Chapter 12: Terrain Mapping

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Chapter 12Terrain Mapping Analysis

• Paul Sutton
• psutton_at_du.edu
• Department of Geography
• University of Denver

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Outline

• Definition Creation of DEMs and TINs
• Terrain Mapping with DEMs and TINs
• Terrain Analysis slope, aspect, viewshed,
  watershed, surface curvature
• Comparing DEMs and TINs for terrain mapping and
  analysis

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Digital Elevation Model (DEM)

• Digital elevation model
• (DEM) data consist of a
• sampled array of regularly
• spaced elevation values
• referenced horizontally either
• to a Universal Transverse
• Mercator (UTM) projection
• or to a geographic coordinate
• system. The grid cells are
• spaced at regular intervals
• along south to north profiles
• that are ordered from west to
• east

A DEM is a raster dataset in which The numbers in
the cells represent Elevation (usually above seal
level) What might this crude DEM represent?
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Data Quality of DEMs

• USGS grades Level 1-4
• Level 1 RMSE avg 7 meters RMSE max 15 m
• Level 2 RMSE max ½ contour interval
• Level 3 RMSE max 1/3 contour interval
• - Most DEM data is Level 1 or 2
• Global or Relative Error
• Global Error (aka Systematic) all values too hi
  or low
• Relative Error bogus sinks, ridges, spikes etc.

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Triangulated Irregular Networks (TINs)
A TIN approximates the land Surface with a series
of non-overlapping triangles. In contrast to
DEMs TINs are Based on an irregular distribution
of elevation points.
TIN (in Black) of Colorado derived from 1 km DEM
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ArcView Default TIN representation of Colorado
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Creating TINs

• TINs can be created from DEMs, surveyed elevation
  points, contour lines, and breaklines
  (breaklines streams, shorelines, ridges, roads)
• Algorithms for Picking Points
• VIP (Very Important Points) (see Chang text also)
  
• Fowler Little
• Max Z-tolerance (see Chang text only)
• Building Triangles from Chosen Points
• Having selected a set of TIN points, these will
  become the vertices of the triangle network.
  There are several ways to connect vertices into
  triangles
• "fat" triangles with angles close to 60 degrees
  are preferred since this ensures that any point
  on the surface is as close as possible to a
  vertex. This is important because the surface
  representation is likely most accurate at the
  vertices
• Distance Ordering
• Delaunay Triangulation

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Choosing the Points IThe Fowler Little
Algorithm

• This approach is based on the concept of
  surface-specific points which play a specific
  role in the surface (e.g. represent features such
  as peaks and pits)
• Procedure first examine the surface using a 3x3
  window, looking at a small array of 9 points at
  each step label the 8 neighbors of the central
  point if higher, - if lower a point is a peak
  if its 8 neighbors are all lower (8 s) a point
  is a pit if its 8 neighbors are all higher (8 -s)
  a point is a pass if the s and -s alternate
  around the point with at least two complete
  cycles, e.g
• - -
  
• - - -
  -
• - (2 cycles) -
  (4 cycles)
• next the surface is examined using a 2x2
  window except at the edges, every point appears
  in four positions of the window a point is a
  potential ridge point if it is never lowest in
  any position of the window a point is a potential
  channel point if it is never highest in any
  position of the window
• then starting at a pass, search through
  adjacent ridge points until a peak is reached
  similarly, search from the pass through adjacent
  channel points until a pit is reached
• Finishing the TIN
• The result of this process is a connected set of
  peaks, pits, passes, ridge lines and channel
  lines
• Fowler and Little recommend that the number of
  points in each ridge and channel line be reduced
  by thinning using a standard thinning algorithm
  it may be desirable to add additional points from
  the DEM which are not on ridges or channels if we
  can significantly reduce any substantial
  differences from the real surface by doing so
  triangles are built between all selected points
• the resulting surface will differ from the
  original DEM, perhaps substantially in some areas
  

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Choosing the Points IIThe Very Important Point
algorithm (VIP)

• Unlike the previous algorithm which tries to
  identify the major features of the terrain, VIP
  works by examining the surface locally using a
  window this is a simplification of the technique
  used in ESRI's ARC/INFO
• Procedure
• Each point has 8 neighbors, forming 4
  diametrically
• opposite pairs, i.e. up and down, right and left,
  upper
• left and lower right, and upper right and lower
  left
• For each point, examine each of these pairs
  of
• neighbors in turn connect the two neighbors by a
• straight line, and compute the perpendicular
  distance
• of the central point from this line diagram.
• Average the four distances to obtain a
  measure of
• "significance" for the point Delete points from
  the
• DEM in order of increasing significance, deleting
  the least significant first
• this continues until one of two
  conditions is met
• 1) the number of points reaches a
  predetermined limit
• 2) the significance reaches a
  predetermined limit
• Comments
• Because of its local nature, this method is
  best when the proportion of points deleted is low
  
• Because of its emphasis on straight lines,
  and the TIN's use of planes, it is less
  satisfactory on curved surfaces

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Making The Triangles IDistance Ordering

• Procedure
• Compute the distance between all pairs of points,
  and sort from lowest to highest
• 1) connect the closest pair of points
• 2) connect the next closest pair if the
  resulting line does not cross earlier lines
• 3) repeat until no further lines can be
  selected
• The points will now be connected with
  triangles
• This tends to produce many skinny triangles
  instead of the preferred "fat" triangles

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Making the Triangles IIDelaunay Triangulation

• By definition, 3 points form a Delaunay triangle
  if and only if the circle which passes through
  them contains no other point. Another way to
  define the Delaunay triangulation is as follows
• 1) partition the map by assigning all
  locations to the nearest vertex the boundaries
  created in this process form a set of polygons
  called Thiessen polygons or Voronoi or Dirichlet
  regions

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Terrain Mapping

• Contours Close together steep, curved in
  upstream direction, should not intersect
• Vertical Profiling (e.g. changes in stream
  elevation along a tributary)
• Hill Shading (shine the sun on the land)
• Hypsometric Tinting (colors to elevation zones)
• Perspective Views (3-D visualization)

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Contour Map of Colorado derived from DEM
County lines Green 500 m Intervals Red 100 m
intervals Black
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Vertical Profiling
This graphic was created using the
SurfaceProfile command in ArcPlot. Can you
explain what it is all about? How might this be
used?
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Hillshading a DEM of ColoradoLet the Sun Shine
in

• Azimuth What direction is the sun coming from on
  the ground (e.g. SouthWest, South, North, etc.
  What possibilities are real?)
• Elevation How high is the sun in the Sky?
• Slope of the Ground Surface
• Aspect of the Ground Surface

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3 different Hillshadings of Colorado
A
B
Fair Test Question Match Images to Hillshade
Parameters 1) Azimuth 0 Elevation 45 2) Azimuth
245 Elevation 15 3) Azimuth 110 Elevation 10
C
Which hillshade is Unphysical?
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Hypsometrically Tinted TIN of CO
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3-D Visualization of a TIN of Colorado
Parameters you can control Viewing Azimuth,
Viewing Angle, Viewing Distance, Z-scale (e.g.
vertical exageration) , draping of multiple layers
You will play with this functionality in Lab
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Terrain Analysis

• Slope and Aspect Algorithms
• Useful in studies of watershed units, landscape
  units, morphometric measures, forest inventory,
  soil erosion, etc.
• Surface Curvature
• Hydrological studies often need to know about
  concavity.
• Viewshed Analysis
• Useful for Cell Phone Tower siting
• Watershed Analysis
• Useful for flood plain mapping

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What will this filter calculate?(This is a
neighborhood operator described in Chapter 10)
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Applying a slope algorithm to a DEM of Colorado
Slope of Colorado
DEM of Colorado
How do we interpret the red areas in the slope
image?
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Algorithms Unambiguous rules for performing an
operation

• There are many mathematical algorithms for
  calculating slope, aspect, curvature, and other
  properties of images.
• Several of these are described in the Chang text.
  
• For further study of these take Remote Sensing
  and digital image processing.

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An Aspect filter applied to a Colorado DEM
When I bought my house what color of this Map was
I trying to find my house in? Could you build
and aspect filter?
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Viewshed Analysis
What can be seen from the Location indicated by
the Red dot in South Park?
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Watershed Analysis(aka Hydrological Modeling)
Creating Watersheds Filled Elevation Grid Flow
direction Grid Flow Accumulation Grid
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Watershed functions for CO
From this DEM of CO
Flow Accumulation
Watersheds
Flow Direction
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Next Week

• Chapter 13 Spatial Interpolation
• Chapter 14 GIS Modeling