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Spatial Analysis
Digital Elevation Model (DEM)
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DEM Derivatives
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Slope
Aspect
Hillshade
DEM Analysis: http://www.youtube.com/watch?v=ukk2ciG2tDY
Slope and aspect
Slope and aspect are calculated at each point in the grid, by comparing the point’s elevation to that of its neighbors Slope is the incline or steepness of a surface
(measured in degrees 0 – 90, or as a percentage of a rise divided by a run)
Aspect is the compass direction that a topographic slope faces usually measured in degrees from north
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Draping
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Buffering
Creates a new object consisting of areas within a user-defined distance of an existing object, for example: To determine areas impacted by a proposed
highway To determine the service area of a proposed
hospital Can be done for both a raster and a vector
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Buffering
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Point
Polyline
Polygon
Point-in-polygon transformation Determine whether a point lies inside or
outside a polygon generalization: assign many points to containing
polygons used to assign crimes to police precincts, voters
to voting districts, accidents to reporting counties
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Point-In-Polygon
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Map Algebra
A language that allows to transform a raster map or combine two or more raster maps by applying mathematical operations and analytical functions
Local: cell-by-cell operations Focal: operations performed on a user-defined
neighborhood of the focus cell Zonal: process all cells within a user-defined
regions (zones) Global: the cell values for the output grid can be
dependent upon all the cells in the input grid
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Map Algebra Example: Sum
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Map Algebra Example: Sum
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Spatial interpolation(Tobler’s First Law of Geogaphy) The process of using points with known values
to estimate values at other points. These points with known values are called known points, control points, sample points, or observations.
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Spatial interpolation
Distance Decay
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Importance of the Density of Sample Points Imagine this elevation cross section: If each dashed line
represented a sample point, this spacing would miss the major local sources of variation, like the gorge
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Importance of the Density of Sample Points If you increase the sampling rate (take samples closer
together), the local variation will be more accurately captured
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Importance of the Density of Sample Points
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Kriging
Kriging is a spatial interpolation technique that assumes that the spatial variation of an attribute may consist of three components: a spatially correlated component, representing the variation of the regionalized variable; a ‘drift’ or structure, representing a trend; and a random error term.
Developed by Georges Matheron to evaluate new GOLD mines with a limited number of borholes.
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Density estimation
Spatial interpolation is used to fill the gaps in a field
Density estimation creates a field from discrete objects. The field’s value at any point is an estimate of the density of discrete objects at that point E.g. estimating a map of population density (a field)
from a map of individual people (discrete objects)
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Kernel Density Surfaces
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Search radius: 20K km2 Search radius: 100K km2