Given a scenario of global mean radiative forcing, the next step is to compute the resultant transient (time-varying) climatic change. This depends on both the climate sensitivity and on the rate of absorption of heat by the oceans. For the projections of global mean temperature (and sea level) change resulting from the IS92 emissions scenarios presented in SAR WGI (Section 6.3 and 7.5.2), a variant of the one-dimensional upwellingdiffusion model (described in Section 3.1) was used. This variant consists essentially of two one-dimensional upwellingdiffusion models strapped together, one for the northern hemisphere (NH) and one for the southern hemisphere (SH). and distinguishes between land and sea. It is illustrated in Figure 9. The original version of this variant is described in Wigley and Raper (1993), although it had been modified for the SAR WGI to include different climate sensitivities for land and ocean and a variable upwelling rate (see Raper and Cubasch, 1996 and SAR WGI: Section 6.3.1). A limited number of sea level cases was also presented (in SAR WGI: Section 7.5.3) using the two-dimensional ocean and one-dimensional atmospheric model of de Wolde, et al., (1995) and Bintanja (1995). which was also introduced in Section 3.1.

There are four key parameters in the upwelling-diffusion model (and the variant shown in Figure 9): (a) the infrared radiative damping factor, which governs the change in infrared emission to space with temperature. This factor includes the effect of feedbacks involving water vapour, atmospheric temperature structure, and clouds, which are explicitly computed in more

UPWELLING

Figure 9. Illustration of a variant of the one-dimensional upwellingdiffusion model having separate land and sea boxes within each hemisphere, and separate polar sinking and upwelling in each hemisphere. This variant was used in the SAR WGI (Section 6.3 and 7.5.2).

complex models. Because the infrared radiative damping to space is a key determinant of climate sensitivity, the model climate sensitivity can be readily altered - to match observational constraints or the results of other models - by changing the value of this factor; (b) the intensity of the thermohaline circulation, which consists of water sinking in polar regions (at a temperature which is prescribed in the model) and upwelling throughout the rest of the ocean; (c) the strength of vertical ocean mixing by turbulent eddies, which is represented as a diffusion process; and (d) the ratio of warming in the polar regions (which are not explicitly represented in the model) to the global mean surface layer warming, which determines the change in temperature of water in the sinking branch of the thermohaline circulation.

The other model used in the SAR WGI for climatic change projections (other than coupled AOGCMs) is the atmosphereocean climate model of de Wolde, et al., (1995) and Bintanja (1995). The oceanic part of this model is a two-dimensional upwelling diffusion model, in that it contains both vertical heat diffusion and the thermohaline overturning (as in the onedimensional upwelling-diffusion model). This model has horizontal resolution and includes parametrizations of northsouth heat transport, as well as simple representations of sea ice and land snow cover. The ratio of polar to global mean surface warming is not directly specified in this model, but is determined by changes in north-south heat transport, ice and snow distribution, and vertical heat fluxes. The climate sensitivity also is not directly specified, but arises from the interaction of a number of different model processes. As in the one-dimensional upwelling-diffusion model, the intensity of the ocean thermohaline overturning and the value of the vertical diffusion coefficient must be directly specified.

Diffusive mixing produces a downward heat flux (from the warm surface to cooler sub-surface water). The thermohaline

overturning, in contrast, produces an upward heat flux because it entails sinking of cold polar water and the upwelling of less cold water elsewhere. This shall be referred to here as the advective heat flux. In steady state, the net heat flux between the surface and deep ocean is zero (that is, the diffusive and advective heat fluxes exactly cancel).

As the surface and atmosphere warm in response to a radiative heating perturbation, the downward diffusive heat flux increases, which tends to slow down the subsequent rate of surface warming. The upward advective heat flux can increase or decrease as the climate warms, depending on the rate of warming of the downwelling source water in polar regions relative to the global mean surface layer and on changes in the sinking flux/upwelling velocity. The greater the specified (or computed) polar warming relative to the mean warming, the slower the mean surface temperature response to a heating perturbation. Similarly, variations in the upwelling velocity as a function of time or as a function of surface warming can be imposed in both the one-dimensional and two-dimensional upwelling-diffusion models, based on the variation in upwelling observed in coupled AOGCM experiments. A reduction in the upwelling velocity in response to surface warming tends to slow the surface temperature response, since this reduces the net heat flux toward the surface layer. Conversely. a strengthening of the thermohaline overturning will accelerate the surface temperature response, and can even cause a temporary overshoot of the equilibrium response (see Harvey and Schneider, 1985; and Harvey, 1994).

A third, minor, feedback that can be imposed in both the onedimensional and two-dimensional upwelling-diffusion models is between the vertical diffusion coefficient and the vertical temperature gradient. It is expected that an increase in the temperature gradient (associated with greater initial warming at the surface) will lead to a weaker diffusion coefficient, which in turn will permit a slightly faster surface warming. However, this feedback was not included for the SAR WGI projections; rather, the diffusion coefficient is assumed to be constant both in the vertical and with time.

It should be stressed that neither alteration in the polar/global mean surface warming ratio in the one-dimensional upwellingdiffusion model, nor feedback between surface temperature and the thermohaline overturning or vertical diffusion coefficient, has any effect on the steady-state surface temperature response to an external forcing change. This is because, in steady state, there is no net heat flux to or from the deep ocean, and the global mean surface-atmosphere steady-state temperature

6 In the case of the two-dimensional upwelling diffusion model, the global mean temperature response will depend slightly on the imposed variation in the thermohaline overtuning. since such changes will modify the north-south heat transport and lead to somewhat different changes in the amount of ice and snow than if the thermohaline overturning is held fixed.

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response is governed by radiative damping to space. However, these three factors do strongly influence the rate of approach to steady state, as noted above. Furthermore, each of these factors strongly influences the steady-state deep ocean temperature. Thus, the greater the polar sea warming, the greater the mean deep ocean warming. An increase in thermohaline overturning intensity results in a smaller deep ocean warming, while a reduction in overturning intensity leads to greater deep ocean warming. Finally, a reduction in the vertical diffusion coefficient will lead to smaller deep ocean warming. These differences in deep ocean warming can lead to dramatic differences in the thermal expansion component of global mean sea level rise associated with a given surface warming (see also Section 5).

It is assumed in both models that the global mean temperature response to a radiative forcing perturbation depends only on the global mean value of the perturbation, and that the climate sensitivity is the same irrespective of the magnitude or direction of the radiative forcing. As discussed in Section 2.3.4, the dependence of climate sensitivity on the magnitude, direction, and nature of the forcing is thought to be small, in most cases, compared to the underlying uncertainty in the sensitivity itself (a factor of three).

The two most important uncertainties in projections of future global mean temperature change are the climate sensitivity and the aerosol forcing, which partly offsets the heating due to increasing greenhouse gas concentrations. Figures 10a and b (SAR WGI: Figure 8.4) illustrate the impact of alternative assumptions concerning climate sensitivity and aerosol forcing, as computed using a one-dimensional upwelling-diffusion model. Comparison with Figure 10c shows that solar variability may also be an important contributor to past observed global mean changes, and its incorporation improves the agreement between model and global mean observations. The effect of uncertainties in the climate sensitivity and aerosol forcing for future climatic change is illustrated in Figure 11 for the central IPCC (1992) emission scenario, IS92a. The figure shows temperature changes over 1990 to 2100 for climate sensitivities of 1.5, 2.5 and 4.5°C, for the changing aerosol (full lines) and constant aerosol (dashed lines) cases. The central sensitivity value gives a warming of 2.0°C (changing aerosols) to 2.4°C (constant aerosols). The range in warming due to uncertainty in the climate sensitivity is large, and aerosol-related uncertainties are larger for higher sensitivities.

Consistency Between Biogeochemical and Energy Balance Model Components

An ideal, fully integrated model, at any level of complexity, should have both chemical (e.g., CO2) and climate (e.g., temperature, sea level) outputs that are derived simultaneously using the same physics, where appropriate. At the simple model level, consistency between the carbon cycle and energy balance components requires, as a minimum, that

The thermal expansion component of sea level rise is computed from the variation of globally-averaged ocean temperature change with depth. The most important model parameter controlling thermal expansion over the next one hundred years is the climate model sensitivity, which strongly influences the heat flux into the ocean. The ratio of polar to mean surface layer warming and the change in the thermohaline overturning intensity are also important to sea level rise, as discussed in Section 4.2, particularly on longer time-scales. For the one-dimensional model calculations presented in the SAR WGI, it was assumed that the polar source regions for downwelling water warm by 20 per cent of the global mean surface layer warming, and that the thermohaline overturning weakens slightly as the climate warms (as in some coupled AOGCMs). The resultant thermal expansion component of sea level rise, associated with the surface temperature response curves of Figure 11 with changing aerosols, is 20, 28 and 40 cm for climate model sensitivities of 1.5, 2.5 and 4.5°C, respectively.

For the calculation of the land-based ice contribution to sea level rise, the ice masses were divided into three groups: the glaciers and ice-caps, the Greenland ice sheet, and the Antarctic

ice sheet.

For the glaciers and ice-caps, a simple model which relates glacier volume to temperature change was used (Wigley and Raper, 1995). There are three important parameters in this model: (a) the initial (1880) global ice volume, which was assumed to be 30 cm sea level equivalent; (b) the minimum temperature increase which, if it were maintained, would cause a given glacier to eventually disappear, and (c) the glacier response time. Because there is a distribution of critical temperature warmings and glacier response times in nature, a distribution of minimum temperature increases required for disappearance of a glacier, and of glacier response times, is assumed in the calculations. As the simulated global mean temperature increases, greater melting of glaciers within the model distribution occurs. The ranges of glacier response times and warmings required for eventual disappearance of small glaciers are themselves uncertain, so different sets of assumptions have been adopted and are listed in Appendix 3. The assumptions listed as "high" in Appendix 3 will give a

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relatively large contribution to sea level rise, while those listed as “low” will give a relatively small contribution to sea level rise.

The assumed initial glacier and ice-cap volume is important because it sets an upper limit to the sea level rise from this source. However, the correct value of this parameter is controversial; a value of 50±10 cm is given in Table 7.1 of the SAR WGI. The difference between this range and the value adopted for the SCM sea level projections (30 cm) reflects the difficulty in estimating this parameter. The initial ice volume and other parameter values were chosen so as to match, as the central value, the estimated contribution to sea level rise during the period 1900-1961 of 1.6 cm sea level, equivalent. Estimates of the past contribution to sea level rise of glaciers and ice-caps based on direct observations over the last century are uncertain by a factor of two. There are many reasons for this uncertainty, including: (a) different time periods used in the analysis; (b) differences in the total estimated glacier areas; (c) incomplete climatic data from the glaciated regions; (d) crude approximations to dynamic feedbacks; and (e) neglect of refreezing of meltwater and of iceberg calving. The central value used bere of 1.6 cm sea level equivalent over 1900-1961 is at the low end of the range of the estimates of 0.35 mm/yr with uncertainty of at least ± 0.1 mm/yr, over 1890-1990, given in the SAR WGI (Section 7.3.2.2). The estimated contribution of glaciers and ice-caps to sea level rise for 1990 to 2100, when climate sensitivities of 1.5, 2.5 and 4.5°C are combined with the low, medium, and high ice parameters of Appendix 3, respectively, are 7, 16 and 25 cm, respectively (again using the temperature response curves of Figure 11 with changing aerosols).

The response time of the Greenland and Antarctic ice sheets is long compared to the time-scale considered here, so, for simplicity, the areas of the ice sheets are assumed to be constant and effects related to ice flow are neglected. However, the uncertainties even in the present mass balance of the ice sheets are large. The SAR WGI (Section 7.3.3.2) concludes that an imbalance between accumulation and losses of the ice sheets of up to 25 per cent cannot be detected by current methods using currently available data.

For modelling purposes, the mass balance of both ice sheets is divided into two components (Wigley and Raper, 1993). The first represents the gain or loss of ice due to the initial state of the ice sheet, and has units mm/yr sea level rise. If the ice sheet was initially in equilibrium with the climate in 1880 (the initial time), this component would be zero, but if it was not in equilibrium but still reacting to a previous temperature change, then it would be non-zero. This component is denoted by the symbol ABO in Appendix 3, where the values used for the low, medium, and high sea level rise cases are given.

The second component is assumed to be linearly dependent on the temperature change relative to the initial state, and has units mm/yr/C sea level rise. The values used are given in Appendix 3 and are based on estimates of the sensitivity of the ice sheets to a 1'C climatic warming as computed by the