Description
Eckert IV is an equal-area pseudocylindrical map projection for world maps. The lateral meridians are semicircles, which give the projection a rounded shape and smooth corners where the lateral meridians meet the pole lines. This projection is commonly used for thematic and other world maps requiring accurate areas.
The projection was introduced by Max Eckert in 1906. It is available in ArcGIS Pro 1.0 and later and in ArcGIS Desktop 8.0 and later.
Projection properties
The subsections below describe the Eckert IV projection properties.
Graticule
Eckert IV is a pseudocylindric projection. The meridians are regularly distributed semiellipses concave toward the central meridian. The lateral meridians are semicircles, which give the graticule boundary a rounded shape. The central meridian is a straight line, half the length of the projected equator. The parallels are unequally distributed straight lines perpendicular to the central meridian. The poles are straight lines half the length of the equator. The corners where lateral meridians meet the pole lines are smooth. The graticule is symmetric across the equator and the central meridian.
Distortion
Eckert IV is an equal-area (equivalent) projection. Shapes, directions, angles, and distances are distorted and stretched north-south in tropical and midlatitude areas. Nearer the poles, features are compressed in the north-south direction. Points 40°30' north and south at the central meridian have zero distortion. The scale is correct along the 40°30' north and south parallel and constant along any given parallel. Distortion values are symmetric across the equator and the central meridian.
Usage
The Eckert IV projection is appropriate for small-scale mapping, especially for thematic world maps illustrating area characteristics and analysis requiring accurate areas.
Variants
There are two variants available in ArcGIS. Both variants correctly support sphere-based Earth models.
- The Eckert IV variant is available in ArcGIS Pro 1.0 and later and in ArcGIS Desktop 8.0 and later. For ellipsoids, it uses the semimajor axis and spherical equations.
- The Eckert IV auxiliary sphere variant is available in ArcGIS Pro 1.0 and later and in ArcGIS Desktop 9.3 and later. For ellipsoids, it uses a sphere specified by the Auxiliary Sphere Type parameter and spherical equations.
Limitations
For an ellipsoid of revolution, the equal-area property is only maintained with the Eckert IV auxiliary sphere variant when the Auxiliary Sphere Type 3 is used. Otherwise, areas are not maintained for ellipsoids.
Parameters
Eckert IV parameters are as follows:
- False Easting
- False Northing
- Central Meridian
Eckert IV auxiliary sphere parameters are as follows:
- False Easting
- False Northing
- Central Meridian
- Auxiliary Sphere Type, with values as follows:
- 0 = use semimajor axis of the geographic coordinate system
- 1 = use semiminor axis
- 2 = calculate and use authalic radius
- 3 = use authalic radius and convert geodetic latitudes to authalic latitudes
Note:
If the geographic coordinate system uses a sphere, the Auxiliary Sphere Type uses the radius of the sphere in all four cases.
Sources
Snyder, J. P. (1987). Map Projections: A Working Manual. U.S. Geological Survey Professional Paper 1395. Washington, DC: United States Government Printing Office.
Snyder, J. P. (1993). Flattening the Earth. Two Thousand Years of Map Projections. Chicago and London: University of Chicago Press.
Snyder, J. P. and Voxland, P. M. (1989). An Album of Map Projections. U.S. Geological Survey Professional Paper 1453. Washington, DC: United States Government Printing Office.