# GEOG 400, Advanced GIS, Fall 2020; Week 8 Lecture 1

October 12, 2020

## Transcript

1. ### GEOG 400: Advanced GIS - Raster Week 8 – Lecture

1 Interpolation (Again) and Terrain Analysis, Part I
2. ### GEOG 400: Advanced GIS - Raster Interpolation (Again) and Terrain

Analysis, Part I A review of spatial interpolation, specifically spline and trend methods, along with natural neighbors, which we saw in lab last week. LAST LECTURE TODAY In-Situ measurements acquire information about an object when the distance between the object and the sensor is comparable to or smaller than any linear dimension of the sensor. Spatial Interpolation is the process by which we generate continuous raster data from discrete vector (i.e., point-based) measurements using remote and in-situ techniques. The beginnings of terrain analysis, which will be this week’s lecture and lab topic; we probably won’t get all the way through terrain analysis today!
3. ### • Spline • This technique is based on the method

formerly used to draw curves for engineering and design purposes • Long, thin, flexible strips of wood, plastic, or metal bent between nails (or “knots”) causing a nice, smoothly-curving shape • The specific shape would be dictated by number and placement of knots, and tension of the spline Spatial Interpolation
4. ### Spatial Interpolation • Spline • In spatial spline interpolation, the

same principles apply • Surface is generated based on a curved, smooth surface
5. ### Spatial Interpolation • Spline • In spatial spline interpolation, the

same principles apply • Surface is generated based on a curved, smooth surface Slide #5
6. ### •Spline • Has several parameters… • Regularized vs. tension spline

• Regularized produces a generally smoother surface • Tension produces a generally more rigid surface • Weight • For regularized, higher weights mean smoother output • For tension, higher weights mean rougher output • Number of points • For both, the number of nearest neighboring points used to create the localized spline Spatial Interpolation
7. ### •Trend • Trend interpolation is based on regression • Regression

analysis is the optimized fitting of a line or curve to derive a mathematical function that best fits the raw data • Linear regression • y = ax + b • Predicting a dependent variable (y) based on an independent variable (x) Spatial Interpolation
8. ### •Trend • However, sometimes the data are not linear in

nature, and thus require polynomial regression • 1st order: y = ax + b • 2nd order: y = ax + bx2 + c • 3rd order: y = ax + bx2 + cx3 + d • etc. Spatial Interpolation
9. ### •Trend • In general, in statistics, we aim for the

simplest explanations • Higher-order polynomials will always increase the model fit, but at the risk of over-fitting your model • i.e. instead of looking at the broader trend, your function is so specific that it won’t be generalizable to another, similar dataset Spatial Interpolation
10. ### • Trend • Trend spatial interpolation is just regression in

two dimensions raw data 1st order polynomial trend surface First-order (y = x); some constant value Actual Landscape The higher-order polynomial, the more complex terrain you can reproduce (but it takes more time)
11. ### • Trend • Trend spatial interpolation is just regression in

two dimensions raw data 2nd order polynomial trend surface second-order (y = x2 + x) Actual Landscape The higher-order polynomial, the more complex terrain you can reproduce (but it takes more time)
12. ### • Trend • Trend spatial interpolation is just regression in

two dimensions raw data 3rd order polynomial trend surface third-order (y = x3 + x2 + x) Actual Landscape The higher-order polynomial, the more complex terrain you can reproduce (but it takes more time)
13. ### • Trend • Trend spatial interpolation is just regression in

two dimensions raw data 4th order polynomial trend surface fourth-order (y = x4+ x3 + x2 + x) Actual Landscape The higher-order polynomial, the more complex terrain you can reproduce (but it takes more time)
14. ### • Trend • Trend spatial interpolation is just regression in

two dimensions raw data 5th order polynomial trend surface fifth-order (y = x5 + x4+ x3 + x2 + x) Actual Landscape The higher-order polynomial, the more complex terrain you can reproduce (but it takes more time)
15. ### • Trend • Trend spatial interpolation is just regression in

two dimensions raw data 6th order polynomial trend surface sixth-order (y = x6 + x5 + x4+ x3 + x2 + x) Actual Landscape The higher-order polynomial, the more complex terrain you can reproduce (but it takes more time)
16. ### • Trend • Trend spatial interpolation is just regression in

two dimensions raw data 7th order polynomial trend surface seventh-order (y = x7 + x6 + x5 + x4+ x3 + x2 + x) Actual Landscape The higher-order polynomial, the more complex terrain you can reproduce (but it takes more time)
17. ### •Trend • Trend interpolation is useful when conditions vary gradually

over relatively broad areas • So, elevation is a bad example • But, atmospheric conditions (temperature, humidity, pollution, etc.) and aquatic conditions (temperature, pH, salinity) are good examples • Can also be used to “remove” broad-scale trends to reveal local phenomena • e.g. compare ambient (background) levels of O3 to local levels Spatial Interpolation
18. ### •Trend • Trend interpolation is useful when conditions vary gradually

over relatively broad areas • So, elevation is a bad example • But, atmospheric conditions (temperature, humidity, pollution, etc.) and aquatic conditions (temperature, pH, salinity) are good examples • Can also be used to “remove” broad-scale trends to reveal local phenomena • e.g. compare ambient (background) levels of O3 to local levels Spatial Interpolation
19. ### Terrain Modeling • Introduction • We’ve been talking a lot

about digital elevation models (DEMs) • What they are • Who creates and maintains them • How they’re created • Where they’re currently available • The focus of today’s lecture is the next, logical question: • What can we do with them?! • Terrain modeling applications in ArcGIS Deriving additional descriptors of land shape (i.e., morphometry) from elevation/terrain data.
20. ### Terrain Modeling •Introduction • Today we’re going to cover an

array of different analysis techniques • What they mean, how they work, when/why they might be useful... • Contour • Hillshade • Solar Radiation • Slope • Aspect • Curvature • Cut Fill • Viewshed
21. ### Terrain Modeling •Contour • As you probably already know from

GEOG 310, contour lines are lines of equal elevation • They are a form of isoline • Lines that connect areas of equal value
22. ### Terrain Modeling •Contour • As you probably already know from

GEOG 310, contour lines are lines of equal elevation • They are a form of isoline • Lines that connect areas of equal value • There are many others... • Isobars • Lines of equal atmospheric pressure
23. ### Terrain Modeling •Contour • As you probably already know from

GEOG 310, contour lines are lines of equal elevation • They are a form of isoline • Lines that connect areas of equal value • There are many others... • Isotherm • Lines of equal temperature
24. ### Terrain Modeling •Contour • As you probably already know from

GEOG 310, contour lines are lines of equal elevation • They are a form of isoline • Lines that connect areas of equal value • There are many others... • Isobaths • Lines of equal underwater elevation (bathymetry)
25. ### Terrain Modeling •Contour • As you probably already know from

GEOG 310, contour lines are lines of equal elevation • They are a form of isoline • Lines that connect areas of equal value • There are many others... • Isobathytherms • Lines of equal water temperature
26. ### Terrain Modeling •Contour • As you probably already know from

GEOG 310, contour lines are lines of equal elevation • They are a form of isoline • Lines that connect areas of equal value • There are many others... • Isochrones • Lines of equal time
27. ### Terrain Modeling •Contour • As you probably already know from

GEOG 310, contour lines are lines of equal elevation • They are a form of isoline • Lines that connect areas of equal value • There are many others... • Isotachs • Lines of equal wind speed
28. ### Terrain Modeling •Contour • As you probably already know from

GEOG 310, contour lines are lines of equal elevation • They are a form of isoline • Lines that connect areas of equal value • There are many others... • Isohyets • Lines of equal precipitation
29. ### Terrain Modeling •Contour • As you probably remember from last

week, interpolation of contour lines is how most DEM data was first created... • So, in a sense, it’s kind of strange to use a DEM to generate contour lines • Kind of like building a house and then tearing it down to use the wood...
30. ### Terrain Modeling • Contour • But(!) contour lines can be

an excellent visualization tool • To generate contours in ArcGIS, you can use the Contour tool • Input raster • Usually DEM, but again, could be any continuous variable • Contour type • Can generate line or polygon output • Polygons could be useful (e.g. how much area is between 100 and 150 m?)
31. ### Terrain Modeling • Contour List • If you just want

a few, specific contours, you can use the Contour List tool...
32. ### Terrain Modeling •Hillshade • Next on the list of tools

that aren’t super useful for analysis but are great for visualization... HILLSHADE! • Hillshade simulates the solar illumination of the terrain based on solar geometry • Two important parameters • Solar elevation (aka altitude) (αs ) • More about time of year (0° – 90°) observer sun
33. ### Terrain Modeling •Hillshade • Next on the list of tools

that aren’t super useful for analysis but are great for visualization... HILLSHADE! • Hillshade simulates the solar illumination of the terrain based on solar geometry • Two important parameters • Solar elevation (aka altitude) (αs ) • More about time of year (0° – 90°) • Solar azimuth (γs ) • More about time of day (0° - 360°) observer sun N W S E
34. ### Terrain Modeling •Hillshade • Although the calculations can be done

manually(!) (and you know I like a good manual calculation...), there are many, simple online calculators to determine solar geometry at any location/time • Useful if you want to depict terrain- driven solar illumination conditions at a certain time of day/year • E.g. “will my house receive direct sunlight in summer?” observer sun N W S E
35. ### Terrain Modeling •Hillshade • Hillshades simulated throughout the day near

Mount Elbert • Tuesday, November 2nd, 2018 • 6am – 4pm, hourly
36. ### Terrain Modeling • Hillshade • Behind the scenes, in addition

to solar geometry, hillshade is taking into account slope and aspect • The more perpendicular a slope is to the solar altitude, the more illumination (solar irradiance) it will receive • The more parallel an aspect is to the solar azimuth, the more illumination it will receive • More on these shortly…
37. ### Terrain Modeling • Hillshade • Hillshade can be generated using

the... Hillshade tool • Only important parameter not yet discussed... Model shadows
38. ### Terrain Modeling •Hillshade • Again, not very useful from an

analytical standpoint, but a great visualization tool • Particularly if displayed in conjunction with a semi- transparent DEM
39. ### Terrain Modeling •Hillshade • Again, not very useful from an

analytical standpoint, but a great visualization tool • Particularly if displayed in conjunction with a semi- transparent DEM • Or really any semi-transparent basemap...
40. ### Terrain Modeling •Hillshade • Why is it not super useful?

• Because it doesn’t provide any true measure of solar radiation • Just an 8-bit value (0-255) representing relative illumination
41. ### Terrain Modeling • Solar Radiation Tools • That being said...

There is a Solar Radiation toolbox built into ArcGIS software that allows you to calculate true measures of solar irradiance • Very advanced set of tools that take into account direct and diffuse radiation • Excellent resource for understanding light availability for photosynthesis • Excellent resource for optimizing placement of solar panels • Unfortunately, the tools are very slow...
42. ### Terrain Modeling • Slope • One of the most useful

terrain modeling tools • A focal analysis method! • Simply, calculates rise over run • However, it does so in two dimensions (x and y), which complicates matters... • Here’s slope in one direction... Simple ϴ Δelev Δdist tan = ∆ ∆ = tan−1 ∆ ∆
43. ### Terrain Modeling • Slope • Here’s how ArcGIS calculates slope

in two directions... • Uses a 3x3 focal neighborhood to calculate slope of the target cell NW N NE W E SW S SE reference analysis window 3 x 3 neighborhood target analysis cell
44. ### Terrain Modeling • Slope • Here’s how ArcGIS calculates slope

in two directions... • Uses a 3x3 focal neighborhood to calculate slope of the target cell 315° 0° 360° 45° 270° 90° 225° 180° 135° reference analysis window 3 x 3 neighborhood target analysis cell
45. ### Terrain Modeling • Slope • Here’s how ArcGIS calculates slope

in two directions... • Uses a 3x3 focal neighborhood to calculate slope of the target cell a b c d e f g h i reference analysis window 3 x 3 neighborhood target analysis cell
46. ### Terrain Modeling • Slope • Here’s how ArcGIS calculates slope

in two directions... x y z slopex = 0° slopey = 0°
47. ### Terrain Modeling • Slope • Here’s how ArcGIS calculates slope

in two directions... x y z slopex = 15° slopey = 0°
48. ### Terrain Modeling • Slope • Here’s how ArcGIS calculates slope

in two directions... x y z slopex = -15° slopey = 0°
49. ### Terrain Modeling • Slope • Here’s how ArcGIS calculates slope

in two directions... x y z slopex = 0° slopey = 15°
50. ### Terrain Modeling • Slope • Here’s how ArcGIS calculates slope

in two directions... x y z slopex = 0° slopey = -15°
51. ### Terrain Modeling • Slope • Here’s how ArcGIS calculates slope

in two directions... x y z slopex = 15° slopey = 15°
52. ### Terrain Modeling • Slope • Here’s how ArcGIS calculates slope

in two directions... x y z slopex = -15° slopey = 15°
53. ### Terrain Modeling • Slope • Here’s how ArcGIS calculates slope

in two directions... x y z slopex = 15° slopey = -15°
54. ### Terrain Modeling • Slope • Here’s how ArcGIS calculates slope

in two directions... x y z slopex = -15° slopey = -15°
55. ### Terrain Modeling •Slope • Here’s how ArcGIS calculates slope in

two directions... • Calculate Δz / Δx • Rise over run in x • ∆ = + 2 + − ( ) + 2 + • Notice the focal weighting (stronger influence of directly E and W) • ∆ = 8 × ( 𝑠𝑠𝑠𝑠) • ∆ ∆ = +2+𝑖𝑖 −(+2+) 8×(𝑐𝑐𝑐𝑐𝑐𝑐 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠) Δz Δx ϴ
56. ### Terrain Modeling •Slope • Here’s how ArcGIS calculates slope in

two directions... • Calculate Δz / Δy • Rise over run in y • ∆ = + 2 + − ( + 2ℎ + ) • Notice the focal weighting (stronger influence of directly N and S) • ∆ = 8 × ( 𝑠𝑠𝑠𝑠) • ∆ ∆ = +2+ −(+2ℎ+𝑖𝑖) 8×(𝑐𝑐𝑐𝑐𝑐𝑐 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠) Δz Δy ϴ
57. ### Terrain Modeling •Slope • Here’s how ArcGIS calculates slope in

two directions... • Then calculate overall slope • ∆ ∆ = ∆ ∆ 2 + ∆ ∆𝑦𝑦 2 • = tan−1 ∆ ∆ • Usually need to convert back to degrees • 𝑑𝑑𝑑𝑑 = 𝑟𝑟𝑟𝑟 × 180 Δz / Δx Δz / Δy
58. ### Terrain Modeling • Slope • So now you know how

ArcGIS calculates slope... • BUT(!) ArcGIS is just one GIS application • There are many different algorithms for doing so • For example, what if you have 25-cm resolution imagery? • Using a 3x3 neighborhood, as ArcGIS does, to calculate slope, will not give you a representation of “slope” as you would interpret it in the field...
59. ### Terrain Modeling • Slope • There are a few important

parameters of the Slope tool... • Output measurement • Percent (0%-∞%) • Rise over run • Degree (0°-90°) • Arctangent of rise over run
60. ### Terrain Modeling • Slope • There are a few important

parameters of the Slope tool... • Method • Planar • Assumes flat earth, suitable for local-scale analyses • Geodesic • Assumes ellipsoid earth, better for broad-scale analyses
61. ### Terrain Modeling • Slope • There are a few important

parameters of the Slope tool... • Z factor • By default, most of the Surface Tools assume that your DEM’s x-y units (e.g. meters) are the same as your z units (also meters) • But, if you convert a DEM’s z units to something else (e.g. feet), then you’d need to adjust the Z factor • Rise and run need to be in the same units

63. ### Terrain Modeling •Slope • Applications… • Wildland fire behavior •

Building site suitability • Habitat suitability • Landslide risk • Avalanche risk • Trail/road building
64. ### Terrain Modeling •Roughness • variability or irregularity in elevation •

the ‘bumpiness’ of the landscape • a measure of landscape complexity • a measure of habitat complexity
65. ### Terrain Modeling •Roughness • variability or irregularity in elevation •

the ‘bumpiness’ of the landscape • many, many ways to calculate terrain roughness - variability (focal stats) of slope - standard deviation of elevation - various ‘ruggedness’ indicies - we’ll try these out in lab this week
66. ### Terrain Modeling •Aspect • In addition to the angle of

inclination (slope), you often want to know the direction of inclination • ...This is also known as the aspect • The azimuth direction of prevailing slope, downhill • Can be described qualitatively N E S W NE SE SW NW NNE ENE ESE SSE SSW WSW WNW NNW
67. ### Terrain Modeling •Aspect • In addition to the angle of

inclination (slope), you often want to know the direction of inclination • ...This is also known as the aspect • The azimuthal direction of prevailing slope, downhill • Can be described qualitatively • Can also be described quantitatively 0°,360° 90° 180° 270° 45 ° 135° 225° 315 ° 22.5° 67.5° 112.5° 157.5° 202.5° 247.5° 292.5° 337.5°
68. ### Terrain Modeling • Aspect x y z slopex = 0°

slopey = 0° aspect = NA
69. ### Terrain Modeling • Aspect x y z slopex = 15°

slopey = 0° aspect = W
70. ### Terrain Modeling • Aspect x y z slopex = -15°

slopey = 0° aspect = E
71. ### Terrain Modeling • Aspect x y z slopex = 0°

slopey = 15° aspect = S
72. ### Terrain Modeling • Aspect x y z slopex = 0°

slopey = -15° aspect = N
73. ### Terrain Modeling • Aspect x y z slopex = 15°

slopey = 15° aspect = SW
74. ### Terrain Modeling • Aspect x y z slopex = -15°

slopey = 15° aspect = SE
75. ### Terrain Modeling • Aspect x y z slopex = 15°

slopey = -15° aspect = NW
76. ### Terrain Modeling • Aspect x y z slopex = -15°

slopey = -15° aspect = NE
77. ### Terrain Modeling •Aspect • The Aspect tool is very simple

• One input, one output • And, planar vs. geodesic again

79. ### Terrain Modeling •Cut Fill • Cut Fill allows you to

assess how terrain (or any three-dimensional structural variable) has changed over time • Specifically, it provides an estimate of the volumetric difference between two elevation models
80. ### Terrain Modeling • Cut Fill • For example… Lake Nighthorse

before Lake Nighthorse after
81. ### Terrain Modeling •Cut Fill • Useful for assessing volumetric changes

that result from: • Volcanoes • Debris flows • Mining • Biomass removal • Damming reservoirs • Glacial retreat
82. ### Terrain Modeling •Viewshed analysis • The last technique we’ll cover

today is viewshed analysis • A viewshed determines, on a cell-by-cell basis, what can and cannot be seen from a given point, set of points, or line, based on a DEM • Conceptually, very simple… not visible visible
83. ### Terrain Modeling •Viewshed analysis • Example… • View from Animas

City Mountain peak
84. ### Terrain Modeling •Viewshed analysis • Example… • View from Animas

City Mountain peak • Result • Pink = not visible • Green = visible
85. ### Terrain Modeling •Viewshed analysis • Example… • View from Animas

City Mountain peak • Result • Pink = not visible • Green = visible • Optionally, can output a “how much taller would I need to be to see this?” raster
86. ### Terrain Modeling •Viewshed analysis • Whereas the Viewshed tool simply

says “yes” or “no”, regardless of how many points/lines you input as your viewing locations, Observer Points allows you to determine which points can see which areas
87. ### Terrain Modeling • Viewshed analysis • Example… • View from

various peaks around town
88. ### Terrain Modeling • Viewshed analysis • Example… • View from

various peaks around town • Result
89. ### Terrain Modeling •Viewshed analysis • Applications… • Fire towers •

Lighthouses • Hiding unsightly things • Scenic overlook planning • Trail building • Building mountain home