intro. to gis lecture 9 terrain analysis april 24 th , 2013
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Intro. To GIS Lecture 9 Terrain Analysis April 24 th , 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 - PowerPoint PPT PresentationTRANSCRIPT
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Intro. To GISLecture 9
TerrainAnalysis
April 24th, 2013
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Reminders
• Please turn in your homework
• Final Project guidelines are available
• Two labs next week (Mon and Wed)
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REVIEW: Raster Data
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Applications of neighborhood functions (spatial filters)
• Removing odd values• Smooth the data• Edge detection• Edge sharpening • Spatial variability
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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
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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?
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How to represent the real world in 3D?
• Ways of spatial sampling
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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
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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
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Surface Representation• Regardless of
vector or raster:• Point elevations• Triangular
Irregular Networks (TINs)
• Contour lines• Digital Elevation
Models (DEMs)
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Vector representation (of surfaces)
• Triangular Irregular Network (TIN)
• TIN can be used to– Generate contour lines– Slope– Aspect
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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
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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.
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Delaunay triangulation
Delaunay triangles: all satisfy the condition Delaunay NOT satisfied
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09_03_Figure
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More about TINs• No interpolation required, all elevation
values are based on direct measurements
• Visualized using hillshade for a 3D effect
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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
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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
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Interpolation• Linear• Polynomial
• In GIS (to generate raster):– Nearest Neighbor– Inverse Distance
Weighted (IDW)– Kriging– Splining
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• 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
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Linear interpolation• Assume that the value for an unknown location
between two known points can be estimated based on a linear assumption
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Polynomial Interpolation• Assume that the value for an unknown location
between two known points can be estimated based on a non-linear assumption
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Spatial Interpolation• Generating surface from points
(samples) based upon: – Nearest Neighbor– Inverse Distance Weighted (IDW)– Kriging– Splining
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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
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Nearest-Neighbor
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Inverse Distance Weighted (IDW)
• Spatial Autocorrelation– Near objects are
more similar than far objects
• IDW weights point values based on distance
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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.
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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 ….?)
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Inverse Distance Weighted
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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
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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)
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Generating Semivariogram
• To generate a semivariogram, semivariance between pairs of points (for various distances/lags) are to be calculated
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09_09_Figure
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Semivariance: Example
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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
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Kriging
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Spline Interpolation
• Curves fit through control points
• Interpolated values may exceed actual elevation values
• Regularized vs. Tension options
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09_13_Figure
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Spline Interpolation
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Comparing Interpolations
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OK…• Which one works better?
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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
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Terrain Functions
• Slope• Aspect• Hillshade• Curvature
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Slope: How it is done!• Equations applied in neighborhoods for
a focal cell
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Viewshed Analysis
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Watershed Delineation
• How much land area drains to a specific point?
• Can be delineated manually from a topo map
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Watershed Basics• Basin/Catchment, Drainage Divide,
Pour Points
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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.
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Delineation Methodology
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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.
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Flow Direction
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Flow Accumulation
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Raster to Vector Streams
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Stream Link
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Stream Order
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Snapping Pour Points
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Watershed Delineation
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Homework & Lab
• Chapter 9: Questions 1 and 4
• Lab on Monday (29th): Raster• Lab on Wednesday: Terrain Analysis– Processing DEM data– Delineating a watershed