The Surface Analysis tool calculates slope, aspect, and curvature from a continuous raster.
A slope represents the "steepness" or the maximum rate of change in value from that cell to its neighbors. This tool analyzes the eight cells surrounding a central cell and determines the slope angle in degrees or the slope direction for each grid cell. The slope angle or direction is then stored as the cell value for the output grid.
An aspect represents the rate of change in the cell value from each cell to its neighbors in the steepest downhill direction. An aspect is the orientation of slope, measured clockwise in degrees from 0 to 360, where 0 is north-facing, 90 is east-facing, 180 is south-facing, and 270 is west-facing. The values of each cell in the output grid lie between 0 to 360, indicating the compass direction.
You will use the slope and aspect in the following fields:
- Automobile design - to design automobiles according to gradeability, i.e., ability to descend slopes of varying degrees.
- Environmental planning
- Designing of railway tracks
- Disaster management
- Wildlife management
- Airport design
- ..and many more
How is Slope Calculated
The rate of change of the surface in the horizontal (dz/dx) and vertical (dz/dy) directions from the central cell determines the slope. The algorithm to calculate slope is:
Slope(in Degree) = ATAN(sqrt((dz/dx)^2 + (dz/dy)^2))*(180/PI)
For example, consider the 3x3 grid, where the values of all nine cells range from a to i. The cell with value e is the central cell with the rest of the cells as its neighbors.
The rate of change in x direction for cell e is calculated as:
dz/dx = ((c + 2f + i) – (a + 2d + g)) / (8 * cellsizeX)
The rate of change in y direction for cell e is calculated as:
dz/dy = ((g + 2h + i) – (a + 2b + c)) / (8 * cellsizeY)
How is Aspect Calculated
Aspect is measured in degrees clockwise from the grid Y (north) axis. The slope direction indicates the downwards direction of the maximum gradient (slope) of the cell.
Aspect(in Degree) = (180/PI)*ATAN2(dz/dy, -dz/dx)
If calculated Aspect is in negative value, the aspect value is then converted to compass direction values (0-360 degrees), as described below.
cell value = 360-abs(Aspect)
Curvature
Curvature calculates the second derivative value of the input surface on a cell-by-cell basis.