A Combined Use of TSVD and Tikhonov Regularization for Mass Flux Solution in Tibetan Plateau

Tianyi Chen,Yunzhong Shen,Jürgen Kusche,Qiujie Chen

doi:10.3390/rs12122045

Abstract

Limited by the Gravity Recovery and Climate Experiment (GRACE) and GRACE Follow-On (GRACE-FO) measurement principle and sensors, the spatial resolution of mass flux solutions is about 2–3° in mid-latitudes at monthly intervals. To retrieve a mass flux solution in the Tibetan Plateau (TP) with better visual spatial resolution, we combined truncated singular value decomposition (TSVD) and Tikhonov regularization to solve for a mascon modeling. The monthly mass flux parameters resolved at 1° are smoothed to about 2° by truncating the eigen-spectrum of the normal equation (i.e., using the TSVD approach), and then Tikhonov regularization is applied to the truncated normal equation. As a result, the terms beyond the native resolution of GRACE/GRACE-FO data are truncated, and the errors in higher degree and order components are dampened by Tikhonov regularization. In terms of root mean squared errors, the improvements are 27.2% and 12.7% for the combined method over TSVD and Tikhonov regularization, respectively. We confirm a decreasing secular trend with −5.6 ± 4.2 Gt/year for the entire TP and provide maps with 1° resolution from April 2002 to April 2019, generated with the combined TSVD and Tikhonov regularization method.

Highlights

Since the launch of Gravity Recovery and Climate Experiment Follow-On (GRACE-FO) in May 2018 [1], the number of monthly products of time-variable gravity fields has grown, which provides the opportunity to further investigate large-scale secular and seasonal geophysical signals [2,3,4]
To compare the performance of each method in the parameter space, we calculated the mean squared error (MSE) roots of 946 mascons in the Tibetan Plateau (TP) using the combined method with Equation (12), those by truncated singular value decomposition (TSVD) according to Xu [32], and those by Tikhonov regularization according to Shen and colleagues [33]
We introduced a combined TSVD and Tikhonov regularization method to retrieve mass flux solutions at 1° resolution in the TP

Summary

Introduction

Since the launch of Gravity Recovery and Climate Experiment Follow-On (GRACE-FO) in May 2018 [1], the number of monthly products of time-variable gravity fields has grown, which provides the opportunity to further investigate large-scale secular and seasonal geophysical signals [2,3,4]. Several post-processing techniques, such as applying Gaussian filters [10,11], decorrelation filters [12], and DDK filters [13,14], have been developed to constrain the errors in high degree and order They tend to cause an attenuation of real geophysical signals [15]. Another option of recovering mass variations from GRACE data while avoiding the use of post-processing techniques is to use mass concentration approaches applied to GRACE inter-satellite range-rate measurements [16], or range-acceleration data [2,17], or spherical harmonic coefficients [8,18]. The native spatial resolution of the mass flux solutions derived from GRACE data is about 2–3◦ (63,000 km2) at an error level of 2 cm in terms of equivalent water height (EWH) at monthly intervals [19]

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Conclusion