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Terrain Mapping and Analysis

Data for Terrain Mapping and AnalysisDigital Terrain Model (DEM)DEM represents an array of elevation points.The quality of DEM influences the accuracy of terrain measures such as slope and aspect.

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Triangulated Irregular Network (TIN)

TIN approximates land surface with a series of non-overlapping triangles.Elevation values (z values) along with x, y –coordinates are stored at the nodes that make up the triangles.The input data to a TIN come from:– DEM, – Surveyed elevation points,contour lines,– Breaklines: line features that represent changes of

the land surface such as streams, shorelines, ridges, and roads. (Figure 12.2)

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Not every points in DEM are used to create TIN.Selected points are selected using algorithms e.g., VIP, z-tolerance.

VIP (very important points)Used by Arc/info.Convert DEM into grid and then evaluate the important of each point (each cell in the evaluation grid) by how well its value can be estimated from the neighboring cells).See Figure 12.1VIP uses the average value of four offset distance s, of each pair of neighbors around the point of interest, P in Figure 12.1 as indicator of significance for P.

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VIP computes the significant values for each cell in the elevation grid.The selection of points by VIP can be based on either a desired number or a specified significant level.

Maximum z-tolerance AlgorithmSelect the points from the elevation grid such that the difference between the original elevation and the estimated elevation from a TIN is within the specified maximum z-tolerance.The algorithm uses an iterative process.

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Terrain Mapping

ContouringMost common method for terrain mapping.Contour lines connect points of equal elevation.Contour interval represents the vertical distance between contour lines.Automated contouring follows two basic steps:

(1) Detecting a contour line intersecting a grid cell or a triangle.

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(2) Drawing the contour line through the grid cell or triangle.

Given a contour line, every triangle edge is examined to determine if the contour line should pass through the edge. If it does determine contour position by a linear interpolation. (Figure 12.3)The straight line segment can be smoothed by splining (fitting a mathematical function to a point).

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Vertical ProfilingA vertical profile shows changes in elevation along a line, such as a stream or a road.Steps: – Draw a line on a contour map.– Mark each intersection between a contour

and the profile line and records its elevation.

– Raise each intersection point to a height proportional to its elevation, and

– Plot the vertical profile by connecting the points. (Figure 12.5)

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Hill Shading (Shaded Relief)

Simulate how the terrain looks with the interaction between the sunlight and surface features. (Figure 12.6)Four factors control the visual effects of hill shading:

– Sun azimuth: the direction of the incoming light, ranging from 0 to 3600

degree in a clockwise direction.

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– The sun’s altitude: The angle of the incoming sunlight measured above the horizon between 00 to 900.

– The surface slope: ranges from 00 to 900. – The aspect: ranges from 00 to 3600.

Use the following equation to compute the relative radiance for every cell in the elevation grid or for every triangle in a TIN.

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( ) sfsfsff HHHHAAR sincoscossincos +−=

Where Rf = the relative radiance value of a facet (grid cell or a triangle).

Af = the facet’s aspect.As = the sun’s azimuth.Hf = the facet’s slope.Hs = the sun’s altitude.

Rf ranges in the value from 0 to 1.0If = Rf x 255, the If value of 255 would

results in white and 0 results in black.

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Perspective View

3-D view of the terrain (Figure 12.7).Four parameters can control the appearance of a 3-D view. (Figure 12.8)– Viewing azimuth: the direction from the

observer to the surface, range from 00 and 3600 in a clockwise direction.

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– Viewing angle: The angle measured from the horizon to the altitude of the observer, ranging between 0 to 900.• 900 means viewing directly from above.• 00 means viewing surface directly

ahead.– Viewing distance: the distance between the

viewer and the surface.

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– Z-scale (exaggeration factor): the ratio between the vertical scale and the horizontal scale. Useful for highlighting minor features.

GIS users can rotate the surface, navigate the surface, or take a close-up view of the surface.The users can superimpose thematic layers such as land cover, or roads in a 3-D draping process. (Figure 12.9)

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Terrain Analysis

Slope and AspectSlope measures the rate of change of elevation at the surface location. (Figure 12.10)

( ) 5.022 )/()/( yzxzS ∂∂+∂∂=

Where s = slope expressed as percent or degreez = elevation at x, y location

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Aspect is the directional measure of slope. (Figure 12.11)

( ))//()/(arctan xzyzA ∂∂∂∂=

Where A = aspect= directional measure in degree

starts with 00 at the north and ends with 3600

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Aspect is the circular measure, the users often transform aspect measures before they can use in numerical analysis.The common method is to transform into fouror eight principal directions, and treat aspects as categorical data or principal direction. (Figure 12.12)Slope and aspects are used for studies landform, watershed units, soil erosion, habitat suitability, site analysis, and many other fields.

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Computing Algorithms for Slope and Aspect Using Grid

We can measure the slope and aspect for a cell in the elevation grid by the quantity and direction of the tilt of the cell’s normal vector.Given a normal vector (nx, ny, nz), see Figure 12.13)

( )xy

zyx

nnAnnns

/arctan/)( 5.022

=

+=

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Approximation Methods

Ritter’s AlgorithmUse 3x3 moving windowsThe slope of the center cell can be estimated by the four immediate members. See Figure 12.14

( )

( ))/()(arctan

2/)()(

3124

5.0224

231

eeeeD

deeeeS

−−=

−+−=

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S is slope gradient if multiply S by 100, the unit is in percent slope.D is measured in radian with respect to x-axis, can be converted into degree from a north base of 00 using algorithm (see text in Chang’s Chapter 12, page 228).

Horn’s AlgorithmUsed in Arc/Info and ArcView.Use 8 neighboring cells and applies weight of 1 to 4 corner cells. See Figure 12.15.

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( )deeeeee

eeeeeeS8/)))2()2((

))2()2((5.02

321876

2853641

++−++

+++−++=

)))2()2((/))2()2arctan(((

853641

321876

eeeeeeeeeeeeD

++−++++−++=

Horn’s Algorithm

Used in Arc/Info and ArcView.Use 8 neighboring cells and applies weight of 1 to 4 corner cells. See Figure 12.15.

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Computing Algorithms using TIN

Use bi-directional normal vector (vector perpendicular to the triangular surface).Suppose a triangle is made of the three nodes:• A (x1, y1, z1), B (x2, y2, z2),and C (x3,

y3, z3)

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The normal vector are:• AB, (x2-x1), (y2-y1), (z2-z1) and • AC, (x3-x1), (y3-y1), (z3-z1).

The three components of the normal vector are:• 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)

)/arctan(

/)( 5.022

xy

zyx

nnaspectnnnslope

=

+=

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IHyGxFxyEyDxyCxyBxyAxz

++++++++= 222222

Surface Curvature

Determine if the surface is upwardly convex or concave.Use 3x3 widows with a quadratic polynomial equation.

Coefficients A to I can be estimated usingthe elevation values in 3x3 window and the grid cell size. See Box 12.6

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Three curvature measures can be computed from the coefficients:• Profile curvature = -2 ((DG2+EH2+FGH)/

(G2+H2))• Plan Curvature = 2((DH2+EG2-FGH)/(G2+H2)• Curvature = 2(D+E)

Profile curvature estimates along the direction of maximum slope.Plan curvature estimates across the direction of maximum slope.The curvature is (profile curvature – plan curvature).

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Viewshed Analysis

Viewshed is the areas of the land surface that are visible from an observation point(s).Applications:– Siting forest lookout station, – Selecting location for resort area development,– Evaluate scenic quality along the highway.– Help locate antennas for wireless

communication.See Figure 12.71a,b

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Watershed Analysis

A watershed is an area that drains water and other substance to a common outlet.Also called basin or catchment.Watershed analysis requires 3 datasets:– A filled elevation grid– A flow direction grid (Figure 12.18)– A flow accumulation grid (Figure 12.19).

Watersheds can be delineated for selected points or for an entire grid (Figure 12.19b).

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Grid versus TIN

Main Advantage of TINFlexibility with input data sources– DEM, breaklines, contour lines, GPS data,

or survey data– User can add elevation point to TIN at their

precise locations, or add features such as ridgelines, streams or shorelines to define surface discontinuity.

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TIN is an excellent data model for 3-D display, better define land surface than elevation grid.

Main Advantages of Elevation GridComputational efficiencyTIN made of sampled points from a DEM is less accurate than the full DEM.