1. Calculating Visual Connectivity …an animated series of slides demonstrating 2D and 3D visual connectivity from increasing viewer height (0’ to 20,000’) Prepared by Joseph K. Berry Keck Scholar in Geosciences, University of Denver Principal, Berry & Associates // Spatial Information Systems (BASIS) Fort Collins — jberry@innovativegis.comjberry@innovativegis.com Website www.innovativegis.com/basis

2. Digital Elevation Model (DEM) (Grid Surface configured as 466 rows by 327 columns with 30m cells ) North  0 miles 6 miles 466 row 327 col First Ridge 6,312 Feet Second Ridge 7,799 Feet + + Mount St. Helens Topography (project area) Raster Image 7,799 Feet 6,312 Feet Viewer Location 3,219 feet Point of Interest 3,267 feet

3. Viewer Elevation 3,219 Feet Seen Not Seen (300c, 114r) Point of Interest Viewer Location (33c, 454r). Viewshed at 0 feet rise North  0 miles 6 miles Point of Interest Viewer Location + First Ridge Elevation (134c, 325r) 6,312 Feet First Ridge + Minimum Visible Elevation 11,380 Feet Calculating Visual Connectivity (Approach) Similar triangles can be used to determine the minimum POI height needed to be visibly connected … Tangent = Rise / Run 1 POI Elevation = (Tangent * Run 2 ) + Viewer Elevation Similar triangles can be used to determine the minimum POI height needed to be visibly connected … Tangent = Rise / Run 1 POI Elevation = (Tangent * Run 2 ) + Viewer Elevation Rise Run 2 Run 1 POI Height N

4. Viewer Elevation 3,219 Feet Seen Not Seen (300c, 114r) Point of Interest Viewer Location (33c, 454r). Viewshed at 0 feet rise North  0 miles 6 miles Point of Interest Viewer Location + First Ridge Elevation (134c, 325r) 6,312 Feet First Ridge + Minimum Visible Elevation 11,380 Feet Calculating Visual Connectivity (Approach) N Similar triangles can be used to determine the minimum POI height needed to be visibly connected … Tangent = Rise / Run = (6312 ft – 3219 ft) / (SQRT[(134 – 33) 2 + (454 – 325) 2 ] * 98.4251 ft) = 3093 ft / (163.835 * 98.4251 ft) = 3893 ft / 16125 ft = 0.1918 Height = (Tangent * Run) + Viewer Height = (0.1918 * (SQRT[(300 – 33) 2 + (454 – 114) 2 ] * 98.4251 ft)) + 3219 ft = (0.1918 * 432.307 * 98.4251 ft) + 3219 = 11,380 Feet Similar triangles can be used to determine the minimum POI height needed to be visibly connected … Tangent = Rise / Run = (6312 ft – 3219 ft) / (SQRT[(134 – 33) 2 + (454 – 325) 2 ] * 98.4251 ft) = 3093 ft / (163.835 * 98.4251 ft) = 3893 ft / 16125 ft = 0.1918 Height = (Tangent * Run) + Viewer Height = (0.1918 * (SQRT[(300 – 33) 2 + (454 – 114) 2 ] * 98.4251 ft)) + 3219 ft = (0.1918 * 432.307 * 98.4251 ft) + 3219 = 11,380 Feet

5. 3,219 + 500 = 3,719 Feet Seen Viewshed at 500 feet rise Point of Interest Viewer Location. First Ridge 6,312 Feet North  0 miles 6 miles + + …an animated series of “viewsheds” from increasing viewer heights demonstrates the importance of a 3-dimensional GIS …advance slides for 1000’ viewer height increases  Visual Connectivity (500’ above the terrain) N

6. 3,219 + 1,000 = 4,219 Feet Seen North  0 miles 6 miles Second Ridge Elevation (187c, 258r) 7,799 Feet Viewshed at 1000 feet rise Point of Interest Viewer Location. Second Ridge + + Visual Connectivity (1000’ above the terrain) N

7. 3,219 + 2,000 = 5,219 Feet Seen North  0 miles 6 miles Second Ridge 7,799 Feet Viewshed at 2000 feet rise Point of Interest Viewer Location. + + Visual Connectivity (2000’ above the terrain) N

8. 3,219 + 3,000 = 6,219 Feet Seen North  0 miles 6 miles Viewshed at 3000 feet rise Point of Interest Viewer Location. + + Second Ridge 7,799 Feet Visual Connectivity (3000’ above the terrain) N

9. 3,219 + 4,000 = 7,219 Feet Seen North  0 miles 6 miles Viewshed at 4000 feet rise Point of Interest Viewer Location. + + Second Ridge 7,799 Feet Visual Connectivity (4000’ above the terrain) N

10. 3,219 + 5,000 = 8,219 Feet Seen North  0 miles 6 miles Viewshed at 5000 feet rise Point of Interest Viewer Location. + + Second Ridge 7,799 Feet Visual Connectivity (5000’ above the terrain) N

11. 3,219 + 6,000 = 9,219 Feet Seen Viewshed at 6000 feet rise Point of Interest Viewer Location. North  0 miles 6 miles + + Second Ridge 7,799 Feet Visual Connectivity (6000’ above the terrain) N

12. 3,219 + 7,000 = 10,219 Feet Seen Viewshed at 7000 feet rise Point of Interest Viewer Location. North  0 miles 6 miles + + Second Ridge 7,799 Feet Visual Connectivity (7000’ above the terrain) N

13. 3,219 + 8,000 = 11,219 Feet Seen Viewshed at 8000 feet rise Point of Interest Viewer Location. North  0 miles 6 miles + + Second Ridge 7,799 Feet Visual Connectivity (8000’ above the terrain) N

14. 3,219 + 9,000 = 12,219 Feet Seen Viewshed at 9000 feet rise Point of Interest Viewer Location. North  0 miles 6 miles + + Second Ridge 7,799 Feet Visual Connectivity (9000’ above the terrain) N

15. 3,219 + 10,000 = 13,219 Feet Seen Viewshed at 10000 feet rise Point of Interest Viewer Location. North  0 miles 6 miles + + Second Ridge 7,799 Feet Visual Connectivity (10000’ above the terrain) N

16. 3,219 + 11,000 = 14,219 Feet Viewshed at 11000 feet rise Point of Interest Viewer Location. Surface Seen + North  0 miles 6 miles + Second Ridge 7,799 Feet Visual Connectivity (11000’ above the terrain) Tangent = 0, therefore POI surface location is seen N

17. 3,219 + 11,000 = 14,219 Feet. Viewer Location Representing Geographic Space (2D and 3D) Visual Exposure (VE) …a count of the number of times seen from specified viewer positions (0 – 11,000 feet above the terrain) 2D Plane (Pixel) 1 Seen 1 Time All surface locations are assigned a VE value Increasing Viewer Height (1000’ increments) …from 0 Feet Viewer Height Seen 12 times 3D Volume (Voxel) 12 All volume locations are assigned a VE value 3-D Grid Data Structure is a direct expansion of the 2D structure with X, Y and Z coordinates defining the position in a 3-dimensional data matrix plus a value representing the characteristic or condition (attribute) associated with that location. Point of Interest

18. 3,219 + 12,000 = 15,219 Feet Viewshed at 12000 feet rise Viewer Location. North  0 miles 6 miles …continue advancing slides for viewsheds of viewer height increases to 20,000’ Visual Connectivity (12000’ above the terrain) N

19. 3,219 + 13,000 = 16,219 Feet Viewshed at 13000 feet rise Viewer Location. North  0 miles 6 miles Visual Connectivity (13000’ above the terrain) N

20. 3,219 + 14,000 = 17,219 Feet Viewshed at 14000 feet rise Viewer Location. North  0 miles 6 miles Visual Connectivity (14000’ above the terrain) N

21. 3,219 + 15,000 = 18,219 Feet Viewshed at 15000 feet rise Viewer Location. North  0 miles 6 miles Visual Connectivity (15000’ above the terrain) N

22. 3,219 + 16,000 = 19,219 Feet Viewshed at 16000 feet rise Viewer Location. North  0 miles 6 miles Visual Connectivity (16000’ above the terrain) N

23. 3,219 + 17,000 = 20,219 Feet Viewshed at 17000 feet rise Viewer Location. North  0 miles 6 miles Visual Connectivity (17000’ above the terrain) N

24. 3,219 + 18,000 = 21,219 Feet Viewer Location. Viewshed at 18000 feet rise North  0 miles 6 miles Visual Connectivity (18000’ above the terrain) N

25. 3,219 + 19,000 = 22,219 Feet Viewer Location. North  0 miles 6 miles Visual Connectivity (19000’ above the terrain) N Viewshed at 19000 feet rise

26. 3,219 + 20,000 = 23,219 Feet Viewer Location. North  0 miles 6 miles Visual Connectivity (20000’ above the terrain) N Viewshed at 20000 feet rise