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### r.walk: Outputs a raster map layer showing the anisotropic cumulative cost of moving between different geographic locations on

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## 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[-knr]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=integer] [null_cost=float] [percent_memory=integer] [nseg=integer] [walk_coeff=a,b,c,d] [lambda=float] [slope_factor=float] [--overwrite] [--verbose] [--quiet]Flags: -kUse the 'Knight's move'; slower, but more accurate-nKeep null values in output map-rStart with values in raster map--overwriteAllow output files to overwrite existing files--verboseVerbose module output--quietQuiet module outputParameters: elevation=stringName of elevation input raster mapfriction=stringName of input raster map containing friction costsoutput=stringName of raster map to contain resultsstart_points=stringStarting points vector mapstop_points=stringStop points vector mapcoordinate=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=integerAn optional maximum cumulative cost Default:0 null_cost=floatCost assigned to null cells. By default, null cells are excludedpercent_memory=integerPercent of map to keep in memory Default:100 nseg=integerNumber of the segment to create (segment library) Default:4 walk_coeff=a,b,c,dCoefficients for walking energy formula parameters a,b,c,d Default:0.72,6.0,1.9998,-1.9998 lambda=floatLambda coefficients for combining walking energy and friction cost Default:1.0 slope_factor=floatSlope factor determines travel energy cost per height step Default:-0.2125DESCRIPTION

r.walkoutputs 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 tor.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 ofr.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 seer.cost, that uses the same algorithm). Oncer.walkcomputes 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.draincan 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'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: 2008-05-16 21:09:06 +0200 (Fri, 16 May 2008) $ Full index (C) 2003-2010 GRASS Development Team R.WALK(1)

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