Comparison of Terrestrial Water Storage Changes in the Tibetan Plateau and Its Surroundings Derived from Gravity Recovery and Climate Experiment (GRACE) Solutions of Different Processing Centers

Abstract

The GRACE twin satellite gravity mission from 2002 to 2017 has considerably improved investigations on global and regional hydrological changes. However, there are different GRACE solutions and products available which may yield different results for certain regions despite applying the same postprocessing and time span. This is especially the case for the Tibetan Plateau (TP) with its special hydrological conditions represented by localized but strong signals that can overlap or merge with signals inside the plateau, which can falsify the determination of terrestrial water storage (TWS) changes in the TP area. To investigate the effect of GRACE solution selection on inverted TWS changes, we analyze quantitatively the secular and monthly changes for 14 glacier areas and 10 water basins in and around the TP area that have been calculated from 16 different available GRACE solutions. Our analysis provides expectable results. While trend results from different spherical harmonic (SH) GRACE solutions match well, there are significant differences to and between mascon GRACE solutions. This is related to the different processing concepts of mascon solutions and their forced handling in our comparisons. SH solution time series match each other when mass changes are strong with a large amplitude and regular periodicity. However, for regions where small TWS changes are associated with small amplitudes, trends, and/or unstable signal periods, SH solutions can also yield different results. Such behavior is known from a time series analysis. Interestingly though, we find that the COST-G and ITSG SH GRACE solutions are closest to the average of all solutions. Therefore, these solutions appear to be preferable for TWS investigations in regions with highly variable hydrological conditions, such as in the Tibetan Plateau and its surroundings. This also indicates that combined solutions such as COST-G provide a promising pathway for an improved TWS analysis, which should be further elaborated.

1. Introduction

The Tibetan Plateau (TP) in Central Asia is a unique area. Geographically, it is both the highest and the largest plateau in the world. Hydrologically, it contains the largest ice fields outside of the Arctic and Antarctica, as well as a wide distribution of natural lakes and permafrost, so that it is often regarded as ‘the water tower of Asia’ [1,2,3,4,5,6,7]. The climatic conditions in the TP and its surroundings are governed by the Indian monsoon and the westerlies in the summer and winter, respectively, as well as the East Asian monsoon [3,8,9,10]. Global warming and changes in the atmospheric circulation patterns have led to severe hydrological changes in recent decades, such as continual lake expansion [1,11], glacier (and snow) retreat [12,13], changes in soil moisture [14,15], and permafrost degradation [6], ultimately increasing groundwater [16].

The Gravity Recovery and Climate Experiment (GRACE) twin-satellite mission is a very reliable and convenient tool to determine terrestrial water storage (TWS) changes in the TP as it helps to overcome the sparsity of ground measurements. The mission was launched in 2002, and the GRACE results were originally provided by three institutions, namely the Center of Space Research (CSR) in Austin, Texas, USA, the Jet Propulsion Laboratory (JPL) in Pasadena, California, USA, and the Geoforschungszentrum (GFZ) in Potsdam, Germany, in the form of spherical harmonic (SH) coefficients that are part of the so-called Level-2 products calculated from earlier processed Level-0, Level-1A, and Level-1B products; here, basically, binary encoded satellite measurements together with other data are converted, preprocessed, and combined to correctly obtain time-tagged and sample-rate-reduced results with appropriate units. Then, adequate postprocessing must be applied to calculate gravity changes and to extract the signal of interest. Over the last two decades, more institutions have started providing Level-2 and even Level-3 products. The latter are already postprocessed gravity changes which are ready for analysis. The large amount of more than a dozen various Level-2 and -3 products may confuse a potential user because each product is based on different processing strategies with different corrections. Moreover, results may show significant discrepancies as has been found for the TP [17,18]. Measurement noises, orbit errors, and different strategies for producing GRACE solutions have led to inconsistencies among different solutions. Furthermore, the special hydrological conditions that small TWS changes are surrounded by much larger glacier melting and groundwater extraction can disturb TWS signals inside the plateau by stronger surrounding TWS signals during a data inversion.

Xiang et al. [17] tested a large set of GRACE solution-filter combinations and mascon models to identify the best combination whose filtered results matched the produced (so-called) aggregated hydrology signals (AHS) of TWS changes based on independent hydrological observations, however, the tests were limited to a trend analysis because not enough reliable observations and model data were available. In addition, the comparison results were rather preliminary compared to the TWS changes in water basins. Therefore, on the basis of the results of Xiang et al. [17], we study the effects of the selection of a GRACE solution on basin-scale inverted TWS changes in the Tibetan Plateau and its surroundings. We select 14 glacier areas and 10 water basins (see Figure 1) according to Xiang et al. [19] and provide basin-scale inverted TWS changes time series. Note that our focus is a comparison of the different products to identify those with the best performance. We are not discussing the results of TWS changes in detail, nor do we compare them with the results of previous studies. In Section 2, the GRACE solutions, destriping filters, as well as the inversion approach are briefly introduced. We present and discuss the results in Section 3. Finally, we summarize our findings in Section 4.

2. Data and Methodology

We investigate GRACE Level-2 and Level-3 products, which we introduce in the next Section 2.1. The Level-2 SH solutions need dedicated processing with destriping filters to show the spatial TWS changes. This is explained in Section 2.2. For comparison with Level-3 mascon solutions, the TWS changes from the SH solutions must be inverted to basin scale, i.e., the special mascons shown in Figure 1. Our computation approach for this inversion is presented in Section 2.3.

2.1. GRACE Solutions

From the many different GRACE products that are currently available (see e.g., http://icgem.gfz-potsdam.de/series, accessed on 17 April 2023 for the SH solutions), we selected the 12 most commonly used SH solutions (Level-2 products) and four so-called mascon solutions (Level-3 products) (Table 1). All the products have different start and end dates but cover the time span between January 2003 and December 2015, therefore, we set this as our time span.

The 12 SH solutions are provided with different maximum degree/order (d/o) Stokes coefficients and need destriping and spatial smoothing filters to reduce the high-frequency noises and correlated errors (see Section 2.2). The common spectral range is from 2 to 60, and thus was used here. The glacial isostatic adjustment (GIA) effects were removed from the monthly Stokes coefficients according to the GIA model ICE-6G_C(VM5a) [20]. Considering the absence of degree-1 coefficients (C10, C11, and S11) and inaccuracy of C20 (degree 2 order 0) and C30 (degree 3 order 0), we complemented the GRACE SH solutions with newly released C10, C11, and S11 coefficients [21], and replaced the native GRACE C20 and C30 coefficients with the latest SLR-derived version [22]. We note that the C30 coefficients were replaced when the time series passed March 2012, where the SLR-derived C30 starts in the data set according to Loomis et al. [22].

The four mascon solutions provide gridded TWS changes. As they are Level-3 products, they can be used directly without further processing but have different accuracies and spatial resolutions due to different strategies in their development. For the comparison in our study, all four mascon solution grids were regridded to match the mascons outlined in Figure 1.

Table 1. Information of the 16 different GRACE solutions used in this study. The organizations are expressed in abbreviations. The resolution is maximum degree/order Stokes coefficients of different versions for SH solutions and spatial resolutions for mascon solutions.

GRACE Solution	Organization	Time Span	Resolution	Reference
ITSG	TU Graz	April 2002–June 2017	60, 96, 120	Kvas et al. [23]
CSR	UT CSR	April 2002–June 2017	60, 96	Bettadpur et al. [24]
COST-G	AIUB	April 2002–June 2017	90	Meyer et al. [25]
GFZ	GFZ	April 2002–June 2017	60, 96	Dahle et al. [26]
JPL	JPL	April 2002–June 2017	60, 96	Watkins et al. [27]
Tongji	TJU	April 20024–August 2016	96	Chen et al. [28]
WHU	WHU	August 2002–July 2016	96	Zhong et al. [29]
HUST	HUST	January 2003–July 2016	60, 90	Zhou et al. [30]
GRGS	CNES-GRGS	September 2002–May 2017	90	Lemoine et al. [31]
IGG	IGG	April 2002–July 2016	60	Wang et al. [32]
AIUB	AIUB	April 2002–June 2017	90	Darbeheshti et al. [33]
XISM	XISM&SSTC	April 2002–March 2016	60	Xiao et al. [34]
CSR_M	UT CSR	April 2002–June 2017	1°	Save et al. [35]
JPL_M	JPL	April 2002–June 2017	3°	Watkins et al. [27]
GSFC_M	NASA/GSFC	January 2003–July 2016	1°	Loomis et al. [36]
ANU_M	ANU	August 2002–July 2016	3°, 2°	Tregoning et al. [37]

Note: Organization abbreviations are defined as follows: TU Graz, Graz University of Technology; UT CSR, Center for Space Research, University of Texas at Austin; AIUB, Astronomical Institute University of Bern; GFZ, GFZ German Research Centre for Geosciences; JPL, NASA Jet Propulsion Laboratory; TJU, Tongji University; WHU, Wuhan University; HUST, Huazhong University of Science and Technology; CNES-GRGS, Centre National d’Etudes Spatiales, Groupe de Recherches de Géodésie Spatiale; IGG, Institute of Geodesy and Geophysics, Chinese Academy of Sciences; XISM&SSTC, Xian Research Institute of Surveying and Mapping and Space Star Technology Co., LTD.; NASA/GSFC, NASA Goddard Space Flight Center; ANU, Australian National University, Canberra, ACT, Australia.

Table 1. Information of the 16 different GRACE solutions used in this study. The organizations are expressed in abbreviations. The resolution is maximum degree/order Stokes coefficients of different versions for SH solutions and spatial resolutions for mascon solutions.

GRACE Solution	Organization	Time Span	Resolution	Reference
ITSG	TU Graz	April 2002–June 2017	60, 96, 120	Kvas et al. [23]
CSR	UT CSR	April 2002–June 2017	60, 96	Bettadpur et al. [24]
COST-G	AIUB	April 2002–June 2017	90	Meyer et al. [25]
GFZ	GFZ	April 2002–June 2017	60, 96	Dahle et al. [26]
JPL	JPL	April 2002–June 2017	60, 96	Watkins et al. [27]
Tongji	TJU	April 20024–August 2016	96	Chen et al. [28]
WHU	WHU	August 2002–July 2016	96	Zhong et al. [29]
HUST	HUST	January 2003–July 2016	60, 90	Zhou et al. [30]
GRGS	CNES-GRGS	September 2002–May 2017	90	Lemoine et al. [31]
IGG	IGG	April 2002–July 2016	60	Wang et al. [32]
AIUB	AIUB	April 2002–June 2017	90	Darbeheshti et al. [33]
XISM	XISM&SSTC	April 2002–March 2016	60	Xiao et al. [34]
CSR_M	UT CSR	April 2002–June 2017	1°	Save et al. [35]
JPL_M	JPL	April 2002–June 2017	3°	Watkins et al. [27]
GSFC_M	NASA/GSFC	January 2003–July 2016	1°	Loomis et al. [36]
ANU_M	ANU	August 2002–July 2016	3°, 2°	Tregoning et al. [37]

Note: Organization abbreviations are defined as follows: TU Graz, Graz University of Technology; UT CSR, Center for Space Research, University of Texas at Austin; AIUB, Astronomical Institute University of Bern; GFZ, GFZ German Research Centre for Geosciences; JPL, NASA Jet Propulsion Laboratory; TJU, Tongji University; WHU, Wuhan University; HUST, Huazhong University of Science and Technology; CNES-GRGS, Centre National d’Etudes Spatiales, Groupe de Recherches de Géodésie Spatiale; IGG, Institute of Geodesy and Geophysics, Chinese Academy of Sciences; XISM&SSTC, Xian Research Institute of Surveying and Mapping and Space Star Technology Co., LTD.; NASA/GSFC, NASA Goddard Space Flight Center; ANU, Australian National University, Canberra, ACT, Australia.

2.2. Destriping Filters

According to Xiang et al. [17], ‘S&W P3M8’ proposed by Swenson and Wahr [38] for destriping together with a 340 km averaging radius Gaussian smoothing filter [39] have been found to be the best filter combination for the identification of TWS changes in the Tibetan Plateau and its surroundings. It removes spatially correlated errors effectively.

‘S&W P3M8’ uses moving filtering windows [38], whereas the window width w is calculated using:

$$w=\max \left\{A{e}^{-\frac{m}{K}}+1, 5\right\},$$

(1)

dependent upon the order $m$ of the Stokes coefficients and the parameters $\left(A,K\right)$ taking the values (30, 10).

2.3. Computation of Mass Changes from Spherical Harmonic Solutions

We compare all solutions in 24 specially designed mascons for our basins under investigation. While Level-3 mascon solutions only need regridding to align to these 24 basins, the TWS changes from the SH solutions must be calculated first, and then inverted to our mascons. These two computation steps are presented in the following Section 2.3.1 and Section 2.3.2, respectively.

2.3.1. Terrestrial Water Storage Changes from Spherical Harmonic Coefficients

The mass change at any time is usually defined with respect to an unchanged earth mass, which can be calculated by the averages of the Stokes coefficients during the observation time span. The mass change (in equivalent water thickness (EWT)) at any time and at an arbitrary site with co-latitude $\theta$ and longitude $\phi$, can be calculated by a synthesis of SH coefficients [40]:

$$∆\mathrm{EWT}\left(\theta , \phi \right)=\frac{a{\rho }_{ave}}{3{\rho }_w}{\displaystyle \sum }_{l=0}^{lmax}{\displaystyle \sum }_{m=0}^l\frac{2l+1}{1+k_l}\times \left(∆c_{lm}\mathit{cos}m\phi +∆s_{lm}\mathit{sin}m\phi \right){\tilde{P}}_{lm}\left(\mathit{cos}\theta \right)$$

(2)

where $∆c_{lm}$ and $∆s_{lm}$ are the changes in Stokes coefficients from GRACE gravity SH solutions, $k_l$ is the degree $l$ elastic load Love number for potential perturbation [41], ${\tilde{P}}_{lm}\left(\mathit{cos}\theta \right)$ is the lth degree and mth order normalized associated Legendre polynomial ($lmax=60$), ${\rho }_{ave}$ is the average density of the earth (5.517 g/cm³), ${\rho }_w$ is the water density (1 g/cm³), and $a$ is the average radius of the Earth.

If the TWS changes from the SH solutions are simply used to estimate the total TWS change for a region of interest, the results are inevitably affected by signal leakages due to the truncation of higher harmonic degree terms and necessary filtering (e.g., using Gaussian filter [39]) and rescaling. Therefore, we used a mascon fitting treatment (Jacob et al. [42]), which could avoid the problem to a large degree.

2.3.2. Mascon Inverted Terrestrial Water Storage Changes

Following Jacob et al. [42] and Xiang et al. [19], the study area was divided into a total number of $M=700$ independent mascons, with 14 irregular glacier mascons (see Figure 1) combined with regular $2°\times 2°$ mascons. Each mascon is supposed to be covered by a uniformly distributed unit EWT, which can be decomposed into SH coefficients $∆c{\prime }_{lm}^i$ and $∆s{\prime }_{lm}^i$ ($i$ = 1, 2,..., $M$) with Equations (4) or (5) by Xiang et al. [16]. According to Jacob et al. [42] and Yi and Sun [8], the mass change in each mascon at any time minimizes the standard least squares merit function using the spectral domain inverse method:

$$min\left|\right|A^G-Bm{\left|\right|}_2^2,$$

(3)

where $A^G$ is a group of the changes in Stokes coefficients for a month or the trend of GRACE data during the study time span, and thus rewritten as ${\left({\omega }_1∆c_{1,0}, {\omega }_1∆c_{1,1},\cdots ,{\omega }_l∆c_{l,l},{\omega }_1∆s_{1,1}, {\omega }_2∆s_{2,1},\cdots ,{\omega }_l∆s_{l,l}\right)}^T$, excluding the coefficient for l = 0, with the length of ${\left(l+1\right)}^2-1$, which is 3720 for lmax = 60. Smoothing factor ${\omega }_l$ is the degree coefficient of the Jekeli’s Gaussian averaging function for Legendre expansion [39]. $B$ is the matrix composed of $M$ columns, with the jth column $B_{.,j}=A_j^{mas}$. $A_j^{mas}$ is a column vector like $A^G$, but for the Stokes coefficients decomposed from the jth mascon, which also considered ${\omega }_l$ matching with $A^G$, and rewritten as ${\left({\omega }_1∆c{\prime }_{1,0}^j, {\omega }_1∆c{\prime }_{1,1}^j,\cdots ,{\omega }_l∆c{\prime }_{l,l}^j,{\omega }_1∆s{\prime }_{1,1}^j, {\omega }_2∆s{\prime }_{2,1}^j,\cdots ,{\omega }_l∆s{\prime }_{l,l}^j\right)}^T$.

Singularity is always a problem in reverse problems in a geophysical inversion, and regularization is usually applied [8]. The regularized iterative algorithm (RIA) method is one simple and effective regularization approach which has been suggested by Li et al. [43] and Mao and Yang [44]. According to their studies, the RIA method can be expressed as:

$$\left(B^{T}B+\alpha I\right)m^k=B^T{A}^G+\alpha m^{k-1},$$

(4)

where $\alpha$ is a nonzero smoothing constant, $I$ is a unit matrix (same order as $B^{T}B$), and $k\left(=1, 2, 3, \dots \right)$ represents the number of iterations. The vector m is supposed to converge to the true solution [44]. The RIA performed very well in a comparison with three other regularization methods [19], and thus was preferred by us here.

Yi and Sun [8] have pointed out that the fitting residue for the regional area is heavily disturbed by the global signals using the spectral domain inverse method with GRACE SH solutions directly. Following Xiang et al. [16], we enlarged the area of concern by 5 degrees outwards and synthesized the grid TWS changes in these areas, then decomposed them into SH coefficients up to d/o 60, providing $A^G$ used in Equation (4).

3. Results and Discussion

TWS changes from SH solutions using Equation (2) are the intermediate results where we can verify the effectiveness of the destriping filter. This is examined first in Section 3.1.1. After that, the inversion processing frame with the RIA method using Equation (4) is adopted to provide basin-scale inverted TWS change trends and time series at the selected 14 glacier mascons and 10 water basins (Figure 1). We not only investigate the difference in their trends (Section 3.1.2), but also the time series (Section 3.2) of the 24 typical mass change regions to better understand the effects of GRACE solutions on the inverted results.

3.1. Effects on Terrestrial Water Storage Change Trends

In the next section, TWS change trends are first analyzed as derived directly from SH coefficients after application of the destriping filter. Thereafter, in Section 3.1.2, we investigate the effects of GRACE solution selection on the TWS change trends at the mascon level.

3.1.1. Effects on TWS Changes Derived from Spherical Harmonic Coefficients

For a first clear view on spatial details, we do not apply a Gaussian smoothing filter, although omitting it allows high-frequency noises spatially. Figure 2 shows GRACE observed gravity changes and patterns after destriping, representing a visual display and a check of the intermediate results based on which the subsequent mascon inversion processing is performed. So, these TWS change trends in Figure 2 are not the final results due to possible truncation and signal leakage effects and other residual errors in processing.

Figure 2 shows no obvious spatial stripes highlighting the effectiveness of ‘S&W P3M8’ for the SH solutions. Outside of the TP, we identify four strong negative signals. The first two negative signals are very strong and continuous from Northwest India to the Bengal Basin due to excessive use of groundwater, which merge visually into one signal with the negative signal caused by glacier melting from the Himalayas due to the distance being too close and signal leakage. The third is in the southeast of the TP and is mainly caused by serious glacier melting. The fourth one is in the Tien Shan due to increased ice melting [16,17,45]. A dumbbell-like positive signal is found throughout the northern part of the TP. One signal center is in the eastern TP around the three-rivers source region and the Qaidam Basin, and it is probably the result of an increase in groundwater and soil moisture [16,17]. The other center in the western TP around West Kunlun and Karakoram may be caused by a slight gain in glacier mass.

Figure 2. TWS change trends (in mm of EWT/year) from January 2003 to December 2015 from the 12 SH solutions. Destriping filter ‘S&W P3M8’ with truncation at d/o 60 is used. Note that the trends are without a Gaussian smoothing filter. The 14 black line marked glacier mascons together with the dashed lines delimit the TP and Tien Shan. The blue lines indicate the Yangtze River and the Yellow River, while the gray lines are the 0 contours. In subfigure (a), the purple lines, abbreviations and numbers are the same as in Figure 1.

Figure 2. TWS change trends (in mm of EWT/year) from January 2003 to December 2015 from the 12 SH solutions. Destriping filter ‘S&W P3M8’ with truncation at d/o 60 is used. Note that the trends are without a Gaussian smoothing filter. The 14 black line marked glacier mascons together with the dashed lines delimit the TP and Tien Shan. The blue lines indicate the Yangtze River and the Yellow River, while the gray lines are the 0 contours. In subfigure (a), the purple lines, abbreviations and numbers are the same as in Figure 1.

The TWS change trend signals in Figure 2a–l show similarity in signal patterns and amplitudes. In contrast, more different patterns and amplitudes appear in the TWS change trends derived from mascon solutions (Figure 3m–p), especially the signals in the TP.

3.1.2. Effects on Inverted Terrestrial Water Storage Changes

After inversion with the regularized iterative algorithm method, we obtain the inverted TWS changes for the 12 SH solutions which can also be compared with the four mascon solutions. Figure 3, Figure 4 and Figure 5 and Table 2, Table 3, Table 4 and Table 5 show and list the trends and time series in the TP and its surroundings, from January 2003 to December 2015, based on all 16 tested GRACE solutions. Figure 3 confirms that the inverted TWS change trends generally have high consistency with the corresponding results in Figure 2.

The inverted TWS change trends derived from the GRACE SH solutions (Figure 3a–l) show similar signal patterns with SH synthetic TWS change trends (Figure 2a–l), implying the effectiveness of the SH solutions from different agencies. However, there are also differences in the extent and amplitude of the trend signals. The differences get larger when comparing mascon solutions (Figure 3m–p) for signals inside and outside of the TP. To show the difference quantitatively, we calculate the Pearson’s correlation coefficients (PCCs) (upper triangular of

Table A1. Pearson’s correlation coefficients (PCCs) among the TWS change trends from the inverted solutions shown in Figure 3 and the average of all 16 solutions, marked as ‘AVE’. The PCCs are calculated for the whole study area (upper triangular) and for only inside the TP (lower triangular area).

PCC	COST-G	ITSG	GFZ	CSR	JPL	Tongji	HUST	WHU	IGG	AIUB	GRGS	XISM	CSR_M	JPL_M	GSFC_M	ANU_M	AVE
COST-G	1.0000	0.9961	0.9930	0.9919	0.9797	0.9840	0.9925	0.9747	0.9758	0.9925	0.9942	0.9566	0.8016	0.6372	0.7636	0.7695	0.9857
ITSG	0.9940	1.0000	0.9923	0.9892	0.9817	0.9854	0.9898	0.9752	0.9777	0.9925	0.9946	0.9546	0.7985	0.6346	0.7595	0.7696	0.9849
GFZ	0.9871	0.9876	1.0000	0.9863	0.9775	0.9814	0.9888	0.9696	0.9737	0.9884	0.9887	0.9494	0.7962	0.6326	0.7593	0.7607	0.9814
CSR	0.9845	0.9801	0.9718	1.0000	0.9745	0.9759	0.9894	0.9673	0.9739	0.9839	0.9870	0.9576	0.7923	0.6293	0.7476	0.7629	0.9796
JPL	0.9577	0.9616	0.9632	0.9504	1.0000	0.9675	0.9758	0.9571	0.9693	0.9758	0.9802	0.9516	0.7820	0.6184	0.7417	0.7597	0.9719
Tongji	0.9801	0.9740	0.9748	0.9566	0.9212	1.0000	0.9780	0.9882	0.9717	0.9774	0.9818	0.9560	0.8143	0.6502	0.7908	0.7632	0.9827
HUST	0.9859	0.9868	0.9800	0.9823	0.9570	0.9671	1.0000	0.9678	0.9748	0.9849	0.9899	0.9557	0.7947	0.6273	0.7531	0.7600	0.9804
WHU	0.9697	0.9561	0.9528	0.9459	0.9016	0.9830	0.9526	1.0000	0.9639	0.9650	0.9703	0.9468	0.8166	0.6535	0.7996	0.7550	0.9761
IGG	0.9710	0.9761	0.9800	0.9627	0.9647	0.9465	0.9672	0.9102	1.0000	0.9699	0.9758	0.9683	0.7875	0.6389	0.7567	0.7415	0.9736
AIUB	0.9908	0.9910	0.9853	0.9710	0.9583	0.9719	0.9796	0.9630	0.9718	1.0000	0.9896	0.9457	0.7879	0.6282	0.7513	0.7597	0.9785
GRGS	0.9921	0.9936	0.9859	0.9807	0.9680	0.9665	0.9838	0.9502	0.9763	0.9881	1.0000	0.9560	0.7972	0.6341	0.7567	0.7714	0.9835
XISM	0.9506	0.9532	0.9655	0.9392	0.9472	0.9284	0.9507	0.8850	0.9809	0.9494	0.9565	1.0000	0.8018	0.6520	0.7565	0.7504	0.9631
CSR_M	0.5298	0.5002	0.5173	0.4845	0.4218	0.6052	0.4831	0.6063	0.4560	0.5146	0.4859	0.4413	1.0000	0.8295	0.9137	0.8532	0.8760
JPL_M	0.3569	0.3247	0.3483	0.3052	0.2540	0.4325	0.2949	0.4377	0.3037	0.3471	0.3139	0.3011	0.7739	1.0000	0.7723	0.6898	0.7301
GSFC_M	0.6095	0.5792	0.5978	0.5500	0.4872	0.6895	0.5555	0.6907	0.5187	0.5911	0.5662	0.5059	0.9164	0.7574	1.0000	0.7978	0.8384
ANU_M	0.6064	0.6056	0.5862	0.5848	0.5289	0.6115	0.5659	0.6046	0.5609	0.6089	0.5898	0.5352	0.7273	0.5180	0.6966	1.0000	0.8307
AVE	0.9807	0.9739	0.9750	0.9586	0.9308	0.9825	0.9615	0.9681	0.9518	0.9750	0.9693	0.9335	0.6641	0.4948	0.7252	0.7038	1.0000

) among inverted TWS change trends in the study areas shown in Figure 3. We find that almost all the PCCs between SH solutions are larger than 0.95 while those PCCs between SH solutions and mascon solutions are all, partly very clearly, smaller than 0.85. Since the most noticeable differences appear in the TP (excluding the glacier melting regions, delimited with the red lines in Figure 3a), we also calculate the PCCs focusing on this area only. The results are listed in the lower triangular area of Table A1. Then, the differences with mascon solutions are even larger. Hence, SH solutions appear to depict the main characteristics of TWS change trends better and more consistently than mascon solutions.

Figure 3. Mascon inverted TWS change trends (in EWT/year) (a–l) with the regularized iterative algorithm method and (m–p) as provided by the solution center from January 2003 to December 2015. The subfigures correspond to those in Figure 2, respectively. Note that a 340 km averaging radius Gaussian smoothing filter is used when implementing the inversion for the 12 SH solutions (a–l). In subfigure (a), abbreviations and numbers are the same as in Figure 1. The 14 black line marked glacier mascons together with the dashed lines delimit the TP and Tien Shan. The red lines delimit the inner TP excluding glacier melting regions. The blue lines indicate the Yangtze River and the Yellow River, while the gray lines are the 0 contours.

Figure 3. Mascon inverted TWS change trends (in EWT/year) (a–l) with the regularized iterative algorithm method and (m–p) as provided by the solution center from January 2003 to December 2015. The subfigures correspond to those in Figure 2, respectively. Note that a 340 km averaging radius Gaussian smoothing filter is used when implementing the inversion for the 12 SH solutions (a–l). In subfigure (a), abbreviations and numbers are the same as in Figure 1. The 14 black line marked glacier mascons together with the dashed lines delimit the TP and Tien Shan. The red lines delimit the inner TP excluding glacier melting regions. The blue lines indicate the Yangtze River and the Yellow River, while the gray lines are the 0 contours.

3.2. Effects on Terrestrial Water Storage Change Time Series

We analyze the features of secular and seasonal signals from the monthly TWS changes for 14 glacier mascons and 10 selected water basins during the period from January 2003 to December 2015. We consider the trend, annual, semiannual, and 161 days aliasing variation (from the S2 semidiurnal solar tide) when implementing a least squares regression analysis on the time series. We use the average from all 16 GRACE solutions as a test benchmark to depict the difference of the time series quantitatively. In addition, we also investigate the difference between the inverted monthly TWS changes with their average derived from 12 SH solutions and between the mascon solutions with their average derived from four mascon solutions. We use PCCs and modified relative root mean square errors (defined by Equation (A2) and simply marked as MRRs here). PCCs and MRRs evaluate the correlation and relative difference between results derived from the GRACE solutions and the test benchmarks. We calculate PCCs both without and with removal of secular trends and annual amplitudes from the time series. The latter is done to remove large signals that overprint the absolute errors of each time series, and thus may affect the statistics favorably.

The time series of the inverted TWS changes for 14 glacier mascons are shown in Figure 4. The secular trends and annual amplitudes are listed in Table 2, and the two indices are listed in Table 3 (MRRs),

Table A2. Pearson’s correlation coefficients (PCCs) between the average of all 16 GRACE solutions (PCC1) and 12 SH solutions (for SH solutions) or four mascon solutions (for mascons) (PCC2) and TWS change time series at 14 glacier mascons derived from each of the 16 different GRACE SH solutions.

No.	Mascon	COST-G		ITSG		GFZ		CSR		JPL		Tongji		HUST		WHU
		PCC1	PCC2	PCC1	PCC2	PCC1	PCC2	PCC1	PCC2	PCC1	PCC2	PCC1	PCC2	PCC1	PCC2	PCC1	PCC2
1	Nyainqentanglha	0.99	0.99	0.99	0.99	0.98	0.99	0.97	0.98	0.95	0.95	0.96	0.96	0.97	0.98	0.97	0.95
2	E. Himalayas	0.96	0.96	0.96	0.96	0.97	0.97	0.89	0.89	0.85	0.86	0.95	0.95	0.93	0.93	0.94	0.94
3		0.98	0.99	0.98	0.98	0.98	0.98	0.96	0.96	0.89	0.90	0.97	0.97	0.94	0.94	0.96	0.96
4	W. Himalayas	0.97	0.98	0.98	0.98	0.93	0.94	0.87	0.89	0.90	0.92	0.95	0.94	0.94	0.94	0.97	0.95
5		0.96	0.97	0.97	0.97	0.93	0.93	0.91	0.93	0.47	0.49	0.92	0.89	0.88	0.91	0.89	0.88
6	Karakoram	0.99	0.99	0.98	0.99	0.97	0.98	0.96	0.97	0.80	0.81	0.94	0.93	0.93	0.93	0.95	0.94
7	Hindukush	0.97	0.96	0.98	0.98	0.96	0.96	0.95	0.95	0.85	0.85	0.96	0.96	0.95	0.95	0.94	0.93
8	Pamir	0.98	0.99	0.96	0.97	0.88	0.88	0.91	0.91	0.91	0.92	0.97	0.96	0.93	0.94	0.98	0.96
9	Tien Shan	0.99	0.99	0.99	0.98	0.91	0.91	0.96	0.96	0.91	0.91	0.97	0.97	0.94	0.95	0.97	0.97
10		0.98	0.98	0.98	0.98	0.89	0.90	0.94	0.95	0.94	0.94	0.94	0.94	0.94	0.94	0.97	0.96
11		0.99	0.99	0.99	0.99	0.97	0.97	0.96	0.96	0.97	0.97	0.97	0.97	0.97	0.97	0.98	0.98
12		0.98	0.99	0.98	0.98	0.88	0.89	0.93	0.94	0.90	0.90	0.96	0.96	0.92	0.93	0.97	0.96
13	West Kunlun	0.96	0.96	0.94	0.93	0.86	0.86	0.87	0.87	0.71	0.72	0.94	0.94	0.79	0.80	0.91	0.91
14	Qilian	0.90	0.91	0.77	0.78	0.69	0.68	0.74	0.76	0.63	0.65	0.75	0.73	0.52	0.52	0.65	0.60
No.	Mascon	IGG		AIUB		GRGS		XISM		CSR_M		JPL_M		GSFC_M		ANU_M
		PCC1	PCC2	PCC1	PCC2	PCC1	PCC2	PCC1	PCC2	PCC1	PCC2	PCC1	PCC2	PCC1	PCC2	PCC1	PCC2
1	Nyainqentanglha	0.97	0.97	0.97	0.97	0.98	0.98	0.93	0.94	0.97	0.99	0.91	0.98	0.94	0.98	0.95	0.93
2	E. Himalayas	0.93	0.93	0.93	0.94	0.95	0.96	0.88	0.88	0.95	0.99	0.93	0.96	0.95	0.98	0.87	0.92
3		0.96	0.96	0.95	0.95	0.98	0.98	0.94	0.94	0.97	0.98	0.94	0.96	0.95	0.96	0.88	0.92
4	W. Himalayas	0.93	0.94	0.93	0.93	0.96	0.96	0.89	0.90	0.96	0.98	0.89	0.96	0.95	0.99	0.91	0.95
5		0.88	0.88	0.91	0.93	0.93	0.94	0.84	0.85	0.78	0.98	0.62	0.91	0.79	0.97	0.85	0.92
6	Karakoram	0.95	0.96	0.92	0.92	0.97	0.97	0.93	0.93	0.87	0.98	0.70	0.88	0.93	0.94	0.74	0.94
7	Hindukush	0.94	0.94	0.94	0.95	0.97	0.97	0.88	0.88	0.97	0.99	0.96	0.98	0.97	0.98	0.94	0.96
8	Pamir	0.92	0.93	0.90	0.91	0.91	0.92	0.88	0.90	0.97	0.99	0.97	0.99	0.95	0.98	0.94	0.97
9	Tien Shan	0.97	0.97	0.93	0.93	0.97	0.97	0.91	0.91	0.96	0.98	0.89	0.96	0.93	0.94	0.91	0.97
10		0.93	0.93	0.94	0.94	0.96	0.96	0.87	0.88	0.95	0.99	0.92	0.97	0.91	0.94	0.91	0.95
11		0.96	0.97	0.97	0.97	0.99	0.98	0.95	0.95	0.98	0.99	0.97	0.98	0.97	0.97	0.95	0.97
12		0.93	0.93	0.93	0.94	0.95	0.95	0.90	0.90	0.96	0.98	0.96	0.97	0.93	0.96	0.88	0.95
13	West Kunlun	0.83	0.84	0.85	0.85	0.92	0.92	0.70	0.72	0.91	0.96	0.82	0.93	0.90	0.91	0.33	0.48
14	Qilian	0.66	0.68	0.41	0.43	0.65	0.65	0.68	0.69	0.54	0.75	0.30	0.67	0.23	0.53	0.36	0.46

(PCCs), and

Table A3. Similar to Table A2, but showing the results for the PCCs calculated after the annual signals and trends are removed.

No.	Mascon	COST-G		ITSG		GFZ		CSR		JPL		Tongji		HUST		WHU
		PCC1	PCC2	PCC1	PCC2	PCC1	PCC2	PCC1	PCC2	PCC1	PCC2	PCC1	PCC2	PCC1	PCC2	PCC1	PCC2
1	Nyainqentanglha	0.95	0.96	0.95	0.95	0.90	0.91	0.86	0.88	0.72	0.73	0.83	0.83	0.87	0.89	0.82	0.80
2	E. Himalayas	0.83	0.84	0.77	0.77	0.84	0.85	0.43	0.43	0.59	0.61	0.76	0.76	0.68	0.70	0.70	0.67
3		0.89	0.90	0.84	0.84	0.85	0.86	0.79	0.80	0.57	0.60	0.75	0.74	0.75	0.77	0.80	0.77
4	W. Himalayas	0.93	0.94	0.94	0.94	0.84	0.85	0.76	0.79	0.81	0.83	0.85	0.84	0.85	0.84	0.88	0.84
5		0.95	0.95	0.95	0.94	0.88	0.87	0.87	0.88	0.45	0.47	0.86	0.84	0.84	0.85	0.84	0.82
6	Karakoram	0.97	0.97	0.96	0.96	0.93	0.93	0.90	0.91	0.68	0.69	0.83	0.82	0.83	0.83	0.87	0.85
7	Hindukush	0.89	0.88	0.93	0.93	0.84	0.85	0.82	0.82	0.68	0.70	0.86	0.86	0.81	0.82	0.80	0.77
8	Pamir	0.96	0.97	0.93	0.93	0.79	0.80	0.83	0.84	0.84	0.86	0.93	0.92	0.89	0.90	0.94	0.92
9	Tien Shan	0.97	0.97	0.94	0.93	0.72	0.73	0.85	0.86	0.70	0.72	0.88	0.87	0.82	0.83	0.87	0.85
10		0.96	0.96	0.96	0.95	0.83	0.84	0.89	0.89	0.86	0.88	0.88	0.87	0.87	0.88	0.92	0.91
11		0.90	0.90	0.91	0.91	0.84	0.83	0.73	0.75	0.80	0.80	0.77	0.77	0.75	0.76	0.84	0.83
12		0.95	0.97	0.93	0.94	0.75	0.79	0.85	0.87	0.77	0.78	0.90	0.90	0.81	0.83	0.89	0.86
13	West Kunlun	0.91	0.91	0.84	0.84	0.68	0.68	0.73	0.74	0.57	0.59	0.85	0.83	0.67	0.67	0.78	0.76
14	Qilian	0.90	0.90	0.77	0.77	0.67	0.66	0.73	0.74	0.63	0.65	0.74	0.72	0.51	0.51	0.64	0.60
No.	Mascon	IGG		AIUB		GRGS		XISM		CSR_M		JPL_M		GSFC_M		ANU_M
		PCC1	PCC2	PCC1	PCC2	PCC1	PCC2	PCC1	PCC2	PCC1	PCC2	PCC1	PCC2	PCC1	PCC2	PCC1	PCC2
1	Nyainqentanglha	0.81	0.80	0.87	0.88	0.88	0.88	0.79	0.79	0.85	0.94	0.79	0.94	0.82	0.91	0.63	0.79
2	E. Himalayas	0.67	0.67	0.78	0.79	0.82	0.83	0.60	0.60	0.65	0.89	0.52	0.84	0.68	0.85	0.57	0.71
3		0.70	0.71	0.68	0.68	0.83	0.84	0.71	0.72	0.81	0.88	0.74	0.87	0.81	0.91	0.49	0.70
4	W. Himalayas	0.83	0.84	0.82	0.83	0.87	0.88	0.72	0.74	0.87	0.94	0.75	0.95	0.83	0.94	0.77	0.86
5		0.79	0.78	0.88	0.89	0.89	0.90	0.72	0.72	0.81	0.94	0.83	0.93	0.79	0.91	0.74	0.88
6	Karakoram	0.91	0.91	0.81	0.81	0.92	0.93	0.84	0.85	0.77	0.95	0.64	0.90	0.81	0.89	0.71	0.91
7	Hindukush	0.83	0.85	0.82	0.83	0.90	0.91	0.75	0.76	0.87	0.96	0.90	0.97	0.88	0.94	0.80	0.89
8	Pamir	0.87	0.88	0.82	0.83	0.84	0.84	0.80	0.83	0.92	0.98	0.92	0.99	0.90	0.96	0.85	0.91
9	Tien Shan	0.85	0.85	0.84	0.84	0.89	0.89	0.71	0.72	0.88	0.96	0.81	0.93	0.86	0.88	0.76	0.94
10		0.86	0.87	0.89	0.89	0.91	0.92	0.82	0.83	0.91	0.98	0.88	0.96	0.88	0.92	0.82	0.94
11		0.78	0.79	0.78	0.77	0.84	0.85	0.73	0.73	0.80	0.85	0.67	0.83	0.78	0.81	0.69	0.84
12		0.81	0.81	0.84	0.85	0.86	0.86	0.71	0.70	0.89	0.95	0.90	0.94	0.86	0.91	0.76	0.90
13	West Kunlun	0.71	0.73	0.68	0.68	0.81	0.82	0.60	0.63	0.77	0.91	0.61	0.86	0.75	0.78	0.64	0.83
14	Qilian	0.70	0.71	0.40	0.42	0.68	0.67	0.66	0.67	0.59	0.76	0.50	0.76	0.41	0.58	0.40	0.79

(PCCs after removal of trend and amplitudes). Similarly, the results for 10 selected water basins are shown in Figure 5, and Table 4, Table 5,

Table A4. Similar to Table A2, but showing the results for PCCs at 10 selected water basins.

Area	COST-G		ITSG		GFZ		CSR		JPL		Tongji		HUST		WHU
	PCC1	PCC2	PCC1	PCC2	PCC1	PCC2	PCC1	PCC2	PCC1	PCC2	PCC1	PCC2	PCC1	PCC2	PCC1	PCC2
NWIA	1.00	1.00	0.99	0.99	0.99	0.99	0.98	0.98	0.98	0.98	0.99	0.99	0.99	0.99	0.98	0.98
BBN	1.00	1.00	1.00	1.00	1.00	1.00	0.99	0.99	0.97	0.97	1.00	1.00	0.99	1.00	0.99	1.00
TRM	0.97	0.97	0.94	0.95	0.89	0.90	0.91	0.92	0.85	0.85	0.90	0.91	0.93	0.93	0.95	0.95
QDM	0.99	0.99	0.98	0.98	0.97	0.97	0.95	0.95	0.96	0.96	0.94	0.94	0.93	0.94	0.94	0.94
ENDR	0.97	0.98	0.95	0.96	0.95	0.96	0.89	0.91	0.91	0.90	0.88	0.91	0.90	0.94	0.91	0.94
YLRS	0.97	0.98	0.96	0.97	0.90	0.93	0.89	0.89	0.92	0.92	0.91	0.92	0.90	0.91	0.91	0.88
YZRS	0.98	0.98	0.98	0.98	0.98	0.98	0.94	0.93	0.94	0.95	0.94	0.95	0.94	0.94	0.95	0.96
MKRS	0.95	0.97	0.91	0.93	0.89	0.92	0.81	0.83	0.69	0.74	0.82	0.81	0.73	0.76	0.79	0.79
SWRS	0.98	0.99	0.98	0.98	0.96	0.96	0.93	0.95	0.94	0.94	0.92	0.93	0.95	0.96	0.94	0.94
YZBR	0.99	0.99	0.99	0.99	0.99	0.99	0.97	0.98	0.97	0.97	0.98	0.98	0.99	0.99	0.96	0.96
Area	IGG		AIUB		GRGS		XISM		CSR_M		JPL_M		GSFC_M		ANU_M
	PCC1	PCC2	PCC1	PCC2	PCC1	PCC2	PCC1	PCC2	PCC1	PCC2	PCC1	PCC2	PCC1	PCC2	PCC1	PCC2
NWIA	0.97	0.97	0.99	0.99	0.99	0.99	0.96	0.96	0.99	0.99	0.98	0.99	0.98	0.98	0.97	0.97
BBN	0.98	0.98	0.99	0.99	1.00	1.00	0.98	0.98	0.99	1.00	0.99	1.00	0.99	1.00	0.99	0.99
TRM	0.88	0.88	0.84	0.85	0.88	0.90	0.81	0.78	0.94	0.94	0.92	0.91	0.84	0.81	0.63	0.79
QDM	0.92	0.92	0.92	0.93	0.94	0.94	0.80	0.82	0.93	0.96	0.89	0.93	0.95	0.97	0.86	0.89
ENDR	0.86	0.90	0.90	0.90	0.88	0.89	0.62	0.61	0.92	0.91	0.86	0.96	0.84	0.97	0.49	0.80
YLRS	0.89	0.89	0.91	0.91	0.91	0.93	0.75	0.78	0.80	0.96	0.88	0.94	0.82	0.93	0.65	0.79
YZRS	0.95	0.95	0.90	0.89	0.96	0.96	0.88	0.88	0.84	0.91	0.84	0.95	0.91	0.90	0.73	0.84
MKRS	0.81	0.82	0.84	0.85	0.86	0.89	0.77	0.79	0.17	0.94	0.06	0.93	0.24	0.91	0.42	0.56
SWRS	0.93	0.92	0.95	0.96	0.96	0.96	0.86	0.87	0.93	0.98	0.87	0.95	0.88	0.94	0.70	0.76
YZBR	0.98	0.98	0.98	0.98	0.98	0.98	0.95	0.95	0.98	0.99	0.96	0.97	0.97	0.98	0.91	0.93

, and

Table A5. Similar to Table A3, but showing the results for PCCs at 10 selected water basins.

Area	COST-G		ITSG		GFZ		CSR		JPL		Tongji		HUST		WHU
	PCC1	PCC2	PCC1	PCC2	PCC1	PCC2	PCC1	PCC2	PCC1	PCC2	PCC1	PCC2	PCC1	PCC2	PCC1	PCC2
NWIA	0.99	0.99	0.98	0.98	0.99	0.99	0.95	0.96	0.96	0.96	0.98	0.98	0.97	0.97	0.97	0.97
BBN	0.99	0.99	0.97	0.98	0.98	0.98	0.95	0.95	0.76	0.78	0.96	0.96	0.95	0.95	0.96	0.95
TRM	0.96	0.96	0.91	0.92	0.88	0.89	0.87	0.87	0.80	0.81	0.83	0.84	0.88	0.89	0.90	0.90
QDM	0.96	0.97	0.91	0.91	0.87	0.88	0.78	0.81	0.83	0.84	0.82	0.80	0.75	0.78	0.88	0.86
ENDR	0.97	0.97	0.92	0.93	0.92	0.93	0.83	0.84	0.84	0.84	0.87	0.87	0.89	0.90	0.89	0.90
YLRS	0.96	0.97	0.95	0.95	0.87	0.89	0.83	0.84	0.88	0.88	0.89	0.89	0.86	0.87	0.89	0.88
YZRS	0.92	0.92	0.90	0.91	0.90	0.90	0.76	0.75	0.75	0.76	0.81	0.81	0.79	0.80	0.80	0.81
MKRS	0.93	0.94	0.87	0.86	0.83	0.83	0.71	0.71	0.59	0.61	0.76	0.74	0.64	0.67	0.72	0.68
SWRS	0.96	0.97	0.95	0.95	0.89	0.90	0.88	0.90	0.84	0.84	0.85	0.86	0.88	0.89	0.88	0.87
YZBR	0.96	0.97	0.95	0.95	0.94	0.95	0.86	0.87	0.78	0.78	0.92	0.91	0.91	0.93	0.87	0.87
Area	IGG		AIUB		GRGS		XISM		CSR_M		JPL_M		GSFC_M		ANU_M
	PCC1	PCC2	PCC1	PCC2	PCC1	PCC2	PCC1	PCC2	PCC1	PCC2	PCC1	PCC2	PCC1	PCC2	PCC1	PCC2
NWIA	0.93	0.93	0.97	0.97	0.97	0.97	0.89	0.90	0.96	0.98	0.94	0.98	0.96	0.97	0.93	0.94
BBN	0.81	0.82	0.93	0.94	0.97	0.96	0.83	0.83	0.94	0.97	0.93	0.97	0.95	0.95	0.87	0.92
TRM	0.81	0.82	0.81	0.83	0.80	0.83	0.68	0.65	0.94	0.92	0.87	0.88	0.81	0.83	0.63	0.82
QDM	0.80	0.81	0.73	0.76	0.78	0.79	0.55	0.57	0.85	0.87	0.83	0.89	0.71	0.76	0.52	0.76
ENDR	0.85	0.85	0.85	0.85	0.87	0.87	0.69	0.68	0.86	0.84	0.84	0.85	0.84	0.87	0.50	0.73
YLRS	0.84	0.84	0.87	0.88	0.91	0.91	0.76	0.76	0.89	0.91	0.87	0.91	0.84	0.88	0.73	0.87
YZRS	0.85	0.86	0.72	0.72	0.86	0.87	0.72	0.73	0.83	0.87	0.82	0.93	0.81	0.78	0.66	0.85
MKRS	0.69	0.71	0.74	0.76	0.79	0.79	0.73	0.75	0.56	0.82	0.40	0.76	0.62	0.88	0.52	0.67
SWRS	0.78	0.77	0.89	0.90	0.91	0.91	0.79	0.79	0.82	0.93	0.74	0.89	0.83	0.89	0.60	0.77
YZBR	0.86	0.86	0.91	0.91	0.91	0.92	0.80	0.80	0.90	0.92	0.83	0.92	0.89	0.91	0.73	0.84

.

Figure 4 exhibits consistent signals of approximate trends and periodic fluctuations, however, with the difference from each other at every month, displaying the diversity of TWS change estimates due to the GRACE solution selection. Only a few glacier mascons display somewhat disordered time series curves, e.g., Figure 4i,k,m,n. Here, when comparing the three different test benchmarks visually (Figure A1), the average of four mascon solutions (black line) slightly deviates from the other two lines. Despite that, mascon solutions still perform well when considering the errors (Figure A1).

Focusing on the secular trends and annual amplitudes of the time series in Table 2, the trends and amplitudes of TWS changes derived from SH solutions differ less from each other than those from mascon solutions. The latter vary remarkably or yield opposite signs for trend values of certain regions with relatively small or/and controversial trends, which means large divergences between SH solutions and mascon solutions, and between different mascon solutions. For further analysis, we classify these values in four intervals using one, two, and three standard deviations (1-STD, 2-STD, and 3-STD) and above. We can clearly see that most of the significantly deviating secular trends and annual amplitudes concern mascon solutions, implying huge variability and inconsistency of the TWS changes from mascon solutions themselves. One reason for this difference is that the mascon solutions are not aligned with the basins of our studies, whereas the mascon solutions themselves have different spatial resolutions. We recall that we regridded the mascon solutions to align with glacier and water basin mascons.

Combining the results of Figure 4 and Table 2, time series curves with larger trends and amplitudes with obvious periodicity show more consistent features, and vice versa; the differences of time series at every month are more distinct when the trends and amplitudes are small with no apparent regular periodicity (such as Figure 4i,k,m,n). This is an expected result for a time series analysis, which is further supported when looking at PCCs (Table A2). Most of them are over 0.9, showing strong correlations with small differences due to different solutions. This changes after removing the annual amplitudes and secular trends (Table A3). The PCCs become smaller and show more differences between solutions. Compared to the average of all solutions, the PCCs for COST-G and ITSG are generally greater than the PCCs of other solutions (Table A2 and Table A3), while, when looking at MRRs (Table 3), the corresponding MRRs for COST-G and ITSG are usually smaller than those of other solutions. That COST-G is close to the mean of all solutions is likely because COST-G is based on a weighted combination of individual SH solutions generated by different agencies [25], where ITSG and CSR hold high weights which are usually larger than 0.5 or even sometimes as large as 0.8 (see Figure A2). Again, we note that the discreteness of the inverted TWS changes derived from different GRACE data is more obvious by MRRs (Table 3) when the annual amplitudes are small with less periodicity for various reasons. This is, for example, the case for the central (mascon 9) and eastern (mascon 11) part of Tien Shan, West Kunlun (mascon 13), and Qilian (mascon 14) (Figure 4i,k,m,n) whose MRRs values are usually much larger. However, there are also other separate cases with large MRRs due to solution differences.

Figure 4. Mascon inverted TWS change time series with the regularized iterative algorithm method (in Gt/year) derived from 16 solutions at 14 glacier mascons (a–n) from January 2003 to December 2015. Mascon names can be found in each subfigure.

Figure 4. Mascon inverted TWS change time series with the regularized iterative algorithm method (in Gt/year) derived from 16 solutions at 14 glacier mascons (a–n) from January 2003 to December 2015. Mascon names can be found in each subfigure.

Table 2. Trends and annual amplitudes of inverted TWS changes derived from 16 solutions at 14 glacier mascons. Units are in Gt/year for trends and in Gt for annual amplitude. The ‘AVE’ column in green represents average of all 16 values, while the ‘STD’ column in light green is the standard deviation. Values within the 1-STD (one standard deviation) bounds are in black, within the 2-STD (two standard deviations) bounds in blue, within the 3-STD (three standard deviations) bounds in red, and above that in purple and bold.

No.	Mascon	Secular Trends
		COST-G	ITSG	GFZ	CSR	JPL	Tongji	HUST	WHU	IGG	AIUB	GRGS	XISM	CSR_M	JPL_M	GSFC_M	ANU_M	AVE	STD
1	Nyainqentanglha	−5.85	−6.06	−5.85	−5.82	−6.26	−4.82	−6.03	−4.52	−6.09	−5.98	−5.98	−5.32	−4.24	−5.54	−3.01	−4.45	−5.36	0.88
2	E. Himalayas	−1.87	−1.99	−1.91	−2.08	−1.70	−1.92	−2.04	−1.98	−2.09	−1.71	−1.96	−1.91	−1.77	−1.36	−1.60	−2.18	−1.88	0.20
3		−2.87	−2.98	−3.03	−2.93	−3.06	−2.86	−2.71	−2.25	−3.16	−2.95	−3.06	−3.04	−1.37	−1.40	−1.09	−3.06	−2.61	0.67
4	W. Himalayas	−1.55	−1.59	−1.40	−1.44	−1.44	−1.57	−1.68	−1.66	−1.65	−1.49	−1.77	−1.57	−1.20	−1.51	−1.26	−2.22	−1.56	0.22
5		0.03	−0.09	−0.05	0.10	0.02	−0.48	0.21	−0.22	−0.22	0.13	0.10	−0.20	−1.08	−1.29	−0.96	−0.85	−0.30	0.47
6	Karakoram	1.11	1.20	1.19	1.16	0.82	0.88	1.06	0.95	1.08	0.98	0.90	0.97	−0.19	−0.18	0.28	−0.88	0.71	0.60
7	Hindukush	−0.65	−0.50	−0.47	−0.48	−0.77	−0.57	−0.55	−0.23	−0.24	−0.41	−0.70	−0.19	−0.24	−0.12	−0.12	−1.11	−0.46	0.26
8	Pamir	−1.25	−1.02	−0.69	−1.47	−1.10	−1.16	−1.23	−1.18	−1.94	−1.06	−1.35	−0.21	−1.41	−1.86	−0.81	−1.36	−1.19	0.40
9	Tien Shan	−2.07	−2.02	−1.98	−2.16	−2.21	−2.09	−2.04	−1.98	−2.21	−1.90	−2.09	−2.26	−1.04	−0.63	−0.78	−1.93	−1.84	0.51
10		−1.26	−1.26	−1.16	−1.25	−1.30	−1.46	−1.37	−1.25	−1.20	−1.21	−1.25	−1.09	−0.81	−0.52	−0.47	−1.70	−1.16	0.31
11		−2.74	−2.80	−2.56	−2.88	−2.66	−2.71	−2.88	−2.45	−2.88	−2.77	−2.96	−2.97	−1.77	−1.69	−1.40	−2.43	−2.53	0.47
12		−0.29	−0.29	−0.27	−0.26	−0.24	−0.33	−0.30	−0.26	−0.34	−0.31	−0.28	−0.37	−0.29	−0.17	−0.21	−0.27	−0.28	0.05
13	West Kunlun	0.65	0.76	0.85	0.62	0.63	0.67	0.45	0.66	0.61	0.85	0.63	0.49	0.39	0.89	0.60	−0.08	0.60	0.22
14	Qilian	0.01	−0.03	0.07	0.07	0.01	0.12	0.05	0.12	−0.18	−0.10	−0.07	0.03	0.03	0.13	0.45	−0.33	0.02	0.16
No.	Mascon	Annual Amplitudes
		COST-G	ITSG	GFZ	CSR	JPL	Tongji	HUST	WHU	IGG	AIUB	GRGS	XISM	CSR_M	JPL_M	GSFC_M	ANU_M	AVE	STD
1	Nyainqentanglha	8.52	9.39	9.14	8.81	10.62	9.35	9.32	9.99	9.31	8.58	8.51	8.44	11.69	20.55	11.31	8.30	10.11	2.87
2	E. Himalayas	11.05	11.40	10.70	11.36	10.42	13.48	11.55	15.20	12.36	11.30	9.78	9.21	9.00	11.15	9.10	5.58	10.79	2.06
3		15.84	16.26	16.22	15.74	17.42	17.27	14.52	17.40	17.02	15.92	15.73	14.02	8.91	9.64	8.12	8.05	14.26	3.36
4	W. Himalayas	4.01	3.98	3.46	3.87	3.66	3.13	3.97	4.10	4.10	4.45	4.12	3.05	3.71	5.40	3.27	2.22	3.78	0.68
5		8.90	8.66	8.96	8.89	4.70	7.23	9.05	5.45	8.25	8.71	9.62	9.63	4.77	2.32	4.63	6.72	7.28	2.17
6	Karakoram	14.58	14.54	14.49	14.53	12.93	13.28	15.15	11.03	13.08	15.10	14.52	14.03	8.78	4.01	9.24	9.60	12.43	3.01
7	Hindukush	16.09	15.76	16.27	16.52	15.10	14.01	16.01	11.84	14.87	16.25	16.08	14.52	12.23	15.77	12.13	13.92	14.84	1.54
8	Pamir	12.69	13.13	14.62	12.43	12.77	14.26	12.27	14.57	12.39	13.05	12.67	11.18	18.00	23.66	16.47	19.17	14.58	3.16
9	Tien Shan	3.43	3.25	2.89	3.46	3.12	2.81	3.41	2.19	3.21	3.81	2.75	2.07	1.78	1.06	1.83	1.17	2.64	0.82
10		6.43	6.34	6.26	7.00	7.19	5.87	6.16	5.73	5.70	6.58	6.71	4.63	5.41	3.90	5.52	5.31	5.92	0.83
11		2.36	2.30	3.37	2.25	2.46	3.05	2.26	2.76	1.83	2.63	2.08	1.89	0.81	1.23	1.81	2.46	2.22	0.61
12		0.92	0.91	1.19	0.98	1.14	0.94	0.95	0.86	0.90	0.96	0.89	0.99	1.21	0.71	1.43	1.84	1.05	0.26
13	West Kunlun	3.76	3.49	3.64	3.74	4.36	4.18	3.66	4.19	3.62	4.25	3.42	2.80	1.59	1.86	2.11	0.89	3.22	1.02
14	Qilian	0.74	0.70	0.91	1.09	0.60	0.52	0.60	0.34	0.59	1.10	0.35	1.40	0.23	0.60	0.27	1.45	0.72	0.37

Table 2. Trends and annual amplitudes of inverted TWS changes derived from 16 solutions at 14 glacier mascons. Units are in Gt/year for trends and in Gt for annual amplitude. The ‘AVE’ column in green represents average of all 16 values, while the ‘STD’ column in light green is the standard deviation. Values within the 1-STD (one standard deviation) bounds are in black, within the 2-STD (two standard deviations) bounds in blue, within the 3-STD (three standard deviations) bounds in red, and above that in purple and bold.

No.	Mascon	Secular Trends
		COST-G	ITSG	GFZ	CSR	JPL	Tongji	HUST	WHU	IGG	AIUB	GRGS	XISM	CSR_M	JPL_M	GSFC_M	ANU_M	AVE	STD
1	Nyainqentanglha	−5.85	−6.06	−5.85	−5.82	−6.26	−4.82	−6.03	−4.52	−6.09	−5.98	−5.98	−5.32	−4.24	−5.54	−3.01	−4.45	−5.36	0.88
2	E. Himalayas	−1.87	−1.99	−1.91	−2.08	−1.70	−1.92	−2.04	−1.98	−2.09	−1.71	−1.96	−1.91	−1.77	−1.36	−1.60	−2.18	−1.88	0.20
3		−2.87	−2.98	−3.03	−2.93	−3.06	−2.86	−2.71	−2.25	−3.16	−2.95	−3.06	−3.04	−1.37	−1.40	−1.09	−3.06	−2.61	0.67
4	W. Himalayas	−1.55	−1.59	−1.40	−1.44	−1.44	−1.57	−1.68	−1.66	−1.65	−1.49	−1.77	−1.57	−1.20	−1.51	−1.26	−2.22	−1.56	0.22
5		0.03	−0.09	−0.05	0.10	0.02	−0.48	0.21	−0.22	−0.22	0.13	0.10	−0.20	−1.08	−1.29	−0.96	−0.85	−0.30	0.47
6	Karakoram	1.11	1.20	1.19	1.16	0.82	0.88	1.06	0.95	1.08	0.98	0.90	0.97	−0.19	−0.18	0.28	−0.88	0.71	0.60
7	Hindukush	−0.65	−0.50	−0.47	−0.48	−0.77	−0.57	−0.55	−0.23	−0.24	−0.41	−0.70	−0.19	−0.24	−0.12	−0.12	−1.11	−0.46	0.26
8	Pamir	−1.25	−1.02	−0.69	−1.47	−1.10	−1.16	−1.23	−1.18	−1.94	−1.06	−1.35	−0.21	−1.41	−1.86	−0.81	−1.36	−1.19	0.40
9	Tien Shan	−2.07	−2.02	−1.98	−2.16	−2.21	−2.09	−2.04	−1.98	−2.21	−1.90	−2.09	−2.26	−1.04	−0.63	−0.78	−1.93	−1.84	0.51
10		−1.26	−1.26	−1.16	−1.25	−1.30	−1.46	−1.37	−1.25	−1.20	−1.21	−1.25	−1.09	−0.81	−0.52	−0.47	−1.70	−1.16	0.31
11		−2.74	−2.80	−2.56	−2.88	−2.66	−2.71	−2.88	−2.45	−2.88	−2.77	−2.96	−2.97	−1.77	−1.69	−1.40	−2.43	−2.53	0.47
12		−0.29	−0.29	−0.27	−0.26	−0.24	−0.33	−0.30	−0.26	−0.34	−0.31	−0.28	−0.37	−0.29	−0.17	−0.21	−0.27	−0.28	0.05
13	West Kunlun	0.65	0.76	0.85	0.62	0.63	0.67	0.45	0.66	0.61	0.85	0.63	0.49	0.39	0.89	0.60	−0.08	0.60	0.22
14	Qilian	0.01	−0.03	0.07	0.07	0.01	0.12	0.05	0.12	−0.18	−0.10	−0.07	0.03	0.03	0.13	0.45	−0.33	0.02	0.16
No.	Mascon	Annual Amplitudes
		COST-G	ITSG	GFZ	CSR	JPL	Tongji	HUST	WHU	IGG	AIUB	GRGS	XISM	CSR_M	JPL_M	GSFC_M	ANU_M	AVE	STD
1	Nyainqentanglha	8.52	9.39	9.14	8.81	10.62	9.35	9.32	9.99	9.31	8.58	8.51	8.44	11.69	20.55	11.31	8.30	10.11	2.87
2	E. Himalayas	11.05	11.40	10.70	11.36	10.42	13.48	11.55	15.20	12.36	11.30	9.78	9.21	9.00	11.15	9.10	5.58	10.79	2.06
3		15.84	16.26	16.22	15.74	17.42	17.27	14.52	17.40	17.02	15.92	15.73	14.02	8.91	9.64	8.12	8.05	14.26	3.36
4	W. Himalayas	4.01	3.98	3.46	3.87	3.66	3.13	3.97	4.10	4.10	4.45	4.12	3.05	3.71	5.40	3.27	2.22	3.78	0.68
5		8.90	8.66	8.96	8.89	4.70	7.23	9.05	5.45	8.25	8.71	9.62	9.63	4.77	2.32	4.63	6.72	7.28	2.17
6	Karakoram	14.58	14.54	14.49	14.53	12.93	13.28	15.15	11.03	13.08	15.10	14.52	14.03	8.78	4.01	9.24	9.60	12.43	3.01
7	Hindukush	16.09	15.76	16.27	16.52	15.10	14.01	16.01	11.84	14.87	16.25	16.08	14.52	12.23	15.77	12.13	13.92	14.84	1.54
8	Pamir	12.69	13.13	14.62	12.43	12.77	14.26	12.27	14.57	12.39	13.05	12.67	11.18	18.00	23.66	16.47	19.17	14.58	3.16
9	Tien Shan	3.43	3.25	2.89	3.46	3.12	2.81	3.41	2.19	3.21	3.81	2.75	2.07	1.78	1.06	1.83	1.17	2.64	0.82
10		6.43	6.34	6.26	7.00	7.19	5.87	6.16	5.73	5.70	6.58	6.71	4.63	5.41	3.90	5.52	5.31	5.92	0.83
11		2.36	2.30	3.37	2.25	2.46	3.05	2.26	2.76	1.83	2.63	2.08	1.89	0.81	1.23	1.81	2.46	2.22	0.61
12		0.92	0.91	1.19	0.98	1.14	0.94	0.95	0.86	0.90	0.96	0.89	0.99	1.21	0.71	1.43	1.84	1.05	0.26
13	West Kunlun	3.76	3.49	3.64	3.74	4.36	4.18	3.66	4.19	3.62	4.25	3.42	2.80	1.59	1.86	2.11	0.89	3.22	1.02
14	Qilian	0.74	0.70	0.91	1.09	0.60	0.52	0.60	0.34	0.59	1.10	0.35	1.40	0.23	0.60	0.27	1.45	0.72	0.37

Table 3. Modified relative root mean square errors (MRRs) between the average of all 16 GRACE solutions (MRR1) and 12 SH solutions (for SH solutions) or four mascon solutions (for mascons) (MRR2) and TWS change time series at 14 glacier mascons derived from each of the 16 different GRACE SH solutions.

No.	Mascon	COST-G		ITSG		GFZ		CSR		JPL		Tongji		HUST		WHU
		MRR1	MRR2	MRR1	MRR2	MRR1	MRR2	MRR1	MRR2	MRR1	MRR2	MRR1	MRR2	MRR1	MRR2	MRR1	MRR2
1	Nyainqentanglha	0.42	0.33	0.43	0.38	0.47	0.44	0.65	0.60	0.89	0.91	0.60	0.70	0.67	0.63	0.62	0.83
2	E. Himalayas	0.32	0.27	0.30	0.28	0.28	0.25	0.54	0.51	0.62	0.56	0.43	0.37	0.46	0.41	0.50	0.44
3		0.23	0.17	0.27	0.21	0.28	0.21	0.35	0.28	0.66	0.55	0.33	0.28	0.42	0.36	0.31	0.29
4	W. Himalayas	0.49	0.40	0.40	0.37	0.74	0.70	1.13	1.03	0.94	0.85	0.65	0.67	0.79	0.77	0.55	0.65
5		0.40	0.27	0.32	0.25	0.54	0.43	0.61	0.46	1.66	1.46	0.45	0.46	0.69	0.53	0.46	0.49
6	Karakoram	0.25	0.13	0.28	0.17	0.33	0.22	0.36	0.26	0.79	0.68	0.35	0.32	0.48	0.39	0.28	0.32
7	Hindukush	0.26	0.25	0.20	0.18	0.28	0.26	0.33	0.31	0.57	0.54	0.24	0.24	0.29	0.28	0.29	0.32
8	Pamir	0.20	0.18	0.26	0.28	0.51	0.56	0.44	0.47	0.43	0.45	0.26	0.32	0.36	0.38	0.21	0.29
9	Tien Shan	0.68	0.39	0.68	0.53	1.52	1.25	1.22	0.90	1.72	1.35	0.81	0.67	1.28	1.01	0.74	0.74
10		0.38	0.30	0.37	0.32	0.80	0.72	0.59	0.52	0.61	0.53	0.50	0.50	0.56	0.51	0.35	0.40
11		0.82	0.63	0.85	0.63	1.13	0.99	1.72	1.34	1.39	1.15	1.22	1.05	1.59	1.24	0.90	0.94
12		0.31	0.26	0.32	0.32	0.83	0.86	0.55	0.57	0.70	0.76	0.50	0.51	0.62	0.64	0.39	0.48
13	West Kunlun	0.45	0.34	0.56	0.46	0.94	0.77	0.77	0.63	1.66	1.35	0.53	0.44	1.01	0.84	0.61	0.53
14	Qilian	1.68	1.21	2.23	1.82	3.70	2.97	4.49	3.44	3.48	2.79	2.42	2.09	4.96	4.04	2.46	2.30
No.	Mascon	IGG		AIUB		GRGS		XISM		CSR_M		JPL_M		GSFC_M		ANU_M
		MRR1	MRR2	MRR1	MRR2	MRR1	MRR2	MRR1	MRR2	MRR1	MRR2	MRR1	MRR2	MRR1	MRR2	MRR1	MRR2
1	Nyainqentanglha	0.66	0.68	0.74	0.71	0.55	0.52	0.87	0.89	0.67	0.16	1.12	0.71	1.00	0.44	0.78	0.55
2	E. Himalayas	0.46	0.41	0.39	0.35	0.31	0.28	0.51	0.49	0.32	0.12	0.37	0.30	0.33	0.18	0.49	0.43
3		0.42	0.33	0.38	0.32	0.26	0.20	0.41	0.36	0.46	0.23	0.45	0.31	0.52	0.31	0.48	0.69
4	W. Himalayas	0.85	0.77	0.81	0.76	0.67	0.61	0.99	0.94	0.66	0.49	1.02	0.68	0.67	0.43	1.01	0.91
5		0.63	0.55	0.57	0.43	0.58	0.43	0.81	0.69	0.65	0.27	0.84	0.61	0.63	0.30	0.54	0.64
6	Karakoram	0.33	0.26	0.51	0.42	0.30	0.22	0.42	0.35	0.46	0.19	0.68	0.45	0.39	0.34	0.60	0.48
7	Hindukush	0.32	0.30	0.33	0.30	0.24	0.22	0.47	0.44	0.24	0.13	0.25	0.24	0.27	0.18	0.29	0.26
8	Pamir	0.42	0.44	0.46	0.49	0.43	0.46	0.52	0.53	0.32	0.11	0.64	0.29	0.31	0.22	0.42	0.22
9	Tien Shan	1.11	0.83	1.39	1.12	0.86	0.66	1.79	1.42	1.39	0.68	1.99	1.49	1.69	1.31	1.41	2.87
10		0.57	0.52	0.57	0.52	0.47	0.42	0.75	0.70	0.48	0.19	0.67	0.38	0.63	0.42	0.65	0.76
11		1.62	1.27	1.43	1.18	1.19	0.86	1.98	1.57	1.68	0.84	1.83	1.07	2.18	1.70	1.50	2.87
12		0.63	0.66	0.62	0.64	0.47	0.51	0.79	0.86	0.42	0.27	0.58	0.44	0.56	0.32	1.00	0.62
13	West Kunlun	0.94	0.76	1.15	0.92	0.57	0.48	1.13	0.95	0.64	0.53	0.78	1.44	0.55	0.94	1.25	1.89
14	Qilian	4.18	3.24	5.61	4.55	2.80	2.34	4.80	3.73	2.16	2.36	2.63	3.19	3.84	7.00	4.43	9.67

Table 3. Modified relative root mean square errors (MRRs) between the average of all 16 GRACE solutions (MRR1) and 12 SH solutions (for SH solutions) or four mascon solutions (for mascons) (MRR2) and TWS change time series at 14 glacier mascons derived from each of the 16 different GRACE SH solutions.

No.	Mascon	COST-G		ITSG		GFZ		CSR		JPL		Tongji		HUST		WHU
		MRR1	MRR2	MRR1	MRR2	MRR1	MRR2	MRR1	MRR2	MRR1	MRR2	MRR1	MRR2	MRR1	MRR2	MRR1	MRR2
1	Nyainqentanglha	0.42	0.33	0.43	0.38	0.47	0.44	0.65	0.60	0.89	0.91	0.60	0.70	0.67	0.63	0.62	0.83
2	E. Himalayas	0.32	0.27	0.30	0.28	0.28	0.25	0.54	0.51	0.62	0.56	0.43	0.37	0.46	0.41	0.50	0.44
3		0.23	0.17	0.27	0.21	0.28	0.21	0.35	0.28	0.66	0.55	0.33	0.28	0.42	0.36	0.31	0.29
4	W. Himalayas	0.49	0.40	0.40	0.37	0.74	0.70	1.13	1.03	0.94	0.85	0.65	0.67	0.79	0.77	0.55	0.65
5		0.40	0.27	0.32	0.25	0.54	0.43	0.61	0.46	1.66	1.46	0.45	0.46	0.69	0.53	0.46	0.49
6	Karakoram	0.25	0.13	0.28	0.17	0.33	0.22	0.36	0.26	0.79	0.68	0.35	0.32	0.48	0.39	0.28	0.32
7	Hindukush	0.26	0.25	0.20	0.18	0.28	0.26	0.33	0.31	0.57	0.54	0.24	0.24	0.29	0.28	0.29	0.32
8	Pamir	0.20	0.18	0.26	0.28	0.51	0.56	0.44	0.47	0.43	0.45	0.26	0.32	0.36	0.38	0.21	0.29
9	Tien Shan	0.68	0.39	0.68	0.53	1.52	1.25	1.22	0.90	1.72	1.35	0.81	0.67	1.28	1.01	0.74	0.74
10		0.38	0.30	0.37	0.32	0.80	0.72	0.59	0.52	0.61	0.53	0.50	0.50	0.56	0.51	0.35	0.40
11		0.82	0.63	0.85	0.63	1.13	0.99	1.72	1.34	1.39	1.15	1.22	1.05	1.59	1.24	0.90	0.94
12		0.31	0.26	0.32	0.32	0.83	0.86	0.55	0.57	0.70	0.76	0.50	0.51	0.62	0.64	0.39	0.48
13	West Kunlun	0.45	0.34	0.56	0.46	0.94	0.77	0.77	0.63	1.66	1.35	0.53	0.44	1.01	0.84	0.61	0.53
14	Qilian	1.68	1.21	2.23	1.82	3.70	2.97	4.49	3.44	3.48	2.79	2.42	2.09	4.96	4.04	2.46	2.30
No.	Mascon	IGG		AIUB		GRGS		XISM		CSR_M		JPL_M		GSFC_M		ANU_M
		MRR1	MRR2	MRR1	MRR2	MRR1	MRR2	MRR1	MRR2	MRR1	MRR2	MRR1	MRR2	MRR1	MRR2	MRR1	MRR2
1	Nyainqentanglha	0.66	0.68	0.74	0.71	0.55	0.52	0.87	0.89	0.67	0.16	1.12	0.71	1.00	0.44	0.78	0.55
2	E. Himalayas	0.46	0.41	0.39	0.35	0.31	0.28	0.51	0.49	0.32	0.12	0.37	0.30	0.33	0.18	0.49	0.43
3		0.42	0.33	0.38	0.32	0.26	0.20	0.41	0.36	0.46	0.23	0.45	0.31	0.52	0.31	0.48	0.69
4	W. Himalayas	0.85	0.77	0.81	0.76	0.67	0.61	0.99	0.94	0.66	0.49	1.02	0.68	0.67	0.43	1.01	0.91
5		0.63	0.55	0.57	0.43	0.58	0.43	0.81	0.69	0.65	0.27	0.84	0.61	0.63	0.30	0.54	0.64
6	Karakoram	0.33	0.26	0.51	0.42	0.30	0.22	0.42	0.35	0.46	0.19	0.68	0.45	0.39	0.34	0.60	0.48
7	Hindukush	0.32	0.30	0.33	0.30	0.24	0.22	0.47	0.44	0.24	0.13	0.25	0.24	0.27	0.18	0.29	0.26
8	Pamir	0.42	0.44	0.46	0.49	0.43	0.46	0.52	0.53	0.32	0.11	0.64	0.29	0.31	0.22	0.42	0.22
9	Tien Shan	1.11	0.83	1.39	1.12	0.86	0.66	1.79	1.42	1.39	0.68	1.99	1.49	1.69	1.31	1.41	2.87
10		0.57	0.52	0.57	0.52	0.47	0.42	0.75	0.70	0.48	0.19	0.67	0.38	0.63	0.42	0.65	0.76
11		1.62	1.27	1.43	1.18	1.19	0.86	1.98	1.57	1.68	0.84	1.83	1.07	2.18	1.70	1.50	2.87
12		0.63	0.66	0.62	0.64	0.47	0.51	0.79	0.86	0.42	0.27	0.58	0.44	0.56	0.32	1.00	0.62
13	West Kunlun	0.94	0.76	1.15	0.92	0.57	0.48	1.13	0.95	0.64	0.53	0.78	1.44	0.55	0.94	1.25	1.89
14	Qilian	4.18	3.24	5.61	4.55	2.80	2.34	4.80	3.73	2.16	2.36	2.63	3.19	3.84	7.00	4.43	9.67

For the 10 selected water basins, the time series with stable signal periods and large amplitudes show very good agreement and small differences between the time series from different solutions, i.e., Northwest India (NWIA), Bengal Basin (BBN), and Yarlung Zangbo River Basin (YZBR) (Figure 5a,b,j, respectively). However, for the Tarim Basin (TRM) and other basin areas with weak TWS change signals with small amplitudes, trends and/or no stable signal periods in the TP, the difference is more obvious. This is the case for the Qaidam Basin (QDM), Endorheic Region of the TP (ENDR), Yellow River source region (YLRS), Yangtze River source region (YZRS), Mekong River source region (MKRS), Salween River source region (SWRS), and Yarlung Zangbo River Basin (YZBR) (Figure 5c–i). Looking at Figure A3, the comparison of the three solution averages also exhibits larger deviations for the average from four mascon solutions (black line) for basin areas with weak TWS change signals, although they agree well within errors. An inspection of the secular trends and annual amplitudes in Table 4 shows that most of the larger deviating trends and annual amplitudes are found for the four mascon solutions. In addition, larger differences appear between SH solutions and mascon solutions and between different mascon solutions, mirroring the performance in glacier mascon regions. We recall, however, that mascon solutions were regridded to align with the glacier and water basin mascons of our study. According to Table 5, Table A4, and Table A5, again, the COST-G and ITSG are closest to the average of all solutions and have smaller MRRs than others. This is especially the case when considering all basins including smaller ones. However, we note that the difference between PCCs without and with removal of trends and amplitudes is not as large as that for the glacier basins.

Larger MRRs appear along with time series with small amplitudes and less periodicity. Therefore, in the TP and its surroundings, the effects of GRACE solutions on inverted terrestrial water storage changes are more pronounced when the signals are weak and amplitudes are small with no stable signal periods, while the effects are relatively weak when the signals are strong with stable periods. However, this behavior is expected for a time series.

Figure 5. Similar to Figure 4, but showing results for 10 selected water basins: (a) NWIA, Northwest India; (b) BBN, Bengal Basin; (c) TRM, Tarim Basin; (d) QDM, Qaidam Basin; (e) ENDR, Endorheic Region of the TP; (f) YLRS, Yellow River source region; (g) YZRS, Yangtze River source Region; (h) MKRS, Mekong River source region; (i) SWRS, Salween River source region; (j) YZBR Yarlung Zangbo River Basin.

Figure 5. Similar to Figure 4, but showing results for 10 selected water basins: (a) NWIA, Northwest India; (b) BBN, Bengal Basin; (c) TRM, Tarim Basin; (d) QDM, Qaidam Basin; (e) ENDR, Endorheic Region of the TP; (f) YLRS, Yellow River source region; (g) YZRS, Yangtze River source Region; (h) MKRS, Mekong River source region; (i) SWRS, Salween River source region; (j) YZBR Yarlung Zangbo River Basin.

Table 4. Trends and annual amplitudes of inverted TWS changes derived from 16 solutions at 10 selected water basins. Units are in Gt/year for trends and in Gt for annual amplitude. The ‘AVE’ column in green represents average of all 16 values, while the ‘STD’ column in light green is the standard deviation. Values within the 1-STD (one standard deviation) bounds are in black, within the 2-STD (two standard deviations) bounds in blue, within the 3-STD (three standard deviations) bounds in red, and above that in purple and bold.

Area	Secular Trend
	COST-G	ITSG	GFZ	CSR	JPL	Tongji	HUST	WHU	IGG	AIUB	GRGS	XISM	CSR_M	JPL_M	GSFC_M	ANU_M	AVE	STD
NWIA	−6.07	−5.79	−5.80	−5.85	−5.03	−5.86	−6.44	−5.23	−6.87	−5.77	−6.47	−6.46	−7.50	−8.07	−5.97	−8.47	−6.35	0.96
BBN	−4.71	−4.43	−4.73	−4.60	−2.92	−4.62	−4.74	−3.97	−4.61	−4.51	−4.50	−4.23	−4.35	−4.34	−4.32	−3.57	−4.32	0.48
TRM	−2.39	−2.08	−1.31	−2.11	−1.02	−2.81	−2.68	−2.52	−4.31	−1.98	−2.52	−5.38	−3.49	−3.31	−1.16	−3.48	−2.66	1.15
QDM	2.20	2.27	2.44	2.21	1.82	2.09	2.11	1.85	1.83	2.18	1.97	2.11	1.63	1.82	3.09	2.71	2.15	0.37
ENDR	1.68	1.67	1.75	1.52	2.18	0.95	1.10	1.35	0.83	1.85	1.43	0.86	3.20	4.59	5.21	4.24	2.15	1.39
YLRS	0.79	0.82	0.96	0.76	0.89	0.63	0.83	0.52	0.81	0.72	0.71	1.07	0.53	0.51	0.64	0.29	0.72	0.19
YZRS	1.70	1.70	1.62	1.66	1.57	1.31	1.65	1.42	1.41	1.67	1.61	1.42	0.58	0.51	1.19	0.79	1.36	0.40
MKRS	0.20	0.22	0.21	0.23	0.22	0.12	0.20	0.15	0.16	0.21	0.22	0.17	−0.44	−0.37	−0.24	−0.12	0.07	0.23
SWRS	−0.96	−1.01	−0.95	−0.90	−0.75	−0.83	−0.98	−0.73	−1.04	−1.00	−0.97	−0.86	−0.89	−1.03	−0.51	−0.46	−0.87	0.18
YZBR	−4.36	−4.50	−4.33	−4.47	−3.43	−4.17	−4.53	−3.92	−4.56	−4.30	−4.51	−4.09	−4.27	−3.06	−3.43	−5.14	−4.19	0.52
Area	Annual Amplitudes
	COST-G	ITSG	GFZ	CSR	JPL	Tongji	HUST	WHU	IGG	AIUB	GRGS	XISM	CSR_M	JPL_M	GSFC_M	ANU_M	AVE	STD
NWIA	23.22	22.74	22.18	22.08	21.04	24.77	23.34	25.30	23.49	23.82	23.00	20.76	30.20	36.45	31.50	24.48	24.90	4.24
BBN	76.98	76.26	76.53	77.32	67.07	73.23	76.78	68.02	75.79	77.52	75.79	69.30	72.41	69.46	65.52	64.75	72.67	4.60
TRM	15.44	15.02	17.12	15.59	15.21	17.26	14.50	15.79	12.82	14.08	14.09	14.02	9.54	12.00	17.94	19.16	14.97	2.36
QDM	2.07	2.27	2.17	2.21	1.49	2.06	2.25	3.69	2.18	2.18	1.92	5.57	2.67	4.29	2.29	4.13	2.72	1.10
ENDR	13.92	15.38	14.60	16.31	13.21	16.30	17.53	17.40	15.53	14.81	10.78	2.38	12.76	11.58	7.89	5.37	12.86	4.35
YLRS	1.31	1.34	1.08	1.47	1.02	1.02	1.16	1.88	0.67	1.53	1.95	2.60	3.71	1.86	3.74	2.57	1.81	0.92
YZRS	5.71	5.78	5.39	6.20	5.46	4.84	5.75	4.85	5.56	5.33	5.38	4.51	3.33	2.13	2.04	2.70	4.69	1.36
MKRS	2.08	2.09	2.13	2.20	2.12	1.31	1.77	0.97	2.11	2.19	1.96	1.83	1.45	1.14	1.33	0.36	1.69	0.54
SWRS	1.56	1.91	1.51	1.60	1.78	1.61	1.94	2.00	1.74	1.72	1.20	0.21	2.08	4.15	1.76	0.88	1.73	0.80
YZBR	12.50	13.46	12.44	12.99	11.95	15.23	13.81	17.75	14.03	13.12	10.98	8.67	13.94	14.29	12.94	5.93	12.75	2.65

Table 4. Trends and annual amplitudes of inverted TWS changes derived from 16 solutions at 10 selected water basins. Units are in Gt/year for trends and in Gt for annual amplitude. The ‘AVE’ column in green represents average of all 16 values, while the ‘STD’ column in light green is the standard deviation. Values within the 1-STD (one standard deviation) bounds are in black, within the 2-STD (two standard deviations) bounds in blue, within the 3-STD (three standard deviations) bounds in red, and above that in purple and bold.

Area	Secular Trend
	COST-G	ITSG	GFZ	CSR	JPL	Tongji	HUST	WHU	IGG	AIUB	GRGS	XISM	CSR_M	JPL_M	GSFC_M	ANU_M	AVE	STD
NWIA	−6.07	−5.79	−5.80	−5.85	−5.03	−5.86	−6.44	−5.23	−6.87	−5.77	−6.47	−6.46	−7.50	−8.07	−5.97	−8.47	−6.35	0.96
BBN	−4.71	−4.43	−4.73	−4.60	−2.92	−4.62	−4.74	−3.97	−4.61	−4.51	−4.50	−4.23	−4.35	−4.34	−4.32	−3.57	−4.32	0.48
TRM	−2.39	−2.08	−1.31	−2.11	−1.02	−2.81	−2.68	−2.52	−4.31	−1.98	−2.52	−5.38	−3.49	−3.31	−1.16	−3.48	−2.66	1.15
QDM	2.20	2.27	2.44	2.21	1.82	2.09	2.11	1.85	1.83	2.18	1.97	2.11	1.63	1.82	3.09	2.71	2.15	0.37
ENDR	1.68	1.67	1.75	1.52	2.18	0.95	1.10	1.35	0.83	1.85	1.43	0.86	3.20	4.59	5.21	4.24	2.15	1.39
YLRS	0.79	0.82	0.96	0.76	0.89	0.63	0.83	0.52	0.81	0.72	0.71	1.07	0.53	0.51	0.64	0.29	0.72	0.19
YZRS	1.70	1.70	1.62	1.66	1.57	1.31	1.65	1.42	1.41	1.67	1.61	1.42	0.58	0.51	1.19	0.79	1.36	0.40
MKRS	0.20	0.22	0.21	0.23	0.22	0.12	0.20	0.15	0.16	0.21	0.22	0.17	−0.44	−0.37	−0.24	−0.12	0.07	0.23
SWRS	−0.96	−1.01	−0.95	−0.90	−0.75	−0.83	−0.98	−0.73	−1.04	−1.00	−0.97	−0.86	−0.89	−1.03	−0.51	−0.46	−0.87	0.18
YZBR	−4.36	−4.50	−4.33	−4.47	−3.43	−4.17	−4.53	−3.92	−4.56	−4.30	−4.51	−4.09	−4.27	−3.06	−3.43	−5.14	−4.19	0.52
Area	Annual Amplitudes
	COST-G	ITSG	GFZ	CSR	JPL	Tongji	HUST	WHU	IGG	AIUB	GRGS	XISM	CSR_M	JPL_M	GSFC_M	ANU_M	AVE	STD
NWIA	23.22	22.74	22.18	22.08	21.04	24.77	23.34	25.30	23.49	23.82	23.00	20.76	30.20	36.45	31.50	24.48	24.90	4.24
BBN	76.98	76.26	76.53	77.32	67.07	73.23	76.78	68.02	75.79	77.52	75.79	69.30	72.41	69.46	65.52	64.75	72.67	4.60
TRM	15.44	15.02	17.12	15.59	15.21	17.26	14.50	15.79	12.82	14.08	14.09	14.02	9.54	12.00	17.94	19.16	14.97	2.36
QDM	2.07	2.27	2.17	2.21	1.49	2.06	2.25	3.69	2.18	2.18	1.92	5.57	2.67	4.29	2.29	4.13	2.72	1.10
ENDR	13.92	15.38	14.60	16.31	13.21	16.30	17.53	17.40	15.53	14.81	10.78	2.38	12.76	11.58	7.89	5.37	12.86	4.35
YLRS	1.31	1.34	1.08	1.47	1.02	1.02	1.16	1.88	0.67	1.53	1.95	2.60	3.71	1.86	3.74	2.57	1.81	0.92
YZRS	5.71	5.78	5.39	6.20	5.46	4.84	5.75	4.85	5.56	5.33	5.38	4.51	3.33	2.13	2.04	2.70	4.69	1.36
MKRS	2.08	2.09	2.13	2.20	2.12	1.31	1.77	0.97	2.11	2.19	1.96	1.83	1.45	1.14	1.33	0.36	1.69	0.54
SWRS	1.56	1.91	1.51	1.60	1.78	1.61	1.94	2.00	1.74	1.72	1.20	0.21	2.08	4.15	1.76	0.88	1.73	0.80
YZBR	12.50	13.46	12.44	12.99	11.95	15.23	13.81	17.75	14.03	13.12	10.98	8.67	13.94	14.29	12.94	5.93	12.75	2.65

Table 5. Similar to Table 3, but showing the results for the MRRs at 10 selected water basins.

Area	COST-G		ITSG		GFZ		CSR		JPL		Tongji		HUST		WHU
	MRR1	MRR2	MRR1	MRR2	MRR1	MRR2	MRR1	MRR2	MRR1	MRR2	MRR1	MRR2	MRR1	MRR2	MRR1	MRR2
NWIA	0.13	0.12	0.20	0.20	0.18	0.16	0.28	0.26	0.28	0.26	0.20	0.21	0.24	0.26	0.27	0.26
BBN	0.06	0.05	0.07	0.06	0.07	0.06	0.10	0.09	0.19	0.18	0.07	0.07	0.10	0.09	0.10	0.10
TRM	0.35	0.30	0.51	0.44	0.66	0.58	0.62	0.56	0.79	0.73	0.73	0.66	0.55	0.50	0.48	0.43
QDM	0.65	0.50	0.99	0.83	1.46	1.19	1.63	1.31	1.37	1.16	1.71	1.47	1.77	1.43	1.57	1.39
ENDR	0.34	0.23	0.48	0.35	0.47	0.38	0.74	0.57	0.70	0.61	0.77	0.57	0.72	0.50	0.63	0.44
YLRS	1.29	1.08	1.48	1.36	2.25	2.09	2.34	2.51	2.24	2.30	1.70	1.85	2.39	2.37	1.63	2.22
YZRS	0.47	0.29	0.49	0.31	0.43	0.30	0.78	0.61	0.79	0.58	0.52	0.48	0.77	0.58	0.48	0.42
MKRS	0.60	0.31	0.72	0.46	0.83	0.52	1.25	0.87	1.96	1.39	0.78	0.69	1.45	1.05	0.72	0.72
SWRS	0.69	0.50	0.70	0.61	0.84	0.79	1.17	1.04	1.02	1.04	1.12	1.11	0.99	0.89	0.85	0.98
YZBR	0.21	0.17	0.21	0.19	0.21	0.20	0.38	0.34	0.39	0.38	0.29	0.27	0.29	0.25	0.46	0.42
Area	IGG		AIUB		GRGS		XISM		CSR_M		JPL_M		GSFC_M		ANU_M
	MRR1	MRR2	MRR1	MRR2	MRR1	MRR2	MRR1	MRR2	MRR1	MRR2	MRR1	MRR2	MRR1	MRR2	MRR1	MRR2
NWIA	0.35	0.37	0.24	0.25	0.23	0.24	0.43	0.42	0.37	0.16	0.55	0.25	0.32	0.26	0.49	0.35
BBN	0.17	0.17	0.11	0.10	0.07	0.07	0.17	0.17	0.10	0.08	0.12	0.08	0.11	0.08	0.15	0.10
TRM	0.84	0.78	0.92	0.83	0.72	0.64	1.23	1.19	0.47	0.58	0.55	0.68	0.81	1.08	1.58	1.58
QDM	1.92	1.55	2.02	1.65	1.62	1.32	3.40	2.77	1.78	2.15	2.17	2.31	2.48	2.63	3.37	3.89
ENDR	0.81	0.60	0.84	0.70	0.68	0.57	1.10	0.99	0.58	1.15	0.90	0.90	1.07	1.00	1.58	1.89
YLRS	2.08	2.26	1.94	2.08	2.05	2.00	3.67	3.75	2.46	0.48	2.05	0.51	2.49	0.67	3.37	1.01
YZRS	0.55	0.45	0.99	0.80	0.54	0.40	0.83	0.70	0.89	0.80	0.98	0.69	0.64	1.07	1.08	1.60
MKRS	1.11	0.80	1.16	0.80	0.84	0.57	1.39	0.99	1.67	0.84	1.60	0.69	1.45	0.75	1.26	1.57
SWRS	1.21	1.23	1.10	1.00	0.90	0.81	1.42	1.44	0.96	0.43	1.67	1.06	1.27	0.60	1.84	1.10
YZBR	0.36	0.34	0.33	0.31	0.31	0.28	0.48	0.48	0.28	0.26	0.47	0.39	0.36	0.30	0.68	0.65

Table 5. Similar to Table 3, but showing the results for the MRRs at 10 selected water basins.

Area	COST-G		ITSG		GFZ		CSR		JPL		Tongji		HUST		WHU
	MRR1	MRR2	MRR1	MRR2	MRR1	MRR2	MRR1	MRR2	MRR1	MRR2	MRR1	MRR2	MRR1	MRR2	MRR1	MRR2
NWIA	0.13	0.12	0.20	0.20	0.18	0.16	0.28	0.26	0.28	0.26	0.20	0.21	0.24	0.26	0.27	0.26
BBN	0.06	0.05	0.07	0.06	0.07	0.06	0.10	0.09	0.19	0.18	0.07	0.07	0.10	0.09	0.10	0.10
TRM	0.35	0.30	0.51	0.44	0.66	0.58	0.62	0.56	0.79	0.73	0.73	0.66	0.55	0.50	0.48	0.43
QDM	0.65	0.50	0.99	0.83	1.46	1.19	1.63	1.31	1.37	1.16	1.71	1.47	1.77	1.43	1.57	1.39
ENDR	0.34	0.23	0.48	0.35	0.47	0.38	0.74	0.57	0.70	0.61	0.77	0.57	0.72	0.50	0.63	0.44
YLRS	1.29	1.08	1.48	1.36	2.25	2.09	2.34	2.51	2.24	2.30	1.70	1.85	2.39	2.37	1.63	2.22
YZRS	0.47	0.29	0.49	0.31	0.43	0.30	0.78	0.61	0.79	0.58	0.52	0.48	0.77	0.58	0.48	0.42
MKRS	0.60	0.31	0.72	0.46	0.83	0.52	1.25	0.87	1.96	1.39	0.78	0.69	1.45	1.05	0.72	0.72
SWRS	0.69	0.50	0.70	0.61	0.84	0.79	1.17	1.04	1.02	1.04	1.12	1.11	0.99	0.89	0.85	0.98
YZBR	0.21	0.17	0.21	0.19	0.21	0.20	0.38	0.34	0.39	0.38	0.29	0.27	0.29	0.25	0.46	0.42
Area	IGG		AIUB		GRGS		XISM		CSR_M		JPL_M		GSFC_M		ANU_M
	MRR1	MRR2	MRR1	MRR2	MRR1	MRR2	MRR1	MRR2	MRR1	MRR2	MRR1	MRR2	MRR1	MRR2	MRR1	MRR2
NWIA	0.35	0.37	0.24	0.25	0.23	0.24	0.43	0.42	0.37	0.16	0.55	0.25	0.32	0.26	0.49	0.35
BBN	0.17	0.17	0.11	0.10	0.07	0.07	0.17	0.17	0.10	0.08	0.12	0.08	0.11	0.08	0.15	0.10
TRM	0.84	0.78	0.92	0.83	0.72	0.64	1.23	1.19	0.47	0.58	0.55	0.68	0.81	1.08	1.58	1.58
QDM	1.92	1.55	2.02	1.65	1.62	1.32	3.40	2.77	1.78	2.15	2.17	2.31	2.48	2.63	3.37	3.89
ENDR	0.81	0.60	0.84	0.70	0.68	0.57	1.10	0.99	0.58	1.15	0.90	0.90	1.07	1.00	1.58	1.89
YLRS	2.08	2.26	1.94	2.08	2.05	2.00	3.67	3.75	2.46	0.48	2.05	0.51	2.49	0.67	3.37	1.01
YZRS	0.55	0.45	0.99	0.80	0.54	0.40	0.83	0.70	0.89	0.80	0.98	0.69	0.64	1.07	1.08	1.60
MKRS	1.11	0.80	1.16	0.80	0.84	0.57	1.39	0.99	1.67	0.84	1.60	0.69	1.45	0.75	1.26	1.57
SWRS	1.21	1.23	1.10	1.00	0.90	0.81	1.42	1.44	0.96	0.43	1.67	1.06	1.27	0.60	1.84	1.10
YZBR	0.36	0.34	0.33	0.31	0.31	0.28	0.48	0.48	0.28	0.26	0.47	0.39	0.36	0.30	0.68	0.65

4. Conclusions

In this study, we compared terrestrial water storage (TWS) changes in the Tibetan Plateau (TP) and its surroundings during the period between January 2003 and December 2015 from 16 different GRACE solutions that are classified into 12 spherical harmonic (SH) solutions and four mascon solutions. Differences in trends and time series of the TWS changes exist due to different strategies by different agencies when producing GRACE solutions.

Comparing trends, different SH solutions match well among each other, while there are clear visual differences, especially in the TP, when comparing SH solutions with mascon solutions. When investigating the time series results compared to their averaged result, the COST-G and ITSG SH solutions agree best with the average of all solutions than other SH and all mascon solutions. This is especially the case when secular trends and annual amplitudes are removed before the comparison. The SH solutions lead to different results in the TP and in some glacier mascons where small TWS changes are accompanied with small amplitudes, trends, and/or no stable signal periods. Then, the difference is even larger comparing SH solutions and mascon solutions or between different mascon solutions. In turn, time series usually match each other when the mass change signals are strong with a large amplitude and regular periodicity. This behavior can be expected because any error due to the processing strategy can be significantly overprinted by a strong signal, thus, the apparent error of the time series is lower.

A user certainly wishes to avoid any differences in results that relate to the selection of a GRACE solution. This study is intended to raise a topical discussion on the effect of selecting certain GRACE solutions on TWS changes. Based on the comparison we provide here, the SH solutions of COST-G and ITSG seem preferable for areas with complicated hydrological conditions and where TWS change signals are not distinct in distribution (single and strong signal) and of certain periodicity. Nonetheless, other SH solutions are still performing well as their differences are mostly within one standard deviation only. Hence, a certain SH solution should not be disregarded right away. On another note, the statistical performance of the COST-G SH solution compared to an average of all solutions implies that combined GRACE solutions are an opportunity to develop GRACE products and results further by taking advantage of the best of each solution. However, additional investigations are needed to confirm this implication.

The results from the four mascon solutions studied here were all partly very different (often two standard deviations) from the average of all solutions, even though they can still be considered feasible based on the error statistics (see Figure A1 and Figure A3). Of course, the differences can, to a large part, be related to the fact that we had to regrid the solutions to match our mascons, which would consequently introduce error. However, this makes mascon solutions somewhat less attractive for detailed TWS investigations in the TP and its surroundings.

Based on our preliminary analysis here, we recommend appropriate, i.e., targeted, mascon setting and usage of, if available, combined SH solutions in future GRACE studies on TWS changes in the TP and adjacent areas. Especially, careful setting of known mass change distribution (such as the glacier mascons) appears more suitable for the special situation of the TP.