THIS POST IS REVIEW OF THE LITERATURE ON THE RELATIONSHIP BETWEEN SEA LEVEL RISE AND THE EARTH’S TILT AND ROTATIONAL SPEED.

ONLINE ARTICLES

REFERENCE#1: CHOI 2015: Earth May Spin Faster as Glaciers Melt. By Charles Q. Choi December 11, 2015.
Scientists say a section of the West Antarctic ice sheet has reached a point of inevitable collapse, an event that would eventually raise sea levels more than 3 feet (1 meter). Melting ice triggered by global warming may make Earth whirl faster than before and could shift the axis on which the planet spins, researchers say. This could also affect sunset times, as the length of Earth’s day depends on the speed at which the planet rotates on its axis. Prior research found the rate at which Earth spins has changed over time. For instance, ancient Babylonian, Chinese, Arab and Greek astronomers often recorded when eclipses occurred and where these phenomena were seen. This knowledge, in combination with astronomical models that calculate what the positions of the Earth, sun and moon were on any given date and time, can help reveal how fast Earth must have been spinning. To do so, researchers calculate the speed necessary for the planet to face the sun and moon in ways that allowed those astronomers to observe the eclipses. In general, the gravitational pull of the moon and sun on Earth is relentlessly slowing the planet’s rate of spin. However, in the short term, a variety of different factors can also speed up and slow down how fast Earth whirls. Previous research has found that melting glaciers triggered by global warming helped cause a significant amount of global sea-level rise in the 20th century. In theory, rising sea levels should also have slightly shifted Earth’s axis and increased the rate at which the planet spins. When polar ice caps melt, they remove weight off underlying rock, which then rebounds upward. This makes the poles less flat and the planet more round overall. This should in turn cause Earth to tilt a bit and spin more quickly. However, previous research mysteriously could not find evidence that melting glaciers were triggering a shift in either Earth’s rotation or axis that was as great as predicted. This problem is known as “Munk’s enigma,” after oceanographer Walter Munk at the Scripps Institution of Oceanography in La Jolla, California, who first noted the mystery, in 2002. Now, in a new study, researchers may have solved this enigma and shown that rising sea levels are indeed affecting Earth’s spin and axis. The rise of sea level and the melting of glaciers during the 20th century is confirmed not only by some of the most dramatic changes in the Earth system — for example, catastrophic flooding events, droughts [and] heat waves — but also in some of the most subtle — incredibly small changes in Earth’s rotation rate. First, the scientists noted that recent studies suggested 20th-century glacial melting was about 30 percent less severe than Munk assumed. This should significantly reduce the predicted amount of shift in Earth’s spin and axis. Moreover, the research team’s mathematical calculations and computer simulations found that prior research relied on erroneous models of Earth’s internal structure. This meant previous studies did not correctly account for how much glaciers would deform underlying rock and influence Earth’s spin. Furthermore, interactions between Earth’s rocky mantle and the planet’s molten metal outer core should have helped slow the planet’s spin more than was previously thought. Altogether, these adjustments helped the scientists find that ongoing glacial melting and the resulting sea-level rise are affecting the Earth in ways that match theoretical predictions, astronomical observations, and geodetic or land-survey data. What we believe in regard to melting of glaciers in the 20th century is completely consistent with changes in Earth’s rotation measured by satellites and astronomical methods. This consistency was elusive for a few years, but now the enigma is resolved. Human-induced climate change is of such pressing importance to society that the responsibility on scientists to get things right is enormous. By resolving Munk’s enigma, we further strengthen the already-strong argument that we are impacting climate.

LINK: https://www.livescience.com/53071-melting-glaciers-change-earth-spin.html

Here Choi et al argue that the resoluton of Munk’s Enigma leads to the conclusion that glacial melt and sea level rise should cause the earth’s rotation to speed up. The argument goes that the earth is not a perfect sphere but more like a pumpkin because it is flatter at the poles. It is then argued that since the ice melt that causes sea level rise is mostly at the poles, and since the melting ice causes the underlying rock to pop back up, the ice melt and sea level rise has the net effect of making thee earth more sphericcal than it was when the poles were squished down by ice. And that should cause the earth’s spin rate to increase.

The NASA refernce on this matter says just the opposite – that for example {if the Greenland ice sheet were to completely melt and the meltwater were to completely flow into the oceans, then global sea level would rise by about seven meters (23 feet) and the Earth would rotate more slowly, with the length of the day becoming longer than it is today, by about two milliseconds.}

REFERENCE#2: NASA: The Earth rotates about its axis once a day, but it does not do so uniformly. Instead, the rate of rotation varies by up to a millisecond per day. Like a spinning ice skater whose speed of rotation increases as the skater’s arms are brought closer to their body, the speed of the Earth’s rotation will increase if its mass is brought closer to its axis of rotation. Conversely, the speed of the Earth’s rotation will decrease if its mass is moved away from the rotation axis. Melting land ice, like mountain glaciers and the Greenland and Antarctic ice sheets, will change the Earth’s rotation if the meltwater flows into the oceans. If the meltwater remains close to its source (by being trapped in a glacier lake, for example), then there is no net movement of mass away from the glacier or ice sheet, and the Earth’s rotation won’t change. But if the meltwater flows into the oceans and is dispersed, then there is a net movement of mass and the Earth’s rotation will change. For example, if the Greenland ice sheet were to completely melt and the meltwater were to completely flow into the oceans, then global sea level would rise by about seven meters (23 feet) and the Earth would rotate more slowly, with the length of the day becoming longer than it is today, by about two milliseconds. Melting sea ice, such as the Arctic ice cap, does not change sea level because the ice displaces its volume and, hence, does not change the Earth’s rotation.

LINK: https://climate.nasa.gov/faq/30/if-all-of-earths-ice-melts-and-flows-into-the-ocean-what-would-happen-to-the-planets-rotation/

The NASA reference says that as ice melts and sea level rises, the earth’s rotational speed should slow down.

In the bibliography below we find support for both hypotheses as for example, support for NASA in the various works of Peltier and support for Choi 2015 in for example the various works of Mitrovica. An interesting issue in the bibliography is that the sea level rise measured by other means (tidal guages or satellite, are not taken as a given but adjusted as needed according to observed changes in the rotational speed.

CONCLUSION: Question: What is the effect of sea level rise on the earth’s rotational speed?

Answer: It depends on a lot of things such that the sea level rise data may need to be adjusted to fit the rotation data. As a generalization, the analysis without reference to Munk’s Enigma predict slowing while those that cite Munk’s Enigma predict speeding.

WHAT IS MUNK’S ENIGMA?

In 2002, Munk defined an important enigma of 20th century global mean sea-level (GMSL) rise that has yet to be resolved. First, he listed three canonical observations related to Earth’s rotation [(i) the slowing of Earth’s rotation rate over the last three millennia inferred from ancient eclipse observations, and changes in the (ii) amplitude and (iii) orientation of Earth’s rotation vector over the last century estimated from geodetic and astronomic measurements] and argued that they could all be fit by a model of ongoing glacial isostatic adjustment (GIA) associated with the last ice age. Second, he demonstrated that prevailing estimates of the 20th century GMSL rise (~1.5 to 2.0 mm/year), after correction for the maximum signal from ocean thermal expansion, implied mass flux from ice sheets and glaciers at a level that would grossly misfit the residual GIA-corrected observations of Earth’s rotation. We demonstrate that the combination of lower estimates of the 20th century GMSL rise (up to 1990) improved modeling of the GIA process and that the correction of the eclipse record for a signal due to angular momentum exchange between the fluid outer core and the mantle reconciles all three Earth rotation observations. This resolution adds confidence to recent estimates of individual contributions to 20th century sea-level change and to projections of GMSL rise to the end of the 21st century based on them.

SOURCE: MITROVICA (see bibliography below)

BIBLIOGRAPHY

Church, John A., et al. “Changes in sea level.” , in: JT Houghton, Y. Ding, DJ Griggs, M. Noguer, PJ Van der Linden, X. Dai, K. Maskell, and CA Johnson (eds.): Climate Change 2001: The Scientific Basis: Contribution of Working Group I to the Third Assessment Report of the Intergovernmental Panel. 2001. 639-694. This chapter assesses the current state of knowledge of the rate of change of global-averaged and regional sea-level in relation to climate change. We focus on the 20th and 21st centuries. However, because of the slow response to past conditions of the oceans and ice sheets and the consequent land movements, we consider changes in sea level prior to the historical record, and we also look over a thousand years into the future. Past changes in sea levelFrom recent analyses, our conclusions are as follows: since the Last Glacial Maximum about 20 000 years ago, sea level has risen by over 120 m at locations far from present and former ice sheets, as a result of loss of mass from these ice sheets. There was a rapid rise between 15 000 and 6000 years ago at an average rate of 10 mm/yr.based on geological data, global average sea level may have risen at an average rate of 0.5 mm/yr over the last 6000 years and at an average rate of 0.1 to 0.2 mm/yr over the last 3000 years. vertical land movements are still occurring today as a result of these large transfers of mass from the ice sheets to the ocean.during the last 6000 years, global average sea-level variations on the time scales of a few hundred years and longer are likely to have been less than 0.3 to 0.5 m.based on tide gauge data, the rate of global average sea-level rise during the 20th century is in the range 1.0 to 2.0 mm/yr, with a central value of 1.5 mm/yr (as with other ranges of uncertainty, it is not implied that the central value is the best estimate).based on the few very long tide-gauge records, the average rate of sea-level rise has been larger during the 20th century than the 19th century.no significant acceleration in the rate of sea-level rise during the 20th century has been detected.there is decadal variability in extreme sea levels but no evidence of widespread increases in extremes other than that associated with a change in the mean.Factors affecting present day sea level changeGlobal average sea level is affected by many factors. Our assessment of the most important is as follows.Ocean thermal expansion leads to an increase in ocean volume at constant mass. Observational estimates of about 1 mm/yr over recent decades are similar to values of 0.7 to 1.1 mm/yr obtained from Atmosphere-Ocean General Circulation Models (AOGCMs) over a comparable period. Averaged over the 20th century, AOGCM simulations result in rates of thermal expansion of 0.3 to 0.7 mm/yr.The mass of the ocean, and thus sea level, changes as water is exchanged with glaciers and ice caps. Observational and modelling studies of glaciers and ice-caps indicate a contribution to sea-level rise of 0.2 to 0.4 mm/yr averaged over the 20th century.Climate changes during the 20th century are estimated from modelling studies to have led to contributions of between Ð0.2 and 0.0 mm/yr from Antarctica (the results of increasing precipitation) and 0.0 to 0.1 mm/yr from Greenland (from changes in both precipitation and runoff).Greenland and Antarctica have contributed 0.0 to 0.5 mm/yr over the 20th century as a result of long term adjustment to past climate changes.Changes in terrestrial storage of water over the period 1910 to 1990 are estimated to have contributed from Ð1.1 to +0.4 mm/yr of sea-level rise.The sum of these components indicates a rate of eustatic sea-level rise (corresponding to a change in ocean volume) from 1910 to 1990 ranging from Ð0.8 mm/yr to 2.2 mm/yr, with a central value of 0.7 mm/yr. The upper bound is close to the observational upper bound (2.0 mm/yr), but the central value bound is less than the observational lower bound (1.0 mm/yr), i.e. the sum of components is biased low compared to the observational estimates. The sum of components indicates an acceleration of only 0.2 mm/yr/century, with a range from Ð1.1 to +0.7 mm/yr/century, consistent with observational finding of no acceleration in sea-level rise during the 20th century. The estimated rate of sea-level rise from anthropogenic climate change from 1910 to 1990 (from modelling studies of thermal expansion, glaciers and ice-sheets) ranges from 0.3 to 0.8 mm/yr. It is very likely that 20th century warming has contributed significantly to the observed sea level rise, through thermal expansion of sea water and widespread loss of land ice.Projected sea-level changes from 1990 to 2100Projections of components contributing to sea-level change from 1990 to 2100 (this period is chosen for consistency with the IPCC Second Assessment Report), using a range of AOGCMs following the IS92a scenario (including the direct effect of sulphate aerosol emissions) give:thermal expansion of 0.11 to 0.43 m, accelerating through the 21st century.a glacier contribution of 0.01 to 0.23 m.a Greenland contribution of -0.02 to 0.09 m.an Antarctic contribution of -0.17 to 0.02 m.Including thawing of permafrost, deposition of sediment, and the ongoing contributions from ice sheets as a result of climate change since the Last Glacial Maximum, we obtain a range of global-average sea-level rise from 0.11 to 0.77 m. This range reflects systematic uncertainties in modelling.For the 35 SRES scenarios, we project a sea-level rise of 0.09 to 0.88 m for 1990 to 2100, with a central value of 0.48 m. The central value gives an average rate of 2.2 to 4.4 times the rate over the 20th century. If terrestrial storage continued at its present rates, the projections could be changed by -0.21 to 0.11 m. For an average AOGCM, the SRES scenarios give results which differ by 0.02 m or less for the first half of the 21st century. By 2100, they vary over a range amounting to about 50% of the central value. Beyond the 21st century, sea level rise will depend strongly on the emission scenario.The West Antarctic Ice Sheet (WAIS) has attracted special attention because it contains enough ice to raise sea level by 6 m and because of suggestions that instabilities associated with its being grounded below sea level may result in rapid ice discharge when the surrounding ice shelves are weakened. The range of projections given above makes no allowance for ice-dynamic instability of the WAIS. It is now widely agreed that major loss of grounded ice and accelerated sea-level rise are very unlikely during the 21st century.Our confidence in the regional distribution of sea level change from AOGCMs is low because there is little similarity between models. However, models agree on the qualitative conclusion that the range of regional variation is substantial compared with the global average sea-level rise. Nearly all models project greater than average rise in the Arctic Ocean and less than average rise in the Southern Ocean.Land movements, both isostatic and tectonic, will continue through the 21st century at rates which are unaffected by climate change. It can be expected that by 2100 many regions currently experiencing relative sea-level fall will instead have a rising relative sea level.Extreme high water levels will occur with increasing frequency (i.e. with reducing return period) as a result of mean sea-level rise. Their frequency may be further increased if storms become more frequent or severe as a result of climate change.Longer term changesIf greenhouse gas concentrations were stabilised, sea level would nonetheless continue to rise for hundreds of years. After 500 years, sea-level rise from thermal expansion may have reached only half of its eventual level, which models suggest may lie within ranges of 0.5 to 2.0 m and 1 to 4 m for CO2 levels twice and four times pre-industrial, respectively.Glacier retreat will continue and the loss of a substantial fraction of the total glacier mass is likely. Areas that are currently marginally glaciated are most likely to become ice-free.Ice sheets will continue to react to climate change during the next several thousand years even if the climate is stabilised. Models project that a local annual-average warming of larger than 3°C sustained for millennia would lead to virtually a complete melting of the Greenland ice sheet. For a warming over Greenland of 5.5°C, consistent with mid-range stabilisation scenarios, theGreenland ice sheet contributes about 3 m in 1000 years. For a warming of 8°C, the contribution is about 6 m, the ice sheet being largely eliminated. For smaller warmings, the decay of the ice sheet would be substantially slower.Current ice dynamic models project that the WAIS will contribute no more than 3 mm/yr to sea-level rise over the next thousand years, even if significant changes were to occur in the ice shelves. However, we note that its dynamics are still inadequately understood to make firm projections, especially on the longer time scales.Apart from the possibility of an internal ice dynamic instability, surface melting will affect the long-term viability of the Antarctic ice sheet. For warmings of more than 10°C, simple runoff models predict that an ablation zone would develop on the ice sheet surface. Irreversible disintegration of the WAIS would result because the WAIS cannot retreat to higher ground once its margins are subjected to surface melting and begin to recede. Such a disintegration would take at least a few millennia. Thresholds for total disintegration of the East Antarctic ice sheet by surface melting involve warmings above 20*C, a situation that has not occurred for at least 15 million years and which is far more than predicted by any scenario of climate change currently under consideration.

Peltier, W. R. “Global sea level and Earth rotation.” Science 240.4854 (1988): 895-901. ABSTRACT: Recent analyses of long time scale secular variations of sea level, based on tide gauge observations, have established that sea level is apparently rising at a globally averaged rate somewhat in excess of 1 millimeter per year. It has been suggested that the nonsteric component of this secular rate might be explicable in terms of ongoing mass loss from the small ice sheets and glaciers of the world. Satellite laser ranging and very long baseline interferometry data may be used to deliver strong constraints on this important scenario because of the information that these systems provide on variations of the length of day and of the position of the rotation pole with respect to the earth’s surface geography. These data demonstrate that the hypothesis of mass loss is plausible if the Barents Sea was covered by a substantial ice sheet at the last maximum of the current ice age 18,000 years ago.

Peltier, W. R. “Global sea level rise and glacial isostatic adjustment.” Global and Planetary Change 20.2-3 (1999): 93-123. ABSTRACT: The fact that the ongoing global process of glacial isostatic adjustment (GIA) contributes significantly to present-day observed rates of secular sea level change that are recorded on tide gauges is now rather well established. There is a continuing discussion, however, of the magnitude of the globally averaged rate of relative sea level rise that is residual to this GIA related `contamination’. Accurate estimation of this residual is clearly important to the understanding of ongoing global change in the earth system. In the analyses presented herein, following a review of the global theory of the GIA process that focuses on the issue of rotational feedback, I begin by revisiting the issue of estimating this residual on the basis of secular sea level change measurements derived from long time series of annually averaged tide gauge recordings. These observations, all from the US east coast, are then decontaminated by subtracting estimates of the GIA effect determined on the basis of analysis of 14C dated relative sea level histories to infer a (climate related?) residual signal. Also discussed herein, from a global modelling perspective, is the issue of the extent to which a globally averaged rate of sea level rise based upon TOPEX/POSEIDON type altimetric data (or secular gravity field data from the future GRACE mission) is expected to be contaminated by the GIA process. This issue has not been addressed previously and our analyses show that this contamination of the satellite altimeter estimated rate of global sea level rise will also be significantly influenced, locally, by ongoing glacial isostatic adjustment. However, when this signal is averaged over the surface track of TOPEX/POSEIDON we find that the extent to which this instrument’s measure of the globally averaged rate of sea level rise is contaminated by the GIA process is small.

Jerry X. Mitrovica, Carling C. Hay, Eric Morrow, Robert E. Kopp, Mathieu Dumberry, Sabine Stanley: Science Advances, Reconciling past changes in Earth’s rotation with 20th century global sea-level rise: Resolving Munk’s enigma,11 Dec 2015: Vol. 1, no. 11, e1500679, DOI: 10.1126/sciadv.1500679: ABSTRACT: In 2002, Munk defined an important enigma of 20th century global mean sea-level (GMSL) rise that has yet to be resolved. First, he listed three canonical observations related to Earth’s rotation [(i) the slowing of Earth’s rotation rate over the last three millennia inferred from ancient eclipse observations, and changes in the (ii) amplitude and (iii) orientation of Earth’s rotation vector over the last century estimated from geodetic and astronomic measurements] and argued that they could all be fit by a model of ongoing glacial isostatic adjustment (GIA) associated with the last ice age. Second, he demonstrated that prevailing estimates of the 20th century GMSL rise (~1.5 to 2.0 mm/year), after correction for the maximum signal from ocean thermal expansion, implied mass flux from ice sheets and glaciers at a level that would grossly misfit the residual GIA-corrected observations of Earth’s rotation. We demonstrate that the combination of lower estimates of the 20th century GMSL rise (up to 1990) improved modeling of the GIA process and that the correction of the eclipse record for a signal due to angular momentum exchange between the fluid outer core and the mantle reconciles all three Earth rotation observations. This resolution adds confidence to recent estimates of individual contributions to 20th century sea-level change and to projections of GMSL rise to the end of the 21st century based on them.

Milne, Glenn A., and Jerry X. Mitrovica. “Postglacial sea-level change on a rotating Earth: first results from a gravitationally self-consistent sea-level equation.” Geophysical Journal International 126.3 (1996): F13-F20. ABSTRACT: We present and solve a gravitationally self-consistent sea-level equation which governs postglacial sea-level variations on a spherically symmetric, self-gravitating, viscoelastic and rotating Earth. We find that the inclusion of a glacio-isostatically induced rotational excitation can significantly affect previous predictions of both present-day sea-level rates and postglacial sea-level histories which were based on a theory that assumed a non-rotating Earth model. To illustrate, we consider present-day sea-level rates (and tide-gauge corrections) along the US east coast, and relative sea-level curves in the far field of the late Pleistocene ice sheets.