UMES Geographical Information Systems Discussion

1)What is a spatial analysis in GIS? What is a spatial problem?

2) What is continuous raster data? Please provide examples.

3) What is a qualitative flow map? What is a quantitative flow map? Please provide examples.

4) There is an increasing trend for the integration of Desktop GIS, Web, and mobile technologies. Describe an example of such development.

References

Kang-Tsung Chang (2016) Introduction to Geographic Information Systems, 9th edition, NY: McGraw-Hill ISBN19: 978-1-259-92964-9

Additional Reading Materials:

Paul Longley, Michael Goodchild, David Maguire, David Rhind “Geographic Information Science and Systems”, 2014, Wiley, ISBN: 978-1118676950

Kathryn Keranen, Robert Kolvoord “Making Spatial Decisions Using ArcGIS PRO”, 2017, ESRI Press, ISBN 9781589484849;

David W. Allen “Getting To Know Model Builder”, 2011, ESRI Press, ISBN: 9781589482555

It is expected that students will make extensive use of the following journals:

International Journal of Geographical Information Systems;

Geospatial Solutions;

Geo-World;

ESRI Press: Arc User & Arc News

GIS Certificate: Second course
LECTURE 5:
Spatial Analysis using
Continuous Fields
Professor, Dr. Sergei Andronikov
Spatial Analysis using Discrete &
Continuous Fields
Lecture outline:
1. Basic operations for spatial analysis.
2. The Goods on Grids.
3. Map Algebra.
4. Point operations.
5. Spatial Operations
6. Practical Application.
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Operations for spatial analysis
with
discretized
continuous
fields.
Two main ways to represent continuous fields:
1. The TIN of digital elevation modeling;
2. Regular, square rasters -grids used in raster GIS and image
analysis.
Each Attribute in raster is represented by a separate overlay, and
each grid cell is allowed to take a different, scalar value.
It is much easier to maintain the database and to compute new
attributes if all the data are referenced to a uniform geometry regular square grid.
1. Rasterizing smooth polygon boundaries vs. creation new
polygons by intersection.
2. RS Imaginary as input.
3. Each attribute – a separate overlay.
Thus, any math operation on once attribute for the same cell can be
applied to all cells in the overlay.
Graphic Data Structure

TWO fundamental methods of indication
geographical space.
Spatial Analyst Extension
The Spatial Analyst extension adds spatial analysis
capabilities that are performed on:
 Feature themes;
 Grid themes
 It represents Geographic Phenomenon with cellbased grid themes (instead of points, lines,
polygons)
 Spatial Analyst creates, displays, queries, and
analyzes cell-based data
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Raster Graphic Data Structure
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RASTERS consist of spatial data stored as individual
cells in an array.
Rasters saved in the special GRID format.
GRID is also a generic term for Raster datasets
Grids are a matrix of square cells. The cells store a
NUMERIC value representing a geographic feature
Raster Data structure do not provide precise locational
information.
Rasters and vectors can be flat
files … if they are simple
Vector-based line
Raster-based line
Flat File
4753456 623412
4753436 623424
4753462 623478
4753432 623482
4753405 623429
4753401 623508
4753462 623555
4753398 623634
Flat File
0000000000000000
0001100000100000
1010100001010000
1100100001010000
0000100010001000
0000100010000100
0001000100000010
0010000100000001
0111001000000001
0000111000000000
0000000000000000
Generic structure for a grid
Grid extent
Rows
Grid
cell
Resolution
Columns
Generic structure for a grid
RASTER
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Advantage. The data form their own map in the
computer’s memory. Comparing grid cells require
looking at the values in the next and preceding row and
column of the grid cells.
Disadvantage. Grids are poor at representing points,
lines and areas, but good at surfaces.
Grids are good only at very localized topology, and
weak otherwise.
Grids are a natural for scanned or remotely sensed data.
Grids suffer from the mixed pixel problem.
Grids must often include redundant or missing data.
Grid compression techniques used in GIS are run-length
encoding and quad trees.
The mixed pixel problem
Water dominates
Winner takes all
Edges separate
W W
G
W G
G
W E
G
W W
G
W W
G
W E
G
W W
G
W G
G
E
G
E
The quad-tree structure
210
0
1
2
3
0
2
0
2
1
3
1
3
quadrant
number
The quad-tree structure. Reference to code 210.
Spatial Analyst Application areas

Environmental Analysis
 Vegetation Cover Mapping
 Wildlife Habitat Display
 Hazardous-Waste Cleanup
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Business Analysis
 Location Analysis and Site Selection
 Proximity to Transportation Analysis
 Healthcare and Insurance
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Social Analysis
 Census Data Exploration
 Housing Studies
 Disease Spread Prediction
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Agricultural Analysis
 Forestry
 Precision Farming
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Hydrological Analysis
Spatial Analyst Functions
Perform Overlay Analysis
 Create Buffer Distance and Proximity
Themes
 Create Contours or Surface Themes from
sample points
 Display and Query Grid themes
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Overlay Spatial Analysis
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Determines where and How much feature overlap
each other
How much residential land in the flood zone?
Is there more vacant or commercial land in the
flood zone?
Result in a Chart and a Table of descriptive
Information
Compares relationships between 2 or more themes
Where is the cheap, vacant land outside the flood?
Results in a new theme.
Operations for spatial analysis
with discretized continuous fields.
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You can use the same algebraic notation to operate on
gridded data as on single numbers.
This method is called MAP ALGEBRA. The procedure of
using algebraic techniques to build models for spatial
analysis – CARTOGRAPHIC MODELING.
The methods of map algebra means that you need only to
SPECIFY the spatial operations to be used, and the names
of the SOURCE overlays, and the result – the PC program
applies the operation to all cells in the overlays.
NEW MAP = MAP1 + MAP2 + MAP3 (the SUM of the
values);
NEW MAP = (MAP1 + MAP2 + MAP3): 3 (AVERAGE);
You compute new values on a cell-by-cell basis.
Map Algebra
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Rainfall 97
Rainfall 96
CHANGE
7
5
3
3
2
3
4
3
0
4
3
3
4
3
3
0
0
0
7
7
4
3
4
4
4
3
0
7
5
7
7
1
3
0
4
4
–
=
Working with Distances & Surfaces
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Calculates distances from every locations to
selected
 How
far is it to the airport or bus route?
 How many customers are within 1 mile of my store?
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Creates contour lines or surfaces from, sample
points
 Is
the home in a high noise area?
 Where are the hills and valleys?
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Analyze hazardous chemical spills
Spread of disease through a vegetation type
Erosion Studies
Vegetation sunlight studies using aspect
GRID Themes
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VECTOR better addresses problems where the
OBJECT is of greater concern and the
LOCATION of the object.
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RASTER better addresses analysis of an object’s
neighborhood, and how that neighborhood may
have some influence on the object’s attributes.
GRID Themes
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Similar to feature themes
Advantage:
The ability to represent continuous surfaces
The ability to store points, lines, polygons, and surfaces
UNIFORMLY. All features are treated the same.
You may analyze a continuous surface of elevation, a zone of
pine forest, a lake location, well locations, and a distance to
rivers all in the same map query, overlay, or map algebra
expression.
BUT… accuracy may be sacrificed because each feature type is
a cell. The resolution of a cell will determine how much
accuracy is lost.
The second drawback is the raster ability to store attributes.
GRID Themes
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Grid Themes are stored with a Cartesian
coordinate system
Positions on the grid have real-world locations
Each cell can be referenced by an x, y location
All cells are the same in size.
Spatial Analyst automatically resample and
reproject the grids to match each other. Raster
projection is slow. “First come… first serve”
rule.
y-axis
x-axis
GRID Themes and Cells
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Cells store a numeric value
Cell Values are either integer (3; 5; 8) or floating
points (2.343; 3.453) numeric values.
Cells with the same value make up a ZONE. One
VAT (Value Attribute Table) per zone
A REGION is a zone where all the cells are
contiguous (RegionGroup Request)
7
4
7
7
5
3
3
3
7
4
5
7
Cell Values
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Values are:
1. INTEGER. Discrete.
Often uses a code that identify a cell and its category:
1- Water, 2 – Forest. Have a Theme Table called a
VAT – value attribute table
2. FLOATING POINT VALUES. Continuous.
A Floating point grid represents ONE phenomenon
like elevation, rainfall, noise level
Each cell stores a value for the phenomenon.
HAVE NO theme table.
3. NO DATA. Insufficient information
Cell Values
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Values are:
1. INTEGER. Discrete.
Often uses a code that identify a cell and its category:
1- Water, 2 – Forest. Have a Theme Table called a
VAT
–5 value
7
3 attribute table
0.007
No data
0.007
2.4FLOATING
3
3 POINT VALUES.
0.307 No data Continuous.
0.307
A7Floating
point
grid represents
ONE
phenomenon
7
4
0.000
0.008
0.007
like elevation, rainfall, noise level
7
5
7
1.678
0.065
0.092
Each cell stores a value for the phenomenon.
HAVE NO theme table.
3. NO DATA. Insufficient information
Grid Theme Tables
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ONLY integer grids have a table. Only integer
grids can be converted to polygons!
Grid Theme Tables are always INFO format tables.
Contain at least 2 fields: value and count.
Value stores the value assigned to each zone in a
grid theme. Do not edit it.
Count – total number of cells in a zone. Do not
edit!
Limits: no more than 500 unique values, and the
range does not exceed 100,000.
MAP QUERY creates a new grid theme that
contains values 0 & 1. 1is assigned to all cells that
met the query requirements. [Landuse.Type]=
“Residential”
The Working Directory
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Use the W.D./Source Manager to copy, delete, and
rename grids. Set up your Working Directory!
DO NOT use any operating commands to move, copy,
or delete grid data sets because each grid data sets
stores some of its files in a different directory (e.g.
INFO)
TEMPORARY GRIDS
Created as a result of performing analysis. Deleted
when a corresponding theme is deleted. Become
permanent when the project is saved.
Raster Analysis
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Local Functions. Calculated on a cell-by-cell basis
Focal Functions. Based on a moving target area
(window) of specific shape and size. 3×3 averaging
filter.
Zonal Functions. Employ a target area called a zone,
which can be of any shape and size. The function
calculates a specific statistic for all cells in each zone
and summarizes the results in a table. Zones are
specified by an additional layer of input. E.g. each
parcel in a housing development has its own parcel #
and would be considered a zone.
Global Functions. Use the cells in the grid to
calculate the result for all raster. Act on an entire grid.
E.g. travel route across the surface
Spatial Operations
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FIRST & HIGHER ORDER DERIVATIVES.
Gridded surface – mathematically continuous. Possible to
derive the math. derivatives at any location.
The 2 first order derivatives are
THE SLOPE and THE ASPECT.
The 2 second order – are the PROFILE CONVEXITY &
PLAN CONVEXITY
Slope is defined by a plane tangent to a surface at any point
and comprises 2 components: GRADIENT – the max rate
of change of altitude, and ASPECT – the compass direction
of this max rate of change.
Gradient – in degrees, %, or radians. Aspect – degrees.
Converted to a compass bearing.
Convexity – the rate of change of slope, in degrees per unit
of distance (concavity – negative convexity).
Spatial Operations – 2
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Before analyzing quantitatively drainage basins you need to automatically
derive surface topology.
Local Drain Directions (LDD)- several algorithms for calculating the
direction of steepest downhill descent (the flow of the material).
CLUMPING.
As a result of a Boolean selection or classification on the attributes of
cells, there are some cells that cannot be identified as a part of sp. entity.
The clump operator examines every cell in a 3 x 3 window to assign to
the same class.
Identifying all ridges via the upstream element map
VIEWSHEDS, SHADED RELIEF, IRRADIANCE
Methods concern the computation of the paths of light between a light
source on the DEM , and its effect at other locations.
Concern with establishing new attributes that refer to the 3D form of the
continuous surface.
Binary variable: 1 – visible, 0- invisible. The collective distribution of all
the ‘true’ points – viewshed.
Practical application.
Soil Erosion Hazard.
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S.erosion has been treated as a static process. Each site has been evaluated separately. No
attention to transport & deposition of sediment. Modeled as sets of independent entities
(polygons or pixels). Physically unrealistic.
Erosion as a process, rather than as a descriptor, using a data model of continuous
variation than as an attribute of crisp entities.
The potential erosion for each cell may be computed using the point models.
Then the transport capacity of each cell determines how much of the potentially eroded
soil can be moved to the neighboring cell.
As each cell is TOPOLOGICALLY connected to upstream neighbors it will also receive
sediment. If the amount of received sediment is greater than that discharged, then
deposition. If not – net erosion.
The transport capacity of the network depends on geometrical aspects of landform, and
potential and kinetic energy of the water.
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Easy to add a transport component once a ldd spatial network has been established, and demonstrates
the deposition in valleys. Never – with the point model.
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Highlighting combinations of steep slopes, shallow soils, aggressive water flows – indicate
the location of erosion potential.
LECTURE 6.
Fuzzy Sets & Fuzzy
Geographical Objects.
David O’Sullivan, David Unwin “Geographic
Information Analysis”, chapter 11, pp. 316-356
Peter Burrough, Rachael McDonnell “Principles
of GIS”, chapter 11, pp. 265 – 297
Fuzzy Sets & Fuzzy
Geographical Objects
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Lecture outline:
Imprecision as a way of thought.
I’m fuzzy…..
Fuzzy objects.
Operations on several fuzzy sets
Combining fuzzy
boundaries & fuzzy attributes
Fuzzy k-means
Advantages & Disadvantages
Application of fuzzy classification
BASICS
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To model geographical phenomena – first necessary to
divide the world either into CRISP ENTITIES or into
CONTONUOUS FIELDS.
These fundamental spatial entities
– points, lines, polygons, pixels – are described by their:
location,
attributes,
topology.
All these statements in conventional logic can have only 2
values: TRUE & FALSE: 0 & 1.
The principles of 2-valued logic.
Lies at the heart of most of mathematics & computer
science.
BASICS
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Many geographical phenomena are not simple clear-cut entities.
The patterns vary over many spatial and temporal scales.
Defined by many interacting attributes.
Until recently we had no means in GIS, apart from
statistics, for dealing with entities that are not crispy
defined.
By limiting the rules of logic to binary decisions we limit the
retrieval and classification of data to situations in which
ONLY A COMPLETE MATCH is possible.
In real life we make compromises based on the DEGREE
with which an object meets our specifications.
E.g. House. Rock types, soil/vegetation classes, socio-economic
groupings, decisions in law courts (guilty, not, or not proven),
nationality, even the borders of the nation state
Imprecision
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The Law of the EXCLUDED middle and its role in
mathematical proof – of paramount importance in scientific
& philosophical development.
The rules of logic used in PC query languages are based on
EXACT ideas of truth or falsehood.
In environmental data this is not necessarily so…
“He says that he always lies” Neither true nor false. It is a
paradox.
Many users of Geo Info have a clear notion of what they need.
Land users & evaluators.
Imprecisely formulated requests (which areas are under the threat
of flooding?).
Must be translated in terms of the basic units of information
available. Not all information is EXACT !!!
Geographical phenomena
& Imprecision
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Geo phenomena are more complicated.
We must consider grouping both in ATTRIBUTE
(whether all entities are of the same kind) &
GEOGRAPHIC space(whether entities of the same
kind occupy a region).
Very often we ‘ve concentrated only on building
class definitions from attributes with assumption
that similar entities will cluster together…
This may be the case, BUT…
How to deal with imprecision in overlapping
attribute classes ?????
Fuzzy Sets &
Fuzzy objects
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Conventional or crisp sets allow ONLY binary membership
functions (T or F). CRISP BOOLEAN SETS.
An individual IS or IS NOT a member of any set. All
members match the class concept, the class boundaries
are SHARP.
Fuzzy sets admits the possibility of partial membership.
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The class boundaries are NOT or CANNOT be SHARPLY defined.
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• Boolean CRISP Set.
FUZZY Set.
Fuzzy Sets &
Fuzzy objects
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In Fuzzy sets the grade of membership is expressed in terms of a
scale that can vary CONTINUOUSLY between 0 & 1.
Individuals to different degrees can be members of more
than one set…
THE BOUNDARY VALUES based on attributes.
In CRISP sets: – on the basis of expert knowledge; – using
methods of numerical taxonomy.
Both options are possible with FUZZY sets.
1. Uses a priori membership function with which individuals
can be assigned a membership grade.
The Semantic Import Approach or Model SI
2. The value of the membership function is a function of the
classifier used. METHOD of FUZZY K-MEANS
Membership Functions
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1. THE SEMANTIC IMPORT APPROACH – SI
Useful in situations where users have a very good,
QUALITATIVE IDEA of how to group data,
but for various reasons – difficulties with exactness.
The membership function should ensure that the GRADE of
membership is 1.00 at the center of the set, that it falls off
through the fuzzy boundaries to the regions outside the set,
where it takes the value 0.
Boolean
Fuzzy
1.0
1.0
Not
A
0.0
A
Not
A
0.0
Not
A
A
Not
A
Membership Functions
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The SI approach to polygon boundaries.
You can incorporate information about the nature
of the boundaries and also to calculate sensible
area measures.
2 separate approaches: the map-unit, and the
individual boundary approach.
The SI approach can be used to add information
about the abruptness of boundaries to a polygon
database.
Picture of spatial variation across and along
boundaries.
Membership Functions
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2. FUZZY K-MEANS.
Very often users may not know which classification is
useful and appropriate.
Continuous classification.
Soil science, geohydrology, vegetation mapping.
Translating a multiple attribute description of an
object into k membership values to k classes or
clusters.
Rainforest types, heavy metal pollution.
Advantages &
disadvantages
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SI approach to exactly delineated polygons can
improve their information content, providing
information about the nature of the sharpness or
diffuseness of the identified boundaries.
Results are more congruent with reality.
Membership values can be easily interpolated
over space.
THE GREATEST DIFFICULTIES come with
choosing the values of the control parameters to
obtain the best results: the kind of membership
functions, boundary values, transition widths, etc.
Applications
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In situations where a well-defined and functional
scheme – SI APPROACH.
SI continuous classes are more robust and less
prone to errors and extremes than simple Boolean
classes that use the same attribute boundaries.
Fuzzy k-means approach is appropriate when
information about the number and definition of
classes is lacking.
Fuzzy k-means methods yield sets of optimal,
overlapping classes that can be also mapped in
data space and in geographical space.
CONGRATULATIONS!!!
You completed the
second course in a set
of courses to obtain
CERTIFICATE in
GeoSpatial Intelligence
Just one more course
left!
CONGRATULATIONS!!!