Lecture 10:Projections and Coordinate Systems,

Continued

By Austin Troy

------Using GIS--Introduction to GIS

Datums•Necessary for understanding coordinate systems

•Definition: a three dimensional surface from which latitude, longitude and elevation are calculated

•Datum roughly approximates the surface of the earth at some mean sea level value

•Interesting fact: before satellites, datums were known to all be wrong, but geodesists agreed how to be wrong

Introduction to GIS

Datums vs. spheroids•A datum is essentially the model that is used to translate a spheroid into locations on the earth

•A different datum is generally used for each spheroid.

•Prior to satellites, datums were realized by referenced survey monuments (250,000+) with known position. These monuments were connected by a network of measurements enabling the computation of a position.

•Based on that survey, a location was chosen where the spheroid meets the earth. That translation between model and reality is the datum

Introduction to GIS

Datums as a point•In the old days, determined the lat/long of a location by measuring it relative to a known reference point

•That reference point was known in relation to another reference point.

•The datum is essentially the “ultimate reference point.”

•In the old days, they used pendulums, magnetometers, sextants, etc. to try to determine its precise location.

•Eventually the whole system of linked reference and subrefence points came to be known as the datum.

Introduction to GIS

Surface Based Datums•These pre-satellite datums are surface based.

•A given datum has the spheroid meet the earth in a specified location somewhere.

•Datum is most accurate near the touching point, less accurate as move away (remember, this is different from a projection surface because the ellipsoid is 3D)

•Different surface datums can result in different lat/long values for the same location on the earth.

•So, just giving lat and long is not enough!!!

Introduction to GIS

Satellite Based Datums•The errors of these datums stem from fact they used the surface of the earth as the reference point

•With satellite measurements the center of the spheroid can be matched with the center of the earth.

•This gives a spheroid that when used as a datum correctly maps the earth such that all Latitude/Longitude measurements from all maps created with that datum agree.

Introduction to GIS

Common Datums•Previously, the most common spheroid was Clarke 1866; the North American Datum of 1927 (NAD27) is based on that spheroid, and has its center in Kansas.

•A newer, satellite measured spheroid is the World Geodetic System 1984 (WGS84) spheroid, which is more or less identical to Geodetic Reference System 1980 (GRS80). The GPS system uses WGS84.

•NAD83 is based on these spheroids and is measured from the center of the spheroid, rather than the surface.

•WGS84 is considered to be a datum and a spheroid

Introduction to GIS

Spheroids and Datums

Spheroids

GRS 1980 Satellite derived - Ellipsoid Centered - NAD 1983

WGS 1984 Satellite derived - Ellipsoid Centered – WGS 1984

Clarke1866 Initial point - origin Meads Ranch, Kansas - NAD 1927

Everest 1830 Initial point - India 1960

Additional WGS-84 based datums exist in other parts of the world, like the Geocentric Datum of Australia (GDA 94)

Introduction to GIS

Major Datums

Click here for a listing of all world datums from Peter Dana

Datums•NAD83 is superior to NAD 27 because:

•NAD83 is more accurate

•NAD27 can result in a significant horizontal shift

•The error in going from a surface-oriented datum to a spheroid-based datum is called datum shift

•That error varies with location: 10 to 100 m in the cont. US, 400 m in Hawaii, 35 m in Vermont

Introduction to GIS

Datums-things to remember•Lat/long coordinates calculated with one datum are valid only with reference to that datum.

•This means those coordinates calculated with NAD 27 are in reference to a NAD 27 earth surface, not a NAD 83 earth surface.

•To be viewed in NAD 83, their position must be recalculated and they will be given new coordinates.

Introduction to GIS

Coordinate Systems•Map projections, like we discussed in last lecture provide the means for viewing small-scale maps, such as maps of the world or a continent or country (1:1,000,000 or smaller)

•Plane coordinate systems are typically used for much larger-scale mapping (1:100,000 or bigger)

Introduction to GIS

Coordinate Systems•Projections are designed to minimize distortions of the four properties we talked about, because as scale decreases, error increases

•Coordinate systems are more about accurate positioning (relative and absolute positioning)

•To maintain their accuracy, coordinate systems are generally divided into zones where each zone is based on a separate map projection

Introduction to GIS

Coordinate Systems•The four most commonly used coordinate systems in the US:

•Universal Transverse Mercator (UTM) grid system

•The Universal Polar Stereographic (UPS) grid system

•State Plane Coordinate System (SPC)

•And the Public Land Survey System (PLSS)

Introduction to GIS

UTM•Universal Transverse Mercator is a very common projection

•UTM is based on the Transverse Mercator projection (remember, that’s using a cylinder turned on its side)

•It generally uses either the NAD 27 or NAD83 datums, so you will often see a layer as projected in “UTM83” or “UTM27”

Introduction to GIS

UTM•UTM divides the earth between 84°N and 80°S into 60 zones, each of which covers 6 degrees of longitude

•Zone 1 begins at 180 ° W longitude.

Introduction to GIS

World UTM zones

UTM

•US UTM zones

Introduction to GIS

UTM•Each UTM zone is projected separately

•There is a false origin (zero point) in each zone

•In the transverse Mercator projection, the “cylinder” touches at two secants, so there is a slight bulge in the middle, at the central meridian. This bulge is very very slight, so the scale factor is only .9996

•The standard meridians, where the cylinder touches

Introduction to GIS

UTM•Because each zone is big, UTM can result in significant errors as get further away from the center of a zone, corresponding to the central line

Introduction to GIS

UTM•Scale factors are .9996 in the middle and 1 at the secants

Introduction to GIS

Earth surface

Projection surface

.9996

Central meridian

Standard meridians

UTM•In the N hemisphere, UTM coordinates are measured from a false origin at the equator and 500,000 meters west of the central meridian

•In the S hemisphere, they are measured from a false origin 10,000,000 meters south of the equator and 500,000 meters west of the central meridian

•Accuracy: 1 in 2,500

Introduction to GIS

UTM•UTM is used for large scale mapping applications the world over, when the unit of analysis is fairly small, like a state

•For portraying large land units, like Alaska or the 48 states, a projection is usually used, like Albers Equal Area Conic

Introduction to GIS

UPS Grid•The Universal Polar Stereographic Grid system cover the polar areas and uses the stereographic projection, centered on the pole

•Used to divide the polar area into a series of 100,000 meter squares

Introduction to GIS

SPC System•State Plane Coordinate System is one of the most common coordinate systems in use in the US

•It was developed in the 1930s to record original land survey monument locations in the US

•More accurate than UTM, with required accuracy of 1 part in 10,000

•Hence, zones are much smaller—many states have two or more zones

Introduction to GIS

SPC System•Transverse Mercator projection is used for zones that have a north south access.

•Lambert conformal conic is used for zones that are elongated in the east-west direction. Why?

•Units of measurement are feet, which are measured from a false origin.

•SPC maps are found based on both NAD 27 and NAD 83, like with UTM, but SPC 83 is in meters, while SPC 27 is in feet

Introduction to GIS

SPC System•Note how a conic projection is used here, since the errors indicate an east-west central line

Introduction to GIS

Polygon errors-state plane

SPC System•Many States have their own version of SPC

•Vermont has the Vermont State Plane Coordinate System, which is in meters and based on NAD 83

•In 1997, VSGI converted all their data from SPC 27 to SPC 83

•Vermont uses Transverse Mercator because of its north-south orientation

Introduction to GIS

•Here are some State Plane zone maps

Introduction to GIS

SPC System

•Here are some State Plane zone maps

Introduction to GIS

SPC System