Contour line

A contour line is a curve that connects points sharing a constant value.

In mathematics, this is a line on a two-dimensional graph representing a three-dimensional surface.

These lines are also known by several other names. They might be called isolines, isopleths, isoquants, or isarithms. In the field of cartography, a contour line typically joins points of equal elevation. This elevation is usually measured as height above a specific level, such as mean sea level.

By using these lines, a map can illustrate the physical shape of the Earth.

To understand how they work, imagine a three-dimensional surface being sliced by horizontal planes. Each slice creates a cross-section that appears as a contour line on a flat map.

The lines can be straight, curved, or a mixture of both. A key concept is the gradient, which represents the rate of change in value. The gradient is always perpendicular to the contour lines. When the lines are placed very close together, it indicates a large magnitude of the gradient. This means the variation in the surface is very steep. Conversely, when the lines are far apart, the slope is gentle. The vertical distance between two successive lines is called the contour interval.

There are different ways to create these maps. One method involves tracing lines directly on a visible three-dimensional model. This is often done by a photogrammetrist viewing a stereo-model. Another method is called interpolation. In this process, a computer program threads lines through a network of observation points. This is used when scientists have estimated surface elevations rather than direct measurements. The specific method of interpolation can affect how reliably the lines portray peaks, pits, or slopes.

History shows that the idea of lines joining equal values was discovered many times. The oldest known example is an isobath, which is a contour line of constant water depth. This was found on a 1584 map of the river Spaarne near Haarlem. In 1701, Edmond Halley used isogons to map variations in magnetism.

In 1727, Nicholas Cruquius drew the river Merwede using isobaths at one-fathom intervals. By 1843, the Ordnance Survey began recording contour lines regularly in Great Britain and Ireland. This followed years of use in various European countries.

Because different people invented these techniques independently, many names emerged. In 1889, Francis Galton proposed the term "isogram" for lines showing equal physical quantities. During the early 20th century, "isopleth" became common in the United States. Meanwhile, "isarithm" was frequently used in Europe. Other terms like "isoline" and "isometric line" also appeared. Despite many attempts to choose one standard name, all these alternatives still exist today. This variety reflects the many different ways humans apply the concept.

Specific names are often used depending on what is being measured. In meteorology, the prefix "iso-" is used to identify different variables. For example, an isotherm connects points with the same temperature.

An isotherm at 0 °C is known as the freezing level. An isohyet is a line joining points of equal rainfall.

An isobar is a line of constant atmospheric pressure.

These isobars help scientists predict wind patterns and future weather. There are even lines for solar radiation called isohels.

Modern applications have expanded far beyond simple land maps. We now use contour lines to map complex environmental data. For instance, maps can show levels of air quality or noise pollution. These types of maps first appeared in the United States around 1970. This was partly due to national laws requiring the mapping of these specific parameters. Today, contour lines remain a vital tool for turning complex, scattered data into clear, visual patterns.