Isopleth

Also called: Isoline, Isopleth map · Topic: Graphical Representation of Data and Thematic Maps · NCERT: Class 12, Ch 3 "Graphical Representation of Data"

Meaning

An isopleth (also called an isoline) is a line on a map that joins places with the same value of something that changes smoothly across space, like temperature, rainfall, pressure, slope or height. An isopleth map uses many such lines and ignores state and district borders. It shows how a natural feature rises and falls over a whole region, which a table of numbers cannot show.

Explanation

What it shows and why the lines are drawn

• Some data change smoothly across space.
• Slope, temperature, rainfall and pressure do not stop at a state or district border.

• So the map ignores administrative borders (the borders of states, districts and other government units) and follows the data.

• Word origin: Iso = equal. NCERT says pleth means "lines". The Greek root plethos actually means "quantity", so an isopleth is a "line of equal quantity".

• Input = values at points. These points are weather stations, rain gauges or spot heights (points on a map where the exact height is written). The lines are drawn between these points.
• Basic rule: lines of different values never cross. One place cannot have two values at the same time.

Types of isopleths

Isopleth	Joins places of equal…	Source
Isotherm	temperature	NCERT
Isobar	atmospheric pressure	NCERT
Isohyet	rainfall over a set period (a month, a season, a year)	NCERT
Isoneph	cloudiness (cloud cover)	NCERT
Isohel	sunshine (hours of bright sunshine)	NCERT
Contour	height above mean sea level	NCERT
Isobath	depth below a water surface	NCERT
Isohaline	salinity (salt content) of sea water	NCERT
Isoseismal	earthquake intensity	Beyond NCERT
Isochrone	travel time from a point	Beyond NCERT
Isogonic line	magnetic declination (the angle between true north and magnetic north)	Beyond NCERT

• Isobath: works like a contour line, but under water. It measures depth, not height. It shows the continental shelf, the slope and the ocean deeps.
• Isohaline: salinity is usually given in parts per thousand (‰).
• Isoseismal: joins places that felt the same intensity of shaking. Intensity measures damage and the effect on people. It does not measure the energy released.
• Usually, intensity falls as you move away from the epicentre. So isoseismals form nested rings, with each higher-intensity zone inside the next lower one [4].
• Older isoseismal maps used contour lines to separate areas of equal whole-number intensity. The USGS "Did You Feel It?" (DYFI) maps today are numerically interpolated (worked out by computer), so they show continuous values [4].
• The US uses the Modified Mercalli Intensity (MMI) scale, written in Roman numerals [4].

How to draw one: requirements and rules

• What you need:
• A base map with the point locations marked.
• Data for one fixed period at every point, such as mean January temperature or annual rainfall. You cannot mix values from different periods.

• Drawing instruments, especially a French curve (a plastic template with many curves, used to draw smooth lines).

• Rules:

• Use equal intervals. An interval of 5, 10 or 20 is ideal (for example 20°, 25°, 30°C, or 100, 120, 140 cm).
• Write each line's value on one side of the line or in a break in the line.
• Draw smooth lines that never cross.
• Draw the lowest-value isopleth first, then the higher ones in order.

Interpolation: placing the line between stations

• Interpolation means estimating values between two observed points, in proportion to distance. It assumes the value changes evenly from one point to the next.
• Why it is needed: a station rarely records exactly 30°C or 100 cm. So the line for a round value has to be placed between stations.
• NCERT formula: Position of the isopleth = (distance between the two points ÷ difference between their values) × interval.

• Here the "interval" is the gap between the lower station's value and the value of the isopleth you want.

• Steps: 1. Join two neighbouring stations with a faint pencil line. 2. Work out how many millimetres stand for one unit of value (distance ÷ value difference). 3. Multiply this by the gap between the lower station's value and the isopleth value. 4. Measure that distance from the lower-value station and mark a point. 5. Repeat for every pair of stations. Join the marks with a smooth curve using the French curve.

• NCERT worked example (Fig. 3.15):

• Station A = 28°C, station B = 33°C, map distance = 10 mm.
• Value difference = 5°C, so 1°C = 10 ÷ 5 = 2 mm.
• For the 30°C isotherm: gap from A = 30 − 28 = 2°C. Position = 2 × 2 = 4 mm from A.

• On the same line, the 31°C isotherm falls 6 mm from A and the 32°C isotherm falls 8 mm from A.

• Computer version (GIS): a GIS (Geographic Information System: software that stores, analyses and maps data tied to places) does interpolation automatically. It makes a gridded surface, which is a regular net of cells, each with an estimated value.

• Inverse distance weighting (IDW): a nearby station counts for more than a far one. The weight goes down as distance goes up, often as 1 ÷ distance².
• Kriging: a statistical method. It first uses a semivariogram (a graph showing how values become less alike as points get farther apart) to measure how fast values change with distance. Then it uses this to set the weights.
• The USGS ShakeMap system weights its station and felt-report data by distance using spatial semivariograms. It also allows for uncertainty in the data, called the "nugget effect" [5].
• Isohyets and isotherms are then drawn on the grid as contours. This is the same job as the hand method, done at thousands of points at once.

Where it occurs

• Isohyets of India: on the annual rainfall map, the lines bunch close together over the Western Ghats and Meghalaya, where rain is very heavy. They spread far apart over western Rajasthan, where rain is very low.

• Isohyets also show the sharp drop in rainfall from the windward Western Ghats (the side facing the moist wind) to the rain-shadow Deccan (the dry side behind the mountains).

• Isohalines in Indian seas: they show that the Bay of Bengal is less salty than the Arabian Sea, because many large rivers pour fresh water into the Bay.

• Isobaths: on sea-floor maps they show the continental shelf, the slope and the ocean deeps.
• IMD gridded rainfall (India's example of IDW):
• IMD Pune built a daily rainfall grid at 0.25° × 0.25° (latitude × longitude) for 1901–2010, using 6,955 rain-gauge stations. Up to then, no study of this kind had used more stations (Pai et al., MAUSAM, 2014) [2].
• Gauge values were spread onto the grid with Shepard's (1968) inverse-distance weighting [2].

• The fine grid shows orographic rain zones (areas where moist wind rises over mountains and drops rain) much better than older, coarser datasets. Examples are the Western Ghats and North-East India [2].

• Free data: IMD Pune's Climate Data Service Portal offers free download of gridded rainfall and temperature data of India [3].

• USA: USGS "Did You Feel It?" maps and ShakeMap turn felt reports and station readings into intensity surfaces after earthquakes [4] [5].

Don't confuse with

• Choropleth map: shades or colours whole administrative units (for example, population density by district) using values for areas. An isopleth map draws lines from values at points and ignores borders.
• Contour vs isobath: a contour joins equal height above mean sea level. An isobath joins equal depth below a water surface.
• Isoseismal vs magnitude: an isoseismal joins equal intensity (damage and how strongly people felt the shaking). It does not show magnitude (energy released).
• Interpolation vs extrapolation: interpolation estimates values between observed points. Extrapolation estimates values beyond the last observed point.

Prelims Hooks

• Isohyet = equal rainfall. Isohel = equal sunshine. Isoneph = equal cloudiness. These three are the pairs most often swapped in matching questions.
• Isobath = equal depth. Contour = equal height above sea level. Isohaline = equal salinity. Isogonic line = equal magnetic declination. Isochrone = equal travel time.
• Isoseismal = equal earthquake intensity, not magnitude. The US measures intensity on the Modified Mercalli Intensity (MMI) scale [4].
• NCERT says the ideal intervals are 5, 10 or 20. Smooth lines are drawn with a French curve, and the lowest-value line is drawn first.
• NCERT example: stations at 28°C and 33°C, 10 mm apart. The 30°C isotherm lies 4 mm from the 28°C station.
• IMD gridded rainfall: 0.25° × 0.25°, 6,955 rain gauges, 1901–2010, built with Shepard's inverse-distance weighting [2].

Mains Points

• Why isopleths suit climate and relief data (GS-I):
• Rainfall, temperature and pressure depend on physical controls such as latitude, relief, distance from the sea and winds. They do not depend on state borders.

• Isohyets show the sharp fall from the windward Western Ghats to the rain-shadow Deccan. Maps like this guide crop planning, mapping of drought-prone areas and the design of irrigation projects.

• Limits of interpolation:

• It assumes values change evenly between stations. Where gauges are few (Himalaya, Thar Desert, oceans), estimates are less reliable.

• Steep relief can create local highs and lows that no station records. So a denser station network gives a more accurate map, which is why IMD's 6,955-gauge network makes the 0.25° rainfall grid more realistic in hilly areas [2].

• Disaster and resource uses (GS-III):

• Isoseismal maps outline damage zones after an earthquake. This helps relief work and the making of building codes [4].
• Free gridded rainfall and temperature data from IMD's portal feed flood and drought monitoring, heatwave studies and climate-trend analysis [3].
• NCERT's hand method of placing lines by distance is the basic idea behind IDW and kriging. These modern methods add distance weighting and an allowance for uncertainty, which turns point readings into maps that planners can act on [5].

Related concepts

• Isohyet
• Isohaline
• Isobath
• Interpolation

Read more

• Isopleth maps and interpolation