## Dt

1 dQ

Dt PrefCw dZ

where cw is the heat capacity of water (see Table 9.3), and Q and E are, respectively, the turbulent vertical flux of heat and freshwater driven by air-sea exchange, convection, ice formation, and vertical mixing in the ocean (as sketched in Fig. 9.11). At the surface Q = Qnet, the net heat flux across the sea surface (see Eq. 11-5) and E = Esurface = E - P (evaporation minus precipitation, including that due to river runoff and ice formation processes) is the net fresh water flux across the sea surface. Typically Q and E decay with depth over the mixed layer from these surface values. Note that the minus sign in Eq. 11-2 ensures that if heat is lost from the ocean (Qnet > 0), its temperature decreases.

The buoyancy equation can be deduced by taking D/Dt of Eq. 11-1 and using Eqs. 9-5,11-2, and 11-3 to obtain

Db Dt

Pref dB

aL dQ

Cw dZ

,dÂ£ dz where B is the vertical buoyancy flux, allowing us to identify the air-sea buoyancy flux thus:

Bsurface _

Pref

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