Geography 70  Basic Geodesy  Map Projections  Coordinate Systems  Scale Locating Positions on the Earth

Geographic Data  Features must be referenced to some real world location  Known as georeferencing

Geographic Data & Position  GOAL: To assign a location to all features  Important elements must agree: – ellipsoid – datum – projection – coordinate system – scale

Position/location  To determine position on the Earth, it is necessary to understand how those elements relate to one another  Begin with geodesy

What is Geodesy? Geodesy “A branch of applied mathematics which determines by observation and measurement the exact positions of points and the figures and areas of large portions of Earth's surface, the shape and size of the Earth, and the variations of terrestrial gravity."

What is Geodesy? More simply, geodesy is the study of the Earth’s size and shape.

The Earth is Not Flat

Eratosthenes  ( B.C.) Measured the height of an obelisk in Alexandria and determined the circumference of the earth. His measurement: 25,000 Miles Modern Measurement: 24,860 Miles

So the Earth is Round, Right?

The Earth is Irregular Not perfectly round due to: – Distortion due to the Earth’s rotation – Small irregularities on the surface such as mountains, basins, etc. – Irregularities due to variations in gravity

The Earth is Irregular  Slightly flattened at the poles  Equator bulges  Southern Hemisphere slightly larger than Northern Hemisphere

The Earth is: A SpheroidAn Ellipsoid A Geoid

The Earth as a Sphere  Geographic coordinates (latitude/longitude) used to specify locations.  Treating the Earth as a sphere is accurate enough for small maps of large areas of the Earth (i.e. very small scale maps)

The Earth as a Sphere  Spheroid model: – short range navigation – global distance approximations  The slight flattening at the poles result in a 20 km difference at the poles from the average spherical radius

The Earth as an Ellipsoid  Ellipsoid is a flattened sphere  Ellipsoid is created by rotating a 2 - dimensional ellipse around an axis.

The Earth as an Ellipsoid  Every ellipsoid has a semi-major (a) and semi-minor axis (b)  The amount of flattening is defined as a value f, which is calculated using the semi-axes

The Earth as an Ellipsoid  a = semi-major axis  b= semi-minor axis  f = ((a-b)/a) = flattening

The Earth as an Ellipsoid: WGS84 Ellipsoid b a f =

The Earth as an Ellipsoid

Differences in Lat / Long  On a spheroid, lines of latitude (parallels) are equal distance apart  On an ellipsoid, the distance between parallels slightly increases as latitude increases

The Earth as a Geoid  The only thing shaped like the Earth is the Earth  Geoid means “Earth Like”  Shape is based on gravity field corrected by the centrifugal force of the earth’s rotation.

The Earth as a Geoid  Geoid -- The surface on which gravity is the same as its strength at mean sea level  Coincides with the surface to which the oceans would conform over the entire earth if it were made only of water.

The Earth as Geoid  If the Earth were completely uniform in its geological composition, landforms and density, then the geoid would match the ellipsoid exactly

Interaction SpheroidEllipsoid Geoid

Relationship of Geoid to its reference ellipsoid

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

Geodetic Datum  Geodetic datum – The information that ties an ellipsoid model to the geoid model – Horizontal datum (most common used) – Vertical datum

Horizontal Datum  Parameters of the ellipsoid – axis length – flattening value  Parameters that tie the ellipsoid to the origin point (known place on the Earth) Components

Review  Sphere – The simplest 3D model of the earth  Ellipsoid – A more accurate model that takes into account some of the Earth’s irregularity  Geoid – The most accurate, most complex model of the Earth, taking into account the Earth’s minor variations from an ellipsoid  Datum – The information that ties an ellipsoid model to a known place on the Earth

Geodetic Control Networks  Geodesists and surveyors create geodetic control networks to precisely link a set of known locations to each other and to the ellipsoid/geoid at a datum origin.

Geodetic Control Networks  Surveyors use these known points in the control networks for surveys and mapping.  Control Points are referenced to specific datums.

Geodetic Control Network  How do surveyors and others know where these points are?

Geodetic Control Network  They mark it.

Common Ellipsoids, Datums

Geodetic Datums  The purpose of all of this is to end up with a very, very accurate map.  Not all maps need this accuracy, but some do.

Geodetic Datums

Review  Sphere – The simplest 3D model of the earth  Ellipsoid – A more accurate model that takes into account some of the Earth’s irregularity  Geoid – The most accurate, most complex model of the Earth, taking into account the Earth’s minor variations from an ellipsoid  Datum – The information that ties an ellipsoid model to a known place on the Earth