Gis analysis data methods

1. INTERNATIONAL INSTITUTE FOR GEO-INFORMATION SCIENCE AND EARTH OBSERVATION
Spatial data analysis (2)

2. Overview of this lesson
Three topics will be discussed:
1. Neighbourhood functions
2. Network analysis
3. Error propagation
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3. 1. Neighborhood functions
 Will find out
characteristics of
the vicinity
(neighborhood) of a
location
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4. 1. Neighborhood functions
 To perform
neighborhood analysis
we must
 State which target
locations are of interest to
us, and what is their
spatial extent
 Define how to determine
the neighborhood for each
target
 Define which
characteristic(s) must be
computed for each
neighborhood
1. Target: medical clinics
2. Neighborhood
2 km distance
In a straight line
2 km travel distance
3. Characteristics
• How many people live in the area
• What is their average household
income
• Are there any high-risk industries
located in the neighborhood
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5. 1. Neighborhood functions
 Proximity computation
makes use of the
geometric distance
function
 Spread computation
assumes that the
phenomenon spreads in
all directions, but not
necessarily equally
easily in all direction.
 In seek computation the
phenomenon will choose
a least-resistance path.
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Geometric
distance
Spread
computation
Seek
computation

6. 1. Neighborhood functions
1. Neighborhood functions
1.1 Buffer generation (Vector and Raster)
1.2 Thiessen polygons (Vector)
1.3 Spread computation (Raster)
1.4 Seek computation (Raster)
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7. 1.1 Buffer zone generation
 Principle is simple, we
select one or more
target locations and
determine the area
around them.
 Buffer generation can
be performed on vector
as well as raster data.
 Target locations can be
point, lines or polygons
in a vector environment
Buffer of 500 meters around the Main
Roads
Buffer of 1 km around the Highways
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8. 1.1 Buffer zone generation
 Buffers can be simple,
or zonated.
 With a zonated buffer
the buffer consists of
multiple rings each
representing a different
distance
 In vector buffer
generation the buffer
will become a new
polygon in the output
layer
Between
0- 100 m
Between
100-200 m
Between
200-300 m
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9. 1.1 Buffer zone generation
raster layers:
 Need target cell(s)
 The distance function
applies the Pythagorean
distance between the cell
centers.
 Using cell resolution as
the unit
 The distance from a non-
target cell to the target is
the minimal distance one
can find between that
non-target cell and any
target cell.
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10. 1.2. Thiessen polygons
Thiessen polygons
 Divide an area into
polygons, so that each
polygon contains locations
that are closer to the
midpoint than to any other
midpoint
 It will generate a polygon
around each target
location that identifies all
those locations that ‘
belong to’ that target
For each store, identify the
area for which this store is
the closest. This is the
service area for that store
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11. 1.3. Spread computation
 Picture landfill
pollution should be
scanned.
 In spread
computation the
neighbourhood of a
target location not
only depends on
distance but also on
direction and
differences in the
terrain
 Examples are
pollutions and radio
waves
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12. 1.3 Spread computation
 Spread computation
involves one or more
target locations, which
are better called source
location in this context,
as they may be for
example the pollution
source
 Spread computation also
involves a local
resistance raster, which
for each cell provides a
value that indicates how
difficult it is to pass by
that cell.
Source Locations
Local resistance raster
A high value,
indicate that it
is very
difficult to
pass this cell
(resistance is
high)
1 1 1 2 8
4 4 5 4 9
4 3 3 2 10
4 5 6 8 8
4 2 1 1 1
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13. 1.3 Spread computation
 While computing
total resistance, The
GIS takes proper
care of correct
spread path lengths.
 The spread from a
cell to its neighbour
cell to the east is
shorter than to its
northeast neighbour
Path length to the east is equal
to the cell size
Path length to the north east is cell
size * √ 2
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14. 1.3 Spread computation
 The GIS computes the
total resistance for
spreading from csrc to cn
as ½(val (csrc) + val (cn))
 This is half of the
resistance value of the
source cell (csrc),
because this cell is only
traveled half, plus half
of the resistance value
of the cell north of it
 The value of the source
cell of course is 0.
(4+4)/2 = 4
?
0.00
Minimal total resistance
Resistance layer
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15. 1.3 Spread computation
 The GIS computes the
total minimal resistance
raster for a diagonal
neighbour as ½ (val
(csrc) + val (Cne)) * √2
 This is half of the
resistance value of the
source cell plus half of
the resistance value of
the cell to the north-
east multiplied by the
square root of 2
4.00 ?
0.00
Resistance layer
(4+5)/2 * sqrt(2) =
6.36
Minimal total resistance
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16. 1.3 Spread computation
 Since the source
material has the habit
of taking the easiest
route to spread, we
must determine the
minimal cost.
 We must consider all
possible paths to
reach the cell and
assign the minimal
value
Total resistance via the black
path(4+5)/2 * sqrt(2) = 6.36
Total resistance via the blue
path(4+4)/2 + (4+5)/2 = 8.5
Total resistance via the red
path(4+2)/2 + (2+5)/2 = 6.5
Lowest value
Resistance layer
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17. 1.3 Spread computation
 Note that the
accumulated resistance
along a path of cells is
simply the sum of these
incurred resistances.
 We can use the value
4.00 and add the
resistance for moving
from this cell to its
north east neighbour
cell
?
4.00 6.36
0.00 3.00
4.00 + (½ (4+3) *
√2) = 8.95
Resistance layer
Minimal
total
resistance
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18. 1.4 Seek computation
 Seek computation
applies when a
phenomenon does
not spread in all
directions, but
chooses a least-cost
path.
 A typical example is
a drainage pattern in
a catchment.
Drainage pattern from a volcano
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19. 1.4 Seek computation
 Input for a seek
computation is an
elevation raster
 For each cell the
steepest downward
slope to a neighbour
cell is determined
 The direction of this
downward slope is
stored in the flow
direction raster
elevation
Flow direction
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20. 1.4 Seek computation
134 112
106 88
1. For each cell first
eliminate all cells that
are not downhill (have
a higher elevation
value)
2. You have to types of
neighbours direct
neighbours and
diogonal ones. For
each type pick the
steepest.
3. Compensate for the
difference in path
length.
134
106 88
134 – 106 = 28
134 - 88 = 46 / √2 =32
Step 1
Step 2
Step 3:
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21. 1.4 Seek computation
 From the flow
direction raster the
GIS will calculate
the accumulated
flow count raster
 Cells with a high
accumulated flow
count represent
streams.
Flow direction
Flow accumulation
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22. 1.4 Seek computation
 The value of the
accumulated flow
for each cell is the
number of cells that
flow into this
particular cell.
 Cells with a value 0
have no other cells
flowing into them,
and represent higher
areas.
All the cells flowing
into this cell are
marked in red the
value of this cell will
be 7
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23. 1. Summary – proximity computation
Method Data
structure
Input output
Buffer Geometric
distance
Vector and
raster
Target points Buffer polygon
or raster
Thiessen
polygons
Geometric
distance
Vector Target points Polygon layer
Spread
computation
Cost distance Raster Target points and
resistance raster
Minimal total
resistance
Seek
computation
Least cost path Raster Elevation raster
Direction raster
Accumulated
flow count

24. 2.Network analysis
 2.1 Types of networks
 Directed network and undirected network
 Planar network and non-planar network
 Two types of analysis
 2. 2 Optimal path finding
 Ordered
 Unordered
 2.3 Network partitioning
 Network allocation
 Trace analysis
 2.4 Turntables
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25. 2.1 Types of Networks
 Network is a set of
connecting lines
 Network can represent
rivers, roads, pipelines,
telecommunication lines
etc.
 Network analysis
analyze the way ‘goods’
can be transported
along these lines
 Network analysis can be
done in raster or in
vector.
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26. 2.1 Types of Networks
 Networks can be
directed ,
transportation is
only in one
direction, for
example rivers, or it
can be undirected,
the goods can be
transported in both
directions (roads)
Directed network (pipelines),
the arrows indicate the
direction of flow
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27. 2.1 Types of Networks
 Networks can be
planar, this means
they are 2-
dimensional
 Planar networks do
not have overpasses
or underpasses
 Example of a planar
networks are rivers
Embedded in a
2-dimensional
plane
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28. 2.1 Types of Networks
 Non-planar networks
have multi-level
crossings, underpasses
and overpasses.
 When they are modeled
in 2-D these overpasses
and underpasses should
be modeled in a special
way
 Example of non-planar
networks are roads.
Non-Planar
Multi-level
crossings
Underpasses
Overpasses
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29. Analysis on networks
 Optimal path finding
Which generates a least cost-path on a network
between a pair of predefined locations using
both geometric and attribute data.
 Network partitioning
Which assigns network elements (nodes or line
segments) to different location using
predefined criteria.
 Network allocation
 Trace
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30. 2.2 Optimal path finding
 Optimal path finding is used
when a least cost path between
two nodes in a network must be
found.
 You need a cost function!
 Also called Impedance.
 One of the attributes in the
feature attribute table.
 Length, travel time, etc.
 The least-cost path is the
one that has the min. value
of the total cost between
two nodes
11.5
6.3
8.7
6.7
4.1
6.0 9.5
In purple you see the two point location
1 and 2, one is your origin and the other
the destination. In red you see the least
cost path. The numbers in black
indicate the cost for traveling each line
segment. Total cost is 52.8 seconds.
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31. 2.2 Optimal path finding
Cost factors
 The cost can be
defined on both lines
and nodes.
 For lines, the cost can
be same or different
along and against the
line direction.
 The cost on nodes is
used to define the
turns.
27
35
0.81 min.
0.81 min.
One cost field for both directions
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32. 2.2 Optimal path finding
 Two costs, one for
each driving
direction can be
applied in rush hour.
In the morning it
takes much longer to
go into the city than
it takes to drive in
the opposite
direction.
37
36
0.31
min
0.38 minutes
Two different cost fields, one for each
direction Ft is from- to, Tf means to-from.
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33. 2.2 Optimal path finding
 Cost can be
associated with line
segments, but also
with nodes
 Passing a traffic light
for example can take
a considerable
amount of time.
Node 71
Arc 119
Arc 89
0.50 minutes
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34. 2.2 Optimal path finding
 Ordered optimal
path finding: the
sequence in which
the places have to
be visited matters.
 Unordered optimal
path finding: the
sequence does not
matter.
1
2
3
4
1
3
2
4
Unordered path finding
Ordered path finding
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35. 2.3 Network partitioning
 In network partitioning, the purpose is to
assign lines and nodes (parts of the network)
to a number of target locations (for example
which part of the network belongs to a
hospital, school or fire station).
 There are two types of network partitioning
problems:
 2.3.1 network allocation
 2.3.2 trace analysis
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36. 2.3.1 network allocation
 We have a number of
resource centers, and
the problem is which
part of the network can
be assigned to which
service center.
 In principle this is a
simple problem, each
line segment is assigned
to the service center
that is the nearest.
Three blue circles (police stations), with
their services areas in blue, purple and
green
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37. 2.3.1 network allocation
Problems associated with
network allocation are:
 The capacity with which
a centre can produce
the resources
 The consumption of the
resources which may
vary amongst lines or
line segments.
Large police station with three
times the capacity of the other two.
Number of
citizens in this
area is much
less than in
the other two.
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38. 2.3.2 Trace analysis
 Trace analysis is
performed when we
want to understand
which part of a network
is connected to the
trace origin.
 A condition can be
applied for example,
trace only in the
direction of the origin
(upstream)
The PowerStation is indicated with
a green square (right), and arrows
show the direction of flow. The red
line is a trace upstream.
Utility network.
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39. 2. Summary – network analysis
Directed/un-
directed
networks
Input output Other
requirements
Optimal
path finding
both At least two
points (origin
– destination)
Path One or two
cost fields
Network
allocation
both Min. one
point, source
of the
service area
A set of street
segments, or
polygon
covering these
segments
One or two
cost fields,
maximum
distance
Trace
analysis
directed Trace origin path Condition
(maximum
distance,
direction or
capacity)

40. 3. Error propagation
How errors propagate:
 Errors already present in
the input data will
propagate through the
manipulations.
 New errors arise from
the computer processing
(analytical operations
performed)
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41. 3. Error propagation
 Error propagation
analysis:
 Testing the accuracy
of each state by
measurement against
the real world
 Modeling error
propagation, either
analytically or by
means of simulation
techniques.
178

42. 3. Error propagation
 Initially the complexity
of spatial data led to
the development of
mathematical models
describing only the
propagation of attribute
errors.
 Modern models
incorporate both spatial
and attribute erros.
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