Environ. Sci. Technol. 2006, 40, 931-938
Assessing Sites Contaminated with Unexploded Ordnance: Statistical Modeling of Ordnance Spatial Distribution JACQUELINE A. MACDONALD* AND MITCHELL J. SMALL Department of Civil and Environmental Engineering and Department of Engineering and Public Policy, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213-3890
km2
More than 40 000 of former military land in the United States are contaminated with unexploded ordnance (UXO). Cleanup costs are estimated to total as much as $140 billion. The amount of contaminated acreage and total costs are likely to increase as the U.S. Department of Defense (DOD) follows through on recently announced plans to close an additional 22 domestic military bases. The U.S. Environmental Protection Agency (EPA) and DOD disagree on how these sites should be characterized to assess their risks and plan for cleanup. As a result, much potentially valuable land remains idle while remediation decisions are pending. One of the sources of disagreement is how the locations of UXO should be characterized, given that the exact spatial distribution of UXO is unknown in advance of cleanup. In this paper, we propose and test a new model to represent the spatial distribution of UXO. Unlike existing DOD models, the new model accounts for the tendency of UXO to cluster, presumably around targets at which soldiers aimed during training. We fit the cluster model to geographic data on UXO locations at two former military installations and show that it describes key characteristics of the data more accurately than the existing DOD model. We discuss how the choice of a UXO spatial distribution model could affect important decisions about cleaning up and reusing UXO-affected property.
Introduction The U.S. Department of Defense (DOD) faces a legacy of contamination at former military installations across the United States where soldiers once trained with or tested weapons. These sites, now designated or already being used for civilian activities, are contaminated with unexploded mortars, rockets, grenades, bombs, and other munitions, known as “unexploded ordnance,” or UXO (Figure 1). Many of these UXO items are live, i.e., prone to detonating if they are disturbed. For more than a decade, the DOD and the U.S. Environmental Protection Agency (EPA) have been unable to agree on the magnitude of the risks these sites pose, how best to clean them up, and their safety for civilian uses (1). * Corresponding author present address: Department of Engineering and Public Policy and Department of Civil and Environmental Engineering, Baker Hall Room 129, Carnegie Mellon University, Pittsburgh, PA 15213-3890; phone: (412) 268-5607; fax (412) 2683757; e-mail:
[email protected]. 10.1021/es051168t CCC: $33.50 Published on Web 12/15/2005
2006 American Chemical Society
FIGURE 1. UXO uncovered during the cleanup of Fort McClellan, a closed military base in Alabama.
FIGURE 2. At 26 closed Army bases included in one study, less than 10% of land containing UXO is being reused by civilians; the rest awaits resolution of disagreements about site characterization and remediation (2). For example, a recent RAND Corp. study found that more than 90% of UXO-contaminated land at Army bases closed under the Base Realignment and Closure Program between 1988 and 1995 remains off limits for redevelopment, pending final decisions about cleanup (Figure 2) (2). As a result, civilian activities are affected, and sometimes entirely prohibited, thereby slowing economic redevelopment and depressing property values. This paper focuses on one aspect of characterizing UXO sites prior to cleanup that needs to be resolved to enable remediation decisions to go forward: the statistical modeling of how UXO is scattered across the land surface. An adequate statistical characterization of UXO spatial distribution is critical to assessing risks of UXO sites and making remediation decisions, because the locations of individual UXO items are not known in advance of cleanup and land reuse. The DOD has developed a model for characterizing UXO spatial distribution, but the EPA disagrees with this model. This disagreement is one of the factors contributing to the delays in making final remediation decisions at many UXO sites. In this paper, we first provide background on the extent of the UXO problem in the United States, the difficulties associated with cleanup, and previous efforts to model UXO spatial distribution. Then, we suggest a new statistical model for representing UXO locations. We test both DOD’s existing UXO spatial model and the alternative model using data from two UXO sites. Finally, we discuss how the choice of a spatial VOL. 40, NO. 3, 2006 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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model will affect decisions related to site risk and the need for remediation.
Background Extent and Costs of UXO Contamination. An estimated 1765 sites at closed or closing military bases in the United States are contaminated with UXO (3). All told, about 40 000 km2s an area the size of Massachusetts, Connecticut, Rhode Island, and Delaware combinedsare affected (3). The DOD currently estimates that costs to clean up all known UXO sites in the United States will total $19.9 billion (4), but a review by the Government Accountability Office suggests much higher costs, from $40-140 billion (5). New UXO sites continue to be found, as ordnance still occasionally surfaces in areas that were long ago used for military training, but where records of this activity were lost or incomplete, or where cleanups were conducted but UXO continues to surface (1). The number of sites, acreage affected, and total cleanup costs all are likely to increase as DOD follows through on plans, finalized in September 2005, to close an additional 22 major domestic military bases. UXO sometimes remains from the burial of unused munitions, but most UXO contamination is a result of the failure of munitions to detonate after they are fired. Such failures can occur due to either a malfunction in the arming process or operator error (such as failure to remove the safety pin or hit the target). The dud rate varies with the type of munition, its age, and the climate and terrain. Fuses on modern munitions fail about 3-8% of the time (3); failure rates on older munitions may be as high as 10-30% (6). Even though a munition may have failed to explode when initially launched, it can remain live and prone to detonation if it is disturbed. As an example, an Army Corps of Engineers review of records from about half of the known UXO sites in the United States found reports of 38 civilian deaths and 64 injuries between 1913 and 2002 (7). The potential for injuries will increase as more closed bases are converted to civilian uses. Limitations of Remediation Technologies. The primary tool used in the search for UXOsmuch of which is buriedsis the metal detector. Due to performance limitations of these tools, no amount of searching, short of complete excavation down to the maximum depth of UXO penetration, can ensure that all UXO has been found (3, 8). The complete excavation approach generally is cost prohibitive because of the size of the affected areas and the depths at which UXO may be buried: sometimes more than 6m (20 ft) for certain combinations of munitions and soil types (8, 9). Metal detectors have two important limitations as the primary instruments for locating UXO. One is that they usually do not find all the UXO (3, 10). For example, results from a controlled field test at a former training range in Fort Ord, California, showed that when crews dug holes of radius 0.5 m (1.6 ft) around each anomaly signaled by the metal detector, they found anywhere from 24 to 99% of buried UXO (11). Factors such as the detector brand; how it is tuned; the metal content, burial depth, and orientation (vertical, horizontal, or angled) of the ordnance; operator skill and training; and the area’s soil type all affect performance. The second limitation of metal detectors is their high false-alarm rate (3, 10, 12). Shrapnel, scrap from targets, hubcaps, cans, belt buckles, wire, and rocks containing iron comprise most of the “finds” of UXO clearance crews. State-of-the-art geophysical mapping and data analysis tools have markedly decreased the false-alarm rate, but it is still extremely high. According to the Defense Science Board Task Force on UXO, as many as 99% of the objects excavated in searching for UXO are nonhazardous metal items (3). UXO detection crews must trade off decreases in the falsealarm rate against improvements in the probability of 932
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detection (10, 12). For any given class of metal detector, decreasing the false-alarm rate increases the chance of missing some UXO. For example, in the Fort Ord study mentioned above, the instrument with the highest probability of detection across all sites also had the highest false-alarm rate. Researchers concluded that 63-79% of the UXO items this detector located were chance discoveries, unearthed by accident as the crew searched for clutter items that had triggered a detector signal (11). Existing Site Characterization Approach. Due to the limitations of UXO detection technologies, one can never be sure that all UXO has been removed after cleanup. Further, the locations of individual UXO items cannot be determined definitively until the items are found, either by cleanup crews or by accident. The DOD and EPA, which are both involved in establishing policies for remediation and reuse of UXOcontaminated land, have been unable to agree on how best to address the uncertainties associated with the distribution of UXO across a site, the associated risks, and the effectiveness of different cleanup strategies (1, 2, 13). In particular, EPA has raised objections to DOD’s approach to characterizing the spatial distribution of UXO, given that the exact distribution can never be known. The DOD has developed two tools intended to characterize the UXO spatial distribution at individual sites: “SiteStats/ GridStats” and “UXO Calculator” (14-16). Both are software packages that field crews use in real time, on laptop computers, to estimate the density of UXO itemssdefined as the number of UXO items per unit of land area. Both use the same statistical model to represent how UXO is distributed across the land surface. The statistical term for the model is “complete spatial randomness” (CSR). For CSR to hold, the spatial arrangement of UXO must exhibit the following two properties (17, 18): 1. The number of UXO items in a region with area |A| must follow a Poisson distribution with mean λ|A|, where λ represents the average number of UXO items per unit area. In other words, the probability that the number of UXO items in any area of size |A| equals some integer k is given by
Pr(N ) k) )
(λ|A|)ke-λ|A| k!
k ) 0, 1, 2, 3, . . .
(1)
2. The specific locations of UXO in planar region A are an independent random sample from the uniform distribution on A. These assumptions imply that (1) the average number of UXO items per unit area is constant across the site and (2) any given location on the site has an equal chance as any other of containing UXO. EPA’s primary objection to the CSR model is that it does not adequately represent the physical phenomena that lead to the deposition of UXO (16, 19). Since soldiers aim their weapons at targets, EPA contends, one would expect a higher density of UXO near targets and a lower density farther away from targets. The CSR assumption, in contrast, implies that soldiers fire at random, without regard to target locations. In a letter to DOD’s Under Secretary of Defense for Environmental Security, EPA Assistant Administrator Timothy Fields, Jr., noted, “The statistical grid sampling approach used by the USACE [U.S. Army Corps of Engineers] would only be appropriate if one expected a relatively uniform distribution of UXO, which is not the case at military ranges” (19). A technical review of SiteStats/GridStats and UXO Calculator conducted on behalf of EPA noted that the CSR assumption forms the basis for all the subsequent modeling that occurs in these programs and that “If this assumption is not true, the resulting conclusions and consequently all subsequent
UXO sector density information, UXO interval estimation, and risk estimates may be inadequate” (16).
New Model of UXO Spatial Distribution The key limitation of the existing approach to modeling the spatial distribution of UXO is that it fails to capture the expectation that UXO items will be clustered around targets. The problem of modeling clusters of spatially distributed objects or events is common to a range of scientific disciplines, from cosmology to botany. For example, statisticians have developed models to represent the clustering of galaxies in the universe (20), trees in forests (18), and incidences of disease (21). Models developed for these other applications can be applied to the problem of UXO site characterization. The research reported here focused on testing the fit of one particular class of statistical model commonly used to represent spatial clustering: the “Poisson cluster model” (17, 18, 21). Neyman and Scott developed this model during the mid-twentieth century and showed that it could represent the spatial distribution of galaxies in the universe (20). At the time, galaxy locations were determined by counting images of the faint light reaching the earth from distant galaxies, as captured on two-dimensional photographs of the night sky. Whereas previous modelers had assumed that galaxies are CSR distributed, this assumption conflicted with observations of local clusters of galaxies. Neyman and Scott’s model effectively represented the observation that centers of clusters of galaxies appear to be homogeneously distributed, while at the smaller scale galaxies group around these cluster centers. This same model has the potential to be useful for UXO site modeling because it can represent firing targets as cluster centers (analogous to the cluster centers of galaxies) and UXO locations as “offspring” of these cluster centers (analogous to locations of specific galaxies). The Poisson cluster model assumes the following (18): 1. Cluster centers (known as “parents”) form a Poisson process with intensity F. In other words, the number of parents in any area of size |A| is a Poisson random variable with expected value F|A|. 2. Associated with each parent is a random number a of offspring, with this number independent of all the other parents. 3. The positions of the offspring relative to their parents are independently and identically distributed according to a bivariate, continuous probability density function. We consider a special class of Poisson cluster process in which a, the number of events per parent (UXOs per target), has a Poisson distribution and in which events are distributed around each parent according to a radially symmetric Gaussian distribution (18, 22). Three parameters are needed to specify this model: (1) the average number of parents (in this case, targets) per unit of land area, represented by F; (2) the average number of offspring (UXO) per parent, denoted as a; and (3) the standard deviation, σ, of the distance from each offspring to its parent. In recent research for the DOD’s Strategic Environmental Research and Development Program, investigators have assumed that a Poisson cluster model might be appropriate to represent the UXO spatial distribution, but they have not verified that the model provides a statistically significant fit to actual UXO data sets. As an example, Ostrouchov et al. (23) proposed that a spatial cluster model might be appropriate for UXO sites because it can represent target placement and the scatter of objects about targets as separate processes. Ostrouchov et al. used a cluster model of the same type tested here as the basis for simulating UXO sites, but they did not assess the extent to which it statistically represents data from actual sites or attempt to estimate model parameters based on site data. Similarly, McKenna et al. used
FIGURE 3. UXO locations at Fort Ord sample area. a model in which UXO items are clustered around a single target according to a radially symmetric Gaussian distribution as the starting point for an effort to model UXO data from former bombing ranges (24-26). However, they did not verify the statistical fit of such a model to a data set, nor did they use it as the output of their UXO site characterization method. Instead, they converted data on UXO locations to a single, continuous random variable: the UXO “density” (number per unit area) at any given point in the continuous x,y-plane. This approach results in a loss of pattern information because it requires the transformation of a discrete variable (the locations of UXO items) to a continuous variable (the UXO density) (17, p 591).
Method for Testing the Model We compared the ability of the CSR and cluster models to represent data on UXO locations at two former military training ranges: Fort Ord, California, and Tobyhanna State Park (formerly Tobyhanna Artillery Range), Pennsylvania. In each case, our goal was to determine whether the CSR model (DOD’s current model) or the cluster model (the proposed alternative) better characterizes the spatial distribution of UXO. Data Sources. The basis for our analysis at Fort Ord was an Army Corps of Engineers database with a complete listing of the geographic coordinates of all UXO items found to date. Fort Ord was used for Army training from 1917 until its closure in 1994. Approximately 12 000 of Fort Ord’s 28 000 acres contain UXO; almost all of this acreage is awaiting cleanup and transfer (2). We used data on UXO locations from two adjoining areas (known as OE-53 and OE-53-EXP), both of which have been fully surveyed and excavated for UXO. We chose a square of side 335 m (1 100 ft) that encompasses a large portion of these two areas. Figure 3 shows the UXO locations in this area. The items shown are all unexploded munitions. At Tobyhanna State Park, the basis for our analysis was a similar database (compiled by Weston Solutions, Inc.), but in this case we evaluated all ordnance-related metallic anomalies, including fragments of exploded or partially exploded munitions. We included all ordnance-related metallic objects because information about the pattern of such objects may help in the development of algorithms for distinguishing areas with UXO from clean areas. [Typically, when initial surveys of UXO sites are conducted, the result is a map of all metallic anomalies found. Such anomalies will be present at clean sites (due to metallic objects such as ferrous rocks, bottle caps, coins, and other cultural debris). VOL. 40, NO. 3, 2006 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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For the CSR model, the K function is given by (17)
K(h) )
πh2 × λ ) πh2 λ
(5)
That is, the expected number of extra events increases linearly with the area of the circular region of radius h around a particular event. For the specific type of Poisson cluster model we are considering, the K function is given by
[
1 - exp
K(h) ) πh2 +
F
( )] -h2 4σ2
(6)
where F and σ are the model parameters, as described above (18). We estimated the cluster model parameters by minimizing the least squared error in the K function (18, 22), using
∫
a2
a1
FIGURE 4. Locations of UXO and ordnance-related items at Tobyhanna State Park sample area. We are currently beginning an investigation of whether the pattern of metal detector responses in UXO-free areas differs statistically from the pattern in UXO-affected areas. If these patterns are statistically different, then statistical analyses can be used to help distinguish areas with UXO from those without it, prior to any excavation.] Tobyhanna State Park was used for artillery training between 1912 and 1949, when it was transferred to the Commonwealth of Pennsylvania. The area was slated for cleanup in 1997, after a camper using a metal detector found 53 unexploded 37-mm artillery rounds (27). We used data from a square of side 2438 m (8000 ft) that has been carefully surveyed for metallic objects. Figure 4 shows the locations of the UXO-related anomalies in the square area we studied. Parameter Estimation Methods. For the CSR model, only one parameter is required: the intensity (the average number of UXO or UXO-related items per unit area). Considering at Fort Ord the sample area is a square of side 335 m (1100 ft), and 199 UXO items were found in this square, the estimated intensity for the CSR model of Fort Ord is
λˆ )
199 ) 1.77 × 10-3/m2 ) 1.64 × 10-4/ft2 (335 m)2
(2)
At Tobyhanna, with 805 UXO-related items in a square of side 2438 m (8000 ft), the estimated intensity is
λˆ )
805 ) 1.35 × 10-4/m2 ) 1.26 × 10-5/ft2 (3) (2438 m)2
Estimation of the parameters for the Poisson cluster model is more difficult, because tractable equations for computing parameter estimates from sample data are not available (18). However, iterative methods for parameter estimation are available and have been applied to other spatial data sets. We used the method described in Diggle (18) and Moller and Waagepetersen (22). The parameter estimation method is based on what spatial statisticians call the “K function.” The K function is a property of a spatial point process (17, 18) and is defined for any distance h as
K(h) ) (Expected number of extra events within distance h of given event)/(λ) (4) where λ is the intensity, as defined above for the CSR model. 934
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{K ˆ (h) - K(h)}2dh )
∫
a2
a1
{
(
(K ˆ (h) - πh2) - 1 - exp
( )) }
2 -h2 /F dh (7) 2 4σ
Here, a1 and a2 (the limits of integration) can be chosen over any region where the estimated K function does not exhibit extreme fluctuations. [We used (a1, a2) ) 43 m, 152 m) ) (140 ft, 500 ft) for the Fort Ord data and (a1, a2) ) (0 m, 1340 m) ) (0 ft, 4400 ft) for the Tobyhanna data.] As Moller and Waagepetersen recommend (22), we solved the above minimization by setting
C(σ2) )
D(σ2) )
∫
a2
a1
[
∫
a2
a1
[
1 - exp
( )] -h2 4σ2
2
(K ˆ (h) - πh2)(1 - exp
dh
(8)
( )]
(9)
-h2 dh 4σ2
With this method, σ2 is chosen to maximize D2/C; F is set equal to C/D; and R is estimated from
R ˆ)
λˆ Fˆ
(10)
where λ is the intensity. We determined K ˆ for different distances h from the data using a built-in algorithm provided with the spatial statistics module for the software package S+. Methods for Assessing Model Fit. To compare the fit of the two spatial models (cluster and CSR) to the data, we used three graphical methods and two goodness-of-fit tests as recommended by Diggle (18). The methods employ three different functions that describe the spatial distribution of point patterns in two dimensions: (1) the “nearest-neighbor” cumulative probability distribution function, G(h); (2) the “point-to-nearest-event” cumulative probability distribution function, F(h); and (3) the K function, K(h) (eqs 5 and 6). For each of these functions, one can assess model fit by checking how well the predicted values for different distances h correspond to actual values as determined from the data. Also, using G(h) and F(h), it is possible to estimate goodnessof-fit statistics that describe how well a particular model fits the data. The nearest-neighbor distribution function, G(h), represents the cumulative probability that the distance between an event (in this case, a UXO) and its nearest neighbor is less than or equal to h (17, 18). The G(h) curve for a spatial data set can be compared to the curve expected for a given model with given parameters to assess whether the model is
TABLE 1. Parameter Estimates for the Two Models of UXO Spatial Distribution data set model
parameter
CSR cluster
a
Fort Ord
λ (items per unit area) F (cluster centers per unit area) σ (cluster radius)a R (items per cluster center)
10-3/m2
1.8 × 1.3 × 10-4/m2 27 m 13
Tobyhanna 1.4 × 10-4/m2 8.9 × 10-7/m2 43 m 161
The cluster radius is the standard deviation of the distance between UXOs and their associated cluster centers.
consistent with the data (18). Also, G(h) is the basis for a test statistic, gi, that indicates the strength of the model fit, much as the t statistic measures the likelihood that a sample mean represents the mean of a larger population. This statistic is defined as (18)
gi )
∫ {Gˆ (y) - Gh (y)} dy ∞
0
2
i
i
(11)
where G ˆ 1(y) is the G-function for the data, G ˆ i(y) (i ) 2, 3,..., s) are the G functions for s-1 simulations of the model, and G h i(y) is the average of all the simulated values (except the ith simulation). The point-to-nearest-event distribution function, denoted by F(h), represents the distances from each of m sample points to the nearest of the n events (UXO items). The sample points m typically are determined by overlaying a k × k grid, with k ) n0.5 (where n is the total number of events), on the area of interest and selecting the points at the origin of each square of the grid (18, 28). Theoretical and empirical values of F for different distances h, and a test statistic fi based on F, can be determined in much the same manner as for G (for details, see 18 and 28). While F(h) and G(h) are useful indicators of clustering in a spatial point pattern, these statistics do not capture how clustering varies with spatial scale (17). This drawback results from the reliance of both G and F on information only about the single nearest event to another event or a point on the plane, rather than on second-nearest events, third-nearest events, and so on. Cressie (17) recommends assessing model fit by plotting K as a function of h for the model and for the empirical data and comparing how well these two plots correspond.
Results Parameter Estimates. Table 1 summarizes the parameter estimates for the CSR and cluster models at Fort Ord and Tobyhanna. As shown, if the cluster model is valid at Fort Ord, there are 1.3 × 10-4 targets (i.e., parents) per m2, or 15 targets in the whole area. The standard deviation of the distance from each UXO to its associated target is 27 m. On average, 13 UXO items are associated with each target. At Tobyhanna, the cluster model implies that there are about 5 targets total (equivalent to a parent density of 8.9 × 10-7/ m2), each with a radius of about 43 m, with 161 items per target. The greater number of items associated with each hypothetical target in the case of Tobyhanna makes sense, given that at Fort Ord the data points correspond only to whole UXO, whereas at Tobyhanna the data points correspond to pieces of exploded ordnance, as well as UXO. Evaluation of Model Fit. Figure 5 shows the comparison of the two spatial models to the Fort Ord data set using K(h). The 98% confidence interval represents the upper 99% and lower 1% values for K computed in 100 simulations of the postulated models. The top half of the figure shows that the data are entirely outside the 98% confidence interval for the CSR model. In contrast, the bottom half shows that the data are entirely contained within this confidence interval for the cluster model. (Note that the cluster model has much wider
FIGURE 5. Comparison of CSR (upper graph) and cluster (lower graph) model fits to the Fort Ord UXO data using the K function. The cluster model provides a statistically close fit, while the data are outside the 98% confidence interval for the CSR model. confidence intervals than the CSR model because it accounts for more sources of variability.) This result appears to rule out the CSR model as an accurate representation of the Fort Ord data set, while the cluster model appears to be consistent with the data. Similar analyses using F(h) and G(h) also show that the cluster model is consistent with the data, while the CSR model is not; results are provided with the Supporting Information for this paper. Figure 6 shows similar results for the Tobyhanna data: empirical results are outside the 98% confidence interval for the CSR model. In contrast, the data are within this confidence interval for the cluster model. The confidence interval is very wide for the cluster model because of the large uncertainty represented in this model (greater than at Fort Ord due to the small number of cluster centers). The results were the same in analyses using the F and G functions, with the data points outside the 98% confidence intervals for the CSR model VOL. 40, NO. 3, 2006 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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FIGURE 6. Comparison of CSR (upper graph) and cluster (lower graph) model fits to the Tobyhanna data using the K function. The data are within the 98% confidence interval for the cluster model but outside of it for the CSR model. and within them for the cluster model (see Supporting Information). The goodness-of-fit statistics fi and gi provide further evidence that the cluster model represents both the Fort Ord and Tobyhanna data sets. For the Fort Ord data, using 100 simulations of the cluster model these statistics give 0.05 e p e 0.14, where p represents the smallest level of significance at which one would reject the hypothesis that the cluster model fits the data. For the Tobyhanna data, again using 100 simulations, the statistics indicate 0.14 e p e 0.36. If we choose a 5% level of significance, the hypotheses that the cluster models fit the Fort Ord and Tobyhanna data cannot be rejected.
Discussion: Implications of Model Choice The choice of a spatial point-process modelswhether CSR, Poisson cluster, or some othersto represent the spatial distribution of UXO at former military training ranges could affect key decisions about how best to proceed with site characterization and remediation. Examples of decisions that could change with model choice include the following: 1. What percentage of the total site area must be surveyed without finding UXO to declare an area clean? This question is being debated at many UXO sites. In practice, typically only a small percentage of a site is searched carefully. If no UXO is found in the sampled grids, the entire area is declared to have very low probability of containing UXO, and further cleanup may not be undertaken. For example, at one typical 936
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installation studied by Engelhardt et al. (16), the Army Corps of Engineers based its site characterization on a survey of about 1% of the total acreage. Our research indicates that assuming the CSR model holds when in fact the UXO are clustered increases the risk of incorrectly concluding that an area is clean, based on such selective sampling. Figure 7 shows this effect for both Tobyhanna and Fort Ord. As shown, for both sites the CSR model predicts a nearly 100% chance of finding UXO as long as at least 3% of the site is surveyed. In contrast, the cluster model shows that the probability of finding UXO in a sample area that is 3% of the total area is 70% at Fort Ord and less than 20% at Tobyhanna. Thus the CSR model implies that one needs to sample only a small area to determine whether UXO is present on a larger site, whereas the cluster model indicates the need for more extensive sampling. 2. How risky is it to use a land parcel for some civilian purpose when UXO clearance is incomplete? For example, is it safe to use an area for hiking if only UXO on the surface, or down to one or two feet of depth, have been cleared? How does the risk change with more intensive remediation? Our results suggest that the answers to such questions can change, depending on which statistical model is chosen to represent the UXO distribution. As an example, Figure 8 shows probability distributions for the number of UXO items in a 61-m2 parcel within the Fort Ord area we studied; one distribution assumes that the CSR model applies, while the other assumes the cluster model applies. (In both cases, we used the model parameters shown in Table 1, and we assumed no remediation had yet occurred.) As shown, these probability distributions differ markedly for the two models. For example, the cluster model predicts a much higher probability (34%) that the area will contain no UXO than the CSR model (0.14%), but it also predicts a higher probability than the CSR model that the area will contain a large number of UXO items (e.g., more than a dozen). 3. Is it possible to divide a site into subsections that can be considered homogeneous for purposes of decisionmaking? The documentation for existing methods for statistical characterization of UXO sites says that it is possible to divide a UXO site into sectors such that the UXO distribution can be assumed homogeneous (i.e., CSR) within each sector (14-16). However, the results of our analyses from Fort Ord and Tobyhanna indicate that the CSR assumption is invalid even at extremely small spatial scales. Figures 5 and 6 indicate that at both Fort Ord and Tobyhanna, the data violate the CSR assumption even at scales as small as 15 m (50 ft), which is the minimum length of the side of a sampling area in UXO investigations (29). Thus, this research suggests that it is not reasonable to assume that UXO are homogeneously distributed even within a single sampling gridsmuch less on a parcel of land large enough to be of interest for decision-making purposes. 4. Once the presence of UXO has been confirmed, where should the search for additional UXO begin? Our research suggests that the search for UXO should begin by attempting to locate target areas, or clusters of UXO, rather than by sampling a few grids at random locations and then extrapolating UXO density information from those few grids across the entire site. Indeed, research is currently under way at U.S. Department of Energy (DOE) laboratories to design statistically based sampling plans to locate target areas (2326, 29). The research reported in this paper compliments these efforts in that it confirms that UXO may be clustered. Clustering may occur even where targets were moved repeatedly over time, as was the case at Fort Ord, where historical documents indicate that target locations changed many times over the lifetime of the training range. The results of our analyses could be useful for further work to identify optimal sampling strategies for locating target areas and,
FIGURE 7. Probability that a sample area will contain zero UXO, given that the larger site has UXO. As the two lower curves show, at both installations the CSR models predict that the probability of deciding a site is clean because no UXO were found in the sample area is zero as long as about 3% or more of the total acreage is sampled. On the other hand, the cluster models indicate high probabilities that limited site sampling will fail to detect UXO even if an area is contaminated. Here, |A| is the size of the sample area, and |F| is the size of the full site (in units of length2). The cluster model curves are based on 1000 simulations using the S+ Spatial Stats module and the parameters in Table 1; the CSR model curves are based on the Poisson distribution with intensities as in Table 1.
FIGURE 8. Probability distributions for the number of UXO items in a 61 m × 61 m square within the Fort Ord area studied in this research. As shown, the CSR model predicts a near-zero (0.14%) probability that the area will contain zero UXO and also a near-zero probability (0.33%) that it will contain more than 14 UXO items. In contrast, the cluster model shows a 34% probability that the area will contain zero UXO, but also a 16% probability that it will contain more than 14 UXO. once they are located, deciding how to proceed with characterizing the UXO distribution around the target. Before the findings from Fort Ord and Tobyhanna are generalized, additional research should be undertaken to test whether the cluster model fits data from other installations that have been extensively surveyed and have databases on locations of all UXO items found. Alternative forms of cluster models, such as ones representing the distribution of UXO around targets as asymmetric, could be tested as well. In developing a set of such alternative models to test, physical factors affecting ordnance deposition, such as soldiers’ firing accuracy and munitions flight paths, could be considered. On the basis of the results of such analyses, a database of appropriate model types and typical parameters for different kinds of former training ranges could be prepared. These databases then could be usedsalong with site-specific historical information (if available) such as target locations, types of munitions used, and amount of ordnance fired over timesas a starting point for characterizing the UXO distribution at former training ranges where thorough surveys have not been completed. As an example, consider a range where the Poisson cluster model is determined to be
appropriate. If historical information suggests that a certain number of targets and total quantity of ammunition were used, then this information could provide the basis for initial estimates of cluster center intensity (the parameter F) and the number of UXO items per target (the parameter a), assuming a certain failure rate for the munitions. The cluster radius (σ) then could be determined from sites in the database where similar kinds of munitions were used and where extensive UXO surveys and excavations have already been completed. All the model parameters for the new site could be updated, using Bayesian statistical methods (21), as site data are collected. The research presented here is the beginning of a larger effort to develop a quantitative risk assessment method for UXO sites. A more complete understanding of the risks of UXO, as well as the likely risk reduction achieved by site characterization and remediation programs, must consider a number of factors other than the spatial distribution of UXO. These factors include the depth at which ordnance is found; the probability that civilians will encounter UXO; and the probability that, once encountered, the UXO will detonate. In future research, we will show how spatial point-process models of UXO distribution can be combined with these other variables to produce quantitative estimates of risk at UXO sites under different combinations of remediation method and land reuse.
Supporting Information Available Four figures and text describing additional techniques used to compare the fit of the CSR and cluster models to the data sets at Fort Ord and Tobyhanna. This material is available free of charge via the Internet at http://pubs.acs.org.
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Received for review June 20, 2005. Revised manuscript received October 31, 2005. Accepted November 14, 2005. ES051168T
