Specialised Cartographic Skills: Isolines, Choropleths and Flow Lines

Showing where geographical data occurs

A graph can compare quantities, but a map also shows where those quantities occur. Different map techniques represent different kinds of information: shading compares areas, isolines show a continuously changing variable, dots show distribution, and symbols or lines show quantities at places or moving between them.

When completing a partly drawn map, first read its title and key. Identify the variable, units and scale, then use the same conventions for the missing information. The examples below use invented places and data to demonstrate the methods, not real geographical distributions.

Completing a choropleth map

A choropleth map divides data into classes and gives each class a shade or colour. Each geographical area receives the shade matching its value. A sequence from light to dark usually represents increasing values, allowing areas with high and low values to stand out.

To complete one, match each area's data to the correct class in the key, then shade the whole area consistently within its boundary. If constructing the map from scratch, choose class boundaries that cover the data without gaps or overlaps and add a key showing the ranges and units.

For example, imagine four fictional districts with population densities of 18, 37, 54 and 76 people per square kilometre. With classes of 0–19, 20–39, 40–59 and 60–79 people per square kilometre, the districts receive the first, second, third and fourth shades respectively. The district with a value of 54 does not get its own special shade: it shares a shade with any other district in the 40–59 class.

Choropleths work well for comparing measures such as population density, percentages or average income. However, an area shaded 40–59 does not have the same value everywhere within it. Shading hides internal variation and usually gives a range rather than an exact value. Large areas can also dominate the visual impression even when their values are low.

Completing isolines by estimating between measurements

An isoline joins places with the same value. Contours join points of equal height above sea level; isotherms join points of equal temperature; isobars join points of equal atmospheric pressure.

To complete an isoline map, read the values at the plotted points and identify the interval between lines. Estimate where the required value falls between neighbouring measurements, then connect these estimated positions with smooth lines. Label each line with its value and make the units clear. Lines representing different values must not cross: a point cannot have two different values of the same variable at the same time.

Suppose two fictional temperature measurements are 8°C and 14°C. A 10°C isotherm must pass between them. Assuming a steady change between the measurements, 10°C is 2°C above 8°C within a total difference of 6°C. It therefore lies one-third of the distance from the 8°C point towards the 14°C point. Repeating this process between other pairs of measurements allows the line to be completed.

This estimation is called interpolation. It is useful, but it does not prove that the variable changes evenly between measurements. More observations can reveal local variations that a simple interpolation misses.

Reading value, contour and gradient

A labelled isoline gives the value at every point along that line. A point between the 10°C and 12°C isotherms has a temperature between those values; estimating its exact temperature requires judging its position between the lines.

On a contour map, the labels give height above sea level, usually in metres. If successive contours are labelled 20, 30 and 40 metres, the contour interval is 10 metres. Following these labels shows which direction is uphill and which is downhill.

Gradient describes change with distance. Where equally spaced values are represented by closely packed isolines, the value changes rapidly over a short distance. Where those lines are far apart, the change is slower. On a contour map this means close contours show a steep slope and widely spaced contours show a gentle slope. On an isotherm map it means rapid or gradual temperature change, not steep or gentle land.

Compare spacing only after checking the isoline interval and map scale. A smaller gap between lines is meaningful because it represents a known change over a shorter distance.

Completing dot maps and proportional symbols

A dot map uses a fixed quantity for every dot. Read the dot value before adding symbols, and use dots of the same size as those already drawn.

For a fictional map with a key of one dot representing 100 people, an area containing 500 people needs five dots. Place dots using the location information provided. If only an area total is known, the dots represent distribution within that area rather than verified individual addresses. Clusters indicate concentrations, but overlapping dots can become difficult to count.

A proportional symbol map instead changes symbol size to represent quantity at a location. To complete it, locate the site, determine the required symbol size from the key or supplied sizing guide, and draw the symbol centred on that location.

For circles, it is the area that is proportional to the value. For example, a site with 400 visitors needs a circle with four times the area of the circle for 100 visitors. Its radius is therefore twice as large, not four times as large. Use the same relationship throughout and include a size key. Overlapping symbols can obscure smaller ones, so they must remain distinguishable.

Completing desire lines and flow lines

Both techniques connect places, but they emphasise different information.

Desire lines are straight origin-to-destination connections. For example, they can link the places where customers live to a shop, showing its catchment without suggesting which streets the customers used. Complete a desire-line map by connecting the correct places with straight lines, adding arrows if direction is required and using the stated width scale if quantity is represented.

Flow lines show movement and its volume. Their paths may follow mapped roads or other routes when these are supplied, although a simplified flow map need not show the exact journey taken. To complete one, connect the correct places along the indicated path, use an arrow to show the required direction, and make the line width match the quantity in the key.

Imagine a fictional width scale of 1 millimetre representing 100 journeys per day. A flow of 200 journeys per day needs a 2-millimetre-wide line; a flow of 400 needs a 4-millimetre-wide line. The quantity is represented by width, not by line length: a longer journey does not necessarily involve more travellers.

These examples demonstrate how to complete the techniques. On a real map, transfer the same methods to the actual boundaries, measurement points, origins, destinations and routes provided. The map's key controls how the data should be drawn.

Area shading and equal-value lines

• Choropleth: match each area's value to a class; shade within its boundary. The shade shows a range and hides variation within the area.
• Isoline: interpolate between measurements, join equal values smoothly and label the lines. Different-value lines do not cross.
• Contour: equal height above sea level. Check labels and the contour interval.
• Gradient: close isolines mean rapid change; wide spacing means gradual change, for the same interval and map scale. Close contours mean steep slopes.

Quantities and movement

• Dot map: number of dots = quantity ÷ value per dot. Keep dot sizes consistent.
• Proportional symbols: symbol area represents quantity. Four times the value requires twice the circle radius.
• Desire lines: straight origin-to-destination links, not travelled routes.
• Flow lines: width represents volume; arrows show direction. Follow indicated paths where provided.

Completing a map

Check the title, units, locations and key. Continue the existing classes, symbol sizes, line-width scale and labelling.