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l = slope length α = angle of inclination. The grade (US) or gradient (UK) (also called stepth, slope, incline, mainfall, pitch or rise) of a physical feature, landform or constructed line is either the elevation angle of that surface to the horizontal or its tangent. It is a special case of the slope, where zero indicates horizontality. A ...
On topographic maps, stream gradient can be easily approximated if the scale of the map and the contour intervals are known. Contour lines form a V-shape on the map, pointing upstream. By counting the number of lines that cross a certain segment of a stream, multiplying this by the contour interval, and dividing that quantity by the length of ...
A contour map is a map illustrated with contour lines, for example a topographic map, which thus shows valleys and hills, and the steepness or gentleness of slopes. [4] The contour interval of a contour map is the difference in elevation between successive contour lines. [5] The gradient of the function is always perpendicular to the contour ...
Slope illustrated for y = (3/2)x − 1.Click on to enlarge Slope of a line in coordinates system, from f(x) = −12x + 2 to f(x) = 12x + 2. The slope of a line in the plane containing the x and y axes is generally represented by the letter m, [5] and is defined as the change in the y coordinate divided by the corresponding change in the x coordinate, between two distinct points on the line.
In principle, it is the projection of the gradient onto the horizontal slope. In practice using a raster digital elevation model, it is approximated using one of the same partial derivative approximation methods developed for slope. [12] Then the aspect is calculated as: [15]
A topographic survey is typically based upon a systematic observation and published as a map series, made up of two or more map sheets that combine to form the whole map. A topographic map series uses a common specification that includes the range of cartographic symbols employed, as well as a standard geodetic framework that defines the map ...
USGS topographic map of Stowe, Vermont with contour lines at 20-foot intervals. Terrain cartography or relief mapping is the depiction of the shape of the surface of the Earth on a map, using one or more of several techniques that have been developed.
A topographic profile or topographic cut or elevation profile is a representation of the relief of the terrain that is obtained by cutting transversely the lines of a topographic map. Each contour line can be defined as a closed line joining relief points at equal height above sea level. [ 1 ]