**University of Copenhagen**

**Department of Geophysics.**

C.C.Tscherning.

File: C:\CCTWP\e2m993m.wpd 23 September 1999

**WP 3 progress report "Scientific Data processing algorithms".**

Prepared for the E2M Mid-term Review, Sept. 1999.

**3.1. Software elements.**

The following programs must be available:

(1) program implementing Least-Squares Collocation, and using GOCE-data as well as being
able to estimate systematic errors (biases, tilts). It must be able to "predict" block mean
values of GOCE-observables, spherical harmonic coefficients and error estimates. The
program should be able to handle at least 90000 observations.

Note: such a program (GEOCOL) is available, fulfilling many of the above requirements.

(2) program implementing the integration approach from block averages.

(3) program for gross-error detection.

Note: GEOCOL and GEOGRIDX has this capability. But further development necessary.

**3.2. Software distribution and standards document.**

The Web-based distribution system used in MANICORAL is well suited for GOCE data
reduction. Basically each pise of software must be documented, have test in- and output
available. All source-texts must be available, and test of the software on various platforms
must have been made. Timing estimates should be given.

All programs should be written in C or FORTRAN.

**3.3. Numerical problem areas.**

Obviously the largest problem will be the solution of the system of equations having up to
90000 unknowns. However current studies by G.Moreaux have confirmed that this is
possible. Whether numerical problems (related to the condition number) will occur is
uncertain.

The second severe problem is to make sure that the signal to noise ratio is correct. If a
homogeneous-isotropic statistical model is used, this is not possible for the global approach.
Regional solutions may have a statistical model adapted to the region.

**3.4. Implementation of recent developments.**

The use of preconditioning has been implemented in a separate program, which will have to
be merged with other programs like GEOCOL. It is not necessary the the preconditioning
procedures becomes integrated in the GEOCOL program. An "off-line" solution of the
normal-equations is a possibility being considered.

The prediction of coefficients have been implemented and used in WP 2 for initial studies
using limited datasets. At the moment calculations are done in spherical approximation.

**3.5. Software testing.**

Tests using realistic size data sets are in progress for the preconditioning method.

Controlled tests of coefficient prediction and error-estimation have been made for
coefficients of low degree and order and for a limited number of observations.

Last update 1999-09-23 by cct.