Abstract

On interannual time scales, regional sea level variability is largely determined by changes in the steric component. The relation between the thermosteric and halosteric components is studied by separating the components into contributions from the mixed layer and, below the mixed layer, into the part that is related to isopycnal motion and that contributes to the steric sea level and the inactive part related to changes of spiciness. The decomposition provides a simple diagnostic to detect and understand physical mechanisms leading to regional sea level changes. In most areas of the world’s oceans, steric sea level variability is dominated by the contribution from isopycnal motion to the thermosteric sea level while halosteric variability relates more to spiciness. Because of the salinity minimum at middepth, different spatial salinity gradients above and below the minimum lead to opposing contributions and thus to a small contribution from isopycnal motion to the halosteric sea level. In nonpolar regions, both active components oppose each other, rendering the thermosteric variability larger than the steric variability. In the Arctic, the variability of both components is governed by spiciness in the Eurasian Basin and isopycnal motion in the Amerasian Basin.

1. Introduction

Sea level is one of the most prominent climate variables because it affects many people living in low-lying coastal areas. Regional sea level changes differ substantially from global mean changes. The imprint of the anthropogenic effects is clearly visible in the global mean while current regional patterns appear to be largely caused by natural variability (Stammer et al. 2013). In particular, variability on interannual-to-decadal time scale obscures the attribution of trends to either natural or anthropogenic processes. On interannual time scales, regional sea level changes are mainly determined by the steric component (Cazenave and Llovel 2010), except for some deep extratropical regions and shallow or semienclosed areas (Piecuch et al. 2013) where the bottom pressure signal plays a role. Detecting the associated processes is crucial for understanding sea level variability and for distinguishing between natural and anthropogenically forced changes.

Steric changes are determined by the baroclinic component and are affected by surface fluxes of heat and freshwater, and by wind stress (Suzuki and Ishii 2011). How these various components influence the steric sea level is the subject of many studies. Different forcing mechanisms were studied by Piecuch and Ponte (2011), who addressed, however, only the total steric variability while different forcing mechanisms have different impacts on thermosteric versus halosteric variability. Wind stress acts on different time scales, for example via Ekman pumping, Rossby waves, or via a time-dependent Sverdrup relation (e.g., Kelly et al. 1993; Qiu 2002), while the importance of heat fluxes and freshwater fluxes was demonstrated by Häkkinen and Rhines (2004) and Fukumori and Wang (2013).

Little is known about the relation between thermosteric and halosteric variability, how wind forcing changes affects these individual components, or how locally generated buoyancy anomalies affect remote regions (e.g., Schneider 2000). Modeling studies (e.g., Pardaens et al. 2011) showed that the thermosteric signal prevails in the Southern Ocean whereas halosteric changes dominate in the Arctic and strong compensation between thermosteric and halosteric changes characterizes the Atlantic. Observational investigation is hindered by the fact that for much of the historical record until the recent introduction of salinity-profiling Argo floats, salinity data are sparse and sufficient coverage for determining regional patterns of interannual steric sea level changes exists only for temperature. Regional studies (e.g., Levitus et al. 2000; Lombard et al. 2005) therefore concentrate mainly on signals of heat content and thermosteric sea level. However, for basinwide signals Levitus et al. (2005) and Ishii et al. (2006) have already studied the relation between halosteric and thermosteric sea level variability and noticed regional differences in their conjoint or competing effect on the steric signal.

Analyzing trends from ocean syntheses, Wunsch et al. (2007) and Köhl and Stammer (2008) found that except in high latitudes both components share many common patterns and their generally opposite signs lead to smaller net steric sea level changes than suggested by each field alone. The suggestion that adiabatic horizontal or vertical displacement (i.e., redistribution of water masses) acts as a main contributor to the sea level variability will be revisited here and the contribution from the displacement of isopycnals and the displacement of water masses on isopycnals should be quantified. To this end, the halosteric and thermosteric sea level will be decomposed into the contribution from the mixed layer (ML) and, below the mixed layer, further into their parts related to density and spiciness changes. Temperature and salinity anomalies with a density signature are, for instance, governed by planetary wave dynamics or wind stress curl changes, while density-compensating (spiciness) anomalies can be thought of being advected along isopycnals by the circulation as a passive tracer. The decomposition will contribute to the understanding of which processes determine regional steric sea level and why, for instance, halosteric sea level variability is smaller than thermosteric variability. Prospects for sea level predictability and for reconstruction of freshwater content based on thermosteric and total sea level will also be discussed.

2. The synthesis

The results are based on an ocean synthesis covering the years 1948–2011 from the German contribution to Estimating the Circulation and Climate of the Ocean (GECCO) project. GECCO2 is an extension of the 2002–07 synthesis described by Köhl et al. (2012). A detailed evaluation of GECCO2 is provided by Köhl (2013, manuscript submitted to Quart. J. Roy. Meteor. Soc.). The synthesis uses the adjoint method to bring a global ocean–sea ice model into consistency with the National Centers for Environmental Prediction (NCEP) atmospheric state (Kalnay et al. 1996), satellite data, and the quality-controlled and bias-corrected temperature and salinity profiles from the EN3 database (version v2a; Ingleby and Huddleston 2007). Here, we analyze annual means from iteration 28 for the period 1993–2011 that is comparably well observed, particularly due to the near-global coverage by the satellite altimeter data. The spatial mean of the altimeter data was removed but the time series are not detrended. In this respect, the analysis here differs from that of Piecuch and Ponte (2011), who excluded the signal from longer-term changes by removing the linear trend. To compare the results from GECCO2, an additional analysis is based directly on the EN3 temperature and salinity profiles covering the period 2005–11, for which for the first time sufficient global coverage of salinity data is available to determine the regional halosteric sea level variability.

Figure 1 compares the GECCO2 annual-mean sea level with mapped Archiving, Validation, and Interpretation of Satellite Oceanographic data (AVISO) in terms of their STD (standard deviation) and a skill score metric. Despite the fact that GECCO2 is based on a low-resolution non-eddy-permitting model, in most areas the level of interannual sea level variability of GECCO2 compares well with the AVISO product and regions of high variability are nearly identical. Only along the Antarctic Circumpolar Current (ACC), GECCO2 substantially underestimates the variability. In tropical regions, the phase of large variability matches very well while in higher latitudes, where variability is affected by mesoscale eddies, the correspondence between GECCO and the data is lower. Very low skill exists in regions that are at least partially ice covered throughout the year and where the availability of the data is prone to be biased to one season. Detrending the time series reduces the variability everywhere, particularly in the subpolar North Atlantic and south of the Gulf Stream where the variability of GECCO2 remains larger than AVISO also after detrending (not shown). However, the larger signal south of the Gulf Stream is related to the change in observing system and disappears if the analysis is restricted to the pre-Argo period (1993–2003). Overall, the good agreement between the variability of GECCO2 (Fig. 1a) and AVISO (Fig. 1b) justifies a statistical analysis of steric sea level data. Some restrictions may apply to the use in the eastern North Atlantic and at higher latitudes where the agreement is low and where the mixed layer analysis discussed later suggests large biases.

Fig. 1.

STD of annual-mean sea level anomalies (in cm) from (a) mapped altimeter data from AVISO on a 1° × 1° grid and (b) GECCO2. (c) Skill score based on the STD of the difference of GECCO − AVISO data normalized by the square root of the sum of the respective variances. A value of 1 corresponds to no skill.

Fig. 1.

STD of annual-mean sea level anomalies (in cm) from (a) mapped altimeter data from AVISO on a 1° × 1° grid and (b) GECCO2. (c) Skill score based on the STD of the difference of GECCO − AVISO data normalized by the square root of the sum of the respective variances. A value of 1 corresponds to no skill.

3. Decomposing thermosteric and halosteric anomalies

Following Gill and Niiler (1973), and with Δρ being the local density anomaly, steric sea level anomalies Δη can be decomposed for sufficiently small perturbations of salinity S and potential temperature Θ, according to

 
formula

into the halosteric contribution and thermosteric contribution . Here, α and β are the local thermal expansion and haline contraction coefficients, respectively; ρ0 is a reference density; and H is the total water depth. The linearization is a good approximation for the interannual variability analyzed here. According to Bindoff and McDougall (1994), subsurface water can be altered by either changed properties of subducted mixed layer water through buoyancy fluxes or by isopycnal motion. However, this is a simplified concept as, for instance, the variability of diapycnal mixing (Yeager and Large 2004) may also contribute. For depths below the mixed layer, the effect of potential temperature and salinity anomalies on the steric sea level can be decomposed into components aligned with and perpendicular to the time mean spatial density gradient. To first order, only the aligned part of the changes will contribute to steric sea level changes, while the perpendicular temperature and salinity changes tend to cancel each other out.

Under the assumption that the influence of other processes such as mixing is small, the spiciness anomaly (Δτ = αΔΘ + βΔS) related components are defined as residuals to the projection on the mean density gradient

 
formula
 
formula

with γ being the gradient of the neutral density surfaces (McDougall 1987) and the overbar denoting the time mean. Here, ΔΘτ and ΔSτ are the anomaly of spiciness in temperature and salinity, respectively. On the right-hand sides, the first terms are the total anomalies seen at a fixed location in space and the second terms are the contributions to the temperature or salinity anomalies from the motion of the isopycnal at that location. To restrict the relevant processes to isopycnal motions and motions along isopycnals, this decomposition should be applied only below the mixed layer, where mixing effects can be assumed to be small. To achieve a complete decomposition, the thermosteric and halosteric variability is thus separated into their contribution from the mixed layer and below the maximum of the mixed layer depth (MLD), into isopycnal motion– and spiciness-related parts,

 
formula
 
formula

as the first and second term in the parentheses, respectively. In regions where density gradients do not vanish,

 
formula

it becomes clear that within the linear approximation only the salinity and temperature anomalies associated with isopycnal motion contribute to the steric sea level and that the terms associated with spiciness have to compensate each other. Below the mixed layer, the contribution of temperature and salinity changes to the steric sea level changes is therefore entirely defined by the density changes and their mean properties and how they are related to the mean density gradient.

For each place in the water column, the contribution of a local density anomaly to thermosteric and halosteric anomalies is determined by the terms preceding Δρ in (4) and (5), which are shown after multiplication with ρ0 in Fig. 2 at 500- and 1500-m depth. For temperature, the depths correspond to typical levels above and below the thermocline while for salinity they are above and below the salinity minimum, respectively. In the upper ocean, the thermosteric part contributes most to the steric sea level and the halosteric and thermosteric contribution have the opposite sign. However, in the polar regions both aspects are different and salinity changes contribute more. In the deeper part, the opposite is true and both contributions act conjointly except for the Southern Ocean and regions that are affected by saline overflows from either the Mediterranean or the Red Sea. In regions with large weighting coefficients such as near saline outflows, small steric changes are therefore potentially associated with larger thermosteric and halosteric changes and strong compensation.

Fig. 2.

Weighting coefficients (top) and (bottom) for projecting density anomalies onto temperature and salinity contributions from isopycnal motion according to (4) and (5). Because the parts trivially add to one, in regions with values much larger than one substantial part of both contributions have to compensate each other; contour lines at 1 and −1 are added to distinguish these regions.

Fig. 2.

Weighting coefficients (top) and (bottom) for projecting density anomalies onto temperature and salinity contributions from isopycnal motion according to (4) and (5). Because the parts trivially add to one, in regions with values much larger than one substantial part of both contributions have to compensate each other; contour lines at 1 and −1 are added to distinguish these regions.

Fundamental is the different behavior of the terms above and below the main thermocline and above and below the salinity minimum, respectively. While the contribution from density changes to the thermosteric component adds in a column-integrated sense (Fig. 2, top), for salinity the contributions above and below the minimum tend to compensate (Fig. 2, bottom). Because the density anomalies related to the contribution from isopycnal motion are the same for thermosteric and halosteric sea level, the difference in structure of the spatial gradients of temperature and salinity suggests that the halosteric variability will be much smaller than the thermosteric variability. However, a correlated or anticorrelated contribution from the mixed layer and the spiciness advection may change this.

Because the depth of the maximum mixed layer is an important parameter for the decomposition, a comparison of the mixed layer depths calculated from GECCO2 and EN3 data is provided in Fig. 3. Despite different periods, both estimates agree quite well with each other and with the maximum of the seasonal climatology of Kara et al. (2002). Areas of large mixed layer depth indicate the major mode water regions. Although the water is not vertically homogeneous in GECCO2 in the Weddell, Amundsen, and Ross Seas, the stratification is too low such that the fixed density difference criteria lead to a substantial overestimation of the mixed layer there. Using a smaller density difference leads to a smaller depth but does not suffice to remove the problem. This overestimation has to be kept in mind when interpreting the GECCO2 results.

Fig. 3.

Max MLD (in m) calculated as the depth where the density value is 0.125 kg m−3 larger than the value at 5-m depth (a) over the period 1993–2011 from GECCO2 and (b) over the period 2005–11 from EN3 data.

Fig. 3.

Max MLD (in m) calculated as the depth where the density value is 0.125 kg m−3 larger than the value at 5-m depth (a) over the period 1993–2011 from GECCO2 and (b) over the period 2005–11 from EN3 data.

4. Sea level variability related to spiciness and isopycnal motion

According to the interannual steric sea level variability calculated from GECCO2 over the period 1993–2011 (Fig. 4a), regions with large variability exist in the subtropical gyres of the Northern Hemisphere, the eastern tropical Pacific, and the western parts of the trade wind zones except for in the Atlantic. The thermosteric variability in Fig. 4c is similar but in general slightly larger, except for the northern North Pacific and the Arctic, where halosteric variability (Fig. 4d) dominates. Except for those regions, the halosteric variability is much smaller than the thermosteric variability. From the ratio of the standard deviation of thermosteric to the halosteric components from monthly temperature and salinity analysis, Ishii et al. (2006) concluded that thermosteric component is dominant in low latitudes, while the halosteric STD exceeds thermosteric STD in high latitudes.

Fig. 4.

GECCO2 STD of the total sea level and its thermosteric and halosteric contributions (cm). The latter two are decomposed into their contribution from the ML and for depths below the max ML into their contribution from isopycnal motion and spiciness.

Fig. 4.

GECCO2 STD of the total sea level and its thermosteric and halosteric contributions (cm). The latter two are decomposed into their contribution from the ML and for depths below the max ML into their contribution from isopycnal motion and spiciness.

Contributions from the mixed layer shown in Figs. 4e and 4f are consistent with the mode water regions as they are shown by Talley (1999), except for an additional signal in the central tropical Pacific. These are also the regions in which diffusive mixing is important according to Piecuch and Ponte (2011). As Fig. 3 demonstrates, contributions from the mixed layer are restricted to the top 100–200 m in most regions and therefore affect only a small part of the water column. Only in mode water regions a substantial fraction of the upper ocean, which according to Piecuch and Ponte (2011) explains more than 80% of the sea level variability, is affected.

In areas with large thermosteric variability related to isopycnal motion, the active parts of the halosteric and the thermosteric component (Figs. 4e,f) oppose each other because of the characteristics of the mean thermohaline structure in the upper ocean (see Fig. 2). In the upper ocean, the factors shown in Fig. 2 (left) already suggest a larger thermosteric variability, which is further enhanced by the contribution from the lower layers (Fig. 2, right). For salinity, opposite signs of these factors above and below the salinity maximum result in small halosteric variability. Exceptions are the subpolar North Pacific, North Atlantic, and Arctic, where in fact the halosteric variability dominates.

As a consequence of (6), the spiciness contributions to thermosteric and halosteric variability shown in Fig. 4b are identical, except for the sign and for numerical artifacts in regions of steep density slopes due to the finite difference approximation. Note, that the decomposition is problematic in areas of vertical density-compensated layers, which are isopycnal but not mixed layers (de Boyer Montegut et al. 2004). In these layers, the effect of temperature and salinity gradients on the density gradients exactly compensates, causing an area without density stratification. The spiciness contribution enhances the thermosteric and the halosteric variability in most areas except the North Atlantic (not shown).

In the Atlantic and Indian Oceans, Levitus et al. (2005) found density-compensating linear trends in the thermosteric and halosteric components of steric sea level changes, whereas in the Pacific they see the two components acting in concert. For the interannual variability, our results clearly agree in the Atlantic but only to some extent in the Indian Ocean. Although halosteric variability is dominated by spiciness, the contributions from the mixed layer act in concert in the Indian Ocean. In the Pacific, a clear positive correlation exists only in the subpolar areas while in other areas both isopycnal motion and mixed layer processes are important (not shown).

5. Processes affecting thermosteric and halosteric variability

By comparing the size of the variability associated with isopycnal motion, spiciness, or within the mixed layer (Fig. 4), it becomes clear that thermosteric variability is mostly related to isopycnal motion and in mode water regions to variability within the mixed layer. A direct correlation of the thermosteric and halosteric signal with each of its components reveals how much variability is explained by each part (Fig. 5). Figure 5a generally confirms the importance of isopycnal motion for thermosteric variability. Spiciness becomes an important process adjacent to regions where variability in the mixed layer is dominant (yellow regions framing mode water regions) and in the tropical Atlantic. In the Amerasian Basin (roughly the western Arctic Ocean) isopycnal motion is the dominant process for thermosteric and halosteric variability (Figs. 5a,c). In the Nordic Seas and in the Weddell and Amundsen Sea the mixed layer and in the Eurasian Basin (eastern Arctic) spiciness is more important.

Fig. 5.

Explained STD of the (a),(b) thermosteric STD σΘ and (c),(d) halosteric STD σS by their isopycnal motion I, spiciness τ, and ML (here denoted as “M”) components for (left) GECCO2 (1993–2011) and (right) EN3 profiles (2005–11). The colors denote regions where the explained STD (according to the relation , with X being temperature or salinity and r the correlation, alone or in combination) is larger than 55% of the total. If two combinations are associated with a color, both explain more than 55% of the total. Note that regions where more than one process is required are rare. For the EN3 data, the components were calculated for each profile and the result was mapped with a Gaussian interpolation using a 2° length scale leading to a certain amount of extrapolation.

Fig. 5.

Explained STD of the (a),(b) thermosteric STD σΘ and (c),(d) halosteric STD σS by their isopycnal motion I, spiciness τ, and ML (here denoted as “M”) components for (left) GECCO2 (1993–2011) and (right) EN3 profiles (2005–11). The colors denote regions where the explained STD (according to the relation , with X being temperature or salinity and r the correlation, alone or in combination) is larger than 55% of the total. If two combinations are associated with a color, both explain more than 55% of the total. Note that regions where more than one process is required are rare. For the EN3 data, the components were calculated for each profile and the result was mapped with a Gaussian interpolation using a 2° length scale leading to a certain amount of extrapolation.

Isopycnal motion in the Amerasian Basin is consistent with the wind-driven changes of the water mass structure suggested by Proshutinsky and Johnson (1997) while the spiciness signal in the Eurasian Basin may be associated with the spreading of Atlantic Water anomalies (Dmitrenko et al. 2008). In the tropics and midlatitudes, halosteric variability is dominated by the spiciness signal, although in some parts of the Pacific and in the North Atlantic isopycnal motion is important in GECCO2. This is due to the fact that halosteric contributions from isopycnal motions above and below the salinity minimum compete and render this contribution small in the column-integrated sense. As for the thermosteric variability, mode water regions are characterized by the importance of variability within the mixed layer. An interesting exception is the central tropical Pacific where the maximum mixed layer depth reaches deep enough to catch some of the El Niño variability.

For a comparison, the analysis is also performed on in situ profiles from the EN3 database. To reduce biases due to incomplete sampling of the seasonal cycle, anomalies of the EN3 are defined with respect to climatological temperature and salinity from the World Ocean Atlas 2009 (Levitus et al. 2009), which is also used for the definition of spatial gradients of temperature, salinity and density in (4) and (5).

In comparison to the EN3 results, in GECCO2 the mixed layer is much more relevant in the Southern Ocean because of the excessive mixed layer depth noted in Fig. 3. Although both databases largely lead to consistent results (cf. Fig. 5a with Figs. 5b,d), differences exist for the thermosteric STD in the tropical Atlantic and in the Indian and Pacific sectors of the Southern Ocean. Reasons for differences include deficiencies of GECCO2, insufficient sampling by Argo profiles, particularly the lack of observations below 2000 m, and the different analysis periods (1993–2011 vs 2005–11). We tested the latter two reasons by restricting the GECCO2 analysis first to 0–2000 m and then additionally to the period 2005–11. Differences in the Southern Ocean are explained by lack of Argo data below 2000 m, while restricting the analysis period resolves the difference in the Atlantic (not shown). For halosteric STD, differences exist in the subtropical North Atlantic, in the range 40°S–40°N of the Pacific Ocean and at the southern end of the Southern Ocean. By restricting the analysis to the top 2000 m, differences in the Atlantic are resolved, but differences in the Pacific remain with variability within the mixed layer gaining importance.

6. Conclusions

Because of the lack of salinity data, variability patterns of only thermosteric sea level were considered, for instance by Bergé-Nguyen et al. (2008), to approximate sea level variability patterns for sea level reconstructions. Although the steric variability is dominated by the thermosteric part in many regions, one has to be careful with conclusions drawn from thermosteric part only, because first, it includes an inactive component associated with the advection of spiciness, and second, in most areas the active part of the halosteric component will also reduce the signal. Except for mode water regions and high latitudes, temperature- and salinity-related steric sea level variability are governed by different dynamics: whereas thermosteric variability is dominated by isopycnal motion, which according to Piecuch and Ponte (2011) in extra-equatorial regions is driven primarily by Ekman pumping, the advection of spiciness is more important for halosteric variability. This is due to the fact that density gradients are more controlled by temperature than by salinity gradients and different gradients above and below the salinity minimum tend to reduce the halosteric variability.

Knowing the relation between halosteric and thermosteric variability is important for the use of a combination of temperature and sea level observations to infer synthetic vertical profiles of salinity to study, for instance, freshwater content changes (Levitus et al. 2005). The decomposition presented here provides a simple diagnostic to detect and understand processes that affect regional sea level changes and motivates a way for reconstructing freshwater content changes.

Outside of regions where bottom pressure plays a role, halosteric anomalies can be estimated as the residual between sea level and thermosteric anomalies. However, because haline contraction coefficients are depth dependent, halosteric variability is not directly related to freshwater content changes. With the approximation that isopycnal motion mainly relates to wind stress curl variations, depth-dependent changes in temperature and salinity can be approximated from the associated displacement of the isopycnal and the mean hydrographic properties. The spiciness component has to be treated separately. Below the mixed layer, diagnosing the isopycnal motion component of observed temperature anomalies enables the estimation of their spiciness component as a residual. Because the latter is density compensated, the ratio of thermal expansion to haline contraction gives then the associated local salinity component of the spiciness signal. However, because thermosteric variability is dominated by isopycnal motion, a very high accuracy of diagnosing the associated variability is needed for a successful reconstruction of the spiciness signal, which therefore is prone to large errors. In mode water regions, the contribution from the mixed layer poses a further handicap.

The decomposition presented here enables understanding predictable parts of sea level anomalies. Because sea level variability is primarily caused by wind stress changes, the difficulty in predicting sea level is associated with predicting the atmospheric changes that primarily affect the isopycnal motion. Although thermosteric sea level is dominated by isopycnal motion and therefore, in agreement with Piecuch and Ponte (2011), probably not predictable in many areas, persistent cyclonic or anticyclonic wind stress leads to a build-up of steric anomalies that provide memory. Beyond persistence and because the anomalies can propagate as baroclinic Rossby waves, a part of this signal is predictable even with simple models (e.g., Qiu and Chen 2006). The spiciness-related signal can be thought of as being advected with the mean circulation and should provide long-term predictability. Although this part of the signal does not affect sea level, it provides information on the heat content and is therefore relevant for climate prediction. In mode water regions, where the mixed layer contributes a substantial part to the variability, the heat capacity of the mixed layer acts as an integrator (Frankignoul and Hasselmann 1977) and provides memory for steric sea level. Although the latter should only give rise to persistence, the predictability analysis of sea level by Polkova et al. (2014) indicates additional predictability in mode water regions. A detailed analysis of the predictability of the individual components of steric sea level is a topic for further studies.

Acknowledgments

Support from the Ministry of Science and Education through the project RACE and comments from anonymous reviewers, Iuliia Polkova, and Detlef Stammer are acknowledged. The altimeter products were produced by Ssalto/Duacs and distributed by AVISO with support from CNES.

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