.TH r.walk 1grass "" "GRASS 6.4.4" "Grass User's Manual"
.SH NAME
\fI\fBr.walk\fR\fR  - 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.
.SH KEYWORDS
raster, cost surface, cumulative costs
.SH SYNOPSIS
\fBr.walk\fR
.br
\fBr.walk help\fR
.br
\fBr.walk\fR [\-\fBknr\fR] \fBelevation\fR=\fIstring\fR \fBfriction\fR=\fIstring\fR \fBoutput\fR=\fIstring\fR  [\fBoutdir\fR=\fIstring\fR]   [\fBstart_points\fR=\fIstring\fR]   [\fBstop_points\fR=\fIstring\fR]   [\fBcoordinate\fR=\fIx,y\fR[,\fIx,y\fR,...]]   [\fBstop_coordinate\fR=\fIx,y\fR[,\fIx,y\fR,...]]   [\fBmax_cost\fR=\fIinteger\fR]   [\fBnull_cost\fR=\fIfloat\fR]   [\fBpercent_memory\fR=\fIinteger\fR]   [\fBnseg\fR=\fIinteger\fR]   [\fBwalk_coeff\fR=\fIa,b,c,d\fR]   [\fBlambda\fR=\fIfloat\fR]   [\fBslope_factor\fR=\fIfloat\fR]   [\-\-\fBoverwrite\fR]  [\-\-\fBverbose\fR]  [\-\-\fBquiet\fR] 
.SS Flags:
.IP "\fB\-k\fR" 4m
.br
Use the 'Knight's move'; slower, but more accurate
.IP "\fB\-n\fR" 4m
.br
Keep null values in output map
.IP "\fB\-r\fR" 4m
.br
Start with values in raster map
.IP "\fB\-\-overwrite\fR" 4m
.br
Allow output files to overwrite existing files
.IP "\fB\-\-verbose\fR" 4m
.br
Verbose module output
.IP "\fB\-\-quiet\fR" 4m
.br
Quiet module output
.PP
.SS Parameters:
.IP "\fBelevation\fR=\fIstring\fR" 4m
.br
Name of elevation input raster map
.IP "\fBfriction\fR=\fIstring\fR" 4m
.br
Name of input raster map containing friction costs
.IP "\fBoutput\fR=\fIstring\fR" 4m
.br
Name of raster map to contain results
.IP "\fBoutdir\fR=\fIstring\fR" 4m
.br
Name of output raster map to contain movement directions
.IP "\fBstart_points\fR=\fIstring\fR" 4m
.br
Starting points vector map
.IP "\fBstop_points\fR=\fIstring\fR" 4m
.br
Stop points vector map
.IP "\fBcoordinate\fR=\fIx,y[,\fIx,y\fR,...]\fR" 4m
.br
The map E and N grid coordinates of a starting point (E,N)
.IP "\fBstop_coordinate\fR=\fIx,y[,\fIx,y\fR,...]\fR" 4m
.br
The map E and N grid coordinates of a stopping point (E,N)
.IP "\fBmax_cost\fR=\fIinteger\fR" 4m
.br
An optional maximum cumulative cost
.br
Default: \fI0\fR
.IP "\fBnull_cost\fR=\fIfloat\fR" 4m
.br
Cost assigned to null cells. By default, null cells are excluded
.IP "\fBpercent_memory\fR=\fIinteger\fR" 4m
.br
Percent of map to keep in memory
.br
Default: \fI100\fR
.IP "\fBnseg\fR=\fIinteger\fR" 4m
.br
Number of the segment to create (segment library)
.br
Default: \fI4\fR
.IP "\fBwalk_coeff\fR=\fIa,b,c,d\fR" 4m
.br
Coefficients for walking energy formula parameters a,b,c,d
.br
Default: \fI0.72,6.0,1.9998,-1.9998\fR
.IP "\fBlambda\fR=\fIfloat\fR" 4m
.br
Lambda coefficients for combining walking energy and friction cost
.br
Default: \fI1.0\fR
.IP "\fBslope_factor\fR=\fIfloat\fR" 4m
.br
Slope factor determines travel energy cost per height step
.br
Default: \fI-0.2125\fR
.PP
.SH DESCRIPTION
\fIr.walk\fR 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 \fIr.cost\fR, 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.
.PP
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:
.PP
T= [(a)*(Delta S)] + [(b)*(Delta H uphill)] + [(c)*(Delta H moderate downhill)] + [(d)*(Delta H steep downhill)]
.PP
where:
.br
T is time of movement in seconds,
.br
Delta S is the distance covered in meters,
.br
Delta H is the altitude difference in meter.
.PP
 
The a, b, c, d parameters take in account movement speed in the different
conditions and are linked to:
.RE
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
.RE
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.
.PP
The lambda parameter of the linear equation combining movement and
friction costs:
.br
total cost = movement time cost + (lambda) * friction costs
.br
must be set in the option section of \fIr.walk\fR.
.PP
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.
\fC
.DS
.br
  K   K 
.br
K x x x K
.br
  x O x
.br
K x x x K
.br
  K   K
.br
.DE
\fR
.PP
The minimum cumulative costs are computed using Dijkstra's
algorithm, that find an optimum solution (for more details see
\fIr.cost\fR, that uses the same algorithm).
.SH Movement Direction
.PP
The movement direction surface is created to record the sequence of
movements that created the cost accumulation surface. Without it 
\fIr.drain\fR would not correctly create a path from an end point 
back to the start point. The direction shown in each cell points \fBaway\fR 
from the cell that came before it. The directions are recorded as
\fC
.DS
.br
       112.5 90  67.5         i.e. a cell with the value 135 
.br
157.5  135   0   45   22.5    means the cell \fBbefore\fR it is 
.br
       180   x   0            to the south-east.
.br
202.5  225  270  315  337.5
.br
       247.5     292.5
.br
.DE
\fR
.PP
Once \fIr.walk\fR 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), \fIr.drain\fR
can be used to find the minimum cost path. Make sure to use the \fB-d\fR flag
and the movement direction raster map when running r.drain to ensure
the path is computed according to the proper movement directions.
.SH SEE ALSO
\fIr.cost\fR,
\fIr.drain\fR,
\fIr.in.ascii\fR,
\fIr.mapcalc\fR,
\fIr.out.ascii\fR
.SH REFERENCES
.RS
.IP
Aitken, R. 1977. Wilderness areas in Scotland. Unpublished Ph.D. thesis.
University of Aberdeen.
.IP
 Steno Fontanari, University of Trento, Italy, Ingegneria per l'Ambiente e
il Territorio, 2000-2001.
Svilluppo di metodologie GIS per la determinazione dell'accessibilit&agrave;
territoriale come supporto alle decisioni nella gestione ambientale.
.IP
Langmuir, E. 1984. Mountaincraft and leadership. The Scottish
Sports Council/MLTB. Cordee, Leicester.
.RE
.SH AUTHORS
\fBBased on r.cost written by :\fR
.PP
Antony Awaida,
.br
Intelligent Engineering
.br
Systems Laboratory,
.br
M.I.T.
.br
.br
James Westervelt,
.br
U.S.Army Construction Engineering Research Laboratory
.PP
Updated for Grass 5
.br
Pierre de Mouveaux (pmx@audiovu.com)
.PP
\fBInitial version of r.walk:\fR
.PP
Steno Fontanari, 2002
.PP
\fBCurrent version of r.walk:\fR
.PP
Franceschetti Simone, Sorrentino Diego, Mussi Fabiano and Pasolli Mattia
.br
Correction by: Fontanari Steno, Napolitano Maurizio and  Flor Roberto
.br
In collaboration with: Franchi Matteo, Vaglia Beatrice, Bartucca Luisa, Fava Valentina and Tolotti Mathias, 2004
.PP
\fBUpdated for Grass 6.1\fR
.PP
Roberto Flor and Markus Neteler
.PP
\fILast changed: $Date: 2012-12-31 13:29:35 +0100 (Mon, 31 Dec 2012) $\fR
.PP
Full index
.PP
© 2003-2014 GRASS Development Team