Review of the IMPROVE Equation 

 for 

Estimating Ambient Light Extinction Coefficients 

J. L. Hand and W. C. Malm
TABLE OF CONTENTS 

Abstract........................................................................................................................................... 1 

1. Introduction............................................................................................................................... 1 

2. Sampling Biases........................................................................................................................ 5 

2.1. Nitrate Sampling Issues.................................................................................................. 7

2.2. Ammonium Sampling Issues.......................................................................................... 9 

2.3. Carbonaceous Aerosol Sampling Issues....................................................................... 10 

2.4. Issues Related to Elemental Species and Coarse Mass................................................. 12 

3. Chemical and Physical Forms of Species in the IMPROVE Equation................................... 13 

3.1. Particulate Organic Material (POM)............................................................................. 13 

3.2. Nitrate ........................................................................................................................... 26 

3.3. Sulfate ........................................................................................................................... 31 

3.4. Soil Composition .......................................................................................................... 33 

3.5. Coarse Mass.................................................................................................................. 35 

3.6. Sea Salt.......................................................................................................................... 37 

3.7. Size Distributions.......................................................................................................... 38 

Urban Observations .......................................................................................................... 41 

Rural Observations............................................................................................................ 42 

Recent Observations of Size Distributions Using DMA and OPC Data at National Park 

Service Special Studies..................................................................................................... 43 

Southeastern Aerosol and Visibility Study (SEAVS)................................................... 43 

Grand Canyon Visibility Study (GRAVS) ................................................................... 43 

Big Bend Regional Aerosol and Visibility Observational Study (BRAVO)................ 43 

Yosemite Aerosol Characterization Study (YACS) ..................................................... 44 

4. Hygroscopic Growth............................................................................................................... 44 

5. Mass Scattering Efficiencies................................................................................................... 52 

5.1. Theoretical Discussion.................................................................................................. 52

5.2. Methods for Deriving Mass Scattering Efficiencies..................................................... 59 

5.3. Survey of Mass Scattering Efficiencies........................................................................ 62 

5.3.1. Theoretical Method............................................................................................... 64 

5.3.2. Measurement Method ........................................................................................... 67 

5.3.3. MLR Method ........................................................................................................ 69 

5.3.4. Partial Scattering Method ..................................................................................... 71 

5.3.5. Apportionment Method......................................................................................... 72 

5.3.6. Mass Absorption Efficiencies............................................................................... 75 

5.4. Estimates of Dry Mass Scattering Efficiencies from IMPROVE Data ........................ 78 

6. Evaluation of the Combined Data Set................................................................................... 110 

7. Biases between Reconstructed and Measured Scattering ..................................................... 114 

8. Summary of Suggested Refinements to the IMPROVE Equation........................................ 121 

References................................................................................................................................... 126 

i
LIST OF FIGURES

Figure 1. Mean values of Roc multiplier derived from an ordinary least square multi-linear 

regression analysis (equation 6)........................................................................................ 21 

Figure 2. Mean seasonal values of Roc for all sites. Standard deviations are also shown as upper 

and lower error bars. ......................................................................................................... 22 

Figure 3. (a) Fine mode (Dp < 1 μm) nitrate speciation of NH4NO3, NaNO3 and Ca(NO3)2 at 

several IMPROVE sites. The size of the pie chart reflects the magnitude of the 

concentration of total nitrate in this size mode, which is listed under each chart. (b) Same

as (a) but for Dp < 3.2 μm. (c) Same as (a) but for coarse mode (Dp > 1 μm).................. 27 

Figure 4. Mean values of the soil coefficient from an ordinary least square multi-linear

regression analysis (equation 6)........................................................................................ 35 

Figure 5. (a) f(RH) curves using the “no solids” method for ammonium sulfate, ammonium 

bisulfate, and sulfuric acid (assuming a size distribution with Dg = 0.4 μm and σg = 1.9). 

(b) Sulfate mass scattering efficiencies for ammonium sulfate, ammonium bisulfate, and 

sulfuric acid using the curves in part (a). (c) Ratios of ammonium bisulfate and sulfuric 

acid mass scattering efficiencies to the ammonium sulfate mass scattering efficiency 

shown in (b). ..................................................................................................................... 50 

Figure 6. (a) Diagram contrasting mass scattering efficiencies for internally versus externally 

mixed particles. (b) Partial scattering efficiencies for internally and externally mixed 

particles............................................................................................................................. 56 

Figure 7. Method 1 measured total ambient scattering and reconstructed total scattering using 

equation 25 for Acadia National Park............................................................................... 87 

Figure 8. Method 2 reconstructed mixed scattering (bmix,est, Mm-1) compared to measured mixed 

scattering (bmix, Mm-1) using equation 20 (fine mode contributions) for Acadia National 

Park. .................................................................................................................................. 88 

Figure 9. The comparison of fine mode mixed inorganic and organic mass concentrations (Mmix, 

μg m-3) and the SCF for Acadia National Park. The Thiel regression line is shown. ...... 90 

Figure 10. Comparisons of method 3 reconstructed mixed scattering (bmix,est, Mm-1) to measured 

mixed scattering (bmix, Mm-1) for Acadia National Park................................................... 91 

Figure 11. Method 4 estimates of reconstructed scattering compared to measured scattering (bsp, 

Mm-1) for Acadia National Park........................................................................................ 93 

Figure 12. Map of the mean ammonium sulfate mass scattering efficiencies (m2

 g-1) for the 

United States derived using method 1. The size of the circle reflects the magnitude of the 

efficiency, which is printed next to the circle................................................................... 95 

Figure 13. Map of the mean POM mass scattering efficiencies (m2

 g-1) for the United States

derived using method 1. The size of the circle reflects the magnitude of the efficiency, 

which is printed next to the circle..................................................................................... 96 

Figure 14. Map of inorganic specific mass scattering efficiencies (αinorg, m2

 g-1) for the United

States using method 2. The size of the circle reflects the magnitude of the efficiency, 

which is printed next to the circle..................................................................................... 99 

Figure 15. Map of organic (POM) mass scattering efficiencies (αorg, m2

 g-1) for the United States

using method 2. The size of the circle reflects the magnitude of the efficiency, which is 

printed next to the circle. ................................................................................................ 100 

ii
Figure 16. Map of percent change in specific mass scattering efficiency (for either αinorg or αorg) 

due to a doubling of mixture mass (Mmix) using method 3. The size of the circle reflects 

the magnitude of the change, which is printed next to the circle.................................... 102 

Figure 17. Map of the intercept from the Theil regression in method 3. The size of the circle 

reflects the magnitude of the intercept, which is printed next to the circle. ................... 103 

Figure 18. Map of mean inorganic specific mass scattering efficiencies (αinorg, m

2

 g

-1) from 

method 3. The size of the circle reflects the magnitude of the efficiency, which is printed 

next to the circle.............................................................................................................. 105 

Figure 19. Map of organic mass scattering efficiencies (αorg, m

2

 g

-1) from method 3. The size of 

the circle reflects the magnitude of the efficiency, which is printed next to the circle.. 106 

Figure 20. Map of the mean ammonium sulfate mass scattering efficiencies (αAS, m

2

 g

-1) from

method 4. The size of the circle reflects the magnitude of the efficiency, which is printed 

near the circle.................................................................................................................. 109 

Figure 21. Map of mean POM mass scattering efficiencies (αPOM, m2

 g-1) from method 4. The

size of the circle reflects the magnitude of the efficiency, which is printed near the circle.

......................................................................................................................................... 110 

Figure 22. The average biases for each site corresponding to time periods with low measured 

scattering values (10–20%) (see Table 26)..................................................................... 116 

Figure 23. The average biases for each site corresponding to time periods with median measured 

scattering values (45–55%) (see Table 27)..................................................................... 117 

Figure 24. The average biases for each site corresponding to time periods with high measured 

scattering values (80–90%) (see Table 28)..................................................................... 118 

Figure 25. Average biases for the combined data set (all sites and time) for time periods with 

low (10–20%), median (45–55%), and high (80–90%) scattering ranges, as calculated 

using methods 3 and 4, and the current IMPROVE algorithm. Also shown is the average 

of the per-site biases from Tables 26–28. The f(RH) curves were calculated for

continuous growth from 1 < RH < 90%. ........................................................................ 118 

Figure 26. Average biases for the combined data set (all sites and time) for time periods with 

low (10–20%), median (45–55%), and high (80–90%) scattering ranges, as calculated 

using methods 3, 4, and the current IMPROVE algorithm. The f(RH) curves were 

calculated from 1 < RH < 95% assuming crystallization growth curves........................ 119 

iii
LIST OF TABLES 

Table 1. Statistically significant (95%) regression coefficients using the ordinary least square 

multiple-linear regression analysis (equation 6). Site code is in the first column. The 

remaining columns correspond to coefficients associated with ammonium sulfate (AS), 

ammonium nitrate (AN), particulate organic matter (POM), light-absorbing carbon 

(LAC), soil, and sea salt, respectively. Insignificant coefficients are replaced with “.”. . 16 

Table 6. Summary of mass scattering efficiencies reported in Tables 2 through 5 (Appendix 2). 

The “Apportionment” column refers to results from White (1991). The “IMPROVE”

column lists values used in the current IMPROVE formulation. Entries correspond to the 

fine mode unless otherwise stated in the row header. Sulfate efficiencies correspond to

dry ammonium sulfate, and POM efficiencies have been normalized to an Roc value of 

1.8...................................................................................................................................... 74 

Table 8. Values used for the dry mass scattering efficiencies for the large and small mass size

distributions for each species............................................................................................ 83 

Table 9. A statistical summary of mass concentrations (μg m-3) at Acadia National Park. CM 

and FM refer to gravimetric coarse mass and fine (PM2.5) mass, respectively. AS and AN 

refer to ammonium sulfate and ammonium nitrate, respectively. POM is particulate

organic matter using an Roc factor of 1.8. Mass units are (μg m-3). RH refers to ambient 

relative humidity. The number of nephelelometer data points in a 24-hr average is given 

by N(bsp). The values of the revised f(RH) curves for the ambient RH (f(RH)amb,new) and

the nephelometer chamber RH (f(RH)chamb,new) are also listed. Similar values are reported 

for the current f(RH) curves (f(RH)amb,old and f(RH)chamb,old). ........................................... 84 

Table 10. A summary of bsp (Mm-1) for Acadia National Park. Values correspond to measured 

total ambient scattering (bsp), reconstructed total ambient scattering (bsp_recon), measured 

scattering associated with inorganics and organics (bmix), estimated scattering associated 

with inorganics and organics (bmix_est), scattering due to ammonium sulfate (bsp(AS)), 

ammonium nitrate (bsp(AN)), particulate organic material (bsp(POM)), soil and coarse 

mass (bsp(soil+CM)), sea salt (bsp(SS)), and water (bsp(H20)). Light absorption (bap) was 

computed assuming a mass absorption efficiency of 10 m2

 g

-1. New f(RH) curves were 

used to estimate wet scattering. POM was computed assuming an Roc factor of 1.8 and 

mass scattering efficiency of 3.8 m2

 g

-1............................................................................ 85 

Table 11. Fractional contribution to total ambient scattering at Acadia National Park using 

equation 25. AS corresponds to ammonium sulfate and AN corresponds to ammonium 

nitrate. Particulate organic matter (POM) fraction was computed assuming an Roc factor 

of 1.8. The coarse mode fraction is given by CM............................................................. 86 

Table 12. The results from method 1 for Acadia National Park (see equation 17). The regression 

coefficients (ai) are listed, along with the standard error. Derived mass scattering

efficiencies are also listed for ammonium sulfate (AS), ammonium nitrate (AN), 

particulate organic matter (POM = 1.8·OC), coarse mass combined with soil (soil+CM). 

and sea salt. The number of valid cases was 267 and there were 370 missing data points. 

The r2

 coefficient was 0.95. .............................................................................................. 86 

Table 13. Results for method 2 for estimating specific mass scattering efficiencies for inorganics 

(αinorg) and organics (αorg) for Acadia National Park. See text for full description. ........ 88 

Table 14. Results of the method 3 Thiel regression of SCF versus mass (Mmix = inorganics + 

organics) for Acadia National Park. ................................................................................. 89 

iv
Table 15. Method 3 estimates of the overall mean and upper and lower specific scattering 

efficiencies associated with the 15% upper and lower mass concentrations of mixed 

inorganic and organic mass for Acadia National Park...................................................... 90 

Table 16. Summary of the method 3 SCF and specific mass scattering efficiencies for inorganics 

(αinorg) and organics (αorg) for Acadia National Park. ...................................................... 91 

Table 17. Method 4 estimates of the mean, and the upper and lower mass scattering efficiencies 

(m2 g-1) associated with the 15% upper and lower mass concentrations for Acadia

National Park. ................................................................................................................... 92 

Table 18. Summary of mass scattering efficiencies (m2

 g

-1) and standard errors for all sites using

method 1. Mass scattering efficiencies are listed for ammonium sulfate (AS), ammonium 

nitrate (AN), particulate organic matter (POM = 1.8·OC), soil and coarse mass (soil + 

CM), and sea salt............................................................................................................... 94 

Table 19. Summary of specific mass scattering efficiencies (m2

 g-1) for inorganics (αinorg) and 

organics (αorg) for all sites using method 2....................................................................... 98 

Table 20. Summary of the results from method 3 using the Thiel regression of SCF and mass 

(Mmix) for each site. The fourth column corresponds to the percent change in specific

mass scattering efficiency (either for inorganic or organics) from a doubling of the mixed 

inorganic and organic mass concentration (Mmix). .......................................................... 101 

Table 21. The mean, upper, and lower specific scattering efficiencies for inorganics (αinorg) and 

organics (αorg) computed with method 3. The upper and lower estimates are calculated by 

averaging the specific scattering efficiencies associated with the upper and lower 15% 

mixed mass concentrations (Mmix). The percent change between the upper and lower mass

scattering efficiencies (final column) corresponds to both (αinorg) and (αorg). ............... 104 

Table 22. The mean, upper, and lower specific scattering efficiencies (m2

 g

-1) for ammonium 

sulfate (AS), ammonium nitrate (AN), and particulate organic matter (POM) computed 

with method 4. The upper and lower estimates are calculated by averaging the mass

scattering efficiencies associated with the upper and lower 15% mass concentrations. The

percent changes between the upper and lower mass scattering efficiencies are shown in

the final three columns.................................................................................................... 108 

Table 23. A statistical summary of mass concentrations (μg m-3) for the combined data set (all 

optical monitoring sites except Phoenix and the Virgin Islands). CM and FM refer to 

gravimetric coarse mass and fine (PM2.5) mass, respectively. AS and AN refer to

ammonium sulfate and ammonium nitrate, respectively. POM is particulate organic 

matter using an Roc factor of 1.8. RH refers to ambient relative humidity. The number of

nephelometer data points in a 24-hr average is given by N(bsp). The values of the f(RH)

corresponding to the nephelometer chamber for the ammonium sulfate small mode, large 

mode, current IMPROVE estimate, and NaCl curves are also listed. The contribution to 

fine mass is provided in parentheses............................................................................... 111 

Table 24. A summary of the low, mean, and high mass scattering efficiencies (m2

 g

-1) for the

combined data set with method 4 (M4-C), two statistical corrections to method 4 results 

(M4-C1 and M4-C2, see text), and results from method 3 applied to the combined data 

(M3-C). Results correspond to ammonium sulfate (AS), ammonium nitrate (AN), and 

particulate organic material (POM). ............................................................................... 112 

Table 25. A summary of bsp (Mm

-1) for the combined data set (all monitoring sites except

Phoenix and the Virgin Islands). Values correspond to measured total ambient scattering

(bsp), reconstructed total ambient scattering (bsp_recon), measured scattering associated with 

v
fine mode inorganics and organics (bmix), estimated scattering associated with inorganics 

and organics (bmix_est), scattering due to ammonium sulfate (bsp(AS)), ammonium nitrate 

(bsp(AN)), particulate organic material (bsp(POM)), sea salt (bsp(SS)), and water 

(bsp(H20)). Light absorption (bap) was computed assuming a mass absorption efficiency of 

10 m2

 g-1. New f(RH) curves were used to estimate wet scattering................................ 113 

Table 26. Average biases for time periods with low (10–20%) measured scattering values for 

methods 1–4 and the current IMPROVE equation. ........................................................ 115 

Table 27. Average biases for time periods with the median (45–55%) measured scattering values 

for methods 1–4 and the current IMPROVE equation.................................................... 116 

Table 28. Average biases for time periods with high (80–90%) measured scattering values for 

methods 1–4 and the current IMPROVE equation. ........................................................ 117 

Table 29. Values used for the dry mass scattering efficiencies (m2

 g

-1) for the large and small

mass size distributions for each species (ammonium sulfate, ammonium nitrate, and 

particulate organic material, POM)................................................................................. 124

Disclaimer 

The assumptions, findings, conclusions, judgments, and views presented herein are those of the 

authors and should not be interpreted as necessarily representing the National Park Service 

policies. 

vi
ABSTRACT 

The Interagency Monitoring of Protected Visual Environments (IMPROVE) protocols for 

reconstructing ambient light extinction from measured aerosol species are the basis for 

evaluating compliance under the Regional Haze Rule. We review the assumptions involved in 

computing reconstructed light extinction using the IMPROVE protocol. This review includes 

examining the biases in the measurements of aerosol composition, the assumed chemical forms 

of aerosol species, particle hygroscopicity, and assumed mass scattering efficiencies. We present 

a thorough survey of estimates of mass scattering efficiencies from recent peer-reviewed

literature. Furthermore, we use IMPROVE nephelometry and composition data to estimate mass

scattering efficiencies using a variety of methods. The current mass scattering efficiencies 

applied in the IMPROVE equation are then interpreted in the context of this survey and results

derived from the IMPROVE data analyses. Finally, a summary of provisional recommendations 

for refinements to the IMPROVE equation and a discussion of important uncertainties to

consider in the assumptions are presented. Although tentative recommendations of refinements

to the IMPROVE equation are presented, final refinements to the IMPROVE equation await 

future discussions of the results presented here. 

1. Introduction

The role of aerosols in visibility degradation has been the subject of research for several

decades, but recently interest has intensified with attempts to quantify the optical properties of

aerosols, especially because of the uncertainties surrounding the role of aerosols in climate 

change and because of the need for compliance under the Regional Haze Rule. In most instances,

visibility reduction is primarily due to scattering and absorption by particles. Particle scattering 

and absorption properties can, with a number of limiting assumptions, be calculated using Mie 

theory (Mie, 1908; van de Hulst, 1981). 

1
Compliance under the Regional Haze Rule is based on protocols for reconstructing

aerosol mass and light extinction (bext) from speciated mass concentrations. Reconstruction 

equations are used to estimate PM2.5 mass concentrations (for particles with aerodynamic

diameters less than 2.5 μm) as well as light extinction coefficients. Dry PM2.5 fine mass is 

computed using equations 1 and 2 

PM2.5 = (NH4)2SO4+ NH4NO3 + POM + LAC + Soil (1)

Soil = 2.2Al + 2.49Si + 1.94Ti + 1.63Ca + 2.42Fe (2)

where sulfate is assumed to be fully neutralized ammonium sulfate ((NH4)2SO4), nitrate is

assumed to be in the form of ammonium nitrate (NH4NO3), and organic carbon is included as 

particulate organic material (POM), computed by multiplying organic carbon (OC) 

concentrations by a molecular weight per carbon weight ratio (POM = Roc·OC). Light-absorbing 

carbon is referred to as LAC. We use the term LAC because it is more representative of the 

optical properties of light-absorbing carbon rather than elemental (EC) or black carbon (BC), 

although these terms are often used interchangeably in the literature. Fine soil concentrations

include the contributions from assumed forms of elemental species (equation 2) (Malm et al., 

1994b). Mass concentrations are given in units of μg m-3

. 

The light extinction coefficient (bext) includes the contributions from light scattering by 

particles (bsp) and gases (bsg), and light absorption by particles (bap) and gases (bag). 

bext = bsp + bap + bsg+bag (3) 

The only gas in the atmosphere that absorbs visible light is nitrogen dioxide, NO2. Absorption by 

NO2 at a wavelength of 550 nm is computed as bag = 330[NO2], where the units of bag are Mm-1

(Mm-1 = 10-6 meters

-1) and the units of [NO2] are ppm (Dixon, 1940; Hodkinson, 1966). Light 

scattering by gases (bsg) is described by Rayleigh scattering theory (van de Hulst, 1981). 

2
Rayleigh scattering is isotropic and is nearly completely polarized for light scattering at 90° to 

incoming radiation. Rayleigh scattering is proportional to molecular number density and has a 

strong spectral dependence (λ

-4, where λ is the wavelength of light). Correspondingly, bsg = 12 

Mm-1 at sea level and λ = 550 nm. 

Reconstructed scattering and absorption by particles as formulated in the IMPROVE 

(Interagency Monitoring of Protected Visual Environments) protocol are given by equations 4 

and 5, respectively, assuming an externally mixed aerosol. 

bsp = 3.0 f(RH)AS[AS]+3.0 f(RH)AN[AN]+ 4.0 ROC[OC]+ 1.0 [Soil]+ 0.6 [CM] (4) 

bap = 10.0 [LAC] (5)

Estimates of total ambient bsp in this formulation are in units of Mm-1 and correspond to 

visible wavelengths (λ ~ 550 nm). This formulation assumes that contributions to total ambient 

light scattering are from ammonium sulfate (AS), ammonium nitrate (AN), organic carbon (OC), 

soil, and coarse mass (CM). Each species has a corresponding dry mass scattering or absorption 

efficiency (α) in m2

 g-1. The terms in the brackets correspond to mass concentrations in μg m-3. 

Organic carbon mass is multiplied by an organic aerosol mass to organic carbon ratio, Roc = 1.4, 

to estimate particulate organic matter. The effects of the uptake of water as a function of relative 

humidity (RH) by hygroscopic species are estimated by the f(RH) factor. 

The formulation of the equations used in the IMPROVE reconstructions (equations 1–5) 

requires a number of assumptions. Each assumption has associated uncertainties that obviously

will have consequences for reconstructed extinction, albeit to varying degrees. The purpose of 

this report is to evaluate or comment on each assumption, and when possible, suggest 

refinements. Refinements of many of the assumptions are not suggested at this time because data 

do not currently exist to support modifications, or they would require further measurements to 

3
characterize. Suggested refinements do include increasing the Roc factor used to compute 

particulate organic matter and modifying the f(RH) factor to reflect some water associated with

particles below a relative humidity of 40%. Mass scattering efficiencies for ammonium sulfate 

and POM may also be adjusted to reflect current data. The assumptions and some related 

questions are listed below, along with the section in which they are discussed. Although 

estimating uncertainties and their combined effects on extinction from the assumptions described 

in the following sections is important, it is beyond the scope of this report. 

• Section 2. Sampling biases: definitions and descriptions of their effects on nitrate (2.1), 

ammonium (2.2), carbonaceous aerosols (2.3), and elemental and coarse mass (2.4). 

• Section 3. Chemical and physical forms of species: multiplier used to compute 

particulate organic matter from organic carbon (3.1), nitrate as ammonium nitrate (3.2), 

sulfate as ammonium sulfate (3.3), soil composition (3.4), coarse mass speciation (3.5), 

sea salt (3.6), and size distributions (3.7). 

• Section 4. Hygroscopic growth curves and scattering enhancement curves (f(RH)): 

hygroscopicity of species, assumed growth curves, and relative humidity ranges. 

• Section 5. Mass scattering efficiencies: theoretical discussion of mass scattering 

efficiencies (5.1), review of methods used for deriving efficiencies (5.2), survey of 

reported efficiencies (5.3), and derived values using IMPROVE data (5.4). 

• Section 6. Evaluation of methods for computing mass scattering efficiencies using the 

combined IMPROVE data set. 

• Section 7. Discussion of computed biases between measured and reconstructed 

scattering for various methods of calculating mass scattering efficiencies. 

• Section 8. Suggested refinements of IMPROVE equation. 

4
2. Sampling Biases

Before investigating the assumptions involved for each species included in the 

IMPROVE equation, it is of interest to review any sampling issues or uncertainties related to the 

measurements of these species. The IMPROVE network utilizes four separate sampling modules

to characterize the PM2.5 aerosol composition and total mass. Module A is equipped with Teflon®

filters used for analysis of PM2.5 mass by gravimetry and elemental composition by X-ray 

fluorescence (XRF). In module B, nylon filters are used to collect particles for ion analysis using

ion chromatography (IC). The module is preceded by a denuder designed to capture acidic gases.

Module C incorporates quartz filters for use in quantifying organic and light-absorbing carbon by 

thermal optical reflectance (Chow et al., 1993), and module D uses Teflon® filters to collect 

particles for gravimetric PM10 total mass measurements. 

Sampling artifacts, or biases, are not uncommon with filter sampling. An artifact is 

defined as any increase or decrease in the material being sampled that results in a positive or 

negative bias in the ambient concentration measured. Artifacts can occur due to contamination 

issues (contamination of the filter medium or of the cassettes during transport) or adsorption of 

gases on the filter medium during sampling or transportation and handling. These types of

artifacts are considered positive. Negative sampling artifacts arise from volatilization of gases

from disassociated particles on the filter or during handling after collection (McDade et al., 

2004). Sampling biases affect aerosol species differently, depending on the volatility of the 

particles being measured and the sampling technique being used; therefore applying corrections 

for sampling biases is not always straightforward. 

Corrections of IMPROVE data due to sampling artifacts have been applied as part of the 

routine IMPROVE methodology since the beginning of the network. We will briefly review the 

methodology IMPROVE applies for artifact correction and then discuss recent research about 

5
artifacts that are associated with specific species, such as nitrate, ammonium, and carbonaceous 

aerosols. 

Dynamic field blanks for both Teflon® and nylon filters are collected at all of the sites. 

These filters are treated like network filters in that they are placed in the sampler, but no sample 

air is drawn through them. Concentrations on Teflon® field blanks are statistically insignificant,

so no corrections are made for measurements on Teflon® filters. The concentrations measured on 

the nylon filter field blanks are subtracted from the measured filters. Monthly median artifact

corrections have been applied to the data since the change in IMPROVE data processing from 

seasonal to monthly in June 2002. These corrections are applied separately for each ion. Analysis 

of artifacts on the nylon filter suggests that sulfate ion artifacts are typically less than 10% of the

ambient concentration, and nitrate artifacts range between 10 and 20% (McDade et al., 2004). 

Further discussion of nitrate artifacts, including discussions on denuder efficiency will be 

presented in the next section. 

Quartz field blanks are also collected at all of the sites, but quartz after-filters are

collected at six sites only. The after-filters are placed behind the primary quartz filter and are

designed to capture organic gases (positive artifact). Negative artifacts for carbonaceous aerosols 

are assumed to be insignificant compared to positive artifacts, although other studies suggest

negative artifacts (volatilization) can be important (Turpin et al., 2000). Concentrations from the 

after-filters from the subset of sites are used to correct for positive artifacts from data at all of the 

sites. Monthly median values are also used for quartz filters, and each fraction of organic carbon

has a separate artifact correction. Typical artifacts for organic carbon can correspond to half of 

the reported ambient concentration (McDade et al., 2004). A more in-depth discussion of

carbonaceous aerosol artifacts will be presented in section 2.3.

6
2.1. Nitrate Sampling Issues 

The nylon filters in module B are used for analysis of particulate nitrate because the 

nitrate ion is retained by the filter when ammonium nitrate dissociates under conditions of high

temperature and low relative humidity. Preceding the filter is an annular denuder coated with

Na2CO3 and glycerin to remove gaseous nitric acid that would otherwise be retained by the nylon 

filter. The denuders are serviced once per year during annual maintenance. A positive artifact 

could occur due to degradation of efficiency of the denuder with time, allowing nitric acid to be 

collected on the nylon filter. Therefore characterizing the efficiency of the denuders has been a 

topic of recent study (Ashbaugh et al., 2004; Yu et al., 2005a). Daily samples were collected for

four consecutive weeks during different times of the year at IMPROVE sites, representing areas 

with significant seasonal nitrate contributions to fine mass (Brigantine National Wildlife Refuge 

NJ, Grand Canyon National Park AZ, San Gorgonio Wilderness CA, and Bondville IL). At each 

site a combination of IMPROVE ion modules with different denuder configurations were

operated. The denuder configurations were designed to compare freshly coated denuders to 

denuders that had been previously exposed to high levels of nitric acid. The combination also 

represented different coating options, from the typical IMPROVE coating to no coating. One 

module was operated with no denuder at all. For all the sites, no differences in nitrate 

concentrations due to the different denuder configurations were observed. The denuder 

configuration used regularly as a part of the IMPROVE network was found to be efficiently 

removing HNO3 (Ashbaugh et al., 2004). 

As part of the same study, the extraction efficiency of nitrate from the nylon filter was 

investigated (Yu et al., 2005a). Typically, basic solutions (e.g., sodium bicarbonate) are used to 

extract nitrate on nylon filters; however, this leads to interference from Na+

 ions during ion 

chromatography (IC). Instead, the use of deionized water for extraction of nylon filters has been 

7
investigated. Data from this study suggest that deionized water extraction with ultrasonification 

efficiently extracts nitrate and sulfate ions from nylon filters (Yu et al., 2005a) and successfully

avoids issues of Na+

 and NH4

+

 interference during IC analysis. 

While the previous discussions suggest that nitrate measurements and artifacts from 

denuder-nylon filter configurations are fairly well understood, the effects of nitrate loss on 

Teflon® filters remain a sampling issue and have important implications for measurements of 

fine mass concentrations by gravimetry. Hering and Cass (1999) investigated the effects of 

nitrate loss from the Federal Reference Method (FRM) measurements of PM2.5 mass on Teflon®

filters. They found that nitrate concentrations were 28% lower on Teflon® filters compared to 

nylon filters. Ammonium nitrate particles are volatile and disassociate to form nitric acid gas and 

ammonia gas, and this reaction is very sensitive to temperature, pressure, and relative humidity. 

Changes in these parameters during sampling can cause significant losses of nitrate and 

ammonium from the sampling media, as Teflon® filters do not retain nitric acid as nylon filters

do. Correcting mass concentrations for lost nitrate is difficult because knowledge of the history 

of the equilibrium of ammonium nitrate/nitric acid and ammonia gases at the temperature,

pressure, and relative humidity that the filter substrate experienced during the sampling period is 

required. Recent work by Frank (2005) suggests that applying a thermodynamic model can assist 

in reducing the uncertainties in fine mass due to nitrate volatilization. Diurnal and seasonal 

trends in nitrate loss were observed by Hering and Cass (1999), as well as Ashbaugh and Eldred 

(2004) who performed a similar study. The implications for the negative artifact of sampling 

volatile particles on Teflon® filters are obvious. Underreporting nitrate concentrations results in 

an overemphasis of nonvolatile species such as dust and sulfate when computing mass 

concentrations. Comparisons of reconstructed fine mass using the IMPROVE equation and 

8
gravimetric fine mass could be highly affected by significant underestimations of nitrate due to 

the volatilization of ammonium nitrate from the Teflon® filter used for gravimetric analysis. 

2.2. Ammonium Sampling Issues 

Although ammonium is not routinely analyzed as part of the IMPROVE procedures, it is 

important to review the sampling issues related to ammonium to understand measurements made

during special studies and by other researchers. The effects of ammonium loss from filter media

were studied as part of the nitrate loss study described in the previous section (Yu et al., 2005b). 

Losses of ammonium are affected by sample location (urban versus rural), meteorological 

sampling conditions (e.g., relative humidity, temperature), chemical composition of the sampled

aerosol, and gas-to-particle partitioning. Volatilization of ammonium nitrate can lead to 

ammonium loss from filter media, as can reaction of ammonium nitrate with strong acids. Also,

when ammonium nitrate is captured by the nylon filter, nitrate is bound by the filter but 

ammonium can volatilize. Two filter pack configurations were designed to study ammonium 

loss: denuded nylon-nylon (N-N) and denuded Teflon®-nylon (T-N). Ammonium loss from 

nylon filters was observed at the four sites where measurements were performed (ranging from ~ 

10 to 52%), suggesting a single nylon filter is not sufficient for capturing ammonium nitrate.

Results from the N-N and T-N filter pack systems suggest that the T-N configuration is as good 

as, or better than, the N-N configuration for ammonium retention (Yu et al., 2005b). Applying a

correction factor for the negative bias in ammonium would require estimates of ammonium loss 

at each site, which is a difficult task. Understanding the sampling biases for ammonium is very 

important, especially during special studies when NH4

+

 is measured, because its concentrations

are required in predicting the chemical form of aerosol species, which reduces the uncertainty in

reconstructed fine mass and light extinction. 

9
2.3. Carbonaceous Aerosol Sampling Issues 

Understanding sampling biases for carbonaceous aerosols is important for accurately

quantifying the concentrations of organic and light-absorbing carbon and has been the focus of

several studies. Before we discuss the sampling issues related to quantifying the concentrations 

of carbonaceous aerosols, we provide a brief review of the analytical technique used by the 

IMPROVE network. The Desert Research Institute (DRI) thermal/optical reflectance (TOR) 

technique used for IMPROVE (Chow et al., 1993) is one of the thermal methods available to 

analyze carbonaceous aerosols (also referred to as evolved gas analysis). Typically, for thermal 

methods the sample filter is heated in a step-wise manner in different atmospheres (e.g., oxygen 

or helium) and the volatilized carbon from the filter is detected. For each temperature regime a 

carbon concentration is determined, with the lower temperature concentrations summed for

organic carbon (O1, O2, O3, O4, and OP) and the highest temperature regime corresponding to 

what is typically referred to as elemental or light-absorbing carbon (E1, E2, and E3). A more

representative nomenclature would refer to this high temperature carbon as refractory carbon; 

because of its low volatility it does not evolve without oxidants at lower temperatures. The 

pyrolysis of organic carbon on the filter as the temperature is increased can contribute to the 

concentrations of refractory carbon. To account for this effect, the filter is monitored by the 

reflectance (or transmittance, as is used in thermal optical transmittance methods) of laser light,

which decreases when the filter darkens due to pyrolysis. Once oxygen is introduced into the 

chamber, the pyrolized carbon combusts, the filter lightens, and the laser light returns to its 

original intensity. After this point, the amount of carbon measured is associated with refractory 

(light-absorbing) carbon. The split between organic and light-absorbing carbon is based on the 

conditions for which this process occurs and is dependent on refractory properties of both 

pyrolyzed and light-absorbing carbon. Huebert and Charlson (2000) discuss several of the 

10
uncertainties associated with measurements of thermally defined carbonaceous aerosols, 

especially pointing out that these methods differ from one laboratory to another (e.g., 

temperatures regimes, rate of temperature changes, carrier gases in the chamber), making it very 

difficult to compare results. In section 5.3 we will discuss in more detail the issues related to the 

definitions of OC and LAC by this method. 

Turpin et al. (2000) review the difficulties inherent in measuring particulate organic 

carbon. Interference from gaseous and condensable organics can result in sampling errors due to 

interactions with the filter media. Positive artifacts arise from adsorption of organic gases onto 

the filter, and negative artifacts occur due to volatilization of particulate organics. They report 

artifact contributions to organic carbon mass ranging from -80 to +50%. Positive and negative 

artifacts occur simultaneously, which makes correcting for them difficult. Subramanian et al.

(2004) utilized several sampling approaches in an attempt to estimate these artifacts. Depending 

on the types of denuders and filter configurations, they found that positive artifacts could be

eliminated, or that artifacts may depend on sampling duration and probably also depend on 

sampling location. Huebert and Charlson (2000) state that systematic errors on the order of

±80% are possible using thermal methods. 

The IMPROVE network assumes negative artifacts are insignificant and only corrects for 

positive artifacts that are estimated from quartz after-filters collected at six sites (Chiricahua AZ, 

Grand Canyon AZ, Yosemite CA, Okefenokee GA, Shenandoah VA, and Mount Rainier WA) 

(McDade et al., 2004). The after-filters are placed directly behind the primary quartz filter. 

Quartz filter field blanks are collected at every site and are only used for identification of

problems. Field blank filters and the after-filters have similar concentrations; however, the afterfilters are used because they are exposed to the same air sample as the primary filter. Artifacts 

11
are determined separately for each fraction of organic and light-absorbing carbon from TOR 

analyses. McDade et al. (2004) evaluate the artifacts for O3 and E2, the more prominent

fractions of OC and LAC. The O3 artifact represents nearly half of the reported ambient 

concentration (higher for cleaner conditions), and the E2 artifact decreased to less than 10% of 

ambient concentrations after the IMPROVE sampler switched to version 2 in 2000. Although 

some spatial and seasonal differences are observed in the artifact estimates (the Okefenokee site 

has higher artifacts than the other sites, and summer appears to have higher O3 and E2 artifacts

than winter), the same monthly median artifact value is applied to the entire network. Based on

studies performed at the University of California, Davis, it appears that the positive artifact is 

due to saturation of the quartz filter from exposure to ambient organic acids in the atmosphere 

and would probably affect all filters sent to the field similarly. These results are substantiated by 

Subramanian et al. (2004), who found that quartz after-filters provided a robust estimate of 

positive artifacts for sampling durations of 24 hours, long enough for equilibrium to be achieved.

However, if some volatile organic compounds are being lost from the primary filter to the afterfilter, this correction could be too large. 

2.4. Issues Related to Elemental Species and Coarse Mass 

An X-ray fluorescence (XRF) technique is used to determine concentrations of trace 

elements with atomic mass number (Z) from 11 to 82 (Na-Pb). White et al. (2004) report on the 

uncertainties and detection limits for trace elements. Lower Z elements (e.g., Na, Mg) have much 

higher minimum detection limits (White, personal communication, 2004), and therefore

detectable amounts of those elements can be much more difficult to obtain. Other uncertainties in 

trace elements, especially those corresponding to coarse mode aerosols, arise due to uncertainties 

in the flow rates of the samplers. The size cut of the cyclone used to collect and separate PM2.5 

aerosols is very sensitive to the flow rate of the sampler. Variations in the flow rate (e.g., due to 

12
clogged inlets) can have significant impacts on the size range of aerosols being collected and 

termed “fine”. This issue can be important when interpreting fine mass versus coarse mass

because the soil contribution in the IMPROVE equation typically corresponds to the tail of

coarse mode mineral aerosols. The size distribution of the coarse mode aerosols can vary 

significantly, as shown by Hand et al. (2002). Over a four-month study in Big Bend National 

Park, the volume mean diameter of the coarse mode ranged from ~ 2 μm to 5 μm. The tail of this 

mode that is measured as part of the PM2.5 mass is obviously sensitive to the size distribution 

statistics of the coarse mode aerosols, which complicates any correction that may be applied to 

data with flow rate issues. The interpretation of coarse soil as fine soil has important 

consequences for reconstructed mass as well as reconstructed light extinction because the applied

optical properties are significantly different for each mode (as will be seen in section 5). 

3. Chemical and Physical Forms of Species in the IMPROVE Equation 

Aerosol species included in the reconstructed mass and IMPROVE reconstructed 

extinction equation are assumed to be in specific chemical forms and size ranges. In this section

we investigate whether these assumptions are appropriate. In particular we investigate the 

speciation of POM, sulfate, soil, nitrate, coarse mass, and sea salt. 

3.1. Particulate Organic Material (POM) 

Accurate estimates of particulate organic material (POM) are required in order to 

compute PM2.5 mass closure and to estimate optical properties such as light scattering. 

Estimating the contributions of organic carbon aerosol to mass or scattering requires an estimate 

of the total mass associated with organic carbon. The organic carbon multiplier (Roc) used to 

estimate particulate organic material (POM) is an estimate of the average molecular weight per 

carbon weight for organic carbon aerosol and takes into account contributions from other

elements associated with the organic matter, such as N, O, and H. It is highly spatially and 

13
temporally variable. It is impossible to determine which and how many elements are associated 

with POM without knowing the chemical formula of the organic compound, and it is common 

for ~ 20–40 % of organic aerosol mass to remain unidentified (Turpin and Lim, 2001). 

Because the organic compounds that compose POM are largely unknown, the approach 

for taking into account other elements in POM mass has been to apply an average multiplier. As

Turpin and Lim (2001) review, the often-used value of 1.4 dates back to samples collected in 

Pasadena CA in the early 1970s and 1980s (Grosjean and Friedlander, 1975; White and Roberts,

1977; Van Vaeck and Van Cauwenberghe, 1978; Countess et al., 1980; Japar et al., 1984). More 

recently, Turpin and Lim (2001) have reviewed several estimates of Roc in terms of the types of 

compounds known to compose POM, and that review will not be repeated here. However, to 

summarize their findings, they recommend a factor of 1.6 ± 0.2 for urban organic aerosols, a 

factor of 2.1 ± 0.2 for nonurban organic aerosols, and values ranging from 2.2 to 2.6 for samples

with impacts from biomass burning. Russell (2003) used Fourier Transform Infrared (FTIR) 

spectroscopy to estimate POM from the number of carbon bonds present and the molecular mass

of each functional group associated with the carbon bonds. Over 90% of Roc from estimates from

samples in northeastern Asia and the Caribbean were between 1.2 and 1.6, with mean values 

below 1.4. Values of Roc like those reported by Turpin and Lim (2001) and Russell (2003) are 

derived using techniques that depend on the functional groups and molecular compounds of

organic carbon aerosols. El-Zanan et al. (2005) used solvent extractions from archived 

IMPROVE filters at five sites to directly measure POM mass and carbon content and derive an

average Roc of 1.92 (range of 1.58–2.58). They also used a mass balance approach to estimate the 

Roc ratio using the IMPROVE data that resulted in an average value of 2.07 across the 

IMPROVE network. Other types of methods result in similar findings. Reconstruction of fine

14
mass and light scattering coefficients allow estimates of Roc to be derived, as was done in a twomonth study in Yosemite National Park by Malm et al. (2005a) where POM dominated the fine 

mass. They found that an Roc factor of approximately 1.8 allowed for closure in fine mass and 

light scattering coefficients for periods that encompassed both pristine conditions as well as the 

impacts of biomass burning and regional haze. Poirot and Husar (2004) found better agreement 

between measured and reconstructed fine mass by applying an Roc factor of 1.8 during a biomass 

burning event in the New England and mid-Atlantic state regions. 

Previous investigators have attempted to estimate Roc from comparisons of gravimetric 

and reconstructed mass; however, a number of issues arise with this type of analysis. These

issues originate from the uncertainties in the assumptions involved in the formulation of

reconstructed mass and have been discussed in the literature (Andrews et al., 2000; Rees et al., 

2004; Tanner et al., 2004; El-Zanan et al., 2005); therefore they will be mentioned only briefly

here. Some of the uncertainties inherent in reconstructed mass equations include the assumed 

form of aerosol species. For example, sulfate is typically assumed to be in the form of fully 

neutralized ammonium sulfate, although in reality the form of sulfate could be different (more 

acidic). Nitrate is assumed to be in the form of ammonium nitrate, and as we will show later, this 

assumption may be inappropriate under certain conditions. Water may be retained by 

hygroscopic species on the filters used to determine gravimetric PM2.5 mass. Soil mass requires 

an assumption of soil composition as defined by equation 2, and OC concentrations may be

affected by sampling artifacts and analytical issues regarding the method-dependent definitions

of organic and light-absorbing carbon. El-Zanan et al. (2005) performed sensitivity studies 

related to these issues and found that values of Roc varied between 1.74 and 2.2, although they 

15
believe the lower values are not realistic. They also found higher values of Roc determined from 

mass balance methods in the summer (2.33) compared to the winter (1.87). 

The approach implemented here for estimating Roc from IMPROVE data applies an 

ordinary least square (OLS) multiple-linear regression (MLR) analysis using 

PM2.5,i = a1[(NH4)2SO4]i+ a2[NH4NO3]i + a3[OC]i + a4[LAC]i + a5[soil]i + a6[sea salt]i (6) 

The results of the regression analysis for each site are presented in Appendix 1, including

a statistical summary of gravimetric mass and aerosol species mass concentrations (minimum, 

maximum, mean, and standard deviation). Also presented for each site is the fractional 

contribution of each species to gravimetric mass and a comparison between reconstructed and 

gravimetric mass. The statistically significant (95% level) regression coefficients for each site 

are reported in Table 1, with the mean and standard deviation of the coefficients listed in the 

final two rows. If the mass for each species (other than POM) is accurately estimated and the 

regression is unbiased, then the regression coefficient for a given species should equal 1. The 

regression coefficient for POM corresponds to the Roc factor. Scatter plots of gravimetric and 

reconstructed mass are presented in Appendix 1. Reconstructed mass has been computed using 

equation 1 and using the regression coefficients derived from equation 6. 

Table 1. Statistically significant (95%) regression coefficients using the ordinary least square multiple-linear 

regression analysis (equation 6). Site code is in the first column. The remaining columns correspond to 

coefficients associated with ammonium sulfate (AS), ammonium nitrate (AN), particulate organic matter

(POM), light-absorbing carbon (LAC), soil, and sea salt, respectively. Insignificant coefficients are replaced 

with “.”.

Site AS AN POM LAC Soil Sea Salt

ACAD 1.23 . 1.85 . 1.40 1.02

ADPI 1.23 0.49 1.67 . 1.68 .

AGTI 1.05 0.67 1.63 . 1.09 .

AREN 1.08 0.80 1.70 2.36 0.50 .

BADL 1.14 0.65 1.98 . 1.06 .

BALD 1.29 0.75 1.76 . 1.18 .

BAND 1.21 0.54 1.52 . 1.12 .

BIBE 1.08 0.74 1.84 . 1.02 .

BLIS 1.25 0.54 1.74 . 1.06 .

16
B

LMO1.00 1.09 1.27. 1.09.

BOAP1.18 0.68 1.71 0.65 1.30.

BOND0.98 1.01 1.28. 1.17.

BOWA1.18 0.84 1.88. 1.32.

BRCA1.250.501.401.161.41.

BRET1.16 0.70 1.53. 1.51.

BRID1.31. 1.73. 1.22.

BRIG1.08 0.54 1.99. 1.18 0.95

BRLA0.97. 1.91. 1.52.

BRMA1.04. 1.42. 1.10.

CABA1.17 0.56 1.16 2.52 1.10 1.19

CABI1.46. 2.05. 1.19.

CACO1.25 0.51 1.62. 1.31 0.82

CACR1.11 0.50 1.67. 1.06.

CADI1.22 0.63 1.40 2.77 1.05.

CANY1.10 0.55 1.74. 1.21.

CAPI1.04 0.50 2.07. 1.21.

CEBL1.11 1.14 2.07. 1.11.

CHAS1.17. 1.44 0.90 0.99 0.59

CHER1.11 0.98 1.43. 1.57.

CHIR1.28 0.79 1.36 1.59 1.15 0.88

CLPE1.25. 1.71. 1.38.

COGO1.10 0.57 1.63. 1.10.

COHI1.21 0.63 1.92. 1.68.

COHU1.01 0.33 1.71. 1.16.

CORI1.33 0.60 1.59. 1.14 0.95

CRES1.00 0.98 2.16. 1.14.

CRLA1.68. 1.68 0.48 1.10 1.10

CRMO1.40 0.71 1.96. 1.25.

DENA1.39. 1.89. 0.85 1.13

DEVA1.05 0.70 1.65. 1.25.

DOME0.95 0.81 1.77. 1.36.

DOSO1.16. 1.58. 1.00.

ELDO1.13 0.82 1.44. 1.05.

ELLI1.070.972.07.1.10.

EVER1.00. 1.44 4.40 1.20.

FLAT1.33. 1.74. 1.23.

FOPE1.10 0.49 2.06. 1.27.

GAMO1.20. 1.66. 1.29.

GICL1.22 1.79 1.54. 1.09.

GLAC1.16 0.93 1.58 1.43 1.17.

GRBA1.45 0.58 1.70. 1.35.

GRCA1.29. 1.36 4.66 1.27.

GRGU1.10. 1.65 3.90 0.99.

GRRI1.04 0.96 1.73. 1.34.

GRSA1.34. 1.98. 1.16.

GRSM1.23. 1.71. 1.02.

17
GUM

O1.14. 1.66. 1.02 1.96

HALE1.01 2.05 1.45. 0.97.

HAVO1.61. 1.45. 1.15.

HECA1.01 0.69 1.52. 1.29.

HEGL1.09 0.69 1.75. 1.19.

HILL1.36. 2.04. 1.42.

HOOV1.37. 2.08. 1.59.

IKBA1.12 0.33 1.86. 1.61.

INGA1.12. 1.36. 1.27.

ISLE1.00 0.82 1.67. 0.72 0.51

JARB1.23 0.99 1.49. 1.29.

JARI1.22 0.52 1.66 1.39 0.73.

JOSH1.25 0.74 2.00. 1.03.

KAIS1.11 1.03 1.81. 1.27.

KALM2.25. 2.16. 1.64.

LABE0.86 1.48 1.72. 1.41 0.85

LASU1.10 1.01 1.54. 1.03.

LAVO1.52 0.43 1.41 1.42 1.17.

LIGO1.24. 1.75. 1.07.

LIVO1.26 0.73 1.79. 1.17.

LOST1.16 0.93 1.80. 1.37.

LYBR1.10 0.37 1.63. 1.02.

MACA1.01 0.22 1.81. 1.08.

MELA1.08 0.80 1.84. 1.16.

MEVE1.32 1.27 1.45. 1.00.

MING1.27 0.85 1.45. 1.14.

MKGO1.39 0.66 1.38. 0.40.

MOHO1.36. 1.77. 1.11 1.23

MOMO1.08. 2.04. 1.35.

MONT1.48. 1.74 11.08 2.21.

MOOS1.13 0.62 1.66 0.68 1.50 1.04

MORA1.30 0.76 1.59 1.55 0.90 1.14

MOZI1.25. 1.70. 1.11.

NEBR1.21 0.66 2.06. 1.20.

NOAB0.82. 1.26 4.98 1.30.

NOCA1.62. 1.48. 1.09 1.60

NOCH.. 1.71. 2.64.

OKEF1.12. 1.44 2.51 1.01 0.62

OLTO1.15 0.97 1.29 0.97 1.01 0.66

OLYM1.15 0.96 1.73. 1.36 0.80

PASA1.54. 1.53. 1.21 2.85

PEFO1.35 0.77 1.76 2.13 1.18.

PHOE1.28 0.68 1.29 0.78 1.13.

PINN1.32 0.64 1.66 0.89 1.28 1.15

PMRF1.22 0.54 1.36. 1.02.

PORE1.28 0.74 1.93. 1.26 1.04

PRIS0.93 1.00 1.30. 1.19 0.62

18
PUS

O1.23 0.76 1.35 0.82 1.07 1.21

QUCI1.30 0.64 1.95. 0.40.

QURE1.05 0.28 1.63 2.12 0.87.

QUVA1.17 0.79 2.00. 1.37.

RAFA1.39 0.95 1.57. 0.96 1.20

REDW1.23 1.59 2.16. 1.25 0.92

ROMA1.19. 1.60. 1.20 0.91

ROMO1.27. 1.71. 1.34.

SACR1.30 0.97 1.45. 1.55 2.80

SAFO1.08 0.99 1.63. 0.80.

SAGA1.12 0.60 1.57. 0.91.

SAGO1.00 0.91 1.27. 1.07 1.46

SAGU1.25 0.26 1.50 1.29 1.26.

SAMA1.17. 1.58. 1.42.

SAPE1.08. 1.57. 1.23.

SAWE1.30. 1.50. 1.29.

SAWT1.84. 1.74. 1.20.

SENE1.16 0.70 1.81. 0.72.

SEQU1.29 0.91 1.35 2.93 0.98.

SHEN1.11. 1.97. 0.87.

SHRO1.22. 1.74. 1.10.

SIAN1.10 0.38 1.37 2.25 1.37.

SIKE1.18. 1.53. 1.15.

SIME1.43. 1.28. 1.32 1.16

SIPS1.04. 1.69. 1.04.

SNPA1.33 0.64 1.71. 1.23 1.23

SPOK1.24 0.71 1.66. 1.28.

STAR1.61. 1.11. 1.70.

SULA1.58. 1.63. 1.15.

SWAN1.13. 1.75. 1.33.

SYCA1.43 0.44 1.59. 1.10.

TALL1.05 0.84 1.12 3.34 1.51.

THBA1.00 0.77 1.84. 1.04.

THRO1.13 0.81 1.85. 1.01.

THSI1.75. 1.28. 1.52.

TONT1.17 0.67 1.92. 1.09.

TRCR1.59.1.91.0.62.

TRIN2.08. 1.16. 1.15 1.03

TUXE2.20. 1.91 3.09 0.62 1.05

ULBE0.98 0.91 1.99. 1.17.

UPBU1.10 0.67 1.94. 0.88.

VIIS0.75 2.34 1.44. 1.31.

VILA1.07 1.02 1.27. 0.80.

VOYA1.22 1.01 1.83. 1.32 0.89

WASH1.16 0.82 1.70 0.87 1.04 0.82

WEMI1.41. 1.68. 1.21.

WHIT1.23 1.04 2.19. 1.23.

19
WHPA 1.13 0.96 1.57 . 1.09 .

WHPE 1.05 . 1.66 0.87 1.31 .

WHRI 1.32 . 1.74 . 1.27 .

WICA 1.06 0.55 1.93 . 1.17 .

WIMO 1.23 0.80 1.55 . 1.18 .

YELL 1.12 0.62 1.54 2.57 1.30 .

YOSE 1.15 0.74 1.68 . 1.26 0.99

ZION 1.34 0.64 1.63 . 1.28 .

Avg 1.22 0.78 1.66 2.28 1.18 1.12

Std Dev 0.22 0.32 0.24 2.00 0.26 0.51

The mean values of Roc derived from equation 6 (see Table 1) are shown as a summary in

Figure 1. There are clear spatial trends in the Roc factor. The highest coefficients of 1.8–2.0+ are 

just east of the Rocky Mountain range and may be reflective of wild and prescribed fire activity 

to the west of this region. Both Malm et al. (2005a) and Poirot and Husar (2004) derived Roc

factors near 1.8 at sites with air masses influenced by aged biomass smoke, and higher Roc values 

corresponding to biomass burning were reported by Turpin and Lim (2001). Three of the four 

sites in Alaska (not shown) also have coefficients near 1.9, with the exception of Simeonof 

National Wildlife Refuge on the Alaskan peninsula. Other remote locations have Roc values near 

1.8. Coefficients ranging from 1.6 to 1.8 are found around most of the United States, with 

distinct regions having coefficients less than 1.6. Regions in the Northwest, interior Midwest,

and Northeast are in this category. 

20
Figure 1. Mean values of Roc multiplier derived from an ordinary least square multi-linear regression 

analysis (equation 6). 

The average coefficient over all sites is Roc = 1.66 ± 0.24, with all 158 sites having 

significantly valid coefficients. On a seasonal basis the coefficients do not vary significantly, as 

seen by the mean and standard deviation values presented in Figure 2. The mean summer value 

(Roc ~ 1.7) is near the average value of 1.66, while the lowest values were derived during winter 

(Roc ~ 1.5). Some seasonality in Roc is expected, with higher values in summer due to 

photochemical reactions from warmer temperatures and higher solar insolation. Results from 

these analyses suggest that the existing Roc value of 1.4 in the IMPROVE equation is probably 

too low. Based on estimates reported from other studies and the analysis performed here, we 

recommend an Roc value in the range of 1.7–1.8. 

21
Figure 2. Mean seasonal values of Roc for all sites. Standard deviations are also shown as upper and lower 

error bars. 

As will be discussed in section 5, the particle density is often needed to compute optical 

properties. Inorganic particle densities for species such as ammoniated sulfate are well known; 

however, the density of organic aerosols can range from 1 to 2 g cm-3 or higher, depending on 

the organic composition. Because the composition of organic aerosol is largely unknown, the 

value of organic density has large uncertainties. Turpin and Lim (2001) review densities of 

particle-phase organic compounds and summarize them by compound class. The values they 

report range from 0.77 to 1.64 g cm-3. Values near 1.2 g cm-3 were found for the urban areas of

the Los Angeles Basin, West Los Angeles, downtown Los Angeles, Pasadena, and Roubidoux 

CA (Rogge et al., 1993). However, higher values of organic aerosol density would be expected 

with increased concentrations of carboxylic acids and/or polycyclic aromatic hydrocarbons, or in 

the presence of significant concentrations of amines and amino acids (Turpin and Lim, 2001). 

Investigating mass closure studies can assist in understanding if a particular organic density is 

appropriate, particularly when organic mass fractions are significant. 

22
During the Aerosols99 campaign, Quinn et al. (2001) performed closure studies of mass

and light extinction from cruise-based measurements from Virginia to South Africa. Organic 

carbon was collected using a three-stage impactor and analyzed with thermographic methods. 

Particulate organic material (POM) was computed by assuming an Roc factor for North American 

air masses and a value of 2.1 for all other air masses (Turpin and Lim, 2001). POM was assumed 

to be nonhygroscopic and distributed as non-sea-salt sulfate and the organic density was 1.4 g 

cm-3. The highest submicron POM mass fractions were measured off the coast of North America

(~ 15%) and for biomass burning air masses off the coast of Africa (15–20 %). For both of these 

regions the submicron mass closure was within experimental uncertainty, as was the measured 

and computed light scattering coefficient. 

During INDOEX (Indian Ocean Experiment), Quinn et al. (2002b) used a similar method

to the Aerosols99 campaign, but collected three samples with a seven-stage impactor to obtain 

OC size distributions. An Roc value of 1.6 was applied to all samples. Organics were assumed to 

be nonhygroscopic and an organic aerosol density of 1.4 g cm-3 was applied. The highest 

submicron POM mass fractions were obtained for Arabian air masses (~ 15%). Both calculated

mass and light scattering coefficients agreed with measured values within experimental 

uncertainty.

During the ACE-Asia (Aerosol Characterization Experiment in Asia) study, Quinn et al. 

(2004) used a seven-stage impactor to collect organic carbon and computed POM assuming an 

Roc of 2.1 in marine regions and 1.6 elsewhere. POM was assumed to be nonhygroscopic and a 

density of 1.4 g cm-3 was applied. At most, the POM submicron mass fractions were

approximately 20% and calculated and measured mass and light scattering coefficients agreed 

within experimental uncertainty. 

23
Hand and Kreidenweis (2002) used differential mobility analyzer (DMA), optical particle

counter (OPC), and aerodynamic particle sizer (APS) volume distributions to compute mass

concentration during the Big Bend Regional Aerosol and Visibility Observational (BRAVO)

study. Closure between measured and reconstructed total mass was found between these data, 

assuming an Roc of 1.4 and an organic density of 1.4 g cm-3. On average, POM was 22% of the 

PM2.5 mass. Good agreement between micro-orifice uniform deposit impactor (MOUDI) size 

distributions and DMA volume distributions converted to mass distributions (as a function of

aerodynamic diameter) was also found. 

Ames et al. (2000) computed mass concentrations from OPC volume distributions during 

the Southeastern Aerosol and Visibility Study (SEAVS) in the Great Smoky Mountains National 

Park and found good agreement with measured mass concentrations when assuming Roc = 1.4 

and an organic density of 1.4 g cm-3. Dick et al. (2000) also applied an organic density of 1.4 g 

cm-3 during SEAVS. 

Although the above studies did achieve closure with the assumptions made about organic 

aerosols, it is difficult to glean too much information about organics from closure studies when 

they are not the dominant aerosol type, because the integrated mass or optical properties will be 

less sensitive to what is assumed for organic properties. Very few ground-based closure studies 

exist with a carbon-dominated aerosol, except during extreme smoke events. During a field study 

in Yosemite National Park, the submicron organic mass fraction was 69% on average (Malm et

al., 2005a). McMeeking et al. (2005) used DMA and OPC size distributions in successful closure 

studies of mass concentrations and light scattering coefficients assuming an Roc of 1.8 and 

organic density of 1.4 g cm-3. Similar agreement was found by Malm et al. (2005a) during the 

24
same study, suggesting these estimates were reasonable for organic aerosol properties at this 

location.

Organic aerosol densities typically applied by researchers tend to vary from 1 to 2 g cm-3, 

depending on the application and type of organics (e.g., urban, rural, smoke). Since there are 

large uncertainties on organic compounds themselves (20–40% of organic mass is unidentified, 

Turpin and Lim, 2001), there is also high uncertainty in its density. Furthermore, direct 

measurements of aerosol density do not exist, so these values have to be inferred from other 

measurements. Because this number is not well known, investigators often apply a reasonable 

number. A value of ρ = 1 g cm-3 previously has been used (e.g., Sloane et al., 1991; Zhang et al., 

1993; Neusüß et al., 2002; Adam et al., 2004), as well as ρ = 1.4 g cm-3 (e.g., Ames et al., 2000; 

Dick et al., 2000; Hand, 2001; Quinn et al., 2001, 2002b, 2004; Hand et al., 2002; 2004; Gao et 

al., 2004; McMeeking et al., 2005). Currently a value of ρ = 1.2 g cm-3 often is being applied that 

corresponds to a value recommended by Turpin and Lim (2001) for urban organic aerosol 

measurements in Los Angeles (e.g., Lowenthal et al., 2000; McMurry et al., 2002; Wang et al., 

2002; Fridlind and Jacobson, 2003; Gasparini et al., 2004; Stanier et al., 2004; Zhang et al., 

2005). Reid et al. (2005) report higher densities for specific organic aerosol types, such as

smoke, from various investigators in a review of biomass burning properties. Values between 

0.79 and 1.35 g cm-3 were reported by Stith et al. (1981) for two temperate fires. Densities of 1 g 

cm-3 and 1.53 g cm-3 were reported by Radke et al. (1988, 1991) and Martins et al. (1996), 

respectively, for temperate forest fires, and Reid and Hobbs (1998) report a value of 1.35 g cm-3

for fires in the Amazon. From these estimates, Reid et al. (2005) suggest the average density of 

dry smoke particles range from 1.2 to 1.4 g cm-3. 

25
3.2. Nitrate 

Nitrate is an important seasonal contributor to particulate matter at many locations in the 

United States. Nitrate is assumed to be present in the fine mode as ammonium nitrate; however, 

it can be present in the coarse mode also. Field studies at several IMPROVE monitoring sites 

investigated the speciation and size of aerosol nitrate using a size-resolved impactor (MOUDI) 

and have shown that nitrate is often present as coarse mode nitrate. Lee et al. (2004a) computed 

the speciation of nitrate by first calculating leftover ammonium from (NH4)2SO4. Excess 

ammonium is then associated with nitrate as NH4NO3, and any excess nitrate not associated with 

ammonium is determined. Sodium is first combined with Cl-

 as sea salt, and any excess sodium

is combined with excess nitrate (NaNO3). If additional nitrate is left over, it is associated with

crustal compounds such as Ca+2 or Mg+2 (Ca(NO3)2 or Mg(NO3)2). 

NH4NO3 forms from the reaction of gas phase ammonia and nitric acid and is more 

favorable in regions with high ammonia and nitric acid concentrations and low sulfate 

concentrations. The equilibrium reaction producing aerosol-phase NH4NO3 is sensitive to small

changes in temperature and relative humidity that can shift the equilibrium to the gas phase. 

However, the reaction of gas phase nitric acid with sea salt or calcium carbonate is not an 

equilibrium reaction and results in nitrate being transferred to the aerosol phase and associated 

with coarse mode particles. 

Two estimates of fine mode nitrate for the three forms discussed above have been 

computed by summing the nitrate in the MOUDI size bins corresponding to Dp < 1 and Dp < 3.2 

μm (although the MOUDI does not have a 2.5 μm size bin, we assume that the fine mode

corresponding to Dp < 3.2 μm most closely represents the IMPROVE PM2.5 measurement). Fine 

mode nitrate estimates are presented in Figures 3a and 3b for Dp < 1 and Dp < 3.2 μm,

respectively. Coarse mode nitrate is computed in a similar manner for Dp > 1 μm and is 

26
presented in Figure 3c. The size of the pie charts in Figure 3 represents the total nitrate

concentration in that size range (in these figures, a doubling of the pie size corresponds to 8 

times the concentration), and the total nitrate concentration in that size mode is listed beside its 

chart. 

Figure 3. (a) Fine mode (Dp < 1 μm) nitrate speciation of NH4NO3, NaNO3 and Ca(NO3)2 at several

IMPROVE sites. The size of the pie chart reflects the magnitude of the concentration of total nitrate in this

size mode, which is listed under each chart. (b) Same as (a) but for Dp < 3.2 μm. (c) Same as (a) but for coarse

mode (Dp > 1 μm). 

NH4NO3

NaNO3

Ca(NO3)2

76%

23%

1%

100%

4%

1%

96%

100%

43% 56%

33%

67%

67%

13%

20%

500 ng/m3

Great Smoky Moutains

(summer)

27 ng/m3

Bondville

(winter)

3646 ng/m3

San Gorgonio

(April)

2389 ng/m3

Brigantine

(fall)

630 ng/m3

Yosemite

(summer-fall)

450 ng/m3

Big Bend

(summer)

408 ng/m3

Grand

Canyon

(spring)

233 ng/m3

27
NH4NO3

NaNO3

Ca(NO3)2

71%

26%

3%

87%

7%

2%

1%

63%

63%

2%

61%

38%

14%

86%

35%

35%

6%

500 ng/m3

26%

43%

31% Great Smoky Moutains

(summer)

102 ng/m

Bondville

(winter)

3930 ng/m3

San Gorgonio

(April)

2993 ng/m3

Brigantine

(fall)

953 ng/m3

Yosemite

(summer-fall)

711 ng/m3

Big Bend

(summer)

640 ng/m3

Grand

Canyon

(spring)

606 ng/m3

28
NH4NO3

NaNO3

Ca(NO3)2

64%

6%

69%

2%

30%

32%

24%

6%

17%

44%

12%

91%

9%

29%

77%

64%

24% 36%

64%

6%

500 ng/m3

Great Smoky Moutains

(summer)

389 ng/m3

Bondville

(winter)

453 ng/m3

San Gorgonio

(April)

941 ng/m3

Brigantine

(fall)

651 ng/m3

Yosemite

(summer-fall)

586 ng/m3)

Big Bend

(summer)

256 ng/m3

Grand

Canyon

(spring)

631 ng/m3

The data presented in Figure 3a demonstrate that fine mode (Dp < 1 μm) nitrate is not 

always speciated as ammonium nitrate. For example, during summer in Big Bend National Park 

TX, only 1% of fine mode nitrate was in the form of ammonium nitrate, and during winter in 

Bondville IL, ammonium nitrate accounted for 76% of the nitrate species in the fine mode while 

Ca(NO3)2 accounted for 24%, even though the fine mode total nitrate concentrations in Bondville 

are considerably higher than the other sites. During spring in Grand Canyon National Park AZ, 

NH4NO3 was 67% of fine mode nitrate, and during summer at Great Smoky Mountains National 

Park TN, it was only 33%. However, in both San Gorgonio National Park CA (spring) and 

Yosemite National Park CA (summer), the fine mode nitrate was completely speciated as 

ammonium nitrate, and in Brigantine NJ (autumn), it was nearly all ammonium nitrate (96%). 

29
For the sites where ammonium nitrate was not the dominant form of nitrate in the fine mode, the 

contribution of nitrate ion to PM2.5 mass concentration was less than ~ 20%. 

Coarse mode speciation of nitrate at these sites (see Figure 3c) reflects the reaction 

pathways of nitric acid with mineral aerosols discussed earlier. For example, at several of the 

sites (Brigantine NJ, Yosemite National Park CA, and Big Bend National Park TX), coarse mode

nitrate was associated with sea salt as NaNO3. At Big Bend National Park TX, nitrate had 

replaced Cl-

 in sea salt (NaNO3) (Lee et al., 2004a), and MOUDI data showed that nitrate and 

sodium had similar size distributions. However, at other sites nitrate was associated with crustal 

material (Ca(NO3)2) (Bondville IL, Great Smoky Mountains National Park TN, and Grand 

Canyon National Park AZ). 

At many of the sites, the nitrate concentrations in the coarse mode were higher than in the 

fine mode. For example, data from Grand Canyon National Park (spring) indicate that 

concentrations of nitrate in the coarse mode were almost three times higher than nitrate in the 

fine mode, and roughly 14 times higher in Great Smoky Mountains National Park. Nitrate 

concentrations at Yosemite National Park were comparable for both modes, similarly for

Brigantine NJ. The only sites where fine mode nitrate mass was considerably higher than coarse

mode nitrate mass were Bondville IL and San Gorgonio CA. 

The two estimates of fine mode nitrate for Dp < 1 μm and Dp < 3.2 μm in Figures 3a and 

3b, respectively, were computed to demonstrate the importance of the size cut of the impactor on 

the interpretation of nitrate speciation. For example, shifting the fine mode cutpoint from 1 to 3.2 

μm for data from the Brigantine NJ site results in the speciation of nitrate changing from

predominantly NH4NO3 (96%) to 63% NH4NO3 and 35% NaNO3 because more of the coarse 

mode tail is being included (see Figures 3a–c). Similar behaviors are observed at Grand Canyon 

30
National Park AZ, Big Bend National Park TX, and Great Smoky Mountains National Park TN, 

where the speciation of fine mode nitrate changes significantly because of the inclusion of coarse 

mode nitrate mass. 

Determining or predicting the form of nitrate is not straightforward; it depends on 

meteorological parameters such as temperature and relative humidity, as well as the presence and 

acidity of other species such as sulfate. Also, the amount of coarse mode nitrate being attributed 

to the fine mode also depends on the cutpoint of the impactor, which depends on the accuracy of 

the flow rate. However, for data gathered at the sites shown in Figures 3a–c, when fine mode

total nitrate concentrations were roughly greater than 0.5 μg m-3, ammonium nitrate contributed 

over 70% of the observed total nitrate in the fine mode. Obviously, the form of nitrate is very 

important in accurately accounting for contributions of nitrate to fine mass and to light

extinction—optical properties of fine mode ammonium nitrate (as well as hygroscopic 

properties) are quite different from coarse mode sodium nitrate or calcium nitrate. Accurately

estimating the speciation of nitrate would require measurements of fine mode ammonium and 

speciation of coarse mass. Because these measurements are not currently available at all sites,

and based on the previous discussion that suggests higher levels of nitrate in the fine mode are

probably associated with NH4NO3, we recommend that nitrate remains in the form of ammonium

nitrate in the IMPROVE formulation.

3.3. Sulfate 

Elemental sulfur and the sulfate ion are measured as part of the IMPROVE network. To 

assess the contributions of sulfate to fine mass or light extinction, the molecular form of sulfate 

must be known. The IMPROVE algorithm assumes that sulfate is in the form of fully 

ammoniated sulfate ((NH4)2SO4). The molecular form of sulfate depends on its degree of 

neutralization, for which routine measurements of the ammonium ion are required. The

31
IMPROVE network does not measure the NH4

+

 ion, and as discussed in section 2.2, there are 

inherent sampling issues with respect to ammonium measurements. The molar ratio of

ammonium to sulfate ranges from 2 for fully neutralized ammonium sulfate to 0 for sulfuric acid. 

Many authors have shown that aerosol sulfate acidity can vary temporally and spatially. More 

acidic aerosols have been measured at many locations around the United States (e.g., Gebhart et 

al., 1994; Liu et al., 1996; Day et al., 1997; Lowenthal et al., 2000; Lefer and Talbot, 2001; 

Quinn et al., 2002a; Chu, 2004; Hogrefe et al., 2004; Schwab et al., 2004; Tanner et al., 2004; 

Zhang et al., 2005). Special studies at IMPROVE sites have also demonstrated variability. At 

Great Smoky Mountains National Park during the summer of 1995 (SEAVS), ammonium to

sulfate molar ratios of 1.1 were observed (Hand et al., 2000). During the BRAVO study at Big 

Bend National Park, Lee et al. (2004a) found ammonium to sulfate molar ratios of 1.54 on 

average. Also, on average, fully neutralized ammonium sulfate was observed at Yosemite 

National Park during the summer of 2002 (Malm et al., 2005a). Seasonal and spatial variations in 

aerosol acidity complicate recommendations of a single form of ammoniated sulfate, and regular 

measurements of the NH4

+

 ion at IMPROVE sites do not exist. 

The coefficient (a1) multiplying ammonium sulfate in the regression model described in

section 3.1 provides some indication of the role of sulfate in reconstructed fine mass. A 

coefficient greater than 1 suggests that water mass retained on the gravimetric filter is associated 

with sulfate, because ammonium sulfate is assumed in the regression and it has the highest 

molecular weight of any ammoniated sulfate species. Gravimetric fine mass is measured from 

Teflon® filters that are weighed at a relative humidity of ~ 40%; therefore an acidic sulfate (or 

other) species could be responsible for retained water on the filter. The amount of residual water 

on the filter is a function of the relative humidity at which the filter is weighed and the RH 

32
history to which the aerosol is exposed. Issues related to water on the filter cannot be avoided 

because acidic sulfate species retain water to very low relative humidity. On average, the MLR 

coefficient associated with sulfate was greater than 1 at almost all of the IMPROVE sites (see 

Table 1). Others have found similar results; for example, Andrews et al. (2000) suggested that up

to half of the discrepancy between measured and reconstructed fine mass could be accounted for

by water uptake on the Teflon® filter by sulfate species during the SEAVS study in Great Smoky 

Mountains National Park. As previously stated, it is impossible to know the form of sulfate to 

assume in the IMPROVE equation because ammonium is not measured; therefore we 

recommend that ammonium sulfate remain as the form of sulfate in the IMPROVE equation. 

3.4. Soil Composition 

The composition of soil varies as a function of soil taxonomy at a given location. Soil

taxonomy charts show variability across the United States with soil type, with the southwestern 

United States differing from the eastern United States, and many finer differentiations beyond 

that. Soil composition can also vary due to long-range intercontinental and transcontinental 

transport. Several studies have shown that contributions of Asian dust to U.S. fine soil 

concentrations can be significant episodically, affecting aerosol concentrations and mineralogy 

across the United States (e.g., VanCuren and Cahill, 2002; Jaffe et al., 2003; VanCuren, 2003). 

Transport of North African dust to the United States occurs regularly, affecting aerosol

concentrations in the Virgin Islands, the eastern and southeastern United States (Perry et al., 

1997), and even as far west as Big Bend National Park (Hand et al., 2002). Due to the spatial and 

temporal variability in dust sources, it is very difficult to characterize an appropriate aerosol soil 

composition for each measurement site. Soil mass concentrations are therefore estimated by a 

general method that sums the oxides of elements that are typically associated with soil (Al2O3, 

33
SiO2, CaO, K2O, FeO, Fe2O3, TiO2), with a correction for other compounds such as MgO, Na2O,

H2O and carbonates (Malm et al., 1994b).

Elemental concentrations are multiplied by factors that represent the mass concentrations 

of the oxide forms. Several corrections are also made. Molar concentrations of iron are assumed 

to be equally abundant in the forms of FeO and Fe2O3. Potassium has a nonsoil contribution from 

biomass smoke, so the soil potassium is estimated by using Fe as a surrogate, or [K] = 0.6[Fe]. 

The formula for computing soil concentration is given in equation 2 and has been divided by 

0.86 to take into account missing compounds. Results from the multiple linear regression 

technique described in section 3.1 (see Table 1 and Figure 4) suggest that, on average for all the 

IMPROVE sites, the soil composition is being underestimated by roughly 20%. Spatial 

variability is observed in the soil coefficient from the MLR method, with soil concentrations in 

the western United States being underestimated more than in the Midwest and eastern United 

States. An area of the country from Michigan south through the Ohio River valley appears to 

have overestimated soil concentrations by 10–30%. Although the results from the MLR method 

suggest an underestimation of soil mass on average, the lack of measurements of soil 

composition around the United States and the additional complication of contributions of longrange (Mexico, Asia, and Africa) soil at many U.S. sites do not allow for suggestions for 

refinements to the soil formula at this time. 

34
Figure 4. Mean values of the soil coefficient from an ordinary least square multi-linear regression analysis 

(equation 6). 

Soil multiplier

3.5. Coarse Mass 

Coarse mass is the difference between PM10 and PM2.5 mass concentrations measured

gravimetrically and is not routinely analyzed for speciation; therefore the IMPROVE equation 

treats all of coarse material as nonhygroscopic dust. A few short-term special studies at national 

parks during which coarse mass speciation and aerosol mass size distributions were measured 

have shown that coarse mass consists of a substantial amount (~ 40–50%) of carbonaceous 

material and inorganic salts such as calcium and sodium nitrate (Malm and Day, 2000; Hand, 

2001; Lee et al., 2004a,b). To investigate the speciation of coarse mass, a coarse particle 

speciation network was initiated at nine IMPROVE sites in 2003. Sites were selected to be 

representative of the continental United States and were operated according to IMPROVE 

35
protocol analytic procedures for a period of one year, with additional A, B, and C modules 

operating with PM10 inlets. Preliminary results from one year of data from the sites suggest that 

over 50% of coarse mass is soil (as defined by the IMPROVE soil equation), with soil 

contributions higher in the western than eastern half of the country. Particulate organic material 

is the next highest contributor (15–35%) with fairly homogeneous spatial distribution. Nitrate is 

next highest contributor (5–15%), probably associated with sea salt on the coast and dust in the 

inner and western areas of the country. Sulfate is a minor contributor to coarse mass, although at 

coastal regions in the Northeast it averaged up to 10%, probably related to sea salt. The optical, 

physical, chemical, and hygroscopic properties of coarse mode aerosols can vary significantly, 

depending on the composition and size distribution of coarse mass, and could have important

implications to total scattering, because in some remote areas contributions to total scattering 

from the coarse mode scattering could be comparable to fine mode contributions. For example,

there were several periods during the BRAVO study in Big Bend National Park when up to 80% 

of total scattering was attributable to the coarse mode (Hand, 2001; Hand et al., 2002). 

Several special studies at IMPROVE sites have suggested that the coarse mode aerosol 

composition can affect the fine mode mass because often the tail of the coarse mode is measured

as part of the fine mode. For example, during the BRAVO study at Big Bend National Park, sizesegregated MOUDI impactor measurements (Lee et al., 2004a), as well as particle size 

distribution measurements (Hand et al., 2002), suggested that a 1 μm aerodynamic diameter was 

a much more realistic separation between the fine and coarse mode. Similar results were found in 

Yosemite National Park, San Gorgonio CA, Grand Canyon AZ, Brigantine NJ, and Great Smoky 

Mountains National Park (Lee et al., 2004b). The use of a PM2.5 size cut for IMPROVE samplers 

results in a substantial fraction of the tail of the coarse mode distribution in fine mode samples,

36
and this can vary significantly with a variable sampler flow rate that affects the size cut of the 

cyclone. The implications can be important for understanding the hygroscopicity, optical 

properties, mixing, and trends of fine mode aerosols. 

3.6. Sea Salt 

Although contributions from sea salt to coarse mass (and indirectly to fine mass) are not 

included in the IMPROVE reconstruction equation, sea salt can be a significant fraction of the 

fine mass at many coastal locations, (e.g., the Virgin Islands), as well as contribute significantly 

to light scattering (e.g., Quinn et al., 2001, 2002b, 2004). Sea salt concentrations are typically 

computed from sea salt markers like the sodium ion, chloride ion, or combination of ions (Quinn 

et al., 2001). Difficulties in computing sea salt from data from the IMPROVE network arise 

because positive ions are not analyzed; therefore sodium ion (the strongest indicator of sea salt) 

data are not available. Elemental sodium data are available from XRF analyses; however 

sensitivity issues regarding poor detection of Na result in large uncertainties corresponding to Na

from XRF (White et al., 2004). Issues also arise when using the chloride ion or chlorine to 

estimate sea salt because reaction of gaseous nitric acid with sea salt produces sodium nitrate 

particles and the release of gaseous HCl. The depletion of chloride during this reaction results in 

an underestimation of sea salt when using chloride to compute it. 

For noncoastal sites, the inclusion of sea salt is not expected to have a considerable 

impact on reconstructed light scattering, so underestimating the contribution at those sites is not

significant. However, Lowenthal and Kumar (2003) found that including sea salt (computed

using Na and Cl) in reconstructed fine mass at Point Reyes CA increased reconstructed fine mass

by 30% on average. Because sea salt is hygroscopic, the added effects of water mass to light 

scattering in coastal higher RH environments could be important also. Recent work by 

Lowenthal and Kumar (2005) suggests the possibility of using strontium as a surrogate for sea 

37
salt. Investigations into this possibility are ongoing. The elemental abundance of strontium varies 

depending on the type of soil (Siefert et al., 1999) and estimates of Sr-derived sea salt depend on 

accurate estimates of its crustal abundance in relation to other elements. Because many 

IMPROVE sites have been shown to be influenced by long-range transport of Asian and North 

African dust (e.g., Perry et al., 1997; VanCuren and Cahill, 2002; Jaffe et al., 2003, 2005; 

VanCuren, 2003; Hand et al., 2004) as well as local dust sources, it is very important that the 

contributions to Sr from dust sources versus sea salt be accurately characterized, as both can be 

very important contributors to light scattering. For example, in Barbados (near the Virgin 

Islands), Li et al. (1996) found that for a 10-year mean, dust contributed 56% to light scattering, 

compared to 33% by sea salt. 

The MLR analysis in section 3.1 and summarized in Table 1 included sea salt as 1.6·Cl-

(NaCl). This analysis suggests that east and west coastal sites underestimate sea salt mass by 

about 10% on average, even with some chloride depletion. We recommend that sea salt be 

included in the reconstructed fine mass equation as 1.8·Cl (sea salt is 55% Cl by weight as 

defined by the composition of sea water by Seinfeld and Pandis, 1998) because of the

uncertainties related to sodium measurements. Interestingly, the ratio of the 1.8 and 1.6 factors is

1.12, similar to the average regression coefficient for sea salt, so perhaps some of the

underestimate was related to the sea salt multiplication factor. The contributions of sea salt to the 

light extinction equation (including its hygroscopic properties) should also be included. 

3.7. Size Distributions 

Atmospheric aerosols are typically described by a trimodal size distribution. The three 

modes are commonly referred to as the nucleation mode (0.01 < Dp < 0.1 μm), accumulation 

mode (0.1 < Dp < 1 μm), and the coarse mode (Dp > 1 μm), and each mode is typically 

38
associated with different formation mechanisms. However, several observations have shown that 

bimodal structure can exist in the accumulation mode. 

The existence of a bimodal size distribution was documented by Hering and Friedlander 

(1982) in the urban Los Angeles area. Their measurements of sulfur size distributions using a

low pressure impactor demonstrated two types of distributions. Type I distributions had mass 

mean aerodynamic diameters (Dae) ranging from 0.42 to 0.65 μm and were observed over a wide 

range of sulfur concentrations (5–52 μg m-3), but typically on days with heavy sulfate loadings. 

Type II distributions were associated with smaller mass median diameters (Dae ranging from 0.17 

to 0.22 μm) and occurred on days with low sulfate loadings and lower relative humidity. Their 

calculations suggested that Type I sulfate distributions formed from aerosol phase reactions, 

while Type II distributions formed from gas phase reactions. Later measurements by Hering et 

al. (1997) in southern California during the Southern California Air Quality Study (SCAQS) 

campaign in 1987 suggested that that the total size distribution (in contrast to a single species) 

was bimodal in the accumulation mode with peaks around 0.25 and 0.65 μm in the summer,

while size distributions measured in the fall were more monomodal. 

Other mass size distribution measurements performed during SCAQS by John et al. 

(1990) suggested that typical sulfate size distributions were bimodal with aerodynamic mass

mean diameters around 0.2 and 0.7 μm. The average mode concentration increased with mode

diameter, with the larger size mode corresponding to the highest sulfate concentrations on

average. The transition observed between the modes suggested that the larger size mode was a 

continuation of the smaller mode. 

39
The formation of the two modes observed by Hering and Friedlander (1982), Hering et al. 

(1997), and John et al. (1990) was investigated by Meng and Seinfeld (1994) using modeling. 

The first mode is referred to as the condensation mode (Dae ~ -0.2 μm) and is believed to be 

formed from nucleation and/or condensation processes. The larger size mode is referred to as the 

droplet mode (Dae ~ 0.7 μm). Hering and Friedlander (1982) demonstrated that for ambient

concentrations, coagulation of submicrometer particles to form the droplet mode is too slow to 

account for the droplet mode within normal residence times, as is growth of the condensation 

mode by accretion of water vapor or by gas-phase or aerosol-phase production. Meng and 

Seinfeld (1994) demonstrated that activation of condensation mode particles into fog or cloud 

drops, followed by aqueous phase sulfate formation and then evaporation, is a realistic

mechanism for formation of the droplet mode. This mechanism demonstrates the importance of 

heterogeneous aerosol processing in the formation of the droplet mode. 

The early evidence for the bimodality of the accumulation mode and several of the

following examples that will be discussed are from impactor measurements that typically have 

fairly coarse size resolutions. Inversions of impactor measurements using techniques such as the 

Twomey inversion may provide further size-resolved information, but interpretation of Twomeyinverted size distributions should also be cautioned, as artifacts can result using this method, 

possibly producing spurious modes. Ideally, size distributions measured with finer size 

resolution techniques (e.g., differential mobility analyzer, DMA, and optical particle counter, 

OPC) can be quite useful in observing multi-modes; however, these instruments measure the 

total aerosol and cannot be easily assigned to a single species. Both types of measurements are

included in the following discussion of examples of bimodal accumulation mode size 

40
distributions. It should be pointed out that the type of diameter reported may be different 

depending on the type of measurement, e.g., aerodynamic (Dae) versus geometric size (Dg). 

Although the early observations of bimodality in the accumulation mode were made in

urban regions, John et al. (1990) state that the presence of bimodality in the accumulation mode 

is a general feature of atmospheric aerosols and not just a feature of urban aerosols. The 

following examples are by no means exhaustive, but are provided to demonstrate that these types 

of size distributions are not necessarily assigned to one type of location or aerosol. 

Urban Observations 

Zhuang et al. (1999) performed MOUDI measurements for 22 days in Hong Kong in the 

winter of 1996 and early 1997. These impactor data were analyzed for sulfate, ammonium, and 

nitrate, and fit with lognormals. Sulfate and ammonium size distributions were bimodal with 

aerodynamic mode diameters around 0.2 ± 0.15 μm and 0.58 ± 0.11 μm. The droplet mode

dominated and was associated with high relative humidity and low clouds. During the 2002 

Baltimore field campaign (4–12 July 2002), Adam et al. (2004) observed a haze event that was

due to smoke originating from Canadian forest fires. Size distributions were measured with an 

SMPS (scanning mobility particle sizer) and an APS (aerodynamic particle sizer), and volume

size distributions showed multiple modes in the accumulation mode range. 

MOUDI aerosol size distributions were measured during the Pittsburgh Air Quality Study 

(PAQS) for one year during summer of 2001 through summer 2002. Cabada et al. (2004) showed 

that in summer sulfate size distributions peaked around 0.7 μm, with another peak around 0.2 μm

revealed by the Twomey inverted data. Winter sulfate size distributions were more bimodal (Dae

around 0.2 and 0.7 μm), corresponding to lower sulfate concentrations overall. 

41
Rural Observations 

Aircraft measurements performed by Hegg et al. (1993) in remote regions over the North 

Atlantic Ocean suggested that measurements in clouds show different types of sulfur size 

distribution compared to those in clear air, probably due to heterogeneous aerosol processing by 

clouds. In Point Reyes National Seashore, Rivera-Carpio et al. (1996) measured MOUDI and

DMPS (differential mobility particle sizer) size distributions in October 1993 and summer 1994. 

Low mass sulfate concentrations corresponded to bimodal peaks in the accumulation mode (Dg ~ 

0.1, 0.4 μm), medium mass concentrations corresponded to a monomodal peak (Dg ~ 0.25 μm), 

and high sulfate concentrations corresponded to a mostly monomodal peak around Dg ~ 35 μm.

In October, bimodal sulfate distributions were observed for both low and high mass days, with 

peak diameters around 0.15 and 0.35 μm. Similar measurements were performed at El Yunque in 

Puerto Rico in spring 1992 that indicated two types of sulfate size distributions. Most of the

samples were bimodal with peaks around 0.1 and 0.3 μm, and monomodal size distributions

peaked around 0.3 μm. 

Several size distribution measurements have been performed in the Grand Canyon region. 

Zhang et al. (1994) report sulfate size distributions measured with a low-pressure impactor 

corresponding to Dae around 0.1–0.3 μm and 0.5-1.0 μm, and in some cases bimodal size 

distribution. Malm and Pitchford (1997) report DRUM (Davis rotating universal size-cut 

monitor) size distributions measured at the Grand Canyon in winter 1988 and in summer in 

Shenandoah. Larger geometric mass mean diameters were observed at Shenandoah (0.32 μm) 

than at the Grand Canyon (0.21 μm). Relationships between size parameters and mass

concentrations suggest larger sulfate masses correspond to larger mass mean diameters, 

especially at Shenandoah. At both locations sulfate higher mass concentrations were also 

associated with narrower size distributions. 

42
Recent Observations of Size Distributions Using DMA and OPC Data at National Park 

Service Special Studies 

Southeastern Aerosol and Visibility Study (SEAVS)

During the SEAVS study at Great Smoky Mountains National Park TN in 1995, ASASPX size distributions were measured in the size range from 0.1 to 3 μm (Ames et al., 2000; Hand 

et al., 2000). Because of the multi-valued response of the instrument in the 0.4–0.6 μm range, 

determining bimodality of these distributions is difficult, although there were several periods 

where the presence of multi-modes was indicated. 

Grand Canyon Visibility Study (GRAVS)

Size distribution measurements were made using a DMA and OPC (active scattering 

aerosol spectrometer probe, ASASP-X) during the GRAVS study in Grand Canyon National 

Park AZ in summer 1998 (Hand, unpublished data). These size distributions are not ideal for

investigating bimodality of the accumulation mode because an impactor was used with the DMA

to remove large particles that contribute to multiple-charged particles. The ASASP-X data are 

aligned with the DMA data for sizes greater than 0.5 μm, but the ASASP-X data have 

considerable uncertainty due to calibration issues. However, there are some size distributions that 

do appear to be bimodal in the accumulation mode. 

Big Bend Regional Aerosol and Visibility Observational Study (BRAVO)

Size distribution data were obtained using a DMA, OPC (LASAIR), and APS during the

BRAVO study at Big Bend National Park in 1999 (Hand and Kreidenweis, 2002; Hand et al. 

2002). Bimodal accumulation mode volume size distributions were often observed. Out of 117 

days of hourly size distributions, bimodal structure in the accumulation mode was observed for 

some part or all of the day for 62 days. 

43
Yosemite Aerosol Characterization Study (YACS)

During the Yosemite Aerosol Characterization Study (YACS) of 2002, DMA, and OPC 

size distribution measurements were performed during summer and early fall (McMeeking et al., 

2005). Although less frequently than at BRAVO, bimodal accumulation mode size distributions 

were observed for some portion of eight days during the study. 

4. Hygroscopic Growth 

The hygroscopicity of atmospheric aerosols is an important characteristic that determines 

how a particle will behave in a changing relative humidity (RH) environment. Soluble particles

will uptake water, resulting in increased mass and particle size, both of which determine how 

efficiently particles scatter light, as well as their atmospheric lifetimes. A pure salt particle (e.g., 

ammonium sulfate) exposed to increasing RH will undergo an abrupt change from a solid 

particle to a droplet at a particular relative humidity (referred to as deliquescence) that is specific 

to its chemical composition. Above this point the particle continues to grow exponentially. As 

the RH decreases, the solution droplet will lose water by evaporation and remain in a metastable 

supersaturated state until it effloresces and returns to a solid particle at a lower RH than that at 

which it deliquesced. The metastable state can exist for indefinite periods of time. This behavior 

is also referred to as hysteresis because the particle follows a different path of growth and 

evaporation. 

Although extensive laboratory studies have been performed to characterize the hysteresis 

behavior of hygroscopic aerosols of known composition (e.g., Tang and Munkelwitz, 1994; 

Tang, 1996), many field studies have also been performed to understand the relationship between 

the hygroscopic, optical, and chemical properties of ambient aerosols. These types of

measurements are typically performed by a few different methods. Tandem differential mobility

analyzers (TDMA) arranged in series allow for the selection of a single particle size in the first 

44
DMA (typically a dry size). The particle size is measured in the second DMA after it has been 

exposed to increased (or decreased) relative humidity in a conditioner that separates the two 

DMAs. Growth factors (D/Do) are derived from these measurements as a ratio of a humidified 

particle diameter (D) to the initial dry particle diameter (Do) as a function of relative humidity.

This technique has been employed in many field studies, several of which are reviewed by 

Cocker et al. (2001). The results of most of these studies suggest the presence of particle modes

with varying degrees of solubility and hygroscopic characteristics (“more” or “less” hygroscopic 

modes), reflecting the varying chemical composition and mixing properties of the aerosols. 

Bimodal growth of urban aerosols has been shown to have a less hygroscopic mode with D/Do

ranging from 1.0 to 1.4 (for RH ~ 80–90%) and a more hygroscopic mode with D/Do = 1.1–1.8 

(e.g., Zhang et al., 1993; Busch et al., 1999; Ferron et al., 1999). Carrico et al. (2005) observed 

monomodal, bimodal, and trimodal growth profiles at Yosemite National Park. They found an 

inverse relationship between the mass fraction of POM and hygroscopicity and found that the 

growth factors were significantly lower than expected for ionic components of the aerosol 

composition, especially during periods dominated by biomass smoke. 

Another technique for characterizing particle growth utilizes optical particle counters that

measure aerosol size distributions at changing relative humidities. During SEAVS, Kreisberg et 

al. (2001) used a relative-humidity-moderated differential mobility optical particle size 

spectrometer to measure dry and humidified particle size distributions. Hand et al. (2000) used a 

relative-humidity-controlled optical particle counter to obtain both dry and humidified size 

distributions. Size distributions statistics (such as geometric mean diameter and integrated 

volume concentrations) for both the wet and dry distributions are used to construct diameter 

growth curves (D/Do). This method differs from the TDMA method in that D/Do curves are 

45
determined for an integrated aerosol size distribution, rather than for individual sizes, so

information regarding mixing and “more” and “less” hygroscopic modes is not available. 

Both of the above mentioned techniques to measure growth curves rely on measurements

of particle size in a changing relative humidity environment. Another method for estimating 

particle growth is to condition the aerosol sample in a nephelometry system. Day et al. (2000) 

describe an experimental technique used to measure dry and humidified light scattering 

coefficients from which light scattering growth curves (f(RH) = bsp(RH)/bsp(dry)) have been 

derived for several special studies in national parks (e.g., Day and Malm, 2001; Malm et al., 

2003; Malm et al., 2005b). Several investigators have used a variation on this technique of 

measuring a dry and humidified bsp to compute f(RH) (e.g., Sheridan et al., 2001; Eldering et al., 

2002; Carrico et al., 2003). Growth curves derived from nephelometry systems (f(RH)) and from 

TDMA systems (D/Do) are not directly comparable because, besides being a function of aerosol 

composition and mixing characteristics (similar to D/Do), f(RH) curves are also a function of

aerosol size distributions that could be changing independently of RH effects during a 

measurement cycle and correspond to an average of scattering due to aerosol types growing at 

different rates. 

Laboratory studies suggest that mixed salt particles have a complicated growth behavior 

with multiple deliquescence points (Tang, 1997), but the behavior is fairly well understood and

can be predicted by several equilibrium models (Kim et al., 1993; Clegg et al., 1998a,b; Nenes et 

al., 1998). Less is understood about the hygroscopic properties of organic aerosols or 

inorganic/organic aerosol mixtures. Laboratory and some field studies have investigated the role 

that organic species have in the hygroscopic growth of inorganic salts or minerals and indicate 

that organics can change the deliquescence point of the pure inorganic species (e.g., Andrews 

46
and Larson, 1993; Lightstone et al., 2000) and, depending on the properties and mass fractions of

the organic compounds, can enhance, reduce, or not effect the rate of growth of the inorganic 

species (Andrews and Larson, 1993; Saxena et al., 1995; Hansson, et al., 1998; Lightstone et al., 

2000; Chan and Chan, 2003; Prenni et al., 2003; Brooks et al., 2004; Gysel et al., 2004; Mikhilov 

et al., 2004; Carrico et al., 2005; Malm et al., 2005b). Many organic compounds have been 

shown to have no deliquescent or efflorescent behavior at all (e.g., Peng et al., 2001). Virkkula et 

al. (1999) found during a field study in Spain that internally mixed particles of ammonium

sulfate and organic compounds take up water independently of one another. 

In the atmosphere, the aerosols are a complicated mixture of inorganic and organic 

species with complex growth behaviors that may not be well represented by laboratory studies. It 

is likely that a large fraction of hygroscopic particles exist in supersaturated equilibrium as 

aqueous droplets below their deliquescence RH, based on the numerous studies that report a 

smooth function of particle growth with relative humidity rather than step-wise growth behavior. 

This behavior has been observed for D/Do growth curves in southeast Texas (Santarpia et al., 

2004, 2005), Great Smoky Mountains National Park (Hand et al., 2000), and Yosemite National 

Park (Carrico et al., 2005). Smooth f(RH) curves have also been observed in the Netherlands (ten

Brink et al., 1996), Great Smoky Mountains, Grand Canyon, Big Bend, and Yosemite national 

parks (e.g., Malm and Day, 2001; Malm et al., 2003, 2005b), Portugal (Carrico et al., 2000), 

China (Xu et al., 2002), North Carolina (Im et al., 2001), the Maldives (Eldering et al., 2002), 

and during ACE-Asia (Carrico et al., 2003). Although a variety of aerosol types likely exist at 

these locations, their smooth growth curves suggest these particles exist either in a equilibrium 

state, lacking growth characteristics like deliquescence points due to their nonsoluble/soluble 

47
mixture, or in a supersaturated equilibrium state with a very low efflorescence RH (i.e., acidic

aerosols). In either case, water appears to be associated with these aerosols at low values of RH. 

The difference between f(RH) for ammoniated sulfate states between fully neutralized 

ammonium sulfate and more acidic sulfate is summarized in Figures 5a–c. Figure 5a shows the 

f(RH) “no solids” curves (Clegg et al., 1998b) for ammonium sulfate, bisulfate, and sulfuric acid

for a mass size distribution with Dg = 0.4 μm and σg = 1.9. Notice there is little difference 

between the ammonium sulfate and bisulfate f(RH) curves up to ~ 70% RH, while for RH > 70% 

the bisulfate f(RH) curve is about 1.2 times the ammonium sulfate curve. The sulfuric acid

f(RH) curve is about twice the ammonium sulfate curve for most RH values. However, the dry 

mass scattering efficiencies for ammonium sulfate, bisulfate, and sulfuric acid are 3.72, 3.35, and 

2.66 m2

 g

-1, respectively, offsetting the differences in f(RH) curves at high humidity. The mass

scattering efficiencies for ammonium sulfate, bisulfate, and sulfuric acid are plotted as a function 

of RH in Figure 5b to assess the effective scattering of a fixed amount of sulfate ion interpreted 

as any of these three forms of sulfate. Notice that at low RH the mass scattering efficiency for 

bisulfate is lower than the ammonium sulfate mass scattering efficiency and about equal at 

higher RH. Sulfuric acid mass scattering efficiency is about the same as ammonium sulfate mass 

scattering efficiency at low RH but greater at high RH. Figure 5c summarizes these differences. 

The ratio of the sulfate ion mass scattering efficiency interpreted as ammonium bisulfate and as 

sulfuric acid to the ammonium sulfate efficiency curve is shown as a function of RH. Notice that 

at low RH (10–70%) the bisulfate efficiency is about 20% lower than the ammonium sulfate 

mass scattering efficiency, and at high RH they are about equal. Sulfuric acid mass scattering 

efficiencies are 10–20% greater than ammonium sulfate efficiencies over most of the RH range

and 40% greater at very high RH values (95–98%). 

48
In the IMPROVE formulation, the form of sulfate is assumed to be ammonium sulfate.

From Figure 5c it is evident that this choice of ammonium sulfate can either be an over- or 

underestimate of true sulfate scattering, depending on the ratio of the ammonium to sulfate ion. 

However, the current f(RH) growth curve used in the IMPROVE equation is based on an 

interpolated D/Do curve between the ascending and descending branches of growth for 

ammonium sulfate and reaches a value of 1 at 40% RH (no water is associated with the particles

below 40% RH) (Sisler and Malm, 1994). This curve was derived to approximate smooth growth

curves observed in field studies. We propose applying an f(RH) growth curve corresponding to 

equilibrium calculations for ammonium sulfate below the deliquescence point to 0% RH using 

the Aerosol Inorganics Model (AIM) with the “no solids” option (Clegg et al., 1998b). This 

smooth curve also approximates the behavior observed for mixtures of aerosols as those 

observed in the studies cited above; however, it differs from the current curve in that it allows 

water to be associated with the aerosol for RH values below 40%. Organics are assumed to be 

nonhygroscopic because of the lack of conclusive evidence; however, laboratory and field results 

suggest they are weakly to nonhygroscopic, (Malm et al., 2003; Carrico et al., 2005; Malm et al. 

2005b). Sea salt f(RH) curves are computed using NaCl growth factors derived from the AIM 

model (Clegg et al., 1998b). No water is associated with sea salt below its crystallization point 

(RH = 47%). 

49
Figure 5. (a) f(RH) curves using the “no solids” method for ammonium sulfate, ammonium bisulfate, and

sulfuric acid (assuming a size distribution with Dg = 0.4 μm and σg = 1.9). (b) Sulfate mass scattering

efficiencies for ammonium sulfate, ammonium bisulfate, and sulfuric acid using the curves in part (a). (c) 

Ratios of ammonium bisulfate and sulfuric acid mass scattering efficiencies to the ammonium sulfate mass

scattering efficiency shown in (b). 

5a

50
5b

5c

51
5. Mass Scattering Efficiencies 

In order to review mass scattering efficiencies, it is important to understand the 

terminology used and the impact of assumed aerosol models upon the resulting estimates. We

motivate this section by a theoretical discussion of mass scattering efficiencies, including

derivations and effects of the assumed model on derived estimates. Later we review other 

empirical methods used for estimating mass scattering efficiencies from measurements and how

the assumptions applied in these methods may result in estimates that, although they may be

referred to as mass scattering efficiencies, in fact may actually differ in their physical meaning. 

The final subsections provide a survey of reported measured mass scattering efficiencies using

different methods and estimates derived from IMPROVE data. 

5.1. Theoretical Discussion 

The role of aerosols in visibility degradation or climate forcing has motivated efforts to 

quantify the optical properties of specific aerosol species. The terminology used and the impact 

of assumed models on the amount of change in extinction apportioned to individual aerosol

species have been subjects of debate. For example, ranges in estimates of mass scattering 

efficiency of sulfate aerosol applied in climate forcing models (Penner et al., 1993) arose due to 

the assumptions regarding the presence of other chemical species (e.g., ammonium and/or water) 

or assumptions concerning shifts in the size distribution with changes in aerosol mass in the 

calculation of mass scattering efficiency (Zhang et al., 1993; Anderson et al., 1994; McMurry et 

al., 1996). White (1986) presents a thorough discussion of the definitions of extinction efficiency 

and the consequences of various assumptions of the assumed aerosol microstructure upon the 

apportionment of extinction to its chemical components. 

Mass extinction (or scattering) efficiencies are defined as the total aerosol extinction (or

scattering) divided by the total aerosol mass and can be calculated theoretically for spherical 

52
particles of known composition and size using Mie theory (van de Hulst, 1981). Aerosol models 

typically assume that aerosol species are mixed externally; the simplest example is a particle

composed of a single chemical species such as ammonium sulfate, and for this case the 

extinction efficiency is referred to as a “mass extinction efficiency”. However, realistically, 

particles in the atmosphere comprise a variety of inorganic and organic species. These types of

particles are referred to as internal mixtures, and their extinction efficiencies are termed “specific 

mass extinction efficiencies”. Internally mixed particles can also be externally mixed from other

particle populations; the most obvious case would be internally mixed fine mode aerosols

externally mixed from coarse mode aerosols. 

For the following discussion, the aerosol size distribution refers to an externally mixed 

aerosol of a single chemical component, j. For a corresponding aerosol number distribution 

fN,j(Dp) and complex refractive index nj = m + ik, the light extinction coefficient (bext,j) is 

computed with equation 7 and has units of inverse length. 

∫

∞

=

0

, 2 , ( , , ) ( ) 4 ext j p ext j p N j Dp dDp b D Q n D λ f π (7)

The Mie extinction efficiency is given by Qext(nj,Dp,λ) and is a function of refractive index, 

particle diameter (Dp), and wavelength (λ). Equation 7 can be reformulated in terms of aerosol 

mass size distribution fM,j(Dp) by making the following substitution for the number distribution 

(equation 8), with species particle density given by ρj: 

( ) 6 ( ) , 3 , M j p

j p

N j p f D

D

f D

ρ π = (8)

Substituting equation 8 into equation 7 gives 

53
∫

∞

=

0

, , , ( , , ) ( ) ext j ext j j p M j Dp dDp b α n D λ f (9)

where the single particle mass extinction efficiency (αext,j) has units of m2

 g-1 and is given by 

j p

ext j p

ext j D

Q n D

ρ

λ

α

( , , )

2

3 , = (10) 

Normalizing equation 9 by the total mass concentration of species j (Mj) allows the extinction

efficiency to be written as 

∫

∞

= ′

0

M ext j M j Dp d Dp f j ( ) ( ) α α , , (11) 

where f'M,j(Dp) is the normalized mass distribution. If f'M,j(Dp) does not vary with total mass 

concentration, then the average mass scattering efficiency for species j can be considered a 

constant and the light extinction coefficient corresponding to species j can be written as 

bext,j = α Mj Mj (12) 

The total extinction is then a linear combination of the species mass concentrations. 

bext = Σα Mj Mj (13)

Equation 13 also holds for an internally mixed aerosol where the chemical species are mixed in

fixed proportions to each other, the index of refraction is not a function of composition or size, 

and the aerosol density is independent of volume.

When computing total extinction using Mie theory, the microscopic structure of the

aerosol (that is, the extent of internal or external mixing) is found to be relatively unimportant, so 

that the assumption of internally versus externally mixed particles does not have much impact on 

the predicted results. This insensitivity of total scattering or extinction to the aerosol mixture has 

54
been demonstrated by a number of authors, including Hasan and Dzubay (1983), Sloane (1983), 

Pilinis et al. (1995), and McMurry et al. (1996). 

The mass extinction (or scattering) efficiency is a stronger function of density and size 

than optical properties such as refractive index (see equation 10). Several investigators have 

reported on the size dependence of mass scattering efficiencies (Malm and Pitchford, 1997; Li et 

al., 2000; Hand, 2001; Malm et al., 2003). Other authors report the dependence of mass

scattering on mass concentrations (Malm et al., 2003) or on light scattering coefficients

(Lowenthal and Kumar, 2004); however, these relationships arise due to the dependence of bsp

and mass on particle size. 

Estimating the change in extinction due to the removal or addition of a single species is

different from assigning a fraction of extinction to a chemical species or mixture of species, and 

is referred to as a “partial mass extinction efficiency” (αext,part). 

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

∂

∂

j

ext

ext part M

b

α , = (14) 

The partial extinction efficiency is dependent on change in composition as well as change in 

aerosol size as species are added or removed. For example, McMurry et al. (1996) examined 

αext,part as a function of formation mechanisms for sulfate. If sulfate was formed by gas phase 

reactions, lower humidity conditions led to smaller particles sizes; whereas when sulfate was 

formed in aqueous processes, the higher relative humidity conditions led to larger particle sizes. 

A simple example illustrating some of these concepts is shown in Figure 6 (Malm and 

Kreidenweis, 1997). The insensitivity of the total computed scattering to the mixing assumption 

is presented in Figure 6a. Two aerosol species with the same total volume, size distribution, and 

index of refraction, but with densities differing by a factor of 2, are externally mixed. They have

55
mass scattering efficiencies of 3 m2

 g

-1 and 6 m2 

g

-1, respectively. The externally mixed aerosol 

contains 10 μg m-3 of species 1 and 5 μg m-3 of species 2, with each species contributing 30 

Mm-1 to the total aerosol scattering of 60 Mm-1. 

Figure 6. (a) Diagram contrasting mass scattering efficiencies for internally versus externally mixed

particles. (b) Partial scattering efficiencies for internally and externally mixed particles. 

If species 1 and species 2 are now assumed to be internally mixed (see lower part of 

Figure 6a), the specific mass scattering efficiency for the mixed particle is now required for 

calculation of the total aerosol scattering. The specific mass scattering efficiency can be

computed as the mass-weighted average of the efficiencies of the individual species (4 m2

 g-1), 

assuming several conditions are met. The optical properties of the mixture must be similar to

those for the individual species (which must also be similar; this condition is met, for example,

56
by a mixture of ammonium sulfate and organics, with real refractive indices of 1.53 and 1.5, 

respectively). Volume conservation must be invoked, and the size distribution of the internal

mixture must be similar to the size distributions of the external mixtures. By applying the 

specific mass scattering efficiency, a total aerosol bsp for the sample is again computed as 60 

Mm-1 (see Figure 6a). 

However, the apportionment of scattering to species 1 and 2 is different under these two 

models. Using the externally mixed model, species 1 and 2 each contribute 50% of the total 

scattering. In the internally mixed case, species 1 contributes 66% of the scattering budget (since 

it makes up 66% of the total mass), while species 2 contributes 33%. This discrepancy arises 

because when the species are internally mixed, the same scattering efficiency is assigned to both 

species, although independently they have different efficiencies. This discrepancy can only be 

resolved if the specific mass scattering efficiency of the mixed aerosol is prorated to its chemical 

constituents, based on their relative densities. The apportionment of scattering to specific species 

is therefore independent of whether an externally or internally mixed model is assumed.

This simple example demonstrates that the contribution of each species to total extinction

is sensitive to the assumed microscopic structure of the aerosol. White (1986) refers to this as the 

apportionment problem, distinct from the problem of computing total extinction from estimates 

of size-dependent chemical composition that we just demonstrated to be similar for the two cases 

in Figure 6a. For the externally mixed case, the total extinction for the mixture is calculated by

computing the contribution of each species separately, and the species contribution to the total is

well defined if we know the size distribution of each species. For the internally mixed case, it 

may be misleading to assign a percentage of the total extinction to each species on a massweighted basis, as demonstrated in Figure 6a. 

57
The previous discussion concerns itself with apportioning extinction to a species as it 

resides in the ambient atmosphere. From a regulatory standpoint, the change in total scattering as 

a function of the removal of a species may be of interest. Total scattering can be computed for 

the mixture, and for the case when one species has been removed from the mixture; the

difference between these values provides the contribution of the species to total scattering. As an 

example, we compute the partial scattering efficiency for species 2 under the assumptions of 

externally mixed particles. The partial scattering efficiency is obtained by computing the total 

aerosol scattering assuming only species 1 is present (30 Mm

-1, see Figure 6b). Subtracting this 

value from the total scattering obtained for the mixture (60 Mm-1, see Figure 6a), we deduce that 

species 2 contributed 30 Mm

-1 (half) to the mixed aerosol scattering. The derived partial 

scattering efficiency of 6 m2

 g

-1 for species 2 [∆bsp/∆mass = (60-30 Mm-1)/(5 μg m-3)] is the

same as its mass scattering efficiency from Figure 6a. 

Investigating the same scenario but for the internally mixed case (see the lower part 

Figure 6b), we assume that the removal of one species from the internal mixture would conserve 

particle number concentrations but reduce particle size. This size reduction alters the specific 

scattering efficiency of the mixture, which is now assumed to be 2 m2

 g

-1. The total aerosol 

scattering is thus 20 Mm-1, which leads to the conclusion that the partial scattering efficiency of 

species 2 is 8 m2

 g-1 [∆bsp/∆mass= (60-20 Mm-1)/(5 μg m-3)]. White (1986) presents a thorough 

discussion of the definitions of specific extinction and mass extinction efficiency and of the 

consequences of various assumptions of aerosol microstructure upon the apportionment of 

extinction to its chemical components. 

Issues also arise when apportioning scattering to species that have different hygroscopic 

properties. Consider an external mixture of hygroscopic and nonhygroscopic aerosols species 

58
with similar masses. The mass scattering efficiencies of the dry nonhygroscopic and hygroscopic 

species are each 3 m

2

 g

-1, while that of the wet hygroscopic species is, because of associated 

water, 8 m2

 g-1. When internally mixed, the wet specific mass scattering efficiency will be 3–8 

m

2

 g

-1, depending on the hygroscopic properties of the mixed aerosol. Several authors discuss 

aerosol growth characteristics as a function of RH and have successfully predicted the scattering

characteristics of the mixed particles (Anderson et al., 1994; Sloane, 1983, 1986; Malm and 

Pitchford, 1997; Malm et al., 2000, 2003, 2005b). However, the apportionment of scattering to a 

particular species is still problematic. Typically, one growth curve is developed for the mixed 

species, and scattering due to water is apportioned proportionally among all aerosol components, 

even though only one of the species may be hygroscopic. An example would be a mixture of

ammonium sulfate and a weakly hygroscopic organic species.

5.2. Methods for Deriving Mass Scattering Efficiencies 

The methods typically used to estimate mass scattering efficiencies depend on the type of 

measurements and data available. In this section we will discuss the most common methods

used. We use the term “mass scattering efficiency” to refer to estimates that correspond to a 

single aerosol component such as dry ammonium sulfate, and although one could argue that 

species such as POM and soil correspond to a combination of chemical components, we will use 

this term to correspond to those efficiencies also. We use the term “specific mass scattering 

efficiency” to refer to aerosols composed of more than one species, for example, a “fine mode 

specific mass scattering efficiency”. We will also use this term to refer to aerosols that include 

water mass. For example, if an efficiency for an inorganic salt particle with associated water

mass is reported, we refer to it as a “specific mass scattering efficiency”. 

The simplest method for computing efficiencies is with measured mass concentrations

from filter samples and measured light scattering coefficients from nephelometry. For an aerosol

59
population, a specific mass scattering efficiency αsp_spec can be defined as the ratio of a light 

scattering coefficient corresponding to the mass concentration (M) of that population. 

M

bsp α sp _ spec = (15) 

The average specific mass scattering efficiency can be estimated by dividing the average

scattering coefficient by the average mass concentration for a given set of measurements, or a

linear regression can be performed on the data and the slope of the linear fit can be interpreted as

the specific mass scattering efficiency. Specific mass scattering efficiencies derived in this 

manner represent an average aerosol that could be changing due to variations in relative 

humidity, size distribution, and composition during the sampling period. Mass concentrations

used in this method could be either gravimetric mass or the sum of chemically analyzed masses, 

or be computed from integrated volume distributions using an assumed density. 

A number of investigators have taken advantage of the form of equation 13 (bext = 

ΣαMjMj) to construct a multi-linear regression (MLR) model with bext as the independent 

variable, and the measured aerosol mass concentrations for each species j (Mj) as the dependent 

variables. The regression coefficients are then interpreted as mass extinction (or scattering or 

absorption) efficiencies. The assumptions required in this formulation are that all the components 

contributing to extinction are included, equation 13 is a reasonable approximation to the 

relationship between extinction and the various aerosol species, the number of samples is large 

enough to give stable results, and the concentrations of the species are uncorrelated. 

However, as stated by White (1991), “Model simulations show the procedure to yield 

usefully accurate results under favorable conditions. An important liability is that the availability 

of standard software makes it easy to perform regression under unfavorable conditions.” 

Regression-derived efficiencies are vulnerable to a variety of systematic and random errors. At 

60
the most basic level, there is the issue that meteorologically driven fluctuations of the existing 

aerosol concentrations may cause aerosol mass concentrations of different species to be

collinear. The high degree of collinearity commonly found among aerosol species can make

regression results very sensitive to the choice of species to be included in the analysis. A more

practical difficulty is that regression results can be biased by random uncertainties in the 

measurements. Standard regression models tend to overpredict the coefficients of species that 

have lower uncertainties (e.g., sulfates) and underpredict the coefficients of species with larger 

measurement uncertainties (e.g., organics), similar to the discussion in section 3.1. 

The theoretical approach described at the beginning of this section (see equations 7–10)

is often used to compute mass scattering efficiencies from mass (or number) distributions of

aerosol species from impactor measurements or mobility or optical measurements. However, this 

method requires assumptions of the measured species chemical form and mixing properties of 

the aerosols, as well as their optical properties. Estimates from this method often assume an

externally mixed aerosol, but if the size distribution measurement is obtained by mobility or 

optical measurements (number size distribution), an internally mixed aerosol is assumed, but 

perhaps for separate size modes. This method has been shown to accurately reconstruct light 

scattering. For example, measurements of size distributions have been incorporated with 

estimates of aerosol optical properties to reconstruct measured scattering (and estimate specific

mass scattering efficiencies) on fine time scales (Hand et al., 2002; Malm et al., 2005a; 

McMeeking et al., 2005). These estimates have the added advantage of allowing for the 

investigation of the functional dependence of efficiencies on particle size, composition, and 

humidity. The theoretical method provides the most accurate estimate of efficiencies out of those 

discussed in this section. A disadvantage to this method is that size distribution measurements 

61
are more analytically intensive and not often available for routine monitoring, so computing 

mass scattering efficiencies by this method is not routinely possible. 

Estimating mass scattering efficiencies as the change in bext resulting from the removal

(or addition) of a single species is different from assigning a fraction of measured extinction to a 

chemical species or a mixture of species. The change in extinction resulting from a change in 

aerosol species concentration was described previously (equation 14). As species are added or

removed from an aerosol, the efficiency is dependent on change in composition as well as on 

change in aerosol size. Computing partial mass scattering efficiencies in this context requires a 

model to account for the effects of removal of mass on light scattering coefficients, such as the 

ELSIE (Elastic Light Scattering Interactive Efficiencies) model (Sloane, 1983; Sloane et al., 

1991; Lowenthal et al., 1995; Omar et al., 1999). Among the assumptions in the ELSIE model

are those associated with removing aerosol mass. Mass can be removed or added by assuming 

that the particle size changes but not the particle number, or that the particle number changes but 

not the particle size (Lowenthal et al., 1995). Unless the option is chosen to keep the size 

constant, the efficiencies derived from this method cannot be compared to efficiencies from other

methods. Also, assumptions must be made regarding how to treat water mass associated with a 

removed species. Although this technique is useful in a regulatory context, in practice it is not 

possible to measure the change in light scattering due to a change in mass concentration, so more 

empirical approaches were adopted to estimate mass scattering efficiencies. 

5.3. Survey of Mass Scattering Efficiencies 

A review of ground-based measured mass scattering efficiencies from peer-reviewed 

literature since 1990 includes values derived from the four different methods described above

(theoretical, measurement, multi-linear regression, and partial scattering approach) and are 

summarized by several tables (Tables 2–5 in Appendix 2). The tables can be understood in the

62
following way: the mass scattering efficiencies are listed by species (e.g., sulfate, POM) or as 

specific mass scattering efficiencies for mixtures of aerosols by size mode (i.e., fine, coarse, or 

total). The tables also list the study location, study name, aerosol characteristics (e.g., smoke) if 

noted, and the study time period. Each method table has a corresponding notes table that 

provides details of the measurements, size ranges, the relative humidity of the measurements, 

assumptions, and the wavelength at which the measurements were made if it was other than 550

nm; these can found in Appendix 2. Occasionally this information may also be found in a 

footnote in the mass scattering efficiency method table for quick reference. Citations are

numbered consecutively in alphabetical order (a full citation list can also be found in Appendix 

2). The “note” column in the table refers to the citation number as well as the entry in the notes 

table. When appropriate, we compute the average (and one standard deviation) for values in the 

cited literature and note it in the footnotes. Except for averages, values are listed as found in the

literature, and furthermore, sulfate mass scattering efficiencies have been normalized to dry

ammonium sulfate when possible. This normalization is performed because sulfate efficiencies

are reported under a variety of conditions. For example, they may be reported in terms such as

sulfate ion, ammonium sulfate mass, or ammoniated sulfate mass (depending on the acidity), and 

they may be reported for a range of relative humidity values corresponding to associated water 

mass. Sulfate mass scattering efficiencies reported for RH > 45% were converted to dry 

ammonium sulfate mass scattering efficiencies based on reported ammonium to sulfate molar 

ratios and f(RH) curves corresponding to ammonium sulfate. For all the entries, the original 

sulfate mass scattering efficiencies are reported, along with corrected dry ammonium sulfate 

mass scattering efficiencies in italicized font (if already reported in the cited manuscript), or 

noted with a (†) symbol if we performed the correction to a dry ammonium sulfate basis. 

63
Occasionally there was not enough information available to do this correction. Other corrections

in the table include normalizing the POM efficiencies to a multiplier of 1.8. Most of the

estimates were reported corresponding to POM computed with multipliers of 1.2, 1.4, 1.6, or 2.1 

(see notes table for each method). We normalized the efficiencies to Roc = 1.8 so that estimates

derived in the next section can be directly compared. Both efficiencies are listed in the tables but 

the normalized values are italicized. 

We begin our review with the theoretical method efficiencies so that later discussions of

efficiencies derived by more simple methods can be understood in the context of theoretical

predictions. Theoretical mass scattering efficiencies are reported in Table 2. These efficiencies

are the most representative estimates because the effects of particle size and composition can be 

included in the calculation for a single time period, and as previously mentioned, derived 

efficiencies accurately reconstruct scattering over very fine time resolutions. The theoretical 

method relies on computed scattering that is dependent on Mie theory and corresponding 

assumptions of spherical particles and optical properties. 

5.3.1. Theoretical Method 

The average fine mode dry ammonium sulfate mass scattering efficiency from the 

theoretical method is 2.5 ± 1.1 m2

 g

-1 (see Table 6). Most of the values reported correspond to 

the fine mode, although coarse and total sulfate are reported and noted in Table 2 (see Appendix 

2). The highest value in this table (6.0 m

2

 g-1) was reported for China by Li et al. (2000) and we 

have corrected it from ammonium bisulfate to ammonium sulfate but performed no humidity 

correction. It is unclear at what relative humidity this value is reported, although Li et al. (2000) 

state that particle growth based on Tang (1997) has been assumed. Having some water mass 

associated with this estimate would be consistent with its higher value compared to the other

estimates. For example, wet specific mass scattering efficiencies reported for Hopi Point AZ, 

64
Meadview AZ, Shenandoah National Park, and Great Smoky Mountains National Park 

correspond to different RH values (see notes table) and demonstrate the large effect water mass 

has on efficiencies, especially at Shenandoah where the ambient humidity is high in summer. 

Removing the highest value (6.0 m2 g

-1, reported by Li et al., 2000) from the calculated average 

results in a mean dry ammonium sulfate mass scattering efficiency of 2.2 ± 0.6 m2

 g-1. The 

lowest value in the table (1.12 m2

 g

-1) was observed in the Southern Ocean region south of 

Australia during the ACE-1 (Southern Hemisphere Aerosol Characterization Experiment) study 

(Quinn et al., 1998), corresponding to a small average surface mean diameter of 0.20 ± 0.04 μm. 

It is interesting that given the global distribution in the measurements, a fairly low variability in 

dry ammonium sulfate efficiencies is observed, perhaps a reflection of the robustness of this 

method for computing efficiencies, especially when the optical and hygroscopic properties are 

well understood. 

The average POM mass scattering efficiency without corrections for Roc differences was

5.9 ± 1.0 m2 g

-1 and was most likely affected by the assumptions in computing POM from 

measured organic carbon and the range of types of organics measured. To correct for the 

different multipliers used to compute POM, we normalized these values to an Roc of 1.8, and the

resulting normalized average POM mass scattering efficiency was 5.5 ± 1.6 m2

 g

-1 (see Table 6).

The normalization did not significantly change most of the estimates (see italicized values in the 

table) because most of the studies use Roc values ranging from 1.4 to 2.1. This normalization did 

change the estimate by Li et al. (2000) in China because no Roc was reported in that study, so we

assumed they used a value of 1. Most of the authors in these studies applied Roc values consistent 

with Turpin and Lim’s (2001) suggested values that vary according to aerosol type. For example, 

during the Aerosols99 study, Quinn et al. (2001) reported values for locations ranging from the 

65
Atlantic Ocean off the coast of Virginia to Cape Town, South Africa, with aerosol origins 

ranging from remote marine to African dust and biomass burning. They applied a POM 

multiplier of 1.6 for North American air masses (more urban aerosols) and 2.1 for all other air 

masses. With the exception of Li et al. (2001), these studies did not assume organics were 

hygroscopic; however, the RH corresponding to the value by Li et al. (2001) is unspecified. 

Average fine, coarse, and total (fine + coarse) dust mass scattering efficiencies were 3.4 ± 

0.5, 0.7 ± 0.2, and 1.2 ± 0.3 m2

 g

-1, respectively. It is probable that fine dust corresponds to the 

tail of the coarse mode dust distribution; however, the higher fine mode efficiencies are a result 

of these sizes interacting more efficiently with light, compared to the coarse mode. Mid-range 

values corresponding to the total aerosol mode reflect the integration over all sizes. The 

variability for each of these estimates is fairly low, considering differences in dust composition 

and size distributions, the study locations, and dust origins, which include Asia, the Indian 

Ocean, and off the coast of North Africa (Chiapello et al., 1999; Li et al., 2000; Quinn et al., 

2001, 2002b, 2004). 

The average fine and coarse mode specific mass scattering efficiencies were 4.3 ± 0.7 m2

g

-1 and 1.6 ± 1.0 m2

 g-1, respectively. The fine mode values could include ammoniated salts, 

carbonaceous aerosols, and mineral aerosols. These efficiencies were reported for a range of

humidities, and no corrections to a dry aerosol were performed because of the lack of 

information on the fine mode composition. The cut-off diameter for these modes may also vary 

from study to study, ranging from 1 to 2.5 μm. Given these differences, there is still a fairly 

narrow range of values reported for fine mode specific efficiencies. A much larger variation in

the coarse mode efficiencies was observed. The composition, size distribution, and optical 

properties of the coarse mode may vary considerably given the studies reported here. For 

66
example, the lowest value of 0.6 m2

 g

-1 at Big Bend National Park (Hand, 2001) reflects the fact 

that soil dominated the coarse composition (~ 40% on average). In contrast, the values derived

from the many cruise-based measurements (Quinn et al., 2001, 2002b, 2004) may be influenced 

by sea salt or other species. 

Average fine, coarse, and total sea salt specific mass scattering efficiencies were 5.3 ± 

0.8, 1.2 ± 0.3, and 2.3 ± 0.9 m2

 g

-1, respectively. Sea salt specific mass scattering efficiencies are 

not corrected for relative humidity and include the effects of aerosol water mass. Similar to what

was observed with dust mass scattering efficiencies, the fine mode sea salt specific mass 

scattering efficiencies are larger than the coarse mode, with the total aerosol (fine + coarse) in 

the middle of the range. 

5.3.2. Measurement Method 

Estimates of mass scattering efficiencies for the measurement method are reported in 

Table 3 (see Appendix 2 and Table 6). Most of these values correspond to specific mass

scattering efficiencies for the fine or coarse mode because the measurements were performed for

fine (or coarse) mass and measured light scattering. These values are not averaged together 

because the relative humidity at which the measurements are made, the types of mass data 

(gravimetric or sum of chemically analyzed), and the composition and size ranges corresponding 

to each mode vary; therefore normalizing these data to a common RH or composition is not

possible. Some studies have several values reported (such as in the Maldives during the

INDOEX study) because they are reported for ranges of light scattering coefficients and for 

different measurement methods (land- and cruise-based) by different investigators and averaging 

them together would be inappropriate. Even with these differences, some spatial patterns are 

noticeable. The highest fine mode specific mass scattering efficiencies (> 5 m2

 g-1) are reported 

in urban locations such as Mexico City, Mexico (Chow et al., 2002), Fort Meade MD (Chen et 

67
al., 2003), and the New England–mid-Atlantic region (Poirot and Husar, 2004). These values 

could be high due to relative humidity effects (especially in the eastern United States), or due to 

the aerosol composition. For example, the efficiency of 6 m2

 g-1 reported by Poirot and Husar

(2004) corresponds to smoke aerosol that may have higher efficiencies (Malm et al., 2005a; 

McMeeking et al., 2005). With the exception of sites in Phoenix AZ and sites near Denver CO, 

the urban (e.g., Beijing, China, Atlanta GA, Dallas TX) fine mode specific mass scattering 

efficiencies are greater than 3 m2

 g

-1. Most of the rural sites in the southwestern United States

correspond to lower specific efficiencies (less than ~ 2.5 m2

 g-1) in Meadview AZ, Mount Zirkel 

in Colorado, and Spirit Mountain NV, which are close to the theoretical mass scattering 

efficiencies computed for dry ammonium sulfate. The exceptions to these low values are those 

reported for the northwestern United States (Mount Rainier WA and North Cascades WA) and in 

Bondville IL with efficiencies greater than 4 m2

 g

-1. Higher specific mass scattering efficiencies

(usually greater than 3 m2

 g

-1) were observed during the INDOEX experiment in the Maldives. 

Specific mass scattering efficiencies for this study are ordered as a function of light scattering 

coefficients and no significant difference was observed for low scattering (bsp < 25 Mm-1) 

compared to high scattering periods (bsp > 55 Mm-1), in contrast to the relationship Lowenthal 

and Kumar (2004) observed for data from the IMPROVE network. The specific efficiencies 

reported for the Maldives are for an RH of 33%, so the effects of aerosol water mass are 

probably not significant for these data. Specific efficiencies corresponding to the total aerosol 

mode were reported for Yulin, China (Alfaro et al., 2003), during the ACE-Asia study. Values

were higher during polluted periods compared to periods dominated by dust aerosols, probably 

because of the change in aerosol size distributions. 

68
5.3.3. MLR Method 

Estimates of mass scattering efficiencies obtained using the MLR method are 

summarized in Table 4 (see Appendix 2). These values are subject to variability based on how 

the regressions were performed (with or without intercepts, or accounting for measurement 

uncertainties) and the types of data used. Average fine mode specific mass scattering efficiencies

were 3.1 ± 1.5 m2

 g-1, which were somewhat lower than the average estimate derived from the 

theoretical method, although with much larger variability. The highest values (> 5 m2 g

-1) were 

reported in Israel, and the lowest values (2–3 m2

 g-1) were reported in the southwestern United 

States (Nevada, Arizona, and Colorado), which is similar to the spatial distribution seen with the

results from the measurement method. Average coarse mode specific mass scattering efficiencies 

are 0.7 ± 0.6 m2

 g

-1, ranging from values greater than 1 m2

 g

-1 in Nevada and Arizona to values 

less than 0.5 m

2

 g

-1 in Colorado, Arizona, and Israel. The variability of coarse mode composition 

and size distributions could result in large variability in derived efficiencies. 

The average fine mode dry ammonium sulfate mass scattering efficiency was 

4 ± 3 m2

 g

-1, higher than theoretically predicted for fine mode dry ammonium sulfate and with a 

large variability due to outliers. Removing the outliers (i.e., 10.9 and 8 ± 3 m2

 g-1) results in an 

average dry ammonium sulfate efficiency of 3.2 ± 1.2 m2

 g

-1

, much closer to what has been 

theoretically derived. It is possible that these high values are due to water associated with the

nephelometer data, or due to uncertainties in the nephelometer data. Many of the sulfate mass 

scattering efficiencies reported in the MLR table were corrected to a dry ammonium sulfate 

basis, which could also contribute to uncertainties in these values. Variations in relative humidity 

or aerosol acidity could result in uncertainties in the corrections as these were applied in an

average sense. The lowest value reported in the table (0.83 m2

 g-1) corresponds to the total (Dp < 

10 μm) size distribution, demonstrating the effects of averaging over larger particles (higher

69
mass) that have less efficient light scattering properties. Also, it is probable that the chemical

form of sulfate in the coarse mode was different from ammonium sulfate. 

The unnormalized average value of POM mass scattering efficiency was 3 ± 4 m2

 g-1, 

with the large variability reflecting the range in values reported. The average POM mass 

scattering efficiency normalized to an Roc of 1.8 is 2 ± 3 m2

 g-1. Outliers in these values are

reported for Uniontown PA (12 ± 8 m2

 g

-1, Lowenthal et al., 1995), and removing that outlier 

from the normalized efficiencies results in an average value of 1.6 ± 0.6 m2

 g

-1, which is 

considerably lower than the average value of 5.5 ± 1.6 m2

 g-1 derived with the theoretical 

method. If we remove the cases that were computed assuming organics are somewhat soluble 

during higher RH periods, the average value is 2.3 ± 1.0 m2

 g

-1. Besides the outlier, the highest

value reported is for Bondville IL (4.11 m2

 g

-1) (Koloutsou-Vakakis et al., 2001) and has not 

been normalized because it corresponds to a carbonaceous aerosol that includes both organic and

light-absorbing carbon. The low values of POM mass scattering efficiency derived by this 

method provide a good example of how uncertainties associated with organics may result in an 

underprediction of derived mass scattering efficiencies. 

The average ammonium nitrate mass scattering efficiency was 4 ± 2 m2

 g-1. The highest 

values are reported for Meadview AZ and Mount Zirkel CO. However, no spatial dependence is 

seen, as the lowest values reported are also in the southwestern United States (Grand Canyon 

AZ, Canyonlands UT, and Phoenix AZ). The average fine, coarse, and total dust mass scattering 

efficiencies are 3 ± 2, 0.40 ± 0.08, and 0.7 ± 0.2 m2

 g-1, respectively. Fine mode dust mass 

scattering efficiencies are quite similar to those derived using the theoretical method (3.4 ± 0.5 

m

2

 g

-1); however, coarse mode and total dust efficiencies are somewhat lower for the MLR 

70
method. Given the range of assumptions and different measurements that are incorporated into 

these estimates, the convergence of fine dust efficiencies towards 3 m2

 g

-1 is notable.

The average sea salt specific mass scattering efficiencies for the fine, coarse, and total

modes are 4.0 ± 1.6, 1.6 ± 1.2, and 2.2 (one number reported) m2 g

-1

, respectively. These values

are also quite similar to those reported in the theoretical table. Sea salt is hygroscopic; therefore 

any water associated with measured scattering could be attributed to sea salt in the regression. 

5.3.4. Partial Scattering Method 

Values of mass scattering efficiency derived from the partial scattering approach are 

reported in Table 5 (see Appendix 2). Most of these studies employed the ELSIE model, as 

described previously. Species included in the model are sulfate, POM, nitrate, dust, elemental 

carbon, and fine mode aerosols. The two entries listed in the table per site for the first eight 

entries correspond to model results using two scenarios: (1) assuming a homogeneous 

composition with constant particle size, and (2) a core/shell scenario with constant particle

number. All estimates reported in the table using the constant size assumption are in bold font. It 

is not appropriate to average efficiencies computed with both scenarios because the second 

scenario corresponds to changing size distributions that would also change the efficiency. The 

entries listed for Hopi Point toward the end of the table all correspond to estimates made at

different relative humidities. 

The average dry ammonium sulfate partial scattering efficiency for the first scenario

(including those we corrected) in Table 5 is 2.7 ± 0.4 m2

 g-1, similar to the results from the 

theoretical method, as would be expected because the theoretical basis is the same. Most of the

studies included in this table occurred in the western or southwestern United States with the 

exception of the rural sites of Bondville IL and Uniontown PA. The sites in the Southwest are 

mostly rural with the exception of Phoenix AZ. No strong spatial variation is noticeable. Values 

71
derived in Meadview AZ are somewhat higher than those derived in Hopi Point. Both locations 

are near the Grand Canyon, with Hopi Point on the southern rim of the canyon and Meadview on 

the western edge of the canyon. Observations from Meadview have been used to characterize 

subregional aerosol and visibility in the Southwest (Measurement of Haze and Visual Effects, 

MOHAVE, study) (Turpin et al., 1997; Lowenthal et al., 2000). It is possible that the aerosols 

measured in Meadview were influenced by long-range transport and therefore probably aged, 

resulting in somewhat higher efficiencies. The average normalized POM mass scattering 

efficiency is 3.0 ± 1.4 m2

 g-1. High values were measured in Uniontown PA, Denver CO, and the 

Grand Canyon (Hopi Point), a mix of rural and urban locations. The ELSIE model treats POM 

mass as partly soluble (values for these studies range from 25 to 60% solubility, and that fraction

is as soluble as ammonium sulfate), so a direct comparison of POM partial scattering efficiency 

from this method to the other methods is not appropriate. The average ammonium nitrate partial 

scattering efficiency is 3.8 ± 1.5 m

2

 g

-1, with an outlier value in Denver CO. The average fine 

dust mass scattering efficiency is 2.8 ± 1.0 m2 g

-1. Especially high dust efficiencies were reported

for Uniontown PA. 

5.3.5. Apportionment Method 

As part of the 1991 National Acid Precipitation Assessment Program (NAPAP) Report 

24 on visibility, mass scattering efficiencies were computed from light scattering coefficients and

mass data based on several studies around the United States. Scattering was apportioned to major 

species such as ammonium sulfate and organics (White, 1991). The intention of the 

apportionment scheme was to provide the range of efficiencies based on extreme assumptions. 

Low estimates of sulfate mass scattering efficiencies were derived assuming that sulfates, 

nitrates, and POM scatter twice as efficiently as the remaining aerosol. The high estimates for

sulfates were derived assuming that sulfates alone scatter twice as efficiently as all other fine 

72
aerosols. Low estimates of POM mass scattering efficiency were derived assuming that POM 

and nonsulfate species scatter half as efficiently as sulfates. High POM mass scattering 

efficiencies were derived assuming that POM is three times as efficient, and sulfate is twice as

efficient, as the remaining aerosol in the fine mode. The range of these values is reported in 

Table 6, along with a summary of efficiencies for all the methods. Values for POM mass

scattering efficiencies are normalized to an Roc multiplier of 1.8. The values reported in Table 6 

for the apportionment method are from studies that occurred around urban and rural U.S. 

locations. The average specific mass scattering efficiency for the fine mode was 2.6 ± 0.8 m2

 g-1, 

with higher values in the rural and urban eastern United States (4.5 ± 0.8 and 3.5 ± 0.4 m2

 g

-1, 

respectively). The lowest values were computed for the rural and urban western United States, 

especially San Jose CA (1.83 m2

 g

-1). The apportionment method fine mode specific mass 

scattering efficiency was the lowest of all the methods; however, it was closest to the MLR 

method. Although these values are reported as dry, it is possible that the RH environment where 

the measurements were made has an effect on the values derived, perhaps through associated 

water on the filter or aerosol processing effects. 

73
Table 6. Summary of mass scattering efficiencies reported in Tables 2 through 5 (Appendix 2). The 

“Apportionment” column refers to results from White (1991). The “IMPROVE” column lists values used in 

the current IMPROVE formulation. Entries correspond to the fine mode unless otherwise stated in the row 

header. Sulfate efficiencies correspond to dry ammonium sulfate, and POM efficiencies have been normalized

to an Roc value of 1.8.

Summary of Mass Scattering Efficiencies from All Methods

*

Species/ 

Mode 

Theoretical 

(m2

 g-1) 

MLR 

(m2 g-1) 

Partial 

(m2 g-1) 

Apportionment

** 

(m2 g-1) 

IMPROVE 

Fine 4.3 ± 0.7 

(26) 

3.1 ± 1.5 

(17) 

2.6 ± 0.8 

(30) 

Coarse 1.6 ± 1.0 

(21) 

0.7 ± 0.6 

(13) 

0.6

Total 2.2 ± 1.0 

(9) 

Sulfate 2.5 ± 1.1 

(16) 

3.2 ± 1.2 

(24) 

2.7 ± 0.4 

(6) 

3.0 ± 0.9 – 

3.9 ± 0.9 (30) 

3.0 

Nitrate 4 ± 2 

(16) 

3.8 ± 1.5 

(6) 

3.0

POM 5.5 ± 1.6 

(20) 

2.3 ± 1.0 

(23) 

3.0 ± 1.4 

(6) 

1.5 ± 0.3 – 

3.2 ± 0.9 (30) 

4.0 

Fine Dust 3.4 ± 0.5 

(19) 

3 ± 2 

(19) 

2.8 ± 1.0 

(4) 

Coarse Dust 0.7 ± 0.2 

(21) 

0.40 ± 0.08

(2) 

1.0

Total Dust 1.2 ± 0.3 

(9) 

0.7 ±0.2 

(3) 

Fine Sea

Salt 

5.3 ± 0.8 

(22) 

4.0 ± 1.6 

(3) 

Coarse Sea 

Salt 

1.2 ± 0.3 

(20) 

1.6 ± 1.2 

(3) 

Total Sea 

Salt 

2.3 ± 0.9 

(9) 

2.2 ± 0 

(1) * Number of observations in parentheses ** Apportionment values from Table H-1 in Appendix H in White (1991) and references therein.

Dry ammonium sulfate mass scattering efficiencies derived from the apportionment

method ranged from 3.0 ± 0.9 to 3.9 ± 0.9 m2

 g

-1 for the low and high apportionment strategies, 

respectively. These estimates are similar to the values derived from the other methods but are

still larger than what is derived from the theoretical method. The POM mass scattering 

efficiencies are lower than other estimates reported in Table 6, although the MLR method 

estimates fall within the range of low and high values from the apportionment schemes. It is 

interesting that derived sulfate mass scattering efficiencies are fairly insensitive to the low and 

high apportionment scheme, while the POM efficiencies are approximately double, based on the 

74
apportionment scheme, probably due to uncertainties associated with organic carbon 

measurements. The spatial variability in both sulfate and POM mass scattering efficiencies are 

similar to the fine mode specific efficiency. The highest values are derived in the eastern United

States (both rural and urban) and the lowest values in the urban West. 

5.3.6. Mass Absorption Efficiencies 

Reported estimates of mass scattering and absorption efficiencies of LAC, as well as for 

other species, are reported in Table 7 (see Appendix 2). Efficiencies listed in this table have 

been derived using all the methods described above, which is noted in the first column of the

table. Typically, mass absorption efficiencies are computed by the measurement method, by 

dividing a light absorption coefficient measured by transmittance (measured with an

aethalometer or particle soot absorption photometer) by the mass of LAC from thermal analyses. 

Light absorption coefficients measured with a photoacoustic technique also are used to derive 

mass absorption efficiencies (e.g., Arnott et al., 2003). The theoretical method can be used if the 

size distribution of LAC is measured, or by applying a complex refractive index to number or

volume size distributions in the Mie calculation. In Table 7 the values reported for a wavelength 

other than 550 nm have been corrected to 550 nm assuming a λ

-1 relationship (Bohren and 

Huffman, 1983). It is well known that large uncertainties surround the values of mass absorption 

efficiencies by LAC, as is evidenced by the range of values reported in the table. Much of the 

uncertainty stems from the fact that estimates of LAC mass concentrations are method-dependent 

(as described in section 2.3), as are light absorption efficiencies, on the wavelength at which the 

measurements are performed, due to the spectral dependence of light absorption. Uncertainties 

also arise due to the wide range in optical properties (i.e., complex refractive index) of LAC

applied in theoretical methods. 

75
Reconstructed extinction equations typically treat LAC as externally mixed (see 

equations 4 and 5), as well as assume that it is the only component of the aerosol that is 

absorbing solar radiation in the visible wavelengths. This formulation is based on the assumption 

that LAC refers only to “soot” particles; however, there is substantial evidence that some of the

carbonaceous aerosol, especially biomass smoke, being characterized as LAC by thermal 

methods is not soot and in fact is probably refractory organic carbon. Others have reported that 

light-absorbing carbon and a significant fraction of organic carbon from biomass smoke have

similar volatility and combustion temperatures, causing the split between LAC and OC to be 

poorly defined (and method-dependent) and leading to an overestimation of LAC and an 

underestimation of OC for biomass smoke (e.g., Novakov and Corrigan, 1995; Gelencsér et al., 

2000; Mayol-Bracero et al., 2002; Formenti et al., 2003; Guyon et al., 2003). A previous study 

by Malm et al. (1994a) in the northwestern United States showed that light absorption 

coefficients (as measured independently) correlated well with higher temperature fractions of OC

as well as LAC. Analyses of single particle data from Yosemite National Park (Hand et al., 

2005) showed that both the measured LAC and OC from TOR analysis corresponded to a type of 

nongraphitic refractory carbonaceous particle called tar balls, which are efficient at both 

scattering and absorbing light. Caution should be taken in always interpreting data from TOR 

analyses only as externally mixed OC and LAC particles, because TOR analyses are based on the 

refractory properties of carbon particles and not necessarily on their light-absorbing

characteristics. 

Theoretical calculations performed by Fuller et al. (1999) suggest a reasonable LAC mass

absorption efficiency of 6.5 m2

 g

-1; however, the average value of the empirical values listed in

Table 7 is 13 ± 6 m2

 g

-1. The IMPROVE equation applies a value of 10 m2

 g

-1. The scattering due 

76
to LAC is not considered in the IMPROVE equation. Estimates reported in Table 7 suggest an 

average fine mode LAC mass scattering efficiency of 3.6 ± 1.3 m2

 g

-1. Clearly, more work is 

needed to understand the absorption characteristics of carbonaceous aerosols. 

The summary of the survey results for all methods, including values currently used in the 

IMPROVE formulation, is reported in Table 6. The results suggest that POM mass scattering 

efficiencies are higher than what is applied in the IMPROVE reconstruction equation, even 

though the current IMPROVE formulation assumes an Roc multiplier of 1.4. However, in general,

the IMPROVE efficiencies fall within the range of the variability seen in the survey results. Fine 

soil in the IMPROVE formulation is assumed to correspond to the tail of the coarse dust size 

distribution; therefore the mass scattering efficiency associated with dust in a reconstructed 

PM2.5 bext calculation corresponds to a coarse dust mass scattering efficiency. If the fine dust 

concentration actually corresponds to a size distribution that peaks in the fine mode, the

corresponding mass scattering efficiency would actually be quite higher (~ 3 m2

 g

-1). Size 

distribution measurements at IMPROVE sites suggest this is not typically the case (e.g., Hand et 

al., 2002; Lee et al., 2004a, 2004b). 

Lowenthal and Kumar (2004) suggest that the mass scattering efficiencies applied in the 

IMPROVE formulation should be reevaluated based on a comparison of measured and 

reconstructed scattering that implies that scattering is overestimated 66% of the time on average 

at 20 IMPROVE sites. Dry ammonium sulfate mass scattering efficiencies from the survey are 

somewhat lower and ammonium nitrate efficiencies are somewhat higher than the IMPROVE

values, but the IMPROVE mass scattering efficiencies fall within the variability seen in the

survey results. Coarse mass (CM) efficiency is assumed to be 0.6 m2

 g

-1, and the absorption 

efficiency for light-absorbing carbon (LAC) is 10 m2

 g

-1, both falling within the range of

77
variability reported in the survey. In general the values of dry mass scattering efficiency applied 

in the IMPROVE equation are reasonable, given the range of ground-based values reported in 

the literature since 1990. 

5.4. Estimates of Dry Mass Scattering Efficiencies from IMPROVE Data 

The form of the IMPROVE equation for reconstructing particle extinction is 

bext = (3.0)f(RH){[(NH4)2SO4] + [NH4NO3]} + (4.0)[POM] + 1.0[Soil] + (0.6)[CM] + (10.0)[LAC] (16) 

where bext is the extinction coefficient (Mm-1) and enclosed in the brackets is the aerosol species

mass concentration (μg m-3). The parenthetically enclosed numerals in front of POM, soil, and 

coarse mass (CM) are the optimal dry mass scattering efficiencies as reviewed by White (1990) 

and Malm et al. (1994b). A nominal mass scattering efficiency value of 3.0 m2 g

-1 is applied for

dry ammonium sulfate and dry ammonium nitrate. The ratio of wet and dry scattering as a 

function of RH is the relative humidity scattering enhancement factor f(RH). 

In the IMPROVE monitoring program, nephelometers collocated with particle mass 

samplers have been operated at 22 sites, in some cases for more than 10 years. Therefore the 

validity of the assumptions associated with equation 16 can be explored and possibly refined by

comparing measured and reconstructed scattering. Four methods will be used as part of this 

strategy to estimate mass scattering efficiencies. We describe each method below, followed by a

comparison of results from each method for one site (Acadia National Park) and later for all 

sites. In addition to the uncertainties described in previous sections, the results from these

methods are subject to uncertainties in the bsp values measured by Optec NGN nephelometers at 

a wavelength of 550 nm. 

Method 1 uses a simple linear regression technique that assumes the relationship between 

scattering and species mass concentrations can be represented by equation 17. POM is assumed 

to be 1.8·OC, sea salt is estimated as 1.6·Cl-

, and soil and CM are grouped together. 

78
bsp = ao + a1f(RH)[(NH4)2SO4] + a2f(RH)[NH4NO3] + a3[POM] + a4[soil + CM] + a5[sea salt] (17) 

The regression coefficients are interpreted as the mass scattering efficiencies and the f(RH) 

curves are those associated with ammonium sulfate assuming a mass mean diameter of Dg= 0.4 

μm and geometric standard deviation of 2, and an ammonium sulfate D/Do curve estimated using 

the AIM “no solids” model (assumes equilibrium below the crystallization point). The f(RH) was 

calculated on one-hour intervals and averaged to 24 hours to be commensurate with the one-day 

sampling duration of the aerosol samples. 

Method 2 assumes an aerosol model of a fine mode internal mixture of inorganic 

ammonium salts (sulfate and nitrate) and POM that is externally mixed from soil, coarse mass, 

and sea salt. The measured fine mode mixture scattering (bmix) is approximated by 

bmix = bopen – bCM – bsoil – bSS (18) 

where bopen is measured with the PM10 open air nephelometer, and bCM, bsoil, and bSS (scattering

due to sea salt) are estimated using coarse mass, fine soil, and sea salt mass (1.6·Cl-

),

respectively. Sea salt scattering is estimated by multiplying the sea salt mass by a mass scattering 

efficiency of 1.37 m2

 g

-1and the f(RH) value defined above. If the assumptions are met that allow 

scattering associated with an internal and external mixture to be approximately equal, then 

αmixMmix = [(NH4)2SO4 + NH4NO3]αinorg + 1.27[POM]αinorg (19) 

where the specific mass scattering efficiency αmix of the mixed aerosol mass (Mmix = (NH4)2SO4

+ NH4NO3 + POM) is prorated to its chemical constituents based on their relative densities (1.27

= 1.78/1.4). The specific mass scattering efficiency of ammonium sulfate and ammonium nitrate 

is αinorg, and αPOM corresponds to the mass scattering efficiency of POM. Implicit assumptions 

in equation 19 are that the refractive indices of all the species are similar, the mixing ratios of the 

79
species are independent of the size distribution of the mixed aerosols, and the organic density is 

known. Therefore the estimated scattering of the mixture (bmix_est) is written as 

bmix_est = (3.0)f(RH)[(NH4)2SO4 + NH4NO3] + 3.81 [POM] (20) 

where 3 m2 g

-1 is the nominal mass scattering efficiency assigned to ammonium sulfate and 

ammonium nitrate, and 3.81 m2

 g-1 is the density-weighted mass scattering efficiency of POM 

(3.81 = 1.27·3). A regression is performed for bmix and bmix_est with a regression coefficient of a1. 

The inorganic and organic specific efficiencies can therefore be written as αinorg = a1·3.0 and αorg

= a1·3.81, respectively. 

Both methods 1 and 2 assume that the discrepancy between measured and estimated 

scattering can be accounted for by a single multiplicative constant, either for each species or for

the mixed aerosol. These approaches do not account for the possibility that mass scattering 

efficiencies vary as a function of mass concentration (due to its functional dependence on 

particle size, as described in the section 5.1). Therefore method 3 is used to investigate how mass

scattering efficiencies may vary with mass concentrations. A scattering correction factor (SCF) is 

defined as the ratio of measured scattering of the mixture (bmix) from equation 18 to the estimated 

scattering for the mixture (bmix_est). 

3.0 ( )[( ) ] 3.81[ ] _ f RH NH4 2 SO4 NH4NO3 POM

b b b b

b

b SCF open CM soil SS

mix est

mix

+ +

− − − = = (21) 

The SCF should equal 1 for all mass values if the assumptions used in computing bmix and bmix_est

are appropriate and if there is no functional dependence between mass scattering efficiency and 

Mmix. The functional relationship of SCF with the mixture mass (Mmix) was explored using 

equation 22 

SCF = ao + a1[Mmix] (22) 

80
where ao and a1 are the regression coefficients determined using a Theil regression analysis, and 

SCF is the scattering correction factor computed from equation 21. In this case, a linear

relationship is hypothesized; however, any functional relationship could be assumed. A new 

estimate of b'mix can be calculated using

b'mix_est = SCF'[3f(RH)[(NH4)2SO4 + NH4NO3] + 3.81[POM]] (23) 

where SCF′ is the estimated scaling factor derived from equation 22. New inorganic and organic 

specific mass scattering efficiencies are then calculated as α'inorg = 3.0·SCF' and α'org = 

3.81·SCF'. 

Methods 1–3 rely on statistical regressions between measured scattering coefficients and 

observed aerosol mass concentrations. For most sites, the mass scattering efficiencies increase

as ambient aerosol mass concentrations increase, presumably because of heterogeneous aerosol 

processes that are related to the aging of the aerosol. The increase in mass scattering efficiency is

primarily due to the aerosol size distribution growing into a size range that is more efficient at 

scattering light as mass concentrations increase. Method 4 takes into account changes in mass 

scattering efficiency as a function of mass due to shifts in particle size through a simple physical 

model of a linear combination of bimodal fine mode aerosol mass size distributions. One 

distribution is associated with the small size mode, lower mass concentrations, and lower mass 

scattering efficiencies, while the second size distribution corresponds to a larger size mode often 

observed under higher mass concentrations and higher mass scattering efficiencies. As was

discussed in section 3.7, bimodal size distributions in the fine mode reflect different atmospheric 

processes. However, these processes include not only changes in particle size, but also changes 

in composition as the particles age and undergo processing. The implications for the omission of

81
compositional changes in method 4 will be discussed later for results corresponding to the 

Phoenix site. 

The review of aerosol size distribution data reported in the peer-reviewed literature in

section 3.7 indicates that low aerosol mass concentrations are typically associated with mass size 

distributions with mass mean diameters (Dg) around 0.2 μm and with larger geometric standard 

deviations (σg), while higher mass loadings correspond to size distributions with Dg near 0.5 μm 

and smaller values of σg. Therefore the two mass size distributions were assumed to be

lognormals with a Dg of 0.2 μm and σg of 2.2, and Dg of 0.5 μm and σg of 1.2 for the small and 

large size modes, respectively. These size distributions were applied for all fine mode species 

(e.g., Hering et al., 1997) and used to compute dry mass scattering efficiencies. Humidification 

factors were computed for each size distribution and species also. The ambient scattering

coefficient for a linear combination of the bimodal size distribution is computed using 

( )

( ) ( ) ( )( ) ( ) , l s

j l

l j l

l s

l j

sp j s j s M M

M M

M f RH

M M

M M

b M f RH −

− + −

− = α α (24) 

where αs, αl, Ms, Ml, fs(RH), and fl(RH) are the dry mass scattering efficiencies, mass 

concentrations, and humidification factors associated with the small and large mass size

distributions, respectively. The species mass concentration is given by Mj. The mass scattering 

efficiencies associated with the small and large mass size distributions for each species are 

presented in Table 8. Unless otherwise stated, Ms = 0.0 μg m-3 and Ml = 20.0 μg m-3 for all 

species; when the species mass concentrations exceeded 20 μg m-3, the dry mass scattering 

efficiency was set equal to the large values shown in Table 8.

82
Table 8. Values used for the dry mass scattering efficiencies for the large and small mass size distributions

for each species. 

(m2

 g-1) Ammonium 

Sulfate 

Ammonium 

Nitrate POM 

αs (small) 2.2 2.4 2.8

αl (large) 4.8 5.1 6.1

To demonstrate the differences in these four methods and their effects on reconstructed 

scattering, data from Acadia National Park (ACAD) will be presented for each method.

Reconstructed total scattering (bsp_tot) was computed using 

bsp_tot = (3.0)f(RH)[(NH4)2SO4 + NH4NO3]+ 3.81[POM]+ (1.0)[Soil]+ (0.3)[CM] + (1.0)[Sea salt] (25) 

We applied ammonium sulfate and ammonium nitrate mass scattering efficiencies of 3.0 m2

 g-1, 

a POM mass scattering efficiency of 3.81 m2

 g-1 (assuming a POM multiplier of 1.8), and a CM 

specific efficiency of 0.3 m2

 g-1 to account for coarse particle truncation issues in the 

nephelometer. A statistical summary of the mass concentrations, RH, average number of hours in 

each 24-hour period of useable nephelometer data, average f(RH) using ambient RH and RH 

inside the nephelometer chamber, and new and presently used f(RH) curves for ACAD are 

provided in Table 9. A summary of measured and reconstructed total ambient scattering,

absorption, and contributions to scattering from each species is found in Table 10. Also listed in 

Table 10 is estimated scattering due to absorbed water on the ammoniated salts. Reconstructed 

total ambient scattering associated with dry mass is overestimated by about 15% on average, and 

scattering due to absorbed water is about half of the scattering due to inorganic mass,

emphasizing the importance of selecting an appropriate f(RH) curve (see Appendix 3 for similar

tables for all sites). The final row of Table 10 shows the bias in the calculation of reconstructed 

bsp. 

83
Table 9. A statistical summary of mass concentrations (μg m-3) at Acadia National Park. CM and FM refer to 

gravimetric coarse mass and fine (PM2.5) mass, respectively. AS and AN refer to ammonium sulfate and 

ammonium nitrate, respectively. POM is particulate organic matter using an Roc factor of 1.8. Mass units are 

(μg m-3). RH refers to ambient relative humidity. The number of nephelelometer data points in a 24-hr

average is given by N(bsp). The values of the revised f(RH) curves for the ambient RH (f(RH)amb,new) and the 

nephelometer chamber RH (f(RH)chamb,new) are also listed. Similar values are reported for the current f(RH) 

curves (f(RH)amb,old and f(RH)chamb,old). 

Variable Mean Std Dev Minimum Maximum Valid

CM (μg m-3) 3.77 3.89 -0.45 76.19 1093

FM (μg m-3) 6.15 5.18 0.46 45.58 1120

AS (μg m-3) 2.96 3.12 0.18 28.37 1138

AN (μg m-3) 0.36 0.39 0.01 3.30 1125

POM (μg m-3) 1.87 1.72 0.05 28.43 1132

LAC (μg m-3) 0.24 0.18 -0.01 1.33 1132

Soil (μg m-3) 0.24 0.27 0.00 4.34 1139

Sea Salt (μg m-3) 0.08 0.37 0.00 5.44 1158

RH (%) 68.70 12.31 30.41 89.78 1052

bsp (Mm-1) 21.79 25.46 1.96 240.92 406

N (bsp) 16.29 8.21 1.00 24.00 1158

f(RH)chamb,new 2.28 0.51 1.33 4.26 1038

f(RH)chamb,old 2.08 0.54 1.01 3.65 1038

f(RH)chamb,small 2.29 0.56 1.07 4.35 1038

f(RH)chamb,large 1.94 0.38 1.06 3.22 1038

f(RH)chamb,NaCl 2.89 0.69 1.00 4.78 1038

84
Table 10. A summary of bsp (Mm-1) for Acadia National Park. Values correspond to measured total ambient 

scattering (bsp), reconstructed total ambient scattering (bsp_recon), measured scattering associated with 

inorganics and organics (bmix), estimated scattering associated with inorganics and organics (bmix_est),

scattering due to ammonium sulfate (bsp(AS)), ammonium nitrate (bsp(AN)), particulate organic material

(bsp(POM)), soil and coarse mass (bsp(soil+CM)), sea salt (bsp(SS)), and water (bsp(H20)). Light absorption (bap) 

was computed assuming a mass absorption efficiency of 10 m2

 g-1. New f(RH) curves were used to estimate

wet scattering. POM was computed assuming an Roc factor of 1.8 and mass scattering efficiency of 3.8 m2

 g-1. 

Variable Mean Std Dev Minimum Maximum Valid

bsp 22.22 26.06 2.38 240.92 377

bsp_recon 25.16 23.99 3.78 219.35 377

bmix 20.69 25.75 0.82 240.16 377

bmix_est 23.64 23.56 3.34 218.59 377

bsp(AS) 14.14 18.25 1.28 184.85 377

bsp(AN) 2.45 3.15 0.18 27.76 377

bsp(POM) 7.05 5.94 0.83 67.24 377

bsp(Soil) 0.28 0.22 0.01 2.27 377

bsp(CM) 2.24 3.00 -0.21 45.71 377

bsp(SS) 0.13 0.80 0.00 12.27 377

bsp(soil+CM) 2.52 3.06 -0.07 46.20 377

bap 2.44 1.79 0.42 13.25 377

bsp(H2O) 8.48 11.26 0.75 112.63 377

( )

mix

mix mix est

b

b − b _

-0.14

The fractional contribution of each species to total scattering using equation 25 is 

presented in Table 11. The results from method 1 are reported in Table 12. A comparison of 

measured total ambient scattering and reconstructed total scattering using equation 25 and 

method 1 is shown in Figure 7 (similar tables corresponding to method 1 for all sites can be 

found in Appendix 3 and figures can be found in Appendix 4). Notice that reconstructed 

scattering from equation 25 is underestimated for low values of bsp and overestimated at high 

values of bsp, suggesting that mass scattering efficiencies vary with mass concentration. 

Reconstructed bsp derived from method 1 removes the biases observed at low and high bsp, but at 

the expense of having what appears to be unrealistic mass scattering efficiencies. The soil + CM

specific scattering efficiency is negative, which is unphysical, and the sea salt efficiency is 1.23 

m2

 g-1 (see Table 12), similar to values reported by Quinn et al. (2001, 2002b, 2004) for higher 

RH values. The average ammonium sulfate and POM mass scattering efficiencies of 3.29 m2

 g-1

85
and 3.43 m2

 g-1, respectively, are physically reasonable. However, sulfate mass scattering 

efficiencies may be overestimated and POM mass scattering efficiencies may be underestimated 

due to the relative uncertainties in each of those measurements. 

Table 11. Fractional contribution to total ambient scattering at Acadia National Park using equation 25. AS 

corresponds to ammonium sulfate and AN corresponds to ammonium nitrate. Particulate organic matter 

(POM) fraction was computed assuming an Roc factor of 1.8. The coarse mode fraction is given by CM. 

Species Fraction

of bsp

AS 0.64 

AN 0.11 

POM 0.32 

Soil 0.01 

CM 0.10 

Sea salt 0.01 

Table 12. The results from method 1 for Acadia National Park (see equation 17). The regression coefficients 

(ai) are listed, along with the standard error. Derived mass scattering efficiencies are also listed for 

ammonium sulfate (AS), ammonium nitrate (AN), particulate organic matter (POM = 1.8·OC), coarse mass 

combined with soil (soil+CM). and sea salt. The number of valid cases was 267 and there were 370 missing

data points. The r2

 coefficient was 0.95. 

Acadia National Park 

Variable Coefficient

(ai) 

Standard 

Error 

Derived Mass

Scattering 

Efficiency (m2

 g-1) 

AS 1.10 0.03 3.29

AN 0.62 0.13 1.87

POM 0.90 0.07 3.43

Soil+CM -0.23 0.13 -0.14

Sea salt 1.23 0.50 1.68 

86
Figure 7. Method 1 measured total ambient scattering and reconstructed total scattering using equation 25 

for Acadia National Park. 

Method 1

IMPROVE and Method 1 Scattering (Mm-1)

Measured Scattering (Mm-1)

ACAD

Estimates of specific scattering efficiencies for ammoniated salts (sulfates and nitrates) 

and POM mass scattering efficiency derived from method 2 are reported in the last two rows of 

Table 13. The derived sulfate and nitrate specific efficiency was 2.88 m2

 g-1 and the POM mass

scattering efficiency was 3.65 m2

 g-1. Comparisons of measured mixed bmix to reconstructed

mixed bmix,est using method 2 and equation 20 are shown in Figure 8 (similar tables 

corresponding to all sites for method 2 are found in Appendix 3 and figures are found in 

Appendix 4). The single multiplication factor derived from the regression between bmix and 

bmix_est that was used to correct the inorganic and organic mass scattering efficiencies does not 

87
remove the biases observed at low and high scattering values. It only serves to make the average 

method 2 reconstructed scattering equal that which is measured. 

Figure 8. Method 2 reconstructed mixed scattering (bmix,est, Mm-1) compared to measured mixed scattering 

(bmix, Mm-1) using equation 20 (fine mode contributions) for Acadia National Park. 

Method 2

IMPROVE and Method 2 Scattering (Mm-1)

Measured Scattering (Mm-1)

ACAD

Table 13. Results for method 2 for estimating specific mass scattering efficiencies for inorganics (αinorg) and

organics (αorg) for Acadia National Park. See text for full description. 

Results for Method 2 Regression 

(Acadia National Park)

a1 coefficient 0.96 

Standard error in a1 0.01 

αinorg (m2 g-1) 2.88 

αorg (m2 g-1) 3.65 

Statistical summaries of method 3 for Acadia National Park are reported in Tables 14–16. 

The intercept and slope from the Thiel regression of SCF versus mass (Mmix) are presented in 

88
Table 14. A slope of 0 corresponds to a constant mass scattering efficiency over the entire mass 

range, while the intercept is proportional to the over- or underestimation of the assumed mass 

scattering efficiencies for sulfates and POM (3 and 3.81 m2

 g-1, respectively). An intercept of 1 

and slope of 0 would imply that the assumed values provided good agreement between measured 

and reconstructed mixed (inorganic and POM) scattering. The comparison of fine mode

inorganic and organic mass concentrations and SCF is shown in Figure 9 (similar tables for all 

sites corresponding to method 3 can be found in Appendix 3 and similar figures can be found in 

Appendix 4). The Thiel regression line is also shown, demonstrating a fairly flat slope as 

reported in Table 14. Mass scattering efficiencies for ammoniated salts and POM that are 

associated with the 15% upper and lower mass concentrations are reported in Table 15. Finally,

the comparison of reconstructed and estimated mixed scattering using efficiencies derived from 

method 3 is shown in Figure 10. The summary of derived efficiencies from method 3 and the 

SCF factor are reported in Table 16. Accounting for the dependence of mass scattering efficiency 

on mass with method 3 removes these biases observed at low and high scattering by increasing 

the value of the efficiencies for low mass concentrations, and decreasing efficiencies that 

correspond to high mass concentrations (see Figure 10). As shown in Table 16, the average 

inorganic specific mass scattering efficiency using method 3 at Acadia National Park is 2.51 m2

g-1 (ranging from 2.36 to 3.45 m2

 g-1). The mean POM mass scattering efficiency was 3.18 m2 g1

 (ranging from 3.00 to 4.39 m2 g-1). 

Table 14. Results of the method 3 Thiel regression of SCF versus mass (Mmix = inorganics + organics) for

Acadia National Park. 

Method 3 Theil 

Regression results 

(Acadia National Park)

Intercept 0.78 

Slope 0.011 

Significance 0.04 

89
Figure 9. The comparison of fine mode mixed inorganic and organic mass concentrations (Mmix, μg m-3) and

the SCF for Acadia National Park. The Thiel regression line is shown. 

Inorganics + Organics (:g/m3)

SCF

ACAD

Table 15. Method 3 estimates of the overall mean and upper and lower specific scattering efficiencies

associated with the 15% upper and lower mass concentrations of mixed inorganic and organic mass for 

Acadia National Park. 

Acadia National Park 

Specific Scattering 

Efficiency (m2

 g-1) 

Lower Mean Upper

Inorganics (αinorg) 2.39 2.51 2.77

Organics (αorg) 3.04 3.18 3.51

90
Figure 10. Comparisons of method 3 reconstructed mixed scattering (bmix,est, Mm-1) to measured mixed

scattering (bmix, Mm-1) for Acadia National Park. 

IMPROVE and Method 3 Scattering (Mm-1)

Method 3

Measured Scattering (Mm-1)

ACAD

Table 16. Summary of the method 3 SCF and specific mass scattering efficiencies for inorganics (αinorg) and

organics (αorg) for Acadia National Park.

Acadia National Park 

Variable Mean Std Dev Minimum Maximum Valid data 

SCF 0.84 0.28 0.09 3.06 377

αinorg (m2

 g-1) 

2.51 0.14 2.36 3.45 1119

αorg

(m2 g-1) 

3.18 0.18 3.00 4.39 1119

From the discussion of these methods for data from Acadia National Park, it is clear that 

incorporating the dependence of mass scattering efficiencies on mass concentrations removed the

biases observed between measured and reconstructed extinction, and improved the comparison 

of reconstructed and measured scattering. For most sites, a linear relationship between mass and 

91
SCF appears to be a reasonable assumption, except at Great Smoky National Park (GRSM) 

where there seems to be a distinct nonlinearity. At GRSM the SCF is about 0.5 at lower mass

concentrations (< 5.0 μg m-3) and rapidly approaches one for higher mass concentrations. 

The mass scattering efficiencies computed with method 4, based on a physical model, are 

quite similar to those derived using method 3, a statistical fitting approach. The method 3 

specific mass scattering efficiencies associated with low mass concentrations are 2.39 m2

 g-1and 

3.04 m2

 g-1 for inorganics and organics, respectively. Mass scattering efficiencies derived using 

method 4 are 2.28, 2.21, and 2.89 m2

 g-1 for low concentrations of ammonium sulfate, 

ammonium nitrate, and POM, respectively (see Table 17). The difference between the two 

methods is on the order of 5%. The differences in sulfate mass scattering efficiencies 

corresponding to high mass concentrations between method 3 and method 4 were larger, with a 

difference of 10%. POM mass scattering efficiencies for high mass concentrations POM were 

very similar for both methods. A comparison of measured bsp and reconstructed bsp using method 

4 is shown in Figure 11. The good agreement between the two estimates is demonstrated through 

an OLS regression forced through a zero intercept with a slope of 1.01 ± 0.013 and an R2 = 0.91. 

Table 17. Method 4 estimates of the mean, and the upper and lower mass scattering efficiencies (m2 g-1)

associated with the 15% upper and lower mass concentrations for Acadia National Park. 

Acadia National Park 

Mass Scattering 

Efficiency (m2

 g-1) 

Lower Mean Upper

Ammonium Sulfate 2.28 2.58 3.29

Ammonium Nitrate 2.21 2.25 2.34

POM 2.89 3.10 3.56

92
Figure 11. Method 4 estimates of reconstructed scattering compared to measured scattering (bsp, Mm-1) for 

Acadia National Park. 

Method 4

IMPROVE and Method 4 Scattering (Mm-1)

Measured Scattering (Mm-1)

ACAD

We now summarize and discuss these methods for all of the sites where the analyses 

were performed. The mass scattering efficiencies derived from method 1 are summarized in 

Table 18, along with the standard error associated with each estimate. For ammonium sulfate the 

regression coefficients are all statistically significant at 5%, except for Snoqualamie WA

(SNPA), which is near the Cascade mountain range in the northwestern United States. The 

values are summarized for all sites in Figure 12, where the size of the circle corresponds to the 

magnitude of the mass scattering efficiency. The site in the Columbia River Gorge WA (CORI) 

is influenced by air masses from Portland, is in a high RH environment, and has a dry 

ammonium sulfate mass scattering efficiency that is greater than 3.0 m2

 g-1. However, typically 

93
the highest ammonium sulfate mass scattering efficiencies are found in the eastern United States, 

as well as Big Bend National Park TX (BIBE) where they are typically greater than 3.0 m2

 g-1. 

In the southwestern United States, the values are near 2.0 m2

 g-1 with the site in Sycamore 

Canyon AZ (SYCA) having the lowest value at 1.40 m2 g-1. The average dry ammonium sulfate 

mass scattering efficiency for the sites that are statistically significant at 5% is 2.65 m2

 g-1. This 

value is similar to the average values reported in the literature review of the theoretical method. 

Table 18. Summary of mass scattering efficiencies (m2 g-1) and standard errors for all sites using method 1. 

Mass scattering efficiencies are listed for ammonium sulfate (AS), ammonium nitrate (AN), particulate 

organic matter (POM = 1.8·OC), soil and coarse mass (soil + CM), and sea salt. 

Site AS AS

Std Err 

AN AN

Std Err

POM POM

Std 

Err 

CM + 

Soil 

CM+Soil 

Std Err 

Sea 

Salt 

Sea Salt

Std Err 

ACAD 3.29 0.08 1.87 0.40 3.43 0.28 -0.14 0.08 1.68 0.68

BIBE 3.20 0.08 1.38 0.76 3.58 0.21 0.29 0.02 56.03 58.17

BOWA 3.01 0.47 6.14 0.36 3.45 1.37 -0.56 0.33 2.26 5.98

CORI 3.59 0.24 5.15 0.20 2.54 0.22 0.06 0.05 0.84 0.55

DOSO 3.47 0.27 3.90 1.38 4.51 1.06 -1.19 0.44 0.00 0.00

GICL 1.66 0.15 2.38 1.18 5.73 0.08 0.11 0.04 1.55 24.88

HANC 2.44 0.21 6.68 0.73 3.81 0.20 0.20 0.04 0.00 83.57

GRSM 3.64 0.08 4.58 0.69 3.04 0.37 -0.85 0.19 0.00 532.74

IKBA 1.76 0.26 2.13 0.54 3.22 0.27 0.55 0.02 0.00 16.76

JARB 1.48 0.51 3.34 0.39 5.11 0.24 0.25 0.05 21.75 15.26

LOPE 2.77 0.28 4.77 0.13 3.30 0.23 0.13 0.06 4.48 37.51

MACA 3.36 0.15 4.52 0.23 2.66 0.52 -0.19 0.26 0.00 601.18

MORA 3.23 0.53 4.99 2.90 3.97 0.43 -0.36 0.27 3.45 5.56

OKEF 4.12 0.30 0.77 2.36 3.50 0.84 -0.17 0.29 0.00 0.00

PHOE 1.85 0.18 2.68 0.15 2.56 0.09 0.31 0.02 1.01 3.02

SENY 2.35 0.17 4.23 0.19 4.41 0.56 0.06 0.39 161.48 254.89

SHEN 3.44 0.10 2.64 0.35 2.33 0.51 -0.59 0.25 0.00 4895.51

SNPA 0.40 0.79 7.23 1.06 4.51 0.48 0.24 0.17 0.00 386.12

SYCA 1.40 0.30 5.06 0.85 4.56 0.16 0.24 0.02 -0.94 12.05

THIS 1.44 0.48 2.86 1.05 5.41 0.25 -0.02 0.10 0.59 7.74

UPBU 3.62 0.09 4.86 0.34 1.44 0.43 0.27 0.10 0.00 537.76

VIIS 3.15 0.29 9.47 1.51 -3.46 0.85 0.88 0.05 2.06 0.21

Avg 2.65 3.91 3.67 -0.06 12.10

94
Figure 12. Map of the mean ammonium sulfate mass scattering efficiencies (m2

 g-1) for the United States

derived using method 1. The size of the circle reflects the magnitude of the efficiency, which is printed next to 

the circle. 

The derived mass scattering efficiencies for POM are statistically significant at 5% at all 

sites except at Dolly Sods WV (DOSO). The values are summarized in Figure 13. A negative 

value was derived at the Virgin Islands (VIIS) (not shown), which is unphysical. In the East, as 

with sulfates, the implied mass scattering efficiencies are near 3.0 m2

 g-1 or greater. In the West, 

the coefficients are higher and variable but all within ranges that would be considered physically 

reasonable. Those sites typically influenced by wild fires tend to have higher POM mass

scattering efficiencies, consistent with recent analyses by Malm et al. (2005a) and Poirot and 

Husar (2004). The average POM mass scattering efficiency for statistically significant sites is 

3.67 m2

 g-1 and is within range of the values reported in Table 6, although closest to the MLR 

95
average value. The ratio of ammonium sulfate to POM mass scattering efficiencies on average is

1.38, which is similar to the ratio of POM to ammonium sulfate density of 1.21. 

Figure 13. Map of the mean POM mass scattering efficiencies (m2 g-1) for the United States derived using 

method 1. The size of the circle reflects the magnitude of the efficiency, which is printed next to the circle. 

Many of the ammonium nitrate mass scattering efficiencies are higher than could be 

reasonably expected, possibly because fine nitrate may be a surrogate for coarse particle nitrate 

(see section 3.2). Coarse mass specific mass scattering efficiencies that are statistically

significant vary from a low of 0.06 m2

 g-1 at CORI and Seney MI (SENY) to a high of 0.88 m2 g1

 at VIIS. Sea salt specific mass scattering efficiencies are only statistically significant at two 

locations, ACAD and VIIS. 

The specific mass scattering efficiencies for ammoniated salts (sulfate and nitrate) and 

POM mass scattering efficiencies derived from method 2 are summarized for all of the sites in 

Table 19. The values of αinorg range from 2.02 to 5.41 m2

 g-1, with an average of 2.87 m2 g-1. A

96
summary of the values is shown in Figure 14. The high value is in the Virgin Islands (not shown) 

where there is known to be large contributions to aerosol mass from sea salt and dust, so the 

inorganic salts could be influenced by those contributions. The low value occurred at Phoenix 

AZ (PHOE). The low and high values of efficiencies for POM also occurred at PHOE and VIIS,

with 2.56 and 6.87 m2

 g-1, respectively. These estimates are summarized in Figure 15. 

Throughout most of the United States, POM mass scattering efficiencies vary between about 3.5 

and 4.0 m2 g-1, with the Arizona sites having the lowest values (Figure 15). POM mass scattering 

efficiencies are higher than those for inorganics; however, there is less spatial variability in POM

mass scattering efficiencies compared to method 1 because of the internal mixing assumptions

inherent in method 2. Because only one multiplicative factor is used to scale both the inorganics

and the organics, the bias between measured and reconstructed scattering for low and high mass

concentrations remains. 

97
Table 19. Summary of specific mass scattering efficiencies (m2

 g-1) for inorganics (αinorg) and organics (αorg) 

for all sites using method 2.

Site αinorg

(m2

 g-1)

αorg

(m2

 g-1) 

ACAD 2.87 3.65

BIBE 2.91 3.69

BOWA 3.72 4.72

CORI 2.97 3.78

DOSO 3.06 3.88

GICL 3.35 4.25

HANC 2.81 3.57

GRSM 3.13 3.97

IKBA 2.58 3.27

JARB 3.13 3.97

LOPE 3.21 4.08

MACA 3.11 3.95

MORA 2.85 3.62

OKEF 3.29 4.17

PHOE 2.02 2.56

SENY 2.98 3.79

SHEN 2.82 3.58

SNPA 2.99 3.80

SYCA 2.44 3.10

THIS 3.07 3.90

UPBU 3.14 3.99

VIIS 5.41 6.87

Avg 2.87 3.65

98
Figure 14. Map of inorganic specific mass scattering efficiencies (αinorg, m2

 g-1) for the United States using 

method 2. The size of the circle reflects the magnitude of the efficiency, which is printed next to the circle. 

99
Figure 15. Map of organic (POM) mass scattering efficiencies (αorg, m2

 g-1) for the United States using 

method 2. The size of the circle reflects the magnitude of the efficiency, which is printed next to the circle. 

The results from method 3 using the Thiel regression of SCF and Mmix (intercept, slope, 

and t-values) from method 3 are listed in Table 20 for each site. As previously mentioned, a

slope of 0 corresponds to a constant mass scattering efficiency over the entire mass range, while 

the intercept is proportional to the underestimation of the assumed mass scattering efficiencies 

for sulfates and POM (3 and 3.81 m2

 g-1, respectively). An intercept of 1 and slope of 0 would 

imply that the assumed values provided good agreement between measured and reconstructed 

mixed (inorganic and POM) scattering. The average and one standard deviation intercept for all 

22 sites is 0.76 ± 0.16, while the average slope is 0.02 ± 0.03. 

100
Table 20. Summary of the results from method 3 using the Thiel regression of SCF and mass (Mmix) for each

site. The fourth column corresponds to the percent change in specific mass scattering efficiency (either for

inorganic or organics) from a doubling of the mixed inorganic and organic mass concentration (Mmix). 

Site Intercept slope t-value % change

ACAD 0.78 0.01 0.04 2.62

BIBE 0.66 0.03 0.00 9.54

BOWA 1.01 0.00 0.96 -0.29

CORI 0.57 0.04 0.00 12.15

DOSO 0.78 0.01 0.10 2.75

GICL 0.65 0.05 0.00 13.73

HANC 0.95 -0.01 0.46 -2.52

GRSM 0.64 0.02 0.00 6.05

IKBA 0.47 0.10 0.00 28.96

JARB 0.92 0.01 0.72 3.00

LOPE 0.67 0.04 0.00 11.62

MACA 0.98 0.00 0.55 0.43

MORA 0.82 0.01 0.43 2.66

OKEF 0.65 0.04 0.00 10.55

PHOE 0.63 0.00 0.49 0.66

SENY 1.13 -0.01 0.16 -2.48

SHEN 0.72 0.01 0.00 3.94

SNPA 0.74 0.03 0.09 8.50

SYCA 0.72 0.01 0.37 2.54

THIS 0.69 0.05 0.02 12.05

UPBU 0.80 0.02 0.00 3.76

VIIS 2.52 -0.21 0.01 -20.22

Avg 0.76 0.02 0.21 6.20

Std Dev 0.16 0.03 0.29 7.21

The fourth column in Table 20 corresponds to the percent change in mass scattering 

efficiency (either for inorganic or organics) resulting from a doubling of the mixed inorganic and 

organic mass concentration (Mmix). The results in the final column are shown in graphical form in 

Figure 16. Notice that the percent change in mass scattering efficiency resulting from a doubling 

of mass concentration is lowest in the eastern United States, with only a few percent change

along the Ohio River valley. Great Smoky Mountains National Park TN (GRSM) has a 6% 

change in mass scattering efficiency for a doubling of mass, while OKEF (Okefenokee GA) has 

an 11% change. Sites in the western United States exhibit the largest change in mass scattering

efficiency as a function of mass. Sites in the Northwest and Great Basin region all have percent 

101
changes between about 10 and 15%, while sites in Arizona vary from about a 1% change to as 

high as 29% at IKBA (Ikes Backbone AZ). The intercept data are shown in Figure 18. Sites 

along the Ohio River valley have intercepts between 0.9 and 1.0, implying 3.0 m2

 g-1 and 3.81 m2

g-1 are reasonable choices for dry mass scattering efficiencies. In the western United States, the 

intercepts range between 0.5 and 0.7, with a low value of 0.47 at IKBA, implying a lower mass

scattering efficiency would be more appropriate there. This result is consistent with what is 

observed at other sites in that region. 

Figure 16. Map of percent change in specific mass scattering efficiency (for either αinorg or αorg) due to a

doubling of mixture mass (Mmix) using method 3. The size of the circle reflects the magnitude of the change, 

which is printed next to the circle. 

102
Figure 17. Map of the intercept from the Theil regression in method 3. The size of the circle reflects the 

magnitude of the intercept, which is printed next to the circle. 

The mean, upper, and lower specific mass scattering efficiencies for the mixed 

ammonium salts and POM mass scattering efficiencies are reported in Table 21. The upper and 

lower mass scattering efficiencies are calculated by averaging the mass scattering efficiencies

associated with the upper and lower 15% mixed mass concentrations (Mmix). The percent change

between the upper and lower mass scattering efficiencies (either inorganics or organics) is

reported in the last column. The highest average inorganic specific mass scattering efficiencies

are found in the southeast United States, where they are near 3 m2

 g-1 or less (see Figure 18 for 

spatial distribution). The inorganic specific scattering efficiencies decrease towards the western

United States. The lowest inorganic specific mass scattering efficiencies (near 2.0 m2

 g-1) are 

found in Arizona. (IKBA, PHOE, and SYCA). The average inorganic specific mass scattering 

efficiency is 2.35 ± 0.34 m2

 g-1. 

103
Table 21. The mean, upper, and lower specific scattering efficiencies for inorganics (αinorg) and organics (αorg) 

computed with method 3. The upper and lower estimates are calculated by averaging the specific scattering

efficiencies associated with the upper and lower 15% mixed mass concentrations (Mmix). The percent change

between the upper and lower mass scattering efficiencies (final column) corresponds to both (αinorg) and (αorg). 

αinorg

(m2 g-1) 

αinorg

(m2 g-1) 

αinorg

(m2 g-1) 

αorg

(m2 g-1) 

αorg

(m2 g-1) 

αorg

(m2 g-1) 

Percent 

Change 

αInorg & αOrg

Site Lower Mean Upper Lower Mean Upper

ACAD 2.39 2.51 2.77 3.04 3.18 3.51 15.65

BIBE 2.13 2.48 3.06 2.71 3.15 3.89 43.47

BOWA 2.98 3.01 3.02 3.78 3.82 3.84 1.40

CORI 1.89 2.33 3.16 2.40 2.96 4.01 66.84

DOSO 2.46 2.71 3.17 3.12 3.44 4.02 29.02

GICL 2.10 2.51 3.60 2.67 3.19 4.57 71.51

HANC 2.68 2.77 2.83 3.40 3.52 3.59 5.75

GRSM 2.13 2.58 3.39 2.70 3.27 4.30 59.27

IKBA 1.75 2.25 2.90 2.23 2.85 3.68 65.39

JARB 2.78 2.84 2.97 3.53 3.61 3.77 6.75

LOPE 2.20 2.51 3.08 2.79 3.19 3.91 40.08

MACA 2.98 3.03 3.10 3.79 3.85 3.94 3.95

MORA 2.47 2.58 2.74 3.14 3.27 3.48 10.74

OKEF 2.41 3.00 3.92 3.06 3.81 4.97 62.53

PHOE 1.91 1.94 2.01 2.43 2.47 2.55 5.15

SENY 2.76 3.14 3.32 3.50 3.99 4.21 20.34

SHEN 2.27 2.55 3.04 2.88 3.23 3.86 33.94

SNPA 2.29 2.54 2.97 2.90 3.22 3.77 29.89

SYCA 2.20 2.25 2.36 2.79 2.86 2.99 7.33

THIS 2.11 2.44 3.11 2.68 3.10 3.95 47.15

UPBU 2.54 2.83 3.29 3.22 3.59 4.18 29.87

VIIS 4.90 6.22 6.97 6.22 7.90 8.86 42.34

Avg 2.35 2.61 3.04 2.99 3.31 4.08 31.24

Std Dev 0.34 0.30 0.40 0.44 0.38 0.50 23.70

104
Figure 18. Map of mean inorganic specific mass scattering efficiencies (αinorg, m2

 g-1) from method 3. The size

of the circle reflects the magnitude of the efficiency, which is printed next to the circle.

The spatial distribution of POM mass scattering efficiencies from method 3 is shown in

Figure 19. Inorganic and organic aerosols were assumed to be internally mixed; therefore the

POM scattering efficiencies are scaled to inorganic efficiencies by the ratio of their densities 

(1.31) and the spatial variability across the United States is the same for both. Notice, however, 

that in the central eastern United States the POM scattering efficiencies approach 4.0 m2

 g-1, the

value currently assumed in the Regional Haze Rule guidance. Also note that at GRSM there is

less than a 6% change in mass scattering efficiency for a doubling of mass concentration, but that 

the actual variability in observed mass results in a 60% change in mass scattering efficiency

between the upper and lower estimates when the functional dependence on mass is accounted for 

by this method. The average POM mass scattering efficiency is 3.31 ± 0.38 m2

 g-1, similar to that

derived for inorganics. 

105
Figure 19. Map of organic mass scattering efficiencies (αorg, m2

 g-1) from method 3. The size of the circle 

reflects the magnitude of the efficiency, which is printed next to the circle.. 

In the eastern United States the POM mass scattering efficiencies for method 3 are 

similar to method 1. However, method 3 results are quite different from method 1 in the western 

part of the country, where the efficiencies were near 2.0 m2

 g-1 or lower. One interesting feature

showing up in both analyses is lower mass scattering efficiencies in Arizona compared to 

adjacent monitoring sites. 

Table 22, like Table 20 for method 3, provides the mean, lower, and upper mass

scattering efficiencies for each species as derived using method 4. The upper and lower estimates 

are computed by averaging the mass scattering efficiencies associated with the upper and lower 

15% mass concentrations. Although results for VIIS are reported, calculations of the average and 

standard deviation in mass scattering efficiencies do not include data from VIIS. The results

derived with method 4 are quite similar to those from method 3, with similar values of the 

106
average mean, lower, and upper mass scattering efficiencies for all the sites. However, there is 

much greater variability in the results from method 3 compared to those from method 4. Method

3 also yields a significantly lower POM mass scattering efficiency for the urban area of Phoenix 

compared to method 4 (mean values of 2.47 versus 3.71 m2

 g-1). In fact, method 4 yields the 

highest POM mass scattering efficiencies (3.71 m2

 g-1) compared to other sites because it has

some of the highest POM mass concentrations; however, results from method 3 indicate that

PHOE has the lowest POM mass scattering efficiencies of all the sites. A possible reason for this

discrepancy is the calculation of POM. An Roc factor of 1.8 is used on all sites in methods 3 and 

4; however, the MLR regression in section 3.1 suggests that Phoenix has a much lower average 

Roc factor (1.3). If POM mass is overestimated in Phoenix due to a high Roc factor, the 

efficiencies derived with method 4 will be more strongly affected that those derived using 

method 3 because of how masses are weighted in the respective algorithms. If we correct the 

method 4 Phoenix POM mass scattering efficiency for an Roc factor of 1.3, the value decreases to

2.68 m2

 g-1 and we obtain a closer agreement with method 3 (2.47 m2 g-1). These differences in

mass scattering efficiencies between method 3 and 4 generally occur for all monitoring sites in 

the Southwest, suggesting that the difference in composition of the two size modes, not just the 

change in size, is potentially important and is not included in the method 4 formulation. These 

differences are highlighted by comparing Figures 18 and 19 to Figures 20 and 21 where the mass

scattering efficiencies for each monitoring site and species are shown. The effects of the 

different mass scattering efficiencies on estimated scattering will be investigated in section 7, 

where we present the biases between measured and estimated scattering for all the methods. 

107
Table 22. The mean, upper, and lower specific scattering efficiencies (m2

 g-1) for ammonium sulfate (AS), 

ammonium nitrate (AN), and particulate organic matter (POM) computed with method 4. The upper and 

lower estimates are calculated by averaging the mass scattering efficiencies associated with the upper and

lower 15% mass concentrations. The percent changes between the upper and lower mass scattering

efficiencies are shown in the final three columns. 

m2

 g-1 αAS αAS αAS αAN αAN αAN αPOM αPOM αPOM AS AN POM

Site lower mean upper lower mean upper lower mean upper % diff % diff % diff 

ACAD 2.28 2.58 3.29 2.21 2.25 2.34 2.89 3.10 3.56 43.95 6.03 23.48

BIBE 2.29 2.58 3.06 2.21 2.24 2.30 2.87 3.07 3.50 33.25 4.00 22.05

BOWA 2.26 2.44 2.79 2.20 2.27 2.56 2.86 3.09 3.60 23.49 15.99 25.68

CORI 2.25 2.39 2.62 2.22 2.33 2.72 2.92 3.27 3.95 16.64 22.87 35.49

DOSO 2.40 3.05 4.27 2.21 2.28 2.45 2.98 3.33 3.82 78.28 10.51 28.22

GICL 2.25 2.36 2.53 2.20 2.22 2.25 2.76 3.09 3.85 12.39 1.96 39.59

HANC 2.23 2.31 2.44 2.20 2.23 2.28 2.82 2.99 3.33 9.31 3.32 17.93

GRSM 2.40 3.05 4.22 2.21 2.26 2.41 2.97 3.39 4.02 75.47 8.68 35.29

IKBA 2.25 2.35 2.49 2.21 2.25 2.32 2.88 3.02 3.27 10.77 4.93 13.75

JARB 2.22 2.27 2.34 2.20 2.22 2.26 2.85 3.03 3.45 5.39 2.47 21.25

LOPE 2.25 2.34 2.48 2.22 2.30 2.61 2.89 3.11 3.49 10.08 17.82 20.74

MACA 2.48 3.11 4.20 2.23 2.34 2.65 3.03 3.41 4.02 69.20 19.01 32.90

MORA 2.22 2.35 2.61 2.20 2.23 2.28 2.86 3.20 3.81 17.57 3.33 33.02

OKEF 2.43 2.87 3.62 2.22 2.26 2.33 3.01 3.34 3.87 49.04 5.11 28.78

PHOE 2.29 2.42 2.60 2.24 2.37 2.83 3.14 3.71 4.98 13.24 26.64 58.21

SENY 2.28 2.54 3.24 2.21 2.32 2.76 2.85 3.14 3.69 42.31 25.05 29.25

SHEN 2.37 2.97 4.09 2.22 2.30 2.49 2.92 3.23 3.84 72.77 12.30 31.72

SNPA 2.23 2.35 2.56 2.21 2.25 2.34 2.84 3.10 3.62 15.08 5.85 27.20

SYCA 2.24 2.32 2.43 2.21 2.24 2.30 2.90 3.13 3.57 8.88 4.28 23.03

THIS 2.21 2.29 2.45 2.20 2.22 2.26 2.82 3.11 3.76 10.75 2.45 33.37

UPBU 2.34 2.81 3.67 2.22 2.34 2.66 2.97 3.33 3.93 57.30 19.97 32.19

VIIS 2.26 2.33 2.46 2.21 2.23 2.26 2.8 2.9 3.1 8.85 2.26 10.71

Avg 2.27 2.49 2.91 2.21 2.26 2.39 2.91 3.18 3.74 32.15 10.60 29.20

Std Dev 0.078 0.289 0.689 0.009 0.046 0.190 0.086 0.172 0.353 25.433 8.261 9.293

108
Figure 20. Map of the mean ammonium sulfate mass scattering efficiencies (αAS, m2

 g-1) from method 4. The 

size of the circle reflects the magnitude of the efficiency, which is printed near the circle. 

109
Figure 21. Map of mean POM mass scattering efficiencies (αPOM, m2

 g-1) from method 4. The size of the circle 

reflects the magnitude of the efficiency, which is printed near the circle. 

6. Evaluation of the Combined Data Set 

Section 5 focused on the various methods for estimating mass scattering efficiencies for 

each site individually. We now apply methods 3 and 4 to a combined data set from all the sites.

Data from PHOE and VIIS were not included in this combined data set because the results from 

these sites were consistent outliers. When analyses are performed on a per-site basis, site specific

coefficients are applied to data from each site; however, in this section we apply only one set of

assumptions to the combined data set. We will refer to results from methods 3 and 4 as applied to 

the combined data set as “M3-C” and “M4-C”, respectively. Method 3 yields an intercept and

slope for the combined data set of 0.8 and 0.015, respectively, and can be compared to the values 

110
derived for individual sites from Table 20. The average intercept and slope of all the individual 

sites was 0.69 and 0.04, respectively. 

Table 23 presents a statistical summary of aerosol mass concentrations for each species,

relative humidity, total aerosol scattering, and the average f(RH) estimates corresponding to the 

ammonium sulfate small size mode, large size mode, current IMPROVE estimate, and sodium 

chloride for the combined data from all the sites and time periods (except PHOE and VIIS). 

Ammonium sulfate composes 43% of the fine mass while POM contributes 34%. Soil

contributes 10% of the fine mass, ammonium nitrate is 7%, and light-absorbing carbon is 4%. 

Sea salt contributes less than 1%. 

Table 23. A statistical summary of mass concentrations (μg m-3) for the combined data set (all optical

monitoring sites except Phoenix and the Virgin Islands). CM and FM refer to gravimetric coarse mass and 

fine (PM2.5) mass, respectively. AS and AN refer to ammonium sulfate and ammonium nitrate, respectively. 

POM is particulate organic matter using an Roc factor of 1.8. RH refers to ambient relative humidity. The 

number of nephelometer data points in a 24-hr average is given by N(bsp). The values of the f(RH) 

corresponding to the nephelometer chamber for the ammonium sulfate small mode, large mode, current

IMPROVE estimate, and NaCl curves are also listed. The contribution to fine mass is provided in

parentheses. 

Variable Mean Std Dev Minimum Maximum Valid 

CM (μg/m3 ) 4.71 5.09 -17.74 116.56 13217 

FM (μg/m3 ) 7.15 6.35 -0.71 68.04 13630 

AS (μg/m3 ) 3.05 (43%) 3.90 0.00 46.69 13982 

AN (μg/m3 ) 0.51 (7%) 0.92 -0.06 16.92 13695 

POM (μg/m3 ) 2.45 (34%) 2.68 -0.19 104.41 13794 

LAC (μg/m3 ) 0.30 (4%) 0.30 -0.02 13.39 13768 

Soil (μg/m3 ) 0.68 (10%) 1.34 0.00 29.26 13881 

Sea Salt (μg/m3 ) 0.02 (<1%) 0.14 0.00 5.44 15051 

RH (%) 61.48 18.02 5.85 90.00 13300

bsp (Mm-1) 25.92 31.28 0.04 325.96 5899

N(bsp) 15.86 8.83 1.00 24.00 15051

f(RH)c,small 2.09 0.59 1.04 4.35 12727

f(RH)c,large 1.80 0.40 1.04 3.22 12727

f(RH)c,IMPROVE 1.87 0.59 1.00 3.65 12727

f(RH)c,NaCl 2.54 0.86 1.00 4.78 12727

111
Table 24. A summary of the low, mean, and high mass scattering efficiencies (m2

 g-1) for the combined data 

set with method 4 (M4-C), two statistical corrections to method 4 results (M4-C1 and M4-C2, see text), and 

results from method 3 applied to the combined data (M3-C). Results correspond to ammonium sulfate (AS),

ammonium nitrate (AN), and particulate organic material (POM). 

Using the combined data, we now investigate the performance of method 4 by evaluating 

different statistical regressions between the method 4 estimated and measured scattering. The 

results of the regressions are summarized in Table 24. The mean and lower and upper mass

scattering efficiencies for the combined data set as derived by method 4 are referred to as “M4-

C”. The first statistical approach (M4-C1) corresponds to a regression of the scattering estimates 

from method 4 for each species against the measured scattering, bmix, with adjustments to the 

method 4 dry mass scattering efficiencies by the regression coefficients corresponding to each 

species. The regression coefficients were near 1, indicating that method 4 results in average mass 

scattering efficiencies that are representative of the actual mass scattering efficiencies. The 

statistical approached referred to as “M4-C2” is similar to M4-C1 except the regression is

between fine mode (summed inorganics and organics, bmix_est) scattering from method 4 and 

measured bmix (similar to method 2), resulting in a single regression coefficient instead of

coefficients corresponding to each species. The regression coefficient is not statistically different 

from 1, implying again that dry mass scattering efficiencies derived with method 4 are 

representative of actual values. Finally, results from method 3 applied to the combined data 

(M3-C) are very similar to the results from method 4 (see last row in Table 24). The values in 

Table 24 should be contrasted to those used in the current IMPROVE equation for estimating

α (m2 g-1) AS AN POM

Case low mean high low mean high low mean high

M4-C 2.23 2.52 3.28 2.21 2.25 2.41 2.87 3.18 3.80

M4-C1 2.19 2.47 3.22 4.12 4.21 4.49 2.59 2.87 3.43

M4-C2 2.28 2.57 3.36 2.26 2.31 2.46 2.94 3.25 3.89

M3-C 2.45 2.67 3.14 2.45 2.67 3.14 3.10 3.38 3.97

112
scattering. The current IMPROVE ammonium sulfate, ammonium nitrate, and POM mass 

scattering efficiencies are 3.0, 3.0, and 4.0 m2

 g-1, respectively, roughly 20–25% higher than 

estimates obtained from method 4 (2.52, 2.25, and 3.18 m2

 g-1 for ammonium sulfate, ammonium

nitrate, and POM, respectively). 

A summary of measured and reconstructed total bsp and accumulation mode bmix using 

method 4 is presented in Table 25. Also presented are estimates of scattering associated with 

each species, fine particle absorption, and scattering due to water. There is only about a 3%

difference on average between estimated and measured scattering for both fine and total 

scattering. Ammonium sulfate and POM contribute 41 and 27%, respectively, to total extinction,

while CM contributes 12%. Nitrate and soil each contribute less than 10% of total scattering,

and sea salt contributes less than 0.2 of one percent. 

Table 25. A summary of bsp (Mm-1) for the combined data set (all monitoring sites except Phoenix and the

Virgin Islands). Values correspond to measured total ambient scattering (bsp), reconstructed total ambient

scattering (bsp_recon), measured scattering associated with fine mode inorganics and organics (bmix), estimated

scattering associated with inorganics and organics (bmix_est), scattering due to ammonium sulfate (bsp(AS)), 

ammonium nitrate (bsp(AN)), particulate organic material (bsp(POM)), sea salt (bsp(SS)), and water (bsp(H20)).

Light absorption (bap) was computed assuming a mass absorption efficiency of 10 m2

 g-1. New f(RH) curves 

were used to estimate wet scattering. 

Variable (Mm-1) Mean Std Dev Minimum Maximum Valid 

bsp 25.56 30.00 0.04 273.50 5090

bsp_recon 24.80 27.83 0.27 301.00 5090

bmix 22.74 29.92 -11.01 271.99 5090

bmix_est 21.98 27.61 0.10 298.70 5090

bsp(AS) 11.92 21.84 0.39 292.39 5090

bsp(AN) 2.27 4.90 -0.19 74.16 5090

bsp(POM) 7.79 9.01 -0.36 194.13 5090

bsp(Soil) 1.02 1.66 0.01 29.26 5090

bsp(CM) 3.52 3.68 -3.12 69.94 5090

bsp(SS) 0.04 0.41 0.00 15.12 5090

bap 2.74 2.15 -0.11 30.25 5090

bsp(H2O) 6.31 11.55 0.06 158.15 5090

113
7. Biases between Reconstructed and Measured Scattering 

In this section we present a brief summary of the skill with which each method

reconstructs total scattering as measured by the Optec ambient open air nephelometer. We

compute the average bias as (bsp_recon - bsp_meas)/bsp_meas for time periods with low (10–20%), 

median (45–55%), and high (80–90%) measured scattering values. The results for each of the 

five methods (current IMPROVE and methods 1–4) are presented in Tables 26–28 and Figures 

22–26. 

The poorest performance for all the methods corresponds to time periods with the 10–

20% lowest measured scattering coefficients. The statistical models (methods 1–3) demonstrate 

the weakest performance, with average biases across all sites for method 1 and method 2 of 63 

and 82%, respectively. Methods 3 and 4 perform the best, with average biases of 46 and 44%, 

respectively. The biases for all the methods tend to increase and decrease for each sites similarly 

(see Figure 22). The bias was near 150% at Ikes Backbone AZ (IKBA) and Jarbridge

Wilderness NV (JARB) and near zero at Shenandoah National Park VA (SHEN), Three Sisters 

Wilderness OR (THIS), and Upper Buffalo Wilderness AR (UPBU). The biases corresponding 

to the eastern monitoring sites were the lowest, ranging from 25–30 % for methods 3 and 4. 

The lowest average biases corresponding to time periods with the median (45–55%) 

measured scattering coefficients were 4.3 and 1.2%, corresponding to methods 3 and 4, 

respectively. The highest average biases for this case were 13 and 22%, corresponding to 

methods 1 and 2, respectively. Note that the bias at Phoenix is smallest (<10%) for the methods 

that were applied on a site-by-site basis (methods 1–3), compared to the highest bias (~ 30%) for

method 4, which was applied similarly to the entire data set. Phoenix has relatively high 

concentrations of POM with quite low mass scattering efficiencies, as compared to more remote 

114
nonurban locations; these unique conditions are accounted for in the site-by-site evaluations 

(methods 1–3), but not in the site-independent algorithm applied in method 4. 

Methods 1 and 2 have the lowest biases (1–2%) corresponding to the highest (80–90%) 

scattering values; however, all models performed well under these conditions, with biases of less 

than 10%. Method 4 has an average bias across all sites of -9%. Methods 1–3 perform the best 

for the Phoenix site for the reasons discussed above. 

Table 26. Average biases for time periods with low (10–20%) measured scattering values for methods 1–4 

and the current IMPROVE equation. 

Site Method 1 Method 2 Method 3 Method 4 IMPROVE 

ACAD 0.433 0.510 0.270 0.213 0.320 

BIBE 0.779 0.866 0.402 0.518 0.577 

BOWA 0.440 1.341 0.790 0.485 0.571 

CORI 1.105 1.419 0.640 0.965 1.109 

DOSO 0.637 0.732 0.485 0.308 0.265 

GICL 0.875 1.450 0.478 0.676 0.858 

HANC 0.556 0.568 0.515 0.188 0.359 

GRSM 0.423 0.565 0.097 0.235 0.242 

IKBA 1.455 1.421 0.819 1.199 1.383 

JARB 1.358 1.800 1.328 1.066 1.277 

LOPE 0.521 0.841 0.380 0.345 0.428 

MACA 0.308 0.376 0.318 0.087 0.125 

MORA 1.536 1.530 0.956 1.025 1.157 

OKEF 0.563 0.754 0.374 0.288 0.336 

PHOE 0.109 0.201 0.096 0.421 0.468 

SENY -0.027 0.031 0.140 -0.211 -0.093

SHEN 0.429 0.584 0.317 0.336 0.404 

SNPA 0.405 0.554 0.243 0.225 0.336 

SYCA 0.810 0.837 0.677 0.774 0.857 

THIS 0.327 0.456 0.116 0.099 0.182 

UPBU 0.210 0.398 0.130 0.050 0.099 

Avg 0.631 0.821 0.456 0.442 0.536 

115
Figure 22. The average biases for each site corresponding to time periods with low measured scattering

values (10–20%) (see Table 26).

Bias corresponding to Low Scattering Range 

-0.5

0.0

0.5

1.0

1.5

2.0

ACAD

BIBE

BOWA

CORI

DOSO

GICL

HANC

GRSM

IKBA

JARB

LOPE

MACA

MORA

OKEF

PHOE

SENY

SHEN

SNPA

SYCA

THIS

UPBU

Site

A

verage Bias

Method 1 Method 2 Method 3 IMPROVE Method 4

Table 27. Average biases for time periods with the median (45–55%) measured scattering values for methods

1–4 and the current IMPROVE equation. 

Site Method 1 Method 2 Method 3 Method 4 IMPROVE 

ACAD 0.140 0.186 0.016 -0.028 0.054 

BIBE 0.204 0.232 0.002 0.027 0.038 

BOWA -0.043 0.248 -0.041 -0.208 -0.117

CORI 0.250 0.432 0.052 0.201 0.246 

DOSO 0.362 0.239 0.090 -0.023 -0.057

GICL 0.097 0.489 0.000 0.043 0.123 

HANC 0.232 0.235 0.202 0.014 0.072 

GRSM 0.190 0.258 0.010 0.077 0.045 

IKBA 0.169 0.194 0.020 0.097 0.163 

JARB 0.152 0.299 0.133 -0.011 0.049 

LOPE 0.160 0.392 0.100 0.043 0.080 

MACA 0.110 0.114 0.076 -0.062 -0.072

MORA 0.224 0.218 0.045 0.075 0.093 

OKEF 0.097 0.170 0.027 -0.081 -0.069

PHOE -0.020 0.062 -0.018 0.331 0.299 

SENY -0.118 -0.057 0.028 -0.256 -0.151

SHEN 0.085 0.184 0.037 0.054 0.073 

SNPA 0.187 0.257 0.107 0.042 0.072 

SYCA -0.007 0.035 -0.050 0.003 0.055 

THIS 0.042 0.157 -0.010 -0.087 -0.043

UPBU 0.134 0.231 0.069 -0.010 -0.014

Avg 0.126 0.218 0.043 0.012 0.045 

116
Figure 23. The average biases for each site corresponding to time periods with median measured scattering 

values (45–55%) (see Table 27).

Bias corresponding to Median Scattering Range

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

0.6

ACAD

BIBE

BOWA

CORI

DOSO

GICL

HANC

GRSM

IKBA

JARB

LOPE

MACA

MORA

OKEF

PHOE

SENY

SHEN

SNPA

SYCA

THIS

UPBU

Site

A

verage Bias

Method 1 Method 2 Method 3 IMPROVE Method 4

Table 28. Average biases for time periods with high (80–90%) measured scattering values for methods 1–4 

and the current IMPROVE equation. 

Site Method 1 Method 2 Method 3 Method 4 IMPROVE 

ACAD 0.093 0.119 0.020 -0.016 0.024

BIBE -0.022 -0.020 -0.073 -0.121 -0.152

BOWA -0.006 0.224 -0.027 -0.191 -0.115

CORI -0.054 0.106 -0.057 -0.006 -0.031

DOSO 0.140 0.056 -0.011 -0.098 -0.139

GICL 0.049 0.182 -0.047 -0.117 -0.113

HANC -0.152 -0.149 -0.166 -0.270 -0.254

GRSM 0.002 -0.008 -0.029 -0.016 -0.131

IKBA -0.068 -0.071 -0.007 -0.110 -0.088

JARB -0.144 -0.080 -0.147 -0.275 -0.250

LOPE -0.042 0.025 -0.132 -0.208 -0.181

MACA -0.016 -0.039 -0.063 -0.140 -0.169

MORA -0.012 -0.020 -0.095 -0.093 -0.109

OKEF -0.002 -0.004 0.015 -0.155 -0.194

PHOE -0.057 -0.025 -0.067 0.456 0.193

SENY 0.005 -0.003 0.011 -0.154 -0.108

SHEN -0.006 0.046 0.000 0.028 -0.021

SNPA -0.010 -0.049 -0.096 -0.178 -0.183

SYCA -0.068 -0.072 -0.128 -0.039 -0.056

THIS 0.009 0.045 0.061 -0.088 -0.152

UPBU -0.053 -0.024 -0.069 -0.135 -0.161

Avg -0.020 0.011 -0.053 -0.092 -0.114

117
Figure 24. The average biases for each site corresponding to time periods with high measured scattering 

values (80–90%) (see Table 28).

Bias corresponding to High Scattering Range

-0.4

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

ACAD

BIBE

BOWA

CORI

DOSO

GICL

HANC

GRSM

IKBAJARB

LOPE

MACA

MORA

OKEF

PHOE

SHEN

SENY

SNPA

SYCA

THIS

UPBU

Site

A

verage Bias

Method 1 Method 2 Method 3 IMPROVE MWS

Figure 25. Average biases for the combined data set (all sites and time) for time periods with low (10–20%), 

median (45–55%), and high (80–90%) scattering ranges, as calculated using methods 3 and 4, and the current

IMPROVE algorithm. Also shown is the average of the per-site biases from Tables 26–28. The f(RH) curves

were calculated for continuous growth from 1 < RH < 90%.

Bias for Combined Data

(RH < 90 % cutoff - Continuous Curve)

-0.2

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

0.6

Low Median High

A

verage Bias

Method 4 (M4-C)

Method 3 (M3-C)

IMPROVE

Method 4 (per-site avg)

Method 3 (per-site avg)

IMPROVE (per-site avg)

118
Figure 26. Average biases for the combined data set (all sites and time) for time periods with low (10–20%), 

median (45–55%), and high (80–90%) scattering ranges, as calculated using methods 3, 4, and the current 

IMPROVE algorithm. The f(RH) curves were calculated from 1 < RH < 95% assuming crystallization 

growth curves. 

Bias for Combined Data

(RH < 95 % cutoff - Crystallization Curve)

-0.2

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

Low Median High

A

verage Bias

Method 4 (M4-C)

Method 3 (M3-C)

IMPROVE

The biases were also computed for the combined data set of all sites and time periods. In 

this analysis the bias is calculated for each 24-hour sampling period and then averaged, thus 

biasing the results toward those monitoring sites that have been operating over longer periods of 

time. This approach should be contrasted against the bias computed as the grand average of all 

the site average biases, thus weighting each monitoring site or geographic location equally. 

Figures 25 and 26 show the average bias corresponding to time periods with low, median, and 

high scattering periods for method 4 (MC-4), method 3 (MC-3), and the current IMPROVE

algorithm for the combined data set. Two f(RH) curves were used in these calculations. Because 

the Regional Haze Rule suggests using an RH cutoff of 95%, the bias calculations were 

computed using RH cutoff values of both 90 and 95%. Figure 25 presents the biases computed 

assuming a 90% RH cutoff and continuous (1 < RH < 90%) f(RH) curves for both the combined 

data set and the site-by-site average, while Figure 26 presents the same biases computed with a 

119
95% RH cutoff and f(RH) curves corresponding to the crystallization branch for the combined

data set only. 

For the f(RH) curve corresponding to a 90% cutoff RH, the biases corresponding to the 

low scattering values are the largest for all the methods, ranging from 45 to almost 60%. The

biases corresponding to the median scattering values range from 0–10%, and the biases 

corresponding to the highest scattering values are negative (-10–0%) (see Figure 25). The biases 

computed for an average of all the sites are lower than biases computed for the combined data 

set, by about 10% for the low scattering range, 5% at the median scattering range, and within a 

few percent at the high scattering range. The lower bias corresponding to the averaged per-site 

estimates is consistent with the earlier example of better performance at the Phoenix site when 

analyses are performed on a per-site basis. The biases computed from method 3 as applied to the

combined data set (M3-C) were highest for the low and median scattering range, and the method 

4 average of the per-site analyses had the lowest biases for the low and median scattering ranges.

For the time periods with the highest scattering range, M3-C had the lowest bias, while the 

current IMPROVE formulation had the largest (most negative) bias. Overall, M4 for the per-site 

analyses had the lowest bias. Computing the biases with f(RH) curves corresponding to a higher 

RH cutoff (95%) resulted in lowering the biases for all the methods compared to an RH cutoff of 

90%. This decrease in bias does not imply that the bias was necessarily improved, because a bias

could decrease from -10 to -20%, reflecting a larger difference between measured and predicted 

scattering. The biases corresponding to the low scattering range dropped by about 10%, and the 

median and high bias dropped by about 6–8%. Method 4 (M4-C) results are biased negatively by 

about 14% for the high scattering values, negatively by 6% for the median values, and positively 

by 31% for low scattering values. 

120
8. Summary of Suggested Refinements to the IMPROVE Equation 

The current equation used to estimate extinction associated with measured aerosol 

species is 

bext = αASf(RH)AS[AS]+αANf(RH)AN[AN]+ αPOM[POM]+ αsoil[Soil]+ αCM [CM]+ αLAC[LAC] (25) 

where it is assumed that the dry mass scattering and absorption efficiencies αAS, αAN, αPOM, αsoil,

αCM, and αLAC are 3.0, 3.0, 4.0, 1.0, 0.6, and 10.0 m2 g-1, respectively, and the f(RH) curve is 

calculated on an hourly basis and averaged to 24 hours to be commensurate with the 24-hour

average aerosol mass measurements. The f(RH) curve is a “smoothed” ammonium sulfate curve 

that reflects continuous particle growth starting at 40% RH. The forms assumed for each of the 

aerosol species are ammonium sulfate and ammonium nitrate, 1.4·OC, soil, and gravimetric 

coarse mass (PM10–PM2.5). 

Uncertainty in estimated extinction is dependent on not only the assumed forms of each 

of the aerosol species and their respective mass scattering efficiencies and growth factors, but 

also on measurement and analytic accuracy and precision. One uncertainty of special concern is

the variation in flow rate associated with the IMPROVE monitoring system, because 

uncertainties in the flow rate affect the cutpoint of the inlet. The IMPROVE 2.5 μm inlet 

intersects the size range corresponding to the coarse mode; therefore any changes in the cutpoint 

of the inlet (due to variations in the flow rate) cause significant and varying amounts of coarse 

material to be characterized as fine mass. The fine mode mass scattering efficiency associated 

with the fine tail of the coarse mode can vary significantly. This issue is especially important for 

sites where soil mass contributes significantly to estimated extinction (e.g., most sites in the

West during spring months) and for sites where coarse particle nitrate concentrations are high.

Some of the issues associated with measurement uncertainty have been discussed, but this report 

121
does not make any recommendations on changes in measurement methodology or analytic 

procedures. 

Another significant uncertainty in reconstructed bext is the chemical form of each of the 

aerosol species. Again, this issue is discussed in some detail in this report, but because the 

ammonium ion is not measured, the current assumption of interpreting sulfate and nitrate in the 

fine mode as ammonium sulfate and ammonium nitrate is not changed. However, the 

multiplication factor (Roc = 1.4) used to estimate particulate organic material from measured 

organic carbon mass in the current equation is undoubtedly low. Based on recent literature 

review and an analysis of IMPROVE data, we recommend a value of 1.8. We also recommend 

the inclusion of fine sea salt in the IMPROVE equation as 1.8·Cl per the above discussion. 

Recognizing that fine sea salt is probably the fine tail of coarse mode sea salt, a new f(RH) 

function and dry mass scattering efficiency for sea salt was developed. No new recommendation 

of fine mass absorption efficiency is made. 

Because coarse mass is not speciated, we cannot recommend a change in coarse mass 

scattering efficiency. Coarse mass is not composed only of crustal material but also contains 

significant fractions of organic and inorganic species, some of which are hygroscopic and light 

absorbing and therefore have mass scattering efficiencies that differ significantly from the 

currently assumed value of 0.6 m2

 g-1. Thus it should be recognized that coarse mass extinction is

only a very rough estimate. Coarse mass concentrations are also only approximate because the 

PM2.5 cutpoint intersects the size range that corresponds to the peak of the coarse mode mass size

distribution, and flow rate variability can cause the cutpoint to vary substantially. 

At most monitoring sites, dry mass scattering efficiencies increase with increasing mass 

concentration. This relationship was observed at most of the rural sites and at the one urban site 

122
(Phoenix) in the optical monitoring network. The trend toward increasing mass scattering 

efficiency with mass concentrations was treated with two separate approaches. A variety of 

statistical regressions of mass concentration and scattering coefficients were applied (methods 1–

3); however, results from statistical regressions are only as robust as the data themselves. 

Therefore the second approach (method 4) was based on a physical model of a bimodal fine 

mode size distribution. The small size mode corresponds to lower mass concentrations and 

particles that are less efficient at scattering light, while the large size mode is associated with 

higher mass concentrations and particles that are more efficient at scattering light. The mass 

scattering efficiencies were computed for a simple linear mixing of these size modes as a 

function of mass. This model was applied to those species typically found in the fine (Dp < 2.5 

μm) mode, namely sulfates, nitrates, and POM. 

The fine mode bimodal mass size distributions were assumed to be lognormal

distributions with mass mean diameters (Dg) of 0.2 μm and 0.5 μm for the small and large size

modes, respectively, and with geometric standard deviations (σg) of 2.2 and 1.2, respectively, 

consistent with what is reported in the literature. The ambient scattering coefficient for each 

species is calculated using the same size distribution parameters. An ammonium sulfate f(RH) 

curve is calculated for each size distribution and the ambient scattering for each species is 

calculated using 

( )

( ) ( ) ( )

( ) ( ) , l s

j l

l j l

l s

l j

sp j s j s M M

M M

M f RH

M M

M M

b M f RH −

− + −

− = α α (26) 

where αs, αl, Ms, Ml, fs(RH), and fl(RH) are the dry mass scattering efficiencies, mass 

concentrations, and humidification factors associated with the small and large mode mass size 

distributions, respectively. The species mass concentration is given by Mj. The mass scattering 

efficiencies associated with the small and large mass size distributions for each species are 

123
presented in Table 29. Unless otherwise stated, Ms = 0.0 μg m-3 and Ml = 20.0 μg m-3; when the 

species mass concentrations exceeded 20 μg m-3, the dry mass scattering efficiency was set equal 

to the large values shown in Table 29. 

Table 29. Values used for the dry mass scattering efficiencies (m2 g-1) for the large and small mass size

distributions for each species (ammonium sulfate, ammonium nitrate, and particulate organic material,

POM). 

m2 g-1 Ammonium

sulfate 

Ammonium 

nitrate 

POM 

αs (small) 2.2 2.4 2.8 

αl (large) 4.8 5.1 6.1 

The bias between modeled and measured scattering is similar for method 3 (statistical 

approach) and method 4 (physically based model) as applied to the combined data set; however 

method 4 has an advantage of being less dependent on the data set in its formulation. 

A substantial number of measurements of D/Do and f(RH) curves indicate that aerosol 

growth occurs at low RH values well below the crystallization points. New f(RH) curves are 

recommended that are based on an ammonium sulfate D/Do “no solids” growth curve with a 

mass size distribution corresponding to those mass size distributions discussed above. The “no 

solids” curve extends the D/Do curve to relative humidity values below the ammonium sulfate 

crystallization point. However, there is little difference in the bias between estimated and 

measured scattering for the case when f(RH) is assumed to be 1 below the crystallization point 

compared to when continuous growth between 1 < RH < 90% is assumed. Currently, organic 

mass is not assumed to be hygroscopic and no change is recommended in this assumption, 

although there is some evidence that ambient organics may be very weakly hygroscopic at high 

RH values (RH > 85%). 

The form of the extinction equation using method 4, and including site-specific Rayleigh 

scattering and absorption by gaseous NO2, is 

124
[ ] [ ]

[ ] [

[ ] [ ]

[ ]

[ ]

[ ]

[ ]

[ ] 2 2

4 3 4 3

4 2 4 4 2 4

( )

0.6

1.4 ( )

1

10

2.8 6.1 arg

2.4 ( ) 5.1 ( ) arg

2.2 ( ) ( ) 4.8 ( ) arg ( )

EE NO

Rayleigh Scattering Site Specific

Coarse Mass

f RH Sea Salt

Fine Soil

Elemental Carbon

Small POM L e POM

f RH Small NH NO f RH L e NH NO

b f RH Small NH SO f RH L e NH SO

NO

SS

S L

ext S L

+ ×

+

+ ×

+ × ×

+ ×

+ ×

+ × + ×

+ × × + × × ]

≈ × × + × ×

 (27) 

The apportionment of the total concentrations of ammonium sulfate ((NH4)2SO4) into the 

concentrations of the small and large size fractions is accomplished using the following 

equations: 

[ ] [ ] [ ] 4 2 4

4 2 4

4 2 4 ( ) 20

( ) arg ( ) Total NH SO Total NH SO L e NH SO = × (28) 

[ ] [ ] [ ] 4 2 4 4 2 4 4 2 4 Small (NH ) SO = Total (NH ) SO − Large (NH ) SO (29) 

Similar equations are used to apportion total ammonium nitrate (NH4NO3) and total particulate 

organic material (POM = 1.8·OC) concentrations into the small and large size fractions. 

125
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