x+‐2.39;Rsq=0.97LosAngeles,CAy=1.08*x+‐3.01;Rsq=0.99y=1.04*x+‐1.62;Rsq=1y=1.02*x+0.31;Rsq=0.99y=1.05*x+‐3;Rsq=0.99y=1*x+0.89;Rsq=1y=1.05*x+‐2.16;Rsq=0.99y=1.03*x+‐0.3;Rsq=0.99y=1.03*x+‐0.34;Rsq=0.99y=1.06*x+‐1.65;Rsq=0.99y=1.08*x+‐3.22;Rsq=0.99y=1.06*x+‐0.62;Rsq=1y=1.04*x+‐0.14;Rsq=0.99NewYork,NYy=1*x+‐0.52;Rsq=1y=1.01*x+‐0.82;Rsq=1y=0.99*x+0.86;Rsq=1y=1.03*x+‐0.26;Rsq=1y=1*x+0.17;Rsq=0.99y=1.07*x+‐3.4;Rsq=0.99y=1.03*x+‐4.03;Rsq=0.99y=1.02*x+‐2.4;Rsq=0.99y=1.01*x+‐0.93;Rsq=1y=1.06*x+‐3.4;Rsq=0.99y=1.02*x+‐0.84;Rsq=1y=1*x+‐1.08;Rsq=120Month123456789101112Philadelphia,PAy=1.03*x+‐1.63;Rsq=0.99y=1.02*x+‐2.07;Rsq=0.99y=1.02*x+‐0.65;Rsq=1y=1.05*x+‐1.63;Rsq=0.98y=0.99*x+0.1;Rsq=1y=0.99*x+0.42;Rsq=1y=1.02*x+0.32;Rsq=0.98y=0.99*x+2.35;Rsq=0.99y=0.96*x+1.39;Rsq=0.99y=1.01*x+0.84;Rsq=1y=1.02*x+‐0.83;Rsq=1y=1*x+‐0.41;Rsq=1Phoenix,AZy=1.17*x+‐3.94;Rsq=0.93y=0.95*x+1.15;Rsq=0.99y=0.84*x+1.91;Rsq=0.97y=0.9*x+1.35;Rsq=0.94y=0.98*x+0.6;Rsq=0.96y=0.98*x+0.63;Rsq=0.98y=0.88*x+3.02;Rsq=0.81y=0.94*x+1.07;Rsq=0.99y=0.97*x+0.28;Rsq=0.98y=0.98*x+1.01;Rsq=0.89y=0.98*x+0.03;Rsq=0.96y=1.06*x+‐3.32;Rsq=0.97Pittsburgh,PAy=1.04*x+‐0.57;Rsq=0.97y=1*x+0.78;Rsq=0.99y=1.01*x+0.29;Rsq=1y=1.05*x+‐0.59;Rsq=0.99y=1.01*x+‐0.88;Rsq=0.99y=1*x+0.02;Rsq=0.99y=1.02*x+‐3.12;Rsq=0.99y=1.04*x+‐3.96;Rsq=0.99y=1.02*x+‐1.58;Rsq=0.99y=0.98*x+2.1;Rsq=0.98y=1.05*x+‐2.23;Rsq=0.99y=0.95*x+4.33;Rsq=0.98SaltLakeCity,UTy=1*x+1;Rsq=1y=1.02*x+‐0.82;Rsq=1y=1.07*x+‐0.81;Rsq=0.99y=1.05*x+‐0.51;Rsq=0.95y=0.98*x+0.79;Rsq=0.96y=1.02*x+‐0.44;Rsq=0.99y=0.97*x+0.77;Rsq=0.99y=0.96*x+0.74;Rsq=0.96y=0.75*x+8.1;Rsq=0.8y=0.97*x+1.37;Rsq=0.99y=1*x+‐0.22;Rsq=1y=1*x+‐0.24;Rsq=1StLouis,MOy=1.04*x+‐0.73;Rsq=0.99y=1.03*x+‐0.62;Rsq=1y=1.08*x+‐4.01;Rsq=0.99y=1.08*x+‐2.89;Rsq=0.98y=1.04*x+‐1.27;Rsq=0.97y=0.99*x+0.5;Rsq=0.99y=1.03*x+‐1.96;Rsq=0.99y=1.02*x+‐3.12;Rsq=0.99y=1*x+‐0.23;Rsq=0.99y=1*x+1.02;Rsq=0.99y=0.93*x+4.74;Rsq=0.98y=1.09*x+‐4.55;Rsq=0.98Tacoma,WAy=0.97*x+1.51;Rsq=1y=1.08*x+3.92;Rsq=0.73y=1.02*x+0.31;Rsq=0.97y=1.03*x+‐0.72;Rsq=0.99y=1.02*x+‐0.71;Rsq=0.98y=1.02*x+‐0.21;Rsq=0.99y=1.04*x+‐0.37;Rsq=0.98y=1.03*x+‐0.58;Rsq=0.99y=0.98*x+1.41;Rsq=0.98y=0.97*x+0.92;Rsq=0.99y=1.02*x+‐0.03;Rsq=1y=0.99*x+2.77;Rsq=0.97

# 21 PM 2.5 

# Mass Concentration Used Alone to Calculate PM 2.5 

# Light Extinction

Approach I predicts PM 2.5 

# light extinction by merely multiplying the same hourly PM 2.5 

# values

as used in approach A (continuous PM 2.5 

# instrument normalized to match the FRM 24-hour

concentration) by a constant, 4.35 m 2 

# /g. 12 

# As shown in Figures 4 and 5, the results are not nearly

as comparable as those calculated using appr oach 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 R 2 

# values that are

often below 0.9 and as low as 0.4.

Figure 4. Box and whisker plot of the pe rcent difference in calculated hourly PM 2.5 

# light extinction between

approaches I and A by urban area.

12 

# The value of 4.35 m 2 

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

more careful analysis would be appropriate, including anal ysis 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 PM 2.5 

# light extinction for approach I versus approach A

(“original”) for four selected urban areas.23Table 5.Linear regression equation and R2values for relating hourly PM2.5light extinction values calculated using approach I (x in the equation) tothose using approach A (y in the equation) by month for 15 urban areas.Month123456789101112Atlanta,GAy=1.49*x+‐6.01;Rsq=0.91y=1.45*x+‐6.61;Rsq=0.85y=1.25*x+‐8.03;Rsq=0.85y=1.33*x+‐11.91;Rsq=0.85y=1.2*x+‐7.04;Rsq=0.77y=1.06*x+5.99;Rsq=0.65y=0.87*x+25.82;Rsq=0.55y=1.06*x+8.1;Rsq=0.62y=1.21*x+‐2.64;Rsq=0.75y=1.22*x+‐2.26;Rsq=0.89y=1.53*x+‐12.49;Rsq=0.91y=1.56*x+‐13.12;Rsq=0.93Baltimore,MDy=1.28*x+‐8.13;Rsq=0.88y=1.65*x+‐31.12;Rsq=0.84y=1.47*x+‐17.18;Rsq=0.79y=1.03*x+0.1;Rsq=0.79y=1.05*x+6.54;Rsq=0.62y=1.23*x+‐6.26;Rsq=0.7y=1.1*x+‐1.47;Rsq=0.74y=1.09*x+7.77;Rsq=0.85y=1.33*x+‐8.8;Rsq=0.81y=1.49*x+‐7.7;Rsq=0.72y=1.66*x+‐14.72;Rsq=0.94y=1.34*x+‐5.97;Rsq=0.72Birmingham,ALy=1.29*x+‐5.76;Rsq=0.8y=1.31*x+‐7.25;Rsq=0.85y=1.11*x+‐5.05;Rsq=0.89y=1.05*x+‐2.93;Rsq=0.85y=1.06*x+‐6.34;Rsq=0.9y=1*x+‐2.72;Rsq=0.82y=1.09*x+‐0.42;Rsq=0.77y=0.95*x+2.44;Rsq=0.77y=1.16*x+‐13.85;Rsq=0.8y=1.24*x+‐7.38;Rsq=0.87y=1.17*x+‐4.96;Rsq=0.89y=1.2*x+‐0.65;Rsq=0.92Dallas,TXy=1.68*x+‐8.85;Rsq=0.84y=1.93*x+‐21.66;Rsq=0.88y=1.53*x+‐12.91;Rsq=0.79y=1.34*x+‐10.87;Rsq=0.75y=1.16*x+‐2.83;Rsq=0.69y=0.86*x+3.04;Rsq=0.74y=0.86*x+3.72;Rsq=0.75y=0.96*x+‐2.36;Rsq=0.7y=1.04*x+‐2.03;Rsq=0.71y=1.19*x+‐2.94;Rsq=0.81y=1.15*x+‐2.83;Rsq=0.8y=1.63*x+‐9.61;Rsq=0.93Detroit,MIy=1.19*x+11.68;Rsq=0.72y=1.26*x+5.08;Rsq=0.85y=1.12*x+7.21;Rsq=0.67y=1.16*x+‐5.67;Rsq=0.86y=0.79*x+11.4;Rsq=0.82y=0.78*x+14.2;Rsq=0.84y=0.99*x+8.98;Rsq=0.73y=1.22*x+1.21;Rsq=0.55y=1.22*x+‐11.05;Rsq=0.72y=1.42*x+‐6.23;Rsq=0.79y=1.69*x+‐24.95;Rsq=0.92y=1.13*x+18.7;Rsq=0.77Fresno,CAy=1.2*x+2.32;Rsq=0.83y=1.26*x+1.71;Rsq=0.84y=1.43*x+0.17;Rsq=0.83y=1.29*x+‐2.1;Rsq=0.67y=0.98*x+4.24;Rsq=0.54y=1.01*x+‐1.51;Rsq=0.68y=0.94*x+‐1.1;Rsq=0.93y=1.13*x+‐5.1;Rsq=0.73y=1.24*x+‐4.61;Rsq=0.73y=1.6*x+‐7.84;Rsq=0.71y=1.22*x+8.23;Rsq=0.82y=1.3*x+2.8;Rsq=0.87Houston,TXy=1.29*x+‐2.32;Rsq=0.87y=1.35*x+‐6.35;Rsq=0.81y=1.23*x+‐7.63;Rsq=0.85y=1.38*x+‐18.36;Rsq=0.82y=1.33*x+‐19.81;Rsq=0.76y=1.07*x+‐2.13;Rsq=0.77y=0.54*x+20.69;Rsq=0.57y=0.75*x+11.34;Rsq=0.43y=1.21*x+‐12.05;Rsq=0.82y=1.3*x+‐10.7;Rsq=0.95y=1.21*x+‐7.66;Rsq=0.86y=1.32*x+‐4.95;Rsq=0.88LosAngeles,CAy=1.41*x+‐5.87;Rsq=0.87y=1.19*x+3.9;Rsq=0.85y=1.24*x+6.92;Rsq=0.8y=1.41*x+‐5.96;Rsq=0.78y=1.4*x+‐3.52;Rsq=0.78y=1.7*x+‐25.06;Rsq=0.57y=1.22*x+5.35;Rsq=0.59y=1.57*x+‐21.03;Rsq=0.5y=1.38*x+‐6.02;Rsq=0.71y=1.43*x+‐13.45;Rsq=0.81y=1.47*x+‐12.56;Rsq=0.86y=1.17*x+6.8;Rsq=0.86NewYork,NYy=1.49*x+‐13.85;Rsq=0.9y=1.17*x+‐5.14;Rsq=0.92y=1.39*x+‐5.93;Rsq=0.87y=1.21*x+‐1.68;Rsq=0.89y=1.2*x+‐2.33;Rsq=0.8y=1.35*x+‐9.03;Rsq=0.78y=1.17*x+0.72;Rsq=0.65y=1.29*x+‐12.79;Rsq=0.79y=1.37*x+‐5.7;Rsq=0.89y=1.89*x+‐21.25;Rsq=0.83y=1.39*x+0.87;Rsq=0.92y=1.3*x+0.85;Rsq=0.8724Month123456789101112Philadelphia,PAy=1.36*x+‐8.52;Rsq=0.77y=1.1*x+2.02;Rsq=0.79y=1.03*x+1.75;Rsq=0.83y=0.81*x+7.79;Rsq=0.68y=0.88*x+4.55;Rsq=0.85y=0.97*x+3.07;Rsq=0.78y=1.03*x+1.63;Rsq=0.82y=0.79*x+34.86;Rsq=0.69y=0.8*x+10.76;Rsq=0.64y=1.01*x+8;Rsq=0.86y=1.27*x+1.02;Rsq=0.86y=1.06*x+10.01;Rsq=0.76Phoenix,AZy=0.83*x+‐2.5;Rsq=0.89y=0.76*x+‐1.53;Rsq=0.97y=0.65*x+1.46;Rsq=0.96y=0.56*x+2.12;Rsq=0.92y=0.6*x+1.7;Rsq=0.88y=0.62*x+1.11;Rsq=0.96y=0.5*x+5.73;Rsq=0.61y=0.69*x+0.51;Rsq=0.97y=0.6*x+0.85;Rsq=0.95y=0.6*x+2.35;Rsq=0.58y=0.76*x+‐0.91;Rsq=0.91y=0.97*x+‐2.05;Rsq=0.89Pittsburgh,PAy=1.6*x+‐7.37;Rsq=0.75y=1.22*x+0.01;Rsq=0.77y=1.18*x+‐1.9;Rsq=0.76y=1.06*x+0.12;Rsq=0.74y=1.06*x+0.38;Rsq=0.56y=0.97*x+11.89;Rsq=0.67y=1.06*x+10.46;Rsq=0.51y=1.28*x+‐9.71;Rsq=0.74y=1.18*x+‐2.72;Rsq=0.62y=1.16*x+2.65;Rsq=0.72y=1.4*x+‐9.03;Rsq=0.82y=1.47*x+‐6.82;Rsq=0.83SaltLakeCity,UTy=1.38*x+‐4.77;Rsq=0.93y=1.25*x+‐0.91;Rsq=0.92y=1.23*x+‐0.88;Rsq=0.87y=0.92*x+2.08;Rsq=0.75y=0.73*x+4.3;Rsq=0.69y=0.83*x+2.88;Rsq=0.79y=0.9*x+0.11;Rsq=0.98y=0.88*x+‐0.16;Rsq=0.96y=0.79*x+5.83;Rsq=0.87y=1.1*x+2.25;Rsq=0.82y=1.06*x+2.85;Rsq=0.92y=1.12*x+9.08;Rsq=0.94StLouis,,MOy=1.5*x+‐0.32;Rsq=0.91y=1.69*x+‐23.16;Rsq=0.87y=1.78*x+‐23.32;Rsq=0.83y=1.29*x+‐5.92;Rsq=0.69y=1.24*x+‐7.67;Rsq=0.73y=0.88*x+8.95;Rsq=0.74y=1.12*x+‐5.02;Rsq=0.75y=1.07*x+‐2.69;Rsq=0.72y=1.03*x+2.61;Rsq=0.74y=1.7*x+‐15.07;Rsq=0.79y=1.64*x+‐13.94;Rsq=0.94y=1.74*x+‐14.71;Rsq=0.82Tacoma,WAy=1.1*x+2.32;Rsq=0.98y=1.52*x+‐2.25;Rsq=0.94y=1.28*x+0.12;Rsq=0.92y=1.37*x+‐3.6;Rsq=0.86y=1.15*x+‐1.92;Rsq=0.71y=1.1*x+2.17;Rsq=0.63y=1.03*x+2.64;Rsq=0.81y=1.3*x+‐2.74;Rsq=0.68y=1.07*x+2.74;Rsq=0.84y=1.36*x+‐0.96;Rsq=0.91y=1.35*x+‐1.99;Rsq=0.98y=1.16*x+2.4;Rsq=0.96