Introduction to GIS Modeling Week 3 — Reclassifying and Overlaying Maps GEOG 3110 –University of Denver Suitability Modeling Logic Reclassifying Maps (position, initial value, size, shape and contiguity) Overlaying Maps (point-by-point, region-wide and map-wide) Presented by Joseph K. Berry W. M. Keck Scholar, Department of Geography, University of Denver …but we didn’t finish last week’s material!!!

Display Settings for Grid-based Maps Let’s look at some example displays in the Bighorn.rgs data base… (Berry)

Reclassify and Overlay Operations Covertype (Input map)Covertype_size (Output map) Size (Command) SIZE Covertype FOR Covertype_size …make sure your map display is “appropriate” –not simply the default (Berry)

Evaluating Habitat Suitability Manual Map Overlay (Binary) Ranking Overlay (Binary Sum) Rating Overlay (Rating Average) Generating maps of animal habitat… (digital slide show Hugag) Hugag Assumptions – Hugags like… gentle slopes, gentle slopes, southerly aspects, and southerly aspects, and lower elevations lower elevations (See Beyond Mapping III online book, “Topic 23” for more information) Topic 23Topic 23 (Berry)

Covertype Water Mask 0= No, 1= Yes Habitat Rating 0= No-go 1 to 9 Good Constraint Map SolutionMap Habitat Rating Bad 1 to 9 Good (Times 1) (1) (1) Conveying Suitability Model Logic (See Beyond Mapping III online book, “Topic 22” for more information) Topic 22Topic 22 InterpretedMaps gentle slopes Slope Preference Bad 1 to 9 Good Aspect Preference Bad 1 to 9 Good Elevation Preference Bad 1 to 9 Good southerly aspects lower elevations Derived Maps Slope Aspect Base Maps Elevation …while Reclassify and Overlay commands are not very exciting, they are some of the most frequently used operations FactJudgment CalibrateAlgorithmWeight Rows  Model Criteria Columns  Analysis Levels Levels (Berry) Reclassify Overlay Lines  Processing Steps Processing Steps (Commands) (Commands)

Extending Model Criteria Additional criteria can be added… forests Forest Preference Bad 1 to 9 Good Forest Proximity Forests —Hugags would prefer to be in/near forested areas water Water Preference Bad 1 to 9 Good Water Proximity Water —Hugags would prefer to be near water —Hugags are 10 times more concerned with slope, forest and water criteria than aspect and elevation (Times 10) (10) (10) (1) (1) (Berry) Habitat Rating Bad 1 to 9 Good gentle slopes Slope Preference Bad 1 to 9 Good Aspect Preference Bad 1 to 9 Good Elevation Preference Bad 1 to 9 Good southerly aspects lower elevations Slope Aspect Elevation Lines  Processing Steps Processing Steps (Commands) (Commands) Rows  Model Criteria Columns  Analysis Levels Levels

Optional Questions 3-1) Flowchart of Binary Habitat Model 3-2) “Simply” and “Completely” Crosstab Tables 3-3) Average Suitability Rating for each Covertype parcel Using PowerPoint as a “graphics package” 3-4) Average and Coefficient of Variation maps for the 200 foot contour polygons of Elevation (statistical model) 3-5) Average Wildfire Fuel Loading index for each management District (mathematical model) (Berry)

Creating a Flowchart (using PowerPoint) Under the Home tab, 1) use the Rectangle drawing tool to create and size a box to represent a map in the flowchart and 2) use the Text box drawing tool to enter the map name in the Rectangle. Select both and use Format  Group to group the two objects. Enter map title 12 Enter other map title Slope Copy and Paste the Rectangle to form other maps. Use the Line drawing tool to connect the boxes. Use the Text box drawing tool to enter the command, rotate and place over the Line. Enter yet another map title Repeat the process to add additional maps (boxes) and processing steps (lines) to complete the flowchart containing the logic of the GIS model. There are a lot of other things you can do to make the graphic a bit more unique, such as borders, transparency, shadowing and animation (viewed as a slide show). Also, keep in mind that Format  Align can be used to align multiple graphic objects if things get out of whack. (Berry)

Compound Graphic (Campground model results) Use SnagIt to capture one of the graphic elements, such as the S_Pref map then Paste and Size at the appropriate location on the “canvas” (white background shape). Repeat for all of the other graphic elements. Use the Text Box tool to embed text as appropriate. Group the figure elements in logical groupings and then use the Custom Animation tool to control their sequencing for display if you intend to present as a PowerPoint slide deck. Campground Suitability (Berry)

Big Picture of Map Analysis and Modeling Nanotechnology GEOTECHNOLOGY Biotechnology Global Positioning System GEOGRAPHIC INFORMATION SYSTEMS Remote Sensing ANALYSIS and MODELIN G (Grid-based) Mapping and Geo-query (Vector-based) SPATIAL ANALYSIS (Geographic Relationships) SPATIAL STATISTICS (Numeric Relationships) Reclassify and Overlay Distance and Neighbors Surface Modeling Spatial Data Mining GISer’sPerspectives Week 3 Week 4 Week 5 GIS Modeling Weeks 6 and 7 Week 8 Week 9 Future Directions Week 10 Mathematician’s Perspective: Basic GridMath & Map Algebra Advanced GridMath Map Calculus Map Geometry Plane Geometry Connectivity Solid Geometry Connectivity Unique Map Analytics Math/StatPerspectives (SpatialSTEM) Statistician’s Perspective: Basic Descriptive Statistics Basic Classification Map Comparison Unique Map Statistics Surface Modeling Advanced Classification Predictive Statistics See Topic 30, Beyond Mapping IIITopic 30 (Berry)

Grid-Based Map Analysis Spatial analysis investigates the “contextual” relationships in mapped data… Reclassify — reassigning map values (position; value; size, shape; contiguity) Reclassify — reassigning map values (position; value; size, shape; contiguity) Overlay — map overlay (point-by-point; region-wide; map-wide) Overlay — map overlay (point-by-point; region-wide; map-wide) Distance — proximity and connectivity (movement; optimal paths; visibility) Distance — proximity and connectivity (movement; optimal paths; visibility) Neighbors — ”roving windows” (slope/aspect; diversity; anomaly) Neighbors — ”roving windows” (slope/aspect; diversity; anomaly) Data mining investigates the “numerical” relationships in mapped data… Descriptive — aggregate statistics (e.g., average/stdev, similarity, clustering) Descriptive — aggregate statistics (e.g., average/stdev, similarity, clustering) Predictive — relationships among maps (e.g., regression) Predictive — relationships among maps (e.g., regression) Prescriptive — appropriate actions (e.g., optimization) Prescriptive — appropriate actions (e.g., optimization) Surface modeling maps the spatial distribution and pattern of point data… Map Generalization — characterizes spatial trends (e.g., titled plane) Map Generalization — characterizes spatial trends (e.g., titled plane) Spatial Interpolation — deriving spatial distributions (e.g., IDW, Krig) Spatial Interpolation — deriving spatial distributions (e.g., IDW, Krig) Other — roving window/facets (e.g., density surface; tessellation) Other — roving window/facets (e.g., density surface; tessellation) Spatial statistics Weeks 3,4,5 Weeks,8,9 (Berry)

…recall Map Analysis organization and evolution discussion from Week 1 class presentation/reading (GIS Modeling Framework paper) GIS Modeling FrameworkGIS Modeling Framework An Analytic Framework for GIS Modeling Reclassify operations involve reassigning map values to reflect new information about existing map features (Berry)

Reclassifying Maps (Berry)

CLUMP -- Assigns new values to contiguous groups of cells within each map category. CONFIGURE -- Assigns new values characterizing the shape of the area associated with each category. RENUMBER -- Assigns new values to the categories of a map. SIZE -- Assigns new values according to the size of the area associated with each map category. SLICE -- Assigns new values by dividing the range of values on a map into specified intervals (contouring). The most frequently used map analysis operation …and one of the most dangerous!!! ContiguityShape InitialValue Size InitialValue (Berry)

Renumber Operation Renumber — assigns new values to the categories of a map. RENUMBER Elevation ASSIGNING 1 TO 500 THRU 1800 ASSIGNING 1 TO 500 THRU 1800 ASSIGNING 0 TO 1800 THRU 2500 ASSIGNING 0 TO 1800 THRU 2500 FOR E_Pref FOR E_Pref …context Help provides information on function and use of operations …context Help provides information on function and use of operations MapCalc ManualMapCalc Manual …any real number from -3.4E 38 to + 3.4E 38 can be assigned to any existing value on a map …often integer values are assigned based on user reasoning (as in this example) Note: PMAP_NULL is a special value that can be assigned indicating “no data” and the grid location will be ignored in processing and display (Berry)

Slice Operation Slice — assigns new values by dividing the range of values on a map into specified intervals (“Equal Ranges” contouring) … Slice is often used to collapse a map with a large set of map values to just a few intervals for a quick view of the pattern of the spatial data distribution …a user can specify the minimum and maximum values of the range– SLICE Elevation INTO 20 SLICE Elevation INTO 20 FROM 1000 THRU 1200 ZeroFill FROM 1000 THRU 1200 ZeroFill FOR Relief_10ft FOR Relief_10ft …Map Range = Max_Value – Min_Value = 2500 – 500= 2000 feet = 2500 – 500= 2000 feet …Contour Interval = Map Range / # ranges = 2000 / 20 = 100 feet = 2000 / 20 = 100 feet SLICE Elevation into 20 FOR Relief_100ft (Berry)

Size Operation …the Size operation assigns the number of cells comprising each map region (category/value) …in this instance there are three map regions (Open Water= 1, Meadow= 2, Forest= 3)– note that Water occurs at two different places. …to calculate the actual area of each map region multiply the size map times the area per grid cell– 10,000 m 2 or 1 ha in this case …to calculate the size/area of each occurrence you must first Clump the map “regions”, then use the Size command Size — assigns new values according to the size of the area associated with each map category. SIZE Covertype FOR Coverype_size (Berry)

Clump Operation …a map “category” identifies all locations with the same characteristic or condition– e.g., Open Water, Meadow, Forest …a “clump” is a contiguous group (individual spatial instance of a map “category”)–e.g., five cover type clumps with two instances of Open Water Clump — assigns new values to contiguous groups of cells within each map category. CLUMP Covertype AT 1 DIAGONALLY FOR Coverype_clumps “At” identifies how far to reach in defining clumps “Orthogonally” reaches horizontally and vertically only; “Diagonally” includes off angles (Berry)

Configure Operation Spatial Integrity Configure — assigns new values characterizing the shape and integrity of the area associated with each map category. Boundary Configuration Edge cells CONFIGURE Covertype Edges FOR Covertype_edges FOR Covertype_edges Convexity is the ratio of the Edge to the Area (Size) and normalized to that of a circle of the same area Euler = (# Holes) – (1-#Fragments) (Berry)

Some Reclassifying Things to Keep in Mind The Covertype map contains Nominal data that is Discretely (Choropleth) distributed in geographic space. As such, it is best displayed in 2D using cells (Grid) and with layer mesh on as the stored values do not form gradients in either numerical or geographic space. The Size command assigns new values according to the size of the area (# of cells) associated with each map category. In this instance the input map is Covertype (Nominal/Discrete data) and the output map is Covertype_size (Ratio/Discrete data). The size algorithm “counts” the number of cells for each map category (stored map value). …identifies that “one cell in size” elevation values occur in 64% of the map area (384/1= 384 times; each value is unique). “Three cells in size” areas occur in 2.88% of the analysis window (18/3= 6 times; six sets of the same value). Size works on Nominal data (Categorical) but usually is not appropriate for ratio data as far to many values (decimal places); results in most of the map being assigned the cell size value of 1 because elevation values with decimal points rarely are the same. For example, sizing the Elevation map… (Berry)

An Analytic Framework for GIS Modeling Overlay operations involve characterizing the spatial coincidence of mapped data …recall Map Analysis organization and evolution discussion from Week 1 class presentation/reading (GIS Modeling Framework paper) GIS Modeling FrameworkGIS Modeling Framework (Berry)

Overlaying Maps (conceptual approaches) (Berry)

Overlaying Maps (accessing the data) Overlaying maps involves one of four basic techniques for accessing/organizing geo-registered data for analysis— (Tomlin’s organizational framework) Local …collects data on a cell-by-cell basis and reports a single value on a cell-by-cell basis “Spearing” Map1 Map2 Focal …collects data on a neighborhood basis and reports a single value on a cell-by-cell basis “Funneling” Map1 Map2 Global …collects data on a map-wide basis and reports results on a map-wide or cell-by-cell basis “Plunging” Map1 Map2 Entire Area Zonal …collects data on a region-wide basis and reports summary on a region-wide basis “Lacing” Map1 Map2 Template Map (Berry)

Overlaying Maps COMPOSITE -- Creates a map summarizing values from one map which coincide with the categories of another. CALCULATE and COMPUTE -- Creates a map as the mathematical or statistical function of two or more maps. COVER -- Creates a new map where nonzero values of the top map replace the values on the previous (bottom) map, or stack of maps. CROSSTAB -- Generates a spatial coincidence table of two maps. INTERSECT -- Creates a map that assigns new values to pair-wise combinations of values on two maps. …true “map-ematics” Region-widePoint-by-Point Point-by-Point Point-by-Point Point-by-Point …Map-wide overlay involves spatial statistics (spatial data mining) (Berry)

Compute/Calculate Operation All of the basic mathematical operations on a typical pocket calculator can be performed on grid maps… …including Add, Subtract, Multiply, Divide, Exponentiation, Square, Square Root, Max, Min, And, Or, & Trig functions …other math operations? …other math operations? …in this example one map is multiplied by 10 then added to another map, thereby creating a 2-digit code indicating the first map’s categories as the tens digit followed by the second map’s categories as the one’s digit Compute/Calculate — creates a new map as the mathematical function of two or more maps. COMPUTE Covertype TIMES 10 Plus Water FOR Coverype_Water CALCULATE ((Covertype * 10) + Water) FOR Covertype_Water (Berry)

Crosstab — generates a spatial coincidence table of two maps. Map1 = Districts Map2 = Covertype Crosstab Operation …the maps are compared “cell-by-cell” and the number of joint occurrences between the map categories are summarized in a table CROSSTAB Districts WITH Covertype Simply TO Newtextfile.txt In this example there are… 58 cells classified as District 1 on the Districts map 58 cells classified as District 1 on the Districts map 82 cells classified as Open Water on the Covertype map 82 cells classified as Open Water on the Covertype map 58 cells identified as having the joint condition of District 1 and Open Water representing 9.28 percent of the entire map area. 58 cells identified as having the joint condition of District 1 and Open Water representing 9.28 percent of the entire map area. Note: all of the District 1 cells are in Open Water Note: all of the District 1 cells are in Open Water Optional Question 3-2(Berry)

Intersect Operation …if “completely” is specified all combinations are automatically identified using unique sequential numbering for map values Note: Intersect is similar to geo-query operations in desktop mapping packages by identifying all locations having specified category (map-value) combinations …“zerofill” assigns 0 to all combinations that are not specified … “oldfill” retains 1 st map values for non-specified combinations Intersect — creates a map that assigns new values to pair- wise combinations of values on two maps. Map 1 = Districts Map 2 = Covertype The maps are compared “cell-by-cell” and a user specified number is assigned to designated category combinations… INTERSECT Districts WITH Covertype ASSIGN 1 to 1, 1 Zerofill FOR Districts1_Cover1 (Berry)

Cover — creates a new map where the non-zero values of the top map replace the values on the previous (bottom) map, or stack of maps. 4 Water 4 Cover 1 Water Covertype Cover Operation …in the example coincidence 4,1  4 because 4 is non-zero and replaces what is beneath it …0,3  3 because zero is ignored and does not replace the previous value in the map stack …the maps are compared “cell-by-cell” and the value in the top-most cell replaces the previous values unless that value is zero, then the top most non-zero value in the map stack is retained (Berry)

Composite Operation …data summary procedures include Average, Standard deviation, Average, Standard deviation, Coefficient of variation, Total, Coefficient of variation, Total, Maximum, Minimum, Median Maximum, Minimum, Median Majority, Minority, Diversity, Majority, Minority, Diversity, Deviation and Proportion Deviation and Proportion “Cookie-cutter” Template Map Data Map Composite — creates a map summarizing values from one map that coincide with the categories (termed regions) identified on another map …the regions identified by category values on one map serve as cookie-cutter shapes (Template map) for summarizing data contained on another map (Data map) COMPOSITE Districts WITH Slope Average IGNORE PMAP_NULL FOR Districts_avgSlope (Berry)

Thematic Mapping (Average elevation by district) Best Worst Average Elevation of Districts “Thematic Mapping” (Discrete Spatial Object) (0)(39) (9) (29) (21) (9) (24) …include Coffvar in Thematic Mapping results (Berry)

Map Accuracy (Error Propagation– simple overlay) Soil Type Forest Type Joint Probability — likelihood of two conditions occurring together… VectorRaster P(x,y) = P(x) * P(y) …evaluated cell-by-cell P(x) P(y)P(x,y) Joint Probability (See Beyond Mapping II, “Topic 4, “Toward and Honest GIS”) Beyond Mapping IIBeyond Mapping II Topological Overlay Coincidence Search 100% certain everywhere in the derived polygon? IntersectPolygons Spatial Table Attribute Table JoinData Believable? (digital slide show Honest) Honest (Berry)