Groundwater pressure mapping
Introduction
An isoline (also called isopleth, contour line, isogram or isaritma), for a function of several variables, is a curve that connects the points where the function has the same constant value.
Isolines represented on a map are straight lines, curves or a mixture of both, which describe on a map the intersection of a real or hypothetical surface with one or more horizontal planes. Setting these contours allows map readers to infer the relative gradient of the variable or parameter and estimate a value at a given location. Contours can be plotted on a visible three-dimensional model of the surface, as when a photogrammetrist observing a stereoscopic model plots elevation contours, or interpolated from estimated elevations of the surface, as when a computer program threads contours through a network of area centroid observation points. In the latter case, the interpolation method affects the reliability of the individual isolines and their representation of slope, troughs and peaks.[1].
The gradient of the function is always perpendicular to the isoline. When the lines are very close, the length of the gradient is large: the variation is accentuated. If adjacent isolines have the same line thickness, the direction of the gradient cannot be determined and therefore different thicknesses are used or they are labeled or labeled numerically: in this way the direction of the gradient can be easily appreciated.
The most common use of isolines is in cartography and meteorology. A topographic map (or contour map) uses isolines that join points of equal altitude and thus shows the shape of valleys and hills, and the slope of slopes. In meteorology, it is common to show curves of equal atmospheric pressure called isobars.
History
The idea of using lines that join points of equal value was rediscovered on several occasions throughout history. The oldest known isobath (isoline of depth) is found on a 1584 map of the River Spaarne, near Haarlem, by the Dutch surveyor Pieter Bruinsz. depth (isobats), in intervals of 1 fathom "Fathom (unit)");[2] and in 1737, Philippe Buache, used an interval of 10 fathoms to prepare a map of the English Channel that was published in 1752.
The use of these lines (the contour line) to describe the earth's surface was studied theoretically by Ducarla in 1771, and Charles Hutton used it in calculating the volume of a hill in 1777. In 1791, J. L. Dupain-Triel made a map of France, which reflected the contour lines every 20 meters of interval. In 1801, the also Frenchman and head of the Corps of Engineers, Haxo"), used the contour line on a larger scale, 1:500 in a plan for his project for the Rocca de Aufo.[3][4][5].