GEOG 400, Advanced GIS, Fall 2020; Week 6 Lecture 2

Transcript

1. GEOG 400: Advanced GIS - Raster Week 6 – Lecture 2 Global Raster Operations
2. GEOG 400: Advanced GIS - Raster 1. Local Operations 4. Global Operations 2. Focal Operations 3. Zonal Operations There are four types of raster operations we’ll discuss this week and next: Operations that work on single cell locations one at a time Operations that work on cells within a neighborhood Operations that work on cells within particular zones Operations that work on all cells within the raster at the same time
3. GEOG 400: Advanced GIS - Raster 1. Local Operations 4. Global Operations 2. Focal Operations 3. Zonal Operations There are four types of raster operations we’ll discuss this week and next: Operations that work on single cell locations one at a time Operations that work on cells within a neighborhood Operations that work on cells within particular zones Operations that work on all cells within the raster at the same time
4. 1. Local analyses A spatial/mathematical operation is performed on every single cell, individually, independent of surrounding cells 81 59 2 65 35 50 53 73 82 23 97 47 48 72 39 38 input raster operation [divide by 2] output raster 40.5 29.5 1 32.5 17.5 25 26.5 36.5 41 11.5 48.5 23.5 24 36 19.5 19 There are four types of raster operations we’ll discuss this week and next:
5. 81 59 2 65 35 50 53 73 82 23 97 47 48 72 39 38 input raster operation [mean] output raster 53.6 neighborhood 2. Focal analyses A spatial/mathematical operation is performed on every single cell, individually, based on some pre-defined neighborhood There are four types of raster operations we’ll discuss this week and next:
6. [mean] 53.6 53.6 53.6 53.6 53.6 53.6 53.6 53.6 53.6 3. Zonal analyses A spatial/mathematical operation is performed on groups of cells at the same time, based on some pre-defined neighborhood There are four types of raster operations we’ll discuss this week and next: input raster operation output raster neighborhood 81 59 2 65 35 50 53 73 82 23 97 47 48 72 39 38
7. • Introduction • We’ve now covered local analyses • Raster analyses where some operation is performed on every cell independent of any other cell • e.g. reclassification, conditional analyses, map algebra
8. • Introduction • We’ve now covered local analyses • Raster analyses where some operation is performed on every cell independent of any other cell • e.g. reclassification, conditional analyses, map algebra • We’ve now covered focal analyses • Raster analyses where some operation is performed on every cell based on the cells that surround it in some pre-defined neighborhood size and shape • e.g. focal mean, max, min, range, majority, etc.
9. • Introduction • We’ve now covered local analyses • Raster analyses where some operation is performed on every cell independent of any other cell • e.g. reclassification, conditional analyses, map algebra • We’ve now covered focal analyses • Raster analyses where some operation is performed on every cell based on the cells that surround it in some pre-defined neighborhood size and shape • e.g. focal mean, max, min, range, majority, etc. • We’ve now covered zonal analyses • Raster analyses where some operation is performed on every cell within some set of fixed geometric features (zones) of interest • e.g. zonal mean, max, min, range, majority, etc.
10. • Introduction • The most common type of global analysis is distance analysis • Other types include watershed analysis and viewshed analysis, but we’ll talk about them later 81 59 2 65 35 50 53 73 82 23 97 47 48 72 39 38 input raster operation [distance from cell R1C1] output raster 0 1 2 3 1 1.4 2.2 3.2 2 2.2 2.8 3.6 3 3.2 3.6 4.2 Global Operations in ArcGIS
11. • Types of distance • There are two primary types of distance used in global analyses: • Unweighted distance • Distance measure where only the x and y coordinates of source/destination matter • “level playing field” distance • Weighted distance • Distance measure where both x-y distance and some sort of impedance measure (cost) are considered • “unlevel playing field” distance unweighted distance weighted distance Global Operations in ArcGIS
12. • Types of distance • There are two primary types of distance used in global analyses: • Unweighted distance • Distance measure where only the x and y coordinates of source/destination matter • “level playing field” distance weighted distance Global Operations in ArcGIS unweighted distance
13. • Unweighted distance • (Believe it or not) there are several different ways to calculate unweighted distance 1.41 1 1.41 1 1 1.41 1 1.41 Euclidean distance 1 1 1 1 1 1 1 1 Chebyshev distance 2 1 2 1 1 2 1 2 Manhattan distance Global Operations in ArcGIS
14. • Unweighted distance • Euclidean distance • This is the distance measure we are most familiar with • The “truest” representation of distance in continuous x-y space • Can be calculated in n dimensions • In GIS world, 2D 1.41 1 1.41 1 1 1.41 1 1.41 Euclidean distance = 2 − 1 2 + 2 − 1 2 Global Operations in ArcGIS
15. • Unweighted distance • Euclidean distance • Example • Find the distance between a and b = 2 − 1 2 + 2 − 1 2 y x a b Global Operations in ArcGIS
16. • Unweighted distance • Euclidean distance • Euclidean distance in continuous space Global Operations in ArcGIS
17. • Unweighted distance • Chebyshev distance • Also known as “chessboard distance”, as in the movements of a king piece in chess • Not nearly as common as Euclidean distance • More common in statistics, measuring similarity or difference between variables 𝐶𝐶𝐶𝐶 = max 2 − 1 , 2 − 1 1 1 1 1 1 1 1 1 Chebyshev distance Global Operations in ArcGIS
18. • Unweighted distance • Chebyshev distance • Example • Find the distance between a and b 𝐶𝐶𝐶𝐶 = max 2 − 1 , 2 − 1 y x a b Global Operations in ArcGIS
19. • Unweighted distance • Chebyshev distance • Chebyshev distance in continuous space Global Operations in ArcGIS
20. • Unweighted distance • Manhattan distance • Also known as “taxicab distance”, as in the movements of cabs in the streets of NY (or any gridded city) • More common than Chebyshev, less common than Euclidean 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀 = 2 − 1 + 2 − 1 2 1 2 1 1 2 1 2 Manhattan distance Global Operations in ArcGIS
21. • Unweighted distance • Manhattan distance • Example • Find the distance between a and b 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀 = 2 − 1 + 2 − 1 y x a b Global Operations in ArcGIS
22. • Unweighted distance • Manhattan distance • Manhattan distance in continuous space Global Operations in ArcGIS
23. • Unweighted distance • The only one of these three built into ArcGIS is Euclidean Distance • Implemented in the Euclidean Distance tool Global Operations in ArcGIS
24. • Unweighted distance • Example • Only one input (and parameters) Global Operations in ArcGIS
25. • Unweighted distance • Example • Results Global Operations in ArcGIS
26. • Unweighted distance • Example • Results Global Operations in ArcGIS
27. • Types of distance • There are two primary types of distance used in global analyses: • Unweighted distance • Distance measure where only the x and y coordinates of source/destination matter • “level playing field” distance • Weighted distance • Distance measure where both x-y distance and some sort of impedance measure (cost) are considered • “unlevel playing field” distance unweighted distance weighted distance Global Operations in ArcGIS
28. • Types of distance • There are two primary types of distance used in global analyses: • Unweighted distance • Distance measure where only the x and y coordinates of source/destination matter • “level playing field” distance • Weighted distance • Distance measure where both x-y distance and some sort of impedance measure (cost) are considered • “unlevel playing field” distance unweighted distance weighted distance Global Operations in ArcGIS
29. • Weighted distance • Weighting can be thought of in any number of ways in GIS… • Increased distance • e.g. traveling up a steep slope will effectively increase the distance traveled (c = sqrt(a2 + b2) • Increased “cost” • “cost” used to describe a variety of factors in GIS • Effort – e.g. physical toll it takes to travel over rough terrain • Difficulty – e.g. logistical challenge associated with navigating through an environment • Time – e.g. time it will take to build a trail through dense vegetation • Actual Cost – e.g. cost it will take to build a pipeline through varying property values • Other words for cost include impedance and friction Global Operations in ArcGIS
30. • Weighted distance • Two types of costs/weights/impedances/friction forces ISOTROPIC costs are the same no matter which direction you’re crossing a cell in ANISOTROPIC costs vary depending on the direction in which you’re crossing a cell Global Operations in ArcGIS
31. • Weighted distance • Two types of costs/weights/impedances/friction forces ISOTROPIC ANISOTROPIC Global Operations in ArcGIS
32. • Isotropic costs • In ArcGIS, isotropic costs are simulated using the Cost Distance tool Global Operations in ArcGIS
33. • Isotropic costs • Example • You live in Three Springs • You hate biking along Hwy 160 • You want to build a trail from Three Springs to Fort Lewis College campus • How much is it going to cost? • Cost distance analysis! (what you want to be doing) Global Operations in ArcGIS
34. • Isotropic costs • Example • Need to know: • Property value of all eligible land • Price per whatever raster resolution you’re analyzing • Think of each cell as an individual piece of land • Starting location (aka “Source”) • Three Springs • Ending location (aka “Destination”) • Fort Lewis College • Cheapest path between (what you want to be doing) Global Operations in ArcGIS
35. • Isotropic costs • Example Global Operations in ArcGIS
36. • Isotropic costs • Example Global Operations in ArcGIS
37. • Isotropic costs • Example • Results • Accumulative cost from Three Springs • Notice how costs go up with distance from Three Springs • Also notice how the rate of increase is not at all Euclidean Global Operations in ArcGIS
38. • Isotropic costs • Example • Results • Accumulative cost from Three Springs • Notice how costs go up with distance from Three Spring • Also notice how the rate of increase is not at all Euclidean • Backlink • Insane looking thing that allows you to figure out the least-cost path • Sort of like a cost “aspect” layer – figures out the least-cost neighboring cell for every other cell in the dataset (focal!) Global Operations in ArcGIS
39. • Isotropic costs • Example • To calculate the least-cost path (path of least resistance), we can use the Cost Path tool Global Operations in ArcGIS
40. • Isotropic costs • Example Global Operations in ArcGIS
41. • Isotropic costs • Example • Results • Again, notice how this is definitely not the Euclidean shortest path • But, according to parcel data, it is the least cost path (LCP) • In fact, the resulting attribute table of the LCP contains exactly how much it will cost (assuming you can purchase a bunch of 10x10m areas through other peoples’ properties…) Global Operations in ArcGIS
42. • Isotropic costs • Other examples of isotropic cost • There are many others… • Soil/geology type • Vegetation type • Existing built infrastructure • Habitat/aesthetic value • Protected status • etc. Global Operations in ArcGIS
43. • Weighted distance • Two types of costs/weights/impedances/friction forces ISOTROPIC costs are the same no matter which direction you’re crossing a cell in ANISOTROPIC costs vary depending on the direction in which you’re crossing a cell Global Operations in ArcGIS
44. • Anisotropic costs • Again, whereas isotropic costs don’t have a directionality (e.g. vegetation is dense regardless of movement direction), anisotropic costs are directionally-dependent • The most common example of anisotropy is terrain slope! vs Global Operations in ArcGIS
45. • Anisotropic costs • The anisotropic costs of slope manifest themselves in two ways: • Increased travel distance • By traveling on sloped terrain, you are not simply moving in the x-y direction, you’re also moving up and downhill • a2 + b2 = c2 • Increased travel effort/time • Steeper slopes, generally more physically demanding • However, the effects of uphill travel on effort/time are not identical to those of downhill travel – anisotropy! Global Operations in ArcGIS
46. • Anisotropic costs • Slope distance • “True” measures of ground distance must include the effects of slope • Most distance estimators calculate distance based on x-y alone (e.g. Euclidean distance) • Navigation apps like Google Maps, AllTrails, etc. • Most analyses in ArcGIS Global Operations in ArcGIS
47. • Anisotropic costs • Slope distance • In reality, the effects of slope are fairly negligible for most applications • Durango to Silverton example • Horizontal distance • 48.2 miles • Vertical distance • Silverton: 9318’ • Durango: 6512’ • Difference = 2806’ • Slope distance • sqrt(48.22+0.532) = 48.203 miles • 0.003 miles = 16 feet Durango Silverton 48.2 miles 0.53 miles Global Operations in ArcGIS
48. • Anisotropic costs • Slope distance • However, over shorter (and steeper!) distances, it can make a notable difference… • Haflin Creek trail example • Horizontal distance • 3.8 miles (one way) • Vertical distance • 2916’ • Slope distance • sqrt(3.82+0.552) = 3.84 miles • 0.04 miles = 211 feet • Not huge, but not insignificant! Trailhead Trail end 3.8 miles 0.55 miles Global Operations in ArcGIS
49. • Anisotropic costs • Slope distance • So how is this anisotropic? • A right triangle’s a right triangle, right? • …Yes and no • It is anisotropic because you don’t always have to travel in the direction of slope! • Think about switchbacks… • You’re hiking uphill, but you’re not hiking directly uphill Global Operations in ArcGIS
50. • Anisotropic costs • Slope distance can be analyzed using the Path Distance tool in ArcGIS Global Operations in ArcGIS
51. • Anisotropic costs • Example Global Operations in ArcGIS
52. • Anisotropic costs • Example Global Operations in ArcGIS
53. • Anisotropic costs • Movement in a raster environment • There are three options King’s case (4 directions) Queen’s case (8 directions) Knight’s case (16 directions) (sort of a misnomer..) this is what ArcGIS uses Global Operations in ArcGIS
54. • Anisotropic costs • Slope effects on effort/travel time • Many researchers have attempted to quantify this relationship • All generally say the same thing… • Steeper slopes, up and down, slower movement • For one reason or another, they’re all flawed Global Operations in ArcGIS
55. • Anisotropic costs • Slope effects on effort/travel time • So how do we apply this in ArcGIS?! • Again, using the Path Distance tool – just with a few more parameters Global Operations in ArcGIS
56. • Anisotropic costs • Example Global Operations in ArcGIS
57. • Anisotropic costs • Example Global Operations in ArcGIS
58. • Anisotropic costs • Example Global Operations in ArcGIS
59. • Anisotropic costs • Example Here, you need a text file, containing two columns:  Slope (in degrees) on the left  Time it takes to traverse that slope  So, if your function is in m/s, you need to convert it to s/m  1 divided by your slope-travel rate function Global Operations in ArcGIS
60. • Anisotropic costs • Results travel time from center point black lines represent hours Global Operations in ArcGIS
61. • Anisotropic costs • Other examples of anisotropic cost… • Wind • e.g. the amount of fuel a plane has to expend to fly in head winds vs. tail winds Global Operations in ArcGIS
62. • Anisotropic costs • Other examples of anisotropic cost… • Wind • e.g. the amount of fuel a plane has to expend to fly in head winds vs. tail winds • Ocean currents • e.g. the amount of time it takes a ship to cross the ocean with or against prevailing currents Global Operations in ArcGIS