Bridging the gap between GRACE and GRACE follow-on monthly gravity field solutions using improved multichannel singular spectrum analysis

Highlights

• A new way to bridge the gap between GRACE and GRACE-FO missions.

• The infilled gaps by improved MSSA agree well with the Swarm solutions.

• Improved MSSA can fill the gap reliably in 25 river basins by simulation.

Abstract

The gap between the Gravity Recovery and Climate Experiment (GRACE) and GRACE Follow-on mission (GRACE-FO) is a crucial problem, leading to discontinuous global mass change information from time-variable gravity field solutions. We aim to use the improved Multichannel Singular Spectrum Analysis (MSSA) to fill the gap and reconstruct the continual global mass change signals in this study. The one-year gravity field gap is filled with improved MSSA based on the Release 06 (RL06) monthly gravity field models provided by Center for Space Research (CSR) truncated to d/o 60 and further compared with Swarm monthly solutions (d/o 40). The results show that the infilled gravity field models agree with the Swarm solutions, indicating that improved MSSA can reliably bridge the gap between GRACE and GRACE-FO missions. Moreover, relative to the Global Land Data Assimilation System (GLDAS) Noah model, the infilled gravity field models have higher correlation coefficients and smaller root mean squared errors than Swarm solutions for the mass change signals over Congo, Lena and Fraser river basins. According to the simulation results using the same gap as GRACE and GRACE-FO, improved MSSA can fill the gap very efficiently and reliably in 25 major river basins over the World.

Introduction

The monthly gravity field models, derived from the Gravity Recovery and Climate Experiment (GRACE) satellite mission (Tapley et al., 2004) spanning March 2002 to October 2017, were commonly applied in many areas such as hydrology, climatology, marine science, and geophysics for its high resolution and accuracy. For example, GRACE has provided new insights into the Total Water Storage Change (TWSC) (Syed et al., 2008, Landerer and Swenson, 2012, Guo et al., 2018), hydrological mass variations (Abd-Elbaky and Jin, 2019, Chen, 2019, Chandan and Nagesh, 2018), drought or flood detection (Yirdaw et al., 2008, Thomas et al., 2014, Forootan et al., 2019), and global ocean mass change (Chen et al., 2018a, Tamisiea, 2011, Cazenave, 2018), the Antarctic ice sheet mass changes (Chen et al., 2009, Gao et al., 2015, Tapley et al., 2019), the Glacial Isostatic Adjustment (GIA) (Steffen et al., 2008), etc. However, the GRACE mission operated from March 2002 to October 2017, and then the GRACE-FO mission was launched in May 2018. Therefore, there exists about one year of missing data between the two GRACE missions (Li et al., 2020), which leads to the inability to supply continuous geophysical information. How to bridge the gap effectively is valuable to acquire continual GRACE geophysical signals.

Many efforts were carried out to explore the potential of bridging the gap between the two GRACE missions with some alternative observations or approaches. In general, the gap-filling methods can be classified into three aspects. Firstly, satellite laser ranging (SLR) or GPS (Global Positioning System) observations to low Earth-orbiting satellites, such as Swarm, can provide the temporal gravity solutions with a lower spatial resolution (Bezděk et al., 2016, Jäggi et al., 2016, Lück et al., 2018, Teixeira et al., 2019), which provides an opportunity to bridge the gap (Forootan et al., 2020). The potential to bridge the gap of the two GRACE missions with Swarm was investigated by Lück et al., 2018, Forootan et al., 2020 and successfully implemented by Meyer et al. (2019). Secondly, one can reconstruct the GRACE TWSC by determining the relationships between TWSC and corresponding climatic and hydrological variables specifically including rainfall, temperature, etc, which is normally called data-driven approaches (Humphry & Gudmundsson, 2019, Hasan et al., 2019, Hasan & Tarhule, 2020). For example, the Artificial Neural Network (ANN) was adopted to learn the relationship between TWSC and related variables (Ahmed et al., 2019). Forootan et al. (2014) first applied the Independent Component Analysis (ICA) (Forootan and Kusche, 2012) to separate the GRACE signals into their original sources, then produced the reconstruction and derived the relations based on the autoregressive exogenous (ARX) (Ljung, 1987). Li et al. (2020) applied data-driven methods for reconstructing and predicting GRACE-Like gridded TWSC using climate inputs. Besides, other approaches, including the Multiple Linear Regression (MLR) approach (Myers, 1986), Convolutional Neural Network (CNN) (Sun et al., 2019) and Principal Component Analysis (PCA) (Wold, 1987), were also used to extrapolate the GRACE time series of gridded TWSC outside the GRACE period by constructing relationship models with indicators such as precipitation, land surface temperature etc (Li et al., 2020).

Besides the above approaches, many interpolation methods, such as linear interpolation (Zotov and Shum, 2010, Zotov, 2012), cubic spline interpolation (Guo et al., 2018) and least-squares fitting (Rangelova et al., 2010), were used to interpolate missing data with neighboring data. However, the performance of filling gap with these interpolation approaches is basically dependent on the lengths of time series and gaps, availability of neighboring data, and so on (Semiromi and Koch, 2019). In contrast to the above methods, a data-adaptive method SSA\MSSA, can better decompose the time series into a trend, periodic components and noise, and distinguish spatiotemporal patterns (Zotov and Shum, 2010, Zotov, 2012). Three classified SSA-based approaches have been proposed for filling the data gap. The first approach is an iterative interpolation that first needs to fill the missing data with arbitrary numbers (Golyandina, 2010, Golyandina and Zhigljavsky, 2013, Prevost et al., 2019, Wang et al., 2020). The second one is an SSA-based forecasting approach, used for bridging the TWSA gap of two GRACE missions (Li et al., 2019). The third approach named Improved SSA (ISSA) was first proposed in Shen et al. (2015) for stationary time series and performed the algorithm only with available observations. It should be noted that all three SSA-based approaches assumed that the reconstructed or forecasted component can be approximately represented by a time series with finite rank (Golyandina and Zhigljavsky, 2013).

The improved MSSA (Wang et al., 2020), which is the extension of ISSA (Shen et al., 2015), has been successfully used to process the incomplete GRACE monthly solutions. The improved MSSA can fill the missing data especially for consecutive data gaps more exact than the other interpolation and iteration MSSA approaches (Wang et al., 2020). This will provide a new method to fill the large gap between the two GRACE missions accurately. The missing months between GRACE and GRACE-FO account for 14.35% of the total data from April 2002 to March 2020. To test whether improved MSSA can effectively fill the large gap, we will deeply investigate it in this study. As we know that the GRACE gravity field solutions can be validated by comparing with some independent geophysical data, for example, the in-situ data such as ocean bottom pressure and Global Navigation Satellite Systems (GNSS)-derived vertical loads (Chambers and Willis, 2010, Chen et al., 2018b), and the hydrological models such as GLDAS Noah and WGHM data (Li et al., 2020), etc. However, according to Forootan et al. (2020), the in-situ data is more suited to evaluate the low degree spectral variations. Therefore, we use the GLDAS Noah models to demonstrate the performance of improved MSSA and Swarm solutions. The rest of this paper is organized as follows: the datasets used in this study are briefly described in Section 2. We briefly introduced the improved MSSA in Section 3. The results of the filled gap using improved MSSA are presented and compared with the Swarm data in Section 4, the simulation experiment is performed in Section 5 for further evaluating the improved MSSA and finally, the conclusions are shown in Section 6.