The Lambert projections are a family of map projections devised by the Swiss‑French mathematician and astronomer Johann Heinrich Lambert in the late 18th century. In his 1772 work Anmerkungen und Zusätze zur Entwerfung der Land‑ und Himmelscharten (Notes and Comments on the Composition of Terrestrial and Celestial Maps) Lambert introduced several conic, cylindrical and azimuthal projections that bear his name. The most widely used of these are the Lambert conformal conic projection (LCC), the Lambert cylindrical equal‑area projection, and the Lambert azimuthal equal‑area projection.
General characteristics
All Lambert projections are conformal (preserving local shape) or equal‑area (preserving relative area), depending on the specific variant. They are defined mathematically by projecting the surface of the Earth onto a geometric surface (a cone, a cylinder, or a plane) that is then unrolled to produce a flat map. By selecting appropriate standard parallels or reference latitudes, distortion can be minimized within a region of interest.
Major variants
| Projection | Geometry used | Primary property | Typical applications |
|---|---|---|---|
| Lambert conformal conic (LCC) | Cone tangent or secant to the globe | Conformal (shape‑preserving) | Aeronautical charts, U.S. State Plane Coordinate System, national/regional mapping of east‑west‑oriented regions |
| Lambert cylindrical equal‑area | Cylinder tangent at the equator | Equal‑area (area‑preserving) | Global thematic maps (e.g., climate, population) where accurate area representation is essential |
| Lambert azimuthal equal‑area | Plane tangent at a chosen point (azimuthal) | Equal‑area with true distances from the center | Polar maps, continental‑scale thematic mapping, GIS data sets requiring area fidelity |
Lambert conformal conic (LCC)
The LCC projects the Earth onto a cone that intersects the globe along one or two standard parallels where scale is exact. The cone is then unrolled, yielding a map in which meridians are straight lines converging toward a pole and parallels are arcs of circles. The projection is defined by a set of trigonometric equations (see Wikipedia entry “Lambert conformal conic projection”) that relate geographic latitude φ and longitude λ to planar coordinates (x, y). Because great‑circle routes appear as near‑straight lines, pilots use LCC charts for navigation. It is also the basis of many national grid systems, such as France’s Lambert‑93 (EPSG:2154) and the U.S. State Plane Coordinate System for states elongated east‑west.
Lambert cylindrical equal‑area
In this cylindrical projection the Earth is projected onto a cylinder tangent at the equator, then unwrapped. The resulting map has parallels as straight, equally spaced horizontal lines and meridians as vertical lines. Scale is true along the equator, and area is preserved everywhere, making it suitable for global thematic displays where area distortion would mislead interpretation.
Lambert azimuthal equal‑area
An azimuthal projection centered on a chosen point (often a pole), the Lambert azimuthal equal‑area projects the globe onto a plane. Distances from the central point are accurate, and areas are preserved across the map. It is frequently employed for polar region mapping and for GIS layers that require area‑preserving transformations.
Historical context
Lambert’s contributions (1772) were among the earliest systematic treatments of map projection mathematics. His work laid the foundation for later developments in cartography and geodesy, influencing the formulation of modern coordinate reference systems. The LCC, in particular, remains one of the seven projections originally described by Lambert and continues to be implemented in contemporary GIS software (e.g., PROJ, ArcGIS, Matplotlib Basemap).
References
- Wikipedia, “Lambert conformal conic projection.”
- Encyclopædia Britannica, “Lambert conformal projection.”
- Lambert, J. H. (1772). Anmerkungen und Zusätze zur Entwerfung der Land‑ und Himmelscharten.
- U.S. National Geodetic Survey, State Plane Coordinate System of 1983 (NOAA Manual NOS NGS 5).
These sources collectively document the definition, mathematical formulation, and practical uses of the Lambert family of map projections.