The ocean flux is generally evaluated using a CAM 3.0 control simulation driven by prescribed sea surface temperature and sea ice distributions. Let

(5.12) |

over ocean (regardless of whether the ocean surface is open or ice covered), for each of 12 ensemble mean months (n=1,...,12). The Q flux distribution for each month n is then evaluated: (note that here we use the CAM 3.0 sign convention on the Q flux).

(5.13) |

where:

(5.14) |

(5.15) |

where is the number of days in each month, is the latent heat of fusion for ice, and is the regionally specified ice thickness. We then define an annual average using the monthly mean data:

(5.16) |

By definition

(5.17) |

(5.18) |

so that

(5.19) |

Since is the monthly mean flux into the ocean directly from the control, must be constrained to ensure that the actual applied in the SOM configuration has the same annual mean as . Otherwise, the application of the flux would introduce a source or sink of heat with respect to the control.

The actual applied in the SOM configuration is based on linear
interpolation between monthly means, taken as midpoints. Since the
months have different lengths, in general the annual mean of the
flux applied to the SOM *will not* equal
. Thus, we
must define another annual mean, based on the time interpolated ,
to ensure that the SOM applied Q has the identical annual mean as the
fluxes from the control run.