1. Grid-based Map Analysis Techniques and Modeling Workshop
Workshop on GIS Modeling (Part 2)
Grid-based Map Analysis Techniques and Modeling Workshop
Part 1 – Maps as Data
Part 2– Surface Modeling
Point density analysis
Spatial interpolation
Map comparison
Part 3 – Spatial Data Mining
Part 4 – Spatial Analysis
Part 5 – GIS Modeling
Joseph K. Berry, BA_SIS, Inc. All Rights Reserved.

2. Grid-Based Map Analysis
Surface Modeling maps the spatial distribution and pattern of point data…
Map Generalization— characterizes spatial trends (e.g., titled plane)
Spatial Interpolation— deriving spatial distributions (e.g., IDW, Krig)
Other— roving window/facets (e.g., density surface; tessellation)
Data Mining investigates the “numerical” relationships in mapped data…
Descriptive— aggregate statistics (e.g., average/stdev, similarity, clustering)
Predictive— relationships among maps (e.g., regression)
Prescriptive— appropriate actions (e.g., optimization)
Spatial Analysis investigates the “contextual” relationships in mapped data…
Reclassify— reassigning map values (position; value; size, shape; contiguity)
Overlay— map overlay (point-by-point; region-wide; map-wide)
Distance— proximity and connectivity (movement; optimal paths; visibility)
Neighbors— ”roving windows” (slope/aspect; diversity; anomaly)
(Berry)

3. Point Density Analysis
Point Density analysis identifies the number of points within
a specified distance of each grid location
Roving
Window
…areas of high customer density can be isolated and transferred to a standard desktop mapping system
(See Map Analysis, “Topic 17” for more information)
(Berry)

4. Spatial Interpolation (Smoothing the Variability)
The “iterative smoothing” process is similar to slapping a big chunk of modeler’s clay over the “data spikes,” then taking a knife and cutting away the excess to leave a continuous surface that encapsulates the peaks and valleys implied in the original field samples
…repeated smoothing slowly “erodes” the data surface to a flat plane = AVERAGE
(digital slide show SSTAT)
(Berry)

5. Spatial Interpolation Techniques
Characterizes the spatial distribution by fitting a mathematical
equation to localized portions of the data (roving window)
Interpolation techniques fit “locally controlled” map surfaces.
The various techniques produce different renderings based on
how they define and summarize neighboring sample values. Assumptions of data trends and interpolation/extrapolation characteristics of the algorithms result in different prediction
surfaces for a given set of field data
…no one technique is best for all data.
Inverse Distance Weighted (IDW) identifies
sample values within a specified distance then
weight- averages the values with less influence from
more distant values (1/d2 weighting factor equation)
(Berry)

6. Spatial Interpolation (Evaluating performance)
Residual Analysis
…the best map is the
one that has the “best
guesses”
(See Map Analysis, Topic 2 for more information)
(Berry)

7. Spatial Interpolation (Characterizing error)
A Map of Error (Residual Map)
…shows you where your estimates are likely good/bad
The residuals for the kriging interpolation (posted values) are themselves interpolated to generate a map of interpolation error. Note the upper right portion (NE) contains wide disparities (steep slopes in 3D plot and close contours in 2D display) indicating widely changing error patterns.
(Berry)

8. Spatial Dependency
Spatial Interpolation
…understanding relationships within a single map layer
the conditions of that variable at nearby locations, termed Spatial Autocorrelation (intra-variable dependence)
Spatial Dependence— what occurs at a location in geographic space is related to:
the conditions of other variables at that location, termed Spatial Correlation (inter-variable dependence; Spatial Data Mining …understanding relationships among sets of map layers)
(Berry)

9. Characterizing Spatial Autocorrelation
Quick Test— similarity among neighbors vs. overall similarity in the data set (compare Nearest Neighbor to data set Average)
Avg [ |Value – NNeighbor| ]
Avg [ |Value – Average| ]
SAindex =
Variogram— plot of similarity as a function of distance between samples
…curve-fitting an equation establishes a data-based weighting factor equation
(See Map Analysis, “Topic 8” for more information)
(Berry)

10. Spatial Interpolation
Spatial Interpolation is similar to throwing a blanket over the “data spikes” to conforming to the geographic pattern of the data.
…all interpolation algorithms assume that 1) “nearby things are more alike than distant things” (spatial autocorrelation), 2) appropriate sampling intensity, and 3) suitable sampling pattern.
…the interpolated surfaces “map the spatial variation” in the data samples.
(Berry)

11. Comparing Spatial Interpolation Results
Comparison of the interpolated surface to the whole field average shows large differences in localized estimates
…yellow band is +/- 1 unit
Average - IDW
Comparison of the IDW and Krig interpolated surfaces shows small differences in in localized estimates
…yellow band is +/- 1 unit
IDW - Krig
(See Map Analysis, “Topic 17” for more information)
(Berry)

12. Workshop on GIS Modeling (Part 2)
Interpolation Methods
Nearest Neighbor— assigns the value of the nearest sample point (iteratively smoothed)
Inverse Distance to a Power— weighted average of samples in the summary window such that the influence of a sample point declines with “simple” distance
Modified Shepard’s Method— uses an inverse distance “least squares” method that reduces the “bull’s-eye” effect around sample points
Radial Basis Function— uses non-linear functions of “simple” distance to determine weights
Kriging— summary of samples based on distance and angular trends in the data
Natural Neighbor—weighted average of neighboring samples where the weights are proportional to the “borrowed area” from the surrounding points (based on differences in Thiessen polygon sets)
Triangulation— identifies the “optimal” set of triangles (facets) connecting all of the sample points, then converts to a grid
Minimum Curvature— analogous to fitting a thin, elastic plate through each sample point using a minimum amount of bending
Polynomial Regression— fits an equation to the entire set of sample points (not true interpolation, but map generalization procedure)
Thiessen Polygons
(Berry)
Joseph K. Berry, BA_SIS, Inc. All Rights Reserved.