Towards the Development of a Continuous Spatio-Temporal Finite Element Based Representation of the Mean Sea Surface

Abstract

The mean sea surface 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 spatio-temporal mean sea surface 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 C¹-smooth finite element space to represent the mean sea surface. 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 mean sea surface, the temporal component is used to absorb the ocean variability.<br> Within a proof-of-concept study 10 years of satellite altimetry from CryoSat–2 and Jason 1–3 over the period 2010 to 2019 are used and analyzed in two study regions with different spatial resolutions. Besides the static mean sea surface, the temporal component which is estimated covers a linear trend and the annual period. The comparison of the static component to the global CNES_CLS15 MSS shows a reasonable agreement with a root mean square error below 10 cm over the entire North Atlantic. But still, systematic differences occur especially in regions with a high temporal variability. Comparisons of the temporal component with gridded sea level anomaly products show a good agreement in areas of low ocean variability, but highlights that in regions of large ocean variability the temporal basis function chosen in this initial study must be further investigated. In general, it is demonstrated that the proposed approach can be an alternative to the well established mean sea surface estimation procedures.