Refinement of Spatio-Temporal Finite Element Spaces for Mean Sea Surface and Sea Level Anomaly Estimation

Abstract

AbstractThe mean sea surface (MSS) is an important reference surface for oceanographic or geodetic applications such as sea level studies or the geodetic determination of the steady-state ocean circulation. Models of the MSS are derived from averaged along-track radar altimetry which provides instantaneous measurements of the sea surface heights (SSH). SSH observations corrected for tides and other physical signals and can be modeled as the sum of the MSS and sea level anomalies (SLA) which describe the temporal variability of the ocean. The typical MSS products are defined as grids of heights at a specific reference epoch and result from spatial and temporal prediction and filtering of the along-track SSH observations, whereas SLA products are computed with respect to an MSS model and are also defined as e.g. daily or averaged monthly grids.In this contribution a one-step least-squares approach is used to estimate a continuous spatio-temporal model of the MSS and filtered SLAs from along-track altimetric SSH measurements using C1-smooth finite element spaces for the spatial representation. The finite elements are defined on triangulations with different edge lengths and, thus, different spatial resolutions for MSS and SLA modeling. To model the temporal ocean variability finite B-Splines base functions are combined with the spatial finite elements to construct a spatio-temporal model. This contribution presents a concept to adapt the triangulations to the spatial characteristics of the signal of the MSS and SLA in a study region south of Africa. Least-squares residuals are studied to detect areas which show unmodeled spatial signal. These serve as input for the refinement of the triangulation. The results show that the residuals are indeed a good indicator for unmodeled signal, but as they are significantly influenced by unmodeled temporal signals as well, the refinement has only a small local impact on the obtained MSS and SLA models.