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Johnson and Ettinger Attenuation Factor

The attenuation factor, &#945, is a proportionality constant relating indoor air concentrations to soil or groundwater concentrations:

C_{indoor air} = &#945_SG x C_{soil gas} or C_{indoor air} = &#945_GW x C_groundwater x H

This attenuation of vapor phase concentrations from the subsurface to indoor air can be computed by the simplified Johnson and Ettinger (1991) relationship:

A larger &#945 indicates less attenuation and a smaller value indicates more attenuation. For example, at an &#945 = 0.001 a subsurface concentration of 1000 [&#956g/m³] will attenuate to an indoor air concentration of 1 [&#956g/m³]. At an &#945 = 0.1, the same subsurface concentration of 1000 [&#956g/m³] will only attenuate to an indoor air concentration of 100 [&#956g/m³]. Note that different attenuation factors will be produced for soil gas and groundwater contamination sources (because of different D_T ^eff values as explained below).

Building Terms:

A_B is the area of the enclosed space that is in contact with soil [m²]. This includes both floor and wall-space that contacts the subsurface.
Q_B is the building ventilation rate [m³hr^-1], which is usually estimated to be the product of the enclosed-space volume (V_B [m³]) and the indoor air exchange rate with outdoor air (E_B [hr^-1]).
L_T is the distance (depth) from the bottom of the foundation to the vapor source (for soil gas contamination) or water table (for groundwater contamination) [m].
&#951 is the fraction of the enclosed space surface area open to vapor intrusion [unitless].

Subsurface Terms:

Q_soil is the pressure-driven soil gas flow rate into the building [L/min].
D_T ^eff is the effective diffusion coefficient through the unsaturated zone (for soil gas contamination) or through both the capillary and unsaturated zones (for groundwater contamination). This term incorporates soil and compound-specific parameters and is computed using the Millington approximation.
D_crack ^eff is the effective diffusion coefficient through the foundation cracks. It is assumed that the foundation cracks are dry, therefore D_crack ^eff is set equal to D_T ^eff.