Improvement of Least-Squares Collocation Error Estimates Using Local GOCE Tzz Signal Standard Deviations

The method of Least-Squares Collocation (LSC) may be used for the modeling of the anomalous gravity potential (T) and for the computation (prediction) of quantities related to T by a linear functional. Errors may also be estimated. However, when using an isotropic covariance function or equivalent reproducing kernel, the error estimates will be nearly constant if the used data have a good (regular) distribution. In this case the error estimate will vary only if the data distribution changes (e.g. for satellite data as a function of latitude), if data are missing in an area, or if predictions are made outside the data area. On the other hand, a comparison of predicted quantities with observed values show that the error also varies depending on the local data standard deviation. This quantity may be (and has been) estimated using the GOCE second order vertical derivative, T-zz, in the area covered by the satellite. The ratio between the nearly constant standard deviations of a predicted quantity (e.g. in a 25 degrees x 25 degrees area) and the standard deviations of T-zz in smaller cells (e.g., 1 degrees x 1 degrees) have been used as a scale factor in order to obtain more realistic error estimates. This procedure has been applied on gravity anomalies (at 10 km altitude) predicted from GOCE T-zz. This has given an improved agreement between errors based on the differences between values derived from EGM2008 (to degree 512) and predicted gravity anomalies.