INTRODUCTIONTop

The global mean sea level (MSL) has been rising since the beginning of the twentieth century (IPCC 2013Intergovernmental Panel on Climate Change (IPCC). 2013. Climate Change 2013: The Physical Science Basis. Contribution of Working Group I to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change. Stocker T.F., Qin D., et al. (eds), Cambridge University Press, Cambridge, United Kingdom and New York, NY, USA. 1585 pp.) and more rapidly during the last 20 years (Chen et al. 2017Chen X., Zhang X., Church J.A., et al. 2017. The increasing rate of global mean sea-level rise during 1993-2014. Nat. Clim. Change 7: 492-495.). Quantifying the rate and patterns of MSL change is of great importance (Jevrejeva et al. 2009Jevrejeva S., Grinsted A., Moore J.C. 2009. Anthropogenic forcing dominates sea level rise since 1850. Geophys. Res. Lett. 36: L20706., Marcos and Amores 2014Marcos M., Amores A. 2014. Quantifying anthropogenic and natural contributions to thermosteric sea level rise. Geophys. Res. Lett. 41: 2502-2507., Luu et al. 2018Luu Q.H., Wu Q., Tkalich P. et al. 2018. Global mean sea level rise during the recent warming hiatus from satellite-based data. Remote Sens. Lett. 9: 497-506.) but is still challenging (Hay et al. 2015Hay C.C., Morrow E., Kopp R.E., et al. 2015. Probabilistic reanalysis of twentieth-century sea-level rise. Nature 517: 481-484.), mostly due to uncertainty in the measurement (Cazenave et al. 2014Cazenave A., Dieng H.B., Meyssignac B., et al. 2014. The rate of sea-level rise. Nat. Clim. Change 4: 358-361., Bos et al. 2014Bos M.S., Williams S.D.P., Araujo I.B., et al. 2014. The effect of temporal correlated noise on the sea level rate and acceleration uncertainty. Geophys. J. Int. 196: 1423-1430., Dieng et al. 2017Dieng H.B., Cazenave A., Meyssignac B., et al. 2017. New estimate of the current rate of sea level rise from a sea level budget approach. Geophys. Res. Lett. 44: 3744-3751.) and interpretation (Visser et al. 2015Visser H., Dangendorf S., Petersen A.C. 2015. A review of trend models applied to sea level data with reference to the “acceleration-deceleration debate”. J. Geophys. Res. Oceans 120: 3873-3895, Dangendorf et al. 2017Dangendorf S, Marcos M., Wöppelmann G., et al. 2017. Reassessment of 20th century global mean sea level rise. Proc. Nat. Acad. Sci. 114: 5946-5951., Royston et al. 2018Royston S., Watson C.S., Legresy B., et al. 2018. Sea-level trend uncertainty with Pacific climatic variability and temporally-correlated noise. J. Geophys. Res. Oceans 123: 1978-1993.) of sea level data. Dating back to the eighteenth century, tide gauge records have long been a source of the spatio-temporal rates of MSL change. However, their limitations are sparseness, uneven geographic distribution, high sensitivity to local geodynamic and hydrological influences and, notably, unavailability in the open oceans. The launch of oceanographic satellites since 1993 provided an unprecedented opportunity to reveal the spatial patterns of sea level change with global coverage, capturing the non-uniformity in trend and variability (Ablain et al. 2015Ablain M., Cazenave A., Larnicol G., et al. 2015. Improved sea level record over the satellite altimetry era (1993-2010) from the Climate Change Initiative project. Ocean Sci. 11: 67-82., 2017Ablain M., Legeais J.F., Prandi P., et al. 2017. Satellite altimetry-based sea level at global and regional scales. Surv. Geophys. 38: 7-31., Nerem et al. 2018Nerem R.S., Beckley B.D., Fasullo J.T., et al. 2018. Climate-change–driven accelerated sea-level rise detected in the altimeter era. Proc. Nat. Acad. Sci. 115: 2022-2025.).

In some regions of the western tropical Pacific Ocean, the MSL change rate has been shown to be 3 to 4 times higher than the global rate for the period 1993-2011, thanks to the exploitation of altimetric data (Zhang and Church 2012Zhang X., Church J.A. 2012. Sea level trends, interannual and decadal variability in the Pacific Ocean. Geophys. Res. Lett. 39: L21701., Frankcombe et al. 2015Frankcombe L.M., McGregor S., England M.H. 2015. Robustness of the modes of Indo-Pacific sea level variability. Clim. Dyn. 45: 1281-1298.). Regional change of MSL results from a complicated combination of several climatic factors at different timescales and geographical distributions (Hughes and Williams 2010Hughes C.W., Williams S.D.P. 2010. The color of sea level: Importance of spatial variations in spectral shape for assessing the significance of trends. J. Geophys. Res. 115: C10048., Stammer et al. 2013Stammer D., Cazenave A., Ponte R.M., et al. 2013. Causes for contemporary regional sea level changes. Annu. Rev. Mar. Sci. 5: 21-46., Chen et al. 2018Chen G., Peng L., Ma C. 2018. Climatology and seasonality of upper ocean salinity: a three-dimensional view from argo floats, Clim. Dyn. 50: 2169-2182.). The El Niño Southern Oscillation (ENSO) is a major global driver of interannual sea level variability, being prominent in the Pacific Ocean and the Indian Ocean (Landerer et al. 2008Landerer F.W., Jungclaus J.H., Marotzke J. 2008. El Niño–Southern Oscillation signals in sea level, surface mass redistribution, and degree-two geoid coefficients. J. Geophys. Res. Oceans 113: C08014., Chen et al. 2010Chen G., Wang Z., Qian C., et al. 2010. Seasonal-to-decadal modes of global sea level variability derived from merged altimeter data. Remote Sens. Env. 114: 2524-2535., Boening et al. 2012Boening C., Willis J.K. Landerer F.W. et al. 2012. The 2011 La Niña: So strong, the oceans fell. Geophys. Res. Lett. 39: L19602.), which during some extreme events show a local rise in level of approximately 30 cm (Becker et al. 2012Becker M., Meyssignac B., Letetrel C., et al. 2012. Sea level variations at tropical Pacific islands since 1950. Glob. Planet. Change 80: 85-98., McGregor et al. 2012McGregor S., Gupta A.S., England M.H. 2012. Constraining wind stress products with sea surface height observations and implications for Pacific Ocean sea level trend attribution. J. Clim. 25: 8164-8176., Widlansky et al. 2014Widlansky M.J., Timmermann A., McGregor S., et al. 2014. An interhemispheric tropical sea level seesaw due to El Niño Taimasa. J. Clim. 27: 1070-1081.). The Pacific Decadal Oscillations (PDO) also affect sea level variability, especially in the North Pacific region, where this climate fluctuation could modulate the sea level by 10 cm in some regions (Hamlington et al. 2013Hamlington B.D., Leben R.R., Strassburg M.W., et al. 2013. Contribution of the Pacific Decadal Oscillation to global mean sea level trends. Geophys. Res. Lett. 40: 5171-5175., Luu and Tkalich 2014Luu Q.H., Tkalich P. 2014. Reconstruction of gappy mean sea level data. Ind. J. Geo-Mar. Sci. 43: 1316-1321., Frankcombe et al. 2015Frankcombe L.M., McGregor S., England M.H. 2015. Robustness of the modes of Indo-Pacific sea level variability. Clim. Dyn. 45: 1281-1298.). Qualifying the regional MSL change may also have an alternative social implication, such as determining land areas subject to a sovereignty claim in the South China Sea (Lyons et al. 2018Lyons Y., Luu Q.H. Tkalich P. 2018. Determining high-tide features (or islands) in the South China Sea under Article 121(1): a legal and oceanography perspective. In: Jayakumar S., Koh T. et al. (eds), The South China Sea Arbitration: The Legal Dimension, Edward Elgar Publ., pp. 128-153.).

While many efforts have been made to derive the globally averaged MSL rise rate linked to global warming (e.g. Dangendorf et al. 2015Dangendorf S., Marcos M., Muller M., et al. 2015. Detecting anthropogenic footprints in sea level rise. Nat. Comm. 6: 7849., Slangen et al. 2016Slangen A.B.A., Church J.A., Agosta C., et al. 2016. Anthropogenic forcing dominates global mean sea-level rise since 1970. Nat. Clim. Change 6: 701-705., Wu et al. 2017Wu Q., Luu Q.H., Tkalich P. et al. 2017. An improved empirical dynamic control system model of global mean sea level rise and surface temperature change. Theo. Appl. Clim. 132: 375-385.), its regional patterns have received less attention. The separation of regional trend and variability required a sufficiently long period for two reasons. Firstly, climate oscillations may increase the MSL by 50 mm or higher within a year, which was significantly greater than the annual increase (<5 mm) linked to global warming (Han et al. 2010Han W., Meehl G.A., Rajagopalan B., et al. 2010. Patterns of Indian Ocean sea-level change in a warming climate. Nat. Geos. 3: 546-550., Tkalich et al. 2013Tkalich P., Vethamony P., Luu Q.H., et al. 2013. Sea level trend and variability in the Singapore Strait. Ocean Sci. 9: 293-300., Luu et al. 2015Luu Q.H., Tkalich P., Tay T.W. 2015. Sea level trend and variability around Peninsular Malaysia. Ocean. Sci. 11: 617-628.). Secondly, each climate factor has a different spatial impact on the Earth’s oceans. Many works (Zhang and Church 2012Zhang X., Church J.A. 2012. Sea level trends, interannual and decadal variability in the Pacific Ocean. Geophys. Res. Lett. 39: L21701., Palanisamy et al. 2015Palanisamy H., Cazenave A., Delcroix T., et al. 2015. Spatial trend patterns in the Pacific Ocean sea level during the altimetry era: the contribution of thermocline depth change and internal climate variability. Ocean Dyn. 65: 341-356.) attribute a large part (>12 mm year^–1) of the MSL rise observed in the western tropical Pacific to climate variability. In a recent analysis using climate model ensembles, Fasullo and Nerem (2018)Fasullo J.T. Nerem R.S. 2018. Altimeter-era emergence of the patterns of forced sea-level rise in climate models and implications for the future. Proc. Nat. Acad. Sci. 115: 12944-12949. showed that climate forcing associated with the ENSO and the PDO contribute significantly to the spatial patterns of global MSL rise.

In this study, we extend the work of Zhang and Church (2012)Zhang X., Church J.A. 2012. Sea level trends, interannual and decadal variability in the Pacific Ocean. Geophys. Res. Lett. 39: L21701. using satellite altimetry data in three aspects. First, our domain consists of not only the Pacific Ocean, but also the Indian and Atlantic oceans. Second, we took four dominant modes of sea level variability into consideration instead of two modes, accompanied by a better statistical model to correct for autocorrelation. Lastly, we further considered the lagged times to represent the delayed response of climate impact on sea level.

DATA AND METHODTop

Monthly sea level data from the Ssalto/Duacs delay-time product provided by the Archiving, Validation and Interpretation of Satellite Oceanographic Data service (AVISO, http://www.aviso.altimetry.fr/en/data.html) for the period 1993-2015 were obtained. The product was reconstructed from ten satellite missions having fine spatial bins and delivering data at a grid resolution of 1/4°×1/4°. We removed the seasonal cycle, applied a 5-month moving average for time series and smoothed spatial patterns to a resolution of 1°×1° covering the domain 0-360°, 50°S-60°N. To correlate with climate fluctuations, we decomposed the time series of sea level at each grid point into decadal and interannual components, as suggested by previous studies (Vimont 2005Vimont D.J. 2005. The contribution of the interannual ENSO cycle to the spatial pattern of decadal ENSO-like variability. J. Clim. 18: 2080-2092., Zhang and Church 2012Zhang X., Church J.A. 2012. Sea level trends, interannual and decadal variability in the Pacific Ocean. Geophys. Res. Lett. 39: L21701.). The decadal dataset was obtained by applying 25-month moving averages followed by another 37-month smoothing on the original time series at each grid point, while the interannual dataset was achieved by subtracting the decadal components from the time series, as suggested by Zhang and Church (2012)Zhang X., Church J.A. 2012. Sea level trends, interannual and decadal variability in the Pacific Ocean. Geophys. Res. Lett. 39: L21701.. For discussion, we further used the sea level data provided by the Commonwealth Scientific and Industrial Research Organization (CSIRO), which combined data from four satellite measurements TOPEX/Poseidon, Jason-1, Jason-2/OSTM and Jason-3, available from http://www.cmar.csiro.au/sealevel/sl_data_cmar.html).

We used different climate indices to associate with dominant modes of sea level variability. The highest correlated forcings are the ENSO, the Central Pacific ENSO (CP ENSO) and the PDO. The multivariate ENSO index (MEI; http://www.esrl.noaa.gov/psd/enso/mei/) was chosen as a proxy of the ENSO (Wolter and Timlin 1998Wolter K., Timlin M.S. 1998. Measuring the strength of ENSO events: how does 1997/98 rank? Weather 53: 315-324.) that has a strong correlation with interannual changes in sea level (Luu et al. 2015Luu Q.H., Tkalich P., Tay T.W. 2015. Sea level trend and variability around Peninsular Malaysia. Ocean. Sci. 11: 617-628., Wu et al. 2017Wu Q., Luu Q.H., Tkalich P. et al. 2017. An improved empirical dynamic control system model of global mean sea level rise and surface temperature change. Theo. Appl. Clim. 132: 375-385.). The PDO index was adopted (from http://research.jisao.washington.edu/pdo/) alongside CP ENSO, as an alternative climate factor akin to the ENSO (Kao and Yu 2009Kao H.Y., Yu J.Y. 2009. Contrasting eastern-Pacific and central-Pacific types of ENSO. J. Clim. 22: 615-632., available at http://www.ess.uci.edu/~yu/2OSC/). The solar radiation data used by Luu et al. (2018)Luu Q.H., Wu Q., Tkalich P. et al. 2018. Global mean sea level rise during the recent warming hiatus from satellite-based data. Remote Sens. Lett. 9: 497-506. are not considered in this study.

To ease the autocorrelation problem arising from the original least square fitting, the first-order autoregressive and first-order moving average (ARMA(1, 1)) was applied instead of the commonly used first-order autoregressive (AR(1)) model. As pointed out by Foster and Brown (2015)Foster G., Brown P.T. 2015. Time and tide: analysis of sea level time series. Clim. Dyn. 45: 291-308., its advantage over the AR(1) model is its capability to resolve the underestimation of standard errors. All statistical values in our study were computed for a two-tailed Student t-test at a 95% significance interval. Note that the corrected confidence intervals are associated with smoothed data and might consist of unavoidable dominant uncertainties, including observational errors in the satellite orbit corrections applied (Ablain et al. 2015Ablain M., Cazenave A., Larnicol G., et al. 2015. Improved sea level record over the satellite altimetry era (1993-2010) from the Climate Change Initiative project. Ocean Sci. 11: 67-82.).

MODES OF SEA LEVEL VARIABILITYTop

The empirical orthogonal functions (EOF) technique has been applied successfully in various climate studies (e.g. Bjornsson and Venegas 1997Bjornsson H., Venegas S.A. 1997. A manual for EOF and SVD analyses of climatic data, McGill University, 53 pp., Church and White 2011Church J.A., White N.J. 2011. Sea-level rise from the late 19th to the early 21st century. Surv. Geophys. 32: 585-602.). Its advantage is its ability to decompose the spatio-temporal signals into dominant modes associated with spatial patterns and time series by means of orthogonal basis functions. We used the PCAtool developed in Matlab software by Guillaume Maze (given at https://au.mathworks.com/matlabcentral/fileexchange/17915-pcatool) to implement a regular (non-rotating) EOF analysis on sea level variability. Four dominant modes were detected from this analysis: the leading mode from decadal time series and three modes from interannual signals. They were then associated with well-identified climatic drivers that have high correlations, as described below.

For the decadal dataset, the first three leading EOF modes explained 61.2% of total variance. Accounting for 39.8% of the signals, the most dominant mode (EOF1-D) exhibited seesaw patterns in the Pacific Ocean extending symmetrically to mid-latitudes, and in the Indian Ocean (Fig. 1A). Positive values were observed in the eastern Pacific region (180-100°W; 15°S-20°N) and the western Indian Ocean (50-90°E; 0-20°S), while negative values were observed near the western Pacific-eastern Indian areas (110-150°E; 20°S-20°N) and in the central North Pacific (160°E-140°W; 20-40°N). Its temporal evolution was highly correlated (Pearson’s correlation coefficient, r=0.92) with the fluctuations of the low-pass-filtered PDO index (Fig. 1B). We attributed this mode to the PDO, which was consistent with previous findings (Zhang and Church 2012Zhang X., Church J.A. 2012. Sea level trends, interannual and decadal variability in the Pacific Ocean. Geophys. Res. Lett. 39: L21701., Frankcombe et al. 2015Frankcombe L.M., McGregor S., England M.H. 2015. Robustness of the modes of Indo-Pacific sea level variability. Clim. Dyn. 45: 1281-1298.).

Three leading modes revealed from the interannual dataset explained 39.9% of total variance. The largest principal mode (EOF1-I) accounted for 26.8% of net signals and was related to the ENSO influence due to a significant correlation (r=0.94) between spatio-temporal patterns of this mode and the high-pass-filtered ENSO index (Fig. 2B). For example, in the Pacific Ocean, a narrow seesaw pattern was found, comprising a negative anomaly in the west of the tropical equator (120-170°E; 5°S-15°N) and a positive anomaly extending from the middle of the Pacific toward the western coast of the American continent (180-65°W; 10°S-10°N). The results were similar to the ENSO-induced sea level in the tropical Pacific Ocean revealed in other studies (e.g. Hamlington et al. 2011Hamlington B.D., Leben R.R., Nerem R.S., et al. 2011. Reconstructing sea level using cyclostationary empirical orthogonal functions. J. Geophys. Res. Oceans 116: C12015., Widlansky et al. 2014Widlansky M.J., Timmermann A., McGregor S., et al. 2014. An interhemispheric tropical sea level seesaw due to El Niño Taimasa. J. Clim. 27: 1070-1081.). In contrast, a high anomaly was depicted around the western part of the Indian Ocean (40-100°E; 10°S-10°N), while a negative one was detected in its eastern part. These patterns were linked to the ENSO in earlier studies (Hamlington et al. 2011Hamlington B.D., Leben R.R., Nerem R.S., et al. 2011. Reconstructing sea level using cyclostationary empirical orthogonal functions. J. Geophys. Res. Oceans 116: C12015., Zhang and Church 2012Zhang X., Church J.A. 2012. Sea level trends, interannual and decadal variability in the Pacific Ocean. Geophys. Res. Lett. 39: L21701.).

The second principal mode (EOF2-I) showed a smaller contribution to the interannual variance (8.8%) and had a complicated structure. In the Pacific, it comprised a narrow negative equatorial belt bounded between 5°S and 5°N, a positive bar mirrored over the latitudinal line of 10°N, and a significantly negative trace appearing in the South Pacific Convergence Zone (SPCZ). Adoption of the MEI yielded the best correlation of 0.90 for a 7-month lag (Fig. 2D). This half-year lag was consistent with the findings of Widlansky et al. (2014)Widlansky M.J., Timmermann A., McGregor S., et al. 2014. An interhemispheric tropical sea level seesaw due to El Niño Taimasa. J. Clim. 27: 1070-1081., who observed an interaction between sea level in the northwest and southwest Pacific tropical regions and the ENSO extreme events. Meanwhile, the third principal mode (EOF3-I) depicted a strong positive anomaly in the Niño-4 region (5°S-5°N, 160°E-150°W) shown in Fig. 2E. This anomaly was previously reported by Kug et al. (2009)Kug J.S., Jin F.F., An S.I. 2009. Two types of El Niño events: cold tongue El Niño and warm pool El Niño. J. Clim. 22: 1499-1515., who pointed to the CP ENSO influence. The highest correlation between the temporal evolution of the CP ENSO and the mode was 0.56 after a 2-month lag (Fig. 2F and Table 1), contributing 4.3% to total variance.

The time lags between climate indices and principal modes of sea level variability are summarized in Table 1. To further examine the sensitivity of these time lags, we repeated the EOF analysis on the sea level dataset provided by CSIRO and obtained similar results (Table 1).

REGRESSION ANALYSISTop

Regression models

In the simple model, the sea level change rate was derived from a single-value linear regression (SVLR) analysis. At a given geographic location (x,y), the geocentric sea level H(x,y,t) with respect to its long-term mean at the given time t is described by the equation:

H(x,y,t) = sSVLR(x,y)t + cSVLR (x,y)

(1)

where s_SVLR is the linear rate of sea level rate over the considered period, and c_SVLR is a constant in the SVLR analysis. By calculating the rates at different geographic locations, we established a global map showing rates of sea level change during the given period (Fig. 3A). The analysis was carried out on the monthly time-series from each of 360×180 grid points.

In the second model, we further considered more variables in the equation using multiple linear regression (MVLR) analysis. These variables were defined from above dominant climate indices, which have been shown in the EOF analysis to have high correlations with the sea level. Table 1 presents definitions of the Interannual Climate Indices (ICIs) and the Decadal Climate Indices (DCIs) based on the MEI, the CP ENSO and the PDO. Using the defined climate indices, we estimated the linear rate of change (s_MVLR) from the equation

H(x,y,t) = sMVLR(x,y)t + cMVLR (x,y) + i1(x,y)ICI1 + i2(x,y)ICI2 + i3(x,y)ICI3 + d1(x,y)DCI1

(2)

where s_SVLR(x,y) is the sea level rise rate; i_k(x,y) (k=1, 2, 3) and d_k(x,y) (l=1) are the coefficients representing the contributions from ICIs and DCIs; and c_SVLR(x,y) is a constant.

Model performance and contribution of climate factors

We used the coefficient of determination (R2) to measure the goodness-of-fit of the models. It is computed as a percentage from the ratio of explained variance (derived from the regression model) to total variance, resulting in a value between 0% and 100%. Table 2 and Figure 4 show the coefficients computed from the regression models: SVLR, MVLR with two dominant modes, and MVLR with four dominant modes.

For the AVISO dataset, the SVLR model explained 24% of the globally averaged variance. The use of the MVLR model with all dominant modes significantly doubled the R2 to 47% (Table 2). The MVLR model provides better results than the SVLR in the Pacific Ocean, where the goodness-of-fit difference was almost three-fold. The variance in the Atlantic Ocean was well explained by the SVLR (35%), in which the involvement of four additional variables enhanced the estimates by only 7%. A similar success of the MVLR over the SVLR was observed in the CSIRO dataset (Table 2).

Figure 4 depicts relative influences of the dominant ICI and DCI modes in the MVLR models for the AVISO dataset. The coefficient of determination in the MVLR model using the ICIs was 41%, which is 6% higher than that of the DCIs. This means that the contribution of the interannual indices was greater than that of the decadal components in the overall MVLR model. When both ICIs and DCIs were included in the regression (Fig. 4D), the R2 ratio was the highest among the MVLR models considered, reaching 50%. Notable improvements are observed in the tropical Pacific Ocean and part of the mid-latitude regions (R2>80%). In the Pacific Ocean, ICIs dominated the regional variance. In the Atlantic Ocean, the two indices were equally important in contributing to total variance.

The best model depicting the rates of regional sea level rise is MVLR using the dominant modes of both the ICIs and the DCIs (Fig. 5), which was used to derive the characteristics of regional sea level rise rates to be discussed in the next section.

REGIONAL SEA LEVEL CHANGETop

Spatial patterns of sea level change

Figure 3A displays the observed patterns of sea level rise in global oceans for the period 1993-2012. The rate was high (>10 mm year^–1) in the western areas of the Pacific Ocean, whereas a marginal decreasing rate was seen in the eastern areas. In contrast, the increasing tendency was observed in the Indian and Atlantic oceans, except for a few small regions at high latitude. In overall, the highest rates (>6 mm year^–1) were found in the tropical regions (40-120°E; 10-30°S) and at mid-latitudes (around 40°S) in the Indian Ocean and tropical Pacific (150°E-125°W; 20°S-20°N). However, these high rates failed to pass the significance test, implying that the SVLR model did not explain changes in sea level well.

The regional rate after the MVLR analysis is displayed in Figure 3B. A significant adjustment was noted in the Pacific Ocean. The positive change in sea level (>10 mm year^–1) shifted from its western basin to the tropical areas (150°E-125°W; 20°S-20°N), with weakened extremes. The rise became stronger in some areas of the Indian Ocean (around 15°S) and the Atlantic tropics (0-60°W; 0-20°N). The areas with a negative rate in the eastern Pacific were diminished.

In comparison, the aliasing (Fig. 3C) was defined by subtracting the MVLR regional rate (Fig. 3B) from the SVLR one (Fig. 3A), which demonstrated the influence of climate variability on the regional rate of sea level chance. The largest deviations (>9 mm year^–1) in aliasing were found in the Indo-Pacific tropics. The aliasing was unlikely to have been caused by the ICIs because no noticeable rates were observed in their indices. Instead, it was mainly attributed to decadal variability.

Meridional and zonal change in sea level

To further examine the spatial variability, sea level change rates were averaged in the meridional (Fig. 6A) and zonal (Fig. 6C) directions. In the meridional axis, the largest discrepancy was observed in the region between 90°E and 100°W, which includes mainly the Pacific Ocean. When the pattern was compared with the climate factors averaged over the entire available latitudinal range (Fig. 6B), it was apparent that the contribution probably resulted from the PDO. Meanwhile, meridional distribution of the aliasing in the Indian Ocean and the Atlantic Ocean was smaller.

In the zonal axis, the MSL rose faster in the Southern Hemisphere than in the Northern Hemisphere (Fig. 6C). Along the equator (between 10°S and 10°N), the MSL rose at a rate of about 3.5 mm year^–1, which was 1.0 mm year^–1 higher than estimated in the SVLR model (Fig. 6C). The PDO was also responsible for the high rate in latitudinal regions covering the subtropics (30 to 50°S and 30 to 50°N). The zonal influence of interannual components was negligible for the long-term trend (Fig. 6D).

Temporal variability of mean sea level

Time series of the MSL change are depicted in Figure 7A. The main finding is that, while the sea level rise rates over the period 1993-2012 were slightly altered, their corresponding 95% confidence intervals were narrowed significantly. In the Pacific and Atlantic Oceans, the rates for the same episode were marginally higher (by 3-4%), with the confidence bands narrowed by 16 to 27%. The noticeable change was in the Indian Ocean, where the rate was 20% higher than for the simple linear regression, accompanied by a better (i.e. narrower) estimation of confidence band of 0.56 mm year^–1, which was 46% smaller.

To examine the role of each climatic factor, we removed the index from the multiple linear regression (Eq. 2) and computed the contribution as the sea level difference between the modified and original MVLR models (Fig. 7B). It was found that the ENSO exhibited a prevailing impact in year-to-year sea level changes in all oceanic basins, causing the greatest interannual variability. The influence of the PDO (i.e. DCI1) was the strongest, and probably caused an alteration of the apparent sea level rise in the Indian Ocean. Although the contribution of the CP ENSO (ICI2) was insignificant in the long term, it had a noticeable impact on the interannual scale, for instance, over the period 1997-1998.

CONCLUSION AND DISCUSSIONTop

Regional changes in sea level over a 20-year period were partitioned by taking advantage of high-resolution satellite altimeter data. To determine the components of sea level variability, its dominant modes were identified from interannual and decadal time series by means of an EOF method, which linked three leading interannual modes to the ENSO and the CP ENSO, and the principal decadal mode to the PDO. MVLR models were used to separate the trend and variability, which showed an improvement versus the SVLR in two statistical measures. Firstly, the use of the multivariate model improved the coefficients of determination for two datasets used, namely AVISO and CSIRO. Secondly, the MVLR model also significantly eased the statistical uncertainty in estimating the sea level change rate. The MVLR model was then employed to display the patterns and temporal variability of regional sea level change.

Significant adjustments were visible in the Pacific Ocean, where the positive change in sea level (>10 mm year^–1) shifted from its western basin to the tropical areas (150°E-125°W; 20°S-20°N), while the negative rate on its eastern side diminished. The rise became stronger in some areas of the Indian Ocean (around 15°S) and Atlantic tropics (0-60°W; 0-20°N). Along the meridional axis, the largest discrepancy was observed in the Pacific Ocean, which is mainly contributed by the PDO. The MSL rose faster in the Southern Hemisphere than in the Northern Hemisphere. In the temporal change, the ENSO exhibited prevailing impacts in interannual sea level variations in all oceanic basins. Despite being insignificant in the long term, the CP ENSO made a noticeable contribution at the interannual scale, for instance, over the period 1997-1998.

We derived the regional patterns of sea level change by means of a statistical approach using satellite data. Our results are consistent with the conclusion from a recent study by Fasullo and Nerem (2018)Fasullo J.T. Nerem R.S. 2018. Altimeter-era emergence of the patterns of forced sea-level rise in climate models and implications for the future. Proc. Nat. Acad. Sci. 115: 12944-12949., who used climate model ensembles and came to the similar conclusion that external climate forcing including the ENSO and the PDO is probably a main contributor to the observed non-uniform patterns of sea level rise in the global oceans. They further suggested that these patterns might remain for decades, and will probably be intensified under the changing climate.

For future studies, the fairly low significant level in some regions and the small variances explained by interannual modes suggested that improvements are desirable. These may include the introduction of other climatic and non-climatic factors and a more suitable regression model, as there are still a lot of interannual and decadal variabilities left after applying the MVLR model, which alias into the trend estimates. In fact, this is a great challenge, since a quantitative relationship between regional sea level change and climate fluctuations is undeterminable outside the context of the Earth’s sophisticated climate system, which is driven by both deterministic and stochastic processes. As a result, further continuing efforts are needed to give deeper insights into not only the statistical decomposition technique to attain the rate, but also the establishment of non-deterministic mathematical relationships between sea level variability and other physical components of the climate system, including ice sheet melts and volcano eruptions (Slangen et al. 2016Slangen A.B.A., Church J.A., Agosta C., et al. 2016. Anthropogenic forcing dominates global mean sea-level rise since 1970. Nat. Clim. Change 6: 701-705., Marcos et al. 2017Marcos M., Marzeion B., Dangendorf S., et al. 2017. Internal variability versus anthropogenic forcing on sea level and its components. Surv. Geophys. 38: 329-348., Huang et al. 2018Huang J., Zhang X, Zhang Q., et al. 2018. Recently amplified arctic warming has contributed to a continual global warming trend. Nat. Clim. Change 7: 875-879.).

ACKNOWLEDGEMENTSTop

Chen G. and Wu Q. were jointly supported by the Natural Science Foundation of China under Grant Nos. 41331172, U1406404 and 61361136001, and by the National Laboratory for Marine Science and Technology under the Outstanding Scientist Project of the Ao-Shan Talents Programme (No. 2015ASTP-OS15). The analysis was conducted using the PCAtool developed by Guillaume Maze. The authors acknowledge the careful review and constructive comments from Prof. D. Vaqué, Dr. A. Alvera, Dr T. Frederikse and anonymous reviewer(s). We thank Prof. S.P.H. Ng, Dr M.F. Lau and Prof. P.H.H. Then for providing computational facilities. Thanks are extended to V.M. Albéniz, A. Lounds and the Scientia Marina editorial office for the support with submission, and F.A.A. Freddy and T.N. Nguyen for their help with the Spanish translation.

ReferencesTop

Ablain M., Cazenave A., Larnicol G., et al. 2015. Improved sea level record over the satellite altimetry era (1993-2010) from the Climate Change Initiative project. Ocean Sci. 11: 67-82.
https://doi.org/10.5194/os-11-67-2015

Ablain M., Legeais J.F., Prandi P., et al. 2017. Satellite altimetry-based sea level at global and regional scales. Surv. Geophys. 38: 7-31.
https://doi.org/10.1007/s10712-016-9389-8

Becker M., Meyssignac B., Letetrel C., et al. 2012. Sea level variations at tropical Pacific islands since 1950. Glob. Planet. Change 80: 85-98.
https://doi.org/10.1016/j.gloplacha.2011.09.004

Bjornsson H., Venegas S.A. 1997. A manual for EOF and SVD analyses of climatic data, McGill University, 53 pp.

Boening C., Willis J.K. Landerer F.W. et al. 2012. The 2011 La Niña: So strong, the oceans fell. Geophys. Res. Lett. 39: L19602.
https://doi.org/10.1029/2012GL053055

Bos M.S., Williams S.D.P., Araujo I.B., et al. 2014. The effect of temporal correlated noise on the sea level rate and acceleration uncertainty. Geophys. J. Int. 196: 1423-1430.
https://doi.org/10.1093/gji/ggt481

Cazenave A., Dieng H.B., Meyssignac B., et al. 2014. The rate of sea-level rise. Nat. Clim. Change 4: 358-361.
https://doi.org/10.1038/nclimate2159

Chen G., Wang Z., Qian C., et al. 2010. Seasonal-to-decadal modes of global sea level variability derived from merged altimeter data. Remote Sens. Env. 114: 2524-2535.
https://doi.org/10.1016/j.rse.2010.05.028

Chen G., Peng L., Ma C. 2018. Climatology and seasonality of upper ocean salinity: a three-dimensional view from argo floats, Clim. Dyn. 50: 2169-2182.
https://doi.org/10.1007/s00382-017-3742-6

Chen X., Zhang X., Church J.A., et al. 2017. The increasing rate of global mean sea-level rise during 1993-2014. Nat. Clim. Change 7: 492-495.
https://doi.org/10.1038/nclimate3325

Church J.A., White N.J. 2011. Sea-level rise from the late 19th to the early 21st century. Surv. Geophys. 32: 585-602.
https://doi.org/10.1007/s10712-011-9119-1

Dieng H.B., Cazenave A., Meyssignac B., et al. 2017. New estimate of the current rate of sea level rise from a sea level budget approach. Geophys. Res. Lett. 44: 3744-3751.
https://doi.org/10.1002/2017GL073308

Dangendorf S., Marcos M., Muller M., et al. 2015. Detecting anthropogenic footprints in sea level rise. Nat. Comm. 6: 7849.
https://doi.org/10.1038/ncomms8849

Dangendorf S, Marcos M., Wöppelmann G., et al. 2017. Reassessment of 20th century global mean sea level rise. Proc. Nat. Acad. Sci. 114: 5946-5951.
https://doi.org/10.1073/pnas.1616007114

Fasullo J.T. Nerem R.S. 2018. Altimeter-era emergence of the patterns of forced sea-level rise in climate models and implications for the future. Proc. Nat. Acad. Sci. 115: 12944-12949.
https://doi.org/10.1073/pnas.1813233115

Foster G., Brown P.T. 2015. Time and tide: analysis of sea level time series. Clim. Dyn. 45: 291-308.
https://doi.org/10.1007/s00382-014-2224-3

Frankcombe L.M., McGregor S., England M.H. 2015. Robustness of the modes of Indo-Pacific sea level variability. Clim. Dyn. 45: 1281-1298.
https://doi.org/10.1007/s00382-014-2377-0

Hamlington B.D., Leben R.R., Nerem R.S., et al. 2011. Reconstructing sea level using cyclostationary empirical orthogonal functions. J. Geophys. Res. Oceans 116: C12015.
https://doi.org/10.1029/2011JC007529

Hamlington B.D., Leben R.R., Strassburg M.W., et al. 2013. Contribution of the Pacific Decadal Oscillation to global mean sea level trends. Geophys. Res. Lett. 40: 5171-5175.
https://doi.org/10.1002/grl.50950

Han W., Meehl G.A., Rajagopalan B., et al. 2010. Patterns of Indian Ocean sea-level change in a warming climate. Nat. Geos. 3: 546-550.
https://doi.org/10.1038/ngeo901

Hay C.C., Morrow E., Kopp R.E., et al. 2015. Probabilistic reanalysis of twentieth-century sea-level rise. Nature 517: 481-484.
https://doi.org/10.1038/nature14093

Huang J., Zhang X, Zhang Q., et al. 2018. Recently amplified arctic warming has contributed to a continual global warming trend. Nat. Clim. Change 7: 875-879.
https://doi.org/10.1038/s41558-017-0009-5

Hughes C.W., Williams S.D.P. 2010. The color of sea level: Importance of spatial variations in spectral shape for assessing the significance of trends. J. Geophys. Res. 115: C10048.
https://doi.org/10.1029/2010JC006102

Intergovernmental Panel on Climate Change (IPCC). 2013. Climate Change 2013: The Physical Science Basis. Contribution of Working Group I to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change. Stocker T.F., Qin D., et al. (eds), Cambridge University Press, Cambridge, United Kingdom and New York, NY, USA. 1585 pp.
https://www.ipcc.ch/report/ar5/wg1/

Jevrejeva S., Grinsted A., Moore J.C. 2009. Anthropogenic forcing dominates sea level rise since 1850. Geophys. Res. Lett. 36: L20706.
https://doi.org/10.1029/2009GL040216

Kao H.Y., Yu J.Y. 2009. Contrasting eastern-Pacific and central-Pacific types of ENSO. J. Clim. 22: 615-632.
https://doi.org/10.1175/2008JCLI2309.1

Kug J.S., Jin F.F., An S.I. 2009. Two types of El Niño events: cold tongue El Niño and warm pool El Niño. J. Clim. 22: 1499-1515.
https://doi.org/10.1175/2008JCLI2624.1

Landerer F.W., Jungclaus J.H., Marotzke J. 2008. El Niño–Southern Oscillation signals in sea level, surface mass redistribution, and degree-two geoid coefficients. J. Geophys. Res. Oceans 113: C08014.
https://doi.org/10.1029/2008JC004767

Luu Q.H., Tkalich P. 2014. Reconstruction of gappy mean sea level data. Ind. J. Geo-Mar. Sci. 43: 1316-1321.

Luu Q.H., Tkalich P., Tay T.W. 2015. Sea level trend and variability around Peninsular Malaysia. Ocean. Sci. 11: 617-628.
https://doi.org/10.5194/os-11-617-2015

Luu Q.H., Wu Q., Tkalich P. et al. 2018. Global mean sea level rise during the recent warming hiatus from satellite-based data. Remote Sens. Lett. 9: 497-506.
https://doi.org/10.1080/2150704X.2018.1437291

Lyons Y., Luu Q.H. Tkalich P. 2018. Determining high-tide features (or islands) in the South China Sea under Article 121(1): a legal and oceanography perspective. In: Jayakumar S., Koh T. et al. (eds), The South China Sea Arbitration: The Legal Dimension, Edward Elgar Publ., pp. 128-153.
https://doi.org/10.4337/9781788116275.00015

Marcos M., Amores A. 2014. Quantifying anthropogenic and natural contributions to thermosteric sea level rise. Geophys. Res. Lett. 41: 2502-2507.
https://doi.org/10.1002/2014GL059766

Marcos M., Marzeion B., Dangendorf S., et al. 2017. Internal variability versus anthropogenic forcing on sea level and its components. Surv. Geophys. 38: 329-348.
https://doi.org/10.1007/s10712-016-9373-3

McGregor S., Gupta A.S., England M.H. 2012. Constraining wind stress products with sea surface height observations and implications for Pacific Ocean sea level trend attribution. J. Clim. 25: 8164-8176.
https://doi.org/10.1175/JCLI-D-12-00105.1

Nerem R.S., Beckley B.D., Fasullo J.T., et al. 2018. Climate-change–driven accelerated sea-level rise detected in the altimeter era. Proc. Nat. Acad. Sci. 115: 2022-2025.
https://doi.org/10.1073/pnas.1717312115

Palanisamy H., Cazenave A., Delcroix T., et al. 2015. Spatial trend patterns in the Pacific Ocean sea level during the altimetry era: the contribution of thermocline depth change and internal climate variability. Ocean Dyn. 65: 341-356.
https://doi.org/10.1007/s10236-014-0805-7

Royston S., Watson C.S., Legresy B., et al. 2018. Sea-level trend uncertainty with Pacific climatic variability and temporally-correlated noise. J. Geophys. Res. Oceans 123: 1978-1993.
https://doi.org/10.1002/2017JC013655

Slangen A.B.A., Church J.A., Agosta C., et al. 2016. Anthropogenic forcing dominates global mean sea-level rise since 1970. Nat. Clim. Change 6: 701-705.
https://doi.org/10.1038/nclimate2991

Stammer D., Cazenave A., Ponte R.M., et al. 2013. Causes for contemporary regional sea level changes. Annu. Rev. Mar. Sci. 5: 21-46.
https://doi.org/10.1146/annurev-marine-121211-172406

Tkalich P., Vethamony P., Luu Q.H., et al. 2013. Sea level trend and variability in the Singapore Strait. Ocean Sci. 9: 293-300.
https://doi.org/10.5194/os-9-293-2013

Vimont D.J. 2005. The contribution of the interannual ENSO cycle to the spatial pattern of decadal ENSO-like variability. J. Clim. 18: 2080-2092.
https://doi.org/10.1175/JCLI3365.1

Visser H., Dangendorf S., Petersen A.C. 2015. A review of trend models applied to sea level data with reference to the “acceleration-deceleration debate”. J. Geophys. Res. Oceans 120: 3873-3895.
https://doi.org/10.1002/2015JC010716

Widlansky M.J., Timmermann A., McGregor S., et al. 2014. An interhemispheric tropical sea level seesaw due to El Niño Taimasa. J. Clim. 27: 1070-1081.
https://doi.org/10.1175/JCLI-D-13-00276.1

Wolter K., Timlin M.S. 1998. Measuring the strength of ENSO events: how does 1997/98 rank? Weather 53: 315-324.
https://doi.org/10.1002/j.1477-8696.1998.tb06408.x

Wu Q., Luu Q.H., Tkalich P. et al. 2017. An improved empirical dynamic control system model of global mean sea level rise and surface temperature change. Theo. Appl. Clim. 132: 375-385.
https://doi.org/10.1007/s00704-017-2039-3

Zhang X., Church J.A. 2012. Sea level trends, interannual and decadal variability in the Pacific Ocean. Geophys. Res. Lett. 39: L21701.
https://doi.org/10.1029/2012GL053240