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.

LIDARLIDAR 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 TINsGIS 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.

Ph

A 

B C

H P D

G F E

G P C

Pe

ds

a

b

  

 

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

1. Contouring

2. Vertical profiling

3. Hill shading

4. Hypsometric tinting

5. Perspective view

950

850

900

1000

800

850

                           

 

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

1. Slope and Aspect

2. Surface curvature

3. Viewshed analysis

4. Watershed analysis

θ

a

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

E

S

W

N

NE

E

SE

S

SW

W

NW

 

Aspect is a directional measure in degrees. Aspect measures are often grouped into 4 principal directions (top) or 8 principal directions (bottom).

X

Z

South

NorthY

Aspect

Slope

 

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.)

   e2  

e1 C0 e3

  e4  

Ritter’s algorithm for computing slope and aspect at C0 uses the four immediate neighbors of C0.

d2/)ee()ee(s 224

231

))ee/()eearctan((D 3124

Slope

Aspect

 

e1 e2 e3

e4 C0 e5

e6 e7 e8

                     

Horn’s algorithm for computing slope and aspect at C0 uses the eight neighboring cells of C0. The algorithm also applies a weight of 2 to e2, e4, e5, and e7, and a weight of 1 to e1, e6, e3, and e8.

d8/))ee2e()ee2e(())ee2e()ee2e((S 2321876

2853641

)))ee2e()ee2e/(())ee2e()ee2earctan(((D 853641321876

Slope

Aspect

     

A(X1,Y1,Z1)

C(X3,Y3,Z3)

B(X2,Y2,Z2)

 

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.

nx = (y2 - y1) (z3 - z1) - (y3 - y1) (z2 - z1)

ny = (z2 - z1) (x3 - x1) - (z3 - z1) (x2 - x1)

nz = (x2 - x1) (y3 - y1) - (x3 - x1) (y2 - y1)

z2

y2

x n/nnS

)n/narctan(D xy

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

1019 1015 1007

1025 1021 1012

+1 +4 +11

-4 +8

-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

1019 999

1025 1003

1033 1029 1020 1003

0

0

1015 1007

1021 1012

0 0 1 2

0 6

0 3

0 1 2 3

2

2

(a)

(b)

(c)

 

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_Maps_(I_Series)/I_2206/usa_dem.gif

USGS’ National Hydrography Dataset

http://nhd.usgs.gov/

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