NAME
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.
KEYWORDS
raster
SYNOPSIS
r.walk
r.walk help
r.walk [-vknr] elevation=string friction=string output=string [start_points=string] [stop_points=string] [coordinate=x,y[,x,y,...]] [stop_coordinate=x,y[,x,y,...]] [max_cost=cost] [null_cost=null cost] [percent_memory=percent memory] [nseg=nseg] [walk_coeff=a,b,c,d] lambda=lambda [slope_factor=slope_factor] [--overwrite]
Flags:
- -v
- Run verbosely
- -k
- Use the 'Knight's move'; slower, but more accurate
- -n
- Keep null values in output map
- -r
- Start with values in raster map
- --overwrite
- Force overwrite of output files
Parameters:
- elevation=string
- Name of elevation input raster map
- friction=string
- Name of input raster map containing friction costs
- output=string
- Name of raster map to contain results
- start_points=string
- Starting points vector map
- stop_points=string
- Stop points vector map
- coordinate=x,y[,x,y,...]
- The map E and N grid coordinates of a starting point (E,N)
- stop_coordinate=x,y[,x,y,...]
- The map E and N grid coordinates of a stopping point (E,N)
- max_cost=cost
- An optional maximum cumulative cost
- Default: 0
- null_cost=null cost
- Cost assigned to null cells. By default, null cells are excluded
- percent_memory=percent memory
- Percent of map to keep in memory
- Default: 100
- nseg=nseg
- Number of the segment to create (segment library)
- Default: 4
- 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=lambda
- Lambda coefficients for combining walking energy and friction cost
- slope_factor=slope_factor
- Slope factor determines travel energy cost per height step
- Default: -0.2125
DESCRIPTION
r.walk outputs a raster map layer showing the lowest
cumulative cost of moving between each cell and the user-specified
starting points. 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)]
where:
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).
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.
SEE ALSO
r.cost,
r.drain,
r.in.ascii,
r.mapcalc,
r.out.ascii
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'accessibilitÃ
territoriale come supporto alle decisioni nella gestione ambientale.
- Langmuir, E. 1984. Mountaincraft and leadership. The Scottish
Sports Council/MLTB. Cordee, Leicester.
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
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
Last changed: $Date: 2005/12/16 21:04:29 $
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