Hi Seth,
When using the Transverse Mercator projection, the scale factor
parameter (k) is typically used to 'spread' the scale distortion more
evenly across the map. In its standard form the central meridian of a
Transverse Mercator map represents the line - indeed the only line -
along which there is zero scale distortion. Thus, if your map is plotted
at a scale of, say, 1:100,000 then this scale applies only along the
central meridian. At all other points on the map the scale differs from
this 'nominal' scale; in fact the scale distortion increases
dramatically the further one move aways from the central meridian
(recall how scale distortion increaases towards the poles in the normal
Mercator projection).
The scale factor is usually used to reduce the scale at the central
meridian, which has the effect of producing on the projected map two
lines parallel to the central meridian along which the scale factor is 1
(i.e. k = 1.0). These two lines are now free from scale distortion and,
using our earlier example, represent the locus of points at which the
nominal scale of 1:100,000 applies. If a scale factor is not specified,
then the default value of 1 is assumed by most (all?) map projection
applications.
By way of a more concrete example, the 6 degree zones used in the UTM
coordinate reference system, and the Transverse Mercator projection used
in the British National Grid, both employ a scale factor of k=0.9996 at
the central meridian. This means that the two lines of zero scale
distortion are approximately 180 km either side of the central meridian.
Whether of not you choose to utilise a scale factor will depend on the
scale and intended usage of your map. If the map is not going to be used
for navigation or measurement then assigning a scale factor is probably
not required. Likewise, for qualitative interpretation of
regional/global data a scale factor would not be useful, but then you
would almost certainly choose a different map projection for this
purpose, one with more favourable scale distortion characteristics.
In answer then to your question, yes, the scale factor is a single
positive number, typically close to 1.0 (the default value).
Hope this is helpful.
Regards,
Phil
On Fri, 2007-09-14 at 15:58 -0600, mcginnis at ucar.edu wrote:
> Hi all,
>
> If one is using a transverse Mercator grid mapping, how does the
> attribute scale_factor_at_central_meridian work? In particular, is it
> a single number, or is it an array of values? My guess is that it's
> just one number, but it's not clear from the description in table F.1
> of the conventions doc.
>
> Thanks!
>
> Seth McGinnis
> Associate Scientist
> ISSE / NCAR
>
> ----------------------------------------------------------------
>
>
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