Estimation of Generic Subslab Attenuation Factors for Vapor Intrusion Investigations

Generic indoor air:subslab soil gas attenuation factors (SSAFs) are important for rapid screening of potential vapor intrusion risks in buildings that overlie soil and groundwater contaminated with volatile chemicals. Insufficiently conservative SSAFs can allow high‐risk sites to be prematurely excluded from further investigation. Excessively conservative SSAFs can lead to costly, time‐consuming, and often inconclusive actions at an inordinate number of low‐risk sites. This paper reviews two of the most commonly used approaches to develop SSAFs: (1) comparison of paired, indoor air and subslab soil gas data in empirical databases and (2) comparison of estimated subslab vapor entry rates and indoor air exchange rates (IAERs). Potential error associated with databases includes interference from indoor and outdoor sources, reliance on data from basements, and seasonal variability. Heterogeneity in subsurface vapor plumes combined with uncertainty regarding vapor entry points calls into question the representativeness of limited subslab data and diminishes the technical defensibility of SSAFs extracted from databases. The use of reasonably conservative vapor entry rates and IAERs offers a more technically defensible approach for the development of generic SSAF values for screening. Consideration of seasonal variability in building leakage rates, air exchange rates, and interpolated vapor entry rates allows for the development of generic SSAFs at both local and regional scales. Limitations include applicability of the default IAERs and vapor entry rates to site‐specific vapor intrusion investigations and uncertainty regarding applicability of generic SSAFs to assess potential short‐term (e.g., intraday) variability of impacts to indoor air.


Introduction
Risk-based screening levels for soil, groundwater, and soil gas are often included in vapor intrusion guidance documents. Such screening levels, particularly for groundwater and soil gas, are important tools for rapid identification of potential vapor intrusion risks (VIRs) as well as for expediting the clearance of low-risk sites from additional agency oversight. A key parameter in calculating these screening levels is the indoor air:subslab soil gas attenuation factor (SSAF). This factor reflects the degree of mixing and dilution of intruding soil gas with indoor air (Figure 1) and can be calculated empirically as follows: SSAF = Concentration in indoor air ____________________________ Concentration in subslab soil gas .
(1) Subslab soil gas screening levels are generated by selecting a default attenuation factor and indoor air concentration into this equation and solving for the subslab concentration: Subslab soil gas screening level = Indoor air screening level ______________________ SSAF . (2) Fate and transport models can be used to develop equivalent screening levels for soil and groundwater, based on the target concentration of the volatile organic compound (VOC) in subslab soil gas and the equilibrium partitioning characteristics of the targeted chemical (e.g., U.S. Environmental Protection Agency [USEPA] 2004).
This paper evaluates two of the most commonly used approaches for developing default SSAFs for use in vapor intrusion guidance: (1) direct measurement of apparent attenuation based on empirical databases of paired indoor air and subslab soil gas data and (2) estimation of attenuation factors based on vapor entry rates and indoor air exchange rates (IAERs). In the first case, the SSAF is estimated by dividing the measured chemical concentration in indoor air by its subslab soil gas concentration. In the second case, the SSAF is estimated by dividing the vapor entry rate by the IAER in terms of volume per unit of time. The vapor entry rate is referred to as "Q soil " in United States Environmental Protection Agency (USEPA) guidance (USEPA 2004), although a more accurate term would be "Q floor " since vapor flow through the floor (rather than out of the soil) is the primary parameter of interest. This modification recognizes that the model can also be used for buildings with crawl spaces. The IAER for a building represents the number of times that the total volume of air in the building is replaced with fresh air each hour and straightforward; that is, the concentration of a volatile measured in indoor air is divided by its subslab concentration (see Equation 1). This approach is used to estimate a subslab vapor attenuation factor for more than 1000 buildings included in the USEPA database (USEPA 2012b). The range and frequency of estimated attenuation factors are presented in Figure 2. Different plots on the graph reflect different filters applied to the database, with the purple plot representing data sets where VOCs in subslab soil gas samples were 50 times greater than the anticipated indoor air background. Statistical analysis of this particular set of data is used to generate generic SSAFs for general screening purposes, resulting in a median value of 0.003 and a 95th percentile value of 0.03. (Note that the reported median value also appears to be approximately coincidental with the mode.) While elegant in its apparent simplicity, this approach requires two important assumptions (see also USEPA 2012a): (1) indoor air data are representative of vapor impacts and (2) subslab soil gas represents intruding vapors associated with those impacts. If these criteria cannot be established within a reasonable degree of accuracy for each data pair, then the estimated SSAF becomes questionable, as does any statistical evaluation of the database as a whole.

Indoor Air Data
The risk posed to building occupants by intruding vapors is typically assessed in terms of long-term impacts to indoor air. The objective of indoor air sampling is to estimate the associated long-term average concentration of intrusion-related VOCs in areas of the building that a person regularly occupies. The degree to which the indoor air data included in the USEPA (2012b) vapor intrusion database meets this objective is hampered by a number of potential sources of error, including: (1) masking of low-level vapor intrusion impacts by VOCs from indoor and/or outdoor sources, (2) collection of samples from rooms not representative of normally occupied areas, and (3) reliance in most cases on a single sample to characterize this area (refer to Table 1 in the USEPA document).
Note that the reported concentrations of VOCs in indoor air were within the assumed background levels for most of is traditionally presented in terms of the number of building air exchanges per unit time (e.g., exchanges per hour; USEPA 2004USEPA , 2011). An IAER of 1/h, for example, indicates that indoor air is replaced once every hour. A default indoor air volume of 244 m 3 for a one-story, single-family residence is recommended in USEPA vapor intrusion guidance (100 m 2 floor area and 2.44 m height; USEPA 2004).
Selection of one approach over the other for developing generic SSAFs profoundly affects the assumed VIR. Inadequately conservative attenuation factors can allow high-risk sites to be prematurely excluded from further investigation. Excessively conservative attenuation factors can lead to costly and often inconclusive investigations.
A large database of groundwater, soil gas, and indoor air data has been compiled by the USEPA (2012b) and is the primary source of data being used to develop empirically based attenuation factors. This paper focuses on the paired, subslab, and indoor air data in the database used to derive SSAFs. Concerns highlighted for the technical basis of proposed subslab attenuation factors also likely apply to deeper soil gas and groundwater data (e.g., Yao et al. 2013a). However, the authors consider the subslab data to be most prone to potential errors in decision making, and an important starting point for a more detailed review of the adequacy of the database for the development of technically defensible, attenuation factors in general.  More than 75% of the indoor air samples included in the database were collected from residential basements. Basements are an important potential source of indoor air contaminants due to the upward flow of air when the lower living area of the house is depressurized with respect to outdoor air, for example when the house is heated (Dodson et al. 2007;USEPA 2007a). The ventilation of basements relative to upper levels is not recorded in the USEPA database, and the representativeness of the samples from upper levels cannot be quantitatively assessed. As discussed subsequently, minimum ventilation standards for regularly occupied areas are required under the building permit (American Society of Heating, Refrigerating and Air-Conditioning Engineers [ASHRAE] 2013a, 2013b). A higher air exchange rate in upper areas of the building would further attenuate vapors due to leakage and ventilation, making indoor air data from these areas more representative of risk to occupants.
Reliance on a single indoor air sample for most of the pairs in the database poses an additional source of potential error. Studies where large numbers of concurrent indoor air samples are collected indicate that VOC concentrations can vary spatially within the same building by up to four orders of magnitude for large commercial buildings and by a factor of three for smaller residential buildings (Otson and Fellin 1992;Eklund et al. 2008;Folkes et al. 2009;USEPA 2011USEPA , 2012b. Concentrations of volatiles in indoor air at vapor intrusion sites have also been demonstrated to vary by as much as three orders of magnitude over time (Folkes et al. 2009;Song et al. 2011;Holton et al. 2013).
Spatial variability can be addressed in part by the collection of a sample over a longer period that accounts for natural circulation and mixing of indoor air. To meet this objective, 24-h samples are often considered adequate (e.g., California Environmental Protection Agency [CalEPA] 2011). Longer duration samples also take into account diurnal effects of vapor intrusion. However, the duration of sample collection for each subject building is not discussed in the USEPA database report, introducing another potential source of error into the data used to derive the SSAFs. the samples in the database. Of the samples that exceeded the anticipated background levels, the majority were still within an order of magnitude of these values. This is compensated for in the USEPA (2012b) database report in part by filtering the data with respect to the assumed range of background VOCs in indoor air. Of the original 1231 sets of paired subslab and indoor air data sets, 464 were filtered out in order to address known or suspected indoor sources, concentrations of VOCs in the subslab soil gas sample that are less than that reported for indoor air, and other potentially complicating factors. All but 320 sets of paired data were eliminated after screening out indoor air data that fell within the assumed background range of a VOC.
This compromises the representativeness of SSAFs extracted from the database since sites with very low SSAFs and sites where vapor intrusion was not occurring were excluded from further consideration. Contributions from indoor or ambient sources can cause subslab attenuation to be underestimated and can misrepresent cases where vapor intrusion is not occurring. The median, mean, and 95th percentile attenuation factors presented in the USEPA (2012b) report are, therefore, biased toward cases with less attenuation (higher attenuation factors) and do not reflect the database population as a whole.
The USEPA (2012b) database assessment includes an alternate filter that focuses on subslab soil gas data greater than various multiples of the anticipated background (e.g., 100; see Figure 2). However, this again does not address uncertainty in the representativeness of the "high source strength" soil gas data in terms of vapors that actually intruded into the structure and impacted indoor air. Variability of vapor concentrations in the subslab could lead to the presence of both "low source strength" and "high source strength" areas under the same slab. Whether impacts to indoor air were tied to a high vs. low source strength would depend on the location of the vapor entry point rather than where the subslab sample was collected. The reliability of an SSAF derived for an apparent "high source strength" data pair would be no more reliable than an SSAF derived for an apparent "low source strength" data pair.  USDOD 2009;CalEPA 2012;USEPA 2012aUSEPA , 2012b. Data for buildings where large numbers of subslab soil gas samples have been collected suggest that spatial variability of one to several orders of magnitude in VOC concentrations at the scale of a building slab (i.e., across the slab as a whole) is likely to be the rule rather than the exception (Widdowson et al. 1997;Choi and Smith 2005;McHugh et al. 2007;Luo et al. 2009;Johnson et al. 2012;Lutes et al. 2012;Schmidt 2012;O'Neill 2013;Yao et al. 2013aYao et al. , 2013bYao et al. , 2013cShen et al. 2013; see also McHugh et al. 2006;Tillman and Weaver 2006;USEPA 2012a). It is reasonable to assume that the reported concentration of a VOC in a small (e.g., 1 L) subslab soil gas sample represents the immediate area. However, closely spaced grids of passive soil gas samples in outdoor areas routinely identify order-of-magnitude variability over distances of a few feet (e.g., O'Neill 2013; Whetzel et al. 2009; see also American Society for Testing and Materials [ASTM] 2011). Similar variability has been identified in radon gas studies (e.g., Bunzl et al. 1998;Winkler et al. 2001). Variability in VOC concentrations in subslab soil gas is likely to be greatest when vapors are associated with small, isolated pockets of contaminated soil but can also be considerable for vapors attributed only to contaminated groundwater.
This inherent spatial variability of subslab vapors will have profound effects on the calculation of SSAFs based on empirical data. Figure 3 illustrates one example. The figure summarizes data for total petroleum hydrocarbons (TPH) The USEPA document acknowledges these sources of potential error for indoor air samples in the database (USEPA 2012b; see also USEPA 2012a). The representativeness of indoor air data is difficult to quantify, and confidence in estimated SSAFs is difficult to ascertain. However, potential error associated with the representativeness of subslab soil gas data in the database likely far outweighs the error associated with the indoor air data.

Subslab Soil Gas Data
Assessing the representativeness of subslab data in the USEPA database is more challenging than for indoor air. Potential sources of error include: (1) uncertainty in the relation between vapors currently under the slab with vapors previously intruded to indoor air; (2) uncertainty in the duration, entry rate, and volume of vapors intruded to indoor air; (3) potential discrepancies between vapor entry points and sample locations; and (4) reliance in most cases on a single subslab sample to characterize all of the vapors beneath a building.
Evaluating the representativeness of soil gas data first requires that the target population be identified, but this is less straightforward than for indoor air. Direct testing of the vapor that impacted the indoor air is, of course, not possible since the two have already mixed. Instead, vapors under the structure are assumed to represent vapors that intruded earlier, which introduces error in the SSAF calculations (USEPA 2012b; see also USEPA 2007b).
Uncertainty in the population of subslab soil vapors to be targeted for characterization introduces additional error into the database. Indoor vapors could be assumed to reflect the volume of vapor that intruded during the previous exchange of indoor air. For example, an IAER of 0.5/h (CalEPA 2011) and a vapor entry rate of 5 L/min (USEPA 2004) equate to a vapor entry rate of 600 L per air exchange (i.e., 2 h) for each 100 m 2 of building footprint (USEPA 2012a). Alternately, an assumed time period of 24 h would take into account diurnal effects (CalEPA 2011). Assuming a vapor entry rate of 5 L/min, this equates to a vapor plume volume of 7200 L.
Another option might be to assume that the volume of vapors immediately beneath the entire slab area represents the population of interest. The volume of air-filled pore spaces in the first 15 cm of soil beneath a 100 m 2 slab is approximately 4200 L, assuming an air-filled porosity of 28% (default parameter values are included in the USEPA vapor intrusion model; see USEPA 2004USEPA , 2012a. Some guidance documents suggest a source area of vapors beneath slabs as thick as 3 feet (e.g., CalEPA 2011), corresponding to a volume of soil gas of approximately 25,000 L.
A third source of potential error in subslab soil gas data in the USEPA database is the relationship between vapor entry points and sample locations. The specific location of subslab vapor samples in terms of potential vapor entry routes is not recorded in the USEPA database and in most cases is presumably unknown.
The total error associated with these factors alone is difficult or impossible to quantify. Acceptance of the SSAF with any reasonable degree of precision and accuracy requires a leap of faith that the sole subslab sample represents the hundreds or thousands of liters of vapors that subsurface is reasonably homogeneous (uniform)." It goes on to provide an alternative, "site-specific" approach for calculating SSAF values based on the use of default vapor entry rates and IAERs. This is discussed in the following section.
The USEPA (2012b, 16) report continues, "Considering this variability, a statistical approach to characterizing the empirical attenuation factors was adopted...." However, this statement is misleading. Statistical evaluation of the database only addresses the variability between individual homes and buildings, not variability and error within a single data point. Any data set, accurate or not, can yield a pattern amenable to statistical analysis. Statistical analysis of a database is valid only if the individual data points represent their intended purpose within a quantifiable range of error (Silver 2012). This is clearly not the case for the paired indoor air and subslab soil gas samples in the USEPA (2012b) database.
This variability highlights the perils of applying statistical approaches designed to evaluate databases in which the error associated with individual data points can reasonably be assumed to be minimal (e.g., age, height, weight, etc.) vs. databases in which the reproducibility of individual data points is uncertain (see Silver 2012). The Central Limit Theorem in this case no longer applies, and statistical analysis of the database cannot compensate for the unknown error. Although seemingly straightforward, the frequency graph presented in the USEPA database report (see Figure 2) cannot reliably be assumed to reflect the distribution of SSAFs for the individual homes and buildings included in the database. Subsequently, there is no technically defensible basis for using the 95th percentile SSAF value of 0.03 extracted from the database (see also McHugh et al. 2007). As discussed in the following section, the reported median ratio of 0.003 is similar to SSAFs calculated as the ratio of vapor flow to indoor air exchange in this paper. Whether this is coincidental or accurately reflects attenuation is uncertain and is not examined in detail.

Calculation of Subslab Attenuation Factors
An SSAF for a building can also be calculated from the ratio of the rate of subsurface vapor intrusion ("vapor entry rate") to the rate of fresh air entering the building over the same time period, as represented by the IAER: . ( The vapor entry rate is traditionally expressed in terms of a default building floor area of 100 m 2 (USEPA 2012a). In this sense, the term might be more appropriately defined as a "flux" rate. The term "entry" is, however, retained for use in this paper with the understanding that the value presented applies to a specific area of floor space. This mass balance approach is indirectly incorporated into the vapor intrusion models published by USEPA (2002USEPA ( , 2004, with the SSAF in vapors beneath a 210 m 2 building slab (after Luo et al. 2009). Note that the concentration of TPH measured in 17 1-L soil gas samples collected beneath the slab of the building ranged from 0 to 145 mg/L (145,000,000 µg/m 3 ). The maximum detected concentration exceeds the published, risk-based screening levels for TPH in subslab soil gas by up to three orders of magnitude (e.g., see Brewer et al. 2013) and suggests potentially significant vapor intrusion concerns. This could be possible if the lower level of the structure was depressurized with respect to the subslab air space, and if upward attenuation was insufficient to reduce TPH concentrations below the levels of concern before the vapors were drawn through entry points in the slab.
As evident in Figure 3, any estimate of an SSAF for the building depends on the location of the subslab sample and could vary by orders of magnitude. As succinctly concluded by Luo et al. (2009, 89): "Random sampling of a few locations might not reveal the true range of concentrations… Even if one had precise knowledge of the subslab soil gas distribution, it is not clear how it would be used to assess pathway significance without knowledge of the vapor entry points to the building and soil gas entry rates through those points." The concentration of the VOC reported for the sole soil gas sample collected beneath the building could well simply reflect random "noise" in the vapor plume rather than the "signal" directly tied to vapor intrusion, that is, rather than the mean concentration of the VOC in soil gas tied to the measured impacts to indoor air (see also Silver 2012). The potential for multiple vapor entry points from areas under the slab with differing VOC concentrations and different entry rates further compromises the database reliability for estimation of the SSAF.

Confidence in USEPA Database SSAFs
Of the potential sources of error in the USEPA vapor intrusion database, spatial variability of VOC concentrations in subslab soil gas is likely the most significant, in particular at the scale of a single 1-L sample. The effect of spatial (and temporal) variability on the reliability of attenuation factors extracted from the database is recognized but perhaps not fully appreciated in the USEPA (2012b, 15) report: These factors may impart bias when calculating concentration ratios, depending on the extent to which the samples accurately represent the spatial and temporal variability of the indoor air concentrations and the subsurface vapor concentrations affecting the building… The spatial and temporal variability in observed subsurface and indoor air concentrations within and among buildings mean that for every site, and every structure (emphasis added) in an area of similar subsurface contamination, a range of empirical attenuation factors would likely be calculated from a series of discrete indoor air and subsurface vapor concentrations measured at different points in space or at different times.
This potential shortcoming of the database is similarly anticipated in vapor intrusion guidance published by the California Department of Toxic Substances Control. This guidance includes a default SSAF of 0.05 derived from earlier versions of the USEPA database (CalEPA 2011, 16): "The default attenuation factors assume [that] …the

IECC Climate Zones and Designation of Vapor Intrusion Risk Regions
A "Climate Zone" approach similar to that used by Murray and Burmaster (1995) combined with the Köppen-Geiger (Peel et al. 2007) and Trewartha (Trewartha and Horn 1980) climate-classification schemes is used in combination with International Energy Conservation Code (IECC) maps (International Code Council [ICC] 2012) to subdivide the country into four, distinct "VIR" regions ( Figure 4): (1) Region A (cold), (2) Region B (warm), (3) Region C (Mediterranean), and (4) Region D (tropical). Region B includes the coastal marine areas of northern California, Oregon, and Washington. Other specific areas included in the regions are discussed as follows.
The IECC climate zones characterize different regions of the United States in terms of "heating degree days" (HDD) and "cooling degree days" (CDD). Climate zone boundaries follow county boundary lines (see also U.S. Department of Energy [USDOE] 2010). The climate zones closely approximate climate-classification boundaries designated by the Köppen-Geiger (Peel et al. 2007) and Trewartha schemes (Trewartha and Horn 1980). An HDD value for a given day represents the difference between the average daily temperature and a base temperature of 65°F when the daily average temperature is below 65 °F. For example, if the average temperature for a given day is 40 °F, then the HDD value for that day is 25. Individual daily HDD values are summed to generate an annual HDD value for the location. Higher annual HDD values indicate a greater need for heating in comparison to locations with lower values. A CDD is a measure of how hot a location is over a period of time, relative to a base temperature of 50 °F (65 °F used by some entities). The CDD is the difference between that day's average temperature and a temperature of 50 °F, if the daily average temperature is equal to the ratio of the average vapor entry rate into a building (Q soil ) and the Building Ventilation Rate (Q building ) when vapor flow into the building is dominated by advection (see also Song et al. 2011). This same approach is used to develop generic screening levels by several states (e.g., CalEPA 2008CalEPA , 2011Hawaii Department of Health [HDOH] 2011; see also ITRC 2005). Note that the USEPA vapor intrusion models calculate a single "Infinite Source Indoor Attenuation Coefficient (alpha)" that takes into account total attenuation from the source area to indoor air, rather than separate attenuation factors for the source and subslab vapors and then for the subslab vapors and indoor air.
Calculation of the SSAF requires that the IAER be converted to units of volume and time identical to that used for vapor entry, or liters per minute: The term "Volume" represents the interior volume of the structure.
As discussed next, the flow of subsurface vapors into homes and buildings has been extensively studied and is reasonably well understood. IAERs are understood within a relatively narrow range of error (Supporting Information, Appendix S1). Models and field studies have demonstrated that a building's ventilation rate and soil gas entry rate are positively correlated (Cavallo et al. 1992;Song et al. 2014; see also Hers et al. 2001). In combination, they offer a technically defensible and more robust approach for estimating region-specific SSAFs that can be used to develop tools for vapor intrusion screening. An example of this approach is presented in the next section. this exchange rate (see Hers et al. 2001;Gilbert et al. 2008;ASHRAE 2013a). Lower IAERs likewise indicate inadequate ventilation that should be identified and corrected as part of a vapor intrusion investigation.

VIR Region B ("Warm") Default IAER
A default IAER of 0.50/h is assigned to VIR Region B, including the south, southwest, and the southernmost and Central Valley areas of California (IECC Climate Zones 2, 3, and 4 with the exception of coastal central California; ICC 2012; see Figure 4). This area is characterized by having less than 5,400 HDD per year. The default IAER again approximates the annual median air exchange rates estimated by Murray and Burmaster (1995) for their Climate Regions 3 and 4 (i.e., 0.44/h and 0.65/h, respectively). Yamamoto et al. (2010) similarly estimated that the median air exchange rate for homes in Texas was 0.47/h. Lower IAERs are primarily associated with tighter, newer homes in which air conditioning is used for most of the year (Sherman and Matson 2011). This should be accompanied by a lower to negligible vapor entry rate due to pressurization of the lower portions of the home (see also McHugh et al. 2012;Song et al. 2014).
California's climate is highly diverse, with the southeastern corner of the state characterized by a hot desertto-steppe climate, the coastal area stretching from the U.S.-Mexico border to just north of Los Angeles characterized by a Mediterranean climate with hot summers, and the southern half of the Central Valley characterized by a semiarid steppe climate (Kaufmann 2003). These areas were included in VIR Region B due to the potential for heating during brief but cold winters. Studies specific to California estimate a range of IAERs from 0.5 to 1.5 times per hour (e.g., Wilson et al. 1996). The default IAER of 0.50/h assigned to VIR Region B corresponds to the default IAER recommended for the state as a whole in vapor intrusion guidance by the California Department of Toxic Substances Control (CalEPA 2011).
The Marine West Coast climate of coastal northern California (Humboldt, Trinity, and Del Norte counties) and coastal Oregon and Washington is also included in VIR Region B (Taylor and Hannan 1999; ICC 2012; see Figure 4). This area falls within IECC Climate Zone 4C (3600< HDD <5400; ICC 2012). These areas are classified as Mediterranean under the 1899 Köppen-Geiger scheme (Peel et al. 2007). The areas are more appropriately classified as Temperate Ocean Marine (Trewartha and Horn 1980) and are distinct from the true Mediterranean climate of coastal central California (see below) by having cooler temperatures and significantly higher rainfall. This can be expected to result in less ventilation from open windows and doors in comparison to VIR Region C, as well as an increased use of heating, resulting in lower average IAERs and, as discussed in the following, a higher annual-average subsurface vapor entry rate.
Residential IAERs in these areas as a whole are somewhat higher in comparison to IECC Climate Zones 5 to 8 due in part to increased periods of the year when open windows and doors are used for ventilation (refer to the aforementioned discussion and Murray and Burmaster 1995). Air exchange rates in the warmest regions, extending from greater than 50 °F (see ICC 2012). Daily CDD values are summed to generate an annual CDD value for the location. Higher annual CDD values indicate a greater need for cooling in comparison to locations with lower values.
The IECC climate zones are useful approximations of variation in regional IAERs. "Building leakage" models can be used to approximate a default, IAER, and vapor entry rate for each VIR region. The ratio of vapor entry rate to the IAER is then used to assign an SSAF to each VIR region.

Published Studies
Indoor air exchange takes place through a combination of three processes: (1) leakage of outdoor air into the structure around windows, doors, and rooflines and through cracks, gaps, and other openings; (2) natural ventilation via open windows, doors, and other openings; and (3) forced or mechanical ventilation driven by fans. IAER can be measured in the field using tracer tests (e.g., ASTM 1990;ASTM 2000;ASHRAE 2002ASHRAE , 2006ASHRAE , 2013aBatterman et al. 2006;Bennett et al. 2012). Regional variations in IAER can be predicted by models that consider the types and sizes of houses, typical leakage properties, and representative weather conditions (e.g., Sherman and Matson 2011).
A review of published IAERs for different regions of the country is provided in Appendix S1. The example IAERs presented in the following section are based on a review of the noted references. Alternatively, less or more conservative IAERs could be applied on a more site-specific basis (e.g., refer to upper-and lower-bound distribution of air exchange rates summarized in USEPA 2011). However, coinciding vapor entry rates would require similar adjustment to correspond with the change in overall building leakage. Nonetheless, an assessment of the adequacy of building ventilation should be a fundamental part of all vapor intrusion investigations.

VIR Region A ("Cold") Default IAER
A default IAER of 0.35/h is assigned to VIR Region A, including the northeastern, north central, and Rocky Mountain areas of the country as well as the inland area of Oregon and Washington and all of Alaska (IECC Climates Zones 5, 6, 7, and 8; ICC 2012). This area is characterized by the need to heat buildings for most of the year, with decreased periods when windows and doors are likely to be left open.
An IAER of 0.35/h corresponds to the minimum ventilation rate required for residential structures in the United States (ASHRAE 2013b; see also Lawrence Berkeley National Laboratory [LBNL] 1998;USDOE 2002;Manufactured Housing Research Alliance [MHRA] 2003;ASHRAE 2010;USEPA 2010). The IAER is similar to median, annual air exchange rates estimated by Murray and Burmaster (1995) for colder regions that have more than 5400 HDD per year (i.e., 0.32/h and 0.40/h for Climate Regions 1 and 2, respectively). Lower annual-average IAERs are possible but should be accompanied by proportionally lower vapor entry rates, offsetting the potential VIRs. Impacts to indoor air quality by indoor sources also become increasingly likely to mask and outweigh risks posed by vapor intrusion below This rate is considered to be reasonable for conditions when advection is the dominant mechanism for vapor transport across a foundation. This value is supported both by conservative models and through comparison to radon and tracer studies (USEPA 2012a; see also CalEPA 2011). The USEPA (2012a) Conceptual Site Model document for vapor intrusion clarifies that the entry rate ("soil gas advection rate") applies to each 100 m 2 footprint of a building and must be proportionally corrected for building size.
The USEPA (2012a) Conceptual Site Model document notes that impacts to indoor air are relatively constant for higher vapor entry rates (e.g., >5 L/min per 100 m 2 footprint). Increasing the vapor entry rate will not increase impacts to indoor air. This is because VOC transport into the advective zone is limited by the rate of VOC diffusion away from the source (USEPA 2012a). A vapor entry rate of 5 L/min thus represents a reasonable maximum value.
As is the case for IAERs, annual-average vapor entry rates can be anticipated to vary across seasons and between different climate zones. Song et al. (2014) evaluated seasonal changes in vapor entry rates by linking vapor intrusion models to building leakage models, which are used to assess energy efficiency (see Sherman and Matson 2011). The models generate a worst-case indoor-outdoor pressure differential of 40 g/cm-s 2 for periods when a home is being heated, identical to the default value incorporated into the USEPA vapor intrusion guidance (USEPA 2004). Significantly lower pressure differentials are calculated for warmer periods of the year, with values approaching zero for summer periods when the home is being cooled.
These day-to-day pressure differentials are entered into the USEPA (2004) vapor intrusion model to estimate daily vapor entry rates. The models suggest a peak vapor entry of approximately 3 to 5 L/min (per 100 m 2 ) during the cold winter months when a structure is being heated (Song et al. 2014). This corresponds well with the default vapor entry rate recommended by the USEPA (2004). However, vapor entry rates in the range of 0 to 2 L/min are characteristic of warm summer months, when the structure is being cooled and the pressure differential between indoor and outdoor air is significantly less. This lower entry rate corresponds well with radon field studies, which indicated a fivefold reduction in radon entry rates when a building is cooled by open windows and doors (Cavallo et al. 1992). The use of air conditioning will typically pressurize a building and largely negate the advective intrusion of subsurface vapor (ASHRAE 2009(ASHRAE , 2013asee also MHRA 2003;USEPA 2010USEPA , 2012Song et al. 2014; Appendix S1). Note that this could result in the outward leakage of indoor air in subslab soils (McHugh et al. 2006(McHugh et al. , 2012. Taking these studies into consideration, a default average vapor entry rate of 5 L/min is reasonably conservative for cold periods of the year, when a building is likely to be heated for at least part of the day (e.g., mean daily temperature <65 °F). Similarly, a default vapor entry rate of 2 L/min is reasonable for periods when a building is being cooled (e.g., mean daily temperature less than HDD default of 65 °F). For screening purposes, it is reasonable to apply the more conservative vapor entry rate to intermittent periods (e.g., spring and fall) when a building might be either heated Florida to western Texas, are lower than might be expected due to tighter homes and the use of air conditioning for most of the year, compared to more moderate areas.

VIR Region C (Mediterranean) Default IAER
A default annual-average IAER of 1.0/h is assigned to VIR Region C. This includes the coastal central California and a thin sliver of land along the western edge of the Sierra Mountains, which is characterized by a Mediterranean climate with cool summers (Kauffman 2003; see Figure 4, Sierra area not depicted due to scale). The areas fall into IECC Climate Zone 3C (ICC 2012) and Climate Regions 3 and 4 of Murray and Burmaster (1995).
The area is distinct from Region B in terms of cooling and particularly heating. The selected IAER reflects yearround moderate temperatures and an increased use of windows and doors for ventilation, as well as minimal heating requirements during the winter. This is in agreement with the mid-range of IAERs identified for coastal areas (e.g., see Wilson et al. 1996;California Energy Commission [CEC] 2001;and Yamamoto et al. 2010) and is either consistent with or more conservative than peer-reviewed vapor intrusion guidance published by regulatory agencies located in these areas (e.g., Oakland Environmental Services Division 2000; CalEPA 2008). Natural ventilation is usually preferred to mechanical ventilation in these areas (Sherman 1995;ASHRAE 2013a). The IECC climate zone classification also reflects a reduced use of heating in coastal central California (Climate Zone 3C; HDD <3600) in comparison to interior California (Climate Zone 3B; HDD <5400). This helps to explain the comparatively higher IAERs for this area, even though the mean daily temperature dips slightly below the IECC HDD default of 65 °F for most of the year.

VIR Region D (Tropical) Default IAER
An annual-average IAER of 1.0/h is assigned to VIR Region D. This area includes southernmost Florida, Hawai'i, Puerto Rico, the United States Virgin Islands, and Guam (see Figure 4; latter areas not depicted) and falls into IECC Climate Zone 1 (ICC 2012). The default air exchange rate corresponds to the value incorporated into vapor intrusion guidance published by the State of Hawai'i (HDOH 2011). Natural ventilation is generally preferred for ventilation of residences primarily due to a mean temperature of >65 °F throughout the year (Desert Research Institute [DRI] 2013). Heating is only occasionally used in sparsely populated, highelevation areas of the islands of Maui and Hawai'i. Although detailed studies of IAERs have not been published for the state, the annual-average IAERs can reasonably be assumed to be at least as high as those of coastal central California.

Climate-Weighted Vapor Entry Rates
An overview of factors related to building leakage and vapor intrusion under different climate and ventilation scenarios is included in Appendix S1. The USEPA (2004) vapor intrusion guidance recommends a default, subsurface vapor entry rate of 5 L/min into buildings for general screening purposes (i.e., 83 cm 3 /s or 7200 L/d).
weighted vapor entry rates on a more area-specific basis (see also USDOE 2010).

Estimation of VIR Region SSAFs
Default SSAFs can now be calculated and assigned to each of the VIR regions in Figure 4. The selected IAERs, vapor entry rates, and associated SSAFs are preliminary and illustrate regional differences in VIRs. A more detailed analysis similar to that of Song et al. (2014) could be carried out for individual regions or subparts of these regions. Note that the SSAF values presented may not reflect the views of regulatory agencies that oversee vapor intrusion investigations in the region, except as specifically referenced.
Region-specific IAERs assigned in terms of IAER must be converted to volume per unit time for comparison to vapor entry rates for a floor area of 100 m 2 . Assuming a default indoor house volume of 244 m 3 or 244,000 L (USEPA 2012a), conversion of the assigned IAERs of 0.35/h (VIR Region A), 0.50/h (VIR Region B), and 1.0/h (VIR Regions C and D) to liters per minute yields default IAERs of 1423, 2033, and 4067 L/min, respectively (Table 2).
Default SSAFs are generated for VIR regions using Equation 4 (Table 2). An SSAF of 0.0032 is calculated for the colder areas of VIR Region A. This agrees well with an annual-average attenuation factor of 0.003 estimated for residential buildings in northeastern states by Song et al. (2014). A slightly lower SSAF of 0.0020 is calculated for the warmer areas of VIR Region B. An SSAF of 0.0008 is calculated for VIR Region C, the Mediterranean climate areas of coastal California with its cool summers. The lowest SSAF of 0.0005 is calculated for VIR Region D, including the tropical islands of Hawai'i, southernmost Florida, Puerto Rico, the United States Virgin Islands, and Guam.
The range of attenuation factors predicted agrees well with previous estimates of SSAFs based on estimated vapor entry rates and IAERs (e.g., USEPA 2004). The region boundaries depicted in Figure 4 could be evaluated at a more local scale by referring to the IECC Climate Zone database (ICC 2012; see also ASHRAE 2010 and USDOE 2010) and Köppen-Geiger and Trewartha climate-classification maps or cooled but wind effects and closed doors and windows could depressurize the structure.

Default Vapor Entry Rates for VIR Regions
This approach allows the calculation of seasonally weighted vapor entry rates based on the average number of heating days and cooling days per year for a targeted area and an appropriate temperature to approximate the cutoff for that area. Heating is also less likely to be used during this period. Although somewhat subjective, an alternative cutoff of 55 °F is considered to be reasonable for the estimation of CDD vs. HDD values in Region C. As noted in Table 1, this yields a total of 166 d during which homes might be heated during the year.
Assignment of a default vapor entry rate of 2 L/min for "cooling days" and an entry rate of 5 L/min for the remaining parts of the year (i.e., heating or otherwise "noncooling days") generates weighted year-average vapor entry rates of 4.5, 4.0, 3.4, and 2.0 L/min for the cold, warm, Mediterranean, and tropical climate regions, respectively (see Table 1). Climate data and models similar to those published by Song et al. (2014) could be used to develop  Figure 4). 2 Annual-average vapor entry rate (see Table 1 as well as SSAFs, can vary significantly both between and within buildings (see Appendix S1; see also Johnson 2002Johnson , 2005. IAERs are well studied but could vary by an order of magnitude, depending on the age and design of the structure; the method being used for heating, cooling, and ventilation; and other factors (Appendix S1). Effective vapor entry rates can vary by wide margins for similar reasons, including the presence or absence of floor cracks and gaps in different areas of an individual building. Site-specific measurement of vapor flow into buildings and IAERs is difficult if not impossible for typical vapor intrusion investigations. However, potential error associated with building-specific variability of IAERs and vapor entry rates does not necessarily carry over to estimation of annual-average SSAFs. Long-term vapor entry rates and IAERs are positively correlated. Although sufficient quantitative field data are still lacking, especially for "Q soil ," an increase in the vapor entry rate should be accompanied by an offsetting increase in the IAER (see Cavallo et al. 1992;Song et al. 2014; see also Hers et al. 2001). This relationship and the use of reasonably conservative values for both parameters minimize the risk that the generic SSAFs could significantly underpredict the magnitude of long-term vapor intrusion impacts to indoor air.
The applicability of the generic SSAFs presented in this paper to short-term impacts to indoor air (e.g., intraday) is uncertain. Short-term temporal and/or spatial variability of both IAERs and vapor entry rates could be significant due to sudden changes in weather conditions (e.g., high winds) or changes in building ventilation (e.g., heating or air conditioning turned off at night). This could affect short-term SSAFs and lead to temporarily decreased or increased impacts to indoor air. A detailed evaluation of the short-term variability of impacts to indoor air related to vapor intrusion was, however, beyond the scope of this paper.

Summary and Conclusions
This paper illustrates that the disparity between the two approaches for estimation of SSAFs is most likely attributable to error associated with individual data points incorporated into the USEPA (2012b) empirical database. Spatial variability in subslab soil gas, uncertainty in vapor entry points, and the limited number of sample points per structure (typically one) introduces unavoidable and unquantifiable error into the calculated SSAFs. Temporal and spatial variability of VOCs in indoor air, the potential for unrecognized indoor sources of VOCs, and the limited number of sample points (again typically one) per structure introduce additional and unquantifiable error. Statistical analysis of the data does not solve this problem and merely assesses the variability between individual homes and buildings rather than the potential error associated with individual building data points.
These irresolvable problems invalidate the use of the USEPA (2012b) vapor intrusion database for development of defensible and reproducible SSAFs within a reasonable degree of accuracy. Error associated with the representativeness of subslab soil gas data and/or indoor air data in the USEPA VI database is directly carried over into calculation of an SSAF, and it is impossible to assess on a building-specific basis. The potential variability of VOC concentrations in (e.g., Trewartha and Horn 1980;Peel et al. 2007) as well as local building leakage studies. The mean daily temperature across much of the Gulf Coast, for example, exceeds 65 °F during the months of April and October, while temperatures are still well below this level for more northern areas of the "warm" climate region during these months. A lower number of heating days and ultimately a lower SSAF would be warranted for these areas in comparison to the rest of the warm climate region.
Alaska is included in the same climate region as Iowa, even though the mean daily temperature across the majority of Alaska never exceeds 65 °F. The overall SSAF of 0.0032 generated for Region A might, therefore, be insufficiently conservative for this state, but it is close to a maximum SSAF value of 0.0035, due to a vapor entry rate of 5 L/min and an IAER of 0.35/h.

Comparison to Database-Derived SSAFs
The discrepancies between the above-estimated default SSAFs and those extracted from the USEPA (2012b) empirical database (e.g., 95th percentile SSAF) are tied to several factors, including: (1) error in the database associated with spatial (and temporal) subslab vapor heterogeneity, (2) error in the database associated with masking of low but probably typical SSAFs due to interference from indoor air sources of VOCs, and (3) attempts to develop a single IAER, vapor entry rate, and SSAF for the highly variable climate regions of the United States. The conflict is recognized but not fully reconciled in the database report: Using the median values for residential building volume and air exchange rates (395 m 3 and 0.45 air changes per hour, respectively) provided in the Exposure Factors Handbook 2011 Edition … and a central value of 5 L/min for Q soil in sandy materials … the median value of the subslab soil gas attenuation factor … is expected to be approximately 0.002. (USEPA 2012b, 50) The CalEPA (2011) vapor intrusion guidance recommends a default SSAF of 0.05 for California as a whole, based on earlier interpretation of the USEPA database. This SSAF suffers from the same problems as aforementioned for more recent interpretations of the USEPA (2012b) database. The same guidance, however, recommended a default vapor entry rate, house volume, and an IAER of 5 L/min, 244 m 3 , and 0.5/h, respectively, for a more site-specific evaluation of existing or future residential buildings. This generates a more technically defensible SSAF of 0.0025 and corresponds well to the default SSAF of 0.0020 estimated in this paper for VIR Region B (see Table 2).
Oregon was likewise cautious regarding the seemingly high 95 th percentile SSAF of 0.03 proposed for the USEPA (2012b) database. An SSAF of 0.005, closer to the median of the database, was ultimately selected for inclusion in that state's vapor intrusion guidance (ORDEQ 2010).

Limitations
The IAERs and vapor entry rates assigned to individual regions for calculation of generic SSAFs cannot be assumed to be applicable to individual buildings as part of a site-specific vapor intrusion investigation. Vapor entry rates and IAERs, Assessment of VOC concentrations in targeted areas beneath a slab is still feasible, in spite of the problems caused by larger scale variability in subslab vapor. The variability of VOC concentrations in vapors within any given subarea beneath a slab is likely to be relatively low in comparison to variability across the slab as a whole, due to the diffusive properties of the chemicals. Recommendations to collect soil gas data from the center of a building in the area of the highest anticipated vapor concentration, between the center and the suspected source, and near vapor entry points (e.g., utility gaps in the downwind side of the slab) seem reasonable for screening-level vapor intrusion investigations (e.g., ORDEQ 2010; CalEPA 2011; USEPA 2012a; Yao et al. 2013b; see also Luo et al. 2009). Whether these vapors are representative of vapors actually intruding into the building is probably unknowable with any degree of certainty. The representativeness of subslab data from these areas will improve as more cost-effective methods for the collection of a larger number of samples or larger sample volumes from targeted areas continue to be developed.

Disclaimer
Guidance published by the Hawai'i Department of Health and referenced in this paper was funded partly through the use of U.S. EPA State Response Program Grant funds. Its contents do not necessarily reflect the policies, actions, or positions of the U.S. Environmental Protection Agency. The Hawai'i Department of Health does not speak for or represent the U.S. Environmental Protection Agency.
There are no known conflicts of interest or financial interests associated with this manuscript.

Supporting Information
The following supporting information is available for this article: Appendix S1. Overview of indoor air exchange rates and vapor intrusion and building leakage.
Additional Supporting Information may be found in the online version of this article.
vapor plumes alone suggests that error could exceed two orders of magnitude for an individual building.
A similar conclusion was drawn by Yao et al. (2013a) after a more detailed review of data trends and uncertainty regarding potential error associated with indoor air concentrations used to estimate attenuation factors. In particular, estimates of SSAFs based on the 95th percentile of the database could simply represent this level of disparity between signal and noise in indoor and subslab vapor concentrations. The median ratio of VOCs in indoor air to subslab soil gas extracted from the database (0.003, similar to the apparent mode) is similar to the SSAF value estimated in this paper for the same area of the country (VIR Region A; 0.0032). Whether this is coincidental or real is impossible to evaluate, however, given the uncertainty in the representativeness of the individual data points in the database. If accurate, then deviations away from this SSAF value in the database (i.e., above or below the median) could simply reflect increasing error in the data.
Uncertainty and error associated with the calculation of SSAFs from reasonably conservative vapor entry rates and IAERs are considerably lower. This approach, already incorporated into the USEPA (2004) vapor intrusion models and numerous state guidance documents, is more practical and technically defensible for development of region-specific SSAFs and screening levels. The approach also allows for estimation of region-specific SSAFs based on climate data, building designs, and heating and cooling needs, rather than applying a single, generic SSAF to the country as a whole. Default IAERs used to estimate generic SSAFs are considered to be reasonably conservative and reflect either values currently used by individual states for vapor intrusion guidance or the minimum rates required for building ventilation. Climate-weighted, vapor entry rates are conservatively biased to reflect upper limits on diffusive VOC transport away from source areas. Error is most likely to be associated with overestimation of potential, long-term vapor intrusion impacts, especially in areas where buildings are air conditioned for most of the year and over pressurization of lower floors negates significant subsurface vapor entry. This paper also emphasizes the need to understand seasonal variability in building ventilation mechanics as an essential part of vapor intrusion studies. For example, more site-specific studies might consider a lower average subslab vapor flow into buildings due to reduced or even negative flow during periods when the building is air conditioned and pressurized. The associated flow of indoor air into subslab soil during these periods also has implications for both the collection of subslab soil vapor samples and the estimation of the vapor attenuation (e.g., McHugh et al. 2006McHugh et al. , 2012USEPA 2012b). Misinterpretation of the cause of low VOC concentrations beneath a slab could lead to erroneously high estimates of upward vapor attenuation due to natural degradation processes, as well as mistaken assumptions regarding the presence of a permanent, well-oxygenated zone beneath the slab that could be absent when the building is heated. Potential variability in building pressurization supports the need to collect subslab soil gas over different seasons to assess conditions when the building might be under positive, neutral, or negative pressure. The resulting data can be used to assess VIR averaged over the year.