r.walk(1grass) GRASS GIS User's Manual r.walk(1grass)
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_coordi-
nates=east,north[,east,north,...]] [stop_coordi-
nates=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 cate-
gory 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 repre-
sent elevation, combined with a second input raster map whose cell val-
ues 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 de-
creasing cost)
• d: additional walking time in seconds, per meter of elevation
loss on steep downhill slopes (use negative value for increas-
ing 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 ad-
ditional 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 (al-
though it is more time consuming). In the diagram below, the center lo-
cation (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 neigh-
bours 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 di-
rection 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 to-
wards 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 metodolo-
gie 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 Mat-
tia
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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GRASS 7.8.7 r.walk(1grass)
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