EPSG Dataset :: v12.054

Polar Stereographic (variant A)

Coordinate Operation Method Details [VALID]

Name:

Polar Stereographic (variant A)

Code:

9810

Operation is Reversible:

Yes

Formula:

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.

For the forward conversion from latitude and longitude, for the south pole case

E = FE + rho * sin(lon – lonO)
N = FN + rho * cos(lon – lonO)
where
t = tan(pi/4 + lat/2) / {[(1 + e sin(lat)) / (1 – e sin(lat))]^(e/2)}
rho = 2*a*ko*t / {[(1+e)^(1+e) (1–e)^(1–e)]^0.5}

For the north pole case,
rho and E are found as for the south pole case but
t = tan(pi/4 – lat/2) * {[(1 + e sin(lat)) / (1 – e sin(lat))]^(e/2)}
N = FN – rho * cos(lon – lonO)

For the reverse conversion from easting and northing to latitude and longitude,
lat = chi + (e^2/2 + 5e^4/24 + e^6/12 + 13e^8/360) sin(2 chi)
+ (7e^4/48 + 29e^6/240 + 811e^8/11520) sin(4 chi)
+ (7e^6/120 + 81e^8/1120) sin(6 chi) + (4279e^8/161280) sin(8 chi)

where rho' = [(E-FE)^2 + (N – FN)^2]^0.5
t' =rho' {[(1+e)^(1+e) * (1– e)^(1-e)]^0.5} / (2 a ko)
and for the south pole case
chi = 2 atan(t' ) – pi/2
but for the north pole case
chi = pi/2 - 2 atan(t')

Then for for both north and south cases if E = FE, lon = lonO
else for the south pole case
lon = lonO + atan2[(E – FE),(N – FN)]
and for the north pole case
lon = lonO + atan2[(E – FE),(FN – N)] (see GN7-2 implementation notes in preface for atan2 convention)

Example:

For Projected Coordinate Reference System: WGS 84 / UPS North

Parameters:
Ellipsoid: WGS 84
a = 6378137.0 metre
1/f = 298.2572236
then e = 0.081819191

Latitude of natural origin (latO): 90°00'00.000"N =1.570796327 rad
Longitude of origin (longO): 0°00'00.000"E=0.0 rad
Scale factor at natural origin (ko): 0.994
False easting (FE) 2000000.00 metre
False northing (FN) 2000000.00 metre

Forward calculation for:
Latitude (lat) =73°N =1.274090354 rad
Longitude (lon) =44°E =0.767944871 rad

t = 0.150412808
rho = 1900814.564
whence
E = 3320416.75 m
N = 632668.43 m

Reverse calculation for the same Easting and Northing (3320416.75 E, 632668.43 N) first gives:
rho' = 1900814.566
t' = 0.150412808
chi = 1.2722090

Then
Latitude (lat) = 73°00'00.000"N
Longitude (lon) = 44°00'00.000"E

Method
Parameters:

Parameter Name	Parameter Code	Sign reversal	Parameter Description
Latitude of natural origin	8801	No	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).
Longitude of natural origin	8802	No	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)".
Scale factor at natural origin	8805	No	The factor by which the map grid is reduced or enlarged during the projection process, defined by its value at the natural origin.
False easting	8806	No	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.
False northing	8807	No	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.

Meta Data

Remarks:

Latitude of natural origin must be either 90 degrees or -90 degrees (or equivalent in alternative angle unit).

Information Source:

EPSG guidance note #7-2, http://www.epsg.org

Data Source:

EPSG

Revision Date:

August 29, 2018

Change ID:

[2003.22] [2010.054] [2017.024]

Wildcard	Example
% or *	Any wildcard characters
? or _	One wildcard character
[ - ]	[ - ] Range e.g. N[a-c] will return all geodetic objects that contains a string starting with the letter 'N' or 'n' followed by any of the letters contained within the range specified within the square bracket, e.g. letters a, b and c.
\|	Or e.g. E[a\|e]M will return all geodetic objects that contains a string starting with the letter E(e), ends with the letter M(m) and also contain either the letter a or letter e.