1 Introduction

A rise in sea surface height (SSH) has a potentially devastating impact on coastal societies, resulting in flooding, coastal erosion, salinization of surface and ground waters, and degradation of coastal wetlands habitats (Nicholls 2011). Variations in SSH are largely the result of two processes: one involves steric variations (henceforth denoted as SSHsteric) due to changes in temperature and salinity, and the other involves changes in water mass (henceforth denoted as SSHmass) as a result of either ocean mass redistribution or water mass flux (Cazenave and Nerem 2004; Carton et al. 2005; Chambers 2006; Calafat et al. 2010). Altimetry-based estimates of global SSH beginning in1993 have provided a means of measuring the combined effects of steric and mass variation. Objective analysis and ocean data assimilation allow the steric component to be examined alone (Carton et al. 2005; Ishii et al. 2006). Since 2002, the Gravity Recovery and Climate Experiment (GRACE) mission has provided an independent tool to monitor water mass change in the ocean (Nerem et al. 2003; Wahr et al. 2004).

Low-frequency fluctuations in SSHmass (Fig. 1) are strong in the Southern Ocean, North Pacific and semi-enclosed areas at various latitudes (e.g., Indonesian seas, Mediterranean Sea), where the correlation between ocean bottom pressure and SSH is significant (Piecuch et al. 2013). SSHmass variability in the Southern Ocean and North Pacific are mainly driven by changes in wind stress curl (Boening et al. 2011; Cheng et al. 2013). In addition to the GRACE studies in the open ocean, several works have focused on the annual SSHmass cycle in shallow waters such as the Mediterranean Sea, the Gulf of Thailand, and the South China Sea (García et al. 2006; Wouters and Chambers 2010; Cheng and Qi 2010).

Fig. 1
figure 1

Standard deviation of SSHmass (cm) derived from GRACE over the period 2003–2011, with its annual cycle removed

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Strong variations in SSHmass are present in the Gulf of Carpentaria (hereinafter referred to as the GOC) (Fig. 1). The GOC is enclosed on three sides by northern Australia and bounded on the north by the Arafura Sea. It comprises a water area of approximately 300,000 km2, with a general depth of between 55 and 66 m and a maximum depth of 82 m (Fig. 2). This gulf features a multi-million-dollar prawn industry—the most valuable prawn industry managed by the Australian government (McLoughlin 2004)—as well as onshore mineral resources including bauxite, silver and manganese, and unique ecosystems that include submerged reefs supporting diverse coral communities (Harris 2007). As such, understanding the variations in SSH here may be important for the sustainable management of this region. From a scientific perspective, investigating the features of SSH variations in the GOC and related mechanisms will help to improve our knowledge of how the regional ocean responds to large-scale climate modes such as the El Niño-Southern Oscillation (ENSO) and Pacific Decadal Oscillation (PDO).

Fig. 2
figure 2

Bathymetry in Gulf of Carpentaria. The white circles show the tide gauge locations: (1) Groote Eylandt, (2) Karumba, and (3) Weipa. The black box over the Gulf of Carpentaria encloses the area of interest (136°E–142°E, 18°S–8°S) used to calculate the gulf-mean signal, and the red box denotes the area chosen to calculate offshore SSHsteric

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Several studies have investigated SSH variations in the GOC. For example, Forbes and Church (1983) studied annual SSH variations in the GOC based on observations of current and SSH from sea bed drifters and buoys. The largest annual range of monthly mean sea level estimates in the GOC is 75 cm, in the southeast corner, and 70 % of observed variations were attributable to the cumulative effects of atmospheric pressure, winds and steric variation. This annual signal was also detected by the GRACE mission at an amplitude of approximately 0.4 m; a comparison of the GRACE estimates with observations from a nearby tide gauge shows a correlation of 0.93, indicating that the GRGS (Groupe de Recherche en Géodesie Spatiale) GRACE solutions capture well the regional annual signal (Tregoning et al. 2008).

Using a nonlinear barotropic numerical model, Oliver and Thompson (2011) pointed out that the intraseasonal variations of the SSH field in the GOC are driven by surface wind stress variability related to the Madden–Julian Oscillation (MJO), while its low-frequency variability is propagated from the western equatorial Pacific, which is related to ENSO.

The studies mentioned above have provided a description of the annual cycle of SSHmass and intraseasonal, interannual variations of the SSH in the GOC. However, aside from the work by Oliver and Thompson (2011), the interannual and decadal variability of SSHmass, as well as its contribution to sea level change, have seldom been discussed. This study investigates variations in SSH in the GOC on interannual to decadal timescales by decomposing SSH into mass-induced and steric-related components, and explores their response to the ENSO and PDO via ocean processes.

This paper is structured as follows: the datasets used are described in Sect. 2, followed by the results in Sect. 3 on the variations in SSH on seasonal to decadal timescales. A discussion of the results and our conclusions are presented in Sect. 4.

2 Data and method

2.1 Global observations of SSH

SSH observations used in this study are based on a merged product from multiple satellite missions (T/P and ERS-1/2, followed by Jason-1/2 and Envisat) distributed on the Archiving, Validation, and Interpretation of Satellite Oceanographic (AVISO, http://www.aviso.oceanobs.com/) database system. Standard geophysical and environmental corrections, including ionosphere delay, dry and wet tropospheric corrections, electromagnetic bias, solid earth and ocean tides, ocean tide loading, pole tide, inverted barometer correction, sea state bias and instrumental corrections, have been applied (Le Traon et al. 1998; Le Traon and Ogor 1998). The product is available on a 1/3° Mercator grid at monthly intervals.

2.2 Global observations of SSHmass

To estimate the mass component of the SSH budget, we use the monthly GRACE data (Release-04 solutions) produced by the Center for Space Research (CSR), University of Texas at Austin (http://grace.jpl.nasa.gov/data/mass/). The data, which is on a 1° × 1° spatial grid, is smoothed spatially using a 500-km Gaussian filter.

2.3 Global observations of SSHsteric

The monthly 1° × 1° gridded temperature and salinity dataset (Ishii et al. 2006) is used to calculate SSHsteric variations in the GOC. This data covers the period from 1945 to 2011 at a depth from the surface to 700 m.

2.4 Coastal observations of SSH

The presence of observed monthly SSH records at three tide stations (including Milner Bay, Karumba and Weipa; see their locations on Fig. 2) along the coast of Gulf of Carpentaria is from Permanent Service for Mean Sea Level (PSMSL) (http://www.psmsl.org/) (Holgate et al. 2013; PSMSL 2014). It provides an independent measure of the magnitude of the SSH variations against which the altimetry estimates can be validated.

2.5 Global observations of surface wind

For the global fields of zonal and meridional surface winds, we use data on a 0.25° × 0.25° grid obtained from the Environmental Research Division Data Access Program (ERDDAP) and the National Oceanic and Atmospheric Administration's National Climatic Data Center (NOAA/NCDC). The gridded data is generated from multiple satellite observations of the Department of Defense (DOD), NOAA, and the National Aeronautics and Space Administration (NASA), and wind retrievals of remote sensing systems (RSS), with monthly resolution from January 2003 to September 2011. To estimate the response of SSH to wind stress in the GOC, the local wind setup on sea surface height (WSSH) was calculated following Oliver and Thompson (2010).

2.6 Eddy-resolving model

To reveal the decadal and long-term variability of SSHmass and SSH, we used OFES [OGCM for the Earth Simulator] output. The OFES products (Masumoto et al. 2004; Sasaki et al. 2008) are based on the Modular Ocean Model version 3 (MOM3), with a near-global domain extending from 75°S to 75°N, but excluding the Arctic regions. Its horizontal resolution is 0.1°, and it has 54 vertical levels. In this study, hindcast simulation for the period 1955–2013 is used, with its daily atmospheric forcing from NCEP/NCAR Reanalysis data. When the multi-year average is removed, the variable sea surface height of OFES output is transformed into the model-based sea surface height (MSSH). Temperature and salinity outputs are used to calculate the OFES-based steric component (MSSHsteric). Thus the mass-induced term of the OFES version (MSSHmass) is available when MSSH steric is subtracted from MSSH.

2.7 Data processing

The anomalies are obtained by subtracting the climatological monthly means and subsequently filtering out the intraseasonal cycle using a 3-month running mean. The interannual components are the de-trended anomalies. Taking SSH as an example, the de-trended SSH anomalies are what we call interannual SSH. Similarly, the decadal components are the low-pass filtered (with a cutoff period at 7 years) anomalies. Study on the long-term variations of SSH, SSHmass, SSHsteric, MSSH, MSSHmass and MSSHsteric target the corresponding anomalies.

3 Results

3.1 Seasonal variability in SSHmass over the GOC

Sea level records from tide gauges, altimetry observations and OFES output (Fig. 3) are quite well-matched in terms of amplitude and phase, suggesting that both altimetry observations and OFES results effectively capture the SSH signal in the GOC.

Fig. 3
figure 3

Sea level records of altimetry (black lines), tide gauges (blue lines) and OFES (red lines) during the period 2003–2011 for (from top to bottom) Groote Eylandt, Karumba and Weipa

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The time series of SSH in the GOC shows significant seasonal variability (Fig. 3). Along with the southeasterly trade winds in austral winter, negative SSHmass occupies the entire domain, while the northwesterly monsoon causes a significant rise in gulf-wide SSHmass during the austral summer (Fig. 4). As it is dominated by SSHmass, SSH exhibits a pattern that is similar to that of SSHmass. It exerts strong seasonal variability which is attributable to the Ekman transport driven by the seasonally reversing monsoon. The same mechanism has been discussed for the western South China Sea (Cheng and Qi 2010), in agreement with Oliver and Thompson (2011), in which a good coherence between SSH variability and local wind variability is found on the seasonal timescale. Tregoning et al. (2008) carried out similar work using GRACE estimates over the period June 2002–May 2007. With better and longer-term GRACE observations, the climatological means in this study would be expected to be improved.

Fig. 4
figure 4

Maps of seasonal mean SSH (a–d), SSHmass (e–h) and SSHsteric (i–l) (cm, shaded), overlaid by climatological seasonal mean surface winds (m/s, vectors)

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3.2 Interannual variations in gulf-wide SSHmass

On an interannual timescale, the temporal evolution of gulf-mean SSHmass matches well with that of observed SSH (Fig. 5, r = 0.92, significant at the 95 % confidence level), consistent with the results of Piecuch et al. (2013), who reported a significant interannual coherence between observed bottom pressure and SSH over shallow or semi-enclosed areas. However, the authors did not elucidate the reason for the good correlation or the cause of the interannual variability. In the Arafura Sea, just west of the region of interest in our study, interannual SSH and SSHmass variations occur with a peak-to-peak amplitude of a few centimeters and periods of a couple of years (Piecuch et al. 2013). The correlation between the SSHsteric and SSH anomalies in the GOC is also significant (Fig. 5, r = 0.47, significant at 95 % confidence level), while the amplitude of SSHsteric is too weak to affect interannual SSH variability. Unlike seasonal variations, variation in local wind set-up on sea surface height (WSSH) is almost zero amplitude, with the exception of April 2006, when a severe tropical cyclonic hit the GOC. Neither SSHmass nor SSH is significantly correlated with the WSSH, indicating that local wind cannot explain interannual variations in SSHmass and SSH.

Fig. 5
figure 5

Time series of interannual SSH (black), SSHsteric (red) and SSHmass (blue), averaged over the area denoted by the black box in Fig. 2 (136°E–142°E, 18°S–8°S). The green curve and the light blue shading represent the local wind set-up on sea surface height (here denoted as WSSH) anomalies and the Niño 3.4 index, respectively

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Recent studies have suggested that a significant portion of interannual sea level variation along the Australian coast originates from the western Pacific and is closely related to ENSO (Wijffels and Meyers 2004; Oliver and Thompson 2011). The curve denoting the temporal evolution of the Niño 3.4 index (sea surface temperature anomalies in 5°S–5°N, 170°–120°W, Fig. 5) is used to examine the relationship between SSH (including its two components) and ENSO. Three El Niño events (2004/2005, 2006/2007 and 2009/2010) and two La Niña events (2007/2008 and 2010/2011) took place during the study period. During the El Niño (La Niña) events, both SSH and SSHmass experienced negative (positive) anomalies. Similar SSH variations were revealed in the waters surrounding Indonesia (Nerem et al. 1999) and along the southwestern coast of the Australian continent (Feng et al. 2004), where steric components dominate changes in SSH. Further analysis shows that both SSH and SSHmass in the GOC are significantly correlated with the Niño 3.4 index (Fig. 5), with correlation coefficients of −0.71 and −0.75, respectively. Interestingly, the GOC is the very region where interannual SSHmass is highly correlated to ENSO (Fig. 6). In the equatorial western Pacific, easterly (westerly) wind anomalies deepen (shoal) the thermocline during La Niña (El Niño) events, thereby increasing (decreasing) the steric component and, consequently, the total sea level. In contrast, the ENSO-related wind in the GOC leads to the divergence (convergence) of water during La Niña (El Niño) events (Fig. 7), which plays a negative role in variations of SSH and SSHmass. Therefore, ENSO is expected to affect the interannual variability of SSH and SSHmass via ocean processes.

Fig. 6
figure 6

Map of the correlation coefficient between interannual SSHmass and Niño 3.4 index. White contours denote a 95 % confidence level

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Fig. 7
figure 7

Regression coefficients of interannual SSH (a, d), SSHmass (b, e), SSHsteric (c, f) (cm, shaded) and NCDC 10-m winds (m/s, vectors) against the normalized negative Niño 3.4 index. Right panels are their corresponding values over the Gulf of Carpentaria

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3.3 Decadal and long-term variability in SSHmass

In this section, we further identify the decadal and long-term variability in gulf-scale SSHmass and SSH. Figure 8 shows long-term trends in SSH and SSHmass in the GOC for 2003–2011, with maxima reaching ~20 mm/year for SSH and >8.0 mm/year for SSHmass, whereas SSHsteric shows no significant trend. Gulf-mean SSH rises at a rate of 16.9 ± 3.2 mm/year. SSHmass alone has a positive trend of 8.0 ± 1.5 mm/year, four times the rate of the rise in global SSHmass, which was 2.0 mm/year during 2003–2012 (Johnson and Chambers 2013), while the linear trend of SSHsteric is not significant at a 95 % level (Fig. 9a). Significant correlation is found between SSHmass and SSH (r = 0.96, significant at the 99 % level), whereas SSHsteric correlates to SSH at 0.34. The correlation coefficient between SSH and the sum of its two components is 0.96, indicating good agreement between SSH and its two components, and SSHmass dominates the sea level change in terms of long-term variations in the GOC. The sum of SSHmass and SSHsteric explain about half of the observed total sea level rise during 2003–2011. The discrepancy between the SSH and the sum of its two components may be due to uncertainties in the altimetry and GRACE data and subsurface temperature and salinity analyses. The GRACE data has a relatively low signal-to-noise ratio in the tropics (Wahr et al. 2004) and greatly underestimates the SSHmass in the GOC. Quinn and Ponte (2010) noted uncertainty in ocean mass trends of up to ~2.5 mm/year over 2003–2008 from GRACE observations.

Fig. 8
figure 8

Linear trends for SSH (a), SSHmass (b) and SSHsteric (c) over the period 2003–2011 (mm/year, shaded), imposed on the linear trend of 10-m winds from NCDC/NOAA (m/s/year, vectors). Right panels are their corresponding values over the Gulf of Carpentaria

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Fig. 9
figure 9

a Time series of gulf-mean anomalies of SSH (black), SSHsteric (red) and SSHmass (blue) averaged over the area denoted by the black box in Fig. 3 (136°E–142°E, 18°S–8°S). The dotted curves are the corresponding OFES estimates. b Time series of gulf-mean decadal MSSH (black), MSSHsteric (red) and MSSHmass (blue). The light blue shading represents the negative PDO index (right axis)

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Surface winds can be used to explain SSHmass in the Southern Ocean (Boening et al. 2011) and the northwestern North Pacific (Cheng et al. 2013). However, atmospheric circulation during this period in the GOC had a cyclonic trend (Fig. 8), which cannot explain the rise in SSHmass over the region, suggesting that other processes are responsible for the rise in sea level in the basin.

Recent studies have indicated that the PDO accounts for a significant portion of SSH inter-decadal variability and decadal trends in the western equatorial Pacific (Bromirski et al. 2011; Merrifield et al. 2012). In the GOC, just east of the Arafura Sea, the decadal trend may be affected by the PDO. Assuming that the PDO does affect the decadal trend in the GOC, the above-mentioned long-term linear trends may be partly due to large-scale climate modes in the ocean–atmosphere system. Therefore, it is necessary to assess the decadal variability in SSH and SSHmass, which is helpful for isolating the contribution of climate modes to the rise in sea level over the last decade.

Figure 9a shows that both gulf-mean SSH and SSHmass closely correlate with the PDO (r = −0.66), while the correlation between SSHsteric and PDO is not significant (r = 0.11). Since the GRACE data is not of adequate length to explore the relationship between lower-frequency variability of SSH and the PDO, we use the OFES model output. This model covers a longer period and provides a good reproduction of the gulf-scale long-term SSH variations (including the total and its two components) (Fig. 9a). The MSSH, MSSHmass and MSSHsteric correlate to their corresponding observations at 0.95, 0.92 and 0.74. Moreover, the sea level budget in the OPES model is closed, unlike in the observations. The MSSH maintains a rising trend of 13.8 ± 3.4 mm/year over 2003–2011, with 12.8 ± 2.9 mm/year and 1.1 ± 0.9 mm/year for the MSSHmass and MSSHsteric, respectively. The model-derived linear trend is ~3 mm/year less than that of the altimetry observations, which is approximately the rate of the rise in global mean SSHmass due to ice melting (Johnson and Chambers 2013), and this component is not taken into account in the OFES. In the model, mass-induced sea level variations dominate total sea level change in terms of long-term variations.

On a decadal timescale, gulf-mean MSSH and MSSHmass fell during 1955–1968, and then rose until 1975, reaching a high level. They then fell again, reaching the lowest level in 1993, and then rose rapidly over the last two decades. Between 1955 and 2013, the decadal MSSH and MSSHmass from the OFES model correlate to the PDO at −0.76 and −0.75, respectively (Fig. 9b). The good correlations between sea level and the PDO indicate that decadal variability of MSSH and MSSHmass may be modulated by the PDO, which can affect the sea level trend over a relative short period. Similar to interannual variations, the PDO-related wind, exhibiting a cyclonic pattern (Fig. 10), leads to divergence, and consequently drives a drop in sea level. This it cannot explain the decadal and long-term variability of SSHmass and SSH. Which mechanism related to the PDO, then, can explain the high rising rate of the SSHmass (SSH) in the GOC?

Fig. 10
figure 10

Regression coefficients of SSH anomalies (a, d), SSHmass anomalies (b, e), SSHsteric anomalies (c, f) (cm, shaded) and NCDC 10-m wind anomalies (m/s, vectors) against the normalized negative PDO index

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3.4 Origin of low-frequency variability in SSHmass

Previous studies have shown that westward equatorial Rossby waves, excited by trade wind variations, can propagate through the Ombai Strait and then poleward northwesterly to the western Australian coast as coastal-trapped waves (Meyers 1996; Holgate and Woodworth 2004; Wijffels and Meyers 2004). These waves transmit fluctuations in the thermocline and thus lead to SSHsteric variations along their paths. The equatorial easterly anomalies exhibit an intensified pattern. Note that in this case, the SSHsteric variations do maintain a high rising rate of about 15.0 mm/year, the same magnitude as altimetry observations just to the west in the shallow waters of the Arafura Sea, Timor Sea and GOC (See Fig. 8) in this given atmospheric context. Landerer et al. (2007) demonstrated that net mass transfers could occur between shallow and deep zones as a result of steric changes in the ocean. In other words, the high positive SSHsteric anomalies west of the GOC could lead to a sharp pressure gradient between deep regions and the nearby shallow waters. The difference could push the flow of water from deep into shallow regions, resulting in a mass gain in the GOC and a mass loss in the adjacent deep waters. This joint theory can also explain the interannual variations in SSHmass, in which stronger equatorial easterly anomalies lead to higher SSHmass (SSH) during the negative ENSO phase (see Fig. 7), and vice versa.

To quantitatively test this hypothesis, we first compared the gulf-mean MSSHmass against the offshore MSSHsteric (represented by the value averaged over 130°E–133°E and 7°S–3°S, just right in the wave path and northwest of the GOC, the red box in Fig. 2). Secondly, we calculated the volume transport into and out of the GOC using the rough estimate of the 136°E section (denoted by 136°E VT). On an interannual timescale, MSSHmass correlates significantly with the offshore MSSHsteric, at 0.84. The good correlation implies that the offshore MSSHsteric along the wave path may affect the MSSHmass. On such a timescale, therefore, the rough volume transport into and out of the GOC varies almost in phase with the gulf-mean MSSHmass, with a correlation coefficient of 0.54 (Fig. 11a). The MSSHmass is further compared against the volume transport at the 143°E section (denoted by the 143°E VT), with the latter representing the water exchange between the GOC and the South Pacific. On an interannual timescale, the amplitude of the 143°E VT is smaller than that at 136°E. The former has a negative contribution to the gulf-mean MSSHmass variations and varies out of phase with MSSHmass. These results suggest that the hypothesis is accurate for interannual variations. Similarly, it holds true on the decadal timescale: firstly, the correlation between MSSHmass and MSSHsteric was 0.79 and between MSSHmass and 136°E VT was 0.87; secondly, the water exchange between the GOC and the South Pacific shows an out-of-phase relationship with MSSHmass (Fig. 11b).

Fig. 11
figure 11

a Interannual component of the basin-wide MSSHmass (blue), offshore MSSHsteric (red) averaged over the area in the red box in Fig. 2 (130°E–133°E, 7°S–3°S), and the volume transport (denoted as VT) at 136°E (solid gray line) and 143°E (dashed gray line) calculated from OFES zonal and meridional velocity. b The same as (a) but for the decadal component

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4 Conclusions and discussion

In this study, a dome-like rising trend in SSHmass anomalies in the GOC was revealed by GRACE estimates. In conjunction with satellite altimetry and steric budget derived from subsurface temperature and salinity analyses, mass-induced sea level variations in the GOC on multiple timescales were investigated. Seasonal gulf-scale variations in SSH can be attributed to SSHmass variations and local winds acting as the dynamic driver. With regard to interannual and long-term variations, the pattern of SSHmass variability resembles that of SSH, and is related to large-scale climate modes including ENSO and PDO. The local wind anomalies associated with ENSO and PDO cannot explain such low-frequency variability in SSHmass. Oceanic waves propagating from the western Pacific cause changes in SSHsteric west of the Arafura Sea and the GOC, resulting in a sharp pressure gradient between deep regions and the GOC, which drives an exchange of water mass.

The observed mean sea level in the GOC was significantly correlated with the PDO over the period 2003–2011 (r = −0.66), indicating that linear sea level trends over the past 9 years may have been greatly affected by low-frequency variability associated with the PDO. To what extent, then, can the PDO explain the rise in SSH in the GOC during the period 2003–2011? Multivariable linear regression (MVLR) analysis is used here to determine the contribution of the PDO (Zhang and Church 2012), which returns two values: one is the pure linear trend and the other is the linear trend associated with the PDO. Results show that the contribution of the PDO to the gulf-scale SSH (SSHmass) trend was approximately 11.0 mm/year (5.0 mm/year) in 2003–2011. After removing the trend associated with the PDO, the linear trends for SSH and SSHmass drop to 5.9 ± 3.3 and 2.8 ± 1.5 mm/year, respectively (Fig. 12). The PDO appears to account for about 65 % of the sea level rise in the GOC during 2003–2011. Thus, a portion of the rise in SSH is the regional sea adjustment to the PDO phase shift.

Fig. 12
figure 12

a Time series of the basin-wide SSH anomalies (solid black), and the residual with the PDO effect removed (solid blue), with the corresponding dashed lines representing the linear trends. b The same as (a) for SSHmass

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