Transcript Document
Topic 5: Terrain Analysis
第五讲
地 形 分 析
Chapter 12
12.1 Introduction 12.2 Data for Terrain Mapping and Analysis 12.2.1 DEM 12.2.2 TIN 12.3 Terrain Mapping 12.3.1 Contouring 12.3.2 Vertical Profiling 12.3.3 Hill Shading 12.3.4 Hypsometric Tinting 12.3.5 Perspective View
12.4 Terrain Analysis 12.4.1 Slope and Aspect 12.4.1.1 Computing Algorithms for Slope and Aspect Using Grid 12.4.1.2 Computing Algorithms for Slope and Aspect Using TIN 12.4.1.3 Factors Influencing Slope and Aspect Measures 12.4.2 Surface Curvature 12.4.3 Viewshed Analysis 12.4.4 Watershed Analysis 12.5 Grid versus TIN
Applications: Terrain Mapping and Analysis
Task 1: Use DEM for Terrain Mapping Task 2: Perform Viewshed Analysis Task 3: Create a New Lookout Shapefile for Viewshed Analysis Task 4: Delineate Watersheds Task 5: Build and Display a TIN in ArcView
Data for Terrain Mapping and Analysis
DEM TIN
DEMs
The USGS (U.S. Geological Survey) classifies the quality of 7.5 minute DEMS into three levels, with Level 1 having the poorest quality. Level-1 accuracy has a RMSE (root mean square error) target of 7 meters and a maximum RMSE of 15 meters. Level-2 accuracy has a maximum RMSE of one half the contour interval. And Level-3 accuracy has a maximum RMSE of one-third of a contour interval—not to exceed 7 meters. Most USGS DEMs in use are either Level 1 or Level 2.
Global DEMs
DEMs at different resolutions are now available on the global scale. ETOPO5 (Earth Topography-5 Minute) data cover both the land surface and ocean floor of the Earth, with a grid spacing of 5 minutes of latitude by 5 minutes of longitude (http://edcwww.cr.usgs.gov/glis/hyper/guide/etopo5). Both GTOPO30 ( http://edcdaac.usgs.gov/gtopo30/gtopo30.html/ ) and GLOBE ( http://www.ngdc.noaa.gov/seg/topo/globe.shtml/ ) offer global DEMs with a horizontal grid spacing of 30 arc seconds or approximately 1 kilometer.
LIDAR
LIDAR data have the advantage over USGS DEMs in providing high-quality DEMs with a spatial resolution of 0.5 to 2 meters and a vertical accuracy of about 15 centimeters.
a – Canopy elevation b – Ground elevation c – Estimated tree height
TIN
A TIN approximates the land surface with a series of non overlapping triangles. Elevation values (
z
values) along with
x-
,
y
coordinates are stored at nodes that make up the triangles. In contrast to DEMs, TINs are based on an irregular distribution of elevation points.
Data Sources for TINs
GIS users typically compile TINs using DEMs as the primary data source in a process sometimes referred to as conversion of DEM to TIN. Additional point data may include surveyed elevation points, GPS (Global Positioning System), and LIDAR data. Line data may include contour lines and breaklines.
Breaklines
are line features that represent changes of the land surface such as streams, shorelines, ridges, and roads. And area data may include lakes and reservoirs.
DEM to TIN Conversion
1. VIP
(Very Important Points) used by ArcInfo Workstation
2. Maximum z-tolerance
used by 3D Analyst and ArcInfo Workstation.
b a A H G B C P F D E s P h d P e G P C VIP evaluates the significance of an elevation point by measuring how well its value can be estimated from the neighboring point values. Figure 12.1b shows the case of using elevations at G and C to estimate the elevation at P. Pe is the estimated elevation, Ph is the actual elevation, and d represents the offset between Pe and Ph. Rather than using d as the measure of significance, VIP uses s.
Maximum Z-tolerance
The maximum
z
-tolerance algorithm selects points from an elevation grid to construct a TIN such that, for every point in the elevation grid, the difference between the original elevation and the estimated elevation from the TIN is within the specified maximum
z
-tolerance. The algorithm uses an iterative process.
TIN to DEM Conversion
The process requires each elevation point of the DEM to be estimated (interpolated) from its neighboring nodes that make up the TIN. Each of these nodes has its
x-
,
y
coordinates as well as a Z (elevation) value. The default method used by ArcGIS to convert a TIN to a DEM is local first-order polynomial interpolation .
Terrain Mapping
950 900 1000 850 850 800 The contour line of 900 connects points that are interpolated to have the value of 900 along the triangle edges.
A vertical profile showing changes in elevation along a stream tributary. The profile has a vertical exaggeration factor of 1.0 (i.e., or no vertical exaggeration).
An example of hill shading, with the sun’s azimuth at 3150 (NW) and the sun’s altitude at 450
An example of a 3-D perspective view
An example of 3-D draping. In this case, streams and shorelines are draped on a 3-D surface
Terrain Analysis
a θ b
Percent slope in the diagram is 100 x (a/b). a is the vertical distance or rise, and b is the horizontal distance or run. Degree slope can be calculated by arctan (a/b).
N W E NW W SW S N S NE E SE Aspect is a directional measure in degrees. Aspect measures are often grouped into 4 principal directions (top) or 8 principal directions (bottom).
Z
Slope
Y North
Aspect
X South
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 vol. 25, no. 3, pp. 173–185; reprinted with the permission of the American Congress on Surveying and Mapping.)
e 1 e 2 C 0 e 4 e 3 Slope
s
( e 1
e 3 ) 2
( e 4
e 2 ) 2 / 2 d
Aspect
D
arctan(( e
4
e
2
) /( e
1
e
3
))
Ritter’s algorithm for computing slope and aspect at C 0 uses the four immediate neighbors of C 0 .
e 1 e 4 e 6 e 2 C 0 e 7 e 3 e 5 e 8 Slope
S
(( e 1
2 e 4
e 6 )
( e 3
2 e 5
e 8 )) 2
(( e 6
2 e 7
e 8 )
( e 1
2 e 2
e 3 )) 2 / 8 d
Aspect
D
arctan((( e 6
2 e 7
e 8 )
( e 1
2 e 2
e 3 )) /(( e 1
2 e 4
e 6 )
( e 3
2 e 5
e 8 )))
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 6 , e 3 , and e 8 .
A (X 1 ,Y 1 ,Z 1 ) B (X 2 ,Y 2 ,Z 2 ) C (X 3 ,Y 3 ,Z 3 ) n
x =
(
y
2 -
y
1 ) (
z
3 -
z
1 ) - (
y
3 -
y
1 ) (
z
2 -
z
1 ) n
y =
(
z
2 -
z
1 ) (
x
3 -
x
1 ) - (
z
3 -
z
1 ) (
x
2 -
x
1 ) n
z =
(
x
2 -
x
1 ) (
y
3 -
y
1 ) - (
x
3 -
x
1 ) (
y
2 -
y
1 )
S
n x 2
n y 2 / n z
D
arctan( n
y
/ n
x
)
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.
Surface Curvature
GIS applications in hydrological studies often require computation of surface curvature to determine if the surface at a cell location is upwardly convex or concave.
Viewshed analysis divides the study area into (1) not visible from observation points and (2) visible from observation points.
Viewshed analysis is based on the line of sight operation.
1014 1011 1004 +1 +4 +11 1019 1015 1007 -4 +8 1025 1021 1012 -10 -6 +3 (a) (b) (c) The flow direction of the center cell in (a) is determined by first calculating the distance-weighted gradient to each of its eight neighbors. For the four immediate neighbors, the gradient is calculated by dividing the elevation difference between the center cell and the neighbor by 1. For the four corner neighbors, the gradient is calculated by dividing the elevation difference by 1.414. The results in (b) show that the steepest gradient, and therefore the flow direction, is from the center cell to the right cell (+8).
1014 1011 1004 996 (a) 1019 1015 1007 999 1025 1021 1012 1003 1033 1029 1020 1003 (b) (c) 0 0 0 0 0 1 0 0 2 2 1 2 2 6 3 3 The illustration shows a filled elevation grid (a), a flow direction grid (b), and a flow accumulation grid (c). Both shaded cells in (c) have the same flow accumulation value of 2. The top cell receives its flow from its left and lower left cells. The bottom cell receives its flow from its lower left cell, which already has a flow accumulation value of 1.
A flow accumulation grid is shown in (a). The darkness of the symbol corresponds to the flow accumulation value. A drainage network derived from the flow accumulation grid using a threshold value of 500 cells is shown in (b). The delineation of watersheds is shown in (c).
A watershed (shaded area) is derived for each of the three pour points.
Grid or TIN?
Advantages of using TIN
A main advantage of using a TIN lies in the flexibility with input data sources. One can construct a TIN using inputs from DEM, contour lines, GPS data, LIDAR data, and survey data. The user can add elevation points to a TIN at their precise locations and add breaklines, such as streams, roads, ridgelines, and shorelines, to define surface discontinuities. Besides data flexibility, TIN is also an excellent data model for terrain mapping and 3-D display . The triangular facets of a TIN better define the land surface than an elevation grid and create a sharper image. Most GIS users seem to prefer the look of a map based on a TIN rather than an elevation grid.
Grid or TIN?
Advantages of using Grid Computational efficiency is the main advantage of using grids for terrain analysis. The simple data structure makes it relatively easy to perform neighborhood operations on an elevation grid.
Thelin and Pike’s (1991) digital shaded-relief map of the United States http://www.usgs.gov/reports/misc/Misc._Investigations_Series_M
aps_(I_Series)/I_2206/usa_dem.gif
USGS’ National Hydrography Dataset http://nhd.usgs.gov/