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.