FEDERAL LAND MANAGERS' AIR QUALITY RELATED VALUES WORKGROUP (FLAG)
PHASE I REPORT
(December 2000)

Appendix 2.A

Visibility Parameters

Visibility is usually characterized by either visual range (VR) (the greatest distance that a large dark object can be seen) or by the light-extinction coefficient (b_ext) (the attenuation of light per unit distance due to scattering and absorption by gases and particles in the atmosphere) (IMPROVE, 1996). Under certain assumed conditions, these parameters are inversely related to each other by Equation 1; a long visual range corresponds to a low extinction. Visual range is useful for safety reasons such as to direct aircraft traffic near airports, but is not particularly useful for assessing the quality of scenic vistas. Nonetheless, visual range remains a useful measure for describing visibility, especially for communication with the general public. The dimensions of VR are length and the dimensions of b_ext are 1/length. Visual range is usually expressed in kilometers. The extinction coefficient is sometimes expressed as "inverse kilometers" (km^-1) or as "inverse megameters" (Mm^-1) (the reciprocal of 1 million meters). If b_ext is expressed in Mm^-1 the coefficient 3.912 becomes 3912 as in Equation 1.

Equation 1. Relationship between visual range and light-extinction coefficient.

Other visibility parameters frequently used include ΔE and contrast. These metrics relate to the color difference or contrast, respectively, of a plume or haze with respect to some viewing background.

Calculating the Extinction Coefficient

Visibility is degraded by visible light scattered into and out of the line of sight and by light absorbed along the line of sight. Light extinction is the sum of light scattering and absorption, and is usually quantified using the light extinction coefficient (b_ext). Extinction can be measured directly or it can be calculated from representative aerosol measurements. Using a generalized approach to estimating visibility effects, one can calculate the extinction coefficient as the sum of its parts, i.e., b_ext = b_scat + b_abs, where b_scat and b_abs are the light scattering and absorption coefficients. The light scattering and absorption coefficients can be further broken down by their respective components. The scattering coefficient is affected by light scattering (Rayleigh scattering (b_Ray)) from air molecules and from particle scattering (b_sp); the particles can be natural aerosol or result from air pollutants. The absorption coefficient is affected by gaseous absorption (b_ag) and particulate absorption (b_ap). Nitrogen dioxide is the only major light-absorbing gas in the lower atmosphere; it generally does not affect hazes, although it can be an important element in a coherent plume assessment. Therefore, only particle absorption is considered in the suggested far-field visibility analyses, although nitrogen dioxide absorption should be considered when this technique is applied to sources in the near field.

Particle scattering can be broken down by the contributions of different particulate species. It has been convenient to consider the scattering coefficients of fine particles (PM_2.5) (particles with mass mean diameters less than or equal to 2.5 µm) and coarse particles (mass mean diameters greater than 2.5µm but less than or equal to 10µm). The fine particle scattering coefficient can be further defined by the sum of the scattering coefficient due to sulfates (b_SO4 ), nitrates (b_NO3), organic aerosols (b_OC), and soil (b_Soil); the coarse scattering coefficient (b_Coarse) is not refined any further. Thus the particle scattering coefficient (b_sp) can be expressed as in Equation 2.

b_sp = b_SO4 + b_NO3 + b_OC + b_Soil + b_Coarse

Equation 2. Components of particle scattering.

Each of the particle scattering coefficients can be related to the mass of the components using the relationships in Equation 3.

b_SO4 = 3[(NH₄)₂SO₄]f(RH)

b_NO3 = 3[NH₄NO₃]f(RH)

b_OC = 4[OC]

b_Soil =1[Soil]

b_Coarse = 0.6[Coarse Mass]

Equation 3. Relationship between particle scattering and mass of each species.

The quantities in brackets are the masses expressed in µ g/m³. (It is assumed that the forms of the SO₄⁼ and NO₃^- are ammonium sulfate [(NH₄)₂SO₄] and ammonium nitrate [NH₄NO₃].) The numeric coefficients are the "dry" scattering efficiencies (m²/g). The term f(RH) is the relative humidity adjustment factor. The extinction coefficients are in Mm^-1. If the "dry" scattering efficiencies are divided by 1000 (i.e., 0.003 instead of 3) the resultant extinction coefficients will be in km^-1.

Particle absorption (b_ap) is primarily due to elemental carbon (soot). Similarly, absorption by gases (b_ag) is primarily from nitrogen dioxide (NO₂). For purposes of analyzing the effects of soot or NO₂ on visibility in a modeling analysis, the relationships in Equation 4 should be used. Again, the quantities in brackets are the masses of elemental carbon or nitrogen dioxide in µg/m³ and 10 and 0.17 are the extinction efficiencies. Nitrogen dioxide absorption is usually only an issue in the near-field, therefore, it is usually not considered in an analysis for distant sources.

b_ap = 10[EC]

b_ag = 0.17[NO₂]

Equation 4. Relationship between particle absorption and elemental carbon.

The total atmospheric extinction can be expressed as in Equation 5, where b_Ray is the Rayleigh scattering component, which is assumed to be 10 Mm^-1.

b_ext = b_SO4 + b_NO3 +b_OC + b_soil + b_Coarse + b_ap (+ b_ag)^* + b_Ray

Equation 5. Components of Extinction (^*b_ag is usually only considered in near-field analyses).

To the extent that a source contributes to the formation of some of these constituents, those contributions can be summed to yield the source's contribution to extinction. This will be discussed in more detail below.

Examination of Equation 3 reveals that the sulfate and nitrate components of the extinction coefficient are dependent upon relative humidity. These aerosols are hygroscopic and the addition of water enhances their scattering efficiencies. It is sometimes convenient to consider the sulfate and nitrate components of extinction separately from the remaining components of Equation 5 and to keep the relative humidity adjustment factor (f(RH)) separate. Equation 5 can then be rewritten as in Equation 6, where b_hygro is the combined extinction coefficient of sulfate and nitrate, excluding the relative humidity adjustment factor, and b_non-hygro is the sum of b_OC, b_Soil, b_Coarse, b_ap, and b_ag.

b_ext = b_hygrof(RH) + b_non-hygro + b_Ray

Equation 6. Extinction coefficient expressed as the sulfate and nitrate contribution (b_hygro =3[(NH₄)₂SO₄ + NH₄NO₃]) and non-hygroscopic components (b_non-hygro = b_OC+b_Soil+b_Coarse+b_ap+b_ag).

The relative humidity adjustment factor requires some further explanation. The variation of the effect of relative humidity on the extinction efficiency, f(RH), of sulfates and nitrates is given numerically in Table 2.B-1. As can be seen, the effect of relative humidity on the extinction efficiency of these aerosols is non-linear, and is several times greater at higher relative humidity than at lower humidity.

FLAG proposes that the relative humidity adjustment to the "dry" scattering efficiencies (unadjusted for relative humidity) for hygroscopic particles are made as follow:

• The preferred alternative is to apply day-by-day f(RH) adjustment factors to the analysis. For this alternative hourly relative humidity data are needed. Hourly f(RH) values should be averaged to generate a 24-hour relevant f(RH) factor. FLAG recommends, however, that if the hourly relative humidity exceeds 98%, that it be rolled back to 98%, so that there will be no f(RH) factors applied that are greater than f(98).
• For screening analyses the adjustment factor can be based on historic averages of f(RH) for the Class I area(s) of concern (Table 2.B-1).

Table 2.A-1. f(RH) values for various values of relative humidity ^*

^*The values in Table 2.A-1 are only appropriate for averaging times of 1 hour or less.
* The values for 99% and 100% RH are rolled back to the value for 98%.