Transcript Surfaces - Department of Civil, Architectural and Environmental

Surface terrain model for city of Austin, TX
ArcGIS 3-D Analyst
Shoal creek
Waller creek
Triangulated Irregular Network (TIN)
Algorithm for interpolating irregularly-spaced data in
terrain modeling
UT Campus
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
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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
A Mesh of Triangles in 2-D
Triangle is the only
polygon that is always
planar in 3-D
Points
Lines
Surfaces
TIN Triangles in 3-D
(x3, y3, z3)
(x1, y1, z1)
(x2, y2, z2)
z
y
Projection in (x,y) plane
x
Delauney Triangulation
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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
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
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
Inputs for Creating a TIN
Mass Points
Soft Breaklines
Hard Breaklines
• 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.
TIN with Linear Surface Features
Classroom
Waller Creek
UT Football
Stadium
City of Austin digitized all the buildings to get emergency vehicles quickly
A Portion of the TIN in Large View
Input data for this portion
Mass Points
not inside building
Soft Breaklines
along the hills
Hard Breaklines
along the roads
TIN Vertices and Triangles
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
TIN Surface Model
Waller
Creek
Street and
Bridge
Data Sources to Develop TINs
• LIDAR (Light Detection and Ranging; or
Laser Imaging Detection and Ranging)
• Aerial photogrammetry
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
EAARL LIDAR Topography of Platte River and Floodplain Near Overton, NE
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
3-D ArcScene, Austin, TX
Aerial photogrammetry
3-D Scene with Buildings
LIDAR Terrain Surface for
Powder River, Wyoming
Source: Roberto Gutierrez, UT Bureau of Economic Geology
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
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
Why interpolate to raster?
Analogy: Spatially distributed objects are
spatially correlated; things that are close
together tend to have similar characteristics
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.
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
Using the ArcGIS Spatial Analyst to create a
surface using IDW interpolation
5
Zˆ ( yellow )   i (d yellow, redi )  Z (red i )
i 1
IDW weights
i
assigned arbitrarily

di
5
p
dj
i 1
p
Topo to Raster interpolation
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
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
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
5
Zˆ ( yellow )   i (d yellow, redi )  Z (red i )
i 1
SemiVariagram
Captures spatial dependence between
samples by plotting semivariance against
seperation distance


1
zi  z j

2 i, j

2
• 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 )
SemiVariagram
h = separation distance
between i an j

1
   zi  z j
2 i, j

2
What information does it provide?
• The γ between samples
separated by no distance is
about 1.5E-4
• Points influence each other
within 60 km, beyond that
they don’t
• 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
Case Study: Estimating Fecal Coliform
Levels in Galveston Bay, TX
Observed fecal coliform concentrations for January 1999
(MPN fecal coliform colonies/100ml of water )
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
Exploratory Spatial Data Analysis
in Geostatistical Analysis
• Histogram
• Normal Q-Q (QuantileQuantile) plot
• Trend Analysis
• Voronoi Map
• Semivariogram Cloud
• General Q-Q Plot
• Crosscovariance Cloud
1. Histogram
2. Normal Q-Q plot
Log of bacteria conc.
Standard normal distribution
 2 1
 0
2. Normal Q-Q plot
Log of bacteria conc.
Standard normal distribution
 2 1
 0
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
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 largescale trends that the
modeler might want to
remove prior to
estimation
Geostatistical Analysis: Selection of
Methods
Defining the Semivariogram
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
Cross Validation
Predicted Fecal Coliform
Concentration
Average Fecal Coliform Concentration
in each Bay