Estimating Background Threshold Values for Risk Assessment

Environmental due diligence in the United States often begins with a Phase I Environmental Site Assessment to identify potential releases of hazardous substances or petroleum products. If a concern is identified (i.e., potential impact from a release), this may lead to the performance of a site investigation tailored to the most applicable risk-based corrective action (RBCA) program. RBCA programs use federal (i.e., screening using United States Environmental Protection Agency [USEPA] regional screening levels [RSLs]), state, or local government criteria to determine if a release is present or requires corrective action. All RBCA programs rely on contaminant fate and transport models to develop pre-calculated soil screening values that use a conservative set of site-specific parameters (e.g., soil type, soil pH, and depth to groundwater) (USEPA 1996a, 1996b). For example, the soil-to-groundwater leaching pathway is often associated with the most conservative screening value in soil for metals such as lead (USEPA, 1999) due to how a partition (distribution) coefficient (K_d) is used for modeling purposes. Whereas the USEPA (1999) (Page iii) notes that “soil scientists and geochemists knowledgeable of sorption processes in natural environments have long known that generic or default partition coefficient values found in the literature can result in significant errors when used to predict the absolute impacts of contaminant migration or site-remediation option,” many state-based programs continue to use overly conservative K_d values for screening. As a result, nationally, this model produces soil-to-groundwater protection screening values for lead that range from 3 mg/kg in Texas (30 TAC §350; Texas Commission on Environmental Quality [TCEQ], 1999), which is lower than 99.6 percent of soil samples in Texas (United States Geological Survey [USGS]; Smith et al., 2013; and Tramm, 2024), to being defined as “immobile” at any concentration (USEPA, 1996; New Jersey Department of Environmental Protection, 2008, 2021; Hawaii Department of Health, 2007). Figure 1 provides a visual representation of the same lead data set for Texas recommended by the USEPA for screening (USEPA, 2023; 5 cm interval–USGS 2013), confirming there are no lead samples meeting this criterion. Additionally, half of Texas is expected to exceed the singular median “background” value of 15 mg/kg currently offered as an “action level” (TCEQ, 2010). This approach neglects that “spatial variability of soil is not an academic question. It is a real landscape attribute; our unwillingness or inability to identify it in no way decreases its magnitude or existence. … As scientists we must document the magnitude and form of soil variability; accommodate its existence in models of soils; and transmit accurately the expected pattern and implication of spatial changes to users of soil resources” (USEPA, 1992b; Wilding, 1985).

Two key conservative modeling decisions used in Texas’ RBCA program that resulted in such a conservative value (i.e., 3 mg/kg) are the assumptions that soil has a pH of 4.9 s.u. and is sand (S). Both of these are contrary to USEPA guidance (USEPA, 1996b; USEPA, personal communication, July 10, 2023), which directs modeling to use an assumed pH of 6.8 s.u. and soil type of Sandy Loam (SL). Further, the USEPA specifically notes lead to be one of the “least mobile” metals and “at pH values above 6, lead is either adsorbed on clay surfaces or forms lead carbonate (USEPA, 1992a), and currently, “at sites in the early stage of investigation, EPA now recommends investigating areas where the amount of lead in soil is 200 parts per million (ppm) [mg/kg] or more.” (USEPA, 2024b). For context, the election to use a pH 4.9 and sandy soil in Texas’ RBCA modeling is consistent with approximately three percent of Texas surface soil (Walkinshaw et al., 2022). Figure 2 provides a summary of actual soil conditions in surface soil across Texas.

Knowing these pre-calculated screening values can be significantly lower than many naturally occurring metal concentrations (e.g., lead and arsenic), it is important to develop background values to inform the screening of investigation results so a release determination can be made.

Unfortunately, most RBCA programs have little to no background data to complete this screening, leaving the regulated community to repeat this work independently and at their expense. Undertaking a site-specific background study for every investigation effort should not be the outcome intended by regulators for simple baseline assessments for which metals screening is necessary; therefore, this paper provides an approach that can be undertaken using existing data sets. For example, whereas the USEPA (1996b) directs users to “compare available data to background,” it offers no pre-calculated values considering naturally or anthropogenically occurring conditions or clear approaches for developing a background threshold value (BTV). Even when state-based guidance does offer background values, these may be too conservative and result in unacceptable Type I errors (false positives) (USEPA, 1992c, 1995a, 1995b; Vosnakis and Perry, 2009). For example, the TCEQ (1999) acknowledges the median values offered under the Texas Risk Reduction Program as “background” had “no scientific basis for drawing inferences about the distribution of background concentrations on a specific affected property based on a value which represents a median concentration for the entire state,” yet the TCEQ continues to use it for release determination (TCEQ, 2010). One Texas municipality estimated the direct result of having to use a state-wide median background value was in excess of $250,000 annually in unnecessary soil testing, management, and even disposal even though there was no release (Tramm, Minter, and Seaton, 2023).

The absence of readily available BTVs is primarily a result of the complexity and variety of statistical tools available for evaluating data sets as well as the variability inherent within types of geology and resulting soils from across the United States (USGS, 1985; Díez et al., 2009). However, with new, widely accepted tools (i.e., the USEPA’s ProUCL) and availability of spatially relevant data (i.e., USGS data) to the larger scientific community, it is now possible to develop BTVs using a few conservative principles. It should be noted that the utilization of USGS data sets is not in any way suggested to replace a thorough site investigation of specific source areas but rather to provide a tool to utilize for metals comparison values and for delineation purposes for specific metals of concern. During a risk-based assessment, the application of this technique should be considered on a case-by-case basis, taking into consideration the availability of the information in the site area and the source and nature of the potential release to the environment.

The objective of this article is to set forth a simple process with clear decision parameters to aid the selection and censoring of representative data sets for BTV estimation using publicly available data and tools. Note that this emphasis is to selectively censor data sets in an effort to optimize parametric performance and deliver conservative values that would generally be accepted by regulators for screening purposes (i.e., minimize subpopulation bias suspected of adding to a right-tailed distribution). It is often the case that less “normal” or even non-parametric data sets will be sufficient under a more in-depth statistical demonstration to develop BTVs. But these instances should have the benefit of regulatory input concerning any corrective action or remedial decisions. Accordingly, it is recognized that censoring, for the approach set forth in this article, may require the exclusion of naturally occurring values as outliers for the benefit of defensible screening-level BTVs.

The USEPA notes, “USGS datasets for soil provide a baseline for the amount and distribution of chemical elements and minerals against which scientists can measure future changes from natural processes or human activities” (USEPA, 2023). The USEPA is also clear that “published data” from prior site investigations, local federal and state surveys, and universities are acceptable (USEPA, 1995b) for developing BTVs.

Two national USGS data sets have been part of many prior background metals values. This includes a 1981 USGS data set representing soil samples analyzed between 1958 and 1980 that were converted to a database format in 1996 by USGS that offers geospatial information needed for BTV development. The full 1981 USGS study included 1,323 samples (∼1 per 6,000 km²) collected across the conterminous U.S. at a depth of 20 cm (8 in.) below grade (Boerngen and Shacklette, 1981). Expanded versions of 1981 data sets are presented later with more data and/or improved spatial presentations (Shacklette and Boerngen, 1984; Gustavsson et al., 2001).

In 2013, the USGS published a study inclusive of sampling completed between 2007 and 2010 that utilized a highly detailed process for sample point collection through analysis that included avoidance of anthropogenic sources (i.e., not sampling within 200 m of a major highway or within 5,000 m within industrial activities), high sampling density (∼1 per 1,600 km²), multiple depths (e.g., 5 cm, Horizon A, Horizon C), and extensive use of quality control procedures within the laboratory analysis (Smith et al., 2013). The 2013 USGS effort included more than 4,800 sample points (more than 14,400 samples) with analysis of 45 major and trace elements.

Whereas there are subtle differences between the USGS methods utilized in these studies and USEPA methods more commonly used in risk assessment, sufficient verification has been performed (Hydrometrics, 2013; Brooks, 2021) concerning the study performance for lead and arsenic to allow use for BTV development. However, review of USGS vs. USEPA method performance suggests a very high bias in USGS data should be expected for aluminum (i.e., >100 percent) with lesser, but significant, high bias observed within barium, chromium, and vanadium results (Anderson and Yacucci, 2021; Tramm, Minter, and Seaton, 2023). Likewise, the USGS method for mercury is biased low when compared with the USEPA method as preservation techniques are not involved to address volatilization.

If developing a sediment-specific BTV or looking to supplement soil-specific data, the USGS National Geochemical Survey (NGS) offers data at a very high density (goal of ∼1 sample per 290 km²). Whereas much of this data set was initially collected to support the National Uranium Resource Evaluation (NURE) program and a related Hydrogeochemical and Stream Sediment Reconnaissance (HSSR) effort in the 1970s and 1980s, poor laboratory performance rendered the initial data difficult for use. Since the initial evaluation, the USGS has added to the original NURE and HSSR effort by reanalyzing many samples under improved quality assurance programs and extending the initial sampling density for the current NGS (USGS, 2004).

Many state entities may have suitable data for BTV development. For this review, a 2012 state-specific and single-interval data set prepared by the cooperation of USGS, Natural Resource Conservation Service, Wisconsin Department of Natural Resources, and Wisconsin Department of Health Services was selected (Stensvold, 2012) that focused on Wisconsin. This 2012 study included 664 soil samples collected at a depth of approximately 15 cm (6 in.) and analyzed for 17 trace elements. Efforts to avoid anthropogenic interference included only “undisturbed” locations at least 20 feet from a fence line, 100 feet from historical construction sites, and not within 300 feet of suspected arsenic contamination sources (e.g., orchards, cattle dipping, wood preservation activities, paper mills, or poultry/swine manure). Analyses were performed using EPA Method 200.7 after oven drying, grinding for homogeneity, and acid preservation/digestion.

Whereas the authors did not perform sampling to represent a region or specific site for this effort, spatially relevant USGS data has been isolated (Smith et al., 2013) that was appropriately collected, analyzed, subject to quality assurance evaluations and that offers regional data sufficient for BTV development. Similar site-specific data collection could be used to inform BTV development within a more localized area if needed.

The USEPA established an acceptable Type I error rate (false positive) goal in 1996 of 0.05 (five percent) (USEPA, 1996b) for selection of representative background conditions. To meet Type I error rate goals, the authors only estimated BTVs using the specified confidence coefficient of 0.95 within a selected data set being used for BTV development. This is the default setting within the USEPA’s ProUCL as well.

In 2022, the Interstate Technology Regulatory Council (ITRC, 2022) released guidance on the development of BTVs that included input from 16 separate state regulatory agencies, the USEPA, USGS, and United States Army Corps of Engineers in cooperation with multiple universities, industry representatives, and private engineering firms.

The ITRC and USEPA recognize that the 95 percent upper tolerance limit (UTL) “has become the most common measure of BTV in practice” with the 95 percent upper simultaneous limit (USL) presented when there are minimal statistical outliers. Moreover, the USL can be “specifically used to mitigate the issue of excessive false positive error rate in point-by-point comparisons” (ITRC, 2022). A third and “unrealistically conservative” tool for BTV purposes, per the ITRC, is the 95 percent upper prediction limit (UPL).

The UTL represents the value at which 95 percent of recorded samples are expected to fall below it 95 percent of the time. The USL is the statistic at which all potential observations (present and future) from the selected population are less than or equal to it with 95 percent confidence (Singh and Nocerino, 1997). The UPL establishes a limit that classifies future observations at or below this limit as being taken from the same population with a 95 percent confidence.

The ITRC notes that minimum sample sizes acceptable to the USEPA and all involved state regulatory agencies range from 8 to 20 samples to ensure that sufficient statistical power and representation of soil heterogeneity are present. To meet this goal, the authors suggest that BTV development on regional or larger areas include at least 20 samples if the USL is to be considered. A minimum of eight samples is recommended for consideration of the UPL and UTL. Site-specific BTVs may be acceptable to a regulatory agency with fewer samples, but non–site specific BTVs require a suitable statistical power to address expected heterogeneity. Although it is beyond the scope of this article, any risk assessor working across multiple physiographic provinces should understand the significance of varying geomorphological conditions affecting soil types. For example, soils derived from shale (hydrolyzates) can have more than five times the arsenic or lead concentrations compared with soils derived from sedimentary formations (resistates) (USGS, 1985).

For screening purposes, the authors developed UPL, UTL, and USL values for consideration as BTV estimators. For consistency, all statistical calculations were performed within USEPA’s ProUCL (version 5.2), which utilizes adjusted formulas based on population distributions. Once identified, raw data from each arsenic and lead data set are then evaluated using ProUCL. The sample number (n), mean (⁠⁠), median (M), standard deviation (σ), minimum, and maximum observations within each data set, along with the corresponding UPL, UTL, and USL, are provided for each data set. Formulas are provided as Supplemental Material Figure S1. Supplemental Material associated with this article can be found online at https://www.aegweb.org/e-eg-supplements. If the data set contains non-detect results, it is suggested that half the detection limit be applied for each sample (USEPA, 2006). However, if the data set contains more than 15 percent non-detect samples, the simplified screening approach presented in this article is not suggested, and more robust statistical analysis is needed (USEPA, 2000, 2002b) that are consistent with the governing regulatory authority’s expectations. Alternately, other data sets should be sought for BTV estimation that utilize a more appropriate sample detection limit.

Note that, although not utilized for this effort, if a BTV is being developed using USGS data for aluminum, the highest BTV estimator recommended is the mean. Likewise, if a BTV is being developed using USGS data for barium, chromium, or vanadium, the highest estimator recommended is the 95 percent upper confidence limit. These recommendations are based on observed USGS method performance (i.e., high bias) when compared with USEPA method performance within other national studies and an expectation that risk assessment will rely on USEPA method performance for all risk determinations. It is worth noting that all USGS method results for mercury should be considered biased low if they do not include preservation steps to address this element’s volatility.

Within the screening, the authors visually examined individual quantile-quantile (Q-Q) plots to identify possible right-tail outliers (presence of breaks/gaps) as this “unarguably is one of the most powerful diagnostic tools in the hands of a researcher” (Singh et al., 1994). This visual examination is combined with review of statistical distribution (e.g., normal or lognormal) along with minimum population statistics that include a linear correlation coefficient (R) of ≥|0.7| (Naval Facilities Engineering Command, 2002) and a coefficient of variance (CV) of ≤1.0 (USEPA, 2022a, 2022b) to confirm that the data set normality thresholds were acceptable to allow the proposed statistical testing. This is consistent with the USEPA CV requirement for censoring data (USEPA, 2006) and represents the USEPA’s recommended maximum CV when diverse soil types are anticipated (USEPA, 1995a). Another benefit of weighing CV performance in BTV estimator selection is that, as CV values decrease, lognormal distributions become very similar to that of normally distributed data sets (USEPA, 2002a). The USEPA also emphasizes the importance of understanding your data set’s mean and median relative to each other. More specifically, the “mean and median provides another method of identifying the shape of the data. If the mean is approximately equal to the median, then the data are distributed symmetrically. If the mean is greater han the median, then the data are right-skewed; if the mean is less than the median, then the data are left-skewed” (USEPA, 2006). As an additional conservative step in BTV estimation, the authors utilized only the ProUCL-developed values calculated “assuming normal distribution.” It is important to note that naturally occurring environmental data will commonly exhibit right-skewed lognormal, gamma, or non-parametric distributions (USEPA, 2022a) and the outliers electively removed may indeed be a portion of a background data set. Whereas the censored and uncensored data sets are often lognormal and/or gamma in distribution with expected right-tailed distributions, ProUCL presents a less conservative estimator under these tailored estimators and may require regulatory concurrence to allow use. Additionally, only the highest observed concentrations were considered for censoring. It may be appropriate, when within a regulatory program, to consider equal censoring at the highest and lowest observed concentrations, use of formal outlier detection methods (e.g., Dixon or Rosner), alternate treatment of non-detect samples, or other statistical processes tailored to a data set (Daniel, 2015).

This screening was inclusive of outlier censoring based on visual (i.e., Q-Q plots) and numerical considerations in an effort to yield the largest responsive BTV estimator for a given data set as outlined in Table 1. Note that it is intentional that the screening round to the specific performance goal based on the significant digits noted.

A normality quadrant graph (NQG) was provided with each data set screening to illustrate the performance of the resulting R and CV values with and without censoring. Data sets within the upper left quadrant of the NQG were considered suitable for further statistical testing and development of the BTVs. Data sets falling outside the upper left quadrant require censoring and/or further evaluation using non-parametric methods, which is outside the scope of this article.

Boundaries selected for study included a detailed example for four states and two regional areas. Additionally, calibration of the proposed normality performance goals (Table 1) included a full evaluation of the 2013 USGS data set for each state in the conterminous United States. A summary of viable BTVs for lead and arsenic within each state are also provided from this effort.

• Oklahoma: 2013 USGS data sets were isolated, and all vertical intervals were evaluated.

• Louisiana: 2013 USGS data sets were isolated, and all vertical intervals were evaluated.

• Wyoming: 2013 USGS data sets were isolated, and all vertical intervals were evaluated.

• Wisconsin: 2012 data sets (Stensvold, 2012) and 2013 USGS data set.

• San Antonio, Texas, area: 2013 USGS data sets were isolated, and all vertical intervals were evaluated.

• Dallas–Fort Worth, Texas, area: 2013 USGS data sets were isolated, and all vertical intervals were evaluated.

• Summary of conterminous U.S. states: 2013 USGS data sets were isolated, and all vertical intervals evaluated.

The Oklahoma data set included 333 soil samples. The results of iterative censoring and the resulting statistical performance are detailed in Table 2 (Oklahoma: Arsenic and lead BTV estimation) and Figure 3 (Normality quadrant graph [Oklahoma]).

The largest (i.e., most inclusive) BTV estimators for lead and arsenic meeting normality goals were 34.05 mg/kg and 13.00 mg/kg, respectively. Figure 3 provides a clear summary of data set normality improvements seen with censoring. Whereas significant normality improvements were seen within the Oklahoma lead data set censoring at 45 mg/kg and 30 mg/kg, each allowing use of a more conservative estimator, the largest defensible screening-level BTV value meeting normality goals was the UPL as this is a conservative statistic allowing for an inclusive data set. Minimal normality improvements were seen within the Oklahoma arsenic data set censoring, and the full data set allowed use of the UTL.

The Oklahoma Department of Environmental Quality (2023) utilizes the USEPA’s RSLs, which have no background values for metals as the basis of release determinations. Smaller state-wide studies were identified that ranged from 6 to 30 soil samples collected state-wide that exhibited similar mean (⁠⁠) concentrations for lead (10.25–18.3 mg/kg) and arsenic (3.44–7.29 mg/kg) but did not develop BTV estimates (Richards et al., 2012).

The value of a representative BTV is immediately apparent when considering that the current residential USEPA RSL for arsenic in soil is 0.68 mg/kg (target cancer risk of 10⁻⁶, target hazard quotient of 1), yet none of the 333 USGS soil samples would meet this modeled risk criteria (USEPA, 2024a).

The Louisiana data set included 225 soil samples. The results of iterative censoring and the corresponding statistical performance are detailed in Table 3 (Louisiana: Arsenic and lead BTV estimation) and Figure 4 (Normality quadrant graph [Louisiana]).

The largest (i.e., most inclusive) BTV estimators for lead and arsenic meeting normality goals were 45.44 mg/kg and 16.41 mg/kg, respectively. Figure 4 provides a clear summary of data set normality improvements seen with censoring. Significant normality improvements were seen within the Louisiana lead data set when censored at 50 mg/kg and demonstrating the largest defensible screening-level BTV to be the USL. The Louisiana arsenic data set was best represented with the USL following sufficient censoring to obtain CV normality performance goals. Here, rounding to the required significant digit performance for a CV of 0.5 met performance goals and allowed use of the USL. See Table 3 for an illustration of this point.

The Louisiana Department of Environmental Quality (LDEQ, 2003) currently offers a background value of 11.5 mg/kg, rounded to 12 mg/kg in the LDEQ’s screening table under the Risk Evaluation Corrective Action Program (RECAP). RECAP establishes an acceptable background as the mean (⁠⁠) plus one standard deviation (σ). If evaluating in a similar manner from this same data set, the resulting RECAP-based value would be 11.28 mg/kg. Although RECAP does not offer a published background value for lead, the RECAP-based value for lead (⁠⁠) using the USGS data set yields 28.9 mg/kg as background. In 2021, the LDEQ (2021) began allowing quantitative use of the 2013 USGS data set for background evaluation.

The Wyoming data set included 481 soil samples. The results of iterative censoring and the resulting statistical performance are detailed in Table 4 (Wyoming: Arsenic and lead BTV estimation) and Figure 5 (Normality quadrant graph [Wyoming]).

The largest (i.e., most inclusive) BTV estimators for lead and arsenic meeting normality goals were 38.65 and 14.82 mg/kg, respectively. Figure 5 provides a clear summary of data set normality improvements seen with censoring. Given the highly normal performance of the full lead data set, minimal improvements in normality were noted from censoring, whereas sufficient censoring of the arsenic data set to address the risk of remaining outliers or subpopulations allowed consideration of the USL at <15 mg/kg. The USL proved to be the most representative BTV estimator for lead and arsenic.

The Wyoming Department of Environmental Quality (WDEQ) utilizes its Wyoming Environmental Quality Act and supplements it with the USEPA’s RSL, which offers no background values for metals. However, the WDEQ published BTVs for arsenic (12 mg/kg), lead (32 mg/kg), and selenium (1.4 mg/kg) in 2015 and outlined a formal process for other metal BTV development similar to that used in this study (WDEQ, 2015, 2016). The WDEQ BTVs incorporated the same 2013 USGS data sets evaluated for this study with selected project data from prior investigations across Wyoming and selected the UTL as its BTV estimator. Similar to Oklahoma, the value of a representative BTV is immediately apparent when considering the current residential “cleanup level” for arsenic in soil is 0.29 mg/kg (target cancer risk of 10⁻⁶, target hazard quotient of 1) (WDEQ, 2024).

The 2012 Wisconsin data set included 664 soil samples. The 2013 Wisconsin data set included 264 soil samples. The results of iterative censoring and the resulting statistical performance are detailed in Table 5 (Wisconsin: Arsenic and lead BTV estimation [2012]), Table 6 (Wisconsin: Arsenic and lead BTV estimation [2013]), and Figure 6 (Normality quadrant graph [Wisconsin]).

As noted on the NQG for Wisconsin’s data sets (Figure 6), none of these initial data sets met normality performance criteria to allow use in BTV estimation. The largest (i.e., most inclusive) BTV estimators for lead from the 2012 and 2013 data sets were 36.11 mg/kg (censored at 100 mg/kg) and 37.75 mg/kg (censored at 41 mg/kg), respectively. Although the 2012 arsenic data set does not meet the normality performance criteria established for this method with an excess of 15 percent of the data being non-detect (32 percent), the evaluation process was completed for instructional value. If honored, the 2012 data set could yield an arsenic BTV of 5.21 mg/kg, demonstrating the conservative nature of the approach set forth in this study. The 2013 data set offered a slightly lower detection limit for arsenic and yielded a defensible screening-level BTV of 9.6 mg/kg from the UPL when censored at 49 mg/kg. Please note the failure of the 10 percent RPD normality performance goal that precludes allowance of the USL estimate of 10.21 mg/kg.

The 2012 study (Stensvold, 2012) established a BTV for arsenic of 8 mg/kg after applying non-parametric evaluation methods and removing 10 outliers. This BTV is accepted by the Wisconsin Department of Natural Resources (WDNR, 2014) for screening releases. The 2012 study exhibited slightly lower mean (⁠⁠) values for lead (13.5 mg/kg) and arsenic (2.3 mg/kg) when compared with the 2013 USGS data set.

Similar to in Oklahoma and Wyoming, the WDNR relies on the USEPA’s RSLs but supplements with pre-published BTVs for select metals such as aluminum (28,721 mg/kg), arsenic (8 mg/kg), barium (9,364 mg/kg), cadmium (1 mg/kg), chromium (44 mg/kg), copper (35 mg/kg), and lead (52 mg/kg) to minimize Type I errors (false positives) (WDNR, 2014).

The San Antonio data set included 54 soil samples collected from 17 counties. The Dallas–Fort Worth data set included 48 soil samples collected from 13 counties. The results of any iterative censoring and the resulting statistical performance are detailed in Table 7 (San Antonio and Dallas–Fort Worth areas: Arsenic and lead BTV estimation) and Figure 7 (Normality quadrant graph [San Antonio and DFW areas]).

As noted on the NQG for the San Antonio and Dallas–Fort Worth data sets (Figure 7), all of the full data sets are within UTL (DFW arsenic) or USL (DFW lead, San Antonio lead and arsenic) estimator regions. The BTV estimator for lead and arsenic within the San Antonio area are 37.01 and 18.21 mg/kg, respectively. The BTV estimator for lead and arsenic in the Dallas–Fort Worth area are 36.08 and 19.49 mg/kg, respectively. Sufficient normality improvements were seen within the Dallas–Fort Worth area arsenic data set censoring at <18 mg/kg to allow use of the USL. Note that diminishing normality performance is seen in the DFW arsenic data set from further censoring (i.e., decreasing R values).

As outlined previously, release determinations in Texas currently utilize a single median value for screening purposes despite there being high variability across the state (TCEQ, 2010; Tramm, Minter, and Seaton, 2023). As a result, early investigation screening incorrectly requires lead over 15 mg/kg (see Figure 1) or arsenic over 5.9 mg/kg to trigger additional effort despite being well below the conservative BTVs established for these regional areas or, as highlighted subsequently, for the full state of Texas (e.g., lead BTV of 38.4 mg/kg; arsenic BTV of 16.79 mg/kg). It is notable that even the actual mean (⁠⁠) and median (M) values demonstrated in the 2013 USGS data exceed the TCEQ’s current release determination criteria.

Calibration of the BTV estimation method set forth in this article includes a robust data processing effort using data sets across the conterminous U.S. state data sets ranging from 1,237 soil samples for Texas to just six soil samples from Rhode Island and Delaware. The highest arsenic (1,100 mg/kg) and lead (12,400 mg/kg) were identified as obvious outliers from the Nevada data sets. The arsenic data set for Florida exhibited too many non-detect results to allow consideration under the BTV estimation approach set forth in this article; however, the mean (1.96 mg/kg) derived from the normally distributed detections data set is selected as a conservative surrogate for screening purposes as it is consistent with the current regulatory criteria and extensive research on arsenic occurrence in Florida (Missimer et al., 2018). Additionally, too few samples were available for Rhode Island and Delaware to allow BTV estimation consistent with this article. However, the closest sample point from the adjacent state was used to increase the sample size and allow BTV estimation for these states. The results of any iterative censoring and the corresponding statistical performance are detailed in the provided Supplemental Material. Supplemental Material associated with this article can be found online at https://www.aegweb.org/e-eg-supplements. BTVs for lead and arsenic ranged from 13.06 (Florida) mg/kg to 102.5 mg/kg (New Hampshire) and 1.96 mg/kg (Florida) to 26.33 mg/kg (Ohio), respectively. Figures 8 and 9 depict the results of all BTV estimation efforts across the United States (rounded to the nearest whole number).

Based on the results of this study, the proposed procedure for developing BTV estimators was demonstrated to be an efficient way to quickly develop defensible BTVs for screening through the use of publicly available and widely accepted tools and data sets. The approach was intentionally conservative to increase the likelihood of regulator acceptance and ensure only a limited understanding of statistical methods was required for the environmental practitioner. It is essential that any BTV development exercise incorporate both visual (e.g., Q-Q plots, NQGs) and numerical (e.g., R, CV, RPD of the mean [] and median [M]) elements. The approach to BTV estimation outlined in this study can be applied to any investigation effort in which sufficient existing and/or newly obtained data allows an evaluation. The application of more rigorous and project-specific statistical methods should be considered when warranted.

The authors thank Modern Geosciences for allowing staff hours and resources needed to complete this paper. Additionally, the review and input from Harrison P. Tramm, Lauren Gayre, Zachary Tondre, Megan Wingard, Rusty L. Simpson, and Truth Hippman were helpful in completing this article.

Supplemental Material associated with this article can be found online at https://doi.org/10.2113/EEG-D-24-00009, https://www.aegweb.org/e-eg-supplements.