Albers projection

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Albers projection of the world with standard parallels 20°N and 50°N.
The Albers projection with standard parallels 15°N and 45°N, with Tissot's indicatrix of deformation
An Albers projection shows areas accurately, but distorts shapes.

The Albers equal-area conic projection, or Albers projection (named after Heinrich C. Albers), is a conic, equal area map projection that uses two standard parallels. Although scale and shape are not preserved, distortion is minimal between the standard parallels.

The Albers projection is used by the United States Geological Survey and the United States Census Bureau.[1] Most of the maps in the National Atlas of the United States use the Albers projection.[2] It is also one of the standard projections used by the government of British Columbia,[3] and the sole governmental projection for the Yukon.[4]

Formulas

For Sphere

Snyder[5] describes generating formulae for the projection, as well as the projection's characteristics. Coordinates from a spherical datum can be transformed into Albers equal-area conic projection coordinates with the following formulas, where [math]\displaystyle{ {R} }[/math] is the radius, [math]\displaystyle{ \lambda }[/math] is the longitude, [math]\displaystyle{ \lambda_0 }[/math] the reference longitude, [math]\displaystyle{ \varphi }[/math] the latitude, [math]\displaystyle{ \varphi_0 }[/math] the reference latitude and [math]\displaystyle{ \varphi_1 }[/math] and [math]\displaystyle{ \varphi_2 }[/math] the standard parallels:

[math]\displaystyle{ \begin{align} x &= \rho \sin\theta \\ y &= \rho_0 - \rho \cos\theta \end{align} }[/math]

where

[math]\displaystyle{ \begin{align} n &= \tfrac12 \left(\sin\varphi_1+\sin\varphi_2\right) \\ \theta &= n \left(\lambda - \lambda_0\right) \\ C &= \cos^2 \varphi_1 + 2 n \sin \varphi_1 \\ \rho &= \tfrac{R}{n}\sqrt{C - 2 n \sin \varphi} \\ \rho_0 &= \tfrac{R}{n}\sqrt{C - 2 n \sin \varphi_0} \end{align} }[/math]

Lambert equal-area conic

If just one of the two standard parallels of the Albers projection is placed on a pole, the result is the Lambert equal-area conic projection.[6]

See also

References

  1. "Projection Reference". Bill Rankin. http://www.radicalcartography.net/?projectionref. 
  2. Snyder, John P. (1987). Map Projections – A Working Manual. U.S. Geological Survey Professional Paper 1395. Washington, D.C.: United States Government Printing Office. p. 2. https://pubs.er.usgs.gov/pubs/pp/pp1395. Retrieved 2017-08-28. 
  3. [1]
  4. "Support & Info: Common Questions". Geomatics Yukon. Government of Yukon. http://www.geomaticsyukon.ca/info/common-questions. 
  5. Snyder, John P. (1987). "Chapter 14: ALBERS EQUAL-AREA CONIC PROJECTION". Map Projections – A Working Manual. U.S. Geological Survey Professional Paper 1395. Washington, D.C.: United States Government Printing Office. p. 100. https://pubs.er.usgs.gov/publication/pp1395. Retrieved 2017-08-28. 
  6. "Directory of Map Projections". "Lambert equal-area conic".

External links