Development of a continuous spatiotemporal finite element-based representation of the mean sea surface

The mean sea surface (MSS) has an important role, both, in the calculation of the mean dynamic topography and in the area of sea-level change as a reference surface. This paper presents a new approach to estimate a continuous spatiotemporal MSS from along-track altimetric sea surface height measurements. A parametric function continuously defined in the spatial as well as temporal domain is constructed from a C^1 -smooth finite element space to represent the MSS. Least-squares observation equations are set up, to estimate the unknown scaling coefficients from the sea surface height measurements as collected by altimetric exact repeat missions and geodetic missions. An advantage of the proposed method is that the surface is represented by an analytic model and the unknown parameters can be physically interpreted. Whereas the static component of the function represents the MSS, the temporal component is used to absorb the ocean variability. Within this initial study, 10 years of satellite altimetry over the period 2010–2019 are analyzed in a small study region around the Agulhas Current. To obtain the best possible data coverage, all missions available via AVISO, which provide data in the study region and period, are included, i.e., geodetic missions and mission phases as well as exact repeat missions. Besides the static MSS, the temporal component, which is co-estimated to absorb the dominating ocean variability, is modeled with different basis functions to study their performance. On the one hand, global basis functions considering a linear trend and periodic functions are compared with B-Spline basis functions. The comparison of the static component to the global CNES_CLS15 MSS shows a reasonable agreement with a root-mean-square error in the range of 1–4 cm for the well-suited model configurations. To validate the modeling approach and the different analyzed configurations, the temporal model component is compared to gridded sea-level anomaly products. Although it is not (yet) a target quantity, the analysis can serve as a quality check of the MSS and the proposed modeling approach as well. It is shown that in regions with relatively low ocean variability the combination of a linear trend with an annual period is well suited to model the dominant temporal signal, whereas it is not sufficient in regions with strong ocean variability, e.g., close to the Agulhas Current. In those regions, the scenario which utilizes B-Splines in the temporal domain performs significantly better. In general, it is demonstrated that the proposed approach can be an alternative to the well-established MSS estimation procedures.