How the climate drives sea-level changes

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How the climate drives sea-level changes

Glenn Milne

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Reader in the Department of Earth Sciences, University of Durham (g.a.milne@durham.ac.uk).

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Abstract

Sea-level change associated with climate change involves various interactions between different components of the Earth system — primarily oceans, ice sheets and the solid Earth. As a consequence, sea-level science is highly multi- and interdisciplinary, requiring collaboration between scientists who measure and model properties of and processes within these various subsystems. This paper provides a broad and cursory glimpse into the processes underlying climate-driven sea-level change. A key message of this paper is that, contrary to popular belief, climate-driven sea-level change is not spatially uniform. This is a doubled-edged sword: it complicates the processes of producing well-constrained estimates of future sea-level rise at regional to local scales, but it provides the opportunity to better understand past climate change through modelling observations of sea-level changes.
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Sea-level change is a topic of interest to a broad audience for the simple reason that it can influence people directly: around 200 million people live in coastal floodplains. This interest has been heightened by the relatively recent media focus on climate change and the possible environmental and socio-economic consequences if the current warming trend were to continue in the coming centuries. Sea-level rise is, of course, one of the hazards associated with future global warming. This point was made very clear in the recent Stern Review (Stern 2007) which concluded, for example, that 2 million km2 of land and $1 trillion worth of assets are less than 1 m above current sea level and a warming of 3 °C will flood between 7 and 70 million people.

A common misconception among both the wider scientific community and the general public is that sea-level rise associated with a warming climate would be the same everywhere. For example, concern about the future response of the large ice sheets to projected warming often leads to statements regarding the potential sea-level rise associated with the demise of the Greenland or West Antarctic ice sheets — approximately 7 m and 5 m, respectively. However, if either of these ice sheets were to lose even a fraction of their mass, the resulting sea-level change would not be spatially uniform. Current models of sea-level change associated with changes in continental ice volume demonstrate that there is, in fact, a sea-level fall in the vicinity of a melting ice sheet or glacier. If the Greenland ice sheet were to melt significantly in the next few hundred years, the sea-level change around the UK would be effectively zero as a result of the spatial non-uniformity in the sea-level response.

This spatial non-uniformity in the sea-level response to climate change is, of course, a serious issue when considering the sea-level hazard from future global warming. In the coming century, some areas will experience a considerable sea-level rise, whereas others will experience little change or even a considerable fall. It is important for governments and policy makers to be aware of this variability so that appropriate action can be made to plan and implement appropriate mitigatory procedures. This topic will be discussed in the final section of this paper.

While the spatial variability of sea-level change is a complicating factor when making predictions of future changes, it presents a unique opportunity to use observations of sea-level changes to understand better the evolution of the climate system in the recent and distant past. This understanding underpins our ability to make accurate predictions of future changes.

The height of the ocean surface (sea level) can be defined and measured in two ways: relative to the land surface (known as relative sea level) and relative to the Earth’s centre of mass (known as absolute sea level). Satellite measurements of absolute sea level have provided unprecedented spatial cover of sea-level changes over the past ˜15 years. The discussion in this article focuses, however, on relative sea-level change because it is these data that provide the temporal coverage necessary to study climate-driven sea-level change: several decades to millennia. For the past few centuries, measurements obtained using tide gauges have been the most commonly employed for this purpose. Various proxy techniques are employed to reconstruct sea-level changes prior to this, on millennial to decadal timescales. Most of these proxy techniques rely on using the fossil remains of plants and animals that live close to or within the tidal zone as well as morphological indicators formed by erosional or depositional processes (Shennan 2007). Sea-level fingerprinting is a method used to infer the melt sources responsible for observed sea-level change, based on the understanding of the various factors influencing these data.
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Sea-level fingerprinting

Because sea-level change associated with climate variation is not spatially uniform, it is possible to look for patterns in observations of past changes to infer dominant melt sources or constrain the relative importance of steric changes (sea-level changes arising from expansion and contraction of the water as temperature or salinity changes; see box on p2.26) compared to ice melt/growth. A recent application of this type considered a carefully selected subset of tide gauge records to look for a signal related to melting of land ice during the 20th century (Mitrovica 2001). The basis of this study is the pattern of global sea-level change when assuming melt from three distinct sources: Greenland, Antarctica and smaller ice masses such as mountain glaciers and ice caps.

As an example, figure 1 shows the predicted pattern (or “fingerprint”) of sea-level change associated with melting of the Greenland and West Antarctic ice sheets. In the immediate vicinity of a melting ice sheet, the predicted sea-level fall is a consequence of the gravitational influence of the loss of ice mass and the uplift of the solid Earth. At greater distances, the gravitational effect of the ice mass change dominates. If either of the West Antarctic or Greenland ice sheets lost a significant amount of mass during the 20th century, then the patterns shown in figure 1 would be evident in the tide gauge data. The data considered in this study are consistent with a relatively large melt of the Greenland ice sheet because a significant amount of the spatial variability could be accounted for with this scenario (see figure 3 in Mitrovica et al.). The data considered had very limited distribution in the southern hemisphere and so it was not possible to detect a potential fingerprint associated with the Antarctic ice sheet. This lack of data in the southern hemisphere remains a limitation.
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Predicted sea-level change (mm yr−1) assuming that the Greenland (top) or West Antarctic (bottom) ice sheets melt at 1 mm yr−1 (or 10 cm per century). (Adapted from Mitrovica . 2001)
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Linear trends in sea-level change (in mm yr−1) due to the thermosteric effect during the period 1955 to 2003. Note the large spatial variability in the sea-level change. (From Ishii . 2006)

As indicated by Mitrovica et al., uncertainty regarding the magnitude of the thermosteric signal at the data sites limited the interpretation of the observations in terms of ice melt. Determining the accuracy of methods currently used to estimate the thermosteric signal at coastal sites remains an important issue for contemporary research. These methods apply a simplistic method that includes no consideration of ocean dynamics when extrapolating the thermosteric signal (inferred from temperature data in adjacent deeper ocean) across the continental shelf to coastal areas. Once this question has been addressed, it will be possible to remove spatial variability due to ocean temperature changes and obtain a more robust estimate of the ice melt contribution.
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How fast can sea level rise?

An important question to consider with regard to predicting future sea-level change is: how fast can sea levels rise? This question can be answered in two ways: from a theoretical/modelling perspective or from an observational perspective. We consider the latter here. Of the two processes that contribute to climate-driven sea-level change, instabilities in ice reservoirs — particularly the large ice sheets — represent the greatest risk of producing sudden and rapid changes in sea level.

Observations of past sea-level change from low-latitude areas (distant from major glaciation centres) provide evidence for the occurrence of very rapid and large sea-level rise at distinct times. These events, which punctuate periods of relatively steady sea-level change, are known as meltwater pulses. Sea-level records from two locations — Barbados (Bard 1990) and Sunda Shelf (Hanebuth 2000) — provide evidence for a meltwater pulse around 14 000 years ago. This event, known as meltwater pulse IA (mwp-IA), involved a global mean sea-level rise of 20–25 m in about 500 years. During the occurence of mwp-IA, rates of sea-level rise approached values of 40 mm yr−1 in some areas (compared to a rate of almost 2 mm yr−1 in the past 50 years). This event happened at a time of rapid and large climate variability when there was significantly more ice on the planet. It is highly unlikely for an event of this magnitude (20–25 m) to happen in the immediate future (given the high stability of the East Antarctic ice sheet). However, it is not so clear if the rate of sea-level rise measured during mwp-IA and other meltwater pulses can be discounted as a possibility in the coming centuries.
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Will it happen again?

There are several questions regarding meltwater pulse IA that need to be addressed in order to determine if rates of sea-level rise on the order of 10s of mm yr−1 could be possible in the future. Improved constraints on the melt sources responsible for past meltwater pulses are necessary. If the event was sourced primarily from a single ice sheet then this would suggest that similar rates are feasible in the future. If the event can be sourced to a particular ice sheet then what mechanism, or forcing, was responsible for such a sudden and rapid reduction in ice volume? Determining the source distribution of meltwater pulse IA remains a topic of focused research. The method of sea-level fingerprinting has provided some important constraints and will continue to do so as new data are obtained that provide a measure of sea-level change during and after the mwp-IA event.

The principle is the same as that applied for constraining ice melt during the 20th century. The main difference is that there are more potential melt sources (there were ice sheets covering North America and northern Eurasia at this time), the signal is much larger and the data sampling much poorer (currently, data from only two sites capture mwp-IA). The primary constraint from data obtained from Barbados and Sunda Shelf is that the rise associated with mwp-IA is approximately the same at each site. A study by Clark (2002) used this observation to consider what constraint these data imposed on the source geometry of mwp-IA. A primary conclusion from this study was that the data constraint is not compatible with a dominant source from the massive Laurentide ice sheet covering large parts of Canada and the USA. A model prediction, or fingerprint, produces a difference in sea-level rise between the sites of ˜10 m, which is incompatible with the observations.

Clark et al. demonstrated that melt scenarios in which the Antarctic ice sheet contributed part or all of the melt are compatible with the current data. This conclusion was supported by a later study that applied a more complicated model to consider the sea-level response both during and following mwp-IA (Bassett 2005). By considering sea-level change both during and after mwp-IA, a larger data set comprising observations from four sites can be employed. The conclusion of this later study was that the sea-level observations can be fit only with a melt model that includes a dominant (˜15 m eustatic sea-level equivalent) Antarctic source component to mwp-IA. However, it is difficult to reconcile such a large and rapid melt of the Antarctic ice sheet with both field observations of ice sheet extent and glaciological models of ice sheet evolution. Reconciling the constraints from these various approaches is a key focus of ongoing research. The mwp-IA event was one of the largest and most rapid climate events in recent Earth history, so it is important to understand better the forcing and mechanisms responsible for its occurrence. This understanding will enable scientists to evaluate more accurately the possibility of such events happening in the future.
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Predicting future sea-level change

At present, the large ice sheets contain mass equivalent to almost 70 m of eustatic sea-level rise (˜60 m in Antarctica and ˜7 m in Greenland). Smaller bodies of ice (glaciers and ice caps) contain much less water (equivalent to <1 m). However, in the past ˜50 years, melting of these smaller ice reservoirs is thought to have dominated over contributions from the large ice sheets. This is because, due to their smaller size, they respond quicker to a given climate forcing. If current retreat rates of mountain glaciers are sustained (and this is expected) there won't be many left in a few centuries time. The greatest potential for sea-level rise from ice melting in the coming centuries and millennia is the large ice sheets. The East Antarctic ice sheet (˜55 m) is stable and will most likely grow as the climate warms due to an increase in atmospheric moisture content and therefore increased snowfall in this region. The Greenland and West Antarctic ice sheets are less stable and could lose a significant amount of mass in the coming centuries (Meehl 2007).

How much mass they will lose is difficult to quantify. Recent measurements of the Greenland ice sheet, for example, have indicated that the fastest flowing parts of the ice sheet (known as outlet glaciers) are far more dynamic than previously thought in terms of how fast they can flow and how quickly then can respond to climate forcing (e.g. Bamber 2007). Glaciological models that consider the response of ice sheets to climate forcing have yet to account adequately for this highly dynamic behaviour. The measurements that revealed this limitation in our understanding of these systems cover a relatively short time period, so it is not yet clear if the recent acceleration in these outlet glaciers is a transient phenomenon or will be sustained in the coming decades. These issues are a central focus of contemporary research into the monitoring and modelling of ice sheets.

Estimating the future contribution of the steric component of sea-level change, particularly the thermosteric component, is less problematic in terms of our understanding of the underlying physical processes. The steric component can be predicted by running a climate model (or Atmosphere–Ocean General Circulation Model) for a specified greenhouse gas emission scenario. Uncertainty in future greenhouse gas emissions is a major limitation in arriving at a well-constrained estimate of this signal. In the most recent report of the Intergovernmental Panel on Climate Change (IPCC), a range of plausible and distinct emission scenarios were adopted to estimate future thermosteric sea-level change using a range of current models (see figure 10.31 of Meehl 2007). These results indicate that the thermosteric signal is expected to contribute between 10 and 40 cm of global mean sea-level rise in the coming century.
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Spatial variability

As discussed above, future sea-level change will not be globally uniform. This is recognized in the most recent IPCC report in which results are shown to illustrate the spatial variability associated with the thermosteric effect. However, given the differences in predictions of the thermosteric signal between various climate models (for a given emission scenario) and the uncertainty related to future mass changes of the ice sheets, placing useful bounds on the spatial variability of future sea-level rise remains an important goal of contemporary research. Until this uncertainty can be reduced, it remains important to raise awareness of the fact that there will be large spatial variability in future sea-level rise — to the extent that some areas will experience a rise that will be considerably larger than the projected global average.

For example, taking the sea-level projections from the recent IPCC report gives a “worst case” scenario of ˜0.6 m rise in global mean sea level by the end of this century. Spatial variability in the thermosteric signal alone could increase this prediction by more than 30% in some areas. If these areas are also experiencing significant subsidence, a net rise of ˜1 m is not implausible. In addition, this amplification to the projected global mean rise will be amplified further by shorter timescale processes such as tides and storm surges. Governments and local planning authorities need to be aware that regional to local sea-level change can depart significantly from the global mean. This departure should be factored into “worst case” scenarios in order to plan and carry out appropriate mitigation procedures.
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The good news

To end on a lighter note, it is worth keeping in mind that the spatial variability will result in a reduced sea-level rise, or even fall, in some areas. A good example of this, already mentioned in this article, is the sea-level change associated with mass loss from the Greenland ice sheet. The model prediction shown in figure 1 (top frame) shows that the consequence for UK coastal communities would be relatively insignificant. The predictions shown in figure 1 can be scaled for any assumed melt or melt rate. For example, in the extreme case that the Greenland ice will contribute 1 m of eustatic sea-level in the next century, the contours would represent total sea-level change in metres. Note that the UK is bisected by the zero contour, indicating that sea levels would not be significantly affected.
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Measuring and modelling sea-level change

Given that relative sea-level is defined as the vertical height between the sea surface and sea floor at a given location, it follows that a height shift of either bounding surface will affect a change in sea level. Figure 2 gives a schematic depiction of an ocean basin and processes that result in sea-level change. Vertical motion of the sea surface due to processes such as interactions between the atmosphere and the ocean, dynamic flow within the ocean, gravitational influence of the Moon and Sun (i.e. tides) result in sea-level changes at relatively short timescales (seconds to years). In contrast, vertical motion of the solid (rocky) Earth due to internal buoyancy stresses (mantle convection and tectonic processes) and stresses associated with surface mass redistribution (erosion, deposition, ice sheet growth/melting) result in sea-level changes on much longer timescales: thousands to millions of years. Earthquakes and landslides on the ocean floor are, of course, exceptions to this as they involve a very rapid motion of the lower bounding surface that results in often destructive sea-level changes known as tsunamis.
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Schematic depiction of an ocean basin and processes that result in sea-level change over a wide range of timescales (from seconds to millions of years).

The influence of climate change on sea level is apparent at intermediate timescales, from several decades to 100s of millenia. As discussed below, this reflects the fact that climate processes can influence sea level through the displacement of both the sea surface and the sea floor. Climate change influences sea level directly through two processes. (There are other, non-direct mechanisms, but these are generally of second order and so will not be discussed here.) Changes in the temperature and salinity of seawater result in a sea-level change due to the expansion/contraction of the water and the influence of the density changes on dynamic flow of the ocean. The former effect, known as steric sea-level change, dominates over timescales greater than a decade. The thermal component of steric sea-level change is known as the thermosteric effect and the saline component is known as the halosteric effect. The second process is mass exchange between continental ice reservoirs (ice sheets and mountain glaciers) and the oceans. Both of these processes are believed to have been significant contributors to sea-level change during the 20th century and so must be considered in projections of future changes. Over the more distant past (10s–100s of millennia), the influence of growing and melting ice sheets during glacial cycles dominates the sea-level response at most locations.
Steric sea-level change

Sea-level changes associated with the thermosteric effect have been calculated using in situ measurements of ocean temperature. These analyses have concluded that this process accounts for ˜0.4 mm yr−1, or 25% of the mean global rise observed from tide gauge records for this period (e.g. Levitus 2005). The contribution to the global mean rise from salinity changes cannot be calculated reliably because of data sampling limitations, but it is expected to be considerably less (although it is worth noting that this process can be significant or dominant in specific areas). Maps of the thermosteric signal show large spatial variability. For example, in figure 3, compare the rate of sea-level rise between the east coast of North America and Japan. Steric processes are expected to be an important, if not dominant, contributor to sea-level change during the 21st century (Meehl 2007).
Ice melt or growth

A common, first-order model often applied to estimate sea-level change associated with an increase or decrease in continental ice volume is known as the “eustatic model”. This model is based on mass conservation: when an ice sheet loses/gains mass, the oceans gain/lose the same amount. This relationship is written
Formula

where ΔS is the eustatic sea-level change, ρice and ρwater are the densities of ice and water, respectively; ΔV is the change in grounded continental ice volume and A is the area of the ocean. (The factor of ρice/ρwater accounts for the volume change when water melts or freezes.) As a result of interactions between ice sheets, oceans and the solid Earth, the actual sea-level change due to changes in continental ice volume can depart significantly (by between metres and 100s of metres) from the eustatic value. These interactions, and their influence on sea level, are considered in studies of glacial isostatic adjustment (e.g. see Milne and Shennan 2007 and references therein). The remainder of this section will be devoted to a general discussion of the processes contributing to spatial variability in sea-level change through continental ice mass changes.

One effect is due to the gravitational attraction between ice and ocean water, as well as the self-gravitation of water with itself. This effect is illustrated in figure 4, which shows how sea levels are raised in the vicinity of a large ice mass due to this gravitational effect. If the ice sheet were to lose mass, this attraction would be reduced, causing a fall of the sea surface in a large area centred on the region of mass loss. This region of fall becomes a region of rise greater than the eustatic rise as one moves further from the ice mass. This gravitational effect due to mass distribution between ice sheets and oceans can result in a global sea-surface signature for large ice sheets (see figure 1 and related discussion).
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Schematic diagram illustrating the (exaggerated) gravitational attraction between a large ice mass and surrounding ocean water. (Adapted from Tamisiea . 2003)

Another effect involves the deformation of the solid (rocky) Earth in response to the surface mass exchange between ice sheets and oceans. This process, known as isostasy, leads to a global signature in the sea-level response associated with the ice loading (glacio-isostasy) and the ocean loading (hydro-isostasy). Figure 5 shows a model prediction of vertical motion of the solid Earth in response to the most recent deglaciation of the current ice age which occurred between about 20–6 thousand years ago and involved a mass transfer equivalent to about 130 m of eustatic sea-level change. During this event, large ice sheets covering North America and Eurasia completely melted and the ice sheets over Greenland and Antarctica lost a significant amount of mass. This loss of ice mass is most clearly reflected in the present-day uplift of these regions. For example, in Fennoscandinavia and Canada, the solid Earth is uplifting at rates reaching more than 1 cm yr−1 in some areas (e.g. Milne 2001). Compared to the deformation associated with the ice loading, that due to ocean loading is smaller in magnitude but more spatially extensive. One consequence of the ocean loading is a subtle crustal uplift around the perimeter of continents. This is most evident in regions far removed from the influence of ice loading, such as Africa and Australia.
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Rates of uplift (mm yr−1) of the Earth's solid surface (crust) predicted using a model of glacial isostatic adjustment. Note the rapid uplift in regions once covered by large ice sheets (e.g. North America and Fennoscandinavia).

The vertical motion of the solid Earth because of both past and present mass changes in ice sheets adds significantly to the spatial pattern of sea-level change due to changes in continental ice. Note that the redistribution of mass within the solid Earth associated with this isostatic deformation also influences the surface gravity field and so perturbs the sea surface (in the same manner as discussed above for the gravitational influence of ice and water on sea level).

A third process, associated with the sea-level response to changes in continental ice, arises from Earth rotation. As a rotating body, the Earth has an associated rotational potential — causing our planet to be an oblate spheroid (“fatter” in equatorial regions). Mass exchange between ice sheets and oceans, as well as the consequent deformation of the solid Earth, perturb the Earth's inertia tensor and result in a relative motion between the rotation vector (and therefore the rotational potential) and the solid Earth. The perturbation to the rotational potential associated with this relative motion (termed “true polar wander”) causes a distinctive, global-scale pattern of sea-level change which is schematically illustrated in figure 6.
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Schematic illustration of the result of a clockwise motion of the rotation pole relative to the solid Earth. Grey areas indicate a sea-level rise and white areas a fall. (From Mound and Mitrovica 1998)
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Acknowledgments

Many thanks to the colleagues and students I've had the pleasure of working with over the years. With regard to the research discussed in this paper, special thanks go to Sophie Bassett, Peter Clark, Jerry Mitrovica and Mark Tamisiea. I'm grateful to the British Geophysical Association for recognizing my work and giving me the opportunity to bring sea level science to a wider audience. My research was supported by NERC and the Royal Society. ⇑ was kindly drafted by Chris Orton, Department of Geography, Durham University.

The Bullerwell Lecture is awarded annually by the British Geophysical Association (http://www.geophysics.org.uk).
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Footnotes

↵In the 2007 Bullerwell Lecture, Glenn Milne considers the mechanisms and consequences of sea-level changes driven by climate change and finds a surprisingly variable response, worldwide.

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3 thoughts on “How the climate drives sea-level changes

  1. Neville

    4 April, 2013

    i HAVE POSTED THIS FOR THE BENEFIT OF THOSE WHO MAY NOT ACCEPT NON-UNIFORMITY IN SEA-LEVEL RISES.tHIS LENGHTY ARTICLE
    GIVES FULL DETAILS OF THE REASONS FOR THIS.

  2. I submit that building storm walls and levees is a serious waste of time.

    They will be broached as the great glaciers in Greenland and the Antarctic start to melt

    This promises multi-metre SLR

    Better to start moving basic infrastructure to higher levels NOW.

    John

  3. Neville

    4 April, 2013

    This comment from Dr Andrew Glisnock makes no sense and as
    John says removing residents to safe ground is the logical solution

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