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APPLICATION OF REMOTE SENSING AND
GEOGRAPHICAL INFORMATION SYSTEM IN
CIVIL ENGINEERING
Date:
INSTRUCTORS
DR. MOHSIN SIDDIQUE
ASSIST. PROFESSOR
DEPARTMENT OF CIVIL ENGINEERING
Geographic query and analysis
How many
houses are
within 50m of
this junction?
How many
children live in
this 100m grid
square?
Which house
holds falls within
the floodplain?
2
Spatial analysis is a set of methods whose results change when the locations
of the objects being analyzed change
Spatial analysis is the crux of GIS. Spatial analysts can reveal things that might
otherwise be invisible – it can make what is implicit explicit.
Methods of spatial analysis can be very sophisticated, but they can also be
very simple
There are many possible ways of defining spatial analysis, but all in one way
or another express the basic idea that information on locations is essential –
that analysis carried out without knowledge of locations is not spatial analysis
Spatial analysis can be used to further the aims of science, by revealing
patterns that were not previously recognized, and that hint at undiscovered
generalities and laws
Spatial Analysis
3
In the 1850s cholera was very poorly
understood
An outbreak in London in 1854 in the
Soho district was typical of the time,
and the deaths it caused are mapped in
Figure
Dr. John Snow conceived the hypothesis
that cholera was transmitted through the
drinking of polluted water, rather than
through the air, as was commonly
believed
He noticed that the outbreak appeared
to be centered on a public drinking
water pump in Broad Street, and if his
hypothesis was correct, the pattern
shown on the map would reflect the
locations of people who drank the
pump’s water
Dr. John Snow and the causes of cholera
Dr. John Snow and the causes of
cholera in London
4
There are nine methods for testing spatial relations between geometric
objects. Each takes as input two geometries and evaluates whether the
relation is true or not.
1. Equals – are the geometries the same.
2. Disjoint – do the geometries share a common point
3. Intersects – do the geometries intersect
4. Touches – do the geometries intersect at their boundaries
5. Crosses – do the geometries overlap
6. Within – do the geometries within another
7. Contains – does one geometry completely contain another
8. Overlaps – do the geometries overlap
9. Relate – are the intersections between the interior, boundary or exterior
of the geometries.
Spatial relations and analysis on geometric objects
5
Seven methods support spatial analysis on these geometries:
1: Distance – determines the shortest distance between any two points in two
geometries.
2: Buffer – returns a geometry that represents all the points whose distance
from the geometry is less than or equal to a user defi ned distance.
3: Convex hull – returns a geometry representing the convex hull of a
geometry (convex hull is the smallest polygon that can enclose another
geometry without any concave areas).
Spatial relations and analysis on geometric objects
6
4: Intersection – returns a geometry that contains just the points common to
both input geometries.
5: Union – returns a geometry that contains all the points in both input
geometries.
6: Difference – returns a geometry containing the points that are different
between the two geometries.
7: SymDifference – returns a geometry containing the points that are in either
of the input geometries, but not both.
Spatial relations and analysis on geometric objects
7
Spatial relations and analysis on geometric objects
Examples of possible relations for two geographic database.
8
Spatial relations and analysis on geometric objects
Examples of spatial analysis methods on geometries.
9
Spatial relations and analysis on geometric objects
Examples of spatial analysis methods on geometries.
10
Queries and reasoning
Measurements
Transformations
Descriptive summaries
Optimization techniques
Hypothesis testing
Types of Spatial Analysis
11
Queries and reasoning are the most basic of analysis operations, in which
the GIS is used to answer simple questions posed by the user.
No changes occur in the database, and no new data are produced.
The operations vary from simple and well-defined queries like
‘how many houses are found within 1 km of this point’,
to vaguer questions ‘which is the closest city to Lahore going east’, where
the response may depend on the system’s ability to understand what the
user means by ‘going east’.
Interrogations/queries may involve pointing at a map, typing a question or
pulling down a menu and clicking some buttons or sending formal SQL request
to database.
The term reasoning encompasses a collection of methods designed to respond
to more complex forms of query and interrogation.
Queries and reasoning
12
Measurements are simple numerical values that describe aspects of
geographic data.
They include measurement of simple properties of objects, like
length,
area, or
shape,
and of the relationships between pairs of objects, like distance or
direction.
Measurements
13
Transformations are simple methods of spatial analysis that change datasets,
combining them or comparing them to obtain new datasets, and eventually
new insights.
Transformations use simple geometric, arithmetic, or logical rules, and they
include operations that convert raster data into vector data, or vice versa.
They may also create fields from collections of objects, or detect collections of
objects in fields.
Buffering
One of the most important transformations available to the GIS user is the
buffer operation called buffering
Given any set of objects, which may include points, lines, or areas, a buffer
operation builds a new object or objects by identifying all areas that are
within a certain specified distance of the original objects.
Buffering is possible in both raster and vector GIS, in the raster case
Transformations
14
Transformations
Buffers of constant width drawn around a point, line and a polygon
15
Transformations
A raster generalization of the buffer function where changes may be
controlled by some variable (example is of travel speed, whose value is
recorded in every raster cell)
16
Point in polygon: In its simplest
form, the point in polygon operation
determines whether a given point
lies inside or outside a given
polygon.
In more elaborate forms there may
be many polygons, and many points,
and the task is to assign points to
polygons.
If the polygons overlap, it is possible
that a given point lies in one, many,
or no polygons, depending on its
location.
Transformations
The point in polygon problem.
17
Polygon overlay is similar to point in polygon transformation in the sense that
two sets of objects are involved, but in this case both are polygons.
It exists in two forms, depending on whether a field or discrete object
perspective is taken.
From the discrete object perspective, the task is to determine whether two
area objects overlap, to determine the area of overlap, and to define the
area formed by the overlap as one or more new area objects
This operation is useful to determine answers to such queries as:
How much area lies in the shaded zone?
How much of this land parcel is shaded but not the white polygon?
What proportion of the land area outside the shaded but inside the white
polygon?
Transformations
18
From the field perspective the task is
somewhat different.
Figure shows two datasets, both
representations of fields–one
differentiates areas according to
land ownership, and the other
differentiates the same region
according to land cover class.
There are numerous queries that
require simultaneous access to both
datasets, for example:
⇒⇒⇒⇒ What is the total area of land owned
by A and with land cover class X?
⇒⇒⇒⇒ Where are the areas that is owned by
C and have land cover class Y?
⇒⇒⇒⇒ What is the land cover class and who
is the owner of the point indicated by
the user?
Transformations
Polygon overlay in the field case. Where a
dataset representing two types of land
cover. It is overlaid on a dataset showing
three land parcels owned by three
different persons. The overlay result will be
a single dataset in which every point
is identified with one land cover type and
one ownership type. There will be five
polygons, as land over X intersects two
ownership types and land cover y
intersects with three.
19
Spatial interpolation is a pervasive operation in GIS.
Although it is often used explicitly in analysis, it is also used implicitly, in
various operations such as the preparation of a contour map display, where
spatial interpolation is invoked without the user’s direct involvement.
Spatial interpolation is a process of intelligent guesswork, in which the
investigator attempts to make a reasonable estimate of the value of a field at
places where the field has not actually been measured.
Spatial interpolation is an operation that makes sense only from the field
perspective.
Spatial interpolation
20
Spatial interpolation finds applications in many areas:
In contouring, when it is necessary to guess where to place contours in
between measured locations.
In estimating the elevation of the surface in between the measured
locations of a DEM.
In estimating rainfall, temperature, and other attributes at places that are
not weather stations, and where no direct measurements of these
variables are available.
In resampling rasters, the operation that must take place whenever raster
data must be transformed to another grid.
Two commonly used methods of spatial interpolation are inverse distance
weighting (IDW) and Kriging
Spatial interpolation
21
Inverse distance weighting (IDW)
is the workhorse of spatial
interpolation, the method that is
most often used by GIS analysts.
It employs the Tobler law by
estimating unknown measurements
as weighted averages over the
known measurements at nearby
points, giving the greatest weight to
the nearest points.
IDW provides a simple way of
guessing the values of a field at
locations where no measurement is
available.
Inverse distance weighting
Notation used in the equations
defining spatial interpolation.
22
Inverse distance weighting
IDW interpolation
23
Kriging: Of all of the common
methods of spatial interpolation it is
Kriging that makes the most
convincing claim to be grounded in
good theoretical principles.
The basic idea is to discover
something about the general
properties of the surface, as
revealed by the measured values,
and then to apply these properties
in estimating the missing parts of the
surface.
Smoothness is the most important
property, and it is operationalized
in Kriging in a statistically
meaningful way.
Kriging
A semivariogram, here each
cross represents a pair of points.
The solid circles are obtained by
averaging within the ranges of
the distance axis. The dashed
line is the best fit to the five
points.
24
Density estimation is in many ways the logical twin of spatial interpolation –
it begins with points, and ends with a surface.
But conceptually the two approaches could not be more different, because
one seeks to estimate the missing parts of a field from samples of the field
taken at data points, while the other creates a field from discrete objects.
Density estimation
Two identical datasets but with different representations.
A – represents a field of atmospheric temperature recorded at nine sample points.
B – nine discrete objects representing population of different settlements in thousands.
Spatial interpolation is appropriate for case A, while for case B density estimation is
suitable.
25
Density estimation could be applied to any type of discrete spatial object, it
is most often applied to the estimation of point density, and that is the focus
here.
The most obvious example is the estimation of population density, and but it
could be equally well applied to the density of different kinds of diseases, or
animals, or any other set of well-defined points.
Density estimation
Density estimation using two different distance parameters in the
respective kernel functions, displaying smoother and less peaked nature of
the surface that results from the larger distance parameter.
26
Descriptive summaries attempt to capture the essence of a dataset in one or
two numbers.
They are the spatial equivalent of the descriptive statistics commonly used in
statistical analysis, including the mean and standard deviation.
Centers: To analyze the numerical summaries generally we measure by
methods of central tendency.
Like mean is one method which is broadly citing the average of data
series, similarly median, where the value is as such that one half of the
numbers are larger and one half are smaller.
Dispersion: Central tendency is the obvious choice if a set of numbers are to
be summarized in a single value, but where there is opportunity for a second
summary value standard deviation or the variance is often used.
Standard deviation and variance are more appropriate measures of
dispersion than the range because as averages they are less sensitive to
the specific values of the extremes
Descriptive summaries
27
Histograms and Pie Charts: Histograms (bar graphs) and pie charts are two
of many ways of visualizing the content of a geographic database.
A histogram shows the relative frequencies of different value of an attribute
by ordering them on the X axis and displaying frequency through the length
of a bar parallel to the Y axis.
Attributes should have interval or ratio properties, although ordinal properties
are sufficient to allow the values to be ranked and histogram based on
ordinal data is useful representation.
A pie chart is useful for nominal data and is used to display the relative
frequencies of distinct values, with no necessity for ranking.
Pie charts are also useful in dealing with attributes measured on cyclic scales.
Both take a single attribute and organize its values in a form that allow quick
comprehension.
Descriptive summaries
28
Scatterplots are useful visual summaries of relationships between attributes. It
display the value of one attribute plotted against the other.
If both sets of attributes belong to the same objects then the construction of a
scatter plot is straight.
Spatial Dependence: The fundamental problem of spatial analysis is selecting
appropriate digital representations from the real world.
The Tobler’s first law of geography states that everything is related to
everything else but near things are more related than distant things.
A dataset can exhibit positive spatial dependence at one scale but negative
at another scale.
Spatial dependence is a very useful descriptive summary of geographic data
and a fundamental part of its nature
Descriptive summaries
29
Fragmentation and Fractional Dimension: In GIS, maps may show many
patches with each patch representing an area of uniform class and this may
be bounded by patch of different class.
For example, a soil map where we may be interested in the degree to which
the landscape can be fragmented (meaning breaking in small or large
patches).
Fragmentation statistics provide the numerical basis for this purpose. Here we
can analyze the number of patches, their shape or size etc, as a way of
summarizing the geographic details.
The concept of fractals is used as a way of summarizing the relationship
between apparent length and level of geographic detail in the form of
fractional dimensions.
Descriptive summaries
30
Optimization techniques are normative in nature, designed to select ideal
locations for objects given certain well-defined criteria.
They are widely used in market research, in the package delivery industry,
and in a host of other applications.
Optimization is a prime example of GIS utility to support spatial decisions. It
can be by many ways like optimum location of points, routing on a network,
selection of optimum paths across continuous space, locating facilities etc.
The methods of optimization also divide between those that are designed
to locate points and routes on network
and those designed to locate points and routes in continuous space without
respect to the existence of roads or other links. E.g., Point Locations,
Routing Problems, and Optimum Paths
Optimization techniques
31
Point Locations: It is an instance of location in continuous space and
identifying location that minimizes total distance with respect to a number of
points.
The analogous problem on a network would involve finding that location on
the network which minimize total distance to a number of points, also located
on the network, using routes that are considered on the network using routes
that are constrained to the network.
Location allocation involves two types of decisions – where to locate and how
to allocate demand for service.
Optimization techniques
32
Routing Problems: This is another area of optimization where routing and
scheduling or decisions about he optimum tracks are considered.
At the root of all routing problem is the shortest path, the path through the
network between a defined origin and destination that minimizes distance or
travel time.
Attributes such as length, travel speed, restrictions on travel direction and level
of congestion are taken into account.
A GIS can be very effective at solving routing problems because it is able to
examine vast numbers of possible solutions quickly.
Optimization techniques
33
Optimum Paths: Here the concern is for finding optimum path across
continuous space for linear facilities like highways, pipelines or even airline
path etc.
Again emphasis would be on shortest route may be to save fuel, time or
avoiding the restrictions if there are any.
These are normally sorted in raster, where each cell may be assigned a
friction value, equal to the cost or time associated with moving across the cell
in the horizontal or vertical directions.
Optimization techniques
34
Hypothesis testing focuses on the process of reasoning from the results of a
limited sample to make generalizations about an entire population.
It allows us, for example, to determine whether a pattern of points could have
arisen by chance, based on the information from a sample.
Hypothesis testing is based on two concepts – confidence limits and inferential
tests, which are basically statistical testing.
Hypothesis testing
35
Comments….
Questions….
Suggestions….
36
I am greatly thankful to all the information sources
(regarding remote sensing and GIS) on internet that I
accessed and utilized for the preparation of present
lecture.
Thank you !

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Geographic query and analysis

  • 1. APPLICATION OF REMOTE SENSING AND GEOGRAPHICAL INFORMATION SYSTEM IN CIVIL ENGINEERING Date: INSTRUCTORS DR. MOHSIN SIDDIQUE ASSIST. PROFESSOR DEPARTMENT OF CIVIL ENGINEERING
  • 2. Geographic query and analysis How many houses are within 50m of this junction? How many children live in this 100m grid square? Which house holds falls within the floodplain? 2
  • 3. Spatial analysis is a set of methods whose results change when the locations of the objects being analyzed change Spatial analysis is the crux of GIS. Spatial analysts can reveal things that might otherwise be invisible – it can make what is implicit explicit. Methods of spatial analysis can be very sophisticated, but they can also be very simple There are many possible ways of defining spatial analysis, but all in one way or another express the basic idea that information on locations is essential – that analysis carried out without knowledge of locations is not spatial analysis Spatial analysis can be used to further the aims of science, by revealing patterns that were not previously recognized, and that hint at undiscovered generalities and laws Spatial Analysis 3
  • 4. In the 1850s cholera was very poorly understood An outbreak in London in 1854 in the Soho district was typical of the time, and the deaths it caused are mapped in Figure Dr. John Snow conceived the hypothesis that cholera was transmitted through the drinking of polluted water, rather than through the air, as was commonly believed He noticed that the outbreak appeared to be centered on a public drinking water pump in Broad Street, and if his hypothesis was correct, the pattern shown on the map would reflect the locations of people who drank the pump’s water Dr. John Snow and the causes of cholera Dr. John Snow and the causes of cholera in London 4
  • 5. There are nine methods for testing spatial relations between geometric objects. Each takes as input two geometries and evaluates whether the relation is true or not. 1. Equals – are the geometries the same. 2. Disjoint – do the geometries share a common point 3. Intersects – do the geometries intersect 4. Touches – do the geometries intersect at their boundaries 5. Crosses – do the geometries overlap 6. Within – do the geometries within another 7. Contains – does one geometry completely contain another 8. Overlaps – do the geometries overlap 9. Relate – are the intersections between the interior, boundary or exterior of the geometries. Spatial relations and analysis on geometric objects 5
  • 6. Seven methods support spatial analysis on these geometries: 1: Distance – determines the shortest distance between any two points in two geometries. 2: Buffer – returns a geometry that represents all the points whose distance from the geometry is less than or equal to a user defi ned distance. 3: Convex hull – returns a geometry representing the convex hull of a geometry (convex hull is the smallest polygon that can enclose another geometry without any concave areas). Spatial relations and analysis on geometric objects 6
  • 7. 4: Intersection – returns a geometry that contains just the points common to both input geometries. 5: Union – returns a geometry that contains all the points in both input geometries. 6: Difference – returns a geometry containing the points that are different between the two geometries. 7: SymDifference – returns a geometry containing the points that are in either of the input geometries, but not both. Spatial relations and analysis on geometric objects 7
  • 8. Spatial relations and analysis on geometric objects Examples of possible relations for two geographic database. 8
  • 9. Spatial relations and analysis on geometric objects Examples of spatial analysis methods on geometries. 9
  • 10. Spatial relations and analysis on geometric objects Examples of spatial analysis methods on geometries. 10
  • 11. Queries and reasoning Measurements Transformations Descriptive summaries Optimization techniques Hypothesis testing Types of Spatial Analysis 11
  • 12. Queries and reasoning are the most basic of analysis operations, in which the GIS is used to answer simple questions posed by the user. No changes occur in the database, and no new data are produced. The operations vary from simple and well-defined queries like ‘how many houses are found within 1 km of this point’, to vaguer questions ‘which is the closest city to Lahore going east’, where the response may depend on the system’s ability to understand what the user means by ‘going east’. Interrogations/queries may involve pointing at a map, typing a question or pulling down a menu and clicking some buttons or sending formal SQL request to database. The term reasoning encompasses a collection of methods designed to respond to more complex forms of query and interrogation. Queries and reasoning 12
  • 13. Measurements are simple numerical values that describe aspects of geographic data. They include measurement of simple properties of objects, like length, area, or shape, and of the relationships between pairs of objects, like distance or direction. Measurements 13
  • 14. Transformations are simple methods of spatial analysis that change datasets, combining them or comparing them to obtain new datasets, and eventually new insights. Transformations use simple geometric, arithmetic, or logical rules, and they include operations that convert raster data into vector data, or vice versa. They may also create fields from collections of objects, or detect collections of objects in fields. Buffering One of the most important transformations available to the GIS user is the buffer operation called buffering Given any set of objects, which may include points, lines, or areas, a buffer operation builds a new object or objects by identifying all areas that are within a certain specified distance of the original objects. Buffering is possible in both raster and vector GIS, in the raster case Transformations 14
  • 15. Transformations Buffers of constant width drawn around a point, line and a polygon 15
  • 16. Transformations A raster generalization of the buffer function where changes may be controlled by some variable (example is of travel speed, whose value is recorded in every raster cell) 16
  • 17. Point in polygon: In its simplest form, the point in polygon operation determines whether a given point lies inside or outside a given polygon. In more elaborate forms there may be many polygons, and many points, and the task is to assign points to polygons. If the polygons overlap, it is possible that a given point lies in one, many, or no polygons, depending on its location. Transformations The point in polygon problem. 17
  • 18. Polygon overlay is similar to point in polygon transformation in the sense that two sets of objects are involved, but in this case both are polygons. It exists in two forms, depending on whether a field or discrete object perspective is taken. From the discrete object perspective, the task is to determine whether two area objects overlap, to determine the area of overlap, and to define the area formed by the overlap as one or more new area objects This operation is useful to determine answers to such queries as: How much area lies in the shaded zone? How much of this land parcel is shaded but not the white polygon? What proportion of the land area outside the shaded but inside the white polygon? Transformations 18
  • 19. From the field perspective the task is somewhat different. Figure shows two datasets, both representations of fields–one differentiates areas according to land ownership, and the other differentiates the same region according to land cover class. There are numerous queries that require simultaneous access to both datasets, for example: ⇒⇒⇒⇒ What is the total area of land owned by A and with land cover class X? ⇒⇒⇒⇒ Where are the areas that is owned by C and have land cover class Y? ⇒⇒⇒⇒ What is the land cover class and who is the owner of the point indicated by the user? Transformations Polygon overlay in the field case. Where a dataset representing two types of land cover. It is overlaid on a dataset showing three land parcels owned by three different persons. The overlay result will be a single dataset in which every point is identified with one land cover type and one ownership type. There will be five polygons, as land over X intersects two ownership types and land cover y intersects with three. 19
  • 20. Spatial interpolation is a pervasive operation in GIS. Although it is often used explicitly in analysis, it is also used implicitly, in various operations such as the preparation of a contour map display, where spatial interpolation is invoked without the user’s direct involvement. Spatial interpolation is a process of intelligent guesswork, in which the investigator attempts to make a reasonable estimate of the value of a field at places where the field has not actually been measured. Spatial interpolation is an operation that makes sense only from the field perspective. Spatial interpolation 20
  • 21. Spatial interpolation finds applications in many areas: In contouring, when it is necessary to guess where to place contours in between measured locations. In estimating the elevation of the surface in between the measured locations of a DEM. In estimating rainfall, temperature, and other attributes at places that are not weather stations, and where no direct measurements of these variables are available. In resampling rasters, the operation that must take place whenever raster data must be transformed to another grid. Two commonly used methods of spatial interpolation are inverse distance weighting (IDW) and Kriging Spatial interpolation 21
  • 22. Inverse distance weighting (IDW) is the workhorse of spatial interpolation, the method that is most often used by GIS analysts. It employs the Tobler law by estimating unknown measurements as weighted averages over the known measurements at nearby points, giving the greatest weight to the nearest points. IDW provides a simple way of guessing the values of a field at locations where no measurement is available. Inverse distance weighting Notation used in the equations defining spatial interpolation. 22
  • 23. Inverse distance weighting IDW interpolation 23
  • 24. Kriging: Of all of the common methods of spatial interpolation it is Kriging that makes the most convincing claim to be grounded in good theoretical principles. The basic idea is to discover something about the general properties of the surface, as revealed by the measured values, and then to apply these properties in estimating the missing parts of the surface. Smoothness is the most important property, and it is operationalized in Kriging in a statistically meaningful way. Kriging A semivariogram, here each cross represents a pair of points. The solid circles are obtained by averaging within the ranges of the distance axis. The dashed line is the best fit to the five points. 24
  • 25. Density estimation is in many ways the logical twin of spatial interpolation – it begins with points, and ends with a surface. But conceptually the two approaches could not be more different, because one seeks to estimate the missing parts of a field from samples of the field taken at data points, while the other creates a field from discrete objects. Density estimation Two identical datasets but with different representations. A – represents a field of atmospheric temperature recorded at nine sample points. B – nine discrete objects representing population of different settlements in thousands. Spatial interpolation is appropriate for case A, while for case B density estimation is suitable. 25
  • 26. Density estimation could be applied to any type of discrete spatial object, it is most often applied to the estimation of point density, and that is the focus here. The most obvious example is the estimation of population density, and but it could be equally well applied to the density of different kinds of diseases, or animals, or any other set of well-defined points. Density estimation Density estimation using two different distance parameters in the respective kernel functions, displaying smoother and less peaked nature of the surface that results from the larger distance parameter. 26
  • 27. Descriptive summaries attempt to capture the essence of a dataset in one or two numbers. They are the spatial equivalent of the descriptive statistics commonly used in statistical analysis, including the mean and standard deviation. Centers: To analyze the numerical summaries generally we measure by methods of central tendency. Like mean is one method which is broadly citing the average of data series, similarly median, where the value is as such that one half of the numbers are larger and one half are smaller. Dispersion: Central tendency is the obvious choice if a set of numbers are to be summarized in a single value, but where there is opportunity for a second summary value standard deviation or the variance is often used. Standard deviation and variance are more appropriate measures of dispersion than the range because as averages they are less sensitive to the specific values of the extremes Descriptive summaries 27
  • 28. Histograms and Pie Charts: Histograms (bar graphs) and pie charts are two of many ways of visualizing the content of a geographic database. A histogram shows the relative frequencies of different value of an attribute by ordering them on the X axis and displaying frequency through the length of a bar parallel to the Y axis. Attributes should have interval or ratio properties, although ordinal properties are sufficient to allow the values to be ranked and histogram based on ordinal data is useful representation. A pie chart is useful for nominal data and is used to display the relative frequencies of distinct values, with no necessity for ranking. Pie charts are also useful in dealing with attributes measured on cyclic scales. Both take a single attribute and organize its values in a form that allow quick comprehension. Descriptive summaries 28
  • 29. Scatterplots are useful visual summaries of relationships between attributes. It display the value of one attribute plotted against the other. If both sets of attributes belong to the same objects then the construction of a scatter plot is straight. Spatial Dependence: The fundamental problem of spatial analysis is selecting appropriate digital representations from the real world. The Tobler’s first law of geography states that everything is related to everything else but near things are more related than distant things. A dataset can exhibit positive spatial dependence at one scale but negative at another scale. Spatial dependence is a very useful descriptive summary of geographic data and a fundamental part of its nature Descriptive summaries 29
  • 30. Fragmentation and Fractional Dimension: In GIS, maps may show many patches with each patch representing an area of uniform class and this may be bounded by patch of different class. For example, a soil map where we may be interested in the degree to which the landscape can be fragmented (meaning breaking in small or large patches). Fragmentation statistics provide the numerical basis for this purpose. Here we can analyze the number of patches, their shape or size etc, as a way of summarizing the geographic details. The concept of fractals is used as a way of summarizing the relationship between apparent length and level of geographic detail in the form of fractional dimensions. Descriptive summaries 30
  • 31. Optimization techniques are normative in nature, designed to select ideal locations for objects given certain well-defined criteria. They are widely used in market research, in the package delivery industry, and in a host of other applications. Optimization is a prime example of GIS utility to support spatial decisions. It can be by many ways like optimum location of points, routing on a network, selection of optimum paths across continuous space, locating facilities etc. The methods of optimization also divide between those that are designed to locate points and routes on network and those designed to locate points and routes in continuous space without respect to the existence of roads or other links. E.g., Point Locations, Routing Problems, and Optimum Paths Optimization techniques 31
  • 32. Point Locations: It is an instance of location in continuous space and identifying location that minimizes total distance with respect to a number of points. The analogous problem on a network would involve finding that location on the network which minimize total distance to a number of points, also located on the network, using routes that are considered on the network using routes that are constrained to the network. Location allocation involves two types of decisions – where to locate and how to allocate demand for service. Optimization techniques 32
  • 33. Routing Problems: This is another area of optimization where routing and scheduling or decisions about he optimum tracks are considered. At the root of all routing problem is the shortest path, the path through the network between a defined origin and destination that minimizes distance or travel time. Attributes such as length, travel speed, restrictions on travel direction and level of congestion are taken into account. A GIS can be very effective at solving routing problems because it is able to examine vast numbers of possible solutions quickly. Optimization techniques 33
  • 34. Optimum Paths: Here the concern is for finding optimum path across continuous space for linear facilities like highways, pipelines or even airline path etc. Again emphasis would be on shortest route may be to save fuel, time or avoiding the restrictions if there are any. These are normally sorted in raster, where each cell may be assigned a friction value, equal to the cost or time associated with moving across the cell in the horizontal or vertical directions. Optimization techniques 34
  • 35. Hypothesis testing focuses on the process of reasoning from the results of a limited sample to make generalizations about an entire population. It allows us, for example, to determine whether a pattern of points could have arisen by chance, based on the information from a sample. Hypothesis testing is based on two concepts – confidence limits and inferential tests, which are basically statistical testing. Hypothesis testing 35
  • 36. Comments…. Questions…. Suggestions…. 36 I am greatly thankful to all the information sources (regarding remote sensing and GIS) on internet that I accessed and utilized for the preparation of present lecture. Thank you !