What is Geodesy? Types of Geodesy terrestrial or classical geodesy space geodesy theoretical geodesy

Transcription

1 What is Geodesy? Geodesy is the study of: The size, shape and motion of the earth The 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 Geodesy terrestrial or classical geodesy space geodesy theoretical geodesy

2 Basic Geodesy Facts Geographic/true directions determined by the orientation of the graticule on the earths' surface Magnetic 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

3 Horizontal Geodetic Control 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 NAD adjustment of 1927 datum to reflect higher accuracy, 2 million + control points, tie to WGS84 ellipsoid - NAD83

4 Vertical 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 ,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

5 General Concepts Earth is three- dimensional Map (screen) is 2- D Geographic coordinate system (Datum) locates in 3- D Map Projection converts 3- D to 2- D 3- D to 2- D causes distortions

6 Coordinate Systems Geographical coordinate system: Older of two systems now in general use Uses latitude and longitude to locate positions on the uniformly curved surface of the earth Primary system used for navigation and surveying Rectangular/plane coordinate systems: Used for locating positions on a flat map Evolved from cartesian coordinates

7 Geographic Coordinate System The Equator and Prime Meridian are the reference points Latitude/ longitude measure angles Latitude (parallels) 0 º -90 º Longitude (meridians) 0 º º Defines locations on 3- D surface Units are degrees (or grads) Not a map projection!

8 Prime Meridians Origin of Longitude lines Usually Greenwich, England Others include Paris, Bogota, Ferro City Meridian Athens, Greece 23 42' " E Bern, Switzerland 7 26' 22".5 E Bogota, Colombia 74 04' 51".3 W Brussels, Belgium 4 22' 04".71 E Ferro (El Hierro) 17 40' 00" W Jakarta, Indonesia ' 27".79 E Lisbon, Portugal 9 07' 54".862 W Madrid, Spain 3 41' 16".58 W Paris, France 2 20' 14".025 E Rome, Italy 12 27' 08".4 E Stockholm, Sweden 18 03' 29".8 E

9 Latitude/ Longitude Not uniform units of measure Meridians converge near Poles 1 longitude at Equator = 111 km at 60 lat. = 55.8 km at 90 lat. = 0 km

10 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.

11 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 = degrees (30/3600) Add up the degrees to get the answer: = DD

12 Cartesian Coordinate System Used for locating positions on a flat map Coordinates tell you how far away from the origin of the axes you are Referenced as (X,Y) pairs In 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

13 3D Cartesian Coordinates Cartesian 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.

14 Local 3D Cartesian Coordinates This 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)

15 GCS is defined by:

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

17 Shape of the Earth Earth as sphere simplifies math small- scale maps (less than 1: 5,000,000) Earth as spheroid maintains accuracy for larger- scale maps (greater than 1: 1,000,000)

18 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 Geoid Authalic Sphere - a sphere that has the same surface area as a particular oblate ellipsoid of revolution representing the figure of the Earth

19 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 interchangeably For most spheroids, the difference between its semi-major axis and its semi-minor axis is less than 0.34 percent.

20 How About a Few Ellipsoids

21 Why Do We Need More Than One Spheroid (Ellipsoid)? The earth's surface is not perfectly symmetrical the semi-major and semi-minor axes that fit one geographical region do not necessarily fit another one.

22 What is the best Ellipsoid for you? After James R. Smith, page 98

23 Shape of the Earth

24 Relation of Geoid to Ellipsoid From James R. Smith, page 34

25 Vertical Deflection Important to surveyors Deflection of the Vertical = difference between the vertical and the ellipsoidal normal Described by the component tilts in the northerly and easterly directions.

26 Measuring Height Traditionally measured as height above sea level (Geoid) but is changing due to GPS The distance between the geoid and the spheroid is referred to as the geoidspheroid separation or geoidal undulation Can convert but it is mathematically complex

27 Datums (simplified) Reference frame for locating points on Earth s surface Defines origin & orientation of latitude/ longitude lines Defined by spheroid and spheroid s position relative to Earth s center

28 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 Australia geodetic latitudes and longitudes depend on both the reference spheroid and coordinate datum often 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 WGS84 the orientation and scale of the spheroid is defined using further geodetic observations horizontal 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

29 Creating a Datum Pick a spheroid Pick a point on the Earth s surface All other control points are located relative to the origin point The datum s center may not coincide with the Earth s center

30 Datums, cont. 2 types of datums Earth- centered (WGS84, NAD83) Local (NAD27, ED50)

31

32 Relationship between 2 datums

33 Why so many datums? Many estimates of Earth s size and shape Improved accuracy Designed for local regions

34 North American Datums NAD27 Clarke 1866 spheroid Meades Ranch, KS 1880 s NAD83 GRS80 spheroid Earth- centered datum GPS- compatible

35 North American Datums HPGN / HARN GPS readjustment of NAD83 in the US Also known as NAD91 or NAD93 27 states & 2 territories (42 states in PE) NAD27 (1976) & CGQ77 Redefinitions for Ontario and Quebec NAD83 (CSRS98) GPS readjustment

36 International datums Defined for countries, regions, or the world World: WGS84, WGS72 Regional: ED50 (European Datum 1950) Arc 1950 (Africa) Countries: GDA 1994 (Australia) Tokyo

37 Datum transformations Grid- based NADCON / HARN (US), NT v1 / NT v2 (Canada, Australia, NZ) Equation- based Molodensky, Bursa- Wolf, Coordinate Frame, Three Parameter, Seven Parameter

38 Method accuracies NADCON HARN/ HPGN CNT (NTv1) Seven parameter Three parameter 15 cm 5 cm 10 cm 1-2 m 4-5 m

39 GPS Uses WGS84 datum Other datums are transformed and not as accurate Know what transformation method is being used