Description

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

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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.

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

Raster Graphic Data Structure

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

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

Business Analysis

Location Analysis and Site Selection

Proximity to Transportation Analysis

Healthcare and Insurance

Social Analysis

Census Data Exploration

Housing Studies

Disease Spread Prediction

Agricultural Analysis

Forestry

Precision Farming

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

Overlay Spatial Analysis

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.

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

Rainfall 97

Rainfall 96

CHANGE

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5

3

3

2

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0

4

3

3

4

3

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0

0

0

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4

3

4

4

4

3

0

7

5

7

7

1

3

0

4

4

–

=

Working with Distances & Surfaces

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?

Creates contour lines or surfaces from, sample

points

Is

the home in a high noise area?

Where are the hills and valleys?

Analyze hazardous chemical spills

Spread of disease through a vegetation type

Erosion Studies

Vegetation sunlight studies using aspect

GRID Themes

VECTOR better addresses problems where the

OBJECT is of greater concern and the

LOCATION of the object.

RASTER better addresses analysis of an object’s

neighborhood, and how that neighborhood may

have some influence on the object’s attributes.

GRID Themes

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

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

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

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Cell Values

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

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

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

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

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

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

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.

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.

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.

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

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

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

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

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

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

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.

The class boundaries are NOT or CANNOT be SHARPLY defined.

• Boolean CRISP Set.

FUZZY Set.

Fuzzy Sets &

Fuzzy objects

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

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

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

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

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

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!!!

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