5.1: The Oceanic Heat Budget

Changes in energy stored in the upper ocean result from an imbalance between input and output of heat through the sea surface. This transfer of heat across or through a surface is called a heat flux. The flux of heat and water also changes the density of surface waters, and hence their buoyancy. As a result, the sum of the heat and water fluxes is often called the buoyancy flux.

The flux of energy to deeper layers is usually much smaller than the flux through the surface. And, the total flux of energy into and out of the ocean must be zero, otherwise the ocean as a whole would heat up or cool down. The sum of the heat fluxes into or out of a volume of water is the heat budget.

The major terms in the budget at the sea surface are:

1. Insolation, \(Q_{SW}\), the flux of solar energy into the sea;
2. Net Infrared Radiation, \(Q_{LW}\), net flux of infrared radiation from the sea
3. Sensible Heat Flus, \(Q_{S}\), the flux of heat out of the sea due to conduction;
4. Latent Heat Flux, \(Q_{L}\), the flux of energy carried by evaporated water; and
5. Advection, \(Q_{V}\), heat carried away by currents.

Conservation of heat requires: \[Q = Q_{SW} + Q_{LW} + Q_{S} + Q_{L} + Q_{V} \nonumber \]

where \(Q\) is the resultant heat gain or loss. Units for heat fluxes are watts/m². Flux multiplied by surface area multiplied by time is energy in joules. The change in temperature \((\Delta t)\) of the water is related to change in energy \((\Delta E)\) through: \[\Delta E = C_{p} m \Delta t \nonumber \]

where \(m\) is the mass of water being warmed or cooled, and \(C_{p}\) is the specific heat of sea water at constant pressure. \[C_{p} \approx 4.0 \times 10^{3} \ \text{J} \cdot \text{kg}^{-1} \cdot ^{\circ} \text{C}^{-1} \nonumber \]

Thus, 4,000 joules of energy are required to heat 1.0 kilogram of sea water by 1.0\(^{\circ}\)C (figure \(\PageIndex{1}\)).

Figure \(\PageIndex{1}\): Specific heat of sea water at atmospheric pressure, \(C_{p}\), in joules per gram per degree Celsius as a function of temperature in Celsius and salinity, calculated from the empirical formula given by Millero et al. (1973) using algorithms in Fofonoff and Millard (1983). The lower line is the freezing point of salt water.

Importance of the Ocean in Earth’s Heat Budget

To understand the importance of the ocean in Earth’s heat budget, let’s make a comparison of the heat stored in the ocean with heat stored on land during an annual cycle. During the cycle, heat is stored in summer and released in the winter. The point is to show that the ocean store and release much more heat than the land.

To begin, use \((\PageIndex{3})\) and the heat capacity of soil and rocks: \[C_{p(rock)} = 800 \ \text{J} \cdot \text{kg}^{-1} \cdot ^{\circ} \text{C}^{-1} \nonumber \]

to obtain \(C_{p(rock)} \approx 0.2 C_{p(water)}\).

The volume of water which exchanges heat with the atmosphere on a seasonal cycle is 100 m³ per square meter of surface, i.e. that mass from the surface to a depth of 100 meters. The density of water is 1000 kg/m³ , and the mass in contact with the atmosphere is density × volume = \(m_{water}\) = 100,000 kg. The volume of land which exchanges heat with the atmosphere on a seasonal cycle is 1 m³. Because the density of rock is 3,000 kg/m³, the mass of the soil and rock in contact with the atmosphere is 3,000 kg.

The seasonal heat storage values for the ocean and land are therefore:

\[\begin{align*} \Delta E_{ocean} &= C_{p(water)} m_{water} \Delta t \quad\quad\quad\quad \Delta t = 10^{\circ} \text{C} \\ &= (4000)(10^{5})(10^{\circ}) \ \text{Joules} \\ &= 4.0 \times 10^{9} \ \text{Joules} \\ \Delta E_{land} &= C_{p(rock)} m_{rock} \Delta t \quad\quad\quad\quad \Delta t = 20^{\circ} \text{C} \\ &= (800)(3000)(20^{\circ}) \ \text{Joules} \\ &= 4.8 \times 10^{7} \ \text{Joules} \\ \frac{\Delta E_{ocean}}{\Delta E_{land}} &= 100 \end{align*} \]

where \(\Delta t\) is the typical change in temperature from summer to winter.

The large storage of heat in the ocean compared with the land has important consequences. The seasonal range of air temperatures on land increases with distance from the ocean, and it can exceed 40\(^{\circ}\)C in the center of continents, reaching 60\(^{\circ}\)C in Siberia. Typical range of temperature over the ocean and along coasts is less than 10\(^{\circ}\)C. The variability of water temperatures is still smaller (see figure \(6.3.2\), bottom).