城市空间信息技术 第十三章 地形制图与分析 胡嘉骢 不动产学院 博士 副教授 城市规划系主任 手机 : （ ） QQ:

2 Chapter 14: TERRAIN MAPPING AND ANALYSIS 14.1 Data for Terrain Mapping and Analysis 14.2 Terrain Mapping 14.3 Slope and Aspect 14.4 Surface Curvature 14.5 Raster versus TIN

3 Chapter 14: TERRAIN MAPPING AND ANALYSIS Terrain - undulating, continuous surface Terrain mapping techniques include contouring, hill shading （晕渲法）, hypsometric tinting （分 层设色法）, 3-D perspectives GIS packages contain terrain mapping features that allow it to be used in a variety of applications Elevation is z-value at a given x-, y-coordinate location

4 Applications of Terrain Mapping and Analysis Hydrologic modeling Snow cover evaluation Soil mapping Landslide delineation Soil erosion Vegetation communities

Data for Terrain Mapping and Analysis DEM - raster-based TIN - vector-based

DEM Digital elevation model Regular array of elevation points U.S. Geological Survey (USGS) Also from satellite images, radar data, LIDAR( 激 光雷达） Point-based DEM converted to software-specific raster data before being used for terrain mapping and analysis

7 DEM Quality Influence accuracy of terrain measurements –Level 1 is poorest quality (maximum RMS error of 15 meters), 30-meter resolution –Level 2 maximum RMS error of 1/2 contour interval, 10-and 30-meter resolution –Level 3 maximum error of 1/3 contour interval, not to exceed 7 meters Most USGS DEMs are level 1 and 2

8 DEM Errors Level 1 - global or relative –Global - displacement of DEM, mismatching of elevations along boundaries of adjacent DEM –Relative - local but significant errors relative to neighboring elevations and can only be corrected by editing Level 2 - most errors already corrected

9 LIDAR Advantage of greater resolution –0.5-2 meters, 15 cm vertical accuracy Ideal for floodplain mapping, telecommunications, transportation, ecosystems, forest structure studies

TIN Triangulated Irregular Network Series of nonoverlapping triangles elevations (z-coordinates) of triangle nodes are stored along with their x- and y-coordinates

11 TIN DEMs - regular grid of points TIN - irregular grid DEMs are primary data source for preliminary TIN Surveyed points, GPS data, LIDAR Contour lines, breaklines Maximum z-tolerance

12 Figure 14.1 P e is the estimated elevation, P h is the actual elevation, and d is the offset between P e and P h at cell P. VIP uses s, a distance between P h and the hypothetical surface between G and C, for measuring the significance of P.

13 Figure 14.2 A breakline, shown as a dashed line in (b), subdivides the triangles in (a) into a series of smaller triangles in (c).

14 DEM to TIN Most of discussion deals with converting DEM to TIN Can also convert TIN to DEM. Must interpolate (estimate) elevations of intermediate points

Terrain Mapping Techniques include contouring, vertical profiling, hill shading, hypsometric tinting, perspective views

Contour Mapping Most common method Contour lines connect points of equal elevation Contour interval vertical distance between contour lines –Constant on a given map Base contour - contour from which contouring starts

17 Figure 14.3 A contour line map.

18 Contouring Arrangement and pattern of contour lines reflect the topography –Closely-spaced contours represent steep slopes –Widely spaced contour lines represent gentle slopes –Contours curved in an upstream direction along streams (rule of Vs)

19 Automated Contouring Detect a contour line intersecting a raster cell or TIN triangle Draw contour line through the raster cell or triangle Interpolation

20 Figure 14.4 The contour line of 900 connects points that are interpolated to have the value of 900 along the triangle edges.

21 Contour Lines Do not intersect one another Do not stop in the middle of a map Close in the case of a hill or depression Do not split

Vertical Profiling Graph that shows change in elevation with change in horizontal position –Along a trail, road, or stream Figure 14.5 A vertical profile.

23 Manual Profiling Method 1. Draw profile line on contour map 2. Mark intersection of contour and profile line and record its elevation 3. Raise each intersection point to a height proportional to its elevation 4. Plot vertical profile by connecting elevated points Automated profiling follows same procedure but substitutes contour map with a DEM or TIN

Hill Shading Shaded relief map Simulates terrain appearance with interaction between sunlight and surface features –Slope facing sunlight will be illuminated, slopes away from sunlight will be shaded May be mapped alone or in conjunction with terrain or thematic information

25 Hill Shading Computer generated Four factors control visual effect of shading –Sun’s azimuth (315° is default) –Sun elevation –Slope angle –Slope aspect

26 Figure 14.6 An example of hill shading, with the sun’s azimuth at 315° (NW) and the sun’s altitude at 45°.

27 Pseudoscopic Effect （ 反立体） Hills appear as valleys, valleys appear as raised elevations To appear correct, shadows must fall toward viewer This is the reason a sun azimuth of 315° is used

Hypsometric Tinting Depicts distribution of Earth’s mass with elevation Also known as layer tinting Applies color tinting to different elevation zones

29 Figure 14.7 A hypsometric map. Different elevation zones are shown in different gray symbols.

Perspective Views Oblique view, similar to view from an airplane

31 Figure 14.8 A 3-D perspective view.

32 Parameters Four parameters –Viewing azimuth –Viewing angel –Viewing distance –z-scale

33 Viewing Azimuth Compass direction from observer to the surface

34 Viewing Angle Angle measured from horizon to altitude of observer

35 Viewing Distance Distance from viewer to surface

36 z-scale Ratio between vertical and horizontal scales Vertical exaggeration （夸张）

37 Figure 14.9 Three controlling parameters of the appearance of a 3-D view: the viewing azimuth a is measured clockwise from the north, the viewing angle u is measured from the horizon, and the viewing distance d is measured between the observation point and the 3-D surface.

Slope and Aspect Slope - rate of change of elevation at a surface location –Slope angle, gradient Aspect - Directional measurement of a slope

39 Slope and Aspect Basic elements for analyzing and visualizing terrain Important is studies of watershed units, landscape, morphometric measurements, forestry, soil erosion, wildlife habitat suitability, site analysis, others

40 Figure Slope, either measured in percent or degrees, can be calculated from the vertical distance a and the horizontal distance b.

41 Figure Aspect measures are often grouped into the four principal directions (top) or eight principal directions (bottom).

42 Figure Transformation methods to capture the N–S direction (a), the NE–SW direction (b), the E–W direction (c), and the NW–SE direction (d).

Computer Algorithms for Slope and Aspect using Raster Measured by quantity and direction of tilt of cell’s normal vector

44 Figure The normal vector to the cell is the directed line perpendicular to the cell. The quantity and direction of tilt of the normal vector determine the slope and aspect of the cell. (Redrawn from Hodgson, 1998, CaGIS 25, (3): pp. 173–185; reprinted with the permission of the American Congress on Surveying and Mapping.)

45 Approximation Methods 3-by-3 moving window to estimate slope and aspect of center cell by comparison with neighbors

46 Figure Ritter’s algorithm for computing slope and aspect at C 0 uses the four immediate neighbors of C 0.

47 Figure Horn’s algorithm for computing slope and aspect at C 0 uses the eight neighboring cells of C 0. The algorithm also applies a weight of 2 to e 2, e 4, e 5, and e 7, and a weight of 1 to e 1, e 3, e 6, and e 8.

Computing Algorithms for Slope and Aspect using TIN Figure The algorithm for computing slope and aspect of a triangle in a TIN uses the x, y, and z values at the three nodes of the triangle.

Factors Influencing Slope and Aspect Measures DEM resolution DEM quality Computer algorithm Local topography

50 Figure DEMs at three different resolutions: USGS 30-meter DEM (a), USGS 10-meter DEM (b), and 1.83-meter DEM derived from LIDAR data (c).

51 Figure Slope layers derived from the three DEMs in Figure The darkness of the symbol increases as the slope becomes steeper.

Slope Curvature Hydrology studies - surface curvature –Convex or concave upward Algorithms available for calculating these parameters

Raster Versus TIN GIS packages can convert from one to the other Differ in data flexibility and computational accuracy Advantage of TIN - flexibility with input data sources Raster - fixed with given cell size. Cannot add new points

54 Raster Versus TIN TIN also excellent data model for terrain mapping and 3-D display Main advantage of raster is computational efficiency The more accurate? Depends on how TIN or DEM was made

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