On the capabilities of the multi-channel singular spectrum method for extracting the main periodic and non-periodic variability from weekly GRACE data

We study the capabilities of the method of multi-channel singular spectrum analysis (MSSA) to extract periodic signals from the Gravity Recovery and Climate Experiment (GRACE) gravity field solutions. As a non-parametric method and because of the data-adaptive nature of the base functions, the MSSA allows for modelling of non-periodic variations. In addition, it can identify modulated oscillations in the presence of noise. In our study, we analyze a complete 6-year weekly time series of the GFZ-produced GRACE spherical harmonic coefficients of degree and order 30. The MSSA filtering reduces the average root-mean-square (RMS) of the 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. While the high variance annual signal can be extracted from the GRACE data straightforwardly, the semi-annual and long-term modes identified in the low variance portion of the data eigen-spectrum are mixed. Moreover, the semi-annual variability is contaminated by the S2 tidal alias signal shown in an example for the Hudson Bay region to possibly alter the typical two-peak seasonal cycle of the water mass anomalies. Also, some long-term modes indicate that a variation exists with a 2.1–2.5 years period, possibly of a hydrology origin, which was found by previous studies in the GFZ GRACE data.On land, we analyze time series of basin averages in Amazon, Congo, Mississippi and Nelson rivers basins computed from the filtered GRACE and Global Land Data Assimilation System (GLDAS)/Noah model coefficients. The analysis is performed in two steps: (1) an approximation of the series of basin average is computed from the identified annual, semi-annual and long-term variations in the spherical harmonic coefficients and (2) to improve the approximation, the residual variability in the basin average series is analyzed by means of singular spectrum analysis. Time lags between the hydrology model and observations are found for the Amazon (4 weeks) and Mississippi and Nelson (2 weeks) basins, where GLDAS is generally ahead of GRACE. Significant differences in the water content for particular years, for example, during the 2007–2008 time period in Congo, are observed, as well.The use of the MSSA method in the analysis of the GRACE mass variations is not pertinent to the low resolution weekly solutions. The same approach can be applied to the monthly GRACE solutions of a much higher degree and order in the search for local signals. Here, we traded off the spatial resolution for the time resolution and we determined the time lag of the model water mass anomalies and observations with a nominal weekly resolution.