Sea Level Changes: Determination and Effects
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For example, sea level in the North Atlantic is believed to have risen by 3 cm between and , with much of the increase occurring over a few months Figure 7.
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The geophysical processes considered here include post-glacial-rebound for the entire globe: North America, Scandinavia, Greenland, and Antarctica; and assuming a lower-mantle viscosity of E21 Pa-sec ; present-day changes in Antarctic and Greenland ice, at a level to cause a global sea-level change of 1. Carton and Miller, Figure B.
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For identifying the causes of such basin-scale anomalies, a vitally needed piece of information is the relative contribution of thermal expansion compared with an overall increase in mass. Thus again, satellite measurements of the increase in mass would be invaluable in sorting out the causes of sea-level rise. The masses of glaciers, ice caps, and ice sheets the term ''ice sheet" is reserved for the vast ice covers of Antarctica and Greenland vary temporally through the exchange of water with the oceans.
These ice bodies on land can shrink in two ways—by excess melting and liquid water runoff and by breaking off as icebergs. In either case the mass lost soon reaches the ocean. Thus, the measurement of the total mass balance deviation from constant mass through time of the ice on land is a direct, though partial, measure of the changes of water mass in the oceans. There are two important advantages of gravity measurements for large-scale mass-balance studies. The first is that, since gravity depends simply on mass, changes in gravity provide a direct measure of ice-mass balance that is independent of changes in the mean density of the ice bodies, which can change with time.
Secondly, gravity serves as an automatic integrating tool, thus obviating the huge difficulty that glaciologists face in extrapolating results from field studies in a few areas to much larger regions, especially to the entirety of the vast ice sheets. For both these reasons, glaciologists eagerly await future satellite-gravity missions.
Currently, the large-scale mass balances of Greenland and Antarctica are poorly known. Both upper bounds correspond to geoid amplitudes of 2. In the eastern North Atlantic, a warming of sea-surface temperature is reflected in a rise of sea level. These results include the effects of the Earth's elastic response to the changes in ice load, as described in Appendix B. Note that the results rise well above the uncertainties for a 5-year SST mission at values of l below 25 corresponding to half-wavelengths greater than km , and for a 5-year SSI mission at values of l below 40 half-wavelengths greater than km.
Approximating Antarctica and Greenland as squares about km and km on a side, respectively, we estimate from Figure B. The water thickness results from Figure B. A 5-year SSI mission would be about an order of magnitude more sensitive. It is important to note, however, that there are ambiguities in interpreting gravity signals over ice sheets because of problems in separating the effects of ice-sheet changes from the effects of isostatic rebound, interannual variations in snow accumulation rates, and atmospheric pressure.
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These problems are discussed in turn below. It is difficult to distinguish between effects of present-day changes in ice-sheet mass and effects of the Earth's visco-elastic response to changes in ice mass over the past few hundred to several thousand years, particularly in Antarctica. In principle, one could correct for the isostatic uplift by measuring it on exposed rock. Although most of Antarctica is ice-covered, there are many exposures in the extensive Transantarctic Mountains, which cut through the continent from the Atlantic to the Pacific Figure 7.
The problem is, however, that crustal uplift rates measured for the Transantarctic Mountains, which occupy only a small fraction of the total area of Antarctica, would likely not be representative of the average uplift rates for the entire continent. It is thus probable that the best use of such GPS measurements would be to help assess independent models of the rebound, which would then be used to remove the effects at all locations.
Rebound models in their current state of development would not suffice to solve the problem. At first glance, this result suggests that a gravity mission would not improve the global sea-level change estimates of Warrick et al. However, it is likely that a dedicated gravity mission would lead to a solution for secular changes in the gravity field over northern Canada that would greatly improve our knowledge of the Earth's viscosity profile see Chapter 5.
In that case, the main source of uncertainty in the Antarctic visco-elastic change would be the detailed time evolution of the Antarctic ice sheet itself. The level of that uncertainty would depend on the Earth's viscosity profile. If the lower-mantle viscosity is 4. At larger values of lower-mantle viscosity e. Uncertainty estimates this small would indeed lead to improved estimates of the Antarctic contributions to sea-level change, though any such result would be representative of the ice sheet for only the relatively brief duration of the satellite mission. Another interpretation difficulty arises from the consideration of interannual variations in the rate of snow accumulation on the ice-sheet surfaces Figure 7.
The interannual variability in outflow is much less than this because outflow is principally by solid ice discharge into the ocean. Fortunately, this error can be reduced in two ways. Bromwich, personal communication. Furthermore, a substantial portion of the uncertainties would be systematic, i. Note that the s Antarctica and Greenland differ by about a factor of two; Greenland is comparable in size to East Antarctica.
Secondly, the gravity measurements themselves can help determine the interannual variations, at least for the period of the mission. According to our calculation, geoid amplitudes could well vary by 1 mm or more over both Antarctica and Greenland Figure 1. We conclude from Figure B.
For a nominal SSI mission, those numbers are 0. This still would represent a great improvement over current methods of determining changes in snowfall over time. We consider the effect of atmospheric pressure next. Yet another problem arises, particularly in Antarctica, from the fact that the gravity satellite will sense the mass of the atmosphere as well as the masses of the ice sheet and the solid Earth.
The mean atmospheric pressure over the ice sheet which reflects the overlying mass must be determined from a very small number of measuring points; consequently there may be an error as large as 1 mbar about equal to 10 mm of ice or 0.
This could be a relatively static error, however, so it would not notably affect a calculation of secular change rates. There still remains a random-error component, which is on the order of a millibar on annual averages Chen et al.
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Bromwich, personal communication , hence presumably is less than 0. The uncertainties in mean pressures can best be reduced by extending the number of automatic weather stations over the Antarctic surface and assuring that data from them are available and used in mean-pressure calculations. The situation is less serious in Greenland because Greenland is smaller and contains a better distribution of weather stations. Estimates of mass balance could be further improved if the present-day changes in the heights of the ice sheets could be determined separately using laser altimeter measurements from an orbiting satellite—specifically, NASA's planned Laser Altimetry Mission.
For a given mass increase, the surface height changes would be in the ratio of If the cause were atmospheric pressure changes there would be no change in height at all the response of the ice to pressure fluctuations is negligible. It follows that measurements of both change in height and change in gravity should, in principle, make it possible to distinguish between uplift and changes in mass of the ice sheet.
Neither satellite gravity nor satellite laser altimetry has that capability alone—the two types of measurement are strongly complementary. The laser altimeter measurements are subject to most of the same uncertainties about causes as the gravity measurements, but with different sensitivities. Without better knowledge of the isostatic-rebound and snowfall-variation effects, such as could be obtained using satellite gravity, estimates from laser altimetry of the ice sheet contributions to sea level would probably be on the order of 0.
Ice sheets are complex composites of individual drainage systems or basins, some of which are characterized by fast-moving, low-gradient ice streams bordered by slowly flowing ice, some by huge outlet glaciers through peripheral mountain ranges, and some by broad expanses of open sheet flow with only small, local glaciers. Although from a direct societal standpoint the total mass balance of the ice on land is the most relevant quantity to measure, from a glaciological standpoint it is equally important to measure the mass.
A complicating factor is that the dynamic behavior of a particular drainage system may be nearly independent of the dynamic behavior of even its nearest neighbors. The ice sheets are so large that satellite gravity can provide a valuable approach to the study of subdivisions like individual drainage systems as well as entire ice sheets. For example, the mass of ice in the large drainage system that empties into the east side of the Ross Ice Shelf is suspected to have fluctuated dramatically in the past because of unstable dynamic behavior, including a rapid retreat at the end of the last ice age that may even be continuing at present, albeit at a reduced rate.
The determination of secular changes in the masses of this and other large drainage systems would allow models of ice-sheet dynamics to be tested. Unfortunately, the same problems arise with the interpretation of gravity changes over a drainage system as with the interpretation of changes over the encompassing ice sheet as a whole, and the same approaches to alleviating those problems mostly apply. There is a special situation to note with respect to isostatic rebound, however.
Isostatic rebound models, such as those based on the ICE4G model of Peltier , that incorporate the results of analyses of ice-sheet dynamics, show an isostatic rebound rate on the east side of the Ross Ice Shelf in West Antarctica that is much greater than the Antarctic average because of the major modeled ice-sheet retreat there at the end of the last ice age. It is no coincidence that the highest modeled uplift rates are focused on the regions where the greatest likelihood of rapid change from a glaciological perspective exists today—it is the same high glaciological sensitivity of concern today that presumably led to large changes in ice mass in these areas in the past.
Fortunately, the Transantarctic Mountains cut through the regions showing large modeled uplift rates, so GPS surveys in those mountains of the type recommended above would provide an excellent check on the models. Furthermore, because the rates of change that might be attributed to either changing ice mass or isostatic rebound are so large, this region is particularly well suited to testing by comparing results from a gravity satellite with those from a satellite-borne laser altimeter. Satellite gravity could also be used to study secular, interannual, and seasonal changes in the mass balance of ice and snow in regions characterized by a concentration of a large number of glaciers and ice caps.
These systems are important for inferring sea-level change because, even though their masses are much smaller than those of the ice sheets, they are capable of much more rapid response to climate change. Consequently, they may at present be contributing at least as much to sea-level change as the ice sheets cf. Table 7. An example of a large glacial system that could change sufficiently in mass to be detected by a gravity satellite is the system of glaciers that runs from the Kenai Peninsula in southern Alaska down along the Coastal Ranges of the Yukon and British Columbia.
What do we mean by sea level?
This region is characterized by unusually heavy snowfall, particularly in the winter; field observations suggest that the thickness of the glaciers varies annually with an amplitude of about 2. This would produce a geoid signal that varies annually by as much as 20 mm over the region an area equivalent to a square about km on a side Figure 1. For comparison, we estimate from Figure B. For the nominal SSI mission, the accuracy is much better—about 5 mm see Appendix B for a description of how these accuracies were estimated.
Sea Level Changes: Determination and Effects | Geophysical Monograph Series
The secular trend in this system could total about 0. Although this glacier system is likely to have the largest annually-varying signal of any system around the world, there are other large glacier systems that could have comparable secular effects. These estimates for the detection of the seasonal changes in glaciers are somewhat misleading, because there is also a large wintertime snowfall on the surrounding non-glaciated region and there is no good way of knowing what proportion of the seasonal signal to attribute to snow on the glaciers.
A gravity mission would provide the total seasonal signal over the entire glaciated and non-glaciated region, which would help constrain estimates of the seasonal snowfall in the region. Seasonal snow is not a problem on ice sheets because the area of exposed land is so small compared with the area of the ice sheet. The sources of global sea-level rise measured by tide gauges to be between 1. Most of the likely mechanisms involve mass redistribution from the continents to the oceans; gravity measurements can give unique insights through the continual monitoring of geoid changes, not only on global scales, but also on regional and basin scales.
The measurement and interpretation of changes in Greenland and Antarctica is a complex issue, given the complex nature of the phenomena involved: secular changes in ice-sheet mass, post-glacial rebound, interannual variability in snowfall, and the effect of atmospheric pressure trends. When the term "relative" is used, it means change relative to a fixed point in the sediment pile. The term "eustatic" refers to global changes in sea level relative to a fixed point, such as the centre of the earth, for example as a result of melting ice-caps.
The term "steric" refers to global changes in sea level due to thermal expansion and salinity variations. The term "isostatic" refers to changes in the level of the land relative to a fixed point in the earth, possibly due to thermal buoyancy or tectonic effects; it implies no change in the volume of water in the oceans.