slope

GIS software, calculating slope from a Digital Elevation Model, will use a matrix of 5 points to determine slope at each point. For example, for the points

   ___________________
   |     |     |     |
   |  x  | 500 |     |
   |_____|_____|_____|
   |     |     |     |
   | 500 | 700 | 900 |
   |_____|_____|_____|
   |     |     |     |
   |  y  | 900 |     |
   |_____|_____|_____|

the GIS software would see that the average difference in elevation between the center point and those surrounding it (I made each difference 200 meters here for simplicity) was 200 meters. It would then divide that by the distance between the points—the raster cell size—Imagine the cell size is 600 meters, and you get a (200m/600m=)33% slope, quite steep. Important to note is that the slope is attributed to the center point. To calculate, for example, the slope of the bolded 500-meter point on the left, one would compare it to a different 5-cell matrix centered on it, along with cells x and y, the 700-meter high cell, and a cell to the left not pictured on the matrix shown here.

cf. aspect

Slope (?), n. [Formed (like abode fr. abide) from OE. slipen. See Slip, v. i.]

1.

An oblique direction; a line or direction including from a horizontal line or direction; also, sometimes, an inclination, as of one line or surface to another.

2.

Any ground whose surface forms an angle with the plane of the horizon.

buildings the summit and slope of a hill.
Macaulay.

Under the slopes of Pisgah.
Deut. iv. 49. (Rev. Ver.).

⇒ A slope, considered as descending, is a declivity; considered as ascending, an acclivity.

Slope of a plane (Geom.), the direction of the plane; as, parallel planes have the same slope.

 

© Webster 1913

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Slope, a.

Sloping. "Down the slope hills." Milton.

A bank not steep, but gently slope.
Bacon.

 

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Slope, adv.

In a sloping manner. [Obs.] Milton.

 

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Slope, v. t. [imp. & p. p. Sloped (?); p. pr. & vb. n. Sloping.]

To form with a slope; to give an oblique or slanting direction to; to direct obliquely; to incline; to slant; as, to slope the ground in a garden; to slope a piece of cloth in cutting a garment.

 

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Slope, v. i.

1.

To take an oblique direction; to be at an angle with the plane of the horizon; to incline; as, the ground slopes.

2.

To depart; to disappear suddenly. [Slang]

 

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Slope, n.

The part of a continent descending toward, and draining to, a particular ocean; as, the Pacific slope.

 

© Webster 1913