SECTION 4

4.  LOCATION AND RELIEF

4.1  Location

On the curved surface of the earth, position is defined by the universal system of latitude and longitude. All international and most national geographic gazetteers use this system for locating listed features. Small-scale maps and marine charts usually display a graticule (network) of meridians and parallels to assist in locating features using their geographical coordinates.

Marine chart graticules are based on points whose latitude and longitude have been fixed by astronomical or satellite observations. In contrast, topographic maps are surveyed and tied to the local national geodetic datum which is a reference network for horizontal locations. This sometimes results in a discrepancy in the position of the graticule shown on a coastal marine chart as compared to that shown on a topographic map. This is one of the main reasons for the current efforts to develop a world geodetic datum based on satellite observations.

4.2  Horizontal Control

Establishing the primary, horizontal control network requires the determination of the latitudinal and longitudinal positions of the control points through a process known as triangulation (Figure 4.1). This involves defining a starting line, called a baseline, and finding the latitude and longitude of its end points. From this baseline a network of straight lines is extended to the desired control points. The angles formed throughout this network are measured, and trigonometrical calculations are used to determine distances and locations within the network. Corrections must be made for the curvature of the earth through calculations based on spherical trigonometry.

The network that is measured to the highest level of accuracy is called the first-order or primary network. Once this is established, second and third-order networks can be built up within it. These new networks provide a denser array of control points as needed for local surveys. Usually first-order surveys are measured to an accuracy of 1 part in 25,000, second-order to 1 in 10,000, and third-order to 1 part in 5,000. Less accurate fourth-order measurements are used if they do not result in appreciable map error.

4.3  Coordinate Systems

The rotational motion of the earth spinning on its axis provides two natural points, the poles, upon which to base coordinate systems. These systems are networks of intersecting lines (graticules) inscribed upon the globe to permit the precise location of surface features. They are a method of organizing the concepts of direction and distance so that a comprehensive system of relationships can be established. Two types of systems are in general usage for reference mapping: a geographical coordinate system which uses lines of longitude and latitude to fix positions, and a rectangular coordinate system, such as the Universal Transverse Mercator (UTM) Grid System, which uses eastings and northings as the locational technique. Navigation charts, in contrast to their terrestrial partner, the topographic map, may be overlaid with another geo-referencing system, the Loran-C network lattice (refer to Section 5.2.3).

Figure 4.1   The principle of triangulation. (After A.N.Strahler, 1963)

Figure 4.2   A great and a small circle. (After H.S. Robin, 1969)

The terminology associated with coordinate systems includes the following:

i)   Great circle: A plane passing through the centre of the earth cutting the surface in a great circle (Figure 4.2), e.g., all meridians and the equator. An arc of a great circle is the shortest distance between two points on the earth's surface;

ii)  Small circle: A plane passing through the earth, other than through the centre (Figure 4.2), e.g., parallels of latitude;

iii)  Poles: Terminii (north and south) of the earth's axis;

iv)  Meridians (lines of longitude): A set of north-south lines connecting the poles. Each meridian is half a circle. Two opposite meridians make a great circle (Figure 4.3);

v)   Equator: The only great circle perpendicular to the earth's axis, and dividing the earth into northern and southern hemispheres;

vi)  Parallels (lines of latitude): A set of east-west lines running parallel to the equator (Figure 4.3);

vii)  Latitude: The angle (north and south) subtended by two imaginary straight lines, one extending from a given place inwards to the earth's centre, and the other from the earth's centre to the equator (Figure 4.4);

viii)  Longitude: The angle (east or west of the prime meridian) subtended by two imaginary straight lines, one extending inwards to the earth's axis, and the other from the earth's axis to the prime meridian (PM), i.e. the meridian chosen for 0° which passes through Greenwich, U.K. (Figures 4.4 and 4.5). Going east from the PM, the meridians are numbered up to 180° East (the eastern hemisphere). Going west from the PM, the meridians are numbered up to 180° West (the western hemisphere) (Figure 4.4). Because the meridians converge at the poles, the 1° longitude interval decreases from 111 kilometres at the equator to 56 kilometres at 60° North or South and zero kilometres at the poles (Table 4.1);

ix)  Graticule: A network of lines representing parallels and meridians on paper, i.e. geographic coordinates which are defined in degrees, minutes and seconds;

x)  Grid: Two sets of parallel lines crossing at right angles to form squares, i.e. grid coordinates.

Figure 4.3   (a) Meridians; (b) parallels. (After A.N. Strahler, 1963)

Figure 4.4   The geographic grid of parallels and meridians. Point A has a latitude of 50 North and a longitude of 75 West. (After A.N. Strahler, 1963)

Based on Clarke ellipsoid of 1866, from U.S. Geological Survey Bulletin 650, “Geographic Tables and Formulas” by S.S. Gannett, 1916, pp. 36–37. (After A.N. Strahler, 1975)

Figure 4.5   The prime (0°) and other meridians from the perspective of the North Pole. (After A.R. Grime, 1978–80)

4.3.1  Geographical coordinate system

The geographical coordinate system was developed from concepts originated by Greek philosophers before the Christian era. It is the primary system used for basic locational reckoning, such as navigation and surveying. The system is basically one of spherical coordinates, the meridians and parallels being neither straight nor equally spaced. It is useful for mapping large areas and the measurement of distances and directions in angular measure of degrees, minutes and seconds. A rectangular coordinate system which is far simpler in construction and usage may be superimposed on the geographical coordinate system.

4.3.2  Rectangular coordinate system

The Universal Transverse Mercator (UTM) Grid System is an international system which provides rectangular grid zones for the globe between latitude 80° South and 80° North. Poleward of 80°, the Universal Polar Stereographic Grid System is used. These systems are named after the map projections on which they are based. The UTM Grid System consists of 60 grid zones, each 6° of longitude in width (Figure 4.6). The origin (0°) of the grid zone is the intersection of the central meridian and the equator, both straight lines. The grid is a network of 1,000 metre, 10,000 metre or 100,000 metre squares, each identified by the grid coordinates of its lower left hand corner. In stating grid coordinates, the number of metres east or eastings (right) is given first, followed by the number of metres north or northings (up). The procedure for reading UTM grid coordinates is explained in Figure 4.7. In order to have all eastings increase towards the right across the entire zone, the central meridian is given the arbitrary value of 500,000 metres east. The equator is given the value of 0 metres north as the reference line for northings increasing up to the 80th parallel north. For the southern hemisphere, the equator is given the arbitrary northing of 10 million metres north, so that northings begin with their lowest value at 80° South latitude and increase northward to attain that figure at the equator. The Universal Transverse Mercator Grid System has now been widely adopted for topographic maps, referencing of satellite imagery, natural resource data bases and similar applications which require precise positioning.

4.4  Vertical Datum and Control

The first step in setting up a vertical control network is the determination of a starting level, or datum. The most desirable level for this purpose is the surface of the geoid; if there were no tides, the surface of the ocean would provide the required surface. For this reason, measurements that eliminate sea level variations due to tidal action are used to establish the sea level datum. The establishment of this level or datum requires the recording of tidal levels every hour over a 19 year period. These readings are then averaged to establish a mean datum known as Mean Sea Level. The North American Datum based on Mean Sea Level has so far been adjusted twice, in 1929 and again in 1983. Mean Sea Level (MSL) is in fact a datum which fluctuates according to atmospheric pressure changes, winds, tidal forces, etc. Variations of up to one metre have been noted. Despite this, MSL has been adopted by most countries as their topographic vertical reference datum.

Figure 4.6   The UTM grid zone near the equator and at 45° North. (After A.N. Strahler, 1969)

Figure 4.7  The procedure for reading UTM grid coordinates. (After Canada, Department of Energy, Mines and Resources, n.d.)

In contrast to topographic maps, marine charts must show heights and depths above and below the water surface at any given time. Thus marine charts use two datums other than MSL to meet these requirements.

The most important information on a marine chart is the minimum depth of water at any given point. Therefore the primary reference datum used for marine charts is Lowest Normal Water Level. Depths below this level are known as soundings. In the intertidal zones, heights are measured upwards from the same level and are normally underlined on the face of the chart. Some charts use the word “dries” next to these figures and refer to them as drying heights.

The other datum is chosen to identify the land areas on these charts. The phenomenon of spring tides, the twice monthly peak of tidal range, is generally used to determine this datum. It may be labelled as Higher Water Ordinary Spring Tides, Mean High Water Springs, Highest Astronomical Tide, Mean Higher High Water, etc. The variety of mapping and charting datums is illustrated in Figure 4.8.

On lake charts, the horizontal datum, projection and grid are usually identical to surrounding topographic maps. As with sea charts, however, the lowest water level must be adopted as datum for vertical control. Many lakes have a wide seasonal variation, particularly those with no outlet. The elevation of this datum above Mean Sea Level should always be quoted. The choice of chart datum is usually more difficult in inland waters than coastal waters because the former lack the stabilizing influence the ocean exerts on the mean water level. Because a river descends from its source to its mouth, chart datum must slope similarly to the water surface of the river at low stage to avoid constant datum variations throughout the length of the river.

In contrast to depth measurements, the elevations of prominent targets (e.g., beacons) and clearances under obstacles (e.g., bridges) are referred to the datum for elevations (Figure 4.8). On most Canadian charts this is the HHWLT (Higher High Water, Large Tide).

Benchmarks (BM) are fixed elevation markers. In Canada, the Geodetic Survey of Canada locate geodetic benchmarks in relation to the national geodetic datum. Similarly the Canadian Hydrographic Service is responsible for hydrographic benchmarks which identify locally the elevation of the physical surface used as chart datum. Although it is not necessary for charting purposes, it is desirable that chart datum be referenced to geodetic datum, so that the geodetic elevation of chart datum can be supplied to surveyors and documented on charts.

4.5  Relief - The Third Dimension

Most people think of location only in horizontal terms, being unaware of the important third dimension of our environment - the vertical. For certain applications the vertical dimension is an important and sometimes critical factor which cartographers must portray within their two-dimensional graphics. In the marine environment, huge and unwieldy ships must maneuver a scant few metres above unseen and potentially lethal terrain. An up-to-date nautical chart will show a navigator the topography of the ocean bottom so that he can safely navigate the underwater valleys and ridges.

Figure 4.8   Relation between tidal surfaces, charting datums and physical features. (After W.D. Forrester, 1983)

4.5.1  Spot values

The simplest representation of surface elevation is the use of spot values to indicate the measurement of height or depth which applies at that particular point. The spot is represented by a small point symbol with a number beside it indicating the height or depth above or below a reference value or datum. On topographic maps and aeronautical charts the measurement of height is relative to Mean Sea Level; on marine charts depth and height are relative to the selected chart datum.

On topographic maps, spot values known as spot heights, are shown for some physically monumented bench marks on the ground. Other significant locations such as hilltops, mountain passes and road intersections are also given spot heights (Figure 4.9). On nautical charts, depth soundings are spot values that show the depth of water (Figure 4.10). Spot heights and depth soundings are very simple and are accurate for the specific point chosen. They do not, however, provide a graphic effect of shape, nor do they indicate values located between the spots. Because of this limitation the map viewer cannot easily visualize the characteristics of the surface being displayed. Spot heights and depth soundings are most often used as an information supplement to some other technique of showing surface elevation.

Nautical charts have traditionally shown a large number of depth soundings, in addition to isolines or depth contours, to indicate to the mariner the reliability of the information from which the chart was derived. With the increased accuracy of detail of modern marine surveys, however, many marine charting organizations are now dropping this practice which simplifies both the production and usage of these visually more appealing products.

4.5.2  Contours

Contours, or isolines, are by far the most widely used method of portraying relief or depths on maps and charts (Figure 4.9). They may be defined as lines of constant elevation or depth; they are imaginary but they appear on the map as real lines.

Contours can be obtained in several ways, including:

Unfortunately, it is rarely possible to determine the origin and nature of contours on a given map. In particular, the reliability of interpolated or sketched contours will vary from map to map and with the skills of the map maker. Contours on many older maps should be treated with suspicion unless details of the accuracy are provided. Obtaining accurate contours by traditional survey techniques is tedious and will often double the cost of a given survey. Hence, many contours have been interpolated from minimal survey data. Generally speaking, modern photogrammetrically plotted contours are drawn with a large amount of detail, therefore their accuracy will often reveal the errors existing on older mapping.

Figure 4.9  Relief as portrayed by contours. (After Canada, Department of Energy, Mines and Resources, n.d.)

Figure 4.10  Nautical chart showing depth soundings. (Canadian Hydrographic Service, Chart no. 4332)

4.5.2.1  Marine contours (Figure 4.11):

Surveying the ocean floor is still subject to considerable difficulty, as boats and water surfaces are normally in motion during a survey. Accuracy of positions at sea, until the advent of satellites, depended on the distance from shore. High seas positioning historically depended on astronomic observations using sextants, which were not noted for their accuracy.

Depth measurements are taken relative to an artificial datum surface because the actual sea level is constantly fluctuating. There are also several different reference datums in usage, for example, those used by Britain and France vary by 0.6 metres. For reasons of safety the French use the Approximate Lowest Low Water, while Britain has used one which is 0.6 metres below Low Water Mean Spring Tide.

Most nautical charts are notable for the density of spot depths, but the spots are not evenly distributed, being concentrated along navigation routes, at river mouths and shallow areas (Figure 4.10).

It is important to note that hydrographic charts, designed for navigation, and bathymetric charts, designed to depict marine topography, will be contoured differently using the same data. Hydrographic charts emphasize shallow water zones as a deliberate safety factor. Bathymetric charts are the marine equivalent of topographic maps; the interpolation of contours is based strictly on the spot depth values and the distance between them.

The accuracy standards of marine mapping are even more varied than that of land mapping. In general, the continental shelves of the world have been poorly mapped by modern standards. In Canada, for instance, only 50% of those areas carrying commercial maritime traffic are up to modern mapping standards, and in Arctic waters it is less than 20%.

4.5.2.2.  Vertical or contour interval

This is the vertical distance between two adjacent contour lines. It is usually a constant unit on topographic maps whereas many hydrographic charts utilize a number of differing intervals. This latter system is of great benefit to the map user because it is the vertical interval which largely controls the effectiveness of contours in representing the terrain. Any feature whose height is less than the vertical interval will probably not be identified by the contour pattern, therefore a great deal of “microrelief” information that may be of interest to some people is lost on standard topographic mapping. Selecting a smaller contour interval in areas of low relief is an obvious solution which is not used enough in these days of standardized presentations. Conversely, in mountainous regions the contour interval should be kept larger to prevent overcrowding. Since varying contour intervals could lead to consistency problems in series mapping, a system to select contour spacings for various map scales is necessary. The most comprehensive system for that purpose was developed by the noted German cartographer, Eduard Imhof. See Table 4.2.

Figure 4.11  Example of bathymetric contours. (Canadian Hydrographic Service, Chart no. 15062)

Key :

A:   STEEP RELIEF (slopes up to 45°)

B:   MEDIUM RELIEF (slopes up to 26°)

6.   Recommended contour interval.

C:   LOW RELIEF (slopes up to 9°)

7.   Recommended contour interval.

Intermediate or auxiliary contours are a solution to the problem posed above. They are inserted between contours of standard vertical intervals to illustrate significant minor features. To ensure that their non-standard nature does not confuse the reader, they are drawn with broken or dotted lines or, occasionally, in another colour.

A contour line is of little use to a map reader unless its value can be easily identified. Numerical values are placed in short gaps in the appropriate line and aligned with the local orientation of that line. Two different conventions have been developed for numbering contours:

i)   the “top” of the number indicating the up-slope direction (upslope);

ii)   numbers placed such that they can be easily read from the normal base viewing position of the map (upright).

There is no rule which controls the number of contour numbers on a map sheet. The only guide is that the map user must be able to obtain the accurate relevant information required with a minimum of effort. The frequency of the number placement must be judged accordingly. The visual ladder effect created by long strings of numbers should be avoided because it is highly disruptive. In contrast, totally random number placement is difficult for map readers to interpret.

4.5.2.3  Index lines:

Many maps have a high density of complex isolines or contours. Without a visual aid the reader can become disoriented and misinterpret the information. Convention has every fourth or fifth line drawn visibly wider to aid in interpretation. The selection of the fourth or fifth line as the index depends on the contour interval. The most rounded and convenient contour interval should be selected, for example, a map with 25 metre contour intervals would show the fourth or 100 metre line as an index.

4.5.2.4  Contour accuracy:

As indicated earlier this is not easy to ascertain. The most reliable contours are normally those derived photogrammetrically, although their standards can vary widely. In North America the absolute accuracy standard specifies that contour lines must be positioned within a band representing one half the contour interval above and below the true elevation. This is adequate for most engineering purposes but contours cannot show true slope or variation in the terrain, unless the interval is much smaller than the absolute accuracy standard. Intermediate contours should not be interpolated between the contours of an existing topographic map because the land does not necessarily slope evenly between two contours.

4.5.2.5  Contour characteristics:

The following is a list of contour characteristics:

 i)   Contours are always horizontal and perpendicular to the dip of the land, i.e. the direction in which water would run at that location;

Figure 4.12   Hachures constructions. (After International Cartographic Association, 1984

ii)   All contours are closed lines, unless cut off by the margin of the map;

iii)   Contours become closer as the slope of the terrain steepens;

iv)   On crossing rivers, contours will point upstream except on a few alluvial fans;

v)   If the contour interval is too large, low relief will not be recorded;

vi)  Neighbouring contours do not cross or touch each other, with the exception of cliffs and overhangs.

4.5.3  Hachures

Hachures have historically been a very important and common method of showing relief and slopes (Figure 4.12). They consist of short (often tiny) lines arranged so that they face “downhill”. Each hachure line lies in the direction of the steepest slope. On steep slopes they are short but close together, and on flatter slopes they are longer but further apart. They can also be drawn with a variety of line widths, heavier lines indicating steeper slopes.

These techniques can be quite precise and produce a good visual impression of relief. They are, however, extremely time consuming, and cartographers need considerable practice to use the technique effectively. Also the black hachure lines on the map face tend to hide other detail. For most applications the cost and time involved in producing these symbols are prohibitive, especially as there are better methods of showing relief.

4.5.4  Other techniques for showing relief

There are a growing variety of shading techniques, such as illuminated contours, hill shading and step surface shading, which are replacing hachures as a means of showing relief. Complex terrain can also be portrayed by illustrative techniques, for example, rock drawing and the use of physiographic and landform symbols. Details of these relatively sophisticated cartographic techniques can be obtained from more specialized texts.