[GRASS-dev] small changes to r.walk

[Michael Barton]

  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
>>
>>
>>
>>
>>
>>
>>
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