A map shows where things are. But a road, a canal or a dam depends just as much on how high the ground is — and a flat sheet of paper has no obvious way to show that.
Contour lines solve the problem, and they do it so effectively that they have become the standard way of representing terrain.
Why Relief Must Be Shown
The relative positions of points in a plane are represented by a map. The value of the map is even more if the relief — the variation in the elevation of the earth’s surface — is also included along with their relative positions.
A plan giving only horizontal positions answers half the question. Where should the road go? You cannot say without knowing the gradients. Where will water collect? You cannot say without knowing what is high and what is low.
Two Ways of Presenting the Ground
There are two methods by which the conformation of the ground may be presented on a map:
| Method | How It Works | Elevations Given? |
|---|---|---|
| (a) Shading | Delineating the surface slopes by shading, intended to give an impression of relative relief | No — relative elevations are not indicated |
| (b) Contour lines | Plotting imaginary lines passing through points of equal elevation | Yes |
Why Contours Won
Shading produces something an eye can interpret at a glance — you can see that a region is hilly. But you cannot measure anything from it. There are no numbers.
Contour lines, by contrast, are arranged such that the form of the earth’s surface can be portrayed with greater accuracy and thoroughness, and can be readily interpreted. They give both the visual impression and the numerical values.
That combination is why contours are used by engineers in so many ways, and why shading survives only as an artistic supplement.
Definition of a Contour
Two definitions are given, and they describe the same thing from different directions.
Definition 1
A contour may be defined as an imaginary line passing through points of equal elevation on the earth’s surface.
Definition 2
A contour line may also be defined as the intersection of a level surface with the surface of the earth.
Why the Second Definition Is the More Powerful One
The first definition tells you what a contour is. The second tells you why it behaves as it does, and almost every characteristic of contour lines follows from it.
Recall from levelling that a level surface is one of constant height above mean sea level. Now imagine slicing the landscape with such a surface — like a perfectly horizontal sheet of water rising to a given height. Wherever that sheet meets the ground, it traces a line.
That line is the contour. And this picture immediately explains several rules:
- A contour must be closed, because the intersection of two surfaces cannot simply stop in mid-air.
- Two contours cannot cross, because a single point of ground cannot be at two different elevations at once.
- Contours cannot merge, for the same reason.
The shoreline of a lake is the clearest real example — it is literally a level surface meeting the land.
Submarine Contours
When contours are drawn underwater, they are termed submarine contours, fathoms, or bathymetric curves.
These are the contours of the sea bed rather than the land, and they connect directly to hydrographic surveying — whose purpose includes determining the shape of the area under the water surface and the depth of channels.
The term fathom reflects the traditional unit of water depth, and bathymetric comes from the Greek for depth measurement.
Contours Are Invisible
Note: generally contours are not visible on the ground, except in the case of shorelines.
Why the Shoreline Is the Exception
This note is more instructive than it first appears.
A contour is an imaginary line — there is nothing on the ground to mark it. Walk across a hillside and you will not see any line at your feet, however carefully you look.
But a shoreline is a contour you can actually see. Still water forms a level surface, so the line where it meets the land is precisely the intersection described in the second definition. The zero metre contour is the coastline itself.
This is why a lake edge or a coastline is the standard way of explaining contours to someone meeting them for the first time — it is the one case where the abstraction becomes visible.
The Seven Uses of Contours
| No. | Use |
|---|---|
| (a) | Proper and precise location of engineering works such as roads, canals, etc. |
| (b) | In location of water supply and water distribution, and to solve problems of stream pollution |
| (c) | In planning and designing of dams, reservoirs, aqueducts and transmission lines |
| (d) | In selection of sites for new industrial plants |
| (e) | Determining the intervisibility of stations |
| (f) | Determining the profile of the country along any direction |
| (g) | To estimate the quantity of cutting, filling, and the capacity of reservoirs |
Grouping the Uses
The seven fall into three natural families, which makes them easier to recall.
Choosing where to build (a, c, d). Roads and canals need particular gradients; dams need a valley of the right shape; industrial plants need level ground with drainage. In each case the contour map answers the siting question before any ground is broken.
Understanding how water behaves (b, c, g). Water flows downhill, always perpendicular to the contours. So a contour map is effectively a map of where water will go — which is why it serves water supply, distribution, stream pollution and reservoir capacity alike.
Extracting information the map does not directly show (e, f, g). These three are computations performed on the contours rather than readings from them.
Three Uses Worth Explaining
Intervisibility of stations (e). Can a surveyor at station A see station B? This matters enormously — direct ranging requires intervisible ends, and a theodolite must see its target. Contours let you answer the question from the office, by checking whether any intervening ground rises above the line joining the two stations. Without contours you would have to walk the ground to find out.
Profile of the country along any direction (f). Draw any line across a contour map, note the elevation where it crosses each contour, and plot those heights against distance. You have a section through the ground along that line — obtained without any fieldwork at all. This is the basis of longitudinal sections for roads and railways.
Quantities of cutting and filling, and reservoir capacity (g). The area enclosed by each contour can be measured with a planimeter. Multiply areas by the contour interval and you obtain volumes — the earthwork to be moved, or the water a reservoir will hold at each level.
Note that this last use requires the contour interval to be known and constant, which is exactly why a constant contour interval is desirable.
Quick Revision Notes
- Relief means the variation in the elevation of the earth’s surface.
- Two methods of showing ground form: shading (gives an impression only, no elevations) and contour lines (accurate and readily interpreted).
- A contour is an imaginary line passing through points of equal elevation.
- It may also be defined as the intersection of a level surface with the surface of the earth.
- Underwater contours are called submarine contours, fathoms or bathymetric curves.
- Contours are not visible on the ground except in the case of shorelines.
- Seven uses: locating engineering works; water supply, distribution and stream pollution; designing dams, reservoirs, aqueducts and transmission lines; selecting industrial plant sites; determining intervisibility of stations; determining the profile of the country; estimating cutting, filling and reservoir capacity.
Mistakes Students Commonly Make
- Giving only one definition of a contour. The level surface intersection definition explains the behaviour of contour lines and is the more useful one.
- Saying shading shows relative elevations. It gives only an impression of relief; no elevations are indicated.
- Thinking contours can be seen on the ground. They are imaginary, visible only as shorelines.
- Forgetting the alternative names for underwater contours — fathoms and bathymetric curves.
- Omitting intervisibility of stations from the list of uses.
- Overlooking that contours give volumes as well as heights, through areas multiplied by the contour interval.
Conclusion
A contour is the line traced where a level surface cuts the ground — which is why contours close on themselves, never cross and never merge. That single idea turns a flat map into a three-dimensional description of the landscape, accurate enough to site a dam, trace where water will flow, check whether two stations can see one another, cut a section through the country in any direction, and compute the earthwork or reservoir capacity involved. Only at a shoreline does the imaginary line become something you can actually see.
Frequently Asked Questions
What is a contour?
An imaginary line passing through points of equal elevation on the earth’s surface. It may also be defined as the intersection of a level surface with the surface of the earth.
What is relief?
The variation in the elevation of the earth’s surface.
What are the two methods of presenting ground form on a map?
By delineating the surface slopes with shading, which gives an impression of relative relief but no elevations, and by plotting contour lines, which portray the surface accurately and can be readily interpreted.
What are submarine contours?
Contours drawn underwater. They are also called fathoms or bathymetric curves.
Are contours visible on the ground?
Generally no, since they are imaginary lines. The exception is shorelines, where still water forms a level surface meeting the land, making the contour visible.
What are the uses of contours?
Locating engineering works such as roads and canals; locating water supply and distribution and solving stream pollution problems; planning dams, reservoirs, aqueducts and transmission lines; selecting industrial plant sites; determining intervisibility of stations; determining the profile of the country in any direction; and estimating cutting, filling and reservoir capacity.
How do contours help determine intervisibility?
By showing whether any intervening ground rises above the line joining two stations, which allows the question to be answered from the map rather than by walking the ground.
How are volumes estimated from contours?
By measuring the area enclosed by each contour and multiplying by the contour interval, which gives the volume of earthwork or the capacity of a reservoir at each level.
Why can two contour lines not cross?
Because a contour is the intersection of a level surface with the ground, and a single point of ground cannot be at two different elevations at the same time.