Reduced misclosure of global sea-level budget with updated Tongji-Grace2018 solution

The global sea-level budget is studied using the Gravity Recovery and Climate Experiment (GRACE) solutions, Satellite Altimetry and Argo observations based on the updated budget equation. When the global ocean mass change is estimated with the updated Tongji-Grace2018 solution, the misclosure of the global sea-level budget can be reduced by 0.11–0.22 mm/year compared to four other recent solutions (i.e. CSR RL06, GFZ RL06, JPL RL06 and ITSG-Grace2018) over the period January 2005 to December 2016. When the same missing months as the GRACE solution are deleted from altimetry and Argo data, the misclosure will be reduced by 0.06 mm/year. Once retained the GRACE C20 term, the linear trends of Tongji-Grace2018 and ITSG-Grace2018 solutions are 2.60 ± 0.16 and 2.54 ± 0.16 mm/year, closer to 2.60 ± 0.14 mm/year from Altimetry–Argo than the three RL06 official solutions. Therefore, the Tongji-Grace2018 solution can reduce the misclosure between altimetry, Argo and GRACE data, regardless of whether the C20 term is replaced or not, since the low-degree spherical harmonic coefficients of the Tongji-Grace2018 solution can capture more ocean signals, which are confirmed by the statistical results of the time series of global mean ocean mass change derived from five GRACE solutions with the spherical harmonic coefficients truncated to different degrees and orders.

The global sea-level variations have been accurately measured by satellite altimetry since 1 1992, which mainly contain two components: mass-induced variation due to mass exchange among the oceans, land and atmosphere 2 and steric variation due to the changes in seawater temperature and salinity, which can be directly measured by the Argo project (with a reasonable global spatial coverage after 2005) 3 . Therefore, by subtracting the steric variation from the total variation (Altimetry-Argo), one can derive the global ocean mass variation 4 . Since the launch of the twin-satellites of Gravity Recovery and Climate Experiment (GRACE) in 2002, the global ocean mass change can be directly estimated by using GRACE solutions 5 , which provided the possibility to investigate the misclosure of the global sea-level budget between the GRACE derived ocean mass and Altimetry-Argo one [6][7][8] .
Conventional sea-level budget equates the total Sea Surface Height (SSH) change to a sum of mass and steric sea level change 8 . The conventional sea-level budget equation is expressed as follows 9 , where SL steric refers to the contribution of ocean thermal expansion and salinity to sea-level change, and SL mass refers to the sea-level change due to the mass change in the oceans,ε is the difference often described as the misclosure. Many previous studies tried to close the global sea-level budget, however, there exist significant differences among the results, mainly due to the larger uncertainty of early released GRACE solutions 4 . With the released GRACE RL05 and RL06 solutions, the misclosure of the global sea-level budget has been significantly reduced among GRACE, Argo and Altimetry data 4,10-12 , normally within the uncertainty (about 0.30 mm/year for trend) of the observations during the satellite era 13 . Since the ocean thermal expansion and salinity are only measured up to the upper 2000 m of the ocean by Argo floats and the ocean mass change will cause Ocean Bottom Deformation (OBD), Frederikse et al. 14 and Vishwakarma et al. 9 pointed out that OBD and deep-ocean steric sea-level change (> 2000 m) should be considered in the global sea-level budget equation as follows 9 , (1) SL total =SL steric + SL mass + ε (2) SL total −SL OBD =SL steric + SL deep steric + SL mass + ε Data and processing strategies GRACE gravity data (ocean mass change). We adopt the new Tongji-Grace2018 solution, CSR RL06, GFZ RL06, JPL RL06 and ITSG-Grace2018 to estimate the GMOM changes. The Spherical Harmonic (SH) coefficients of GRACE solutions up to degrees and orders (d/o) 60 are downloaded from the website of the International Centre for Global Earth Models (ICGEM) (http:// icgem. gfz-potsd am. de). Note that the Tongji-Grace2018 solution was not directly downloaded from the ICGEM website, but recalculated for extending the period from April 2002 to December 2016. We adopt similar post-processing strategies as Chen et al. 4 , including the P4M6 decorrelation filter 24 , 300-km Gaussian smoothing, 500-km buffer zone for reducing signal leakage from land to ocean, replacing GRACE C 20 term with that from the NASA Goddard Space Flight Center (GSFC) 25 , correcting GIA effects with ICE6G-D model 26 , and correcting the geocenter motion effects using the degree-1 products, etc. Three degree-1 products of CSR, GFZ and JPL solutions are taken from GRACE Technical Note 13 27 (TN-13) and the degree-1 products corresponding to Tongji-Grace2018 and ITSG-Grace2018 solutions are computed using the same method as GRACE TN-13 that was proposed by Sun et al. 28 . Besides, there exists a systematic annual phase lag (~ 10°) between Altimetry-Argo and GRACE estimates due to the total mass of the atmosphere is not conserved 12 . Therefore we removed the global mean atmosphere mass change using the GRACE GAA products to correct the annual phase lag following the method of Chen et al. 12 . Note that only GFZ and JPL provide the GAA products, we use the GAA product from GFZ for the correction of CSR RL06, ITSG-Grace2018 and Tongji-Grace2018 solutions. To be consistent with satellite altimetry and Argo observations, the time series of GMOM change is computed by averaging all grids between latitudes 64.5 o S ~ 64.5 o N, with the cosine latitude weighting. The time series of GRACE, altimetry and Argo observations are all fitted with least-squares fitting by introducing the offset, linear trend, annual and semi-annual terms. Note that the periods of 161 days and 3.73 years are removed for correcting the S2 and K2 ocean tide aliasing [29][30][31] . Altimetry data (total sea level change). Satellite altimetry observations of global SSH are available since 1992 when the TOPEX/Poseidon radar altimeter mission was launched. The merged Mean Sea Level Anomalies (MSLA) from TOPEX/Poseidon, Jason-1/2, ERS-1/2, and Envisat observations are provided by the Archiving, Validation, and Interpretation of Satellite Oceanographic (AVISO) data (called Altimetry a ) (http:// www. aviso. ocean obs. com/). The 0.25° × 0.25° daily altimetry SSH data (Altimetry b ) are averaged into monthly intervals to compute the total global sea-level change (https:// cds. clima te. coper nicus. eu/), Besides, we further use the 0.25° × 0.25° grid SSH data of the CMEMS (Copernicus Marine Environment Monitoring Service) global ocean ensemble reanalysis products (Altimetry c ), which are produced with a numerical ocean model constrained with data assimilation of satellite and in situ observations (http:// marine. coper nicus. eu/). The monthly Global Mean Total Sea Level (GMTSL) changes are computed from the three altimetry SSH anomaly grids over the global ocean between latitudes of 64.5°S and 64.5°N. Normally the GIA impact over oceans is directed corrected by adding a constant value of − 0.30 mm/year 32,33 . Considering a 500-km buffer zone from coastal lines is introduced, the mean GIA impact is recomputed as − 0.28 mm/year using the data downloaded from https:// www. atmosp. physi cs. utoro nto. ca/ ~pelti er/ data. php in our study. Besides considering that the OBD effect cannot be observed by Altimetry, we compute the OBD effect using GRACE solutions as Vishwakarma et al. 9 and the details can be referred to Ref. 9 where ρ 0 is the mean density of seawater (1028 kg/m 3 ), and �ρ the density change as a function of temperature (T), salinity (S) and Pressure (P) 34 . Here we compute the average steric sea-level changes over global oceans with the latitudes from 64.5° S to 64.5° N using three Argo products IPRC, SIO and CSIO, except for that from the Japan Agency for Marin-Earth Science and Technology (JAMSTEC) due to its available latitude from 60.5° S to 70.5° N. Same as Vishwakarma et al. 9 and World Climate Research Programme Sea Level Budget Group 13 , the deep-ocean steric sea-level change is taken as + 0.10 mm/year over the period from Jan. 2005 to Dec. 2016.

Results and analysis
Global mean ocean mass change from altimetry and argo. Three altimetry products are adopted to compute the time series of GMTSL change for the period from Jan. 2005 to Dec. 2016. The averaged GMTSL time series of three altimetry products is computed and the GMTSL change rate is 3.75 ± 0.12 mm/year. Then we use three Argo products provided by IPRC, SIO and CSIO to compute the Global Mean Steric Sea Level (GMSSL) change rate between the latitude 64.5° S and 64.5° N, which is 1.19 ± 0.08 mm/year (including deep steric sea-level contribution + 0.10 mm/year). The OBD effects are estimated with five GRACE solutions (same post-processing strategies as "GRACE gravity data (ocean mass)" section), the results are presented in Table 1 and the average linear trend of the OBD effects is − 0.10 ± 0.01 mm/year. Hence, the OBD effect to the global mean sea-level change rate is equal to that of deep-ocean steric sea-level change (> 2000 m) (+ 0.10 mm/year), which results in the same misclosure between Eqs. (1) and (2). After the linear trend of OBD effects is deducted, the GMTSL change rate is 3.85 ± 0.12 mm/year. The GMTSL and GMSSL time series are shown in Fig. 1a, and the time series of GMOM change derived by GMTSL minus GMSSL is also shown in Fig. 1b with the rate of 2.66 ± 0.14 mm/year. Considering there exist 17 missing months in the GRACE solutions from Jan. 2005 to Dec. 2016, if the same missing months are deleted from the altimetry data, the recomputed GMTSL change rate is 3.76 ± 0.12 mm/year, with a 0.09 mm/year smaller relative to 3.85 ± 0.12 mm/year. However, if the same missing months are deleted from the Argo data, the re-estimated GMSSL change rate will be 1.16 ± 0.08 mm/year, slightly smaller than 1.19 ± 0.08 mm/year. Therefore, the correspondent GMOM change rate derived from Altimetry-Argo is 2.60 ± 0.14 mm/year, with a 0.06 mm/year smaller than 2.66 ± 0.14 mm/year before deleting the GRACE missing months. Note that the amplitudes of annual and semi-annual components and linear trends are estimated by the least-squares fitting approach, the results are presented in Table 2 for the individual and averaged Altimetry and Argo data.  Fig. 2b. We can find from Fig. 2 that the linear trend of GMOM change derived from Altimetry-Argo is larger than the GRACE counterparts. The least-squares fitting results of the GMOM changes from Altimetry-Argo and five GRACE solutions are shown in Table 3, where the annual components from GRACE solutions agree well with those from Altimetry-Argo, however, the semi-annual components have a relatively larger difference, especially for the phase components. Moreover, after deleting the GRACE missing months from Altimetry-Argo data the misclosure of the linear trend is reduced by 0.06 mm/year relative to the five GRACE solutions. Compared to the other four GRACE solutions with the GMOM change rates ranging from 2.21 ± 0.14 mm/year to 2.32 ± 0.14 mm/year, Tongji-Grace2018 solution with the change rate of 2.43 ± 0.14 mm/year is the closest to 2.60 ± 0.14 mm/year from Altimetry-Argo, with the misclosure of the global sea level budget reduced about 0.11-0.22 mm/year.
Normally the GRACE C 20 term is replaced with that by satellite laser ranging (SLR) 35 , however, Chen et al. 4 found that the misclosure of the global sea-level budget derived from CSR RL06 will be reduced when the www.nature.com/scientificreports/ GRACE C 20 term is retained. Therefore, we further re-estimate the GMOM changes by retaining the C 20 terms for all GRACE solutions and present the results in Fig. 3 and Table 4. From Table 4, we can find that the linear trends of all GRACE solutions become larger except for the JPL RL06 solution. The re-estimated linear trends are 2.41 ± 0.14 mm/year for CSR RL06, 2.60 ± 0.16 mm/year for Tongji-Grace2018 and 2.54 ± 0.16 mm/year for ITSG-Grace2018, respectively, all of them are better closed relative to 2.60 ± 0.14 mm/year for Altimetry-Argo after retaining the GRACE C 20 term, however, just the opposite for JPL RL06 model. In addition, when the GRACE C 20 term is retained, the uncertainties of the linear trend, annual and semi-annual amplitudes are almost all larger than those in Table 3 except for CSR and JPL RL06 model.

Contribution of low-degree SH coefficients to GMOM change.
To understand why ITSG-  Normally the GRACE C 20 coefficient is replaced by that from the SLR solution due to its relatively large uncertainty. To analyze the contribution of the C 20 term more clearly, we show the C 20 coefficients of five GRACE solutions and NASA GSFC SLR solution in Fig. 5 and the annual and semi-annual amplitudes and phases and linear trends of GMOM change derived from the six C 20 coefficients in Table 6. In Table 6, the linear trend from the C 20 term of ITSG-Grace2018 solution reaches 0.68 ± 0.06 mm/year, significantly larger than 0.35 ± 0.01 mm/year of NASA GSFC SLR solution, resulting in an obvious increasing trend from 2.21 ± 0.14 mm/year (Table 3) to 2.54 ± 0.16 mm/year (Table 4) after retaining the C 20 term. Except for the C 20 term, the low-degree SH coefficients of the ITSG-Grace2018 solution will be further investigated in the next sub-section to show whether it has an obvious difference from the RL06 official solutions and Tongji-Grace2018.
Other low-degree SH coefficients. To better understand the contributions of other low-degree SH coefficients of five GRACE solutions to GMOM change, the filtered GRACE SH coefficients from 2 to 60 degrees and orders (d/o) except for C 20 term are transformed to 1 • × 1 • gridded maps of Equivalent Water Height (EWH) respectively. Then the GMOM change time series is computed by averaging all grids over the global oceans between the latitudes 64.5° S-64.5° N excluding ocean grids within 500-km from the coastal lines. The squared variance σ (n) of GMOM change derived from the SH coefficients truncated to d/o n is computed to evaluate the ocean signals as, where, GMOM n (t) stand for the GMOM change derived from the SH coefficients up to d/o n, N is the number of available months. The squared variances of the five GRACE solutions are shown in Fig. 6 for the SH coefficients truncated to different degrees and orders. From Fig. 6 Table 7 (linear trends), Table 8 (annual amplitude) and Table 9 (semi-annual amplitude). In Table 7, the linear trends truncated to d/o 15 and 20 are very close to those of d/o 60 SH coefficients. Therefore, we can conclude that the Tongji-Grace2018 solution can reduce the misclosure of the global sea-level budget because its low-degree SH coefficients can capture more ocean signals than the other solutions.

Conclusions
The new solution Tongji-Grace2018 is used to estimate the GMOM change together with the other four solutions (CSR RL06, GFZ RL06, JPL RL06 and ITSG-Grace 2018), and investigate the misclosure relative to the GMOM change from Altimetry-Argo. The same post-processing strategies as Refs. 4 Figure 5. Comparison of C 20 from five GRACE solutions and NASA GSFC SLR solution.