Parametrische Beschreibung der Dynamischen Ozeantopographie aus Beobachtungen von Geoid, altimetrischer Meereshöhe und radialen SAR Oberflächengeschwindigkeiten
Zusammenfassung der Projektergebnisse
The mean dynamic ocean topography (MDT), which is defined as the difference between the temporal mean of the sea surface heights and the geoid can be related to the large scale steady-state ocean circulation. It can be determined from spaceborne measurements using the so called geodetic approach: The sea surface height (SSH) is measured by satellite altimetry since decades, the geoid can be determined from dedicated gravity field missions like CHAMP, GRACE and GOCE. The challenging task is a classical signal separation problem – the temporally and spatially averaged altimetric SSH have to be split into the contribution by the geoid (O (±100 m)) and the contribution of the MDT (O (±1 m)), which is two orders of magnitude smaller. This becomes possible, if complementary information is available sensitive either to the geoid or the MDT only. In the classical geodetic approach, the complementary information is the geoid derived from a global gravity field model derived from the satellite missions mentioned above. This models have a limited accuracy and an insufficient spatial resolution. This leads to the problem that the data sets are spectrally inconsistent. Explicit or implicit filtering is required to obtain the MDT from the difference between the mean sea surface and the geoid. Compared to the established approaches which use discrete grid-based representations for geoid and MDT, a parametric approach is developed in this project which allows to represent the MDT as a continuous mathematical function. As the function space is unknown, we propose to use an approximation by two dimensional finite element based basis functions on triangulations. The project implemented, applied and studied the use different finite elements for the approximation task to find well suited parameterization of the MDT. As the geostrophic ocean currents are linked to the gradient of the MDT, focus is on C 1 -smooth elements. The performed studies in the project found that the Argyris element is best suited. Having parametric representations for both, the finite elements for the MDT and – as established in geodesy – spherical harmonics for the geoid allows to solve the signal-separation problem as a leastsquares parameter estimation problem. Whereas the satellite-based information is directly available in spherical harmonics, least-squares observation equations for the along-track altimetric SSH measurements are developed, e.g. co-estimating a spatio-temporal model to compensate for ocean variability. This spatio-temporal model is designed in a generic way via a composition by separable basis function, again finite elements in spatial and a large set of functions in the temporal domain. The least-squares adjustment takes care of (implicit) temporal averaging of the SSH and the spatial resolution of the finite elements is responsible for the spatial filtering. To obtain smoothed MDT estimates, additional regularization can be directly applied. This joint estimation procedure does not only estimate the MDT but updates the geoid in the study area as well. The chosen problem formulation as a least-squares adjustment allows to include additional data sets, sensitive to the geoid, the MDT or both in a straightforward way. Especially, as the MDT is represented by a C 1 -smooth functions, observations which can be linked to the ocean currents can be included in geostrophic approximation. For instance, observation equations for in-situ surface drifter derived currents can – in geostrophic approximation – analytically derived and used. A promising space borne alternative are Synthetic Aperture Radar (SAR) derived Radial Surface Velocities (RSV) which can be derived from a residual Doppler shift. Over ocean areas, these are line-of-sight projections of the surface velocity, which after calibration and some corrections can be linked in geostrophic approximation to the line-of-sight surface current. This observables can be (theoretically) derived from any SAR satellite and became an official data set of the Sentinel-1 mission (ocean product). Therefore a good spatial and temporal coverage is realistic. Although the measurements from a single pass do not observe the full current, even this kind of ’incomplete’ measurement can be used in the parametric approach. The required observation equations are developed and implemented in the project for different SAR modes (wave mode and interferometric wide swath, IW) and are used as observations sensitive to the MDT. In the proposal, it was planned to use the Sentinel-1 real data products as distributed by Copernicus. During the project it turned out that the real data is not usable as the calibration is insufficient. Instead, the project used simulated data sets to study the potential of the RSV from the wave mode for MDT and geoid determination. In addition, there exists a one year re-calibrated real data set for the densely sampled IW mode, which was successfully used in a proof-of-concept and sensitivity study in the project. For both, the simulation studies and the real data experiments, it could be shown that RSV data contains valuable information for the signal separation. Assuming a proper calibration, it has – due to its coverage compared e.g. to surface drifters – a high potential to improve both, the geoid as well as the MDT.
Projektbezogene Publikationen (Auswahl)
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An Improved Model of the Earth’s Static Gravity Field Solely Derived from Reprocessed GOCE Data. Surveys in Geophysics, 42(2), 277-316.
Brockmann, Jan Martin; Schubert, Till & Schuh, Wolf-Dieter
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Development of a continuous spatiotemporal finite element-based representation of the mean sea surface. Journal of Geodesy, 97(2).
Borlinghaus, Moritz; Neyers, Christian & Brockmann, Jan Martin
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On the Coestimation of Long-Term Spatio-Temporal Signals to Reduce the Aliasing Effect in Parametric Geodetic Mean Dynamic Topography Estimation. International Association of Geodesy Symposia, 129-137. Springer International Publishing.
Brockmann, Jan Martin; Borlinghaus, Moritz; Neyers, Christian & Schuh, Wolf-Dieter
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Refinement of Spatio-Temporal Finite Element Spaces for Mean Sea Surface and Sea Level Anomaly Estimation. International Association of Geodesy Symposia, 119-128. Springer International Publishing.
Borlinghaus, Moritz; Neyers, Christian & Brockmann, Jan Martin
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Radial surface currents from space: An opportunity for mean dynamic topography estimation?. Advances in Space Research, 74(4), 1563-1575.
Neyers, Christian & Brockmann, Jan Martin
