Preliminary Plan for Collaboration on gravity field modelling.
2002-09-14.
The main purpose is to repeat earlier local and global investigations
using a realistic orbit (IAG SC7) for GOCE.
Data should be generated using EGM96 to degree 300. From this
data we subtract EGM96 to degree 24.
First we use Tzz only. Subsequently we use one component more,
probably Txx-Tyy. (Requires changes in GEOCOL).
The SC7 data have positions given in the inertial frame. They
must be converted to geodetic coordinates in an earth-fixed frame
(program /cct/goce/reformat.f ). There are totally 518401 records
in the file /cct/goce/Tensor .
1) a first the test should use noise-free nata in a ENU-frame.
a) then data with correlated noise should be used. The noise is given
through the covariance function as a fourier series with the
time difference as a parameter. The coeffficients are called c(i).
Noise is generated by randomly perturbing the coefficients of
the fourier series. As variances are used c(i)/2 to generate the
coefficients a(i) and b(i) in the series expressing the noise.
so noise(t)= sum i,n (a(i)*sin(i*t/n)+b(i)*cos(i*t/n) (period
must be fixed).
2) subsequent tests should use data in a frame given by the
velocity vector, v. x-along track, x-z plan spanned by v and r.
For both cases a global 0.5 deg. grid of Tzz is generated using
GEOCOL in the 22.5 deg * 22.5 deg. blocks for which we already have the
covariance function parameters. Spherical approximation is used.
But we must check that there are no problems in the overlap area.
Otherwise we must use a global covariance function.
We then use the program sphgrid to generate spherical harmonic
coefficients to degree 300. (The coeffieients up to and inclusive
deg. 24 will be corrections).
In a later test GEOCOL should be used globally. I will apply for access
to a super-computer.
Questions to be answered:
Are we able to recover the EGM96 coefficients and what are the error-
estimates.
Will we be able to determine/eliminate/reduce the noise ?
What is the effect of the noise on the data ?
Do we get different results from sphgrid and GEOCOL ?
Does the an-isotropy (that we use different covariance functions in
different blocks) cause problems ?
Finally another problem:
Do we calculate the potential of the sun and the moon correctly, see
/cct/dgravsoft/stat2pot.f.
In practical terms:
Convert SC7 format to gravsoft format. Make file time, lat., long, ellipsoidal
height.
Use geocol to compute Tzz in the points.
Set up jobs using GEOCOL for each block which predicts
Tzz in a grid at mean satellite altitude.
Reformat all the grids to one big one, with North-west corner
about 83 deg. lat. and 0 deg. long.
Run sphgrid with a global covariance function. (EGM96 error-degree-variances
from deg. 2 - 24, EGM96/GPM98 degree variances from deg. 25 - 720).
Repeat process with Tzz in v-frame.
Repeat process with Tzz and Txx-Tyy (or other component).
Generate correlated noise. (We have to change program).
Add noise and repeat whole procedure.