APPENDIX II. LINEARIZATION OF BULK FORMULAE

The idea developed by Haney (1971) to simplify the algorithm used to compute the surface heat fluxes for modelling proposes is derived from the Taylor expansion of the bulk formulae respect to the sea temperature and evaluating them at the air temperature. With this idea, Q_b and Q_e can be estimated as

and

Now, using

and

where q_h = ρ_aC_pwC_h, and ρ_a, C_p, w and C_h have the same meaning as in equation (27).

Q can be estimated as

Defining T_a^* = T_a + Q₁/q, the previous equation reduces to

This equation is the one used for numerical modelling. T_a^* as well as q are then functions of time and space derived from climatological data (the COADS data in our case) and T_s is the temperature of the first layer of the model. However, in our case we can evaluate the derivatives in the Taylor series using climatological values of the SST instead of air temperatures.