Transcript Inferential Spatial Statistics

Spatial Analysis
1
Digital Elevation Model (DEM)
2
DEM Derivatives
Slope
Hillshade
Aspect
DEM Analysis: http://www.youtube.com/watch?v=ukk2ciG2tDY
3
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
4
Draping
5
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
6
Buffering
Point
Polyline
Polygon
7
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
8
Point-In-Polygon
9
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
10
Map Algebra Example: Sum
11
Map Algebra Example: Sum
12
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.
13
Spatial interpolation

Distance Decay
14
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
15
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
16
Importance of the Density of Sample Points
17
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.
18
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)
19
Kernel Density Surfaces
Search radius: 20K km2
Search radius: 100K km2
20