What is Geodesy?Geodesy is the study of:

The size, shape and motion of the earthThe measurement of the position and motion of points on the earth's surface, and The study of the earth's gravity field and its temporal variations

Types of Geodesyterrestrial or classical geodesyspace geodesytheoretical geodesy

Basic Geodesy FactsGeographic/true directions determined by the orientation of the graticule on the earths' surfaceMagnetic directions must take into account the compass variation (magnetic declination)Great circle – arc formed by the intersection of the earth with a plane passing through any two surface points and the center of the earth (equator)Rhumb line, loxodrome or constant azimuth – line which makes a fixed angle with all meridians; spirals to pole

For North America:

Horizontal – 200,000+ points marked by bronze survey monument – measured on the geoid, adjusted for height to lie on ellipsoid

1833 – U.S. Coast & Geodetic Survey established the first baseline; networks of lines triangulated from this baseline

1927 – all U.S., Canadian, Mexican networks adjusted and integrated into single network – NAD27

1983 – adjustment of 1927 datum to reflect higher accuracy, 2 million + control points, tie to WGS84 ellipsoid - NAD83

Horizontal Geodetic Control

For North America:

Vertical – beginning in 1856, vertical control point marked by bronze benchmark; level lines created between two endpoints, measured on geoid relative to mean sea level

1929 – 67,000 + miles of level lines in U.S. And Canada (500,000+ control points) adjusted and combined to National Geodetic Vertical Datum of 1929 (NGVD29)

1983 – National Vertical Datum of 1983, adjustment of all (now) 388,000+ miles of level lines (NVD83)

GPS elevations made relative to GRS80 or WGS84 ellipsoid

Vertical Geodetic Control

General ConceptsEarth is three- dimensionalMap (screen) is 2- DGeographic coordinate system (Datum) locates in 3- DMap Projection converts 3- D to 2- D3- D to 2- D causes distortions

Geographical coordinate system:

Older of two systems now in general useUses latitude and longitude to locate positions on theuniformly curved surface of the earthPrimary system – used for navigation and surveying

Rectangular/plane coordinate systems:

Used for locating positions on a flat mapEvolved from cartesian coordinates

Coordinate Systems

Geographic Coordinate SystemThe Equator and Prime Meridian are the reference pointsLatitude/ longitude measure angles

Latitude (parallels) 0º - 90º

Longitude (meridians) 0º - 180º

Defines locations on 3- D surfaceUnits are degrees (or grads)Not a map projection!

Prime MeridiansOrigin of Longitude linesUsually Greenwich, EnglandOthers include Paris, Bogota, Ferro

City MeridianAthens, Greece 23° 42' 58.815" EBern, Switzerland 7° 26' 22".5 EBogota, Colombia 74° 04' 51".3 WBrussels, Belgium 4° 22' 04".71 EFerro (El Hierro) 17° 40' 00" WJakarta, Indonesia 106° 48' 27".79 ELisbon, Portugal 9° 07' 54".862 WMadrid, Spain 3° 41' 16".58 WParis, France 2° 20' 14".025 ERome, Italy 12° 27' 08".4 EStockholm, Sweden 18° 03' 29".8 E

Latitude/ LongitudeNot uniform units of measureMeridians converge near Poles1° longitude at Equator = 111 km

at 60° lat. = 55.8 kmat 90° lat. = 0 km

Decimal Degrees (DD)Decimal degrees are similar to degrees/minutes/seconds (DMS) except that minutes and seconds are expressed as decimal values. Decimal degrees make digital storage of coordinates easier and computations faster.

Conversion from DMS to DD:Example coordinate is 37° 36' 30" (DMS) Divide each value by the number of minutes or seconds in a degree:

36 minutes = .60 degrees (36/60) 30 seconds = .00833 degrees (30/3600)

Add up the degrees to get the answer: 37° + .60° + .00833° = 37.60833 DD

Cartesian Coordinate SystemUsed for locating positions on a flat mapCoordinates tell you how far away from the origin of the axes you are

Referenced as (X,Y) pairsIn cartography and surveying, the X axis coordinates are known as Eastings, and the Y axis coordinates as Northings.

False easting and northings are typically added to coordinate values to keep coordinates in the upper right hand quadrant of the ‘graph’ – positive values

3D Cartesian CoordinatesCartesian Coordinates can define a point in space, that is, in three dimensions. To do this, the Z axis must be introduced. This axis will represent a height above above or below the surface defined by the x and y axes.

Local 3D Cartesian CoordinatesThis diagram shows the earth with two local coordinate systems defined on either side of the earth. The Z axis points directly up into the sky.Instead of (X,Y) it is (X,Y,Z)

GCS is defined by:

The Earth is Not RoundFirst the earth was flat 500 BC Pythagoras declared it was a sphereIn the late 1600’s Sir Issac Newton hypothesized that the true shape of the earth was really closer to an ellipseMore precisely an Oblate Ellipsoid (squashed at the poles and fat around the equator)And he was right!

Shape of the EarthEarth as sphere

simplifies mathsmall- scale maps (less than 1: 5,000,000)

Earth as spheroidmaintains accuracy for larger- scale maps (greater than 1: 1,000,000)

Geoid, Ellipsoid & Sphere

Geoid - estimates the earth's surface using mean sea level of the ocean with all continents are removed

It is an equipotential surface - potential gravity is the same at every point on its surface

Ellipsoid - It is a mathematical approximation of the GeoidAuthalic Sphere - a sphere that has the same surface area as a particular oblate ellipsoid of revolution representing the figure of the Earth

Spheroid or Ellipsoid?What is a Spheroid anyway?

An ellipsoid that approximates the shape of a sphere Although the earth is an ellipsoid, its major and minor axes do not vary greatly. In fact, its shape is so close to a sphere that it is often called a spheroid rather than an ellipsoid. ESRI calls it a spheroid but the two can be used interchangeablyFor most spheroids, the difference between its semi-major axis and its semi-minor axis is less than 0.34 percent.

How About a Few Ellipsoids

Why Do We Need More Than One Spheroid (Ellipsoid)?

The earth's surface is not perfectly symmetricalthe semi-major and semi-minor axes that fit one geographical region do not necessarily fit another one.

After James R. Smith, page 98

What is the best Ellipsoid for you?

Shape of the Earth

From James R. Smith, page 34

Relation of Geoid to Ellipsoid

Vertical DeflectionImportant to surveyorsDeflection of the Vertical = difference between the vertical and the ellipsoidal normalDescribed by the component tilts in the northerly and easterly directions.

Measuring HeightTraditionally measured as height above sea level (Geoid) but is changing due to GPSThe distance between the geoid and the spheroid is referred to as the geoid-spheroid separation or geoidal undulationCan convert but it is mathematically complex

Datums (simplified)Reference frame for locating points on Earth’s surfaceDefines origin & orientation of latitude/ longitude linesDefined by spheroid and spheroid’s position relative to Earth’s center

Geodetic Datums (complex)consists of an initial origin; the azimuth for one line; the parameters of the reference ellipsoid and the geoid separation at the origin. The deflection of the vertical and geoid-spheroid separation are set to zero at an origin point eg Johnson in Australiageodetic latitudes and longitudes depend on both the reference spheroid and coordinate datumoften the spheroid is implicitly linked to the datum, so it has become common to use the datum name to imply the spheroid and vice versa eg WGS84the orientation and scale of the spheroid is defined using further geodetic observationshorizontal and vertical(θ, φ, ρ) = (theta , phi, roe) roe describes the distance from the origin, theta is the angle from the XY plane and phi is the angle from the Z axis

Creating a DatumPick a spheroidPick a point on the Earth’s surfaceAll other control points are located relative to the origin pointThe datum’s center may not coincide with the Earth’s center

Datums, cont.2 types of datums

Earth- centered(WGS84, NAD83)

Local(NAD27, ED50)

Relationship between 2 datums

Why so many datums?Many estimates of Earth’s size and shapeImproved accuracyDesigned for local regions

North American DatumsNAD27

Clarke 1866 spheroidMeades Ranch, KS1880’s

NAD83GRS80 spheroidEarth- centered datumGPS- compatible

North American DatumsHPGN / HARN

GPS readjustment of NAD83 in the USAlso known as ‘NAD91’ or ‘NAD93’27 states & 2 territories (42 states in PE)

NAD27 (1976) & CGQ77Redefinitions for Ontario and Quebec

NAD83 (CSRS98) – GPS readjustment

International datumsDefined for countries, regions, or the worldWorld: WGS84, WGS72Regional:

ED50 (European Datum 1950)Arc 1950 (Africa)

Countries:GDA 1994 (Australia)Tokyo

Datum transformationsGrid- based

NADCON / HARN (US),NT v1 / NT v2 (Canada, Australia, NZ)

Equation- basedMolodensky, Bursa- Wolf,Coordinate Frame, Three Parameter,Seven Parameter

Method accuraciesNADCON HARN/ HPGN CNT (NTv1) Seven parameterThree parameter

15 cm5 cm

10 cm1- 2 m4- 5 m

GPSUses WGS84 datumOther datums are transformed and not as accurateKnow what transformation method is being used