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NAME

       r.walk   -  Creates a raster map showing the anisotropic cumulative cost of moving between
       different geographic locations on an input raster map whose cell category values represent
       cost.

KEYWORDS

       raster, cost surface, cumulative costs, cost allocation

SYNOPSIS

       r.walk
       r.walk --help
       r.walk  [-knrib]  elevation=name friction=name output=name  [solver=name]   [nearest=name]
       [outdir=name]       [start_points=name]       [stop_points=name]       [start_raster=name]
       [start_coordinates=east,north[,east,north,...]]
       [stop_coordinates=east,north[,east,north,...]]     [max_cost=value]      [null_cost=value]
       [memory=memory   in  MB]    [walk_coeff=a,b,c,d]    [lambda=float]    [slope_factor=float]
       [--overwrite]  [--help]  [--verbose]  [--quiet]  [--ui]

   Flags:
       -k
           Use the ’Knight’s move’; slower, but more accurate

       -n
           Keep null values in output raster map

       -r
           Start with values in raster map

       -i
           Print info about disk space and memory requirements and exit

       -b
           Create bitmask encoded directions

       --overwrite
           Allow output files to overwrite existing files

       --help
           Print usage summary

       --verbose
           Verbose module output

       --quiet
           Quiet module output

       --ui
           Force launching GUI dialog

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

       friction=name [required]
           Name of input raster map containing friction costs

       output=name [required]
           Name for output raster map to contain walking costs

       solver=name
           Name of input raster map solving equal costs
           Helper variable to pick a direction if two  directions  have  equal  cumulative  costs
           (smaller is better)

       nearest=name
           Name for output raster map with nearest start point

       outdir=name
           Name for output raster map to contain movement directions

       start_points=name
           Name of starting vector points map
           Or data source for direct OGR access

       stop_points=name
           Name of stopping vector points map
           Or data source for direct OGR access

       start_raster=name
           Name of starting raster points map

       start_coordinates=east,north[,east,north,...]
           Coordinates of starting point(s) (E,N)

       stop_coordinates=east,north[,east,north,...]
           Coordinates of stopping point(s) (E,N)

       max_cost=value
           Maximum cumulative cost
           Default: 0

       null_cost=value
           Cost assigned to null cells. By default, null cells are excluded

       memory=memory in MB
           Maximum memory to be used (in MB)
           Cache size for raster rows
           Default: 300

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

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

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

DESCRIPTION

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

       r.walk outputs 1) a raster map showing the lowest cumulative cost (time) of moving between
       each cell and the user-specified starting points and 2) a second raster  map  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 whose  cell  category  values  represent
       elevation,  combined  with  a second input raster map whose cell values represent friction
       costs.

       This function is similar to r.cost, but in addition to a friction  map,  it  considers  an
       anisotropic  travel  time  due to the different walking speed associated with downhill and
       uphill movements.

NOTES

       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
       where:

           •   T is time of movement in seconds,

           •   delta S is the horizontal distance covered in meters,

           •   delta H is the altitude difference in meters.

       The  a,  b,  c,  d  walk_coeff  parameters take in account movement speed in the different
       conditions and are linked to:

           •   a: time in seconds it takes to walk for 1 meter a flat surface (1/walking speed)

           •   b: additional walking time in seconds, per  meter  of  elevation  gain  on  uphill
               slopes

           •   c:  additional  walking  time  in seconds, per meter of elevation loss on moderate
               downhill slopes (use positive value for decreasing cost)

           •   d: additional walking time in seconds,  per  meter  of  elevation  loss  on  steep
               downhill slopes (use negative value for increasing cost)
       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  walk_coeff  parameters  are  those proposed by Langmuir (0.72, 6.0, 1.9998,
       -1.9998), based on man walking effort in standard conditions.

       The friction cost parameter represents a time penalty in  seconds  of  additional  walking
       time to cross 1 meter distance.

       The lambda parameter is a dimensionless scaling factor of the friction cost:
       total cost = movement time cost + lambda * friction costs * delta_S

       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. This movement direction surface can be used by r.path to
       recover a path from an end point back to the start point.   The  direction  of  each  cell
       points towards the next cell.  The directions are recorded as degrees CCW from East:
              112.5      67.5         i.e. a cell with the value 135
       157.5  135   90   45   22.5    means the next cell is to the north-west
              180   x   360
       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),  the  associated  movement direction map can be used by r.path to find the minimum
       cost path.

       r.walk, like most all GRASS raster programs, is also made to be run on  maps  larger  that
       can  fit  in available computer memory. As the algorithm works through the dynamic list of
       cells it can move almost randomly around the entire area. r.walk divides the  entire  area
       into  a number of pieces and swaps these pieces in and out of memory (to and from disk) as
       needed. This provides a virtual memory approach optimally designed for  2-D  raster  maps.
       The  amount  of  memory  to  be  used  by r.walk can be controlled with the memory option,
       default is 300 MB. For systems with less memory this value will have to be set to a  lower
       value.

EXAMPLES

       We  compute  a  map showing how far a lost person could get from the point where he or she
       was last seen while taking into account the topography and landcover.
       g.region swwake_30m -p
       # create friction map based on land cover
       r.recode landclass96 out=friction rules=- << EOF
       1:3:0.1:0.1
       4:5:10.:10.
       6:6:1000.0:1000.0
       7:7:0.3:0.3
       EOF
       r.walk -k elevation=elev_ned_30m friction=friction output=walkcost \
           start_coordinates=635576,216485 lambda=0.5 max=10000
       # compute contours on the cost surface to better understand
       # how far the person can get in certain time (1000 is in seconds)
       r.contour walkcost output=walkcost step=1000

REFERENCES

           •   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’accessibilità  territoriale  come  supporto  alle  decisioni  nella  gestione
               ambientale.

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

SEE ALSO

        r.cost, r.path, r.in.ascii, r.mapcalc, r.recode, r.out.ascii

AUTHORS

       Based on r.cost written by :
       Antony Awaida, Intelligent Engineering, Systems Laboratory, M.I.T.
       James Westervelt, U.S.Army Construction Engineering Research Laboratory
       Updated for Grass 5 by Pierre de Mouveaux (pmx@audiovu.com)

       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

       Updated for GRASS GIS 7:
       Markus Metz
       Multiple path directions sponsored by mundialis

SOURCE CODE

       Available at: r.walk source code (history)

       Accessed: unknown

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