## DESCRIPTION

r.slope.aspect generates raster maps of slope, aspect, curvatures and first and second order partial derivatives from a raster map of true elevation values. The user must specify the input elevation raster map and at least one output raster maps. The user can also specify the format for slope (degrees, percent; default=degrees), and the zscale: multiplicative factor to convert elevation units to horizontal units; (default 1.0).

The elevation input raster map specified by the user must contain true elevation values, not rescaled or categorized data. If the elevation values are in other units than in the horizontal units, they must be converted to horizontal units using the parameter zscale. In GRASS GIS 7, vertical units are not assumed to be meters any more. For example, if both your vertical and horizontal units are feet, parameter zscale must not be used.

The aspect output raster map indicates the direction that slopes are facing counterclockwise from East: 90 degrees is North, 180 is West, 270 is South, 360 is East. Zero aspect indicates flat areas with zero slope. Category and color table files are also generated for the aspect raster map.
Note: These values can be transformed to azimuth values (90 is East, 180 is South, 270 is West, 360 is North) using r.mapcalc:

    # convert angles from CCW from East to CW from North
    # modulus (%) can not be used with floating point aspect values
    r.mapcalc "azimuth_aspect = if(ccw_aspect == 0, 0, \
                                if(ccw_aspect < 90, 90 - ccw_aspect, \
                                450 - ccw_aspect)))"

Alternatively, the -n flag can be used to produce aspect as degrees CW from North. Aspect for flat areas is then set to -9999 (default: 0). Note: The reason for using -9999 is to be compliant with gdaldem which uses -9999 by default as the nodata value.

The aspect for slope equal to zero (flat areas) is set to zero (-9999 with -n flag). Thus, most cells with a very small slope end up having category 0, 45, ..., 360 in aspect output. It is possible to reduce the bias in these directions by filtering out the aspect in areas where the terrain is almost flat. A option min_slope can be used to specify the minimum slope for which aspect is computed. For all cells with slope < min_slope, both slope and aspect are set to zero.

The slope output raster map contains slope values, stated in degrees of inclination from the horizontal if format=degrees option (the default) is chosen, and in percent rise if format=percent option is chosen. Category and color table files are generated.

Profile and tangential curvatures are the curvatures in the direction of steepest slope and in the direction of the contour tangent respectively. The curvatures are expressed as 1/metres, e.g. a curvature of 0.05 corresponds to a radius of curvature of 20m. Convex form values are positive and concave form values are negative.

Example DEM |
Slope (degree) from example DEM | Aspect (degree) from example DEM
Tangential curvature (m-1) from example DEM | Profile curvature (m-1) from example DEM |

For some applications, the user will wish to use a reclassified raster map of slope that groups slope values into ranges of slope. This can be done using r.reclass. An example of a useful reclassification is given below:

              category      range   category labels
                         (in degrees)    (in percent)

                 1         0-  1             0-  2%
                 2         2-  3             3-  5%
                 3         4-  5             6- 10%
                 4         6-  8            11- 15%
                 5         9- 11            16- 20%
                 6        12- 14            21- 25%
                 7        15- 90            26% and higher

         The following color table works well with the above
         reclassification.

              category   red   green   blue

                 0       179    179     179
                 1         0    102       0
                 2         0    153       0
                 3       128    153       0
                 4       204    179       0
                 5       128     51      51
                 6       255      0       0
                 7         0      0       0

## NOTES

To ensure that the raster elevation map is not inappropriately resampled, the settings for the current region are modified slightly (for the execution of the program only): the resolution is set to match the resolution of the elevation raster map and the edges of the region (i.e. the north, south, east and west) are shifted, if necessary, to line up along edges of the nearest cells in the elevation map. If the user really wants the raster elevation map resampled to the current region resolution, the -a flag should be specified.

The current mask is ignored.

The algorithm used to determine slope and aspect uses a 3x3 neighborhood around each cell in the raster elevation map. Thus, slope and aspect are not determineed for cells adjacent to the edges and NULL cells in the elevation map layer. These cells are by default set to nodata in output raster maps. With the -e flag, output values are estimated for these cells, avoiding cropping along the edges.

Horn's formula is used to find the first order derivatives in x and y directions.

Only when using integer elevation models, the aspect is biased in 0, 45, 90, 180, 225, 270, 315, and 360 directions; i.e., the distribution of aspect categories is very uneven, with peaks at 0, 45,..., 360 categories. When working with floating point elevation models, no such aspect bias occurs.

### PERFORMANCE

To enable parallel processing, the user can specify the number of threads to be used with the nprocs parameter (default 1). The memory parameter (default 300) can also be provided to determine the size of the buffer for computation.
Figure: Benchmark on the left shows execution time for different number of cells, benchmark on the right shows execution time for different memory size for 5000x5000 raster. See benchmark scripts in source code. (Intel Core i9-10940X CPU @ 3.30GHz x 28)

To reduce the memory requirements to minimum, set option memory to zero. To take advantage of the parallelization, GRASS GIS needs to compiled with OpenMP enabled.

## EXAMPLES

### Calculation of slope, aspect, profile and tangential curvature

In this example a slope, aspect, profile and tangential curvature map are computed from an elevation raster map (North Carolina sample dataset):

    g.region raster=elevation
    r.slope.aspect elevation=elevation slope=slope aspect=aspect pcurvature=pcurv tcurvature=tcurv

    # set nice color tables for output raster maps
    r.colors -n map=slope color=sepia
    r.colors map=aspect color=aspectcolr
    r.colors map=pcurv color=curvature
    r.colors map=tcurv color=curvature

Figure: Slope, aspect, profile and tangential curvature raster map (North Carolina dataset)

### Classification of major aspect directions in compass orientation

In the following example (based on the North Carolina sample dataset) we first generate the standard aspect map (oriented CCW from East), then convert it to compass orientation, and finally classify four major aspect directions (N, E, S, W):

    g.region raster=elevation -p

    # generate integer aspect map with degrees CCW from East
    r.slope.aspect elevation=elevation aspect=myaspect precision=CELL

    # generate compass orientation and classify four major directions (N, E, S, W)
    r.mapcalc "aspect_4_directions = eval( \\
       compass=(450 - myaspect ) % 360, \\
         if(compass >=0. && compass < 45., 1)  \\
       + if(compass >=45. && compass < 135., 2) \\
       + if(compass >=135. && compass < 225., 3) \\
       + if(compass >=225. && compass < 315., 4) \\
       + if(compass >=315., 1) \\
    )"

    # assign text labels
    r.category aspect_4_directions separator=comma rules=- << EOF
    1,north
    2,east
    3,south
    4,west
    EOF

    # assign color table
    r.colors aspect_4_directions rules=- << EOF
    1 253,184,99
    2 178,171,210
    3 230,97,1
    4 94,60,153
    EOF

Aspect map classified to four major compass directions (zoomed subset shown)

## REFERENCES

- Horn, B. K. P. (1981). Hill Shading and the Reflectance Map, Proceedings of the IEEE, 69(1):14-47.
- Mitasova, H. (1985). Cartographic aspects of computer surface modeling. PhD thesis. Slovak Technical University , Bratislava
- Hofierka, J., Mitasova, H., Neteler, M., 2009. Geomorphometry in GRASS GIS. In: Hengl, T. and Reuter, H.I. (Eds), Geomorphometry: Concepts, Software, Applications. Developments in Soil Science, vol. 33, Elsevier, 387-410 pp, http://www.geomorphometry.org

## SEE ALSO

r.mapcalc, r.neighbors, r.reclass, r.rescale

## AUTHORS

Michael Shapiro, U.S.Army Construction Engineering Research Laboratory
Olga Waupotitsch, U.S.Army Construction Engineering Research Laboratory