1 Method Application Hierarchy Routine Activities Visual data

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1 Method Application Hierarchy Routine Activities § Visual data assessment § § Contour maps

1 Method Application Hierarchy Routine Activities § Visual data assessment § § Contour maps 3 D or Numeric Model Surfaces Requires More Scientific Rigor § § Sample Plan Design LTM Optimization Mass/Volume Calcs Remedial Footprint § § Uncertainty analysis Litigation Resource estimation Risk assessment Delineation All Methods Surfer, Arc. GIS, VSP, MAROS, GMS Rockware, EVS/MVS 1 Requires Expert Level Approach Advanced Methods Arc. GIS, Isatis, SGe. MS, R, SAS

2 Characteristics of Interpolation Methods Trend, Anisotropy, Search Neighborhood u Exact versus Inexact Interpolation

2 Characteristics of Interpolation Methods Trend, Anisotropy, Search Neighborhood u Exact versus Inexact Interpolation u Interpolation Boundary Conditions u Interpolation Gridding u

3 Trend: Large-Scale Systemic Changes Created by Physical Processes Common in Water Level Data

3 Trend: Large-Scale Systemic Changes Created by Physical Processes Common in Water Level Data Remove to Preserve Stationarity © 2013 by Taylor & Francis Group, LLC

4 Anisotropy § § § 4 Directional dependence of spatial correlation Traditional: range of

4 Anisotropy § § § 4 Directional dependence of spatial correlation Traditional: range of correlation varies with direction Zonal: sill (variance) varies with direction Kitanidis, 1997; Goovaerts, 1997 © 1997 by Oxford Press © 1997 by Cambridge Press

5 Search Neighborhood § Defines the area over which data points are considered when

5 Search Neighborhood § Defines the area over which data points are considered when interpolating a value at a new location § § 5 Smaller area emphasizes nearby measurements Anisotropy incorporated through elliptical search neighborhood

6 Exact vs. Inexact Interpolation § Exact interpolation: predictions exactly match measured values at

6 Exact vs. Inexact Interpolation § Exact interpolation: predictions exactly match measured values at measurement locations § § Most simple methods are exact interpolators When nugget > 0, kriging is an inexact interpolator – incorporates error § § Locational error Lab and field sample error § Duplicate samples? Issue: People Like Contours with Exact Interpolation 6

7 Interpolation Boundary Conditions § Surface water features, concentration source zones, impermeable boundaries (slurry

7 Interpolation Boundary Conditions § Surface water features, concentration source zones, impermeable boundaries (slurry walls), faults § § 7 Rely on conceptual site model Failure to incorporate can result in mis-application

8 Interpolation Gridding § Interpolation creates a grid of continuous predictions from a sample

8 Interpolation Gridding § Interpolation creates a grid of continuous predictions from a sample set of discrete point measurements § § 8 Grid types: Rectangular, curvilinear, unstructured/finite element mesh Grid spacing must factor in sample density, scale of problem at hand