projected
Nuna Technologies on behalf of armap.org
2007-01-20
true
false
http://www.opengis.net/def/crs/EPSG/0/3572
WGS 84 / North Pole LAEA Alaska
For studies of Alaskan area.
Northern hemisphere - north of 45°N, including Arctic.
-180
180
45
90
OGP
2008-09-19
false
false
http://www.opengis.net/def/area/EPSG/0/3480
World - north of 45°N
Arctic research.
conversion
Nuna Technologies on behalf of armap.org
2007-01-20
true
false
http://www.opengis.net/def/coordinateOperation/EPSG/0/17296
North Pole Lambert Azimuthal Equal Area (Alaska)
For studies of Alaskan area.
Northern hemisphere - north of 45°N, including Arctic.
-180
180
45
90
OGP
2008-09-19
false
false
http://www.opengis.net/def/area/EPSG/0/3480
World - north of 45°N
Arctic research.
ISO 1000.
1995-06-02
false
http://www.opengis.net/def/uom/EPSG/0/9001
metre
Also known as International metre. SI standard unit.
length
0
USGS Professional Paper 1395, "Map Projections - A Working Manual" by John P. Snyder.
2007-01-12
false
true
For Projected Coordinate Reference System: ETRS89 / ETRS-LAEA
Parameters:
Ellipsoid:GRS 1980 a = 6378137.0 metres 1/f = 298.2572221
then e = 0.081819191
Latitude of natural origin (latO): 52°00'00.000"N = 0.907571211 rad
Longitude of natural origin (lonO): 10°00'00.000"E = 0.174532925 rad
False easting (FE): 4321000.00 metres
False northing (FN) 3210000.00 metres
Forward calculation for:
Latitude (lat) = 50°00'00.000"N = 0.872664626 rad
Longitude(lon) = 5°00'00.000"E = 0.087266463 rad
First gives
qP = 1.995531087
qO = 1.569825704
q = 1.525832247
Rq = 6371007.181
betaO = 0.905397517
beta = 0.870458708
D = 1.000425395
B = 6374393.455
whence
E = 3962799.45 m
N = 2999718.85 m
Reverse calculation for the same Easting and Northing (3962799.45 E, 2999718.85 N) first gives:
rho = 415276.208
C = 0.065193736
beta' = 0.870458708
Then Latitude = 50°00'00.000"N
Longitude = 5°00'00.000"E
http://www.opengis.net/def/method/EPSG/0/9820
Lambert Azimuthal Equal Area
This is the ellipsoidal form of the projection.
Note: These formulas have been transcribed from EPSG Guidance Note #7-2. Users are encouraged to use that document rather than the text which follows as reference because limitations in the transcription will be avoided.
Oblique aspect
To derive the projected coordinates of a point, geodetic latitude (lat) is converted to authalic latitude (ß). The formulae to convert geodetic latitude and longitude (lat,lon) to Easting and Northing are:
Easting, E = FE + {(B . D) . [cos ß . sin(lon ? lonO)]}
Northing, N = FN + (B / D) . {(cos ßO . sin ß) ? [sin ßO . cos ß . cos(lon ? lonO)]}
where
B = Rq . (2 / {1 + sin ßO . sin ß + [cos ßO . cos ß . cos(lon ? lonO)]})^0.5
D = a . [cos latO / (1 ? e2 sin2 latO)^0.5] / (Rq . cos ßO)
Rq = a . (qP / 2)^0.5
ß = asin (q / qP)
ßO = asin (qO / qP)
q = (1 ? e^2) . ([sin(lat) / (1 ? e^2 sin^2(lat))] ? {[1/(2e)] . ln [(1 ? e sin(lat)) / (1 + e sin(lat))]})
qO = (1 ? e^2) . ([sin(latO) / (1 ? e^2 sin^2(latO))] ? {[1/(2e)] . ln [(1 ? e sin(latO)) / (1 + e sin(latO))]})
qP = (1 ? e^2) . ([sin(latP) / (1 ? e^2 sin^2(latP))] ? {[1/(2e)] . ln [(1 ? e sin(latP)) / (1 + e sin(latP))]})
where *P = p/2 radians, thus
qP = (1 ? e^2) . ([1 / (1 ? e^2)] ? {[1/(2e)] . ln [(1 ? e) / (1 + e)]})
The reverse formulas to derive the geodetic latitude and longitude of a point from its Easting and Northing values are:
lat = ß' + [(e^2/3 + 31e^4/180 + 517e^6/5040) . sin 2ß'] + [(23e^4/360 + 251e^6/3780) . sin 4ß'] + [(761e^6/45360) . sin 6ß']
lon = lonO + atan {(E-FE) . sin C / [D. rho . cos ßO . cos C ? D^2. (N-FN) . sin ßO . sin C]}
where
ß' = asin{(cosC . sin ßO) + [(D . (N-FN) . sinC . cos ßO) / rho]}
C = 2 . asin(rho / 2 . Rq)
rho = {[(E-FE)/D]^2 + [D . (N ?FN)]^2}^0.5
and D, Rq, and ßO are as in the forward equations.
Polar aspect
For the polar aspect of the Lambert Azimuthal Equal Area projection, some of the above equations are indeterminate. Instead, for the forward case from latitude and longitude (lat, lon) to Easting (E) and Northing (N):
For the north polar case:
Easting, E = FE + [rho sin(lon ? lonO)]
Northing, N = FN ? [rho cos(lon ? lonO)]
where
rho = a (qP ? q)^0.5
and qP and q are found as for the general case above.
For the south polar case:
Easting, E = FE + [rho . sin(lon ? lonO)]
Northing, N = FN + [rho . cos(lon ? lonO)]
where
rho = a (qP + q)^0.5
and qP and q are found as for the general case above.
For the reverse formulas to derive the geodetic latitude and longitude of a point from its Easting and Northing:
lat = ß' + [(e^2/3 + 31e^4/180 + 517e^6/5040) sin 2ß'] + [(23e^4/360 + 251e^6/3780) sin 4ß'] + [(761e^6/45360) sin 6ß']
as for the oblique case, but where
ß' = ±asin [1? rho^2 / (a^2{1? [(1? e^2)/2e)) ln[(1-e)/(1+ e)]})], taking the sign of latO
and rho = {[(E ?FE)]^2 + [(N ? FN)]^2}^0.5
Then
lon = lonO + atan [(E ?FE)] / (N ?FN)] for the south pole case
and
lon = lonO + atan [(E ?FE)] / ? (N ?FN)] for the north pole case.
2
2
90
EPSG guidance note number 7.
1999-09-09
false
The latitude of the point from which the values of both the geographical coordinates on the ellipsoid and the grid coordinates on the projection are deemed to increment or decrement for computational purposes. Alternatively it may be considered as the latitude of the point which in the absence of application of false coordinates has grid coordinates of (0,0).
http://www.opengis.net/def/parameter/EPSG/0/8801
Latitude of natural origin
-150
Abbeviated as "CM".
Abbreviation for "Central Meridian".
EPSG guidance note number 7.
2002-06-22
false
The longitude of the point from which the values of both the geographical coordinates on the ellipsoid and the grid coordinates on the projection are deemed to increment or decrement for computational purposes. Alternatively it may be considered as the longitude of the point which in the absence of application of false coordinates has grid coordinates of (0,0). Sometimes known as "central meridian (CM)".
http://www.opengis.net/def/parameter/EPSG/0/8802
Longitude of natural origin
0
This alias applies only in the case of projection methods which have an axis positive west, e.g. Transverse Mercator (South Orientated).
EPSG guidance note number 7.
2002-07-31
false
Since the natural origin may be at or near the centre of the projection and under normal coordinate circumstances would thus give rise to negative coordinates over parts of the mapped area, this origin is usually given false coordinates which are large enough to avoid this inconvenience. The False Easting, FE, is the value assigned to the abscissa (east or west) axis of the projection grid at the natural origin.
http://www.opengis.net/def/parameter/EPSG/0/8806
False easting
0
This alias applies only in the case of projection methods which have an axis positive south, e.g. Transverse Mercator (South Orientated).
EPSG guidance note number 7.
2002-07-31
false
Since the natural origin may be at or near the centre of the projection and under normal coordinate circumstances would thus give rise to negative coordinates over parts of the mapped area, this origin is usually given false coordinates which are large enough to avoid this inconvenience. The False Northing, FN, is the value assigned to the ordinate (north or south) axis of the projection grid at the natural origin.
http://www.opengis.net/def/parameter/EPSG/0/8807
False northing
geographic 2D
EPSG. See 3D CRS for original information source.
2007-08-27
true
false
http://www.opengis.net/def/crs/EPSG/0/4326
WGS 84
World.
-180
180
-90
90
OGP
2001-06-05
false
false
http://www.opengis.net/def/area/EPSG/0/1262
World
Horizontal component of 3D system. Used by the GPS satellite navigation system and for NATO military geodetic surveying.
ellipsoidal
OGP
2008-06-23
false
http://www.opengis.net/def/cs/EPSG/0/6422
Ellipsoidal 2D CS. Axes: latitude, longitude. Orientations: north, east. UoM: degree
Coordinates referenced to this CS are in degrees. Any degree representation (e.g. DMSH, decimal, etc.) may be used but that used must be declared for the user by the supplier of data. Used in geographic 2D coordinate reference systems.
http://www.opengis.net/def/axis/EPSG/0/106
Lat
north
http://www.opengis.net/def/axis/EPSG/0/107
Long
east
geodetic
NIMA TR8350.2 June 2004 revision. http://earth-info.nga.mil/GandG/publications/tr8350.2/tr8350_2.html and
http://gis-lab.info/docs/nima-tr8350.2-addendum.pdf
2013-06-15
true
false
http://www.opengis.net/def/datum/EPSG/0/6326
World Geodetic System 1984
EPSG::6326 has been the then current realisation. No distinction is made between the original and subsequent (G730, G873, G1150 and G1674) WGS 84 frames. Since 1997, WGS 84 has been maintained within 10cm of the then current ITRF.
Satellite navigation.
Defined through a consistent set of station coordinates. These have changed with time: by 0.7m on 29/06/1994 (G730), a further 0.2m on 29/01/1997 (G873) and a further 0.06m on 20/01/2002 (G1150) and on 8/02/2012 (G1674).
1984-01-01
Cartesian
OGP
2008-06-23
false
http://www.opengis.net/def/cs/EPSG/0/4467
Cartesian 2D CS for north polar azimuthal lonO 150°W. Axes: X,Y. Orientations: X along 60°W, Y along 30°E meridians. UoM: m.
Used for North Pole tangential and secant projections.
http://www.opengis.net/def/axis/EPSG/0/203
X
South along 60°W
http://www.opengis.net/def/axis/EPSG/0/204
Y
South along 30°E