Spatial Data Mapping: Choropleth, Isoline, and Flow Maps

Thematic mapping shows how a phenomenon varies across space, and the main map types are choropleth maps (areas shaded by value), isoline maps (lines joining points of equal value) and flow maps (lines or arrows whose width shows the size of a movement between places). In brief: choropleth maps should show rates or ratios (such as people per km²) and not raw totals, and their appearance depends on how the data are divided into classes. Isolines, such as contours and isotherms, show continuous surfaces and are drawn by interpolating between measured points. Flow maps, such as Minard’s map of Napoleon’s army, show movement of people, goods or information.

Choosing the right map type and design affects how readers see patterns and whether they are misled. This guide explains choropleth, isoline and flow maps, other map types, classification methods and colors, compares the types in a table, works through classification and interpolation calculations, outlines the history and corrects common mistakes.

How do choropleth maps work?

A choropleth map shades or colors areas, such as countries, regions or wards, according to the value of a variable in each. It is good for showing patterns in data that are collected by area, such as unemployment rates, population density or voting results. Several rules apply:

• Use rates or densities, not totals: a large region will have a large total of almost anything, so use a standardized measure, such as people per km², a percentage or a rate per 1,000 people.
• Classify the data: the values are grouped into classes, usually 4 to 7. The main methods are equal interval (classes of the same width), quantile (the same number of areas in each class), natural breaks (Jenks, which finds gaps in the data) and manual classes at meaningful thresholds. The choice can change the map’s message.
• Use a suitable color scheme: a sequential scheme (light to dark in one hue) for values from low to high, and a diverging scheme (two hues meeting at a neutral midpoint) for data with a meaningful center, such as change above and below zero. Darker should mean more, and colors should be distinguishable by people with color blindness.
• Be aware of limitations: the map suggests that the value is uniform within each area, which is rarely true, and large areas dominate the visual impression even if they have few people. The modifiable areal unit problem (MAUP) means that results can change with the choice of boundaries.

How do isoline maps work?

An isoline (or isopleth) connects points of equal value, and the spacing of lines shows the rate of change: lines close together show a steep gradient, and wide spacing shows a gentle one. Common types are contours (height), isobars (pressure), isotherms (temperature), isohyets (rainfall) and isochrones (equal travel time). Isolines assume that the variable is continuous and varies smoothly, so they suit physical data such as temperature, but not abrupt data such as land use. Measurements are made at a limited number of points, so the lines are drawn by interpolation: estimating values between the known points, usually by assuming a straight-line change. Computers use methods such as inverse distance weighting, kriging or splines. Isolines can be extended to show density surfaces, such as population or crime.

How do flow maps work?

A flow map shows movements, such as migration, trade, traffic or river discharge, using lines or arrows between places, with the width of the line proportional to the quantity and sometimes the color to the type. Charles Joseph Minard’s map of 1869, which shows the size of Napoleon’s army in 1812–1813 as a band that narrows from about 422,000 men to 10,000, along with the temperature during the retreat, is a famous example. Flow maps can become cluttered when there are many flows, so mapmakers may show only major flows, combine lines going in the same direction (bundling), or use a matrix instead. Related maps are desire line maps, which show straight lines between origin and destination.

What other thematic maps are used?

• Proportional symbol maps: symbols such as circles whose size is proportional to the value at a place, good for totals (population of cities).
• Dot maps: each dot represents a number of items (such as 1,000 people) and shows the distribution and density.
• Cartograms: maps in which area is distorted in proportion to a value, such as a map of the world’s countries sized by population.
• Heat maps and density surfaces: color-coded concentration of points.
• Dasymetric maps: improved choropleths that use extra information (such as land cover) to place the population more realistically within areas.

Map types compared

Worked example: classes, interpolation and flow widths

The data are hypothetical. Ten areas have these unemployment rates (%): 2.1, 3.4, 4.0, 5.5, 6.2, 7.9, 8.4, 9.6, 12.3 and 14.0.

1. Equal interval, 5 classes: the range is 14.0 − 2.1 = 11.9, so the class width is 11.9 ÷ 5 = 2.38. The classes are 2.1–4.48, 4.48–6.86, 6.86–9.24, 9.24–11.62 and 11.62–14.0. The numbers of areas in the classes are 3 (2.1, 3.4, 4.0), 2 (5.5, 6.2), 2 (7.9, 8.4), 1 (9.6) and 2 (12.3, 14.0), a total of 10.
2. Quantile, 5 classes: with 10 areas, each class has 2: (2.1, 3.4), (4.0, 5.5), (6.2, 7.9), (8.4, 9.6) and (12.3, 14.0). The class limits are chosen between the groups, for example at 3.7, 5.85, 8.15 and 10.95.
3. Comparing the two: the equal-interval map puts the 9.6 area in a class of its own and groups three low-rate areas, while the quantile map gives each color the same number of areas. The two maps give different impressions of the same data.
4. Interpolating a contour: two spot heights are 540 m at point A and 620 m at point B, which are 4 km apart. The 600 m contour lies where the height has risen by 600 − 540 = 60 m of the 80 m total, which is 60 ÷ 80 = 0.75 of the distance, so 0.75 × 4 = 3 km from A.
5. Interpolating temperature: two stations are 20 km apart with 12 °C and 20 °C. The 16 °C isotherm is halfway, 10 km from each, since (16 − 12) ÷ (20 − 12) = 0.5. The gradient is 8 °C over 20 km, or 0.4 °C per km.
6. Flow map width: a scale of 1 mm for each 10,000 migrants gives a line 4.5 mm wide for 45,000 migrants and 12 mm for 120,000. The second flow is 120 ÷ 45 = 2.7 times as wide.

How did thematic mapping develop?

The first thematic maps appeared in the 17th and 18th centuries, such as Edmond Halley’s map of the trade winds (1686) and his map of magnetic variation with isolines (1701). Charles Dupin made one of the first choropleth maps in 1826, which showed the level of education in France. John Snow’s 1854 map of cholera in London used dots to show deaths. Minard’s flow maps appeared in the 1860s, and Arthur Robinson’s The Look of Maps (1952) and Jacques Bertin’s Semiology of Graphics (1967) set out principles of map design. Since the 1980s, GIS has made it possible for anyone to produce thematic maps, and web mapping and open data have made interactive maps common, but the same questions of classification, scale and honesty apply.

Which mistakes are common?

Mistake 1: Mapping raw totals on a choropleth

Totals reflect the size of the area or population. Use rates, percentages or densities to compare places fairly.

Mistake 2: Assuming that the classification does not matter

The method and number of classes can change the pattern. Check several methods and choose one that fits the data and purpose, and state it on the map.

Mistake 3: Drawing isolines for data that do not vary smoothly

Isolines are suitable for continuous variables. Using them for abrupt or categorical data, such as land use, is misleading.

Mistake 4: Letting flow lines hide the pattern

Too many overlapping flows can create clutter. Show the major flows, use clear scales and consider simplifying the map.