The Earth's topography is a prime example of the last restriction. Customary methods for viewing terrain do not simultaneously provide broad coverage and accurate detail. The Earth's surface cannot be seen at 1:1 scale in its entirety and all at once, but only in many small areas visited sequentially in the field. Spatial continuity and context can be obtained only at greatly reduced scales: on contour maps and photographs or on radar images, or -often obscured by vegetation, cultural features, and clouds- at even smaller scales on satellite images.
Topography, essential to much geologic analysis, contains embedded clues to solving many problems, particularly those of regional tectonics and geomorphology. Although geologists increasingly depend upon research tools invisible to the unaided eye, for example, radiometric ages and magnetic-field reversals, the study of such familiar macroscopic features as the Earth's landforms still contributes vitally to answering geologic questions. Computer visualization by relief-shading thus far is the easiest way to obtain both the large-area (synoptic) context, so effective for interpreting surface features, and the accurate detail required to ensure geologic significance (Batson and others, 1975; Pike, 1991).
Recent advances in computer technology -fast machines, spatial-analysis software, mass-produced elevation data, and graphic input/output devices -have converged to extend the visualization of landform detail to large areas (Burrough, 1987; Kennie and McLaren, 1988). Much of the information encoded in topography can now be extracted by the image-processing of digital elevation models (DEM's), large high-density X,Y-gridded arrays of terrain heights. This chapter briefly revi ews the synoptic mapping of topographic relief, provides a key to the literature, and illustrates the discussion with computer- shaded relief images made in recent work by the U.S. Geological Survey at several scales.
Two artistic approaches have been particularly effective. Pictorial relief symbolizes morphology by repeated line sketches of discrete and stylized terrain types. It was most fully developed in the 50 landform classes of Raisz (1931). Shaded relief, or an alytical hill-shading, shows topography by the intensity of shadows cast from a light source (Imhof, 1965). First drafted by pencil, pen, or brush, it has been executed by airbrush, dark-plate, and photography of raised-relief models. However, topographic detail at a esolution useful for geologic interpretation is much too complex to be mapped both accurately and economically over large areas by either manual approach.
The processing of digitized elevations by computer has revolutionized the art of landform representation by mechanizing, if not yet fully automating, the hill-shading technique. The resulting image -an accurate physiographic panorama, usually in vertical perspective -can be computed much more rapidly from stored files of elevations than pictorial- relief drawings can be prepared by a skilled artist from contour maps or photographs of the same area.
Digitally shaded relief maps resemble cloud-free aerial photographs but actually are matrices of small, gray squares (Yoeli, 1965). Each square, or picture element (pixel), represents a theoretical reflected-light intensity computed from a relation between ground-slope angle and direction, Sun position, and location of the observer (figs. 1 and 2). The lightest and darkest tones in the image show the steepest areas; intermediate gray tones are gentle terrain. The inverse process, termed photoclinometry, extracts topographic form from a shaded image (Horn and Brooks, 1989).
The relief-shading of fine detail was impractical for large areas until Yoeli (1965) developed a modern analytical version for DEM's and adapted it to computer processing (Yoeli, 1967). Batson and others (1975) made the first economical application to large matrices of elevations. Relief-shading has since proven equally effective in portraying gravity, aeromagnetic, geoid, and other geophysical information (Arvidson and others, 1982). The approach is fully applicable to sea-floor bathymetry and extraterrestrial surfaces.
The equivalence of one pixel to one elevation yields great efficiency in computation because the locations in an X,Y array are implicit rather than individually stored and addressed. The resulting economy is twofold. Elevation and its derivatives can be mapped rapidly over large areas, and existing image-processing algorithms can be used (Arvidson and others, 1982; Thelin and Pike, 1991). Thus, large raster files of shaded relief, slope angle, and other measures of surface form are easily calculated for screen display, hard-copy output, and storage for further analysis of topography -such as registration with similarly gridded nontopographic data (Moore and Mark, 1986; Burrough, 1987; Pike and Thelin, 1989).
The technique of relief-shading maps topographic form according to variations in the mathematically determined intensity of reflected light I at each elevation located on the ground in an X,Y grid (fig. 2). This relation, thephotometric function, has many variants (Brassel, 1974; Batson and others, 1975; Horn, 1981). The simplest case is the cosine law of Lambert:
I = kd cos(i),
where i is the angle between incident light (the Sun) and a vector normal to the sloping ground, and kd is a coefficient describing reflectivity of the surface material (here, a perfect diffuser of incident light; Greenberg, 1989). The position of the viewer is (usually) directly overhead; the simulated Sun is typically placed 20o to 30o above a western to northwestern horizon. Ground slope and its facing azimuth are estimated from a DEM in various ways, using two to eight points surrounding each pixel ( fig. 3; Mark and Aitken, 1990). Repeating these calculations pixel-by-pixel over a large DEM yields a reflectance map, a continuous X,Y array of brightness values (Horn, 1981).
Some ambient light, which strikes and reflects from a surface equally in all directions, often is added to improve the appearance of the final image (Greenberg, 1989). Shadows cast by steep terrain can be incorporated into the calculation, and even atmospheric effects can be simulated (Brassel, 1974). The advanced computer graphics used in industry to digitally depict virtually any object with photorealistic quality (Whitted, 1982; Greenberg, 1989) can also be adapted to shaded-relief portrayal (Kennie and McLaren, 1988).
Attractiveness of the final map depends on several factors. The optimum scale for a shaded-relief graphic is the largest consistent with visual merging of pixels into a continuous surface. Resolution (the length of a pixel edge) of the new United States map ( fig. 4; Thelin and Pike, 1991), for example, is 0.23 millimeters (mm), essentially the value initially proposed by Yoeli (1965). Conventional (paper-map) plotters do not create the most pleasing output. The best images are obtained by reading the brightness values into a film recorder/scanner and making a photographic negative in 255 gray tones.
The new United States map ( fig. 4) exemplifies current practice in assembling a synoptic data set. The elevations came from digitized contours, spot heights, and stream and ridge lines read from 1:250,000-scale topographic sheets (by the U.S. Army). Digitizing the maps by semiautomated methods at 0.01 inches (0.25 mm) resolution, 3 arc-seconds or about 200 ft (63 m) on the ground, accounted for 1/6 of the approximately two billion elevations. The remaining 5/6 were interpolated between digitized contours by computer. This large DEM was thinned down (Godson, 1981) to a more easily manipulated file of 12 million elevations spaced 30 arc-seconds apart, nominally 0.8 km on the ground.
No machine-compiled DEM is wholly free of error (Batson and others, 1975; Acevedo, 1991), although the accuracy of mass-produced data is improving. DEM errors, most of them systematic, appear as flaws in shaded-relief maps (less evident at small scales shown here). Star-burst patterns and rectilinear and stair-step textures arise from inaccurate interpolation between contours, the result of suboptimal gridding algorithms and a contour interval too coarse for the terrain. Widely spaced N-S and E-W lines mark the edges of imperfectly mosaicked DEM subquadrangles. The inaccuracies inherent in stereo-profiling characteristically show up in the images as fine parallel stripes.
Digital image-processing excels as a screening device for DEM quality. Errors in the data can be located from both statistical analysis of the elevations (Pike and Thelin, 1989) and visual identification of obviously false patterns in an image (Acevedo, 1991; Thelin and Pike, 1991). The most visible nonsystematic artifacts in a map can be repaired by editing flawed portions of the DEM and changing elevations pixel-by-pixel. Systematic errors, however, are virtually impossible to eliminate. To retain maximum local detail in an image, it is usually unwise to change elevations globally, by digitally filtering the entire DEM, although such filters may remove the worst errors that are spaced at constant intervals (Pan, 1989).
Detailed images of topographic form have now been computed for areas of even continental extent. The 1:3,500,000-scale shaded-relief map of the conterminous United States ( fig. 4; Thelin and Pike, 1991) is the largest single-sheet graphic of relief for this area since the hand- drawn, high-oblique map by Raisz (1939). More topographic information is evident in the new digital image than could, in all practicality, be included in synoptic portrayals of the Nation's terrain at so fine a resolution by any manual technique; the map represents one point every 3 mm on each of over 450 1:250,000-scale topographic sheets. Some of the detail simply reflects the map's large size (140 cm by 90 cm), but much of it derives from the comparatively high density of the DEM (essentially the data set of Godson, 1981) and the computer's ability to rapidly process so much information.
The new shaded-relief map of Italy takes synoptic imaging of topography a step further ( fig. 5 ; only Sicily is shown). At a 1:1,200,000 scale and a pixel size of only 0.19 mm, it is the most detailed map of an entire nation state yet calculated by digital relief-shading (Reichenbach and others, 1992). Ground resolution (230 m) is 3.5m~ that of the United States map (800 m) and twice that of the map of Sweden (500 m). The 5,886m~4,546-pixel array was so large that a 32-bit Unix graphics workstation was required to process it. The new data set, an 8-million-point digital- elevation model of all Italy was assembled from 280 1:100,000-scale blocks of terrain heights digitized from 1:25,000-scale contour maps for the Italian Geological Service.
Submarine morphology can be visualized, and information about it communicated, by computer images in much the same way as subaerial topography ( fig. 6). However, detail has been limited by the low 5-arc-minute resolution of the current world-wide data set (Moore and Mark, 1986; Simkin and others, 1989). A relief-shaded image made from a new digital depth model (DDM) provides a fresh view of regional tectonism and geomorphology for the entire Mediterranean seabed (Mark and others, 1991). Figure 6 is the most detailed synoptic portrait of the area to date -its only precursors are two relief panoramas painted by artists in 1968 and 1982. The 1-km-resolution DDM of some 3 million values was created by digitizing contours on 1:1,000,000-scale bathymetric charts (in Europe) and then gridding the contours at USGS. The technique is equally applicable to the larger scale bathymetry gathered in the Exclusive Economic Zone of the United States and other areas. The synoptic capabilities of the relief-shading technique truly become evident when large subaerial and submarine data sets are combined. The 230-m-resolution DEM of Italy ( fig. 5, Sicily only) was resampled at 1 km (by Robert Mark) and added to the 1-km DDM of the neighboring sea floor ( fig. 6). The shaded-relief map computed from the combined data ( fig. 7) shows the entire Tyrrhenian Sea region -bounded by Italy, Sicily, Corsica, and Sardinia -in one view of submarine and land surfaces together, under identical conditions, and without the distraction of a coastline. Discontinuous alignments of onshore and sea-floor relief elements are among the features of possible tectonic significance revealed in this image.
A digitally sampled surface that can be expressed perceptually, by relief-shading, can also be represented parametrically, by a suite of measures calculated from the same DEM (Pike and Thelin, 1989). Computer maps of slope angle, local relief, and other d erivatives of elevation can then be combined statistically to identify distinctive topographic units and rapidly classify entire regions (Pike and Acevedo, 1988; Reichenbach and others, 1992). For example, the surface morphology of the large San Jose, Cal if., 1:100,000-scale quadrangle ( fig. 8) has been mapped from a new DEM, the first of a USGS series that will supplant the less accurate 1:250,000-scale DEM's (Acevedo, 1991). The resulting suite of some 20 digital images, which contain many fewer flaws than similar maps made from the older DEM, supports a regional geologic analysis of the San Jose area (Pike and others, 1992). Such derivative maps, made for the single quadrangle shown here in shaded relief, can be generated for even larger DEM's comprising several mosaicked quadrangles (Pike and Acevedo, 1988; Mark and Aitken, 1990).
A property unique to digital relief-shading is the ease with which Sun position can be varied to obtain contrasting views of the same area (Moore and Simpson, 1982). This flexibility enables landforms to be studied under lighting conditions that never occur in nature, such as a north-facing Sun, and thus permits otherwise unavailable information to be obtained on a particular feature or piece of topography. Figure 9 shows how differently a small sample area can appear to the eye under eight different Sun azimuths (Sun elevation was held constant at 30 degrees). Such multiple representations of topographic detail can be computed just as readily for images that cover much more area.
Synoptic images of relief are widely applicable tools for interpreting topography, but they are particularly germane to structural geology, tectonics, and geomorphology (Moore and Simpson, 1982; Moore and Mark, 1986; Pike and Thelin, 1989; Pike, 1991). Surface features in digital relief may be examined by all the standard techniques of photointerpretation (stereoscopic pairs can be created; Batson and others, 1975). The images also provide an excellent cartographic base for mapping cultural and earth-science information at any scale commensurate with resolution of the source DEM: local (Mark and Aitken, 1990) to global (Simkin and others, 1989).
Further advances in topographic visualization are assured as more demanding applications of computer-relief images are explored. For example, shaded relief and other derivatives of large DEM's can be combined with different types of spatially based data, using geographic information systems technology, for examining such complex natural processes as the movement of air masses and the hydrologic response of large fluvial systems.
Progress depends upon better topographic coverage of larger areas. The new digital chart of the world, which includes all the 1,000-foot contours on 270 1:1,000,000-scale maps and is available on CD-ROM (Danko, 1991), only begins to satisfy this demand. The growing need to model physical systems both globally and in detail indicates that Earth's surface should be visualized from truly high-quality DEM's. Such systematic measurements may eventually be forthcoming from a satellite mission fully dedicated to terrain mapping (Committee on Global Change, 1990, p. 137).
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