Methods of relief representation and the datum of height

Detail

What "relief" means

• Relief means the highs and lows of the earth's surface: hills, valleys, plateaus and plains.
• A map is flat, so the mapmaker needs special signs to show height and slope on it.
• The methods of relief representation are the ways of showing height on a flat map. There are six:
• hachures
• hill shading
• layer tints
• bench marks
• spot heights

• contours

• On topographical maps (large-scale maps that show both natural and man-made features of a small area in detail, such as Survey of India sheets), contours and spot heights are the main methods.

Hachures

• Hachures are short, thin lines drawn along the direction of steepest slope. This is the path water would take if it ran straight downhill.
• They run across the contours (at right angles to them), not along them.
• How to read them:
• Steep ground → the lines are thick and close together.
• Gentle ground → the lines are thin and wide apart.

• Flat ground (plain or plateau top) → no lines are drawn.

• They give a good feel for slope, but they show no exact heights.

• They need a lot of drawing work and can hide other details on the map. So modern topographical sheets rarely use them.

Hill shading

• Hill shading shades slopes as if a light were shining on the land, usually from the north-west (the top-left corner of the map).
• How it works:
• The light is imagined to come from the north-west.
• Slopes facing the light stay pale.
• Slopes facing away (the south-eastern sides) look dark.

• Ridges and valleys therefore stand out as if in 3-D.

• It is vivid and easy to read, but it gives no exact heights.

• It is often used together with contours to make relief "pop out".

Layer tints

• Layer tints give each height zone its own colour.
• The usual colour order, from lowest to highest:

Height zone	Usual colour
Sea depths (below sea level)	Blues: darker blue for deeper water
Lowlands and plains	Greens
Higher land (uplands, plateaus, hills)	Yellows, then browns
Highest peaks, snow and ice	White

• Layer tints show broad height zones at a glance, so atlas and wall maps use them a lot.
• They do not give the exact height of a single point. A colour only tells you the height range the point falls in.
• Trap: green means low, not "forest" or "fertile". A green desert lowland and a green delta are coloured the same.

Bench mark (BM)

• A bench mark (BM) is a permanent mark fixed on a building, pillar or rock. Its exact height above sea level has been found by careful surveying.
• On a topographical sheet it is shown with the letters BM and a height figure, e.g. "BM 212".
• It is used as a reference point for levelling (levelling: measuring the height difference between two points with a levelling instrument, step by step). Surveyors start at a known BM and carry the height forward to new points.
• How India's bench marks were built up:
• Survey of India began precise spirit levelling in 1858 [2].
• Levelling done from 1858 to 1909 was adjusted into the First Level Net of India, with about 10,000 bench marks [2].

• Even the GT (Great Trigonometrical Survey) stations on hilltops got their heights from angle readings taken from the nearest bench mark. That bench mark's height had been levelled up from mean sea level [2].

• Present problem: about 70% of the old bench marks no longer exist or have been disturbed (status in 2014) [3]. The causes are plate movement and construction work [2].

Spot height

• A spot height is a dot with a number next to it. The number gives the exact height of that one point above mean sea level.
• It is usually placed on a hilltop, a pass or a point on a road.
• How it differs from a bench mark:
• A bench mark is a physical mark you can find on the ground.
• A spot height is only marked on the map. Nothing is fixed on the ground.

Contours (the main method)

• A contour is a line joining places of equal height above mean sea level.
• Contours and spot heights together give exact heights and also the shape of slopes:
• contours close together → steep slope

• contours far apart → gentle slope

• The contour interval is the fixed vertical gap between two neighbouring contours on a sheet.

Comparison of the six methods

Method	Gives exact height?	Shows slope well?	Main use
Hachures	No	Yes (thickness and spacing)	Old maps; feel of steepness
Hill shading	No	Yes (light and shade, NW light)	3-D effect on relief maps
Layer tints	Only a height range	Partly	Atlases, wall maps
Bench mark	Yes (surveyed, on ground)	No	Reference for levelling
Spot height	Yes (one point)	No	Hilltops, road points
Contours	Yes (along the line)	Yes (spacing)	Main method on topographical maps

Mean sea level: the zero datum

• Mean sea level (MSL) is the average sea surface between high and low tide, measured over many years.
• It is the zero datum (the starting level, height = 0) for all contours, spot heights and bench marks.
• Why a long period is needed: tides go through a full cycle of the moon's position that lasts 18.61 years. So Survey of India defines MSL as the mean of hourly tide heights over 18.61 years at a tide station [2]. A 29-day or 1-year record can give MSL too, but it is less accurate [2].
• Most countries, India included, use MSL as the datum for height [2].
• Survey of India has carried out systematic tidal observation since 1877. The earliest Indian tide records come from Khidirpur Dock on the Hugli river (1806-27) and Sagar Island (1828-29) [2].
• Survey of India runs a network of 36 permanent tidal stations: 30 on the mainland, 4 in Andaman and Nicobar and 2 in Lakshadweep. Only 23 were working in 2024 [2].
• Chart Datum (CD) is a different datum from MSL. It is the lowest low-tide level at a place. Sea-depth (bathymetric) contours on navigation charts are measured from it, not from MSL [2]. Survey of India had fixed the Chart Datum for 272 ports by 2024 [2].

India's vertical datum: how it has changed

• Vertical datum means the reference surface from which all heights in a country are measured.
• First Level Net (1909):
• The datum was defined in 1905 [3].
• It was fixed to the MSL of 9 ports: four on the east coast, four on the west coast, and Karachi [2].

• This 100-year-old data is still in use [2].

• Flaw in the old datum:

• All 9 ports were assumed to have MSL at 0.000 m.
• In fact, MSL on the east and west coasts differs by about 40 cm.
• This is mainly because the water of the Arabian Sea and the Bay of Bengal have different salinity [2].

• So the old heights cannot be used for exact studies such as sea-level rise [2].

• Second Level Net:

• It used the local MSL of Bombay, from 38 years of records with a mean epoch of 1955 (epoch: the reference date the average is centred on).

• It was never released to users [2].

• Redefined Indian Vertical Datum (RIVD):

• The project started in 2006 [2][3].
• Heights are computed from a Type 'P' standard bench mark at Mumbai, tied to the local MSL of the Apollo Bunder tidal observatory, Mumbai (1978-1994) [2].
• Gravity was measured at bench marks every 3-5 km [2]. Heights now follow real gravity, so they tell correctly which way water will flow.
• About 46,000 linear km of high-precision levelling (Phase I) was done by 2014 [3].
• Phase II plans to add about 1,00,000 linear km to make the network denser [3].

Beyond the map: GPS heights, the ellipsoid and the geoid

• Ellipsoid: a smooth mathematical model of the earth's shape. It is a slightly flattened sphere.
• WGS-84 (World Geodetic System 1984) is the ellipsoid used by GPS [4].

• Its centre is at the earth's centre, so it is called geocentric [2].

• Geoid: the surface of equal gravity that best fits global mean sea level [4]. You can think of it as "sea level extended under the land".

• Two kinds of height:
• Ellipsoid height (h): height above the WGS-84 ellipsoid. This is what a GPS receiver gives [4].

• Orthometric height (H): height above the geoid, which is the familiar "height above sea level" printed on maps [4].

• How to convert: subtract the geoid height (N), the gap between ellipsoid and geoid at that place: H = h − N [5].

• So a raw GPS height is not the same as the map height.

• A geoid model is needed to convert one into the other.

• India's geoid work:

• The first geoid model of India (the 1980s) was accurate only to metres [2].

• Hybrid geoid models with about 10 cm accuracy have since been released for several states (status in 2024) [2].

• Link to Open Series and Defence Series Maps:

• Old Survey of India sheets used the Everest ellipsoid. It was fixed in 1830 with its origin at Kalyanpur, Madhya Pradesh (24°07′N, 77°39′E), and it is not centred on the earth's centre [2].
• In the early 2000s, India changed over to WGS-84 [2].

• Old topographical maps were converted, with 3-5 m accuracy. The converted sheets became the Open Series Maps (OSM) and Defence Series Maps (DSM) [2].

• Datums differ by country:

• The USA uses NAVD88, fixed to one tide station at Father Point/Rimouski, Quebec.
• Japan uses a bench mark at Tokyo as its fixed point.

• Australia uses MSL from 30 tide gauges around its coast [2].

• CORS network:

• CORS (Continuously Operating Reference Stations) are fixed GNSS stations that record satellite signals all the time.
• Survey of India has 1,042 CORS stations. They let a field receiver find its position in real time to about 1 cm (status in 2024) [2].

Prelims Hooks

• On topographical maps, the main methods of relief are contours and spot heights. Hachures, hill shading and layer tints give no exact heights.
• Hachures run along the direction of steepest slope, across the contours. They are thick and close on steep ground and thin and wide apart on gentle ground.
• In hill shading, light is assumed to come from the north-west, so south-east-facing slopes look dark.
• Layer tint order (low → high): blue (sea depths) → green (lowlands) → yellow → brown → white (snow).
• Bench mark vs spot height: a BM is a physical surveyed mark on a building, pillar or rock. A spot height is only a dot on the map.
• MSL is the zero datum for contours, spot heights and BMs. Survey of India computes it as the mean of hourly tides over 18.61 years [2].
• Sea-depth contours on navigation charts are measured from Chart Datum (lowest low tide), not from MSL [2].
• India's old (1909) level net was fixed to 9 ports, including Karachi. The Redefined Indian Vertical Datum (from 2006) uses a bench mark at Mumbai, tied to MSL at Apollo Bunder [2].
• GPS height is measured above the WGS-84 ellipsoid, and map height is measured above the geoid/MSL. Orthometric height H = h − N [4][5].
• The Everest ellipsoid had its origin at Kalyanpur (Madhya Pradesh). OSM and DSM are sheets converted to WGS-84 [2].

Mains Points

• Why an accurate height datum matters for development (GS-III, infrastructure and disasters):
• Dams, canals, flood maps and coastal-zone plans need heights correct to a few centimetres. Water flows according to gravity, and an error of half a metre can flood the wrong area [2][3].

• India's heights still rest largely on the 1905-09 datum, and about 70% of the old bench marks are lost [3]. This weakens inundation mapping and sea-level-rise studies [2][3].

• East-west coast MSL gap (GS-I, physical geography):

• The salinity of the Arabian Sea and the Bay of Bengal differs.
• So the sea surface stands about 40 cm apart on the two coasts [2].

• One single "sea level" for all ports is therefore a simplification. Modern datums use one fixed origin plus gravity (RIVD, NAVD88, Japan) [2].

• Change from old to new methods:

• Older drawn methods (hachures, hill shading, layer tints) gave a visual feel for relief.
• Survey-based methods (bench marks, spot heights, contours) gave measurable heights.

• Today, GNSS + CORS + geoid models give heights quickly and cheaply. But they still need a good geoid model to turn GPS heights into sea-level heights [2][5].

• Policy angle: better tide gauges, a denser RIVD network, ~10 cm state geoid models and open release of levelling data would help coastal hazard warning (tsunami, storm surge) and disaster planning. Tidal data were shared with INCOIS after the 2004 tsunami [2].