r.walkgrass - Online in the Cloud

PROGRAM:

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 [-knri] elevation=name friction=name output=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=value] [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

--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

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=value
Maximum memory to be used in MB
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 addiction 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. Without it r.drain would not correctly create 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), 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.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 << 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.

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