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, Qb and Qe can be estimated as
where qh = ρaCpwCh, and ρa, Cp, w and Ch have the same meaning as in equation (27).
Q can be estimated as
Defining Ta* = Ta + Q1/q, the previous equation reduces to
This equation is the one used for numerical modelling. Ta* as well as q are then functions of time and space derived from climatological data (the COADS data in our case) and Ts 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.