Contours and slopes

In this note

Detail

Contour line: an imaginary line on a map that joins places of equal height above mean sea level. Mean sea level is the average level of the sea surface, taken as zero height.
Contours are also called "level lines". If you walked along one on the ground, you would never go up or down.
How contours are drawn:
Earlier: from ground survey and levelling (measuring height differences between points with instruments in the field).
Today: from aerial photographs and satellite data.
Contours do two jobs on a map:
they give the height of a place
their spacing shows the slope (how steep the land is).
Survey of India Open Series Maps (OSM) are topographic sheets at 1:50,000 scale. They are available as free PDF downloads for every Indian state and union territory, including Ladakh, Arunachal Pradesh and the Andaman and Nicobar Islands [2].
Each OSM sheet carries two numbers. One is the older sheet number (e.g. 39L/12). The other is a new OSM number (e.g. H42W12) [2].

Term	Meaning	Does it change on one map?	Example
Contour interval / Vertical Interval (VI)	The fixed height gap between two contours that come one after another	No. It is usually constant on one map	20 m, 50 m or 100 m
Horizontal Equivalent (HE)	The ground distance (measured flat, along the map) between two contours that come one after another	Yes. It changes with slope	Large on gentle slopes, small on steep slopes

The link between VI and HE:
VI stays the same everywhere on the sheet.
So when the land is steep, you climb one VI in a short distance. HE is small and the contours sit close together.
When the land is gentle, you need a long distance to climb the same VI. HE is large and the contours spread apart.
Gradient (steepness written as a ratio) = VI ÷ HE.
Example: VI = 20 m and HE = 400 m gives a gradient of 1 in 20.
Contour types used on survey maps (United States Geological Survey (USGS) practice):
Index contour: a thick, bold line drawn at every fifth contour and labelled with its height [3].
Intermediate contour: a thinner line between index contours, drawn at the contour interval [3][4].
Supplementary contour: an extra line drawn between two regular contours. It shows small landforms that the normal interval would miss [3][4].
On USGS maps, contours are printed in brown [3].

Close contours mean a steep slope. Wide contours mean a gentle slope.
Very wide spacing, or no contours at all, means the ground is almost level [3].
Merging contours mean a vertical face. Examples are a cliff or a waterfall, where several heights stack on top of one another.
Contours of different heights do not normally cross. One spot on the ground cannot have two heights. The rare exception is an overhanging cliff.
Hill: a set of closed contours whose values rise inward. The highest value sits at the centre.
Depression: a set of closed contours whose values fall inward (a hollow, pit or basin).
A depression is often marked with ticks or hachures: short lines drawn at right angles to the contour [4].
On USGS maps these hashes point towards the lower ground [4].
USGS uses three kinds of depression contour: depression index, depression intermediate and depression supplemental [4].

In the table, "bottom" means the low-value contours and "top" means the high-value contours.

Slope	Contour spacing	What the ground is like	View from the top
Gentle slope	Far apart, evenly spaced	Land rises slowly	—
Steep slope	Close together, evenly spaced	Land rises sharply	—
Concave slope	Wide at the bottom, close at the top	Gentle below, steep above; the slope curves inward like the inside of a bowl	Valley floor can be seen
Convex slope	Close at the bottom, wide at the top	Steep below, gentle above; the slope bulges outward like the outside of a ball	Valley floor is hidden
Undulating / irregular slope	Uneven: close in some stretches, wide in others	Land rises and falls in waves	Varies

Concave slope:
The lower part is gentle, so the low-value contours are spread out.
The upper part is steep, so the high-value contours crowd together.
Standing at the top, nothing bulges in front of you, so you can see the valley below.
Convex slope:
The lower part is steep, so the low-value contours crowd together.
The upper part is gentle, so the high-value contours are spread out.
Standing at the top, the bulge of the slope hides the valley floor.
Classic trap: students often swap concave and convex.
Memory aid: from the top of a con-CAVE slope you can see the valley floor, as if you were looking into a cave. A convex slope hides it.
Always read the contour values first to find which end is "bottom" and which is "top". Spacing alone is not enough.

Contour line joins points of equal height above mean sea level. Its other name is "level line".
VI (contour interval) is constant on one map. HE (horizontal equivalent) changes with slope: large on gentle slopes, small on steep ones.
Close contours = steep slope. Wide contours = gentle slope. Merging contours = cliff or waterfall.
Concave slope = wide spacing at the bottom and close spacing at the top (gentle below, steep above). Convex slope = the reverse. The trap is swapping the two.
From the top of a concave slope the valley floor is visible. A convex slope hides it.
Closed contours rising inward = hill. Closed contours falling inward = depression, marked with ticks or hachures pointing downslope [4].
Index contour = every fifth contour, drawn thick and labelled with its height [3].
Survey of India Open Series Maps are at 1:50,000, free to download as PDF. Sheet number 39L/12 corresponds to OSM number H42W12 [2].
Contours of different heights do not normally cross. "Contours often intersect on steep slopes" is a false statement.
Gradient = VI ÷ HE. Example: 20 m ÷ 400 m = 1 in 20.

Planning roads and railways in hills: close contours mean steep gradients.
Engineers read HE to plan hairpin bends (zig-zag turns), tunnels and cuttings that keep the gradient gentle.
This applies to roads in the Himalaya and to ghat sections in the Western Ghats.
Disaster risk (GS-III): close or merging contours mark cliffs and steep convex slopes.
These are zones prone to landslides and rockfall.
Contour-based slope maps feed into landslide zoning and decisions on where to allow building in hill states.
Agriculture and water: gentle slopes (wide contours) suit farming and settlement.
On steeper slopes farmers build contour bunds and terraces along the contour lines. These slow down run-off and cut soil erosion.
Depressions shown by contours mark possible sites for ponds and water storage.
Changing map-making: contours were once drawn by ground levelling. Today they come from aerial photographs and satellite data.
Free 1:50,000 Open Series Maps from Survey of India now make this terrain data openly available for planning [2].