Albers cone projection

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Albers cone projection with two standard parallels at 15 ° and 75 ° north latitude.

The Albers cone projection is an equal-area map network design in which the earth's surface is projected onto a cone . The cone, more precisely the truncated cone, touches the surface either in a circle of latitude ( standard parallel ) or intersects it in two standard parallels . The latter method is used almost exclusively. The tip of the cone is usually on the earth's axis . This projection is suitable for regions with greater east-west than north-south expansion. The most important properties are:

  • Area fidelity, ie areas are displayed correctly;
  • Meridians are straight lines, are equidistant from one another and intersect the circles of latitude at right angles;
  • The parallels of latitude are parallel to each other, but the distances between them vary;
  • Parallels of intersection are shown true to length.

history

Heinrich C. Albers (1773–1833), son of a merchant from Lüneburg, published this form of the conical image in an article in Zach's monthly Correspondence magazine in November 1805 and has since been considered the inventor. Albers noticed deficiencies in the representation by Patrick Murdoch's († 1774) earlier cone projection, in which partial areas are not depicted true to area. In February he wrote about Murdoch's draft in the same sheet:

"I now ask what it can help that the entire cone zone has the same content as the sphere zone, if each individual zone differs significantly from it. For in every country that is not delimited by the meridians and parallel circles themselves, the map can never show the true area in this way; and where does such a land, bounded by four right-angled lines, exist? "

In the publication of his own design, Albers concludes with the words:

“One can see that my cone projection affords all the advantages of Murdoch's without admitting more of its deficiencies than are inevitable. Just as the advantages I have given [...] belong to mine alone as well. So I think I can rightly flatter myself that I have first satisfactorily solved the problem of a possibly perfect cone projection. "

- Heinrich Christian Albers

Maps with Albers projection

In 1806 Albers drew his chart of the East Indies on the basis of Arrowsmith's Map of India from 1804. It is questionable whether he used his own projection for this. It appeared in Gotha as a single sheet. A contemporary wrote that the card had "a pure, clean engraving, very legible writing, and very clear and plausible border illumination". The following year, Albers anonymously reviewed Arrowsmith's card in the monthly correspondence . Efforts to include his card in the publication were unsuccessful. In the near future, the card appeared as a supplement to the special reprint of the review, spread over six sheets. After a few years, the map was reprinted again, together with a list of the area of ​​the individual Indian areas, in Zimmermann's pocket book of journeys , "because it seems to be used less than it deserves".

Reichard's map of the USA from 1809

1809–1818: The Lobenstein cartographer Christian Gottlieb Reichard was probably the first to do the projection. He is known to have published several maps based on Albers' projection, published a few years apart. The earliest example is Reichard's map of the United States of North America in Albers' projection and was published in Nuremberg in 1809. After that, the projection was initially forgotten.

Albers' work does not seem to have been rediscovered until the turn of the century. The Military Geography Institute in Vienna planned a 40-sheet new overview map of Europe 1: 750,000 with a projection to Albers. By 1903 two sheets had been published and five more were in progress, a total of twelve sheets were completed. The ninth and final edition of Sohr- Berghaus ' Handatlas covering all parts of the world appeared for the first time in the 1900s with maps designed using Albers projection.

As early as the 1920s, Oscar Adams of the US Coast and Geodetic Survey had spoken of "an equal area representation", "which is as good as any other and in many ways better than any other". Thereafter, the USGS used the Albers projection without exception for maps of the fifty US states in the National Atlas of 1970 with standard parallels at 29.5 ° and 45.5 ° N (excluding Alaska and Hawaii). The revised map with the USDA climate zones appeared in 1990.

literature

  • HC Albers: About Murdoch's three cone projections. In: FX Zach (Hrsg.): Monthly correspondence for the transport of the earth and sky customer (11th volume). Beckersche Buchhandlung, Gotha 1805, pp. 97–114 u. 240–250 1st part in Google book search, 2nd part in Google book search
  • HC Albers: Description of a new cone projection. In: FX Zach (Hrsg.): Monthly correspondence for the transport of the earth and sky customer (12th volume). Beckersche Buchhandlung, Gotha 1805, pp. 450–459 full text in the Google book search
  • HC Albers: Map of India, compiled from various interesting and valuable materials [etc.] In: FX Zach (Hrsg.): Monthly correspondence for the conveyance of earth and sky knowledge (16. Bd.). Beckersche Buchhandlung, Gotha 1807, p. 340. Review of the Arrowsmith map in the Google book search
  • W. Bonacker, E. Anliker: Heinrich Christian Albers, the originator of the equal-area conical trunk projection. In: Paul Langhans (Ed.): Dr. A. Petermann's communications from Justus Perthes' geographical institute . Justus Perthes, Gotha 1930, vol. 76, pp. 238-240. Digitized ThULB Jena
  • Frederick Pearson: Map Projections: Theory and Applications . CRC Press, Boca Raton 1990, ISBN 0-8493-6888-X .
  • Karl Zoeppritz: Guide the card design Administration I . 3. Edition. Teubner, Leipzig / Berlin 1912, pp. 130–137: Albers' equal-area cone (trunk) projection with two equal-length parallel circles. ( archive.org ).

Individual evidence

  1. ^ A b John P. Snyder: Map Projections — A Working Manual (= USGS Professional Paper 1395). Washington 1987, pp. 98-103: Albers Equal-Area Conic Projection . Full text in Google Book Search
  2. ↑ Patrick Murdoch: Of the best Form of Geographical Maps . In: Philosophical Transactions. London 1759, Volume 50, Part II, pp. 553-562. Full text in Google Book Search
  3. ^ Albers, monthly correspondence , Volume 11, pp. 113 f.
  4. ^ Albers, monthly correspondence, volume 12, p. 459.
  5. ^ HC Albers: Chart of the East Indies this side of the Ganges . Becker, Gotha 1806 (1 sheet 39 × 45 cm, approx. 1: 7,200,000) - HC Albers, Aaron Arrowsmith: Chart of the East Indies on this side of the Ganges in the current state drawn in six sheets tapered according to Arrowsmith's latest chart. Becker, Gotha 1807 (6 sheets 39 × 45 cm, approx. 1: 7,400,000)
  6. ↑ For example, the map does not show meridians as straight lines, so it obviously cannot be the Albers cone projection. Bonacker and Anliker suspected that "the main impetus" for Albers' work on projection arose "from the need for a suitable projection base" for this map of India.
  7. ↑ FJ Bertuch (Ed.): General Geographical Ephemeris . Volume 25, Landes-Industrie-Comptoir, Weimar 1808, p. 336. Full text in the Google book search
  8. ^ Albers, Monthly Correspondence. Volume 16, p. 340. See Bonacker / Anliker.
  9. ^ EAW Zimmermann: Taschenbuch der Reisen or entertaining presentation of the discoveries of the 18th century [etc.] 12th year, 1st department, Gerhard Fleischer d. J., Leipzig 1813, p. 346 f. Full text, map not expanded in Google Book search
  10. ↑ The cards from CG Reichard are:
    • The United States of North America according to the safest regulations, the latest news and charts, designed in Alber's projection. Homanns Erben, Nuremberg 1809 (1 sheet 58 × 70 cm, approx. 1: 4,300,000). Digitized by the Norman B. Leventhal Map Center (Boston Public Library) - a later edition by Christoph Fembo, Nuremberg 1818 (1 sheet 57 × 70 cm, approx. 1: 4,300,000)
    • Germany In Albers'scher Projection (= Carte De L'Allemagne D'Après La Projection De Mr. Albers). Homann heirs, Nuremberg 1811 ( 54 × 50 cm, approx. 1: 2,200,000)
    • The Kingdom of Würtemberg, Grand Duchy of Baden, and the Principality of Hohenzollern, in Albers'scher projection (= Charte geographique du Royaume de Wurtemberg, du Grand-Duché de Bade et de la Principauté de Hohenzollern ). Homanns Erben, Nuremberg 1813. (2 sheets 71 × 42 cm, approx. 1: 330,000). Digitized , SuUB Bremen
    • Europe . Fr. Campe, Nuremberg 1817 ( 22.8 × 24 cm, 1: 20,000,000). For the projection see Bonacker / Anliker.
    • The European part of the Turkish Empire. Friedrich Campe, Nuremberg 1817 (1 sheet 75 × 55 cm, approx. 1: 2,000,000). According to the BSB catalog in Albersian projection.
    • China in Albersian projection. Beyerlein, Nuremberg [around 1850] Reprint? (1 sheet 51 × 56 cm, approx. 1: 5,300,000)
  11. ^ Albers, Heinrich Christian. In: New German Biography (NDB). Volume 1, Duncker & Humblot, Berlin 1953, ISBN 3-428-00182-6 , p. 126 ( digitized version ).
  12. ^ Meyer's Large Conversational Lexicon at Zeno.org .
  13. ↑ Overview of historical maps. Federal Office for Metrology and Surveying, October 1, 2010, accessed on January 20, 2013 ( sample sheet Linz , ZIP 35 MB).
  14. ↑ Zöppritz, p. 137
  15. ↑ M. Witkam: Sohr-Berghaus' Atlas hand, 9e druk (1902-1906). 2007, accessed January 20, 2013 .
  16. ^ Oscar S. Adams: Tables for Albers Projection (= US Coast and Geodetic Survey Special Publication No. 130). Washington 1927, p. 1 ( docs.lib.noaa.gov ( memento of the original dated February 20, 2013 in the Internet Archive ) Info: The archive link has been inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this note. PDF; 1.44 MB, accessed on January 20, 2013) @1@ 2Template: Webachiv / IABot / docs.lib.noaa.gov
  17. ↑ USDA plans hardiness zone map 1990 (= USDA Miscellaneous Publication No. 1475). Washington 1990, standard parallel 29.5 ° and 45.5 ° n.B., 118 × 116 cm, approx. 1: 6,000,000. Digitized

Web links

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