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Relative sea-level changes due to ocean bottom pressure changes caused by thermal expansion

Gisela Estermann1,2, Kurt Lambeck1,2 and Herb McQueen1

1 Research School of Earth Sciences, Australian National University, Canberra, ACT 0200, Australia
2 Antarctic Climate & Ecosystems, Cooperative Research Centre, Hobart, Tasmania 7001, Australia


Figure 1.

Ocean thermal expansion does not alter the total global ocean mass but can nevertheless result in relative sea-level changes. The heat uptake by the ocean (in the case of a warming climate) varies locally both horizontally and in depth. In a simplified model the total water column in the deep ocean tends to expand more than in shallow areas (illustrated with arrow 1 in Figure 1). In order to maintain an equipotential surface, water has to flow from the deep ocean to the shallow areas. This redistribution of water (illustrated with arrows 2 in Figure 1) consequently results in a spatial change in ocean bottom pressure. These ocean bottom pressure changes result in relative sea-level changes.

Atmospheric CO2 concentrations and projected global sea-level rise over the period from 1860 to 2200 used here are based on IPCC scenario simulations (see Figure 2 in Landerer et al., 2007). Landerer et al. (2007) calculated ocean bottom pressure changes caused by secular oceanic mass redistribution due to thermal expansion. They developed a numerical model for the mass transfer from deep open water to coastal (shallow) areas. A data set of ocean bottom pressure changes produced by this model has been provided by Felix Landerer. The variations are expressed as changes of mass load in meters of water and are given on an annual basis from 1860 to 2200 on a 1° x 1° grid. Three examples of 10-year averages are shown in Figure 2a. The plots show an increase in intensity of the redistribution of mass particularly from 2000 onwards.

The plots in Figure 2a show the overall transfer of mass from the southern to the northern hemisphere. In particular, the Arctic Ocean shelves experience an above-average increase in mass load. It appears that there is a good correlation between ocean bottom pressure changes and ocean bathymetry. For the IPCC scenario simulations used here, positive loads of up to 0.4 m by the end of the 21st century and 0.8 m by the end of the 22nd century are projected mostly for the Arctic Sea, while the deeper oceans (especially in the southern hemisphere) experience negative loads of -0.2 m and -0.4 m by 2100 and 2200, respectively. These results represent the redistribution of mass assuming a rigid Earth. Hence, the so-called second order relative sea-level changes as a result of the viscoelastic response of the Earth to the redistribution are now calculated. Since only thermal expansion is considered here, no mass is added or taken away from the ocean and the total change in mass over the oceans is zero.

The bottom pressure changes, expressed as water-mass loads, have been implemented in a sea-level program (the calsea program; Johnston 1993a,b; Lambeck et al., 2003). The resulting relative sea-level changes for 10-year averages are shown in Figure 2b. Changes in relative sea level from this source are negligible until the beginning of the 21st century. By the end of the 22nd century, relative sea-level rise reaches a maximum of approximately 60 mm in the Arctic. This value is expressed relative to the mean of the period 1860-1869, which is assumed to be an unperturbed period. As the spatial distribution of relative sea-level changes (Figure 2b) correlates with the spatial distribution of ocean bottom pressure changes (Figure 2a), a rise in second order relative sea level is predicted mostly in coastal areas, in particular in the Arctic Ocean, whereas second order relative sea level falls in deep ocean areas.

Assuming this climate scenario adequately represents future thermal expansion, relative sea-level changes due to the redistribution of water caused by secular ocean mass redistribution are amplified by about 10% due to these ocean bottom pressure changes. While there is a variety of uncertainties in thermal expansion models (e.g. size of the surface warming, the effectiveness of heat uptake by the oceans for a given warming, and the expansion resulting from a given heat uptake; see Section 11.5 in Church et al., 2001), predicted future sea-level changes will have to be increased by 10% to account for the redistribution of ocean water following thermal expansion.

Figure 2. Click to view at full size.

Church, J. A., Gregory, J. M., Huybrechts, P., Kuhn, M., Lambeck, K., Nhuan, M. T., Qin, D., and Woodworth, P. L. (2001). Changes in Sea Level. In Houghton, J. T., Ding, Y., Griggs, D. J., Noguer, M., van der Linden, P. J., Dai, X., and Johnson, C. A., editors, Climate Change 2001: The Scientific Basis. Contribution of Working Group I to the Third Assessment Report of the Intergovernmental Panel on Climate Change, chapter 11. Cambridge University Press, Cambridge, United Kingdom and New York, NY, USA.

Johnston, P. (1993a). Deformation of the earth by surface loads. PhD thesis, The Australian National University, Canberra.

Johnston, P. (1993b). The effect of spatially non-uniform water loads on prediction of sea-level change. Geophysical Journal International, 114, 615-634.

Lambeck, K., Purcell, A., Johnston, P., Nakada, M., and Yokoyama, Y. (2003). Water-load definition in the glacio-hydro-isostatic sea-level equation. Quaternary Science Reviews, 22, 309-318.

Landerer, F. W., Jungclaus, J. H., and Marotzke, J. (2007). Ocean bottom pressure changes lead to a decreasing length-of-day in a warming climate. Geophysical Research Letters, 34 (L06307).