Technical Evaluation of Natural Resource Damage Assessments (NRDA) of Groundwater Resources John A. Connor, Farrukh Ahmad, and Richard L. Bowers Groundwater Services, Inc, 2211 Norfolk, Suite 1000, Houston, Texas, 77098-4044 Abstract To support a Natural Resource Damage Assessment (NRDA) for groundwater resources impacted by oil or hazardous substances, careful technical evaluation is required to define the nature and volume of the affected groundwater zone and the associated impact on the potential services provided by the affected aquifer and other interconnected water resources. Relative to the baseline beneficial use for which the groundwater resource was suitable prior to the impact, such loss of service may involve both: i) the loss of aquifer “storage,” i.e., the reduction in the volume of groundwater available for beneficial use, and ii) the potential loss in the “future yield” of the aquifer system, i.e., the reduction in the rate at which usable water can be produced due to the presence of the affected groundwater zone. Key technical considerations in this analysis include the actual and predicted water use activities, the nature and extent of the affected water zone, the hydrogeologic properties of the aquifer system and its interconnection with surface water resources, the ability for natural attenuation to restore lost beneficial use, the effectiveness of on-going remediation efforts, the applicability of ex-situ water treatment technologies to meet beneficial use criteria, and the relative contributions of different parties. Based on case studies of alleged damage claims, this paper provides practical guidelines for evaluation of losses in storage and potential future yield, considering each of these key factors and providing recommendations for appropriate use of tools such as Geographic Information Systems (GIS) and associated databases, groundwater data evaluation and interpolation methods, and groundwater fate-and-transport modeling.

Introduction Natural Resource Damage Assessment (NRDA) of Groundwater Resources Under the Comprehensive Environmental Response, Compensation, and Liability Act (CERCLA), the Clean Water Act (CWA), the Oil Pollution Control Act (OPA), and the Marine Sanctuary Act (MSA), federal, state, and local government agencies are designated as natural resource trustees authorized to assess and recover damages for injuries to natural resources. Regulations for implementing Natural Resource Damage Assessments (NRDA) have been promulgated by the U.S. Department of Interior (DOI) in 43 CFR Section 11, which provides detailed technical guidelines for damage assessments due to impacts of hazardous substances on various environmental media, including groundwater, and by the National Oceanic and Atmospheric Administration (NOAA) in 15 CFR Section 990, which specifically addresses oil impacts subject to OPA. Under the DOI process, two types of damage assessments are identified: Type A, which involves smaller release incidents and yield maximum damages of $100K or less and Type B, which involves more complex and costly impacts, for which a three-phase assessment process is identified involving i) Injury Determination, ii) Quantification, and iii) Damage Determination. The technical discussion presented in this paper is most applicable to Type B assessments, for which detailed analysis is required for evaluation of significant aquifer systems and/or interconnected surface water systems. Under the NOI guidelines, quantification of the effects of the impact on a groundwater resource involves the following principal steps (43 CFR 11.71 – 11.73): 1) Extent of Injury: Identify the lateral and vertical extent and the degree of chemical impacts to the

unsaturated zone and the saturated zone, including characterization of affected groundwater plumes, as well as related effects on surface water, air, geologic, or biological resources.

2) Change from Baseline Condition: Investigate aquifer conditions in a nearby unimpacted “control

area” based on available data and additional sampling and analysis as needed to characterize the variability of the chemical of concern with in the unaffected water system.

3) Characterization of Baseline Services: Determine the services normally provided by the

groundwater resource in the absence of the chemical impact, including water use (drinking, agricultural, industrial), groundwater recharge, base stream flow discharge, and other related human or ecological services. This analysis may also include the volume of the affected groundwater pumped from wells or discharged to streams or lakes.

4) Identification of Interdependent Services: Consolidate inter-related services so as not to “double-

count” a loss, such as exceedance of two separate water quality criteria which relate to the same or related beneficial uses.

5) Disruption of Services: Compare services provided with and without the presence of the

groundwater impact to define the nature of the disruption, including the degree and timeframe of the loss in the beneficial use of the groundwater resource, as defined by exceedance of drinking water standards, other applicable water quality standards or beneficial use criteria (irrigation, etc.), and/or loss of service via other natural resources (surface water, air, geologic, or biological resources) afforded by the groundwater impact. To support determination of damages, this assessment should also address both the proportion of the available resource that has been impaired (or will be impaired due to further plume growth during the recovery period) and the

timeframe required for recovery of the lost services based both on applicable remedial action scenarios and natural recovery under a “no-action” scenario.

Based on this quantification, the economic value of damages to the natural resource can be can be estimated based upon the costs required to restore, rehabilitate, or replace the services previously provided by the impaired resource and the compensable value of the services lost to the public until such action is complete. Key Technical Considerations in the Evaluation of Groundwater Resource Impacts The NRDA evaluation process entails consideration of technical information from the full spectrum of the groundwater investigation and remediation process, including delineation of the affected groundwater zone, evaluation of the potential chemical fate and transport mechanisms within the groundwater and surface water flow systems, consideration of natural attenuation effects, and evaluation of alternative remedial measures and associated costs. However, in addition to these conventional corrective action elements, the NRDA assessment can require a particular focus on the following technical issues, as needed to support the quantification and damage determination phases of the assessment process: • Characterization of Baseline Beneficial Use: Evaluate of current water use and characterize

potential water use based on background water quality and well yield. Although the affected groundwater unit may be subject to regulatory remediation criteria that are equivalent to drinking water standards, the unit may not actually be used for or be suitable for use as a drinking water supply.

• Static Characterization of Groundwater Impacts per Applicable Beneficial Uses: Delineate the

existing affected groundwater zone not only with respect to applicable remediation criteria, but for other applicable beneficial use criteria, such as agricultural use or applicable industrial uses. Impairment of the resource for use as drinking water may not necessarily impair its use for irrigation, and the associated affected groundwater zones for these alternatives uses may be different in area and volume.

• Dynamic Characterization of Groundwater Impacts: Evaluate the potential effects of the

groundwater plume on water supply wells (or other users) under pumping conditions, as well as future plume migrations patterns. Wells located near, but outside of, the affected groundwater zone could be impacted by plume migration or could be subject to restricted yields or relocation to avoid such impacts.

• Evaluation of Natural Attenuation Effects and Timeframe: Estimate time required for natural

attenuation processes to reduce chemical concentrations to levels consistent with applicable beneficial use criteria and thereby restore lost services. Accurate estimation of site-specific attenuation rates may require time-series monitoring of plume dimensions and concentrations.

• Restoration of Service vs. Remediation: In addition to evaluation of remediation technologies for

the affected groundwater plume, identify alternatives that are targeted toward timely restoration or replacement of the lost services, such as treatment of the extracted groundwater to meet beneficial use criteria or installation of an alternative water supply. Such actions serve to address the disruption of service in a shorter timeframe than may be involved in remediation of the affected groundwater zone as required under applicable regulations.

The conventional tools used for conducting groundwater corrective action projects, including use of Geographical Information Systems (GIS) and associated databases, data interpolation algorithms for estimation of plume dimensions and concentration distributions, and fate and transport modeling to assess dynamic conditions, apply equally to evaluation of the key technical issues related to quantification of impacts for NRDA purposes. However, given the higher cost-sensitivity of the NRDA assessment, a greater degree of accuracy and precision may be required than is commonly needed for remedial action design, particularly with regard to estimation of the volume and duration of the impacted zone. For example, although a rough delineation of the existing groundwater plume and use of a conservative screening-level model may suffice to support design of a pump-and-treat remediation system, per applicable regulatory requirements, such an analysis may serve to greatly over-estimate the associated loss of services and the time required for recovery. In all cases, the level of sophistication of the technical analyses should be commensurate with the magnitude of the potential damages involved, and the user should estimate and communicate the accuracy and reliability of the quantification upon which the economic damages assessment will be based. To support development of reliable assessments of groundwater resource damages, this paper reviews the key technical considerations identified above as they relate to water supply aquifers and presents practical guidelines for application of groundwater data evaluation tools, specifically, GIS and database systems, data interpolation methods, and fate and transport modeling, to NRDA assessments. Quantification of Loss of Service from Water Supply Aquifers Quantifying the potential loss of service from a water supply aquifer involves assessment of two key components: i) the loss of aquifer “storage,” i.e., the reduction in the volume of groundwater available for beneficial use, and ii) the potential loss in the “future yield” of the aquifer system, i.e., the reduction in the rate at which usable water can be produced due to the presence of the affected groundwater zone. Technical considerations for each of these categories are described below. Technical Analysis of Potential Loss of Storage The potential loss of “storage” within a groundwater aquifer due to chemical impacts is a function of: i) the current volume of groundwater within the aquifer that is usable for the proposed beneficial use (e.g., meeting applicable drinking water standards), ii) the portion of this usable water volume that can actually be produced, considering the physical and the practical limitations (e.g., prevention of unacceptable aquifer consolidation and associated land surface subsidence due to excessive withdrawals, or upconing of water from basal saline zone), iii) the current dimensions of the affected groundwater zone in excess of applicable beneficial use criteria, iv) the potential future dimensions of the affected groundwater zone, considering the effects of solute transport, natural attenuation, and current or proposed remediation systems, and v) the limitations, if any, imposed on water production outside the affected groundwater zone, due to potential impacts on the water produced by nearby pumping wells. If the affected groundwater will not discharge to surface water, potential impacts will be limited to groundwater resources and will not entail consideration of ecological impacts. Furthermore, in all cases, the “loss” of storage will depend on the feasibility of treating the affected water to meet the previous beneficial use criteria, a practice that has been successfully applied for many water supply systems in the U.S. Predicted storage loss must also be reconciled with actual water use activities to determine if such impairment actually has been observed and, if so, if actions have already been taken to address such impacts.

Technical Analysis of Potential Loss of Future Yield In addition to the loss of storage, the loss of future yield may represent a separate or modifying consideration when the presence of the affected groundwater zone serves to reduce the rate at which the groundwater could otherwise have been enjoyed and/or requires a modification of the current water pumping strategy so as to continue to meet water supply demands. As noted under NOI guidelines, care needs to be taken not to “double-count” the water impact, claiming loss of the same water volume both as it resides in the aquifer and as it is withdrawn from the aquifer. However, depending on the hydrogeologic characteristics of the aquifer, the current wellfield configuration, and the size and location of the affected groundwater zone, the presence of the affected groundwater zone could impede the future productivity of the aquifer in a manner that would not be cured simply by compensation for the loss in water storage (i.e., the current affected water volume). Evaluation of loss in future yield involves analysis of the water budget for the aquifer system and the effect of the affected groundwater zone on this water budget, if any, and on the methods of water production (well placement, depth, pumping rates, etc.). In many cases, the potential loss of yield can be cured simply by relocating pumping wells and/or treating the affected groundwater as it is produced from the aquifer. Tools for Quantification of Groundwater Resource Impacts Key tools for evaluating potential losses of storage and future yield in groundwater supply aquifers include: spatial database development to support GIS spatial characterization of actual measured groundwater quality conditions, statistical data interpolation methods to estimate the boundaries of affected groundwater zones in excess of applicable beneficial use criteria, and groundwater fate and transport modeling to predict future plume dimensions. In all cases, the predictions of lost storage or yield should be compared to actual water use patterns to “ground-truth” results of calculations or modeling results. The paper provides procedures and examples of these analyses, emphasizing practical measures to assess confidence in modeling and calculation results and appropriately apply these results to evaluation of NRDA claims. Database and Geographic Informational Systems (GIS) Development This section describes the two key elements in the storage and management of spatio-temporal data: databases and GIS. These elements are intimately linked to each other and together provide a powerful means of displaying and analyzing complex datasets for use in evaluation of the extent and degree of impact to an affected groundwater system and in calibrating and “ground-truthing” groundwater fate and transport models. Database or Spreadsheet? Although site data can be archived either in a database (i.e., a database management system [DBMS]) or a “flat table” (i.e., a spreadsheet), a database provides the distinct advantage of sophisticated data querying tools for sorting and understanding the data. Additionally, the large size of environmental datasets arising from arrays of multiple sampling events, locations, and contaminants of concern (COCs) make them highly memory intensive, especially when stored in spreadsheets. The main problem associated with a spreadsheet data system is the large degree of repetition of large portions of the data. This problem of data redundancy can be overcome by utilizing a “relational" system where data are stored in a large table that is linked by common fields to several “key” tables (e.g., sampling locations table or a COC table). Such a relational database management system (RDBMS)

also allows for simpler data entry requirements. Hence, clearly the best system for the storage of environmental site data is a RDBMS where the data consume the least amount of memory and are easily accessible via querying. Database Design Issues: Data Conflicts, Duplicates, Referential Integrity, and Null Values Data conflicts can occur within a data field when data are reported in variety of units, spatial coordinate systems, location names, and COC names. Such conflicts can be easily circumvented by early planning in the database design phase to designate standard reporting units and protocols, or it can be less easily addressed later in the database compilation process by setting up data conversion queries. In either case, data fields should established that report results consistently, in standard media-specific units or non-redundant COC names such as CASRNs (i.e., Chemical Abstracts Registry Numbers). Removing data conflicts provides the added benefit of greatly simplifying the task of data querying. Duplicate records can occur in a database when the same data are uploaded from different sources. Often, data from the different sources have field conflicts precluding their automatic removal as duplicate records upon file uploading. Duplicate records can inflate the size of the database and yield erroneous censored data statistics (e.g., means or medians). For such data, an agreed upon record uniqueness criterion must be established so that duplicate records can be identified and removed. A uniqueness criterion can include fields that report sampling date and time, sampling location coordinates, environmental media, CASRN, sample type, analytical method, laboratory name, analysis time, etc. It is best to consult an environmental chemist for developing the record uniqueness criterion as laboratory QA/QC data are often erroneously loaded into the database. An important concept in the design of an efficient RDBMS is the maintenance of “referential integrity”. For example, if a data table lists a COC that is not present in the COC table, then a number of “dangling records” are created in the database13,15. The recovery of such data depends on which COC field (i.e., the one in the COC table or that in the data table) is referenced in the query. A lack of referential integrity can also confound query results. For example, in the query for “sampling locations where the groundwater MCL has been exceeded” the results will show null values for COCs that are present in dangling records in the data table but not the COC table. Null values are often used in fields either to indicate that a value is unknown, or to suggest that a value is inapplicable for that particular record in the context of the field. It is important to note that fields with null values cannot be used as indexed or primary-key fields (i.e., fields in which each value is unique). This property is also known as “entity integrity” and precludes the use of null values in the definition of uniqueness criteria for identifying duplicate records13. For example, when null values are used in the analytical result value field, then the result value cannot be used to differentiate between two records that are otherwise identical based on the record uniqueness criterion. GIS: Advantages and Limitations A geographic information system (GIS) is a spatial data management tool that allows the collation of complex environmental site investigation data. Traditionally, GIS has been used for its mapping and data analysis capabilities. This entails displaying data with user-selected attributes onto a 2-dimensional site base map (e.g., an aerial photo or a facility layout). The data attributes are selected by querying a linked database that contains the spatially-defined environmental data. Since spatial relationships between data points are displayed in GIS, it is imperative that all data be present in a consistent coordinate system. Moreover, because the data are to be overlayed onto base maps, it is

important that base maps, aerial photographs, and shape files (e.g., property boundaries, utilities, and other) are properly georeferenced. The main limitation of traditional GIS is that it is a 2-dimensional system. Therefore, data collected at the same 2-D point but at different depths must be depth-discretized by assigning either vertical coordinates or geologically defined layers. More recently, various 3-D data visualization and surface interpolation modules have been made available by GIS software vendors. These features allow GIS software to offer functionalities that were originally available only through more specialized software. Application of Data Interpolation Methods to NRDA Assessments Mathematical interpolation is the process of estimating unknown values from a set of known values. In the context of spatial interpolation of environmental concentrations, this process entails creating a regularly-spaced grid of estimated concentrations based on a set of irregularly-spaced data points. Eventually, interpolated grids are used to establish plume boundaries via contouring, provided the data points determined from the site investigation have completely delineated the elevated concentrations to the desired boundary threshold (e.g., MCL). For NRDA applications, interpolated grids can be used to estimate the area or the volume of environmental media that has been impacted above the applicable beneficial use threshold. The following sub-sections discuss various aspects of conducting interpolations using environmental data. Common Interpolation Methods All interpolation methods rely, to some extent, on an inverse relationship between the influence of a known data point concentration and its distance from the unknown point being estimated. In other words, a known data point located far away from the unknown point will have far less of an effect on the estimated value than a known data point that is located much closer. The simplest of these routines falls into the category of “inverse distance weighted (IDW)” methods, also known as Shepard’s Method8,16. In IDW, as in all interpolations, weights are assigned to each of the data points based on their distance from the unknown point. The unknown point is estimated using a simple summation of the product of the weight and concentration of the data points:

CwC i

n

iierpolated ∑

=

=1

int (1)

where,

Cinterpolated = Interpolated concentration at a grid node wi = Weight assigned to a given data point i Ci = Concentration of data point i n = Total number of data points.

The actual formula for determining a normalized weight for a given data point “i” is as follows:

∑=

=

n

jpj

pi

i

h

hw1

1

1 (2)

where,

hi = Distance between the known data point i and the interpolated point p = an integer power; usually 2 for Shepard’s Method.

Many variations of the IDW Method exist, with most utilizing a higher power to enhance the smoothing effect. One important point about the traditional IDW routine is that all points in the dataset have at least some influence on the interpolated point. An exception to this general rule is the Franke-Nielson or Modified Shepard Method8,10,16, which localizes the interpolation by assigning a weight of zero to the point farthest away from the interpolated point. Measured environmental data have a range of values that span several orders of magnitude, from a hotspot located in the source area to non-detects along the plume perimeter. In fact, the univariate statistical distribution more closely resembles a log-Normal distribution than one that is Normal12. Hence, one of the chief concerns in interpolation is to limit the influence of distant points that have high values by making the interpolation more local. The Natural Neighbor and kriging methods of interpolation, as discussed below, are especially good at addressing this concern. Natural Neighbor Method: The Natural Neighbor Method assigns a weight of zero to all points not local to the estimated point. This method creates a Thiessen polygon network (See Figure 1) between the measured data points by employing a tessellation (i.e., Delauney Triangulation ) routine. When an estimated grid point is inserted in between data points, a local “disturbance” is created in the polygon network and the polygon network is redrawn. Only those local data points whose Thiessen polygons need to be redrawn because of the disturbance are included in the interpolation of the estimated point, and all other points are assigned a weight of zero. This method is especially useful for interpolating with clustered data. A complete explanation of the mathematical equations of the Nearest Neighbor Method is beyond the scope of this paper and interested readers should consult Sibson17 for a more detailed explanation. Kriging: The most sophisticated of the interpolation methods commonly applied to groundwater data is ordinary kriging. Developed by the French mathematician Matheron, kriging is a method that is based on three key steps. The first step involves developing a spatial relationship between all available data points. This step is accomplished by running a random function called an estimator (e.g., a semivariogram, covariogram, or other) on the data. In the second step, a mathematical model for conducting the actual interpolation is selected by fitting the spatial relationship defined in Step 1, and anisotropy trends in the data are modeled to establish interpolation search parameters. In the final step, the interpolation is performed to a preselected grid, using the fitted mathematical model and search parameters determined in Step 2. The interpolation itself (i.e., Step 3) involves a Lagrangian optimization routine that yields not only the best values at the grid points, but also estimation variance values for each point6. By incorporating the spatial relationship between the data points, kriging offers a significant advantage over simpler interpolation methods such as IDW and Natural Neighbor. Consider the two cases shown in Figure 2. For both cases, the individual distances of the known data points, A, B, and C, from the unknown point, X, are identical; however, the spatial relationship between the known points changes from one case to the next. IDW and Natural Neighbor would produce identical estimated values of X for both cases, but kriging would take into account the changing spatial pattern and reflect these changes in the estimation of the value at point X. Typically, when properly applied, kriging outperforms all other interpolation methods10 because: i) unlike other interpolation methods,

kriging accounts for spatial relationships in the data, including spatial anisotropy, and ii) kriging incorporates an optimization routine that matches the estimated values at the measured points to a user selected tolerance, thereby serving as an exact interpolator. A complete mathematical treatment of ordinary kriging is beyond the scope of this paper and interested readers can consult a variety of references3,5,11. A stepwise procedure for the practice of ordinary kriging is detailed in a subsection below. Other forms of kriging, such as universal kriging, zonal kriging, and co-kriging, are beyond the scope of this publication and, therefore, are not discussed. Interpolation versus Extrapolation The difference between “interpolation” and “extrapolation” is clearly defined in mathematical terms in grid estimation literature and represents an important consideration in the application of plume estimation methods to NRDA assessments. To understand the difference between these two terms, one must first understand the meaning of another term called the “convex hull”. This is a shape created by the outermost sides of a Delauney triangulation network. To describe it visually in 2-D, it is a rubber band stretched around the outermost lying data points in a data set7. In 3-D, it is a prismatic shape whose surface touches all the outermost points. By definition, “interpolation” is when a point is estimated inside the convex hull, and, conversely, “extrapolation” is when a point is estimated outside the convex hull. The mathematical methods described in the previous subsections are interpolation routines and, as a sound practice, should not be applied to extrapolation because at significant distances beyond the convex hull, there are insufficient data upon which to base a reliable estimation of grid values, such as groundwater plume concentrations. For proper plume delineation in the field, all points in contact with the convex hull must have concentration values below the beneficial use criterion to which the plume is to be delineated (e.g., drinking water MCL). Unfortunately, this is not always the case in datasets from environmental site investigations. Locations where the convex hull of the dataset is not bound by values below the minimum beneficial use criterion may require additional sampling to completely delineate affected groundwater plume. The Natural Neighbor Method is inherently unable to perform extrapolation because it relies on Delauney triangulation and Thiessen polygons. However, both IDW and kriging will estimate points outside the convex hull unless the software being used offers controls to limit such extrapolation. Several commercial softwares provide such controls to the user. It is important to note that extrapolation has some limited validity in the case of kriging (with decreasing reliability with distance from the convex hull) , because kriging is based on a spatial relationship between the data points. However, extrapolation is never suitable for IDW routines because, in IDW interpolation, each estimated point is derived from all of the data points. Extrapolation with IDW methods can result in a very significant over-estimation of plume areas and volumes that give a substantial error upon cross-validation (discussed later in the text). Dataset Preparation for Interpolation Duplicate records at any given location pose a grave problem for spatial interpolation. As discussed earlier, environmental subsurface investigations require sampling at different depths and also require continual sampling over long periods of time (e.g., groundwater monitoring). As a result of such sampling, environmental datasets possess large numbers spatial and temporal duplicates. Raw environmental data must be put through spatial and temporal consolidation so that single values exist for each point in the dataset. Spatial consolidation of data is needed in two cases: i) when 2-D interpolation is to be performed using a 3-D dataset; and ii) when a representative elevation point is needed in a 3-D dataset for a

groundwater well that has a lengthy wellscreen. For both cases, the data consolidation procedure is dependent on the project objective. For instance, if the interpolation is to be performed to develop a conservative worst-case-scenario, then the maximum value along the z-coordinate (vertical) should be used. If the goal is to independently interpolate different stratified geologic layers, then data points falling between the desired layer elevations can be used (see Figure 3 for an example of this type of interpolation). More generally, the statistical mean or median value is selected, with the median usually preferred because it is less prone to influence by outliers. For the second case, typically the mid-point of the screen is selected as the elevation. A potentially confusing situation can occur when a well is screened over more than one hydrogeologic layer. No guidelines exist for assigning an elevation for this type of special case. For temporal consolidation of the data, the statistical mean or median is usually selected. Median values are preferred for reasons that were cited earlier. The choice of the time step for the temporal consolidation is completely arbitrary as there are no clear guidelines in literature for its selection. In practice, typically the sampling frequency (e.g., annual or quarterly) is often selected as a logical time step. However, at complex sites where multiple potentially-responsible parties (PRPs) exist and several site investigations have occurred under different schedules, it becomes impossible to pick out a single consistent sampling frequency. At such sites, multiple local sampling frequencies might exist and the spatial coverage of the entire area might vary historically. A methodology for selecting an appropriate temporal data consolidation time-step for complex sites is currently under development by the authors1. An additional issue that is related to dataset preparation, but not to data consolidation, is the selection of surrogate numerical values for parameters whose results have some degree of uncertainty. The main example of this issue is the selection of numeric values for non-detects. Non-detects represent values that are unknown but are lower than a maximum threshold (i.e., the method detection limit [MDL]). The substitution of surrogate values such as zero or half the MDL for non-detects is common in literature. Other values used include other fractions of the MDL, or a constant value when the MDL is not available. The selection of non-detect values is of particular importance to kriging because it determines whether the non-detects will be incorporated into the determination of spatial relationships from the data (i.e., calculation of the omni-directional or experimental variogram). The Practice of Ordinary Kriging The steps involved in taking raw environmental data and completing ordinary kriging interpolation on it are outlined in Figure 4. The first step of Dataset Preparation was discussed extensively in the previous sub-section. The second step of Data Sufficiency becomes important when the parent dataset is divided up into several subsets to perform multiple interpolations. For example, this problem can arise when different hydrogeologic are kriged separately. It is not possible to justify a fixed number of data points as a minimum limit for data sufficiency for kriging, because this property is a function of a combination of other factors. These factors include the number of data pairs, the size of the estimator lag (a characteristic of the random function), and the data density. The third step in the process involves an exploratory analysis of the data. As part of this step, univariate statistical analysis is conducted to determine whether the data would require transformation. Additionally, the average distance between data pairs9 and the areal coverage of the data are calculated. These two calculations help in the sizing the interpolation grid and selecting a rough initial estimate of the estimator’s properties, respectively.

In the next step an experimental or omni-directional variogram is computed. The experimental variogram represents the overall spatial relationship among the data points. After this step, the dataset in analyzed for anisotropy using directional variograms. If the kriging is being done in 2-D, then the anisotropy analysis in conducted in a single plane. However, if 3-D kriging is being done then the anisotropy of the data must be analyzed in two perpendicular planes (i.e., horizontal and vertical). Anisotropy analysis yields two key parameters that are used for setting the search criteria for ordinary kriging interpolation. They are the principal axis or azimuth and the anisotropy ratio(s). For groundwater contamination data, the azimuth typically corresponds to the principal direction of groundwater flow. The anisotropy ratio(s) determines the shape of the search ellipse (2-D) or ellipsoid (3-D). Following this step, the omni-directional variogram is curve-fitted with a mathematical model. This mathematical model selected, together with the search parameters determined in the anisotropy analysis step, are then used to perform the actual interpolation. Error Analysis Error analysis for any interpolation can be performed by running an automated routine called “cross-validation”. In cross-validation, data points are removed one at a time and interpolations are carried out using the user-defined interpolation criteria in order to estimate a value at the location of the missing data point. In this way, an array of residuals (i.e., difference between measured and estimated values) is created for the estimation grid, which is then used to calculate an aggregate error. Aggregate errors typically calculated include the Mean Error (ME), Root-Mean-Squared error (RMSE), and the Mean-Absolute error (MAE)3,14. Applications of Interpolated Grids Interpolated grids can be utilized to estimate the total mass and the total volume of the contamination in the plume. To calculate the bulk volume, the cells where the concentration exceeds the value of interest (e.g., MCL) are simply counted, and this cell number is then multiplied by the constant grid cell volume. The actual volume of groundwater contaminated can be determined by multiplying this value by the formation porosity. To calculate the mass, the concentrations in cells above MCL are summed, and then the sum is multiplied by the cell volume. In the special case of kriging, statistical confidence values for plume volume and mass can be calculated using the kriging estimation variance grids after assuming a Normal distribution around the optimized concentration value at each grid node. Groundwater Fate and Transport Modeling For purposes of assessing damages, fate and transport modeling can be used to assess losses of storage and future yield associated with zones of impacted groundwater, based on predicted plume dimensions. Depending on the complexity of the hydrogeologic site conditions and the availability of sufficient input data, either 2D or 3D numerical models are commonly employed. The appropriate model or models will depend on the specific technical issue to be addressed, the adequacy of the database, and the level of sophistication required, with many options available for simulating groundwater flow (e.g., MODFLOW, PLASM) and dissolved-phase contaminant transport (e.g. MT3D, RT3D), for combined groundwater flow and transport models (e.g., FEMWATER), or for multi-phase flow and transport models (e.g. UTCHEM). With regard to assessment of groundwater impacts, DOI NRDA regulations (43 CFR 11.64(8)) stipulate the following:

i) Groundwater modeling shall be based on hydrogeologic literature and current practice;

ii) The applicability of models should demonstrated, including the physical processes simulated and analysis methods and computer code employed; and

iii) The validity of models should be established, including boundary conditions, hydrogeologic characterization, grid size and geometry, sources of data, initial conditions, stress periods and time increments, calibration and verification procedures and results (including predicted vs. measured fluxes of water and solutes), and sensitivity analyses.

To achieve these goals, the modeler may apply the various ASTM standards, which address the key considerations and procedures involved in the development and use of groundwater models. Specifically, ASTM standard D5447-93 details the primary steps involved in the application of groundwater models to a site-specific problem, with additional detail regarding individual modeling steps provided in other ASTM standards (see Table 1). Figure 5 illustrates the sequential and iterative steps involved in application of this modeling process and identifies problems that can undermine the accuracy or reliability of models results when applied to NRDA assessments. Step 1: Define Study Objectives Definition of the study objectives is a critical first step to any modeling endeavor, as this process will guide decision-making with regard to all subsequent steps described below, such as identification of processes to be simulated (physical, chemical, and biological), the required level of detail and accuracy, identification of appropriate modeling codes, and model calibration requirements. To assess future groundwater plume dimensions for NRDA purposes, the primary modeling objective should be to match the predicted extent of the plume to the observed extent of the plume over time, where the extent of the plume is defined based upon the applicable beneficial use criteria. In addition, the model outcome should match the observed groundwater heads and contaminant concentrations within the plume. Meeting this objective requires multiple calibration criteria to assess the model’s ability to accurately predict concentrations toward the edges of the plume as well as concentrations near the source area or center of the plume. Where data are available, calibration targets should also de employed to check the predicted versus observed flux of groundwater and contaminant mass at key boundary points (e.g., to wells or surface water discharges). Step 2: Conceptual Model A conceptual model is a simplified interpretation or representation of the system to be modeled2,4, which is developed based on the collection and organization of regional and site-specific data. For NRDA applications, the conceptual model should realistically represent the physical characteristics of the modeled system for purposes of estimating the extent of groundwater impacts. To meet the specific study objectives, the conceptual model should identify and describe to a sufficient degree the key features of the modeled system, which will affect the migration of groundwater and its chemical constituents. Key components of this characterization include the hydrogeologic framework (e.g., lithology, flow system boundaries and hydraulic properties), media type (e.g., porous vs. fractured), and sources and sinks of water and contaminants. In addition, the conceptual model should identify specific contaminants of concern (based on prevalence, mobility, toxicity, etc.), their physical and chemical properties, and physical processes (e.g. natural attenuation) that affect their migration. Development of the conceptual model is often iterative, as it may be continually refined throughout the modeling process.

Step 3: Code Selection An appropriate model code (computer software algorithm) should be selected based on its compatibility with the conceptual model and its ability to meet the study objectives. Key considerations during code selection include the media type, required dimensionality (2D vs. 3D), processes to be simulated, and whether the code has been verified or has a proven track record with other field studies. Oftentimes, more than one code may be utilized, such as a groundwater flow model (e.g., MODFLOW) coupled with a dissolved-phase fate and transport model (e.g., MT3D or RT3D). Step 4: Model Construction Model construction is the process of converting the conceptual model into a mathematical representation4, including developing the model grid (spatial discretization) and assigning boundary conditions (e.g. hydrologic boundaries or sources and sinks of water or contaminants), initial conditions (groundwater elevations and contaminant concentrations), aquifer properties, stress periods, and time increments (temporal discretization). The model must be defined as either steady-state, assuming a long-term equilibrium will be established, or transient, where boundary conditions and model stresses (e.g., pumping) are varied over time. For NRDA applications, spatial discretization is a key concern, as the volume of impacted groundwater is directly related to the grid block volume. Grid blocks must be sized such that predicted plume volumes are not overly exaggerated in either lateral or vertical extent. In particular, model layers should not be excessively thick relative to the observed thickness of the groundwater plume, as the entire thickness of a model grid block is assumed to contain a uniform concentration of contaminant. During model construction, assignment of hydraulic boundary conditions, especially when they do not represent a physical hydrologic boundary, warrant special attention. For example, constant head cells must be used with caution so as not to allow the model to predict unrealistic flux of groundwater into the flow system when stresses (e.g. large simulated pumping rates) are applied in the model. Initial conditions, such as groundwater elevations and contaminant concentrations, should reflect as closely as possible the observed field conditions for the model starting time. Initial conditions must be specified for each grid block and can generally be estimated using spatial analysis techniques, such as kriging , when appropriate. Step 5: Calibration, Verification, and Sensitivity Model calibration is an iterative (usually trial-and-error) process involving the adjustment of hydraulic properties, boundary conditions, and initial conditions within reasonable ranges to obtain a match between predicted and observed conditions within a level of tolerance identified in the study objectives4. Calibration is evaluated by an analysis of “residuals,” which represent the difference in predicted and observed values of simulated variables, such as groundwater elevations or fluxes, contaminant concentrations, and other observed variables, such as plume dimensions. Commonly used metrics for analysis of residuals include the mean absolute value, mean squared value, root mean square value, standard deviation, and variance. Criteria for an acceptable calibration are generally expressed in terms of a selected metric of overall residuals being within a specified percentage of the

range of observations of each simulated variable. In addition, the spatial distribution of residuals should exhibit no significant trend, so as not to incorporate bias in the model results. As discussed above, for NRDA applications, criteria for an acceptable fate and transport model calibration must address the ability of the model to accurately simulate the extent of the modeled plume, as defined by the zone of groundwater exceeding applicable beneficial use criteria. Some variables, such as contaminant concentrations, typically exhibit a range of observed values spanning orders of magnitude. As a result, a calibrated fate and transport model that exhibits an acceptable overall calibration statistic based on concentration residuals may actually provide a poor characterization of the extent of the plume. This is because high concentration residuals associated with poorly simulated calibration targets near the edge of the plume, where concentrations are the lowest, can be offset and obscured by low residuals in the center of the plume, where concentrations are the highest but the match is the best. Consequently, in all cases, the user should separately “ground truth” the predicted dimensions of the plume with regard to the observed monitoring results, with a particular focus on the plume boundary line. Verification, or validation, of modeling results involves testing the ability of the calibrated model to match a different set of field observations than were used for the initial calibration. In many cases, model verification may not be possible due to limited data; however, a successful verification of model predictions lends a higher degree of confidence in the model predictions. Nonetheless, a calibrated but unverified model may still be used for predictive simulations, where uncertainty can be assessed by a sensitivity analysis4. Sensitivity analysis is used to quantify the sensitivity of model results (i.e., plume extents) to changes in model input parameter value and thereby determine the uncertainty in the calibrated model caused by estimates of model input parameters, including hydraulic properties, boundary conditions, initial conditions, stresses, etc.4. Often, this sensitivity analysis can be conducted concurrently with model calibration in order to determine the level of parameter adjustments required to calibrate the model. During this process, particular attention should be paid to the sensitivity of the model to boundary conditions, especially when large hydrologic stresses, such as large pumping rates, are included in the model simulations. Step 6: Predictive Simulations Predictive simulations are run to evaluate future scenarios involving potential changes in model stresses and boundary conditions. For transient models, model predictions represent an extrapolation forward in time based on the calibration data and assumed future conditions, with increasing uncertainty in modeling results with time past the end of the calibration period. General guidelines indicate that chemical fate and transport models can reliably predict into the future for a time period equal to that for which they have been calibrated in the past (i.e., 10 years into the future based on 10 years of past calibration data). In many cases, insufficient historical monitoring data is available to apply this rule of thumb. Nevertheless, the modeler should evaluate the accuracy of future model predictions and communicate this information to those who will rely on these data to estimate resource damages, particularly in cases where variability related to input parameter uncertainties model sensitivities corresponds to a significant change in the estimated disruption of service (in terms of volume and/or time) and the associated damage estimate.

Biographical Sketches John A. Connor, P.E., P.G., D.E.E.: Mr. Connor is President of Groundwater Services, Inc. He received an M.S. degree in Civil Engineering from Stanford University and has over 24 years of experience in environmental engineering, with specialization in risk assessment, fate and transport modeling, and corrective action design. Mr. Connor has served as an expert on numerous legal cases, involving evaluation of soil, groundwater and surface water impacts; associated human health or ecological risks; appropriate remedial measures and costs; and evaluation of potential impacts on natural resources. Address: 2211 Norfolk, Suite 1000, Houston, Texas, 77098-4044, Phone: 713-522-6300, Fax: 713-522-8010, email: jaconnor@gsi-net.com. Farrukh Ahmad, Ph.D., P.E.: Dr. Ahmad received a Ph.D. in Environmental Engineering from Rice University and has over 9 years of environmental project experience in environmental consulting and over 5 years in academic research. His project experience includes laboratory- and field-scale bioremediation studies, biogeochemistry, analytical chemistry, environmental forensics, contaminant transport modeling, and the application of geostatistics to environmental data. Address: 2211 Norfolk, Suite 1000, Houston, Texas, 77098-4044, Phone: 713-522-6300, Fax: 713-522-8010, email: fahmad@gsi-net.com. Richard L. Bowers, P.E.: Mr. Bowers received an M.S. degree in Civil/Environmental Engineering from the University of Texas and has over 10 years of professional experience, with emphasis in groundwater fate-and transport modeling and water resource analysis. He is the primary developer of the GSI “RBCA Tool Kit software and has conducted training session in risk assessment and environmental modeling throughput the U.S. and internationally. Address: 2211 Norfolk, Suite 1000, Houston, Texas, 77098-4044, Phone: 713-522-6300, Fax: 713-522-8010, email: rlbowers@gsi-net.com. References 1. Ahmad, F. and Connor, J. A., A procedure for the selection of data consolidation time-steps for

geostatistical and contaminant modeling applications, Under Preparation, 2005. 2. Anderson, M. P. and Woessner, W. W., Applied Groundwater Modeling: Simulation of Flow and

Advective Transport, Academic Press, San Diego, 1992. 3. Armstrong, M., Basic Linear Geostatistics, Springer-Verlag, Berlin, 1998. 4. American Society for Testing and Materials (ASTM), Standard Guide for Application of a Ground-

Water Flow Model to a Site-Specific Problem, ASTM D 5447-04, West Conshohocken, PA, 2004.

5. Cressie, N. A. C., Statistics for Spatial Data, Revised ed., John Wiley & Sons Inc., New York, 1993.

6. Davis, J. C., Statistics and Data Analysis in Geology, Second ed., John Wiley & Sons, New York, 1986.

7. Davis, P. J., Interpolation & Approximation, Dover, New York, 1975. 8. Golden_Software_Inc., Surfer 7 Users Guide, Golden Software Inc., Golden, Colorado, 1999. 9. Isaaks, E. H. and Srivastava, R. M., An Introduction to Applied Geostatistics, Oxford University

Press, New York, 1989. 10. Jones, N. L., Davis, R. J., and Sabbah, W., A comparison of three-dimensional interpolation

techniques for plume characterization, Ground Water 41 (4), 411-419, 2003. 11. Kitanidis, P. K., Introduction to Geostatistics: Applications in Hydrogeology, Cambridge

University Press, Cambridge, 1997.

12. Kitanidis, P. K. and Shen, K.-F., Geostatistical interpolation of chemical concentration, Advances in Water Resources 19 (6), 369-378, 1996.

13. Pratt, P. J. and Adamski, J. J., Database Systems Management and Design, Third ed., International Thomson Publishing (ITP), Cambridge, 1994.

14. Reed, P. M., Ellsworth, T. R., and Minsker, B. S., Spatial interpolation methods for nonstationary plume data, Ground Water 42 (2), 190-202, 2004.

15. Roman, S., Access Database Design & Programming, O'Reilly, Cambridge, 1999. 16. Shepard, D., A two dimensional interpolation function for irregularly spaced data, in ACM 23rd

National Conference, 1968, pp. 517-523. 17. Sibson, R., A Brief Description of the Natural Neighbor Interpolation, in Interpreting

Multivariate Data, Barnett, V., John Wiley & Sons, New York, 1981, pp. 21-36. Figure 1. Delauney Triangulation Defines the “Convex Hull” of Spatial Data. Delauney triangulation routines define the convex hull of a spatial dataset. The convex hull is a boundary beyond which estimated points are considered to be extrapolated. The triangulation routine can be further used to determine the Thiessen polygon network, which is used in the Natural Neighbor interpolation method.

DelauneyTriangle

ThiessenPolygon

DelauneyTriangle

ThiessenPolygon

Figure 2. Evaluation of Spatial Relationships: Kriging vs. Other Interpolation Methods. The above 2 cases ((i) and (ii)) show 3 measured data points (A, B, and C) at the same independent distances from the point to be estimated, X. The concentric rings depict radii from point X, which are increasing by a constant value. Inverse Distance Weighted (IDW) and Natural Neighbor interpolation would produce the same value in the 2 cases because they are based on independent relationships between X and each measured point, A, B, and C. Kriging will produce different values for X because it will take into account the changing relationship between the data points from case (i) to case (ii).

Figure 3. Example of 2-D Kriging for Multiple Hydrogeologic Layers.

X

A

BC

X

A

B

C

A > B > C A > B > C

( i ) ( ii )

X

A

BC

X

A

B

C

A > B > C A > B > C

( i ) ( ii )

Figure 4. Ordinary Kriging Process Flowchart. The decision diagram depicts the key steps for conducting ordinary kriging interpolation for an environmental dataset. The boxes on the right show potential errors that practitioners can make and their final effect on a NRDA metric, the plume volume.

ORDINARY KRIGING PROCEDURES AND POTENTIAL ERRORS

DATA COLLECTION &PREPARATION

SUFFICIENT DATA?

DEVELOPEXPERIMENTAL VARIOGRAM

SELECT MODEL VARIOGRAM

SPATIAL ANISOTROPYANALYSIS

SEARCH PARAMETERSELECTION &

INTERPOLATION

EXPLORATORY DATA ANALYSIS

ERROR ANALYSIS

YES

NO

Distance Between PairsMin./Max. CoordinatesUnivariate StatisticsData Transformation

Time Period SelectionData Censoring (mean or

median)Treatment of Non-detects

Directional VariogramsAzimuthAnisotropy Factor

Cross ValidationEstimation Variance PlotsConfidence Level Plots

Mathematical ModelRange and SillNugget

Lag and Lag ToleranceAzimuth ToleranceVariogram Estimator

Use of a subset of the data that does not completely delineate the contaminant plume.

Effect on Estimated

Plume VolumePotential Errors

Use of a subset of the data that does not completely delineate the contaminant plume.

Effect on Estimated

Plume VolumePotential Errors

Removal of non-detects: Forces high spatial continuity where none existed.

Removal of non-detects: Forces high spatial continuity where none existed.

No anisotropy modeling conducted: Assumes no dominant direction of GW flow, resulting in “circular” plumes.

No anisotropy modeling conducted: Assumes no dominant direction of GW flow, resulting in “circular” plumes.

Experimental variogram inappropriately fitted with model, e.g., fitted to latter part of curve rather than initial part.

Experimental variogram inappropriately fitted with model, e.g., fitted to latter part of curve rather than initial part.

Search radius substantially larger than range.Search circle rather than ellipse

Search radius substantially larger than range.Search circle rather than ellipse

Not conducted.No evaluation of estimation variance or confidence level.

Not conducted.No evaluation of estimation variance or confidence level.

Not conducted or incompletely performed: Discrepancies with additional sampling.

Not conducted or incompletely performed: Discrepancies with additional sampling.

Figure 5. The decision diagram depicts the key steps for predictive groundwater modeling. The graphics on the right show potential errors that practitioners can make, even with “calibrated” fate and transport models. NRDA damage claims can be seriously inflated, with regard to predicted plume volumes, when calibration criteria are not adequately defined for a model to match observed plume extents, in addition to overall observed concentrations. Extrapolation of model predictions into the future are generally not considered reliable beyond a timeframe equal to the period of time for which calibration was performed.

Table 1: ASTM Standards for Groundwater Modeling

D5447-93 Standard Guide for Application of a Ground-Water Flow Model to a Site- Specific Problem

D5490-93 Standard Guide for Comparing Ground-Water Flow Model Simulations to Site-Specific Information

D5609-94 Standard Guide for Defining Boundary Conditions in Ground-Water Flow Modeling

D5610-94 Standard Guide for Defining Initial Conditions in Ground-Water Flow Modeling

D5611-94 Standard Guide for Conducting a Sensitivity Analysis for a Ground-Water Flow Model Application

D5718-95 Standard Guide for Documenting a Ground-Water Flow Model Application

D5719-95 Standard Guide for Simulation of Subsurface Airflow Using Ground-Water Flow Modeling Codes

D5880-95 Standard Guide for Subsurface Flow and Transport Modeling

D5981-96 Standard Guide for Calibrating a Ground-Water Flow Model Application

D6025-96 Standard Guide for Developing and Evaluating Ground-Water Modeling Codes

D6033-96 Standard Guide for Describing the Functionality of a Ground-Water Modeling Code

D6170-97e1 Standard Guide for Selecting a Ground Water Modeling Code

D6171-97 Standard Guide for Documenting a Ground-Water Modeling Code

E1689-95 Standard Guide for Developing Conceptual Site Models for Contaminated Sites

E978-92 Standard Practice for Evaluating Mathematical Models for the Environmental Fate of Chemicals

WK225 Test Method for Ground Water Flow Modeling in Karst and Fractured Rock Terraines

Source: NGWA, 2005