Underlying drivers of decade-long fluctuation in the global mean sea-level rise

Natural climate variability can mask the background trend of global mean sea-level (GMSL) caused by global warming. Recent advances in satellite measurements and ocean heat-content estimates have enabled the monitoring of GMSL budget components and provide insights into ocean effects on the Earth’s energy imbalance and hydrology. We observed a decadal fluctuation in GMSL rise, which coincides with an increasing trend in the 2010s after the warming ‘hiatus’ during the 2000s, and demonstrated that the rate of sea-level rise can be attributed to climate-related decadal fluctuations in ocean heat storage and hydrology. Since ∼2011, the decadal climate variability has 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), increasing 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 mean sea level has increased ∼20 cm over the past century, and has been rising by nearly 3 mm yr −1 during the period of 1993-2017 (Church et al 2013, Ablain et al 2017, WCRP Global Sea Level Budget Group 2018). The change in the global mean sea level (GMSL) rate has been primarily attributed to the effect of thermal expansion in ocean, mass loss from glaciers and ice sheets, and changing land water storage (LWS) (Shepherd et al 2012, Wada et al 2012, Gardner et al 2013, Marzeion et al 2014. The GMSL budget was estimated by WCRP (2018), comparing the sum of all sea-level components with the observed GMSL. The altimetry-based sea-level products showed an average rate of 3.1 mm yr −1 in the GMSL trend over the altimeter era. The rate of sea-level rise has increased over the recent decades and has been faster since 2010s. The increases in the rate of sea-level rise are also not globally uniform (e.g. Church et al 2013). These results indicate that the rate of GMSL rise is perturbed by internal climate modes in the complex Earth's climate system. Although the secular trend of GMSL rise is a crucial indicator of ongoing global warming, the fluctuations on interannual to decadal timescales superimposed on this trend can also provide important clues for the role of oceans in Earth's energy imbalance (EEI) and global hydrological cycle.
Natural climate variability on interannual to decadal timescales masks the background trend of the detected sea level, thereby changing the acceleration values over short timescales. Previous studies have shown that the GMSL responds to the interannual El Niño-Southern Oscillation (ENSO) variability (Boening et al 2012, Fasullo et al 2013, Nerem et al 2018, Hamlington et al 2020. It has been reported that the sea level variations related to the ENSO are closely linked to the dominant changes in ocean heat storage and global hydrological cycle; however, the relative importance of these two contributions to GMSL variability has remained unclear. Piecuch and Quinn (2016) also raised the question of why the GMSL response to El Niño in 2015/2016 was much stronger than 1997/1998, although these two events were comparable in ENSO amplitude. They speculated in their discussion that other climate modes, like Pacific Decadal Oscillation (PDO), exert an impact on GMSL (Newman et al 2016).
One factor that makes it difficult to understand the ENSO-related GMSL changes is the presence of decadal modes associated with the climate variability (Zhang and Church 2012, Hamlington et al 2019, Moreira et al 2021. The GMSL showed a sluggish rate of ∼2.4 mm yr −1 during the 2000s (WCRP 2018), despite the ocean gaining mass from ice sheets and glaciers. Climate-driven water exchanges between ocean and land contributed to this slowdown , Reager et al 2016. This decade-long decrease in GMSL rate is also consistent with a pause in the global mean surface temperature increase, which is commonly called as the recent warming 'hiatus' (England et al 2014, Maher et al 2018. The global ocean has been suggested to absorb extra heat because of anthropogenic radiative forcing during the hiatus period (Chen and Tung 2014). However, more recent analyses and observations revealed that the ocean heat uptake has slowed down over the 2000s hiatus as compared to the recent decade after 2011 (Xie et al 2016, Von Schuckmann et al 2020, Loeb et al 2021. The rate of GMSL is increasing again after the surface warming hiatus (Yi et al 2015, Moreira et al 2021, along with a shift in the Pacific climate variability that has been shown to play a role in GMSL acceleration occurring on decadal time scales (Hamlington et al 2019). Based on analyses of ocean temperature data, Von Schuckmann et al (2020) revealed that the rates of ocean heat gain have been steadily increased over the past decades, but a rapid increase after the recent hiatus. More recently, a comparison between satellite observations of topof-atmosphere (TOA) net radiation and in situ observations showed a decadal increase in EEI from mid-2005 to mid-2019 (Loeb et al 2021). These results indicated that heat gain in the oceans is increasing over the recent decade, but a direct comparison with the sea-level budget components and their relationship with natural climate variability is lacking.
Because the ocean stores over 90% of EEI in the form of ocean heat content (OHC) and reflects the changes in mass between the ocean and land, natural changes in OHC and exchange of water mass significantly affect the decadal trends of GMSL rise. Therefore, estimating climate-driven sea-level variations is essential to improve our understanding of ocean responses to the global climate system and associated rising sea levels in the future. Despite the significance of determining GMSL and its changes, the following aspects still remain unclear: (a) what are the internal modes that represent the changes in the GMSL rate on decadal timescales (Hamlington et

Data and methods
We considered six different altimetry GMSL products from 1993 to 2018 to estimate GMSL budget during the altimetry era. These products were corrected for the effect of glacial isostatic adjustment and TOPEX-A instrumental drift (see details on the altimetry-based sea-level products in supplementary material). For a steric component of GMSL, we used three following reanalysis products: Ishii and Kimoto (2009) (hereafter IK), EN4 product from Good et al (2013), and NOAA product from Levitus To extract time-varying trends in all components of sea-level budget, we used an ensemble empirical mode decomposition (EEMD) method, which has been widely used in many geophysical climatology applications (Huang and Wu 2008, Ezer 2013, Ji et al 2014, Chen et al 2017. The EEMD is an advanced method that improved the mode mixing problem in empirical mode decomposition. This method is designed to separate the original signals into several intrinsic mode functions (IMFs) and a secular trend, i.e. a residual (Huang et al 1998). The IMFs of EEMD have been acquired as an ensemble average of IMFs separated from the original data sets added by Gaussian white noise. Figure S2 (available online at stacks.iop.org/ERL/16/124064/mmedia) shows the EEMD results for all components, which demonstrate seven IMFs and residual trend in ascending order from high to low frequency. Based on spectral analysis, the EEMD-derived IMFs can be grouped into four major time-scale components: High-frequency, ENSO-scale Interannual variability, decadal-scale variability and a residual as the intrinsic trend. Details about EEMD method and the results of significance test and ending effect of a large El Niño in 2015/2016 are also given in supplementary material.

Temporal evolution of sea-level rise rate
We assessed the GMSL budget in terms of different contributions, using a number of available datasets for altimetry-based sea levels as well as mass and steric components (figure 1(a)). Ensemble means were applied for all sea-level budget components. The temporal evolution of altimetric GMSL agrees well with the sum of all the components (figure 1(a), upper) and the linear trend difference between the two GMSLs is small (0.01 mm yr −1 ), thereby representing the GMSL budget closure and consistency of different datasets. These records show the sea-level fluctuations superimposed on the dominant background trend, with particularly significant ENSOrelated changes in the GMSL rise.
To diagnose the temporal change of sea-level rise rate over recent decades, we extracted decadal-scale variability from all components of the GMSL budget by using EEMD method. Throughout the altimeter era, a distinct decade-long fluctuation with a peak period of ∼12 years was identified in the ensemble mean GMSL as well as in the sum of all components (figure 1(b), upper), which were in phase with a downward shift during the recent hiatus in the 2000s and in phase with an upward shift subsequently (figure 1(b), bottom). Without an intrinsic trend (i.e. a residual trend), the GMSL rates display a transition trend from positive to negative during the surface warming slowdown; however, this trend transitioned back to positive in 2011 (see figure S3(b)), which corresponds to a recent resumption of surface warming after the decade-long hiatus (Hu et al 2019, Lenssen et al 2019). This decadal fluctuation extracted from the EEMD method is also supported by the first mode of the empirical orthogonal function (EOF) analysis, which is derived using a successive five year running mean of the altimetric sea-level data with a linear trend removed (figure S5). The decadal pattern from the EOF analysis is very similar to a decadal fingerprint, which is represented by the sea-level regression in regard to the EEMD-determined decadal mode (figure S6(a)), indicating the robustness of decadal sea level variability from EEMD analysis. These results show that the decadal GMSL fluctuation is separated

Decadal GMSL fluctuation associated with Pacific climate variability
We further identified a strong relationship between the decadal modes of sea-levels and the Pacific decadal variability obtained from the EEMD of the PDO (figure 2). Over the altimeter period, the transition times agreed well between the sea level components and the Pacific decadal variability, showing a distinct transition around 2011 that is consistent with the recent resumption of surface warming after the 2000s hiatus. The Pacific decadal mode has its largest correlation with both the GMSL and steric sea level at near-zero lag; however, there is a seven month lag with the LWS. The spatial patterns of the regressed EEMD-derived decadal GMSL and PDO mode are also agree (figures S6(a) and (b)), suggesting a relationship between sea level and natural variability on decadal timescale. This suggests that the climate-driven decadal mode strongly contributed to slowing the GMSL rise rate during the hiatus and increasing the trend rate after the hiatus. Furthermore, there is a possible link between these climatedriven fluctuations and sunspot activity (dashed red line in figure 2), which is known to exhibit a cycle that lasts approximately 11 years (Hathaway 2015). It has been noted that the cycle of solar forcing can be amplified to produce a measurable climate response on decadal timescale through at least two mechanisms of 'top-down' stratospheric response and 'bottomup' coupled ocean-atmosphere surface response (e.g. Because of the complex processes in air-sea feedback, the physical mechanisms that lead to the impact of the solar cycle on the climate are not fully understood, and thus further investigations are required in the future; nevertheless, the findings from previous studies showed that the solar cycle on decadal timescale can be a relevant source of decadal climate variability both on global and regional scales. These comparisons suggest that the decadal fluctuation in GMSL reported here is a distinct and robust signal associated with the earth's climate system, which is different from the ENSO-related interannual variability. We also note that the climate decadal mode can result in the modulation of GMSL response to ENSO  3). The El Niño in 2015/2016 was one of the strongest events in history, which was comparable to the El Niño events in 1997/1998. The strengths of amplitude were comparable between these two events; however, the sea-level response to El Niño was weaker during the 1997/1998 El Niño than during the 2015/2016 El Niño (figure 3(a)) as previously discussed in Piecuch and Quinn (2016) and WCRP Global Sea Level Budget Group (2018). To examine how the decadal mode modulates with the GMSL response to ENSO events, the contributions of interannual and decadal variability to the observed three-month mean GMSL (with an intrinsic trend removed) were analyzed ( figure 3(b)). The decadal mode contributed to ∼23% of a decline in GMSL during the El Niño in 1997/1998, but made a positive contribution of ∼21% to the GMSL rise

Climate-driven LWS
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 GRACE record that extends back to 2002, global hydrological models estimated the trend and fluctuation of total LWS. However, there were still uncertainties regarding the ability of model to simulate the interannual to decadal variability in global LWS (Scanlon et al 2018). Moreover, the 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 (Durack et al 2014). Therefore, we used the GRACE and Argo-based products to estimate the global patterns of decadal trends in the LWS and OHC for the two analysis periods. The global estimate of the GRACE trend over 2002-2010 revealed an increasing LWS (wetting) at low latitudes, and decreasing LWS (drying) at the mid-latitude of the southern hemisphere (figure 4); these results coincides with previous GRACE studies (Chen et al 2010, Reager et al 2016. The latitudinal trends in LWS shifted since 2011 and showed a distinct pattern of low latitude drying and midlatitude wetting, which is more prominent in the southern hemisphere. The decadal trend shift resulted from changes in the LWS regime since 2011; that is, the wet conditions transformed to dry conditions at low latitudes, while the opposite effect was observed at mid-latitudes (Hamlington et al 2017). The spatial distributions of the LWS trend strongly resembled the LWS pattern regressed on the EEMDdetermined decadal mode of the PDO ( figure 5(a)), thereby implying an important decadal persistence in the Earth's climate systems (Hamlington et al 2017). The GRACE-derived LWS was consistent with the observed land precipitation from the Global Precipitation Climatology Project in the decadal trends and in its interannual variations throughout the GRACE period ( figure 4(c)). There was a delayed (maximum correlation at seven months) response of LWS to the precipitation in land. When the precipitation falls onto land, much of it soaks into the ground as infiltration and some water infiltrates deep into the ground and recharges groundwater in aquifer. This process can make a time lag response of LWS to precipitation (Eagleson 1978). Previous studies demonstrated a delayed response between LWS and precipitation (Humphrey et al 2016, Zhang et al 2019. The lags between LWS and precipitation are about 1-3 months in the low-and mid-latitude basins. However, the effect of seasonal snowpack accumulation and the melting process causes the longer lag (6-9 months) response of LWS to precipitation at high latitude (Humphrey et al 2016, Zhang et al 2019).
The glacier-free LWS contributed 0.14 ± 0.11 and 1.04 ± 0.21 mm yr −1 to the sea level rise during the first and second decades of the GRACE period, respectively (figure 6). Because the net LWS changes estimated here include human-and climatedriven components in storage, an Intergovernmental Panel on Climate Change estimate (Church et al 2013) of direct human-induced LWS changes (0.38 ± 0.12 mm yr −1 ) was used to calculate the climate-driven LWS contribution to GMSL (Reager et al 2016). Therefore, the climate-driven LWS suppressed the GMSL rise (−0.23 ± 0.16 mm yr −1 ) during the hiatus period and 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 variations in the water exchange between ocean and land, thereby supporting the findings of several studies mentioned above.

Ocean effect on the earth energy imbalance
The steric contribution to the rise in GMSL arises from changes in OHC, which is the major factor sequestering the EEI resulting from rising CO 2 concentrations. To elucidate OHC fluctuations contributing to the rate of GMSL rise, we analyzed the temperature profiles recorded by Argo array floats since 2005, which provided a reliable OHC estimate over 0-2000 m (Cheng et al 2015). Global maps of OHC (derived from the SCRIPPS product) trends over the two decadal periods revealed that since 2011, the trend has been changing toward an opposite trend compared to that of the preceding period (figure 7). It is manifest from the regression pattern of the EEMDdetermined decadal mode of the PDO that there are global ocean responses to Pacific climate variability ( figure 5(b)), which agree with the linear trend patterns of the OHC. In 2005-2010, the OHC showed strong warming trends in the eastern/southeastern Indian and western tropical Pacific oceans; a warming structure was also centered in the western/central North Pacific, and surrounded by cooling along the west coast of North America. With the PDO transitioning back to positive since 2011, the spatial patterns of the OHC trend were reversed; this was accompanied by a positive (warming) trend in the EP ocean and a negative (cooling) trend in the western tropical Pacific and northern and southeastern Indian oceans. The Pacific patterns of the decadal OHC trend are linked to the PDO-related trade trends on a decadal timescale, i.e. a strengthening of trade winds during the 2000s, followed by a weakening trend of trade winds since 2011. Climate-altered trade wind results in changes of the upper-ocean circulations, redistributing heat in the Pacific (Merrifield et al 2012, Moon et al 2013, England et al 2014, Hamlington et al 2014, Cha et al 2018, Maher et al 2018. The trend reversal was also observed in the North Atlantic, with warming in the subtropical gyre and cooling in the subpolar gyre; this result indicates a significant influence of ocean circulation on heat redistribution. It is worth noting that the decadal OHC trend of subpolar gyre in the North Atlantic may be attributed to the shifts in the melting rate of Greenland Ice Sheet (GIS). For instance, the cooling in the subpolar gyre since 2011 contributed to the slowdown of mass loss in the GIS, which is consistent with the findings of a recent study (IMBIE Team 2020) that identified a persistent increase in ice loss rate prior to 2012. The combined impacts of warming and cooling regions in the OHC resulted in a GMSL fluctuation that can be caused by decadal-scale climate variability. The other two datasets (i.e. IPRC and JAMSTEC) also show the decadal trend shifts of global OHC, which generally  To illustrate the OHC contribution to the Earth's energy budget, we estimated the EEI during and after the warming hiatus in terms of the heating rate applied over the Earth's surface area; this was achieved by combining Argo-observed upper-2000 m OHC with previously published estimates of heat uptake, using the deep ocean and non-ocean terms (figure 8). The global volume-integrated OHC trend (figure 7(c)) demonstrates that the planetary heating rates are 0.37 ± 0.15 W m −2 over 2005-2010 and 0.65 ± 0.18 W m −2 over 2011-2017 (per unit of Earth's surface of 5.1 × 10 14 m 2 ). Considering a constant heating rate of 0.099 ± 0.066 W m −2 at ocean depths below 2000 m depth (Purkey and Johnson 2010), as well as the sum of non-ocean terms by Von Schuckmann et al (2020), we obtained a net heat uptake of 0.55 ± 0.12 and 0.85 ± 0.10 W m −2 for 2005-2010 and 2011-2017, respectively. The comparison between the two periods indicates that the global ocean gained more heat energy from 2011 onwards (0.30 ± 0.16 W m −2 ), as compared with the previous period. The EEI estimated from the latest release of CERES satellite data was 0.60 ± 0.10 W m −2 for 2005-2010 and 0.95 ± 0.10 W m −2 for 2011-2017, which indicates a close correspondence between two completely independent EEI estimates on decadal time scales. These EEI estimates were not distinguishable within the uncertainty and thus, the increase in the ocean heat uptake since 2011 seems to be robust. The benefits of these two independent approaches are also demonstrated in a recent study by Loeb et al (2021) that showed a robust positive trend in EEI from mid-2005 to mid-2019 due to mainly changes in clouds, water vapor, and trace gases. Figure 8 further demonstrates the agreement with the EEI obtained from the altimetry minus GRACE residual approach (Levitus et al 2012, Fu 2016. These results enhance the confidence in all three complementary climate observing systems (Meyssignac 2019). Furthermore, the consistency shown here suggests that there was no shortfall in closing the global energy budget during the 2000s; this was in contrast to the so-called 'missing energy' problem (Trenberth and Fasullo 2010).

Conclusion and discussions
Understanding the GMSL responses to natural variability can provide important information on the ocean's role in controlling the Earth climate system (Trenberth andFasullo 2010, Leuliette andWillis 2011). In this study, we conducted observational analyses to examine the decade-scale fluctuation in GMSL rate and its connection to variations in ENSO, while discussing the impact of climate decadal variability on the Earth's energy budget and global hydrological cycle. The resulting relationship among sealevel rise, precipitation, ocean warming, and TOA net flux demonstrates a physically consistent expression of decadal climate variability on global scales. Based on the analysis conducted here, the following results can be highlighted: (a) a distinct decadal fluctuation in the rate of GMSL has been identified; (b) the GMSL responses to interannual ENSO signals can be modulated at times of transition in the Pacific decadal mode; (c) both the steric and LWS components account for a large fraction of the decadal fluctuation in the GMSL rate; and (d) the change in ocean heat uptake before and after 2011 is consistent with TOA net energy flux within observation uncertainties and linked to the Pacific decadal climate variability.
Our results can further clarify the ocean's role in EEI, global hydrology, 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 the cross validation of EEI by emphasizing the consistency of thermal energy in the Earth system (Loeb et al 2021). Although systematic errors of space observations and in situ uncertainties still remain large owing to unsampled regions and/or mapping choice, efforts to extend both satellite measurements and Argo records with ongoing development of Deep Argo floats (Johnson et al 2015) will allow better monitoring of EEI changes and give accurate datasets to estimate the role of ocean in the Earth's energy and GMSL rise in the future (Llovel and Terray 2016).

Data availability statement
All data that support the findings of this study are included within the article (and any supplementary files).