[GRASS-user] Question about units and points of reference

[Glynn Clements]

Wayde Allen wrote:

> > I am using 6.2.1, and g.region -p gives the info:
> >
> > projection: 1 (UTM)
> > zone:       10
> > datum:      nad83
> > ellipsoid:  grs80
> > north:      4269999
> > south:      4180119
> > west:       598614
> > east:       651978
> > nsres:      3
> > ewres:      3
> > rows:       29960
> > cols:       17788
> > cells:      532928480
> 
> I've very new to all of this, so please forgive what may be a very obvious 
> question, but can someone explain the units for these coordinates?  I'm 
> thinking that "north: 4269999" must indicate the distance North of some 
> reference location, perhaps the equator?  It this in feet, meters, miles, 
> kilometers, or something else entirely?

In most cases, coordinates are in metres. Some coordinate systems use
feet (normally US survey feet; any countries which historically used
Imperial feet have long since gone metric for cartographic purposes),
but UTM is always in metres.

Sometimes the zero value is meaningful (e.g. a specific parallel or
meridian), sometimes it isn't. Many coordinate systems add a fixed
constant (false easting/northing) to ensure that coordinates are
always positive.

For UTM, the "base" origin is the intersection of the zone's central
meridian (127W for zone 10) with the equator, but a false easting of
500,000m is added. For the southern hemisphere a false northing of
10,000,000m is added.

So, in the above case, the north-west corner (4269999, 598614) is
~4,270 km north of the equator, and ~98.6 km east of the 127W
meridian.

However, the process of mapping an ellipsoid to a plane introduces
distortion, so the coordinates don't exactly correspond to distances. 
E.g. the transverse Mercator projection exaggerates north-south
distances as you move further from the central meridian. To
compensate, a scale factor of 0.9996 is applied to northings, so that
the overall scale factor varies from 0.9996 at the central meridian to
~1.0010 at the boundaries.

-- 
Glynn Clements <glynn at gclements.plus.com>