Climate Change 2001:
Working Group I: The Scientific Basis
Other reports in this collection Models of thermal expansion

Figure 11.1:
Global average sea level changes from thermal expansion simulated in AOGCM experiments with historical concentrations of greenhouse gases in the 20th century, then following the IS92a scenario for the 21st century, including the direct effect of sulphate aerosols.
See Tables 8.1 and 9.1 for further details of models and experiments

A variety of ocean models have been employed for estimates of ocean thermal expansion. The simplest and most frequently quoted is the one-dimensional (depth) upwelling-diffusion (UD) model (Hoffert et al., 1980; Wigley and Raper, 1987, 1992, 1993; Schlesinger and Jiang, 1990; Raper et al., 1996), which represents the variation of temperature with depth. Kattenberg et al. (1996) demonstated that results from the GFDL AOGCM could be reproduced by the UD model of Raper et al. (1996). Using this model, the best estimate of thermal expansion from 1880 to 1990 was 43 mm (with a range of 31 to 57 mm) (Warrick et al., 1996). Raper and Cubasch (1996) and Raper et al. (2001) discuss ways in which the UD model requires modification to reproduce the results of other AOGCMs. The latter work shows that a UD model of the type used in the SAR may be inadequate to represent heat uptake into the deep ocean on the time-scale of centuries. De Wolde et al. (1995, 1997) developed a two dimensional (latitude-depth, zonally averaged) ocean model, with similar physics to the UD model. Their best estimate of ocean thermal expansion in a model forced by observed sea surface temperatures over the last 100 years was 35 mm (with a range of 22 to 51 mm). Church et al. (1991) developed a subduction model in which heat is carried into the ocean interior through an advective process, which they argued better represented the oceans with movement of water along density surfaces and little vertical mixing. Jackett et al. (2000) developed this model further and tuned it by comparison with an AOGCM, obtaining an estimate of 50 mm of thermal expansion over the last 100 years.


The advantage of these simple models is that they require less computing power than AOGCMs and so the sensitivity of results to a range of uncertainties can easily be examined. However, the simplifications imply that important processes controlling the penetration of heat from the surface into the ocean interior are not reproduced and they cannot provide information on the regional distribution of sea level rise. The most satisfactory way of estimating ocean thermal expansion is through the use of AOGCMs (Chapter 8, Section 8.3) (Gregory, 1993; Cubasch et al., 1994; Bryan, 1996; Jackett et al., 2000; Russell et al., 2000; Gregory and Lowe, 2000). Improvements over the last decade relate particularly to the representation of the effect on mixing by processes which operate on scales too small to be resolved in global models, but which may have an important influence on heat uptake (see Section The geographical distribution of sea level change due to density and circulation changes can be obtained from AOGCM results (various methods are used; see Gregory et al., 2001). The ability of AOGCMs to simulate decadal variability in the ocean interior has not yet been demonstrated adequately, partly because of the scarcity of observations of decadal variability in the ocean for testing these models. This is not only an issue of evaluation of model performance; it is also relevant for deciding whether observed trends in sea level and interior ocean temperatures represent a change which is significantly larger than the natural internal variability of the climate system.

Table 11.2: Rate and acceleration of global-average sea level rise due to thermal expansion during the 20th century from AOGCM experiments with historical concentrations of greenhouse gases, including the direct effect of sulphate aerosols. See Tables 8.1 and 9.1 for further details of models and experiments. The rates are means over the periods indicated, while a quadratic fit is used to obtain the acceleration, assumed constant. Under this assumption, the rates apply to the midpoints (1950 and 1975) of the periods. Since the midpoints are 25 years apart, the difference between the rates is 25 times the acceleration. This relation is not exact because of interannual variability and non-constant acceleration.
Rate of sea level rise
1910a to 1990b
1960 to 1990b
1910a to 1990b
0.7 0.2
0.5 0.3
1.1 0.2
CSM 1.3 GS
1.2 0.3
1.0 0.5
1.4 0.4
1.1 0.3
1.2 0.3
0.8 0.2
1.3 0.4
0.8 0.4
a The choice of 1910 (rather than 1900) is made to accommodate the start date of some of the model integrations.
b The choice of 1990 (rather than 2000) is made because observational estimates referred to here do not generally include much data from the 1990s.

A number of model simulations of the 20th century (Table 9.1) have recently been completed using realistic greenhouse gas and aerosol forcings. Results for global average thermal expansion over periods during the 20th century are given in Figure 11.1 and Table 11.2. They suggest that over the last hundred years the average rate of sea level rise due to thermal expansion was of the order of 0.3 to 0.7 mm/yr, a range which encompasses the simple model estimates, rising to 0.6 to 1.1 mm/yr in recent decades, similar to the observational estimates (Section

Table 11.3: Some physical characteristics of ice on Earth.
  Glaciers Ice caps Glaciers and ice capsa Greenland ice sheetb Antarctic ice sheetb
Number >160 000 70      
Area (106 km2) 0.43 0.24 0.68 1.71 12.37
Volume (106 km3) 0.08 0.10 0.18 0.04 2.85 25.71
Sea-level rise equivalentd 0.24 0.27 0.50 0.10 7.2c 61.1c
Accumulation (sea-level equivalent, mm/yr)d     1.9 0.3 1.4 0.1 5.1 0.2
Data sources: Meier and Bahr (1996), Warrick et al. (1996), Reeh et al. (1999), Huybrechts et al. (2000), Tables 11.5 and 11.6.
a Including glaciers and ice caps on the margins of Greenland and the Antarctic Peninsula, which have a total area of 0.14 x 106 km2 (Weideck and Morris, 1996). The total area of glaciers and ice-caps outside Greenland and Antarctica is 0.54 x 106 km2 (Dyurgerov and Meier, 1997a). The glaciers and ice caps of Greenland and Antarctica are included again in the next two columns.
b Grounded ice only, including glaciers and small ice caps.
c For the ice sheets, sea level rise equivalent is calculated with allowance for isostatic rebound and sea water replacing grounded ice, and this therefore is less than the sea level equivalent of the ice volume.
d Assuming an oceanic area of 3.62 x 108 km2.

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