Changes In Ocean Volume Research Articles

Sea-level rise in Denmark: paleo context, recent projections and policy implications

We present the most recent Intergovernmental Panel on Climate Change Sixth Assessment Report (AR6) sea-level projections for four Danish cities (Aarhus, Copenhagen, Esbjerg and Hirtshals) under the Shared Socioeconomic Pathway (SSP) family of climate scenarios. These sea-level changes projected over the next century are up to an order of magnitude larger than those observed over the previous century. At these cities, year 2150 sea-level changes of between 29 and 55 cm are projected under the very low emissions scenario (SSP1-1.9), while changes of between 99 and 123 cm are projected under the very high emissions scenario (SSP5-8.5). These differences highlight the potentially significant impact of remaining opportunities for climate change mitigation. Due to this increase in mean sea level, the mean recurrence time between historically extreme events is expected to decrease. Under the very high emissions scenario, the historical 100-year storm flood event will become a 1- to 5-year event at most Danish harbours by 2100. There is considerable uncertainty associated with these sea-level projections, primarily driven by uncertainty in the future evolution of the Antarctic ice sheet and future sterodynamic changes in ocean volume. The AR6 characterises collapse of the West Antarctic ice sheet as a low-probability but high-impact event that could cause several metres of sea-level rise around Denmark by 2150. In climate adaptation policy, the scientific landscape is shifting fast. There has been a tremendous proliferation of diverse sea-level projections in recent years, with the most relevant planning target for Denmark increasing c. 50 cm in the past two decades. Translating sea-level rise projections into planning targets requires value judgments about acceptable sea-level risk that depend on local geography, planning timeline and climate pathway. This highlights the need for an overarching national sea-level adaptation plan to ensure municipal plans conform to risk and action standards.

Late Holocene sea-level changes in eastern Québec and potential drivers

Late Holocene sea-level changes can be reconstructed from salt-marsh sediments with decimetre-scale precision and decadal-scale resolution. These records of relative sea-level changes comprise the net sea-level contributions from mechanisms that act across local, regional and global scales. Recent efforts help to constrain the relative significance of these mechanisms that include sediment dynamics and isostasy, which cause relative sea-level changes via vertical land motion, ocean-atmosphere processes that influence regional-scale ocean mass redistribution, and ocean-cryosphere and steric interactions that drive global scale ocean-volume changes. There remains a paucity of high-resolution Late Holocene sea-level data from eastern Canada. This precludes an interrogation of the mechanisms that define sea-level changes over recent centuries and millennia in a region sensitive to oceanic (Atlantic Multidecadal Variability, Atlantic Meridional Overturning Circulation), atmospheric (North Atlantic Oscillation, Arctic Oscillation) and cryospheric (ice-mass balance) changes. We present new relative sea-level data that span the past three millennia from Baie des Chaleurs in the Gulf of St. Lawrence generated using salt-marsh foraminifera supported with plant macrofossil analyses. The accompanying chronology is based on radiocarbon and radionuclide analyses, which are independently verified using trace metal and microcharcoal records. Relative sea level has risen at a mean rate of 0.93 ± 1.25 mm yr−1 over the past ∼1500 years. Residual structure within the reconstruction (‘internal variability’) has contributed up to an additional 0.61 ± 0.46 mm yr−1 of short-lived RSL rise prior to 1800 CE. Following a sea-level low stand during the Little Ice Age, acceleration in relative sea-level rise is identified between 1800 and 1900 CE within the estimates of internal variability and from 1950 CE to present in both the secular and residual trends. Phases of relative sea-level changes in the Gulf of St. Lawrence are concomitant with periods of glacier mass loss following the Little Ice Age, phase periods of the North Atlantic Oscillation and the Atlantic Meridional Overturning Circulation and Northern Hemisphere warming. Quantifying the individual effects of these different mechanisms is important for understanding how ocean-atmosphere processes redistribute ocean-mass upon larger scale background ocean-volume changes.

Rapid glaciation and a two-step sea level plunge into the Last Glacial Maximum.

The approximately 10,000-year-long Last Glacial Maximum, before the termination of the last ice age, was the coldest period in Earth's recent climate history1. Relative to the Holocene epoch, atmospheric carbon dioxide was about 100 parts per million lower and tropical sea surface temperatures were about 3 to 5 degrees Celsius lower2,3. The Last Glacial Maximum began when global mean sea level (GMSL) abruptly dropped by about 40 metres around 31,000 years ago4 and was followed by about 10,000 years of rapid deglaciation into the Holocene1. The masses of the melting polar ice sheets and the change in ocean volume, and hence in GMSL, are primary constraints for climate models constructed to describe the transition between the Last Glacial Maximum and the Holocene, and future changes; but the rate, timing and magnitude of this transition remain uncertain. Here we show that sea level at the shelf edge of the Great Barrier Reef dropped by around 20 metres between 21,900 and 20,500 years ago, to -118 metres relative to the modern level. Our findings are based on recovered and radiometrically dated fossil corals and coralline algae assemblages, and represent relative sea level at the Great Barrier Reef, rather than GMSL. Subsequently, relative sea level rose at a rate of about 3.5 millimetres per year for around 4,000 years. The rise is consistent with the warming previously observed at 19,000 years ago1,5, but we now show that it occurred just after the 20-metre drop in relative sea level and the related increase in global ice volumes. The detailed structure of our record is robust because the Great Barrier Reef is remote from former ice sheets and tectonic activity. Relative sea level can be influenced by Earth's response to regional changes in ice and water loadings and may differ greatly from GMSL. Consequently, we used glacio-isostatic models to derive GMSL, and find that the Last Glacial Maximum culminated 20,500 years agoin a GMSL low of about -125 to -130 metres.

Bias in Estimates of Global Mean Sea Level Change Inferred from Satellite Altimetry

Estimates of regional and global average sea level change remain a focus of climate change research. One complication in obtaining coherent estimates is that geodetic datasets measure different aspects of the sea level field. Satellite altimetry constrains changes in the sea surface height (SSH; or absolute sea level), whereas tide gauge data provide a measure of changes in SSH relative to the crust (i.e., relative sea level). The latter is a direct measure of changes in ocean volume (and the combined impacts of ice sheet melt and steric effects), but the former is not since it does not account for crustal deformation. Nevertheless, the literature commonly conflates the two estimates by directly comparing them. We demonstrate that using satellite altimetry records to estimate global ocean volume changes can lead to biases that can exceed 15%. The level of bias will depend on the relative contributions to sea level changes from the Antarctic and Greenland Ice Sheets. The bias is also more sensitive to the detailed geometry of mass flux from the Antarctic Ice Sheet than the Greenland Ice Sheet due to rotational effects on sea level. Finally, in a regional sense, altimetry estimates should not be compared to relative sea level changes because radial crustal motions driven by polar ice mass flux are nonnegligible globally.

Tyrrhenian sea level at 2000 BP: evidence from Roman age fish tanks and their geological calibration

Following the pioneering work of Schmiedt et al. (1972) on establishing the level of the Tyrrhenian Sea in Antiquity, a number of studies have examined this evidence from Roman Period fish tanks but with significantly different outcomes due primarily to different interpretations of the functional level of these pools at the time of their construction. As part of a longer term project to understand the causes of sea-level change around the Italian coast, we have reexamined and resurveyed 12 well-documented fish tanks, all based on the same construction principles, from the Tyrrhenian coast (between Formia and Orbetello) for which it can be established that they were in open contact with the sea at the time of operation. The structural features that tidally control the exchange of water used to define the ancient local sea level are identified as the channel thresholds, the sluice gate and sliding post positions, and the lowest level crepido. These are consistent for all the tanks examined, permitting the local sea-level change over the past 2000 years to be established at each location with a precision of ± 20 cm and against which other coastal archaeological features can be calibrated. We conclude that published local sea levels that are based on the present-day elevations of the foundations of protective walls constructed around the tanks and lie ~ 50 cm above our inferred levels are inconsistent with the successful functioning of the water exchange and have to be rejected. In one case, for Santa Liberata, we have been able to calibrate our interpretation against sedimentary evidence from the nearby Orbetello Lagoon that confirm our interpretation of the functional control level of the tanks and we conclude that the accuracy of our local sea levels is also ± 20 cm. The causes of sea-level change along this section of the coast are several, including land motion driven by tectonic and glacio-isostatic processes and any change in ocean volume. The individual estimates for the observed local sea levels range from − 0.9 to − 1.5 m with a mean value of − 1.22 ± 0.20 m. These values show that the spatial variability of the local levels is small and consistent with model-inferences of the glacio-isostatic process that indicate near-constant contributions for this section of coast and with tectonic inference from the elevations of the Last Interglacial shoreline.

Noble gases as proxies of mean ocean temperature: sensitivity studies using a climate model of reduced complexity

Past global mean ocean temperature may be reconstructed from measurements of atmospheric noble gas concentrations in ice core bubbles. Assuming conservation of noble gases in the atmosphere-ocean system, the total concentration within the ocean mostly depends on solubility which itself is temperature dependent. Therefore, the colder the ocean, the more gas can be dissolved and the less remains in the atmosphere. Here, the characteristics of this novel paleoclimatic proxy are explored by implementing krypton, xenon, argon, and N 2 into a reduced-complexity climate model. The relationship between noble gas concentrations and global mean ocean temperature is investigated and their sensitivities to changes in ocean volume, ocean salinity, sea-level pressure and geothermal heat flux are quantified. We conclude that atmospheric noble gas concentrations are suitable proxies of global mean ocean temperature. Changes in ocean volume need to be considered when reconstructing ocean temperatures from noble gases. Calibration curves are provided to translate ice-core measurements of krypton, xenon, and argon into a global mean ocean temperature change. Simulated noble gas-to-nitrogen ratios for the last glacial maximum are δKr atm = −1.10‰, δXe atm = −3.25‰, and δAr atm = −0.29‰. The uncertainty of the krypton calibration curve due to uncertainties of the ocean saturation concentrations is estimated to be ±0.3 °C. An additional ±0.3 °C uncertainty must be added for the last deglaciation and up to ±0.4 °C for earlier transitions due to age-scale uncertainties in the sea-level reconstructions. Finally, the fingerprint of idealized Dansgaard-Oeschger events in the atmospheric krypton-to-nitrogen ratio is presented. A δKr atm change of up to 0.34‰ is simulated for a 2 kyr Dansgaard-Oeschger event, and a change of up to 0.48‰ is simulated for a 4 kyr event.

Quantifying extension of passive margins: Implications for sea level change

[1] Passive margins form by rifting and extension of continental crust. Extension of continental crust, associated with subduction elsewhere, decreases ocean basin volume, forcing sea level to rise. The amount that the continental crust has been extended can be quantified using total tectonic subsidence, which is determined using sediment thickness and water depth data coupled with a model of the rifting process. We calculate total tectonic subsidence, the amount of extension or stretching factor, and thickness of extended continental crust at a 5 min grid resolution for passive margins between 77°N and 70°S. Our modeled crustal thicknesses correlate well with seismic refraction data from North America and Australia and can be used to estimate the change in ocean volume and the impact of extension on sea level. The duration of extension is constrained by estimating the onset of rifting and the breakup age, which is the time when rifting ceased and seafloor spreading began. Our results indicate that extension of continental crust has increased sea level by 20.8 m since the start of Pangea rifting.

Sea level change and vertical land movements since the last two millennia along the coasts of southwestern Turkey and Israel

This paper provides new relative sea level data inferred from coastal archaeological sites located along the Turkish coasts of the Gulf of Fethye (8 sites), and Israel, between Akziv and Caesarea (5 sites). The structures selected are those that, for effective functioning, can be accurately related to sea level at the time of their construction. Thus their positions with respect to present sea level provide a measure of the relative sea level change since their time of construction. Useful information was obtained from the investigated sites spanning an age range of ˜2.3–˜1.6 ka BP. The inferred changes in relative sea level for the two areas are distinctly different, from a rise of 2.41 to 4.50 m in Turkey and from 0 to 0.18 m in Israel. Sea level change is the combination of several processes, including vertical tectonics, glacio–hydro-isostatic signals associated with the last glacial cycle, and changes in ocean volume. For the Israel section, the present elevations of the MIS-5.5 Tyrrhenian terraces occur at a few meters above present sea level and vertical tectonic displacements are small. Data from GPS and tide gauge measurements also indicate that any recent vertical movements are small. The MIS-5.5 shorelines are absent from the investigated section of the Turkish coast, consistent with crustal subsidence associated with the Hellenic Arc. The isostatic signals for the Israel section of the coast are also small (ranging from −0.11 mm/yr to 0.14 mm/yr, depending on site and earth model) and the observed (eustatic) average sea level change, corrected for this contribution, is a rise of 13.5 ± 2.6 cm during the past ˜2 ka. This is attributed to the time-integrated contribution to sea level from a combination of thermal expansion and other increases in ocean volume. The observed sea levels from the Turkish sites, in contrast, indicate a much greater rise of up to 2.2 mm/yr since 2.3 ka BP occurring in a wide area between Knidos and Kekova. The isostatic signal here is also one of a rising sea level (of up to ˜1 mm/yr and site and earth-model dependent) and the corrected tectonic rate of land subsidence is ˜1.48 mm/yr. This is the primary cause of dramatic relative sea level rise for this part of the coast.

The gyre-scale circulation of the North Atlantic and sea level at Brest

Abstract. The relationship between the gyre-scale circulation of the North Atlantic, represented by air pressure near to the centre of the sub-tropical gyre, and sea level measured at the eastern boundary of the ocean has been investigated using records commencing in the middle of the 18th century. These time series are twice as long as those employed in an earlier study of this relationship. Near-continuous values of annual mean sea level and mean high water from Brest, and air pressure fields for the eastern North Atlantic derived from terrestrial instrumental pressure records and ship logbook information, have been used to demonstrate that sea level on the eastern boundary does indeed appear to be related to air pressure at the centre of the gyre (subject to reservations concerning short sub-sections of data near to the ends of the records). These findings confirm the earlier conclusions but over much longer timescales. This relationship can explain at least part of the century timescale accelerations in European sea level records obtained from tide gauge and saltmarsh data. This finding has important implications for interpretation of the observed sea level rise and acceleration on the European Atlantic coast, suggesting that redistribution of water could play an important role instead of (or as well as) change in ocean volume.

ESR DATING PLEISTOCENE BARNACLES FROM BC AND MAINE: A NEW METHOD FOR TRACKING SEA LEVEL CHANGE

Barnacles have never been successfully dated by electron spin resonance (ESR). Living mainly in the intertidal zone, barnacles die when sea level changes cause their permanent exposure. Thus, dating the barnacles dates past sea level changes. From this, we can measure apparent sea level changes that occur due to ocean volume changes, crustal isostasy, and tectonics. ESR can date aragonitic mollusc shells ranging in age from 5 ka to at least 500 ka. By modifying the standard ESR method for molluscs to chemically dissolve 20 microm from off the shells, six barnacle samples from Norridgewock, Maine, and Khyex River, British Columbia, were tested for suitability for ESR dating. Due to Mn2+ interference peaks, the four Maine barnacle samples were not datable by ESR. Two barnacles from BC, which lacked Mn2+ interference, yielded a mean ESR age of 15.1 +/- 1.0 ka. These ages agree well with 14C dates on the barnacles themselves and wood in the overlying glaciomarine sediment. Although stability tests to calculate the mean dating signal lifetime and more ESR calibration tests against other barnacles of known age are needed to ensure the method's accuracy, ESR can indeed date Balanus, and thus, sea level changes.

Twentieth century sea level: An enigma

Changes in sea level (relative to the moving crust) are associated with changes in ocean volume (mostly thermal expansion) and in ocean mass (melting and continental storage): zeta(t) = zeta(steric)(t) + zeta(eustatic)(t). Recent compilations of global ocean temperatures by Levitus and coworkers are in accord with coupled ocean/atmosphere modeling of greenhouse warming; they yield an increase in 20th century ocean heat content by 2 x 10(23) J (compared to 0.1 x 10(23) J of atmospheric storage), which corresponds to zeta(greenhouse)(2000) = 3 cm. The greenhouse-related rate is accelerating, with a present value zeta(greenhouse)(2000) approximately 6 cm/century. Tide records going back to the 19th century show no measurable acceleration throughout the late 19th and first half of the 20th century; we take zeta(historic) = 18 cm/century. The Intergovernmental Panel on Climate Change attributes about 6 cm/century to melting and other eustatic processes, leaving a residual of 12 cm of 20th century rise to be accounted for. The Levitus compilation has virtually foreclosed the attribution of the residual rise to ocean warming (notwithstanding our ignorance of the abyssal and Southern Oceans): the historic rise started too early, has too linear a trend, and is too large. Melting of polar ice sheets at the upper limit of the Intergovernmental Panel on Climate Change estimates could close the gap, but severe limits are imposed by the observed perturbations in Earth rotation. Among possible resolutions of the enigma are: a substantial reduction from traditional estimates (including ours) of 1.5-2 mm/y global sea level rise; a substantial increase in the estimates of 20th century ocean heat storage; and a substantial change in the interpretation of the astronomic record.

The Ka'ena Highstand of O'ahu, Hawai'i: Further Evidence of Antarctic Ice Collapse during the Middle Pleistocene

The Ka'ena Highstand of O'ahu, Hawai'i:Further Evidence of Antarctic Ice Collapse during the Middle Pleistocene1 Paul J. Hearty Abstract Marine isotope stage (MIS) 11 may well represent one of the most significant interglacial highstand events of the past million years. Ocean volume changes charted from coastal exposures imply partial or complete melting of some of the world's major ice caps during a middle Pleistocene interglacial. The coastal geology of both Bermuda and the Bahamas yields evidence of an MIS 11 highstand 20 m higher than present. Further support for this catastrophic episode in sea-level history is revealed in subtidal and intertidal deposits at +28±2 m in O'ahu, Hawai'i. The stratigraphy, petrology, and uplift history of the Hawaiian deposits strongly suggest a correlation with MIS 11, and a compilation of amino acid racemization, uranium/thorium (alpha and mass spectrometry), and electron spin resonance ages shows a scatter between 300 and 550 kyr. When corrected for uplift, the Ka'ena Highstand succession at Wai'anae Health Center (OWH1) reveals a "stepping up" of sea level through the interglaciation, similar to that described in the Bahamas. Previous studies on O'ahu attributed all 28 m elevation of the Ka'ena Highstand to uplift since 0.5 Ma, but now it appears that only 8 m of that was caused by uplift, and the remaining 20 m by eustatic sea-level rise. These findings from O'ahu strengthen evidence for the complete disintegration of the Greenland and West Antarctic ice sheets and partial melting of the East Antarctic ice sheet during the middle Pleistocene. If the instability of polar ice sheets can be linked to prolonged warm interglaciations as the data suggest, then existing conservative predictions for the magnitude of sea-level change by future "greenhouse" warming are seriously underestimated. A key to evaluating the potential threat of abrupt sea-level rise may be in understanding the behavior of ice sheets during past very warm and/or prolonged interglaciations. Of particular interest in assessing the Holocene climate, because of similar insolation values at that time, is marine isotopic stage (MIS) 11, which the deep-sea oxygen isotope records of ODP Site 677 (Shackleton et al. 1990) and SPECMAP (Imbrie et al. 1984) suggest occurred between 423 and 362 kyr (Figure 1) and lasted for 60 kyr. The deep-sea oceanographic evidence is compelling, yet remains at best an indirect or circumstantial measure of sea-level change during MIS 11. Other than direct studies at or beneath the ice sheet (Sherer et al. 1998), ocean volume changes in response to ice melting are best measured along stable shorelines or at locations where the tectonic element is well understood. Direct dating of MIS 11 tectonically elevated deposits near Rome, Italy, indicate that the interglacial highstand persisted for 15-37 kyr (Karner et al. 1999) and ended around 400 kyr ago (Karner and Renne 1998). A sequence of coral reefs and shoreline deposits of middle Pleistocene age between modern sea level and +28±2 m are well exposed along the west and northwest coasts between Ka'ena Point and Wai'anae town (Figure 2) and at lower [End Page 65] elevations (e.g., Black Point) elsewhere on O'ahu. Click for larger view View full resolution Figure 1. Planktonic oxygen isotope data from ODP Site 677 for the past million years (Shackleton et al. 1990). MIS 11 stands out as the isotopically lightest interglaciation over this interval of the Quaternary. Reviews concerning the sea-level, oceanographic, and ice history of MIS 11 are available (Burckle 1993, Oppenheimer 1998, Poore et al. 1999). On the North Slope of Alaska, Kaufman and Brigham-Grette (1993) and Brigham-Grette (1999) identified a +22 to +23 m middle Pleistoceneage shoreline and interpreted it to be associated with the Wainwrightian transgression. Similarly, in southern Britain, Bowen (1999) estimated an uplift-corrected sea-level highstand of +23 m and correlated this with MIS 11 on the basis of amino acid racemization (AAR) age estimates. Outcrops in Bermuda and the Bahamas reveal strong evidence of an important interglacial highstand with a rise of sea level to approximately +20 m during the middle Pleistocene. This...

Constraints on the age and duration of the last interglacial period and on sea-level variations

The relation between height and age of shorelines formed during the last interglacial period, as revealed by coral reefs, cannot be related directly to changes in ocean volume because of the effect of isostatic uplift in response to changes in ice-sheet loading. Sea-level changes at sites near the melting ice sheet, such as Bermuda and the Caribbean islands, differ from those along the Australian margin. Modelling of these differences constrains the times of onset and termination of the last interglacial, which are at variance with those deduced from oxygen-isotope studies of deep-sea cores.

Correlation of east Australian Pleistocene shorelines with deep-sea core stages: A basis for a coastal chronology

A review of recent attempts to relate emerged shorelines to deep-sea core stages indicates that correlations based on radiometric ages must be treated carefully, for stratigraphic control is often lacking. Radiometric ages help field interpretation, but some authors question the geology before questioning the dates. The view that oxygen-isotope values in deep-sea sediment cores reflect changes in ocean volume is used to interpret sequences of stranded shorelines in Gippsland (Victoria), southeast Queensland, New Zealand, South Carolina (United States), and Morocco. As a basis for study, it is accepted that all of the shorelines in the areas compared result from global changes of sea level superimposed on continuously emerging land masses that have been rising uniformly, but at different rates, in the different localities. Five stands of the sea, ending at the last interglacial maximum, are recognized and correlated with dated deep-sea core stages as follows: G11 (Gippsland) = Woorim (Queensland) = Awatuna 1 (New Zealand) = Silver Bluff (South Carolina) = Ouljian (Morocco) = core substage 5e, 125,000 yr; G26 = Bribie (Qld) = Karoro (NZ) = Princess Anne = Harounian = core stage 7,220,000 yr; G37 = Poyungan (Qld) = Albion 113 (NZ) = Pamlico = Anfatian (G2) = stage 9,330,000 yr; G65 = Ungowa (Qld) = Albion 165 (NZ) = Bethera = stage 11, 430,000 yr; G70 = Albion 183 (NZ) = Talbot = Anfatian (Thomas quarry) = stage 13,480,000 yr. Implied rates of uplift are used to date and correlate six earlier shorelines: G125 = Penholoway = late Maarifian = 1.02 m.y.; G160 = Wicomico = Maarifian = 1.18 m.y.; G260 = Okefenokee = Haj Salah = 1.43 m.y.; G360 = Sunderland = Sidi Messaoud = 1.64 m.y.; G420 = Coharie = Bouchaib bel Kamel = 1.80 m.y.; A600 = Orange-burg = Fouaratian = 2.35 m.y.

Shallowing-upward cycles in the Middle Proterozoic Altyn Formation.

Phanerozoic carbonate rocks commonly contain cycles, a few metres thick, which were deposited during progressive shallowing of their oceanic environment1. Each cycle represents a deepening of water in a nearshore area, followed by the accumulation of sediments up to sea level. The causes of the water deepening which begins each cycle are rarely known. Possibilities include tectonic activity that affected the depositional basin and changes in ocean volume due to the expansion and contraction of ice sheets. I report here that similar cycles occur in the Middle Proterozoic Altyn Formation, part of the Belt Supergroup2. The cycles are probably related to vertical tectonic activity which influenced sedimentation in the Belt basin. The presence of shallowing-upward cycles in the Altyn Formation shows that such cycles are not confined to the Phanerozoic. Other Precambrian sequences should be examined to see if they too contain cycles. Where such cycles are found they may give important information about Precambrian tectonism and glaciation.

Predicted relative sea-level changes (18,000 years B.P. to present) caused by late-glacial retreat of the Antarctic Ice Sheet

Predictions of global changes in relative sea level caused by retreat of the Antarctic Ice Sheet from its 18,000 yr B.P. maximum to its present size are calculated numerically. When combined with the global predictions of relative sea-level change resulting from retreat of the Northern Hemisphere ice sheets, the results may be compared directly to observations of sea-level change on the Antarctic continent as well as at distant localities. The comparison of predictions to the few observations of sea-level change on Antarctica supports the view that the Antarctic Ice Sheet was larger 18,000 years ago than at present. The contribution of the Antarctic Ice Sheet to the total eustatic sea-level rise is assumed to be 25 m (25% of the assumed total eustatic rise). If as little as 0.7 m of this 25-m rise occurred between 5000 yr B.P. and the present, few mid-oceanic islands would emerge. If the Antarctic Ice Sheet attained its present dimensions by 6000 yr B.P., however, and if the volume of the ocean has remained constant for the past 5000 years, numerous islands throughout the Southern Hemisphere would emerge. It is suggested that a thorough study of Pacific islands, believed by some to have slightly emerged shorelines of Holocene age, would yield useful information about ocean volume changes during the past 5000 years, and hence on the glacial history of the Antarctic Ice Sheet.

Global changes in postglacial sea level: A numerical calculation

The sea-level rise due to ice-sheet melting since the last glacial maximum was not uniform everywhere because of the deformation of the Earth's surface and its geoid by changing ice and water loads. A numerical model is employed to calculate global changes in relative sea level on a spherical viscoelastic Earth as northern hemisphere ice sheets melt and fill the ocean basins with meltwater. Predictions for the past 16,000 years explain a large proportion of the global variance in the sea-level record, particularly during the Holocene. Results indicate that the oceans can be divided into six zones, each of which is characterized by a specific form of the relative sea-level curve. In four of these zones emerged beaches are predicted, and these may form even at considerable distance from the ice sheets themselves. In the remaining zones submergence is dominant, and no emerged beaches are expected. The close agreement of these predictions with the data suggests that, contrary to the beliefs of many, no net change in ocean volume has occurred during the past 5000 years. Predictions for localities close to the ice sheets are the most in error, suggesting that slight modifications of the assumed melting history and/or the rheological model of the Earth's interior are necessary.

Tidal dissipation in the oceans: astronomical, geophysical and oceanographic consequences

The most precise way of estimating the dissipation of tidal energy in the oceans is by evaluating the rate at which work is done by the tidal forces and this quantity is completely described by the fundamental harmonic in the ocean tide expansion that has the same degree and order as the forcing function. The contribution of all other harmonics to the work integral must vanish. These harmonics have been estimated for the principal M 2 tide using several available numerical models and despite the often significant difference in the detail of the models, in the treatment of the boundary conditions and in the way dissipating forces are introduced, the results for the rate at which energy is dissipated are in good agreement. Equivalent phase lags, representing the global ocean-solid Earth response to the tidal forces and the rates of energy dissipation have been computed for other tidal frequencies, including the atmospheric tide, by using available tide models, age of tide observations and equilibrium theory. Orbits of close Earth satellites are periodically perturbed by the combined solid Earth and ocean tide and the delay of these perturbations compared with the tide potential defines the same terms as enter into the tidal dissipation problem. They provide, therefore, an independent estimate of dissipation. The results agree with the tide calculations and with the astronomical estimates. The satellite results are independent of dissipation in the Moon and a comparison of astronomical, satellite and tidal estimates of dissipation permits a separation of energy sinks in the solid Earth, the Moon and in the oceans. A precise separation is not yet possible since dissipation in the oceans dominates the other two sinks: dissipation occurs almost exclusively in the oceans and neither the solid Earth nor the Moon are important energy sinks. Lower limits to the Q of the solid Earth can be estimated by comparing the satellite results with the ocean calculations and by comparing the astronomical results with the latter. They result in Q > 120. The lunar acceleration n , the Earth’s tidal acceleration O T and the total rate of energy dissipation E estimated by the three methods give astronomical based estimate —1.36 —28±3 —7.2 ± 0.7 4.1±0.4 satellite based estimate —1.03 —24 ±5 — 6.4 ± 1.5 3.6±0.8 numerical tide model — 1.49 —30 ±3 —7.5± 0.8 4.5±0.5 The mean value for O T corresponds to an increase in the length of day of 2.7 ms cy -1 . The non-tidal acceleration of the Earth is (1.8 ± 1.0) 10 -22 s ~2 , resulting in a decrease in the length of day of 0.7 ± 0.4 ms cy -1 and is barely significant. This quantity remains the most unsatisfactory of the accelerations. The nature of the dissipating mechanism remains unclear but whatever it is it must also control the phase of the second degree harmonic in the ocean expansion. It is this harmonic that permits the transfer of angular momentum from the Earth to the Moon but the energy dissipation occurs at frequencies at the other end of the tide’s spatial spectrum. The efficacity of the break-up of the second degree term into the higher modes governs the amount of energy that is eventually dissipated. It appears that the break-up is controlled by global ocean characteristics such as the ocean­-continent geometry and sea floor topography. Friction in a few shallow seas does not appear to be as important as previously thought: New estimates for dissipation in the Bering Sea being almost an order of magnitude smaller than earlier estimates. If bottom friction is important then it must be more uniformly distributed over the world's continental shelves. Likewise, if turbulence provides an important dissipation mechanism it must be fairly uniformly distributed along, for example, coastlines or along continental margins. Such a global distribution of the dissipation makes it improbable that there has been a change in the rate of dissipation during the last few millennium as there is no evidence of changes in ocean volume, or ocean geometry or sea level beyond a few metres. It also suggests that the time scale problem can be resolved if past ocean-continent geometries led to a less efficient breakdown of the second degree harmonic into higher degree harmonics.

Isostasy, eustasy and crustal sensitivity

Studies in Southern Scandinavia have revealed a “high crustal sensitivity” even to minor changes in the load of ice (glacio-isostasy) and water (hydro-isostasy). Therefore, one might expect that coast, shelves and even ocean floors were hydro-isostatically deformed by the rising ocean level after the last ice age. There are, in fact, strong indications that the increasing load in connection with the rising ocean level really deformed not only several coasts and shelves of the world but also the ocean floor in general. Therefore, “ocean volume changes” (new term) are not equivalent to eustatic changes as earlier assumed DOI: 10.1111/j.2153-3490.1972.tb01586.x