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A graphical representation of all or a portion of the earth or a similarly vast environment. Until the advent of digital computing, this concise definition applied equally well to maps in general, all of which were visible arrangements of labels and graphic symbols. Most discussions of maps in a geographical context still refer to visual compositions, but widespread use of electronic storage often demands a distinction between the structured geographical information in an electronic database and the map images that might — or might not — be generated to display or analyse data. Although visual analysis is often desirable, some geographical information systems let the user measure and compare maps without looking at them.
All map images have three principal elements: scale, projection, and symbolization. scale is defined as the ratio of distance on the map to the corresponding distance on the ground. When recorded as a ratio or fraction, the scale expresses both distances in identical units of measurement, with the map distance reported first as one unit, as in 1:10,000 or 1/ 10,000, which means that a centimetre on the map represents 10,000 cm on the ground. (A dimensionless number, 1/10,000 also indicates that an inch on the map represents 10,000 inches on the ground.) Scale may be expressed verbally, as in \'one inch represents one mile\', which users might find more convenient than the equivalent ratio 1:63,360. Maps often include a graphical scale, on which a carefully measured line, commonly subdivided with appropriately labelled ticks, portrays one or more typical distances. Unlike ratio or verbal scales, a graphical scale remains true if the map is enlarged or reduced on a photocopier.
Fractional representations of scale afford a distinction between large scales, like 1/5,000, and small scales with much larger denominators. At scales of 1/250,000 or smaller, maps that compress huge territories onto small sheets or computer monitors incur a substantial loss of detail especially apparent in the simplification and smoothing of rivers and shorelines (Jenks, 1981). Generalization is particularly severe on page-size world maps with scales of 1/200,000,000 or less. By contrast, scales of 1/10,000 or more can accommodate a wider range of features as well as usefully detailed descriptions of irregular curves and complex patterns. In general, small-scale maps afford a broader geographic scope, whereas large-scale maps can provide a more realistic depiction of the landscape (Goodchild and Proctor, 1997). Whatever its scale, the map serves the geographer much like the microscope serves the biologist, albeit through reduction rather than enlargement.
Only on a globe is scale constant everywhere. Because fitting a curved surface onto a flat map requires stretching or compressing some parts of the globe more than others, scale typically varies with direction as well as from point to point. These distortions are usually negligible on large-scale maps because the stretching required to represent a small city or neighbourhood is far less troublesome than distortions caused by map generalization or the paper\'s sensitivity to moisture. Not so for small-scale maps of continents and other vast areas. Because of substantial geographical variation in stretching — some maps even stretch the poles into lines as long as the equator — world maps typically omit graphic scales, which invite misleading estimates of distance. And a ratio scale, if included, refers only to so-called standard lines, at which a hypothetical globe with the stated scale intersects the plane, cylinder or cone onto which the map\'s projection transfers coastlines, boundaries and other features.
Map projection is easily understood as a two-stage computational process. In the first stage, the planet is reduced to a globe, which establishes the map\'s scale. In the second stage, an algorithm transfers meridians, parallels and other geographical features onto a simple geometric surface that is either flat or easily flattened by cutting. A plane, cylinder or cone avoids needless mathematical complexity yet affords flexibility in positioning the projection\'s standard lines, where the surface meets the globe and around which distortion is comparatively low. Conic projections are particularly suitable for mid-latitude continents like Europe or Australia, for which a single carefully chosen standard parallel can limit overall distortion. Even so, a secant cone, which intersects the globe along two standard parallels, can control distortion more than a tangent cone, which merely touches the globe along a single parallel. For polar regions, the plane provides a realistic view on which meridians converge at the pole, whereas for regions that straddle the equator, like Africa and south Asia, the cylinder affords a secant projection with standard parallels equidistant from the equator. A cylinder secant at 10° N and S, for instance, positions features in Africa closer to a standard line, on average, than would a cylinder tangent at the equator.
Cylindrical projections centred on the equator are widely used for world maps. The simplest cylindrical projection is the plane chart, also called the equirectangular projection, on which evenly spaced straight-line meridians intersect evenly spaced straight-line parallels. North-south scale is constant throughout the map but east-west scale escalates to infinity at the poles, where area and shape are severely distorted. In 1772, mathematician J.H. Lambert proposed a cylindrical equivalent (equal-area) projection, which compensates for the poleward exaggeration of area with ever greater reductions in north-south scale (Snyder, 1993, pp. 85-7). Lambert\'s solution eliminated areal distortion at the expense of more pronounced east-west stretching in polar regions. Although secant cylindrical projections can achieve equivalence of area with mid-latitude belts of low distortion, these solutions incur marked north-south stretching near the equator. A typical example is the rectangular equal-area projection secant at 45°, devised by Scottish minister James Gall in 1855. In the late 1960s, German historian Arno Peters proposed an identical projection as the first world map to eliminate areal distortions that diminished the apparent importance of developing nations (Vujakovic, 1989; Crampton, 1994).
Another mathematical modification of cylindrical projection attacked the plane chart\'s poleward distortion of angles and small shapes. In 1599, English mathematician Edward Wright described an equatorially centred cylindrical projection that kept scale constant in all directions at a point — cartographers call this property conformality — and rendered true angles at all points. Wright\'s name is rarely mentioned because he merely worked out the mathematics for a projection introduced less rigorously thirty years earlier by the famed atlas publisher Gerardus Mercator (Snyder, 1993, pp. 43-9). Although seldom appreciated for its wide use in large-scale topographic mapping, the Mercator projection gained deep respect among mariners. Because straight lines on the Mercator represent lines of constant geographical direction, also called rhumb lines or loxodromes, a navigator need only plot a course\'s origin and destination, connect the points with a straight line, and measure the angle between the line and a meridian to find the bearing. This benefit has a cost: in achieving conformality, the projection incurs an outrageous poleward distortion of area. But because sailing ships rarely ventured into polar latitudes, map-makers truncated the Mercator world map in northern Greenland and just south of the Shetland Islands, and conveniently ignored the absurdity of poles located at infinity.
Another solution to the areal distortion of the plane chart is the pseudocylindrical projection, so called because its meridians bend inward to compensate for areal exaggeration near the poles (Maling, 1968). This strategy, it turns out, is older than Lambert\'s clever rearrangement of parallels: in 1570 the mariner Jehan Cossin of Dieppe produced a world map on the sinusoidal projection, characterized by equidistant straight-line parallels and evenly spaced curved meridians (Snyder, 1993, p. 50). In 1805, Karl Mollweide introduced the pseudocylindrical projection that bears his name. With unevenly spaced parallels and semi-elliptical meridians, the Mollweide projection provides a more pleasing equivalent world map than the sinusoidal projection, on which rapidly converging meridians greatly distort shape near the poles. In addition to a standard line at the equator, the sinusoidal and Mollweide projections have low distortion along the central meridian, which remains a straight line. Even so, these projections severely distort shape and angles at places well removed from both the equator and the central meridian.
The compromises and trade-offs of map projection are readily apparent in interrupted projections, which split the world into lobes that meet along the equator (Dahlberg, 1962). By interrupting over water, these composite equal-area projections lessen the distortion of continents and provide a whole-world base map especially useful for phenomena occurring on land. An exemplar is the homolosine equal-area projection of J. Paul Goode (1925), who centred northern lobes on North America and Eurasia, and southern lobes on the South Pacific Ocean, South America, Africa and Australia. To further limit distortion of shape and angles over land, Goode established standard parallels at 40°44′11.8″N and S, where he further conserved shape by dividing each lobe into an equatorial zone represented with a sinusoidal projection and a polar zone with a Mollweide. Although the resulting land-biased map is poor for portraying ocean currents and shipping routes, Goode demonstrated the versatility of composite projections with an oceanic variant, interrupted over land to conserve the continuity of continents.
In a further demonstration of the flexibility of map projection, Arthur Robinson (1974) devised a non-interrupted pseudocylindrical projection that lessened the maximum amount of angular shear as well as the apparent distortion of continental areas. His projection is neither conformal nor equivalent. Using an iterative trial-and-error approach informed by computer plots and measurements of areal and angular distortion, he adjusted the projection\'s parameters to make the world \'look right\'. In 1988, the National Geographic Society adopted the Robinson projection for its physical and political maps of the world. Although the Society\'s projection is a Euro-centric version centred on the Greenwich meridian, useful variations of the Robinson projection can be centred on East Asia or the Americas.
By relieving the numerical drudgery that impeded the use of customized map projections, computer-assisted cartography helps map authors tailor a map\'s perspective to a specific distribution or part of the world (Robinson and Snyder, 1991). In addition to balancing distortions of angles, area, distance, direction and the gross shape of continents, software users can centre projections on areas of interest and compose maps that engage as well as communicate. Software can also assist in the development of area cartograms, which provide base maps focused on population size, wealth or economic clout rather than land area (Dent, 1996, pp. 202-16).
symbolization, the third element of all maps, refers to the graphic codes — pictorial, geometric or verbal — used to portray geographic features and spatial phenomena. Non-verbal symbols rely on one or more visual variables to communicate differences in kind or degree. Jacques Bertin (1983) defined six retinal variables: shape, pattern, hue, orientation, size and graytone value. Of these, shape, hue and pattern are most appropriate for showing qualitative differences; size and value are most suited to quantitative differences; and orientation (as apparent in arrows and isolines) is ideal for showing direction. A mismatch between the data and the retinal variable, such as widely varied hues to show differences in rate or density, can be inefficient if not misleading (Monmonier, 1996, pp. 19-24). Map authors can also misrepresent quantitative data by ignoring the logical links between intensity data (for example, population density, median income and rates of growth) and graytone symbols, as on choropleth maps, and between count data (for example, number of people, total payroll and amount of increase) and magnitude symbols like graduated circles.
Some map symbols demand a specific kind of projection. A world map of climatic regions, for instance, needs an equivalent projection, which more accurately shows the relative areas of various climatic regions, whereas a world map of weather or individual climatic elements benefits from a conformal projection, which preserves the angles that meridians and isobars make with winds and ocean currents. Similarly, an equivalent projection is essential if a dot-distribution map, on which each dot represents a specified number of people, dairy cattle or tornadoes, is to show worldwide or regional variation in density.
Classifications based on dimensionality and conventional practices do not readily accommodate image maps ranging from black-and-white aerial photographs to colour-infrared satellite imagery (cf. remote sensing). Distinguished from traditional \'cartographic line maps\' by their photo-like tonal variations, these high-altitude portraits of land, oceans and atmosphere reflect nearly a century of progress in optics, aeronautics and electronic image processing. Image maps acquire the trappings of conventional maps through the addition of labels, a grid, coastlines and other cartographic symbols as well as through the removal of geometric distortions characteristic of aerial cameras and orbiting scanners. Orthophotomaps and orthophotoquadrangle maps — geometrically accurate photomaps that capture subtle but significant features like paths and vegetation boundaries — have become a valuable complement to the traditional topographic map (Thrower and Jensen, 1976).
Image maps are but one of many new cartographic forms. Dynamic maps that incorporate time and motion as visual variables provide animated descriptions of spatial processes, and interactive maps afford point-and-click access to highly customized maps, complementary graphs and diagrams, detailed explanations of data and even the map-maker\'s raw data, heretofore available largely to other insiders. Especially promising are maps adapted to colour-impaired users (Olson and Brewer, 1997). No longer must all users settle for a single static map.
In addition to radically changing the nature of graphic maps, cartography\'s digital transition promises to alter fundamentally the relationship between map-maker and map user (Monmonier, 1985). Because of inexpensive personal computers, innovations originally intended only for map-makers are commonplace. And because of the Internet and its worldwide computer-oriented telecommunications network, map users can acquire map images, software and data from a rich variety of institutions and individuals, radical as well as traditional (Peterson, 1997). Despite these promising solutions, the new electronic cartography cannot escape contentious policy issues of public access, privacy, intellectual property and liability (Onsrud and Rushton, 1995).
Equally persistent is the notion that maps are rhetorical communications, readily adapted to the map-maker\'s agenda and customarily accorded respect, if not awe, by users ill-equipped to question motives or authority (Monmonier, 1996). As a graphic representation, the map acquires persuasiveness from the crispness of its lines, the implied precision of grid and scale, and the self-proclaimed accuracy of basic information the user already knows, or presumes to know. Users who understand the constraints of cartographic generalization and the opportunities for manipulation will approach with caution a map\'s silences as well as its facts: the history of cartography is rich in examples of maps that reify the territorial assertions of map authors who deliberately suppressed or conveniently ignored competing claims (Harley, 1988; Black, 1998). While electronic cartography seems likely to intensify, not lessen, the use of maps as propaganda, the new media afford broader opportunities for interrogating data and exploring alternative views. (MM)
References Bertin, J. 1983: Semiology of graphics: diagrams, networks, maps, trans. W.J. Berg. Madison: University of Wisconsin Press. Black, J. 1998: Maps and politics. London: Reaktion Books. Crampton, J. 1994: Cartography\'s defining moment: the Peters projection controversy, 1974-1990. Cartographica 31(4): 16-32. Dahlberg, R.E. 1962: Evolution of interrupted map projections. International Yearbook of Cartography 2: 36-53. Dent, B.D. 1996: Cartography: thematic map design, 4th edn. Dubuque, Iowa: William C. Brown. Goodchild, M.F. and Proctor, J. 1997: Scale in a digital world. Geographical and Environmental Modelling 1: 5-23. Goode, J.P. 1925: The homolosine projection: a new device for portraying the earth\'s surface entire. Annals of the Association of American Geographers 15: 119-25. Harley, J.B. 1988: Silences and secrecy: the hidden agenda of cartography in early modern Europe. Imago Mundi 40: 57-76. Jenks, G.F. 1981: Lines, computers, and human frailties. Annals of the Association of American Geographers 71: 1-10. Maling, D.H. 1968: The terminology of map projections. International Yearbook of Cartography 8: 11-64. Monmonier, M. 1985: Technological transition in cartography. Madison, Wisc.: University of Wisconsin Press. Monmonier, M. 1996: How to lie with maps, 2nd edn. Chicago: University of Chicago Press. Olson, J.M. and Brewer, C.A. 1997: An evaluation of color selections to accommodate map users with color-vision impairments. Annals of the Association of American Geographers 87: 103-34. Onsrud, H.J. and Rushton, G., eds, 1995: Sharing geographic information. New Brunswick, NJ: Rutgers University Press. Peterson, M.P. 1997: Cartography and the Internet: introduction and research agenda. Cartographic Perspectives 26: 3-12. Robinson, A.H. 1974: A new map projection: its development and characteristics. International Yearbook of Cartography 14: 145-55. Robinson, A.H. and Snyder, J.P., eds, 1991: Matching the map projection to the need. Rockville, MD: American Congress on Surveying and Mapping. Snyder, J.P. 1993: Flattening the earth: two thousand years of map projections. Chicago: University of Chicago Press. Thrower, N.J.W. and Jensen, J.R. 1976: The orthophoto and orthophotomap: characteristics, development and application. The American Cartographer 3: 39-56. Vujakovic, P. 1989: Mapping for world development. Geography 74: 97-105.
Suggested Reading Hall, S.S. 1992: Mapping the next millennium. New York: Random House. Keates, J.S. 1996: Understanding maps, 2nd edn. London: Longman. MacEachren, A.M. 1995: How maps work: representation, visualization, and design. New York: Guilford Press. Monmonier, M. 1993: Mapping it out: expository cartography for the humanities and social sciences. Chicago: University of Chicago Press. Robinson, A.H. et al. 1995: Elements of cartography, 6th edn. New York: John Wiley and Sons. |
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