1

Spatial Analysis

Digital Elevation Model (DEM)

2

DEM Derivatives

3

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

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

7

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

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

20

Search radius: 20K km2 Search radius: 100K km2