The Meridian Projection (also known as the Equirectangular Cylindrical or Plate Carrée variant) is a cylindrical map projection in which meridians are mapped to equally spaced vertical lines, and parallels to horizontal lines. It is one of the oldest known projections and remains foundational in digital cartography, meteorology, and global coordinate systems[1].
Unlike conformal or equal-area projections, the Meridian Projection prioritizes mathematical simplicity and grid regularity, making it ideal for computational modeling, satellite imagery tiling, and educational visualization[2].
Historical Development
The geometric principles underlying the Meridian Projection trace back to Hecataeus of Miletus in the 5th century BCE, though formalized mathematical treatment emerged during the Hellenistic period. Ptolemy referenced similar gridding methods in his Geographia (2nd century CE), using rectangular coordinate systems for regional mapping[3].
During the Age of Exploration, navigators adopted simplified meridian grids for portolan charts. The term "Plate Carrée" was later coined by 16th-century French cartographers to describe its unadorned, flat-earth appearance, despite its spherical foundations[4].
Mathematical Formulation
The projection maps a sphere (or ellipsoid) onto a cylinder tangent at the equator. For a sphere of radius R, longitude λ, and latitude φ, the Cartesian coordinates (x, y) on the projected plane are:
y = R · arcsin(sin(φ₀)·sin(φ) + cos(φ₀)·cos(φ)·cos(λ − λ₀))
For standard equatorial form (φ₀ = 0):
x = R · (λ − λ₀)
y = R · φ
Where λ₀ is the central meridian. The linear scaling preserves angular relationships along the equator but introduces progressive distortion toward the poles[5].
Distortion & Properties
The Meridian Projection is neither conformal nor equal-area. It exhibits:
- Scale distortion: Increases with latitude, stretching areas near the poles by a factor of sec(φ)
- Shape preservation: Local angles are preserved only along the equator and central meridian
- Grid regularity: Orthogonal intersection of meridians and parallels simplifies coordinate lookup
- Computational efficiency: Forward/inverse transformations require no iterative solving
These characteristics make it unsuitable for precise area comparison or navigation at high latitudes, but optimal for raster data alignment and global tiling systems[6].
Modern Applications
Despite its age, the Meridian Projection remains actively deployed in:
Digital Earth Platforms — Google Earth, NASA Worldview, and the European Space Agency's Copernicus program use equirectangular variants for seamless global imagery mosaics.
Climate Modeling — Global circulation models (GCMs) rely on regular lat-long grids for atmospheric and oceanic simulation.
Web Mapping Standards — The WGS84 equirectangular specification underpins many open-data initiatives and GIS education tools.
Archival Restoration — Digitization of historical atlases often requires reprojection to the Meridian grid for cross-referencing[7].
Limitations & Alternatives
At latitudes beyond ±60°, the projection's areal distortion exceeds 150%, rendering it inappropriate for polar mapping or demographic visualization. Alternatives include:
- Mollweide / Hammer: Equal-area, elliptical bounds
- Mercator: Conformal, preserves bearing for navigation
- Winkel Tripel: Compromise projection favored by National Geographic
- Gnomonic: Straight-line great circles for flight routing
Selection depends on use-case priorities: topology, scale, shape, or computational simplicity[8].
References
- Snyder, J.P. (1987). Map Projections—A Working Manual. USGS Professional Paper 1395. Washington, D.C.
- National Imagery Transmission Formats (NITF) Standard 2.1A. (2014). DoD Image Formats. Defense Intelligence Agency.
- Ptolemy. (150 CE). Geographia. Translated by Eric R. Latham. Penguin Classics, 2018.
- Bertin, J. (1967). Semiologie Graphique. Gauthier-Villars. Paris.
- Sphere & Ellipsoid Projection Derivations. International Cartographic Association (ICA) Technical Report, 2021.
- Craster, R., & Frazier, R. (2010). Atlas of World Map Projections. CRC Press.
- Copernicus Global Land Service. (2023). Harmonised Land Cover Layers. European Commission Joint Research Centre.
- Tobler, W.R. (1993). Three Presentations on Classical Cartography. University of California Press.