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Low-Frequency Sea Level Variability and the Inverted Barometer Effect

️Rui M. Ponte
️Sat Apr 01 2006

1. Introduction

Observations from the global array of tide gauges and more recently from satellite altimetry reveal a continuum of low-frequency sea level variability, from well-defined seasonal cycles and large interannual and decadal fluctuations to more subtle secular trends. Part of this variability is directly related to changes in the circulation and heat and freshwater contents of the oceans and can thus provide fundamental clues toward understanding the oceans' role in climate. Other signals do not carry any such relevant dynamic or thermodynamic information and are better off subtracted from the records if possible. Such can be the case with sea level fluctuations induced by surface atmospheric pressure (P_a).

At seasonal and longer time scales, apart from the possible excitation of oceanic resonances, sea level η is expected to react as an inverted barometer (IB) to changes in P_a (Ponte 1992; Wunsch and Stammer 1997). Such isostatic response is described simply by

where the overbar denotes a spatial average over the global oceans, ρ is surface density, and g is acceleration of gravity. According to the IB approximation (1), the sea level adjustment implies essentially negligible surface pressure gradients and currents resulting from P_a fluctuations. Any η^ib variability, if not accounted for correctly in the records, can be misinterpreted as corresponding to circulation or subsurface density signals. An easy correction is provided by (1), if one has good estimates of P_a (range of variability in ρg factor is only a few percent and can be neglected).

The importance of accounting for low-frequency effects of η^ib in sea level data analysis has been long recognized, particularly for the seasonal cycle (Patullo et al. 1955; Rossiter 1962), but the lack of P_a records collocated with the measurements or uncertainties in the available P_a fields can be a problem. In recent years, multidecadal P_a fields have become available from reanalyses projects at the National Centers for Environmental Prediction–National Center for Atmospheric Research (NCEP–NCAR) and the European Centre for Medium-Range Weather Forecasts (ECMWF). The reanalyses fields, given on a global 2.5° × 2.5° grid, constitute an alternative to compilations of P_a observations previously used in η analysis (e.g., Mathers and Woodworth 2001), which have typically coarser resolution and sometimes even incomplete coverage due to lack of data. Here, we assess the usefulness of the reanalyses P_a products for estimating η^ib signals at seasonal and longer time scales and for analyzing the sea level record. Contrasting results based on NCEP–NCAR and ECMWF fields also provides a way of assessing the level of uncertainty in estimates of η^ib.

In studies of low-frequency variability in the tide gauge record, the effects of P_a are often inferred using regression analysis, as an attempt to validate the IB relation or understand the origin of the observed signals (e.g., Rossiter 1962; Thompson 1986; Trupin and Wahr 1990; Mathers and Woodworth 2001). Interpretation of results is not trivial, as P_a fields are usually correlated with other forcing fields, such as surface winds. Multiple regressions using both winds and P_a as input have also been tried (e.g., Thompson 1986; Woodworth 1987). Our approach here is different. We want to separate out the IB signals and set the stage for later modeling and analysis of any residual dynamic signals. In particular, we are not concerned with the validity of the IB assumption. Even if the response to P_a contains a dynamic component, applying an IB correction is always useful, as the gradients of η^ib merely balance out P_a gradients and are thus not dynamically significant. For the same reason, removal of η^ib signals still leaves any relevant dynamic signals in the records. Thus, we simply apply IB corrections to the tide gauge record and analyze how such corrections affect its low-frequency variability and trends.

The paper is organized as follows. Section 2 describes in detail the NCEP–NCAR and ECMWF P_a fields and the tide gauge data used, and section 3 discusses the η^ib estimates and respective uncertainties over the global ocean. Both monthly and annual mean estimates are used to assess seasonal and longer-period variability in η^ib. Separate treatment is given to linear trends in η^ib, which may amount to only 0.1 or 0.2 mm yr⁻¹ over a century but can be more substantial over a few decades (Woodworth 1987; Tsimplis and Josey 2001; Church et al. 2001). The effects of η^ib on the variability and trends of tide gauge records are explored in section 4, followed by a summary of results and implications in the final section.

2. Data

A global record of the state of the atmosphere since 1948 is available from the NCEP–NCAR reanalysis project (Kalnay et al. 1996; Kistler et al. 2001). The overall quality and limitations of such a record, which includes gridded estimates of P_a variability every 6 h, is documented in the above references. A similar reanalysis product dating back to 1958 has more recently become available from ECMWF, following earlier calculations performed for a shorter 15-yr period. The later fields are only now beginning to be documented and studied (Marshall 2003; Trenberth and Smith 2005), and we use them as a different estimate of P_a for comparison with those of NCEP–NCAR and for assessing uncertainty in the estimates of η^ib. Where results based on NCEP–NCAR and ECMWF fields are very similar, only the former are shown. Important differences do occur (e.g., in linear trends), and those are discussed where appropriate.

As the models used in the reanalyses remain the same throughout the period of integration, the quality of the products tends to be tied to the amount of assimilated data. With much fewer data available for constraining the analyses until 1958, the first 10 yr of NCEP–NCAR reanalysis are thought to be less reliable (Kistler et al. 2001). The era of satellite data brought another jump in data coverage around 1979. The last two decades of records are thus considered to have the best quality. In this study, the period of analysis is restricted to 1958–2000, for which we have both NCEP–NCAR and ECMWF fields, and thus excludes the period 1948–57, which has more extreme data deficiencies.

Monthly mean sea level P_a values on a 2.5° × 2.5° horizontal grid for both NCEP–NCAR and ECMWF reanalyses are used to calculate η^ib from (1). Monthly P_a means are created as simple averages of 6-hourly values for each month. Values of are estimated using the ocean–land mask provided with the P_a data. From previous studies, the problems in the NCEP–NCAR reanalysis related to the errors in assimilating Australian pseudo-observations (1979–92) and surface pressure observations (1948–67) are expected to have little impact on the quality of monthly P_a values (Marshall and Harangozo 2000; Marshall 2003). There is, however, evidence for spurious P_a variability, particularly long-term trends, in southern mid- and high latitudes. These regions have very sparse data coverage compared to the rest of the globe and are thus prone to having larger errors. Results at those latitudes should be treated with caution. Comparisons of results based on NCEP–NCAR and ECMWF will highlight some of these issues and provide a measure of uncertainty in our findings.

Besides characterizing the IB effects over the global oceans using the gridded P_a fields, we also analyze those effects in relation to the extensive tide gauge record available. For these purposes, we calculate time series of η^ib at the tide gauge locations in Fig. 1 by bilinearly interpolating the gridded fields to the latitude and longitude of interest. The monthly η records were obtained from the Permanent Service for Mean Sea Level (PSMSL) in Bidston, England (Woodworth and Player 2003). A total of 1950 sites are available, but the data span, continuity, and quality varies widely. In this study, we only include tide gauges that have been reduced to a common datum [so-called revised local reference (RLR) dataset most appropriate for scientific inquiry] and that have more than 240 points (equivalent to 20 yr of nonconsecutive data) overlapping the P_a series. With these restrictions, a total of 593 records are used (Fig. 1). Coverage is good for European, North American, and east Asian coasts. In contrast, African, South American, and Australian coasts are very sparsely sampled, and only one series is available for Antarctica. Island gauges provide a few data points over the deep oceans, with most located in the tropical Pacific.

3. Characteristics of IB signals

a. Variability

Figure 2a shows the standard deviation σ of η^ib calculated from the NCEP–NCAR monthly mean time series after detrending, to exclude contributions from long-term drifts analyzed separately below. [Discussions of η^ib can be readily interpreted in terms of P_a variability; from (1) an increase of 1 cm in η^ib is equivalent to a decrease of ∼1 hPa in P_a.] There is a general poleward increase in σ from ∼1 to 7 cm, with largest values occurring in the region of the Aleutian low in the North Pacific, in the Pacific sector of the Southern Ocean, and in the northern North Atlantic. Enhanced variability is also seen in the Arabian Sea, the Bay of Bengal, and the east Asian coast.

A substantial part of η^ib variability in Fig. 2a is related to seasonal time scales. For results based on annual mean series (Fig. 2b), maximum values of σ are smaller by a factor of 2 or 3, with typical values ranging from <0.5 cm at low latitudes to >2 cm at mid- and high latitudes. There is no trace of enhanced variability around Asia for annual mean analysis. Such features in Fig. 2a are likely related to the strong atmospheric seasonal cycle and monsoonal circulations of those regions. Besides these differences, the places of maximum variability and the increase away from the Tropics are quite similar in Figs. 2a and 2b.

The effects of on η^ib are assessed in Fig. 3. The time series of is marked by a clear seasonal cycle with peak-to-peak amplitude of 1–2 hPa, somewhat variable from year to year (cf. Dorandeu and Le Traon 1999). Comparison with time series of average pressure over land (not shown) indicates that a large portion of the seasonal cycle in results from the shifting of air mass between land and ocean, with any residual signal being due to changes in the total water vapor content of the atmosphere (Trenberth and Smith 2005). Variability of the annual mean series is very small (σ = 0.15 hPa). Comparing to η^ib variability in Fig. 2, for both seasonal and longer periods the importance of is confined to the lowest latitudes.

A crude assessment of uncertainty in the values of η^ib is provided in Fig. 4 by calculating the root-mean-square (rms) difference between the two reanalyses P_a fields, after both series are detrended and demeaned. Values are divided by 2 and can represent the average rms error in the reanalyses in the case of uncorrelated noise, or a lower bound on that error in the presence of noise common to both reanalyses. Results based on both monthly and annual means are shown for comparison with Fig. 2. Over most regions, estimated uncertainties are under 0.4 hPa (0.2 hPa) for monthly (yearly) values. Much larger values are found in southern mid- and high latitudes, however, where the quality of the reanalyses is expected to be influenced by weaker data constraints. Relative to the size of the η^ib signals in Fig. 2, the estimated signal-to-noise ratio is likely to be best in the North Atlantic and North Pacific and worst in the Southern Ocean.

b. Linear trends

Trends are an important element of analysis of the sea level record. Linear trends for η^ib calculated over the 43 yr of analysis (Fig. 5) reveal a large-scale pattern of decreasing sea level in the Tropics and increasing at high latitudes. With the noticeable exception of the southern high latitudes, typical values are between ±0.6 mm yr⁻¹ or ±3 cm over 43 yr, similar to findings based on P_a observations (Rossiter 1962; Woodworth 1987; Church et al. 2001). The trend contributed by (Fig. 3) is equivalent to only ∼−0.06 mm yr⁻¹. Formal trend uncertainties (not shown) range from <0.05 mm yr⁻¹ in tropical areas to 0.3 mm yr⁻¹ in high latitudes. Comparison of NCEP–NCAR and ECMWF results in Fig. 5 also provides a measure of how well constrained the trends are. Differences between the two reanalyses are relatively small over the Northern Hemisphere but are substantially larger close to Antarctica and also near the southern tip of South America. At high southern latitudes, trends are expected to be less well determined (Marshall 2003; Marshall and Harangozo 2000).

Increasingly large trends occur south of 40°S, as one approaches Antarctica. Values as large as 2 mm yr⁻¹ for NCEP–NCAR imply a decrease in P_a of more than 8 hPa over the period of analysis. Values for ECMWF are about half as large. Reanalysis trends over the Southern Ocean have been linked to “jumps” in P_a introduced by the start of satellite data assimilation around 1979 (Trenberth and Smith 2005). However, trends calculated for the period 1979–2000 (not shown) reveal very similar patterns and amplitudes to those shown in Fig. 5. Marshall (2003) has used comparisons with data to conclude that NCEP–NCAR trends are indeed too large in the Southern Ocean and that the ECMWF reanalysis gives a much-improved representation of such trends.

Although differences in detail are clear, particularly in the Southern Hemisphere, the pattern of decreasing (increasing) η^ib at low (high) latitudes is a robust feature of both NCEP–NCAR and ECMWF results. The implied opposite trends in P_a fields, particularly those at high latitudes, can be expected from atmospheric circulation changes under global warming scenarios (Fyfe et al. 1999) and are an active subject of climate change research (Marshall 2003; Trenberth and Smith 2005). Other robust features in Fig. 5 include the maximum in negative trends over the central North Atlantic and in positive trends over the Bering Sea. The similarity of patterns and amplitudes of NCEP–NCAR and ECMWF trends in the North Atlantic and Pacific Oceans indicate that they are better constrained than those in the Southern Ocean. Similar trends have been seen previously in analysis of P_a data (Ostermeier and Wallace 2003).

4. Analysis of the tide gauge record

a. Variability

Sea level time series collected by the tide gauge network in Fig. 1 contain many different signals, including those related to fluctuations in P_a, winds, and heat fluxes, as well as those caused by land movements and instrument noise that can blur the interpretation of the former. The relative importance of η^ib signals is assessed in Fig. 6 by showing the ratio of the variance in η^ib to the observed variance at each tide gauge. Both η^ib and tide gauge series were detrended prior to the analysis. For results based on monthly series, typical ratios are <0.1 in the Tropics and increase to larger values at higher latitudes, as expected from the latitudinal gradients in η^ib variability (Fig. 2). The largest ratios near 20°–30°N occur for stations in the Arabian and China Seas, where there is a strong runoff signal in η associated with the monsoon and a related large seasonal cycle in P_a (Fig. 2), consistent with earlier findings (Patullo et al. 1955). In many extratropical sites, monthly η^ib series have variances that exceed 30% of the observed η variance. Ratios based on annual series are generally smaller (mostly <0.2), and thus relative contributions of η^ib to observed variability tend to be smaller at the lowest frequencies.

Mathers and Woodworth (2001) performed extensive regression analyses of the PSMSL dataset on P_a observations. As motivated in the introduction, regression coefficients are not discussed here. Instead, we assess quantitatively the effects of applying an IB correction to the records by calculating the respective percent variance change in the data, computed as 100(σ²_η − σ²_η−η^ib)/σ²_η. Calculations based on detrended monthly and annual series are shown in Fig. 7. For the great majority of tide gauges analyzed, subtracting η^ib leads to a reduction in variance. In the case of the monthly series, decreases of more than 40% can be found in records from the northern North Atlantic and Arctic Ocean islands, the northern European coasts, the Gulf of Alaska and Aleutian Islands, and the East China and Yellow Seas. Other areas, such as the southern Gulf of Mexico, southern Australia and New Zealand, Southeast Asia, and India, show an increase in variance upon subtracting η^ib, with the most substantial gains (>40%, not shown) in some of the stations in India and Southeast Asia. Seasonal η^ib corrections have been noted to result in larger amplitudes of the seasonal cycle in most of these regions (Patullo et al. 1955), and the results based on annual series indeed show a much smaller number of stations with variance increases. At interannual time scales, still a substantial part of the variability in η can be attributed to η^ib. For many tide gauges in Europe, including those in the Mediterranean and the British Isles, in the northwest coast of North America and the Aleutian Islands, and in Australia, η^ib can explain between 20% and 60% of the observed interannual variance.

b. Linear trends

Studies based on P_a and tide gauge observations (Woodworth 1987; Tsimplis and Josey 2001; Church et al. 2001) have shown that accounting for η^ib signals can measurably affect estimates of sea level trends and their formal uncertainties. Such findings are very much dependent on region and length of record considered, and they are revisited here in the context of the reanalyses-based η^ib fields.

Linear trends in η^ib for both the NCEP–NCAR and ECMWF cases are compared to observed trends in Fig. 8. Calculations are done over the period with available data for each tide gauge. Results are similar for NCEP–NCAR and ECMWF fields, but the latter tend to yield smaller trends. The range of amplitudes in η^ib trends is about 10% of that in the observations, showing mostly negative (positive) trends equatorward (poleward) of ∼60°, as expected from the results shown in Fig. 5. There is, however, a significant scatter of values, with several sites exhibiting trends near ±1 mm yr⁻¹ and larger. The largest negative trends between 40° and 50°N correspond to sites in the Mediterranean.

With the large concentration of stations in mid-northern latitudes, the overall mean trend is negative (−0.18 mm yr⁻¹ for NCEP–NCAR and −0.07 mm yr⁻¹ for ECMWF). For comparison, a similar mean trend for the tide gauge data yields 1.23 mm yr⁻¹. Most stations used in studies are confined to within ±60° of the equator (e.g., Douglas 2001). Over these latitudes, the mean trend in η^ib increases to −0.26 mm yr⁻¹ for NCEP–NCAR and −0.14 mm yr⁻¹ for ECMWF. These values represent a potential negative bias introduced in estimates of trends that use tide gauge data not corrected for η^ib signals, but given the dependence on region, the impact of η^ib variability and trends on studies of will be specific to the particular tide gauges used.

Without attempting to add another entry to the long list of rise estimates, we provide here an illustrative example of the possible impact of correcting tide gauge series for η^ib signals based on reanalyses P_a fields. Table 1 displays linear trends and formal error estimates for the stations used in a comprehensive study of rise (Douglas 2001; Peltier 2001), before and after correcting for η^ib. As intended originally (Douglas 2001), stations in Table 1 are grouped in regional clusters and represent 10 different regions, but more than half are in fact located in the North Atlantic. Stations at Dunedin and Wellington (New Zealand) used by Douglas (2001) had no RLR data and were excluded here. The original study was carried out on records 70+ yr long, but only 43 yr at most are considered here, which is appropriate for testing the benefits of correcting shorter-length records for η^ib.

Accounting for P_a effects leads in the great majority of cases to an increase in the trend estimates in Table 1. The increases are most substantial for the Mediterranean records; the overall mean value of 0.20 mm yr⁻¹ for the uncorrected data changes to 1.13 and 0.66 mm yr⁻¹ when corrected by NCEP–NCAR and ECMWF η^ib fields, respectively. Substantial impact of η^ib is also observed at Newlyn (United Kingdom), Brest (France), Cascais (Portugal), and Lagos (Portugal), for which an uncorrected average trend of 1.06 mm yr⁻¹ increases to 1.58 mm yr⁻¹ (NCEP–NCAR) and 1.49 mm yr⁻¹ (ECMWF). The differences between results based on the two reanalyses, which are considerable in the case of Mediterranean sites but smaller in the eastern North Atlantic, give a measure of uncertainty in the η^ib correction. In any case, the inferred negative bias is consistent with P_a trends deduced from observations (Ostermeier and Wallace 2003). Moreover, these results are consistent with those of Tsimplis and Josey (2001), who used P_a station data to show the importance of η^ib trends in explaining the relatively weak sea level trends in the western Mediterranean over the last decades of the twentieth century.

In addition to changing the trends, by removing low-frequency variance from the records η^ib corrections lead to generally smaller uncertainties (Table 1). These effects are particularly important for stations in the eastern North Atlantic with relatively strong η^ib variability: formal error bars are 20%–40% smaller after subtracting η^ib from the data, consistent with the large variance reduction seen in Fig. 7. These results reproduce some of Woodworth's (1987) findings based on P_a observations.

Taking the average over the 10 clusters in Table 1 gives 1.66, 1.91, and 1.84 mm yr⁻¹ for uncorrected, NCEP–NCAR-corrected, and ECMWF-corrected data, respectively. Over the 43-yr period analyzed here, the differences introduced by η^ib corrections are of the same order as those resulting from accounting for glacial rebound effects (Peltier 2001). Note also that the present uncorrected cluster average is very similar to the value of 1.71 mm yr⁻¹ reported by Peltier (2001), which points to the stability of the estimate under shorter periods of analysis.

5. Discussion and summary

Any η^ib series is only as good as the P_a fields used to calculate it. Excessive errors in η^ib series can erase the benefits of their use for dynamic η analysis. Our comparisons of the NCEP–NCAR and ECMWF reanalyses provide a window into the quality of their P_a and respective η^ib series. Regarding the estimated η^ib variability, results suggest good signal-to-noise ratios, with the exception of the highest latitudes in the Southern Ocean. When applying η^ib corrections to the tide gauge dataset, both reanalyses produce very similar results and seem equally well suited to analysis of η variability. Results for η^ib trends are more difficult to assess, but data comparisons suggest that ECMWF fields are more reliable than those of NCEP–NCAR in the Southern Ocean (Marshall 2003). Good estimates of P_a trends are essential for understanding climate variability over the last few decades, and extensive research in this area should provide better-constrained η^ib trends in the future.

Results based on NCEP–NCAR and ECMWF reanalyses confirm the importance of accounting for η^ib seasonal signals in the analysis of η, particularly in mid- and high latitudes but also in tropical regions (e.g., Arabian Sea, Bay of Bengal, China Sea). In addition, we find that interannual η^ib variability is sufficiently large to measurably affect the variance in many mid- and high-latitude η records. Given the agreement in η^ib estimates from the two reanalyses, IB corrections based on such series should allow for improved analysis and interpretation of dynamic η signals in the records, which are associated with circulation changes and most likely driven by processes other than P_a fluctuations.

For record lengths spanning only a few decades, as considered here, treatment of η^ib trends permits a cleaner interpretation of residual trends in terms of steric or eustatic η changes. Accounting for η^ib effects can lead to substantially different and less uncertain trend estimates in areas like the western Mediterranean and the northeast North Atlantic (Woodworth 1987; Tsimplis and Josey 2001). One might expect even more important effects for shorter (decade-long) records, such as those available from altimeter measurements (Nerem and Mitchum 2001). As an example, trend estimates shown in Fig. 9, calculated for the period 1993–2000 overlapping the altimeter record, are on the order of a few millimeters per year and are comparable to observed local trends (cf. the latest altimeter results, available online at http://sealevel.colorado.edu/).

Given the large-scale pattern in η^ib trends shown in Fig. 5 and the undersampling of many regions in the tide gauge record, we find that η^ib trends at the local level can measurably affect estimates of commonly obtained by averaging local trend estimates. These effects can be as important as those from land movements associated with postglacial rebound over the 40+ yr considered. A true estimate of , however, should not depend on η^ib: consistent with conservation of mass, the spatial integral of (1) over the global ocean is time invariant. Measurements by TOPEX/Poseidon and Jason altimeters come close to yielding a true estimate of , given their nearly global coverage (±66° latitude). The effect of missing high latitudes, as well as of regions that are ice-covered for part of the year, is usually neglected, and published altimeter estimates of have been computed without applying an IB correction (Nerem and Mitchum 2001), but the analysis of Dorandeu and Le Traon (1999) hints at possible non-negligible effects.

An estimate of η^ib averaged over ±66° (Fig. 10) yields a trend of only −0.06 mm yr⁻¹, or −2.6 mm over the 43 yr of analysis. Given the patterns in Fig. 5, these results are sensitive to the latitudinal span of the data (e.g., η^ib averaged over ±60° would imply substantially larger negative trends). Larger trends can also result when considering shorter (decadal) spans, like those provided by altimetry. Apart from trends, the series shown in Fig. 10 contains seasonal and longer-period variability with a standard deviation of 2.3 mm, which is comparable with that of altimeter-based series with 60-day smoothing (Nerem and Mitchum 2001). Accounting for η^ib effects should remove some of the variance in the altimeter-derived series, decreasing trend uncertainties and allowing for better interpretation of the residual low-frequency fluctuations. More detailed exploration of η^ib effects on altimeter studies of seems warranted.

As a final point, we recall that reanalyses P_a fields examined here only extend back to 1948. If IB corrections are to be applied to earlier, longer η records, other P_a datasets, such as that described by Basnett and Parker (1997), must be used. Comparisons of available P_a datasets with the reanalyses over recent decades of overlap should provide an extra consistency check on the results presented here. The impact of IB corrections on longer (∼100 yr) tide gauge records is left for future study.

Acknowledgments

Support for this research has been provided by NASA Physical Oceanography Program under Grant NAG5-12742, with additional support from the NASA Jason-1 project under Contract 1206432 with JPL. The author thanks C. Wunsch, D. Stammer, and P. Woodworth for comments on an earlier version of the manuscript.

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Fig. 2.

Standard deviation of detrended inverted barometer sea level η^ib based on NCEP–NCAR fields for (top) monthly and (bottom) annual mean series. Contour interval is (top) 1 cm and (bottom) 0.5 cm.