Intro. To GISLecture 9

TerrainAnalysis

April 24th, 2013

Reminders

• Please turn in your homework

• Final Project guidelines are available

• Two labs next week (Mon and Wed)

REVIEW: Raster Data

Applications of neighborhood functions (spatial filters)

• Removing odd values• Smooth the data• Edge detection• Edge sharpening • Spatial variability

How to represent the real world in 3D?

• Data points are used to generate a continuous surface. In the below example, a color coded surface is generated from sample values

How to represent the real world in 3D?

• Two ways to generate real world surfaces from point data (sample values)– Vector– raster

• Whatever the method, what kind of data are available to represent the world?

How to represent the real world in 3D?

• Ways of spatial sampling

Samples could represent any quantity (value)

• Elevation• Climate data– Temperature– Precipitation– Wind– CO2 flux

• Others– Ice thickness– Spatial samples (of some quantity) in a city– Gold concentrations– LiDAR data points

Elevation Data

• Collected by several methods– Topographic survey (very accurate)– LiDAR data (pretty accurate)– Satellite radar (surprisingly accurate)– GPS survey (much less accurate)

• Elevations (z-values) recorded at points

Surface Representation

• Regardless of vector or raster:

• Point elevations• Triangular

Irregular Networks (TINs)

• Contour lines• Digital Elevation

Models (DEMs)

Vector representation (of surfaces)

• Triangular Irregular Network (TIN)

• TIN can be used to– Generate contour lines– Slope– Aspect

Triangular Irregular Network

• Way of representing surfaces (vector)

• Elevation points connected by lines to form triangles

• Size of triangles may vary

• Each face created by a triangle is called a facet

Triangular Irregular Network

• The triangulation is based on the Delaunay triangulation

• A Delaunay triangulation is a triangulation such that no sample (point) out of all samples is inside the circumcircle of any triangle. Delaunay triangulations maximize the minimum angle of all the angles of the triangles in the triangulation; they tend to avoid skinny triangles.

Delaunay triangulation

Delaunay triangles: all satisfy the condition Delaunay NOT satisfied

09_03_Figure

More about TINs

• No interpolation required, all elevation values are based on direct measurements

• Visualized using hillshade for a 3D effect

More about TINs

• Hillshade is one of the most common ways of displaying/visualizing TINs. Commonly Sun is shining from northwest (315deg) from 45deg above horizon.

• Each facet will be assigned with a color based on its orientation

• Products – Contour lines – Slope and aspect can be derived from

Raster Representation (of surfaces)

• The most commonly used term for raster representation is Digital Elevation Model (DEM)

• Any digital model for any other variable could be generated

• For DEM, each cell has an elevation (z-value)• To generate DEM from sample points, interpolation is

used to fill in between surveyed elevations – several methods to choose from

Interpolation

• Linear• Polynomial

• In GIS (to generate raster):– Nearest Neighbor– Inverse Distance

Weighted (IDW)– Kriging– Splining

• Comes from the word “inter” meaning between and “pole” which represent two sample points. So, you want to find a value between two points.

• Extrapolation is finding a value for the outside of the two points

Interpolation

Linear interpolation

• Assume that the value for an unknown location between two known points can be estimated based on a linear assumption

Polynomial Interpolation

• Assume that the value for an unknown location between two known points can be estimated based on a non-linear assumption

Spatial Interpolation

• Generating surface from points (samples) based upon: – Nearest Neighbor– Inverse Distance Weighted (IDW)– Kriging– Splining

Nearest-Neighbor

• Uses elevations (or another quantity) from a specified number of nearby control points

Sample with Known value

Pixel (grid cell) with unknown value

Nearest-Neighbor

Inverse Distance Weighted (IDW)

• Spatial Autocorrelation– Near objects are

more similar than far objects

• IDW weights point values based on distance

Inverse Distance Weighted (IDW)

• Estimating an unknown value for a pixel (p) by weighting the sample values based on their distance to (p)

i=8 in this example

j

• In the above equation, n is the power. It is usually equals to 2, i.e., n=2. But you can pick n=1, n=1.5, etc.

IDW – Choosing the Power

• Power setting influences interpolation results• Lower power results in smoother surfaces• Higher power results in rugged surface (it

become more like ….?)

Inverse Distance Weighted

Kriging

• Statistical regression method, whose process consists of two main components– Spatial autocorrelation

(semivariance)– Some weighting scheme

• Advanced interpolation function, can adapt to trends in elevation data

Kriging and Semivariogram

• Semivarigram is a graph describing the semivariance (or simply variance) between pairs of samples at different distances (lags)

• The idea comes from intuition:– Things that are spatially close are more

correlated than those are far way (similar to IDW)

Generating Semivariogram

• To generate a semivariogram, semivariance between pairs of points (for various distances/lags) are to be calculated

09_09_Figure

Semivariance: Example

Kriging and Semivariogram

• The first step in the kriging algorithm is to compute an average semivariogram for the entire dataset. This is done by going through each single point in the dataset and calculate semivariogram. Then the semivariogram are averaged.

• The second step is to calculate the weights associated with each point

Kriging

Spline Interpolation

• Curves fit through control points

• Interpolated values may exceed actual elevation values

• Regularized vs. Tension options

09_13_Figure

Spline Interpolation

Comparing Interpolations

OK…

• Which one works better?

Evaluation of the generated surface

• Independent samples must be preserved for accuracy assessment of the predicted (generated) surface. These points are called check points.

• In other words, if you have 100 samples in the area, you’d use 90 to create the surface and 10 of them to evaluate how accurately the surface represents the actual world

Terrain Functions

• Slope• Aspect• Hillshade• Curvature

Slope: How it is done!

• Equations applied in neighborhoods for a focal cell

Viewshed Analysis

Watershed Delineation

• How much land area drains to a specific point?

• Can be delineated manually from a topo map

Watershed Basics

• Basin/Catchment, Drainage Divide, Pour Points

Watershed Delineation

• The key property of a watershed boundary is that it completely and uniquely defines the area from which the (surface) water drains to the watershed outlet.

Delineation Methodology

Detail on Watershed Analysis

• Determine flow direction grid (DEM derived property).

• Determine flow accumulation grid (DEM derived property).

• Specify a "stream" threshold on the flow accumulation grid. This operation will identify all the cells in the flow accumulation grid that are greater than the provided threshold. A new grid is formed from those cells ("stream" grid). This grid will be an indication of the drainage network. Higher thresholds will result in less dense network and less internal subwatersheds, while lower thresholds will result in dense network and more internal subwatersheds.

• Stream grid is converted into stream segments, where each head segment and segment between the junctions has a unique identifier.

• Subwatersheds (in grid format) are defined for each of the stream links in the stream link grid.

• Subwatershed and stream grids are vectorized to produce subwatershed and stream polygon and polyline themes respectively. Additional vector processing might be needed to clean-up the data and insure correct connectivity and directionality.

Flow Direction

Flow Accumulation

Raster to Vector Streams

Stream Link

Stream Order

Snapping Pour Points

Watershed Delineation

Homework & Lab

• Chapter 9: Questions 1 and 4

• Lab on Monday (29th): Raster• Lab on Wednesday: Terrain Analysis– Processing DEM data– Delineating a watershed