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       r.slope.aspect   -  Generates  raster  maps  of  slope,  aspect,  curvatures  and  partial
       derivatives from an elevation raster map.
       Aspect is calculated counterclockwise from east.


       raster, terrain, aspect, slope, curvature


       r.slope.aspect --help
       r.slope.aspect  [-aen]  elevation=name   [slope=name]    [aspect=name]     [format=string]
       [precision=string]     [pcurvature=name]     [tcurvature=name]     [dx=name]     [dy=name]
       [dxx=name]   [dyy=name]   [dxy=name]   [zscale=float]   [min_slope=float]    [--overwrite]
       [--help]  [--verbose]  [--quiet]  [--ui]

           Do not align the current region to the raster elevation map

           Compute output at edges and near NULL values

           Create aspect as degrees clockwise from North (azimuth), with flat = -9999
           Default: degrees counter-clockwise from East, with flat = 0

           Allow output files to overwrite existing files

           Print usage summary

           Verbose module output

           Quiet module output

           Force launching GUI dialog

       elevation=name [required]
           Name of input elevation raster map

           Name for output slope raster map

           Name for output aspect raster map

           Format for reporting the slope
           Options: degrees, percent
           Default: degrees

           Type of output aspect and slope maps
           Storage type for resultant raster map
           Options: CELL, FCELL, DCELL
           Default: FCELL
           CELL: Integer
           FCELL: Single precision floating point
           DCELL: Double precision floating point

           Name for output profile curvature raster map

           Name for output tangential curvature raster map

           Name for output first order partial derivative dx (E-W slope) raster map

           Name for output first order partial derivative dy (N-S slope) raster map

           Name for output second order partial derivative dxx raster map

           Name for output second order partial derivative dyy raster map

           Name for output second order partial derivative dxy raster map

           Multiplicative factor to convert elevation units to horizontal units
           Default: 1.0

           Minimum slope value (in percent) for which aspect is computed
           Default: 0.0


       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).

       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
                 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


       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.


   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

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


           ·   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,


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


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


       Available at: r.slope.aspect source code (history)

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