1. Surface terrain model for city of Austin, TX ArcGIS 3-D Analyst
Shoal creek
Waller creek

2. Triangulated Irregular Network (TIN) Algorithm for interpolating irregularly-spaced data in terrain modeling
UT Campus

3. Steps to Form a Surface From 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

4. A Mesh of Triangles in 2-D
Triangle is the only
polygon that is always
planar in 3-D
Points
Lines
Surfaces

5. TIN Triangles in 3-D (x3, y3, z3) (x1, y1, z1) (x2, y2, z2) z y
Projection in (x,y) plane x

6. 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

7. 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

8. 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

9. 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.

10. TIN with Linear Surface Features
Classroom
UT Football
Stadium
Waller Creek
City of Austin digitized all the buildings to get emergency vehicles quickly

11. A Portion of the TIN in Large View

12. Input data for this portion
Mass Points
not inside building
Soft Breaklines
along the hills
Hard Breaklines
along the roads

13. TIN Vertices and Triangles

14. 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,

15. TIN Surface Model
Waller
Creek
Street and
Bridge

16. Data Sources to Develop TINs
LIDAR (Light Detection and Ranging; or Laser Imaging Detection and Ranging)
Aerial photogrammetry

17. 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

18. EAARL LIDAR Topography of Platte River and Floodplain Near Overton, NE

19. 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

20. 3-D ArcScene, Austin, TX Aerial photogrammetry

21. 3-D Scene with Buildings

22. LIDAR Terrain Surface for Powder River, Wyoming
Source: Roberto Gutierrez, UT Bureau of Economic Geology

23. NCALM National Center for Airborne Laser Mapping
Sponsored by the National Science Foundation (NSF) (
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

24. 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

25. Why interpolate to raster?
Analogy: Spatially distributed objects are spatially correlated; things that are close together tend to have similar characteristics

26. 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.

27. 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

28. Using the ArcGIS Spatial Analyst to create a surface using IDW interpolation
IDW weights
assigned arbitrarily

29. Topo to Raster interpolation

30. 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

31. 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

32. 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

33. 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 )

34. SemiVariagram
h = separation distance
between i an j

35. 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

36. Case Study: Estimating Fecal Coliform Levels in Galveston Bay, TX
Observed fecal coliform concentrations for January 1999
(MPN fecal coliform colonies/100ml of water )

37. 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

38. Exploratory Spatial Data Analysis in Geostatistical Analysis
Histogram
Normal Q-Q (Quantile-Quantile) plot
Trend Analysis
Voronoi Map
Semivariogram Cloud
General Q-Q Plot
Crosscovariance Cloud

39. 1. Histogram

40. 2. Normal Q-Q plot
Standard normal distribution
Log of bacteria conc.

41. 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

42. 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

43. Geostatistical Analysis: Selection of Methods

44. Defining the Semivariogram

45. 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

46. Cross Validation

47. Predicted Fecal Coliform Concentration

48. Average Fecal Coliform Concentration in each Bay