APPENDIX I. HEAT FLUXES ESTIMATION

The surface heat flux computation was made based on bulk formulae. The net heat flux Q through the sea surface is given by

where Q_s, Q_b, Q_e, and Q_h are the heat flux due to the short wave radiation, long wave radiation, latent heat, and sensible heat respectively.

1. Incoming short wave radiation

The short wave radiation was estimated following Reed (1977)

where C is the fraction of sky covered by clouds in tenths, is the altitude of the sun from the horizontal at noon (in degrees), A = 0.06 is the albedo, is computed with the relation sin = sin l sin[23.87 sin(2π(t–82)/365)] + cos l cos[23.87 sin(2π(t-82)/365)], where l is the latitude (Reed, 1977). The radiation under clear sky (Q_c), is computed with the formula

from Seckel and Beaudry (1973), cited in Reed (1977). In equation (21), ɸ = (2π/365)(t–21) is a function related to the day of the year in which t is the Julian day. The coefficients in equation (24) were computed following Reed (1983).

2. Long wave radiation

The long wave radiation was computed as Reed (1983):

In this equation σ = 5.67 x 10^-8 Wm^–2K^–4 is the Stefan Boltzman constant, is the emissivity of the sea surface, T is the temperature in degrees Kelvin, e_a is the water vapor pressure (in millibars) computed following Gill (1982) and is given by

with H the percentage of relative humidity, and e_w is the saturation vapor pressure computed as

where P is the atmospheric pressure at sea level in millibars and γ = (0.7859 + 0.03477t_s)/(1 + 0.00412t_s), in which t_s is the temperature in Celsius.

3. Latent heat flux

The latent heat flux was computed with the relation

In this relation ρ_a is the air density, C_E is the turbulent coefficient, L is the latent heat of vaporization, w is the wind speed, q_s is the saturation specific humidity and q_a the specific humidity at anemometer level. The latent heat was calculated following Gill (1982) as L = 2.5008 x 10⁶ - (2.3 x 10³)T_s; ρ_a = 1.25 Kg m^–3, q_s and q_a, the saturation specific humidity at sea surface and the specific humidity of air were calculated as Gill (1982):

In this work, a constant value of C_E = 1.4 x 10^–3 is used, following Geernaert (1990).

4. Sensible heat flux

The sensible heat flux was calculated with the formulae

with C_H the sensible heat turbulent coefficient, C_p is the specific heat of air, T_s the sea surface temperature, and T_a the air temperature at ship deck level. We use a constant value of C_H = 1.4 x 10^–3, as Geernaert (1990).