Geography 370

The size and shape of the Earth

(Ellipsoid, Geoid, Latitude/longitude) Datum Map projection

Locating Positions on the Locating Positions on the EarthEarth

So the Earth is Round, Right?

Eratosthenes

(276-196 B.C.)

Measured the circumference of the earth.

His measurement: 40,250 km

Modern Measurement: 38,762 km

Eratosthenes

Size and shape of the Earth

17th and 18th centuries

The Earth’s shape

A Spheroid An Ellipsoid

r2=1

r1=1 r1=2r2=1

f = (r1-r2)/r1

Flatten factor?

The Earth as an Ellipsoid

Why not use the same ellipsoid?

Earth’s true shape diverges from the shape of an ellipsoid

Ellipsoidal parameters were fit for each continent or large survey area

Different sets of measurements in each region or continent

Globally applicable ellipsoids

WGS72 WGS84 GRS80

Continuing measurements from satellite and GPS may lead to further ellipsoid refinements.

The Earth as Geoid

The Earth as a Geoid Geoid -- The surface on which gravity is the

same as its strength at mean sea level

The surface that would exist if the sea was admitted under the land portion of the earth by small frictionless channels.

Earth Surfaces The topographical surface of the earth is the

actual surface of the land and sea at some moment in time.

Gravity models attempt to describe in detail the variations in the gravity field. Local variations in gravity, caused by variations in the earth's core and surface materials, cause this gravity surface to be irregular.

http://www.colorado.edu/geography/gcraft/notes/datum/datum_f.html

Reference for elevation:

• Ellipsoid

• Geoid

• Local sea level

Spatial Location and Reference: Latitude / Longitude Most commonly-used coordinate system Lines of latitude are called parallels Lines of longitude are called meridians

Latitude / Longitude

Prime Meridian & Equator are the reference points used to define latitude and longitude

Determine distance between any pair of points

Great circle

Geodetic Datum

Datum -- n. (dat - m) \ any numerical or geometric quantity which serves as a reference or base for other quantities

ee•Horizontal datum •Vertical datum

Geodetic Control Networks

Surveyors use these known points in the control networks for surveys and mapping.

Geodetic Control Network

Three main horizontal datums

North American Datum of 1927 (NAD27) 26,000 survey stations in United States and Canada.

North American Datum of 1983 (NAD83) 250,000 stations and 2,000,000 distance measures

World Geodetic System of 1984 (WGS84) (updated based on satellite measurements)

Ellipsoids & Datums: Importance

Differences exist between different ellipsoids & datums– Coordinates different in each can be

significant distance

– Elevation can be major differences at large scales

Note: Be aware of the ellipsoid & datum for datasets you are working with