The bulk formulas used to determine the turbulent fluxes of momentum (stress), water (evaporation, or latent heat), and sensible heat into the atmosphere over ocean surfaces are

where is atmospheric surface density and is the specific heat. Since CAM2 does not allow for motion of the ocean surface, the velocity difference between surface and atmosphere is , the velocity of the lowest model level. The potential temperature difference is , where is the surface temperature. The specific humidity difference is , where is the saturation specific humidity at the sea-surface temperature.

In (4.427), the transfer coefficients between the ocean surface and the atmosphere are computed at a height and are functions of the stability, :

where is von Kármán's constant and is the roughness length for momentum, evaporation, or heat, respectively. The integrated flux profiles, for momentum and for scalars, under stable conditions () are

For unstable conditions (), the flux profiles are

The stability parameter used in (4.429)-(4.432) is

where the virtual potential temperature is ; and are the lowest level atmospheric humidity and potential temperature, respectively; and . The turbulent velocity scales in (4.433) are

Over oceans, m under all conditions and m for , m for , which are given in Large and Pond [1982]. The momentum roughness length depends on the wind speed evaluated at 10 m as

where m s, , m s, and the required drag coefficient at 10-m height and neutral stability is as given by Large et al. [1994].

The transfer coefficients in (4.427) and (4.428) depend on the stability following (4.429)-(4.432), which itself depends on the surface fluxes (4.433) and (4.434). The transfer coefficients also depend on the momentum roughness, which itself varies with the surface fluxes over oceans (4.435). The above system of equations is solved by iteration.