projections examples of different projections coordinate...
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Projections and Coordinate Systems
Overview
Projections
Examples of different projections
Coordinate systems
Datums
Projections
Overview
• GIS must accurately represent locations of features
from the earth’s surface on a map
• This requires a reference system, or coordinate
system
Projections and Coordinate
Systems
The earth is a spheroid
The best model of the earth is a globe
Drawbacks:
•not easy to carry
•not good for making
planimetric measurement
(distance, area, angle)
Maps are flat
easy to carry
good for measurement
scaleable
A map projection is a method
for mapping spatial patterns
on a curved surface (the
Earth’s surface) to a flat
surface.
Definitions I
• Coordinate System (CS) – provides a frame of
reference to define locations
– Geographic CS – Used for 3D (sphere or globe),
locations defined by latitude and longitude, usually in
decimal degrees
– Projected CS – Used for 2D (maps), locations
defined by x,y measured from some origin (0,0),
usually in meters, sometimes in feet
Definitions II
• Spheroid – A simplified model of the shape of the earth
– Spheroid is used interchangeably with ellipsoid
• Datum – Defines the spheroid being used and aligns the
spheroid, optimizing fit either for a specific area, or
overall globally. This also defines the origin point of the
coordinate system.
Introductio
Definitions III
• Projection – A mathematical equation to convert from
spherical (3-D) to planar (2-D) coordinates
– Every projection will cause some form of spatial
distortion in shape, area, distance, and/or direction
– Common projections used in the US:
� Albers Equal Area for national scale
� State Plane and UTM for state and local scales
North American Datums
• Common North American datums are:
– NAD27, Clarke 1866 spheroid and Meade’s Ranch, KS as
the origin point
– NAD83, GRS80 (GRS = Geodetic Reference System)
spheroid and the earth’s center of mass as it’s origin
– WGS84, WGS84 spheroid and the earth’s center of mass
as it’s origin. This datum is used globally
• In North America, WGS84 is virtually identical to NAD83
– Other datum changes will change coordinates of spatial
features (e.g. NAD83 to NAD27)
Types of Projections
• Imagine a globe with a light source inside that projects
features on the earth’s surface onto a flat surface
• That flat surface can be configured a number of ways – as a
cylinder, a cone, or a plane
�an imaginary light is “projected” onto a “developable surface”
�a variety of different projection models exist
secant cone
tangent cone
cone as developable surface
tangent cylinders
cylinder as developable surface
plane as developable surface
Map projections always introduce error
and distortion
Map projections always introduce error
and distortion
Map projections always introduce error
and distortion
Map projections always introduce error
and distortion
Distortion may be minimized in one or
more of the following properties:
o Shape … conformal
o Distance … equidistant
o Direction … true direction
o Area … equal area
input output
unprojected projected
angles (lat/long) Cartesian coordinates
Exactly what are map projections?
Sets of mathematical equations that convert coordinates from one system to another
y)(x,y)(x, ff
→
How do projections work on a
programmatic level?
o each set of "coordinates" is transformed using a specific
projection equation from one system to another
o angular measurements can be converted to Cartesian
coordinates
o one set of Cartesian coordinates can be converted to a
different measurement framework
Projection, zone, datum (units) X Y
geographic, NAD27 (decimal degrees) -122.35° 47.62°
UTM, Zone 10, NAD27 (meters) 548843.5049 5274052.0957
State Plane, WA-N, NAD83 (feet) 1266092.5471 229783.3093
Geographic “projection”
Examples of different projections
• Albers
(Conic)
Shape Shape along the standard parallels is accurate and minimally distorted in the region between
the standard parallels and those regions just beyond. The 90-degree angles between
meridians and parallels are preserved, but because the scale along the lines of longitude
does not match the scale along lines of latitude, the final projection is not conformal.
Area All areas are proportional to the same areas on the Earth.
Direction Locally true along the standard parallels.
Distance Distances are best in the middle latitudes. Along parallels, scale is reduced between the
standard parallels and increased beyond them. Along meridians, scale follows an opposite
pattern.
Examples of different projections
• Lambert
Azimuthal
Equal
Area
(Planar)
Shape Shape is true along the standard parallels of the normal aspect (Type 1), or the standard
lines of the transverse and oblique aspects (Types 2 and 3). Distortion is severe near the
poles of the normal aspect or 90° from the central line in the transverse and oblique
aspects.
Area There is no area distortion on any of the projections.
Direction Local angles are correct along standard parallels or standard lines. Direction is distorted
elsewhere.
Distance Scale is true along the Equator (Type 1), or the standard lines of the transverse and oblique
aspects (Types 2 and 3). Scale distortion is severe near the poles of the normal aspect or
90° from the central line in the transverse and oblique aspects.
Examples of different projections
•Mercator(Cylindrical)
Shape Conformal. Small shapes are well represented because this projection maintains the local angular
relationships.
Area Increasingly distorted toward the polar regions. For example, in the Mercator projection, although
Greenland is only one-eighth the size of South America, Greenland appears to be larger.
Direction Any straight line drawn on this projection represents an actual compass bearing. These true direction
lines are rhumb lines, and generally do not describe the shortest distance between points.
Distance Scale is true along the Equator, or along the secant latitudes.
Examples of different projections
•Miller(Cylindrical)
Shape Minimally distorted between 45th parallels, increasingly toward the poles. Land masses are stretched
more east to west than they are north to south.
Area Distortion increases from the Equator toward the poles.
Direction Local angles are correct only along the Equator.
Distance Correct distance is measured along the Equator.
Examples of different projections
• Mollweide
(Pseudo-
cylindrical)
Shape Shape is not distorted at the intersection of the central meridian and latitudes 40° 44' N and S.
Distortion increases outward from these points and becomes severe at the edges of the projection.
Area Equal-area.
Direction Local angles are true only at the intersection of the central meridian and latitudes 40° 44' N and S.
Direction is distorted elsewhere.
Distance Scale is true along latitudes 40°44' N and S. Distortion increases with distance from these lines and
becomes severe at the edges of the projection.
Examples of different projections
• Orthographic
Shape Minimal distortion near the center; maximal distortion near the edge.
Area The areal scale decreases with distance from the center. Areal scale is zero at the edge of the
hemisphere.
Direction True direction from the central point.
Distance The radial scale decreases with distance from the center and becomes zero on the edges. The scale
perpendicular to the radii, along the parallels of the polar aspect, is accurate.
Coordinate Systems
Coordinates
� Features on spherical surfaces are not easy to
measure
� Features on planes are easy to measure and
calculate
� distance
� angle
� area
� Coordinate systems provide a measurement
framework
Coordinates
�Lat/long system measures angles on
spherical surfaces
�60º east of PM
�55º north of equator
Lat/long values are NOT Cartesian (X, Y)
coordinates
constant angular deviations do not have constant
distance deviations
1° of longitude at the equator ≠ 1° of longitude
near the poles
Coordinate systems
Examples of different coordinate/projection
systems
� State Plane
� Universal Transverse Mercator (UTM)
Coordinate systems
State Plane
� Codified in 1930s
� Use of numeric zones for shorthand
� SPCS (State Plane Coordinate System)
� FIPS (Federal Information Processing System)
� Uses one or more of 3 different projections:
� Lambert Conformal Conic (east-west orientation )
� Transverse Mercator (north-south orientation)
� Oblique Mercator (nw-se or ne-sw orientation)
Coordinate systems
projection.ppt 42
Pennsylvania State Plane zone definitions
ZoneSPCS
Zone #
FIPS
Zone #Projection
1st Std.
Parallel
2nd Std.
Parallel
Central
MeridianOrigin
False
Easting (m)
False
Northing
(m)
PA_N 5126 3701 Lambert Conformal Conic 40 10 00 40 53 00 -77 45 00 47 00 00 600000 0
PA_S 5151 3702 Lambert Conformal Conic 39 56 00 40 58 00 -120 30 00 39 20 00 600000 0
Coordinate systems
Universal Transverse Mercator
(UTM)
� Based on the Transverse
Mercator projection
� 60 zones (each 6° wide)
� false eastings
� Y-0 set at south pole or equator
Coordinate systems
Every place on earth falls in a particular zone
Pennsylvania is has 2 UTM Zones (18 and 19)
Universal Transverse Mercator (UTM)
Scale
A .30 mm line on a 1:200,000 scale map is almost 2,000 ft on the ground
Map measurement and true ground measurement
( ) ( ) 50' * * 0.025"12"1'
1"
24,000" =
A 1/40th in line on a 1:24,000 scale map is 50 ft on the ground
( ) ( ) ( ) ( ) 1,969' * * * * mm 0.3012"1'
2.54cm1"
mm 101cm
1
2,000,000 =
Scale
Map Scale
Scale refers to the relationship or ratio between a distance on a map and the
distance on the earth it represents. Maps should display accurate distances
and locations, and should be in a convenient and usable size.
Map scales can be expressed as
representative fraction or ratio: 1:100,000 or 1/100,000
graphical scale:
verbal-style scale:
1 inch in map equal to 2000 feet on the ground or
1 inch = 2000 feet
GIS is Scale less
In GIS, the scale can be easily enlarged and
reduced to any size that is appropriate.
However, if we get farther and farther from the
original scale of the layer, problems appear:
details no appear in an enlarged map
too dense in a reduced map
The scale of the original map determines the largest
map scale at which the data can be used.
Road map 1:50,000 scale can NOT be used
accurately at the 1:24,000 scale.
Water coverage at 1:250,000 scale can NOT be
used accurately at the 1:50,000 scale
Scale in attention
1:100,000 scale data from USGS DLG
Data from different sources and scales can vary widely
Scale in attention
1:1,000,000 scale data from DCW (DMA)
Data from different sources and scales can vary widely
Scale in attention
1:2,000,000 scale data from USGS DLG
Data from different sources and scales can vary widely
Scale in attention
one inch on the map equals 200 inches on the ground?
or
one inch on the map equals 200 feet on the ground?
“one to two-hundred”: does this mean
Beware of scale statements
Projections in ArcGIS
Projections in ArcGIS
• All geographic datasets have a GCS
• Many also have a PCS
• Unprojected (GCS) data is generally inappropriate for GIS
analyses
• The first layer added to ArcMap defines the projection and
datum for the data frame. This can be changed in the data
frame properties.
• All subsequent layers are projected on-the-fly (if necessary)
to match the data frame projection. The GCS of the layer
must match the data frame or a transformation is required.
How does ArcGIS handle map projections in data frames?
o Project data frames to see or measure features under different projection parameters
o Applying a projection on a data frame projects data “on the fly.”
o ArcGIS’s data frame projection equations can handle any input projection.
o However, sometimes on-the-fly projected data do not properly overlap.
Applying a projection to a data frame is like putting on a pair of glasses
You see the map differently, but the data have
not changed
How does ArcGIS handle map projections
for data?
� Projecting data creates a new data set on the file
system
� Data can be projected so that incompatibly projected
data sets can be made to match.
� ArcGIS’s projection engine can go in and out of a large
number of different projections, coordinate systems, and
datums.
Projection Metadata
• Stored in:
– A .prj file for shapefiles
– A table in geodatabases
– A prj.adf in coverages and grids
– A header for other raster formats. This can be either a
separate file (.hdr, .tifw) or embedded in the raster file
itself
• Data have a GCS and may have a PCS even if the
metadata is missing. These data have an unknown
coordinate system.
Projection Metadata
• CS information can be viewed in ArcMap (layer
properties>source tab) and ArcCatalog (Description tab)
Data with Unknown
Coordinate Systems
• Cannot be projected on-the-fly
• Will generate a warning when added to ArcMap
• Layer will be added, but may not align with other data
• Can be fixed with Define Projection tool if you know the CS
• If you don’t, you can try:
– contacting the source
– adding the layer to a map with a known CS. If the new
layer is registered with existing layers, it is the same CS.
Projecting Raster Data
• Because projections cause distortions in size and shape, and raster data must have square cells, cells in projected rasters represent different areas on the surface of the earth
• Resampling is used to assign values to projected cells.
– Nearest neighbor is fastest and must be used for categorical data like land cover
– Bilinear interpolation uses a weighted distance average of surrounding cells. Smooths values moderately, useful for continuous data like elevation
– Cubic convolution fits a curve through surrounding points. Can smooth data significantly and is slower
Map Units vs. Display Units
• Coordinates of the dataset are stored in map units.
Geographic generally uses decimal degrees, while a PCS
will usually use meters or feet. Map units can only be
changed by changing the CS of the data (Project tool).
• Display units are independent of map units and are set in
the data frame properties. ArcMap reports coordinate
values and measurements in display units.
Points to Remember
• Choose a PCS for each project. When new data is
acquired, be sure it is in that PCS or convert it using the
Project tool. It is best not to rely on projection on-the-fly in
ArcMap. It is especially important to have all data in the
same PCS when doing analyses.
• Try and avoid changing the CS of raster data
• Use the Project tool to change the CS of data, but use the
Define Projection tool to add metadata about the CS
• CS should be defined for all spatial data