A study on the capabilities of the multi-channel singular spectrum method for extracting the main water mass anomaly information from GRACE and hydrology models

We study the capabilities of the method of (multi-channel) singular spectrum analysis (MSSA), which is mathematically equivalent to the extended empirical orthogonal functions (EOFs), to extract persistent oscillations (such as annual and semi-annual cycles) from noisy GRACE gravity field solutions. As a non-parametric method, MSSA also allows for modelling inter-annual, intra-annual and trend variations because of the data-adaptive nature of the base functions. In addition, it can identify modulated oscillations in the presence of noise. In our study, we analyze simultaneously a complete 6-year weekly time series of GFZ GRACE spherical harmonic coefficients of degree and order 30. The use of the standard de-correlation filtering is avoided and thus no geophysical signal is removed together with the correlated GRACE errors, which ensures a more fair comparison with geophysical models. Our filtering method reduces the average rms of mass variability over the oceans by more than 60 % when all but the annual, semi-annual and long-term variations in the spherical harmonic coefficients are filtered out. Although MSSA removes the bulk of the correlated errors, additional isotropic smoothing is still required. On land, we analyze time series of basin averages in few of the main river basins, i.e., Amazon, Congo and Mississippi, which are computed from the filtered GRACE and GLDAS coefficients. Generally fair agreement between GRACE and GLDAS data exist but some differences such as phase lags (Amazon) and differences in the water content for particular years (Congo) are found.