URBS 335 Final

Mapping

Science of mapping
Scales
Coordinates
projections
Control datums

Info databases

Spatial
Non-spatial

Computer hardware and software, models

People- users, researchers, managers, committees

About mapping what’s around you- mapped water bodies
Was refound to be important in 1492

1960- 1st satellite, 1st GIS
1965- SYMAP
1969- ESRI created
1980- personal computers
1990- GIS goes mainstream
Global positioning systems
2005- Google maps/ earth

Centuries of hand-drawn map overlay techniques and cartographic analysis

Computing development in the 50s, 60s: massive cost reduction of materials and increase in performance

Geographical data production and dissemination in the 70s

Quantitative geography in 60s and 70s

Historically (1960-1980): schools, government, military
As time when on businesses (1980- 1995)
And then the general public (1995- today)

Static: elevation, mountains→ things that can not and will not move
Mobile: traffic

static/ mobile
Changing at different rates
perennial/ seasonal
visible/invisible
simple/complex
Measurable vs not

Continuous: spatial features that exist between observations. The ‘concentration’ of such phenomena can be measured on each location of a surface
- temperature, elevation

Discrete: spatial features that do not exist between observations (individually distinguishable)- they have defined boundaries
- rivers, buildings

Points, line, polygons

Spatial analysis that can be performed:
Contiguity
Is the line on the polygon, is the dot in the polygon

Connectivity

Containment
Is the dot within the polygon?
Can only be done with polygons

Georeferencing or Heads-up- digitizing

2 mathematical:
Scale- large to small
Projection- spheroid to plane

2 cognitive
Map production- interpretation of the reality
Map reading- interpretation of the map

to simultaneously communicate the relationships between 3 dimensions

additive- screen
The more RGB layered= white
No colour= black

subtractive- print
Take away all colour= white

Elevation
Top- white (just for snow peaks)
Button- black

Temperature
Water and water labels- blue
Landmass- tan
forest/park- green
Land Use Colours (APA Standard)
Colour contrast

Le Corbusier Colour Concepts
Naturally pigmented colours and alternating them with darker ones to create depth
Thought colours provoked emotions

Based on the ratio of the 2 radii

Flattening ellipsoid- f=1-b/a
Where a= semi-major axis and b=semi-minor axis
Inverse flattening ration is often used to quickly understand the level of flatting of an ellipsoid
Larger the inverse f the less flat it is

A point, straight line or plane, used as a reference when measuring a 2d surface

Used in GIS as a CRS for referencing earth surface features or positions over an ellipsoid

Locates a new, arbitrary, center of the earth

Its a ‘regional surface model’ of the earth

Projection from datum differences can be sometimes misleading

NAD 27- north american 1927, state plane system

NAD 83 used for topo maps in North america including canada and quebec
Based on GRS 80: geodesic reference system measured accepted
Determined from satellite orbital (more accurate); reference: the center of earth

WGS72 and WGS84- world geodetic system is now the more common reference (GPS ref.) (based on GRS 80)

Google earth/ virtual earth use a spherical datum based on WGS84 without flattening
Both radius use the semi-major axis

One ellipsoid can be used for several datum
lat/long coordinates calculated with one datum are valid only with reference to that datum
To be viewed in another datum, their position must be recalculated (reprojected’) and they will be given new coordinates
When you recalculate or reproject coordinate from one datum to another, the shape and position of the recalculated area changes or shifts

is related to a coordinate system and an origin
numerical

refers to discrete geographic earth surface units .e.g., street addresses, or zip codes

nominal and ordinal

Is a non-projected
Based on lat/long
lat/long correspond to angles at the center of earth based on a defined origin
And based on a specific datum/ellipoid
How to represent 3d on a 2d?
By ignoring that they are angles..and pretending they are x,y values
This gives the basic Equirectangular “projection” (360° E/W and 180 ° N/S) (“Geographic Projection”) (aka Plate-carrée)

Reality: Earth
Mathematical approximation: ellipsoid/datum
Serve to transform geographic coordinate into plane coordinates
They are different types of projected coordinate reference system, based on projection surfaces
3 major projection surfaces- Flanar, cylindrical and conical

In 1772 Johann Heinrich Lambert modifies the Mercator projection into its transverse form
Minimizing the distorsion in narrow strips running from pole to pole
Became widely used in the US after World War II
Divides earth (between 84 N and 80S of lat) into 60 zones, each of which covers a width of 6 degrees
Zones are numbered from 1-60, with zone 1 beginning at 180
Canada has 16 UTM zones, from 7-22
Montreal is zone 18

Limitations
Error and distortion increase for regions that span more than one UTM zone. UTM is not designed for areas that span more than a few zones. (not Equivalent)
USGS 1:100,000 scale topographic maps
Canada: Topographical maps (1:50,000 and 1:250,000)

Shape - are preserved in small areas (Conformal)
Area - Minimal distortion of larger shapes occurs within the same zone.
Distance – Scale is constant along the central meridian
Direction - local angles are true

Montreal in zone 8
Used in Quebec & Atlantic provinces (topo map 1:20,000) (Forestry)
Based on the UTM: Province of Quebec is divided into 8 zones of 3º of longitude each (from 3 to 10 starting on the East coast)
Each zone is centered on a meridian with 1.5 º from each side

Cylindrical equal-area projection
Created by Arno Peters (historian) in 1967 based on James Gall projection (1885)
Challenged the Mercator projection used for centuries
Highlight the importance of the size of southern continent

The Lambert Azimuthal Equal-Area projection of North America
Albers Conic Equal-Area projection of North America
The Lambert Conformal Conic projection

They are a grid like representation of data in terms of rows and columns, presented in different styles
Contains a range of cells
Can be presented in different formats
They are a basis for one of the most important components of GIS
When created well, makes your life easier

Friendly data table
Consistent use of Space and Case
Format and Coding of Data
The structure of the file read by your software

+, - , *, /, ^

>, =, <, >=, <=

AND: intersection of 2 sets
OR: union of 2 sets-
XOR:exclusive OR (belong to A or B, but not both)
NOT: difference operator (belong to A but not to b)
In raster say AND NOT

Can be used for attribute or spatial

Powerful language to isolate, count and locate individual
Use quotation marks for field names, single quotation marks for text and nothing for numbers
Use logical operators (eg >), to select string values based pm sorting order

Describe the characteristics of spatial features
2 major types:
Textual
Numerical

4 measurement levels
Nominal
Ordinal
Interval
Ratio

Nominal
Categorical: describe different categories of data ie dataset has difference categories such as race, age, gender, city
Most qualitative and non numeric
Ranked

Ordinal
Categorical
Mostly quantitative or numerical
Discrete (real or integer), statistical eg mean, median
Meaningful ranking order (often continuous)
Could be binary

Interval
Qualitative and quantitative
Known intervals between values
Allows numerical comparisons between data eg temperature

Ratio
Quantitative
Known intervals between values eg intervals between 2 times steps, age groups etc
Allows numerical comparisons between data, zero is absolute
Statistical
deals with non- negative numbers

Database: a system for collecting, organising, and storing data electronically

5 types:
Hierarchical
Ranked according to levels

Network
Linkage between multiple data networks

Object oriented
Info is represented in the form of an object, most often linked with object oriented programming where everything is defined as an object

Relational
Information stored within the database are mostly related ie datasets are most related to one another

NoSQL: non-tabular databases, where data are stored in formats different from relational databases eg storing data in documents rather than tables

Tables are linked through an ID
One ID for each geographic feature
Field ID is NUMERICAL
Each ID is UNIQUE
Evolving (designed to integrate future data)
Standard (data exchanges)
Tables CAN NOT be linked through FID (feature ID)
FID are computer generated for polygons, lines

Each row represents a spatial feature, and each column describes a characteristic
The connection between tables is made through a key
A key (or ID) is a common field whose values can uniquely identify a record in a table
The Feature ID (FID) is an indicator of the order of which object were created.
Each table can be managed separately from other tables

Types of relationships
One to one
One to many
Many to one
Many to many

Link together two tables by using a common key
E.g. joining nonspatial table(s) to a feature attribute table
Recommended for one-to-one (and many-to-one)

Inner joins; which return matching rows taking into consideration values in Table 1 (left) present in Table 2 (right)

Left join; returns all rows in the left Table including those without a match on the right, with unmatched values from the right filled with null values

Right join; returns all rows in the right Table including those without a match on the left, with unmatched values from the left filled with null values

Full join; returns all matched rows in both right and left tables, with all unmatched values from both Tables filled with null values

Keeps the tables physically separate
Appropriate for all four types of relationships
Slow down data access

Absolute is integer or real number values
Raw numbers
Relative is standardized data- eg %, or ratio values
Standardized data may be derived from the attribute itself or generated with statistics from total of the attribute column or with 2 attribute columns (by putting one over the other = ratio)
density= population/census tract area

Dot density
Isarathic map
Proportional symbols
Graduated symbols
Proportional vs graduate
Graduated symbol points
Cartograms

choropleth

1. Determine number of classes
Based on: volume of data (subjects), type of data, the public (expert viewer= higher number of classes)
Less than 20- 3 or 4 classes, more than a 100= 5 to 8 classes

2. Which classification scheme?
Think of the public (goal of map), data distribution, ease of understanding map/ legend, unique map or multiple maps
Context and data distribution should drive classification

Space segment
Satellite
Need at least 24 us gov satellites distributed in 6 orbital planes circling the earth every 12 hours

Control segment
What's on the ground and communicates with satellite

User segment
How do we use gps coordinates received by a gps receiver?

Gps unit around 200$ Gps uses a minimum of 4 satellites to map on ground locations Error of 5-10 meters Set coordinate systems and control datum the same as other GIS layers About 2 days to learn how to use a GPS unit

Radar- radio detection and ranging
LiDAR-
UAV- unmanned aerial vehicles
SONAR- sound navigation and ranging
Aerial photos or orthophotos
Multispectral remote sensing

light detection and ranging

Plane with sensor generates an image
Using how long it took to get from one point to another to map the length of object

Aerial photos are do not fit reality perfectly
Orthophotos have been rectified to fit perfectly

Points 0- dimensional
Basic shape, defines the essence of all 3 forms

Lines 1- dimensional
Is a set of connected points (vertices)

Polygons 2- dimensional
Is a closed shape (1st and last point have same coordinates)

“Spaghetti model”
Can be retrieved and rendered on screen very quickly
Interoperable (can be used across different software packages)
Inefficient for modelling relationships between geographical objects (eg road network)

Shapefile
No files describe the spatial relationship between the geometric objects
Shapefile polygons have duplicate arcs for shared boundaries
Shapefiles can be converted into topological vector data (eg coverage) and vice-versa

In GIS it has 2 major functions
Validates the geometry of vector entities
Allows spatial operations based on connectivity and neighboring (contiguity) relations

Topology: a geometry without coordinates
Based on relationships

More efficient way of storing data, fewer coordinates than in simple structure (eg a line may serve for several adjacent polygons but the actual coordinate for each line is stored only once)... but more tables for each file

It studies the arrangement of geometric objects and the relationships between objects

It is based on directed line (arcs, not intersected) and the points where arcs meet or end (nodes- intersections)

arcs= line component/ boundaries, nodes= intersections/ end points, vertices= corners at edge of shape

Connectivity: the degree to which lines in a network are linked to one another
Contiguity: link between polygons based on the existence of common lines

Key for applying the concept of planar enforcement (process of converting simple data model into typology):

1. All the space of a map must be filled
2. Line split at intersections
3. Polygons must not overlap

Buffer: zone created around an initial entity (measuring distance)
Can be applied to points, lines, polygons
Performed in vector and raster environments
Can be a simple (uniform) distance or a variable buffer (based on attributes), donut buffer (buffer around buffer/ ring buffer)
Buffering with no dissolve= 100s on polygons
Buffering (dissolve)= 1 polygon with multi parts

Intersect- AND
Union- OR
Complement- XOR (symmetrical difference)
Identity- retains original data but cuts it up my identifying layer→ cookie cutter

Spatial configuration

Contiguous regions
Aka single part polygons

Fragmented regions
Aka multi part polygons

Perforated regions

Transferring known data from one set of polygons (source) to another set of polygons (target)

1. Overlay both layers
2.Query the areal proportion of each source polygon (eg census tract) that is within each target polygon (eg school district)
3.Apportion the data from source polygon (eg population) to target polygon according to the areal proportion
4.Sum the apportioned data from each source for each target polygon

Line is based on a set of vertices
These vertices cane be used to calculate:
Length
Azimuthal direction (spherical trigonometry between each set of points)
Shape or sinuosity (ratio of the length to its straight line length)
Lines can be selected based on these measurements (eg select river with a sinuosity < 3)

Based on vertices

Vertices can be used to calculate:
Length
Area (based on the trapezoid)
Orientation
Convexity
Centroid- Center of gravity,Note: a centroid can also fall outside a concave polygon
Geometric center- Trapezoidal rule, Can not be outside
Mean center

Mean center: find the center if several polygons or points
Could be weighted: each coordinate pair has a different importance

Satellite
Digital orthophotos
Digital raster graphics

Origin is (1,1) at top, left corner

Transforms a raster file into a vector file (features)
Every neighboring cells are connected together to define lines or polygons boundaries
The center of the raster cell becomes a point

The value of each cell is based on the value of ONE selected field
Different methods to determine the value of cell sharing multiple polygons
Errors are common in the converting process
Can not go back and forth- once converted it can not go back

Cell size = resolution
Higher resolution is more accurate, but heavier

Ex:
A 10m cell is 10mx10m (ie cover 100 m^2 on the ground)
Higher resolution
A 30m cell is 30mx30m (ie covers 900m^2 on the ground)

Disadvantage of large cells
Not very precise spatially
Not very accurate thematically (mixed pixel problem)

Disadvantages of small cells (high resolution)
More storage requires much more computer power to be viewed and processed
For an equal number of pixels, a high resolution grid covers a smaller area

Applies to the center of the cell (eg distance measurement) or entire cell (overlay)
Can be used to represented continuous fields as well as discrete objects
Appropriate for continuous phenomena with fuzzy limits

Each cell is usually associated with one numerical value
Integer usually represent categorical data- eg land cover
Floating-point represent continuous data- eg precipitation

In a grid never trust the colours, only the values because there can be classes

This problem is related to the fact that each cell only has one value

2 general methods
Largest share of the cell area (most common)
The central point

Run-length encoding
Say there X of one colour, back to back for each row

Block codes
Requires 3 number per code
Each block is encoded by string its size on one side + its origins in x,y coordinates

Operations on a single shape are easy (area and perimeter operations)
Compact way to store polygons information
Useful to convert raster polygons to vector polygons
Operations on several shapes are more complex (merging, intersection; easier to convert back to uncompressed raster data)
Efficient only if many large areas have the same value

Local: those that work on single cell locations- local functions
Focal: those that work on cell locations within a neighbourhood- focal function
Zonal: those that work on cell locations within zones- zonal functions
Global: those that work on all cells within the raster- global function
Application: those that perform a specific application

Combine 2 or more raster files
You may need to reclassify one (or more) of the files to create a useful overlay
You can use arithmetic, logical and boolean operators
Produce a new raster layer
More powerful than the vector overlaying
Allows for combinations of several grids

Allows the selection of pixels from one grid based on pixels from another grid (mask)
The mask grid must be binary (0,1)
The mask can be used to “clip” other layers
Multiply original data set to only show values that you are interested in from the 2nd set of data

It is estimated more than calculated

perimeter= number of cells faces of the perimeter * resolution

Depending on how the data is encoded the perimeter may be coded in the inside middle or outside
Which one you choose is based on situation

Problem: the more complex the polygon the more grid cells will be at a diagonal to their neighbors and the less accurate your results will be

For each cell, the distance is calculated to the source cell(s) by calculating the hypotenuse of the square triangle
This derives from the true euclidean distance
Does not have to go through center of cells

Calculate the distance from the origin through the center of neighboring cells
Have to go though center points of cells
Useful to calculate the costs distance- shortest distance

Measuring euclidean distance is essential
But the chance of encountering a totally isotropic surface (where no obstructions or frictional changes exist) in the reality is practically non existent
Non euclidean distance (eg cell distance) may be more meaningful
Movement across non-isotropic surfaces incurs a cost: cost distance

Discrete obstacles that interfere with movement across a surface

Can be:
Absolute (eg cliffs, fenced areas, lakes)
Permeable (eg bridge over streams)
Impermeable (cost value= 9999 CU)

Lateral link: 1* ((Ci + Cj)/2)
Straight line
Diagonal link= 1.414 * ((Ci + Cj)/2)
Where Ci = cost of cell i and Cj= cost of cell j

Assets:
Simple to use
Software are usually cheap
More and more data available (eg satellite images)
Powerful for overlaying and neighboring analysis
Relevant for fuzzy analysis

Limits
Size of files
Not designed to join attribute tables
Resolution is determined a priori
Low resolution: not very aesthetic for mapping

“Surfaces are features that are most often thought of as contain g height values called Z values distributed throughout an area defined by sets of X and Y coordinate pairs”

Z values constitutes a statistical representation of the magnitude of the feature
Often elevation

Vector
Used to create and represent surfaces in GIS based on interpolation
Set of irregularly distributed mass points with x, y, and z
constructed based on the Delaunay triangulation

Advantages
Incorporate the original sample points
Efficient way of storing the data
Easy to calculate slope, aspect, etc
Photo-realistic views of landscapes (when draped with images) (eg visualization of urban form)

Limits
Very susceptible to very high and low values
“Unconventional representations

Circles around 3 points and whichever circle does not contain the 4th point will pass

A raster surface which cell values represent elevation
Spatial interpolation
A way to create a continuous surface from sample points so that the surface can be used for analysis

Creating a DEM by Spatial interpolation
1. Input a point layer and select the number of points to be used or (distance of analysis) in interpolation
2. Set the desired size of your output raster cells (resolution)
3.Select the interpolation algorithm

1. Near-neighbour
Target cell get value of the nearest control point

2. Inverse distance-weighting
Average of surrounding value inversely weighted by distance to target cell

3. Kriging
Spatial autocorrelations of surrounding cells are considered in conjunction to the IDW in the interpolation of the target cell
4. Splining
A flexible ‘surface’ attached to the control points and this surface is used to interpolate the value of the target cell
Ex: Georeferencing lab

In raster common methods use a 3-by-3 moving window (kernel)
Kernel passes over every pixel of the grid to calculate the maximum rate of change of value (slope)based on its neighboring cell
either use 4 closest cells or all 8 cells

Compare the 4 adjacent cell to determine the rise values of the central cell (2 axes)
Keep the highest riseun value
Calculate its slope in percentage

Orientation (aspect) of a pixel is derived from the slope
Aspect identifies the down slope direction of the maximum rate if change in value from each cell to its neighbors
Aspect can be thought of as slope direction
The values of the output raster will be the compass direction of the aspect

Compare the 4 rise values (4 axes)
Keep the highest riseun value
Estimate the direction of the slope (aspect)

if you can see something from one object then you can see the other object from that one

Each objects can be seen from all others

Inputs
A point layer
Elevation layer (raster DEM or vector TIN)

Parameters
The viewpoint (fixed or to be selected)
The height of the observer/observation point
Viewing azimuth
Viewing radius
Vertical angle limits to the scan
Object height

Algorithm
Line of sight/ sight line operation (basis of viewshed analysis)
Connects the view point to the target point
Determines if target is visible or not based on elevations of intermediate cells
Line of sight is expanded to every cell in the raster (each cell is a sight line ‘target’) to determine which are visible/ invisible

Output
View shed map
1= visible from viewpoint
0= not visible from viewpoint

Calculate quick surface areas

Creates dashed lines to connect adjacent gages, soldering lines are perpendicular bisectors of those lines, and heavier solid lines are the portions of the bisectors that constitute polygon boundaries. Points in each subregion are closer to the gage near the polygon center than any other gage

Kurtosis- from greek meaning ‘bulging’
0- normal, greater than 0- peak distribution, less than 0- flat distribution
Higher kurtosis= smaller standard deviation

“Everything is related to everything else, but near things are more related than distant things”

If it is clustered= 1, random= 0, dispersed= -1

Random and dispersed distribution

Average distance of nearest neighbour indicates
If value nears, then (1/2sqroot(density)) → random distribution
If value (1.07453/ sqroot(density)) → dispersed distribution

The expected average distance/ the expected random distribution
Like a t test by for differences between observed and expected NN distance

To FSA- 3 digit postal code
To postal code areas- 6 digit
To province-
To census metropolitan area
To census tracts
To dissemination block