Grid-based Map Analysis Techniques and Modeling Workshop Part 1 – Maps as Data Part 2– Surface Modeling Part 3 – Spatial Data Mining Part 4 – Spatial Analysis Suitability mapping Measuring effective distance/connectivity Visual exposure analysis Analyzing landscape structure Characterizing terrain features Part 5 – GIS Modeling

Grid-Based Map Analysis 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 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) (Berry)

Generating maps of animal habitat… Evaluating Habitat Suitability (Berry) Assumptions – Hugags like gentle slopes, southerly aspects and lower elevations Manual Map OverlayRanking OverlayRating Overlay

Covertype Water Mask 0= No, 1= Yes Habitat Rating 0= No, 1 to 9 Good Constraint Map Habitat Rating Bad 1 to 9 GoodWeightSolutionMap gentle slopes InterpretedMapsCalibrate 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 AspectAlgorithm Derived Maps Conveying Suitability Model Logic (Berry) Elevation Base Maps FactJudgment (See map Analysis, “Topic 22” for more information) Topic 22Topic 22

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 Extending Model Criteria (Berry) Elevation 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)

Establishing Distance and Connectivity (digital slide show DIST) DIST (Berry)

Orthogonal distances are the same as calculated by the Pythagorean Theorem and align with a circle of a given radius… …other distances contain slight “rounding” errors Point Grid-based Simple Proximity Surfaces (Berry) Proximity Ripples for a large steps away from a starting location align fairly well with an exact circle… with an exact circle… PointsLinesPolygons …an excellent technique for generating simple and effective proximity surfaces respecting absolute and relative barriers to movement from sets of points, lines and polygons (impossible to do with the Pythagorean Theorem ) …but poorly align for small steps

Simple Proximity …as the crow flies Calculating Effective Distance (Demo) (Berry) Effective Proximity …as the crow walks 0= not able to cross 2= two min. to cross 7 = seven min. to cross …the Splash Algorithm is like tossing a rock into a still pond with increasing distance rings that abut and bend around absolute and relative barriers

Generating an Effective Travel-time Buffer (Berry) (a)superimposition of an analysis grid over the area of interest (b)“burns” the store location into its corresponding grid cell (c)“burns” primary and residential streets are identified (d)travel-time buffer derived from the two grid layers

Travel-Time Connectivity (Berry) …increasing distance from a point forms bowl-shaped accumulation surface …steepest downhill path identifies the optimal path– wave front that got there first. …SPREADing from multiple locations identifies catchment areas– locations closest to starting locations …what do you think the ridges represent?

Accumulation Surface Analysis (Berry) (See Map Analysis, “Topic 5” and “Topic 17” for more information) Map AnalysisMap Analysis …increasing distance from a point forms bowl-shaped accumulation surface Simple distance – symmetrical bowl Absolute barrier – abrupt pillars Relative barrier – gradual humps …subtracting two proximity surfaces identifies relative advantage Zero – equidistant Zero – equidistant Sign – which has the advantage Sign – which has the advantage Magnitude – strength of advantage Magnitude – strength of advantage …what would get if you added the two surfaces?

Establishing Visual Connectivity …like measuring proximity, it starts somewhere (starter cell) and moves through geographic space by steps (wave front) evaluating whether the moving tangent is beat— …if so, the location is marked as “seen” and its tangent is assigned as the one to beat Seen if new tangent exceeds all previous tangents along the line of sight— At At Thru ) Thru ) Onto Onto (Berry) Radiate – visual exposure is calculated bay a series of “waves” that carry the tangent to beat. Simply – viewshed Completely – number of “viewers” that see each location Weighted – viewer cell value is added

Calculating Visual Exposure (# Times Seen) Visual exposure identifies how many times each map location is seen from a set of viewer locations (Berry)

Visual Exposure from Extended Features A visual exposure map identifies how many times each location is seen from an “extended eyeball” composed of numerous viewer locations (road network) (Berry)

Weighted Visual Exposure (Sum of Viewer Weights) Different road types are weighted by the relative number of cars per unit of time …the total “number of cars” replaces the “number of times seen” for each grid location (See Map Analysis, Topic 15, “Deriving and Using Visual Exposure Maps” for more information) Map AnalysisMap Analysis (Berry)

Viewshed …as the crow sees (seen or not seen) Calculating Visual Exposure (Demo) (Berry) Visual Exposure …as the flock sees (# times seen) Weighted Visual Exposure …as the flock sees (not all in the flock are the same)

Real-World Visual Analysis Weighted visual exposure map for an ongoing visual assessment in a national recreation area— the project developed visual vulnerability maps from the reservoir in the center of the park and a major highway running through the park. In addition, aesthetic maps were generated based on visual exposure to pretty and ugly places in the park (Senior Honors Thesis by University of Denver Geography student Chris Martin, 2003) (Berry)

Neighborhood Techniques (Covertype Diversity Map) …a DIVERSITY map indicates the number of different map values (categories) that occur within a window… e.g., cover types As the window is enlarged, the diversity generally increases (Berry)

Neighbor Techniques (Demo) Housing Density by Districts Average housing density for each district –SCAN Covertype diversity within 3 for Cover_diversity3 –SCAN Slope coffvar with 2 for Roughness –SCAN Housing total with 5 for Housing_density –RENUMBER Housing_density for High_hdensity assign 0 to 0 thru 15 assign 1 to 15 thru 50 assign 0 to 0 thru 15 assign 1 to 15 thru 50 –COMPOSITE Districts with Housing_density average for Districts_HDavg for Districts_HDavg (Berry)

Neighborhood Variability (Berry) (See MapCalc Applications, “Assessing Cover Type Diversity and Delineating Core Area” and “Assessing Covertype Diversity” for more information) MapCalc ApplicationsMapCalc Applications

Spatial Analysis of Landscape Structure Area Metrics (6), Patch Density, Size and Variability Metrics (5), Edge Metrics (8), Shape Metrics (8), Core Area Metrics (15), Nearest Neighbor Metrics (6), Diversity Metrics (9), Contagion and Interspersion Metrics (2) …59 individual indices (US Forest Service 1995 Report PNW-GTR-351) …59 individual indices (US Forest Service 1995 Report PNW-GTR-351) For example, Area Metrics Area Metrics …Area per patch …Area per patch Shape Metrics Shape Metrics …Shape Index per patch …Shape Index per patch Edge Metrics Edge Metrics …Edge Contrast per patch Size of individual patches is an important first-order assessment of landscape structure The amount and type of edge tracks the nature of the patch interface P/A ratio tracks patch shape… boundaryirregularity(Berry) See for more information (digital slide show FRAG) FRAG (digital slide show NN_statistics) NN_statistics

Grid-Based Map Analysis 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 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) (Berry)