GRASS GIS manual: r.walk

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, cost surface, cumulative costs

SYNOPSIS

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

Flags:

-k: Use the 'Knight's move'; slower, but more accurate
-n: Keep null values in output map
-r: Start with values in raster map
-i: Only print info about disk space and memory requirements
--overwrite: Allow output files to overwrite existing files
--verbose: Verbose module output
--quiet: Quiet module output

Parameters:

elevation=name: Name of elevation input raster map
friction=name: Name of input raster map containing friction costs
output=name: output map with walking costs; Name of output raster map to contain walking costs
outdir=string: Name of output raster map to contain movement directions
start_points=string: Starting points vector map
stop_points=string: Stop points vector map
start_rast=string: Starting points raster 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=integer: An optional maximum cumulative cost; Default: 0
null_cost=float: Cost assigned to null cells. By default, null cells are excluded
percent_memory=integer: Percent of map to keep in memory; Default: 100
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 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)]

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).

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 GRASS standard directions:

       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.

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.

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: 2009-04-07 13:23:53 -0700 (Tue, 07 Apr 2009) $

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