Glacial rebound

@article{gutenberg1941changes,
    author = "GUTENBERG, B.",
    title = "Changes in sea level, postglacial uplift, and mobility of the earth's interior",
    year = "1941",
    journal = "Geological Society of America Bulletin",
    url = "https://doi.org/10.1130/gsab-52-721",
    doi = "10.1130/gsab-52-721",
    number = "5",
    openalex = "W1989830935",
    pages = "721-772",
    volume = "52"
}

@techreport{gutenberg1941changes2,
    author = "Gutenberg, B",
    title = "Changes in sea level, post-glacial uplift, and mobility of the earth's interior",
    year = "1941",
    howpublished = "Geological Society of America Bulletin, v. 52, p. 721-772",
    note = "talkorigins\_source = {true}; raw\_reference = {Gutenberg, B., 1941, Changes in sea level, post-glacial uplift, and mobility of the earth's interior: Geological Society of America Bulletin, v. 52, p. 721-772.}"
}

@article{broecker1962the,
    author = "Broecker, Wallace S.",
    title = "The contribution of pressure-induced phase changes to glacial rebound",
    year = "1962",
    journal = "Journal of Geophysical Research",
    url = "https://doi.org/10.1029/jz067i012p04837",
    doi = "10.1029/jz067i012p04837",
    number = "12",
    openalex = "W2116457481",
    pages = "4837-4842",
    volume = "67",
    references = "doi101029tr039i005p00947, doi10106313057117, doi10108000291955908551761, doi101086626809, doi1023071791535, doi102475ajs2552115, doi102475ajs2603181, doi105962bhltitle45550, openalexw2426368118"
}

@article{farrand1962postglacial1,
    author = "Farrand, W. R",
    title = "Postglacial rebound in North America",
    year = "1962",
    journal = "American Journal of Science, v. 260, p. 181-198",
    note = "talkorigins\_source = {true}; raw\_reference = {Farrand, W. R., 1962, Postglacial rebound in North America: American Journal of Science, v. 260, p. 181-198.}"
}

A simple isostatic model explaining the pattern of deformation of the shorelines of proglacial lakes has been developed. The rate of glacial retreat before the formation of the shoreline can be derived from the curvature of its uplifted portion. The rate calculated in this way for the retreat preceding the formation of Lake Algonquin is 120 km/103 yr, a value not in conflict with the radiocarbon chronology for this interval. The agreement between the uplift predicted at the iceward extreme of the shoreline (260 meters) and the actual maximum uplift (250±50 meters) provides an independent check on the validity of the model. If the model proves to be correct, the implications are as follows. (1) The continental ice sheets had shapes and total thicknesses during their retreat phases not dissimilar to those observed for present-day ice masses on Greenland and Antarctica, i.e., dynamic equilibrium was maintained; (2) rebound at the edge of large continental ice sheets is a simple isostatic process occurring with the Washburn-Stuiver time constant of about 700 years; and (3) the strength of the crust is sufficiently small to prevent the lateral influence of a continental ice sheet from extending more than a few tens of kilometers beyond its margins.

@article{doi101029jz071i020p04777,
    author = "Broecker, Wallace S.",
    title = "Glacial rebound and the deformation of the shorelines of proglacial lakes",
    year = "1966",
    journal = "Journal of Geophysical Research Atmospheres",
    abstract = "A simple isostatic model explaining the pattern of deformation of the shorelines of proglacial lakes has been developed. The rate of glacial retreat before the formation of the shoreline can be derived from the curvature of its uplifted portion. The rate calculated in this way for the retreat preceding the formation of Lake Algonquin is 120 km/103 yr, a value not in conflict with the radiocarbon chronology for this interval. The agreement between the uplift predicted at the iceward extreme of the shoreline (260 meters) and the actual maximum uplift (250±50 meters) provides an independent check on the validity of the model. If the model proves to be correct, the implications are as follows. (1) The continental ice sheets had shapes and total thicknesses during their retreat phases not dissimilar to those observed for present-day ice masses on Greenland and Antarctica, i.e., dynamic equilibrium was maintained; (2) rebound at the edge of large continental ice sheets is a simple isostatic process occurring with the Washburn-Stuiver time constant of about 700 years; and (3) the strength of the crust is sufficiently small to prevent the lateral influence of a continental ice sheet from extending more than a few tens of kilometers beyond its margins.",
    url = "https://doi.org/10.1029/jz071i020p04777",
    doi = "10.1029/jz071i020p04777",
    openalex = "W1984765750",
    references = "broecker1962the, doi101029jz067i012p04837"
}

Contained within the 4th Edition (1974) of the Atlas of Canada is a set of two maps. One shows the maximum post-glacial marine limit in feet above present sea level and the second shows the maximum height of post-glacial rebound in feet above present sea level. Both maps show existing glaciers and are accompanied by a detailed text providing background information on the post-glacial marine limit, post-glacial rebound and the production of these two maps.

@misc{crossref1972postglacial,
    title = "Post-Glacial Rebound",
    year = "1972",
    abstract = "Contained within the 4th Edition (1974) of the Atlas of Canada is a set of two maps. One shows the maximum post-glacial marine limit in feet above present sea level and the second shows the maximum height of post-glacial rebound in feet above present sea level. Both maps show existing glaciers and are accompanied by a detailed text providing background information on the post-glacial marine limit, post-glacial rebound and the production of these two maps.",
    url = "https://doi.org/10.4095/294445",
    doi = "10.4095/294445",
    openalex = "W2902944798"
}

From 18,000 to 6500 years ago the ice sheets covering North America melted, and sea level rose almost 100 meters. Since that time, sea level has remained almost constant, but the earth has not yet completed its adjustment to the removal of the ice load. In the center of the uplifted region the ground has risen 138 meters in the last 6000 years and is rising at a rate of 2 ± 0.5 cm/yr today; there may be another 300 ± 120 meters of vertical motion left before isostatic equilibrium is reached. This review collects the evidence of vertical movements in northern and eastern North America from different sources and disciplines to provide in one publication the quantitative data important for geophysical analyses of glacio‐isostatic rebound. The paper covers evidence from the area of uplift and the peripheral zone of submergence and from the past movements and instrumentally recorded recent trends, provides a discussion of the eustatic rise in sea level, and gives an updated free‐air gravity anomaly map of the deglaciated region.

@article{doi101029rg010i004p00849,
    author = "Walcott, R. I.",
    title = "Late Quaternary vertical movements in eastern North America: Quantitative evidence of glacio‐isostatic rebound",
    year = "1972",
    journal = "Reviews of Geophysics",
    abstract = "From 18,000 to 6500 years ago the ice sheets covering North America melted, and sea level rose almost 100 meters. Since that time, sea level has remained almost constant, but the earth has not yet completed its adjustment to the removal of the ice load. In the center of the uplifted region the ground has risen 138 meters in the last 6000 years and is rising at a rate of 2 ± 0.5 cm/yr today; there may be another 300 ± 120 meters of vertical motion left before isostatic equilibrium is reached. This review collects the evidence of vertical movements in northern and eastern North America from different sources and disciplines to provide in one publication the quantitative data important for geophysical analyses of glacio‐isostatic rebound. The paper covers evidence from the area of uplift and the peripheral zone of submergence and from the past movements and instrumentally recorded recent trends, provides a discussion of the eustatic rise in sea level, and gives an updated free‐air gravity anomaly map of the deglaciated region.",
    url = "https://doi.org/10.1029/rg010i004p00849",
    doi = "10.1029/rg010i004p00849",
    openalex = "W2072475588",
    references = "doi101029jb073i022p07089, doi101029jb075i020p03941, doi101038195984a0, doi101073pnas48101728, doi101126science16238581121, doi101130001676061970811895psotpa20co2, doi101130gsab52721, doi101139e70070, doi1023072422948, doi1023072423416, doi102475ajs2603181, gutenberg1941changes, openalexw1904021077"
}

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.

@article{doi1010160033589478900339,
    author = "Clark, J. A. and Farrell, William E. and Peltier, W. R.",
    title = "Global Changes in Postglacial Sea Level: A Numerical Calculation",
    year = "1978",
    journal = "Quaternary Research",
    abstract = "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.",
    url = "https://doi.org/10.1016/0033-5894(78)90033-9",
    doi = "10.1016/0033-5894(78)90033-9",
    openalex = "W2094666610",
    references = "doi1010160079194661900040, doi101017s0022143000027386, doi101029jb073i022p07089, doi101029rg010i003p00761, doi101029rg010i004p00849, doi101029rg012i004p00649, doi101111j1365246x1976tb01251x, doi101111j1365246x1976tb01252x, doi101111j1365246x1976tb01253x, doi101126science1914225353, doi1011300016760619647563lqscac20co2, doi101130001676061970811895psotpa20co2, doi1023071550617"
}

This paper is concerned with an analysis of the effect of the Pleistocene glacial cycle upon the Earth's rotation. We demonstrate that two important geophysical observables may be explained as aspects of the rotational response to surface mass loading by ice sheets. These are the astronomically observed non-tidal component of the acceleration of planetary rotation and the secular drift of the rotation pole relative to the surface geography which is evident in the ILS pole path. The former observation is shown to provide an unambiguous constraint upon the viscosity of the planetary mantle and requires a depth dependence of this parameter which is the same as that which has previously been inferred in studies of the relative sea-level variations and free air gravity anomalies associated with post-glacial rebound. The observed secular drift of the pole cannot provide an independent estimate of the viscosity of the mantle because it depends jointly upon mantle viscosity and lithospheric thickness. With the viscosity profile fixed by the rebound data, the observed speed of polar wander suggests a continental lithospheric thickness which is in excess of that appropriate for old ocean basins but nevertheless in accord with independent constraints.

@article{doi101111j1365246x1984tb01920x,
    author = "Wu, Patrick and Peltier, W. R.",
    title = "Pleistocene deglaciation and the Earth's rotation: a new analysis",
    year = "1984",
    journal = "Geophysical Journal International",
    abstract = "This paper is concerned with an analysis of the effect of the Pleistocene glacial cycle upon the Earth's rotation. We demonstrate that two important geophysical observables may be explained as aspects of the rotational response to surface mass loading by ice sheets. These are the astronomically observed non-tidal component of the acceleration of planetary rotation and the secular drift of the rotation pole relative to the surface geography which is evident in the ILS pole path. The former observation is shown to provide an unambiguous constraint upon the viscosity of the planetary mantle and requires a depth dependence of this parameter which is the same as that which has previously been inferred in studies of the relative sea-level variations and free air gravity anomalies associated with post-glacial rebound. The observed secular drift of the pole cannot provide an independent estimate of the viscosity of the mantle because it depends jointly upon mantle viscosity and lithospheric thickness. With the viscosity profile fixed by the rebound data, the observed speed of polar wander suggests a continental lithospheric thickness which is in excess of that appropriate for old ocean basins but nevertheless in accord with independent constraints.",
    url = "https://doi.org/10.1111/j.1365-246x.1984.tb01920.x",
    doi = "10.1111/j.1365-246x.1984.tb01920.x",
    openalex = "W2104024913",
    references = "doi101111j1365246x1982tb04976x"
}

Abstract Stratigraphic, micropalaeontologic and radiocarbon data show that since c. 6500 BP the Fenland has been influenced by 7 periods of positive sea‐level tendencies and by 6 periods of negative sea‐level tendencies. Despite the numerous problems associated with the reconstruction of past altitudes of sea level the periods of positive sea‐level tendencies were clearly characterised by a rise in sea level, the development of transgressive overlaps and a landward movement of the coastline. The periods of negative sea‐level tendencies were characterised by the development of regressive overlaps, a seaward movement of the coastline and a reduced or negative rate of sea‐level rise. The various altitudinal errors do not permit the incontrovertible distinction of periods of falling sea levels. All changes within the Fenland were not synchronous and local factors influenced the exact nature of each sea‐level indicator. Dominant regional and local factors have been identified for different areas and different time periods. The chronological and spatial characteristics of the sequences within the Fenland are best explained by a palaeocoastline without supratidal barriers controlling sedimentation. The data indicate an average crustal subsidence in the Fenland of 0.9m/1000 years since c. 6500 BP and the pattern of positive and negative tendencies of sea‐level movement is also seen in the chronologies for north west England and north east Scotland.

@article{doi101002jqs3390010205,
    author = "Shennan, Ian",
    title = "Flandrian sea‐level changes in the Fenland. II: Tendencies of sea‐level movement, altitudinal changes, and local and regional factors",
    year = "1986",
    journal = "Journal of Quaternary Science",
    abstract = "Abstract Stratigraphic, micropalaeontologic and radiocarbon data show that since c. 6500 BP the Fenland has been influenced by 7 periods of positive sea‐level tendencies and by 6 periods of negative sea‐level tendencies. Despite the numerous problems associated with the reconstruction of past altitudes of sea level the periods of positive sea‐level tendencies were clearly characterised by a rise in sea level, the development of transgressive overlaps and a landward movement of the coastline. The periods of negative sea‐level tendencies were characterised by the development of regressive overlaps, a seaward movement of the coastline and a reduced or negative rate of sea‐level rise. The various altitudinal errors do not permit the incontrovertible distinction of periods of falling sea levels. All changes within the Fenland were not synchronous and local factors influenced the exact nature of each sea‐level indicator. Dominant regional and local factors have been identified for different areas and different time periods. The chronological and spatial characteristics of the sequences within the Fenland are best explained by a palaeocoastline without supratidal barriers controlling sedimentation. The data indicate an average crustal subsidence in the Fenland of 0.9m/1000 years since c. 6500 BP and the pattern of positive and negative tendencies of sea‐level movement is also seen in the chronologies for north west England and north east Scotland.",
    url = "https://doi.org/10.1002/jqs.3390010205",
    doi = "10.1002/jqs.3390010205",
    openalex = "W2053864207"
}

General circulation model experiments at 3000-year intervals for the past 18 000 years were made to estimate the magnitude, timing, and pattern of the climatic response to prescribed changes of orbital parameters (date of perihelion, axial tilt, eccentricity) and glacial-age lower boundary conditions (ice sheets, land albedo, sea ice and sea surface temperature). The experiments used the Community Climate Model (CCM) of the National Center for Atmospheric Research (NCAR). The response of monsoon circulations and tropical precipitation to the orbitally produced solar radiation changes was much larger than the response to changes of glacial-age boundary conditions. The continental interior of Eurasia was 2–4 K warmer in summer, and summer monsoon precipitation of North Africa-South Asia was increased by 10–20% between 12 000 and 6000 yr BP (before present) when perihelion occurred during northern summer (rather than in winter as now) and the earth's axial tilt was larger than now. Southern Hemisphere summer monsoons were weaker during the same period. In northern midlatitudes, glacial-age features such as the North American ice shed exerted a strong influence on the climate until 9000 yr BP. Much of the climatic change of the period 12 000 to 6000 yr BP can be described as an amplified (weakened) seasonal cycle in response to the larger (smaller) seasonal radiation extremes of the Northern (Southern) Hemisphere. Summers were warmer and winters colder in Northern Hemisphere lands, but there was little change in annual average temperature. However, because of the nonlinear relationship between saturation vapor pressure and temperature, the sensitivity of the hydrologic cycle to orbital parameter changes was larger in summer than in winter (and in the tropics rather than high latitudes); in the northern tropics, this led to a net increase in estimated annual average precipitation and precipitation minus evaporation. Many features of the results are in agreement with geologic evidence.

@article{doi1011751520046919860431726tiocop20co2,
    author = "Kutzbach, John E. and Guetter, P. J.",
    title = "The Influence of Changing Orbital Parameters and Surface Boundary Conditions on Climate Simulations for the Past 18 000 Years",
    year = "1986",
    journal = "Journal of the Atmospheric Sciences",
    abstract = "General circulation model experiments at 3000-year intervals for the past 18 000 years were made to estimate the magnitude, timing, and pattern of the climatic response to prescribed changes of orbital parameters (date of perihelion, axial tilt, eccentricity) and glacial-age lower boundary conditions (ice sheets, land albedo, sea ice and sea surface temperature). The experiments used the Community Climate Model (CCM) of the National Center for Atmospheric Research (NCAR). The response of monsoon circulations and tropical precipitation to the orbitally produced solar radiation changes was much larger than the response to changes of glacial-age boundary conditions. The continental interior of Eurasia was 2–4 K warmer in summer, and summer monsoon precipitation of North Africa-South Asia was increased by 10–20\% between 12 000 and 6000 yr BP (before present) when perihelion occurred during northern summer (rather than in winter as now) and the earth's axial tilt was larger than now. Southern Hemisphere summer monsoons were weaker during the same period. In northern midlatitudes, glacial-age features such as the North American ice shed exerted a strong influence on the climate until 9000 yr BP. Much of the climatic change of the period 12 000 to 6000 yr BP can be described as an amplified (weakened) seasonal cycle in response to the larger (smaller) seasonal radiation extremes of the Northern (Southern) Hemisphere. Summers were warmer and winters colder in Northern Hemisphere lands, but there was little change in annual average temperature. However, because of the nonlinear relationship between saturation vapor pressure and temperature, the sensitivity of the hydrologic cycle to orbital parameter changes was larger in summer than in winter (and in the tropics rather than high latitudes); in the northern tropics, this led to a net increase in estimated annual average precipitation and precipitation minus evaporation. Many features of the results are in agreement with geologic evidence.",
    url = "https://doi.org/10.1175/1520-0469(1986)043<1726:tiocop>2.0.co;2",
    doi = "10.1175/1520-0469(1986)043<1726:tiocop>2.0.co;2",
    openalex = "W2078721910"
}

Oceanography is considered a young science with roots going back only to the first half of the nineteenth century. Sometimes as late a year as 1872, when the first scientific cruise of a modern nature, the famous Challenger Expedition, began its work in the oceans, is regarded as the opening year of oceanographic research. However, in this connection it must always be kept in mind that there is an important and interesting field within the boundaries of modern oceanography which has a considerab1y more respectable pedigree. This significant field consists of the studies on sea level and its variations. Research on the tides, especially on their theoretical aspects must, of course, be mentioned first. Nevertheless, there are other phenomena connected with sea-level changes which have been commonly known and studied for centuries. It may suffice to refer to two examples: the disastrous floods described, if not always in a scientific way, by many ancient peoples; and the land uplift characteristic of large areas in the northern hemi-sphere. The latter phenomenon has been known and studied, at least in the Fennoscandian countries, since the beginning of the eighteenth century. It gave, in the middle of the nineteenth century, the first impulse to the erection of sea-level measuring poles and thus laid the first firm foundation for purely scientific studies of sea-level changes, such as they appear in nature. Sea-level research mayat a first cursory glance be considered a rather unitary and well-limited field of scientific studies. The conclusion could easily be drawn that the contemporary tendency for specialization has created within the wide framework of oceanography a scientific branch which may allow the investigator to follow his own independent way. Nothing could be more erroneous than su ch an interpretation. It will be made clear, in the particular chapters of this book, that students of sea level and its variations are forced to consider in their work a considerable number of different elements, factors and phenomena which form a substantial part of many very different sciences. It may be sufficient to mention in this connection a few of these elements and phenomena. Hydrography of oceanography, in the more restricted sense of these terms, contribute such elements as temperature and salinity, and consequently also the density of sea water, currents and long waves; meteorology, atmospheric pressure, different wind effects, evaporation and precipitation; hydrology, water discharged from rivers; geology, land uplift and land subsidence; astronomy, gravitation and tide-generating forces; seismology, tsunami waves; and, finally, glaciology, the eustatic changes.

@book{openalexw41072897,
    author = "Lisitzin, Eugénie",
    title = "Sea-Level Changes",
    year = "1987",
    journal = "Medical Entomology and Zoology",
    abstract = "Oceanography is considered a young science with roots going back only to the first half of the nineteenth century. Sometimes as late a year as 1872, when the first scientific cruise of a modern nature, the famous Challenger Expedition, began its work in the oceans, is regarded as the opening year of oceanographic research. However, in this connection it must always be kept in mind that there is an important and interesting field within the boundaries of modern oceanography which has a considerab1y more respectable pedigree. This significant field consists of the studies on sea level and its variations. Research on the tides, especially on their theoretical aspects must, of course, be mentioned first. Nevertheless, there are other phenomena connected with sea-level changes which have been commonly known and studied for centuries. It may suffice to refer to two examples: the disastrous floods described, if not always in a scientific way, by many ancient peoples; and the land uplift characteristic of large areas in the northern hemi-sphere. The latter phenomenon has been known and studied, at least in the Fennoscandian countries, since the beginning of the eighteenth century. It gave, in the middle of the nineteenth century, the first impulse to the erection of sea-level measuring poles and thus laid the first firm foundation for purely scientific studies of sea-level changes, such as they appear in nature. Sea-level research mayat a first cursory glance be considered a rather unitary and well-limited field of scientific studies. The conclusion could easily be drawn that the contemporary tendency for specialization has created within the wide framework of oceanography a scientific branch which may allow the investigator to follow his own independent way. Nothing could be more erroneous than su ch an interpretation. It will be made clear, in the particular chapters of this book, that students of sea level and its variations are forced to consider in their work a considerable number of different elements, factors and phenomena which form a substantial part of many very different sciences. It may be sufficient to mention in this connection a few of these elements and phenomena. Hydrography of oceanography, in the more restricted sense of these terms, contribute such elements as temperature and salinity, and consequently also the density of sea water, currents and long waves; meteorology, atmospheric pressure, different wind effects, evaporation and precipitation; hydrology, water discharged from rivers; geology, land uplift and land subsidence; astronomy, gravitation and tide-generating forces; seismology, tsunami waves; and, finally, glaciology, the eustatic changes.",
    openalex = "W41072897"
}

Changes in solar radiation arising from changes in the orientation of the earth's axis had pronounced effects on tropical monsoons and mid-latitude climates as well as on ice-sheet configuration during the last 18,000 years. COHMAP (Cooperative Holocene Mapping Project) has assembled a global array of well-dated paleoclimatic data and used general-circulation models to identify and evaluate causes and mechanisms of climatic change. For the northern tropics, particularly in Africa and Asia, data and model results show that the orbitally induced increase in solar radiation in summer 12,000 to 6,000 years ago enhanced the thermal contrast between land and sea and thus produced strong summer monsoons, which raised lake levels in regions that are arid today. In middle to high latitudes the climatic response to both the insolation changes and to the retreating ice sheets led to readjustments in the vegetation in both the Northern and Southern hemispheres. Model results show that the large North American ice sheet split the westerly jet stream into northern and southern branches over North America. An increase in storms associated with the southern branch helps explain high lake levels and increased woodlands in the southwestern United States during full-glacial conditions. Comparisons of paleoclimatic data with the model simulations are important because models provide a theoretical framework for evaluating mechanisms of climatic change, and such comparisons help to evaluate the potential of general circulation models for predicting future climates.

@article{doi101126science24148691043,
    author = "Members, COHMAP",
    title = "Climatic Changes of the Last 18,000 Years: Observations and Model Simulations",
    year = "1988",
    journal = "Science",
    abstract = "Changes in solar radiation arising from changes in the orientation of the earth's axis had pronounced effects on tropical monsoons and mid-latitude climates as well as on ice-sheet configuration during the last 18,000 years. COHMAP (Cooperative Holocene Mapping Project) has assembled a global array of well-dated paleoclimatic data and used general-circulation models to identify and evaluate causes and mechanisms of climatic change. For the northern tropics, particularly in Africa and Asia, data and model results show that the orbitally induced increase in solar radiation in summer 12,000 to 6,000 years ago enhanced the thermal contrast between land and sea and thus produced strong summer monsoons, which raised lake levels in regions that are arid today. In middle to high latitudes the climatic response to both the insolation changes and to the retreating ice sheets led to readjustments in the vegetation in both the Northern and Southern hemispheres. Model results show that the large North American ice sheet split the westerly jet stream into northern and southern branches over North America. An increase in storms associated with the southern branch helps explain high lake levels and increased woodlands in the southwestern United States during full-glacial conditions. Comparisons of paleoclimatic data with the model simulations are important because models provide a theoretical framework for evaluating mechanisms of climatic change, and such comparisons help to evaluate the potential of general circulation models for predicting future climates.",
    url = "https://doi.org/10.1126/science.241.4869.1043",
    doi = "10.1126/science.241.4869.1043",
    openalex = "W1654234791",
    references = "doi1010160033589478900649, doi1010160033589479900929, doi101029jd090id01p02167, doi101029jd092id07p08411, doi101038329408a0, doi101126science19142321131, doi101126science19442701121, doi101126science2074434943, doi101126science214451659, doi101130dnaggnak3, doi1011751520046919860431726tiocop20co2, doi1023071551023, openalexw1934430962"
}

A new high resolution global model of late Pleistocene deglaciation is inferred on the basis of geophysical predictions of postglacial relative sea level variations in which the ice‐ocean‐solid Earth interaction is treated in a gravitationally self‐consistent fashion. For the purpose of these analyses the radial viscoelastic structure of the planet is assumed known on the basis of previously published sensitivity tests on solutions of the forward problem. Only radiocarbon controlled relative sea level histories from sites that were actually ice covered (with one or two additions) are employed to constrain the model, leaving relative sea level (RSL) data from sites that were not ice covered to be employed to confirm its consistency. Results for these confirmatory analyses are reported elsewhere. Here the new deglaciation model, referred to as ICE‐3G, is compared to previous models derived by several independent means and tested against a number of additional observations other than sea level histories, including geologically controlled retreat isochrones, oxygen‐isotope data from deep‐sea sedimentary cores, and coral terrace elevations. The latter two observations strongly constrain the net sea level rise that has occurred since the onset of deglaciation and therefore the mass of ice that melted during the last glacial‐interglacial transition.

@article{doi10102990jb01583,
    author = "Tushingham, A. M. and Peltier, W. R.",
    title = "Ice‐3G: A new global model of Late Pleistocene deglaciation based upon geophysical predictions of post‐glacial relative sea level change",
    year = "1991",
    journal = "Journal of Geophysical Research Atmospheres",
    abstract = "A new high resolution global model of late Pleistocene deglaciation is inferred on the basis of geophysical predictions of postglacial relative sea level variations in which the ice‐ocean‐solid Earth interaction is treated in a gravitationally self‐consistent fashion. For the purpose of these analyses the radial viscoelastic structure of the planet is assumed known on the basis of previously published sensitivity tests on solutions of the forward problem. Only radiocarbon controlled relative sea level histories from sites that were actually ice covered (with one or two additions) are employed to constrain the model, leaving relative sea level (RSL) data from sites that were not ice covered to be employed to confirm its consistency. Results for these confirmatory analyses are reported elsewhere. Here the new deglaciation model, referred to as ICE‐3G, is compared to previous models derived by several independent means and tested against a number of additional observations other than sea level histories, including geologically controlled retreat isochrones, oxygen‐isotope data from deep‐sea sedimentary cores, and coral terrace elevations. The latter two observations strongly constrain the net sea level rise that has occurred since the onset of deglaciation and therefore the mass of ice that melted during the last glacial‐interglacial transition.",
    url = "https://doi.org/10.1029/90jb01583",
    doi = "10.1029/90jb01583",
    openalex = "W2018139159",
    references = "doi1010160012825272900384, doi1010160031920181900467, doi1010160033589473900525, doi1010160033589478900339, doi101029jb073i022p07089, doi101029rg012i004p00649, doi101038324137a0, doi101038342637a0, doi101038345405a0, doi101039jr9470000562, doi101086626295, doi101098rsta19750025, doi101111j1365246x1976tb01251x, doi101111j1365246x1976tb01253x, doi101126science1673919862, doi101126science19442701121, doi101130mem145p449"
}

Observations of sea levels around the coastline of the British Isles for the past 10,000–15,000 years exhibit a major regional variation and provide an important data base for testing models of glacial rebound as well as models of the Late Devensian ice sheet. A high‐resolution rebound model has been developed which is consistent with both the spatial and temporal patterns of sea‐level change and which demonstrates that the observations are the result of (i) the glacio‐isostatic crustal rebound in response to the unloading of the ice sheet over Britain and, to a lesser degree, of the ice sheet over Fennoscandia, and (ii) the rise in sea‐level from the melting Late Pleistocene ice sheets, including the response of the crust to the water loading (the hydro‐isostatic effect). The agreement between model and observations is such that there is no need to invoke vertical crustal movements for Great Britain and Ireland of other than glacio‐hydro‐isostatic origin. The rebound contributions are important throughout the region and nowhere is it sufficiently small for the sea‐level change to approximate the eustatic sea‐level rise. The observational data distribution around the periphery as well as from sites near the centre of the former ice sheet is sufficient to permit constraints to be established on both earth model parameters specifying the mantle viscosity and lithospheric thickness and the extent and volume of the ice sheet at the time of the last glaciation. Preliminary solutions are presented which indicate an upper mantle viscosity of (3–5)10 20 Pas, a lithospheric thickness of about 100 km or less, and an ice model that was not confluent with the Scandinavian ice sheet during the last glaciation and whose maximum thickness over Scotland is unlikely to have exceeded about 1500 m.

@article{lambeck1991glacial,
    author = "Lambeck, Kurt",
    title = "Glacial rebound and sea‐level change in the British Isles",
    year = "1991",
    journal = "Terra Nova",
    abstract = "Observations of sea levels around the coastline of the British Isles for the past 10,000–15,000 years exhibit a major regional variation and provide an important data base for testing models of glacial rebound as well as models of the Late Devensian ice sheet. A high‐resolution rebound model has been developed which is consistent with both the spatial and temporal patterns of sea‐level change and which demonstrates that the observations are the result of (i) the glacio‐isostatic crustal rebound in response to the unloading of the ice sheet over Britain and, to a lesser degree, of the ice sheet over Fennoscandia, and (ii) the rise in sea‐level from the melting Late Pleistocene ice sheets, including the response of the crust to the water loading (the hydro‐isostatic effect). The agreement between model and observations is such that there is no need to invoke vertical crustal movements for Great Britain and Ireland of other than glacio‐hydro‐isostatic origin. The rebound contributions are important throughout the region and nowhere is it sufficiently small for the sea‐level change to approximate the eustatic sea‐level rise. The observational data distribution around the periphery as well as from sites near the centre of the former ice sheet is sufficient to permit constraints to be established on both earth model parameters specifying the mantle viscosity and lithospheric thickness and the extent and volume of the ice sheet at the time of the last glaciation. Preliminary solutions are presented which indicate an upper mantle viscosity of (3–5)10 20 Pas, a lithospheric thickness of about 100 km or less, and an ice model that was not confluent with the Scandinavian ice sheet during the last glaciation and whose maximum thickness over Scotland is unlikely to have exceeded about 1500 m.",
    url = "https://doi.org/10.1111/j.1365-3121.1991.tb00166.x",
    doi = "10.1111/j.1365-3121.1991.tb00166.x",
    number = "4",
    openalex = "W2104963560",
    pages = "379-389",
    volume = "3",
    references = "doi101002jqs3390010205, doi101016003101829090056d, doi101038333036a0, doi101111j1365246x1976tb01251x, doi101111j1365246x1989tb06010x, doi101144gsjgs14230447, doi1023071792449, doi1023073241856, doi1023073673075, openalexw578925996"
}

A R Y We analyse the influences of a viscosity increase in the transition zone between 420 and 670 km on the geophysical signatures induced by post-glacial rebound, ranging from the perturbations in the Earth's rotation to the short wavelength features associated with the migration of the peripheral bulge. A seif-gravitating model is adopted, consisting of an elastic lithosphere, a three-layer viscoelastic mantle and an inviscid core.

@article{doi101111j1365246x1992tb00125x,
    author = "Spada, Giorgio and Sabadini, R. and Yuen, David A. and Ricard, Yanick",
    title = "Effects on post-glacial rebound from the hard rheology in the transition zone",
    year = "1992",
    journal = "Geophysical Journal International",
    abstract = "A R Y We analyse the influences of a viscosity increase in the transition zone between 420 and 670 km on the geophysical signatures induced by post-glacial rebound, ranging from the perturbations in the Earth's rotation to the short wavelength features associated with the migration of the peripheral bulge. A seif-gravitating model is adopted, consisting of an elastic lithosphere, a three-layer viscoelastic mantle and an inviscid core.",
    url = "https://doi.org/10.1111/j.1365-246x.1992.tb00125.x",
    doi = "10.1111/j.1365-246x.1992.tb00125.x",
    openalex = "W2092924956"
}

Sea-level change around the British Isles since the time of the last glacial maximum is largely due to of the crustal rebound from the glacial unloading of northern Britain and the concomitant melt-water loading of the adjacent seas and Atlantic Ocean. Minor, but not insignificant, contributions also result from the rebound caused by the unloading of the distant ice sheets, including Fennoscandia and North America. Observations of sea-level change for this period constrain the glacio-hydro-isostatic rebound model parameters describing the effective lithospheric thickness or rigidity and the effective mantle viscosity, as well as certain ice sheet characteristics such as the ice thickness at the time of the last glacial maximum. The models permit palaeobathymetry and palaeoshorelines to be predicted for the British Isles region, including the North Sea. The resulting evolution of the coastlines exhibits a complex behaviour through time, one that is quite different from the usual models in which sea-level change is assumed to be a function of time only. In part this is because of the delayed response of the mantle to the spatially variable and time-dependent ice and water loads, and in part because the unloading history of the British ice sheet is different from those of the major global ice sheets. Thus, maximum emergence of the North Sea occurred after deglaciation had started and lasted for an extended period from about 15 000 to 12 000 (radiocarbon) years BP. During this relative sea-level still-stand shoreline features could have formed, for example, along the western edge of the Norwegian Trough when access to the firths of eastern Scotland would have been via a long and shallow marine inlet. Shoreline retreat across the North Sea became relatively rapid after about 10000 years. The model predictions for the Irish and Celtic Seas also suggest a complex behaviour, with the formation of a wide land bridge between about 20000 and 13 000 years ago. The model also suggests that as long as the Scottish ice extended across the northern Irish Sea, until about 14 000 years ago, there would have been a large freshwater periglacial lake located further south. Both the predicted sea-level height-age relations and the shoreline positions are consistent with a large body of observational evidence but some discrepancies occur, particularly in northern Scotland and Ireland where the ice heights may have been somewhat greater than assumed in the model.

@article{doi101144gsjgs15230437,
    author = "Lambeck, Kurt",
    title = "Late Devensian and Holocene shorelines of the British Isles and North Sea from models of glacio-hydro-isostatic rebound",
    year = "1995",
    journal = "Journal of the Geological Society",
    abstract = "Sea-level change around the British Isles since the time of the last glacial maximum is largely due to of the crustal rebound from the glacial unloading of northern Britain and the concomitant melt-water loading of the adjacent seas and Atlantic Ocean. Minor, but not insignificant, contributions also result from the rebound caused by the unloading of the distant ice sheets, including Fennoscandia and North America. Observations of sea-level change for this period constrain the glacio-hydro-isostatic rebound model parameters describing the effective lithospheric thickness or rigidity and the effective mantle viscosity, as well as certain ice sheet characteristics such as the ice thickness at the time of the last glacial maximum. The models permit palaeobathymetry and palaeoshorelines to be predicted for the British Isles region, including the North Sea. The resulting evolution of the coastlines exhibits a complex behaviour through time, one that is quite different from the usual models in which sea-level change is assumed to be a function of time only. In part this is because of the delayed response of the mantle to the spatially variable and time-dependent ice and water loads, and in part because the unloading history of the British ice sheet is different from those of the major global ice sheets. Thus, maximum emergence of the North Sea occurred after deglaciation had started and lasted for an extended period from about 15 000 to 12 000 (radiocarbon) years BP. During this relative sea-level still-stand shoreline features could have formed, for example, along the western edge of the Norwegian Trough when access to the firths of eastern Scotland would have been via a long and shallow marine inlet. Shoreline retreat across the North Sea became relatively rapid after about 10000 years. The model predictions for the Irish and Celtic Seas also suggest a complex behaviour, with the formation of a wide land bridge between about 20000 and 13 000 years ago. The model also suggests that as long as the Scottish ice extended across the northern Irish Sea, until about 14 000 years ago, there would have been a large freshwater periglacial lake located further south. Both the predicted sea-level height-age relations and the shoreline positions are consistent with a large body of observational evidence but some discrepancies occur, particularly in northern Scotland and Ireland where the ice heights may have been somewhat greater than assumed in the model.",
    url = "https://doi.org/10.1144/gsjgs.152.3.0437",
    doi = "10.1144/gsjgs.152.3.0437",
    openalex = "W2111069348",
    references = "doi101002jqs3390010205, doi101002jqs3390070209, doi101016003101829090056d, doi10102990jb01583, doi101038345405a0, doi101111j1365246x1976tb01251x, doi101111j1365246x1989tb06010x, doi101144gsjgs14230447, doi1023071550617, openalexw578925996"
}

Throughout the latter half of the Pleistocene epoch of Earth history, beginning ∼900 kyr ago, the climate system has been dominated by an intense oscillation between full glacial and interglacial conditions. During each glacial stage, global sea level fell by ∼120 m on average, as extensive ice sheets formed and thickened on the surfaces of the continents at high northern (primarily) and southern latitudes. Within each cycle this glaciation phase lasted ∼90 kyr and was followed by a much more rapid deglaciation event which terminated after ∼10 kyr and which returned the system to the interglacial state. The period of the canonical glacial cycle has remained very close to 100 kyr since its inception in mid‐Pleistocene time. Because of the magnitude of the mass that was redistributed over the surface of the Earth during each such glacial cycle and because of the viscoelastic nature of the rheology of the planetary mantle, these shifts in surface mass load induced variations in the shape of the planet that have been indelibly transcribed into the geological record of sea level variability. Indeed, the geological, geophysical, and even astronomical signatures of this process, which is continuing today, are now being measured with unprecedented precision using the methods of space geodesy and have thereby begun to provide important new scientific insight and understanding, both of the interior of the solid Earth and of the climate system variability with which the ice ages themselves are associated. In this article my purpose is to bring together, in a single review, an assessment of where we currently stand scientifically with regard to understanding both of these aspects of the ice ages. Although the discussion will not address in any detail the fascinating issue of ice age climate, since this topic is sufficiently complex of itself to require a detailed review of its own, I will nevertheless attempt to briefly summarize the current state of understanding of the physical processes that are responsible for the occurrence of the ice age cycle, by way of providing a more complete context in which to appreciate the main lines of argument that will be developed.

@article{doi10102998rg02638,
    author = "Peltier, W. R.",
    title = "Postglacial variations in the level of the sea: Implications for climate dynamics and solid‐Earth geophysics",
    year = "1998",
    journal = "Reviews of Geophysics",
    abstract = "Throughout the latter half of the Pleistocene epoch of Earth history, beginning ∼900 kyr ago, the climate system has been dominated by an intense oscillation between full glacial and interglacial conditions. During each glacial stage, global sea level fell by ∼120 m on average, as extensive ice sheets formed and thickened on the surfaces of the continents at high northern (primarily) and southern latitudes. Within each cycle this glaciation phase lasted ∼90 kyr and was followed by a much more rapid deglaciation event which terminated after ∼10 kyr and which returned the system to the interglacial state. The period of the canonical glacial cycle has remained very close to 100 kyr since its inception in mid‐Pleistocene time. Because of the magnitude of the mass that was redistributed over the surface of the Earth during each such glacial cycle and because of the viscoelastic nature of the rheology of the planetary mantle, these shifts in surface mass load induced variations in the shape of the planet that have been indelibly transcribed into the geological record of sea level variability. Indeed, the geological, geophysical, and even astronomical signatures of this process, which is continuing today, are now being measured with unprecedented precision using the methods of space geodesy and have thereby begun to provide important new scientific insight and understanding, both of the interior of the solid Earth and of the climate system variability with which the ice ages themselves are associated. In this article my purpose is to bring together, in a single review, an assessment of where we currently stand scientifically with regard to understanding both of these aspects of the ice ages. Although the discussion will not address in any detail the fascinating issue of ice age climate, since this topic is sufficiently complex of itself to require a detailed review of its own, I will nevertheless attempt to briefly summarize the current state of understanding of the physical processes that are responsible for the occurrence of the ice age cycle, by way of providing a more complete context in which to appreciate the main lines of argument that will be developed.",
    url = "https://doi.org/10.1029/98rg02638",
    doi = "10.1029/98rg02638",
    openalex = "W2165736211",
    references = "doi10102995jb03208, doi101029jb073i022p07089, doi101029jb089ib07p05987, doi101111j1365246x1982tb04976x, doi101144gsljgs1865021010224, openalexw623436458"
}

Northwestern Europe remains a key region for testing models of glacial isostasy because of the good geological record of crustal response to the glacial unloading since the time of the Last Glacial Maximum. Models for this rebound and associated sealevel change require a detailed knowledge of the ice-sheet geometry, including the ice thickness through time. Existing ice-sheet reconstructions are strongly model-dependent, and inversions of sea-level data for the mantle response may be a function of the model assumptions. Thus inverse solutions for the sea-level data are sought that include both ice-and earth-model parameters as unknowns. Sea-level data from Fennoscandia, the North Sea, the British Isles and the Atlantic and English Channel coasts have been evaluated and incorporated into the solutions. The starting ice sheet for Fennoscandia is based on a reconstruction of a model by Denton & Hughes (1981) that is characterized by quasi-parabolic cross-sections and symmetry about the load centre. Both global (northwestern Europe as a whole) and regional (subsets of the data) solutions have been made for earth-model parameters and ice-height scaling parameters.

@article{doi101046j1365246x199800541x,
    author = "Lambeck, Kurt and Smither, Catherine and Johnston, Paul",
    title = "Sea-level change, glacial rebound and mantle viscosity fornorthern Europe",
    year = "1998",
    journal = "Geophysical Journal International",
    abstract = "Northwestern Europe remains a key region for testing models of glacial isostasy because of the good geological record of crustal response to the glacial unloading since the time of the Last Glacial Maximum. Models for this rebound and associated sealevel change require a detailed knowledge of the ice-sheet geometry, including the ice thickness through time. Existing ice-sheet reconstructions are strongly model-dependent, and inversions of sea-level data for the mantle response may be a function of the model assumptions. Thus inverse solutions for the sea-level data are sought that include both ice-and earth-model parameters as unknowns. Sea-level data from Fennoscandia, the North Sea, the British Isles and the Atlantic and English Channel coasts have been evaluated and incorporated into the solutions. The starting ice sheet for Fennoscandia is based on a reconstruction of a model by Denton \& Hughes (1981) that is characterized by quasi-parabolic cross-sections and symmetry about the load centre. Both global (northwestern Europe as a whole) and regional (subsets of the data) solutions have been made for earth-model parameters and ice-height scaling parameters.",
    url = "https://doi.org/10.1046/j.1365-246x.1998.00541.x",
    doi = "10.1046/j.1365-246x.1998.00541.x",
    openalex = "W1964286915",
    references = "boulton1985glacial, doi1010160031920181900467, doi1010160277379187900035, doi101016104061829400057c, doi10102990jb01583, doi10102995jb03208, doi101126science2655169195, doi101126science27452901155, doi101144gsjgs14230447, doi101144gsjgs15230437, doi1023073673075, gutenberg1941changes"
}

We present a complete derivation of the equation governing long-term sea-level variations on a spherically symmetric, self-gravitating, Maxwell viscoelastic planet. This new ‘sea-level equation’ extends earlier work by incorporating, in a gravitationally self-consistent manner, both a time-dependent ocean—continent geometry and the influence of contemporaneous perturbations to the rotation vector of the planet. We also outline an efficient, pseudo-spectral, numerical methodology for the solution of this equation, and present a variety of predictions, based on a suite of earth models, of relative sea level (RSL) variations due to glacial isostatic adjustment (GIA). These results show that the contribution to the predicted RSL signal from GIA-induced perturbations to the rotation vector can reach 7–8 m over the postglacial period in geographic regions where the rotationally induced signal is a maximum. This result is sensitive to variations in the adopted lower-mantle viscosity and is relatively insensitive to variations in the adopted lithospheric thickness. We also show that the rotationally induced component of RSL change is sufficient to influence previous estimates of Late Holocene melting eventsand ongoing sea-level change due to GIA which were based on a RSL theory for a non-rotating Earth. In particular, estimates of Antarctic melting over the last 5 kyr, based on the amplitude of sea-level highstands from the Australian region, may require an adjustment downwards of the order of 0.5 m of equivalent sea-level rise. Furthermore, present-day rates of sea-level change are perturbed by as much as ∼0.2 mm yr−1 by the rotational component of sea-level change, and this has implications for GIA corrections of the global tide gauge record. Over the period from the last glacial maximum to the present, we predict a distinctly non-monotonic variation in the rotation-induced component of RSL. This is in agreement with our previouspreliminary study (Milne & Mitrovica 1996), but contrasts significantly with predictions presented by Han & Wahr (1989) and Bills & James (1996). We demonstrate that the disagreement arises as a consequence of approximations adopted in the latter studies. We furthermore refute an assertion by Bills & James (1996) that previously published constraints on mantle viscosity and ice-sheet histories which did not incorporate a rotation-induced RSL component are ‘largely invalidated’ by this omission.

@article{doi101046j1365246x19981331455x,
    author = "Milne, Glenn A. and Mitrovica, J. X.",
    title = "Postglacial sea-level change on a rotating Earth",
    year = "1998",
    journal = "Geophysical Journal International",
    abstract = "We present a complete derivation of the equation governing long-term sea-level variations on a spherically symmetric, self-gravitating, Maxwell viscoelastic planet. This new ‘sea-level equation’ extends earlier work by incorporating, in a gravitationally self-consistent manner, both a time-dependent ocean—continent geometry and the influence of contemporaneous perturbations to the rotation vector of the planet. We also outline an efficient, pseudo-spectral, numerical methodology for the solution of this equation, and present a variety of predictions, based on a suite of earth models, of relative sea level (RSL) variations due to glacial isostatic adjustment (GIA). These results show that the contribution to the predicted RSL signal from GIA-induced perturbations to the rotation vector can reach 7–8 m over the postglacial period in geographic regions where the rotationally induced signal is a maximum. This result is sensitive to variations in the adopted lower-mantle viscosity and is relatively insensitive to variations in the adopted lithospheric thickness. We also show that the rotationally induced component of RSL change is sufficient to influence previous estimates of Late Holocene melting eventsand ongoing sea-level change due to GIA which were based on a RSL theory for a non-rotating Earth. In particular, estimates of Antarctic melting over the last 5 kyr, based on the amplitude of sea-level highstands from the Australian region, may require an adjustment downwards of the order of 0.5 m of equivalent sea-level rise. Furthermore, present-day rates of sea-level change are perturbed by as much as ∼0.2 mm yr−1 by the rotational component of sea-level change, and this has implications for GIA corrections of the global tide gauge record. Over the period from the last glacial maximum to the present, we predict a distinctly non-monotonic variation in the rotation-induced component of RSL. This is in agreement with our previouspreliminary study (Milne \& Mitrovica 1996), but contrasts significantly with predictions presented by Han \& Wahr (1989) and Bills \& James (1996). We demonstrate that the disagreement arises as a consequence of approximations adopted in the latter studies. We furthermore refute an assertion by Bills \& James (1996) that previously published constraints on mantle viscosity and ice-sheet histories which did not incorporate a rotation-induced RSL component are ‘largely invalidated’ by this omission.",
    url = "https://doi.org/10.1046/j.1365-246x.1998.1331455.x",
    doi = "10.1046/j.1365-246x.1998.1331455.x",
    openalex = "W2143784106",
    references = "doi101029rg010i004p00849"
}

The increase in sea level from the last glacial maximum has been derived from a siliciclastic system on the tectonically stable Sunda Shelf in Southeast Asia. The time from 21 to 14 thousand calendar years before the present has been poorly covered in other records. The record generally confirms sea-level reconstructions from coral reefs. The rise of sea level during meltwater pulse 1A was as much as 16 meters within 300 years (14.6 to 14.3 thousand years ago).

@article{doi101126science28854681033,
    author = "Hanebuth, Till J J and Stattegger, Karl and Grootes, Pieter Meiert",
    title = "Rapid Flooding of the Sunda Shelf: A Late-Glacial Sea-Level Record",
    year = "2000",
    journal = "Science",
    abstract = "The increase in sea level from the last glacial maximum has been derived from a siliciclastic system on the tectonically stable Sunda Shelf in Southeast Asia. The time from 21 to 14 thousand calendar years before the present has been poorly covered in other records. The record generally confirms sea-level reconstructions from coral reefs. The rise of sea level during meltwater pulse 1A was as much as 16 meters within 300 years (14.6 to 14.3 thousand years ago).",
    url = "https://doi.org/10.1126/science.288.5468.1033",
    doi = "10.1126/science.288.5468.1033",
    openalex = "W2013430677",
    references = "doi101016s0012821x98001988"
}

Sea level change during the Quaternary is primarily a consequence of the cyclic growth and decay of ice sheets, resulting in a complex spatial and temporal pattern. Observations of this variability provide constraints on the timing, rates, and magnitudes of the changes in ice mass during a glacial cycle, as well as more limited information on the distribution of ice between the major ice sheets at any time. Observations of glacially induced sea level changes also provide information on the response of the mantle to surface loading on time scales of 10(3) to 10(5) years. Regional analyses indicate that the earth-response function is depth dependent as well as spatially variable. Comprehensive models of sea level change enable the migration of coastlines to be predicted during glacial cycles, including the anthropologically important period from about 60,000 to 20,000 years ago.

@article{doi101126science1059549,
    author = "Lambeck, Kurt and Chappell, John",
    title = "Sea Level Change Through the Last Glacial Cycle",
    year = "2001",
    journal = "Science",
    abstract = "Sea level change during the Quaternary is primarily a consequence of the cyclic growth and decay of ice sheets, resulting in a complex spatial and temporal pattern. Observations of this variability provide constraints on the timing, rates, and magnitudes of the changes in ice mass during a glacial cycle, as well as more limited information on the distribution of ice between the major ice sheets at any time. Observations of glacially induced sea level changes also provide information on the response of the mantle to surface loading on time scales of 10(3) to 10(5) years. Regional analyses indicate that the earth-response function is depth dependent as well as spatially variable. Comprehensive models of sea level change enable the migration of coastlines to be predicted during glacial cycles, including the anthropologically important period from about 60,000 to 20,000 years ago.",
    url = "https://doi.org/10.1126/science.1059549",
    doi = "10.1126/science.1059549",
    openalex = "W2109459276",
    references = "doi1010160012821x96000623, doi10102990jb01583, doi10102995jb03208, doi101029jb089ib07p06003, doi101029rg012i004p00649, doi101038324137a0, doi101038342637a0, doi10103835021035, doi101038365143a0, doi101038382241a0, doi101046j1365246x199800541x, doi101111j1365246x1976tb01252x, doi101111j1365246x1989tb06010x, doi101126science2655169195, doi101126science28854681033, doi101126science28954861897, doi101144gsjgs15230437, doi101146annurevea12050184001225, doi1023073673075, openalexw2260624936"
}

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, andwe 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.

@article{openalexw2177590044,
    author = "Church, John and Gregory, Jonathan M. and Huybrechts, Philippe and Kühn, Michael and Lambeck, Kurt and Nhuận, Mai Trọng and Qin, D. and Woodworth, Philip",
    title = "Changes in Sea Level",
    year = "2001",
    journal = "Helmholtz-Zentrum für Polar-und Meeresforschung (Alfred-Wegener-Institut)",
    abstract = "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, andwe 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.",
    openalex = "W2177590044"
}

@article{doi101016s0277379101000828,
    author = "Huybrechts, Philippe",
    title = "Sea-level changes at the LGM from ice-dynamic reconstructions of the Greenland and Antarctic ice sheets during the glacial cycles",
    year = "2002",
    journal = "Quaternary Science Reviews",
    url = "https://doi.org/10.1016/s0277-3791(01)00082-8",
    doi = "10.1016/s0277-3791(01)00082-8",
    openalex = "W2115178268",
    references = "doi10102990jb01583, doi101029rg026i001p00149"
}

▪ Abstract The 100 kyr quasiperiodic variation of continental ice cover, which has been a persistent feature of climate system evolution throughout the most recent 900 kyr of Earth history, has occurred as a consequence of changes in the seasonal insolation regime forced by the influence of gravitational n-body effects in the Solar System on the geometry of Earth's orbit around the Sun. The impacts of the changing surface ice load upon both Earth's shape and gravitational field, as well as upon sea-level history, have come to be measurable using a variety of geological and geophysical techniques. These observations are invertible to obtain useful information on both the internal viscoelastic structure of the solid Earth and on the detailed spatiotemporal characteristics of glaciation history. This review focuses upon the most recent advances that have been achieved in each of these areas, advances that have proven to be central to the construction of the refined model of the global process of glacial isostatic adjustment, denoted ICE-5G (VM2). A significant test of this new global model will be provided by the global measurement of the time dependence of the gravity field of the planet that will be delivered by the GRACE satellite system that is now in space.

@article{doi101146annurevearth32082503144359,
    author = "Peltier, W. R.",
    title = "GLOBAL GLACIAL ISOSTASY AND THE SURFACE OF THE ICE-AGE EARTH: The ICE-5G (VM2) Model and GRACE",
    year = "2004",
    journal = "Annual Review of Earth and Planetary Sciences",
    abstract = "▪ Abstract The 100 kyr quasiperiodic variation of continental ice cover, which has been a persistent feature of climate system evolution throughout the most recent 900 kyr of Earth history, has occurred as a consequence of changes in the seasonal insolation regime forced by the influence of gravitational n-body effects in the Solar System on the geometry of Earth's orbit around the Sun. The impacts of the changing surface ice load upon both Earth's shape and gravitational field, as well as upon sea-level history, have come to be measurable using a variety of geological and geophysical techniques. These observations are invertible to obtain useful information on both the internal viscoelastic structure of the solid Earth and on the detailed spatiotemporal characteristics of glaciation history. This review focuses upon the most recent advances that have been achieved in each of these areas, advances that have proven to be central to the construction of the refined model of the global process of glacial isostatic adjustment, denoted ICE-5G (VM2). A significant test of this new global model will be provided by the global measurement of the time dependence of the gravity field of the planet that will be delivered by the GRACE satellite system that is now in space.",
    url = "https://doi.org/10.1146/annurev.earth.32.082503.144359",
    doi = "10.1146/annurev.earth.32.082503.144359",
    openalex = "W2112363056",
    references = "doi1010160031920181900467, doi1010160033589478900339, doi101017s0033822200019123, doi10102990jb01583, doi101029jb073i022p07089, doi101029rg010i003p00761, doi101029rg012i004p00649, doi101029rg020i002p00219, doi101038342637a0, doi101038345405a0, doi10103835021035, doi101038364218a0, doi101046j1365246x199800541x, doi101111j1365246x1976tb01251x, doi101111j1365246x1976tb01253x, doi101111j1365246x1982tb04976x, doi101126science1072497, doi101126science2605109771, doi101126science2655169195, doi101126science28754612225, doi101126science28954861897, doi101144gsjgs15230437"
}

Efforts to mathematically model the Earth's post‐glacial rebound, or, in general, long‐term planetary‐scale viscoelastic deformations, have been ongoing for several decades. Unfortunately, research in the post‐glacial rebound community has not been characterized by much exchange of knowledge. Groups around the world have developed their code independently, sometimes with profoundly different approaches, occasionally leading to inconsistent results [e.g., Boschi et al., 1999]. Postglacial Rebound Calculator (TABOO) is a post‐glacial rebound software that is being made freely available (through Samizdat Press at http://samizdat.mines.edu/taboo/) in the hope that it might become a common reference for all post‐glacial rebound researchers. TABOO is portable and has been tested on Unix, Linux, and Windows systems; all it requires is a Fortran90 compiler supporting quadruple precision. The software is easy to use. It comes with a detailed guide that can work as a quick reference cookbook, and it is also accompanied by a textbook, The Theory Behind TABOO, collecting the most significant theoretical results from post‐glacial rebound literature. TABOO is not a “black‐box,” although it may easily be used as such. The entire source code is provided and should be easy to understand for intermediate‐level Fortran programmers.

@article{spada2004modeling,
    author = "Spada, Giorgio and Antonioli, Andrea and Boschi, Lapo and Boschi, Lapo and Brandi, Valter and Cianetti, Spina and Galvani, Gabrielle and Giunchi, Carlo and Perniola, Bruna and Agostinetti, Nicola Piana and Piersanti, Antonio and Stocchi, Paolo",
    title = "Modeling Earth's post‐glacial rebound",
    year = "2004",
    journal = "Eos, Transactions American Geophysical Union",
    abstract = "Efforts to mathematically model the Earth's post‐glacial rebound, or, in general, long‐term planetary‐scale viscoelastic deformations, have been ongoing for several decades. Unfortunately, research in the post‐glacial rebound community has not been characterized by much exchange of knowledge. Groups around the world have developed their code independently, sometimes with profoundly different approaches, occasionally leading to inconsistent results [e.g., Boschi et al., 1999]. Postglacial Rebound Calculator (TABOO) is a post‐glacial rebound software that is being made freely available (through Samizdat Press at http://samizdat.mines.edu/taboo/) in the hope that it might become a common reference for all post‐glacial rebound researchers. TABOO is portable and has been tested on Unix, Linux, and Windows systems; all it requires is a Fortran90 compiler supporting quadruple precision. The software is easy to use. It comes with a detailed guide that can work as a quick reference cookbook, and it is also accompanied by a textbook, The Theory Behind TABOO, collecting the most significant theoretical results from post‐glacial rebound literature. TABOO is not a “black‐box,” although it may easily be used as such. The entire source code is provided and should be easy to understand for intermediate‐level Fortran programmers.",
    url = "https://doi.org/10.1029/2004eo060007",
    doi = "10.1029/2004eo060007",
    number = "6",
    openalex = "W2003927156",
    pages = "62-64",
    volume = "85",
    references = "doi10102990jb01583, doi101029rg012i004p00649, doi101046j1365246x199900644x, doi101046j1365246x200000027x, doi101111j1365246x1992tb00125x, doi101111j1365246x1997tb04492x"
}

@article{doi101002jqs1049,
    author = "Shennan, Ian and Bradley, Sarah and Milne, Glenn A. and Brooks, Anthony and Bassett, S. E. and Hamilton, Sarah",
    title = "Relative sea‐level changes, glacial isostatic modelling and ice‐sheet reconstructions from the British Isles since the Last Glacial Maximum",
    year = "2006",
    journal = "Journal of Quaternary Science",
    url = "https://doi.org/10.1002/jqs.1049",
    doi = "10.1002/jqs.1049",
    openalex = "W2170884910",
    references = "lambeck1991glacial"
}

@article{doi101002jqs1119,
    author = "Brooks, Anthony and Bradley, Sarah and Edwards, Robin and Milne, Glenn A. and Horton, Benjamin P. and Shennan, Ian",
    title = "Postglacial relative sea‐level observations from Ireland and their role in glacial rebound modelling",
    year = "2007",
    journal = "Journal of Quaternary Science",
    url = "https://doi.org/10.1002/jqs.1119",
    doi = "10.1002/jqs.1119",
    openalex = "W2115595032",
    references = "lambeck1991glacial"
}

We develop a 3-D finite-element model to study the viscoelastic response of a compressible Earth to surface loads. The effects of centre of mass motion, polar wander feedback, and self-consistent ocean loading are implemented. To assess the model's accuracy, we benchmark the numerical results against a semi-analytic solution for spherically symmetric structure. We force our model with the ICE-5G global ice loading history to study the effects of laterally varying viscosity structure on several glacial isostatic adjustment (GIA) observables, including relative sea-level (RSL) measurements in Canada, and present-day time-variable gravity and uplift rates in Antarctica. Canadian RSL observations have been used to determine the Earth's globally averaged viscosity profile. Antarctic GPS uplift rates have been used to constrain Antarctic GIA models. And GIA time-variable gravity and uplift signals are error sources for GRACE and altimeter estimates of present-day Antarctic ice mass loss, and must be modelled and removed from those estimates. Computing GIA results for a 3-D viscosity profile derived from a realistic seismic tomography model, and comparing with results computed for 1-D averages of that 3-D profile, we conclude that: (1) a GIA viscosity model based on Canadian relative sea-level data is more likely to represent a Canadian average than a true global average; (2) the effects of 3-D viscosity structure on GRACE estimates of present-day Antarctic mass loss are probably smaller than the difference between GIA models based on different Antarctic deglaciation histories and (3) the effects of 3-D viscosity structure on Antarctic GPS observations of present-day uplift rate can be significant, and can complicate efforts to use GPS observations to constrain 1-D GIA models.

@article{doi101093gjiggs030,
    author = "Geruo, A and Wahr, John and Zhong, Shijie",
    title = "Computations of the viscoelastic response of a 3-D compressible Earth to surface loading: an application to Glacial Isostatic Adjustment in Antarctica and Canada",
    year = "2012",
    journal = "Geophysical Journal International",
    abstract = "We develop a 3-D finite-element model to study the viscoelastic response of a compressible Earth to surface loads. The effects of centre of mass motion, polar wander feedback, and self-consistent ocean loading are implemented. To assess the model's accuracy, we benchmark the numerical results against a semi-analytic solution for spherically symmetric structure. We force our model with the ICE-5G global ice loading history to study the effects of laterally varying viscosity structure on several glacial isostatic adjustment (GIA) observables, including relative sea-level (RSL) measurements in Canada, and present-day time-variable gravity and uplift rates in Antarctica. Canadian RSL observations have been used to determine the Earth's globally averaged viscosity profile. Antarctic GPS uplift rates have been used to constrain Antarctic GIA models. And GIA time-variable gravity and uplift signals are error sources for GRACE and altimeter estimates of present-day Antarctic ice mass loss, and must be modelled and removed from those estimates. Computing GIA results for a 3-D viscosity profile derived from a realistic seismic tomography model, and comparing with results computed for 1-D averages of that 3-D profile, we conclude that: (1) a GIA viscosity model based on Canadian relative sea-level data is more likely to represent a Canadian average than a true global average; (2) the effects of 3-D viscosity structure on GRACE estimates of present-day Antarctic mass loss are probably smaller than the difference between GIA models based on different Antarctic deglaciation histories and (3) the effects of 3-D viscosity structure on Antarctic GPS observations of present-day uplift rate can be significant, and can complicate efforts to use GPS observations to constrain 1-D GIA models.",
    url = "https://doi.org/10.1093/gji/ggs030",
    doi = "10.1093/gji/ggs030",
    openalex = "W2022712506",
    references = "doi101111j1365246x1982tb04976x"
}

We present a glacial isostatic adjustment (GIA) model for Antarctica. This is driven by anew deglaciation history that has been developed using a numerical ice-sheet model, and isconstrained to fit observations of past ice extent. We test the sensitivity of the GIA model touncertainties in the deglaciation history, and seek earth model parameters that minimize themisfit of model predictions to relative sea-level observations from Antarctica. We find thatthe relative sea-level predictions are fairly insensitive to changes in lithospheric thickness andlower mantle viscosity, but show high sensitivity to changes in upper mantle viscosity andconstrain this value (95 per cent confidence) to lie in the range 0.82.0 10 21 Pa s. Significantmisfits at several sites may be due to errors in the deglaciation history, or unmodelled effects oflateral variations in Earth structure. When we compare our GIA model predictions with elastic correctedGPS uplift rates we find that the predicted rates are biased high (weighted meanbias = 1.8mm yr 1) and there is a weighted root-mean-square (WRMS) error of 2.9mm yr 1.In particular, our model systematically over-predicts uplift rates in the Antarctica Peninsula,and we attempt to address this by adjusting the Late Holocene loading history in this region,within the bounds of uncertainty of the deglaciation model. Using this adjusted model theweighted mean bias improves from 1.8 to 1.2mm yr 1, and the WRMS error is reduced to2.3mm yr 1, compared with 4.9mm yr 1 for ICE-5G v1.2 and 5.0mm yr 1 for IJ05. Finally,we place spatially variable error bars on our GIA uplift rate predictions, taking into accountuncertainties in both the deglaciation history and modelled Earth viscosity structure. Thiswork provides a new GIA correction for the GRACE data in Antarctica, thus permitting moreaccurate constraints to be placed on current ice-mass change.

@article{doi101111j1365246x201205557x,
    author = "Whitehouse, Pippa L. and Bentley, Michael J. and Milne, Glenn A. and King, Matt A. and Thomas, Ian",
    title = "A new glacial isostatic adjustment model for Antarctica: calibrated and tested using observations of relative sea-level change and present-day uplift rates",
    year = "2012",
    journal = "Geophysical Journal International",
    abstract = "We present a glacial isostatic adjustment (GIA) model for Antarctica. This is driven by anew deglaciation history that has been developed using a numerical ice-sheet model, and isconstrained to fit observations of past ice extent. We test the sensitivity of the GIA model touncertainties in the deglaciation history, and seek earth model parameters that minimize themisfit of model predictions to relative sea-level observations from Antarctica. We find thatthe relative sea-level predictions are fairly insensitive to changes in lithospheric thickness andlower mantle viscosity, but show high sensitivity to changes in upper mantle viscosity andconstrain this value (95 per cent confidence) to lie in the range 0.82.0 10 21 Pa s. Significantmisfits at several sites may be due to errors in the deglaciation history, or unmodelled effects oflateral variations in Earth structure. When we compare our GIA model predictions with elastic correctedGPS uplift rates we find that the predicted rates are biased high (weighted meanbias = 1.8mm yr 1) and there is a weighted root-mean-square (WRMS) error of 2.9mm yr 1.In particular, our model systematically over-predicts uplift rates in the Antarctica Peninsula,and we attempt to address this by adjusting the Late Holocene loading history in this region,within the bounds of uncertainty of the deglaciation model. Using this adjusted model theweighted mean bias improves from 1.8 to 1.2mm yr 1, and the WRMS error is reduced to2.3mm yr 1, compared with 4.9mm yr 1 for ICE-5G v1.2 and 5.0mm yr 1 for IJ05. Finally,we place spatially variable error bars on our GIA uplift rate predictions, taking into accountuncertainties in both the deglaciation history and modelled Earth viscosity structure. Thiswork provides a new GIA correction for the GRACE data in Antarctica, thus permitting moreaccurate constraints to be placed on current ice-mass change.",
    url = "https://doi.org/10.1111/j.1365-246x.2012.05557.x",
    doi = "10.1111/j.1365-246x.2012.05557.x",
    openalex = "W2108434249"
}

There have been significant changes in sea level over the past two million years, and a complete understanding of natural cycles of change as well as anthropogenic effects is imperative for future global development. This book reviews the history of research into these sea-level changes and summarises the methods and analytical approaches used to interpret evidence for sea-level changes. It provides an overview of changing climates during the Quaternary, examines processes responsible for global variability of sea-level records, and presents detailed reviews of sea-level changes for the Pleistocene and Holocene. The book concludes by discussing current trends in sea levels and likely future sea-level changes. This is an important and authoritative resource for academic researchers and graduate and advanced undergraduate students working in tectonics, stratigraphy, geomorphology, physical geography, environmental science and other aspects of Quaternary studies.

@book{doi101017cbo9781139024440,
    author = "Murray‐Wallace, Colin V. and Woodroffe, Colin D.",
    title = "Quaternary Sea-Level Changes: A Global Perspective",
    year = "2014",
    booktitle = "Research Online (University of Wollongong)",
    abstract = "There have been significant changes in sea level over the past two million years, and a complete understanding of natural cycles of change as well as anthropogenic effects is imperative for future global development. This book reviews the history of research into these sea-level changes and summarises the methods and analytical approaches used to interpret evidence for sea-level changes. It provides an overview of changing climates during the Quaternary, examines processes responsible for global variability of sea-level records, and presents detailed reviews of sea-level changes for the Pleistocene and Holocene. The book concludes by discussing current trends in sea levels and likely future sea-level changes. This is an important and authoritative resource for academic researchers and graduate and advanced undergraduate students working in tectonics, stratigraphy, geomorphology, physical geography, environmental science and other aspects of Quaternary studies.",
    url = "https://doi.org/10.1017/cbo9781139024440",
    doi = "10.1017/cbo9781139024440",
    openalex = "W46210259",
    references = "doi1010160025322770900496, doi1010160025322789901278, doi1010160033589479900760, doi101016s001282520100054x, doi101130gsab23377, doi101130gsab52721, doi101144gsljgs1865021010224, doi105860choice440326, gutenberg1941changes"
}

Understanding sea-level processes, such as ocean tides, storm surges, tsunamis, El Nino and rises caused by climate change, is key to planning effective coastal defence. Building on David Pugh's classic book Tides, Surges and Mean Sea-Level, this substantially expanded, full-colour book now incorporates major recent technological advances in the areas of satellite altimetry and other geodetic techniques (particularly GPS), tsunami science, measurement of mean sea level and analyses of extreme sea levels. The authors discuss how each surveying and measuring technique complements others in providing an understanding of present-day sea-level change and more reliable forecasts of future changes. Giving the how and the why of sea-level change on timescales from hours to centuries, this authoritative and exciting book is ideal for graduate students and researchers in oceanography, marine engineering, geodesy, marine geology, marine biology and climatology. It will also be of key interest to coastal engineers and governmental policy-makers.

@book{doi101017cbo9781139235778,
    author = "Pugh, David and Woodworth, Philip",
    title = "Sea-Level Science: Understanding Tides, Surges, Tsunamis and Mean Sea-Level Changes",
    year = "2014",
    abstract = "Understanding sea-level processes, such as ocean tides, storm surges, tsunamis, El Nino and rises caused by climate change, is key to planning effective coastal defence. Building on David Pugh's classic book Tides, Surges and Mean Sea-Level, this substantially expanded, full-colour book now incorporates major recent technological advances in the areas of satellite altimetry and other geodetic techniques (particularly GPS), tsunami science, measurement of mean sea level and analyses of extreme sea levels. The authors discuss how each surveying and measuring technique complements others in providing an understanding of present-day sea-level change and more reliable forecasts of future changes. Giving the how and the why of sea-level change on timescales from hours to centuries, this authoritative and exciting book is ideal for graduate students and researchers in oceanography, marine engineering, geodesy, marine geology, marine biology and climatology. It will also be of key interest to coastal engineers and governmental policy-makers.",
    url = "https://doi.org/10.1017/cbo9781139235778",
    doi = "10.1017/cbo9781139235778",
    openalex = "W619339943",
    references = "doi101007bf02520477, doi101007s0038201110576, doi101007s1162500800433, doi101016s0074614208x60024, doi101017cbo9781107415324013, doi1010292004gl019920, doi10102996rg03038, doi10102998gl00950, doi101126science27753341956, doi1011751520042620020190183eimobo20co2, doi1011751520044220000131000amitec20co2, doi101785bssa0750041135, doi1018901015101, doi104835025539, doi105962bhltitle128554, openalexw1548396839, oro1990the"
}

The major cause of sea-level change during ice ages is the exchange of water between ice and ocean and the planet's dynamic response to the changing surface load. Inversion of ∼1,000 observations for the past 35,000 y from localities far from former ice margins has provided new constraints on the fluctuation of ice volume in this interval. Key results are: (i) a rapid final fall in global sea level of ∼40 m in <2,000 y at the onset of the glacial maximum ∼30,000 y before present (30 ka BP); (ii) a slow fall to -134 m from 29 to 21 ka BP with a maximum grounded ice volume of ∼52 × 10(6) km(3) greater than today; (iii) after an initial short duration rapid rise and a short interval of near-constant sea level, the main phase of deglaciation occurred from ∼16.5 ka BP to ∼8.2 ka BP at an average rate of rise of 12 m⋅ka(-1) punctuated by periods of greater, particularly at 14.5-14.0 ka BP at ≥40 mm⋅y(-1) (MWP-1A), and lesser, from 12.5 to 11.5 ka BP (Younger Dryas), rates; (iv) no evidence for a global MWP-1B event at ∼11.3 ka BP; and (v) a progressive decrease in the rate of rise from 8.2 ka to ∼2.5 ka BP, after which ocean volumes remained nearly constant until the renewed sea-level rise at 100-150 y ago, with no evidence of oscillations exceeding ∼15-20 cm in time intervals ≥200 y from 6 to 0.15 ka BP.

@article{doi101073pnas1411762111,
    author = "Lambeck, Kurt and Rouby, Hélène and Purcell, Anthony and Sun, Yiying and Sambridge, Malcolm",
    title = "Sea level and global ice volumes from the Last Glacial Maximum to the Holocene",
    year = "2014",
    journal = "Proceedings of the National Academy of Sciences",
    abstract = "The major cause of sea-level change during ice ages is the exchange of water between ice and ocean and the planet's dynamic response to the changing surface load. Inversion of ∼1,000 observations for the past 35,000 y from localities far from former ice margins has provided new constraints on the fluctuation of ice volume in this interval. Key results are: (i) a rapid final fall in global sea level of ∼40 m in <2,000 y at the onset of the glacial maximum ∼30,000 y before present (30 ka BP); (ii) a slow fall to -134 m from 29 to 21 ka BP with a maximum grounded ice volume of ∼52 × 10(6) km(3) greater than today; (iii) after an initial short duration rapid rise and a short interval of near-constant sea level, the main phase of deglaciation occurred from ∼16.5 ka BP to ∼8.2 ka BP at an average rate of rise of 12 m⋅ka(-1) punctuated by periods of greater, particularly at 14.5-14.0 ka BP at ≥40 mm⋅y(-1) (MWP-1A), and lesser, from 12.5 to 11.5 ka BP (Younger Dryas), rates; (iv) no evidence for a global MWP-1B event at ∼11.3 ka BP; and (v) a progressive decrease in the rate of rise from 8.2 ka to ∼2.5 ka BP, after which ocean volumes remained nearly constant until the renewed sea-level rise at 100-150 y ago, with no evidence of oscillations exceeding ∼15-20 cm in time intervals ≥200 y from 6 to 0.15 ka BP.",
    url = "https://doi.org/10.1073/pnas.1411762111",
    doi = "10.1073/pnas.1411762111",
    openalex = "W2094350389",
    references = "doi1010160012821x83901620, doi1010160277379187900035, doi101016s0277379101000713, doi101016s0277379101001019, doi101017s0033822200034202, doi1010292003rg000128, doi1010292004pa001071, doi101029rg012i004p00649, doi101038324137a0, doi101038342637a0, doi10103835021035, doi101038nature01690, doi101038nature08686, doi101046j1365246x199800541x, doi101111j1365246x1976tb01251x, doi101126science1059549, doi1011300091761319970250483hciapw23co2, doi1023073673075, openalexw2070611029"
}

Abstract Vertical land motions are a key element in understanding how sea levels have changed over the past century and how future sea levels may impact coastal areas. Ideally, to be useful in long‐term sea level studies, vertical land motion should be determined with standard errors that are 1 order of magnitude lower than the contemporary climate signals of 1 to 3 mm/yr observed on average in sea level records, either using tide gauges or satellites. This metrological requirement constitutes a challenge in geodesy. Here we review the most successful instrumental methods that have been used to determine vertical displacements at the Earth's surface, so that the objectives of understanding and anticipating sea levels can be addressed adequately in terms of accuracy. In this respect, the required level of uncertainty is examined in two case studies (global and local). A special focus is given to the use of the Global Positioning System (GPS) and to the combination of satellite radar altimetry with tide gauge data. We update previous data analyses and assess the quality of global satellite altimetry products available to the users for coastal applications. Despite recent advances, a near‐plateau level of accuracy has been reached. The major limitation is the realization of the terrestrial reference frame, whose physical parameters, the origin and the scale factor, are beyond the scope of a unique technique such as the GPS. Additional practical but nonetheless important issues are associated with the installation of GPS antennas, such as ensuring that there is no unknown differential vertical motion with the tide gauge.

@article{doi1010022015rg000502,
    author = "Wöppelmann, Guy and Marcos, Marta",
    title = "Vertical land motion as a key to understanding sea level change and variability",
    year = "2015",
    journal = "Reviews of Geophysics",
    abstract = "Abstract Vertical land motions are a key element in understanding how sea levels have changed over the past century and how future sea levels may impact coastal areas. Ideally, to be useful in long‐term sea level studies, vertical land motion should be determined with standard errors that are 1 order of magnitude lower than the contemporary climate signals of 1 to 3 mm/yr observed on average in sea level records, either using tide gauges or satellites. This metrological requirement constitutes a challenge in geodesy. Here we review the most successful instrumental methods that have been used to determine vertical displacements at the Earth's surface, so that the objectives of understanding and anticipating sea levels can be addressed adequately in terms of accuracy. In this respect, the required level of uncertainty is examined in two case studies (global and local). A special focus is given to the use of the Global Positioning System (GPS) and to the combination of satellite radar altimetry with tide gauge data. We update previous data analyses and assess the quality of global satellite altimetry products available to the users for coastal applications. Despite recent advances, a near‐plateau level of accuracy has been reached. The major limitation is the realization of the terrestrial reference frame, whose physical parameters, the origin and the scale factor, are beyond the scope of a unique technique such as the GPS. Additional practical but nonetheless important issues are associated with the installation of GPS antennas, such as ensuring that there is no unknown differential vertical motion with the tide gauge.",
    url = "https://doi.org/10.1002/2015rg000502",
    doi = "10.1002/2015rg000502",
    openalex = "W2260016662",
    references = "doi1010022015gl063306, doi101007s0019000803003, doi101007s0019001104444, doi101007s1071201191191, doi1010292005jb003629, doi1010292007jb004949, doi101038nclimate1979, doi101111j1365246x201104952x, doi101126science21545401611, doi101146annurevearth32082503144359, doi102112jcoastresd12001751, gutenberg1941changes, openalexw2986345846"
}

@article{doi101016jquascirev201803031,
    author = "Shennan, Ian and Bradley, Sarah and Edwards, Robin",
    title = "Relative sea-level changes and crustal movements in Britain and Ireland since the Last Glacial Maximum",
    year = "2018",
    journal = "Quaternary Science Reviews",
    url = "https://doi.org/10.1016/j.quascirev.2018.03.031",
    doi = "10.1016/j.quascirev.2018.03.031",
    openalex = "W2797343474",
    references = "lambeck1991glacial"
}

We review the characteristics of sea level variability at the coast focussing on how it differs from the variability in the nearby deep ocean. Sea level variability occurs on all timescales, with processes at higher frequencies tending to have a larger magnitude at the coast due to resonance and other dynamics. In the case of some processes, such as the tides, the presence of the coast and the shallow waters of the shelves results in the processes being considerably more complex than offshore. However, 'coastal variability' should not always be considered as 'short spatial scale variability' but can be the result of signals transmitted along the coast from 1000s km away. Fortunately, thanks to tide gauges being necessarily located at the coast, many aspects of coastal sea level variability can be claimed to be better understood than those in the deep ocean. Nevertheless, certain aspects of coastal variability remain under-researched, including how changes in some processes (e.g., wave setup, river runoff) may have contributed to the historical mean sea level records obtained from tide gauges which are now used routinely in large-scale climate research.

@article{doi101007s10712019095311,
    author = "Woodworth, Philip and Melet, Angélique and Marcos, Marta and Ray, Richard D. and Wöppelmann, Guy and Sasaki, Yoshi N. and Cirano, Mauro and Hibbert, Angela and Huthnance, John M. and Monserrat, S. and Merrifield, M. A.",
    title = "Forcing Factors Affecting Sea Level Changes at the Coast",
    year = "2019",
    journal = "Surveys in Geophysics",
    abstract = "We review the characteristics of sea level variability at the coast focussing on how it differs from the variability in the nearby deep ocean. Sea level variability occurs on all timescales, with processes at higher frequencies tending to have a larger magnitude at the coast due to resonance and other dynamics. In the case of some processes, such as the tides, the presence of the coast and the shallow waters of the shelves results in the processes being considerably more complex than offshore. However, 'coastal variability' should not always be considered as 'short spatial scale variability' but can be the result of signals transmitted along the coast from 1000s km away. Fortunately, thanks to tide gauges being necessarily located at the coast, many aspects of coastal sea level variability can be claimed to be better understood than those in the deep ocean. Nevertheless, certain aspects of coastal variability remain under-researched, including how changes in some processes (e.g., wave setup, river runoff) may have contributed to the historical mean sea level records obtained from tide gauges which are now used routinely in large-scale climate research.",
    url = "https://doi.org/10.1007/s10712-019-09531-1",
    doi = "10.1007/s10712-019-09531-1",
    openalex = "W2944017778",
    references = "doi1010022015rg000502, doi101017cbo9781139235778, doi101029tr041i004p00629"
}

Abstract. We present SELEN4 (SealEveL EquatioN solver), an open-source program written in Fortran 90 that simulates the glacial isostatic adjustment (GIA) process in response to the melting of the Late Pleistocene ice sheets. Using a pseudo-spectral approach complemented by a spatial discretization on an icosahedron-based spherical geodesic grid, SELEN4 solves a generalized sea-level equation (SLE) for a spherically symmetric Earth with linear viscoelastic rheology, taking the migration of the shorelines and the rotational feedback on sea level into account. The approach is gravitationally and topographically self-consistent, since it considers the gravitational interactions between the solid Earth, the cryosphere, and the oceans, and it accounts for the evolution of the Earth's topography in response to changes in sea level. The SELEN4 program can be employed to study a broad range of geophysical effects of GIA, including past relative sea-level variations induced by the melting of the Late Pleistocene ice sheets, the time evolution of paleogeography and of the ocean function since the Last Glacial Maximum, the history of the Earth's rotational variations, present-day geodetic signals observed by Global Navigation Satellite Systems, and gravity field variations detected by satellite gravity missions like GRACE (the Gravity Recovery and Climate Experiment). The “GIA fingerprints” constitute a standard output of SELEN4. Along with the source code, we provide a supplementary document with a full account of the theory, some numerical results obtained from a standard run, and a user guide. Originally, the SELEN program was conceived by Giorgio Spada (GS) in 2005 as a tool for students eager to learn about GIA, and it has been the first SLE solver made available to the community.

@article{doi105194gmd1250552019,
    author = "Spada, Giorgio and Melini, Daniele",
    title = "SELEN 4 (SELEN version 4.0): a Fortran program for solving the gravitationally and topographically self-consistent sea-level equation in glacial isostatic adjustment modeling",
    year = "2019",
    journal = "Geoscientific model development",
    abstract = "Abstract. We present SELEN4 (SealEveL EquatioN solver), an open-source program written in Fortran 90 that simulates the glacial isostatic adjustment (GIA) process in response to the melting of the Late Pleistocene ice sheets. Using a pseudo-spectral approach complemented by a spatial discretization on an icosahedron-based spherical geodesic grid, SELEN4 solves a generalized sea-level equation (SLE) for a spherically symmetric Earth with linear viscoelastic rheology, taking the migration of the shorelines and the rotational feedback on sea level into account. The approach is gravitationally and topographically self-consistent, since it considers the gravitational interactions between the solid Earth, the cryosphere, and the oceans, and it accounts for the evolution of the Earth's topography in response to changes in sea level. The SELEN4 program can be employed to study a broad range of geophysical effects of GIA, including past relative sea-level variations induced by the melting of the Late Pleistocene ice sheets, the time evolution of paleogeography and of the ocean function since the Last Glacial Maximum, the history of the Earth's rotational variations, present-day geodetic signals observed by Global Navigation Satellite Systems, and gravity field variations detected by satellite gravity missions like GRACE (the Gravity Recovery and Climate Experiment). The “GIA fingerprints” constitute a standard output of SELEN4. Along with the source code, we provide a supplementary document with a full account of the theory, some numerical results obtained from a standard run, and a user guide. Originally, the SELEN program was conceived by Giorgio Spada (GS) in 2005 as a tool for students eager to learn about GIA, and it has been the first SLE solver made available to the community.",
    url = "https://doi.org/10.5194/gmd-12-5055-2019",
    doi = "10.5194/gmd-12-5055-2019",
    openalex = "W2964145352",
    references = "spada2004modeling"
}

Abstract Glacial‐isostatic adjustment (GIA) is the key process controlling relative sea‐level (RSL) and paleo‐topography. The viscoelastic response of the solid Earth is controlled by its viscosity structure. Therefore, the appropriate choice of Earth structure for GIA models is still an important area of research in geodynamics. We construct 18 3D Earth structures that are derived from seismic tomography models and are geodynamically constrained. We consider uncertainties in 3D viscosity structures that arise from variations in the conversion from seismic velocity to temperature variations (factor r) and radial viscosity profiles (RVP). We apply these Earth models to a 3D GIA model, VILMA, to investigate the influence of such structure on RSL predictions. The variabilities in 3D Earth structures and RSL predictions are investigated for globally distributed sites and applied for comparisons with regional 1D models for ice center (North America, Antarctica) and peripheral regions (Central Oregon Coast, San Jorge Gulf). The results from 1D and 3D models reveal substantial influence of lateral viscosity variations on RSL. Depending on time and location, the influence of factor r and/or RVP can be reverse, for example, the same RVP causes lowest RSL in Churchill and largest RSL in Oregon. Regional 1D models representing the structure beneath the ice and 3D models show similar influence of factor r and RVP on RSL prediction. This is not the case for regional 1D models representing the structure beneath peripheral regions indicating the dependence on the 3D Earth structure. The 3D Earth structures of this study are made available.

@article{doi1010292021gc009853,
    author = "Bagge, Meike and Klemann, Volker and Steinberger, Bernhard and Latinović, Milena and Thomas, Maik",
    title = "Glacial‐Isostatic Adjustment Models Using Geodynamically Constrained 3D Earth Structures",
    year = "2021",
    journal = "Geochemistry Geophysics Geosystems",
    abstract = "Abstract Glacial‐isostatic adjustment (GIA) is the key process controlling relative sea‐level (RSL) and paleo‐topography. The viscoelastic response of the solid Earth is controlled by its viscosity structure. Therefore, the appropriate choice of Earth structure for GIA models is still an important area of research in geodynamics. We construct 18 3D Earth structures that are derived from seismic tomography models and are geodynamically constrained. We consider uncertainties in 3D viscosity structures that arise from variations in the conversion from seismic velocity to temperature variations (factor r) and radial viscosity profiles (RVP). We apply these Earth models to a 3D GIA model, VILMA, to investigate the influence of such structure on RSL predictions. The variabilities in 3D Earth structures and RSL predictions are investigated for globally distributed sites and applied for comparisons with regional 1D models for ice center (North America, Antarctica) and peripheral regions (Central Oregon Coast, San Jorge Gulf). The results from 1D and 3D models reveal substantial influence of lateral viscosity variations on RSL. Depending on time and location, the influence of factor r and/or RVP can be reverse, for example, the same RVP causes lowest RSL in Churchill and largest RSL in Oregon. Regional 1D models representing the structure beneath the ice and 3D models show similar influence of factor r and RVP on RSL prediction. This is not the case for regional 1D models representing the structure beneath peripheral regions indicating the dependence on the 3D Earth structure. The 3D Earth structures of this study are made available.",
    url = "https://doi.org/10.1029/2021gc009853",
    doi = "10.1029/2021gc009853",
    openalex = "W3208036139",
    references = "doi1010022014jb011176, doi1010160031920181900467, doi1010292001gc000252, doi10102995eo00198, doi10102997jb02122, doi10102998eo00426, doi101073pnas1411762111, doi101093gjiggt095, doi101098rsta20021077, doi101146annurevearth32082503144359"
}

SUMMARY Studies of glacial isostatic adjustment (GIA) provide important constraints on the Earth's mantle viscosity. Most GIA models assume Newtonian viscosity through the mantle, but laboratory experimental studies of rock deformation, observational studies of seismic anisotropy, and modelling studies of mantle dynamics show that in the upper mantle non-Newtonian viscosity may be important. This study explores the non-Newtonian effects on the GIA induced variations in mantle stress and viscosity and on surface observables including vertical displacement, relative sea level (RSL) and gravity change. The recently updated and fully benchmarked software package CitcomSVE is used for GIA simulations. We adopt the ICE-6G ice deglaciation history, VM5a lower mantle and lithospheric viscosities, and a composite rheology that combines Newtonian and non-Newtonian viscosities for the upper mantle. Our results show that: (1) The mantle stress beneath glaciated regions increases significantly during deglaciation, leading to regionally reduced upper mantle viscosity by more than an order of magnitude. Such effects can be rather localized at the periphery of glaciated regions. However, non-Newtonian effects on far-field mantle viscosity are negligibly small. GIA induced stress is also significant in the lithosphere (∼30 MPa) and lower mantle (∼2 MPa). (2) The predicted RSL changes from non-Newtonian models display distinct features in comparison with the Newtonian model, including more rapid sea level falls associated with the rapid deglaciation at ∼14 000 yr ago followed by a more gradual sea level variation for sites near the centres of formerly glaciated regions, and an additional phase of sea level falls for the last ∼8000 yr for sites at the ice margins. Similar time-dependence associated with the deglaciation is also seen for rate of vertical displacement, suggesting a relatively slow present-day rates of vertical displacement and gravity change. These features can be explained by the non-Newtonian effects associated with a loading event which manifest a fast relaxation stage followed by a relative slow relaxation stage. Our results may provide GIA diagnoses for distinguishing non-Newtonian and Newtonian rheology.

@article{doi101093gjiggab428,
    author = "Kang, Kaixuan and Zhong, Shijie and Geruo, A and Mao, Wei",
    title = "The effects of non-Newtonian rheology in the upper mantle on relative sea level change and geodetic observables induced by glacial isostatic adjustment process",
    year = "2021",
    journal = "Geophysical Journal International",
    abstract = "SUMMARY Studies of glacial isostatic adjustment (GIA) provide important constraints on the Earth's mantle viscosity. Most GIA models assume Newtonian viscosity through the mantle, but laboratory experimental studies of rock deformation, observational studies of seismic anisotropy, and modelling studies of mantle dynamics show that in the upper mantle non-Newtonian viscosity may be important. This study explores the non-Newtonian effects on the GIA induced variations in mantle stress and viscosity and on surface observables including vertical displacement, relative sea level (RSL) and gravity change. The recently updated and fully benchmarked software package CitcomSVE is used for GIA simulations. We adopt the ICE-6G ice deglaciation history, VM5a lower mantle and lithospheric viscosities, and a composite rheology that combines Newtonian and non-Newtonian viscosities for the upper mantle. Our results show that: (1) The mantle stress beneath glaciated regions increases significantly during deglaciation, leading to regionally reduced upper mantle viscosity by more than an order of magnitude. Such effects can be rather localized at the periphery of glaciated regions. However, non-Newtonian effects on far-field mantle viscosity are negligibly small. GIA induced stress is also significant in the lithosphere (∼30 MPa) and lower mantle (∼2 MPa). (2) The predicted RSL changes from non-Newtonian models display distinct features in comparison with the Newtonian model, including more rapid sea level falls associated with the rapid deglaciation at ∼14 000 yr ago followed by a more gradual sea level variation for sites near the centres of formerly glaciated regions, and an additional phase of sea level falls for the last ∼8000 yr for sites at the ice margins. Similar time-dependence associated with the deglaciation is also seen for rate of vertical displacement, suggesting a relatively slow present-day rates of vertical displacement and gravity change. These features can be explained by the non-Newtonian effects associated with a loading event which manifest a fast relaxation stage followed by a relative slow relaxation stage. Our results may provide GIA diagnoses for distinguishing non-Newtonian and Newtonian rheology.",
    url = "https://doi.org/10.1093/gji/ggab428",
    doi = "10.1093/gji/ggab428",
    openalex = "W3210496754",
    references = "doi1010292022gc010359"
}

Abstract The redistribution of past and present ice and ocean loading on Earth's surface causes solid Earth deformation and geoid changes, known as glacial isostatic adjustment. The deformation is controlled by elastic and viscous material parameters, which are inhomogeneous in the Earth. We present a new viscoelastic solid Earth deformation model in ASPECT (Advanced Solver for Problems in Earth's ConvecTion): a modern, massively parallel, open‐source finite element code originally designed to simulate convection in the Earth's mantle. We show the performance of solid Earth deformation in ASPECT and compare solutions to TABOO, a semianalytical code, and Abaqus, a commercial finite element code. The maximum deformation and deformation rates using ASPECT agree within 2.6% for the average percentage difference with TABOO and Abaqus on glacial cycle (∼100 kyr) and contemporary ice melt (∼100 years) timescales. This gives confidence in the performance of our new solid Earth deformation model. We also demonstrate the computational efficiency of using adaptively refined meshes, which is a great advantage for solid Earth deformation modeling. Furthermore, we demonstrate the model performance in the presence of lateral viscosity variations in the upper mantle and report on parallel scalability of the code. This benchmarked code can now be used to investigate regional solid Earth deformation rates from ice age and contemporary ice melt. This is especially interesting for low‐viscosity regions in the upper mantle beneath Antarctica and Greenland, where it is not fully understood how ice age and contemporary ice melting contribute to geodetic measurements of solid Earth deformation.

@article{doi1010292022gc010813,
    author = "Weerdesteijn, Maaike and Naliboff, John and Conrad, Clinton P. and Reusen, Jesse and Steffen, Rebekka and Heister, Timo and Zhang, Jiaqi",
    title = "Modeling Viscoelastic Solid Earth Deformation Due To Ice Age and Contemporary Glacial Mass Changes in ASPECT",
    year = "2023",
    journal = "Geochemistry Geophysics Geosystems",
    abstract = "Abstract The redistribution of past and present ice and ocean loading on Earth's surface causes solid Earth deformation and geoid changes, known as glacial isostatic adjustment. The deformation is controlled by elastic and viscous material parameters, which are inhomogeneous in the Earth. We present a new viscoelastic solid Earth deformation model in ASPECT (Advanced Solver for Problems in Earth's ConvecTion): a modern, massively parallel, open‐source finite element code originally designed to simulate convection in the Earth's mantle. We show the performance of solid Earth deformation in ASPECT and compare solutions to TABOO, a semianalytical code, and Abaqus, a commercial finite element code. The maximum deformation and deformation rates using ASPECT agree within 2.6\% for the average percentage difference with TABOO and Abaqus on glacial cycle (∼100 kyr) and contemporary ice melt (∼100 years) timescales. This gives confidence in the performance of our new solid Earth deformation model. We also demonstrate the computational efficiency of using adaptively refined meshes, which is a great advantage for solid Earth deformation modeling. Furthermore, we demonstrate the model performance in the presence of lateral viscosity variations in the upper mantle and report on parallel scalability of the code. This benchmarked code can now be used to investigate regional solid Earth deformation rates from ice age and contemporary ice melt. This is especially interesting for low‐viscosity regions in the upper mantle beneath Antarctica and Greenland, where it is not fully understood how ice age and contemporary ice melting contribute to geodetic measurements of solid Earth deformation.",
    url = "https://doi.org/10.1029/2022gc010813",
    doi = "10.1029/2022gc010813",
    openalex = "W4322766262",
    references = "doi101016s0021999102000311, doi1010292021gc009853, doi1010292022gc010359, doi101029rg012i004p00649, doi101038s415860180179y, doi101038s4158601918552, doi101093gjiggs030, doi101093gjiggx195, doi101111j1365246x1982tb04976x, doi101111j1365246x201205557x, doi101111j1365246x201205609x, doi105194tc815392014"
}

Abstract. It has been previously proposed that glacial inception represents a bifurcation transition between interglacial and glacial states and is governed by the nonlinear dynamics of the climate–cryosphere system. To trigger glacial inception, the orbital forcing (defined as the maximum of summer insolation at 65° N and determined by Earth’s orbital parameters) must be lower than a critical level, which depends on the atmospheric CO2 concentration. While paleoclimatic data do not provide a strong constraint on the dependence between CO2 and critical insolation, its accurate estimation is of fundamental importance for predicting future glaciations and the effect that anthropogenic CO2 emissions might have on them. In this study, we use the novel Earth system model of intermediate complexity CLIMBER-X with interactive ice sheets to produce a new estimation of the critical insolation–CO2 relationship for triggering glacial inception. We perform a series of experiments in which different combinations of orbital forcing and atmospheric CO2 concentration are maintained constant in time. We analyze for which combinations of orbital forcing and CO2 glacial inception occurs and trace the critical relationship between them, separating conditions under which glacial inception is possible from those where glacial inception is not materialized. We also provide a theoretical foundation for the proposed critical insolation–CO2 relation. We find that the use of the maximum summer insolation at 65° N as a single metric for orbital forcing is adequate for tracing the glacial inception bifurcation. Moreover, we find that the temporal and spatial patterns of ice sheet growth during glacial inception are not always the same but depend on the critical insolation and CO2 level. The experiments evidence the fact that during glacial inception, ice sheets grow mostly in North America, and only under low CO2 conditions are ice sheets also formed over Scandinavia. The latter is associated with a weak Atlantic Meridional Overturning Circulation (AMOC) for low CO2. We find that the strength of AMOC also affects the rate of ice sheet growth during glacial inception.

@article{doi105194cp2013492024,
    author = "Talento, Stefanie and Willeit, Matteo and Ganopolski, Andrey",
    title = "New estimation of critical insolation–CO 2 relationship for triggering glacial inception",
    year = "2024",
    journal = "Climate of the past",
    abstract = "Abstract. It has been previously proposed that glacial inception represents a bifurcation transition between interglacial and glacial states and is governed by the nonlinear dynamics of the climate–cryosphere system. To trigger glacial inception, the orbital forcing (defined as the maximum of summer insolation at 65° N and determined by Earth’s orbital parameters) must be lower than a critical level, which depends on the atmospheric CO2 concentration. While paleoclimatic data do not provide a strong constraint on the dependence between CO2 and critical insolation, its accurate estimation is of fundamental importance for predicting future glaciations and the effect that anthropogenic CO2 emissions might have on them. In this study, we use the novel Earth system model of intermediate complexity CLIMBER-X with interactive ice sheets to produce a new estimation of the critical insolation–CO2 relationship for triggering glacial inception. We perform a series of experiments in which different combinations of orbital forcing and atmospheric CO2 concentration are maintained constant in time. We analyze for which combinations of orbital forcing and CO2 glacial inception occurs and trace the critical relationship between them, separating conditions under which glacial inception is possible from those where glacial inception is not materialized. We also provide a theoretical foundation for the proposed critical insolation–CO2 relation. We find that the use of the maximum summer insolation at 65° N as a single metric for orbital forcing is adequate for tracing the glacial inception bifurcation. Moreover, we find that the temporal and spatial patterns of ice sheet growth during glacial inception are not always the same but depend on the critical insolation and CO2 level. The experiments evidence the fact that during glacial inception, ice sheets grow mostly in North America, and only under low CO2 conditions are ice sheets also formed over Scandinavia. The latter is associated with a weak Atlantic Meridional Overturning Circulation (AMOC) for low CO2. We find that the strength of AMOC also affects the rate of ice sheet growth during glacial inception.",
    url = "https://doi.org/10.5194/cp-20-1349-2024",
    doi = "10.5194/cp-20-1349-2024",
    openalex = "W4399747868",
    references = "doi105194cp205972024"
}

Abstract. We present transient simulations of the last glacial inception using the Earth system model CLIMBER-X with dynamic vegetation, interactive ice sheets, and visco-elastic solid Earth responses. The simulations are initialized at the middle of the Eemian interglacial (125 kiloyears before present, ka) and run until 100 ka, driven by prescribed changes in Earth's orbital parameters and greenhouse gas concentrations from ice core data. CLIMBER-X simulates a rapid increase in Northern Hemisphere ice sheet area through MIS5d, with ice sheets expanding over northern North America and Scandinavia, in broad agreement with proxy reconstructions. While most of the increase in ice sheet area occurs over a relatively short period between 119 and 117 ka, the larger part of the increase in ice volume occurs afterwards with an almost constant ice sheet extent. We show that the vegetation feedback plays a fundamental role in controlling the ice sheet expansion during the last glacial inception. In particular, with prescribed present-day vegetation the model simulates a global sea level drop of only ∼ 20 m, compared with the ∼ 35 m decrease in sea level with dynamic vegetation response. The ice sheet and carbon cycle feedbacks play only a minor role during the ice sheet expansion phase prior to ∼ 115 ka but are important in limiting the deglaciation during the following phase characterized by increasing summer insolation. The model results are sensitive to climate model biases and to the parameterization of snow albedo, while they show only a weak dependence on changes in the ice sheet model resolution and the acceleration factor used to speed up the climate component. Overall, our simulations confirm and refine previous results showing that climate–vegetation–cryosphere feedbacks play a fundamental role in the transition from interglacial to glacial states characterizing Quaternary glacial cycles.

@article{doi105194cp205972024,
    author = "Willeit, Matteo and Calov, Reinhard and Talento, Stefanie and Greve, Ralf and Bernales, Jorjo and Klemann, Volker and Bagge, Meike and Ganopolski, Andrey",
    title = "Glacial inception through rapid ice area increase driven by albedo and vegetation feedbacks",
    year = "2024",
    journal = "Climate of the past",
    abstract = "Abstract. We present transient simulations of the last glacial inception using the Earth system model CLIMBER-X with dynamic vegetation, interactive ice sheets, and visco-elastic solid Earth responses. The simulations are initialized at the middle of the Eemian interglacial (125 kiloyears before present, ka) and run until 100 ka, driven by prescribed changes in Earth's orbital parameters and greenhouse gas concentrations from ice core data. CLIMBER-X simulates a rapid increase in Northern Hemisphere ice sheet area through MIS5d, with ice sheets expanding over northern North America and Scandinavia, in broad agreement with proxy reconstructions. While most of the increase in ice sheet area occurs over a relatively short period between 119 and 117 ka, the larger part of the increase in ice volume occurs afterwards with an almost constant ice sheet extent. We show that the vegetation feedback plays a fundamental role in controlling the ice sheet expansion during the last glacial inception. In particular, with prescribed present-day vegetation the model simulates a global sea level drop of only ∼ 20 m, compared with the ∼ 35 m decrease in sea level with dynamic vegetation response. The ice sheet and carbon cycle feedbacks play only a minor role during the ice sheet expansion phase prior to ∼ 115 ka but are important in limiting the deglaciation during the following phase characterized by increasing summer insolation. The model results are sensitive to climate model biases and to the parameterization of snow albedo, while they show only a weak dependence on changes in the ice sheet model resolution and the acceleration factor used to speed up the climate component. Overall, our simulations confirm and refine previous results showing that climate–vegetation–cryosphere feedbacks play a fundamental role in the transition from interglacial to glacial states characterizing Quaternary glacial cycles.",
    url = "https://doi.org/10.5194/cp-20-597-2024",
    doi = "10.5194/cp-20-597-2024",
    openalex = "W4392913422",
    references = "doi101002qj3803, doi101002qj828, doi101016s0277379101000828, doi1010292021gc009853, doi1010292022gl101827, doi101038nature12374, doi1010510004636120041335, doi101111j1365246x1976tb01252x, doi1011751520046919800372712amftsa20co2, doi1011751520046919800372734amftsa20co2, doi1031892014jog13j176, doi105194cp1210792016"
}

Abstract. The vast majority of ice-sheet modelling studies rely on simplified representations of the glacial isostatic adjustment (GIA), which, among other limitations, do not account for lateral variations in the lithospheric thickness and upper-mantle viscosity. In studies of the last glacial cycle using 3D GIA models, this has however been shown to have major impacts on the dynamics of marine-based sectors of Antarctica, which are likely to be the greatest contributors to sea-level rise in the coming centuries. This gap in comprehensiveness is explained by the fact that 3D GIA models are computationally expensive, rarely open-source and require a complex coupling scheme. To close this gap between “best” and “tractable” GIA models, we propose FastIsostasy here, a regional GIA model capturing lateral variations in the lithospheric thickness and mantle viscosity. By means of fast Fourier transforms and a hybrid collocation scheme to solve its underlying partial differential equation, FastIsostasy can simulate 100 000 years of high-resolution bedrock displacement in only minutes of single-CPU computation, including the changes in sea-surface height due to mass redistribution. Despite its 2D grid, FastIsostasy parameterises the depth-dependent viscosity and therefore represents the depth dimension to a certain extent. FastIsostasy is benchmarked here against analytical, as well as 1D and 3D numerical solutions, and shows good agreement with them. For a simulation of the last glacial cycle, its mean and maximal error over time and space respectively yield less than 5 % and 16 % compared to a 3D GIA model over the regional solution domain. FastIsostasy is open-source, is documented with many examples and provides a straightforward interface for coupling to an ice-sheet model. The model is benchmarked here based on its implementation in Julia, while a Fortran version is also provided to allow for compatibility with most existing ice-sheet models. The Julia version provides additional features, including a vast library of adaptive time-stepping methods and GPU support.

@article{doi105194gmd1752632024,
    author = "Swierczek-Jereczek, Jan and Montoya, Marisa and Latychev, Konstantin and Robinson, Alexander and Álvarez-Solas, Jorge and Mitrovica, J. X.",
    title = "FastIsostasy v1.0 – a regional, accelerated 2D glacial isostatic adjustment (GIA) model accounting for the lateral variability of the solid Earth",
    year = "2024",
    journal = "Geoscientific model development",
    abstract = "Abstract. The vast majority of ice-sheet modelling studies rely on simplified representations of the glacial isostatic adjustment (GIA), which, among other limitations, do not account for lateral variations in the lithospheric thickness and upper-mantle viscosity. In studies of the last glacial cycle using 3D GIA models, this has however been shown to have major impacts on the dynamics of marine-based sectors of Antarctica, which are likely to be the greatest contributors to sea-level rise in the coming centuries. This gap in comprehensiveness is explained by the fact that 3D GIA models are computationally expensive, rarely open-source and require a complex coupling scheme. To close this gap between “best” and “tractable” GIA models, we propose FastIsostasy here, a regional GIA model capturing lateral variations in the lithospheric thickness and mantle viscosity. By means of fast Fourier transforms and a hybrid collocation scheme to solve its underlying partial differential equation, FastIsostasy can simulate 100 000 years of high-resolution bedrock displacement in only minutes of single-CPU computation, including the changes in sea-surface height due to mass redistribution. Despite its 2D grid, FastIsostasy parameterises the depth-dependent viscosity and therefore represents the depth dimension to a certain extent. FastIsostasy is benchmarked here against analytical, as well as 1D and 3D numerical solutions, and shows good agreement with them. For a simulation of the last glacial cycle, its mean and maximal error over time and space respectively yield less than 5 \% and 16 \% compared to a 3D GIA model over the regional solution domain. FastIsostasy is open-source, is documented with many examples and provides a straightforward interface for coupling to an ice-sheet model. The model is benchmarked here based on its implementation in Julia, while a Fortran version is also provided to allow for compatibility with most existing ice-sheet models. The Julia version provides additional features, including a vast library of adaptive time-stepping methods and GPU support.",
    url = "https://doi.org/10.5194/gmd-17-5263-2024",
    doi = "10.5194/gmd-17-5263-2024",
    openalex = "W4400507616",
    references = "doi1010292022gc010359, doi1010292022gc010813"
}

Abstract. The dynamics of the ice sheets on glacial timescales are highly controlled by interactions with the solid Earth, i.e., the glacial isostatic adjustment (GIA). Particularly at marine ice sheets, competing feedback mechanisms govern the migration of the ice sheet's grounding line (GL) and hence the ice sheet stability. For this study, we developed a coupling scheme and performed a suite of coupled ice sheet–solid Earth simulations over the last two glacial cycles. To represent ice sheet dynamics we apply the Parallel Ice Sheet Model (PISM), and to represent the solid Earth response we apply the 3D VIscoelastic Lithosphere and MAntle model (VILMA), which, in addition to load deformation and rotation changes, considers the gravitationally consistent redistribution of water (the sea-level equation). We decided on an offline coupling between the two model components. By convergence of trajectories of the Antarctic Ice Sheet deglaciation we determine optimal coupling time step and spatial resolution of the GIA model and compare patterns of inferred relative sea-level change since the Last Glacial Maximum with the results from previous studies. With our coupling setup we evaluate the relevance of feedback mechanisms for the glaciation and deglaciation phases in Antarctica considering different 3D Earth structures resulting in a range of load-response timescales. For rather long timescales, in a glacial climate associated with the far-field sea-level low stand, we find GL advance up to the edge of the continental shelf mainly in West Antarctica, dominated by a self-amplifying GIA feedback, which we call the “forebulge feedback”. For the much shorter timescale of deglaciation, dominated by the marine ice sheet instability, our simulations suggest that the stabilizing sea-level feedback can significantly slow down GL retreat in the Ross sector, which is dominated by a very weak Earth structure (i.e., low mantle viscosity and thin lithosphere). This delaying effect prevents a Holocene GL retreat beyond its present-day position, which is discussed in the scientific community and supported by observational evidence at the Siple Coast and by previous model simulations. The applied coupled framework, PISM–VILMA, allows for defining restart states to run multiple sensitivity simulations from. It can be easily implemented in Earth system models (ESMs) and provides the tools to gain a better understanding of ice sheet stability on glacial timescales as well as in a warmer future climate.

@article{doi105194tc1842332024,
    author = "Albrecht, Torsten and Bagge, Meike and Klemann, Volker",
    title = "Feedback mechanisms controlling Antarctic glacial-cycle dynamics simulated with a coupled ice sheet–solid Earth model",
    year = "2024",
    journal = "˜The œcryosphere",
    abstract = "Abstract. The dynamics of the ice sheets on glacial timescales are highly controlled by interactions with the solid Earth, i.e., the glacial isostatic adjustment (GIA). Particularly at marine ice sheets, competing feedback mechanisms govern the migration of the ice sheet's grounding line (GL) and hence the ice sheet stability. For this study, we developed a coupling scheme and performed a suite of coupled ice sheet–solid Earth simulations over the last two glacial cycles. To represent ice sheet dynamics we apply the Parallel Ice Sheet Model (PISM), and to represent the solid Earth response we apply the 3D VIscoelastic Lithosphere and MAntle model (VILMA), which, in addition to load deformation and rotation changes, considers the gravitationally consistent redistribution of water (the sea-level equation). We decided on an offline coupling between the two model components. By convergence of trajectories of the Antarctic Ice Sheet deglaciation we determine optimal coupling time step and spatial resolution of the GIA model and compare patterns of inferred relative sea-level change since the Last Glacial Maximum with the results from previous studies. With our coupling setup we evaluate the relevance of feedback mechanisms for the glaciation and deglaciation phases in Antarctica considering different 3D Earth structures resulting in a range of load-response timescales. For rather long timescales, in a glacial climate associated with the far-field sea-level low stand, we find GL advance up to the edge of the continental shelf mainly in West Antarctica, dominated by a self-amplifying GIA feedback, which we call the “forebulge feedback”. For the much shorter timescale of deglaciation, dominated by the marine ice sheet instability, our simulations suggest that the stabilizing sea-level feedback can significantly slow down GL retreat in the Ross sector, which is dominated by a very weak Earth structure (i.e., low mantle viscosity and thin lithosphere). This delaying effect prevents a Holocene GL retreat beyond its present-day position, which is discussed in the scientific community and supported by observational evidence at the Siple Coast and by previous model simulations. The applied coupled framework, PISM–VILMA, allows for defining restart states to run multiple sensitivity simulations from. It can be easily implemented in Earth system models (ESMs) and provides the tools to gain a better understanding of ice sheet stability on glacial timescales as well as in a warmer future climate.",
    url = "https://doi.org/10.5194/tc-18-4233-2024",
    doi = "10.5194/tc-18-4233-2024",
    openalex = "W4402650595",
    references = "doi1010022014jb011176, doi1010160031920181900467, doi1010292006jf000664, doi1010292021gc009853, doi1010292022gc010359, doi101038271321a0, doi101038nature17145, doi101038s4156101905108, doi101073pnas1812883116, doi101126science1172873, doi101126scienceabn7950, doi105194tc73752013"
}

Abstract A glacial forebulge is a bending‐related upheaval of the lithosphere outside a glaciated area that co‐occurs to the depression of the lithosphere below an ice sheet. The forebulge of the last glaciation attracted attention over more than one century, but quantitative descriptions on the geometry of the forebulge are rare. While many studies mention forebulge dynamics as a possible cause for a certain observation, very few studies provide a detailed and systematic exploration of the forebulge's precise dynamics. That way the forebulge became occasionally a rather mysterious structure with many unknowns. We aim to shed light into the forebulge discussion. After reviewing the history of forebulge research, we outline the theory behind the spatio‐temporal forebulge development including controlling factors, and present forebulge observations in geological and geodetic records of North America and the northern parts of Central Europe. We use a state‐of‐the art finite‐element model that can fit multiple observations of the last glaciation simultaneously, to illustrate forebulge development in North America and northern Central Europe and address the issue of whether the zero‐uplift hinge line is a good indication of the location of the forebulge front. Finally, we discuss effects of the forebulge on the sea‐level change pattern and the evolution of lithospheric stresses, which can induce intraplate earthquakes. We also show that the existence of a glacial forebulge outside the ice margin is not consistent with the assumption of isostatic equilibrium at the Last Glacial Maximum, and there is no strain rate‐stress paradox.

@article{doi1010292024rg000852,
    author = "Brandes, Christian and Steffen, Holger and Steffen, Rebekka and Li, Tanghua and Wu, Patrick",
    title = "Effects of the Last Quaternary Glacial Forebulge on Vertical Land Movement, Sea‐Level Change, and Lithospheric Stresses",
    year = "2025",
    journal = "Reviews of Geophysics",
    abstract = "Abstract A glacial forebulge is a bending‐related upheaval of the lithosphere outside a glaciated area that co‐occurs to the depression of the lithosphere below an ice sheet. The forebulge of the last glaciation attracted attention over more than one century, but quantitative descriptions on the geometry of the forebulge are rare. While many studies mention forebulge dynamics as a possible cause for a certain observation, very few studies provide a detailed and systematic exploration of the forebulge's precise dynamics. That way the forebulge became occasionally a rather mysterious structure with many unknowns. We aim to shed light into the forebulge discussion. After reviewing the history of forebulge research, we outline the theory behind the spatio‐temporal forebulge development including controlling factors, and present forebulge observations in geological and geodetic records of North America and the northern parts of Central Europe. We use a state‐of‐the art finite‐element model that can fit multiple observations of the last glaciation simultaneously, to illustrate forebulge development in North America and northern Central Europe and address the issue of whether the zero‐uplift hinge line is a good indication of the location of the forebulge front. Finally, we discuss effects of the forebulge on the sea‐level change pattern and the evolution of lithospheric stresses, which can induce intraplate earthquakes. We also show that the existence of a glacial forebulge outside the ice margin is not consistent with the assumption of isostatic equilibrium at the Last Glacial Maximum, and there is no strain rate‐stress paradox.",
    url = "https://doi.org/10.1029/2024rg000852",
    doi = "10.1029/2024rg000852",
    openalex = "W4411894792",
    references = "doi1010022014jb011176, doi1010160033589478900339, doi1010292002eo000189, doi1010292021gc009853, doi1010292022gc010359, doi101029rg012i004p00649, doi101073pnas1411762111, doi101111j1365246x1976tb01252x, doi101126science19442701121, doi101126science2605109771, doi101146annurevearth32082503144359, doi101146annurevearth36031207124326, doi105194tc1842332024"
}

The solid earth structure beneath Greenland, meaning the rocky part of Earth from the ice-bed interface to depth, has gained increased interest in recent years as it provides a critical boundary condition for the dynamic evolution of the Greenland ice sheet (GrIS), one of the largest sources of sea-level rise contributions since the early 2000s. However, no consensus has been reached regarding the key internal or surface earth properties influencing this boundary condition and thus GrIS behaviour. One important surface property is the subglacial heat flow, which affects sliding conditions of the ice sheet including the onset of major ice streams and is related to subglacial geology. Lithospheric architecture and mantle viscosity structure are internal properties that influence ice sheet evolution through changes in the height and slope of the ice-bed interface caused by glacial isostatic adjustment. Because there is no general agreement regarding crustal and lithospheric structures, some glaciological studies use an ensemble of solid earth models to incorporate uncertainties into their GrIS predictions, but it is unclear how these variations ultimately affect estimates of future sea-level rise. Here we describe the main solid earth properties that are important for GrIS evolution (heat flow, temperature, viscosity), from the base of the ice sheet to the upper mantle, and we provide some perspectives on how future collaborative efforts and integrated studies could lead to better agreement regarding these key characteristics.

@article{doi101144jgs2024291,
    author = "Ebbing, J. and Hopper, John R. and Conrad, Clinton P. and Milne, Glenn A. and Steffen, Rebekka and Afonso, Juan Carlos and Barletta, Valentina R. and Ferreira, Ana M. G. and Freienstein, Judith and Hansen, S. E. and Heincke, Björn and Jones, Glenn and Lebedev, Sergei and Moorkamp, Max and Schutt, D. and Wansing, Agnes",
    title = "Importance of solid earth structure for understanding the evolution of the Greenland ice sheet",
    year = "2025",
    journal = "Journal of the Geological Society",
    abstract = "The solid earth structure beneath Greenland, meaning the rocky part of Earth from the ice-bed interface to depth, has gained increased interest in recent years as it provides a critical boundary condition for the dynamic evolution of the Greenland ice sheet (GrIS), one of the largest sources of sea-level rise contributions since the early 2000s. However, no consensus has been reached regarding the key internal or surface earth properties influencing this boundary condition and thus GrIS behaviour. One important surface property is the subglacial heat flow, which affects sliding conditions of the ice sheet including the onset of major ice streams and is related to subglacial geology. Lithospheric architecture and mantle viscosity structure are internal properties that influence ice sheet evolution through changes in the height and slope of the ice-bed interface caused by glacial isostatic adjustment. Because there is no general agreement regarding crustal and lithospheric structures, some glaciological studies use an ensemble of solid earth models to incorporate uncertainties into their GrIS predictions, but it is unclear how these variations ultimately affect estimates of future sea-level rise. Here we describe the main solid earth properties that are important for GrIS evolution (heat flow, temperature, viscosity), from the base of the ice sheet to the upper mantle, and we provide some perspectives on how future collaborative efforts and integrated studies could lead to better agreement regarding these key characteristics.",
    url = "https://doi.org/10.1144/jgs2024-291",
    doi = "10.1144/jgs2024-291",
    openalex = "W4409550815",
    references = "doi1010292022gc010813, doi105194tc1842332024"
}

Abstract. During the last 20 000 years the climate of the earth has changed from a state much colder than today, with large ice sheets over North America and northwest Eurasia, to its present state. The fully interactive simulation of this transition represents a hitherto unsolved challenge for state-of-the-art climate models. We use a novel coupled comprehensive atmosphere–ocean–vegetation–ice-sheet–solid-earth model to simulate the transient climate evolution from the Last Glacial Maximum to pre-industrial times. The model considers dynamical changes in the glacier mask, land–sea mask, and river routing. An ensemble of transient model simulations successfully captures the main features of the last deglaciation, as depicted by proxy estimates. In addition, our model simulates a series of abrupt climate changes, which can be attributed to different drivers. Sudden weakenings of the Atlantic meridional overturning circulation during the glacial period and the first half of the deglaciation are caused by Heinrich-event like ice-sheet surges, which are part of the model generated internal variability. We show that the timing of these surges depends on the initial state and the model parameters. Abrupt events during the second half of the deglaciation are caused by a long-term shift in the sign of the Arctic freshwater budget, changes in river routing, and/or the opening of ocean passages.

@article{doi105194cp217192025,
    author = "Mikolajewicz, Uwe and Kapsch, Marie‐Luise and Schannwell, Clemens and Six, Katharina and Ziemen, Florian and Bagge, Meike and Baudouin, Jean‐Philippe and Erokhina, Olga and Gayler, Veronika and Klemann, Volker and Meccia, Virna and Mouchet, Anne and Riddick, Thomas",
    title = "Deglaciation and abrupt events in a coupled comprehensive atmosphere–ocean–ice-sheet–solid-earth model",
    year = "2025",
    journal = "Climate of the past",
    abstract = "Abstract. During the last 20 000 years the climate of the earth has changed from a state much colder than today, with large ice sheets over North America and northwest Eurasia, to its present state. The fully interactive simulation of this transition represents a hitherto unsolved challenge for state-of-the-art climate models. We use a novel coupled comprehensive atmosphere–ocean–vegetation–ice-sheet–solid-earth model to simulate the transient climate evolution from the Last Glacial Maximum to pre-industrial times. The model considers dynamical changes in the glacier mask, land–sea mask, and river routing. An ensemble of transient model simulations successfully captures the main features of the last deglaciation, as depicted by proxy estimates. In addition, our model simulates a series of abrupt climate changes, which can be attributed to different drivers. Sudden weakenings of the Atlantic meridional overturning circulation during the glacial period and the first half of the deglaciation are caused by Heinrich-event like ice-sheet surges, which are part of the model generated internal variability. We show that the timing of these surges depends on the initial state and the model parameters. Abrupt events during the second half of the deglaciation are caused by a long-term shift in the sign of the Arctic freshwater budget, changes in river routing, and/or the opening of ocean passages.",
    url = "https://doi.org/10.5194/cp-21-719-2025",
    doi = "10.5194/cp-21-719-2025",
    openalex = "W4409166176",
    references = "doi105194tc1842332024"
}

Abstract. Earth and other terrestrial and icy planetary bodies deform viscoelastically under various forces. Numerical modeling plays a critical role in understanding the nature of various dynamic deformation processes. This article introduces a newly developed open-source package, CitcomSVE-3.0, which efficiently solves the viscoelastic deformation of planetary bodies. Based on its predecessor, CitcomSVE-2.1, CitcomSVE-3.0 is updated to account for three-dimensional elastic compressibility and depth-dependent density, which are particularly important in modeling horizontal displacement for viscoelastic deformation. We benchmark CitcomSVE-3.0 against a semi-analytical code for two types of loading problems: (1) single harmonic loads on the surface or as a tidal force and (2) the glacial isostatic adjustment (GIA) problem with a realistic ice sheet loading history (ICE-6G_D) and an updated version of sea level equations. The benchmark results presented here demonstrate the accuracy and efficiency of this package. CitcomSVE-3.0 shows second-order accuracy in terms of spatial resolution. For typical GIA modeling with a 122 kyr glaciation–deglaciation history, a surface horizontal resolution of ∼50 km, and a time increment of 125 years, this takes ∼3 h on 384 CPU cores to complete, with displacement rate errors of less than 5 %.

@article{doi105194gmd1814452025,
    author = "Yuan, Tao and Zhong, Shijie and Geruo, A",
    title = "CitcomSVE-3.0: a three-dimensional finite-element software package for modeling load-induced deformation and glacial isostatic adjustment for an Earth with a viscoelastic and compressible mantle",
    year = "2025",
    journal = "Geoscientific model development",
    abstract = "Abstract. Earth and other terrestrial and icy planetary bodies deform viscoelastically under various forces. Numerical modeling plays a critical role in understanding the nature of various dynamic deformation processes. This article introduces a newly developed open-source package, CitcomSVE-3.0, which efficiently solves the viscoelastic deformation of planetary bodies. Based on its predecessor, CitcomSVE-2.1, CitcomSVE-3.0 is updated to account for three-dimensional elastic compressibility and depth-dependent density, which are particularly important in modeling horizontal displacement for viscoelastic deformation. We benchmark CitcomSVE-3.0 against a semi-analytical code for two types of loading problems: (1) single harmonic loads on the surface or as a tidal force and (2) the glacial isostatic adjustment (GIA) problem with a realistic ice sheet loading history (ICE-6G\_D) and an updated version of sea level equations. The benchmark results presented here demonstrate the accuracy and efficiency of this package. CitcomSVE-3.0 shows second-order accuracy in terms of spatial resolution. For typical GIA modeling with a 122 kyr glaciation–deglaciation history, a surface horizontal resolution of ∼50 km, and a time increment of 125 years, this takes ∼3 h on 384 CPU cores to complete, with displacement rate errors of less than 5 \%.",
    url = "https://doi.org/10.5194/gmd-18-1445-2025",
    doi = "10.5194/gmd-18-1445-2025",
    openalex = "W4408239833",
    references = "doi1010292022gc010359, doi1010292022gc010813"
}

@incollection{lambeckNoneglacial,
    author = "Lambeck, K.",
    title = "Glacial rebound and sea-level change: An example of deformation of the earth by surface loading",
    year = "None",
    booktitle = "Lecture Notes in Earth Sciences",
    url = "https://doi.org/10.1007/bfb0009885",
    doi = "10.1007/bfb0009885",
    openalex = "W1657896926",
    pages = "111-137",
    references = "doi1010160031920181900467, doi101029rg010i004p00849, doi101029rg012i004p00649, doi101038324137a0, doi101111j1365246x1976tb01251x, doi101111j1365246x1976tb01252x, doi101111j1365246x1989tb06010x, doi1023071550617, openalexw2070611029, openalexw41072897"
}