Sea-Level Rise Model (SLRM)

The impacts of global warming on the global sea level are calculated by the Sea-Level Rise Model of IMAGE 2.2 (SLRM). This model was developed for the MAGICC model by Climate Research Unit (in Norwich, UK) and is described in Raper et al. (1996). In this model the total sea-level rise is influenced by thermal expansion of the oceans and by changing the net mass balance of glaciers and ice sheets. The most important ice sheets of Greenland and Antarctica are taken into account in SLRM. The main model input and output are shown in the table below.

Model input	Global temperature of the oceanic layers and global mean surface temperature change since 1880
Model output	Changes in global sea level through thermal expansion of the oceans and contributions of small glaciers, Greenland and Antarctica

1. Sea-level rise caused by thermal expansion of oceans

As the ocean warms, the density of the ocean decreases and its volume increases. The temperature changes in each ocean layer, calculated in UDCM, are used to determine the expansion coefficient. The thermal expansion is determined by the temperature of each ocean layer. The initial vertical temperature profile is based on observations from Levitus (1982). The initial temperature of the oceanic mixed upper layer is assumed to be 17.2 oC while the temperature of deeper ocean layers is assumed to decrease with depth to a temperature of 1.0oC for the bottom layer.

2. Sea-level rise caused by small glaciers melting

Melting of small glaciers may also contribute to sea-level rise. For the small glaciers a simple approach to relate glacier volume to temperature change is used, as described in detail by Wigley and Raper (1995). The three important parameters in this approach are:

• the initial (1880) global ice volume
• the minimum temperature increase that would cause a given glacier to disappear
• the glacier-response time.

A distribution of values for the minimum temperature and glacier response time is assumed to take different glaciers into account,. The glacier-response time varies from 70 to 130 years and the minimum temperature from 0.7 oC to 3.0 oC. The initial global ice volume is assumed to be 30-cm sea-level equivalent.

3. Sea-level rise caused by melting of the Greenland and Antarctica ice sheets

For Greenland and Antarctica, the ice sheet area is assumed to be constant because the response times are very long and temperature changes are assumed to be moderate. The mass balance of the ice sheets can be divided into two components:

• a constant component that represents the gain or loss of ice as a result of the initial state of the ice sheet
• a component that is linearly dependent on the temperature change relative to the initial state. Just as for small glaciers, the initial state of the ice sheets is assumed to be the year 1880.

The Greenland ice sheet is assumed to be in equilibrium in 1880, so that the constant component is 0.0 cm per year. For Antarctica this component is assumed to be 0.01 cm per year. The sensitivity values for the mass balance are taken as 0.03 cm per year per oC for Greenland and 0.02 cm per year per oC for Antarctica. The sensitivity values are based on estimates of the sensitivity of the ice sheets to 1oC warming as computed by more complex two- and three-dimensional ice sheet models.

4. Uncertainties

The uncertainty in these indicators is large, with ranges for 1990-2100 of 0.11 to 0.43 m for thermal expansion, 0.04 to 0.17 m for the glacier contribution, -0.01 to 0.07 m for the Greenland ice sheet and -0.12 to -0.02 m for the Antarctica contribution.