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Map Projections for Global and Continental Data Sets and An PEER.REVIEWED ARIICTE MapProjections for Global and Gontinental Data Setsand an Analysis of PixelDistortion Caused byReproiection DanielR. Steinwand,John A. Hutchinson,and John P. Snyder Abstract map projection where the North Pole is a point. In such a and data loss will occur at and With growing emphasis on global monitoring, research using cas-e,feature compression causedby changing projec- remotely sensed data and geographic information systems is near the pole. Data degradation but the larger the study area,the increasingly on large rcgions studied at small scales. tions is .rbt always severe, focused can be, These global change sfudies require the integration of data more significant the distortions were to selectmap proiections sets several sources that are reprojected to a common The goals of this study from sets of global, hemispheric, or continental map base. In small-area, large-scole studies the choice of a for use with data introduced (1) during the map projection has Little effect on data quality. In global extent and to identify distortions data to and from different projections,and change studies the effects of map projection properties on transformationof (2) of raster data. data quality are morc apparcnt, and the choice of projection during the reprojection is more significant. To aid compilers of global and continen- tal data sets, six equal-area projections were chosen: the in- MapProjection Ploperties and Classes terrupted Goode Homolosine, the interrupted Mollweide, thetht The distortion characteristicsof a map projection depend on Wagner IV, and the Wagner VII for globol maps; the Lambert its properties.There are severalschemes for classifyingmap Azimuthal Equal-Areafor hemispheremaps; and the Ob- proiectionsbased on their properties,but in this study, pro- Iated Equd-Area and the Lambert Azimuthal Equal-Areafor fections were classifiedas equidistant,conformal, or equal- continental mops. Distortions in small-scale maps caused by iuea, rcprojection, and the additional distortions incurred when re- All maps distort distances,because it is impossible to projecting raster images, were quantified and graphically de- perfectly portray the round Earth on a flat map. Equidistant picted. For raster images, the enors caused by the usual projections,such as the Azimuthal Equidistant, show dis- rcsampling methods (pixel brightness level interpolation) [ancescorrectly through one or two points, but most other werc rcsponsible for much of the additional error where the distancesare distorted (Figure 1). local resolution and scale change were the greatest. Conformal projectionsmanipulate distance distortion to preservelocal anglesor shapes,but not area-s'On a confor- Introduction mal map projection, a very small circle on the globe will not of the same size. The Data transformationand a suitable map projection are neces- project to a circle on the map, but proiections form a sary when registeringremotely senseddata to a map base. ihree most commonly used conformal For studies of small areasat large scale,raster data are often registeredto a topographic map baseusing, for example,the Universal TransverseMercator or Lambert Conformal Conic projections.Errors causedby reproiection are usually not sig- nificant becauseprojection propertieshave less effect on data quality than other factors for study areas that extend only Figure1. AzimuthalEqui- over a topographic quadrangle. distant,centered on the For large study areas,problems causedby map projec- SouthPole. Distances tion characteristicsmay arise that are not signifi.cantfor are showncorrectly smaller study areas.When severalsmall data setsmust be throughthe centerof the merged or large data setsreregistered to a common map projection. base,the distortion due to a map projection changemust be considered.For example, data may be in a projection that representsthe North Pole as a line and are reprojectedto a D.R. Steinwand and J.A. Hutchinson are with Hughes STX Corporation,EROS Data Center,U.S. GeologicalSurvey, Photogrammetric Engineering & Remote Sensing, Sioux Falls,SD 57198. Vol. 61, No. 12, December 1995, pp. 1487-1.497. I.P. Snyder is with the U.S. GeologicalSurvey, Reston,VA 0099-11 1 2/9 5I 61,1,2-1487$3.OO / O 22092. O 1995 American Society for Photogrammetry and Remote Sensing PE&RS PEER.REVIEWED ARIICTE Figure2. Conformalprojections: a smallcircle on the globeprojects to a circleon the map,but of differentsize. The Mercator,Lambert Conformal Conic, and Stereographic(l to r) form a math- ematicallyrelated family of conformalprojections. not necessarilytheir shape or distance,equal-area projections were chosen over conformal or equidistant.The best equal- areamap projection for a global or continental data set is the projection with the least distortion for the area and with the optimum parameters. The latter includes central latitude, longitude, and standard parallels or other constantsaffecting the specific distortion Dattern. fhere are strong indications that the optimum equal-area map projection of a given region will have a line of constant distortion following the limits of the region, a principle proven in the 19th century for conformal maps. When at- tempting to select a projection that most satisfactorilyap- proachesthis ideal for a given region, conflicting situations soon becomeapparent: Figure3. Equalarea projections: a smallcircle on the . For a world mao. the criteria for selection is subiective be- globeprojects to an ellipseon the map,but not of the cause the relative importance of land versus water portions, same size.The Albers Equal-Area Conic (l) and Lambeft of polar versus equatorial regions, and of straight pirallets AzimuthalEqual-Area (r) aretwo equal-areaprojections versus curved parallels affect the decision, as well as the amongthe manyin commonuse. overall appearance; . For continental regions, irregular iines of constant distortion that follow coastlines require complicated formulas and more uncommon projections:and mathematically related family: Mercator, Lambert Conformal o The choice of a map projection is determined by whether the Conic, and Stereographic(Figure 2). map of the region will be used independently or whether it Equal-areaprojections preserveareas and sizes,but not should fit maps of adjacent regions and, therefore, be on the same proiection as that of the larger region; anglesor shapes.A very small circle on the globe will gener- ally project to an ellipse on an equal-areaproiection, but the Equal-area world map proiections have been the subject of ellipse will have the same area as the circle. Just as a circle numerous papers; therefore, projection selection was based can be formed into many different-shaped(but equal-in-area) on these papers and on an evaluation of distortion. If land ellipses, so there are many equal-areaprojections, including and ocean data are not needed on the same maD. an inter- the Albers Equal-AreaConic and the Lambert Azimuthal rupted projection can be used to reduce distortion. In this Equal-Area(Figure 3). case, the interrupted Goode Homolosine or interrupted Moll- No projection can show distances,angles, and areasall weide are recommended. interruoted for land or water in correctly; this is only possible on a globe. Some proiections, standard formats (see Cover tmage). For uninterrupted world however, are neither equidistant, conformal, nor equal-area. maps, recommended projections are Wagner IV (same as Put- For example, the Robinson projection does not preservean- nins P2') or Wagner VII (same as Wagner-Hammer) (Plate 11. gles or areasbut achievesa better look. It avoids the shearing Equal-area hemispheric map projections need little de- near the poles characteristicof many equal-areaprojections, bate. If all parts of a hemisphere are to be given equal impor- without the excessivearea distortion of the conformal Merca- tance, the Lambert Azimuthal Equal-Area projection, tor (Figure4). centered on the center of the hemisphere desired, is ideal be- cause its circular lines of conslant distortion include a line ldentiflcationof Global and Continental Map Ptojections following the limit of the hemisphere [Plate 2). This study primarily involved raster data sets. Because the For maps of continents or oceans, the method of least analysis of raster data is based on the areas of image pixels, squares can be applied to determine a minimum-error projec- 1488 PE&RS PEER.REVIEWED ARIICIE Figure4. Projectionsneither conformal nor equal areaia smallcircle on the globeprojects to an ellipseof a differentshape and sizeon the map.The Robinson(l), PlateCarr6e (r)' andthe AzimuthalEquidistant (figure 1) havespecial properties that precludecorrect depiction of shapesand sizes. with center 48'N' ss'W' tion (within a given category) for the region. Snyder (1985J North America: Oblated Equal-Area shape constants m : 1.33, n - 2.27, rotation used this method for certain conformal map projections, and - 13.95" -or- has now been applied to the oblique the same principle Lambert with center 50"N, 100"W Equal-Area proiection (standard) and its Lambert Azimuthal South America: Lambert with center 15'S, 60"W (re- more general case, the Oblated Equal-Area projection EuroDe: Lambert with center 55"N' 2o"E cently developed) (Snyder, 198B). Africa: Lambert with center 5"N, 20"E Regions benefiting most lrom these proiections are circu- Asia: Lambert with center 45'N' 100"E lar (for the Lambert) and symmetrically oval or rectangular Australasia: Lambert with center 15"S, 135"E (for the Oblated). In principle,
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