The Heatbudget Equation

As discussed in Section 1.1. the Earth as a whole not only receives solar radiation, which is largely short-wave, but also re-emits long-wavelength radiation. This is because all bodies with a temperature above absolute zero emit radiation: the higher the temperature of the body concerned, the greater the total amount of radiant energy emitted. In fact, the intensity (/) of the radiation emitted increases in proportion to the fourth power of the absolute temperature (7); i.e. I = oT4. This is known as Stefan's Law and the constant a is known as Stefan's constant. Furthermore, the higher the temperature of the body concerned, the more the radiation spectrum is shifted towards shorter wavelengths. Thus, the surfaces of the oceans and continents not only absorb and reflect the incoming short-wave solar radiation that has penetrated the atmosphere but also re-emit radiation which is mostly of a much longer wavelength, because of their relatively low temperatures. This longer-wavelength radiation is either lost to space or is absorbed by clouds, water vapour and other gases - especially carbon dioxide and ozone - all of which re-emit long-wave radiant energy in all directions. In calculating the amount of radiant energy absorbed by the oceans, we therefore have to consider not only the incoming short-wave (< 4 pm) radiation (given the symbol (2S) but also the net emission of longwave radiation (also known as back-radiation, and so given the symbol Qb). For all latitudes, Qs - Qh is generally positive, i.e. the oceans absorb more radiant energy than they emit (Figure 6.4), although at higher latitudes the value of (2S - Qb varies significantly with the time of year.

Of the total amount of energy received from the Sun by the world's oceans, about 419r is lost to the atmosphere and. indirectly, to space, as long-wave radiation, and about 549c is lost as latent heat through evaporation from the sea-surface. A relatively small amount - about 59c - is lost to the overlying atmosphere by conduction. Heat loss by evaporation is generally given the symbol Qc. and heat loss by conduction, the symbol Qh.

The temperature of a body is a measure of the thermal energy it possesses. If the average temperature of the oceans is to remain constant, the gains and losses of heat must even out over a period. In other words, the heat budget must balance.

Figure 6.4 The radiation balance (Qs - Qb) at the Earth's surface, in W nr2, averaged over the course of a year. Values have been converted from non-SI units; and contours have been omitted over high ground. The white area shows the approximate winter limit of sea-ice cover.

Figure 6.4 The radiation balance (Qs - Qb) at the Earth's surface, in W nr2, averaged over the course of a year. Values have been converted from non-SI units; and contours have been omitted over high ground. The white area shows the approximate winter limit of sea-ice cover.

QUESTION 6.2 Using I he symbols Q^, Qh, and write down the heal-budget equation (i.e. an equation of ihe form: heat gained = heal lost i lor the oceans as a whole.

Heat is not only being continuously gained and lost from the oceans, but also redistributed within them, by currents and mixing.

Figure 6.5(a) and (h) show the global distributions of sea-surface temperature in Jul; and January. Would you sa\ that these temperature distributions reflect the influence of ocean currents (Figure 3.1)?

Yes. In particular, surface water on the western sides of oceans is generally warmer than the water on the eastern side, particularly in the hemisphere experiencing summer. This is a result of flow around the subtropical gyres, with the western boundary currents carrying warm water from lower latitudes - the effect of the Gulf Stream in transporting relatively warm water across the Atlantic can also be clearly seen, especially in Figure 6.5(a), for the northern summer. By contrast, the eastern boundary currents carrying cold water from higher latitudes cause temperatures on the eastern sides of oceans to be somewhat lower than they would otherwise be. Low temperatures in eastern boundary currents are also a result of upwelling -the effect of the Benguela upwelling is particularly evident, especially in the southern winter (Figure 6.5(a)); so, too is upwelling at the northern edge of the South Equatorial Current in the Pacific and the Atlantic Oceans.

Heat brought into a region of ocean by currents and mixing, i.e. by advection, is given the symbol Qs. The term "advection' (cf. Section 1.1) is normally taken to relate to horizontal transport of water into an area, but water carried to the surface in upwelling currents, or carried away from it in downwelling currents, also contributes to Qs . Indeed, heat transport - like current flow -has areas of convergence and divergence (cf. Figure 3.27). However, while converging surface water tends to sink, a region of convergence of heat (Q\ positive) can result in a rise in temperature leading to heat being lost upwards (as Qh, Qe and Qh) as well as being mixed downwards.

In summary, the heat-budget equation for any part of the ocean should include the following terms:

Qs - solar energy, received by the ocean as short-wave radiation;

Qb - the net loss of energy from the surface of the ocean as long-wave (back-) radiation:

Qc- the heat lost by evaporation from the surface, less any heat gained by condensation at the surface;

Qh - the net amount of heat transferred to the atmosphere by conduction across the air-sea interface (but see later);

Q{ - the amount of surplus heat actually available to increase the temperature of the water: when there is a heat deficit, this term will be negative, and there will be a fall in the temperature of the water;

Qv - the net amount of heat gained from adjacent parts of the ocean by advection (including upwelling or sinking of water) and mixing: when heat is lost by advection. this term will be negative. (For the ocean as a whole, Qv is of course zero as it refers to the redistribution of heat within the ocean.)

Ocean Circulation Distribution Heat

Figure 6.5 The global distribution of sea-surface temperature (b) in January.

Note: Ignore differences in intensity of colour between (a) and (b).

Figure 6.5 The global distribution of sea-surface temperature (b) in January.

Note: Ignore differences in intensity of colour between (a) and (b).

The full heat-budget equation for a part of the oceans is therefore:

Getting Started With Solar

Getting Started With Solar

Do we really want the one thing that gives us its resources unconditionally to suffer even more than it is suffering now? Nature, is a part of our being from the earliest human days. We respect Nature and it gives us its bounty, but in the recent past greedy money hungry corporations have made us all so destructive, so wasteful.

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Responses

  • Sarah
    How is ocean circulation indirectly tied to solar radiation?
    12 months ago

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