5.3: Direct Calculation of Fluxes

Before we can describe the geographical distribution of fluxes into and out of the ocean, we need to know how they are measured or calculated.

Gust-Probe Measurements of Turbulent Fluxes

There is only one accurate method for calculating fluxes of sensible and latent heat and momentum at the sea surface: from direct measurement of turbulent quantities in the atmospheric boundary layer made by gust probes on low-flying aircraft or offshore platforms. Very few such measurements have been made. They are expensive, and they cannot be used to calculate heat fluxes averaged over many days or large areas. The gust-probe measurements are used only to calibrate other methods of calculating fluxes.

1. Measurements must be made in the surface layer of the atmospheric boundary layer (see Section 4.3), usually within 30 m of the sea surface, because fluxes are independent of height in this layer.
2. Measurements must be made by fast-response instruments (gust probes) able to make several observations per second on a tower, or every meter from a plane.
3. Measurements include the horizontal and vertical components of the wind, the humidity, and the air temperature.

Fluxes are calculated from the correlation of vertical wind and horizontal wind, humidity, or temperature. Each type of flux is calculated from different measured variables, \(u'\), \(w'\), \(t'\), and \(q'\): \[\begin{align} T &= \langle \rho_{a} u' w' \rangle = \rho_{a} \langle u'w' \rangle \equiv \rho_{a} u_{*}^{2} \\ Q_{S} &= C_{p} \langle \rho_{a} w't' \rangle = \rho_{a} C_{p} \langle w't' \rangle \\ Q_{L} &= L_{E} \langle w'q' \rangle \end{align} \nonumber \]

where the brackets denotes time or space averages, and the notation is given in table \(\PageIndex{1}\). Note that the specific humidity mentioned in the table is the mass of water vapor per unit mass of air.

Table \(\PageIndex{1}\). Notation Describing Fluxes.

Symbol	Variable	Value and Units
\(C_{p}\)	Specific heat capacity of air	\(1030 \ \text{J} \cdot \text{kg}^{-1} \cdot \text{K}^{-1}\)
\(C_{D}\)	Drag coefficient (see Section 4.3)	\(\left(0.50 + 0.071 U_{10}\right) \times 10^{-3}\)
\(C_{L}\)	Latent heat transfer coefficient	\(1.2 \times 10^{-3}\)
\(C_{S}\)	Sensible heat transfer coefficient	\(1.0 \times 10^{-3}\)
\(L_{E}\)	Latent heat of evaporation	\(2.5 \times 10^{6} \ \text{J/kg}\)
\(q\)	Specific humidity of air	\(\text{kg (water vapor)/kg (air)}\)
\(q_{a}\)	Specific humidity of air 10 m above the sea	\(\text{kg (water vapor)/kg (air)}\)
\(q_{s}\)	Specific humidity of air at the sea surface	\(\text{kg (water vapor)/kg (air)}\)
\(Q_{S}\)	Sensible heat flux	\(\text{W/m}^{2}\)
\(Q_{L}\)	Latent heat flux	\(\text{W/m}^{2}\)
\(T\)	Wind stress	\(\text{Pascals}\)
\(t_{a}\)	Temperature of the air 10 m above the sea	\(\text{K or }^{\circ} \text{C}\)
\(t_{s}\)	Sea-surface temperature	\(\text{K or }^{\circ} \text{C}\)
\(t'\)	Temperature fluctuation	\(^{\circ} \text{C}\)
\(u'\)	Horizontal component of fluctuation of wind	\(\text{m/s}\)
\(u_{*}\)	Friction velocity	\(\text{m/s}\)
\(U_{10}\)	Wind speed at 10 m above the sea	\(\text{m/s}\)
\(w'\)	Vertical component of wind fluctuation	\(\text{m/s}\)
\(\rho_{a}\)	Density of air	\(1.3 \ \text{kg/m}^{3}\)
\(T\)	Vector wind stress	\(\text{Pa}\)

Radiometer Measurements of Radiative Fluxes

Radiometers on ships, offshore platforms, and even small islands are used to make direct measurements of radiative fluxes. Wideband radiometers sensitive to radiation from 0.3 \(\mu\)m to 50 \(\mu\)m can measure incoming solar and infrared radiation with an accuracy of around 3% provided they are well calibrated and maintained. Other, specialized radiometers can measure the incoming solar radiation, the downward infrared radiation, and the upward infrared radiation.