Intro. To GIS Lecture 9 Terrain Analysis April 24 th , 2013

1. Intro. To GISLecture 9TerrainAnalysisApril 24th, 2013

2. Reminders • Please turn in your homework • Final Project guidelines are available • Two labs next week (Mon and Wed)

3. REVIEW: Raster Data

4. Applications of neighborhood functions (spatial filters) • Removing odd values • Smooth the data • Edge detection • Edge sharpening • Spatial variability

5. How to represent the real world in 3D? • Data points are used to generate a continuous surface. In the below example, a color coded surface is generated from sample values

6. How to represent the real world in 3D? • Two ways to generate real world surfaces from point data (sample values) • Vector • raster • Whatever the method, what kind of data are available to represent the world?

7. How to represent the real world in 3D? • Ways of spatial sampling

8. Samples could represent any quantity (value) • Elevation • Climate data • Temperature • Precipitation • Wind • CO2 flux • Others • Ice thickness • Spatial samples (of some quantity) in a city • Gold concentrations • LiDAR data points

9. Elevation Data • Collected by several methods • Topographic survey (very accurate) • LiDAR data (pretty accurate) • Satellite radar (surprisingly accurate) • GPS survey (much less accurate) • Elevations (z-values) recorded at points

10. Surface Representation • Regardless of vector or raster: • Point elevations • Triangular Irregular Networks (TINs) • Contour lines • Digital Elevation Models (DEMs)

11. Vector representation (of surfaces) • Triangular Irregular Network (TIN) • TIN can be used to • Generate contour lines • Slope • Aspect

12. Triangular Irregular Network • Way of representing surfaces (vector) • Elevation points connected by lines to form triangles • Size of triangles may vary • Each face created by a triangle is called a facet

13. Triangular Irregular Network • The triangulation is based on the Delaunay triangulation • ADelaunay triangulationis a triangulation such that no sample (point) out of all samples is inside the circumcircle of any triangle. Delaunay triangulations maximize the minimum angle of all the angles of the triangles in the triangulation; they tend to avoid skinny triangles.

14. Delaunay triangulation Delaunay triangles: all satisfy the condition Delaunay NOT satisfied

15. 09_03_Figure

16. More about TINs • No interpolation required, all elevation values are based on direct measurements • Visualized using hillshade for a 3D effect

17. More about TINs • Hillshade is one of the most common ways of displaying/visualizing TINs. Commonly Sun is shining from northwest (315deg) from 45deg above horizon. • Each facet will be assigned with a color based on its orientation • Products • Contour lines • Slope and aspect can be derived from

18. Raster Representation (of surfaces) • The most commonly used term for raster representation is Digital Elevation Model (DEM) • Any digital model for any other variable could be generated • For DEM, each cell has an elevation (z-value) • To generate DEM from sample points, interpolation is used to fill in between surveyed elevations – several methods to choose from

19. Interpolation • Linear • Polynomial • In GIS (to generate raster): • Nearest Neighbor • Inverse Distance Weighted (IDW) • Kriging • Splining

20. Interpolation • Comes from the word “inter” meaning between and “pole” which represent two sample points. So, you want to find a value between two points. • Extrapolation is finding a value for the outside of the two points

21. Linear interpolation • Assume that the value for an unknown location between two known points can be estimated based on a linear assumption

22. Polynomial Interpolation • Assume that the value for an unknown location between two known points can be estimated based on a non-linear assumption

23. Spatial Interpolation • Generating surface from points (samples) based upon: • Nearest Neighbor • Inverse Distance Weighted (IDW) • Kriging • Splining

24. Nearest-Neighbor • Uses elevations (or another quantity) from a specified number of nearby control points Sample with Known value Pixel (grid cell) with unknown value

25. Nearest-Neighbor

26. Inverse Distance Weighted (IDW) • Spatial Autocorrelation • Near objects are more similar than far objects • IDW weights point values based on distance

27. Inverse Distance Weighted (IDW) • Estimating an unknown value for a pixel (p) by weighting the sample values based on their distance to (p) i=8 in this example j • In the above equation, n is the power. It is usually equals to 2, i.e., n=2. But you can pick n=1, n=1.5, etc.

28. IDW – Choosing the Power • Power setting influences interpolation results • Lower power results in smoother surfaces • Higher power results in rugged surface (it become more like ….?)

29. Inverse Distance Weighted

30. Kriging • Statistical regression method, whose process consists of two main components • Spatial autocorrelation (semivariance) • Some weighting scheme • Advanced interpolation function, can adapt to trends in elevation data

31. Krigingand Semivariogram • Semivarigram is a graph describing the semivariance (or simply variance) between pairs of samples at different distances (lags) • The idea comes from intuition: • Things that are spatially close are more correlated than those are far way (similar to IDW)

32. Generating Semivariogram • To generate a semivariogram, semivariance between pairs of points (for various distances/lags) are to be calculated

33. 09_09_Figure

34. Semivariance: Example

35. Kriging and Semivariogram • The first step in the kriging algorithm is to compute an average semivariogram for the entire dataset. This is done by going through each single point in the dataset and calculate semivariogram. Then the semivariogram are averaged. • The second step is to calculate the weights associated with each point

36. Kriging

37. Spline Interpolation • Curves fit through control points • Interpolated values may exceed actual elevation values • Regularized vs. Tension options

38. 09_13_Figure

39. Spline Interpolation

40. Comparing Interpolations

42. OK… • Which one works better?

43. Evaluation of the generated surface • Independent samples must be preserved for accuracy assessment of the predicted (generated) surface. These points are called check points. • In other words, if you have 100 samples in the area, you’d use 90 to create the surface and 10 of them to evaluate how accurately the surface represents the actual world

44. Terrain Functions • Slope • Aspect • Hillshade • Curvature

45. Slope: How it is done! • Equations applied in neighborhoods for a focal cell

46. Viewshed Analysis

47. Watershed Delineation • How much land area drains to a specific point? • Can be delineated manually from a topo map

48. Watershed Basics • Basin/Catchment, Drainage Divide, Pour Points

49. Watershed Delineation • The key property of a watershed boundary is that it completely and uniquely defines the area from which the (surface) water drains to the watershed outlet.

50. Delineation Methodology