## Thermal expansion of the oceans

A large component of sea level rise is due to thermal expansion of the oceans. Calculation of the precise amount of expansion is complex because it depends critically on the water temperature. For cold water the expansion for a given change of temperature is small. The maximum density of sea water occurs at temperatures close to 0 °C; for a small temperature rise at a temperature close to 0 °C, therefore, the expansion is negligible. At 5 °C (a typical temperature at high latitudes), a rise of 1 °C causes an increase of water volume of about 1 part in 10 000 and at 25 °C (typical of tropical latitudes) the same temperature rise of 1 °C increases the volume by about 3 parts in 10 000. For instance, if the top 100 m of ocean (which is approximately the depth of what is called the mixed layer) was at 25 °C, a rise to 26 °C would increase its depth by about 3 cm.

A further complication is that not all the ocean changes temperature at the same rate. The mixed layer fairly rapidly comes into equilibrium with changes induced by changes in the atmosphere. The rest of the ocean changes comparatively slowly (the whole of the top kilometre will, for instance, take many decades to warm); some parts may not change at all. Therefore, to calculate the sea level rise due to thermal expansion - its global average and its regional variations - it is necessary to employ the results of an ocean climate model, of the kind described in Chapter 5.5

Figure 7.1 Estimates for 1961-2003 (blue) and 1993-2003 (pink) of contributions to global mean sea level change (upper four entries), the sum of these contributions and the observed rate of rise (middle two) and the difference between the observed rate and the estimates (lower). The bars represent a range of uncertainty of 90% probability. Errors of the separate terms have been combined in quadrature to obtain the error on their sum.

Thermal expansion

Glaciers and ice caps m dl

Greenland

Antarctica

Observations

Difference (Obs-Sum)

Rate of sea level rise (mm yr-1)

relative to 1980-99 of 0.21-0.48 m. Apart from a smaller uncertainty range this shows little change from the 0.12-0.7 m range for the A1B scenario given in the IPCC 2001 Report. The overall range covering the six SRES marker scenarios is from 0.18 to 0.59 m. The largest contribution to sea level rise (0.13-0.32 m for A1B) is expected to continue to be from thermal expansion of ocean water

Sea-ice is frozen sea water floating on the surface of the ocean. Some sea-ice is semi-permanent, persisting from year to year, and some is seasonal, melting and refreezing from season to season. The sea-ice cover reaches its minimum extent at the end of each summer and the remaining ice is called the perennial ice cover. The 2007 Arctic summer sea-ice (white) reached the lowest extent of perennial ice cover on record - nearly 25% less than the previous lowest in 2005 (orange). The average minimum sea-ice from 1979 to 2007 is shown in green. The area of perennial ice has been steadily decreasing since the satellite record began in 1979, at a rate of about 10% per decade. Such a dramatic loss has implications for ecology, climate and industry. The 2008 sea-ice extent was even less than that of 2007. With this increasingly rapid rate of change, it is possible that Arctic summer sea-ice could reduce to zero by 2020.

calculated in detail from the ocean component of climate models. The second largest (0.08-0.16 m for A1B) is expected from the melting of glaciers and ice caps outside Greenland and Antarctica. It is derived from estimates of their mass balance - the difference between the amount of snowfall on them (mainly in winter) and melting (mainly in summer); both winter snowfall and average summer temperature are critical and have to be carefully estimated using climate models.

Figure 7.2 Global mean sea level in the past and as projected for the future. From 1870 is a reconstruction of the global mean from tide gauges; the green line is global mean sea level as observed from satellite altimetry. Beyond 2004 is the range of model projections (the 5% to 95% uncertainty range) for the SRES A1B scenario for the twenty-first century relative to the 1980-99 mean from the sum of estimates of the different contributions (major ones identified in Figure 7.1). 1800 1850 1900 1950 2000 2050 2100

Year

The third largest contribution is expected from changes in the Antarctic and Greenland ice-sheets. It is perhaps surprising that the net contribution from them over the twentieth century is small and is still not large (Figure 7.1). For both icesheets there are two competing effects. In a warmer world, there is more water vapour in the atmosphere which leads to more snowfall. But as surface temperature increases, especially at high latitudes, there is also more ablation (erosion by melting) of the ice around the boundaries of the ice-sheets where melting of the ice and calving of icebergs occur during the summer months. During the last few decades, both ice-sheets have been close to balance (Figure 7.1). For the twenty-first century, the IPCC AR4 2007 projects that Antarctica will continue close to balance but that for Greenland, ablation will be greater than accumulation leading to a net loss amounting to less than 0.1 m by the end of the century.

During the last year, many pictures have been published of rapid ice melting and discharge from the Greenland ice cap and concern expressed that the rate of melting could accelerate substantially as the warming progresses. This possibility was recognised in IPCC AR4 where it was pointed out that if ice flow from Greenland increased linearly with temperature rise the upper range of sea level rise in 2100 (Figure 7.2) would increase by 0.1 to 0.2 m. However, the rate of increase may accelerate more rapidly. Four indications of this, the first two suggested by P. Christoffersen and M.J. Hambrey6 and the last two by J. Hansen and his co-authors,7 are:

(1) Observations from satellite radar altimeters show that the total ice-mass loss from the Greenland ice cap rose from 90 km3 in 1996 to 140 km3 in 2000 and 220 km3 in 2005. Similar losses have been observed from the West

Estimates of the past

Instrumental record

Projections of the future

Projections of the future

Antarctic ice-sheet. A loss of 400 km3 per year transfers into a global sea level rise of about 1 mm per year or 0.1 m per century.

(2) Observations of acceleration in the movement of coastal outlet glaciers to now more than 10 km per year. Similar losses and movement are occurring with the West Antarctic ice-sheet.

(3) Observations of increased melt water, from the operation of the ice-albedo feedback (see Chapter 5, page 114), penetrating to the bed of the ice-sheet and through its lubrication enhancing ice motion and instabilities near the ice-sheet base.

(4) Palaeo evidence of periods of rapid melting with associated global sea level rise of up to several metres per century occurring for instance during the recovery from the last ice age about 14 000 years ago.

The possibility of acceleration due to these non-linear processes was acknowledged by IPCC, AR4 although they did not feel able to provide any quantification of their likely size. A careful assessment published in Science8 as this book is going to press concludes with a best estimate, including accelerated conditions of ice melt, of 0.8 m total sea level rise by 2100. It also concludes that a rise of up to 2 m by 2100 'could occur under physically possible glaciological conditions but only if all variables are quickly accelerated to extremely high limits'. Improved quantification should be possible as new satellite data (e.g. from the GRACE gravity mission) is obtained and interpreted.9

If we look into the future beyond the twenty-first century, as temperatures around Greenland rise more than 3 °C above their pre-industrial level, model studies show that meltdown of the ice cap will begin; its complete melting will cause a sea level rise of about 7 m. The time taken for meltdown to occur will depend on the amount of temperature rise; estimates for the time to 50% meltdown vary from a few centuries to more than a millennium.

The portion of the Antarctic ice-sheet that is of most concern is that in the west of Antarctica (around 90° W longitude); its disintegration would result in about a 5-m sea level rise. Because a large portion of it is grounded well below sea level it has been suggested that rapid ice discharge could occur if the surrounding ice shelves are weakened. From studies so far of ice dynamics and flow there is no agreement that rapid disintegration is likely although, as with Greenland, it is recognised that the possibility exists.

The projections in Figure 7.2 apply to the next 100 years. During that period, because of the slow mixing that occurs throughout much of the oceans, only a small part of the ocean will have warmed significantly. Sea level rise resulting from global warming will therefore lag behind temperature change at the surface. During the following centuries, as the rest of the oceans gradually warm, sea level will continue to rise at about the same rate, even if the average temperature at the surface were to be stabilised.

The estimates of average sea level rise in Figure 7.2 provide a general guide as to what can be expected during the twenty-first century. Sea level rise, however, will not be uniform over the globe.10 The effects of thermal expansion in the oceans varies considerably with location. Further, movements of the land occurring for natural reasons due, for instance, to tectonic movements or because of human activities (for instance, the removal of groundwater) can have comparable effects to the rate of sea level rise arising from global warming. At any given place, all these factors have to be taken into account in determining the likely value of future sea level rise.

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### Responses

• maia
How does thermal expansion work in the ocean?
6 months ago
• louis
How would thermal expansion of water in the oceans affect the planet?
5 months ago
• Tancredi
How thermal expansion of oceans effect climate change?
2 months ago