Document: GOCE_s1.doc Date: 2001.05.08, Author: C.C.Tscherning.

1.2.1. Slice 1. GOCE Product and standards definition.

The following input to slice 1 is relates to EGG-C Tasks 3, 5, 6 and 7 and concerns throughout requirements relevant for the use of the space-wise method.

GRAVSOFT Standard.

The basis for some of the specifications proposed below are the so-called GRAVSOFT standards, (Tscherning et al., 1994). In brief they are:

All data are in ASCII code with blanks as delimiters.

Spherical harmonic coefficients:

Degree n, order m, C_{nm}, S_{nm}, s
( C_{nm}, S_{nm } ). Coefficients are unitless. All coefficients are included (also (0,0)).

Geo-located data:

Geographical coordinates:

<Unique id, integer> <latitude, decimal degrees (number of significant digits to be specified)>, <longitude, decimal degrees from 0 to 360 degrees, positive East > < altitude in m, significant digits to be specified , ellipsoidal height or orthometric height must be specified> <data 1> <data 2> ….. <data n >

UTM coordinates: like geographical coordinates, but Northing instead of latitude and Easting instead of longitude.

Cartesian Coordinates:

Like geographical coordinates, but <unique id. >, <X>, <Y>, <Z>, and then data.

Equal-angular grids of data: Data start with a label which describes the extend and spacing of the data grid. Then the data are organized in "bands" of equal latitude (or UTM Northing) from North to South. The coordinates refer to the center of the cell.

Grid label: Geographical coordinates: minimum, maximum latitude, minimum, maximum longitude, spacing in latitude, spacing in longitude. UTM: Northing instead of latitude, Easting instead of longitude, last value is the UTM zone.

Example: Grid with 4 elements.

55.0 56.0 10.0 12.0 2.0 2.0

4.1 5.0

- 5.6

Data-specifications which agree with GRAVSOFT:

Auxiliary data needed are:

A-priori set of spherical harmonic coefficients and associated error-estimates.

Global digital mean terrain/depth data in a 5’ x 5’ grid, globally. Units m.

For all the following data, the horizontal coordinates must be given as geographical coordinates in WGS84/ITRF ??. All associated heights are heights above mean-sea level. (Datum to be specified if not mean value).

5’ mean Free-air gravity anomalies with <data 1> = <gravity anomaly, mgal with 1 decimal>, <data 2> = < standard error>.

Height anomalies from GPS and levelling <data 1> = < height anomaly in units of m with 3 decimals> <data 2> = < error estimates > <data 3> = < datum name (ISO)>

Deflections of the vertical: Meridian and Prime-vertical components.

<data 1> = <Meridian component, arcseconds with 2 decimals >, <data 2> = < Prime-vertical component >, <data 3 > , <data 4> = <error-estimates of the components > <datum id.>

Deflection of the vertical, one component only. As above with only two data-items.

Satellite data:

Geo-located observational data on GRAVSOFT format.

SGG data: Geographical coordinates. Altitude is ellipsoidal height in mm. <data 1> … <data n>, <standard deviations of data 1 … data n> <3 attitude angles: tilt, roll, pitch in decimal degrees with 4 decimals>

SST data: Cartesian coordinates

Corrections to geo-located data on same format.

Products:

Spherical harmonic coefficients and their variance-covariance matrix.

Grids of free-air anomalies, deflections of the vertical and height anomalies referring to the mean terrain height.

Corresponding grids of error-estimates. The grid-labels will tell whether the grids are global or local.

Geo-located and corrected satellite data on the same format as above.

Non-GRAVSOFT data-types.

The gravity field statistics.

The physical correlation of gravity field quantities may be expressed through a global or regional covariance functions. Such functions may be specified using the following parameters:

<error-degree-variance modifiers> < depth to Bjerhammar-sphere (m) > < gravity anomaly variance (mgal^{2}) >. The degree-variance modifiers are the following

< weight factor on error degree-variances > < number of error-degree-variances used > < indicator of whether the scale factor is to be applied on all degree-variances or so that it changes linearly from degree zero to the maximal degree >

A file should be established with the current values (they depend on the a-priori spherical harmonic model used). It should in one record hold the boundaries of the areas of validity and the parameters.

Variance-covariance matrices of a-priori given or estimated quantities.

These matrices must be on binary form, REAL*8. Since the matrices are symmetric, the matrix elements should be stored from column 1 to "N" , from element no. 1 to the diagonal element.

Example: The symmetric 2 x 2 matrix

1 3 becomes 1, 3, 4.

3 4

Reference:

Tscherning, C.C., P.Knudsen and R.Forsberg: Description of the GRAVSOFT package. Geophysical Institute, University of Copenhagen, Technical Report, 1991, 2. Ed. 1992, 3. Ed. 1993, 4. ed, 1994.