TY - GEN
T1 - Improvement of least-squares collocation error estimates using local GOCE Tzz signal standard deviations
AU - Tscherning, Carl Christian
PY - 2015
Y1 - 2015
N2 - 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, Tzz, in the area covered by the satellite. The ratio between the nearly constant standard deviations of a predicted quantity (e.g. in a 25° × 25° area) and the standard deviations of Tzz in smaller cells (e.g., 1° × 1°) 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 Tzz. This has given an improved agreement between errors based on the differences between values derived from EGM2008 (to degree 512) and predicted gravity anomalies.
AB - 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, Tzz, in the area covered by the satellite. The ratio between the nearly constant standard deviations of a predicted quantity (e.g. in a 25° × 25° area) and the standard deviations of Tzz in smaller cells (e.g., 1° × 1°) 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 Tzz. This has given an improved agreement between errors based on the differences between values derived from EGM2008 (to degree 512) and predicted gravity anomalies.
KW - Collocation
KW - Error estimates
KW - Gravity anomalies
KW - Gravity gradients
U2 - 10.1007/1345_2015_70
DO - 10.1007/1345_2015_70
M3 - Article in proceedings
AN - SCOPUS:84971439999
SN - 9783319245485
T3 - International Association of Geodesy Symposia
SP - 27
EP - 32
BT - 8th Hotine-Marussi Symposium on Mathematical Geodesy - Proceedings of the Symposium
PB - Springer
T2 - 8th Hotine-Marussi Symposium on Mathematical Geodesy, 2013
Y2 - 17 June 2013 through 21 June 2013
ER -