[GRASS-dev] small changes to r.walk
Michael Barton
michael.barton at asu.edu
Mon Nov 17 10:59:59 EST 2008
Thanks Colin,
This is all very helpful. The percentage friction map was a wish. It
is clear that it can't be used that way with the current code. At
least now it is very clear how lambda and a friction map interacts
with the rest of the cost calculations. If some empirical tests could
be made, it might be possible to suggest value ranges for a friction
map that would give meaningful time values in the result. It would
probably be good to get some of this information into the manual page.
We will be using r.walk in a number of research settings, so we might
come up with some information. If so, I'll pass it along.
Michael
______________________________
C. Michael Barton, Professor of Anthropology
Director of Graduate Studies
School of Human Evolution & Social Change
Center for Social Dynamics & Complexity
Arizona State University
Tempe, AZ 85287-2402
USA
voice: 480-965-6262; fax: 480-965-7671
www: http://www.public.asu.edu/~cmbarton
On Nov 15, 2008, at 6:06 PM, Colin Nielsen wrote:
> Hi again,
>
>> Thanks again for the info. We're looking into it. I guess we will
>> need to do
>> some empirical tests, but it would be nice if one could specify how
>> to value
>> a friction map so as to still get real time values in the output.
>> Here seems
>> to be the most relevant piece of code.
>>
>> else
>> fcost_dtm = (double)((double)(W_dtm - my_dtm) * c);
>> fcost_cost = ((double)(W_cost + my_cost) / 2.0);
>> min_cost = pres_cell->min_cost + fcost_dtm + (EW_fac * a) +
>> lambda *
>> fcost_cost * EW_fac;
>>
>> fcost_cost is not friction cost per se. Maybe my_cost is the actual
>> friction
>> cost value? It doesn't seem be converted to time units at that
>> point, but
>> this is not clear (What is W_cost?). I guess we need to know this to
>> determine the units/value ranges for the friction map.
>
> Perhaps it would clarify things if I explain exactly how the two costs
> (topographic and friction) are calculated and then how they're
> combined. Beginning with the specified start point, an origin cell is
> selected. The topographic and friction costs are then calculated to
> each of its neighbours (8 or 16). The snippet of code I gave was for
> the western neighbour (ie. W_cost) but it continues with every other
> neighbour as well. In the code, W_dtm = the elevation cell value of
> the western neighbour, W_cost = the friction cell value of the
> neighbour, my_dtm = elevation of origin, my_cost = friction value of
> origin.
>
> The topographic cost is calculated by finding the difference in
> elevation between the origin and its neighbour over the horizontal
> resolution, dtm=digital terrain model: (W_dtm - my_dtm) / EW_fac.
> Depending on the slope and the specified slope_factor it is multiplied
> by one of the specified coefficients b,c,d to convert it to seconds
> (see the attached graph, assuming this list will accept attachments,
> nb. I converted the slope to degrees).
>
> The friction cost is calculated by summing half the friction of each
> of the origin cell and the neighbouring cell: (W_cost + my_cost) /
> 2.0). This is because the "walker" is travelling from cell center to
> cell center and therefore only has to walk across half of each pixel
> (actually in the code it is an average of the two cell values possibly
> to save on calculation time). With the next step, the other half of
> the pixel will be counted.
>
>> Possibly the easiest way to think about a friction map is as a
>> percent of
>> the 'normal' cost (faster or slower)--though that is not how it
>> seems to be
>> added in.
> It might be convenient if it worked that way but since it is added,
> rather than multiplied, I don't think the friction as a percent of
> normal will work currently.
>
>>
>> I'm not sure why you say a friction map would need to only ADD
>> time. If it
>> is included in the calculations BEFORE the final cumulative time
>> map is
>> made, then it could either increase OR decrease the net time to
>> traverse a
>> cell. This is what I was referring to a couple posts back. And this
>> is what
>> seems to be happening here--except that it looks like you can't
>> really make
>> a friction map value LESS than the topographic costs of traversing
>> a cell.
>> Nevertheless, it is good if we model with some factors reducing the
>> time to
>> cross a cell and other factors increasing the time.
>
> I meant the friction is ADDed as opposed to being used as a
> multiplier. As you said, in theory, there is no reason why a negative
> friction cost couldn't be created which would then decrease the net
> time it took to cross the cell.
>
> As for the range of the friction map to create, empirical tests are
> probably the way to go. Possibly mountaineering guides would be a good
> source for this kind of data as well (especially since the r.walk
> equation was taken from one to begin with). Once completed, perhaps
> lambda could be used for a global conversion between friction map
> values and friction time (as I'm guessing it was originally intended
> for this).
>
> I hope you and your students are finding this as interesting to work
> on as I have.
>
> -Colin
>
>
>>
>>
>> On Nov 13, 2008, at 2:46 PM, Colin Nielsen wrote:
>>
>>>> This is a BIG help and an equally big relief.
>>>
>>> Glad to help.
>>>>
>>>> Now the question arises as to what kind of units should the
>>>> friction map
>>>> be
>>>> in to make sense in this kind of calculation.
>>>
>>> While I'm at it I can try this one too. Basically, without careful
>>> consideration, the use of a friction map will render the units of
>>> the
>>> output relative only (ie. unitless). Which isn't necessarily a bad
>>> thing unless you're set on knowing the actual time.
>>>
>>> The only way to avoid this is to make sure the friction map * lambda
>>> can logically be used to ADD time (rather than being used as a
>>> multiplier). I can't think of a dataset that would allow you to do
>>> this and I'm not even sure that adding the time it would take to
>>> cross
>>> a pixel of forest to the topographic time is an accurate way of
>>> representing multiple travel time factors. Good luck!
>>>
>>> -Colin
>>>
>>>>
>>>> Michael
>>>>
>>>> On Nov 13, 2008, at 1:06 PM, Colin Nielsen wrote:
>>>>
>>>>> If I understand your comment correctly then the current r.walk
>>>>> functionality is actually doing what you want it to be doing (ie.
>>>>> there is no problem). r.walk does not create a full cumulative
>>>>> cost
>>>>> map and then add the friction map, rather it combines the
>>>>> cumulative
>>>>> cost and friction cost with each origin pixel to neighbouring
>>>>> pixel
>>>>> calculation. If this was unclear in the help file perhaps an
>>>>> update to
>>>>> clarify is needed.
>>>>>
>>>>> See the snippet of code below from r.walk/main.c where "case 1"
>>>>> represents the consideration of the western neighbour:
>>>>>
>>>>> 1024 switch (neighbor) {
>>>>> 1025 case 1:
>>>>> 1026 dtm_value = &W_dtm;
>>>>> 1027 segment_get(&dtm_in_seg, dtm_value, row,
>>>>> col);
>>>>> 1028 cost_value = &W_cost;
>>>>> 1029 segment_get(&cost_in_seg, cost_value,
>>>>> row, col);
>>>>> 1030 if (G_is_d_null_value(cost_value))
>>>>> 1031 continue;
>>>>> 1032 if (((W_dtm - my_dtm) / EW_fac) >= 0)
>>>>> 1033 fcost_dtm = (double)((double)(W_dtm -
>>>>> my_dtm)
>>>>> * b);
>>>>> 1034 else if (((W_dtm - my_dtm) / EW_fac) <
>>>>> (slope_factor))
>>>>> 1035 fcost_dtm = (double)((double)(W_dtm -
>>>>> my_dtm)
>>>>> * d);
>>>>> 1036 else
>>>>> 1037 fcost_dtm = (double)((double)(W_dtm -
>>>>> my_dtm)
>>>>> * c);
>>>>> 1038 fcost_cost = ((double)(W_cost +
>>>>> my_cost) / 2.0);
>>>>> 1039 min_cost =
>>>>> 1040 pres_cell->min_cost + fcost_dtm +
>>>>> (EW_fac *
>>>>> a)
>>>>> +
>>>>> 1041 lambda * fcost_cost * EW_fac;
>>>>> 1042 break;
>>>>>
>>>>> The last calculation shows that the neighbour's new cost
>>>>> (min_cost)
>>>>> will be equal to the origin's cumulative cost (pres_cell-
>>>>> >min_cost) +
>>>>> the topographic/slope cost to move to the western neighbour
>>>>> (fcost_dtm) + lambda * the friction cost to move to the western
>>>>> neighbour (fcost_cost).
>>>>>
>>>>> I hope that helps and that I wasn't more long winded than was
>>>>> called for
>>>>> :).
>>>>>
>>>>> -Colin
>>>>>
>>>>>
>>>>> On Thu, Nov 13, 2008 at 2:34 PM, Michael Barton <michael.barton at asu.edu
>>>>> >
>>>>> wrote:
>>>>>>
>>>>>> Hi Colin,
>>>>>>
>>>>>>
>>>>>> On Nov 13, 2008, at 11:38 AM, Colin Nielsen wrote:
>>>>>>
>>>>>>> Not that I'm disagreeing with the need to change this
>>>>>>> functionality,
>>>>>>> but based on the way the algorithm incorporates the friction
>>>>>>> map, you
>>>>>>> can currently put zero for lambda and any map for the friction
>>>>>>> to have
>>>>>>> it work on slope alone. This is a little easier than the
>>>>>>> method you
>>>>>>> mentioned.
>>>>>>
>>>>>> This is a handy workaround. However, it is probably better in
>>>>>> the long
>>>>>> run
>>>>>> to fix this than to depend on a workaround.
>>>>>>
>>>>>>
>>>>>>>
>>>>>>>
>>>>>>> ie. total cost = movement time cost + (0 * friction)
>>>>>>>
>>>>>>> Further, I believe to make lambda and friction optional will
>>>>>>> take
>>>>>>> relatively substantial re-writes.
>>>>>>
>>>>>> Hopefully, this won't really take that much effort. However,
>>>>>> while
>>>>>> we're
>>>>>> on
>>>>>> the subject, one of my students noticed something that might
>>>>>> take more
>>>>>> substantial rewrites and I guess I should mention it now.
>>>>>>
>>>>>> If we are correct on how r.cost uses a friction map (and this
>>>>>> is not
>>>>>> 100%
>>>>>> certain), there is a fundamental flaw. A cost distance map
>>>>>> should have
>>>>>> cells
>>>>>> that represent cumulative cost outward from a starting point.
>>>>>> r.walk
>>>>>> automatically calculates this in seconds, making it a really
>>>>>> useful
>>>>>> module
>>>>>> to have in GRASS.
>>>>>>
>>>>>> If the friction map is added in AFTER the initial cumulative
>>>>>> walking
>>>>>> time
>>>>>> cost map is generated, the result will violate the cumulative
>>>>>> nature of
>>>>>> the
>>>>>> cost map. Imagine a map generated by r.walk with a cumulative
>>>>>> time cost
>>>>>> along a line of cells as follows:
>>>>>>
>>>>>> 0 | 100 | 120 | 150 | 250 | 350 |
>>>>>>
>>>>>> Now ADD a friction map to this
>>>>>>
>>>>>> 0 | 0 | 200 | 300 | 0 | -150 |
>>>>>>
>>>>>> Here is the result
>>>>>>
>>>>>> 0 | 100 | 320 | 450 | 250 | 200 |
>>>>>>
>>>>>> The final map is no longer the cumulative time to travel from the
>>>>>> origin.
>>>>>> More distant cells take less time to reach than closer cells.
>>>>>>
>>>>>> The friction map needs to be incorporated into the cost along
>>>>>> with
>>>>>> topographic slope when the initial time map is created, not
>>>>>> afterwards.
>>>>>>
>>>>>> Michael
>>>>>>
>>>>>>
>>>>>>>
>>>>>>>
>>>>>>> -Colin
>>>>>>>
>>>>>>> On Thu, Nov 13, 2008 at 1:16 PM, Michael Barton
>>>>>>> <michael.barton at asu.edu>
>>>>>>> wrote:
>>>>>>>>
>>>>>>>> Several weeks back, Helena gave a very good explanation of
>>>>>>>> how r.walk
>>>>>>>> actually works. It makes very good sense (see below).
>>>>>>>> However, from
>>>>>>>> this
>>>>>>>> explanation, it is clear that lambda and a friction map
>>>>>>>> should be
>>>>>>>> *optional*
>>>>>>>> rather than *required* as they are now.
>>>>>>>> The main part of r.walk calculates the time (in seconds)
>>>>>>>> needed to
>>>>>>>> walk
>>>>>>>> across a landscape.
>>>>>>>> For any cell,
>>>>>>>> total time = (walking time in seconds to traverse the cell
>>>>>>>> given its
>>>>>>>> slope)
>>>>>>>> + (lambda * friction map)
>>>>>>>> Lambda is a weighting coefficient to convert the friction map
>>>>>>>> to
>>>>>>>> units
>>>>>>>> that
>>>>>>>> match the costs due to slope (i.e., units in seconds normally).
>>>>>>>> If you want to calculate walking time to traverse a landscape
>>>>>>>> that is
>>>>>>>> based
>>>>>>>> solely on the topography (i.e., slope), then you need a
>>>>>>>> friction map
>>>>>>>> with
>>>>>>>> a
>>>>>>>> value of 0; lambda can be anything.
>>>>>>>> So this should be optional. Currently, you need to create a 0
>>>>>>>> friction
>>>>>>>> map
>>>>>>>> and try to figure out what lambda should be in order to run
>>>>>>>> r.walk.
>>>>>>>> This
>>>>>>>> is
>>>>>>>> sort of pointless and can cause considerable confusion.
>>>>>>>> So, can lambda and friction map be changed to optional
>>>>>>>> arguments for
>>>>>>>> our
>>>>>>>> upcoming releases?
>>>>>>>> Thanks
>>>>>>>> Michael
>>>>>>>> ____________
>>>>>>>> Begin forwarded message:
>>>>>>>>
>>>>>>>> From: Michael Barton <michael.barton at asu.edu>
>>>>>>>> Date: October 10, 2008 9:27:46 PM GMT-07:00
>>>>>>>> To: Helena Mitasova <hmitaso at unity.ncsu.edu>
>>>>>>>> Cc: grass developers <grass-dev at lists.osgeo.org>, Ullah Isaac
>>>>>>>> <Isaac.Ullah at asu.edu>, David.Quixal at uv.es, Sean Bergin
>>>>>>>> <Sean.Bergin at asu.edu>, Moreno Martín Andrea <andrea.moreno at uv.es
>>>>>>>> >
>>>>>>>> Subject: Re: [GRASS-dev] default for r.walk
>>>>>>>> Thanks very much for this thorough explanation Helena. It is
>>>>>>>> quite
>>>>>>>> helpful.
>>>>>>>> I hope that Roberto can verify (or correct) this.
>>>>>>>>
>>>>>>>> I'm copying some folks who have been working with r.walk
>>>>>>>> recently.
>>>>>>>> Our
>>>>>>>> lab
>>>>>>>> discussions on this caused me to raise these questions.
>>>>>>>>
>>>>>>>> On the issue I first asked about, it seems that lambda should
>>>>>>>> either
>>>>>>>> 1)
>>>>>>>> have
>>>>>>>> a default value of 1 or 2) be optional.
>>>>>>>>
>>>>>>>> Michael
>>>>>>>>
>>>>>>>>
>>>>>>>> On Oct 10, 2008, at 6:09 PM, Helena Mitasova wrote:
>>>>>>>>
>>>>>>>>
>>>>>>>> On Oct 10, 2008, at 7:39 PM, Michael Barton wrote:
>>>>>>>>
>>>>>>>>
>>>>>>>>
>>>>>>>>
>>>>>>>> On Oct 10, 2008, at 11:32 AM, Helena Mitasova wrote:
>>>>>>>>
>>>>>>>> I opened the code and it has it right in header:
>>>>>>>>
>>>>>>>> TOTAL COST = [(WALKING ENERGY ) + (LAMBDA*FRICTION)]
>>>>>>>>
>>>>>>>> maybe this is how it should go into the man page
>>>>>>>>
>>>>>>>> That seems like a good idea.
>>>>>>>>
>>>>>>>> This suggests that friction and lambda should be in some kind
>>>>>>>> of
>>>>>>>> energy
>>>>>>>> units.
>>>>>>>>
>>>>>>>> However, as I understand it, the values in an r.walk map--
>>>>>>>> using the
>>>>>>>> default
>>>>>>>> values--are an estimate of the number of seconds to traverse
>>>>>>>> a cell
>>>>>>>> walking
>>>>>>>> 'normally' (i.e., according to the default values). Is this
>>>>>>>> true
>>>>>>>> anyone?
>>>>>>>> If
>>>>>>>> so, wouldn't the additive friction need to be in time units?
>>>>>>>>
>>>>>>>> I'm not trying to be dense, but trying to get clear about
>>>>>>>> what the
>>>>>>>> output
>>>>>>>> is
>>>>>>>> actually telling us, since it does not seem to be in
>>>>>>>> arbitrary units
>>>>>>>> like
>>>>>>>> r.cost is (unless you do some numerical massaging).
>>>>>>>>
>>>>>>>> these are perfectly valid questions - authors should probably
>>>>>>>> answer
>>>>>>>> them
>>>>>>>> rather than me
>>>>>>>>
>>>>>>>> but we tried to put some explanation based on the manual in
>>>>>>>> to the
>>>>>>>> appendix
>>>>>>>> of GRASSbook
>>>>>>>>
>>>>>>>> and I have just covered it in the class so I had to spend
>>>>>>>> some time
>>>>>>>> trying
>>>>>>>> to understand it.
>>>>>>>>
>>>>>>>> the units are - according to the manual - time - see below
>>>>>>>>
>>>>>>>> S, H are meters but the coefficients a,b,c,d are 1/speed
>>>>>>>> which is
>>>>>>>> sec/meter
>>>>>>>> giving you time in seconds,
>>>>>>>>
>>>>>>>> then friction map can be either in units of time (sec) and
>>>>>>>> lambda is
>>>>>>>> unitless weight
>>>>>>>>
>>>>>>>> or friction is unitless factor and lambda is in seconds which
>>>>>>>> converts
>>>>>>>> it
>>>>>>>> to
>>>>>>>> time.
>>>>>>>>
>>>>>>>> So the results are in seconds - when you derive contours from
>>>>>>>> the
>>>>>>>> results
>>>>>>>> you will get isochrones -
>>>>>>>>
>>>>>>>> so you can delineate an area where the person gets within 2
>>>>>>>> hours or
>>>>>>>> whatever time you chose.
>>>>>>>>
>>>>>>>> But it would be really good to hear from the authors because
>>>>>>>> these
>>>>>>>> are
>>>>>>>> my
>>>>>>>> interpretations
>>>>>>>>
>>>>>>>> of the manual and my experiments with the module. The man
>>>>>>>> page is
>>>>>>>> pretty
>>>>>>>> good it just needs to be more clear that the cost is measured
>>>>>>>> by time
>>>>>>>> (if
>>>>>>>> I
>>>>>>>> understand it correctly)
>>>>>>>>
>>>>>>>> Helena
>>>>>>>>
>>>>>>>>
>>>>>>>> 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 of r.walk.
>>>>>>>>
>>>>>>>>
>>>>>>>>
>>>>>>>>
>>>>>>>> Michael
>>>>>>>>
>>>>>>>>
>>>>>>>>
>>>>>>>>
>>>>>>>>
>>>>>>>>
>>>>>>>> On Oct 10, 2008, at 2:21 PM, Michael Barton wrote:
>>>>>>>>
>>>>>>>> I've been emailing with Helena to try to understand exactly how
>>>>>>>> lambda
>>>>>>>> and a
>>>>>>>> friction surface interacts with information about topography
>>>>>>>> (extracted
>>>>>>>> from
>>>>>>>> a DEM) in r.walk. It seems a good idea to put this back on
>>>>>>>> the list.
>>>>>>>> Perhaps
>>>>>>>> I'm the only one a little in the dark, but maybe it can help
>>>>>>>> others.
>>>>>>>>
>>>>>>>> On Oct 10, 2008, at 10:40 AM, Helena Mitasova wrote:
>>>>>>>>
>>>>>>>>
>>>>>>>> To clarify for me, is it
>>>>>>>>
>>>>>>>> total cost = (movement time cost + lambda) * friction costs
>>>>>>>>
>>>>>>>> OR
>>>>>>>>
>>>>>>>> total cost = movement time cost + (lambda * friction costs)
>>>>>>>>
>>>>>>>> I did not look into the code but if there are no brackets in
>>>>>>>> the
>>>>>>>> code,
>>>>>>>> this
>>>>>>>> second interpretation applies.
>>>>>>>>
>>>>>>>> For anyone familiar with the code, is this the case? If so,
>>>>>>>> should I
>>>>>>>> be
>>>>>>>> thinking in time units for creating a friction map? If I
>>>>>>>> remember,
>>>>>>>> r.walk
>>>>>>>> normally outputs in seconds to traverse the cell.
>>>>>>>>
>>>>>>>> So, should the friction map be in additional seconds to
>>>>>>>> traverse the
>>>>>>>> cell?
>>>>>>>> Or is friction a weighting factor (i.e., multiplicative
>>>>>>>> rather than
>>>>>>>> additive)?
>>>>>>>>
>>>>>>>> Thanks
>>>>>>>>
>>>>>>>> Michael
>>>>>>>>
>>>>>>>>
>>>>>>>>
>>>>>>>>
>>>>>>>>
>>>>>>>>
>>>>>>>>
>>>>>>>> _______________________________________________
>>>>>>>> grass-dev mailing list
>>>>>>>> grass-dev at lists.osgeo.org
>>>>>>>> http://lists.osgeo.org/mailman/listinfo/grass-dev
>>>>>>>>
>>>>>>
>>>>>>
>>>>
>>>>
>>
>>
> <dtm_cost.png>
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