6.5 Ice to Ocean Flux Exchange

This section is only relevant when CAM 3.0 is coupled to a slab ocean. When sea ice is present, only a fraction of the melting potential from heat stored in the ocean actually reaches the ice at the base and side. The melting potential is

(6.33) |

where , , , and are the ocean layer thickness, density, heat capacity, and temperature and is the freezing temperature of the layer (assumed to be -1.8C).

Usually only a fraction of is available to melt ice at the base and side, and these fractions are determined from boundary-layer theories at the ice-ocean interfaces. However, it is critical that the sum of the fractions never exceeds one, otherwise ice formation might become unstable. Hence we compute the upper-limit partitioning of , even though these amounts are rarely reached. The partitioning assumes is dominated by shortwave radiation and that shortwave radiation absorbed in the ocean surface layer above the mean ice thickness causes side melting and below it causes basal melting:

(6.34) |

where , , [134] and and are the fractions of bottom and side melt flux available, respectively. Thus the maximum fluxes available for melt are and . The actual amount used for bottom melting, , is based on boundary layer theory of McPhee [127]:

where the empirical drag coefficient =0.006 and the skin friction speed cm/s [165].

The heat flux for lateral melt is the product of the vertically-summed, thickness-weighted energy of melting of snow and ice with the interfacial melting rate and the total floe perimeter per unit floe area . The interfacial melting rate is taken from the empirical expression of Maykut and Perovich [124] based on Marginal Ice Zone Experiment observations: , where m s deg and . The lead-ice perimeter depends on the ice floe distribution and geometry. For a mean floe diameter and number of floes , and the floe area [154]. Thus the heat flux for lateral melt is , so that the actual amount used is:

where [154]. Based partially on tuning and partially on the results of floe distribution measurements, the mean floe diameter of =300 m was chosen. The ice area, volume, snow volume, and ice energy are all reduced by side melt in time by the fraction .

The heat flux that is actually used by the ice model is then:

(6.37) |

The net flux exchanged between ocean and ice also includes the shortwave flux transmitted to the ocean through sea ice

(6.38) |

(see Eq. 6.45). Hence