# [GRASS-user] negative slope values and movement costs

Michael Barton michael.barton at asu.edu
Thu Feb 1 12:38:07 EST 2007

```If you are calculating round-trip, simply create a slope map and use the
original Tobler algorithm to make a positive (i.e. uphill) cost map and a
negative (downhill) cost map. Then add them together and use the summed
result as the basis for a round-trip cost surface. If you are doing one-way
only you¹ll need an anisotropic algorithm. Perhaps you can modify the
coefficients in r.walk to simulate a Tobler result. If not you can create
the whole thing in the map calculator (e.g., using neighborhood functions)
or the best way would be to work with Markus on r.walk to add the Tobler
algorithm as an option if it is widely used and generally desirable.

Michael

On 2/1/07 9:36 AM, "Miguel Correia" <miguellage.rc at gmail.com> wrote:

> Hello Michael.
> I understand your point. R.walk does create anisotropic cost movements in
> one-way travel, in the sense that calculates differently downhill and uphill
> costs. The problem is that it is based on Naismith's algorithm. For the
> modeling I'm trying to produce, will generate more accurate results another
> algorithm: Tobler's one.
> I guess I already have resolved the problem. In Tobler's hiking function, in
> average, there is a difference of 1km/hr in the same slope value, positive or
> negative. For example, at 10º is estimated 3Km/hr and at -10º, 4km/hr. This
> means that the difference between them is an average distance value of 500
> meters, which in kilometers is expressed 0.05Km. This is the number that
> Tobler sums to the positive slope value to calibrate the anisotropic cost
> movement. For each positive slope value, there is an increment of 0.05km to
> get the average value of its correspondent negative value. This is the
> algorithm:
>
> 6* exp (-3.5 * abs(Slope + 0.05))
>
> And it's logic: if we sum in map algebra, let's say, a cell value of 10º of a
> 'positive slope surface' and the correspondent value in a 'negative slope
> surface', -10º, we would get 3km/hr in the first case and 4km/hr in the second
> case: what is the average? 0.05Km!!!
> What do you think about this, Michael? Do you think I'm right?
> Thanks for your help.
> Miguel.
>
>
> 2007/2/1, Michael Barton <michael.barton at asu.edu>:
>> R.cost creates an isotropic cost surface. If a slope map is used to create a
>> cost surface using r.cost, All slopes of the same magnitude have the same
>> costs (i.e., the cost is the same whether you are going uphill or downhill).
>> This can be OK for 2-way travel (out and back), but can be problematic when
>> calculating 1-way costs.
>>
>> As I understand it, r.walk will calculate an anisotropic cost surface--i.e.,
>> such that uphill and downhill costs are calculated differently. It also
>> allows for inclusion of an additional friction surface to weight costs and
>> input of coefficients to automatically calculate walking (or theoretically
>> other) energy costs.
>>
>> Multiplying a slope map by -1 would only make all slopes negative rather
>> than leaving some positive and some negative. You could multiply by a
>> function of the aspect to make upslope positive, downslope negative, and
>> 'aroundslope' in between.
>>
>> However, what is uphill and what is downhill will depend on the specific
>> route. That is, the uphill direction will vary depending on the direction of
>> travel outward from a point of origin. I believe that r.walk takes this into
>> account.
>>
>> Michael
>>
>>
>> On 2/1/07 1:40 AM, "Gerald Nelson" <gnelson at uiuc.edu> wrote:
>>
>>> > Why do you want negative slope values?
>>> >
>>> > What r.cost does is calculate the smallest cost of moving over a friction
>>> > surface, which could be slope, to one or more destinations.
>>> >
>>> > The manual for the command is here.
>>> >
>>> > http://grass.itc.it/gdp/html_grass63/r.cost.html
>>> >
>>> > Jerry
>>> >
>>> > ---- Original message ----
>>>> >> Date: Thu, 1 Feb 2007 09:05:33 +0100 (CET)
>>>> >> From: mlage at usal.es
>>>> >> Subject: Re: [GRASS-user] negative slope values and movement costs
>>>> >> To: grassuser at grass.itc.it  <mailto:grassuser at grass.itc.it>
>>>> >>
>>>> >> Thank you Jerry.
>>>> >> How does r.cost produce negative slope values?
>>>> >>
>>>> >> Miguel
>>>> >>
>>>> >> _______________________________________________
>>>> >> grassuser mailing list
>>>> >> grassuser at grass.itc.it
>>>> >> http://grass.itc.it/mailman/listinfo/grassuser
>>> > Gerald Nelson
>>> > Professor, Dept. of Agricultural and Consumer Economics
>>> > University of Illinois, Urbana-Champaign
>>> > office: 217-333-6465
>>> > cell: 217-390-7888
>>> > 315 Mumford Hall
>>> > 1301 W. Gregory
>>> > Urbana, IL 61801
>>> >
>>> >
>>
>> __________________________________________
>> Michael Barton, Professor of Anthropology
>> School of Human Evolution & Social Change
>> Center for Social Dynamics & Complexity
>> Arizona State University
>>
>> phone: 480-965-6213
>> fax: 480-965-7671
>> www: http://www.public.asu.edu/~cmbarton
>>
>>
>> _______________________________________________
>> grassuser mailing list
>> grassuser at grass.itc.it
>> http://grass.itc.it/mailman/listinfo/grassuser
>>
>

__________________________________________
Michael Barton, Professor of Anthropology
School of Human Evolution & Social Change
Center for Social Dynamics and Complexity
Arizona State University

phone: 480-965-6213
fax: 480-965-7671
www: http://www.public.asu.edu/~cmbarton

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