GIS Modeling

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					               GIS Modeling
               Week 2 — Maps as Data
            GEOG 3110 –University of Denver

                          Presented by    Joseph K. Berry
               W. M. Keck Scholar, Department of Geography, University of Denver

    Points , lines, polygons and surfaces; Discrete vs.
Continuous data; Map data types and their implications;
Displaying grid data; Contouring implications; Grid map
                    structure and storage
               Who We Are (Class Photo)

                    Annotated Class Roster posted at…
                              <as of Thursday morning>
                           Now, Where Were We?
                                  What GIS Is (and isn’t)
Computer Mapping (70’s) - Spatial dB Management (80’s) - GIS Modeling (90’s)

                                 GIS Modeling
 Spatial Analysis —
   “contextual” relationships
    within and among mapped
    data (Reclassify, Overlay,
    Distance, Neighbors)

 Spatial Statistics — “numerical” relationships within
    and among mapped data (Surface Modeling and Spatial Data Mining)
                                                                                          From mapping to
                                                                                          Spatial Reasoning…

                                                                       …that radically changes our Map Paradigm

        …keeping in mind that the frontier is currently focused on Multimedia Mapping (00’s)               (Berry)
 Campground Suitability Model Review (Logic)
  Prefer Gentle Slopes, Near Roads, Near Water, View of Water and Westerly Oriented
                     …but can’t be too close to water or too steep
                           1             2            3           4
1) Base

2) Derived                                                                        6

3) Interpreted

4) Combined /
Modeled maps

5) Constraint

6) Final map

    Campground Suitability Model Review (Solution)
          A sequencing of map analysis commands are applied to implement model logic—
                          using a command script (Tutor25_Campground.scr)

      Solution set
      of maps are
      created by
      the model                                                              Hands-on
      logic for the                                                          Review
      pattern of
      at each
           …grid cell

                    Basic Map Features
Manual cartography utilizes points, lines and areas as the basic
    building blocks for characterizing geographic space
                                      Based on spatial objects (discrete)

                                                                  New map feature
                                                                   type based on
                                                                     grid cells

…traditionally all maps are composed of three fundamental map features—Points, Lines
     and Areas. The digital map provides additional dimensions of depth and time to
        extend the features to Surfaces, Volumes, hyper-Volumes and fuzzy-Features
Storing Points, Lines and Areas

 …how do you think Vector and Raster data structures store
  Surfaces, Volumes, hyper-Volumes and fuzzy-Features?
                          Spatial Resolution
The concept of Scale (S= MD/GD) does not exist in a GIS                            …heresy!!!

      …replaced by the concept of Resolution (Spatial, Mapping, Thematic and Temporal)

      Minimum Mapping Resolution
…replaced by the concept of Resolution (Spatial, Mapping, Thematic and Temporal)

Thematic and Temporal Resolutions
…replaced by the concept of Resolution (Spatial, Mapping, Thematic and Temporal)

   …so what is the difference between the concepts of PRECISION and ACCURACY
          …and how do these concepts relate to the concept of RESOLUTION?          (Berry)
                      Accuracy versus Precision
    The Wikipedia defines Accuracy as “the degree of veracity” (exactness) while Precision as “the degree of
                                        reproducibility” (repeatable)

   Accuracy describes the closeness of arrows to the bull’s-eye at the target center (actual/correct)

                                                                   Handheld GPS unit
                                        High Accuracy
                                       but Low Precision

Accuracy vs.
…the “target analogy”
compares measurements
to the pattern of arrows
shot at a target
                                        High Precision
                                       but Low Accuracy
                                                                                                  Precision GPS unit

   Precision relates to the size of the cluster of arrows— grouped tightly together is considered precise

Classification versus Delineation (spatial perspective)
                                              Interpreter A
                                              Interpreter B
                                              Interpreter C

                      Vegetation                                   Superimposed
                        Parcel                                     interpretation
                       Mapping                                      boundaries

    Accuracy = classification (What)       Precision = delineation (Where)

          Photo Interpreter A          Photo Interpreter B               Photo Interpreter C
             Cottonwood                 Ponderosa Pine                      Cottonwood

   Classification Accuracy (What)  Delineation Precision (Where)                        (Berry)
Model Accuracy/Precision (spatial modeling perspective)
                Routing Criteria                                                                                                  Calibrate
                Most                        Least                                                                                  Expert
                Preferred               Preferred
                1   2   3   4   5   6      7   8    9
                                                        Housing Density   Road Proximity      Sensitive Areas   Visual Exposure

                            HD & VE times 10                       RP & SA times 10                    HD & RP times 10
                            Homeowners                          Environmentalists                       Engineers

mapping has
no definitive                                                                                                                      Weight
  solution—                                                                                                                       Stakeholder

                                Start                                           Start
                                                               Optimal Path

                    Engineers                                    Optimal
                                                                 Average of
                                                                  the three
                                                                cost surfaces

          Individual                                         Combined
          Solutions                     End                   Solution                  End
                                  Raster Data Types
      It is important to note that the map features in a vector-based mapping system
     identify discrete, irregular spatial objects with sharp abrupt boundaries. Other
       data types — grid surfaces, raster images and pseudo grids — treat
           space in entirely different manner to portray spatially continuous data

                                                    …in a raster image the values stored at each
                                                    map location identify its color (hue, saturation
                                                    and brightness)– constrained integer value

…mapped        GIS Maps contain—
data ready     • Points, lines, polygons
for map        • Grid surfaces
analysis and   • Raster images
               • Pseudo grids

     …in a pseudo grid each grid element
     is treated as a separate polygon (square)
     with spatial and attribute tables defining
                       the set of little polygons
                     Basic Grid Data Structure
 A Grid Map consists of a matrix of numbers with a value                     Map Stack
 indicating the characteristic /condition at each grid cell
 location forming a geo-registered set of Map Layers
 or “Map Stack”
 Lines                   Layer Mesh      Grid Map


                                                     Analysis Frame
The Analysis Frame
provides consistent                                    Col 3, Row 22

“parceling” needed
for map analysis
and extends discrete
point, line and areal
features to continuous
Map Surfaces                                                           Data listing for a
                                                                         Map Stack
                                        Layer Mesh                      Drill-down
Basic Grid Display Types
                                                                        Display Types…
                                                                      Lattice display forms a
                                                                         smooth wireframe
                                                                       Grid display forms
                                                                       chunky extruded grids

                                               …so how is a Contour Map generated?

                                             Contour line

   (See Example Applications, “Display Types” for more information)                         (Berry)
 Thematic Display (Shading Manager)
           MapCalc Shading Manager…
         # Ranges sets the number of intervals
   Equal Ranges has the same range for each interval
Equal Count has the same number of cells for each interval

           (See Example Applications, “Display Types” for more information)   (Berry)
Contouring Mapped Data (Continuous to Discrete)
                                                        Display the elevation surface
                                                        as wireframe (Lattice) with filled
                                                        floor contours
                                                         Set #Ranges to 7 and assign
                                                        yellow as the inflection color
                                                         Redisplay the surface as
                                                         Equal Count, Equal Ranges,
                                                           StDev and User Defined
                                                         …note the dramatic differences in the
                                                          shape and position of the boundary
                                                         lines of the discrete contour intervals

  +/- 1Stdev           Equal Count              Equal Ranges            User Defined (300 Step)

               So which discrete map of elevation surface is CORRECT?                              (Berry)
Matching Data Types & Display Types/Forms

                                                                                                                     Data Type…
                                                                                                                       Data Type toggles
                                                                                                                       between Discrete and
                                                                                                                       Continuous data types

                                                                                                                     Display Type…
                                                                                                                       Use Cells toggles
                                                                                                                       between Lattice and
                                                                                                                       Grid display types

                                                                                                                     Display Form…
                                                                                                                       3D Toggle changes
                                                                                                                       2D and 3D display

 (See Example Applications, “Data Types”, “Color Interval/Pallet”, “3D Display Options” and “Data Inspection and Charting” for related information)

  Numeric and Geographic Data Types
    …all digital maps are composed of organized sets of numbers—
the Data Type determines what “map-ematical” processing can be done
          with the numbers on a map, or stack of map layers

                      Homework Exercise #2
Part 1 –   Understanding Basic Concepts and Terms
• Scale and Resolution. 1) Map Scale, 2) Spatial Resolution, 3) Thematic
Resolution, 4) Minimum Mapping Resolution and 5) Temporal Resolution.

• Data Types. 1) Nominal, 2) Ordinal, 3) Interval, 4) Ratio, 5) Binary, 6) Choropleth,
7) Isopleth data types (be sure to distinguish which data types are Numeric and which are

• Display Considerations. You will generate different map displays of the Slope
and Districts map layers, then identify/comment on the Data Type, Display Type and Display
Form used and discuss the effects/appearance of the different displays

Part 2 –   Characterizing Geographic Space                          …Discrete versus Continuous

•Thematic Mapping                   . You will use the Shading Manager to create different map displays
while investigating the effects of Calculation Mode (Equal Ranges, Equal Count,+/- 1 Standard Deviation
and User Defined), Number of Ranges and Color Ramp assignments.

                        Simple Erosion Model
     (Exercise #2, Part 3)

Create a slope map
Reclassify that map for
slope classes
Create    a flow map
Reclassify    that map for
flow classes

Combine   the maps of
slope classes and flow

…result   is a map with a
2-digit code
     1St digit = flow class
     2nd digit = slope class

                                So Where Are You in GIS?
                                                                                             General and
                                                                                             Innovative Users– uses
                                                                                             understanding of basic
      …changing our Map              Paradigm                                                concepts, capabilities and
                                                                                             considerations in developing
                                                                                             new applications within
The “bookends” of this continuum are
                                                                                             their discipline
the current drivers of Geotechnology
                                                                                                 “…of the Discipline”

           “…of the Computer”                                                            “…of the Application”

Computer                        Solutions                     Systems             Data                 GIS
Programmer–                     Developer–                    Manager–            Provider–            Specialist–
develops GIS                    develops GIS                  develops and        develops GIS         uses discipline
tools; mostly                   applications that             maintains spatial   data layers; good    expertise and
computer science                link GIS to real-             databases and       skills in GPS and    GIS knowledge
with some                       world problems;               connections         remote sensing       for basic GIS
courses in GIS                  mostly GIS/CS                 within (LAN)        with strong skills   applications and
                                with some                     and outside         in GIS data          interacts with
                                disciplinary                  (Internet) the      formats and          solution
                                expertise                     organization; CS    geodetic             developers to
                                                              and GIS balance     referencing          address complex
                                                                                                       spatial problems
(See Beyond Mapping III, Topic 4, “Where Is GIS Education”)
    Vector to/from Raster (direct calculation)
V to R– burning the points, lines and areas into the grid (fat, thin and split)

    R to V– connecting grid centroids, sides and edges (line smoothing)           (Berry)
                   Vector to Raster (centroid implied)
  V to R– uses a point file of cell centroids and converts polygon features that intersect
   Implied Grid with Centroids                Centroid Point File
                                                                                     Vector Map (polygons)

                                                                                     …as the
                                                                                    points fall

Note: this technique
is very sensitive to
cell size (features                                       The corresponding
smaller than cells)                                       grid cell is assigned
and complexity of                                         the value of the
                                                          “point in polygon
boundary shape
…but it is really fast

                                                                                  Polygons with Overlaid Points
                                 Raster Map                                                                       (Berry)
          Exporting MapCalc Data Layers

                                  ESRI GridASCII Format

   just for fun (you are
having fun, right?)—
Export the MapCalc Tutor25.rgs        …browse to an
Elevation map layer in both        appropriate folder and
                                     Save exported file
ESRI GridASCII format and
Surfer ASCII format

                                   Surfer ASCII Format
Grid-based Data Structures/Formats (Esri .asc)
   …open the ELEV.asc file in Notepad to see the data structure (stored as
       an Individual File) <export Elevation as ESRI_elevation.asc and open in NotePad>
                                                                           Map Data (Bottom portion)

                                                        Origin is upper-
                                                        left corner

                                                        …values along
                                                        the row, left to
                                                        right in a block
   General Information (“header” first 6 records)       Each block
                                                        contains all of
                                                        the map values
                       #Col                             for a row
                       Longitude of LL corner
                       Latitude of LL corner
                       Cell size (in decimal degrees)
                       No Data value (null)
                                                        …next row up
                                                        …repeat for all
                                                        rows (625 total)

Grid-based Data Structures/Formats (Surfer .grd)
       …open the ELEV.grd file in Notepad to see the data structure
  (stored as an Individual File) <export Elevation as Surfer_elevation.grd and open in NotePad>

                                                                         Map Data (Bottom portion)

                                                    Origin is lower-
                                                    left corner

                                                    …values along
                                                    the row, left to
                                                    right in a block
   General Information (“header” first 5 records)   Each block
                                                    contains all of
                                                    the map values
                         File Type
                         #Row #Col                  for a row
                         Lon/Lat LL and UR
                         Min and Max Value
                                                    …next row up
                                                    …repeat for all
                                                    rows (625 total)

Grid-based Data Structures/Formats (MapCalc .rgs)
            …open the Tutor25.rgs in Notepad to see the data structure
         (stored as a Data Table)                     …open Tutor25.rgs in Notepad

                                                                      Map Data (Bottom portion)

                                                   Origin is lower-
                                                   left corner

                                                   …values for all
                                                   columns along
                                                   the row, left to
                                                   right (25)

                                                   Each column
General and Map Legend Information (top portion)   contains all of
                                                   the map values
                                                   for a layer

                                                   …next row up
                                                   …repeat for all
                                                   rows (625 total)


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