coordinates vs projections

[mike camann]

GRASS users--

This may be a FAQ, but I haven't seen any recent discussion about it,
so I'll ask anyway.  Last week I posted a question regarding how to set
up a LOCATION using a transverse Mercator projection and a lat-lon
coordinate system.  I gather, after some experimentation, that you
can't (*please* correct me if I'm wrong).  GRASS expects transverse
Mercator locations to be referenced in meters.  This raises several
important issues:

1)  As near as I can tell, GRASS regards lat-lon as a *projection*.
Furthermore, it seems to view lat-lon as a square projection, where all
the grid lines intersect at 90 degrees.  Square-grid projections of the
Earth's surface don't make great maps because of the enormous
distortion they introduce in northern and southern latitudes.  Besides,
latitude and longitude are not a projection at all: they're a
coordinate referencing system, one that uses sexagesimal notation to
reference points.  The coordinate system should be independent of the
projection used to project the elliptical surface of the Earth onto a
plane.

2)  The GRASS restriction that transverse Mercator projections
reference points with coordinates in meters is clumsy, especially when
working at global scale, i.e. maps of North America or of the western
hemisphere.  The base maps used to set up these LOCATIONS usually
reference points in lat-lon; not only is this the result of
long-standing cartographic tradition but it makes perfect sense to use
a sexagesimal coordinate system on spherical (or near spherical)
objects.  Such maps usually lack printed decimal grids or even the
distances between corners, which would move along with the illustrated
coastlines, etc., as the paper moved and distorted the image through
time.  Accurately locating decimal control points can be difficult (or
impossible) when digitizing the base map.  Unfortunately, using a
lat-lon coordinate system, with its printed grid, leads to rhomboidal
DEFAULT_WIND definitions at global scale, and to rasters that are
unequal in size.

3)  Assuming that this is too messy a can of worms to open, how does
GRASS determine where to lay the square (90 degree corners)
DEFAULT_WIND onto the geographic region?  In the case of a transverse
Mercator projection, one sensible way would be to align the geographic
center of the DEFAULT_WIND with the intersection of the central
meridian and the central parallel (the ones requested by g.setproj when
you first define the LOCATION) and to hold the bottom and top edges of
the DEFAULT_WIND at right angles to the central meridian (parallel to
the equator).  Is this the way GRASS does it?  The documentation is
unclear on this point, to say the least.

4)  How is the metric coordinate system set up within the
DEFAULT_WIND?  Is (0,0) in the lower left corner of the window, is it
at the geographic center of the window, or is it at some standard
geographic reference point?  The online documentation omits this
information, but one *has* to know it in order to properly define the
DEFAULT_WIND.

5)  Is there any way to tell GRASS to use metric units other than
meters, i.e. 10 kilometer units?  I realize that this is easy to fudge,
in that a *unit* of measure can be anything I want it to be, but GRASS
explicitly calls these units *meters* which have a distinct formal
definition.  It is inconvenient at best to be forever having to
mentally define a *meter* in one LOCATION to be 10 km while it is 1 km
in another LOCATION and is actually 1 m at another.  At the worst,
someone will forget to make the conversion and import bogus data into
another application.

Thanks in advance.  I hope this stimulates some discussion about
GRASS's apparent confusion over coordinate systems vs map projections,
and that someone can answer my specific questions about how to define
the DEFAULT_WIND under a transverse Mercator projection.

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Michael Camann                          camann at dial.pick.uga.edu
Department of Entomology                camann at phoenix.cs.uga.edu
University of Georgia                   (706) 542-1388
Athens, GA 30602                        (706) 542-2276

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