RECONSTRUCTING LIGHT EXTINCTION FROM AEROSOL MEASUREMENTS

Procedure for reconstructing light extinction from dry aerosol measurements

The light-extinction coefficient, b_ext (expressed as inverse megameters, 1/Mm), is the sum

(3.1)

where b_scat is the sum of scattering by gases and scattering by particles, and b_abs is the sum of absorption by gases and particles. Scattering by gases in the atmosphere, b_sg, is described by the Rayleigh scattering theory [vandeHulst, 1981] and will be referred to as Rayleigh scattering. The IMPROVE program assumes a standard value of 10 1/Mm. Scattering by particles, b_sp, is caused by both fine and coarse aerosol species and is the largest contributor to total light extinction in most locations [Malm et al., 1994a]. Absorption due to gases, b_ag, is primarily due to nitrogen dioxide (NO₂) and is assumed to be negligible because almost all monitoring sites are in rural locations [Trijonis and Pitchford, 1987]. Absorption by particles, b_ap, is caused primarily by carbon containing particles.

A particle in the atmosphere can be a mix (internal mixture) of various aerosol species, or in some cases its compositional structure may be restricted to one species (external mixture) such as (NH₄)₂SO₄. Furthermore, an internally mixed aerosol such as organic/ammoniated sulfate/water particle can be externally mixed from wind-blown dust particles. Whether an aerosol is internally or externally mixed, it scatters and/or absorbs a specific fraction of radiant energy impinging on it. Following the suggestion of White [1986], an aerosol scattering/extinction per unit mass ratio will be referred to as specific scattering/extinction, as in specific gravity.

Most routine aerosol monitoring programs and many special study visibility characterization programs were designed to measure bulk aerosol species mass concentrations such as sulfates, nitrates, carbonaceous material, and selected elements [Heisler et al., 1980; Malm et al., 1994b; Tombach and Thurston, 1994; Watson et al., 1990; Macias et al., 1981]. They were not designed to determine the microphysical and chemical characteristics of these species.

The inherent limitations of estimating aerosol optical properties from bulk aerosol measurements have been addressed, at least in part, by a number of authors. For instance, Ouimette and Flagan [1982] have shown, from basic theoretical considerations, that if an aerosol is mixed externally or if in an internally mixed aerosol the index of refraction is not a function of composition or size, and the aerosol density is independent of volume, then:

(3.2)

where a_i is the specific scattering or absorption efficiency and m_i is the mass of the individual species.

Malm and Kreidenweis [1997] demonstrated from a theoretical perspective, that specific scattering of mixtures of organics and ammoniated sulfates were insensitive to the choice of internal or external mixtures. Sloane [1983, 1984, 1986], Sloane and Wolff [1985], and more recently Lowenthal et al. [1995], Malm [1998], and Malm et al. [1997] have shown that differences in estimated specific scattering between external and internal model assumptions are usually less than about 10%. In the absence of detailed microphysical and chemical structure of ambient aerosols, the above studies demonstrate that a reasonable estimate of aerosol extinction can be achieved by assuming each species is externally mixed.

However, the issue of water uptake by hygroscopic species must be addressed. Implicit to the use of Equation (3.2) is an assumed linear relationship between aerosol mass and extinction. It is well known that sulfates and other hygroscopic species form solution droplets that increase in size as a function of relative humidity (RH). Therefore, if scattering is measured at various relative humidities the relationship between measured scattering and hygroscopic species mass can be quite nonlinear. A number of authors have attempted to linearize the model, in an empirical way, by multiplying the hygroscopic species by such a factor as 1/(1-RH) to account for the presence of water mass [White and Roberts, 1977; Malm et al., 1986]. However, Malm et al. [1989] and Gebhart and Malm [1989] proposed a different approach. They multiplied the hygroscopic species by a relative humidity scattering enhancement factor, f(RH), that is calculated on a sampling-period-by-sampling-period basis using Mie theory and an assumed size distribution and laboratory measured aerosol growth curves.

Measurements of hygroscopic species growth as a function of relative humidity show that species such as ammonium sulfate show zero growth until a relative humidity, referred to as the deliquescent relative humidity, is reached where they spontaneously form a solution droplet that is in equilibrium with water molecules in the ambient atmosphere. Conversely, when the relative humidity is decreased from some value greater than 80% the solution droplet retains water below the deliquescent point to a relative humidity where all water is spontaneously given up. This point is referred to as the crystallization relative humidity.

However, because the growth factor and light-scattering efficiency for ambient aerosols has previously been observed to be rather smooth, [Sloane 1983, 1984, 1986; Wexler and Seinfeld, 1991; Waggoner et al., 1981; Day et al., 2000; Malm et al. 2000] a “best estimate" for the sulfates and nitrates species growth, the laboratory growth curves, as measured by Tang [1996] were smoothed between the deliquescence and crystallization points. Malm [1998] and Malm et al., [1997] have demonstrated that in both the East (Great Smoky Mountains National Park) and West (Grand Canyon National Park) the best estimate growth model, in combination with measured size distributions, yields an f_T(RH) function that results in good agreement between measured and reconstructed scattering for particles less than 2.5 mm.

Therefore, the following equation is used to estimate reconstructed particle scattering:

(3.3)

See Aerosol-Type Equations for definitions of the species in equation 3.3

The brackets indicate the species concentration, 3 m²/g is the dry specific scattering for ammonium sulfate and ammonium nitrate, 4 m²/g for organic carbon, and 1 m²/g and 0.6 m²/g are the respective scattering efficiencies for soil and coarse mass. The efficiencies for fine soil and coarse mass are taken from a literature review by Trijonis and Pitchford [1987].

A dry scattering efficiency of 3 m²/g is a nominal scattering efficiency based on a literature review by Trijonis et al. [1988, 1990] and a review by White [1990]. Trijonis' best estimate for ammonium sulfate and ammonium nitrate is 2.5 m²/g with an error factor of 2, while for organics it is 3.75 m²/g again with an error factor of 2. White took a somewhat different approach in that he reviewed 30 studies in which particle scattering and mass were measured. He then estimated a high and low scattering efficiency by using mass measurements to prorate the measured extinction. For ammonium sulfate, the low estimate was arrived at by assuming sulfates, nitrates, and organics scatter twice as efficiently as all other species, and for the high estimate he assumed that only the ammonium sulfate was twice as efficient. His low and high ammonium sulfate mass scattering efficiencies for the rural west were 3.0 and 3.7 m²/g, respectively. For organics his low estimate assumes organics and other non-sulfate species scatter half as efficiently as ammonium sulfate, and for the high estimate he assumes organics are three, and ammonium sulfate twice as efficient at scattering light as other species. His low and high estimates for organic mass scattering coefficients are 1.8 and 4.1 m²/g. More recently, Malm et al. [1996] demonstrated that an assumption of dry specific scattering values given in Equation (3.3) yielded good agreement between measured and reconstructed extinction across the entire IMPROVE monitoring network.

Various functions for the hygroscopicity of organics have been proposed. Assumptions must not only be made about the solubility of organics but also on the fraction of organics that are soluble. It should be noted, models that treat water uptake for nonideal multicomponent solutions using theoretical and semi‑theoretical thermodynamic relationships have been developed and have been applied to both visibility and climate forcing problems [Saxena and Peterson, 1981; Pilinis et al., 1995; Saxena et al., 1986, 1993]. The correct treatment of the hygroscopicity of species in multicomponent mixtures—especially organic species—remains problematic, not only because of the lack of suitable mixture thermodynamic data but also because of the lack of information about other critical mixture properties. Given the variety of organic species, it is possible that a geographic variation in organic species exists, with large fractions of soluble species occurring in certain parts of the continent and much smaller fractions in other areas. However, field experiments and subsequent data analysis at Great Smoky Mountains and Grand Canyon National Parks [Malm et al., 1997; Malm and Kreidenweis, 1996 Malm et al., 2000] and, more generally, data collected in the IMPROVE Network [Malm et al., 1996] show that to within the uncertainty of the measurements and modeling assumptions, organics are not or are only weakly hygroscopic. Therefore, f_org(RH) for organics was set equal to one.

Equation (3.3) has been shown to give a good estimation of scattering for particles less than 2.5 mm, however, estimating extinction requires a knowledge of particle absorption. Mass absorption efficiencies of carbon vary by more than a factor of two as do direct measurements. Horvath [1993] has reviewed the measurement of absorption, while Fuller et al. [1999] has theoretically explored the variability of absorption efficiency as a function of carbon morphology. Although absorption can be estimated in a variety of ways, there is no one method that is generally accepted by the scientific community. For purposes of this report, carbon absorption is estimated using:

(3.4)

where b_abs is particle absorption, LAC is the concentration of light-absorbing carbon as measured using the Thermal Optical Reflectance (TOR) analysis scheme [Chow et al., 1993], and 10 is the specific absorption for LAC, which has been used by a number of scientists [Horvath, 1993].

Because aerosol concentrations are derived from averages over long periods, the light scattering due to soluble species is derived using hourly RH values less than or equal to 98%, as given by the following equation:

(3.5)

where is the average species concentration, a is the specific scattering, and

(3.6)

Using Equation (3.3), extinction budgets for a time interval may be calculated by replacing f_T(RH) with F_T and by using the average concentration of each species over the same time interval as the mass concentration. Using the data from sites with collocated optical and RH data, a polynomial curve was fitted to the annual and seasonal data as defined by:

F= b₀+b₁(100/(100-RH))+b₂(100/(100-RH))² (3.7)

where b_o = 0.33713, b₁ = 0.58601, and b₂ = 0.09164 with an R-square of 0.93 annually. Figure 3.1 shows the fitted curve plotted against annual average RH for IMPROVE sites with collocated RH data. Table 3.1 lists the regression results for annual and seasonal averaging periods. For those sites without collocated optical and RH data, the annual factors can be calculated using Equation (3.7) and estimates of annual average RH. (Five significant figures are used in the curve fit program used for this report and therefore are included here for reference.)

Figure 3.1 Best-fit relation between a site’s annual average RH and its annual average RH correction factor.

Table 3.1 Parameters of the best-fit equation relating the relative humidity light-extinction correction factors (F_T) to seasonal and annual average site relative humidity (F = b_o + b₁(1/(1-RH)) + b₂(1/(1-RH))².

Season	b₀	b₁	b₂	R²
Spring	-0.01097	0.78095	0.080147	0.93
Summer	-0.18614	0.99211	---	0.91
Autumn	-0.24812	1.01865	0.01074	0.93
Winter	0.34603	0.81984	---	0.77
ANNUAL	0.33713	0.58601	0.09164	0.93

Figure 3.2 is a flowchart, which details the process used to account for the effects of relative humidity at those sites with or without relative humidity sensors.

Figure 3.2 The process by which IMPROVE data is used to develop site specific

seasonal and annual RH correction factors.

The extinction reconstruction process starting with the raw IMPROVE data through to the extinction calculation can be summarized:

At those sites with collocated RH sensors and particle monitors, discard hourly RH values greater than 98% and discard days with less the 16 RH values.
Convert the hourly RH to f(RH) values using the “smoothed” ammonium sulfate f_T(RH) versus RH lookup table shown graphically in Figure 3.3.
Calculate annual and/or seasonal RH and f(RH) averages (F_T) (Equation (3.6)).
Develop an empirical relationship between average RH and average F_T(RH) (Equation (3.7)).
For the desired time period (annual or seasonal) find the average of the following species: ammonium sulfate, ammonium nitrate, organics, light-absorbing carbon, fine soil, and coarse mass.
Using these averages calculate average reconstructed aerosol extinction according to the equation:

(3.8)

where the parameters enclosed in the brackets are the average concentrations of each species.

The use of a 98% RH cutpoint is somewhat arbitrary, but it was chosen to allow for the likelihood that above 98%, precipitation would obscure visibility without regard to pollutant concentrations, and as an expedient measure because f_T(RH) is infinite at 100% RH. The same f_T(RH) was used in the first and second IMPROVE reports [Sisler et al., 1993; Sisler, 1996]. However, the assumptions used for estimating this curve will be investigated in light of more recent growth and particle size distribution data.

There are two ways reconstructed extinction is calculated in this report that are different from the 1996 IMPROVE report. First, the factor f(RH) that accounts for the relative humidity effects on hygroscopic aerosols has been upgraded with new relative humidity data from additional relative humidity monitoring sites and second, absorption is estimated from measurements of light-absorbing carbon rather than from transmission measurements of filter media. Therefore, some differences in aerosol extinction between this and the 1996 report are due to changes other than levels of aerosol mass concentration.

Visibility expressed as reconstructed deciview (dv) can now be calculated. The deciview is a visibility metric based on the light-extinction coefficient that expresses incremental changes in perceived visibility [Pitchford and Malm, 1994]. Because the deciview expresses a relationship between changes in light extinction and perceived visibility, it can be useful in describing visibility trends. A 1-dv change is about a 10% change in extinction coefficient, which is a small but perceptible scenic change under many circumstances. The deciview is defined by the following equation:

(3.9)

The deciview scale is near zero for pristine atmosphere (dv = 0 for Rayleigh condition at about 1.8 km elevation) and increases as visibility is degraded.

Figure 3.3 RH factors (f_T (RH)) derived from Tang’s ammonium sulfate growth curves smoothed between the crystallization and deliquescence points.