1. Introduction

The focus of this paper is on the regional response of sea surface height (SSH) to low-frequency regional and global changes in atmospheric pressure loading associated with climate change. Generally, the ocean reacts to surface wind stress and atmospheric sea level pressure, p_a, with the impact of surface pressure forcing being limited to time scales of only a few days [Willebrand et al. (1980); Ponte (1992); see also Wunsch and Stammer (1997), who discuss in detail the ocean’s response to time-varying atmospheric loading and its effect on altimeter data]. On weekly to seasonal and longer time scales, however, sea level reacts isostatically to first order to changes in p_a, which can be described by an inverted-barometer (IB) response according to

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Here, ρ is the surface density of seawater, g is the acceleration of gravity, and p′_a is defined as the local pressure anomaly:

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relative to the instantaneous sea level pressure averaged over the globally connected ocean domain, . (t). According to Eq. (1), sea level goes up (down) by 1 cm if the local surface pressure, p′_a(x, y, t), increases (decreases) by 1 mbar. This implies that it is not only changes in SSH due to changes of ocean dynamic that matter during climate change discussions, but also it is those changes that are imposed externally through η_ib, if the latter turns out to be of significant amplitude. The recognition of the importance of low-frequency variability of sea level pressure on estimates of SSH change goes back to early studies by Patullo et al. (1955) and Rossiter (1962). The question was revisited recently by Ponte (2006) who analyzed decadal changes in atmospheric sea level pressure in the National Centers for Environmental Prediction–National Center for Atmospheric Research (NCEP–NCAR) 40-Year Reanalysis (RA; Kalnay et al. 1996) and the 40-yr European Centre for Medium-Range Weather Forecasts (ECMWF) Re-Analysis (ERA-40; Uppala et al. 2005) and who demonstrated that associated effects on SSH can lead to incorrect interpretations of long sea level records.

Studies of climate change and the associated changes in sea level are often based on coupled ocean–atmosphere models. As an example, results from climate change scenario runs suggest that through heat uptake, sea level might rise by about 30–40 cm on a global scale during the next century (Church et al. 2001). Among others, a process not included in most model-based sea level studies is the surface pressure forcing, implying that changes in low-frequency IB effects are usually neglected in climate-related SSH predictions. However, a changing atmospheric circulation implies a change in the atmospheric pressure and an associated loading effect, in principle, will contribute to regional sea level change.

Gregory and Lowe (2000) suggested that the IB effect is of comparatively minor consequence in global and regional predictions of SSH change using coupled atmosphere–ocean general circulation models (AOGCMs). More recently, Lowe and Gregory (2006, hereafter LG06) discussed sea level changes in version 3 of the Hadley Centre Coupled Model (HadCM3) AOGCM after quadrupling atmospheric CO₂ concentrations, with a focus on the changes in sea level due to density and circulation changes of the ocean. Although the authors show a map of IB changes, suggesting again that its overall contribution to regional SSH changes is small in their solution, the change of IB was neither discussed quantitatively nor analyzed in terms of contributions arising from atmospheric dynamics or from an increase in moisture content. Moreover, their IB effect has to be put into the context of other model results.

We will here, based on the output of the ECHAM5/MPI-OM coupled atmosphere–ocean general circulation model of the Max Planck Institute for Meteorology (MPI-M; Jungclaus et al. 2006), investigate the extent to which changes in sea level pressure under climate change conditions could potentially affect estimates of future regional SSH changes on decadal to centennial time scales and analyze to which extent one needs to take IB effects into account in future SSH prediction studies. In section 2 we will first describe the model output and the methodology used in our study. In section 3 we will then compare the model results with results from ERA-40 in terms of time mean IB fields and their standard deviation (STD). In section 4 we then investigate possible climate effects on long-period changes in η_ib as well as high-frequency IB fluctuations. Section 5 then investigates causes for sea level pressure changes in terms of dry and moist pressures. A discussion and final remarks are provided in section 6.

2. Data and method

Our study is based on output of the Max Planck Institute for Meteorology coupled atmosphere–ocean general circulation model ECHAM5/MPI-OM (referred to hereafter as the MPI-M model), which is described in detail by Jungclaus et al. (2006). It is a coupled ocean–atmosphere–ice–land model. Its atmospheric component is version 5.2 of the ECHAM model, which is run at a T63 spatial resolution, equivalent to 1.875° resolution in latitude and longitude, with 31 vertical levels. For details of the atmospheric model, see Roeckner et al. (2003). Technical details of the MPI-OM ocean model and the embedded sea ice model can be found in Marsland et al. (2003). In essence, the ocean model is based on the primitive equations for a hydrostatic Boussinesq fluid and is formulated with a free surface on an Arakawa C grid. It is run with 1.5° horizontal grid spacing and with 40 unevenly spaced vertical levels. The model uses an along-isopycnal diffusion following Redi (1982) and Griffies (1998), and isopycnal tracer mixing by unresolved eddies is parameterized following Gent et al. (1995). The dynamic sea ice model is based on a viscous–plastic rheology (Hibler 1979). Its thermodynamics connect changes in sea ice thickness with a balance of radiant, turbulent, and oceanic heat fluxes. Atmosphere, ice, ocean, and land are coupled by means of the Ocean–Atmosphere–Sea Ice–Soil (OASIS) coupler (Valcke et al. 2003). River runoff and calving glaciers are treated interactively in the atmosphere model and the respective freshwater fluxes are passed to the ocean as part of the atmospheric freshwater flux field.

Model output analyzed in this study was taken from the following three MPI-M experiments:

1. Control run (CTRL hereafter): This preindustrial control experiment (PIcntrl) was run for about 500 yr with constant atmospheric composition as of the year 1860. Because subsequent experiments with increased CO₂ started from this control run, it will be used here as a reference against which the impact of increased CO₂ concentrations on SSH will be diagnosed.

2. 2 × CO₂ (2CO₂ hereafter): Starting from the control run in 1860, that is, after 40 yr into the first run, a second run (called 1%to2x) was performed with atmospheric CO₂ concentration increased by 1% yr⁻¹ compounded for 70 yr. The model was integrated forward until a new level of twice the preindustrial atmospheric CO₂ concentration was reached (end of 1930). No further CO₂ was added subsequently while the model continued to be integrated forward for an additional 100 yr.

3. 4 × CO₂ (4CO₂ hereafter): A third run (called 1%to4x) was performed, starting in 1930 from the experiment 1%to2x, by continuing to add CO₂ to the atmosphere at a 1% level per year compounded beyond twice the present-day concentration until an additional 70 yr of integration was completed; the atmospheric CO₂ concentration reached levels of four times the preindustrial conditions in the year 2000. This third run was continued subsequently until 2040 at this new level of CO₂ content.

The atmosphere model dynamically uses only the dry atmospheric pressure, p^dry_a, and the moisture-related sea level pressure, p^ϵ_a, was neither analyzed nor stored. We diagnosed p^ϵ_a from the available output of the vertically integrated water vapor mixing ratio, q, according to

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where g is the gravitational constant and ∫qdp/g represents the vertically integrated water vapor (kg m⁻²). The total sea level pressure, p_a, relevant for the following IB studies, was obtained by adding p^ϵ_a to the available dry pressure:

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All three runs are schematically summarized in Fig. 1, which shows the atmospheric pressure at sea level averaged globally over the ocean, p^ϵ_a, resulting from the vertically integrated moisture content of the simulated atmosphere. As can be seen from the figure, the control experiment preserves its moisture content and associated values of p^ϵ_a throughout the entire run. By adding CO₂ to the model atmosphere, its moisture content globally increased. The associated sea level pressure reached a new equilibrium soon after the atmospheric CO₂ level was kept at a constant level of twice and four times the preindustrial level for the runs 2CO₂ and 4CO₂. Based on Fig. 1, the following three periods were defined, representing typical time-mean conditions of η_ib for the runs CTRL, 2CO₂, and 4CO₂:

1. Period 1: An average of η_ib over the period 1850–60 is used to characterize the atmospheric surface pressure and the associated IB effect of the control run.

2. Period 2: The average of η_ib over the years 1950–60 of run 2CO₂ is used to characterize the sea level pressure and the IB effects for doubled CO₂ concentrations.

3. Period 3: Fields of run 3 were averaged over the period 2010–20 to represent sea level pressure and IB conditions of the quadrupled CO₂ concentration run.

The time-mean η_ib field was computed from p_a according to Eq. (1) and averaged subsequently over the above three 10-yr periods. To investigate how η_ib changes under climate change conditions, the following differences will be used to characterize changes in atmospheric loading under doubled and quadrupled CO₂ conditions:

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with the superscript representing the averaging period.

3. Comparison of IB fields

Before investigating CO₂-induced changes in the atmospheric loading, we will first compare the time mean of η_ib and its standard deviation, STD(η_ib), computed from monthly mean sea level pressure fields of the CTRL run over the period 1958–2000, with similar fields obtained from monthly mean ERA-40 sea level pressure fields. The time-mean η_ib fields, resulting from the ERA-40 surface pressure fields over the period 1958–2000 is given in Fig. 2a (results from the RA are visually similar and will therefore not be shown separately). The figure reveals that sea level is depressed by up to 10 cm underneath quasi-permanent atmospheric high pressure systems, such as the Azores high. Equivalently, sea level is elevated by a similar amount underneath low pressure systems, such as the Icelandic low and by up to 25 cm around the Antarctic continent. Any long-term change in atmospheric pressure systems, either in amplitude and/or through spatial displacements, will cause long-term changes in regional sea level. Similar results, but from the CTRL run, are shown in the bottom panel of Fig. 2. Overall, the two fields agree visually in their patterns, their geographic locations, and the their amplitudes. However, some differences can be seen in the western equatorial Pacific, where the time-mean η_ib field of the CTRL run is lower than that from ERA-40.

The STD of η_ib, evaluated over the same period, is shown in Fig. 3. As for the time-mean Fig. 3 IB, the CTRL run is also capable of producing the ERA-40 IB variability, both in terms of geographic pattern and amplitude. In both fields, the amplitude in the variability is on the order of 10 cm, and highs and lows agree in their geographic locations. Deviations between both maps are related to the fact that variability is maximum in the North Pacific in the CTRL run, while it is maximum in the subpolar North Atlantic in the ERA-40 results. Higher variability than is present in ERA-40 can be found around Antarctica, where changes in the variability pattern, characteristic of the ERA-40 results, are missing in the CTRL run.

For our present purposes, we conclude from Figs. 2 and 3 that the MPI-M model reproduces the ERA-40 results reasonably well in terms of the mean and STD surface pressure distribution, to the point that we can assume that the model can be used to study atmospheric loading effects on sea level.

4. CO₂-induced IB trends

Fields of Δη^2x_ib(x, y) and Δη^4x_ib(x, y) are shown in Fig. 4. Focusing first on Δη^2x_ib(x, y), a maximum increase in SSH of 5 cm occurs around Antarctica. Increased sea level can also be found at high latitudes of the Northern Hemisphere, in association with reduced sea level pressure there. In reaction to decreasing high-latitude atmospheric sea level pressure, sea level decreases at mid- and low latitudes through the effects of the globally averaged sea level pressure in Eq. (2). A maximum depression in sea level can be found all along 40°S in the Pacific Ocean with some contribution reaching into the Atlantic and Indian Ocean sectors at the same latitude. A further depression of similar amplitude is suggested for the western tropical Pacific.

Changes in the atmospheric loading occurring during period 3 relative to the control conditions, Δη^4x_ib(x, y), are overall similar in pattern to those seen in the Δη^2x_ib(x, y) field, but show significantly enhanced amplitudes (Fig. 4b). Maximum increases in η_ib reach 10 cm around Antarctica and enhanced sea level of up to 6 cm can also be found in the Nordic Seas (Greenland–Iceland–Norwegian Sea) and in the vicinity of the Bering Strait. Highest depressions of up to −5 cm are located along 40°S in all ocean basins and off of the Iberian Peninsula. A comparison of Fig. 4 with Fig. 2 confirms that changes in η_ib under climate change conditions can be of the same size as amplitudes in the present time-mean η_ib field itself (Fig. 2).

For a summary description of CO₂-induced IB changes, we show in the bottom panel of Fig. 4 zonal averages of Δη^4x_ib. The relatively symmetric (to the equator) response of increased sea level at high latitudes (due to decreased atmospheric surface pressure there) is obvious, as is the maximum depression between 30° and 50°S in the Southern Hemisphere. A slight depression in sea level due to enhanced loading can also be found at low latitudes centered around the equator. We note that the amplitudes of the loading changes are about twice as high for 4CO₂ as compared to 2CO₂, but that near the equator and in the Southern Hemisphere, dynamical effects lead to local enhancements of the sea level pressure response. In contrast, a relative depression present in Δη^2x_ib near 60°N relaxes back to zero in Δη^4x_ib, that is, back to preindustrial conditions, suggesting regionally dependent nonlinearities in the CO₂ response. Figure 5 shows again the Δη^4x_ib changes, but now as yearly rates of SSH change. In subpolar regions, respective rates of η_ib increase, on average, are of the order of 0.6 mm yr⁻¹ for quadrupled atmospheric CO₂ content. At mid- and low latitudes, sea level will go down at a rate of −0.2 to −0.4 mm yr⁻¹. We note that computing similar quantities from only the CTRL run leads to overall vanishing trends in the IB term.

We have also investigated how the higher-frequency IB (subseasonal to interannual) signal evolves under climate change conditions. For that purpose we detrended the time series of η_ib and computed a spatial RMS variability from deviations from a mean (this computation makes use of the ergodic principle to infer temporal variability from spatial variability). Results are shown in Fig. 6a after normalization by the total RMS variability of the CNTL run; that is, the figure shows a fractional change and the level of one indicates the same variability as is present in the control run. While all three curves show temporal modulations of the variability in p_a of the order of 20% on decadal time scales (variations in the figure are close to a 20-yr period), it appears that the variability levels of p_a increase with increasing CO₂ forcing, suggesting that variability goes up especially at the end of the considered period.

We also computed the local STD from the total, but detrended, η_ib time series from each run. Differences in the resulting STD (η_ib) between 4CO₂ and the CTRL run are shown in Fig. 6b, which reveals small areas of a reduction in sea level pressure variability that are largely limited to midlatitudes. In contrast, an enhanced variability in sea level can be seen in the vicinity of Antarctica. Overall, the figure is consistent with a slight increase in variability suggested by the top panel, suggesting an increase (by about 40%) in intraseasonal sea level pressure variability at low latitudes, especially in the western tropical Pacific. In agreement with Bengtsson et al. (2006), the figure is also consistent with a poleward shift of intraseasonal atmospheric variability and reduced variability amplitudes at midlatitudes.

5. Causes for IB changes

According to Eq. (5), two components contribute to changes in atmospheric loading under enhanced CO₂ forcing: These are 1) changes in dry atmospheric pressure at sea level due to low-frequency changes in the atmospheric flow field and the associated shifts in air mass and 2) an increase of water vapor in the model’s atmosphere due to changes in the atmospheric temperature and moisture content according to Eq. (4). To investigate the relative importance of each of the terms for sea level pressure changes, we computed similar differences as shown before for Δη_ib, but now as Δp^dry_a and Δp_aε, respectively.

Changes in Δp^ϵ_a, expressed as changes in η_ib, are shown in the top panel of Fig. 7 for the 4CO₂ run relative to the CTRL run. A depression of sea level is apparent at low latitudes due to enhanced atmospheric moisture content. In an IB context, those enhanced pressure values have to be balanced elsewhere, through Eq. (2), causing sea level to rise in high latitudes, despite the fact that the atmosphere will show relatively little changes in its moisture content there.

Changes in the dry sea level pressure, again in terms of η_ib changes, are shown in the middle panel of Fig. 7. In contrast to the moisture-induced sea level changes, regions of reduced amplitudes of dry sea level pressure are located at high latitudes where, accordingly, η_ib goes up. Regions of increased dry sea level pressure can be found at midlatitudes where accordingly sea level decreases, especially along 40°S, with regional patterns superimposed. From the figure, it is obvious that a sea level depression, located off the European coast, is caused by the mass redistribution associated with changes in the atmospheric circulation and not through an increase in the atmospheric moisture content (the same holds in the northeast Pacific and along 40°S). Likewise, the large positive increase in η_ib over the poles is again caused by a strong dynamical response of the atmospheric circulation (associated redistribution of air mass) to increased CO₂ forcing.

A summary of the changes in the two atmospheric pressure components, and their relative contributions to the total pressure, is provided in the bottom panel of Fig. 7 showing zonal averages of moisture-associated and dry-airmass-associated η_ib changes. The figure reveals clearly that the total sea level pressure increases at low latitudes due to moisture uptake in the atmosphere and at mid- and high latitudes due to shifts in dry air masses. A secondary effect of atmospheric loading then acts through the impact of local pressure changes on the ocean-mean sea level pressure and the resulting compensating effect on η_ib in Eq. (2). The compensating effect of both components works in the same direction, pushing sea level farther down at low latitudes through the compensating effect of dynamical changes at high latitudes. In contrast, sea level gets further elevated at high latitudes through the compensating effect of the moisture-related pressure change at low latitudes. As a net effect, dry air and moisture-related pressure changes contribute evenly to low-latitude IB changes; however, the high latitudes are dominated by dynamical adjustments with the moisture-related changes being not larger than 10% of the dynamic impacts.

Any increase in globally averaged p^ϵ_a implies a change of atmospheric moisture content, which has to come from land or the ocean, respectively. Assuming that the land is not changing its water content dramatically (terrestrial water sources are small as compared to the ocean), and that most of the enhanced water vapor in the atmosphere would come from the ocean, this would result in a net decrease in global sea level. The moisture content of each run (kg m⁻²) can be obtained by dividing the numbers shown in Fig. 1 by g = 9.81m s⁻². The figure thus implies an increase of vertically integrated moist content of 4 kg m⁻² and 12 kg m⁻², as a global average, for 2CO₂ and 4CO₂ concentrations, respectively. Dividing these numbers by the density of water and accounting for the fact that the ocean covers 70% of the earth’s surface area, suggests a decrease in global sea level of the order of 0.6 cm and 1.7 cm due to the increase of atmospheric moisture for 2CO₂ and 4CO₂ concentrations, respectively.

6. Discussion and concluding remarks

Since the early studies of Patullo et al. (1955) and Rossiter (1962), the effects of surface pressure changes on estimates of seasonal variations in sea level and longer-term trends have been addressed repeatedly, although studies were mostly hampered by the lack of sufficient data. As an example, Woodworth (1987) investigated the effect of atmospheric loading on estimates of mean sea level trends around the British Isles. In addition, Holgate and Woodworth (2004) investigated the evidence for enhanced coastal sea level rise during the 1990s. Church et al. (2001), in their discussion of future sea level change projections, estimated the effects of changes in η_ib to be only of the order of 0.2 mm yr⁻¹ and dismissed this effect as unimportant. Not considered was the potential that through increased changes in atmospheric sea level pressure those effects might increase in amplitude in the future and that changes in the atmospheric loading effect show strong regional variations.

In our analysis we find values of η_ib changes around the British Isles that are consistent with those of Woodworth (1987). However, we find considerably larger rates of η_ib changes in some regions, especially in the Southern Ocean where η_ib increases by about 0.6 mm yr⁻¹ for a quadrupling of CO₂ concentrations. Changes of this order are about 1/4 of the otherwise predicted rates of global sea level change and as such are not negligible in discussions of future sea level change.

Gregory and Lowe (2000) and Church et al. (2001) provide a detailed description of geographic variations of sea level caused through the doubling of CO₂ concentrations [Intergovernmental Panel on Climate Change (IPCC) scenario A1B], which was recently confirmed by Landerer et al. (2007). Through ocean dynamics, a uniform global increase in sea level is significantly altered, ranging from about 30 cm at low latitudes to 50 cm at high latitudes. Our analysis suggests that low-frequency changes in η_ib could be as large as 10%–20% of this value in some regions, notably the high latitudes including the coasts of northern Europe. Through simultaneous changes in the atmospheric loading pattern, those changes could be reduced at low latitude to only 28 cm, while at high latitudes the sea level change might actually increase to 66 cm.

LG06 discussed sea level changes in the HadCM3 AOGCM of the Hadley Centre after quadrupling atmospheric CO₂ concentrations. In their run, 2% of CO₂ compounded over 70 yr was added to reach quadrupled CO₂ concentrations after 70 yr. The authors showed a map of IB changes resulting from their experiment. The map is reproduced here in the top panel of Fig. 8 and can be compared directly with Fig. 4b. Overall, the patterns for changed IB are similar in that high and midlatitudes show increasing and decreasing SSH, respectively. However, significant deviations are present in some regions, for example, in the midlatitudes of the Pacific, where the decrease in SSH is much more pronounced in the results of LG06. Moreover, the increased SSH in the MPI-M solution (by 4 cm) in the Bering Sea is replaced by a depression of similar size. The comparison suggests that IB-related sea level changes can differ substantially between different climate models, even under similar CO₂ forcing conditions.

Ponte (2006) investigated trends in atmospheric sea level pressure present in the NCEP–NCAR and ERA-40 products. His rates of IB change were extrapolated here to cover a 70-yr period like for LG06. Results are shown in the middle panel of Fig. 8. The figure reveals spatial patterns and amplitudes of changes in η_ib that are very similar to what we find here in our analysis of the MPI-M model results. As in our results, the Southern Ocean is more affected, but the Northern Hemisphere shows similar patterns. The ERA-40 fields suggest an increase in η_ib at high latitude of up to 1 mm yr⁻¹ in some regions. A decrease in η_ib is found at low latitudes, again in agreement with our findings.

For a more quantitative comparison of the results from the MPI-M model with those from LG06 and from Ponte (2006), we show in the bottom panel of Fig. 8 zonal averages from Δη^2x_ib and Δη^4x_ib, as were shown above in Figs. 4a and 4b, and we compare them with the zonal averages of the fields shown in the top two panels of Fig. 8 from LG06 and Ponte (2006). The MPI-M Δη^4x_ib agrees with LG06 in the Northern Hemisphere. However, over the Southern Ocean LG06 shows only 1/2 of the amplitude present in Δη^4x_ib. In the same geographic range, Ponte agrees better with Δη^4x_ib; however, in the Northern Hemisphere, Ponte is more in agreement with the zonal averages of Δη^2x_ib. We also note the pronounced differences between Δη^4x_ib and LG06 in the tropics; here, LG06 is close to zero as would be Δη^4x_ib if the moisture-related component would not have been added back, suggesting that the moisture-related component of IB is missing in the LG06 results. The ERA-40 results are missing completely the depression at 30°–50°S.

One interpretation of the agreement between Ponte and results from the MPI-M model and LG06 could be that the NCEP–NCAR and ERA-40 fields already include a signal of global warming forced by a CO₂ increase. However, Fig 8 also suggests that uncertainties in estimates of IB changes from coupled models are substantial. A detailed interpretation of present-day IB changes on decadal and longer time scales therefore has to await further analyses of the spectrum of IPCC models used during the most recent assessment of climate change.