Map projections and Coordinate Systems 

All spatial data are referenced to a datum and coordinate system… either geographic or projected 

Spatail referencing system
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relevant components…


ellipsoid > datum > geographic coordinate system > projected coordinate system 


Mathematical estimation of earth’s general shape, it’s shape is smooth 

Ellipsoid, What does it do? 

establishes the reference system for measuring horizontal location 

Geometric properties of an Ellipsoid 

semi major axis:
the estimated radius of the earth in the equitorial direction
Semi minor axis:
The estimated radius of the earth in the polar direction


Ellipsoid
Flattening Factor


An expression of the degree of “squashing” in the ellipsoid
( a function of the defference between the semimajor and semiminor axes)


Why do we have so many different ellipsoids?
Explain




Ties an estimated ellipsoid to the earth by “fixing” it to the earths surface through a physical network of precisely measured points
( sets the position and oreintation of the ellipsoid, i.e. its center, relative to the earths center (of mass)





Defines the origin of where gratucules of latitude and longitude will lie on the earths surface, i.e. the origin for a geographic coordinate system 


based on astonomical observations, local surface measurements and older estimated ellipsoids as such, the ellipsoid is aligned to closely fit the earths surface only in one particular region; as a result, the origin, or ellipsoid center, is generally offset relative to the earths true center of mass; only applies to a particular area of the earth and not another; North American Datum (NAD) 1927 is a local datum 

Earh centered (geocentric) datum 

Based on satellite measurements and newer ellipsoid estimates (best fitting); as such the ellipsoid is aligned to fit the earths surface globally; as a result the origin, or ellipsoid center, is aligned to the earths true center of mass. Applies tot he entire world; North Americna Datum (NAD) 1983 and WGS 1984 are geocentric datums
GIS natively records horizontal location using WGS 1984 datum


Datum Shift
(motherfucker)


Since different datums are based on different ellipsoids and sets of measurements, the estimated coordinates (location) for benchmark points typically differ between datums
The latitude and longidute estimate of a given location point in one datum will be different from the latitdue and longitude estimate of the same location in a different datum ( as a function of each datum having diff. origins, i.e. ellipsoid centers). The feature has not physically moved, just the estimate of its location has changed.


Geographic (datum) transformatino


Because coordinates are based off of datums and each datum is based on one particular ellipsoid, a change in a datum changes the underlying ellipsoid, and thus the origin of the spatial reference system based off of it.
Geographic transformation converts latitude, longitude from one datum to another through a series of mathematical calculations (transformations) that account for this defference in origins


Geographic Coordinate Systems 

Is is a cartesian coordinate system? NO, it is a spherical (polar) system based on angles from an origin (or baselin)
Latitude and longitude are measured as degrees or angles from the center of the earth, i.e. ellipsoid origin; a geographical coordinate systems origin is always established by a datum
All geographic coordinate systems are based on one particular datum


Map projections and projecte coordinate systems 

Transfer the geographical coordinate system established by a datum, i.e. a particular ellipsoid, to a flat surface (3D to 2D)
 mathematical expressions that transform geodetic coordinates to a flat surface
 generally made on to simple geometric shapes called develoable surfaces
 Why? the shapes can be flattened without stretching thier surfaces
 combine developable surfaces and different perspective views (light) to generate a projection



All map projections involve some level of distortion
spatial properties that are inevidably distorted on a map, shape, area, distances and direction
 size of mapped area influences amount of expected distortion; function of how much of the curvature of the earth must be projected (flattened)
 small scale maps: large area, greater degree of distortion
 large scale maps: small area; minimum degree of distortion expected


Projections by surface (families) 

 conical (cones)
 cylindrical (cylindars)
 azimuthal or planar (planes)


Projections by preservation of property 

 equal area (preserve area)
 conformal (preserve local shape)
 equidistant (preserve distance)
 truedirectional or azimuthal (preserve direction)
No map can be entirely equal area and conformal at the same time


Lines of tangency (standard parallels) of a projection
How/why are they significant to map projections?


 points where the developable surface touches the surface of the earth and comprise areas of zero distortion, areas of true scale
 distortion increases away from the lines of tangency
 lines of tnagency can intersect in one place (tangent) or in two (secant)


Linear Unit of a projection 

 the X and Y values are stored, e.g. meters, feet
 also establishes the unit of measurement, e.g. area, lenght etc. for spatatial data with coordinates stored in that projection



 Sea surface as a function of gravity alone; no tidal, atmospheric or surface influence
 resulting surface is a lumpy and irregular ( from gravitational anomalies) surface that approzimates mean sea level
 establishes the reference system for measurein vertical location ( elevation)
 orthometric height ( height above the geoid; more accurate) ellipsoidal height ( height above the ellipsoid; less accurate)
 GPS measures elevation as hight above the ellipsoid, thus relatively inaccurate way to measure elevation in that regard

