Corresponding author: I. Fukumori, Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California, USA. (email@example.com)
 Regional sea level changes often differ from global mean changes due to geographic variations in surface fluxes and to changes in ocean circulation. Here we study such regional sea level trends from 1993 to 2004 using a synthesis of observations and an ocean general circulation model. Unlike the global mean, steric changes dominate regional trends with negligible contributions from column-integrated mass variations. Regional heat and freshwater anomalies underlying steric changes are in turn distinguished between redistribution of pre-existing anomalies within the ocean and contributions from additional surface fluxes external to the ocean. Internal redistribution accounts for most regional trends but exceptions are found, most notably in the western tropical Pacific Ocean where a warming of external origin dominates the trend. On average, external thermosteric sea level trends are found to be positive in temperate regions while negative at higher latitudes with opposite trends found in halosteric anomalies of external origin.
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 Sea level rise provides one of the most compelling observational evidences of global climate change. Tide gauge records exhibit a global mean sea level rise of approximately 1.7 mm/yr over the 20th century [Church and White, 2011]. Satellite measurements available since the early 1990s show an accelerated mean sea level rise of 2.8 mm/yr from 1993 to 2003 [Leuliette et al., 2004]. The increase in global mean sea level can be ascribed to two origins external to the ocean: (1) thermal expansion of the ocean due to an increase in ocean heat content caused by excess net surface heating and (2) additional ocean mass and volume, for example, due to runoff from increased melting of glaciers and ice sheets on land. Of the 2.8 mm/yr global mean sea level rise from 1993 to 2003, the two are estimated to have contributed 1.6 and 1.2 mm/yr rise, respectively [Willis et al., 2004]. (See, for instance, Bindoff et al.  and Church et al.  for rates estimated for other periods.) Global mean sea level rise is expected to continue, driven by global warming caused by the gradual increase in anthropogenic atmospheric greenhouse gas concentrations. Continued warming may result in additional sea level rise by over 28 cm by the end of the 21st century from thermal expansion alone [Yin, 2012] and possibly an order of magnitude larger rise from melting glaciers and ice sheets [Katsman et al., 2011].
 Sea level rise is of particular concern to low-lying coastal regions and island nations. However, the magnitude of sea level change often varies from region to region with values that can differ significantly from that of the global mean. For instance, sea level observed from 1993 to 2004 based on the gridded data set of the Archiving, Validation, and Interpretation of Satellite Oceanographic data (AVISO) (http://www.aviso.oceanobs.com) increases in excess of 10 mm/yr in many regions of the western Pacific, but decreases in the eastern Pacific, especially in the subpolar North Pacific Ocean (Figure 1a). The observed geographic pattern of sea level change also differs from that expected from gradual global warming [Bryan, 1996; Mitrovica et al., 2001; Stammer, 2008; Yin, 2012]. These differences can be attributed to ocean circulation. At regional scales, in addition to heat and mass from sources external to the ocean that contribute to global mean changes, sea level can also vary due to internal redistribution of pre-existing heat and salt (water masses) such as vertical displacement of isopycnals associated with horizontal convergence and divergence of changing ocean circulation [Wyrtki, 1975; Roemmich et al., 2007; Gille, 2008; Han et al., 2010; Piecuch and Ponte, 2011]. If regional sea level changes are due to internal redistribution, where then are the heat and freshwater changes with origins external to the ocean that contribute to global mean sea level rise? Such distinction is fundamental to understanding observed sea level changes and in assessing their future evolution.
 Here, we study this dichotomy of sea level change, i.e., origins of change that are external to the ocean versus those that are internal to the ocean, using a model-data synthesis of the Consortium for Estimating the Circulation and Climate of the Ocean (ECCO) [Wunsch et al., 2009]. In particular, we revisit the model of Wunsch et al.  who demonstrated a first order consistency between the observed and the model-estimated global and regional sea level trends from 1993 to 2004. In the present study, effects of ocean circulation redistributing pre-existing water masses within the ocean on the one hand and changes in ocean heat and freshwater content from additional surface fluxes on the other, hereafter referred to as changes with origins internal and external to the ocean, respectively, will be distinguished using the model estimate to gain further insight into the nature of regional sea level variability and possible signatures of global climate change.
2 Model and Method
 The ECCO synthesis combines nearly all extant in situ and satellite observations of the ocean into a complete physical description of the ocean state and its variability. These observations include sea level variability from satellite altimetry and temperature and salinity profiles from in situ observations. (See Wunsch et al.  for further details.) The particular model-data synthesis permits closure of heat and freshwater budgets and allows quantitative attribution of processes underlying the observed changes of the ocean, which is critical for the purpose of the present investigation. In this study, we employ simulated passive tracers to identify the origins of heat and freshwater anomalies that underlie regional sea level change. Lowe and Gregory  utilized a similar approach to trace pathways of anomalous heat and freshwater associated with climate change. Here, passive tracers that represent heat and freshwater changes of either external or internal origins to the ocean are followed in time using the 1993–2004 circulation estimate of the ECCO model (i.e., velocity and mixing). For instance, changes of heat that originate from external air-sea fluxes will be evaluated by integrating a passive tracer in time, using the ECCO circulation estimate, forced with surface tracer boundary conditions equivalent to the synthesis' air-sea heat fluxes but from an initial tracer distribution that is nil. Any change in the resulting passive tracer field can be traced back to the air-sea heat fluxes that were employed. In comparison, the contribution of internal redistribution of heat that was present in the ocean at the initial instant is evaluated by integrating another passive tracer using the same circulation estimate but with initial tracer values equivalent to those of the synthesis' initial temperature field and with no air-sea tracer fluxes. Any passive tracer change in this second integration can be attributed to internal heat redistribution from other locations, as there are no sources or sinks for this tracer. The two contributions, i.e., changes originating from external air-sea fluxes and changes associated with redistribution of internal anomalies, are additive and the sum of them is identical to the synthesis' temperature field. Corresponding contributions for external and internal origins of freshwater changes are evaluated in a similar manner using the model's surface freshwater fluxes and initial freshwater (salinity) distribution, respectively.
 Trends of the ECCO model's sea level relative to its global mean are comparable with those observed by satellite altimetry (Figure 1). Some discrepancies between the model and observations are evident in the Southern Ocean where model uncertainties are relatively large due to insufficient observations that were available to constrain the model and the absence of a sea-ice model for this particular model setup [Wunsch et al., 2007]. Based on the hydrostatic relation, barometrically corrected sea level anomalies (Δh) can be separated between those associated with net mass changes of the water column (Δhmass) and those due to steric changes, viz., density variations within the water column (Δhsteric) [Gill and Niiler, 1973]:
 Here Δpbottom is anomaly of ocean bottom pressure, ρ0 a reference density, g gravitational acceleration, H depth of the ocean, Δρ density anomaly, and z vertical coordinate. All anomalies (Δ) are defined relative to corresponding time-mean variables.
 The regional sea level trends resolved by the ECCO estimate can largely be explained by steric changes of the ocean (Δhsteric) as opposed to depth-integrated mass variations (Δhmass), except for some coastal regions especially along Antarctica (Figure 2). Therefore, the issue of understanding the origins of geographically varying sea level change becomes one of analyzing steric sea level variations and processes controlling temperature and salinity changes of the ocean that underlie the density anomalies.
 The origins of temperature and salinity changes in the ECCO estimate are analyzed using the simulated passive tracers discussed above. Contributions of internal water mass redistribution and changes of external origin are often in opposition to each other reflecting the mean state of the ocean in which changes induced by circulation are in first-order balance with those originating from external sources. For example, in the tropics, surface heating warms the ocean in opposition to upwelling that tends to cool the upper water column. Therefore, to distinguish anomalies that give rise to the trends, i.e., imbalances from a stationary state, anomalous contributions are identified as the dominant of the two contributions in excess of the other when changes of internal and external origins are in opposition to one another.
 Figures 3a and 3b illustrate the resulting steric sea level trend decomposition into such anomalous buoyancy changes of external origins and those of internal redistribution, respectively. Steric trend by internal water mass redistribution (Figure 3b) is found to be the larger of the two across most of the globe and accounts for the large positive sea level trends (Figure 1) seen in the extra-tropical regions of the North and South Pacific Oceans, the North Atlantic Ocean, and in the Southern Hemisphere of the Indian Ocean. Most of the negative trends found in the model's sea level change can also be ascribed to internal redistribution such as changes in the Alaskan gyre, the eastern tropical Pacific and its coastal regions, the tropical Indian Ocean, the Southern Ocean south of Africa, and the Brazil-Malvinas Confluence Zone in the South Atlantic Ocean.
 In comparison, steric sea level trends due to buoyancy anomalies of external origin (Figure 3a) are generally smaller than those due to internal redistribution (Figure 3b) and are often of opposite sign, such as in the southern Indian Ocean and the Gulf Stream region. An exception is found in the warm pool region of the western tropical Pacific Ocean and the eastern tropical Indian Ocean where a positive trend of external buoyancy origin dominates the steric sea level rise with little contribution from internal redistribution.
 Each of the anomalies in steric sea level can be further decomposed into separate contributions from temperature and salinity changes by evaluating the corresponding contributions to density anomaly, Δρ in equation ((3)). In particular, the positive sea level trend in the warm pool region noted above can be traced to an anomaly in heat content as opposed to that in freshwater content. A positive thermosteric contribution (Figure 4a) dominates the external steric sea level change in the warm pool region with little halosteric contribution (Figure 4b). The two contributions vary spatially across the globe, often with opposite signs found in neighboring regions, but not necessarily collocated with each other. For instance, external thermosteric and halosteric changes of opposite sign are found in the western subtropical North Atlantic but slightly offset from each other, resulting in a net dipole pattern of steric sea level trend in this region (Figure 3a). The large negative external steric sea level change found in the southern Indian Ocean is associated with anomalies in freshwater content (Figure 4b), which, however, is largely canceled by internal water mass redistribution (Figure 3b). Interestingly, external thermosteric sea level anomalies are generally positive in temperate regions and negative at higher latitudes whereas external halosteric sea level changes are generally opposite with positive trends found at higher latitudes and negative trends in temperate regions.
 A similar decomposition of internal steric sea level changes (Figures 5a and 5b) shows thermosteric contributions accounting for most of the internal variations with smaller halosteric contributions often collocated with thermosteric ones of opposite sign. The differences in magnitude can be attributed to the ocean being primarily thermally stratified, i.e., density stratification having larger dependencies on vertical temperature gradient than on salinity gradient. The opposite sign of the two contributions can be ascribed to vertical temperature and salinity gradients often having the same sign, i.e., warm salty water on top of cold fresh water, resulting in density compensating changes by vertical isopycnals heaving [e.g., Ponte, 2012]. Exceptions where halosteric variations dominate internal steric sea level changes can be found in the Alaskan gyre and the eastern Ross Sea.
4 Summary and Discussion
 The geographic variability of sea level trend from 1993 to 2004 is studied to discern the effects of ocean warming and freshening. The heat and freshwater anomalies underlying the sea level trend are distinguished between those with origins external to the ocean and those from sources within the ocean. The different origins are quantified with simulated passive tracers using an ocean state estimate that combines a comprehensive suite of in situ and satellite observations of the ocean using an ocean general circulation model.
 Unlike the global mean, regional decadal sea level variations are shown to be mostly due to steric changes of the ocean, i.e., sea level changes due to temperature and salinity variations, as opposed to local net mass changes of the water column. Moreover, the steric variations are largely dictated by ocean circulation redistributing internal water mass anomalies in contrast to effects of temperature and/or salinity variations originating from external diabatic sources.
 An exception to the internal redistribution-dominated sea level change is found in the warm pool region of the western tropical Pacific and eastern tropical Indian Oceans where thermosteric changes of external origin account for the decadal sea level rise with little excess contribution from redistribution of pre-existing water mass anomalies. Although smaller in magnitude than effects of internal redistribution, external thermosteric sea level changes are also found to be increasing in several other temperate regions while decreasing at higher latitudes. In comparison, external halosteric sea level changes have decreasing values in temperate regions and increasing values near subpolar regions, often opposite to that of external thermosteric changes but not necessarily coincident in location. The variations imply that, on average, there is excess warming and less freshening (more evaporation) in temperate regions and more cooling and excess freshening at higher latitudes than can be accounted for by redistributing water masses alone. The latitudinal dependence of the implied salinity change is qualitatively similar to that described by Durack et al. , who attributed observed salinity changes to intensification in the global water cycle. However, the present analysis period is too short to assess consistencies between the two studies.
 Note, that the study's distinction between internal water mass redistribution and external sources of diabatic change is not an explanation of causal mechanism but an analysis of the heat and freshwater anomalies' origins. For instance, Merrifield and Maltrud  and Qiu and Chen  have shown that the sea level trend found in the western tropical Pacific Ocean can be explained by the ocean's adjustment to a decadal trend of increasing Pacific trade winds. The strengthening trade winds cause a convergence in the upper ocean with an associated deepening of the thermocline in the western tropical Pacific, resulting in an increase in steric sea level. The present study indicates that there is a diabatic change associated with this wind-driven adjustment and that the heat anomaly originates from air-sea fluxes as opposed to a convergence of warm water from elsewhere. For example, the deepening thermocline reduces the cooling effect of upwelling, resulting in a larger volume of warm water in the western tropical Pacific Ocean than otherwise. That there is a net increase in warm water volume in this region might also be inferred by a lack of decreasing sea level near-by in the analysis of Merrifield and Maltrud [2011, Figure 2a] as would be expected if the change were strictly a result of wind-driven internal water mass redistribution. McGregor et al.  also found significant discrepancies between observed sea level trends in the western tropical Pacific and a wind-driven 1.5-layer shallow water model that only resolves adiabatic redistribution of water masses.
 The present investigation also complements studies of heat and freshwater budgets, such as that of Piecuch and Ponte  who examined such budgets in relation to steric sea level variations using the same ocean model as employed in the present study. Although their budget analysis considered interannual variations about the mean trend, advection was found to be the dominant component contributing to regional sea level changes, consistent with the findings of the present investigation concerning the trend. The two analyses both quantify physical processes underlying the variations but from different perspectives. Whereas the budget study of Piecuch and Ponte  describes a local dynamic balance, the present investigation provides a semi-Lagrangian analysis of heat and freshwater changes by distinguishing, for example, advection of diabatic anomalies of external origin that may have entered the ocean elsewhere from that of redistributing anomalies of internal origin. Although adiabatic changes associated with redistribution, such as wind-driven thermocline heave, are often reversible with the relaxation of their causes, diabatic changes (e.g., mixing) usually are not. Identifying the origins of heat and freshwater content changes is an important element in understanding the nature of the ocean's variability and its future evolution.
 The present findings illustrate some of the challenges in understanding sea level change and in predicting its regional variations. Owing to the dominance of redistribution, regional sea level variations on decadal time scales are often different from changes of their global mean. Future predictions of decadal regional sea level variations will require an accurate estimate of changing ocean circulation in addition to estimates of heat and freshwater input into the ocean. The diabatic effects also vary spatially and contribute to regional differences in sea level change. Monitoring sea level change and understanding its nature will require not only a sustained global observing system of sea level but also one that adequately resolves the spatial and temporal variation of temperature and salinity changes across the global ocean. For consistency with previous studies [e.g., Wunsch et al., 2007; Piecuch and Ponte, 2011], the present investigation focused on the period from 1993 to 2004. Analyses over longer periods of time are left for future investigation.
 This work was carried out at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration (NASA). The authors thank W. Llovel, C. Piecuch, R. Ponte, and J. Willis for their constructive suggestions and helpful discussion. The model setup was kindly provided by P. Heimbach. Valuable comments by two anonymous reviewers are gratefully acknowledged.