Considering the advantage of Empirical Mode Decomposition (EMD) for extracting the geophysical signals and filtering out the noise, this paper will first apply the EMD approach to post-process the Gravity Recovery and Climate Experiment (GRACE) monthly gravity field models. A 14-year time-series of Release 06 (RL06) monthly gravity field models from the Center for Space Research (CSR) truncated to degree and order 60 from the period April 2002 to August 2016 are analyzed using the EMD approach compared with traditional Gaussian smoothing filtering. Almost all fitting errors of GRACE spherical harmonic coefficients by the EMD approach are smaller than those by Gaussian smoothing, indicating that EMD can retain more information of the original spherical harmonic coefficients. The ratios of latitude-weighted RMS over the land and ocean signals are adopted to evaluate the efficiency of eliminating noise. The results show that almost all ratios of RMS for the EMD approach are higher than those of Gaussian smoothing, with the mean ratio of RMS of 3.61 for EMD and 3.41 for Gaussian smoothing, respectively. Therefore, we can conclude that the EMD method can filter noise more effectively than Gaussian smoothing, especially for the high-degree coefficients, and retain more geophysical signals with less leakage effects.
The strong striping and high-frequency noise existed in Gravity Recovery and Climate Experiment (GRACE) solutions drowned the real geophysical signals, which need other signal extraction methods. Considering the advantages of local mean decomposition (LMD) in extracting geophysical signals from noisy time series, we adopt it to filter the noise and estimate the terrestrial water storage (TWS) changes over 25 global main river basins from the time series of 14-year (2002.04~2016.08) Release 06 (RL06) monthly gravity field models provided by Center for Space Research (CSR), together with the empirical mode decomposition (EMD) as a comparison. To evaluate the efficiency of eliminating noise by LMD and EMD, the ratios of the latitude weighted RMS over the land and ocean signals are adopted. The results show that all RMS ratios of land relative to ocean signals derived by LMD are higher than EMD with the mean values 3.4458 and 3.3302, respectively. Moreover, relative to the Global Land Data Assimilation System (GLDAS) Noah model, the extracted TWS changes by LMD approach have smaller root mean squared errors than EMD over 25 global river basins. Therefore, it is reasonable to conclude that LMD approach outperforms EMD in extracting TWS changes and filtering out the strong noise existed in GRACE monthly gravity field solutions.
Due to the strong noise that exists in GRACE (Gravity Recovery and Climate Experiment) temporal gravity field solutions, geophysical signals are normally drowned which need many effective filtering approaches. Considering the advantage of the ensemble empirical mode decomposition (EEMD) approach, we used the EEMD to filter the noise in this study together with the empirical mode decomposition (EMD) for comparisons. EMD method is a spectrum analysis method, which is very effective for non-stationary signals. EMD process is essentially a means to process non-stationary signals. It has been applied in many fields in recent years. Considering the characteristics of the spherical harmonic coefficient model that the noise level higher with the increasing degree, we divided the gravity field solutions into two parts (degrees 2–28 and degrees 29–60) based on the ratios of the latitude-weighted root mean square (RMS) over the land and ocean signals when adopting different truncated degrees. For the real GRACE solution experiments, the results show that the fitting errors of EEMD approach are always smaller than those of EMD approach, and the mean RMS ratio of EEMD is 3.45, larger than 3.40 of EMD. The simulation results show that the latitude weighted root mean square errors for EEMD approach are smaller than those of EMD, indicating that EEMD can extract the geophysical signals more accurately. Therefore, it is reasonable to conclude that EEMD performs better than EMD for filtering GRACE solutions.
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