GIS Analysis Functions

GIS Analysis Functions

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Introduction

Geographic information systems analysis is the cornerstone of what a GIS is all about.

� All sorts of data can be analyzed and processed with this system.

RoutingRouting

Site SelectionSite Selection

PlanningPlanning

PoliciesPolicies

Spatial Analysis Categories

Retrieval, reclassification, and measurement.

Topological overlay.

Buffering operation.

Neighborhood operations.

Connectivity functions.


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Retrieval

Calls up certain records based on criteria of one or more attributes.

� All land parcels zoned for commercial use that cost less than $2,000,000/acre.

It is a selective search using means such as:

� Select by mouse;

� Query builder;

� For example, how many parcels have land value exceeding $100,000?

� Select by theme;

� You can select feature by mouse, or by an “identify “ tool.

� Find;

� Click on it’s button and type your query in the box which pops up.

Spatial Selection by Mouse

Retrieval involves the selective search, manipulation, and output of data without the requirement to modify the geographic location of the features involved.

Retrieval operations occur on both spatial and attribute data.


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Spatial Selection by Query Builder

Land use areas > 400000

Spatial Selection by Theme

If we want to get information about all the houses in four sample neighborhoods and see which ones overlay fire hazard zones.


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Retrieval: Select by Theme

Now with “sample houses” active, we click select by theme and tell it to choose features that intersect the features of fire hazard zone.

Retrieval: Select by Theme

Those that overlay a hazard zone are selected

selected

Not selected


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Retrieval in Raster

Single layer numeric example: elevation > 2000 ft

Retrieval in Raster

Results in a binary true/false layer


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Reclassification

The reclassification operation will:

� Select data layer based on the specified criteria.

� Reclassify the specific attribute.

� Present the selected layer as a new layer with different number of classes.

Reclassification is an attribute generalization technique.

Reclassification

Classes 1, 2, and 3 in the figure are areas of specific types of crop.

You are interested only in where grain crop are grown?

The program will process all areas and present only areas of class 1 as one class.

The features in the new class 1 may differ among themselves in other characteristics, for example, ownership.


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Reclassification

Input data layer with 8 classes, reclassify it to just 4 categories.

Reclassification Based on Attribute


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Measurement

It is the computation of distance between 2 features, area size of 2D features, volume size of 3D features.

We may want to know the total area of parcel of land, or the distance between two points. In principle all of these measurements are obtainable by simple calculations inside a GIS.

Measurements of the area of digitally represented polygon is trivial and totally reliable for the GIS.


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Spatial Analysis

Retrieval, Reclassification, and Measurement.

Topological Overlay.

Buffering Operation.

Neighborhood Operations.

Connectivity Functions.

Topological Overlay

The primary analysis technique used in GIS applications is the topological overlay.

Overlay operators allow for an analysis of how features overlap and intersect.

This could be done if the features of those combining layers occupy the same location.

This requires relatively complex geometrical operations to derive the intersected polygons, and the necessary creation of new nodes(points) and arcs (lines), with their combined attribute values.


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Topological Overlay

The result of this operation is new information - the spatial and attribute data layers are combined to create a new layer with a new attribute table and new spatial data.

Data layers must be geo-referenced in the same system

In some GI systems, you can overlay only two layers at a time. Others, allow the user to overlay multiple data layers.

Cannot overlay points or lines on each other, but overlay them on polygons.

In a vector-based system, overlay operations are much more complex than in a raster-based system.

Overlay Functions

Topological vector overlay operations can be classified via two ways:

� By operation types:

� Arithmetic:

� Union, intersection, complement, identity.

� Addition, subtraction, division, multiplication.

� Logical:

� AND, OR, XOR, NOT etc.

� Arithmetic and logical operations are precisely equivalent to one another.

� Through the elements contained in the layers to be overlaid:

� Point-in-polygon.

� Line-in-polygon.

� Polygon-on-polygon.


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Overlay Arithmetic Operations

Intersection:

� Keeps areas common to both layers.

� Raster: assign zeros to non-layer areas

and use multiplication.

� Boolean: AND.

Union:

� Keeps all areas from both layers.

� Raster: use addition.

� Boolean: OR.

Complement:

� Both layers except the common area.

� Boolean: A XOR B.

Identity:

� Keeps all areas from the first input layer.

� Boolean: A NOT B.

Identity

Boolean Algebra

Boolean logic represents all possible combinations of spatial interaction btw different features.

Boolean operations use Boolean logic (true or false) on the input values.

AND is the intersection of two sets, the entities that belong to both A and B.

OR is the union of two sets, those entities that belong to either set A or to set B.

NOT is the difference operator identifying those entities that belong to A but not to B. (Identity or minus).

XOR (exclusive OR) is the set of objects that belong to one set or another but not to both. (Complement).


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Logical Functions

Based on logic used to query two or more sets of data.

Logical operators AND, OR, XOR, NOT determine whether a particular condition is true or false.

There are several 16 combinations of Boolean operations such as:

� A AND B.

� A OR B.

� A NOT B.

� A XOR B.

Union

The union operation is used in a vector overlay of two coverages;

� The first is a map of land ownership versus renting,

� The second is a land use map showing agricultural versus urban.

The result of this operation is a map of the entire study area, indicating agricultural and urban as well as owned versus rented land.


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Point-in-polygon Overlay

The point in polygon operation is useful to determine whether a point lies inside or outside a polygon or in which polygon are these points?

Knowing the coordinates of the points, GI system would:

� Perform a number of calculations to determine which of the polygon line segment coordinates surround each of these points.

� Determine whether this point is located within the polygon whose outside coordinates match those in the figure.

Point–in-Polygon

Even number of intersections: point is outside.

Odd number of intersections: point is inside.


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Point-in-Polygon

Draw a line from the point to infinity in any direction, and count the number of intersections between this line and each polygon’s boundary.

The polygon with an odd number of intersections is the containing polygon;

All other polygons have an even number of intersections.

Line-in-Polygon Overlay

More complex than point-in-polygon;

� Sometimes one part of the line falls into the polygon and the other parts fall outside the polygon.


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Polygon Overlay

In this example, two polygons are intersected to form 9 new polygons:

� One is formed from both input polygons;

� Four are formed by polygon A and not polygon B;

� Four are formed by polygon B and not polygon A.

AB

Polygon-in-polygon Overlay

Union

Intersect


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Polygon Overlay Types

Intersect:

� Combine the features inside the area common to both layers.

Identity:

� Combine the features inside the area of the first coverage.

Union:

� Combine the polygons from two layers.

Raster Map Overlay

The raster data model performs overlay operations more efficiently than the vector model.

The classes are indicated by a numerical values that are easy to calculate.

In raster data the overlay functions are carried out between corresponding pairs of cells, one from each input raster data layer.

Raster cells have a one-to-one relationship between layers.

Important to consider measurement of input data layers;

� It makes no sense to divide soil class a by land use class b.


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Raster Map Overlay (Calculus)

Output cell value is the result of an arithmetic operation on the input layers.

For example, if a and b are input layers and c is an output layer,c = a + bc = a * b…..

Also any kind of function such as average, sum, min, max, standard deviation.

Raster Map Algebra Overlay

Map algebra calculation can be performed to identify relationships between layers, or to derive indices that describe phenomena.

A and B.

� (Soil_depth_1990) AND (Soil_depth_2000) = common Soil_depth between 1990 and 2000.


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Raster Map Overlay

Raster based GIS overlay does not need a geometrical operation because the classes are indicated by a numerical values which is easy to calculate. +, _, *, /.

Raster Overlay

New values result from applying one of the following operations:

� First + second: corresponding feature attributes(pixels) from the two layers (images) are added.

� First - second: attributes of the second layer are subtracted from those of the first.

� First x second: corresponding attributes from the two layers are multiplied.

� First / second: attributes from the first layer are divided by corresponding attributes from the second.


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Raster Overlay

Overlay: Basic Rules

1. Enumeration rule

Each Attribute preserved in output, Union operation


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2. Contributory rule

each attribute value contributes to result


3. Dominance rule

Only one value win


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4. Interaction rule

pair of values contribute to result

Spatial Analysis







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Buffer

Buffering involves the ability to create a uniform distance in all direction from selected features, be it points, lines, or areas.

To produce the buffer the following are required:

� A selected feature(s),

� A specified distance from that feature,

� A specific attribute of that feature,

� Its purpose

Buffers are created as a separate feature and separate coverage as well.

Examples: The boundaries of areas believed to be contaminated areas by poison gas, nuclear disaster, those borders imposed by law enforcement agencies.

Buffering is also referred to as corridor or zone generation.

What Queries Can Buffer Solve

What is the total number of customers within 10 km of this new store to estimate the potential sales?

What proportion of the wheat crop is within 500 m of the water well?

How many houses lie within 100 m of this stream carrying water-borne diseases to estimate population at risk.


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Buffer Types: Vector

buffer 100 meters Buffer with dissolvingthe interior boundaries

buffer byattribute values

Buffers and Setbacks: Vector

Setback: A zone inside a polygon constructed by a fixed distance from the edge of the polygon


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Buffer Creation: Vector

Buffer: Vector

In vector-based buffer generation, the buffers themselves become polygon features, usually in a separate data layer, that can be used in further spatial analysis.

In this example, a number of main and minor roads were selected, a 75m and 25m noise buffer was computed from them.


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Buffer: RasterThe principle of buffer zone generation involves:

� Selecting one or more target location, then,

� Identifying the area around them within a certain distance.

For example: buffer around habitat of a threatened species.

Feature

Buffer

Buffer: Raster

Vary the distance buffered according to values in a target layer

City limits

Areas reachable in 5 minutes

Areas reachable in 10 minutes

Other areas


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Clip

Within the areal extent of the clip theme includes only those features of the input theme that are inside the area

+ =

Spatial Query

Determine the volume (not as a number) of timber within 100 m distance of a cut-line


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Performing Extraction Analysis

To be scanned

Spatial Analysis







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Neighborhood Analysis Functions

This function evaluates the characteristics of an area surrounding a specific location.

For these operations each location is surrounded by eight adjacent neighbors.

The statistics that can be computed within a neighborhood are: max,min..

The neighborhood function that can be specified are:� A rectangle of any dimension,

� A circle of any radius,

� A doughnut shape,

� Irregular shaped neighborhood.1 2 3

4 X 5

6 7 8

Neighborhood Analysis Functions

Neighborhood analysis basic functions:

� Average, diversity, majority.

� Minimum/maximum, and total.

Neighborhood analysis functions:

� Thiesson polygon.

� Vector model.

� For example, triangulated irregular network (TIN).

� Raster model.

� For example, digital elevation model (DEM).


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Neighborhood Operations

To perform neighborhood analysis, we must:

� State which target locations are of interest to us, and what is their spatial extent.

�What is at the location (e.g. volcano, source of pollution, medical clinic)?

� Define how to determine the neighborhood for each target.

�What is near the location?

� Define which characteristics must be computed for each neighborhood.

� How many people live in the area?

� Are any high-risk industries located in the neighborhood?

� For which residential areas are the location the closest?

Mean: Vector


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Neighborhood Analysis Functions: Raster

Neighborhood characteristics often are obtained via statistical functions that compute values of the cells in the identified neighborhood such as:

� Average (zonal mean).

� Sum (zonal sum).

� …..

Output cell value is a function of a group of neighboring cells in the input raster.

input

output

Maximum: Raster


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Neighborhood Operations

Thiessen polygon

Vector model

� e.g. Triangulated irregular network (TIN)

Raster model

� e.g. Digital elevation model (DEM)

Thiessen PolygonThe analysis of topographic features are categorized as being a Neighborhood operation.

This involves a variety of point interpolation techniques including slope and aspect calculations, contour generation, and Thiessen polygons.

Interpolation is defined as the method of predicting unknown values using known values of neighboring locations.

The input layer is the set of points. From these, Thiessen polygons are defined in which each polygon defines the area closest to the point that lies within it.

The boundary lines are thus lines that are equidistant from two points.


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Triangulated Irregular Network

Irregularly space points are stored in a Triangular Irregular Network (TIN).

A TIN is a vector topological network of triangular facets generated by joining the irregular points with straight line segments.

The TIN structure is utilized when irregular data is available, predominantly in 3D vector based systems.

A triangulated irregular network is a model of a surface.

Triangulated Irregular Network


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Digital Elevation Model (DEM)

An alternative in storing elevation data is the regular point, Digital Elevation Model (DEM).

The term DEM usually refers to a grid of regularly space elevation points.

These points are usually stored with a 3 D raster data model.

Digital Elevation Model (DEM)


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Spatial Analysis- a Process

Spatial Analysis







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Connectivity Functions

Combines adjacent units together when they share a common attribute (dissolving).

Proximity operation.

� Determine distances between sets of points or between points and lines (vector).

� Calculate a surface representing the distance to the nearest target (raster).

� Not restricted to distance; Can be noise, time, pollution, etc.

Distance mapping.

Parameters to define:

� Target location.

� Unit of measure.

� Function to calculate proximity (distance/time/noise).

� Area to be analyzed.

Connectivity Functions (Dissolving)

Removes boundaries between adjacent polygons that have the same value of a selected attribute.


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1. Proximity Mapping

It involves the ability to assign each location to the source it’s nearest to.

For instance, which fire hydrant will serve which area.

Which medical clinic is closest to the village?

Identify which houses are affected by which contaminated water sources (pumps).

Determine the distance from archeological sites to the nearest stream.

2. Distance Mapping

It involves the ability to find how far each location is from the nearest source (e.g. Snow’s cholera maps).

By mapping the locations of deaths and pumps in 1854, Snow concluded that the outbreak of cholera that occurred in a district in London came from contaminated water, not by inhaling vapors as they thought.

Another e.g. Find all fire hydrant within 500m of a burning building.

By selecting these locations that meet the criteria, you can transform the distance map into a buffer.


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Example of working with raster data: Flow & Watershed

DEM


Flow Direction


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Flow Accumulation


Watershed


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Conclusion


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Conclusion

Spatial analysis functions are a powerful tolls for solving a wide range of spatial problems

Maximising the agricultural profit by establishing the relationship between soil chemistry and crop yield.

Defining the best route for gas/oil pipeline or the location for other infrastructure and facilities.

With spatial analysis functions you can execute these tasks.

Slides Courtesy of:

Dr. Bheshem Ramlal

Department of Geomatics Engineering and Land Management

The University of the West Indies

St. Augustine

Date post:	23-Nov-2023
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GIS Analysis Functions

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