A New GRACE Filtering Approach Based on Iterative Image Convolution

Abstract

The Gravity Recovery and Climate Experiment (GRACE) mission and its successor GRACE Follow‐On (GRACE‐FO) mission provide humans with a unique perspective on mass distribution through accurate temporal gravity field models. However, these models suffer from unavoidable stripe errors in the spatial domain. A new approach based on image processing has been developed for filtering GRACE and GRACE‐FO spherical harmonic solutions. In this approach, the gravity fields are treated as noise‐contaminated images, and the stripe errors are expected to be suppressed by convolving the input with an appropriate kernel. To verify the effectiveness of the proposed approach, a closed‐loop simulation environment over the nominal mission lifetime of 5 years is designed. Image processing indicators and geophysical information evaluation results demonstrate the superior performance of the new approach in suppressing stripe errors. In the context of real GRACE data processing, our new approach still yields better results as follows: 1) The comprehensive ability of de‐striping and retaining details has slight advantages over some commonly used filters, as demonstrated through spatial distributions, amplitude spectra, and coefficient spectra. 2) The equivalent water height time series at the basin scale is comparable to the results derived from other filters or Level‐3 products. 3) The estimated signal amplitude of the Mw9.1 2004 Sumatra earthquake co‐seismic gravity change is 52.7% larger than that derived from the Gaussian 300 km filter, which is much closer to the theoretical value derived from the dislocation theory.

Covariance Matrix Reconstruction of GRACE Monthly Solutions Using Common Factors and Individual Formal Errors

“…Moreover, some error peaks, occurred in 2002, 2004, 2010, and 2012, closely resemble the uncertainty peaks observed in the GRACE solutions discussed in Chen et al [50]. These peaks are attributed to the limited ground track coverage caused by orbit resonances as GRACE satellite altitude varied [14]. The reconstructed errors increase during the end phase of GRACE satellite operation (i.e., 2014-2016) because of the gradually decreasing orbit altitude [50].…”

“…The uncertainties of estimated parameters, such as linear trends and annual amplitudes of time series 𝒔, are the square roots of the corresponding diagonal elements of the covariance matrix 𝑸, 𝑸 = σ 0 2 (𝑨 T 𝑨) −1 (14) where 𝜎 0 denotes the standard error with 𝜎 0 = √ 𝜺 T 𝜺 𝑛−𝜇 with 𝑛 and 𝜇 representing the number of months and unknown parameters; The design matrix 𝑨 is defined as,…”

“…he Gravity Recovery and Climate Experiment (GRACE) [1] and its successor GRACE Follow on (GRACE-FO) [2] have been operated since April 2002, providing monthly high-resolution gravity field model, which has been widely used in exploring earth mass variations, including terrestrial water storage (TWS) [3], [4], sea level [5], [6], polar ice caps [7], [8], mountain glaciers [9], [10] and solid earth [11], [12]. However, the time-varying gravity field models are seriously contaminated by the south-north stripe noise, originating from instrumental errors, orbit geometry, imperfect oceanic and atmospheric non-tidal models, as well as the limitations in the data processing strategies [13], [14]. Therefore, efficient post-processing procedures are required to denoise the time-varying gravity field models.…”