[R-sig-Geo] WGS 84 coordinates and the use of Euclidean calculations for short distances--is it ever okay?

[Clint Bowman]

I think I would convert your coordinates to a rectangular one 
(e.g., UTM or a Lambert Conformal) and compute distance 
relationships there.

Clint

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On Sat, 21 May 2011, Thomas Lumley wrote:

> On Sat, May 21, 2011 at 10:07 AM, Megan Marcotte <megotte at gmail.com> wrote:
>> Hello All
>>
>>
>> I am new to the list and am hoping to get some advice.  I am working with
>> statisticians who are doing the programming of a new analysis in R where we
>> are comparing animal tracks with environmental parameters. I was wondering
>> if anyone knows or has an opinion on the following:
>>
>> 1)      a) A rule of thumb or even a hard rule for when you need to start
>> using great circle instead of Euclidian calculations for distances? Just a
>> bit more information for perspective: depending on the animals tracked the
>> distances between fixes could be as small as 20 m or up to 1.5 km. The
>> tracks may be up to 20 km of cumulative length.
>
> When you say "Euclidian" it's not clear whether you mean
> a/ treating the earth as flat
> b/ treating latitude and longitude as a rectangular coordinate system
> c/ treating the degree grid as square.
>
> (a) should be fine on this scale, for (b) and (c) it depends on the latitude
>
>> 2)      b) Are functions based on Euclidian math okay to use with WGS84
>> coordinates if the total distance of the tracks are <20 km, or a max of 0.5
>> degrees of latitude (but usually much less, at latitudes of 25 or or -36
>> degrees). I know that with latitude the length of a degree of longitude
>> changes but at this scale is it a factor?  Any rules for this?
>>
>
> I would have said that it was perfectly ok to treat the earth as flat
> and the degree grid as rectangular on this sort of scale and at these
> latitudes, but that you can't treat the degree grid as square. That
> is, a degree of longitude is about 10% less than a degree of latitude
> at 25 degrees and about 20% less at 36 degrees.
>
>   -thomas
>
>