id	summary	reporter	owner	description	type	status	priority	milestone	component	version	resolution	keywords	cc
462	ECI <--> ECF coordinate transformation needs to account for Earth's precession	Ian Culverwell	Ian Culverwell	"Stig Syndergaard (DMI) has highlighted a problem with EUMETSAT's planned upgrade to the PPF, as follows.
{{{
Hi Dave, Ian,

I think Ian maybe got some info from Chris Marquardt on Friday 
about these things because Chris Burrows was not in office on 
Friday. I'll send some additional info after this email.

Related to ROPP, the bottom line is this:

There are different versions of ECI systems. EUMETSAT uses J2000, 
CDAAC uses something called ITOE, which is a true-of-date system. 
The rotation from J2000 -> ECF is different (and more complex) than 
the rotation from ITOE -> ECF (which is basically just a rotation 
about the z-axis). This page explains nicely about different 
systems and what true-of-date means:
}}} 
http://physics.stackexchange.com/questions/130580/how-to-determine-satellite-position-in-j2000-from-latitude-longitude-and-distan
{{{
ROPP's eci2ecf.f90 and ecf2eci.f90 only does the rotation about the 
z-axis. To process EUMETSAT data from level1a with the 
ropp_pp_occ_tool we need code to do the full J2000 -> ECF 
transformation. The Earth's z-axis in J2000 is tilted about 0.1 deg 
relative to the J2000 frame, and that difference matters. If we 
don't account for it in the ellipsoidal correction, I believe we 
will see regional biases of about 0.5% - what postponed the PPF 
day-2 upgrade.

So I'm thinking that what could be coded are extensions to the 
existing subroutines with an additional argument specifying for 
which ECI reference frame the rotation should be done. These 
subroutines can thus be used for both CDAAC and EUMETSAT data (and 
perhaps with additional implementation of other coordinate systems 
later on - we don't know what GFZ is using, WegC or China). It 
should be sufficient to code what is called the RNP matrix (see 
link above), i.e., not taking into account the so-called ""Earth 
Orientation Parameters"" which are minor corrections, and depends on 
regular Bulletins (see link above) that would be hard to maintain 
for ROPP - well it could be done, I suppose, if the users provides 
these themselves.

More emails to follow.

-Stig
}}}

He further says
{{{
Hi all,

I learned a bit more about coordinate systems and 
precession/nutation over the weekend. It turns out that the Earth's 
precession has the right size to be able to explain the issue. I 
did not know the difference between nutation and precession until a 
few days ago, nor did I know their sizes.

But as I understand it now, the precession has the largest 
contribution and results in that the Earth's spin axis trace out a 
cone in ECI of about 23.5 deg (the well-known tilt relative to the 
normal of the ecliptic plane) over 26000 years. After only 16 years 
since January 1, 2000, we are not far along the trace of the cone, 
but long enough so that it has resulted in a small tilt of the 
Earth's spin axis relative to the J2000 ECI z-axis of about 0.1 deg.

I found the attached chapter from a book on these things. I assume 
it is describing the J2000 ECI, but it is not totally clear. 
Anyways, plugging in 16.3 years (mid April 2016) I got the tilt to 
be 0.0907 deg (theta in eq. 2.16). I tried to confirm this by 
backing out the tilt from the NetCDf4 files from April 17 
using vectors that are given in both coordinate systems. That gave 
me about 0.0903 deg, but with a little daily variation of about 
0.0001 deg that I don't understand. Oh, well!
Maybe it is not exactly J2000 that is described in the attached 
doc, but close enough.

I made the attached drawing trying to explain the issue 
geometrically. This is also based on what Riccardo told me in 
Barcelona when we made a similar drawing on the table at the 
University restaurant.

Hope it helps understanding all this.

Cheers,
-Stig
}}}

The picture and book chapter to which Stig refers are attached.

Clearly this is important; equally clearly, we don't have the resources to do anything about it in the middle of an upgrade of ROPP. So this ticket records the problem but is not assigned to anyone."	enhancement	closed	normal	9.1	ropp_utils	8.0	fixed