Isopleth maps and interpolation

Detail

What an isopleth map shows

• Some data change smoothly across space. They do not stop at state or district borders. Examples are slope, temperature, rainfall and pressure.
• These data are shown by isopleths. An isopleth is a line that joins places having the same value of something.
• Word origin: Iso = equal. NCERT glosses pleth as "lines". The Greek root plethos actually means "quantity", so an isopleth is a "line of equal quantity".
• How it differs from a choropleth map:

Feature	Isopleth map	Choropleth map
Kind of data	Continuous, changes smoothly (rainfall, temperature)	Data counted by administrative unit (population density by district)
Boundaries used	Ignores administrative borders	Follows administrative borders
What is drawn	Lines of equal value	Shades or colours filling each unit
Input	Values at points (weather stations, rain gauges)	Values for areas

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 (duration of bright sunshine)	NCERT
Contour	height above mean sea level	NCERT
Isobath	depth below a water surface; shows sea-floor relief	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

• Isohyet: the line joining places that get the same amount of rain in a given period. On India's annual isohyet map the lines bunch up along the Western Ghats and in Meghalaya, where rain is very heavy, and spread out over western Rajasthan, where rain is very low.
• Isobath: works like a contour line, but under water. It measures depth, not height. Isobaths show the continental shelf, slope and ocean deeps on a sea-floor map.
• Isohaline: joins points of equal sea-water salinity, usually given in parts per thousand (‰). Isohaline maps show, for example, the lower salinity of the Bay of Bengal (many large rivers bring in fresh water) compared with the Arabian Sea.
• Isoseismal: joins places that felt the same intensity of shaking. Intensity measures the damage and the effect on people, not the energy released.
• In the usual case, intensity falls with distance from the epicentre. So isoseismals form nested rings: each higher-intensity zone sits inside the next lower one [4].
• Historical isoseismal maps used contour lines to separate areas of equal whole-number intensities. The USGS "Did You Feel It?" (DYFI) maps today are numerically interpolated, which means they show continuous values [4].
• The US uses the Modified Mercalli Intensity (MMI) scale, written in Roman numerals [4].

Requirements for drawing an isopleth map

• A base map with the point locations marked (weather stations, rain gauges, spot heights).
• Data for a fixed period for every point, such as mean January temperature or annual rainfall. Values from different periods cannot be mixed.
• Drawing instruments, especially a French curve: a plastic template with many curves, used to draw smooth lines.

Rules for drawing isopleths

• Use equal intervals. An interval of 5, 10 or 20 is ideal (for example 20°, 25°, 30°C or 100, 120, 140 cm).
• Write the value of each line along it, either on one side of the line or in a break in the line.
• Isopleths are smooth lines. Lines of different values never cross each other, because one place cannot have two values at the same time.
• Draw the lowest-value isopleth first, then the higher ones in order (Fig. 3.15).

Interpolation: the method

• Interpolation means estimating the values between two observed points, in proportion to distance. We assume the value changes evenly from one point to the next.
• Why it is needed: stations rarely record exactly 30°C or 100 cm. The line of a round value must be placed between stations.
• Formula (NCERT):
• 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 to draw.

• Step by step: 1. Join two neighbouring stations with a faint pencil line. 2. Find how many millimetres on the map stand for each unit of value (distance ÷ value difference). 3. Multiply 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 all station pairs. Join the marked points 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 = 33 − 28 = 5°C, so each 1°C = 10 ÷ 5 = 2 mm.
• For the 30°C isotherm, the gap from A = 30 − 28 = 2°C.
• Position = (10 ÷ 5) × 2 = 4 mm from the 28°C station.
• Check: the 31°C isotherm would fall 6 mm from A. The 32°C isotherm would fall 8 mm from A.

Interpolation in present-day GIS practice

• A GIS (Geographic Information System: computer software that stores, analyses and maps data tied to locations) does interpolation automatically. It produces a gridded surface: a regular net of cells, each with an estimated value.
• Inverse distance weighting (IDW): a nearby station counts for more than a distant one. The weight goes down as distance goes up, often as 1 ÷ distance².
• Kriging: a statistical method. It first measures how quickly similarity between values drops with distance, using a semivariogram (a graph of how values become less alike as points get farther apart). It then uses this to set the weights.

• The USGS ShakeMap system weights its seismic-station and felt-report data by distance through spatial semivariograms, and also allows for data uncertainty (a "nugget effect") [5].

• IMD gridded rainfall (an Indian example of IDW):

• IMD Pune built a daily gridded rainfall dataset at 0.25° × 0.25° (latitude × longitude) for 1901–2010, from 6,955 rain-gauge stations. This was the largest number of stations used by any study of this kind up to then (Pai et al., MAUSAM, 2014) [2].
• Gauge values were interpolated onto the grid with Shepard's (1968) inverse-distance weighting, where weights depend on distance from each grid point [2].

• The fine grid shows heavy-rain zones on hills (orographic zones: areas where moist winds rise over mountains and drop rain) much better than older, coarser datasets. Examples are the Western Ghats and North-East India [2].

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

• Link to the NCERT method: the computer does the same job as the hand method, at thousands of points at once. Isohyets and isotherms are then drawn on the grid as contours.

Prelims Hooks

• Isohyet = equal rainfall; isohel = equal sunshine; isoneph = equal cloudiness. These three are the most often swapped in matching questions.
• Isobath = equal depth below water. Contour = equal height above sea level. Isohaline = equal salinity.
• Isoseismal = equal earthquake intensity, not magnitude. Isogonic line = equal magnetic declination. Isochrone = equal travel time.
• Isopleths suit continuous data that ignore administrative boundaries. Choropleths suit data shown by administrative units.
• NCERT's ideal isopleth intervals are 5, 10 or 20. The tool used to draw smooth isopleths is the French curve.
• NCERT example: stations at 28°C and 33°C, 10 mm apart. The 30°C isotherm lies 4 mm from the 28°C station. Draw the lowest-value isopleth first.
• IMD gridded rainfall: 0.25° × 0.25°, 6,955 rain gauges, period 1901–2010, built with Shepard's inverse-distance weighting [2].
• Trap: interpolation estimates values between observed points. Estimating beyond the last observed point is extrapolation.

Mains Points

• Why isopleths suit climate and relief data: rainfall, temperature and pressure follow physical controls such as latitude, relief, distance from the sea and winds, not state borders.
• Isohyets show the sharp rainfall drop from the windward Western Ghats to the rain-shadow Deccan.

• Such maps guide crop planning, drought-prone area mapping 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 become less reliable.
• Steep relief can create local extremes that no station records.

• So the density of the station network directly controls map accuracy. This 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, which helps relief work and building codes [4].

• Gridded rainfall and temperature data, free on IMD's portal, feed flood and drought monitoring, heatwave studies and climate-trend analysis [3].

• From hand drawing to GIS: the NCERT proportional-distance method is the basic idea behind IDW and kriging. Modern interpolation adds weighting by distance and an allowance for uncertainty, turning point readings into decision-ready surfaces [5].