Sparse DDK: A Data-Driven Decorrelation Filter for GRACE Level-2 Products

Qian, Nijia; Chang, Guobin; Ditmar, Pavel; Gao, Jingxiang; Wei, Zheng-Qiang

doi:10.3390/rs14122810

Cited by 5 publications

(3 citation statements)

References 53 publications

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“…From the proof, we can conclude that in the sparse solution, the zero parameters can be viewed as constants without statistical uncertainty, and the statistically uncertain non-zero parameters can be approximately viewed as Gaussian, with the covariance matrix being N −1 AA [61]. This indicates that both the estimated parameters and the corresponding covariance matrix are sparse in the sparse solution, demonstrating an interesting parallel to the effective number of parameters, whereas the effective number of parameters approximately equals that of the non-zero parameters of the final solution in [59].…”

Section: Covariance Matrix Of the Estimated Parametersmentioning

confidence: 97%

Application of Sparse Regularization in Spherical Radial Basis Functions-Based Regional Geoid Modeling in Colorado

Yu,

Chang,

Zhang

et al. 2023

Remote Sensing

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Spherical radial basis function (SRBF) is an effective method for calculating regional gravity field models. Calculating gravity field models with high accuracy and resolution requires dense basis functions, resulting in complex models. This study investigated the application of sparse regularization in SRBFs-based regional gravity field modeling. L1-norm regularization, also known as the least absolute shrinkage selection operator (LASSO), was employed in the parameter estimation procedure. LASSO differs from L2-norm regularization in that the solution obtained by LASSO is sparse, specifically with a portion of the parameters being zero. A sparse model would be advantageous for improving the numerical efficiency by reducing the number of SRBFs. The optimization problem of the LASSO was solved using the fast iterative shrinkage threshold algorithm, which is known for its high efficiency. The regularization parameter was selected using the Akaike information criterion. It was specifically tailored to the L1-norm regularization problem. An approximate covariance matrix of the estimated parameters in the sparse solution was analytically constructed from a Bayesian viewpoint. Based on the remove–compute–restore technique, a regional geoid model of Colorado (USA) was calculated. The numerical results suggest that the LASSO adopted in this study provided competitive results compared to Tikhonov regularization; however, the number of basis functions in the final model was less than 25% of the Tikhonov regularization. Without significantly reducing model accuracy, the LASSO solution provides a very simple model. This is the first study to apply the LASSO to SRBFs-based modeling of the regional gravity field in real gravity observation data.

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Section: Covariance Matrix Of the Estimated Parametersmentioning

confidence: 97%

Application of Sparse Regularization in Spherical Radial Basis Functions-Based Regional Geoid Modeling in Colorado

Yu,

Chang,

Zhang

et al. 2023

Remote Sensing

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“…where k l denotes the loading Love number, ρ w denotes the water density 1000 kg m −3 and ρ E represents the averaged Earth density 5517 kg m −3 (Qian et al 2022). The noise of the true SH coefficients c lm are generated using the covariance matrix of CSR GRACE RL05 product in January 2008, denoted as lm (Baur & Sneeuw 2011).…”

Section: Simulationmentioning

confidence: 99%

Statistically optimal estimation of surface mass anomalies by directly using GRACE level-2 spherical harmonic coefficients as measurements

Chang

Qian

Bian

2023

Geophysical Journal International

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Summary Point-mass inversion is widely employed in GRACE level-2 data processing. Conventionally, the spherical harmonic (SH) coefficients are used indirectly: a set of pseudo measurements is generated first using the SH coefficients through SH synthesis; then the point-mass inversion is done with these pseudo measurements. To be statistically optimal, the covariance matrix of pseudo measurements should be calculated and used to appropriately weigh the parameter estimation. In this work, we propose a statistically optimal point-mass inversion scheme by directly using the SH coefficients as measurements. We prove the equivalence between this direct approach and the conventional indirect approaches. We also demonstrated their comparable performance through both simulation and real GRACE data processing. Choosing and calculating pseudo measurements, propagating covariance matrix, and potentially dealing with the singularity of the covariance matrix involved in the conventional indirect approaches are avoided in the proposed direct approach. This statistically optimal direct approach can readily be employed in mascon inversion of GRACE data and other radial basis functions-based approaches in regional gravity modeling.

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“…This scalar is often called the variance component, denoted as σ 2 . This variance component does not affect the filtered solution as shown in Equation (1), because it has already been absorbed into the regularization parameter [19]. However, in some accuracy assessments, e.g., global noise standard deviation estimation [20,21], this variance component is needed.…”

Section: Variance and Covariance Analysismentioning

confidence: 99%

Adaptive DDK Filter for GRACE Time-Variable Gravity Field with a Novel Anisotropic Filtering Strength Metric

et al. 2022

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Filtering for GRACE temporal gravity fields is a necessary step before calculating surface mass anomalies. In this study, we propose a new denoising and decorrelation kernel (DDK) filtering scheme called adaptive DDK filter. The involved error covariance matrix (ECM) adopts nothing but the monthly time-variable released by several data centers. The signal covariance matrix (SCM) involved is monthly time-variable also. Specifically, it is parameterized into two parameters, namely the regularization coefficient and the power index of signal covariances, which are adaptively determined from the data themselves according to the generalized cross validation (GCV) criterion. The regularization coefficient controls the global constraint on the signal variances of all degrees, while the power index adjusts the attenuation of the signal variances from low to high degrees, namely local constraint. By tuning these two parameters for the monthly SCM, the adaptability to the data and the optimality of filtering strength can be expected. In addition, we also devise a half-weight polygon area (HWPA) of the filter kernel to measure the filtering strength of the anisotropic filter more reasonably. The proposed adaptive DDK filter and filtering strength metric are tested based on CSR GRACE temporal gravity solutions with their ECMs from January 2004 to December 2010. Results show that the selected optimal power indices range from 3.5 to 6.9, with the corresponding regularization parameters range from 1 × 1014 to 5 × 1019. The adaptive DDK filter can retain comparable/more signal amplitude and suppress more high-degree noise than the conventional DDK filters. Compared with the equivalent smoothing radius (ESR) of filtering strength, the HWPA has stronger a distinguishing ability, especially when the filtering strength is similar.

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Sparse DDK: A Data-Driven Decorrelation Filter for GRACE Level-2 Products

Cited by 5 publications

References 53 publications

Application of Sparse Regularization in Spherical Radial Basis Functions-Based Regional Geoid Modeling in Colorado

Application of Sparse Regularization in Spherical Radial Basis Functions-Based Regional Geoid Modeling in Colorado

Statistically optimal estimation of surface mass anomalies by directly using GRACE level-2 spherical harmonic coefficients as measurements

Adaptive DDK Filter for GRACE Time-Variable Gravity Field with a Novel Anisotropic Filtering Strength Metric

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