Geography 370 Locating Positions on the Earth The size and shape of the Earth (Ellipsoid, Geoid, Latitude/longitude) Datum Map projection

So the Earth is Round, Right? So everyone knows the Earth is round, even Columbus. Case closed right? Not exactly, the earth isn’t perfectly round either. What shape is it?

Eratosthenes (276-196 B.C.) Measured the circumference of the earth. His measurement: 40,250 km Modern Measurement: 38,762 km Era-tos-thenes He had heard of a well in Syene (near modern Aswan Egypt - Tropic of Cancer) where the sun’s reflection could be seen in the water at noon on June 21. -- The sun was directly overhead. At the exact moment the sun could be seen in the well he measured the height of an obelisk in Alexandria. Then using some basic geometry he was then able to calculate the circumference of the earth by creating a triangle between Alexandria, Syene and the Sun. He got pretty close…

Eratosthenes

Size and shape of the Earth 17th and 18th centuries The Earth’s shape A Spheroid An Ellipsoid

f = (r1-r2)/r1 r2=1 r2=1 r1=2 r1=1 Flatten factor?

The Earth as an Ellipsoid Here are some other commonly used ellipsoids. You don’t need to memorize any of this. Just keep in mind the term reference ellipsoid. That’s what an ellipsoid is used for… reference. It’s a starting point to calculating a position on the earth.

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 But the earth is not completely uniform. So we can use a geoid to model the earth’s surface instead of an ellipsoid. And surveyors DO use the geoid to make precise locational calculations. But for our purposes, and for most purposes in GIS, we don’t use the geoid. It’s too complex. Instead, we use an ellipsoidal model.

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 Parallels parallel to each other; circle the globe ew Max value of angular measurement N and S from the equator: 90 degrees Meridians: perpendicular to parallels Prime meridian: Greenwich, England Meridians run 180 degrees E and W of the prime meridian (until reach International Date Line)

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 e Horizontal datum Vertical datum So we have datums. Now, I said we need a simpler way, and simple is a relative term. Datums are complex models in and of themselves. But the key to the Geodetic Datum is that it provides a link between locations on the sphere ellipsoid and geoid. For instance in economics if you want to calculate price indicies you use a base year (1960) that’s an example of datum.

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

Geodetic Control Network Over 800,000 points in the U.S. Sundial -- EZ1375 Keep your eyes out for others as you walk around campus.

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