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

[Thomas Lumley]

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

-- 
Thomas Lumley
Professor of Biostatistics
University of Auckland