Global positioning system.

Funded and controlled by the US department of defense.

Needs 4 satellites for x,y,z.

Reciever computes position, velocity and time.

Architecture improved.

First satellite launched.

System declared operational. 

Architecture approved.

First satellite launched.

System declared operational. 

6 orbital planes (60^o apart)

4 satellites per plane

5-8 satellites visible from any point on earth. 

If we know the distance to satellites,

then 1 satellite results in a sphere.

2 result in a circle.

3 result in 2 points.

 4 results in 1 point.

Only 3 satellites are required in principle.  The 4th satellite corrects for timing errors and is therefore always needed. 

are controlled twice a day.

Minute differences are recorded and sent with the message to the reciever.  A good reciever will understand this message and correct its time. 

Radio signals can pass through:

But not throgh: 

Clouds, glass, plastics and foliage of trees.

Buildings and mountains. 

Dilution of precision.

States that when satellites are far apart the DOP is low and there is a good DOP (angles between satellites are larger).

When satelites are close together the DOP is high and there is a poor DOP (angles between satellites are smaller). 

cm accuracy

uses reference point on Earth (benchmark)

By knowing position of benchmark, combined errors can be corrected.

Animal tracking

Emergency responses

Transportation 

hard copy maps

aerial photographs

remotely-sensed imagery

point data samples from surveys

existing digital data files 

Heads down: digitizing tablet, hard copy map/

Heads up:  on screen digitizing, from images (satellite, air photo, scanned) 

Use a grid of wires embedded in the tablet to generate a magnetic field which is detected by the cursor.

accuracies better than 0.1 mm (better than the 0.5 mm accuracy of the operator) 

Map is placed on digitizing table.

At least 4 control points are used (coordinates of these points are known.  More control points = better map)

Follow selected feature with cursor. 

Digitizing mode in which operator identifies points to be captured by pressing a button.

Advantages/disadvantages:  operator selects points subjectively.  Different operators will select different points. 

digitizing method in which points are captured at set time intervals (usu. 10/sec) or on movement of the cursor by a fixed amount.

Advantages/disadvantages:  generates large number of points (redundancy) and is more demanding on the user. 

If map is removed from digitizing table, reference points must be re-entered.

If map has stretched or shrunk, newly digitzed points will be slightly off in their location.

Errors on the map are entered into the GIS database 

High level of concentration is needed

Discrepancies across map sheet boundaries (edge-matching) 

lines do not  connect

polygons are not closed

potential topology problems 

Creates a dangle

Creates a dangle node

After cleaning dangles, there is a useless line but it does no harm to topology. 

1736.  Started a new branch of mathematics: Topology

GIS topology is a set of rules and behaviours that model how points, lines and polygons share coincident geometry.

transform, stretch, bend

 coordinate system and scale

-adjacent polygons have shared edges

- street centrelines and census blocks share geometry

-adjacent soil polygons share edges.

-no gaps should exist between polygons

-there should be no overlapping features

unconnected chains -  without topology

strings of unconnected lines

no spatial relationship

arcs may not join

intersections may not have connecting nodes

adjacent polygons may overlap or underlap

Topological structure of the digital spaghetti

GIS vector data are constructed with topology.

Adjacency - sharing common boundary

Containment - polygon is enclosed and has an area

Connectivity - common link. Arcs are connected by nodes.  Allows networks and routes.

defined by vertices and nodes

arcs have nodes as endpoints

have direction defined by nodes

from-node and to-node

Use arc and arc direction to combine polygons

Follow arcs in clockwise direction

Arcs have direction and therefore each arc records which polygon lies to the left and right side of its direction

Outside the study area is called the Universe

-Combine attributes (join by location)

-Overlay features (union, intersect, identity)

-process based on spatial relationships (buffer, clip, dissolve, merge, append, find nearest feature)

Interconnected pathways or networks

Features that connect or touch

Nearness

Use of buffer zones

Aggregates (joins) features based on similar attributes

(border lines from 2 files are erased with this feature to make both files appear as one)

Combines input features from multiple sources into a new feature class

(makes rivers from two files into one river file)

Merges multiple feature classes together to create a single feature class

(makes 2 files 1)

Boolean OR

Includes all classes from the input in the output

Boolean AND

Features that overlap in the input will be in the output 

Map extent of input features

Inputfeatures that overlap the identity features will beincluded in the output

where continuous data are required

-distances, proximity, cost surfaces

-elevation models, soils, climate, habitat, vegetation

have names or a code.

eg, land use, soils, county boundary

-fir

-juniper

-pine

-spruce

can be categorized

have names and are ranked

eg. land suitabilty, wildlife suitability, risk

- very good

-good

-moderate

-poor

can be ordered and classed

eg. rainfall, population density

- 700-709

- 710-719

- 720-729

VECTOR: 

models discrete features with precise shapes and boundaries

RASTER: 

models continuous phenomena and images of the earth

aerial photography

GPS recievers

digitized from map manuscripts

sketched on top of raster display

contours from triangulation

CAD drawings

photographed from an airplane

satellite image

converted from triangulation

rasterized from vector data

scanned blueprints, photographs

 Raster vs Vector 2

-original resolution without generalization

-graphic output is more aesthetically pleasing (traditional)

-most data are in vector format

-accurate geographic location of data is maintained

-allows use of topology

-location of each vertex must be stored explicitly

-continuous data are not accurately represented

-spatial analysis and filtering with polygons is impossible

-location of each cell is implied by postion in cell matrix

-no geographic coordinates are stored OTHER THAN the origin point (bottom left corner)

-data analysis is fast

 -ideally suited for mathematical modelling and quantitative analysis

-some discrete data are represented equally as well as continuous data

-integrates the two data types

-cell size determines the resolution at which data are represented

-difficult to represent linear features

-network of linkages are difficult to establish

-raster maps reflect only one attribute

-vector - to - raster conversion is often required.  Problems occur with generalization of grid-cell size

Perform a calculation on single cell at a time.

Neighbouring cells do not influence result

Perform a calculation on a single cell and its neighbouring cells.

Neighbourhoods can return mean, standard deviation, sum or range of values within immediate or extended neighbourhoods

Perform a calculation on a zone, which is a set of cells with a common value.

Cells that form a zone can be discontinuous.

Can be statistical or geometric.

Area, centroid, perimetre, ranges, sum calculations

Perform a computation on a raster as a whole.

eg.  Euclidean distances, weighted cost distances, watershed diliniation.

Identifies maximum rate of change in value from each cell to its neighbours

can be percent slope or degree slope

first derivative of the surface curvature

uses 3x3 neighbourhood window

Percent of slope = rise/run *100

Percent slope *100 = tan (degree slope)

Slope direction

Identifies the down slope direction or maximum rate of change in value of each cell to its neighbours

zero slope aspect assigned value of -1

Assign new values to old cell values

Make a wide range of values into few meaningfull classes

Specifies that any circle around 3 nodes in a triangle will not include any other nodes

Triangles are made and then perpendicular lines are constructed across the centre of the line connecting two points.  then polygons are built.

To calculate density from point estimates of a population

Output density will be occurances of measured quantity per specified unit of area

SIMPLE or KERNAL

calculated same as simple but value found in population field is distributed out from each point.

Smoother looking output

enter aglebra expression

create new themes (grids)

 perform complex analysis

1.  By supplying a name for the output function in dialog box

-[output1] = [input]/1000 ---> creates temporary file

-output2 = [input]/1000 ---> creates permanent file

2.  By creating a temporary result and then making it permanent.  (right click in TOC - Data - Make permanent)

3.  By saving the map document, which makes all temporary files permanent in the working directory, using default output name 

output = con ([waterdist] > 1000, 1, 0)

con - condition (IF)

con (condition, true, false)

If the value of waterdist is  >1000, then the output gets a value of 1, otherwise it gets a value of 0. 

Map algebra operators: Boolean and Relational

Boolean: the integer output grid will contain values of 1 (TRUE) or 0 (FALSE)

Relational:  compare the two numbers. If the result is true, 1 is returned, if it is false,0 is returned.

A continuous grid from point data

Estimation of z values of a surface at an unsampled point based on z values of the surrounding points

Value for every cell in the grid is calculated

-Trend: (polynomial) local, global

-Inverse distance weighting (IDW)

-Spline

-Kriging

Uses all points.  Local neighbours may over or underestimate

May not capture overall sloping plane (trend)

 Minimize error of prediction

To make a bend, use a second order polynomial, for 2 or 3 bends, use third and fourth order polynomials

fit many smaller overlapping planes and use centre of each plane as prediction for each location.

More accurate than global polynomial interpolation

weight of a value decreases as distance increases from a prediction location

Can be accurate IF elevation samples are relatively evenly distributed and surface characteristics do not change across the landscape

-Nearest neighbours - integer value defining minimum number of points to be used for interpolation

-Fixed Radius - distance in map units specifying that all input sample points within the specified radius will be used to perform interpolation

-Power - defining higher powers puts more emphasis onto nearest points.  Nearby data will have most influence and surface will have more detail (will be less smooth)

limiting search radius

limiting maximum number

-Barriers - limit selected set of input sample points used to interpolate output z values to only those samples on the same side of the barrier as the current processing cell

linear discontinuities

Can be used in IDW and Kriging

Surface that captures global trends and local variations

Bend and stretch surface to pass through all points

It is a mathematical function that bends the surface like a rubber sheet to make it pass through sampling points

Minimizes total curvature

Gently varying surface is calculated

Good for surfaces without abrubt changes in elevation or terrain models

REGULARIZED - yields a smooth surface and smooth first derivatives (yields smoother surface)

TENSION - tunes stiffness of interpolant according to character of modelled phenomenon

WEIGHT - between 0 and 0.5.  Higher values will yield coarser surfaces when using tension

NUMBER OF POINTS - smoother surface with more points

IDW is used: when assuming variable being mapped decreases in influence with distance

eg. consumer purchase power for retail site analysis

SPLINE is used:  when variable is a smooth conitinuous surface.  NOT GOOD in areas with large variability over small distances.

eg. water table, terrain, pollution concentration