11:30 AM - 11:45 AM
[G03-3-05] GRACE de-striping by biharmonic thin-plate splines on the sphere
If gravity field solutions are deduced from satellite observations, the gravity field information is only available along the ground tracks of the satellite.
Implicitly, a global spherical harmonics solution leads to polynomial interpolation between these tracks. The oscillation tendency of polynomial interpolation contributes to the undesired striping effect in monthly GRACE solutions.
In the paper an alternative interpolation strategy is tested, which fulfills two requirements
i) It reproduces the observations along the tracks and
ii) it is as smooth as possible between the tracks.
If smoothness is understood as minimal bending energy of an elastic membrane, the strategy results in an spherical thin-plate spline interpolation.
The interpolation problem is solved in two independent ways:
1) As the direct solution of the variational problem and
2) as the solution of the corresponding Euler equation.
In our case the Euler equation is the biharmonic equation on the sphere. For this equation a consistent finite differences approximation is developed and numerically implemented.
Compared to Gaussian smoothed spherical harmonics solution the thin-plate spline solutions shows a better consistency with the observations along the tracks.
Implicitly, a global spherical harmonics solution leads to polynomial interpolation between these tracks. The oscillation tendency of polynomial interpolation contributes to the undesired striping effect in monthly GRACE solutions.
In the paper an alternative interpolation strategy is tested, which fulfills two requirements
i) It reproduces the observations along the tracks and
ii) it is as smooth as possible between the tracks.
If smoothness is understood as minimal bending energy of an elastic membrane, the strategy results in an spherical thin-plate spline interpolation.
The interpolation problem is solved in two independent ways:
1) As the direct solution of the variational problem and
2) as the solution of the corresponding Euler equation.
In our case the Euler equation is the biharmonic equation on the sphere. For this equation a consistent finite differences approximation is developed and numerically implemented.
Compared to Gaussian smoothed spherical harmonics solution the thin-plate spline solutions shows a better consistency with the observations along the tracks.