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Professor has explained the following concepts in these Lecture Slides : Digital Elevation Model, Visualizing Terrain, Surface Data, Visualizing Map, Map Surfaces, Map Analysis Evolution, Analytic Framework, Surface Modeling, Unusually High Density, Geographic Distributions
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Visualizing Terrain Surface Data (Exercise 8 – Part 1)
Mount St. Helens dataset
Question 1 Access SURFER then enter Map Contour Map New Contour Map \Samples Helens2.grd
(Berry)
There are numerous websites that allow you to download a DEM and use SURFER to visualize
…a generally useful procedure that you can use for lots of reports (Optional Exercise)
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Map Analysis Evolution (Revolution)
(Berry)
Forest Inventory Map
Store Travel-Time (Surface)
Minimum= 5.4 ppm Maximum= 103.0 ppm Mean= 22.4 ppm StDev = 15.
Spatial Distribution (Surface)
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An Analytic Framework for GIS Modeling
(Berry)
Surface Modelling operations involve creating continuous spatial distributions from point sampled data. /
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Identifying Unusually High Density
Pockets of unusually high customer density are identified as more than one standard deviation above the mean MapCalc “Renumber” – ESRI GRID/Spatial Analyst “Reclassify”
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…Data Values link the two views—
Click anywhere on the Map and the Histogram interval is highlighted
Click on the Histogram interval and the Map locations are highlighted
Linking Numeric & Geographic Distributions
(See Beyond Mapping III, “Topic 7” for more information) (Berry)
…simply different ways to organize and analyze mapped data
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Assumptions in Non-Spatial Statistics
(Berry)
…uniformly distributed in geographic space (horizontal plane at average; +/- constant)
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Geographic Distribution (surface modeling)
(Berry)
…analogous to fitting a curve (Standard Normal Curve) in numeric space except fitting a map surface in geographic space to explain variation in the data
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Generating a Map of Percent Change (map-ematics)
(Berry)
…maps are organized sets of numbers supporting a robust range of Map Analysis operations that can be used to relate spatial variables (map layers)
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Spatial Relationships (coincidence , proximity, etc.)
(Berry)
…spatial relationships can be utilized to extend understanding
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The Average is Hardly Anywhere
Arithmetic Average – plot of the data average is a horizontal plane in 3-dimensional geographic space with some of the data points balanced above (green) and some below (red) the “typical” value (uniform estimate of the spatial distribution)
Field Collected Data #
87 = P2 sample value
Arithmetic Average knows nothing of Geographic Space
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Surface Modeling (Map generalization)
(Berry)
Map Generalization – fits standard functional forms to the data, such as a Nth^ order polynomial for curved surfaces with several peaks and valleys
Spatial Average balances “half” of the data above and below a Horizontal Plane—
Arithmetic Average balances “half” of the data on either side of a Line—
Yavg
Xavg^ Line Plane
Curved Plane Curved Line
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Surface Modeling Methods (Surfer)
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 summary 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)
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
Nearest Neighbor — assigns the value of the nearest sample point
Triangulation — identifies the “optimal” set of triangles connecting all of the sample points Thiessen Polygons (Berry)
Map Generalization — Mathematical Equation/Surface Fitting
Map Generalization — Geometric facets
Spatial Interpolation — “roving window” localized average
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Surface Modeling Approaches (using point samples)
Spatial Interpolation — these techniques use a roving window to identify Nearby Samples and then Summarize the Samples based on some function of their relative nearness to the location being interpolated.
relationship (inverse distance squared) or a more complex statistical relationship (spatial autocorrelation)
non-exacting estimate sample locations (IDW)
(Berry)
Map Generalization (Equation) — these techniques seek the general trend in the data by Fitting a Polynomial Equation to the entire set of sample data (1 st^ degree polynomial is a plane).
Thiessen Polygons
Map Generalization (Geometric Facets) — Triangulated Irregular Network (TIN) is a form of the tessellated model based on Triangles. The vertices of the triangles form irregularly spaced nodes and unlike the DEM, the TIN allows dense information in complex areas, and sparse information in simpler or more homogeneous areas Docsity.com
