Slope Computation

Znw Zn Zne Zw Z Ze Zsw Zs Zse
Point notation	Slope map overlaid on satellite image

Slope computation on a grid is focal operation on a cell and generally its eight adjacent neighbors (in fact for many algorithms, the actual point's elevation is not used).

The slope is taken as a dZ value divided by a horizontal distance.  The horizontal distance is the data spacing (east-west, north-south, or diagonal).

For an Eight Neighbors Unweighted algorithm, you compute x and y derivatives

dzdx := (zne + ze + zse - zsw - zw - znw) / 6 / UseXSpace;  (this will be the average of three differences in the x direction, each twice the data spacing)

dzdy := (znw + zn + zne - zsw - zs - zse) / 6 / AverageYSpace;  (this will be the average of three differences in the  y direction, each twice the data spacing)

            Slope := sqrt(sqr(dzdx) + sqr(dzdy));  (magnitude of the vector from the Pythagorean theorem)

Aspect, the downhill direction, can be computed as a byproduct of the slope computation, as the arc tangent of the x and y derivatives.

Computed slope is generally done either in degrees, or in percent (the tangent of the angle * 100).

Computed slope will be a function of the data spacing; as the spacing goes up, computed slope decreases.

Sample slope maps

Detailed discussion of alternate slope algorithms.

MICRODEM can do:

• On the fly computation and display of slope as the Display parameter.
• Create derivative grid of slope.

Last revised 7/1/2014