Multivariate variational mode decomposition to extract the stripe noise in GRACE harmonic coefficients

In this work, a novel method has been developed to remove the north-south stripe noise in the Level-2 spherical harmonic coefficient products collected by the Gravity Recovery and Climate Experiment (GRACE) mission. The proposed method extracts the stripe noise from the equivalent water height (EWH) map via the Multivariate Variational Mode Decomposition algorithm. The idea behind our method is to extract the cofrequency mode in multiple-channel series in the longitude direction. The parameters of our method are empirically determined. The investigation in a closed-loop simulation proves the improvement of our methods compared with the Singular Spectrum Analysis Spatial (SSAS) filter. Subsequently, the spatial-domain and spectral-domain investigations are conducted by using real GRACE data. Our method only suppresses stripe noise at low latitudes (30 degrees S-30 degrees N) and imposes an order-dependent impact on spherical harmonic coefficients but with potential oversmoothing. Meanwhile, the well-documented water level proves that our method further reduces outliers in a time-series of localized mass variations compared with the SSAS filter. More importantly, users are allowed to reduce the filtering strength of our method to preserve small-scale strong signals while suppressing stripe noise. Moreover, noise levels over the ocean at low latitudes are evaluated as well. The noise level of our method using empirical parameters is 32.48 mm of EWH, with 31.54 and 53.52 mm for DDK6 and SSAS, respectively. Our work introduces a novel method to address the issue of north-south stripe noise in the spatial domain.