Cartographic Terrain Depiction Methods

The simple rounded dome shape which resembles a mole hill was the most common early cartographic form of a mountain (Figure 3a).These simple shapes were often arranged, even in the earliest maps in row or chains, and often aligned with the axis of the row (Figure 3b). In poor copies of these maps rows of mountain symbols became bands and ridges (Figure 3c). The row arrangement in Figure 3b went out of use during the 15th century and the instead of the symbols having varied orientations they all began to line up with the line of sight of the viewer (Figure 3d). Groupings of the symbols were created following the upright rows of symbols and are described as the fish scale representation (Figure 3e). Further modifications included outlines of cone-shaped, and craggy pointed mountains which became differentiated by size. Shadowing was suggested with lines and the imaginary light source was usually from the left (Figure 3f).

In the 16th century demands on the cartographer increased with the spiritual and intellectual awakening of the Renaissance. Topographic survey methods were evolving to include the compass, measuring chain and measuring cart which provided more accurate metrics for the production of maps. Artists and scientists also became more interested in the natural world and produced maps such as Figure 4 by Leonardo da Vinci. About 50 years later cartographers developed more natural symbology for mountains following da Vinci's example (Figure 5). The previously flattened landscape with isolated mountain symbols gave way to a continuous terrain of differentiated graphical symbology. Forests and fields supported the oblique view of continuous terrain and three dimensionality was achieved through slope lines and the use of shadow hachures.

Another technological development of the 16th century provided finer, smoother and denser lines. The earliest printed maps were produced using the woodcut, but the technique of copper engraving allowed for an increase of topographic content and the character of maps were changed due to the technique. Unfortunately the increases in content were often accompanied by a reduction in drawing skill.

Continued developments in survey techniques during the 17th and 18th century prompted further advancements in cartographic presentation. It was an uneven development as both the technological and artist aspects moved along in separate irregular paths. A noteworthy example of the heights to which the technological and artistic aspects of cartography could attain are the maps by Hans Conrad Gyger during the mid 17th century. See Figure 6. Gyger combined detailed, accurate surveying with a presentation in plan view. The entire map, of which Figure 6 is a small portion, was nearly 5 meters square, naturally colored, and shows excellent 3 dimensional realism. This is the earliest relief map in existence but it did not have an effect on the cartography of the time because it was hidden away as a military secret

Only in the 18th century did real advances such as those seen in Gyger's map begin to appear. France was the leader in cartography with the first modern national triangulation completed in 1774 by Cassini and the advances in geodetic survey and calculation an copper engraving were evident in the maps produced by Cassini and his son. Although the precise planimetric nature of the details could have contributed to advancements in terrain representation the Cassini maps did not. During the 18th century a wide range of cartographic developments coexisted. The transition to a planimetric view took place near the turn of the century. See Figure 7. Although maps were now being created with a planimetric view there was still no means for cartographers of the time to actually see what mountains looked like from above. The restriction imposed by copper engraving still was limiting the drawings essentially to line work in one color. Areas of slope were depicted hachures with the level areas left blank. Hachures were drawn with the rule that the greater the slope and ruggedness, the denser and darker were the hachures (Figure 7). Frederick the Great was quoted as instructing his Prussian military topographers, "Wherever I can't go, let there be a blot". This approach was carried to such an extreme that the convention "the steeper, the thicker and darker the pattern of hachuring" replaced the realistic three dimensional typical style of Gyger (Figure 6

In 1799 the Saxon military topographer, Johann Georg Lehmann, developed a system called slope hachuring. See Figure 8. Hachure lines are drawn in the direction of slope with the hachures broken into nearly even sections. The hachure were arranged so that their end points began and ended on what were assumed to be contour lines with regular vertical intervals. Flatter terrain were drawn with longer hachures and steeper slopes with shorter. The angle of the slope determined the thickness of the hachures. Steep slopes had heavier hachures and gentle slopes had finer. This system allowed for easy identification of the direction of slope and the change from ground level to steep slope and cartographers could produce the hachures in an objective and consistent manner. Slope hachuring became the most means of showing terrain through the 19th century up until the middle of the 20th century.

Meanwhile, in France, Switzerland and a bit in Italy hachuring was also developed but with a tendency towards the use of "left illumination". Heavier hachures were drawn on the shaded slopes and finer hachures were drawn on the illuminated sides. Building upon this was the combination of using Lehmann's arrangements of hachure lines with the three dimensional effect provided by the "left illumination" method. The result is called shadow hachure. The Dufour map seen in Figure 9 is the "finest and clearest map of any high mountain region to have appeared in the last century." This method was in use until the middle of the 20th century for many national and private maps

While the debate over the relative merits of the two methods of hachuring were being debated a new method emerged which would come to dominate the depiction of terrain. The new method was the use of contours and depth contours or isobaths. Contours have the immense advantage over other methods of terrain depiction because they record and convey the geometric form of the terrain including elevations and the angles and directions of slopes. The earliest example of isobaths, or depth contours, was by Pieter Buuinss in 1584. Contours were known and used, mainly in the form of isobaths, while hachure techniques were being developed and used. Contour maps of the land surface had to wait until advances in survey techniques provided the detail required for the production of these maps.

During the past 100 years the demands for content and accuracy have increased until the classical survey methods became inadequate. Photogrammetric methods were developed and these provided the increase in speed and accuracy required for contour maps. These methods have also evolved to make use of satellite imagery as the source of information about the land surface.

Even before these advances, the development of lithography in 1796 and its application to printing maps in 1826 changed the appearance of maps. Multicolored maps were now possible. First hachures were changed to brown while other elements such as contours or different land surfaces could be printed in various colors. Hachures evolved into shading tones, or shadows and areas could now be printed in continuous color. During the latter part of the 19th century maps appeared using regional area coloring as hypsometric tints and naturalistic and symbolic landscape tints.Advances of the recent past 100 years are familiar to us in the form of multicolored maps, standardized use of contours for topographic map series, and hill shaded effects. The older method of hachures has essentially disappeared. Those methods currently in use for the depiction of terrain will be explored in more detail in the following sections.

Contour lines are imaginary lines which represent the intersections that arise from horizontally slicing up landforms into equal vertical intervals like a layer cake. Figure 10. Imhof defines them as, "... lines on the map depicting the metric locations of points on the earth's surface at the same elevation above sea level." Contour lines are measured up from a base datum, usually sea level and the lines measured down from the datum are called depth contours or isobaths. Few contour lines exist in nature with the exception of shorelines and a few man made features. See Figure 10.

The height difference between contours is called the contour interval. In the simplest system there is a single value assigned to the contour interval. The choice of contour interval depends upon several factors. First, the accuracy and completeness of the landform data must be determined. The smallest possible value for the contour interval is determined by the steepest slope to be represented and the fact that individual contours must be easily distinguishable on the map. This value may prove completely unsuitable when a single map or map series covers very different terrain types. Finally the purpose of the map must be determined. Small scale regional maps will have a larger contour interval, and will be less accurate, and very large scale maps used for engineering and planning will have a very small contour interval, and be very accurate.

When a map or map series covers a region of varying terrain relief the choice of contour interval becomes more difficult. Robinson (1995) uses the example of a 1:24,000 map series for the US. A 40 foot contour interval would be appropriate for areas of high relief such as in the western. The same contour interval would obliterate most of the detail in an area of low slope such as Florida where the maximum elevation is only 345 feet. In these cases intermediate, or supplementary contours are used. These contours are a simple fraction of the contour interval are portrayed as dotted or screened lines.

Various attempts have been made to draw contours in such a way that they appear three dimensional since 1870. In 1951 Kitiro Tanaka expanded the principals of construction and ever since his process has been known as the Tanaka method (Imhof, 1982). See Figurs 12 and 13.

Lines that divide up terrain are called skeletal lines (Imhof), structure lines (Weibel), or break lines (ESRI). These lines divide up watersheds, show drainage networks, ridge lines, breaks in slope, etc. Skeletal lines have been used as an independent method for the depiction of terrain. See figure from page 109 Imhof. Skeletal line drawings consisting of mountain crests, ridge lines, and streams are combined with spot elevations, annotation and other text have been used for expedition reports and travel books (Imhof, 1982). Skeletal lines can also be used to improve the visual interpreting of hill and mountain shapes through the addition of stream lines. See Figure 14.

This concept has been used as a constructional aid in the representation of terrain in both manual and automated methods. Imhof, 1982 describes the use of these lines in the manual preparation of drawing contour lines, hachures and hill shading. Weibel, 1992 uses nearly the same concept for describing the essential structure, or signature of terrain features during computer assisted terrain generalization (Figure 15). These features may be automatically extracted from a digital elevation model, extracted from photogrammetric data digitized, or from topographic maps. In the creation of a terrain model in the ARC/INFO software by ESRI these break lines are used in conjuction with elevation values in the form of points, contour lines or a TIN structure to produce a GRID format terrain model.

Skeletal lines can be combined with other display methods such as contour lines or shading to improve the visual interpretation of hill and mountain shape. The use of skeletal lines in a final map product should be limited to those lines which contribute to the effectiveness of the display of terrain such as in the case of stream lines. Excess use of skeletal lines may detract from the final map because they may clutter the map unnecessarily.

The gradation from dark to light in a single color according to specific principals for the purpose of creating a three dimensional effect is called shading. In contrast to the metric accuracy of contour lines, hill shading is primarily used for its visual effects. Imhof (1982) describes three different types of shading. Slope shading operates on the principal that the steeper the slope - the darker the shade. Oblique shading or hill shading is based upon the effect of an oblique light source on a terrain surface. Combined shading combines the effects of slope and hill shading. Additional displays are possible using shading techniques. Moellering and Kimerling (1990) presented a method for the display of slope-aspect maps which retains the three dimensional quality while including the display of slope-aspect. Numerous visualizations have also been produced by combining a hill shades digital terrain model with orthophotos or satellite imagery. See the cover of Robinson et al (1995) for an example.

Slope shading, as mentioned above operates basically on the principal of the steeper - the darker. Historically this has been the case (Figure 16 but some digital versions of the slope map invert the schema so that the it becomes the steeper - the lighter (Figure 17).

"Light reveals all! The same is true for landforms in nature, on the model and in the map. (Imhof, 1985)". See Figures 18, 19, 20and 21 for examples of the lighting effects produced by nature, in the photograph of a physical terrain model, shading manually produced on a map and shading produced by digital methods. All of these examples are very appealing visually. Hill shading provides us with a view that is familiar but not one which we experience in our daily lives (at least most of us). The of computer generated hill shading combined with our inherent fascination with the map produced ensures continued use of this method.

The use of computer methods allows for rapid generation of hill shaded maps by cartographers and non-cartographers alike. Digital methods also handle the problem faced by manual methods of providing sufficient detail. "Detail brings out the character of the relief and there is little fear of destroying the larger form by working on the detail which can be incorporated into the map with ease. (Imhof, 1982)".

The building of physical terrain models is rarely undertaken due to the high costs involoved but it is the most direct way of showing the three dimensional land surface (Figure 19). A recent exception are the models built by the Hammond company for their new world atlas. Physical models are also clumsy and difficult to store. Vacuum formed relief maps are still produced as wall maps. Physical models usually require an exaggeration in vertical scale relative to horizontal scale.

Block diagrams are a pictorial method which used to be used primarily for the portrayal of geologic relationships. Block diagrams show a portion of the earth's surface and crust from an oblique viewing angle. The origins of the block diagram were from 18th century geological report illustrated with cross sections. Pictorial sketching was added to the section to add realism and relate the surface expression with subsurface geology. See the block diagram in Figure 23 witha cross section on the front edge.

Block diagrams are enjoying a rapid phase of development with the advent of computer graphics and surface creation software. The old fashioned geologic block diagram with cross section is now being reformed to display three dimensional shapes within the earth. Various parts of the diagram may be transparent to allow for the three dimensional effect and the suface features may or may not appear (Figure 24).

The gridded perspective map is other popular use of the block diagram is for displaying surface terrain. With a few parameters such as azimuth, viewing height, zenith angle and view point distance a diagram such as Figure 25 can be created and viewed on a computer screen. These rapid views of digital terrain data can be an indispensible means for seeing errors in a data set. The gridded perspetive type block diagram has the same draw backs as the older block diagrams, there is significant planimetric displacement of features due to the oblique viewing angle. Higher elevations will often obscure the view of lower featuress but one the aspects of the digital production method is that the view parameters can be quickly altered to determine the best viewing angle. Surface features from other data sets such as land cover or transportation networks can also be draped over the gridded surface.