# Evaluation of the Consistency of Three GRACE Gap-Filling Data
###### Abstract
Unfortunately, this approach yields only 10-degree gravity field models, which capture only the long-term variability of the large-scale gravity fields [12]. Furthermore, the long-wave variations in the time-varying gravity field can also be monitored by high-low satellite-to-satellite tracking (HLSST) measurements, but this technique provides only the long-wave variations in the gravity field with an approximate spatial resolution of 2000 km [13]. Similarly, orbit data from the geomagnetic satellite constellation Swarm is also able to solve the Earth's large-scale time-varying gravity field [14], but its data quality is only good at low degrees (i.e., below degree 12 [15]). To overcome the low-resolution problems of SLR and HLSST, researchers have proposed various techniques for recovering the time-varying gravity field and filling the 11-month gap between the GRACE and GFO data. Empirical orthogonal decomposition methods [16], machine learning techniques [17; 18; 19; 20], and singular spectrum analysis [21] essentially maintain the spatial resolution of GRACE. The empirical orthogonal function (EOF) analysis method is a way of dimensionality reduction of data to obtain the dominant signal [22]. Except for SLR alone, a time-varying gravity field can be recovered from SLR data using the GRACE EOF decomposition model [16]. Machine learning is a popular branch of artificial intelligence, which is now widely used for solving engineering and science problems. However, machine learning is usually designed for regional gridded observations of hydrological signals, rather than for global and generic SHCs. Singular spectrum analysis methods, which have recently emerged for studying non-linear time series data, promise the availability of simple and generous models with less-computationally intensive solutions and high operability. This approach decomposes a time series into its trend, periodic components, and noise [23; 24], and it opens up an effective way to fill the gaps between GRACE and GFO. The first attempt to fill data gaps with SSA data [25] was targeted at regional terrestrial water storage anomalies in China and was not generalizable to other research fields (i.e., oceanography and solid Earth physics). [PERSON] and [PERSON] (2021) [21] and [PERSON] et al. (2021) [26] improved the existing work by devising new schemes to fill the data gaps with the highly applicable form of SHCs. In general, there are three types of SHC gap-filling datasets: Purely derived from other observations but with limited resolution, fully data-driven approaches that inherit information from GRACE/GFO observations, and hybrid approaches integrating SLR or other data with GRACE. Here, we choose each instance of these three types for comparison: (1) Time-varying gravity field models recovered from a combination of HLSST and SLR ([PERSON], [PERSON] 2019 [27]), (2) interpolations of GRACE observations using the SSA approach ([PERSON] and [PERSON] 2021 [21]), and (3) a hybrid modelling that using EOFs from the GRACE solutions as the base functions to recover time-varying gravity field models from SLR observations (IGG, [PERSON] and [PERSON] 2021 [16]). In this paper, we will scrutinize these three datasets in the spectral and spatial domains, evaluate their consistency, and explore their applicable scenarios.