Decade-long shift in the rate of global mean sea-level rise


 Recent advances in satellite measurements and ocean heat-content estimates have enabled the monitoring of global mean sea level (GMSL) budget components and understanding of ocean effects on the Earth’s energy imbalance and hydrology. We observed a notable accelerating GMSL rise rate in the recent decade after the warming “hiatus” during the 2000s, and demonstrated that this was attributed to decade-long shifts in ocean heat storage and hydrology. Since ~2011, climate-driven changes have resulted in additional ocean mass gain (271±89 Gt yr-1) from glacier-free land water storage and increased ocean heat uptake (0.28±0.17 W m-2), accelerating the GMSL rise rate by 1.4±0.4 mm yr-1. The suggested estimates of sea-level and Earth’s energy budgets highlight the importance of natural variability in understanding the impacts of the ongoing sea-level rise.


Introduction
Globally, the sea level has increased by more than 20 cm over the past century, and has been rising by nearly 3 mm yr -1 during the past two decades 1,2 . An apparent increasing rate of the global mean sea level (GMSL) in the second decade of the altimetry era, i.e. during the 2000s, has been reported, and has been primarily attributed to the increasing ice mass loss in Greenland 3,4 . This accelerated GMSL rise contrasts with the conclusions of previous works that indicate a slowdown of this rate during the 2000s, which was attributed to the climate-driven water mass exchange between ocean and land [5][6][7] . This decade-long decrease in GMSL rate coincides with the pause in the global mean surface temperature warming, commonly known as the recent hiatus [8][9][10] . Furthermore, this decade-long surface warming hiatus has been one of the most debated and researched issues in recent years. During the hiatus period, the global ocean has been suggested to absorb extra heat because of anthropogenic radiative forcing 11-13 . However, more recent analyses and observations have revealed that the ocean heat uptake tended to slow down during the warming hiatus in the 2000s compared to the recent decade after 2011 14,15 .
These disagreements may be linked to natural climate variability, which masks the background trend of the observed sea level and, consequently, changes the acceleration values over short time scales 16,17 . Because the ocean stores over 90% of the Earth's energy imbalance (EEI) in the form of ocean heat content (OHC) and reflects changes in water storage between 3 the land and ocean, natural changes in OHC and exchange of water mass significantly affect the rate of GMSL rise. Therefore, estimating climate-driven sea-level variations is essential to improve our understanding of global ocean responses to the Earth's climate system. In addition, understanding the GMSL response to natural fluctuations can provide a more accurate background to predict sea-level changes in the future.
Despite the significance of determining GMSL and its changes, the following aspects still remain unclear: (i) how natural variability has shifted the rate of GMSL during and after the surface warming hiatus, (ii) whether the sea-level shift will persist or pause in the near future, and (iii) what are the relative steric and barystatic contributions to changes in the GMSL rate, and their relationship to EEI at the top of atmosphere (TOA) 15,[18][19][20] . Herein, these issues are discussed considering the influence of the Earth's energy storage and global hydrological cycle in the closure of the sea-level budget, and in order to distinguish an intrinsic GMSL trend from naturally occurring variability.

Decade-long shift in GMSL
We assessed the sea-level budget in terms of different contributions, using a number of available datasets for altimetry-based sea levels and steric and mass components (Fig. 1a).
Ensemble means were applied for all terms of the sea-level budget, with a correction of TOPEX-A instrumental drift for the altimeter datasets 4,21 . The temporal evolution of altimetric 4 GMSL agrees well with the sum of all components (Fig. 1a, upper), and the linear trend difference between the two GMSLs is small (0.01 mm yr -1 ), indicating the closure of GMSL budget and consistency of different datasets. These records show sea-level fluctuations superimposed on the dominant background trend with small but significant decade-long shift in the GMSL rise. The shifting trend occurred since ~2011, with a notable accelerating rate of GMSL rise, which coincides with a recent resumption of global mean surface temperature 22 (GMST) warming after the decade-long hiatus 23 (Fig. 1a, bottom). To diagnose the rate of GMSL rise over recent decades, we used an ensemble empirical mode decomposition (EEMD) method 24 , which has been widely used for many geophysical applications 3,25-28 . EEMD is an adaptive and temporally local decomposition method that can separate a dataset into a finite number of intrinsic mode functions that represent the non-stationary nature of climate data and residuals (Materials and Methods). Throughout the altimeter era, a distinct decade-long shift was identified in both the ensemble mean GMSL and sum of all components (Fig. 1b, upper), which are in phase with a downward shift during the global warming hiatus in the 2000s and subsequently, in phase with an upward shift (Fig. 1b, bottom). Without a secular trend, the rates of sea-level rise display a transition trend from positive to negative during the surface warming slowdown; however, the trend transitioned back to positive in 2011. The contribution to the decadal shift in the rate of GMSL rise was mostly derived from the steric expansion due to ocean warming and land water storage (LWS) excluding glaciers and ice sheets, with little 5 contribution from other components. For the altimeter period, the contributions of steric and LWS accounted for 71% and 69%, respectively, of the variance in the sum of all components of the GMSL budget, similar to the contributions obtained by Hamlington 20 . The LWS contribution estimated here strongly supports the conclusion of Reager 6 , who showed that glacier-free LWS slowed the rate of GMSL rise in 2002-2014. Our analysis indicates that both steric and LWS components suppressed the GMSL rise during the recent warming slowdown, despite water losses from the ice sheets. However, these two contributors significantly affected the increase in the background trend of GMSL after the end of the hiatus.

Climate-driven Land Water Storage
To investigate the response of global hydrology and ocean heat storage to climate decadal variability, the following two decadal periods were compared: 2002-2010 (i.e. hiatus period) and 2011-2017. Prior to the Gravity Recovery and Climate Experiment (GRACE) record that extends back to only 2002, global hydrological models estimated the trend and fluctuation of total LWS. However, there were still uncertainties regarding the model's ability to reproduce the interannual to decadal variability in global LWS 29 . Moreover, the large uncertainty in the OHC calculation that arises from insufficient sampling and instrumental biases was mainly observed for the period before the early 2000s, that is, the pre-Argo period 30,31 . Therefore, we used the GRACE and Argo-based products to estimate the global patterns of decadal trends in The glacier-free LWS contributed 0.14±0.11 and 1.04±0.21 mm yr -1 to the GMSL during the first and second decades of the GRACE period, respectively (Fig. 4). Because the net LWS 7 changes estimated here include human-and climate-driven components in storage, an Intergovernmental Panel on Climate Change (IPCC) estimate 1 of direct human-induced LWS changes (0.38±0.12 mm yr -1 ) was used to calculate the climate-driven LWS contribution to GMSL, similar to the approach used in Reager 6 . Therefore, the climate-driven LWS suppressed the GMSL rise (-0.23±0.16 mm yr -1 ) over the hiatus period but subsequently enhanced it (0.66±0.24 mm yr -1 ), which suggests that the natural LWS variability significantly contributed to the decade-long shift in the GMSL. These LWS changes determined by GRACE indicate that naturally occurring variability in precipitation leads to decadal changes in the exchange of water between land and ocean.

Ocean effect on the Earth Energy Imbalance
The steric contribution to GMSL rise arises from changes in OHC, which is the major factor sequestering the EEI resulting from rising CO2 concentrations. To elucidate OHC fluctuations contributing to the rate of GMSL rise, we analysed the temperature profiles recorded by Argo array floats since 2005, which provided a reliable OHC estimate over 0-2000 m 30,38 . Global maps of OHC (derived from the Scripps Institution of Oceanography (SCRIPPS) product) trends over the two decadal periods revealed that since 2011, the trend has been shifting toward an opposite pattern compared to that of the preceding period (  2011-2017, which indicates a close correspondence between two completely independent EEI estimates on decadal time scales. The two EEI estimates are not distinguishable within the estimated uncertainty and thus, the increase in the ocean heat uptake since 2011 seems to be robust. Fig. 6 further demonstrates the agreement with the EEI obtained from the altimetry minus GRACE residual approach 45,46 . These results strengthen confidence in all three complementary climate observing systems 47 . Furthermore, the consistency shown here suggests that there was no shortfall in closing the global energy budget during the 2000s, in contrast to the so-called "missing energy" problem 48 .

Summary
The resulting relationship between sea-level rise, precipitation, ocean warming, and TOA net flux demonstrates a physically consistent expression of decadal climate variability on global scales. Our results can further clarify the ocean's role in EEI and hydrological cycle and perspectives on ongoing sea-level change. An ongoing GMSL rise can be influenced by climate-driven signals that can accelerate or decelerate the underlying sea-level trend for decadal time periods. Furthermore, the estimate conducted here illustrates the utility of completely independent datasets for EEI cross validation by emphasising the consistency of thermal energy in the Earth system. Although systematic errors of space observations and in situ uncertainties are likely to remain large owing to unsampled regions and/or mapping choice, 11 efforts to extend both satellite measurements and Argo records with ongoing development of Deep Argo floats 49 will allow better monitoring of EEI changes and provide accurate datasets to investigate the ocean's role in the Earth's energy budget and future sea-level rise 40 .       The EEMD method is based on empirical mode decomposition (EMD), which is designed to separate the time series into a finite number of intrinsic mode functions (IMFs) and residual 26 trend that represents the long-term adaptive trend 25,68 . The IMFs of EEMD is obtained as an ensemble average of IMFs that were decomposed from the original time-series with the addition of Gaussian white noise by EMD. This advanced method resolves the mode mixing problem caused by intermittence signal in the original EMD. Here, we set the white noise with variance σ=0.2 relative to the variance of the original time-series, and the number of ensemble members, N=500. Supplementary Fig. 4 shows the EEMD results for all data sets, which yielded seven IMFs and residual in ascending order from highest-frequency to lowestfrequency. Based on spectral analysis, the EEMD-derived IMFs can be grouped into four major time-scale components: IMFs 1-2 as the high-frequency components of less than a year, IMFs 3-5 as the ENSO-scales frequencies ranging from 1.5 to 7 years, IMF 6-7 as the decadal-scales component with a peak period of ~ 12 years, and taking a residual as the intrinsic trend. Note that the EEMD-determined ENSO signals are clearly separated from the decadal mode and the secular trend. The intrinsic trend is the same unit as the raw time series and the rate of timevarying trend is obtained by taking the first-order time derivative of the trend, in unit of mm y -1 for GMSL.
Time-varying rate of the intrinsic trend of each time series, which was determined by calculating the temporal derivative of the trend (i.e., residual mode), is presented in Supplementary Fig. 5a. A bootstrap method based on random resampling to estimate confidence intervals is used to test the significance of the intrinsic trends obtained from EEMD.  Fig. 5c, ref. 8,28,69 ). It is thus likely that the climate-driven decadal mode strongly contributed to slowing the rate of sea-level rise during the hiatus but accelerating the trend rate after the hiatus.
Significance of the intrinsic trend. The significance of the intrinsic trend is tested using a standard bootstrap method 70 . This method is based on randomly resampling to estimate confidence intervals. The main steps in this method are as follows: 1) create artificial resampled 28 data ( ) by randomly sampling the anomaly for the original data; 2) add the artificial data to the residual ( * = + ); 3) perform the EEMD again on the reconstructed data ( * ) to obtain the artificial trend; 4) repeat the steps 1-3 for M times (in this study, M=1,000 iterations) and the mean artificial trend ( * ̅̅̅ ) can be estimated from individual bootstrap simulations, * ̅̅̅ = 1 ∑ ( * ) =1 . Supplementary Fig. 5a,b show the rates of intrinsic trends and decadal variability in each component, with a 95% confidence interval (within two standard deviations) for 1,000 randomly sampled trends and decadal modes, respectively. The time-varying trends and decadal modes in all components do not change significantly within their confidence intervals, indicating robustness of the EEMD-derived trend and decadal mode.
In addition, to test whether the decadal-scale component was affected by the ending point effect including the significant event like El Niño, similar to Cha 28,71 , we compared the decadalscale components of full record length with gradually shortened records of the same datasets by removing 0-3 years of data from the end of the time series ( Supplementary Fig. 6). The amplitudes of decadal-scale components from satellite altimetry, steric, and LWS show a little change, but their decadal signal persisted regardless of the impact of the El Niño event in 2015/16, indicating that the decadal-scale variability is robust in the GMSL.