Slab ocean model

The slab ocean model is from Codron [2012]. This model uses the same horizontal grid as the GCM and is composed of two layers. The first layer (50 m depth) represents the surface mixed layer, where the exchanges with the atmosphere take place. The second layer (150 m depth) represents the deep ocean. The transport of heat by the ocean circulation is given by two components. First, the impact of subgrid-scale eddies is represented by horizontal diffusion, with a uniform diffusivity in both layers. Then, the mean wind-driven circulation is computed by calculating the Ekman mass fluxes in the surface layer from the surface wind stress and taking an opposite return flow at depth. These mass fluxes are then used to advect the ocean temperature horizontally. In the case of divergent horizontal mass fluxes, the upwelling or downwelling mass flux is obtained by continuity. Other components of the ocean circulation— density-driven circulations and horizontal gyres—are not present in the model. Although they can play an important role regionally on the present Earth, they are weaker on global average, and gyres would be absent in the case of a global ocean. This simplified model reproduces the global meridional oceanic heat transport quite closely compared to a full GCM, both for actual Earth and for a simulated global ocean case [Marshall et al., 2007]. [37] The oceanic model also computes the formation of oceanic ice. Sea ice forms when the ocean temperature falls below –1.8ıC and melts when its temperature rises above freezing. The changes in ice extent and thickness are computed based on energy conservation, keeping the ocean temperature at –1.8ıC as long as ice is present. A layer of snow can be present above the ice. The surface albedo is then that of snow, or for bare ice: A = Amax ice – (Amax ice – Amin ice ) exp(–hice/h0 ice) (11) with A the albedo, Amax ice = 0.65 the maximal albedo, Amin ice = 0.2 the minimal albedo, hice the ice thickness (in m) and h0ice = 0.5 m. The albedo over the ice-free ocean is taken to be equal to 0.07. The value for the maximal sea ice albedo we used (i.e., 0.65) is classical for GCMs. It is a pretty high value for studies of snowball Earth [Abbot et al., 2011], making our results concerning cold climates pretty robust. [38] The transport of sea ice is not taken into account. This has a small impact for the present-day conditions, but it may be more important for different conditions (e.g., a colder climate with more sea ice) [Lewis et al., 2003].

Technical aspects

In the code the slab ocean model is read by ....