Provided by: grass-doc_6.4.3-3_all bug


       r.walk   -  Outputs  a  raster map layer showing the anisotropic cumulative cost of moving
       between different geographic locations on an input elevation raster map layer  whose  cell
       category  values  represent  elevation  combined with an input raster map layer whose cell
       values represent friction cost.


       raster, cost surface, cumulative costs


       r.walk help
       r.walk   [-knr]   elevation=string    friction=string    output=string     [outdir=string]
       [start_points=string]            [stop_points=string]           [coordinate=x,y[,x,y,...]]
       [stop_coordinate=x,y[,x,y,...]]            [max_cost=integer]            [null_cost=float]
       [percent_memory=integer]      [nseg=integer]      [walk_coeff=a,b,c,d]      [lambda=float]
       [slope_factor=float]   [--overwrite]  [--verbose]  [--quiet]

           Use the 'Knight's move'; slower, but more accurate

           Keep null values in output map

           Start with values in raster map

           Allow output files to overwrite existing files

           Verbose module output

           Quiet module output

           Name of elevation input raster map

           Name of input raster map containing friction costs

           Name of raster map to contain results

           Name of output raster map to contain movement directions

           Starting points vector map

           Stop points vector map

           The map E and N grid coordinates of a starting point (E,N)

           The map E and N grid coordinates of a stopping point (E,N)

           An optional maximum cumulative cost
           Default: 0

           Cost assigned to null cells. By default, null cells are excluded

           Percent of map to keep in memory
           Default: 100

           Number of the segment to create (segment library)
           Default: 4

           Coefficients for walking energy formula parameters a,b,c,d
           Default: 0.72,6.0,1.9998,-1.9998

           Lambda coefficients for combining walking energy and friction cost
           Default: 1.0

           Slope factor determines travel energy cost per height step
           Default: -0.2125


       r.walk outputs 1) a raster map layer showing the lowest cumulative cost of moving  between
       each  cell and the user-specified starting points and 2) a second raster map layer showing
       the movement direction to the next cell on the path back to the start point (see  Movement
       Direction).  It  uses  an  input  elevation  raster  map  layer whose cell category values
       represent elevation, combined with a second input  raster  map  layer  whose  cell  values
       represent  friction  costs.   This  function  is  similar to r.cost, but in addiction to a
       friction map, it considers an anisotropic travel time due to the different  walking  speed
       associated with downhill and uphill movements.

       The  formula  from  Aitken 1977/Langmuir 1984 (based on Naismith's rule for walking times)
       has been used to estimate the cost parameters of specific slope intervals:

       T= [(a)*(Delta S)] +  [(b)*(Delta  H  uphill)]  +  [(c)*(Delta  H  moderate  downhill)]  +
       [(d)*(Delta H steep downhill)]

       T is time of movement in seconds,
       Delta S is the distance covered in meters,
       Delta H is the altitude difference in meter.

       The  a,  b, c, d parameters take in account movement speed in the different conditions and
       are linked to:
       a: underfoot condition (a=1/walking_speed) b: underfoot condition and cost  associated  to
       movement  uphill  c: underfoot condition and cost associated to movement moderate downhill
       d: underfoot condition and cost associated to movement steep downhill
       It has been proved that moving downhill  is  favourable  up  to  a  specific  slope  value
       threshold,  after  that  it becomes unfavourable. The default slope value threshold (slope
       factor) is -0.2125, corresponding to tan(-12), calibrated on human behaviour (>5  and  <12
       degrees:  moderate downhill; >12 degrees: steep downhill). The default values for a, b, c,
       d are those proposed by Langmuir (0.72, 6.0, 1.9998, -1.9998), based on man walking effort
       in standard conditions.

       The lambda parameter of the linear equation combining movement and friction costs:
       total cost = movement time cost + (lambda) * friction costs
       must be set in the option section of r.walk.

       For  a  more  accurate result, the "knight's move" option can be used (although it is more
       time consuming). In the diagram below, the center location (O) represents a grid cell from
       which  cumulative  distances  are calculated. Those neighbours marked with an x are always
       considered for cumulative cost updates. With the "knight's move"  option,  the  neighbours
       marked with a K are also considered.
         K   K
       K x x x K
         x O x
       K x x x K
         K   K

       The minimum cumulative costs are computed using Dijkstra's algorithm, that find an optimum
       solution (for more details see r.cost, that uses the same algorithm).

Movement Direction

       The movement direction surface is created to record the sequence of movements that created
       the  cost  accumulation surface. Without it r.drain would not correctly create a path from
       an end point back to the start point. The direction shown in each cell  points  away  from
       the cell that came before it. The directions are recorded as
              112.5 90  67.5         i.e. a cell with the value 135
       157.5  135   0   45   22.5    means the cell before it is
              180   x   0            to the south-east.
       202.5  225  270  315  337.5
              247.5     292.5

       Once  r.walk  computes  the  cumulative  cost map as a linear combination of friction cost
       (from friction map) and the altitude and distance  covered  (from  the  digital  elevation
       model),  r.drain  can  be used to find the minimum cost path. Make sure to use the -d flag
       and the movement direction raster map when running r.drain to ensure the path is  computed
       according to the proper movement directions.


       r.cost, r.drain,, r.mapcalc, r.out.ascii


                     Aitken,  R.  1977.  Wilderness  areas in Scotland. Unpublished Ph.D. thesis.
                     University of Aberdeen.

                      Steno Fontanari, University of Trento, Italy, Ingegneria per  l'Ambiente  e
                     il   Territorio,   2000-2001.    Svilluppo   di   metodologie   GIS  per  la
                     determinazione dell'accessibilit&agrave;  territoriale  come  supporto  alle
                     decisioni nella gestione ambientale.

                     Langmuir,  E.  1984.  Mountaincraft  and  leadership.  The  Scottish  Sports
                     Council/MLTB. Cordee, Leicester.


       Based on r.cost written by :

       Antony Awaida,
       Intelligent Engineering
       Systems Laboratory,
       James Westervelt,
       U.S.Army Construction Engineering Research Laboratory

       Updated for Grass 5
       Pierre de Mouveaux (

       Initial version of r.walk:

       Steno Fontanari, 2002

       Current version of r.walk:

       Franceschetti Simone, Sorrentino Diego, Mussi Fabiano and Pasolli Mattia
       Correction by: Fontanari Steno, Napolitano Maurizio and  Flor Roberto
       In collaboration with: Franchi Matteo, Vaglia Beatrice, Bartucca Luisa, Fava Valentina and
       Tolotti Mathias, 2004

       Updated for Grass 6.1

       Roberto Flor and Markus Neteler

       Last changed: $Date: 2012-12-31 04:29:35 -0800 (Mon, 31 Dec 2012) $

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