[Gdal-dev] Understanding GEOS projected space
retsios at itc.nl
Mon Nov 19 09:33:58 EST 2007
Enrico Zini wrote:
>On Mon, Nov 19, 2007 at 12:21:40PM +0100, Bas Retsios wrote:
>>Note that due to the large area covered by this projection (an entire
>>earth's hemisphere), the "meters" are only correct near the nadir-point.
>>As an example, a box with bounds (xMin=-3500000, xMax=3500000,
>>yMin=-3500000, yMax=3500000) would roughly include the Arfican continent
>>and a great part of the atlantic ocean.
>So we're talking about a virtual kind of metre that is 1 metre long at
>the nadir point but gets smaller as we move further from it.
>The implementation I had (which followed directly from Eumetsat
>documentation) used to work with the scaling function defined at section
>"4.4.4 Scaling Function",
>Switching to proj I need to use ColumnDirGridStep and
>LineDirGridStep, which I didn't see mentioned in Eumetsat's
>documentation about georeferencing. I hope that it's just the same
>quantity scaled differently, and that the precision of georeferentiation
>that I get in the end is the same.
>Now, I need to handle some NetCDF based formats that store this
>georeferentiation information in terms of CFAC and LFAC, and moving to
>GDAL I'd need to rebuild ColumnDirGridStep and LineDirGridStep out of
>Is there a formula (it should be nothing more than a simple scaling
>constant, if I get it right) that allows me to convert back and forth
>from ColumnDirGridStep to CFAC (likewise for line)?
>4.4.4 Scaling Function
> The scaling function provides a linear relation between the
> intermediate coordinates (x,y) and the image coordinates (c,l).
> The definition is as follows:
> c = COFF + nint(x * 2^-16 * CFAC)
> l = LOFF + nint(y * 2^-16 * LFAC)
> Herein, "nint" denotes a nearest integer rounding of the real
> argument. COFF, CFAC, LOFF, LFAC are the (integer) scaling
> coefficients provided with the image navigation record. Each of the
> coefficients may have an integer value between -231 and +231-1.
> LineDirGridStep gives the grid step size in km SSP in the line
> direction. Default value is 3km for VIS and IR, and 1km for HRV. The
> on-ground grid step size of 3 km at the SSP represents an instrument
> scan step of 251.53 microrad divided by 3.
> ColumnDirGridStep gives the grid step size in km SSP in the column
> direction. Default value as for `LineDirGridStep'.
The x and y as mentioned in formula  (4.4.4), the so-called
"intermediate coordinates" are the scan-angle of the satellite. There is
a linear relationship between the c and l (column and line of a pixel in
an MSG-image), and the angle at which this was "seen" from the satellite.
Since c and l also have a linear relationship with X and Y (meters, in
GEOS projection), you must be right when you say that there is also a
linear relationship (scaling + offset) between (x,y) and (X,Y).
Calculate the relationship, given the following:
The ColumnDirGridStep and LineDirGridStep values found in the header
files of the MSG images are 3004.03165817 m for bands 1-11, and
1000.134348869 m for HRV band 12. Thus not exactly 3km / 1km, but
slightly more. These values have never changed, since our institute
installed a receiver for MSG images in 2004.
For bands 1-11, COFF=1856 and CFAC=-13642337, and for band 12, COFF =
5566 and CFAC=-40927014. These values have also remained the same for
all images up to now.
c = COFF + x * CFAC / 65536
c = X / ColumnDirGridStep
Ir. V. (Bas) Retsios
Geo-information Processing Department
International Institute for Geo-information Science and Earth Observation (ITC)
P.O. Box 6, 7500 AA Enschede, The Netherlands
Phone +31 (0)53 4874 573, telefax +31 (0)53 4874 335
E-mail retsios at itc.nl, Internet http://www.itc.nl
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