Difference between revisions of "Slab ocean model"

Revision as of 12:03, 26 February 2024

A brief description of the 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.

In its current form in the Generic-PCM, the slab ocean model handles two key processes, (a) Heat transport by ocean circulation, and (b), Sea ice formation:

Heat transport by ocean circulation

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. This simplified model reproduces the global meridional oceanic heat transport quite closely compared to an Oceanic-GCM.

Other ocean circulation features like density-driven / thermohaline circulation and horizontal gyres are not present in the model. While these features play an important role in shaping regional climates on modern Earth, their effect is weaker on the global average; gyres would be absent in the case of a global ocean.

Sea ice formation

Sea ice forms when the ocean temperature falls below –1.8°C (the freezing point of Earth's sea water, function of salinity) 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 –1.8°C 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 that of bare ice:

$$A = A^\rm{max}_\rm{ice} – (A^\rm{max}_\rm{ice} – A^\rm{min}_\rm{ice} ) e^{\left ( \frac{–h_\rm{ice}}{h^0_\rm{ice}} \right )}$$

Here, $$A$$ is the albedo, $$A^\rm{max}_\rm{ice}$$ = 0.65 is the maximal albedo, $$A^\rm{min}_\rm{ice}$$ = 0.2 is the minimal albedo, $$h_\rm{ice}$$ is the ice thickness (in m) and $$h^0_\rm{ice}$$ = 0.5 m. The albedo over the ice-free ocean is taken to be equal to 0.07. These values for the maximal and minimal sea ice albedos are classical for Earth-based GCMs. However, by definition, the Generic-PCM is meant to handle a more generalised case of planets. It is well known that the albedo of a material (for e.g., ice or snow) is spectral-dependent. Consequently, the albedo value of ice will be different around a star that is unlike the Sun. For instance, the ice/snow albedo climate feedback will be significantly weaker for planets orbiting M-dwarf stars (for e.g., Proxima Centauri b) than for planets orbiting G-type stars like the Sun (see Joshi & Haberle [2012] and Shields [2014]). The Generic-PCM accounts for this by instituting a spectral dependence of albedo.

Indeed, changes in the sea-ice model, or in parameters such as the snow albedo, can have large impacts on the simulated climate. This happens through changes in the ice extent and the global temperature through the ice-albedo feedback. This effect is, however, largely independent of the heat transport schemes presented in this page.

Over each grid point, the sea ice is represented by a uniform layer of depth $$H$$ and fractional area $$f$$. It may be covered by a layer of snow. In the Generic-PCM, this snow layer is assumed to have zero heat capacity, which implies that the snow layer is at the same temperature as that of the sea ice layer below it. The temperature at the bottom of the ice layer is always equal to the freezing temperature of sea water $$T_o$$. The surface temperature, $$T_s$$,

The 2024 version of the slab ocean model

Compared to the old model, the new model has the following changes (non-exhaustive):

        (a) More realistic description of sea ice creation and evolution - simultaneous
            surface, side and bottom melting / freezing depending on fluxes.
        (b) Snow has an effective heat capacity.
        (c) Snow has "weight"; it can sink an ice block if there is too much of it.
        (d) Snow can be blown off by wind.
        (e) The two-layer ocean allows for convective adjustment.
        (f) Diffusion can follow the Gent-McWilliams scheme + Eddy diffusivity.
        (g) Can be used in parallel mode.

Variables of the slab ocean model which can be written as outputs in diagfi.nc

• tslab1, tslab2: temperature of the surface and deep ocean layers respectively (K)
• pctsrf_sic: grid fraction of sea ice
• sea_ice: mass of sea ice (kg/m$$^2$$)
• tsea_ice: temperature of the sea ice surface (K)
• dt_hdiff1, dt_hdiff2: heating of the surface and deep ocean layers by horizontal diffusion (W/m$$^2$$)
• dt_ekman1, dt_ekman2: heating of the surface and deep ocean layers by Ekman transport (W/m$$^2$$)
• dt_gm1, dt_gm2: heating of the surface and deep ocean layers by Gent-McWilliams eddy transport (W/m$$^2$$)

Technical aspects

The slab ocean model is activated in callphys.def with: ok_slab_ocean = .true.

The sea ice model is activated in callphys.def with: ok_slab_sic = .true.

The horizontal heat transport is activated in callphys.def with: ok_slab_heat_transp = .true. The horizontal heat transport cannot be activated in parallel at the moment.

Values of A$$^{max}_{ice}$$ and A$$^{min}_{ice}$$ are fixed in slab_ice_h.F90

rnat is a standard diagfi output, which either represents 0 for oceanic grid points or 1 for continent grid points