Chapter 2: Representation of Relief
In a dry year, when a reservoir shrinks, its banks tell a quiet story. As the water sinks, it leaves pale rings on the exposed slopes — one ring for each level at which the surface paused for a while. Walk down from the tree line to the shrunken pool and you cross ring after ring, each marking where the water once stood.
Look closely at any single ring. Every point along it sits at exactly the same height, because a still water surface is perfectly level. The ring is a line of equal elevation, and the water has drawn it on the land for you.
Now imagine the rings did not fade. Picture dozens of them, evenly spaced in height, wrapping the whole basin. Where the bank is steep, the rings crowd together; where it flattens out, they spread wide apart. Seen from directly above, they would form a set of nested loops — the shape of the basin drawn entirely in lines.
That picture is a contour map. Long before satellites, this was the problem every mapmaker had to solve: the land rises and falls in three dimensions, but paper has only two. A map cannot bulge upward. Somehow the height of every ridge, valley and cliff must be folded flat onto a sheet — and read back off it by anyone, anywhere.
This chapter is about how that is done.
Diagram
Fig. 2.0-1 Caption: Each level at which the water rests leaves a line of equal height; seen from above, those lines become the contours of the basin. Brief: Draw one rounded hill in a shallow basin, shown twice side by side. Left panel — a cut-away side view with the water surface marked at five equal height steps (0, 100, 200, 300, 400 m), each waterline ruled across and labelled with its height, and a small downward arrow beside the surface showing the level falling. Right panel — the plan (top-down) view of the same hill, where each former waterline appears as a closed loop; draw the loops crowded together on the steep side and spread wide on the gentle side, each loop labelled with the matching height. Emphasise with a light tie-line that one loop on the right corresponds to one waterline on the left. Use no place names.
2.1 Showing Relief on Flat Paper
A map is printed on a flat sheet, but the land it describes is not flat. Relief means the differences in height and the shape of the land surface — its mountains, plateaus, plains and valleys. Relief is three-dimensional; paper has only two dimensions. This is the central difficulty of showing the land on a map.
The paper cannot actually rise where the mountain rises. So relief is never copied onto a map — it is coded onto it. Colours, shades and lines are agreed symbols that stand for height, and the reader learns to translate them back into a surface that climbs and falls.
Several methods have been developed, and they answer three different questions. Some give a quick pictorial impression of the land — the colour method, hachures, hill shading and layer tints. Some give the exact height of scattered points — spot heights, bench marks and trigonometrical stations. And one family of lines gives exact height across the whole surface, not just at points; because it is the most accurate, it is developed on its own in Section 2.2.
No single method does everything. Each is a trade-off between a vivid picture and precise measurement, and the right choice depends on what the map is for.
2.1.1 The Colour Method
In the simplest method, a different colour is given to each broad type of relief. Green is used for plains, brown for mountains and highland, white for snow-covered land, and blue for the sea.
Its strength is speed: at a single glance the reader sees the general layout of high and low ground. Its weakness is that the colouring is crude. One colour covers a wide range of land, so differences of height inside that band are lost.
A whole plain is painted the same green whether it rises ten metres or a hundred. The method assigns colour to the kind of feature, not to a measured height — which is exactly the gap that layer tints (Section 2.1.5) later close.
2.1.2 Hachures
Hachures are short, fine lines drawn down the direction of steepest slope, running from high ground towards low. Their thickness and spacing carry the message. On a steep slope they are drawn thick and close together; on a gentle slope they are thin and far apart. A near-vertical face is filled solid black, and flat land is left blank.
The eye therefore reads the density of ink as steepness. Where the page is dark and crowded, the ground is steep; where it is open, the ground is gentle.
Hachures give a good impression of the shape and steepness of the land. But they cannot give actual heights — you can see that a slope is steep without knowing how high it climbs. Heavy hachuring also tends to hide other detail printed underneath it.
Diagram
Fig. 2.1-1 Caption: Hachures crowd together and thicken on the steep face and thin out on the gentle face, so the ink itself records the slope. Brief: Draw a simple asymmetrical hill in plan (top-down) view, hachured. On the steep side draw the down-slope hachure lines thick, short and closely packed; on the gentle side draw them thin, longer and widely spaced. Leave the flat foreground blank. Add a tiny arrow on one hachure showing it runs downhill (high to low). No heights, no place name.
2.1.3 Spot Heights, Bench Marks and Trigonometrical Stations
These three symbols do the opposite of hachures: they give exact heights, but only at single points. All heights are measured above mean sea level — the average level of the sea, taken as the zero from which every land height is counted.
A spot height is the surveyed height of one particular point of ground above mean sea level. It is printed as a dot followed by its height in metres. It fixes a height but says nothing about the ground around it.
A bench mark is a height fixed permanently to a solid object — a pillar, a building or a bridge — so that it can be found again and reused by later surveys. It is marked B.M. with its height. The difference from a spot height is exact: a bench mark gives the height of a mark on an object, while a spot height gives the height of the ground itself.
A trigonometrical station is a point used in triangulation, the survey method that fixes positions across a whole country through a connected network of measured triangles. On the map it is shown as a small triangle with its height. These stations, placed on hilltops, form the master framework to which other heights are tied.
Diagram
Fig. 2.1-2 Caption: Three symbols for the same idea — an exact height fixed at a single point. Brief: Draw the three point symbols in a row, each with a sample number beside it: a filled dot labelled ‘1180’ for a spot height; the letters ‘B.M.’ with a small horizontal mark and ‘1204’ for a bench mark shown resting on a small pillar; a small open triangle labelled ‘1247’ for a trigonometrical station on a hilltop. Add a one-line key beneath naming each. State all heights are in metres above mean sea level. No place name.
Because they give heights only at points, these three are used alongside a method that shows shape. On their own they are a scatter of numbers; joined to contours, they become the skeleton on which an accurate relief map is built.
2.1.4 Hill Shading
Hill shading imitates the light and shadow the land would show if a lamp were shone across it from one fixed direction. The base of the method is light: one part of the surface is treated as lit and the rest as in shadow.
The light is usually imagined coming from the north-west, or falling vertically from directly above. Slopes that face the light are left pale; slopes that face away are shaded dark. The brain reads that pattern of pale and dark as a solid, rounded surface.
If the light falls vertically, flat tops come out bright and all slopes come out dark. If it comes from the north-west, the north-west-facing slopes are lit while the south-east-facing slopes fall into shadow.
The method gives a very vivid, immediate sense of the relief — it is what gives many printed physical maps their three-dimensional look. Its limits are that it gives no actual heights, and that where the range of altitude is large the shading cannot separate every level cleanly.
Diagram
Fig. 2.1-3 Caption: With the light coming from the north-west, slopes that face it stay pale and slopes that turn away fall into shadow. Brief: Draw a rounded hill or short ridge in plan view, shaded to suggest relief. Show a small sun or light-source arrow in the top-left (north-west) corner with an arrow pointing across the hill. Render the north-west-facing slopes pale/unshaded and the south-east-facing slopes progressively darker. Add a small compass rose. No heights, no place name.
2.1.5 Layer Tints
Layer tints, also called hypsometric tints, refine the colour method by tying colour to measured height. A tint fills each band of land that lies between two successive height levels, and the tint deepens step by step as the land rises.
A fixed scheme is followed. Blue is used for the sea, growing darker as the water deepens. Low land begins in a dull green, passing to light green and yellow-green as it rises. Highland is shown in brown, darkening through dark brown and reddish brown up to crimson red for the greatest heights. The highest, glaciated peaks are left white, often with a tinge of blue.
Now colour carries ordered height information: darker brown always means higher ground. This is the difference from the crude colour method, where colour marked only the type of feature. The physical map in a school atlas is a layer-tint map — the green lowlands and brown mountains are reading you their heights.
Layer tints give a vivid picture at a glance and suit atlas and small-scale maps. But when the range of altitude is very large, not every step of colour can be shown distinctly, and the tints only fill the gaps once the underlying height lines have been drawn.
Diagram
Fig. 2.1-4 Caption: In a layer-tint scheme the colour deepens with height, so darker brown always means higher land. Brief: Draw a vertical stepped ladder or staircase of colour bands, lowest at the bottom. From the bottom up: dark blue (deep sea) to light blue (shallow sea) below a sea-level line; then dull green, light green, yellow-green for rising lowland; then light brown, brown, dark brown, reddish brown, crimson for rising highland; then white with a blue tinge at the top for glaciated peaks. Label the sea-level line and mark the direction ‘increasing height’ up the side. No specific figures, no place name.
2.1.6 Form Lines
Form lines are broken lines drawn in the same way as contours — lines of equal height, defined fully in Section 2.2 — but showing only approximate heights where an accurate survey was not possible.
They follow the same principle as contours: the closer the lines lie, the steeper the ground. What they give up is precision. A form line shows the general pattern of the surface rather than a surveyed value you can trust.
They are used where the relief is too broken or too inaccessible to survey exactly, and stand in until proper contours can be drawn. In this they point straight to the next section — the exact, surveyed version of the same idea, which is the contour.
2.2 Contours: The Accurate Method
Of all the methods, the contour is the most popular and the most accurate. Almost every fact about the shape of the ground — its height, its slope, its valleys and ridges — can be read exactly from a contour map.
The earlier methods each gave up something: a picture without heights, or heights without a picture. Contours give both at once, which is why they carry the whole weight of a topographical map. This section builds the idea from its definition up to the point where a student can draw contours from raw survey heights.
2.2.1 What a Contour Is
A contour is an imaginary line that joins all adjacent points standing at the same height above mean sea level. Every point along a single contour is at one, and only one, stated height.
There is a simple way to picture it. Imagine a traveller walking along a hillside at a height of exactly 100 metres, taking care never to climb and never to descend. The path traced by that careful walk is the 100-metre contour.
The idea also follows from the opener’s shrinking reservoir. Picture a hill surrounded by sea and sliced by level planes at equal height intervals, as the falling water sliced the bank in Fig. 2.0-1. Each cut is a closed loop, and each loop, drawn on the map, is one contour.
2.2.2 Vertical Interval and Horizontal Equivalent
Two measurements govern how contours behave, and telling them apart is the key to reading any contour map. One is measured up and down; the other is measured across the ground.
The vertical interval, abbreviated V.I., is the difference in height between two successive contours. Its unit is the metre or the foot. On any one map the V.I. is kept constant — if it is 100 m, the contours are drawn at 0, 100, 200, 300 m and so on.
The horizontal equivalent, abbreviated H.E., is the horizontal distance on the ground between two successive contours. Unlike the V.I., the H.E. changes from place to place: it is small where the slope is steep and large where the slope is gentle.
Here is the whole reading skill in one sentence. Because the V.I. is fixed while the H.E. varies, the spacing of contours on the map tells you the slope of the land — contours crowded close together mean steep ground, contours spread wide apart mean gentle ground.
Diagram
Fig. 2.2-1 Caption: The vertical interval is the same for every step, so where the ground steepens the contours are forced closer together. Brief: Draw a side-view (cross-section) staircase-style slope descending left to right, with horizontal levels marked at 0, 100, 200, 300, 400, 500 m. Show the equal vertical gaps between levels labelled ‘V.I.’ (all equal). Show the horizontal gaps between the points where each level meets the slope labelled ‘H.E.’, drawn short where the slope is steep and long where it is gentle. Use arrows to make clear V.I. is measured vertically and H.E. horizontally. No place name.
The steepness of a slope can be put as a number. The gradient is the vertical rise divided by the horizontal distance over which it is climbed.
\[\text{Gradient} = \frac{\text{Vertical interval (V.I.), in metres}}{\text{Horizontal equivalent (H.E.), in metres}}\]
The gradient is a pure ratio, so it is usually written as ‘1 in n’. Working it out from a map has one extra step, because map distance must first be turned into ground distance.
Suppose two successive contours, with a V.I. of 100 m, appear 1 cm apart on a map drawn to a scale of 1 : 50,000. A scale of 1 : 50,000 means one unit on the map stands for 50,000 of the same units on the ground. The ground distance between the contours is therefore
\[1 \text{ cm} \times 50{,}000 = 50{,}000 \text{ cm} = 500 \text{ m}\]
so the H.E. here is 500 m. The gradient is then
\[\text{Gradient} = \frac{100 \text{ m}}{500 \text{ m}} = \frac{1}{5}\]
The land rises 1 m for every 5 m walked — a moderate slope. Now let the same two contours lie only 0.4 cm apart. The ground distance becomes \(0.4 \text{ cm} \times 50{,}000 = 20{,}000 \text{ cm} = 200 \text{ m}\), and the gradient becomes \(100 \text{ m} \div 200 \text{ m} = 1/2\) — a steep slope. The vertical interval never changed; the closer spacing alone made the slope steeper.
2.2.3 Rules for Drawing Contours
Contours are not drawn freely; a set of rules keeps them consistent from one map to the next. The fixed height gap between them is called the contour interval, which is simply the vertical interval chosen for that map.
The rules are as follows.
Contours are continuous curved lines. Their curvature follows the shape of the land, and they are never broken.
They never begin or end within the map. A contour either closes on itself as a loop or runs off the edge of the sheet.
They are drawn at a constant interval — the contour interval.
They lie close together where the slope is steep and wide apart where the slope is gentle.
They never meet or cross one another, with two exceptions. Where the slope is almost vertical, as at a waterfall or a cliff, contours touch. Where one piece of land overhangs another, as at an overhanging cliff, contours cross.
The value of a contour is written towards the ascending, uphill side, or set into a small break in the line itself where the contours are too crowded to leave space.
Contours are conventionally printed in brown.
2.2.4 Interpolation of Contours
A survey does not hand over finished contours. It hands over a scatter of separate heights — spot heights, bench marks and trigonometrical stations. Interpolation of contours is the process of drawing continuous contours from that scatter of measured point-heights.
The work follows a fixed order. First, mark all the measured heights on the map; the more points there are, the better the result. Next, find the highest and lowest values; the difference between them is the range of elevation, the total spread of height on the map.
The range decides the contour interval, which is chosen in round figures — 10, 20, 50 or 100 metres — to suit it. The contour values are then fixed, also in round figures, starting from the low ground. Finally, each round value is located where it falls between two neighbouring points, and points of the same value are joined into a smooth curve.
Flowchart
Fig. 2.2-2 Caption: Interpolation turns a scatter of point-heights into continuous contour lines, one value at a time. Nodes: Mark all measured point-heights on the map → Find the highest and lowest; their difference is the range of elevation → Choose a contour interval in round figures to suit the range → Fix the contour values in round figures, lowest first → Locate each value between neighbouring points by proportion → Join equal-value points into a smooth curve → more contour values to plot? yes → back to ‘Locate each value between neighbouring points by proportion’; no → finished contour map
The one step that needs arithmetic is locating a value between two points. It is done by simple proportion, on the assumption that the slope between the two points is even.
The midpoint answer held only because we assumed an even slope between A and B. Real ground between two survey points may be concave or convex, so the true 1200 m line can sit a little off the midpoint. This is exactly why interpolation improves with more measured points: each extra height shortens the gap over which an even slope must be assumed. A contour drawn from few points is a reasonable estimate, not a guarantee.
2.3 Drawing a Profile from Contours
A contour map is a plan — a view looking straight down on the land from above. It shows where the ground climbs and falls, but it does not let you see that rise and fall directly. The map has to be turned on its side.
Drawing a profile is the skill of doing exactly that: converting the top-down pattern of contours into a side view of the land. This section defines the profile, then works through the two standard ways of drawing one, and ends with the trick that makes the drawing readable.
2.3.1 What a Profile Shows
A profile, also called a cross-section, is the outline of the ground seen from the side — the shape produced where a vertical plane cuts down through the land along a chosen line.
The idea is easy to feel. When an apple is cut cleanly in two, the fresh flat face of each half is a section. Cut through the ground the same way along a line, and the side view of that cut is its profile.
A profile earns its place because a plan of contours does not, on its own, give a vivid sense of the land. It converts contour spacing into a slope the eye can actually see, showing the heights, the slopes and the hollows along one chosen line.
2.3.2 The Perpendicular Method
This method drops the profile straight from the map. Suppose a section is to be drawn along a line AB across the contour map.
Draw the section line AB so that it crosses the contours; mark the crossing points A, B, C, D and so on.
Below the map, draw a base line equal in length to AB.
On that base, draw a set of parallel horizontal lines, one for each contour height — 100, 200, 300 m and upward — spaced according to the vertical scale you choose.
From every point where AB crosses a contour, drop a perpendicular down to the horizontal line of that same height, and mark the meeting point.
Join the marked points with a smooth free-hand curve. That curve is the profile.
Diagram
Fig. 2.3-1 Caption: Each contour crossing on the section line drops straight down to its own height line, and the marked points join into the profile. Brief: Draw a small contour map of a hill at the top with a straight section line AB ruled across it, crossing several contours; label the crossing points A, B, C, D, E, F. Below, draw a base line the same length as AB with horizontal guide lines at 100, 200, 300, 400, 500 m marked up the left edge. From each crossing point drop a dashed vertical perpendicular to its matching height line and mark a dot. Join the dots with a smooth curve to form the profile. Show the perpendiculars with downward arrows. No place name.
2.3.3 The Paper-Strip Method
This method copies the contour crossings onto a movable strip first. Suppose the section is to run along a line XY.
Lay the straight edge of a paper strip along the section line XY.
Mark on the strip every point where a contour touches the edge, and note the height at each mark.
Draw a framework of parallel horizontal lines to a chosen vertical scale — for instance, letting 0.5 cm stand for 50 m, so the lines read 0, 50, 100, 150 m and upward.
Lay the strip along the lowest line, and from each marked point raise a perpendicular to the height noted for it.
Join the tops of these perpendiculars in a smooth curve to complete the profile.
Diagram
Fig. 2.3-2 Caption: The contour crossings are transferred to a paper strip, raised to their heights on a scaled framework, and joined into the profile. Brief: Draw four small labelled panels left to right. (A) A contour map of a hill with a section line XY ruled across. (B) The same line with a paper strip laid along it, tick-marked where each contour meets it, each tick labelled with its height. (C) A framework of horizontal lines at 50 m spacing with vertical lines raised from each tick to its height, tops marked with dots. (D) The dots joined by a smooth curve — the finished profile. No place name.
The two methods reach the same profile by different routes. The perpendicular method drops its lines straight from the map itself, while the paper-strip method first copies the crossings onto a strip that can be moved about. The strip is handier when the section line is long, or when the map should not be marked on directly.
2.3.4 Vertical Exaggeration
There is a problem hidden in every profile. The heights involved are small — a few hundred metres — while the horizontal distances are large, often several kilometres. Drawn honestly, to the same scale both ways, the profile would flatten into an almost straight line and show nothing.
The cure is vertical exaggeration: the vertical scale of the profile is deliberately made larger than the horizontal scale, so that the ups and downs stand out. The horizontal scale is kept exactly the same as the map; only the vertical scale is stretched.
How much a profile is stretched is measured by the vertical exaggeration, the ratio of the vertical scale to the horizontal scale.
\[\text{Vertical exaggeration} = \frac{\text{Vertical scale}}{\text{Horizontal scale}}\]
Suppose the map has a horizontal scale of 1 : 50,000, and the profile is drawn with a vertical scale of 1 cm to 100 m. That vertical scale is a representative fraction of \(1 : 10{,}000\), because 100 m equals 10,000 cm. The vertical exaggeration is then
\[\text{Vertical exaggeration} = \frac{1/10{,}000}{1/50{,}000} = \frac{50{,}000}{10{,}000} = 5\]
so heights are drawn five times larger than they would be to true scale. In practice the vertical scale is exaggerated about 5 to 10 times, and under no circumstances should the exaggeration go beyond about 20 times, or the profile becomes a caricature of the land.
Diagram
Fig. 2.3-3 Caption: The same hill, drawn at low and high vertical exaggeration — the relief that is invisible on the left becomes dramatic on the right. Brief: Draw the same hill profile twice, side by side, over an identical horizontal length. Left panel — vertical exaggeration about ×1 (true scale), so the hill appears as a very low, almost flat bump; label its vertical scale. Right panel — vertical exaggeration about ×10, so the same hill rises as a tall, sharp peak; label its vertical scale. Add a note that both drawings are of the identical hill. No place name.
This is also the profile’s honest limit. Because the vertical is stretched, the slopes drawn on a profile look steeper than they truly are. A profile faithfully shows the relative rise and fall along a line, but the angles it draws are not the real angles of the ground.
2.4 Reading Slopes from Contour Spacing
Section 2.2 gave the basic rule: close contours mean steep ground, wide contours mean gentle ground. But a slope is rarely the same all the way up — its steepness changes as it climbs. Reading a slope properly means reading how the spacing changes across it, not just whether the lines are close.
The slope of a relief feature is the angle its surface makes with the horizontal. Because the vertical interval is fixed, that angle is written straight into the contour spacing, and several standard kinds of slope can be told apart by their spacing alone.
Steep and Gentle Slopes
A steep slope is one where the land rises or falls sharply — steeper than a gradient of about 1 in 10, which is roughly 6°. Its contours are packed close together, because a large drop is crossed in a short distance on the map.
A gentle slope is the opposite: the change of height is gradual, less than about 1 in 10 or 6°, and its contours are placed wide apart. So the same fixed height gap that crowds the lines on a steep face lets them spread on a gentle one.
Uniform, Concave and Convex Slopes
A uniform slope keeps the same steepness throughout. Because the slope never changes, its contours are evenly spaced from bottom to top — equal gaps all the way.
A concave slope is gentle at the foot but becomes steep near the top, curving inward like the inside of a bowl. Its contours are widely spaced low down and crowd together near the summit.
A convex slope is the mirror image: steep at the foot and gentle at the top, bulging outward. Its contours crowd together low down and spread apart near the top. Concave and convex slopes may run between the very same pair of contours, yet they are opposite shapes — which is why the trend of spacing must be read, not just its average.
The difference is not academic. On a convex slope the ground curves away beneath you, so from the top you cannot see the foot — the lower slope is hidden ‘dead ground’. On a concave slope the whole face is open to view from the top. A map reader can see this danger, or this clear sightline, before ever reaching the hill.
Diagram
Fig. 2.4-1 Caption: Four slopes with the same height range but different spacing signatures — the trend of the spacing tells the shape. Brief: Draw four small panels in a row, each with a contour plan above and its matching side-view section below. (1) Uniform slope — evenly spaced contours; a straight section. (2) Concave slope — contours wide at the foot closing up towards the top; a section curving inward (bowl-shaped). (3) Convex slope — contours close at the foot opening out towards the top; a section bulging outward. (4) Terraced slope — contours in close pairs separated by wide gaps; a stepped section. Label each panel. Contour interval marked. No place name.
Terraced and Undulating Slopes
A terraced slope runs in a series of steps: it rises gently, then steeply, then gently again, and so on. Each steep riser packs its contours into a close pair, while each flat tread leaves a wide gap — so the contours appear drawn in pairs.
An undulating slope, also called an irregular slope, changes over short distances, with some stretches concave and others convex. Its contours therefore lie at irregular distances, neither evenly spaced nor showing a single clean trend. Most real hillsides are undulating, and reading them is simply the practised habit of following the spacing as it tightens and loosens along the line.
2.5 Reading Relief Features from Contour Patterns
Every relief feature leaves its own signature in the contour pattern, because contours are simply the shape of the land seen from above. Learning to read those signatures is the point of the whole chapter — a glance at the loops and Vs on a map should call up the hill, valley or cliff that drew them.
Each feature below is first the land, made by some process, and then the pattern that records it. Read the two together and the flat map begins to stand up off the page.
The Closed Upland Forms
A conical hill rises like a cone — a broad, roughly circular base narrowing to a small peak, with a slope much the same on every side. Such hills are common in volcanic areas, built up by material erupted from a central vent. Its contours are almost circular loops, spaced at roughly regular distances, with the values increasing towards the centre.
A plateau is an elevated area with a nearly level top and steep sides. Its contours are crowded together along the steep edges, while the flat top is almost free of contours — a ring of close lines around an open middle.
A ridge is a long, narrow highland with a crest, falling steeply on both flanks. Its contours are elongated, oval loops, closely spaced down the sides, and a single ridge may carry several peaks and low passes along its length.
Diagram
Fig. 2.5-1 Caption: Three high grounds with rising central values, told apart by the shape of their loops. Brief: Draw three panels, each a contour plan above and a matching section below. (1) Conical hill — near-circular concentric contours, values increasing inward; a cone-shaped section. (2) Plateau — a ring of closely spaced contours around a wide contour-free centre; a flat-topped, steep-sided section. (3) Ridge — long elongated oval contours, closely spaced on both flanks, with two small summit loops; an elongated section with two low peaks. Label each and mark the contour interval. No place name.
The V-Forms: Valley and Spur
A V-shaped valley is a narrow, deep, long trough with a river flowing along its floor; the river’s downward cutting carves the V. On the map its contours bend into V-shapes whose apex — the point of the V — always points upstream, that is, uphill. The outermost contour is the highest and the innermost the lowest, so the values decrease inward, towards the valley floor.
A spur is a tongue of high land projecting from higher ground out into lower ground. Its contours are also V-shaped, which is why it is so easily confused with a valley. The difference is exact and worth memorising: on a spur the V points towards the lower ground, downhill, and the values increase inward, towards the high ground — the reverse of a valley on both counts.
Diagram
Fig. 2.5-2 Caption: Both draw V-shaped contours, but the valley’s V points upstream with falling values, while the spur’s V points downhill with rising values. Brief: Draw two panels side by side, each a contour plan above and a section below. (1) V-shaped valley — contours forming Vs whose points aim uphill/upstream (mark a river arrow flowing down through the apexes); values labelled decreasing inward toward the floor; a deep V section. (2) Spur — contours forming Vs whose points aim downhill toward lower ground; values labelled increasing inward toward the high ground; a section showing a projecting tongue of land. Mark the direction of the V-apex in each. Contour interval marked. No place name.
The Steep Faces
An escarpment, or scarp, is an abrupt, comparatively long and regular steep face of a hill, ridge or plateau. It results from the erosion of tilted rock layers, or from faulting, which lifts one block against another. Its contours run very close together down the steep face — though they do not touch — while the far side falls away as a gentle back-slope with widely spaced contours.
A waterfall forms where a river drops over a near-vertical step, usually where it crosses from hard rock onto softer rock that wears away faster. Its contours resemble a valley’s V, but at the fall itself two or more contours run into one another, because the drop is almost vertical.
A sea cliff is a very steep, almost vertical face of high ground at the coast, cut back by the pounding of waves. Like the waterfall, its steepness makes two or more contours join one another — here along the line where the land meets the sea.
The waterfall and the sea cliff are the living examples of the rule met in Section 2.2.3: where a slope becomes vertical, contours are allowed to touch. The escarpment sits just short of that — steep enough to crowd its contours to the edge of touching, but not vertical, so they still hold apart.
Diagram
Fig. 2.5-3 Caption: Three steep faces — the escarpment crowds its contours to the edge of touching, while the waterfall and sea cliff push them together. Brief: Draw three panels, each a contour plan above and a section below. (1) Escarpment — contours very close on one steep face and wide apart on the gentle back-slope; an asymmetric section (steep scarp, gentle dip slope). (2) Waterfall — valley-style V contours with two or more contours merging into one line at the fall; a section showing a near-vertical drop with the river. (3) Sea cliff — closely spaced contours merging into one another along a coastline, sea shaded on one side; a section showing a vertical cliff face meeting the sea. Label each; contour interval marked. Show the sea as officially shaded water, no disputed boundaries, no place name.
2.6 Summary
Relief — the differences in height and shape of the land — is three-dimensional, but a map is flat. Relief is never copied onto paper; it is coded onto it by symbols the reader learns to translate back.
The pictorial methods — the colour method, hachures, hill shading and layer tints — give a quick impression of the land’s shape and steepness, but none of them gives exact heights.
The point methods — spot heights, bench marks and trigonometrical stations — give exact heights above mean sea level, but only at single points, and so are used alongside a method that shows shape.
A contour joins all adjacent points of the same height. Contours are the most accurate method because a contour map carries the full shape of the ground, height everywhere included.
The vertical interval (the fixed height gap between contours) stays constant while the horizontal equivalent (the ground distance between them) varies with slope. So contour spacing reads as slope, and gradient equals vertical interval divided by horizontal equivalent.
Contours obey fixed rules: they are continuous, they close on themselves or leave the map edge, they keep a constant interval, they crowd on steep ground, and they never cross except where the ground is vertical.
Interpolation draws contours from scattered survey heights by proportion, assuming an even slope between points. More measured points give truer lines, so a contour is a sound estimate, not a guarantee.
A profile is a side view of the land along a chosen line, built from the contours by dropping perpendiculars or by the paper-strip method. It makes visible the landscape the plan only encodes.
Vertical exaggeration stretches the vertical scale (usually 5 to 10 times, never beyond about 20) so relief shows clearly — but the same stretch distorts slopes, so the figure used must be stated.
Slopes are read from the spacing pattern: even spacing is a uniform slope, crowding at the top a concave slope, crowding at the base a convex slope, paired lines a terraced slope, and irregular spacing an undulating slope.
Landforms are read from the contour pattern: near-circular loops a conical hill, elongated loops a ridge, a bare centre a plateau, merging contours a waterfall or sea cliff, a V pointing upstream a valley, and a V pointing downhill a spur.
Flowchart
Fig. 2.6-1 Caption: The whole chapter in one chain — the land is coded onto flat paper, and the reader lifts its shape back off the page. Nodes: Three-dimensional land, height varies everywhere → mapmaker codes height onto flat paper by a chosen method → which kind of method? pictorial (colour, hachures, hill shading, layer tints) → a picture of shape but no exact heights; point (spot heights, bench marks, trig stations) → exact heights only at points; contours → exact height everywhere → contours drawn from survey point-heights by interpolation at a constant vertical interval → reader lifts the shape back off the map → spacing → slope (close = steep, wide = gentle); spacing pattern → slope shape (uniform, concave, convex, terraced, undulating); contour pattern → landform (hill, ridge, plateau, escarpment, valley, spur, waterfall, cliff) → a profile drawn along any line rebuilds the side view, using vertical exaggeration
What This Chapter Cannot Tell You
A contour map is silent about the ground between its lines — any bump, dip or feature smaller than the contour interval simply does not appear. Interpolated contours assume even slopes between measured points, so they are estimates, and a profile’s apparent steepness depends on the vertical exaggeration chosen, not on the land alone. Contours give height and shape, but not what the surface is made of, whether water actually flows in a valley, or how the land came to take its form — those questions need other evidence.
2.7 Key Terms
- Bench mark — a point of known height fixed permanently to a solid object such as a pillar or bridge, shown as B.M. with its height.
- Concave slope — a slope steep at the top and gentle at the base, whose contours crowd near the top and spread near the bottom.
- Conical hill — a cone-shaped hill with a broad circular base and a narrow peak, shown by nearly circular, evenly spaced contours.
- Contour — an imaginary line joining all adjacent points at the same height above mean sea level.
- Contour interval — the fixed height gap chosen between successive contours on a map, equal to the vertical interval.
- Convex slope — a slope gentle at the top and steep at the base, whose contours spread near the top and crowd near the bottom.
- Escarpment — an abrupt, long, steep face of a hill, ridge or plateau, shown by very closely spaced contours that do not touch.
- Form lines — broken lines drawn like contours but showing only approximate, un-surveyed heights.
- Gentle slope — a slope with a gradual change of height, gradient less than 1 in 10, shown by widely spaced contours.
- Gradient — the steepness of a slope, the vertical rise divided by the horizontal distance, written as 1 in n.
- Hachures — short lines drawn down the slope, thick and close on steep ground and thin and far apart on gentle ground.
- Hill shading — shading that imitates light and shadow from one direction to give a three-dimensional impression of relief.
- Horizontal equivalent — the horizontal ground distance between two successive contours, small on steep slopes and large on gentle ones.
- Interpolation of contours — the process of drawing continuous contours from scattered measured point-heights by proportion.
- Layer tints — colours filling each height band between contours and deepening with altitude; also called hypsometric tints.
- Mean sea level — the average level of the sea, taken as the zero from which all land heights are measured.
- Plateau — an elevated tract of nearly level land with steep sides, shown by a contour-free centre ringed by crowded edge contours.
- Profile — the side view of the land along a chosen line, as if the ground were cut vertically; also called a cross-section.
- Range of elevation — the difference between the highest and lowest heights shown on a map.
- Relief — the differences in height and the shape of the land surface, such as mountains, plateaus, plains and valleys.
- Ridge — a long, narrow highland sloping steeply on both sides, shown by elongated, closely spaced contours.
- Sea cliff — a very steep, almost vertical coastal face, shown by two or more contours merging.
- Spot height — the surveyed height of a particular point of ground above mean sea level, shown as a dot with its value.
- Spur — a tongue of high ground projecting into lower ground, shown by V-shaped contours pointing downhill with values rising inward.
- Steep slope — a slope with a sharp change of height, gradient more than 1 in 10, shown by closely spaced contours.
- Terraced slope — a slope that rises in steps, shown by contours grouped in close pairs separated by wide gaps.
- Triangulation — a survey method that fixes positions across a country through a connected network of measured triangles.
- Trigonometrical station — a survey point used in triangulation, shown on the map as a small triangle with its height.
- Undulating slope — an irregular slope, concave in parts and convex in others, shown by unevenly spaced contours.
- Uniform slope — a slope of constant steepness, shown by evenly spaced contours.
- Vertical exaggeration — drawing the vertical scale larger than the horizontal scale so that relief shows clearly on a profile.
- Vertical interval — the fixed difference in height between two successive contours.
- V-shaped valley — a narrow river-cut valley, shown by V-shaped contours pointing upstream with values rising outward.
- Waterfall — a near-vertical drop where a river crosses from hard to soft rock, shown by two or more contours merging.
2.8 Points to Ponder
A map never copies the shape of a mountain; it only stands for it with agreed symbols. If two mapmakers chose different symbols for the very same hill, would they be drawing the same land, or two different lands?
A contour is an imaginary line — no such line is painted anywhere on the hillside. Yet it lets a stranger read the exact height of ground they have never seen. How can something that does not exist on the land carry such reliable information?
Interpolation assumes the slope between two known heights is even, though real ground rarely is. Is a contour map therefore a faithful record of the land, or partly a well-reasoned guess about it — and can adding more survey points ever remove the guessing completely?
The vertical exaggeration that makes a profile readable also makes gentle land look jagged. If every usable profile must distort the very slopes it sets out to show, can a profile ever honestly be called a true picture of the land?
The same V-shaped contours can mean a valley or a spur, and a dry valley looks exactly like a river valley. What does this reveal about the gap between the shape of the land and the life that moves across it — and which of the two can a contour map actually hold?
A contour interval of 20 m hides every rise and dip smaller than 20 m; a larger interval simplifies the map but loses detail, a smaller one shows more but crowds the page. Is there a single ‘correct’ contour interval, or does the right map always depend on the question being asked of it?
2.9 Objective Questions
- The method of showing relief that gives exact heights but only at separate points is:
- hachures
- layer tints
- spot heights
- hill shading [1 mark]
- On a contour map, contours drawn very close together indicate:
- a gentle slope
- a steep slope
- flat land
- the level top of a plateau [1 mark]
- The apex of the V-shaped contours of a river valley always points:
- downstream
- upstream
- straight across the valley
- in no fixed direction [1 mark]
- On a topographical map, contours are conventionally printed in:
- blue
- green
- brown
- black [1 mark]
- Assertion (A): The horizontal equivalent varies from place to place on a contour map. Reason (R): The vertical interval is kept constant on any one contour map.
- Both A and R are true and R is the correct explanation of A.
- Both A and R are true but R is not the correct explanation of A.
- A is true but R is false.
- A is false but R is true. [1 mark]
- Assertion (A): A profile drawn with high vertical exaggeration makes gentle slopes look steep. Reason (R): Vertical exaggeration stretches the vertical scale relative to the horizontal scale.
- Both A and R are true and R is the correct explanation of A.
- Both A and R are true but R is not the correct explanation of A.
- A is true but R is false.
- A is false but R is true. [1 mark]
- Match each relief feature in Column A with its contour signature in Column B:
| Column A | Column B |
|---|---|
| a. Conical hill | i. Two or more contours merge |
| b. Plateau | ii. Nearly circular, evenly spaced contours |
| c. Spur | iii. Contour-free centre ringed by crowded edge contours |
| d. Waterfall | iv. V-shaped contours pointing downhill with values rising inward |
[1 mark]
Fill in the blank: The difference between the highest and lowest heights shown on a map is called the ________. [1 mark]
Fill in the blank: A slope that is steep in its upper part and gentle in its lower part is called a ________ slope. [1 mark]
State whether true or false: Contours may begin or end anywhere within the body of a map. [1 mark]
2.10 Check Your Concepts
Define a contour. State one reason it is regarded as the most accurate method of showing relief. [2 marks]
What is meant by the range of elevation? How does it help in fixing the contour interval? [2 marks]
Differentiate between a bench mark and a spot height. [2 marks]
Differentiate between the vertical interval and the horizontal equivalent, and explain how the relationship between them allows contour spacing to reveal the slope of the land. [3 marks]
Give reasons for the following: (a) contours crowd together on a steep slope; (b) two or more contours merge at a sea cliff. [3 marks]
Distinguish between the contour pattern of a V-shaped valley and that of a spur. [3 marks]
Explain the process of interpolation of contours, giving the steps in order, and illustrate it by placing one contour between two points of known height. [4 marks]
‘Vertical exaggeration makes a profile useful but also makes it misleading.’ Evaluate this claim. [4 marks]
Describe how layer tints show relief, and explain how they improve on the simple colour method. [4 marks]
Describe the different methods of showing relief on a map, and explain why the contour method is preferred for a topographical map. [6 marks]
Explain, with reference to their contour patterns, how a uniform slope, a concave slope, a convex slope and a terraced slope can each be identified on a map. Why does the pattern of spacing, rather than a single measurement, reveal the shape of a slope? [6 marks]
2.11 Map, Diagram & Data Interpretation
Study Fig. 2.5-2, showing a valley and a spur.
- State the direction in which the V of the contours points in each feature. [1]
- In which of the two do the contour values increase inward, towards the centre of the V? [1]
- Name one thing the contours alone cannot tell you about the valley. [1] [3 marks]
On a map drawn to a scale of 1 : 50,000, two successive contours with a vertical interval of 50 m are 2.5 cm apart. Showing every step of your working:
- Find the ground distance between the two contours (the horizontal equivalent). [2]
- Calculate the gradient of the slope. [1]
- State whether the slope is steep or gentle, and give your reason. [1] [4 marks]
Using Fig. 2.4-1, describe how the spacing of contours differs between a concave slope and a convex slope, and state where along each slope the ground is steepest. [3 marks]
Two neighbouring survey points read 640 m and 700 m above mean sea level, with an even slope between them, as in the interpolation of Fig. 2.2-2.
- Which contour values, at a 20 m interval, fall between the two points? [1]
- Show by proportion where the 660 m contour crosses the line joining the two points. [2]
- State one assumption this working depends on. [1] [4 marks]
A contour map shows a set of nearly circular, evenly spaced contours whose values increase towards the centre.
- Name the landform. [1]
- State the type of area where such a landform commonly occurs. [1]
- State one thing this contour pattern cannot tell you about how the landform came to be. [1] [3 marks]