1. Introduction

There is evidence from observations and models that sea level has risen during the last 100 years due to the increase in global mean air temperature (see IPCC 1996, chapter 7 for a review). Future warming is expected to cause an increase in sea level of 0.2 to 0.86 m by the year 2100, with a “best guess” of 0.49 m. The main factors contributing to changes in sea level are changes related to oceanic thermal expansion, glaciers and small ice caps, the large ice sheets of Greenland and Antarctica, and possible changes in ground-water storage. More than half of the projected sea level rise (0.28 of 0.49 m in the year 2100) is expected to be due to oceanic thermal expansion (IPCC 1996). Here we investigate changes in sea level due to this thermal expansion component of global sea level rise and the uncertainties associated with potential circulation changes.

Several types of models have been employed for estimates of ocean thermal expansion, from simple 1D upwelling diffusion energy balance models (Raper et al. 1996), 2D zonally averaged energy balance models (de Wolde et al. 1995, 1997), or the subduction model of Church et al. (1991) to complex 3D atmosphere–ocean GCMs (e.g., Mikolajewicz et al. 1990). Using new parameterizations of the subgrid-scale ocean mixing processes (Redi 1982; Gent and McWilliams 1990), some models simulate reduced convection, improved stratification, and changes in the Southern Ocean overturning circulation, leading to a reduced ocean heat uptake in global warming scenarios (e.g., Hirst et al. 1996; Power and Hirst 1997; Wiebe and Weaver 1999). In a recent study, Weaver and Wiebe (1999) suggest that, based on horizontal diffusion parameterizations, previous Intergovernmental Panel on Climate Change projections of long-term changes in sea level may overestimate the thermal expansion component. They find equilibrium steric sea level rise to be more than two times lower when using more realistic parameterizations for subgrid-scale ocean mixing.

The aim of this paper is to present new results from a zonally averaged coupled ocean–atmosphere model to show how changes in sea level are linked to changes in the atmospheric temperature, to the thermohaline circulation, and to ocean mixing parameterizations. Focussing on the equilibrium changes in sea level due to global warming, we find simple dependences that give a consistent view of our results and the results of Weaver and Wiebe (1999).

2. Model description

We use the zonally averaged three-basin ocean model of Wright and Stocker (1991), with the closure scheme described by Wright et al. (1998). The ocean model consists of three rectangular basins representing the Atlantic, Pacific, and Indian Oceans, connected by an Antarctic circumpolar basin, the Southern Ocean. The geometry is identical to that used by Stocker and Wright (1996). The ocean model is coupled to a one-dimensional, zonally and vertically averaged energy balance model of the atmosphere (Stocker et al. 1992) including an active hydrological cycle (Schmittner and Stocker 1999). The three different subgrid-scale ocean mixing parameterizations used are the same as those described in detail in Knutti et al. (2000). Briefly, we use the version HOR with the traditional horizontal–vertical diffusion scheme (horizontal diffusivity K_H = 1000 m² s⁻¹, constant vertical diffusivity K_V = 5 × 10⁻⁵ m² s⁻¹), the version ISO with an isopycnal diffusion scheme (isopycnal diffusivity K_I = 1000 m² s⁻¹, diapycnal diffusivity K_D = 5 × 10⁻⁵ m² s⁻¹), and the model version GM, which is identical to ISO but with an additional eddy-induced advection (Gent and McWilliams 1990) (Gent–McWilliams parameter κ = 500 m² s⁻¹). The model configuration, all parameters, and the spinup of the model as well as the simulation of the global warming scenarios are identical to those described in detail by Knutti et al. (2000). For the global warming scenarios we assume an exponential increase in atmospheric CO₂, corresponding to a linear increase in the radiative forcing. Once double preindustrial CO₂ concentration (560 ppm) is reached, CO₂ is kept constant and the model is integrated until an equilibrium state is reached (usually 5000 yr). Changes in global mean sea level due to thermal expansion are calculated from the changes in the in situ density distribution (Gregory 1993).

3. Results

Next we investigate the values and sensitivities of the two parameters c and ζ. The additional contribution c is determined by the transition of the thermohaline circulation between different steady states. For the results in Fig. 2, we obtain c = 0.45 m (HOR, filled triangles pointing up) and c = 0.63 m (GM, filled circles) for the transition from NADW formation to shallow NPDW formation. An interesting result is obtained when we start with the steady state of the model and apply a freshwater pulse in the North Atlantic to enforce a collapse of the Atlantic circulation. Although no atmospheric warming occurs, an increase in sea level of c = 0.55 m (HOR) and c = 0.74 m (GM) is observed, consistent with the results for the global warming experiments. The additional increase in sea level, c, is mainly due to the increased ocean heat uptake in the case of an NADW formation collapse due to a temporary reduced surface temperature and therefore reduced emission of longwave radiation. Less than 10% of the additional sea level rise is caused by the nonlinear dependence of density on temperature and salinity; in the case of an NADW formation collapse, we observe a warming mainly in the upper 1000 m of the Atlantic. As the thermal expansion coefficient α = −ρ⁻¹∂ρ/∂T is larger for higher temperatures, this leads to considerable expansion in the upper Atlantic.

Parameter ζ characterizes the sensitivity of global mean sea level in a specific model version to changes in atmospheric mean temperature. We believe this to be one of the most important quantities when comparing changes in sea level in different model versions. Note that we now compare sea level sensitivities of different model spinups, differing in either ocean mixing parameterizations or parameter settings. In Fig. 3, we compare ζ for the different ocean mixing parameterizations by plotting ζ versus the Atlantic overturning of the corresponding spinup steady state. The three ocean mixing versions HOR, ISO, and GM obtained with standard parameter settings are marked with circles. To test the robustness of our result, we calculated ζ for the same mixing parameterizations, but with ocean parameters used in previous studies (Schmittner and Stocker 1999) (squares). In both cases, a strong dependence of ζ on the strength of the thermohaline circulation is observed. These results indicate that an enhanced thermohaline circulation leads to higher values of ζ because of a stronger coupling of the atmosphere and surface ocean to the deep ocean and to a more effective transport of excess heat to the deep ocean, which results in higher sea level rise.

Rather small differences in steric sea level rise between the different ocean mixing parameterizations are found in our global warming simulations. Our results are seemingly inconsistent with those of Weaver and Wiebe (1999, hereafter WW), who observe that sea level rise in a 2 × CO₂ scenario is two times lower when using more realistic Gent–McWilliams mixing (WW–GM hereafter) or HBL mixing (notation as in WW: variable vertical diffusivity, WW–HBL hereafter) parameterizations instead of the classic horizontal–vertical diffusion parameterization (constant vertical diffusivity K_V = 10⁻⁴ m² s⁻¹, WW–H hereafter). However, a consistent picture is obtained when we estimate ζ for the experiments of WW (note that ζ is determined from one single experiment) and compare them with our results (see Fig. 3). Their values for ζ differ by about a factor of 2 for the different mixing versions, but there are large differences in the Atlantic thermohaline circulation as well. For the WW–HBL and WW–GM versions, they observe an Atlantic overturning of only 13 Sv compared to 24 Sv in the WW–H version. An extrapolation of our results in Fig. 3 is in agreement with the low ζ values WW find for their GM and HBL versions. We conclude from these results that the sensitivity of sea level to changes in atmospheric temperature for a particular model version is not necessarily affected by the mixing parameterization that is used, but it may be predominantly determined by the strength of the thermohaline circulation. There is, however, a strong relation of the Atlantic overturning strength to the way ocean mixing is parameterized and to various parameters used in these mixing schemes (e.g., vertical or diapycnal diffusivity, Gent–McWilliams parameter) (Knutti et al. 2000).

4. Summary and discussion

We have shown in a series of model experiments that sea level rise from thermal expansion in global warming scenarios is affected by the thermohaline circulation in two different ways. First, equilibrium sea level rise depends linearly on the atmospheric temperature increase with the slope ζ related to the strength of the circulation. The values for ζ estimated in different studies cover a large range from about 0.2 to 0.5 m K⁻¹, with the average of our model results indicating a best estimate of about 0.3 m K⁻¹ (see Fig. 3). Second, our experiments suggest that a permanent reorganization of the thermohaline circulation pattern could lead to a comparatively large additional contribution to sea level rise of order 0.5 m. Furthermore, we have confirmed previous studies that showed that changes in sea level depend on the way subgrid-scale mixing processes in the ocean are parameterized. However, quantitative results in our experiments are different from those of WW. We suggest that if their GM and H versions had similar Atlantic overturning, differences in projected sea level rise could be significantly smaller. Our results indicate that the equilibrium sensitivity of global mean sea level to atmospheric temperature changes is indirectly affected by the mixing parameterization via the strength of the thermohaline circulation, with a stronger circulation leading to higher sea level rise for the same warming scenario. A precise picture of the modern thermohaline circulation pattern and of expected circulation changes in the future is therefore crucial to reduce the uncertainty in projected sea level rise.