Vector Analysis 

1.0 Overview

Analysis is often considered to be "the heart" of GIS.  Through analysis new information is gained.  As a GIS stores both attribute and spatial data, analysis can be conducted on both types of data – however, it is the spatial analysis capability that sets GIS apart from database applications.

There are a great many GIS analyses that can be conducted.  For convenience sake we often group the analyses into categories.  For the purpose of this course I have decided to create a bit of a hierarchy.  This is done to reflect your lab experiences using GIS.  Our first encounter with GIS analyses is with vector data.  Later we will (hopefully) move into analysis of raster data.  The focus of this module is vector data.  The breakout of vector analysis is as follows:
 

Attribute

Attribute Query - Select by Attribute

Arithmetic Calculation

Statistical Summary

Reclassification

Relating Tables

Spatial Join
 

Spatial

Spatial Query - Select by Location

Spatial Calculation

Spatial Join

Overlay

Buffer

Dissolve

Network Analysis

2.0 Attribute Data Operations

There are many operations that can be conducted on the attribute database (the data tables).  These can be divided into 4 categories: query (or logical), arithmetic, statistical and reclass operations.  I included a short note about relating tables as it enhances our analytical capabilities.  There is also the spatial join function, which straddles attribute and spatial analysis.

2.1 Queries = Select by Attributes

Queries include both comparison (=, >, <, >=, <=, <>) and Boolean (AND, OR and NOT) operators (for a simple but effective visual, check-out the Boolean Machine).  These operators are used to perform queries. 

Example 1: a simple comparison query,

Forest_Age >= 250 (years)

would query for a subset of forest polygons that could be considered ‘old growth’. 

Note the query has 3 parts: field name, operator and value.

Example 2: in Pacific Northwest critical deer winter range has old growth Douglas-fir trees.  The query has two criteria and would look like,

            Forest_Age >= 250 AND Fir% >= 50.

This second query operates on two attribute fields and is more specific (restrictive) than the first – it would yield a smaller subset of polygons as both conditions would have to be met. 

Example 3: if deer simply liked old growth and/or Douglas-fir (a fictitious example), then the query would be

            Forest_Age >= 250 OR Fir% >= 50.

This query is more inclusive as a stand can be either old OR composed of Douglas-fir.

2.2 Arithmetic

Arithmetic operators perform simple mathematical functions on values in the attribute database; operators include:

·        +

·        -

·        /

·        *

·        ⁿ (raised to the power of)

·        √

·        Sin

·        Cos

·        Tan

These operators can be utilized to to calculate values to be placed in a new field:

2.3 Statistics

Statistical operations can also be performed on the attribute data.  There are 2 options available when you right-click on a field name: 'statistics' and 'summarize'.  'Statistics' provides a temporary pop-up table with the typical parameters:

·        count

·        minimum

·        maximum

·        sum

·        mean

·        standard deviation

Plus the data are plotted in a histogram (frequency distribution).

'Summarize' creates a an output data table.  Statistics are based on unique values in a chosen field. selected fields from these operations are placed in a summary table.  In the example below, the field Group was chosen and the statistics count, sum and mean were calculated.

Data Table                                                Summary Table

2.4 Reclassification

Reclassification is another operation that can be conducted on attribute data.   Reclassification results in a generalization (i.e. a simplification) of the original data set.  For instance, raw property values in a data set can be put in 3 classes: lower, middle, and upper class.  We typically use the legend editor (in ArcGIS the Symbology tab of the Layer Properties dialog box) to classify the data - altering the legend is temporary and we can change the colouring at anytime.  (If we want a "permanent reclassification", e.g. a new map, then we would use Merge / Dissolve - this is described in section 3.5 below).

2.5 Table Relations

Relating tables to each other involves joining or linking records between two tables.  This may not be considered ‘an operation’, but it does allow us to relate outside source data to our themes to allow the features in our themes to be analyzed based on ‘outside’ data.  Refer to the database lecture notes.

2.6 Spatial Join

As with relating tables, a spatial join will relate records between two tables.  But the records are not joined based on a common attribute value (usually ID); instead records are joined based on ‘common location’ (as defined by the coordinates of the spatial features).  This type of operation is a combination of spatial and attribute; it is described in more detail in section 3.2 below.

3.0 Spatial/ Geometric Operations

The spatial characteristics of map features (points, lines, polygons) can also be analyzed.  Location, size and shape of the map features, as defined by their coordinates, are basis for these operations.  Spatial operations can be categorized as follows:

3.1 Spatial Query - Select by Location

This is where features in one theme are selected based on their spatial relation (connectivity, containment, intersection, or nearness) to features in a second theme (i.e. select forest stands that contain an eagle’s nest); new data is not created, just a set of features are selected.  A few examples:

3.2 Spatial Calculations

Simple spatial calculations determine areas, perimeters, and distances based on the coordinates (in ArcView these are accessed through the ‘shape’ field as it contains the vertices); the calculations utilize the coordinates that define the features, but the results are stored in the database table (so this operation also straddles both attribute and geometric). 
 

3.3 Spatial Join

As previously stated, this operation is a mix of spatial and attribute operations.  The end result is a join of two database tables, but the basis for the join is ‘coincident space’.  As with a ‘regular join’ the relation has to be one-to-one or many-to-one between records in the ‘destination-to-source tables’.  As an example we could have two themes: Cities and Countries of the world.  A spatial join could be done for cities as the destination theme, as it yields a many-to-one relation (many cities to one country).  A spatial join would thus bring data from the Countries theme to the Cities theme.  A spatial join could not be done with Countries as the destination table as the relation would be one-to-many.

 

3.4 Overlays – bringing together two themes – the line work of the two themes are combined (lines are broken, new nodes and links/arcs are recognized, topology is redone, note that sliver polygons may have to be eliminated) and the fields from both theme databases are combined into one new database.  Three common types of overlays:
 

3.5 Buffers

Buffering creates a new theme with new polygon features (geometric objects) based on a constant measure from features in a source theme; buffers around points are circles, around lines are ‘corridors’ (snake-like with rounded ends) and around polygons are ‘donuts’; buffers can be created based on:

3.6 Dissolve

With dissolve, also known as merge polygons, boundaries between adjacent polygons with the same attribute value (i.e. class = poor) are ‘dissolved’ and the two (or more) polygons are merged into one larger polygon; a new map layer (theme) results with the generalized data.  This is the ‘spatial equivalent’ to reclassification of attribute data.

 

3.7 Network Routing – as the name implies, this type of analysis assesses movement through a network.  Consider the difference between the shortest route and the fastest route.  During the middle of the night the ‘shortest route’ is likely the ‘fastest route’, however, during rush hour I would consider traffic and use the ‘fastest route’ (which may have a longer distance).  The network is modeled using lines (arcs) and intersections (nodes).  Arc-node topology provides information regarding connectivity.  The attribute database would provide additional information regarding impedance to flow (or movement).  Examples would include speed limit and traffic loads at different times of the day.  There is a ‘cost’ to making turns at intersections – i.e. you have to slow down rather than use just two wheels to make the turn.  One-way streets would provide for an absolute barrier.  As well, making a turn off of an overpass onto a highway below would be prohibited.  Other routing examples include most efficient route (for making several stops or deliveries) and location-allocation (where school catchment areas can be determined based on road network and not just a straight-line distance).

Quickest route to Vegas!

Shortest route to Vegas!

Note the difference between the two routes. 

3.8 Summary

The results of these spatial operations take on different forms: item 3.1 is a spatial query and merely results in a selection of map features that meet the ‘spatial criteria/relation’, items 3.2 and 3.3 result in additions/changes to the database tables, items 3.4 - 3.6 generally result in a new theme with line work and a data table based on the spatial operation, and .  Item 3.7 (networks) usually result in a selection of lines within the network that represent the best route.