Distortions • The earth is spherical, and a simple way of mapping it without distortion is to map it on a globe. However, mapping on globes is not possible. • The transformation from the three-dimensional ellipsoid/sphere to the two-dimensional plane (flat) surface is not possible without some form of distortion. • The distortions increase as the distance from the central point of the projection increases • Areas smaller than 25 x 25 km: No distortions • Areas larger than 25 x 25 km: Always distortions • Map projections are used to control/minimize the distortions Classification and properties of map projections Properties of map projections • Areas are everywhere correctly represented • All distances are correctly represented • All directions on the map are the same as on Earth • All angles are correctly represented • The shape of any area is correctly represented (e.g. a circle projected would remain a circle)

16. PROJECTIONS AND COORDINATE SYSTEMS (COORDINATE REFERENCE SYSTEMS
(CRS))
• Spatial reference system is required to define geometric location and shape of entities of the
earth surface
• Geospatial reference system (‘coordinate reference system – CRS’) is required for
modelling:
– The geometry of entities occurring on/below/above the surface of the Earth and
– Terrain
• Two classes of geospatial reference systems
1. Unprojected (Geographic)
2. Projected
3. Very many variants exist for both classes
• Maps, place objects/phenomena on the earth’s
surface in their correct relationship to one another.
• Map can be considered as a Geographic
Information System that gives answers to many questions.
• From Geometric Fundamentals of Mapping, the
earth can be approximated by an ellipsoid or by a sphere
PLANET EARTH

17. The Earth’s shape is irregular
Its positioning needs simplification
• Planet earth = a 3D-body, spherical but (abstraction from relief)
• When abstraction is made from relief, the Earth can be described by:
– The geoid (equipotential surface of gravity force - mean sea level) or by
– A sphere slightly flattened at the poles (spheroid/ellipsoid)

18. • Geographic (unprojected) coordinates:
– Expressed as angles with respect to 2 of 3 axes through the gravity point of the
ellipsoid
– LONGITUDE: 0° (Greenwich) to 180° East and 0° to 180° West measured in the
horizontal plane
– LATITUDE: 0° (Equator) to 90 North and 0° to 90° South) measured in the
vertical plane
– Degrees-Minutes-Seconds or Decimal Degrees:
20° 15’ 15” = 20,2525
• Geoid
– 3D-physical datamodel of the Earth’s surface, based on measurements of the gravity
force
• Local and Global Ellipsoids
– Mathematical 3D-models of the Earth’s surface
– Global ellipsoids are defined to represent the full Earth with overall acceptable accuracy
– Local ellipsoids are defined to represent a part of the Earth’s surface only, with high
accuracy
What is a map projection
• Map projection is a systematic arrangement of the earth’s curved geographic coordinates
(latitudes and longitudes) into rectangular (Cartesian) coordinates (x, y), on a flat surface:
paper or monitor screen.
• Is a mathematical formula by which you can transform a set of spherical Geographic
coordinates (latitudes and longitudes) into a set of Cartesian coordinates (x, y)
representing positions on the two-dimensional surface of the map.
• For each map projection the following equations are available:
x, y = f (,) forward equation
,  = f (x, y) inverse equation

19.  Different map projections result in different spatial relationships between regions
 This cannot be done without some distortion
 There are many kinds of projections, but all involve transfer of the distinctive global
patterns of parallels of latitude and meridians of longitude onto an easily flattened, or
developable, surface
 The three (3) most common developable surfaces are the cylinder, cone, and plane
 A plane is already flat, while a cylinder or cone may be cut and laid out flat, without
stretching
 Thus map projections may be classified into four (4) general families namely:
 cylindrical
 Conical
 planar or azimuthal and
 Miscellaneous projections

20. Note that for any type of map projection during transformation of a spherical surface into a flat
surface some error or distortions on the map are inevitable
Ideally, a distortion-free map has four (4) valuable properties:
• conformality
• equivalence
• equidistance
• true direction
Distortions
• The earth is spherical, and a simple way of mapping it without distortion is to map it on a
globe. However, mapping on globes is not possible.
• The transformation from the three-dimensional ellipsoid/sphere to the two-dimensional
plane (flat) surface is not possible without some form of distortion.
• The distortions increase as the distance from the central point of the projection increases
• Areas smaller than 25 x 25 km:
No distortions
• Areas larger than 25 x 25 km:
Always distortions
• Map projections are used to control/minimize the distortions
Classification and properties of map projections
Properties of map projections
• Areas are everywhere correctly represented
• All distances are correctly represented
• All directions on the map are the same as on Earth
• All angles are correctly represented
• The shape of any area is correctly represented (e.g. a circle projected would remain a
circle)

21. Classification criteria
• Map projections can be categorized on the basis of the followings:
The shape of the projection plane (Class)
The characteristics they retain (Property)
The orientation of the projection plane (Aspect
• Class refers to the shape of the projection plane (developable surface).
• Cylindrical projections result from projecting a spherical surface onto a cylinder.
• Conic projections result from projecting a spherical surface onto a cone.
• Azimuthal/Zenithal projections result from projecting a spherical surface onto a plane.
PROPERTY
• On the basis of the characteristics they retain, map projections are classified as
conformal, equivalent (equal area) or equidistant.
• Conformal: Shapes and angles are correctly represented at infinitely small locations.
• Equivalent: Areas of the sphere are correctly represented on the map.
• Equidistant: Distances between points or along certain lines are correctly represented

22. Aspect
Cylindrical projections
• Cylinder is tangent to the sphere (normal case) contact is along a great circle i.e. the
shortest distance on the earth’s surface. Both parallels and meridians are straight lines
perpendicular to each other.
• Cylinder upon the sphere is projected at right angles to the poles, the cylinder and the
resulting projection are transverse.
• Cylinder at some other, non-orthogonal angle with respect to the poles, the cylinder and
resulting projection is oblique.
Conic and Azimuthal projections
• When the cone is tangent to the sphere (normal case) contact is along a small circle. The
meridians are circular arcs.
• When the plane is tangent to the sphere contact is at a single point on the surface of the
earth. In the normal aspect meridians are straight lines, and parallels are concentric
circles centering on the pole.
MAP PROJECTIONS IN COMMON USE
Projections used in topographic mapping
Universal Transverse Mercator
• The Universal Transverse Mercator (UTM) projection is derived from the Transverse Mercator
projection, which is conformal.

23. • It is a worldwide-accepted projection for topographic mapping purposes. The UTM is primarily a
conformal cylindrical projection, but one with:
a transverse secant cylinder
30 positions of the cylinder each considered twice.
• The UTM covers the area from 80º South to 84º North. The arctic and Antarctic regions are
covered by the Universal Polar Stereographic (UPS) projection.
• Originally the coverage of the UTM system was from 80º S to 80º N but at the request of
Norway, it was extended northwards 4º to enable Spitzbergen to be mapped within the system.
• The UTM-system divides the area between 80º south to 84º north into:- 60 longitudinal zones
Other examples of local datums
UTM GRID ZONES OF THE WORLD

24. Graticule
• Each zone has its own central meridian.
• Each zone the central meridian and the Equator are projected as straight lines.
• Parallels and meridians are curved but intersecting at right angles (a conformal
requirement).
Grid
 Each zone has its own Cartesian coordinate system.
 Central meridian has been given an Easting value of 500,000 m (to avoid negative
coordinates).
 For mapping north of the Equator, the Equator is given a Northing value of 0 m.
 For mapping south of the Equator; the Equator is given a Northing value of 10,000,000
m.
 Lambert Conic Conformal (e.g.France, Spain, Morocco, Algeria)
 Property: conformal

25.  Graticule:
Spacing of parallels increases outside the standard parallels.
Indicate the scale is a little too large along the meridians.
Spacing of parallels decreases in between the standard parallels.
Indicate the scale is a little too small along the meridians
• Parallels and meridians intersect at right angles (a conformal requirement).
Scale:
True along one or two chosen standard parallels
Scale is constant along any given parallels
Scale change is the same in all directions at a given point (indicating conformity).
Distortion:
Area distortion increases away from the standard parallels

26. Stereographic projection (e.g. The Netherlands)
• Property:conformal
• Graticule:
All meridians and parallels are shown as circular arcs or straight lines.
In the polar aspect the meridians are equally spaced straight lines
Parallels are unequally spaced circles centred at the pole.
In equatorial aspect the central meridian and the Equator are straight lines

27. • Scale:
Scale is constant along any circle having its centre at the projection centre.
Scale increases moderately with distance from the centre.
• Distortion:
Areas increase with distance from the projection centre. The ellipses of distortion
remain circles (indicate conformity).
Projection used in navigational charts and atlases
Mercator projection
• Property: conformal
• Graticule:
Parallels and meridians are straight lines intersecting at right angles.
Meridians are equally spaced.
Parallel spacing increases with distance from the Equator.
Poles cannot be shown.

28. • Scale:
True along the Equator or along two parallels equidistant from the Equator (the secant
form).
Scale increases with distance from the Equator, as a function of sec , to infinity at the
poles.
Scale is constant along any given parallel.
• Distortion:
The ellipses of distortion appear as circles (indicating conformity)
Increases in size away from the equator (indicating area distortion).
All loxodromes or rumb-lines make equal angles with all meridians and lines of constant
true bearing –are straight lines.

29. Gnomonic (or central azimuthal) projection
• Property:
Neither conformal nor equal-area. Great circle lines are shown as straight lines.
• Graticule:
In polar aspect the parallels are unequally spaced circles. Spacing increases rapidly away
from the pole.
• Scale:
Increases rapidly with the distance from the centre.
• Distortion: Area and shape distortions are extreme.
Choosing a suitable map projection
• A basic knowledge of projections helps in selecting a map that comes closest to fulfilling
a specific need.

30. Factors influencing map projection selection
The selection of a map projection depends on:
• Purpose of the map
• The shape of the area
• The size of the area
• Location/position of the area to be mapped
Conclusion
• The projection which is best fits a given country is always the minimum-error projection
of the selected class.
• The map projection property depends on the map purpose.
• There are strong arguments in favor to using an international standard projection for
mapping. One problem encountered by many map users is the edge matching of adjacent
regions.
• Map must base on the same ellipsoid or sphere and sometimes have the same standard
parallels or meridians.
• In conclusion, one should realize that there are no good or bad projection but rather,
there are good or bad applications of map projections.
4 .GLOPBAL POSITIONING SYSTEM (GPS)

31. WHAT IS GPS?
• The Global Positioning System (GPS) is a space-based, microwave, 24-hour, all-weather,
global military navigation system designed, deployed, financed and managed by the U.S.
military authorities.
GPS System
• Designed to provide positioning and timing information:
– 24 hours/day, 7 days/week
– under any weather conditions
– anywhere in the world
Consists of:
– Space segment
– Control segment
– User segment
Space segment
• The Space Segment of the system consists of the GPS satellites. These space vehicles
(SVs) send radio signals from space
• 24 space vehicles and spares
• 6 orbital planes with 4 vehicles each
• Vehicles are about 11,500miles above earth
• 5 to 8 SVs visible from anywhere on earth.
• Orbit every 12 hours

32. Control segment
• The Control Segment consists of a system of tracking stations located around the
world
• SVs are controlled by five system tracking stations

33. User segment
• The GPS User Segment consists of the GPS receivers and the user
community. GPS receivers convert SV signals into position, velocity, and
time estimates
• 2 Parts of user Segment
• Civilian
– SPS - Standard Positioning Service (Horizontal error 100m)
• Uses single frequency L1
• Military
– PPS - Precise Positioning Service (Error 22m)
• Uses two frequencies L1/L2
Civil users worldwide use the SPS without charge or restrictions.
Receiver Output
 Position, Velocity, Time (PVT)
 Position
o Latitude ddmm.mmmm
o Longitude dddmm.mmmm
 Altitude m
 Velocity
o Speed knots
o Heading degrees
 Time (UTC)
o Date dd/mm/yy
o Time hh/mm/ss.sss
GPS Position calculation
• Each satellite is continuously radiating a signal that can be picked up with GPS receiver
• The reciever has accurate clock that records when the signal is received
• And encrypted within the signal is the time at which it was sent from the satellite

34. • This allows the time it takes the signal to travel from the staellite to earth, delta T, to be
calculated
• Like electromagnetic radiation, the signal travels at speed of light, C
(186,000 miles per second), so the distance from the satellite to the earth is
given by Δr= CΔt
• If distance Δr1 from only one satellite is known, the object could be
anywhere on a sphere of radius Δr1 centered on that satellite (slide)
• Similarly If distance from a second sattelite is also known, the object lies on
a sphere of radius Δr2 centred on the second satellite .
• The intersection of the two spheres is a circle so with two satellites the
object could be anywhere on this circle of intersection .

35. • The addition of the third satellite provides another such circle, and the
intersection of the two circles yields two potential locations for the object
• The addition of a fourth satellite determines which of the two potential
locations is the actual one

36. Applications for Conservation and LUP
• Map making
– GPS provides a way to collect feature data and either create maps
from scratch or improve existing maps
– Monitoring
– GPS can be used to monitor the landscape and raise an alarm when
there is landscape deterioration or species decline
– Species range, movement mapping (GPS Collars)
• Ground truthing and georeferencing satellite images
– GPS used to collect reference points on the ground for georeferencing
and image classification
– Navigation
– GPS can be used to navigate to points of concern eg for study
GPS Data collection
• Involves recording coordinates of points and lines
– Waypoints
– Tracks
– (some systems allow collecting polygon data)
• Points to note
– Obtain suitable Units
– Plan your field work
– Prepare accompanying forms
– Prepare enough batteries to power units
– Establish naming conventions as needed
– Prepare to record hardcopy backup

37. – Check signal and accuracy before recording position, if necessary move to get
clear view of sky
Downloading GPS data
• Downloading GPS data requires software and cable. These normally come with the unit.
• Install the software first then connect the unit
• Open the software and establish connection. This may involve changing the connection
port.
• Some software utilities (e.g. Garmin DNR) can download the data and put it into the GIS
program
Displaying GPS data
• Data from GPS will normally be in ASCII text format
• After download, edit the data to put it in correct format for GIS
• Add data to GIS and use software tools to display
• Save data in GIS format as desired
OR
Enter data in Excel and save in dbase format
Then proceed in with GIS (e.g. ArcView) software
In ArcView
 Open tables in the Arcview table of contents
 Add table – add the dbase file with your field data
 Close tables and open View in Arcview table of content
 In view-Go to view-add event them
 Identify GPS data standing for point, line and polygon features
 Construct appropriate layers (polygon, line and point) and overlay them

38.  Generate layout map with all necessary map elements on
Choosing a GPS receiver
• Types
– Geodetic
– Mapping
– Handheld
• Considerations
– Price
– Accuracy required
– Environment
– Memory
5.Geoprocessing and spatial analysis
Geoprocessing and spatial analysis
Definitions
Geoprocessing
The term geoprocessing could be defined as the application of core GIS operations that create
new spatial data from existing or derived data
This definition excludes operations such as cartography, data creation and editing, database
scheme management and visualization
Spatial analysis
Spatial analysis is the study of the pattern and relationships between points, lines, areas, and
surfaces
It is about discovering/creating new relationships, (in GIS language) it means creating new maps
(shape files, coverages
GIS functional spatial analyses
Some of the GIS functional spatial analyses adopted from ESRI ArcGIS include operations such
as:
 Dissolve

39.  Clip
 Buffer
 Overlay
 Modelling
Dissolve
 Dissolve combines adjacent features within a feature class based on an attribute value
 it aggregates items that have the same value
 Simplify data based on common attribute values
 You can dissolve either polygon or line feature classes, and the output will contain the
same feature type as the input
Clipping data
 Clip is used to cut out a piece of one layer using one or more of the polygons in another
layer as a cookie cutter
 Use one feature class to define the boundary of another

40.  This is particularly useful for creating a new layer that contains a geographic subset of
the features in another larger layer
 The layer that is having its features clipped can contain points, lines, or polygons
 The cookie cutter or clip layer must contain polygon features only
Buffer
 A buffer is a polygon zone around some geographic feature or set of features
 It is a distance analysis tool for points, lines, and areas
 It creates new polygon representing specified distances
 Answer questions based on proximity e.g. what is outside or inside the buffer polygon?
 Buffer zones can be used to find features contained inside or that fall outside a certain
specified distance
Buffering
• A distance analysis tool for points, lines, and areas
• Create new polygon representing specified distance
• Answer questions based on proximity
– What is outside or inside the buffer polygon?

41. Overlay analysis
 Two or more map layers of vector or raster data are mathematically joined together to
form a new map layer
 If the original map layers had attribute tables (databases) linked to them, then all, part or
none of these attributes can be associated with this new map layer
Three types of overlay analysis
 Point-in-polygon overlay
• To find which point falls inside which polygon, use the point-in-polygon analysis
 Line-in-polygon overlay
• To find the common areas between a line layer and a polygon layer, use line-in-
polygon analysis
 Polygon-on-polygon overlay
• For studying common areas between the two layers, use polygon-on-polygon
overlay analysis

42. In GIS there are three overlay operations which produce different results :
 Intersection
 Identity and
 Union
Topological poly-on-poly overlay: Variants

43. Modelling
• In general, a model is a representation of reality
• Models are simplified, manageable views of reality i.e. the complicated real world.
• Models helps to understand, describe, and predict how things work in the real world
• Models can be extremely useful in automating the most frequently tasks used to describe
the real world
• Below are just a few examples of how models can apply to geoprocessing in GIS.
Suitability models
• GIS is often used to find the best location for something (e.g., school locations,
landfill, emergency evacuation site, potential site for rain water harvesting)
• A set of criteria is applied to the GIS layers to find places (cells) that are
acceptable locations for a certain activity
• Suitability modeling is easy and there is a standard methodology to follow, and
the GIS processing is trivial
• The hardest part is defining the criteria for selecting the site

44. (ABOVE FEGURE)Flow chart for identification of potential sites for different RWH
technologies in Makanya catchment, Same District Northern Tanzania (Source: B.P.
Mbilinyi et al. / Physics and Chemistry of the Earth 32 (2007) 1074–1081)
Typical input maps, for Bangalala and Mwembe villages, Makanya catchment in Same District
Northern Tanzania, used for the development of Decision Support System (DSS) for
identification of potential sites for different RWH technologies. (Source: B.P. Mbilinyi et al. /
Physics and Chemistry of the Earth 32 (2007) 1074–1081)

45. Map of potential sites for different RWH technologies in Bangalala and Mwembe villages,
Makanya catchment in Same District Northern Tanzania. (Source: B.P. Mbilinyi et al. / Physics
and Chemistry of the Earth 32 (2007) 1074–1081) (ABOVE FEGURE)
Process models
• Process models describe the interaction between the geographic objects that are
defined in the representation models
• Examples include predicting the area of inundation behind a proposed dam,
rainfall distribution from elevations, rain erosivity from rainfall distribution,
magnitude of soil erosion etc)
• These types of models are often difficult to design and implement, and there is no
set methodology to follow
• You must know your GIS tools and apply them creatively
Other spatial analysis operations include:
I. NEIGHBOURHOOD OPERATIONS
 Works with immediate neighbours on one coverage; finding neighbours,
topographic functions

46. II. CONNECTIVITY OPERATIONS
 Works with distant neighbours and across the whole coverage; buffers, network
analysis, barriers etc
III. BOOLEAN LOGIC
 Common in land suitability analysis
 Works with any data, consider logical expressions i.e. where a specified set of
conditions occurs or does not occur (true or false
Boolean operators are:
<, >, =, ≤, ≥
e.g. FIND City population >500,000 AND State population > 5,000,000
“City population” and “State population” are operands
AND, OR, NOT, and XOR are called Boolean connectors
FIND all boys in the classroom roster NOT girls
FIND all conifer forest stands that are not tamarack (evergreen)
Conifer AND Evergreen
FIND all soil orders suitable for farming in Morogoro rural district
Mollisols OR Alfisols
I can afford a DVD player XOR a digital camera
SIMPLE DISPLAY AND QUERY
Display
Using points and arcs it is possible to display the locations of all objects stored in GIS
Attributes and entity types can be displayed by varying colours, line patterns and point symbols
Subset of data may also be displayed
• e.g. areas of urban land use with some base map data
•select all political boundaries and highways, but only areas that had urban
land uses

47. How is this achieved?
• e.g. one of the layers in a data base is a “map” of land use called USE
• Area of objects on this layer have several attributes
• One attribute called CLASS identifies the area’s land use
• For urban land use it has the value “U”
• Need to extract boundaries for all areas that have CLASS = “U”
Standard Query Language (SQL)
Different systems use different ways of formulating queries
Standard Query Language (SQL) is used by many systems
The SQL phrase structure is as follows:
SELECT &LTattribute name(s)>FROM &LTtable>WHERE &LTcondition statement>
e.g. SELECT FROM USE WHERE CLASS=“U”
this selects only the objects for display – no attributes are retrieved by
the query
SQL examples using list of students names:
SELECT name FROM list (select all names)
SELECT name FROM list WHERE grade =“A” (selects names of
students receiving an “A”)
SELECT name FROM list WHERE cumgrade>3.0 (selects students with cumulative GPA
greater than 3.0)
SQL operators:
relational: >, &LT, =, <, ≥, ≤, &LT=
arithmetic: =, -, *, /, + (only on numeric fields
Boolean: and, or, not, xor
Boolean operators:
Used to combine conditions

48. WHERE cumgrade>3.0 AND grade=“A” (selects students satisfying both
conditions only)
Boolean operators with spatial meaning in GIS
e.g. two maps overlaid, areas (polygons) that are superimposed have the “AND” condition
A spatial representation is used to illustrate Boolean operators in the study of logic, through the
use of Venn diagrammes
thus GIS area overlay is geographical instance of a Venn diagram A and B,
A or B, A xor B etc
6: DIGITAL ELEVATION MODEL (DEM)
WHAT IS DEM
• Landform is perceived as a continuous varying surface which can be represented by
contours
• To fully model the surface, would need an infinite amount of points
• Any digital representation of the continuous variation of relief over space is called a
digital elevation model (DEM) or digital terrain model (DTM)

49. • The term digital elevation model or DEM is frequently used to refer to any digital
representation of a topographic surface
• Most often it is used to refer specifically to a raster or regular grid of spot heights
• Simply, DEM’s are digital representations of altitude.
• Digital Elevation Models (DEM’s) store continuously varying variables such as
elevation, groundwater depth or soil thickness
• Digital Terrain Models (DTM’s) are
• digital representations of altitude and are frequently used in hydrological, erosion and
engineering geological studies
CREATION OF DEM
DEM’s are made via the following techniques:
Photogrametrical techniques
 Use stereoscopic aerial photographs or satellite images to sample a large number
of points with X,Y and Z values by means of advanced photogrammetrical
equipment
 The sampled points are interpolated into a regular grid (raster)
 The method is time consuming, requires photogrametrical experts, and a set of
very detailed points
 The software for generating DEM from this operation is rather expensive
 In general, it can be said that photogrammetrical methods, whether analogue or
digital, are mainly used by mapping agencies and certain companies specialized in
photogrammetry and map production
Point interpolation techniques
 Use available detailed point data of an area obtained via ground surveys:
theodolites, GPS
 For complex terrain, the interpolation techniques are also rather complex taking
into account breaklines of slope
Interpolation of contour lines
 Contour information on existing topographic maps is commonly the main source for this
technique
 Contour lines are digitised and interpolated
 This is the most common procedure in many GIS operations

50. CREATING DEM BY CONTOUR INTERPOLATION
Use digitised contour lines (segment map)
The digitised contours should extend a little bit outside the study area
The DEM is then created from the segment map as follows:
Segment to raster conversion:
Segment map is converted to raster using georeference, in which the pixel size, the
number of lines and columns, and the minimum X and Y coordinates of the map are
defined
The raster map resulting from the segment to raster conversion will contain values for
those pixels covered by a contour line
All other pixels in the map remain undefined
Contour interpolation:
 A linear interpolation is made between the pixels with altitude values, to obtain
the elevations of the undefined values in between the rasterised contour lines
 The output of the contour interpolation is a raster map in which each pixel in the
map has a value
The calculation is done using the following procedure:
The operation calculates, for each undefined pixel between segments, the shortest
distance towards the two nearest isolines
The height value for each undefined pixel is calculated using the following formula
(Figure 3 ):
h = H2 + (d2/(d1+d2)* (H1-H2))
Where: H1 and H2 = height values of the higher and lower contour lines
d1 and d2 = distances from pixel to the higher and lower contour lines
The programme calculates distances forward and backwards (from top line to bottom and
vice versa) until no more changes occur
Then linear interpolation is performed using the two distance values
This returns the value of the undefined pixels
During this exercise several megabytes of hard disk are used for storing temporary maps;
therefore a good computer with sufficient capacity and memory is required

51. Storage of DEM
DEM can either be stored in vector or raster format
DEM in vector format are always in in the form of Triangulated Irregular Networks (TIN) which
can be seen as a series of polygons in the form of triangle in between three points
Each triangle has a uniform slope steepness and slope direction
The more the complex the terrain the more the number of triangles
DEMs in raster format are represented by pixel values
Each pixel in the raster map contains the altitude of the centre of the pixel
The accuracy of the DEM depends very much on the details of the contour lines
The larger the scale of the map and the smaller the contour interval, the more accurate the DEM
will be
Figure 3: Two contour lines (H1 and H2) and the
shortest distances from pixel P

52. Important applications of DEMs
 Storage of elevation data in national databases
 Cut-and fill problems in road design
 3-dimensional display of landforms for visual purposes (landscape architecture)
 For analysis of cross-country visibility (viewsheds)
 For planning road routes, dam/power line locations
 For statistical analysis and comparisons of terrain types
 For computing slope, aspect, slope distances (calculate runoff and erosion)
 As a background for displaying thematic information
 Provide data for image simulation models
 Substitute z-axis with other variables of choice such as cost, population, noise,
pollution, groundwater or consumption levels
Figure 1: A Triangulated
Irregular Network structure
for a DEM
Figure 2: Data structure
of a TIN (detail)

53. Filters applied on Digital Elevation Models
• Filtering is the calculation of pixel values in an image or a raster map based on the pixel
values of the central pixel and its neighbours
• In other words, filtering is a process in which, usually a window of 3x3 or 5x5 pixels, is
moved over the map, to calculate an output value for the central pixel in the window
according to its neighbours
• Filters are commonly used in image processing but can also be
• applied to raster maps
• A special group of filters can be used to calculate
• slope steepness, slope shape (convex, concave) and shadow from Digital Elevation
Models
• The existing standard filters in ILWIS that can be applied on DEMs are listed hereunder:

54. List of standard filters in ILWIS that can be applied on DEMs
Filter type Application
DFDX Detects slope differences in x-direction.
DFDY Detects slope differences in y-direction.
DFDUP Calculates slope differences in the upward diagonal direction.
DFDDN Calculates slope differences in the downward diagonal direction.
D2FDX2 Detects slope shape differences in x-direction.
D2FDY2 Detects slope shape differences in y-direction.
D2FDXDY Calculates slope shape differences in all diagonal directions
LAPLACE Calculates slope shape differences in all diagonal directions
SHADOW Applies artificial illumination (from the northwest) to the DEM
Creating a hillshading map
In ILWIS standard filter: Shadow is applied on the Digital Elevation Model (DEM) to create a
shaded relief image The shadow filter simulates sun illumination on the surface, with the sun in
the northwest. The shaded relief image can be merely used for display

55. • When you display the map, you can see the relief coming out of the map
• The map shows the representation of the mountains under an artificial illumination, as if
the
• sun is shining from the NW
• Steep slopes directed to the SE are dark, and slopes
• directed to the NW are very bright
Using gradient filters
• The most important types of filters that can be used on a DEM are called gradient filters
• With the help of the gradient filters Dfdx and Dfdy, horizontal and vertical gradients are
calculated for each pixel
• The gradient maps are used to produce slope
• steepness maps as well as slope direction maps

56. • Calculating slope shape in ILWIS
• A number of filters can be used to investigate which parts of the terrain are convex
(showing negative values in the
• output map) or concave (positive values in output map)
• Flat areas and uniform slopes obtain the output value 0
• The following filters can be used:
• - D2FDX2. This 1x5 filter detects slope shape differences in x-direction.
• - D2FDY2. This 5x1 filter detects slope shape differences in y-direction.
• - LAPLACE. This 3x3 filter can be used to detect slope shape differences in both x and y
directions
Products that can be derived from a Digital Elevation Model (DEM)
- Slope steepness, showing the steepness of slopes in degrees, percentages, or radians for
each location (pixel)
- Slope direction maps (also called slope aspect maps), showing the orientation or compass
direction of slopes (between 0°-360°)
Slope convexity/concavity maps, showing the change of slope angles within a short distance.
From these maps you can see if slopes are straight, concave or convex in form.
-Hill shading maps (or shadow maps), showing the terrain under an artificial illumination,
with bright sides and shadows. Hill shading is used to portray relief difference and terrain
morphology in hilly and mountainous areas.
- Three dimensional views showing a bird’s eye view of the terrain from a user defined position
above the terrain.
- Cross-sections indicating the altitude of the terrain along a line and represented in a graph
(distance against altitude).
- Volume maps (or cut-and-fill maps), generated by overlaying two DEMs from different
periods. This allows you to quantify the changes in elevation that took place as a result of slope
flattening, road construction, landslides etc.

57. - Creation of Ortho-images from aerial photographs or satellite images. With the help of DEMs,
aerial photographs and satellite images can be corrected for tilt distortions and relief
displacements
ARC VIEW SOFTWRE
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