Chapter 5 - The Oceanic Heat Budget

The Oceanic Heat Budget

About half the solar energy reaching Earth is absorbed by the ocean and land, where it is temporarily stored near the surface. Only about a fifth of the available solar energy is directly absorbed by the atmosphere. Of the energy absorbed by the ocean, most is released locally to the atmosphere, mostly by evaporation and infrared radiation. The remainder is transported by currents to other areas especially mid latitudes. Note that "heat is the amount of thermal energy transferred from one body to another because of the temperature difference between those bodies" (Donald E. Simanek).

Heat lost by the tropical ocean is the major source of energy needed to drive the atmospheric circulation. And, solar energy stored in the ocean from summer to winter helps ameliorate Earth's climate. The thermal energy transported by ocean currents is not steady, and significant changes in the transport, particularly in the Atlantic, may have been important for the development of the ice ages. For these reasons, oceanic heat budgets and transports are important for understanding Earth's climate and its short and long term variability.

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5.1 The Oceanic Heat Budget

Changes in energy stored in the upper layers of the ocean result from a local imbalance between input and output of heat through the sea surface. This transfer of heat through the 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 sunlight into the sea;
2. Net Infrared Radiation Q_LW, net flux of infrared radiation from the sea;
3. Sensible Heat Flux Q_S, the flux of heat out of the sea due to conduction;
4. Latent Heat Flux Q_L, the flux of heat carried by evaporated water; and
5. Advection Q_V, heat carried away by currents.

Conservation of heat requires:

where Q_T is the resultant heat gain or loss. Units for heat fluxes are watts/m². The product of flux times surface area times time is energy in joules. The change in temperature DT of the water is related to change in energy ΔE through:

where m is the mass of water being warmed or cooled, and C_p is the specific heat of sea water at constant pressure.

Thus, 4,000 joules of energy are required to heat 1.0 kilogram of sea water by 1.0°C (Figure 5.1).

Figure 5.1 Specific heat of sea water at atmospheric pressure Cp in joules per gram per degree Celsius as a function of temperature in Celsius and salinity in practical salinity units, 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 simple 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 oceans store and release much more heat than the land.

To begin, we use (5.3) and the heat capacity of soil and rocks

to obtain C_p(rock) ≈ 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 100m. 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:

ΔEoceans	= Cp(water) mwater ΔT	ΔT = 10°C
	= (4000)(105)(10°) Joules
	= 4.0 X 109 Joules
ΔEland	= Cp(rock) mrock ΔT	ΔT = 20°C
	= (800)(3000)(20°) Joules
	= 4.8 X 107 Joules
	= 100

where ΔT 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°C in the center of continents, reaching 60°C in Siberia. Typical range of temperature over the ocean and along coasts is less than 10°C. The variability of water temperatures is still smaller (see Figure 6.5).

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