Assessing the Consistency Among Three Mascon Solutions and COST-G-Based Grid Products for Characterizing Antarctic Ice Sheet Mass Change

Highlights

What are the main findings?

• The three mainstream mascon as well as COST-G-based grids show good consistency over the AIS, while large differences occurred in APIS.
• Significant differences among these four grids existed in the annual mass change in 2016 and the interannual signals from mid-2016 to mid-2018.

What are the implications of the main findings?

• One or more mascon or COST-G-based grids can be selected for application to perform further studies over the AIS. Caution should be taken when applying these grids over the APIS.
• This study sheds light on the way to improve the quality of GRACE/GRACE-FO grid products; i.e., refining the algorithms for the APIS and updating the grids at the late stage of the GRACE mission.

Abstract

To facilitate easy accessibility to the Gravity Recovery and Climate Experiment (GRACE) and GRACE Follow-On (GRACE-FO) results for the geoscientific community, multiple institutions have successively developed mass anomaly grid products including mass concentration (mascon) grids; these were provided at the Gravity Information Service (GravIS) portal. However, an assessment of their consistency for studying large-scale mass redistribution and transport in Earth’s system is still not available. Here, we compare three major mascon solutions separately from the Center for Space Research (CSR), the Jet Propulsion Laboratory (JPL), the Goddard Space Flight Center (GSFC) and GravIS products based on the Combination Service for Time-variable Gravity fields (COST-G) by analyzing the Antarctic Ice Sheet (AIS) mass changes in four aspects. Our results demonstrate that: (1) the four datasets exhibit strong consistency on the entire AIS mass change time series, with the largest difference occurring in the Antarctic Peninsula; (2) mass trend estimates show better agreement over longer periods and larger regions, but differences with a percentage of 20–40 exist during the late stage of GRACE and the whole GRACE-FO timespan; (3) notable discrepancies arise in the annual statistics of the Eastern AIS in 2016, leading to inconsistency on the sign of annual AIS mass change; (4) good agreement can be seen among these interannual mass variations over the AIS and its three subregions during 2003–2023, excluding the period from mid-2016 to mid-2018. These findings may provide key insights into improving algorithms for mascon solutions and grid products towards refining their applications in ice mass balance studies.

1. Introduction

Since the launch of the Gravity Recovery and Climate Experiment (GRACE) satellite in March 2002 [1,2] and its successor GRACE Follow-On (GRACE-FO) in May 2018 [3], the two missions have provided unprecedented observations of Earth’s time-variable gravity field. However, deriving mass changes from these time-variable gravity fields requires solving an inverse problem which is a non-unique question. To address such a problem and to ease access to GRACE/GRACE-FO data for scientists without a profound geodetic background, multiple institutions have developed grid products, i.e., mass concentration (mascon) products and mass anomaly grid products. The Goddard Space Flight Center (GSFC) pioneered the first mascon product, and conducted case studies in the Amazon basin [4,5]. Subsequently, to improve the estimation of ocean mass changes, the Jet Propulsion Laboratory (JPL) released the mascon product for applications on global mass change [6]. The Center for Space Research (CSR) at the University of Texas developed its version to avoid the complex post-processing of GRACE/GRACE-FO gravity field solutions in terms of spherical harmonics [7]. Currently, these mascon products have been widely applied to investigate mass migrations occurring in multidisciplinary fields such as hydrology [8,9,10,11,12,13,14], the cryosphere [15,16,17,18,19,20,21,22,23,24], and solid Earth geophysics [25,26,27,28,29]. In addition, the Gravity Information Service (GravIS) portal provides user-friendly mass anomaly products based on GRACE/GRACE-FO Level-2 gravity field solutions separately processed at the German Research Centre for Geosciences (GFZ) and the Combination Service for Time-variable Gravity fields (COST-G), aiming at supporting applications on hydrology, glaciology, and oceanography. It has been pointed out that mass anomaly products based on COST-G should have better accuracy since they stem from the approach for combining multiple Level-2 products from different data analysis centers, while those based on GFZ have a shorter latency [30]. Although COST-G-based gridded products were utilized to evaluate the spatial pattern of gridded ice elevation data in Antarctica [31], the comparison among mascon products and COST-G-based ice mass change products is still not available.

The Antarctic ice sheet (AIS), as the largest ice sheet on Earth, is the world’s largest freshwater reservoir. Its changes not only directly affect sea-level rise, but also have significant impacts on ocean surface temperature, salinity, thermal circulation and the global carbon cycle. If the AIS were to melt completely, the global sea level would rise by 58 m [32], which would pose a severe threat to the lives and property safety of all mankind. Therefore, accurately monitoring the AIS mass balance is significant to understand its current status and predict sea level change.

Expressed in an intuitive equivalent water height grid format, mascon data have been widely used for estimating the AIS mass variations. Previously, Pan et al. [33] derived a mass trend of approximately −100 Gt/yr using three mascon products during 2002–2021. Based on CSR mascon data, Wang et al. [34] estimated a mass change rate of −141.8 ± 55.6 Gt/yr for the AIS during 2003–2020. Although their study periods were not exactly the same, there could be apparent discrepancies among estimates of the AIS mass changes derived from mascon data. In addition, mass variations of the AIS fluctuate with relatively large interannual variability and short-term extreme meteorological events [35,36,37]. Using JPL mascon data, Bodart et al. [38] reported anomalous mass gain in West Antarctica during the 2015–2016 extreme El Niño event. Zhang et al. [39] showed that the interannual mass variations over different subregions in the AIS displayed similar or opposite temporal patterns. Whether the same patterns of mass changes can be obtained from different grid products over the AIS is still unknown. Consequently, it is necessary to evaluate the consistency among these grid products towards a better understanding of the uncertainty of the AIS mass changes derived from GRACE/GRACE-FO and potential applications on sea-level rise and climate forcing response analyses.

In this study, we conduct a comprehensive evaluation about the consistency of three mascon products (CSR, JPL, and GSFC) and COST-G-based gridded products to characterize the AIS mass changes on multiple temporal scales. Mass change time series are first separately extracted over the AIS and its three subregions, using the above four grid products. We then compare mass trends separately obtained at a relatively short period, the entire GRACE period, GRACE/GRACE-FO period, and only the GRACE-FO period. The differences among those mass trends are quantified, and the four acceleration maps of mass change during 2003–2023 are compared over the AIS. We also statistically analyze and compare the patterns of mass change over the AIS and its subregions at seasonal, annual and interannual timescales. This study provides critical insights on future grid product refinement and applications in ice sheet mass balance studies.

2. Data and Methods

This study compares four grid products from GRACE/GRACE-FO observations, aiming at investigating their consistency on characterizing the AIS mass variations. The adopted data and methods are provided as follows.

2.1. GRACE/GRACE-FO Data

We use three mascon products, namely CSR, JPL, and GSFC mascon, and COST-G-based gridded products provided by the GravIS to investigate their consistency in characterizing AIS mass change spanning from January 2003 to December 2023. The following are the descriptions of these grid products.

2.1.1. CSR Mascon

In this study, we adopted the latest released CSR mascon data in RL06.3. This dataset incorporates the degree 1 coefficients or geocenter corrections provided in Technical Note 13 (TN-13a) [40]. The degree 2 order 0 (C20) coefficients and the degree 3 order 0 (C30) coefficients are replaced with the C20 and C30 solutions from satellite laser ranging (SLR) [40,41]. The glacial isostatic adjustment (GIA) effect is corrected using the ICE6G-D model [42]. For oceanographic studies, the atmosphere and ocean de-aliasing level-1B (AOD1B) ‘Grid Azimuth Determination (GAD)’ fields represented in the original mascon geodesic grid is added back, which is called GAD Correction. The Tikhonov regularization is used along with L-ribbon approach to compute the regularization parameter [7]. No additional smoothing or empirical de-striping or filtering is applied to this dataset. Finally, CSR mascon data are expressed on an ellipsoidal spherical grid of 0.25° × 0.25° relative to their mean baseline (2004.0000~2009.999) in the form of equivalent water height. The raw data is available from the website: https://www2.csr.utexas.edu/grace/RL06_mascons.html (accessed on 10 February 2025).

2.1.2. JPL Mascon

The GRACE RL06.3Mv04 mascon grids products from the Jet Propulsion Laboratory (https://grace.jpl.nasa.gov/data/get-data/jpl_global_mascons/ (accessed on 10 March 2025)) were used to estimate the mass change of the AIS. The JPL mascon data was calculated based on JPL-processed 1B GRACE/GRACE-FO data. The replacement of C20 and C30 coefficients, degree 1 coefficients, and the GIA corrections were applied as these for the CSR mascon data. However, no GAD correction is mentioned in the user guide for JPL mascon data. The complete mascon solution generated by JPL consists of 4551 independent estimates of surface mass change that have been derived using an equal-area 3-degree grid of individual mascon [6]. Finally, the JPL mascon data is expressed on the surface of an elliptical Earth in a grid of 0.5° × 0.5°, with its effective resolution of 3° × 3°. All reported JPL mascon data are anomalies relative to the 2004.0000~2009.999 time-mean baseline.

2.1.3. GSFC Mascon

GSFC mascon data has applied the same C20 and C30 corrections, degree 1 coefficients corrections, GIA and GAD corrections as those for CSR mascon data. The tidal model, GOT 4.7 to degree and order 90, is further considered. After deducting the average field from 2004.0–2010.0, GSFC’s mascon data is provided at an equal angle 0.5° × 0.5° grid. For GSFC mascon data, its land values are determined with a least squares estimator that conserves mass over each region, while ocean values have been interpolated/extrapolated. In this study, we applied GSFC mascon data in RL06v2.0, which is available from the website: https://earth.gsfc.nasa.gov/geo/data/grace-mascons (accessed on 13 February 2025).

2.1.4. Dataset Based on COST-G from the GravIS

Here we introduced ice mass change data from the COST-G Level-3 product [30] (available at https://gravis.gfz.de/ais, accessed on 6 August 2025) for additional comparison. COST-G is a product center for time-variable gravity fields of IAG’s International Gravity Field Service. It provides consolidated monthly global gravity fields of the GRACE/GRACE-FO satellite missions in spherical harmonic representation (Level-2 products) and thereof derived grids (Level-3 products) of surface mass changes by combining existing solutions or normal equations from COST-G analysis centers and partner analysis centers [43]. In this study, ice mass change product is derived from the latest release of GRACE/GRACE-FO Level-2 products from COST-G. The long-term mean gravity field—derived from 183 monthly solutions available between April 2002 and March 2020—was subtracted from each monthly gravity field model to obtain anomalies relative to this mean state. Subsequently, destriping and smoothing were performed using an anisotropic filter (the VDK filter) [44]. Coefficient replacements were applied for C20 (over the entire GRACE/GRACE-FO time series) and C30 (only for the period from November 2016 to June 2017) [40,41]. Geocenter correction was implemented using the approximate method described by Swenson et al. [45]. During the GravIS Level-2B processing, an empirical correction was applied to mitigate S2 tidal aliasing errors. The ICE-6G_D (VM5a) model [42] was used to correct for GIA effects in the GravIS Level-2B products.

2.2. Methods

To illustrate the methods in this study, we provide the following workflow in Figure 1. Based on mascon solutions (CSR, JPL, GSFC) and the COST-G-based grids, we first generated mass change time series. We then filled in the data gaps through linear interpolation for 1–2 month intervals and singular spectrum analysis (SSA) for the 11-month between-mission gap. Finally, the consistency across the four datasets is quantified at multiple temporal scales using the intraclass correlation coefficient (ICC).

Figure 1. The workflow for intercomparing three mascon (CSR, JPL, GSFC) grids and COST-G-base products.

2.2.1. The Gap-Filling Method

It is known that there are data gaps with a length of one or two months within the respective periods of GRACE and GRACE-FO. These data gaps can be filled by applying linear interpolation in order to continuously analyze the observations from GRACE or GRACE-FO. However, there are 11-month data gaps between GRACE and GRACE-FO missions. As the continuity of GRACE and GRACE-FO data was verified by using surface mass balance combined with ice discharge data [16], this enables us to directly analyze mass change time series from both missions. Previously, the singular spectrum analysis (SSA) method was used to fill the 11-month gap, and its performance was confirmed to be good for analyzing terrestrial water storage change and ice-sheet mass variations [46]. The SSA method is based on singular value decomposition. It can be used to extract trend term, period, seasonal and interannual change signals, and it can also be used for signal decomposition, reconstruction, filling and prediction. In this study, we first applied linear interpolation for filling in isolated or paired data gaps within GRACE or GRACE-FO observation period. Then, as to the 11-month data gap between GRACE and GRACE-FO, the SSA method was applied. Thus, the 20-year-long mass change time series of the AIS can be obtained to characterize patterns of its mass variations.

2.2.2. Method for Extracting Linear Trend and Interannual Variations

In this study, the least squares method can be used to fit mass change time series. At each grid point, we adopt a mathematical model including the linear component and seasonal signals to fit mass variations. This can be written in the equation as the following:

$$M\left(t_i\right)=a+b{t}_i+c_1\sin \left(2\pi t_i\right)+c_2\cos \left(2\pi t_i\right)+d_1\sin \left(4\pi t_i\right)+d_2\cos \left(4\pi t_i\right)$$

(1)

in which $t_i$ is the $i_{th}$ time tag in years, $M\left(t_i\right)$ represents mass change time series at each grid point, the four sinusoids together represent seasonal signals with the periodicity of 1 year and half year, and $a$, $b$, $c_1$, $c_2$, $d_1$ and $d_2$ are unknown parameters to be estimated. Among these parameters, $a$ indicates an offset, and $b$ is a linear time-dependent parameter representing the trend of mass changes. $c_1$ and $c_2$ are associated with the amplitude of a seasonal component with the periodicity of 1 year, and $d_1$ and $d_2$ for a seasonal component with the periodicity of half a year.

After performing least squares, the above unknown parameters can be estimated at each grid point. We then carried out the following steps to extract the inter-annual mass variations: (1) calculate the residuals at each grid point, which are obtained through mass change time series subtracting the linear component and seasonal components; (2) since only the average seasonal variations in the study period have been removed in step (1), while seasonal variations may be different from year to year, we applied a moving average with a one year long window to further remove the remnant seasonal changes. Thus, the interannual mass variations can be obtained at each grid over the AIS.

2.2.3. Correlation Analysis Through ICC

The ICC is a numerical value typically ranging between 0 and 1. It serves as a widely recognized statistical tool employed in various fields, including medical, psychological, biological, and genetic research. The ICC quantifies the correlation within a class of data (i.e., the correlation of repeated weight measurements), as opposed to the correlation between two distinct classes of data (i.e., the correlation between weight and length) [47]. It can be utilized to assess inter-rater consistency and retest reliability. Furthermore, it is appropriate for quantifying the magnitude of measurement error and evaluating the reliability of measurements. Numerous ICC models exist, and we selected the bidirectional random-effects model with absolute agreement based on the characteristics of the three mascon datasets. Given that the three mascon datasets are independent of one another, a single measurement standard was adopted. The following is the calculation formula of the model selected in this study:

$$ICC\left(A,1\right)={\displaystyle \frac{M{S}_R-M{S}_E}{M{S}_R+\left(k-1\right)M{S}_E+\frac{k\left(M{S}_C-M{S}_E\right)}{n}}}$$

(2)

in which $M{S}_R$ is row variable mean square; $M{S}_C$ is column variable mean square; $M{S}_E$ is mean square of error; $n$ is number of subjects; $k$ is number of raters. $A$ represents absolute consistency in the model.

3. Results

3.1. Mass Change Time Series of the AIS and Its Subregions

Based on mascon data from CSR, JPL, and GSFC, and COST-G-based ice-mass change products during 2003–2023, we separately compared mass change time series of the AIS and its three subregions including the Antarctic Peninsula ice sheet (APIS), West Antarctic ice sheet (WAIS) and East Antarctic ice sheet (EAIS), as shown in Figure 2. The division of these three subregions over the AIS was referred to the Antarctic Drainage System provided by NASA’s Goddard Earth Sciences Division (available at https://earth.gsfc.nasa.gov/cryo/data/polar-altimetry/antarctic-and-greenland-drainage-systems; accessed on 10 September 2024). It can be seen that these four mass change time series are consistent with each other over the AIS, APIS, WAIS and EAIS. Such consistency can be reflected by the high ICC values of 0.98, 0.94, 0.99, and 0.97 among these four mass change time series over AIS, APIS, WAIS, and EAIS, respectively (Table 1). However, there are some discrepancies among these mass change time series, i.e., in the AIS (Figure 2a), mass change time series from COST-G show a jump in June 2017, which leads to an apparent difference with mascon results during the data gap period (the slight gray area). In APIS (Figure 2b), a notable decline can be seen from GSFC-derived mass change time series since 2014, and COST-G-based mass change show a similar decline with larger amplitude since 2012. In WAIS (Figure 2c), since 2012, JPL’s results show a more negative trend compared with those from CSR, GSFC and COST-G. In EAIS (Figure 2d), slight differences can be seen in these four mass change time series during the late GRACE period and the time intervals of data gap.

Figure 2. Mass change time series of (a) the entire AIS, (b) the APIS, (c) the WAIS, and (d) the EAIS separately derived from three mascon data, namely CSR (blue lines), JPL (orange lines), and GSFC (yellow lines), and from the COST-G-based grid data (purple lines). The slight gray area indicates the gap between the GRACE and GRACE-FO missions. The regions including the AIS, APIS, WAIS and EAIS, are marked in dark gray.

Table 1. ICC values for mass change time series, annual mass variations and interannual mass variations over the AIS, APIS, WAIS, and EAIS, respectively. To be noted, two cases, namely including gap period (from July 2017 to May 2018) and excluding gap period, are separately considered.

Regions	ICCs for Mass Change Time Series 2003.01–2023.12		ICCs for Annual Mass Variations 2003–2023		ICCs for Interannual Mass Variations 2003.07–2023.07
	With Gap Period	Without Gap Period	With Year 2016, 2017	Without Year 2016, 2017	With Gap Period	Without Gap Period
AIS	0.98	0.98	0.75	0.84	0.87	0.91
APIS	0.94	0.94	0.79	0.77	0.94	0.95
WAIS	0.99	0.99	0.82	0.88	0.96	0.97
EAIS	0.97	0.97	0.79	0.85	0.92	0.94

3.2. Linear Trends and Accelerations of Mass Change in the AIS and Its Subregions

To more carefully analyze the consistency of the AIS mass changes derived from the three mascon grids and COST-G-based grid products, we calculated short-term mass trends of the AIS and its three subregions in five timespans (approximately every four years), as shown in the left side of the blue dashed lines in Figure 3. In the AIS (Figure 3a) and APIS (Figure 3b), negative trends can be seen in the first four spans but a positive trend for the last span. In WAIS (Figure 3c), negative trends are revealed for all the five timespans. In EAIS (Figure 3d), except for a slightly negative trend in the span 2012–2015, positive trends can be found for the other four spans. No difference of sign is found in all the trends derived from these grid data, which to some extent illustrates their good agreement with each other. However, there are some differences among these grid data. In the AIS (Figure 3a), from January 2003 to December 2007, the mass trend from CSR mascon (−26.67 Gt/yr) or COST-G (−36.42 Gt/yr) is more than twice that from JPL (−11.48 Gt/yr). A similar case also appears in the timespan from January 2016 to December 2019, in which the mass trend from JPL mascon (−138.65 Gt/yr) or COST-G (−142.33 Gt/yr) is more than twice those from GSFC (−63.86 Gt/yr), with their difference in absolute value exceeding ~70 Gt/yr. During 2008–2011 and 2012–2015, better consistency can be seen among mass trends from these three data centers and COST-G. In APIS (Figure 3b), more pronounced difference can be found during 2020–2023, compared with the other three timespans. In WAIS (Figure 3c), since 2008, JPL-derived mass trends are more negative than those from CSR, GSFC and COST-G, which agrees with the result shown in Figure 2c. In EAIS (Figure 3d), the JPL-derived mass trend is much smaller than those from CSR and GSFC during 2016–2019, and the COST-G-based mass trend in absolute value is the smallest in all these timespans except for 2008–2011.

Figure 3. Mass trends of (a) the entire AIS, (b) the APIS, (c) the WAIS, and (d) the EAIS separately derived from three mascon data, namely CSR (blue bar), JPL (orange bar), and GSFC (yellow bar) and from COST-G (purple bar). The study period is divided as follows: The left side of the blue imaginal line shows the trends during four periods which are approximately four years, and the right side of the blue imaginal line shows mass trends during the entire GRACE/GRACE-FO period, GRACE period and GRACE-FO period, respectively.

We also calculate mass trends during the entire GRACE/GRACE-FO period, GRACE period and GRACE-FO period, respectively. As provided by the right side of the blue dashed lines in Figure 3, compared with these four-year spans and GRACE-FO period, much better agreement can be seen among mass trends obtained in entire GRACE/GRACE-FO period and GRACE period.

To quantify the differences among the four mass trends in each timespan, we calculated the mean mass trend for each timespan. We then calculated the difference by mass trend from each data center and COST-G subtracting the mean mass trend, respectively. Later, the percentage can be separately computed by the difference divided by the mean mass trend for each timespan. As provided in Figure 4a, the percentage of the difference relative to the mean mass trend in absolute value exceeds 60% for COST-G over the AIS during 2003–2007, 2020–2023, and 2018.06–2023.12, respectively. Also, the CSR-derived mass trend in absolute value is more than 60% smaller than the mean mass trend during 2018.06–2023.12. Over the APIS, as shown in Figure 4b, 14 out of 32 mass trends show a percentage in absolute value larger than 20%. In the eight timespans, there are seven mass trends derived from COST-G with a percentage larger than 20%, which means COST-G-based mass trends are more negative or more positive compared to the corresponding mean mass trend. There are also three mass trends derived from CSR, and two from GSFC showing a percentage less than −20%, which means those mass trends are less positive or less negative than the corresponding mean mass trend. JPL-derived mass trends show one case with a percentage larger than 20% and one case less than −20%. Over the WAIS, all the trends in eight timespans show a percentage in absolute value less than 20%. For the EAIS, the largest difference occurs at the timespan when the mass trend is small relative to other timespans.

Figure 4. The percentage of difference between mass trend and the corresponding mean mass trend relative to the mean mass trend over (a) the entire AIS, (b) the APIS, (c) the WAIS, and (d) the EAIS separately derived from three mascon data, namely CSR (blue bar), JPL (orange bar), and GSFC (yellow bar) and from COST-G (purple bar). The study period is divided like those in Figure 3.

Furthermore, based on these mascon data, we separately estimated acceleration at grid points in order to compare the acceleration maps of the AIS mass variations from 2003 to 2023, as shown in Figure 5. Similar spatial patterns can be seen from these acceleration maps, i.e., a positive acceleration of about 3 Gt/yr² is observed in APIS and George V Land, while a negative acceleration of about −4 Gt/yr² is found in Amundsen Sea Embayment (ASE) and Wilkes Land, illustrating the good consistency among these grid products. Nonetheless, there are some pronounced differences among the four acceleration maps. CSR mascon shows a positive acceleration in parts of coastal regions in ASE but a negative acceleration appeared in JPL and GSFC mascon. The positive acceleration derived from COST-G in ASE shows a much smaller area. In addition, there are also some differences over the interior in EAIS. The above differences could be partly associated with the selection of mascon grid, i.e., CSR mascon data are represented on a 0.25° longitude-latitude grid (Figure 5a), JPL mascon is presented in a 3° × 3°grid (Figure 5b), and GSFC mascon adopts 1-arc-degree equal-area mass concentration cells (Figure 5c). COST-G-based grid products are thought to be accurate, since they stem from the combining multiple Level-2 products from different analysis centers [30].

Figure 5. Acceleration maps of the AIS mass variations from 2003 to 2023, separately derived from three mascon data, namely CSR (a), JPL (b), and GSFC (c), and from COST-G (d). Acceleration rates are estimated from the second order polynomial $y=a_0+a_{1}t+{\displaystyle \frac{1}{2}}{a}_2{t}^2$ fitting to monthly mass change time series.

3.3. Patterns of Seasonal and Annual Mass Change in the AIS

To assess the similarity of patterns of the AIS seasonal mass changes derived from these grid data, we separately compare the climatological mean of the seasonal variation recorded with GRACE and GRACE-FO over the AIS, APIS, WAIS and EAIS. As provided by Figure 6a–d, during GRACE observational interval, patterns of mass gradually decreasing during austral spring (September–November), achieving minimum during austral summer (December–February), and increasing during austral autumn (March–May) as well as slightly decreasing during austral winter (June–August) are revealed by all the grid data. However, there is a difference (~60 Gt) between the mean of mass changes derived by CSR and GSFC in August in the AIS. This difference is caused by differences occurring in WAIS and EAIS in August (Figure 6c,d). During the GRACE-FO observational interval (Figure 6e–h), from austral spring to autumn, patterns of mass decreasing and increasing are similar to those during GRACE period. But for austral winter, mass is increasing except for those from COST-G and CSR in WAIS during GRACE-FO period. It is worthwhile that the amplitude of mass gain from January to April during GRACE-FO period is about twice as that during GRACE period. This is mainly associated with the massive increase occurred in EAIS and APIS during GRACE-FO period.

Figure 6. Average (solid line) and standard deviation (the shaded area) for monthly mass changes derived by CSR (blue lines), JPL (red lines) and GSFC (green lines) as well as COST-G (pink lines), separately in the AIS, APIS, WAIS and EAIS during (a–d) the GRACE periods and (e–h) the GRACE-FO periods.

We further conducted statistical analysis about annual mass change, which is defined as the sum of mass changes that occurred from January to December. For instance, mass change in January 2003 is computed by the mass in January 2003 subtracting that in December 2002, and the mass change in February 2003 is computed by the mass in February subtracting that in January 2003, and so on. The annual mass change in 2003 is the sum of mass changes that occurred from January 2003 to December 2003, as shown in Figure 7a. Good consistency can be found among the annual mass changes derived from the three centers and COST-G over the AIS in most years. The ICCs for AIS, APIS, WAIS, and EAIS among these grid data are 0.75, 0.79, 0.82, and 0.79, respectively. It is worth noting that the sign of annual mass change is opposite between CSR and JPL/GSFC in 2009, 2016, and 2020. Especially for the year 2016, CSR-derived annual mass change was about −350 Gt, while JPL-derived annual mass change was about 170 Gt. By excluding the year 2016 and 2017, the ICC for the AIS, WAIS, and EAIS will increase to be 0.84, 0.88 and 0.85. This suggests that mascon data at the end of GRACE mission and during the GRACE/GRACE-FO gap have an important impact on quantifying their consistencies on annual mass changes.

Figure 7. (a) Annual mass change of the AIS derived separately from CSR (blue bar), JPL (orange bar) and GSFC (yellow bar) mascon data as well as COST-G (purple bar). (b) Ratios of annual mass change of WAIS (blue bar), EAIS (orange bar) and APIS (yellow bar) versus to the sum of annual mass change of WAIS, EAIS, and APIS in absolute value, respectively. Note that the first bar corresponds to results from CSR, the second for JPL, and the third for GSFC in each year in (a).

We further analyze contributions from WAIS, EAIS, and APIS to the annual mass changes of the AIS, as shown in Figure 7b. Except for the year 2016, good consistency can be seen among the ratios of three subregions derived separately from CSR, JPL and GSFC as well as COST-G data. WAIS dominated the annual mass loss of the AIS in recent decades excluding the year 2005. EAIS showed annual mass gain in most years, which can partly compensate for the mass loss that appeared in WAIS. When net mass loss occurred in EAIS, mass loss of the AIS would be large. Such a case can be found in 2007, 2010, 2013, 2014, and 2019. APIS suffered from mass loss in most years, with a relatively small amplitude. However, there are some differences which can be seen in ratios of these subregions. For instance, over the EAIS, an annual mass change of opposite signs can be seen in 2008, 2013, 2015, 2016 and 2017.

3.4. Interannual Mass Variations of the AIS and Its Subregions

We also compare the interannual mass variations of the AIS and its three subregions including APIS, WAIS, and EAIS, as shown in Figure 8. It can be seen that the interannual mass variations derived from CSR and GSFC are consistent with each other over the AIS, APIS, WAIS and EAIS during 2003–2023. JPL-derived interannual mass variations also agree well with those from CSR and GSFC over the AIS and its three subregions when excluding the timespan from 2016 to 2018. COST-G-based interannual mass variations show similar patterns to that from JPL over all the regions except for discrepancies that occurred during 2016–2018 and during 2013–2016 over the APIS. The ICC values among these four interannual variations are 0.87, 0.94, 0.96 and 0.92 for the AIS, APIS, WAIS and EAIS, respectively. If excluding the data gap period (from July 2017 to May 2018), the ICC values among these interannual variations will have a slight increase, i.e., 0.91, 0.95, 0.97 and 0.94 separately for the AIS, APIS, WAIS and EAIS (Table 1). Since an extreme El Niño event occurred during 2015–2016, enhanced precipitation in mass of 210 ± 59 Gt with respect to its long-term trend was reported in the AIS [38]. However, no pronounced increase can be found in CSR/GSFC-derived interannual mass variations in the AIS during the timespan from 2015 to 2016. Although CSR and GSFC mascon show substantial mass gains in the APIS (33.21 Gt and 44.38 Gt, respectively) and WAIS (40.92 Gt and 48.85 Gt) during 2015–2016 (Figure 8b,c), these increases were more than offset by pronounced mass loss in the EAIS (−168.41 Gt and −201.49 Gt; Figure 8d) in the same period. JPL-derived interannual mass variations showed a brief stabilization in mass loss in EAIS. In addition, the above difference appears at the late stage of the GRACE mission, and the relatively large noise of measurements [3,48] may introduce difficulty in accurately monitoring mass change of small amplitude in the EAIS.

Figure 8. Interannual mass variations of (a) the entire AIS, (b) the APIS, (c) the WAIS, and (d) the EAIS separately derived from CSR (blue lines), JPL (orange lines), and GSFC (yellow lines) mascon data as well as COST-G (purple lines) grid products. The slight gray area indicates the data gap between the GRACE and GRACE-FO missions.

4. Discussion

GRACE and GRACE-FO grid products from multiple data centers have been widely applied in studying ice sheet mass changes in recent years. A deep understanding of their consistencies and uncertainties is of vital importance to the geoscientific community. This study systematically evaluated the consistency between three mainstream mascon products and the COST-G-based glacier grid products on revealing characteristics of the AIS mass variations. Our analysis revealed two key findings: (1) there are some differences between the mascon and the COST-G-based ice mass grid products, especially over the APIS where the topography is long and narrow; (2) the ICC value is closely related to the time period of the selected data, especially in the late stage of the GRACE mission and the gap period between GRACE and GRACE-FO missions. This section elucidates the potential causes of these findings and discusses their implications for future research.

The differences among these grid products are not completely surprising, and they can be mainly attributed to the regularization methods which were applied for mascon data and the adopted “thin layer assumption” as well as the post-processing approach for gravity field solutions in spherical harmonic coefficients [49]. It was known that mascon solutions introduce a priori constraints on the spatial or temporal resolution of the target in order to overcome the instability during the inversion procedure. The gridded mass anomaly products from mascon solutions do not exhibit the typical stripes or signal leakage. But it could introduce erroneous signals or not correctly recover small-scale signals [30]. As shown in Figure 5, it is difficult to distinguish the true signals in the interior of the AIS due to the relatively weak signals. The gravity field solutions in spherical harmonic coefficients derived from unconstrained mathematical fitting of global observations are essentially susceptible to measurement errors, which are manifested in the spatial domain as the characteristic north-south fringe patterns [48]. Although using spatial smoothing operators can effectively suppress these errors, they simultaneously attenuate the true geophysical signals, especially at regions with small-scale variations and areas near basin boundaries. As reported by [50], the APIS is such an example region which can suffer from significant signal attenuation. That is why relatively large differences exist among these grid products there. Therefore, we should take caution when applying a single grid product to explain signals with a small amplitude or analyze changes over regions like the APIS. The corresponding uncertainty cannot be neglected.

In addition, we found that the ICC values increase or decreased over some regions when selecting data with a varying period. For instance, ICC value increased over the AIS, WAIS and EAIS but slightly decreased over the APIS when excluding annual mass variation in the years 2016 and 2017. This suggests that the consistency among the annual mass variations in the years 2016 and 2017 is worse than those in other years over the AIS, WAIS and EAIS. This is understandable. The larger the ICC value, the better the consistency. Indeed, the late stage of GRACE (after October 2016) was operated with only one accelerometer mode [48], and this would definitely degrade the accuracy of mass change obtained from GRACE at that period. As to the APIS, it is essentially susceptible to significant signal attenuation. The uncertainty of its mass change was relatively large. In addition, by excluding data during the gap period from July 2017 to May 2018, ICC values remain unchanged or slightly increase over all regions for both monthly mass change time series and interannual variations. This demonstrates that the results generated by SSA has little impact on evaluating the consistency among the four mass change time series and interannual mass variations over the AIS, WAIS, EAIS and APIS, respectively.

5. Conclusions

Based on the mascon data from CSR, JPL and GSFC, and COST-G-based grid products from the GravIS, this study systematically analyzed their consistency in characterizing the spatiotemporal patterns of mass change over the AIS from 2003 to 2023. The findings can be summarized as follows:

(1)

A high degree of consistency is found among these four mass change time series derived separately from CSR, JPL, GSFC, and COST-G over the AIS and its subregions, with ICC values larger than 0.94. Such a consistency is reflected by the similarities shown at multiple temporal scales including the relatively long-term trend, monthly variation, annual variation and the interannual variations. Similar spatial patterns are also found among mass accelerations derived from the four GRACE/GRACE-FO grid products, i.e., the APIS and George V Land show a positive acceleration of approximately 3 Gt/yr², while the ASE and Wilkes Land have a negative acceleration of approximately −4 Gt/yr².

(2)

Significant differences are shown among the annual mass changes of the AIS during the period of 2016–2017. When excluding annual mass changes during 2016–2017, the ICC values among annual mass variations derived from these four datasets increase significantly over the AIS, WAIS and EAIS, respectively. This indicates that mascon and COST-G-based grid data during the late stage of GRACE mission has an important impact on quantifying the consistency among these four gridded data. However, over the APIS, the ICC value slightly decline. This reflects that the consistency among these four datasets in the cases excluding the years 2016 and 2017 is no better than that in the case including the years 2016 and 2017.

(3)

From 2016 to 2018, the interannual signals from JPL mascon and COST-G-based grid products showed significant differences with those from CSR/GSFC mascon data over the AIS. The interannual signals of JPL mascon display the feature of “mass increasing first and later decreasing”, while the interannual signals from CSR/GSFC products show relatively stable mass variations. The above differences are mainly caused by discrepancies among interannual mass variations over the EAIS at the late stage of GRACE mission.

This study not only suggests a clue to improving the consistency of mascon data and COST-G-based grid products in the future, but also provides a reference for selecting grid datasets in multidisciplinary applications.