Description
Goode homolosine is an equal-area pseudocylindrical projection for world maps. It is most commonly used in interrupted form. It is a combination of Mollweide (or homolographic) and sinusoidal projections, hence the name homolosine. The Mollweide projection is used north and south of the 40°44'12'' parallels. The sinusoidal projection is used between those two latitude values for the equatorial part of the world. The projection shows discontinuity in the graticule where both projections join.
The Goode homolosine projection was introduced by J. Paul Goode in 1923. It is available in ArcGIS Pro 1.0 and later and in ArcGIS Desktop 9.2 and later.
Projection properties
The subsections below describe the Goode homolosine projection properties.
Graticule
Goode homolosine is a pseudocylindric projection.
The equator and central meridian are projected as straight lines and the central meridian is 0.44 times the length of the projected equator. The other meridians are concave toward the central meridian and equally spaced sinusoidal curves between 40°44'12'' north and south, and arcs of an ellipse from the 40°44'12'' parallel to the nearest pole. The parallels are straight lines, equally spaced between 40°44'12'' north and south. Their spacing slowly decreases toward the poles beyond those latitudes. The poles are presented as points. The discontinuity of the lateral meridian shows the fusing parallel where the two projections are joined. The graticule is symmetric across the equator and the central meridian.
In the interrupted forms, each lobe has its own straight central meridian 0.22 times as long as projected equator. For the land-oriented version, the straight meridians are -100° and 30° in the northern hemisphere and -160°, -60°, 20°, and 140° in the southern hemisphere. The ocean-oriented version uses -140°, -10°, and 130° meridians in the northern hemisphere and -100°, 20°, and 140° meridians in the southern hemisphere. The poles are presented with two, three, or four points, depending on the interrupted form. The complete graticule is not symmetric across the equator and the central meridian.
Distortion
Goode homolosine is an equal-area (equivalent) projection. Shapes, directions, angles, and distances are generally distorted. The scale along all parallels in the sinusoidal part, between 40°44'12'' north and south, and along the central meridians of the projection is accurate. There is no distortion along the central meridians and the equator. In the uninterrupted form, bulging meridians produce considerable shape distortion toward the edge of the projection. The distortion values are symmetric across the equator and the central meridian only in the uninterrupted form.
Usage
The Goode homolosine projection is appropriate for small-scale mapping requiring accurate areas although its uninterrupted use is not advisable. Interrupted forms can be used for focus maps on land or ocean as originally presented by the inventor. The United States Geological Survey (USGS) Center for Earth Resources Observation and Science (EROS) center provides data in Goode's homolosine projection.
Limitations
The Goode homolosine projection is supported on spheres only. For an ellipsoid, the semimajor axis is used for the radius. The equal-area property and some other distortion properties are not maintained when an ellipsoid is used.
Parameters
Goode Homolosine parameters are as follows:
- False Easting
- False Northing
- Central Meridian, which does not alter the interruption longitudes as specified by the Option parameter.
- Option, used to specify the interruption forms regardless of Central Meridian parameter value, with values as follows:
Option value Result 0 = No interruption
1 = Interrupt oceans to show land masses
2 = Interrupt land masses to show oceans
Sources
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.