[GRASS5] PROJ_INFO and prime meridian

[Markus Neteler]

A projection related question:

Currently I try to geocode a (precisely) scanned map from 1945, 
Northern Italy. The map was made by the US Army in Lambert Conic
Orthomorphic. The map is based on a map from 1931 done by Istituto
Geografico Militare and was enhanced by aerial photo survey (I assume
also reprojected to Lambert Conic Orthomorphic).

Given on the map is:
- prime meridian Monte Mario (old!): 12d27'7.1E (today 12d27'8.4E)
- "spheroid":     Bessel
- Origin:         14E, 45:54N
- False Easing:   800000 meters
- False Northing: 601000 meters
- The map provides the LCC grid and coordinates as well as
  Lat/Long corners in reference to Monte Mario Old and equator.

Using the latest CVS version, I created a location with LCC:
PROJ_INFO
name: Lambert Conformal Conic
towgs84: -104.1,-49.1,-9.9,0.971,-2.917,0.714,-11.68
proj: lcc
ellps: bessel
a: 6377397.1550000003
es: 0.0066743722
f: 299.1528128000
lat_0: 45.9000000000   <- given 45:54N
lat_1: 33.0000000000   <- calculated by GRASS, given 'return'
lat_2: 45.0000000000   <- calculated by GRASS, given 'return'
lon_0: 14.0000000000   <- given 14E
x_0: 800000.0000000000
y_0: 601000.0000000000

Procedure:
- import of scanned map into XY location
- definition of above LCC location
- i.points of 4 points on the LCC grid, typing into the related
  coordinates by keyboard as read from the map
- i.rectify, 1st order into LCC
- r.proj of recent data from Gauss-Boaga (a tmerc derivate) into
  this LCC location

       i.*            r.proj
    XY ======> LCC <======== Gauss-Boaga
   scan       final          recent GIS data

Validation tests:
- the Lat/Long corner coordinates as printed on the map
  match perfectly with d.where -l results
- but the rectified map is shifted compared to new data (see next)

Problems:
- how to define a different prime meridian (monte Mario old/new)?
- the towgs84 may be wrong (no idea what to use, I selected rome40)
- the resulting map is shifted according to recent data (orthophoto 1m):
    - around 400m to North
    - around 800m to East
- there is also a very small rotation

Ideas (comments welcome):
- Lambert Conic Orthomorphic != LCC (I hope not)
- the optional definition of the true prime meridian may solve the
  rotation problem (the map center is around 11 degree East from Monte
  Mario)
- the bessel definition of 1945 may be different from the current bessel
  in GRASS
- the US Army used a different datum for LCC (where to find out?)
- the Gauss-boaga location with recent GIS data is wrong (I hope not)

Sorry for the long mail,

 Markus