Geography 70

Basic Geodesy Map Projections Coordinate Systems Scale

Locating Positions on the Locating Positions on the EarthEarth

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

(276-196 B.C.)

Measured the height of an obeliskin Alexandria and determinedthe 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 Spheroid An 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

bb

aa

f = 0.003353f = 0.003353

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

Spheroid Ellipsoid

Geoid

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

ee

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, DatumsEllipsoid Date Semi-Major

RadiusSemi-minorRadius

Flattening Used for

Clarke 1866 1866 6,378,249.1 6,356,583.8 1/ 294.98 N. AmericaGRS80 1980 6,378,137.0 6,356,752.3 1/ 298.26 WorldWGS84 1984 6,378,137.0 6,356,752.3 1/ 298.26 World/ GPS

Datum Ellipsoid UseNAD1927 Clarke1866 Old USGS Topo maps, old

state and county surveysNAD1983 GRS80 Recent Topo maps -- a

national standardWGS1984 WGS84 Current International

Standard Datum, GPS

Geodetic Datums

The purpose of all of this is to end up with a very, very accurate map.

Not all maps needthis 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