Estimating spatio-temporal characteristics of sea level variations of the South China Sea using the Spherical Slepian functions
Authors: Ma Zhongtian , Tenzer Robert , Fok Hok-Sum 
Published: March 2024

The Gravity Recovery and Climate Experiment (GRACE) has played an important role in sea level observations over the last few decades. However, regional-scale studies of this phenomenon are still challenging due to the potential land-to-ocean leakage along coastlines. In this study, we utilized the Spherical Slepian Functions (SSF) to inverse the regional sea level signal within the South China Sea by incorporating an optimal coastal buffering zone into transform procedures of the original GRACE spherical harmonics (SH). By synthesizing the time series of oceanic and coastal areas with different trends, annual amplitudes and phases, the SSF-inversed signal with a 1&#176; buffering zone was found to be more consistent with synthesized time series than traditional SH-inversed results. Then, the spatiotemporal characteristics of seasonal and residual sea level variations were further analyzed and compared with results from traditional GRACE SH product, GRACE Mascon resolution, the Estimating the Ocean Circulation and Climate (ECCO) model, and the difference between altimetry and a steric sea level model (i.e., Altimetry-Steric data). Temporal analysis shows that the trend and the phase of regional sea level signal within the South China Sea with the 1&#176; buffering zone using the GRACE SSF was 0.28 cm/yr and 108&#176; respectively, which generally agrees with other sea level solutions. However, the SSF-inversed mass sea level amplitude of 4.63 cm was larger (smaller) than that obtained from the SH (Mascon) method by approximately 0.7 cm (0.6 cm), showing relatively better consistency with the 4.47 cm from the ECCO model and 4.23 cm from the Altimetry-Steric data. For the spatial analysis, an extremely high amplitude of sea level signal at the centre of the Gulf of Thailand due to seasonal alternating circulations was observed in all data, except for the GRACE SH solution, which significantly underestimated the signal due to a smoothing effect of filtering. Besides, the SFF-inversed GRACE exceptionally observed an apparent seasonality of sea level signal near the mouth of the Pearl River with an amplitude of ~ 8 cm. Furthermore, the sea level signal along the eastern coasts and the Sunda Shelf was out-of-phase for SSF GRACE and Altimetry-steric data, probably due to the interaction of active tropical eddies nearby. The potential inter-annual sea level variability was also analyzed by decomposing the residual time series through the Multivariate Singular Spectrum Analysis (MSSA) method. Results show that the highest cross-correlation between the decomposed modes of GRACE Mascon mass sea level and Southern Oscillation Index (SOI) reached 0.52 with a time lag of 2 months, considerably larger than 0.14 from GRACE SSF. This finding can be explained by the fact that most of the truncated Spherical Slepian functions capture short-term signals that are mainly attributed to seasonal changes. Consequently, it is difficult to distinguish between a relatively small long-term signal and noise. This may also explain the irregular spatial distribution in the GRACE SSF sea level trends. Nevertheless, this study demonstrates a feasibility of using the Spherical Slepian functions in modelling of mass sea level signal over a medium-sized sea.