Presentation on theme: "Map Projections and Coordinate Systems"— Presentation transcript:
1Map Projections and Coordinate Systems Surveying 101 for GIS Professionals2013 Kentucky GIS ConferenceJeremy Gould – Kentucky Transportation Cabinet11
2Agenda Geographic Coordinate Systems Ellipsoids Geoid Horizontal DatumsProjected Coordinate SystemsProject Datum FactorsVertical Datums
3Geographic Coordinate Systems Geographic Coordinates Systems use radial coordinates to locate a point on a specifically defined sphere (ellipse). These are called spherical coordinates.Cartesian point P can also be represented in spherical coordinates (λ,φ, γ) where:λ= +/- degrees longitudeΦ= +/-degrees latitudeγ= + radial distance from center
5EllipsoidsEllipsoids are flattened spheroids that when referenced to the earth can be rotated and/or shifted to best fit the earth (geoid) either in part or in whole
6GeoidThe geoid is an equipotential gravimetric surface resulting in an irregular and non-mathematical approximation of the earth’s size and shape relative to a base of reference that best fits global mean sea level in a least squares senseThe geoid is a 3 dimensional surface along which the pull of gravity is a specified constantThe geoid is a measured and interpolated surface and not a mathematically defined surfaceDifferences in the density of the Earth cause variation in the strength of the gravitational pull, in turn causing regions to dip or bulge above or below the reference ellipsoid
7GeoidGravity Recovery And Climate Experiment (GRACE) Gravimeters
8Ellipsoids There are Global Ellipsoids and Regional (local) Ellipsoids Two Global ellipsoids are GRS80 and WGS84
9Horizontal Datums A datum is a reference surface A geodetic datum consists of two major componentsEllipsoid with a spherical coordinate system and originSet of points and lines that have been surveyedA geodetic datum is a three dimensional Euclidian reference frame defined relative to an associated ellipsoid oriented to achieve a best fit statistical approximation of the geoid either in part or in whole.The North American Datum (NAD) has been defined by two different ellipsoids, the Clarke ellipsoid of 1866, which was oriented to best fit the North American continent and is the basis of NAD27, and the Global Reference System ellipsoid of 1980 (GRS80) which is a globally defined ellipsoid and the basis of NAD83.
10Ellipsoid, Geoid, and Datum GRS80 Ellipsoid(NAD’83)CLARKE 1866 Ellipsoid(NAD’27)GEOIDEarth Mass CenterApproximately 236 meters
11Horizontal DatumsLat and Long locations of given benchmarks in the NAD27 datum will likely be different from the lat and long of that same benchmark in the NAD83 or WGS84 datum's.The monumented points do not moveThis is described as a datum shiftShift in coordinate locations from WGS84 to NAD83 is often less than 1 meterDatum shifts between NAD27 and NAD83 are often 100’s of meters
12Horizontal Datums Geographic Position (Lat-Long) (variations between datums for same position)Example:Datum 1 may have a long-lat of( °, °)Datum 2 may have a long-lat of( °, °)The same point has different coordinates because of the shift/rotation of the ellipsoid
13Projected Coordinate Systems A mapping projection is a geometric tool that allows a portion of a spherical surface to be represented on a two dimensional surface such as a flat sheet of paper or computer screen in a spatially consistent manner.A State Plane Coordinate System is a specialized mapping projection that allows direct conversion between spherical geographic coordinates of latitude () and longitude (), and rectangular Cartesian coordinates of northing (y) and easting (x).
14Projected Coordinate Systems So how do we get from our Geographic Coordinates to a Projected Coordinate System?
15Projected Coordinate Systems CylindricalConicalPlanar
18Projected Coordinate Systems KENTUCKY PROJECTIONS UTM Zones 16 & 17 Transverse Mercator (Secant Cylinder)UTM Zone 16UTM Zone 17
19Projected Coordinate Systems Lambert Conic Projection (Northern Hemisphere)Polar AxisNorth Standard Parallel (SF = 1)Central MeridianSouth Standard Parallel (SF = 1)Parallel of Grid Origin (Base Parallel)
20State Plane Coordinate Systems State Plane zones are sometimes identified by the Federal Information Processing System (FIPS) Codes as shown below
21Projected Coordinate Systems KENTUCKY PROJECTIONS North and South State Plane Lambert Conformal Conic (Secant Cone)State Plane South ZoneState Plane North Zone
22Projected Coordinate Systems KENTUCKY SINGLE ZONE PROJECTION
23Projected Coordinate Systems KENTUCKY SPCS – NORTH AND SOUTH ZONESNORTH ZONESOUTH ZONE
24Projected Coordinate Systems Kentucky Projections NAD83 State Plane Coordinate System (Lambert Conformal Conic)ParameterSingle ZoneNorth ZoneSouth ZoneCentral Meridian85° 45’ W84° 15’ WNorth Std Parallel38° 40’ N38° 58’ N37° 56’ NSouth Std Parallel37° 05’ N37° 58’ N36° 44’ NBase Parallel36° 20’ N37° 30’ NFalse Northing1,000,000 m0 m500,000 mFalse Easting1,500,000 mLinear unit of measure for all zones is the U.S. Survey Foot (USFt)(1 USFt = meters)
25Projected Coordinate Systems COORDINATE SPACE COMPARISON1,500,000 mft1,250,000 mftNAD'83 SINGLE ZONE1,000,000 mftNORTHING750,000 mftNAD'83 SOUTH ZONE500,000 mftNAD'83 NORTH ZONE250,000 mftNAD'27 NORTH ZONENAD'27 SOUTH ZONE0 m0 ft0 m0 ft250,000 mft500,000 mft750,000 mft1,000,000 mft1,250,000 mft1,500,000 mft1,750,000 mft2,000,000 mftEASTING
26Projected Coordinate Systems Equatorial PlaneTopographic Surface (Ground)EllipsoidE1Axis of RotationS1G1G2E2S2G3E3S3E1 < G1 < S1G2 < E2 < S2E3 < S3 < G3Projection GridNorth Standard ParallelSouth Standard ParallelE = Distance on ellipsoid G = Distance on grid S = Distance on surfaceSF = Grid Scale Factor = Geodetic latitudeSF=1SF<1SF>1
27Project Datum FactorA Project Datum Factor (PDF) converts grid distances (state plane coordinates) to ground/surface distances.If you were to use a total station to measure distance between two points on the ground and then used GPS to measure the location of the same two points and calculate the distance between those two points on the state plane grid, the two distances would be close but not exactly the same. This is due to the curvature of the earth combined with the elevation above sea level of the project location. The grid (state plane projection) is trying to represent the elevated, curved surface of the earth on a flat plane at sea level.The PDF was more prevalent before GPS became popular because total stations were the primary tools used for surveying.Projects were designed using the PDF. This allowed surveyors in the field to measure directly from the designed plans, without having to apply the PDF on the fly in the field.
31Conversion Among Coordinate Systems Exact or approximate mathematical formulas have been developed to convert to and from geographic coordinates (lat and long) to all commonly used coordinate projectionsCare must be taken when converting among projections that use different datumsA datum transformation must be used to convert from one geographic coordinate system to another
32Conversion Among Coordinate Systems Inverse of PDFInverse of PDF