GIS midterm 1

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

Ellipsoid

 

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 semi-major and semi-minor axes)

Why do we have so many different ellipsoids?

Explain

Horizontal Datum

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)

Horizontal datum
Horizontal Datum
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
Local  Datums
 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

Map Distortion

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)
  • true-directional 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

Geoid

 

 

 

 

  • 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