The Interrupted Goode Homolosine projection (Goode's) is an interrupted, pseudocylindrical, equal-area, composite map projection that can present the entire world on one map. Global land masses are presented with their areas in proper proportion, with minimal interruption, and minimal overall distortion.
Vector and raster data in the Goode's projection are available to the spatial data community from a variety of sources. One of these sources is the U.S. Geological Survey's (USGS) EROS Data Center (EDC). EDC currently provides imagery and derived data sets such as the Global Land 1-kilometer Advanced Very High Resolution Radiometer (AVHRR) imagery of the world land masses, a corresponding raster land/water mask generated from World Vector Shoreline and Digital Chart of the World (DCW) drainage layer sources, and the 1-kilometer Global Land Cover Characterization data set. Future imagery such as the Moderate Resolution Imaging Spectrometer (MODIS) and SPOT Vegetation imagery will also be provided in the Goode's map projection. These data can augment scientific investigations, but the user must be able to project data into and from the Goode's map projection in order to use these data sets with data in other map projections.
The Interrupted Goode Homolosine map projection is composed from twelve discrete regions that combine to form six interrupted lobes. The two northern regions are often presented with land areas repeated in both regions, allowing these land areas to be shown without interruption. The Goode's projection currently is not explicitly supported in Geographic Information System (GIS) software packages such as ArcInfo3. Fortunately, it can be simulated by combining twelve instances of the Mollweide and Sinusoidal map projections, both of which usually are supported in GIS software packages. Vector and raster data can be projected into the Goode's projection by splitting it into the appropriate Goode's regions, projecting each region using its component map projection (Mollweide or Sinusoidal) and offsets, and joining the reprojected regions into one data set. Vector data stored in other map projections have been projected into the Goode's projection at product generation time in ARCPLOT. This was accomplished through the use of appropriate logical RESELECTs of features and the repeated use of the MAPPROJECTION environment.
Vector and raster data sets in the Interrupted Goode Homolosine (Goode's) projection are available to the spatial data community from a variety of sources, including the U.S. Geological Survey's (USGS) EROS Data Center (EDC). At EDC, global data sets of remotely-sensed raster imagery are being compiled. The imagery for these data sets are medium-resolution. The Goode's projection was chosen for use with these data because it provides minimal distortion over the world's land areas, helping to preserve the information content of the imagery. These data sets include the Global Land 1-kilometer Advanced Very High Resolution Radiometer (AVHRR) imagery of the world land masses (Figure 1), a corresponding raster land/water mask generated from World Vector Shoreline and Digital Chart of the World (DCW) drainage layer sources, and the 1-kilometer Global Land Cover Characterization data set (Figure 2). Future imagery such as the Moderate Resolution Imaging Spectrometer (MODIS) and SPOT Vegetation imagery will also be provided in the Goode's map projection.
The properties of map projections and the ability of these properties to control distortion have been adequately described in a number of sources. Snyder (1987) presents a more complete discussion of this topic. Snyder and Voxland (1989) provide useful information about map projection properties and present graphics for a number of map projections. Pamphlets such as Robinson (1986), Robinson (1988), and Robinson and others (1991) provide discussions that contribute to a reasonable understanding of the properties of map projections and the control of distortion. Appendix 1 summarizes these properties.
Global monitoring projects using remotely-sensed raster imagery need a map projection that supports the collection, registration, compositing, archiving, analysis, and presentation of this imagery. Each of these tasks has special needs that suggest selecting some map projections and not others. Since it is not currently feasible to change map projections for each activity of a project, it is necessary to compromise on a map projection that serves most of a project's needs.
Of the conformal, equal-area, equidistant, and azimuthal properties, the equal-area property is the most important when dealing with raster imagery. The raster pixels that compose imagery are areal in nature. Each pixel represents the area contribution of its corresponding ground location. Image processing software operates on an image, processing each pixel as yet another unit. The software functions as if the pixels are all the same size. When the imagery is in an equal-area map projection, image processing operations affect similarly-sized ground regions, and area calculations are then simplified.
Gerardus Mercator presented what has come to be known as the Mercator map projection in 1569 as an effective navigational tool that featured straight rhumb lines. While it is an excellent map projection for this purpose, the Mercator projection was never intended to be a general-use world map projection. It can not display the entire Earth on a world map. The north and south poles are not visible because they lie at infinity in the Mercator Cartesian coordinate space. It is inappropriate for the presentation of areal relationships because the Mercator map projection is a conformal, not an equal-area map projection. The sizes and shapes of large regions are distorted, especially near the poles. The Mercator map projection has been commonly (and incorrectly) used for general-purpose world mapping because it nicely fills a rectangular page and is easily constructed. Because it is seen so often, its use is seldom questioned.
J.P. Goode proposed several map projections and variations. The most common of these is the Goode's projection referred to in this paper, the Interrupted Goode Homolosine map projection with cap extensions in the northern regions. The Goode's projection is described and classified as an interrupted, pseudocylindrical, equal-area, composite map projection. It was developed in 1923 to provide an effective alternative to portraying global areal relationships on the Mercator map projection.
Interrupted means that, in an effort to reduce peripheral distortion, the mapped surface of the world has been split into six lobes (Figure 3). Each lobe spans a region of the Earth from the Equator to a pole. The lobes are not symmetrical about the Equator. The six lobes are split along meridians passing through the major oceans, and correspond to five of the major continental land masses and the South Pacific. The intention is to present the world land masses with as little interruption as possible and still hold distortion to a minimum throughout the world. Antarctica is the only major land mass that is split. Strictly speaking, Greenland and northeastern Asia's Chukotski Peninsula and Wrangel Island should also be split because the meridians dividing the northern lobes run through them. These regions are often presented intact by adding cap extensions to the northern lobes. The cap extensions cause some places on Earth to map to two locations in the map projection. Cap extensions also graphically present the relationships of the affected features with their neighboring features in both lobes. Some implementations of the Goode's projection do not support the cap extensions because of the double mapping. The central meridian chosen for the Eurasian land mass provides lower distortion in the regions of Europe and northern Africa, but distortion becomes noticeable in northeastern Asia. The level of this distortion is slightly greater than the level that occurred with the Bonne projection that was commonly used to present Asia when Goode developed the Interrupted Homolosine projection (Goode, 1925).
Pseudocylindrical means that the projection features straight horizontal lines for parallels and has meridians equally spaced along the parallels. Unlike the cylindrical map projections, meridians in pseudocylindrical map projections are usually curved. The central meridians of each lobe in the Goode's map projection are straight lines running from the Equator to the poles. The other meridians curve toward their lobe's central meridian and intersect at the pole. The straight-line, horizontal parallels facilitate the comparative study of world features by latitude. The graticule, or network of lines representing selected parallels and meridians for the Earth, features horizontal lines for the parallels, curved, evenly-spaced vertical lines representing meridians, and poles at the extreme ends of each lobe's central meridian (Figure 4).
Composite means that the Goode's projection is formed from more than one map projection. In this case, the map projections are the Mollweide and the Sinusoidal. The Mollweide projection is used to map the poleward regions of each interrupted lobe. The Sinusoidal projection is used to map the Equatorial regions of each interrupted lobe (Figure 5).
Scale properties are determined by the component projection for each region. The Sinusoidal regions of the projection present true scale along every latitude and along the central meridians of the lobes. This has the effect of evenly spacing the parallels and of making distance measurements accurate along the lines of latitude and the central meridian. The Mollweide regions of the projection present true scale only at ±40° 44' 11.8". Scale is otherwise constant along a given latitude and the same at the corresponding, opposite latitude, but scale varies between latitudes (Figure 4 and Figure 5).
Distortion properties are determined by the component projection for each region. The Sinusoidal regions present no distortion along the Equator and the central meridian of each lobe. Distortion occurs away from these lines, and becomes most severe at high latitudes, away from the central meridians. The Mollweide regions are distortion free only where their respective central meridians intersect the latitudes ±40° 44' 11.8". Distortion is again most severe at high latitudes, away from the central meridians (Figure 4 and Figure 5).
The Goode's map projection offers an effective compromise, balancing the equal-area and minimum distortion needs of global land data sets. The major limitation to its effective use is in the polar regions, where lobe interruptions and the inability to cross over the pole interfere with the formation of a proximal view of the region. Unfortunately, the Goode's projection has not been widely implemented as an integrated map projection in GIS and image processing software. When the Goode's projection has not been implemented in a user's GIS, the user may be able to simulate the projection by appropriately applying its component Sinusoidal and Mollweide map projections.
The Goode's map projection is formed on a Cartesian coordinate plane. Units of measure for the map projection are usually specified in meters. The Cartesian origin, (0,0), coincides with the geographic Longitude/Latitude coordinates of (0° East, 0° North). The Cartesian coordinate space is defined everywhere on the coordinate plane. The geographic coordinate space is undefined in the gaps between the lobes.
The Earth's surface is presented on six lobes, mapped onto the Cartesian plane with appropriate offsets. The lobes join along the Equator. Each lobe is divided into two regions at the parallels ±40° 44' 11.8". Thus, the Goode's projection is formed from 12 separate regions and effectively, 12 separate map projections. Projection of the geographic Longitude/Latitude coordinate space onto the Cartesian coordinate plane is governed by the input geographic location and the Goode's region that it is being projected into. Note that when cap extensions are used, some geographic locations will be mapped to two locations on the Cartesian coordinate plane.
Each component map projection is a world map projection in its own right. As such, it has its own Cartesian coordinate plane. Geographic (Longitude,Latitude) locations are mapped to Cartesian coordinate (x,y) locations for every point on Earth, not just the geographic locations belonging to a Goode's region. The component map projection's origin at (Longitude,Latitude) location (central meridian, Equator) is mapped to the Cartesian origin at (0,0). To map geographic data into any component region of the Goode projection, the geographic data must be clipped to the desired region's boundaries and projected into that component projection. Extending the clipping boundary allows geographic data that falls outside the nominal boundaries of a region to be mapped as an extension to that region. This is one method for handling the cap extensions.
If the component map projections are clipped to the prescribed geographic extents (Appendix 2) and plotted on a common Cartesian coordinate plane, the result appears as in Figure 6. The origins of each component projection are aligned at the Cartesian origin, (0,0), and the plot lays out accordingly. The component regions lie on the proper side of the Equator, but they overlay each other in their northern or southern hemispheres. The polar regions are separated from the Equatorial regions by a gap, but they overlay each other. To place the component regions in their proper locations for the Goode's map projection, appropriate false eastings must be applied to each of the Sinusoidal component map projections. The same false eastings and appropriate false northings must be applied to the Mollweide component projections to align them with the Sinusoidal components and to join them at the respective latitudes ±40° 44' 11.8".
It is useful to refer to the regions of the Goode's projection by an identifying region number. The convention used here (Figure 5) assigns the upper left region the number 1 and proceeds across and down the projection. This results in labeling the North American lobe regions 1 and 3, and labeling the Australian lobe regions 8 and 12. This convention is used in the appendices to identify information for each region.
The Goode's map projection is supported as an integrated map projection in the Land Analysis System (LAS) image processing software package at the EROS Data Center. LAS is used to process remotely-sensed raster imagery from a variety of sensors, including the 1-kilometer AVHRR imagery. Source code for a utility program that converts latitude/longitude coordinates into image line/sample coordinates for Global Land 1-kilometer AVHRR imagery and for the Global Land 1-kilometer AVHRR Pathfinder imagery was developed by Steinwand (1994) and is available on the world-wide-web at
This utility program is written in the C language, and is offered for distribution without support. Note that this implementation provides a one-to-one mapping between locations on Earth and locations in the map projection. It does not support cap extensions.
Because the Goode's projection has not been implemented in many GIS and image processing software packages, it is necessary to simulate the Goode's projection by projecting data into the Goode's Cartesian coordinate space using the Goode's component map projections. Data from each input coverage must first be partitioned into the component Goode's regions. The spatial extents of the Goode's regions are most easily defined in the geographic coordinate space.
A double precision, geographic coverage of the Goode's regions was generated in ARC using a polygon input file (Appendix 2). This file/coverage defines the geographic extents of each of the Goode's regions. Vertices in the resulting coverage are sparse, occurring only at the corners and intersections of the polygons defining the regions. The geographic Earth is partitioned into 14 regions instead of 12. The two extra regions are the portions of Region 1 and Region 2 that must be projected twice to produce the cap extensions.
Polygon topology was built for the generated coverage. Each polygon was assigned a 5-character label to store its Goode's region number. Most of the polygons were labeled with a 2-character region number. The code "01" was used for Goode's region 1, and so on. The leading "0" is added to the single digit region numbers to make it easier to select desired regions. The cap polygons were labeled with "01 02" (Figure 7). The resulting coverage is useful in this form as an overlay template for geographic coverages. If this coverage is to be reprojected for use with input coverages in other projections, it needs to be densified with vertices at least at every degree so that the Goode's boundaries show appropriate curvature in the required map projection.
Twelve projection files are provided (Appendix 3) that establish the MAPPROJECTION environments needed to project geographic features into each region's component map projection. The reader is cautioned that the Mollweide projection is not implemented with false eastings and false northings as part of the map projection parameters. Needed offsets are handled with the XSHIFT and YSHIFT subcommands for PROJECT. If the reader wishes to project from Mollweide back to another map projection, the signs on the XSHIFT and YSHIFT values must be reversed.
The following AML illustrates the procedure for projecting WORLDGOODES, a geographic coverage of the world, into the Goode's projection. WORLDGOODES was created by performing a polygon INTERSECT of a geographic coverage of the world with the geographic coverage of the Goode regions. For disk housekeeping convenience, the 12 projection files were stored in a subdirectory of the current workspace called "projections".
/* world mapextent in Goode's coordinates mapextent -20015500,-8673500,20015500,8673500 linecolor 1 &do i := 1 &to 12 /* loop through each of the regions &if %i% < 10 &then &setvar i := 0%i% /* pad with a leading 0, where necessary clearselect reselect WORLDGOODES poly region cn [quote %i%] mapprojection projections/dd.r%i% /* path to the 12 projection files polys WORLDGOODES mapprojection off &end /* end of do loop &returnPerforming a polygon INTERSECT partitioned the polygon features of the input coverage into Goode's regions, supporting polygon operations like POLYGONSHADES. The polygon INTERSECT had the side effect of adding undesirable lines at ±40° 44' 11.8", at the Equator, and at 180° in Region 2. This made the use of the POLYS command questionable because region boundary lines were plotted even though they were artificial (Figure 5 and Figure 8). This problem was addressed by establishing and using line topology. The input world coverage was built to line topology. It had a perimeter box around the world running at ±180° longitude and ±90° latitude. Because the perimeter box contributed unwanted lines to the output plot in the northeast Asia cap extension, the world coverage was edited and the perimeter box was deleted. A line INTERSECT was performed on the edited world coverage, using the polygon Goode's coverage to split world features into the Goode's regions and assign the Goode's region numbers to the line features. The Goode's region boundaries were not included in the resulting line coverage. This eliminated the offending boundary lines, but it also eliminated the lobe outline that provided closure to the Goode's projection.
A line coverage called GOODESLINES was developed from the polygon Goode's region coverage. GOODESLINES provides a source for the Goode's lobe boundaries. It was intended to be plotted with a world line coverage to provide closure to the Goode's lobes (Figure 3). The polygon Goode's region coverage was copied to a new coverage and edited to delete the internal horizontal lines at ±40° 44' 11.8" and 0°. The vertical line at 180°, north of 40° 44' 11.8" was also deleted. Goode's region number labels like those labeling the Goode's regions in the polygon coverage were assigned to the remaining line segments (Figure 9). Several of the lines were assigned two region numbers because those lines defined the lobe edges of adjacent Goode's regions. GOODESLINES then was densified so that there were vertices at least at every degree. The following AML illustrates the presentation of a geographic world coverage in the Goode's projection, omitting undesired internal Goode's boundary lines.
/* world mapextent in Goode's coordinates mapextent -20015500,-8673500,20015500,8673500 linecolor 1 &do i := 1 &to 12 /* loop through each of the regions &if %i% < 10 &then &setvar i := 0%i% /* pad with a leading 0, where necessary clearselect /* reselect world's arc features reselect WORLDGOODES arc region cn [quote %i%] /* reselect goodesline's arc features reselect GOODESLINES arc region cn [quote %i%] mapprojection projections/dd.r%i% /* path to the 12 projection files arcs WORLDGOODES arcs GOODESLINES mapprojection off &end /* end of do loop &returnPolygon topology was lost with the line INTERSECT operation, but polygon topology is often neither required nor desired when drawing vector data over imagery. Polygon shading usually is unwanted on imagery. When polygon shading is needed, the first AML can be modified to use the POLYGONSHADES and DROPLINE commands. Polygons will break at the Goode's region boundaries, but the polygon shading will hide this if the polygons are not outlined.
The generate file below, the projection files in Appendix 3, and export files of the polygon Goode's coverage and the densified GOODESLINES coverage are available through anonymous ftp. To retrieve these files:
%> ftp edcftp.cr.usgs.gov user> anonymous password> <please enter your email address> ftp> binary ftp> cd /pub/edcuser/lethcoe/goodes ftp> get support.tar.gz /* unix user ftp> get support.exe /* microsoft user ftp> quit
A generate file for the geographic Goode's region polygons
/* Please Note: Comment lines such as these are mixed /* with actual lines from the generate file. /* They are provided to more clearly identify /* each polygon. Reference Figure 7. /* If you want to use this listing without /* retrieving the file by anonymous ftp, /* DO NOT INCLUDE THESE COMMENTS! /* /* East Cap for Eurasia / Western North America /* REGION = "01 02" 1, -170.0000000, 70.0000000 -180.0000000, 50.0000000 -180.0000000, 90.0000000 -160.0000000, 90.0000000 -160.0000000, 50.0000000 end /* /* Northern North America /* REGION = "01 " 2, -100.0000000, 65.0000000 -180.0000000, 40.7366111 -180.0000000, 50.0000000 -160.0000000, 50.0000000 -160.0000000, 90.0000000 -180.0000000, 90.0000000 -50.0000000, 90.0000000 -50.0000000, 60.0000000 -40.0000000, 60.0000000 -40.0000000, 40.7366111 end /* /* East Cap for North America / West Cap for Eurasia /* REGION = "01 02" 3, -30.0000000, 75.0000000 -40.0000000, 60.0000000 -50.0000000, 60.0000000 -50.0000000, 90.0000000 -10.0000000, 90.0000000 -10.0000000, 60.0000000 end /* /* Northern Eurasia /* REGION = "02 " 4, 30.0000000, 65.0000000 -40.0000000, 40.7366111 -40.0000000, 60.0000000 -10.0000000, 60.0000000 -10.0000000, 90.0000000 180.0000000, 90.0000000 180.0000000, 40.7366111 end /* /* Southern North America /* REGION = "03 " 5, -100.0000000, 20.0000000 -180.0000000, 0.0000000 -180.0000000, 40.7366111 -40.0000000, 40.7366111 -40.0000000, 0.0000000 -100.0000000, 0.0000000 end /* /* North Africa / Southeast Asia /* REGION = "04 " 6, 30.0000000, 20.0000000 -40.0000000, 0.0000000 -40.0000000, 40.7366111 180.0000000, 40.7366111 180.0000000, 0.0000000 80.0000000, 0.0000000 -20.0000000, 0.0000000 end /* /* South Pacific /* REGION = "05 " 7, -160.0000000, -20.0000000 -180.0000000, -40.7366111 -180.0000000, 0.0000000 -100.0000000, 0.0000000 -100.0000000, -40.7366111 end /* /* South America /* REGION = "06 " 8, -60.0000000, -20.0000000 -100.0000000, -40.7366111 -100.0000000, 0.0000000 -40.0000000, 0.0000000 -20.0000000, 0.0000000 -20.0000000, -40.7366111 end /* /* Southern Africa /* REGION = "07 " 9, 20.0000000, -20.0000000 -20.0000000, -40.7366111 -20.0000000, 0.0000000 80.0000000, 0.0000000 80.0000000, -40.7366111 end /* /* Australia /* REGION = "08 " 10, 140.0000000, -20.0000000 80.0000000, -40.7366111 80.0000000, 0.0000000 180.0000000, 0.0000000 180.0000000, -40.7366111 end /* /* Western Antarctica /* REGION = "09 " 11, -160.0000000, -65.0000000 -180.0000000, -90.0000000 -180.0000000, -40.7366111 -100.0000000, -40.7366111 -100.0000000, -90.0000000 end /* /* South America / Antarctica /* REGION = "10 " 12, -60.0000000, -65.0000000 -100.0000000, -90.0000000 -100.0000000, -40.7366111 -20.0000000, -40.7366111 -20.0000000, -90.0000000 end /* /* Antarctica South of Africa /* REGION = "11 " 13, 20.0000000, -65.0000000 -20.0000000, -90.0000000 -20.0000000, -40.7366111 80.0000000, -40.7366111 80.0000000, -90.0000000 end /* /* Antarctica South of Australia /* REGION = "12 " 14, 140.0000000, -65.0000000 80.0000000, -90.0000000 80.0000000, -40.7366111 180.0000000, -40.7366111 180.0000000, -90.0000000 end end
Goode's component projection files
input projection GEOGRAPHIC units DD parameters output projection MOLLWEIDE units METERS spheroid SPHERE xshift -11119487.42847 yshift -336410.83237 parameters -100 00 00 end
input projection GEOGRAPHIC units DD parameters output projection MOLLWEIDE units METERS spheroid SPHERE xshift 3335846.22854 yshift -336410.83237 parameters 30 00 00 end
input projection GEOGRAPHIC units DD parameters output projection SINUSOIDAL units METERS parameters 6370997.0 -100 00 00 -11119487.42847 0.0 end
input projection GEOGRAPHIC units DD parameters output projection SINUSOIDAL units METERS parameters 6370997.0 30 00 00 3335846.22854 0.0 end
input projection GEOGRAPHIC units DD parameters output projection SINUSOIDAL units METERS parameters 6370997.0 -160 00 00 -17791179.88555 0.0 end
input projection GEOGRAPHIC units DD parameters output projection SINUSOIDAL units METERS parameters 6370997.0 -60 00 00 -6671692.45708 0.0 end
input projection GEOGRAPHIC units DD parameters output projection SINUSOIDAL units METERS parameters 6370997.0 20 00 00 2223897.48569 0.0 end
input projection GEOGRAPHIC units DD parameters output projection SINUSOIDAL units METERS parameters 6370997.0 140 00 00 15567282.39985 0.0 end
input projection GEOGRAPHIC units DD parameters output projection MOLLWEIDE units METERS spheroid SPHERE xshift -17791179.88555 yshift 336410.83237 parameters -160 00 00 end
input projection GEOGRAPHIC units DD parameters output projection MOLLWEIDE units METERS spheroid SPHERE xshift -6671692.45708 yshift 336410.83237 parameters -60 00 00 end
input projection GEOGRAPHIC units DD parameters output projection MOLLWEIDE units METERS spheroid SPHERE xshift 2223897.48569 yshift 336410.83237 parameters 20 00 00 end
input projection GEOGRAPHIC units DD parameters output projection MOLLWEIDE units METERS spheroid SPHERE xshift 15567282.39985 yshift 336410.83237 parameters 140 00 00 end
Espenshade, E.B. Jr., ed., 1995, Goode's world atlas (19th ed.): Chicago, Rand McNally, 372 p.
The international atlas, 1988: Chicago, Rand McNally, 222 p.
EROS Data Center
Sioux Falls, SD 57198