Physical models aim to describe quantitatively the different physical processes that contribute to sea level rise. Global sea level can be raised in three fundamentally different ways:



(i) By altering the volume of the existing ocean water mass by warming, a process called ‘thermal expansion'.

(ii) By adding water mass. Mass addition comes primarily from melting land ice, i.e. from mountain glaciers, small ice caps and the big ice sheets on Greenland and Antarctica. Melting sea ice hardly affects global sea level, since it already floats on the sea displacing water corresponding to its weight (Archimedes' principle). Mass addition (or removal) can to some extent also come from water stored on land in liquid form, e.g. from storage of water in human-built reservoirs, which corresponds to about 3 cm worth of sea level (Chao et al. 2008), or from pumping up water from deep aquifers for irrigation purposes which ends up in the ocean (Wada et al. 2010).

(iii) By changing the depths of the global ocean basins by movements of the Earth's crust. This is a very long-term process of lesser relevance on the century time scale, but it is currently estimated as causing a drop in sea level at a rate of 3 cm per century due to glacial isostatic adjustment (GIA), i.e. the ongoing adjustment process of the Earth's crust after the big ice sheets of the last Ice Age have disappeared.

We will discuss local sea level changes in a separate section below.

Of these key processes, thermal expansion can be modeled with 3-dimensional ocean circulation models, a standard component of coupled climate models. The crucial factor is how fast heat penetrates from the surface into the ocean, and where. The uncertainty comes, e.g., from the intensity of mixing of different ocean layers and from changes in ocean circulation. For a given emissions scenario, (IPCC 2007) estimates about a factor of two uncertainty in the thermal expansion; for moderate warming (A1B scenario) the best estimate is around 20 cm rise by 2100.

The melting of mountain glaciers is difficult to calculate from physical models because there is such a large number and variety of glaciers - the World Glacier Inventory contains ~123,000 glaciers (Radic and Hock 2010). It is impossible to model the dynamics of each glacier individually, so that semi-empirical scaling laws are used instead. Since satellite imagery reveals only the surface area, even the total volume of glacier ice is uncertain, with estimates ranging from 24 cm (Raper and Braithwaite 2005) to 60 cm (Radic and Hock 2010) sea level equivalent. Hence, the sea level contribution from glacier melt up to the year 2100 could be as little as 5 cm (Raper and Braithwaite 2006), around 10 cm (IPCC 2007), or more than 37 cm (Bahr et al. 2009) for moderate global warming.

Even more uncertain is the contribution of the two huge ice sheets on Greenland and Antarctica. Although they are modeled individually by ice sheet models, these do not yet properly capture the full flow dynamics, especially the small-scale, fast-flowing outlet glaciers that drain ice into the ocean. The part that is more easily modeled is the surface mass balance: the difference between snow accumulation and melting at the ice surface. For Antarctica this is expected to be positive as a result of warming, since snow fall increases more than melting. For Greenland this is moderately negative. Overall, the IPCC report (IPCC 2007) projected a sea level contribution from the ice sheets that is close to zero, due to Greenland losing some mass (roughly between 5 and 10 cm sea level equivalent) and Antarctica gaining a similar amount.

This is at odds with the observed accelerating mass loss from both Greenland and Antarctica (Rignot. 2011), and the IPCC report explicitly stated that its estimates "exclude future rapid dynamical changes in ice flow". With this caveat, the IPCC projected an overall rise between 18-59 cm for the time span 1990 to 2095.But when the different modeled components are added up, their sum falls well short of the observed sea level rise for the past decades (IPCC 2007; Rahmstorf. 2007). At this stage it must be concluded that physical modeling of sea level rise does not yet provide reliable results, which is the motivation to turn to semi-empirical methods.