SADA provides a collection of methods to model contaminant behavior between sampled data points. These methods may estimate attribute values or quantify the uncertainty in estimation. The results serve as a foundation for secondary spatial modeling in human health risk assessment, ecological risk assessment, remedial design (see Area of Concern Maps), and cost assessment (see Cost Benefit Analysis) applications. There are five geospatial interpolation methods currently available: Nearest Neighbor, Natural Neighbor, Inverse Distance, Ordinary Kriging, and Indicator Kriging.
The foundation for geospatial modeling in SADA is a choice of one of the five interpolants and a grid structure, which will partition the site. SADA will estimate the concentrations at the horizontal center of each block and use these values as an estimate for the block concentration. For 3d data, SADA also uses the interpolation point (see set vertical layers) to define block concentration. Further partitioning individual blocks and then averaging resulting values is not currently available. However, the user can currently achieve block estimation by selecting a sub-region of the site with a polygon (see Polygons) and applying the Statistics button.
The premise for each of the available interpolants is that the concentration value at any location is a weighted average of the concentration values around it. Therefore, to estimate the concentration value at a given location requires averaging the weighted values of sampled locations in a nearby neighborhood. This idea can be mathematically expressed as
where v0 is the concentration to be estimated at (x0, y0, z0), N(v0) is the number of sample locations in the neighborhood of v0 , vi are the sample values, and wi are the weights. Generally, the fundamental difference between the interpolation methods is how the weights are determined.
The mathematical basis and description of these methods is beyond the scope of this manual. For a more detailed explanation of these methods, see GSLIB Geostatistical Software Library and User’s Guide by Deutsch and Journel (1992) or An Introduction to Applied Statistics by Isaaks and Srivastava.
The following examples demonstrate output from spatial models. In the first image, the user has provided a set of Arsenic data. With this data, the ordinary kriging model was used to produce the subsequent images.
The supporting samples are distributed as follows:
The next step is to partition the space with a grid system. See set grid specs.
Once the grid has been established, each block in the grid becomes the focus of the geospatial model. The following image shows how the OK model estimates concentration values within each block to produce a map (see interpolate my data).
Using the concentration map as a basis, human health and ecological risk models may be added to transform the concentration map into a contoured risk map. Risk maps are useful for identifying areas that exceed established risk goals.
Note: From a risk perspective, the exposure unit size may not be reasonable, especially for finely partitioned sites. However, once an area of interest is identified with the risk map, a polygon may be used to select the sub-region and define a new exposure area where risk models may be applied more appropriately. See Spatial Risk Issues.
When using ordinary kriging or indicator kriging, uncertainty about site conditions can be quantified. For example, if a cleanup goal is specified, SADA can identify those areas that exceed this goal. Kriging adds another element to the modeling process by producing probability maps. For example, the following map demonstrates the probability of exceeding 1E-6 risk. See Probability Maps.
These modeling results can be extended to identify areas of concern or remedial boundaries. See Area of Concern Maps.
Geospatial modeling also supports Cost Benefit Analysis and Sampling designs.