Elevation contour map

A contour line (also level set, isopleth, isogram or isarithm) for a function of two variables is a curve connecting points where the function has a same particular value. A contour map is a map illustrated with contour lines. Description: Example of a topographic map with contour intervals Source: Sample taken from the public domain USGS Digital Raster Graphic file o44072d6. ... Description: Example of a topographic map with contour intervals Source: Sample taken from the public domain USGS Digital Raster Graphic file o44072d6. ... Basic Definition In geography, the elevation of a geographic location is its height above mean sea level (or some other fixed point). ... In mathematics, a level set of a real-valued function f of n variables is a set of the form { (x1,...,xn) | f(x1,...,xn) = c } where c is a constant. ... In mathematics, the concept of a curve tries to capture the intuitive idea of a geometrical one-dimensional and continuous object. ... Example of a topographic map with contour lines Topographic maps, also called contour maps, topo maps or topo quads (for quadrangles), are maps that show topography, or land contours, by means of contour lines. ... Bold text For other uses, see Map (disambiguation). ...

The gradient of the function is always perpendicular to the contour lines. When the lines are close together the length of the gradient is large: the variation is steep. If adjacent contour lines are of the same line width, the direction of the gradient cannot be determined from the contour lines alone. However if contour lines rotate through three or more widths, or if the lines are numerically labelled, then the direction of the gradient can also be determined from the contour lines. In the above two images, the scalar field is in black and white, black representing higher values, and its corresponding gradient is represented by blue arrows. ...

Various types of contour lines are given different names according to the nature of the variable being mapped:

• air pollutant: isopleth.
• illuminance: isophote.
• dew point: isodrosotherm.
• economic production: isoquant.
• elevation: contour lines on a topographic map or isohypse.
• underwater depth: isobath.
• humidity: isohume.
• liquid precipitation amount: isohyet.
• magnetic declination: isogon.
• presence of linguistic feature: isogloss.
• pressure: isobar.
• solar radiation: isohel.
• sound level: contour line.
• temperature: isotherm.
• volume: isochor.
• wind direction: isogon.
• wind speed: isotach.
• drive time: isochrone.
• frequency of hail storms: isochalaz.
• time of thawing: isotac.
• cost of travel time: isodopane.

"Iso" can be replaced with "isallo" to specify a contour line connecting points where a variable has changed at the same rate during a given time period. This power plant in New Mexico releases sulfur dioxide and particulate matter into the air. ... Contour map A contour line (also isopleth, level set, isogram or isarithm) for a function of two variables is a curve connecting points where the function has a particular value. ... Illuminance is the total luminous flux incident per unit area. ... The dew point or dewpoint of a given parcel of air is the temperature to which the parcel must be cooled, at constant barometric pressure, for the water vapor component to condense into water, called dew. ... An isodrosotherm is a line of equal or constant dew point on a graph, plot, or map; an isopleth of dew point. ... An isoquant map where Q3 > Q2 > Q1. ... Basic Definition In geography, the elevation of a geographic location is its height above mean sea level (or some other fixed point). ... Example of a topographic map with contour lines Topographic maps, also called contour maps, topo maps or topo quads (for quadrangles), are maps that show topography, or land contours, by means of contour lines. ... An isohypse is a line of equal or constant elevation on a graph, plot, or map; an isopleth of elevation. ... Look up depth in Wiktionary, the free dictionary In classical physics, depth is a distance measured vertically from top to bottom (height) or horizontally from outside to inside (thickness). ... An isobath is a line on a map or chart that connects points of equal water depth. ... Humidity is the concentration of water vapor in the air. ... An isohume is a line of equal or constant humidity on a graph, plot, or map; an isopleth of humidity. ... Isohyetal map An isohyet or isohyetal line is a line joining points of equal precipitation on a map. ... The magnetic declination (or magnetic variation) at any point on the earth is a property of the geomagnetic field defined as the angle that must be added or subtracted in converting between two kinds of directional information: the direction of the needle on a magnetic compass located there, and the... Isogonic lines are lines connecting those parts where the declination of the Earths magnetic field is the same in amount. ... Isoglosses on the Faroe Islands An isogloss is the geographical boundary of a certain linguistic feature, e. ... Pressure (symbol: p) is the force per unit area acting on a surface in a direction perpendicular to that surface. ... An isobar is a line of equal or constant pressure on a graph, plot, or map; an isopleth of pressure. ... In meteorology, an isohel is a line of equal or constant solar radiation on a graph, plot, or map; an isopleth of solar radiation. ... A schematic representation of hearing. ... Temperature is also the name of a song by Sean Paul. ... An isotherm is a line of equal or constant temperature on a graph, plot, or map; an isopleth of temperature. ... Volume, also called capacity, is a quantification of how much space an object occupies. ... An isochoric process, also called an isometric process, is a thermodynamic process in which the volume stays constant; . This implies that the process does no pressure-volume work, since such work is defined by , where P is pressure (no minus sign; this is work done by the system). ... In meteorology, an isogon is a line of equal or constant wind direction on a graph, plot, or map; an isopleth of wind direction. ... An isotach is a line of equal or constant wind speed on a graph, plot, or map; an isopleth of wind speed. ... A tautochrone or isochrone curve is the curve for which the time taken by a particle sliding down it under uniform gravity to its lowest point is independent of its starting point. ...

Technical construction factors

To maximize readability of contour maps, there are several design choices available to the map creator, principally line weight, line color, line type and method of numerical marking. Color is an important part of the visual arts. ...

Line weight is simply the darkness or thickness of the line used. This choice is made based upon the least intrusive form of contours that enable the reader to decipher the background information in the map itself. If there is little or no content on the base map, the contour lines may be drawn with relatively heavy thickness. Also, for many forms of contours such as topographic maps, it is common to vary the line weight and/or color, so that a different line characteristic occurs for certain numerical values. For example, in the topgraphic map above, the even hundred foot elevations are shown in a different weight from the twenty foot intervals.

Line color is the choice of any number of pigments that suit the display. Sometimes a sheen or gloss is used as well as color to set the contour lines apart from the base map. In biology, pigment is any material resulting in color in plant or animal cells which is the result of selective absorption. ... Sheen is a place in southwest London nearby to Barnes, Roehampton and Putney to the east and Richmond to the west. ...

Line type refers to whether the basic contour line is solid, dashed, dotted or broken in some other pattern to create the desired effect. Dotted or dashed lines are often used when the underlying base map conveys very important (or difficult to read) information.

Numerical marking is the manner of denoting the arithmetical the values of contour lines. This can be done by placing numbers along some of the contour lines, typically using interpolation for intervening lines. Alternatively a map key can be produced associating the contours with their values. Arithmetic is the current mathematics collaboration of the week! Please help improve it to featured article standard. ... In the mathematical subfield of numerical analysis, interpolation is a method of constructing new data points from a discrete set of known data points. ...

Plan view versus profile view

Most commonly contour lines are drawn in plan view. or as an observer in space would view the earth's surface: ordinary map form. However, some parameters can often be displayed in profile view showing a vertical profile of the parameter mapped. Some of the most common parameters mapped in profile are air pollutant concentrations and sound levels. In each of those cases it may be important to analyze (air pollutant concentrations or sound levels) at varying heights so as to determine the air quality or noise health effects on people at different elevations, for example, living on different floor levels of an urban apartment. One can see an example of vertical contours in the article on noise barriers. In actuality, both plan and profile view contour maps are used in air pollution and noise pollution studies. This power plant in New Mexico releases sulfur dioxide and particulate matter into the air. ... Sound pressure level (SPL) or sound level Lp is a logarithmic measure of the energy of a particular noise relative to a reference noise source. ... Environmental noise can produce irreversible hearing loss Noise health effects, the collection of health consequences of elevated sound levels, constitute one of the most widespread public health threats in industrialized countries. ... Noise barrier earth berm along Highway 12, Sonoma County, California A noise barrier is an exterior structure, normally made of masonry or earth, designed to protect sensitive land uses from noise pollution. ... This power plant in New Mexico releases sulfur dioxide and particulate matter into the air. ... Noise pollution is unwanted human-created sound that disrupts the environment. ...

External links

• Drawing Contour Plots. A lesson plan that deals with drawing various isopleths.
• See also Forthright's Phrontistery for many more different types of isopleths.
• Surfer contour line software