Surface terrain model for city of Austin, TX ArcGIS 3-D Analyst

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Surface terrain model for city of Austin,
TXArcGIS 3-D Analyst
Shoal creek
Waller creek
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Triangulated Irregular Network (TIN)Algorithm
for interpolating irregularly-spaced data in
terrain modeling
UT Campus
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TIN

• Digital representation of the terrain
• Preserves details of a shape on the terrain, more
  accurate representation of urban area
• Break lines represent significant terrain
  features like a lake or cliff that cause a change
  in slope
• Requires a much smaller number of points than a
  gridded DTM (The digital terrain model) in order
  to represent the surface terrain with equal
  accuracy

Steps to Form a Surface From TIN

• A triangular mesh is drawn on the control and
  determined data points
• A perimeter around the data points is first
  established, the convex hull
• To connect the interior points, Delaunay
  triangulation is used
• A surface is created by integrating all of the
  triangles over the domain
• Additional elevation data such as spot elevations
  at summits and depressions and break lines are
  also collected for the TIN model

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A Mesh of Triangles in 2-D
Triangle is the only polygon that is always
planar in 3-D
Lines
Surfaces
Points
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TIN Triangles in 3-D
(x3, y3, z3)
(x1, y1, z1)
(x2, y2, z2)
z
y
Projection in (x,y) plane
x
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Delauney Triangulation

• Developed around 1930 to design the triangles
  efficiently
• Geometrically related to theissen tesselations
• Maximize the minimum interior angle of triangles
  that can be formed
• No point lies within the circumcircle of a
  triangle that is contained in mesh

Yes More uniform representation of terrain
No
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Circumcircle of Triangle

• Draw the perpendicular bisectors of each edge of
  the triangle
• Circumcircle is centered on their intersection
  point
• Radial lines from center have equal length

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Theissen polygon

• Associate each point with the area that is
  associated with that point more closely than any
  other
• Common for getting rainfall
• Widely used without GIS

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Inputs for Creating a TIN

• Mass Points define points anywhere on landscape
• Hard breaklines define locations of abrupt
  surface change (e.g. streams, ridges, road kerbs,
  building footprints, dams)
• Soft breaklines are used to ensure that known z
  values along a linear feature are maintained in
  the tin.

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TIN with Linear Surface Features
Classroom
UT Football Stadium
Waller Creek
City of Austin digitized all the buildings to get
emergency vehicles quickly
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A Portion of the TIN in Large View
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Input data for this portion
Mass Points not inside building
Soft Breaklines along the hills
Hard Breaklines along the roads
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TIN Vertices and Triangles
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ESRI TIN Engine Integrated Terrain Model, ARCGIS
9.2

• Creates varying levels of conditions and points
  to produce pyramid style TINs on the fly
• Provides an efficient methodology for working
  with mass data
• Results in a single dataset that can rapidly
  deploy and visualize TIN based surfaces at
  multiple scale

Courtesy, http//gis.esri.com
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TIN Surface Model
Waller Creek
Street and Bridge
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Data Sources to Develop TINs

• LIDAR (Light Detection and Ranging or Laser
  Imaging Detection and Ranging)
• Aerial photogrammetry

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LIDAR

• An optical remote sensing technology
• Masures properties of scattered light to find
  range and/or other information of a distant
  target
• LIDAR sensor was mounted on-board
• During the flight, the LIDAR sensor pulses a
  narrow, high frequency laser pulse toward the
  earth through a port opening in the bottom of the
  aircraft's fuselage
• The LIDAR sensor records the time difference
  between the emission of the laser beam and the
  return of the reflected laser signal to the
  aircraft
• Range to an object is determined by measuring the
  time delay between transmission of a pulse and
  detection of the reflected signal to the aircraft
• Points are distributed across the space,
  push-broom sensor
• Amazing degrees of details. Resolution is 1/9 arc
  second
• 1 arc second DEM 30 m
• 1/3 arc second DEM 10 m

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EAARL LIDAR Topography of Platte River and
Floodplain Near Overton, NE
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Aerial photogrammetry

• The aerial photos are taken using a stereoscopic
  camera
• Two pictures of a particular area are
  simultaneously taken, but from slightly different
  angles, overlapping photographs
• The overlapping area of the two resulting photos
  is called a stereo pair
• Using a computer, stereoplotter, the stereo pair
  can be viewed as a single image with the
  appearance of depth or relief
• Ground control points are established based on
  ground surveys or aerial triangulation and are
  viewed in the stereoplotter in conjunction with
  the stereo pair
• The image coordinates of any (x,y,z) point in
  stereoscopic image pair can be determined and
  randomly selected and digitized

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3-D ArcScene, Austin, TXAerial photogrammetry
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3-D Scene with Buildings
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LIDAR Terrain Surface for Powder River, Wyoming
Source Roberto Gutierrez, UT Bureau of Economic
Geology
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NCALM National Center for Airborne Laser Mapping

• Sponsored by the National Science Foundation
  (NSF) (http//www.ncalm.org)
• Operated jointly by the Department of Civil and
  Coastal Engineering, College of Engineering,
  University of Florida (UF) and the Department of
  Earth and Planetary Science, University of
  California- Berkeley (UCB)
• Invites proposals from graduate students seeking
  airborne laser swath mapping (ALSM) observations
  covering limited areas (generally no more than 40
  square kilometers) for use in research to earn an
  M.S. or PhD degree.
• Proposals must be submitted on-line by November
  30, 2006

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Some advantages of TINS

• Fewer points are needed to represent the
  topography---less computer disk space
• Points can be concentrated in important areas
  where the topography is variable and a low
  density of points can be used in areas where
  slopes are constant.
• Points of known elevation such as surveyed
  benchmarks can easily be incorporated
• Areas of constant elevation such as lakes can
  easily be incorporated
• Lines of slope inflection such as ridgelines and
  steep canyons streams can be incorporated as
  breaklines in TINS to force the TIN to reflect
  these breaks in topography

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Why interpolate to raster?

• Analogy Spatially distributed objects are
  spatially correlated things that are close
  together tend to have similar characteristics

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Interpolation using Rasters

• Interpolation in Spatial Analyst
• Inverse distance weighting (IDW)
• Spline
• TOPOGRID, Topo to Raster (creation of
  hydrologically correct digital elevation models)
• Kriging (utilize the statistical properties of
  the measured points quantify the spatial
  autocorrelation among measured points )
• Interpolation in Geostatistical Analyst.

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Using the ArcGIS Spatial Analyst to create a
surface using IDW interpolation

• Each input point has a local influence that
  diminishes with distance
• It weights the points closer to the processing
  cell greater than those farther away
• With a fixed radius, the radius of the circle to
  find input points is the same for each
  interpolated cell
• By specifying a minimum count, within the fixed
  radius, at least a minimum number of input points
  is used in the calculation of each interpolated
  cell
• A higher power puts more emphasis on the nearest
  points, creating a surface that has more detail
  but is less smoot
• A lower power gives more influence to surrounding
  points that are farther away, creating a smoother
  surface. Search is more globally

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Using the ArcGIS Spatial Analyst to create a
surface using IDW interpolation
IDW weights assigned arbitrarily
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Topo to Raster interpolation
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ArcGIS Spatial Analyst to create a surface using
Topo to Raster interpolation

• Designed for the creation of hydrologically
  correct digital elevation models
• Interpolates a hydrologically correct surface
  from point, line, and polygon
• Based on the ANUDEM program developed by Michael
  Hutchinson (1988, 1989)
• The ArcGIS 9.x implementation of TopoGrid from
  ArcInfo Workstation 7.x
• The only ArcGIS interpolator designed to work
  intelligently with contour inputs
• Iterative finite difference interpolation
  technique
• It is optimized to have the computational
  efficiency of local interpolation methods, such
  as (IDW) without losing the surface continuity of
  global interpolation methods, such as Kriging and
  Spline

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Using the ArcGIS Spatial Analyst to create a
surface using Spline interpolation

• Best for generating gently varying surfaces such
  as elevation, water table heights, or pollution
  concentrations
• Fits a minimum-curvature surface through the
  input points
• Fits a mathematical function to a specified
  number of nearest input points while passing
  through the sample points
• The REGULARIZED option usually produces smoother
  surfaces than those created with the TENSION
• For the REGULARIZED, higher values used for the
  Weight parameter produce smoother surfaces
• For the TENSION, higher values for the Weight
  parameter result in somewhat coarser surfaces but
  with surfaces that closely conform to the control
  points
• The greater the value of Number of Points, the
  smoother the surface of the output raster

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Interpoloation using Kriging

• Things that are close to one another are more
  alike than those farther away spatial
  autocorrelation
• As the locations get farther away, the measured
  values will have little relationship with the
  value of the prediction location

Kriging weights based on semivariogram
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SemiVariagram
Captures spatial dependence between samples by
plotting semivariance against seperation distance

• Sill The height that the semivariogram reaches
  when it levels off.
• Range The distance at which the semivariogram
  levels off to the sill
• Nugget effect a discontinuity at the origin
  (the measurement error and microscale variation )

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SemiVariagram
h separation distance between i an j
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What information does it provide?

• The ? between samples separated by no distance
  is about 1.5E-4
• Points influence each other within 60 km, beyond
  that they dont
• An unmeasured location can be predicted based on
  its neighboring samples closer than 60 km
• The points separated by 60 km are likely to have
  the same average difference as points separated
  by 100 km or any distance above 60 km

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Case Study Estimating Fecal Coliform Levels in
Galveston Bay, TX
Observed fecal coliform concentrations for
January 1999 (MPN fecal coliform colonies/100ml
of water )
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Study site characteristics
Consists of 5 bay segments 40 Upstream drainage
area 5 managed water quality segments Each
treated differently in TX High Concentration of
bacteria in Urban Concentration is low away from
urban Major area of contamination is associated
with Huston (4 106) Industrial sources
(refinery) Bacteria tend to be local because they
die off pretty past
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Exploratory Spatial Data Analysisin
Geostatistical Analysis

• Histogram
• Normal Q-Q (Quantile-Quantile) plot
• Trend Analysis
• Voronoi Map
• Semivariogram Cloud
• General Q-Q Plot
• Crosscovariance Cloud

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1. Histogram
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2. Normal Q-Q plot
Standard normal distribution
Log of bacteria conc.
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2. Normal Q-Q plot
Standard normal distribution
Log of bacteria conc.
Samples with no detection of bacteria
Mean bacteria C 1.59 log units 40
Decision Criteria for Environmental Management
Task of data exceed certain threshold (43)
Samples with no detection of bacteria conc. 2
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3. Trend Analysis

• 3D plot of the samples and a regression on the
  attribute in the XZ and YZ planes
• Visualize the data and to observe any large-scale
  trends that the modeler might want to remove
  prior to estimation

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Geostatistical Analysis Selection of Methods
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Defining the Semivariogram
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Cross Validation of the Model

• Uses all of the data to estimate the trend and
  autocorrelation models
• It removes each data location, one at a time, and
  predicts the associated data value.
• For example, the diagram below shows 10 randomly
  distributed data points. Cross Validation omits
  red point and calculates the value of this
  location using the remaining blue points
• The predicted and actual values at the location
  of the omitted point are compared
• This procedure is repeated for a second point,
  and so on
• For all points, cross-validation compares the
  measured and predicted values

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Cross Validation
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Predicted Fecal Coliform Concentration
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Average Fecal Coliform Concentration in each Bay