# projections by pengtt

VIEWS: 18 PAGES: 36

• pg 1
```									Datums and Projections:
How to fit a globe onto a
2-dimensional surface
Overview
Ellipsoid
Spheroid
Geoid
Datum
Projection
Coordinate System
Definitions: Ellipsoid
Also referred to as Spheroid, although Earth is not
a sphere but is bulging at the equator and flattened
at the poles
Flattening is about 21.5 km difference between
Ellipsoid model necessary for accurate range and
bearing calculation over long distances  GPS
Best models represent shape of the earth over a
smoothed surface to within 100 meters
Geoid: the true 3-D shape of the earth considered as
a mean sea level extended continuously through the
continents
Approximates mean sea level
WGS 84 Geoid defines geoid heights for the entire
earth
Definition: Datum
A mathematical model that describes the shape of the
ellipsoid
Can be described as a reference mapping surface
Defines the size and shape of the earth and the origin and
orientation of the coordinate system used.
There are datums for different parts of the earth based on
different measurements
Datums are the basis for coordinate systems
Large diversity of datums due to high precision of GPS
Assigning the wrong datum to a coordinate system may
result in errors of hundreds of meters
Commonly used datums

Datum            Spheroid                  Region of use

Central America

WGS 84            WGS 84                      Worldwide

GPS is based on WGS 84 system
GRS 1980 and WGS 84 define the earth’s shape by measuring and
triangulating from an outside perspective, origin is earth’s center of mass
Projection
Method of representing data located on a curved
surface onto a flat plane
All projections involve some degree of distortion
of:
Distance
Direction
Scale
Area
Shape
Determine which parameter is important
Projections can be used with different datums
Projections
The earth is “projected” from an imaginary light source in its
center onto a surface, typically a plate, cone, or cylinder.

Planar or
azimuthal                     Conic                  Cylindrical
Other Projections
Pseudocylindrical
Unprojected or Geographic projection:
Latitude/Longitude
There are over 250 different projections!
Tangency: only
one point
touches surface
Cylindrical:
used for entire world
parallels and meridians
form straight lines
Secancy:
projection surface
cuts through
globe, this reduces
distortion of larger
land areas
Cylindrical
projection

Shapes and angles
within small areas
Distances only true
along equator
Conical:
can only represent one hemisphere
often used to represent areas with
east-west extent (US)
Albers is used by USGS for state
maps and all US maps of
1:2,500,000 or smaller
96 degrees W is central meridian

Lambert is used in State Plane
Coordinate System

Secant at 2 standard
parallels
Distorts scale and distance,
except along standard
parallels
Areas are proportional
Directions are true in
limited areas
Azimuthal:
Often used to show air
route distances
Distances measured
from center are true
Distortion of other
properties increases
away from the center
point
Orthographic:
Used for perspective views of
hemispheres
Area and shape are distorted
Distances true along equator and
parallels

Lambert:
Specific purpose of maintaining equal area
Useful for areas extending equally in all
directions from center (Asia, Atlantic Ocean)
Areas are in true proportion
Direction true only from center point
Scale decreases from center point
Pseudocylindrical:
Used for world maps
Straight and parallel
latitude lines, equally
spaced meridians
Other meridians are
curves

Scale only true along
standard parallel of
40:44 N and 40:44 S

Robinson is compromise
between conformality,
equivalence and
equidistance
Mathematical Relationships
Conformality
Scale is the same in every direction
Parallels and meridians intersect at right angles
Shapes and angles are preserved
Useful for large scale mapping
Examples: Mercator, Lambert Conformal Conic
Equivalence
Map area proportional to area on the earth
Shapes are distorted
Ideal for showing regional distribution of geographic phenomena
(population density, per capita income)
Examples: Albers Conic Equal Area, Lambert Azimuthal Equal
Area, Peters, Mollweide)
Mathematical Relationships
Equidistance
Scale is preserved
Parallels are equidistantly placed
Used for measuring bearings and distances and for representing
small areas without scale distortion
Little angular distortion
Good compromise between conformality and equivalence
Used in atlases as base for reference maps of countries
Examples: Equidistant Conic, Azimuthal Equidistant
Compromise
Compromise between conformality, equivalence and equidistance
Example: Robinson
Projections and Datums
The datum forms the reference for the
projection, so...
Maps in the same projection but different
datums will not overlay correctly
• Tens to hundreds of meters
Maps in the same datum but different
projections will not overlay correctly
• Hundreds to thousands of meters.
Coordinate System
A system that represents points in 2- and 3-
dimensional space
Needed to measure distance and area on a
map
Rectangular grid systems were used as early
Can be divided into global and local
systems
Geographic coordinate system
Global system
Prime meridian and equator are the reference planes to define
spherical coordinates measured in latitude and longitude
Measured in either degrees, minutes, seconds, or decimal
degrees (dd)
Often used over large areas of the globe
Distance between degrees latitude is fairly constant over the
earth
1 degree longitude is 111 km at equator, and 19 km at 80
degrees North
Universal Transverse Mercator
Global system
Mostly used between 80 degrees south
to 84 degrees north latitude
Divided into UTM zones, which are 6
degrees wide (longitudinal strips)
Units are meters
Eastings are measured from central meridian (with
500 km false easting for positive coordinates)
Northing measured from the equator (with 10,000 km
false northing)

Easting 447825 (6 digits)
Northing 5432953 (7 digits)
State Plane Coordinate System
Local system
Developed in the ’30s, based on NAD27
Provide local reference systems tied to a
national datum
Units are feet
Some larger states have several zones
Projections used vary depending on east-
west or north-south extent of state
Which tic marks belong to which grid?

Each of the three coordinate systems
(Lat/Long, UTM, and SPCS) have their own
set of tick marks on 7½ minute quads:
Lat/Long tics are black and extend in from the
map collar
UTM tic marks are blue and 1000 m apart
SPCS tics are black, extend out beyond the map
collar, and are 10,000 ft apart
Other systems
Global systems
Military grid reference system (MGRS)
World geographic reference system (GEOREF)
Local systems
Universal polar stereographic (UPS)
National grid systems
Public land rectangular surveys (township and
sections)
Determining datum or
projection for existing data
May be missing
Opened with text editor
Software
Some allow it, some don’t
Comparison
Overlay may show discrepancies
If locations are approx. 200 m apart N-S and slightly E-W,
Selecting Datums and Projections
Consider the following:
Extent: world, continent, region
Location: polar, equatorial
Axis: N-S, E-W
Select Lambert Conformal Conic for conformal accuracy
and Albers Equal Area for areal accuracy for E-W axis in
temperate zones
Select UTM for conformal accuracy for N-S axis
Select Lambert Azimuthal for areal accuracy for areas with
equal extent in all directions
Often the base layer determines your projections
Summary

There are very significant differences between
datums, coordinate systems and projections,
The correct datum, coordinate system and
projection is especially crucial when matching
one spatial dataset with another spatial dataset.

```
To top