Projections and coordinate systems

Projections and coordinate systems

Projections and coordinate systems

Projections and coordinate systems We think of the earth as a sphere It is actually a spheroid, slightly larger in radius at the equator than at the poles

Projections and coordinate systems Rotate an ellypse around an axis

Projections and coordinate systems

Projections and coordinate systems Reference ellipsoid Because of their relative simplicity, reference ellipsoids are used as a preferred surface on which geodetic network computations are performed and point coordinates such as latitude, longitude, and elevation are defined. Historically, different reference ellipsoids have been defined and adopted by different countries. They are still in use due to technical legacies and juridical issues

Projections and coordinate systems Some reference ellipsoids Name Equatorial axis (m) a Polar axis (m) b Inverse flattening (a-b) / a Airy 1830 6 377 563.4 6 356 256.9 299.324 975 3 Clarke 1866 6 378 206.4 6 356 583.8 294.978 698 2 Bessel 1841 6 377 397.155 6 356 078.965 299.152 843 4 International 1924 6 378 388 6 356 911.9 297 Krasovsky 1940 6 378 245 6 356 863 298.299 738 1 GRS 1980 6 378 137 6 356 752.3141 298.257 222 101 WGS 1984 6 356 752.3142 298.257 223 563

Projections and coordinate systems ...a little problem: gravity

Projections and coordinate systems The Geoid

Projections and coordinate systems Where is the geoid?

Projections and coordinate systems Levelling network Tide gauge

Projections and coordinate systems What is a Datum

Projections and coordinate systems Example of geodetic datums Adindan (Ethiopia, Senegal) Moznet (Mozambique) Arc 1960 (Kenya, Tanzania) ED50 (Iraq) WGS84 is now becoming the International Standard (GPS)

Projections and coordinate systems GPS Initiated by U.S. Department of Defense Military planners wanted a technology where a position could be obtained without the use of radio transmissions Officially named Navigation System with Timing and Ranging (NAVSTAR) First satellite launched in 1974 The GPS Operational Constellation consists of 24 satellites (21 plus 3 operational spares) that orbit the Earth in very precise orbits twice a day. GPS satellites emit continuous navigation signals.

Projections and coordinate systems GPS Each GPS satellite transmits data that indicates its location and the current time. All GPS satellites synchronize operations so that these repeating signals are transmitted at the same instant. Physically the signal is just a complicated digital code, or in other words, a complicated sequence of “on” and “off” pulses. The same pseudo-random sequence is generated by the satellite and the receiver. The receiver compares the two sequences to derive the time difference. The distance from the satellite is the product of this difference by the speed of light.

Projections and coordinate systems GPS

Projections and coordinate systems GPS Precision Satellites use atomic clocks, receivers use quartz clocks -> less expensive Trees, buildings, mountains can prevent or reduce a clear line of sight Signal refraction in the atmosphere Signal interference, e.g. reflection from other surfaces Satellite distribution in the sky (Geometric Diluition of Precision, GDOP)

Projections and coordinate systems GPS Geometric Diluition of Precision Good Poor

Projections and coordinate systems GPS Precision GPS satellites transmit in two frequencies: L1 C/A code (coarse acquisition code) P code (precise code) encrypted Navigation data L2 Standard Positioning System (SPS) Only L1 and only C/A code Precise Positioning System (PPS) Both L1 and L2 (to minimize atmospheric refraction) P code (anti-spoofing)

Projections and coordinate systems GPS Differential GPS One or more ground based station in a known location record or broadcast the difference between the pseudoranges received from satellites and the actual internally computed pseudoranges. The difference can be applied by a rover station (individual, car, airplane etc.) to correct its own pseudoranges Post-processing A dedicated station Real time A network of stations Signal broadcasted by local radio network Signal broadcasted by satellite network (e.g. WAAS, EGNOS)

Projections and coordinate systems GPS

Projections and coordinate systems Other systems GLONASS – Russia's global navigation system. Fully operational worldwide Galileo – a global system being developed by the European Union and other partner countries, planned to be operational by 2014 (and fully deployed by 2019) COMPASS – People's Republic of China's global system, planned to be operational by 2020

Projections and coordinate systems The earth is a spheroid, a map is flat

Projections and coordinate systems Example of projections Cylindrical Conical Azimuthal

Projections and coordinate systems Areas or angles? Mollweide (equivalent) Mercator (conformal)

Projections and coordinate systems Areas or angles? At large scales, most of the commonly used projections are conformal.

Projections and coordinate systems UTM

Projections and coordinate systems UTM

Projections and coordinate systems

Projections and coordinate systems EPSG Geodetic Parameter Dataset European Petroleum Survey Group, now absorbed by the International Association of Oil & Gas Producers (OGP) a collection of definitions of coordinate reference systems and coordinate transformations which may be global, regional, national or local EPSG Geodetic Parameter Registry online at: http://www.epsg-registry.org/ example: EPSG:3857 3857 is the Spatial Reference System Identifier (SRID) WGS 84 / Pseudo-Mercator, used by Google maps

Projections and coordinate systems SRIDs are typically associated with a “well known text” (WKT), i.e. a string definition of the coordinate system “well known text” is a kind of data definition language Example: EPSG:4326 (correspond to WGS84) GEOGCS["WGS 84", DATUM["WGS_1984", SPHEROID["WGS 84",6378137,298.257223563, AUTHORITY["EPSG","7030"]], AUTHORITY["EPSG","6326"]], PRIMEM["Greenwich",0, AUTHORITY["EPSG","8901"]], UNIT["degree",0.01745329251994328, AUTHORITY["EPSG","9122"]], AUTHORITY["EPSG","4326"]]

Projections and coordinate systems There are some websites where you can find complete lists of spatial reference systems and transformations, along with their description and definition in different formats My favorite ones are http://spatialreference.org/ http://epsg.io

Projections and coordinate systems Coordinate conversion A B A C B