GEOG 400, Advanced GIS, Fall 2020; Week 4 Lecture 2

Transcript

1. GEOG 400: Advanced GIS - Raster Week 4 – Lecture 2 Error Modeling and Change Detection
2. GEOG 400: Advanced GIS - Raster Error and Uncertainty This week, we’ll talk about what we don’t know…and how to deal with it. Last time, we talked about sources of UNCERTAINTY and ERRORS in raster data. Today, we’ll talk about ERROR MODELING and CHANGE DETECTION. How can we communicate errors in our raster analysis?
3. Because our rasters are built from point measurements every raster cell inherits those points’ errors!
5. Not only do these things vary in cost, they vary in accuracy Remotely Sensed/Aerial Surveys: Ground-Based/In Situ Surveys: Boat-Based/Bathymetric Surveys: Airborne light detection and ranging (e.g., lidar): +/- 12-25 cm Aerial photogrammetry: +/- 10-15 cm Total Station: +/- 2-10 cm Real-Time Kinematic Global Positioning System (RTK-GPS): +/- 3-12 cm Terrestrial Lidar: +/- 0.5-4 cm Multibeam and Singlebeam sonar: on par with terrestrial lidar How do we know this? By measuring the same point many times.
6. The whole premise of today’s lecture…raster-based change detection 1. Survey a landscape and make a digital elevation model 2. Come back later and survey it again, make a new DEM 3. Subtract (difference) the two DEMs to calculate landscape change
7. DEM Differencing is Everywhere. Ice Caps in Tibet, Neckel et al., 2013
8. DEM Differencing is Everywhere. Coastal Rivers, Suir et al, 2018
9. DEM Differencing is Everywhere. Oso Landslide, Washington, Lato et al., 2018
10. DEM Differencing is Everywhere. Miniature River, Leduc et al., 2019
11. You’d think it would be simple, right? MINUS THE OLD DEM THE NEW DEM 7 m 23 m 10 m 11 m 10 m 3 m 18 m 22 m -1 m -7 m Wheaton, 2010
12. You’d think it would be simple, right? MINUS THE OLD DEM GIVES US A DEM OF DIFFERENCE THE NEW DEM 7 m 23 m 10 m 11 m 10 m 3 m 18 m 22 m -3 m +1 m +7 m -7 m TOTAL “SEDIMENT BUDGET” = -3 + 7 – 7+ 1 = -2 m3
13. You’d think it would be simple, right? MINUS THE OLD DEM THE NEW DEM 7 m ± 2 m 23 m ± 2 m 10 m ± 2 m 11 m ± 2 m 10 m ± 2 m 3 m ± 2 m 18 m ± 2 m 22 m ± 2 m +3 m ± 2 m -1 m ± 2 m -7 m ± 2 m +7 m ± 2 m
14. You’d think it would be simple, right? MINUS THE OLD DEM GIVES US A DEM OF DIFFERENCE THE NEW DEM 7 m ± 2 m 23 m ± 2 m 10 m ± 2 m 11 m ± 2 m 10 m ± 2 m 3 m ± 2 m 18 m ± 2 m 22 m ± 2 m -3 m ± 2 m +1 m ± 2 m +7 m ± 2 m -7 m ± 2 m TOTAL “SEDIMENT BUDGET” IS -3 + 7 - 7 + 1 = -2 m3 ± 2 m3 Maybe it’s -4 m3, maybe it’s 0 m3
15. Some Landscape Terminology 18 m ± 2 m 22 m ± 2 m +3 m ± 2 m -1 m ± 2 m -7 m ± 2 m +7 m ± 2 m …OR: - scour - degradation …OR: - accumulation - aggradation DEPOSITION (+) EROSION (-) NO CHANGE The loss of sediment from a place The gain of sediment at a place
16. You’d think it would be simple, right? MINUS THE OLD DEM GIVES US A DEM OF DIFFERENCE THE NEW DEM 7 m ± 2 m 23 m ± 2 m 10 m ± 2 m 11 m ± 2 m 10 m ± 2 m 3 m ± 2 m 18 m ± 2 m 22 m ± 2 m -3 m ± 2 m +1 m ± 2 m +7 m ± 2 m -7 m ± 2 m TOTAL “SEDIMENT BUDGET” IS -3 + 7 - 7 + 1 = -2 m3 ± 2 m3 Maybe it’s 4 m3, maybe it’s 0 m3 Because our DEMs have error, so will our DEMs of Difference! …and sometimes this error is so large that we can’t tell if a place gained or lost sediment
17. 18 m ± 2 m 22 m ± 2 m +3 m ± 2 m -1 m ± 2 m -7 m ± 2 m +7 m ± 2 m How do we account for error when differencing DEMs? We’ll consider four possibilities: 1. Just ignore it 2. Ignore it, but define some minimum level of detection (minLoD) 3. Treat it as spatially uniform, generate an error surface, and propagate it 4. Treat it as spatially variable, generate an error surface, and propagate it
18. 18 m ± 2 m 22 m ± 2 m +3 m ± 2 m -1 m ± 2 m -7 m ± 2 m +7 m ± 2 m How do we account for error when differencing DEMs? Option 1. Ignore it
19. MINUS THE OLD DEM GIVES US A DEM OF DIFFERENCE THE NEW DEM 7 m ± 2 m 23 m ± 2 m 10 m ± 2 m 11 m ± 2 m 10 m ± 2 m 3 m ± 2 m 18 m ± 2 m 22 m ± 2 m -3 m ± 2 m +1 m ± 2 m +7 m ± 2 m -7 m ± 2 m TOTAL “SEDIMENT BUDGET” IS -3 + 7 - 7 + 1 = -2 m3 ± 2 m3 How do we account for error when differencing DEMs? Option 1. Ignore it
20. MINUS THE OLD DEM GIVES US A DEM OF DIFFERENCE THE NEW DEM 7 m ± 2 m 23 m ± 2 m 10 m ± 2 m 11 m ± 2 m 10 m ± 2 m 3 m ± 2 m 18 m ± 2 m 22 m ± 2 m -3 m ± 2 m +1 m ± 2 m +7 m ± 2 m -7 m ± 2 m TOTAL “SEDIMENT BUDGET” IS -3 + 7 - 7 + 1 = 2 m3 How do we account for error when differencing DEMs? Option 1. Ignore it
21. 18 m ± 2 m 22 m ± 2 m +3 m ± 2 m -1 m ± 2 m -7 m ± 2 m +7 m ± 2 m How do we account for error when differencing DEMs? Option 1. Ignore it Raster calculator is the easiest way to ignore errors in DEM differencing When would we do this? When magnitude of change >>> error in our DEM
22. 18 m ± 2 m 22 m ± 2 m +3 m ± 2 m -1 m ± 2 m -7 m ± 2 m +7 m ± 2 m How do we account for error when differencing DEMs? Option 1. Ignore it Raster calculator is the easiest way to ignore errors in DEM differencing When would we do this? When magnitude of change >>> error in our DEM
23. 18 m ± 2 m 22 m ± 2 m +3 m ± 2 m -1 m ± 2 m -7 m ± 2 m +7 m ± 2 m How do we account for error when differencing DEMs? We’ll consider four possibilities: 1. Just ignore it 2. Ignore it, but define some minimum level of detection (minLoD) 3. Treat it as spatially uniform, generate an error surface, and propagate it 4. Treat it as spatially variable, generate an error surface, and propagate it
24. MINUS THE OLD DEM GIVES US A DEM OF DIFFERENCE THE NEW DEM 7 m 23 m 10 m 11 m 10 m 3 m 18 m 22 m -3 m +1 m +7 m -7 m TOTAL “SEDIMENT BUDGET” IS -3 + 7 - 7 + 1 = -2 m3 How do we account for error when differencing DEMs? Option 2. Ignore it, but define some minimum level of detection (minLoD)
25. MINUS THE OLD DEM GIVES US A DEM OF DIFFERENCE THE NEW DEM 7 m 23 m 10 m 11 m 10 m 3 m 18 m 22 m -3 m +1 m +7 m -7 m TOTAL “SEDIMENT BUDGET” IS -3 + 7 - 7 = -3 m3 How do we account for error when differencing DEMs? Option 2. Ignore it, but define some minimum level of detection (minLoD) Minimum level of detection = 2 m No change
26. 18 m ± 2 m 22 m ± 2 m +3 m ± 2 m -1 m ± 2 m -7 m ± 2 m +7 m ± 2 m How do we account for error when differencing DEMs? Can use raster calculator for minLoD as well! When would we do this? When magnitude of change > potential error in our DEM Option 2. Ignore it, but define some minimum level of detection (minLoD)
27. 18 m ± 2 m 22 m ± 2 m +3 m ± 2 m -1 m ± 2 m -7 m ± 2 m +7 m ± 2 m How do we account for error when differencing DEMs? When would we do this? When magnitude of change > potential error in our DEM Option 2. Ignore it, but define some minimum level of detection (minLoD) Can use raster calculator for minLoD as well!
28. 18 m ± 2 m 22 m ± 2 m +3 m ± 2 m -1 m ± 2 m -7 m ± 2 m +7 m ± 2 m How do we account for error when differencing DEMs? We’ll consider four possibilities: 1. Just ignore it 2. Ignore it, but define some minimum level of detection (minLoD) 3. Treat it as spatially uniform, generate an error surface, and propagate it 4. Treat it as spatially variable, generate an error surface, and propagate it
29. MINUS THE OLD DEM THE NEW DEM 7 m ± 2 m 23 m ± 2 m 10 m ± 2 m 11 m ± 2 m 10 m ± 4 m 3 m ± 4 m 18 m ± 4 m 22 m ± 4 m 3. Treat it as spatially uniform, generate an error surface, and propagate it
30. MINUS THE OLD DEM GIVES US A DEM OF DIFFERENCE THE NEW DEM 7 m ± 2 m 23 m ± 2 m 10 m ± 2 m 11 m ± 2 m 10 m ± 4 m 3 m ± 4 m 18 m ± 4 m 22 m ± 4 m = (𝐷𝐷 1 )2+(𝐷𝐷 2 )2 “Propagated Error is the square root of the sum of squares” = (2)2+(4)2 = 4 + 16 = 4.5 3. Treat it as spatially uniform, generate an error surface, and propagate it -3 m (4.5 m error) +1 m (4.5 m error) +7 m (4.5 m error) -7 m (4.5 m error)
31. MINUS THE OLD DEM GIVES US A DEM OF DIFFERENCE THE NEW DEM 7 m ± 2 m 23 m ± 2 m 10 m ± 2 m 11 m ± 2 m 10 m ± 4 m 3 m ± 4 m 18 m ± 4 m 22 m ± 4 m -3 m (4.5 m error) +1 m (4.5 m error) +7 m (4.5 m error) -7 m (4.5 m error) = (𝐷𝐷 1 )2+(𝐷𝐷 2 )2 “Propagated Error is the square root of the sum of squares” = (2)2+(4)2 = 4 + 16 = 4.5 3. Treat it as spatially uniform, generate an error surface, and propagate it TOTAL “SEDIMENT BUDGET” is 7 m3 - 7 m3 = 0 m3
32. MINUS THE OLD DEM GIVES US A DEM OF DIFFERENCE THE NEW DEM 7 m ± 2 m 23 m ± 2 m 10 m ± 2 m 11 m ± 2 m 10 m ± 4 m 3 m ± 4 m 18 m ± 4 m 22 m ± 4 m TOTAL “SEDIMENT BUDGET” is 7 m3 - 7 m3 = 0 m3 = (𝐷𝐷 1 )2+(𝐷𝐷 2 )2 “Propagated Error is the square root of the sum of squares” = (2)2+(4)2 = 4 + 16 = 4.5 Use this when… We know survey errors exceed the magnitude of changes …but we don’t think they vary (or don’t know how they vary) across the survey region 3. Treat it as spatially uniform, generate an error surface, and propagate it +3 m (4.5 m error) -1 m (4.5 m error) +7 m (4.5 m error) -7 m (4.5 m error)
33. 18 m ± 2 m 22 m ± 2 m +3 m ± 2 m -1 m ± 2 m -7 m ± 2 m How do we account for error when differencing DEMs? We’ll consider four possibilities: 1. Just ignore it 2. Ignore it, but define some minimum level of detection (minLoD) 3. Treat it as spatially uniform, generate an error surface, and propagate it 4. Treat it as spatially variable, generate an error surface, and propagate it
34. 4. Treat it as spatially variable, generate an error surface, and propagate it
35. 4. Treat it as spatially variable, generate an error surface, and propagate it DEM Error varies as a function of surface characteristics: - Error is higher on steep slopes - Error is higher where there are fewer points - Error is higher where the surface roughness is higher
36. 4. Treat it as spatially variable, generate an error surface, and propagate it DEM Error varies as a function of surface characteristics: - Error is higher on steep slopes - Error is higher where there are fewer points - Error is higher where the surface roughness is higher
37. 4. Treat it as spatially variable, generate an error surface, and propagate it DEM Error varies as a function of surface characteristics: - Error is higher on steep slopes - Error is higher where there are fewer points - Error is higher where the surface roughness is higher FUZZY INFERENCE SYSTEM
38. 4. Treat it as spatially variable, generate an error surface, and propagate it DEM Error varies as a function of surface characteristics: - Error is higher on steep slopes - Error is higher where there are fewer points - Error is higher where the surface roughness is higher FUZZY LOGIC IN 3 MINUTES… A set of rules that produces numerical outputs from descriptive inputs
39. 4. Treat it as spatially variable, generate an error surface, and propagate it DEM Error varies as a function of surface characteristics: - Error is higher on steep slopes - Error is higher where there are fewer points - Error is higher where the surface roughness is higher FUZZY LOGIC IN 3 MINUTES… A set of rules that produces numerical outputs from descriptive inputs In the class days of the week, some items clearly belong
40. 4. Treat it as spatially variable, generate an error surface, and propagate it DEM Error varies as a function of surface characteristics: - Error is higher on steep slopes - Error is higher where there are fewer points - Error is higher where the surface roughness is higher FUZZY LOGIC IN 3 MINUTES… A set of rules that produces numerical outputs from descriptive inputs In the class days of the week, some items clearly belong …but some aren’t so clear.
41. 4. Treat it as spatially variable, generate an error surface, and propagate it DEM Error varies as a function of surface characteristics: - Error is higher on steep slopes - Error is higher where there are fewer points - Error is higher where the surface roughness is higher FUZZY LOGIC IN 3 MINUTES… A set of rules that produces numerical outputs from descriptive inputs In the class days of the week, some items clearly belong …but some aren’t so clear.
42. 4. Treat it as spatially variable, generate an error surface, and propagate it DEM Error varies as a function of surface characteristics: - Error is higher on steep slopes - Error is higher where there are fewer points - Error is higher where the surface roughness is higher FUZZY LOGIC IN 3 MINUTES… A set of rules that produces numerical outputs from descriptive inputs In the class days of the week, some items clearly belong …but some aren’t so clear.
43. 4. Treat it as spatially variable, generate an error surface, and propagate it DEM Error varies as a function of surface characteristics: - Error is higher on steep slopes - Error is higher where there are fewer points - Error is higher where the surface roughness is higher FUZZY LOGIC IN 3 MINUTES… A set of rules that produces numerical outputs from descriptive inputs In the class days of the week, some items clearly belong …but some aren’t so clear.
44. 4. Treat it as spatially variable, generate an error surface, and propagate it DEM Error varies as a function of surface characteristics: - Error is higher on steep slopes - Error is higher where there are fewer points - Error is higher where the surface roughness is higher FUZZY LOGIC IN 3 MINUTES… A set of rules that produces numerical outputs from descriptive inputs In the class days of the week, some items clearly belong …but some aren’t so clear.
45. 4. Treat it as spatially variable, generate an error surface, and propagate it DEM Error varies as a function of surface characteristics: - Error is higher on steep slopes - Error is higher where there are fewer points - Error is higher where the surface roughness is higher FUZZY LOGIC IN 3 MINUTES… A set of rules that produces numerical outputs from descriptive inputs In the class days of the week, some items clearly belong …but some aren’t so clear.
46. 4. Treat it as spatially variable, generate an error surface, and propagate it DEM Error varies as a function of surface characteristics: - Error is higher on steep slopes - Error is higher where there are fewer points - Error is higher where the surface roughness is higher FUZZY LOGIC IN 3 MINUTES… A set of rules that produces numerical outputs from descriptive inputs From the descriptive inputs, we come up with a rule set for determining a crisp (numerical) output
47. 4. Treat it as spatially variable, generate an error surface, and propagate it DEM Error varies as a function of surface characteristics: - Error is higher on steep slopes - Error is higher where there are fewer points - Error is higher where the surface roughness is higher FUZZY LOGIC IN 3 MINUTES… A set of rules that produces numerical outputs from descriptive inputs From the descriptive inputs, we come up with a rule set for determining a crisp (numerical) output
48. 4. Treat it as spatially variable, generate an error surface, and propagate it Then, cell-by-cell, propagate the error 𝐷𝐷 𝑐𝑐𝑐𝑐 = (𝐷𝐷 1 )2+(𝐷𝐷 2 )2 And retain only those cells where magnitude of change is greater than magnitude of error
49. 18 m ± 2 m 22 m ± 2 m +3 m ± 2 m -1 m ± 2 m -7 m ± 2 m How do we account for error when differencing DEMs? We’ll consider four possibilities: 1. Just ignore it 2. Ignore it, but define some minimum level of detection (minLoD) 3. Treat it as spatially uniform, generate an error surface, and propagate it 4. Treat it as spatially variable, generate an error surface, and propagate it UNIFORM ERROR VARIABLE ERROR
50. histogram of changes: minLoD example
51. DEPOSITION (+) EROSION (-) NO CHANGE histogram of changes: minLoD example
52. DEPOSITION (+) EROSION (-) NO CHANGE gray is all the pixels where change < minLoD = 0.2 m histogram of changes: minLoD example
53. histogram of changes: propagated error example
54. histogram of changes: propagated error example DEPOSITION (+) EROSION (-) NO CHANGE
55. gray is all the pixels where error > change DEPOSITION (+) EROSION (-) NO CHANGE histogram of changes: propagated error example