# Digital_Terrain_Analysis_saiful_2008 by 1KeLzN7

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```									Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam

Digital Terrain Mapping and
Analysis

Dr. A.K.M. Saiful Islam
Institute of Water and Flood Management (IWFM)
Bangladesh University of Engineering and Technology (BUET)
Lecture Topic
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam

This lecture will focus on
• Geo-referencing
–   Coordinate Systems
–   Map Projections
–   Coordinate Transform
–   Map & Time Distance, Scale and accuracy
–   Interpolation techniques
• Digital Terrain Mapping and Analysis
– DEM
– DTM
Coordinate Systems
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam

Geospatial data should be geographically referenced ( called
georeferenced or geocoded) in a common coordinate system.

 Plane Orthogonal Coordinates
One of the most convenient way of locating points is to use
plane orthogonal coordinates with x (horizontal) and y (vertical)
axis.
 Polar Coordinates
A polar coordinate system with the angle (q ) measured from
the polar axis (x axis) and distance (r) from the pole is used in
some cases.
 3D Orthogonal Coordinates
Three dimensional (3D) orthogonal coordinates are also used
to locate points with the plane coordinates (x, y) and height or
depth (z).
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam

Coordinates
Plane Orthogonal Cartesian
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam

Polar coordinates
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam

3D Coordinate System
The Shape of the Earth
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam

• The shape of the Earth can be represented by an ellipsoid of
rotation (or called a spheroid) with the lengths of the major semi-
axis (a) and the minor semi-axis (b).
• Two type of coordinate system use: (i) Geodetic, (ii) Geocentric
coordinates
Geodetic and Geocentric Latitude
 
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam

Geocentric Latitude – The acute angle measured perpendicular to
the equatorial plane and a line joining the center of the earth and a
point on the surface of the reference ellipsoid.
   Geodetic Latitude – The acute angle between the equator and a line
drawn perpendicular to the tangent of the reference ellipsoid. Map
coordinates are given as longitude and geodetic latitude.

Map Projection
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam

• A map projection is a process of transforming location on
the curved surface of the Earth with the geodetic
coordinates (j , l) to planar map coordinates (x, y).

• More than 400 difference map projections have been
proposed. The map projections are classified by the
following parameters.

–   projection plane: perspective, conical, cylindrical
–   aspect: normal, transverse, oblique
–   property: conformality, equivalence, equidistance
–   size: inside, tangent, secant
Projection property
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam

1. Conformality is the characteristic of true shape, wherein a projection
preserves the shape of any small geographical area. This is
accomplished by exact transformation of angles around points.
– The property of conformality is important in maps which are used for
analyzing, guiding, or recording motion, as in navigation.

2. Equivalence is the characteristic of equal area. Preservation of
equivalence involves an inexact transformation of angles around
points and thus, is mutually exclusive with conformality except along
one or two selected lines.
– The property of equivalence is important in maps which are used for
comparing density and distribution data, as in populations.

3. Equidistance is the characteristic of true distance measuring. The
scale of distance is constant over the entire map.
– Equidistance is important in maps which are used for analyzing
velocity, e.g. ocean currents. Typically, reference lines such as the
equator or a meridian are chosen to have equidistance and are termed
standard parallels or standard meridians.

Perspective Projection
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam

• Perspective projections are classified based on the
projection center or viewpoint.
Conical Projection
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam

• Conical projections are classified by the
aspect as well as the cone size
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam

Conic (secant)
Conic (tangent)
Conic projection
Cylindrical Projections
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam

• Cylindrical projections are classified as in case of conical
projections. One of the most popular cylindrical projections is the
Universal Transverse Mercator (UTM) with a transverse axis, secant
cylinder and conformality (equal angle).
UTM Projection
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam

• Universal Transverse
Mercator (UTM) with a
transverse axis, secant
cylinder and conformality
(equal angle).

• UTM is commonly used for
topographic maps of the
world, devided into 60
zones with a width of 6
degree longitude.
Coordinate Transformation
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam

Coordinate transformation is to transform a
coordinate system (x, y) to another coordinate
system (u, v). The transformation is needed in the
following cases:

– to transform different map projections of many GIS
data sources to an unified map projection in a GIS
database,

– to adjust errors which occur at map digitization
due to shrinkage or distortion of the map
measured, and

– to produce geo-coded image by so called
geometric correction of remote sensing imagery
with geometric errors and distortions.
Reference for Coordinate
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam

Transformation
• Coordinate transformation is executed by a selected
transformation model (or mathematical equation), with
a set of reference points (or control points), that are
selected as tic masks at the corner points, reseau or
ground control points.
Major Transformation
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam

a)   Helmert
Transformation
scale, rotation and shift

b)   Affine Transformation
skew, scale of x and y,and
shift

c)   Pseudo Affine
Transformation
bi-linear distortion

Transformation
parabolic distortion

e)   Perspective Projection
rectification of aerial photo

f)   Cubic Transformation
cubic and distortion)
Distance
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam

•   Distance is one of the important elements in measuring spatial objects in
GIS. Several different concepts of distance are defined as follows.

•   Euclidean Distance
Euclidean distance D is the defined as the distance measured along a
straight line from point (x1, y1 ) to point (x2, y2 ) in Cartesian coordinate
system . D2 = ( x1 - x2 )2 + ( y1- y2 )2

•   Manhattan Distance
Manhattan distance D is defined as the rectilinear rout measured along
parallels to X and Y axes
•   D = | x1 - x2| + | y1-y2|
Distances (Contd..)
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam

•   Great Circle Distance
Great circle distance D is defined as
distance along the great circle of the
spherical Earth surface from a point (1,
1; latitude and longitude) to another
point (2, 2) where R is the radius of the
Earth (R = 6370.3 km) on the assumption
that the Earth is a sphere.

•   Mahalanobis Distance
Mahalanobis distance D is a normalized
distance in the normal distribution from
the center (X0) to a point (X) in case of n
dimensional normal distribution.
Mahalanobis distance is used in the
maximum likelihood method for the
classification of multi-spectral satellite
images. where S: variance-covariance
matrix
Distances (Contd..)
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam

Time Distance

• Time distance is defined as the time required to move from point B
to point A by using specific transportation means.
Scale, Accuracy and Resolution
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam

• Scale of map refers to the ratio of distance on a map over the
corresponding distance on the ground.

• The scale is represented as 1: M or 1/M, where M is called the scale
denominator.

• The larger the scale, the more the detail described by the map and
with higher accuracy.

• Accuracy is generally represented by standard deviation of errors,
that is difference between measurements and the true value.
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam

accuracy and resolution
Relationship between scale,
Principle of Interpolation
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam

Interpolation is the procedure of estimating
the value of properties at unsampled points or
areas using a limited number of sampled
observations.
Interpolation Techniques
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam

• 1. Pointwise interpolation
• 1(a) Thiessen polygon
• 1(b) Weighted Average
• 2. Interpolation by curve fitting
– 2.1 Exact interpolation
• 2. 1(a). Nearest neighbor
• 2. 1.(b) Linear interpolation
• 2. 1(c) Cubic interpolation
– 2.2 Approximate interpolation
• 2.2(a) Moving Average
• 2.2(b) B-spline
• 2.2(c) Curve Fitting by Least Square Method
 3. Interpolation by surface fitting
– 3.1 Regular grid
• 3.1(a) Bilinear Interpolation
• 3.1(b) Bicubic Interpolation
– 3.2 Random points
• 3.2(a) TIN
1. Pointwise Interpolation
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam

 Pointwise interpolation is used in case the sampled
points are not densely located with a limited influence
or continuity in surrounding observations, for example
climate observations such as rainfall and
temperature, or ground water level measurements at
wells.
1(a) Thiessen Polygons
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam

 Thiessen polygons can be generated using distance
operator which creates the polygon boundaries as the
intersections of radial expansions from the observation
points.

 This method is also known as Voronoi tessellation.
1(b) Weighted Average
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam

 A window of circular shape with the radius of
dmax is drawn at a point to be interpolated, so
as to involve six to eight surrounding
observed points.
2. Interpolation by Curve Fitting
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam

 the principle of curve fitting respectively to
interpolate the value at an unsampled point
using surrounding sampled points.
2. Curve Fitting
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam

Curve fitting is an important type of interpolation in
many applications of. Curve fitting is divided into two
categories.

 2.1 exact interpolation : a fitted curve passes through all
given points.

 2.2 approximate interpolation : a fitted curve does not
always pass through all given points.
2.1 Exact interpolation
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam

There are three methods:
2.1(a) nearest neighbor : the same value as that
of the observation is given within the proximal
distance
2.1 Exact interpolation
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam

2.1(b) linear interpolation: a piecewise
linear function is applied between two
2.1 Exact interpolation
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam

• 2.1(c) cubic interpolation : a third order
polynomial is applied between two adjacent points
under the condition that the first and second order
differentials should be continuous.
2.2. Approximate Interpolation
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam

There are three methods;
2.2(a) Moving Average: a window with a range of -d to
+d is set to average the observation within the region
2.2 Approximate Interpolation
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam

2.2(b) B-Spline: a cubic curve is
observations
2.2 Approximate Interpolation
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam

2.2(c) Curve Fitting by Least Square Method.
Least square method (sometimes called regression model) is a
statistical approach to estimate an expected value or function with the
highest probability from the observations with random errors. The
highest probability is replaced by minimizing the sum of square of
residuals in the least square method.
Equation

Y  ax  b
Slope

a
 ( Xi  X )(Y  Y )
 ( Xi  X ) 2

intercept

b  Y  aX
3. Interpolation by Surface Fitting
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam

 the principle of surface fitting respectively to
interpolate the value at an unsampled point
using surrounding sampled points.
3. Surface Fitting
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam

• Surface fitting is widely used for interpolation of points on
continuous surfaces such as digital elevation model
(DEM), geoid, climate model (rainfall, temperature,
pressure etc.) and so on.

• Surface fitting is classified into two categories:
– 3.1 surface fitting for regular grid and
– 3.2 surface fitting for random points.

• 3.1 Surface Fitting for Regular Grid
Following two methods are commonly used.
3.1(a) Bilinear Interpolation
3.1(b) Bicubic Interpolation
3.1 Surface Fitting for Regular Grid
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam

3.1(a) Bilinear Interpolation
Bilinear function is used to interpolate z using the
following formula with respect to normalized
coordinates (u, v) of the original coordinates (x, y)
3.1Surface Fitting for Regular Grid
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam

3.1(b) Bicubic Interpolation
Third order polynomial is used to fit a continuous
surface using 4 x 4 = 16 adjacent points.
3.2 Surface Fitting for random
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam

Points
3.2. (a) Triangular network called as
Triangulated Irregular Network (TIN) is applied
Compare Interpolation methods
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam

• Thiessen polygons are Used for service area analysis of public
facilities such as hospitals. Originally proposed to estimate aerial
averages precipitation in 1985.

• Inverse Distance Weighted can be a good way to take a first look
at an interpolated surface. However, there is no assessment of
prediction errors. Accuracy depends on the selection of a power
value and the neighborhood search strategy. A smaller (6) actually
produce better estimations than a larger number (12).

• Thin-plate Splines (applies to surface) are recommended for
smooth, continuous surfaces such as elevation and water table. Also
used for interpolating mean rainfall surface and land demand
surface.
Kriging
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam

•   Kriging is a geostatistical method for spatial
interpolation.
•   It can assess the quality of prediction with estimated
prediction errors.
•   It uses statistical models that allow a variety of map
outputs including predictions, prediction standard
errors, probability, etc.

•   Semivariogram can be fitted as:
1. Ordinary Kriging models:
Spherical, Circular, Exponential,
Gaussian and Linear.
1. Universal Kriging models:
Linear with Linear drift, and
Semivariogram
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam

• The semivariogram functions
quantifies the assumption that
things nearby tend to be more
similar than things that are
farther apart. Semivariogram
measures the strength of
statistical correlation as a
function of distance.

• Semivariance:
Y(h) = ½ [(Z(xi) - Z(xj)]2

• Covarience = Sill – Y(h)
Data Structure for Continuous
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam

Surface Model
In GIS, continuous surface such as terrain surface, meteorological
observation (rain fall, temperature, pressure etc.) population
density and so on should be modeled

• Grid at regular intervals
– Bi-linear surface with four points or bi-cubic surface with
sixteen points is commonly used
• Random points
– Triangulated irregular network (TIN) is commonly used.
Interpolation by weighted polynomials is also used.
• Contour lines
– Interpolation based on proportional distance between
adjacent contours is used. TIN is also used.
• Profile
– Profiles are observed perpendicular to an alignment or a
curve such as high ways. In case the alignment is a straight
line, grid points will be interpolated. In case the alignment is
a curve, TIN will be generated.
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam

Different Types of DEM
Remote Sensing and GIS in Water Management © Dr. Saiful Islam, IWFM, BUET

DEM
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam

• A DEM (digital elevation model) is digital
representation of topographic surface with the
elevation or ground height above any geodetic
datum. Followings are widely used DEM in GIS:
DTM
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam

    A DTM (digital terrain model) is digital representation of
terrain features including elevation, slope, aspect,
drainage and other terrain attributes.

    Usually a DTM is derived from a DEM or elevation data.

several terrain features including the following DTMs.
1. Slope and Aspect
2. Drainage network
3. Catchment area
6. Slope stability
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam

Examples of DTM
1. Slope and Aspect
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam

(i) Slope
• The steepest slope (s) and the direction from the
east () can be computed from 3 x 3 matrix.
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam

Slope calculation
Slope calculation
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam

 Slope is defined by a plane tangent to a
topographic surface, as modelled by the
DEM at a point (Burrough, 1986).

 Slope is classified as a vector; as such it
has a quantity (gradient) and a direction
(aspect).

 Slope gradient is defined as the maximum
rate of change in altitude (tan )
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam

Example: Slope from elevation data
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam

(ii) Aspect
• The aspect that is, the slope faced to azimuth is
180° opposite to the direction of q
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam

Figure 1. Slope components, note that slope gradient can be
express in percent or in degrees
Aspect calculation
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam

 Aspect identifies the steepest downslope
direction from each cell to its neighbors. It can
be thought of as slope direction or the compass
direction a hill faces.
 It is measured clockwise in degrees from 0 (due
north) to 360, (again due north, coming full
circle). The value of each cell in an aspect
dataset indicates the direction the cell's slope
faces. Flat areas having no downslope direction
are given a value of -1.
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam

data
Example: aspect from the elevation
2. Drainage Network and
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam

Watershed
• The lowest point out of the eight neighbors is
compared with the height of the central point
to determine the flow direction.
Surface Specific points
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam

• + is assigned if the height of the central point is higher than
the one of the eight neighbors and - if lower.
– A peak can be detected if all the eight neighbors are lower.
– A pit or sink is formed if all the eight neighbors are higher
– A pass can be extracted if the + and - alternate around the central
point with at least two complete cycle.
Remote Sensing and GIS in Water Management © Dr. Saiful Islam, IWFM, BUET

Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam

• Shade is defined as reduced reflection depending on
the angle between the terrain surface and the incident
light such as the sun.

• Shadow is projected areas that the incident light cannot
reach because of visual hindrance of objects on terrain
relief
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam

The effect of hill shading on the assumption of an ideally
diffused reflecting surface (called Lambertian surface)
can be computed as follows:
Relative shading = cos  = |nxsx + nysy+ nzsz |≤ 1.0
where  : angle between incident light vector s and surface normal n
Altitude
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam

• The altitude is the slope or angle of the
illumination source above the horizon. The
units are in degrees, from 0 (on the
horizon) to 90 degrees (overhead). The
default is 45 degrees.
Azimuth
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam

• The azimuth is the angular direction of the
sun, measured from north in clockwise
degrees from 0 to 360. An azimuth of 90 is
east. The default is 315 (NW).
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam

below has an
azimuth of 315
and an altitude
of 45 degrees.
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam

maps of Glacier National Park
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam

• By placing an elevation raster on top of a created
hillshade, then making the elevation raster transparent,
you can create realistic images of the landscape.

Generation of Contour Lines
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam

• Contour lines are one of the terrain features which
represent the relief of the terrain with the same
height. There are two types of contour lines in
visualizing GIS data:

• Vector Line Drawing
In case when the terrain points are given in grid, the
simplest method is to divide the square cell into two
triangles mechanically.

• Raster Image
Contour image with painted contour terraces, belts or
lines instead of vector lines will be generated in raster
form.
Interpolation of Elevation from
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam

Contours
• Digital elevation model (DEM) is very often generated by
measuring terrain points along contour lines using a digitizer.
DEM with contour points should be provided with an algorithm
interpolate elevation at arbitrary points. There are several
interpolation methods as follows.

 Profile Method
A profile passing through the point to be interpolated will be
generated and linear or spline curve applied.
 Proportional Distance Method
According to distance to two adjacent contour lines, the
elevation is interpolated proportionally with respect to the
distance ratio.
 Window Method
A circular window is set up around a point to be interpolated and
adjacent terrain points are used to interpolate the value using
second order or third order polynomials.
 TIN Method
TINs are generated using terrain points along contour lines.
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam

Interpolation Methods
Examples: A Digital Elevation Model and
associated contour map of Glacier Nat'l
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam

Park
Automated Generation of DEM
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam

• Automated generation of DEM is achieved by photogrammetric
methods based on stereo aerial photography and satellite stereo
imagery.
• Parallax is defined as difference between left and right photographs or
image coordinates. The higher the elevation is, the bigger the parallax
is. If the parallax is constant, equal elevation or contour lines will be
produced.
Triangulated Irregular Network (TIN)
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam

• Triangulated irregular network or TIN is a DEM with a
network of triangles at randomly located terrain points.

Contouring of TIN is based on
the following procedure:

step 1: find the intersect of contour and a
side.
step 2: assign the "reference point" with
the symbol r to the vertex above the contour
height and the "sub-point" with the symbol
s to the vertex below the contour height.
step 3: shift over to the transversing to find
the third vertex in the triangle by checking
whether it is a reference point (r) or sub-
point (s).
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam

Example: TIN Creation
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam

Thank you

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