Marine Resource Management Hydrographic Module

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Marine Resource ManagementHydrographic Module

• Introduction to GeodesyDatums, Co-ordinate
  Systems, and Map Projections
• Presented by
• David Philip

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Geodesy a definition

• Geodesy is the discipline that deals with the
  measurement and representation of the Earth,
  including its gravity field, in a
  three-dimensional time varying space
• Vanicek and Krakiwsky, Geodesy The Concepts

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Geodesy and Coordinate Integrity Language of
Surveyors
What on Earth ?
Where on Earth ?
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Objectives

• Introduction to Geodesy
• Basic understanding of geodetic datums
• Understanding of map projections coordinate
  systems
• Awareness of coordinate transformations
• Basics of common coordinate systems used in
  marine environment

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Basic Geodesy

• Science of Applied Maths associated with
  describing the Earths surface
• Shape of the Earth
• Mathematical Representation
• Projection onto a Plane Surface
• Components
• Ellipsoids / Spheroids
• Datums
• Projections

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Geoid - the Shape of the Earth

• Irregular Surface
• Oceans/Trenches/Plains/Valleys/Mountains
• Topographical surface
• Geoid Equipotential surface
• based on points of equal gravitational potential
• Imagine surface covered by ocean, ? mean sea
  level
• Not a mathematical shape
• Originally presumed to be flat/disc shaped
• OK for small areas
• Developed to Sphere/Globe -
• Better definition similar to mathematical Earth
  Model
• Oblate Spheroid Flattened at the Poles

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The Geoid
ActualEarths Surface
Sphere
World Spheroid
Geoid
Centre of Local Spheroid
Centre of WorldSpheroid
LocalSpheroid
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Classical Geodesy

• Classical Methods (1800s 1950s)
• Triangulation (Angle measurements)
• Baseline (Invar wires,tapes)
• Laplace Stations
• Control Networks
• Continuous
• Chains
• Derive and then provide First Order control
• Shape
• Scale
• Azimuth

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Geodetic Revolution 1950s to date

• Modern Developments
• EDM (Tellurometer, Geodimeter, Hiran/Shoran)
• Zero order Traverse
• Intercontinental connections
• Satellite Observations
• Satellite Systems
• TRANSIT
• GPS
• Computing Power
• Adjustment
• We can now measure and predict tectonic plate
  movements of a few millimetres per year.

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Ellipsoid/Spheroid Model
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Spheroid Model
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Relationship of Geoid to Ellipsoid/Spheroid
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Choice of Ellipsoid/Spheroid

• Historically, countries choose ellipsoids for
  reasons such as
• It was the best known ellipsoid for the whole
  earth at that time
• It happens to fit the geoid in their area
  particularly well.
• Neighbouring countries have chosen it.
• It was the most recent ellipsoid recommended by
  the International Association of Geodesy

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Choosing an Ellipsoid/Spheroid
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Ellipsoids/Spheroids used in UK

• Mathematical Models
• Define a Best-Fit to the Earth's Surface
• Some examples
• Airy 1830
• UKs best fit for National Mapping
• International (1924)
• for Offshore Block Boundaries on European Datum
• WGS-84
• Global best fit for GPS

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Ellipsoid/Spheroid Reference List
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Spherical Co-ordinate Systems
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Spherical to Cartesian Conversion
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3D Cartesian Co-ordinate System
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Distance Computation in 3D Cartesian
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Spheroidal Co-ordinate System
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Alternative Co-ordinate Systems

• 3D Space
• Cartesian X/Y/Z
• Spherical Latitude/Longitude/Height -?,?,H
• Difficult to use and display
• 2D Plane
• Cartesian X/Y
• Polar Range/Bearing
• 1D Plane
• Height

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Types of coordinate systems
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2D Cartesian Co-ordinate System
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Distance Measurement in 2D Cartesian
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Polar Co-ordinate System
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Relationship Between Polar and Cartesian
Co-ordinate Systems
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Types of Co-ordinate Systems
Types of coordinate system
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Its more than just coordinates...
Geographical Location X, Y, (Z) E,N,Ht
DATA
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Why Projections ? Problems and Pitfall

• Necessary for Preparation of Maps/Charts
• 2D Representation of Earths Surface
• Not all Properties can be retained in the
  transition from spheroid to plane (Map)
• Area/Distance/Shape
• Equal Area
• Area on Spheroid Area on Map Projection
• Equidistant Projections
• Distances on Spheroid Distances on Map
• Conformal Projections
• Shape/Angles on Spheroid Shape/Area on Map
• Of Primary Use to the Surveyor e.g. TM/UTM

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The Map Projection Process
Choice of Datum
Scale Reduction
Cylindrical
Map Projection
Conic
Azimuthal
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Map projections

• Represent 3D-Earth on 2D-Map
• Not possible without distortion

Map
Earth (Ellipsoid)
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Aspects of map projections

• Map projections can have the following effects

straight lines curve
distances change
angles change
areas change
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Map vs. Ellipsoid real differences!!!
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Projections Examples

• Cylindrical
• TM - Transverse Mercator
• UTM - Universal Transverse Mercator
• Conical
• Lambert Conformal Conic
• Azimuthal
• Lambert Azimuthal Equal Area

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Comparison of Projection Types
(Normal) Cylindrical
Conic
Azimuthal
Transverse Cylindrical
Secant Cylindrical
Oblique Cylindrical
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Transverse Mercator Projection
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Transverse Mercator Graticule
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Details of the Transverse Mercator Projection
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Distortion as a result of a map projection
Globular projection
Orthographic projection
Stereographic projection
Mercator projection
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Projection Distortions
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Distortion Mercator v. Peters Projection
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UTM Projection System
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UTM STANDARD PARAMETERS

• Zones are 6 Degrees in width
• Example Zone 31
• Central Meridian 3 Degrees East
• False Easting 500000 metres
• False Northing
• 0 for Northern Hemisphere
• 10000000 metres for Southern Hemisphere
• Scale Factor on Central Meridian 0.9996

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Projection Distortion - Scale
For example UTM
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OS Projection Grid
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Ordnance Survey Grid
Example OSGB36 Latitude Longitude 543052.55N
12755.75W Grid Reference NZ034600013400 Centr
al Meridian 2 Degrees W Origin Latitude 49
Degrees N False Easting 400000 metres False
Northing 100000 metres Scale Factor 0.9996012717
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North reference (1)
Map grid 2 north
True north
Map grid 1 north

• north will be referenced to either True North
  or (map) Grid North.
• the designated choice varies by application.
• if (map) Grid North is designated, there is a
  need to properly identify which map grid is being
  used.

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Projection distortion (2) - direction
Lat / long graticule
Grid north differs from true
north. The difference is known as CONVERGENCE
Projection grid is constructed ... central
meridian is along a line of longitude.
Second projection constructed with central
meridian along a different line of longitude.
Because the meridians converge towards the poles,
the projection grids are rotated relative to
each other.
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North reference (3)
True pole
Latitude / longitude graticule
Magnetic pole (position varies with time)
True north is direction towards geographic north
pole.

• Magnetic north is direction
• towards magnetic north pole.
• varies with time.

• The difference in the direction
• in the horizontal plane between
• true north and magnetic north
• is MAGNETIC DECLINATION.
• positive when magnetic north lies east of true
  north

The difference in the vertical plane is known as
MAGNETIC DIP. The change with time of
declination or dip is known as MAGNETIC
VARIATION.
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North reference (summary)

• All directions must be defined.
• North will be designated to be either true north
  or map grid north. This varies by facility.
• If (map) grid north is chosen, ensure that the
  particular map grid is properly identified
• requires geodetic datum projection zone
• If the correct north is not identified
  directions may be significantly in error.

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Position Co-ordinates - or Where Are We?
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Datums A Frame of Reference for position and
height

• Definition of the-
• Shape of Earth Model
• Position of the Co-ordinate Reference System
• Transformation Between Datums
• e.g. WGS84 to ED50
• OSGB 36
• ED 50
• WGS84

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What about Height Surely thats Easy?
Geoid
Gravity-related
height (h)
Spheroidal Height
(H)
Spheroid
Geoid height
(N)
Spheroidal height (H) is measured from spheroid
along perpendicular passing through point.
Gravity-related height (h) is measured along
direction of gravity from vertical datum at geoid.
Geoid height (N) height of geoid above spheroid.
H h N
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Height Datums

• Examples in UK
• Ordnance Datum
• Based on Mean Sea Level at Newlyn
• Lowest Astronomical Tide (LAT)
• Based on derived tidal constituents at particular
  locations
• EGM 96
• Geoid Model using WGS84 Spheroid

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Geodetic Datum and Latitude
Perpendicular to blue spheroid
Latitude f is angle subtended at equator by a
line perpendicular to spheroid from point
Perpendicular to red spheroid
The same is true for longitude
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Locations with same latitude and longitude
values on three different coordinate systems
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Locations with same latitude and longitude
values on three different coordinate systems
100 metres
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Same Location but three very different sets of
co-ordinates on three different Datums

• ED.50
• Latitude 51d 30m 45.000s N
• Longitude 00d 20m 20.000s W
• Height 10.000m
• WGS84
• Latitude 51d 30m 41.890s N
• Longitude 00d 20m 25.047s W
• Height 76.02m
• OSGB1936
• Latitude 51d 30m 40.038s N
• Longitude 00d 20m 19.329s W
• Height 30.969m

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Datum Shifts Example
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How to produce a dry hole
Actual well at coordinates lat570000N,
lon10000E (GPS coordinate system WGS84)
100-300 m
Planned well at coordinates lat570000 N,
lon10000E (ED50)
Oil/gas
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Example of good practice Know the Datum,
Spheroid, Projection
Geographical coordinates with system
description Latitude 57o 30
12.12 N Longitude 002o 12 48.53 E
Projected coordinates with system
description Easting (X) 452865.852 m
Northing (Y) 6373837.306 m

Geodetic Datum ED50 Spheroid
International 1924 semi-major axis
6378388.0 m reciprocal flattening 1/297.0
Geodetic Datum ED50
Spheroid International 1924
semi-major axis 6378388.0 m reciprocal
flattening 1/297.0
Projection zone UTM zone 31 N latitude of
origin 0o N longitude of origin
3o E scale factor 0.9996 false
easting 500000.0 m false northing
0.0 m projection method
Transverse Mercator
North Diagram
Declination - 5o 12 12.1 8th Feb 2005
Convergence 0o 39 48.2