Plan for testing prediction of coefficients from
point or mean values using LSC.

Prepared by D.Arabelos and C.C.Tscherning 1999-06-05 in Thessaloniki.

The following programs are available for testing:

/disk1/cct/dgravsoft/geocol15.f
/disk1/cct/dgravsoft/spharmt.f
/disk1/cct/cctf/dcovfit/covfit12.f

Test jobs are:

jobnml15a  (and similar names)
covfit12.inp 

(1) Illustration of correlations:

Calculate correlations between some coefficients like,
(i,j) = (5,0), (5,2), (5,-2), (15,0), (15,8), (15,-9)
and geoid at h=0, gravity anomaly at h=0, Tzz at h= 250 km,
in a grid of points covering the earth. Maybe the southern or northern
hemisphere is sufficient. It depends on symmetries.

Probably the grid has to have a resolution equal to  60/max(i,j).

The program covfit12 can be used to calculate the covariances between
the quantities. To obtain correlations, divide with the square-root of
the variances. However it calculates at present
in profiles and not in grids.

A grid-option will be implemented in covfit12.f (action cct).

(2) Test of recovery of spherical harmonic coefficients:

(Using geocol15).

(a) a low degree-and order model (like OSU91 or EGM96 to degree 60)
is used to generate
-  a global 
-  a global, but with polar gaps for Tzz.
-  a regional set (equal-area or equal angular grid) of geoid heights
   at h=0, gravity anomalies at h= 0, Tzz at height = 250 km.

The degree-variances used should then be the degree-variances 
(up to the maximal  degree) calculated from the coefficients.
(NOT the error-degree-variances !).

The generating degree/order should e.g. be 36. The recovery of coef-
ficients from degree 15 to 20 should then be tried from
- the global sets,
- subsets covering areas of continental size.(To simulate taylored models).
Error estimates should also be calculated for the different cases.

The data must probably be assigned an error. This is both to make the
recovery realistic, but also to test the results from GOCE. The Tzz
should then have an error 1 mE/sqrt(Hz). For geoid and gravity anomalies
the errors should depend on the block size, and contingently the
location (high error in the Himalayas, for example).

One or more tries should be made with a very low data noise. However
there is here the problem that the system of equations may be numerically
singular. (A warning will come from the subroutine NES in GEOCOL).

(b) actual data, such as the New Mexico gravity anomalies are used
to test the recovery. Here probably one has to go up to a very high degree,
like 180, if the full 3 deg. x 3 degr. dataset is used. (Probably a
subset should be used or mean values).

The degree-variance model should be generated from the OSU91 error-degree
variances.
 
Error estimates should also be computed. Statistics of the actual error
compared to the error estimates should be made. 

The coefficients which are having estimates below the noise level
should be corrected, and a test should be made that the updated
coefficients agree better with the data used.