1. L2 –Data Models Ch. 2, pp 25-53
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2. Phenomena/entities that exist in the real world
Computer Representation
Entities are represented by spatial features or cartographic objects.
You are making choices, so remember that your choices are introducing a bias What is represented and how it is represented and what properties are recorded depend upon the intended use of the GIS.
This is subjective and adds a bias to the data.
Graphically, the boundary of the wetland may vary.
The attributes you choose depends upon your interest:
A forester might record the type of tree, the diameter at breast height and the health of the tree, where as someone interested in the hydrology might simply record tree.
Machine Code
An abstraction, relevant phenomena and properties 2

3. Data Model
The spatial data model provides a formal means of representing and manipulating spatially-referenced information.
So our data model is how the information is represented on a map and its representation in our database. There are two primary data models. This is example is a vector data model. The lake is represented as a polygon, and our database contains that information. This is the information that is normally visible to the user of the GIS.
Everything else is hidden and is more the concern of computer scientists except for the coordinates of our spatial features.
In order to locate something on the surface of the earth, our spatial feature needs to have either a coordinate pair (x,y) or coordinate triplet (x,y,z).
This information is normally hidden from the user, but we can access it.
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4. Thematic Layers A logical separation of data according to theme.
Each layer reflects a particular use or characteristic.
Overlays.
Most conceptualizations view the world as thematic layers (just layers)
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5. Coordinates
Coordinates are used to define the location and extent of our geographic object.
Coordinates are either (x,y) or (x,y,z).
Polygon [(8,10), (14,5), (5,15), (1, 8), (3,12), (8,10)]
The simplest coordinate system is the Cartesian coordinate system we use in math. On this flat surface we can represent a point A with one coordinate pair. Line AB requires 2 coordinate pairs.
For a polygon we need a coordinate pair for each point making up the line segments with the first and last repeated.
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6. Coordinate Data Latitude & Longitude Spherical Coordinates
Origin (intersection of the Equator and Greenwich meridian)
Spherical Coordinates
Deg., min., sec. (DMS)
Decimal degrees (DD)
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7. Conversion
Convert: 68o 48’ 57” to decimal degrees:
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8. Types of Attribute Data
Attribute data record the non-spatial characteristics of an entity.
Attributes have values
Observed
Measured
Attributes of a pair of jeans:
Observed: color (dark blue sea salt, style :relaxed fit, slim leg, boot cut)
Measured: size 4,6,8,10, length (short, regular, tall)
Llbean.com
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9. Measurement of Attributes
Physical scientists define measurement as the comparison of an object to a standard object.
They define two types of measurements
Extensive/Fundamental Properties (feet)
Derived – by combining extensive properties (feet/second)
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10. Stevens’ Levels of Measurement
Social scientists weren’t satisfied with this classification
Stanley Stevens (1946) proposed a framework for measurement types based upon “levels of measurement”.
He defined measurement as being the assignment of classes or scores to phenomena according to a set of rules.
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11. Stevens’ Levels of Measurement
There are four basic levels according to Stevens:
Nominal – provides descriptive information.
Ordinal – implies a rank order.
Interval – implies order and difference in magnitude.
Ratio - implies order and difference in magnitude and has an absolute 0.
The level of measurement determines the calculations and the analysis that can be performed on the data.
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12. Ordinal
Ordinal Measurement sorts objects in an order or ranked category.
For example, the order of finish in a race, someone gets first place, second place, third place, and so on.
Each object gets categorized based on its position relative to others, ordinal would not measure when, but where in relation to others.
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13. Ordinal You can do comparisons:
If A>B and B>C then the correct increasing order is C, B, A; i.e., establish order
You can establish equality between two orders.
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14. Interval
Interval Measurement puts the object on a number line, so instead of just knowing where, someone finished in relation to others, would also know when, they finished.
But, the number line does not have a zero value, the number line starts arbitrarily.
It would be like writing the times of finish by just looking at a watch, and noting the time they came in. You would know how long between each runner, but not how long the race took over all.
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15. Interval Operations include: Count Equality Order
Addition and Subtraction
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16. Ratio
Ratio Measurement adds the how long, the number line gets a zero value.
So you would know how long and when, and where each runner comes in.
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17. Ratio Operations: Count Equality Order Addition and Subtraction
Multiplication and Division
Higher order operations
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18. Additional Levels of Measurement
Nicholas Chrisman includes several more in his textbook "Exploring Geographic Information Systems."
I will add those here:
Absolute scales – scales bounded on both ends like probability
Cyclical measures – angular measure
Counts are misfits. They are not continuous, but otherwise behave as a ratio scale
Graded membership in categories – Fuzzy set theory; i.e., not all membership within a class must be equal.
A system should handle counts.
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19. Common Spatial Data Models
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20. Raster & Vector Image

21. Vector & Raster Vector is better at representing discrete features.
Raster is better at representing continuous features
A project may contain both vector and raster layers.
Spatial operations can only be performed on one type of layer.
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22. Vector & Raster (cont’d)
The best data model for a given layer depends upon the operations, the experience and the views of the user.
No decision is final, as one can be converted to the other.
Conversion introduces error
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23. Other Data Models Spatial Data Vector Data Raster Data Lecture 2 23
Other Data Models
Vector Data
Raster Data
Non-topological
Topological
Simple Data
Higher-level Data
TIN
Regions
Dynamic Segmentation
Spatial Data
Data Model – A consistent way of defining and representing spatial objects in a database, and of representing the relationships among them
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24. Vector Terminology Lecture 2
Linear features lines, line segments, arcs
How one chooses to represent a feature, is up to the designer of the GIS and the map scale. For example, on a U.S. map, Bangor would not be represented at all, on a map of New England it might be a point, on a map of Maine it could be a point, marked off in line segments or be an area.
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25. Polygon Inclusions
Areas in polygons that are part of the polygon, but different from the rest of the polygon: e.g. Islands in a lake.
Solutions:
Create separate polygons for each inclusion.
Create an attribute column for coding inclusions.
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26. Vector Topology Topology – geometric properties that to not change
with shape: Adjacency, Connectivity, Containment
Early GIS data models were non-topological and so require a lot of careful time consuming editing. The topological data model allows you to set rules such that there can be no overlaps or undershoots.

27. Topology
Topology in the object data model is a set of rules and software tools to define spatial relationships an behaviors, such as:
Polygons must not overlap within a dataset.
Lines must not overlap themselves within a data set.
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28. Three Types of Vector Features
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29. Advantages of Topology
Maintain correct data spatial relationship (Find errors)
Efficient data storage (quickly process large data sets)
Facilitate spatial analysis (Network analysis, Adjacent area analysis, overlay analysis
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30. Encoding Topological Primitives
Polygon Bounding Arcs
A (e,f,g,i,j) (h) (k)
B (a,b,c,-i)
C (-c,d,-j)
D (-k)
Directed arc
External boundaries go clockwise
Internal boundaries are counter clockwise.
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31. Arc Bounding Nodes Left Poly Right Poly
a 1, B
b 2, B
c 3, C B
d 3, C …
k 9, D A

32. Nodes Co-bounding Arcs 1 a,i,-g 2 -a,b 3 -b,d,c 4 -j,d,e 5 -c,j,-i
6 -e,f
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33. Raster Coordinates Coordinate of upper (lower) left corner.
Cell size (Width, Height) – usually square
(Row, Column) 33

34. Calculation (16,23) 10 10 Lecture 2 34
When the cells are square and aligned with the coordinate axis, the coordinate calculation is straight forward. 10 10
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35. Raster – The Storage Space/Resolution Tradeoff
Decreasing the Cell Size by one-half
causes a
Four-fold increase in the storage space required
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36. Rasters – Discrete or Continuous Features
Rasters are better for continuous data.
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37. Raster – The Mixed Pixel Problem
Landcover map –
Two classes, land or water
Cell A is straightforward
What category to assign
For B, C, or D?
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38. Raster Feature & Attribute Tables
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39. Raster Feature & Attribute Tables
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40. Raster Feature & Attribute Tables
Frequently you will see only a cell count when there is a many –to-one relationship
A floating point raster has no attribute table.
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41. Raster vs. Vector
Most current GIS packages have both raster and vector capabilities.
A project may use both spatial data models, but they cannot be combined for analysis.
They are usually better adapted for handling one over the other.
There are advantages and disadvantages to each.
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42. Raster vs Vector Vector Raster Characteristics Positional Precision
Characteristics
Positional Precision
Attribute Precision
Analytical
Capabilities
Data Structures
Storage Requirements
Coordinate conversion
Network Analyses
Output Quality
Can be Precise
Defined by cell size
Poor for continuous data
Good for continuous data
Good for spatial query, adjacency, area, shape analyses. Poor for continuous data. Most analyses limited to intersections. Slower overlays.
Spatial query more difficult, good for local neighborhoods, continuous variable modeling. Rapid overlays.
Often complex
Often quite simple
Relatively small
Often quite large
Usually well-supported
Often difficult, slow
Easily handled
Often difficult
Very good, map like
Fair to poor - aliasing
Vector
Raster
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43. No Decision is Final – We Can Convert
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44. Triangulated Irregular Networks
TINs
Typically used to represent elevations.
Require x,y & z coordinates.
A TIN forms a connected network of triangles (Delaunay triangles)
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45. BUILDING A TIN

46. TIN Parts Points – sample locations Edges – connecting lines Facets –
triangles, “faces”

47. TIN – Triangle Formation
TIN triangles defined such that
Three points on a circle
Circles are empty – they don’t contain another point
These are convergent circles

48. Digital Elevation Models
DEM is point based with elevation at center of a cell.
Each file contains
Elevation,
Header: units, min/max elev, proj, accuracy
Four types
7.5 minute DEM (30 or 10 meter)
30 minute DEM (60 meter)
1 degree DEM (100 meter)
Alaska DEMs
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49. DEM http://rylincolnblaisdell.blogspot.com/2010_12_01_archive.html
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50. Modeling in the Third Dimension
Figure Examples of true 3D data structures
Sources: (a) Rockware Inc., with permission; (b) Centre for Advanced Spatial Analysis (CASA), University College London, with permission
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51. 3 D Demo
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52. Modeling the Fourth Dimension
Four temporal attributes:
Generation time
Duration time
Temporal significance
Temporal scale
Spatial objects may change over time and space (location, size, geometry and orientation)
Time at which the object is created (this may not be known exactly, usually retrospective process)
Degree of permanence – the time during which an object existed.
The importance of the event. This usually determines whether or an event should be included in the database
The ratio between actual time and map time. If an animated sequence takes 6 s to display recorded over a 12 h observation interval 6/(12*3600)=1:7200
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53. Possible Changes of Spatiotemporal Relationships over Time

54. Time Slider Demo
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55. Animation Demo
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