Lecture 4

Understanding Coordinate Systems

Geographic Coordinate systems

GCS

Spherical Ellipsoidal Curved

Projected coordinate systems

GCS

PCS

(PCS) 2D Flat Planar Cartesian

GCS has angular units of measure Degrees

360 per circle Decimal degrees Degree, minute, second

Radians 2 pi per circle ~6.3 per circle (~57 degrees each)

Gradian 400 per circle

Gon Same as gradians To some grad = degree

X -Y +

X +Y +

X -Y -

X +Y -

X

Data

usually here

Y

PCS has linear units of measure Linear units

Meters Feet

X and Y coordinates Length, angles, and areas are constant

Map projection Math to transform GCS

Map projection

Plate Carrée projection

Math to transform GCS to PCS Flattening the earth – round to flat Distortions make geographers SADD

Shape, Area, Distance, and Direction

PCS properties example

Name – NAD 1983 UTM Zone 11N GCS – NAD 1983 Map Projection – Mercator Projection parameters

Central meridian, latitude of origin, scale factor, false easting

Linear unit of measure (i.e., meters)

Geographic coordinate systems Mathematical model of a planetary body - spheroid Parameters describe the spheroid shape

Smooth, without imperfections GCS for earth, planets, and more

Earth Mars IO

GCS properties Spheroid

Major and minor axis Units (lat/long, radians, grads)

GCS properties Spheroid

Major and minor axis Units (lat/long, radians, grads)

Datum Spheroid’s position in relation to actual earth Local datum: spheroid touches edge of earth, good fit there

Great fit here

Bad fit here

Local datum

GCS properties Spheroid

Major and minor axis Units (lat/long, radians, grads)

Datum Spheroid’s position in relation to actual earth Local datum: spheroid touches edge of earth, good fit there Earth-centered: spheroid and earth center match

Great fit here

Bad fit here

Local datum

All around best fit for the entire planet

Earth-centered datum

GCS properties example Name

European Datum 1950 Datum

European Datum 1950 Spheroid

International 1924

Prime Meridian Greenwich

Angular unit of measure Degrees

GCS with a local datum Spheroid

GCS with a local datum Datum

Spheroid’s position in relation to actual earth

GCS with a local datum Datum

Spheroid’s position in relation to actual earth

GCS with a local datum Datum

Spheroid’s position in relation to actual earth

GCS with a local datum Datum

Spheroid’s position in relation to actual earth

GCS with a local datum Datum

Spheroid’s position in relation to actual earth

GCS with a local datum Datum

Spheroid’s position in relation to actual earth

Local datum: spheroid touches edge of earth, good fit there

Bad fit on the other side

GCS with an Earth Centered datum Spheroid

GCS with an Earth Centered datum Datum

Spheroid’s center matched to earth center

GCS with an Earth Centered datum Datum

Spheroid’s center matched to earth center

GCS with an Earth Centered datum Datum

Spheroid’s center matched to earth center

GCS with an Earth Centered datum Datum

Spheroid’s center matched to earth center

GCS with an Earth Centered datum Datum

Spheroid’s center matched to earth center

GCS with an Earth Centered datum Datum

Spheroid’s center matched to earth center

Best fit all around the earth

As measurement gets better, new GCS are defined NAD27 – parameters defined in 1866 (log tables) NAD83 – parameters defined in 1979 (pre-GPS) WGS84 – parameters defined in 1984 (GPS)

Common GCS parameters in use today (US)

North American Datum 1927

North American Datum 1983

World Geodetic Survey 1984

Warning: different geographic coordinate system…

Geographic transformation Math to transform from one GCS to another

NAD 27

34 Degrees

3 Minutes

23.1 Seconds

North

ESRI-Redlands

117 Degrees

11 Minutes

39.2 Seconds

West

Geographic transformation Math to transform from one GCS to another Changing GCS changes the lat/long for same point The same spot on earth has differing coordinates

NAD 27NAD 83

34 Degrees

3 Minutes

23.14 Seconds

North

ESRI-Redlands

117 Degrees

11 Minutes

42.36 Seconds

West

34 Degrees

3 Minutes

23.1 Seconds

North

ESRI-Redlands

117 Degrees

11 Minutes

39.2 Seconds

West

ArcMap’s GCS and PCS behavior Data frame - has both Spatial data - has GCS, may have PCS Metadata - prj, XML, mdb, or none Tools that help

On-the-fly projection

ArcMap data frames have a GCS and a PCS You should set them If not set, data frames take first layer’s GCS/PCS

Data frame: Bonne PCS

On-the-fly projection ArcMap data frames have a GCS and a PCS

You should set them If not set, data frames take first layer’s GCS/PCS

If needed, new layers are projected on-the-fly (to match) If no CS metadata, new layer cannot be projected on-

the-fly

Input layer: Robinson PCS Data frame: Bonne PCS

ArcMap projects data on-the-fly into a data frame

GCS and PCS metadata for spatial data Stored in internal geodatabase tables Stored in projection files

Shapefiles can have a .prj text file (e.g., streets.prj) Coverages can have a prj.adf text file (e.g.,

/rivers/prj.adf) Stored optionally in XML files created by ArcCatalog Non-native ESRI datasets use various other formats

Warning!

GCS and PCS metadata is NOT required You might get data that is missing its

coordinate system metadata If researched and discovered, you can add it If not, use Spatial Adjustment to move the

data into place

Spatial reference problems and solutionsProblem Solution

You know the coordinate system information, but it is missing

Define Projection tool

The PCS is defined correctly,

but is not the one you need

Project tool or data frame project on-the-fly

The GCS is defined, but it is not NAD27 or NAD83

Project tool or set a geographic

transformation in the data frame

properties