APPENDIX III. COMPARISON OF FORMULAE AND DATA SOURCES USED ON THE HEAT FLUXES ESTIMATION IN THE GULF OF MEXICO BY VARIOUS AUTHORS

1. Q_c computations

For the computation of Q_s usually the radiation in clear sky is computed first and with this data the net short-wave radiation is computed including the effect of clouds. The clear sky short-wave radiation (Q_c) has been computed by several authors:

Hastenrath (1968) and Hastenrath and Lamb (1978) takes data from Bernhard and Phillips (1958) maps.

Etter (1983) and Etter et al. (1987) used a combination of results from Bunker (1976) and Hastenrath and Lamb (1978).

Bunker (1976) based its computations on Budyko (1963).

Adem et al. (1993) used data from Budyko (1974).

This work uses Seckel and Beaudry formula: Q_c = A₀ + A₁ cos ɸ + B₁ sin ɸ + A₂ cos 2ɸ + B₂ sin 2ɸ, from Reed (1977) and Reed (1983) for the coefficients values.

2. Q_s estimations

Hastenrath (1968) takes data from Bernhard and Phillips maps (1958). He used A = 6%.

Etter (1983), and Etter et al. (1987) used a combination of results from Bunker (1976) computed with the formula of Budyko and Hastenrath and Lamb (1978) data.

Adem et al. (1993) used the formula given by Budyko (1974), ₁ I = (Q + q)₀(1-(a + bC)C)(1-A), where (Q + q)₀ is the total radiation received by the surface with clear sky with a = 0.35, b = 0.38, (parameters recommended for 25°N), C is the cloud cover in tenths, and A = 6% the albedo at the sea surface.

In this work we follow Reed (1977) using the formula Q_s = Q_c(1 - 0.62C + 0.0019)(1- A).

3. Q_b computations

Hastenrath (1968) used Q_b = Q_b0(1 — 0.60C), where Q_b0 is the long-wave radiation for clear skies, and C the fraction of sky covered by clouds (in tenths). He follow Kuhn (1962) for the computation of Q_b0.

Etter (1983) and Etter et al. (1987) used Hastenrath and Lamb (1978) results.

Adem et al. (1993) used Q_b = -δσT_a⁴[0.254 - 0.0066Ue_s(T_a)](1 - AC) - 4δσT_a³(T - T_a); from Budyko (1974), where δ = 0.96 is the emissivity of the sea surface, A is the cloud cover coefficient (= 0.65 in their computation), U is the relative humidity and e_s the saturation vapor pressure.

In this work we use Q_b = σ∈T_a⁴(0.254 - 0.00495e_a)(1- 0.7C) following Reed (1983).

9.4. Q_e, Q_h, C_E and C_H computations

All works use the formulae: Q_e = ρ_aC_EwL(q_s — q_a) and Q_h = p_aC_pC_Hw(T_s — T_a), or an equivalent set using different unit system, but with different turbulent coefficients.

Hastenrath (1968) used C_E = C_H = 1.4 x 10^–3.

Etter (1983) and Etter et al. (1987) computed Q_e as an average of the results of the work of Budyko (1974), which uses C_E = C_H = 2.1 x 10^–3, and Bunker (1976) with turbulent coefficients computed as a function of the wind speed and the difference of temperature between the air and the sea surface (C_E and C_H get values from 0.071 x 10^–3 to 2.52 x 10^–3).

Adem et al. (1993, 1994) used an equivalent formula, with C_E = C_H = 1.6 x 10^–3.

In this work C_E = C_H = 1.4 x 10^–3, a value slightly higher than those suggested in recent papers (Geernaert, 1990).