Albers projection

File:Albers with Tissot's Indicatrices of Distortion.svg of deformation]]

Image:Usgs map albers equal area conic.PNG

The Albers equal-area conic projection, or Albers projection, 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. It was first described by Heinrich Christian Albers (1773-1833) in a German geography and astronomy periodical in 1805.{{cite journal |last1=Albers |first1=H. C. |title=Beschreibung einer neuen Kegelprojection |journal=(von Zach's) Monatliche Correspondenz zur Beförderung der Erd- und Himmels-Kunde |date=November 1805 |volume=12 |pages=450-459 |url=https://www.digitale-sammlungen.de/de/view/bsb10538604?page=466,467 |access-date=6 December 2024}}

Official adoption

The Albers projection is used by some big countries as "official standard projection" for Census and other applications.

class="wikitable"

!Country

!Agency

Brazil

|federal government, through IBGE, for Census Statistical Grid {{Cite web |title=Grade Estatística |url=https://geoftp.ibge.gov.br/recortes_para_fins_estatisticos/grade_estatistica/censo_2010/grade_estatistica.pdf|year=2016|archive-url=https://web.archive.org/web/20180219033336/https://geoftp.ibge.gov.br/recortes_para_fins_estatisticos/grade_estatistica/censo_2010/grade_estatistica.pdf |archive-date=2018-02-19 }}

Canada

|government of British Columbia{{Cite web |title=Data Catalogue |url=https://catalogue.data.gov.bc.ca/dataset/1-250-000-raster-base-map-bc-albers}}

Canada

|government of the Yukon{{cite web |title=Support & Info: Common Questions |url=http://www.geomaticsyukon.ca/info/common-questions |access-date=15 October 2014 |work=Geomatics Yukon |publisher=Government of Yukon}} (sole governmental projection)

|United States Geological Survey{{cite web |title=Projection Reference |url=http://www.radicalcartography.net/?projectionref |url-status=live |archive-url=https://web.archive.org/web/20090425214731/http://www.radicalcartography.net/?projectionref |archive-date=25 April 2009 |access-date=2009-03-31 |publisher=Bill Rankin}}

|United States Census Bureau

Some "official products" also adopted Albers projection, for example most of the maps in the National Atlas of the United States.

Formulas

=For sphere=

Snyder{{Cite book | author=Snyder, John P. | title=Map Projections – A Working Manual. U.S. Geological Survey Professional Paper 1395 | publisher=United States Government Printing Office | location=Washington, D.C. | year=1987 | chapter=Chapter 14: ALBERS EQUAL-AREA CONIC PROJECTION | page=100 | url=https://pubs.er.usgs.gov/publication/pp1395 | access-date=2017-08-28 | archive-url=https://web.archive.org/web/20080516070706/http://pubs.er.usgs.gov/pubs/pp/pp1395 | archive-date=2008-05-16 | url-status=live }} 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 ${R}$ is the radius, $\lambda$ is the longitude, $\lambda_0$ the reference longitude, $\varphi$ the latitude, $\varphi_0$ the reference latitude and $\varphi_1$ and $\varphi_2$ the standard parallels:

: $\begin{align}
x &= \rho \sin\theta, \\
y &= \rho_0 - \rho \cos\theta,
\end{align}$

where

: $\begin{align}
n &= \tfrac12 (\sin\varphi_1 + \sin\varphi_2), \\
\theta &= n (\lambda - \lambda_0), \\
C &= \cos^2 \varphi_1 + 2 n \sin \varphi_1, \\
\rho &= \tfrac{R}{n} \sqrt{C - 2 n \sin \varphi}, \\
\rho_0 &= \tfrac{R}{n} \sqrt{C - 2 n \sin \varphi_0}.
\end{align}$

= 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.

"Directory of Map Projections".

[https://www.mapthematics.com/ProjectionsList.php?Projection=184 "Lambert equal-area conic"].

References

External links

[http://mathworld.wolfram.com/AlbersEqual-AreaConicProjection.html Mathworld's page on the Albers projection]
[http://www.radicalcartography.net/?projectionref Table of examples and properties of all common projections], from radicalcartography.net
[https://web.archive.org/web/20070927225410/http://www.uff.br/mapprojections/Albers_en.html An interactive Java Applet to study the metric deformations of the Albers Projection].

Category:Equal-area projections