Dynamic topography
5.2 MONSOONAL CIRCULATION
6.1.2 THE HEAT-BUDGET 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 ( I ) o f the radiation emitted increases in proportion to the fourth power of the absolute temperature (73; i.e. I = ~ T 4. This is known as Stefan's Law and the
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Figure 6.4 The radiation balance (Qs- Qb) at the Earth's surface, in W m -2, 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.
constant ~ 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 g a s e s - especially carbon dioxide and o z o n e - 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 Q~) but also the net emission of long- wave radiation (also known as back-radiation, and so given the symbol Qb).
For all latitudes, Q ~ - Qb is generally positive, i.e. the oceans absorb more radiant energy than they emit (Figure 6.4), although at higher latitudes the value of Q~ - Qb varies significantly with the time of year.
Of the total amount of energy received from the Sun by the world's oceans, about 41% is lost to the atmosphere and, indirectly, to space, as long-wave radiation, and about 54% is lost as latent heat through evaporation from the sea-surface. A relatively small amount - about 5% - is lost to the overlying atmosphere by conduction. Heat loss by evaporation is generally given the symbol Qe, 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 b u d g e t must balance.
Heat is not only being continuously gained and lost from the oceans, but also redistributed within them, by currents and mixing.
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 u p w e l l i n g - 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 Q,. 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 Q,. Indeed, heat t r a n s p o r t - like current f l o w - 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 Qb, Qc 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:
Q~- 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;
Q e - 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 t - 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;
Q , - 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, Q,. is of course zero as it refers to the redistribution of heat within the ocean.)
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Figure 6.5 The global distribution of sea-surface temperature (~ (a)in July, (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:
Q,~ + Q,. = Qb + Qh + Qc + Qt (6.1)
Assessing the relative sizes of the quantities in Equation 6.1 has been an ongoing challenge for oceanographers. However, we can review the principles behind the methods for estimating them, and look briefly at some of the problems encountered in practice.
Values for radiation gain (Q~) can be estimated from knowledge of incoming solar radiation (cf. Figures 1.4(a) and 6.2). Values for radiation loss (Qb) can be estimated using the temperature of the surface skin of the ocean. This is often determined by measuring the temperature at a few metres depth, and then applying a correction; this method can give good results as long as a shallow diurnal (i.e. daytime) thermocline has not developed. Sea-surface temperature is also needed to estimate Qh and Qe.
The most accurate results are obtained by using a combination of in situ and satellite measurements. Global scale temperature data are now available through the use of satellite-borne radiometers (cf. Figure 4.31 (a)). These measure the radiation intensity, at different wavelengths, at the top of the atmosphere; the sea-surface temperature itself is determined using assumptions about the effects of cloud cover and about atmospheric concentrations of those variable constituents that absorb and re-emit radiation, in particular water vapour and aerosol droplets.
For many decades, meteorological and oceanographic data have been collected regularly, not only from research vessels, but also from weather ships (now mostly decommissioned), buoys, and enormous numbers of commercial and Admiralty vessels and other 'ships of opportunity', now referred to as Voluntary Observing Ships. Despite the observation code (Section 4.1.1), observational practice and positioning of instruments vary from ship to ship, so care has to be taken in comparing or combining data.
There are also problems regarding the quantity and, in particular, the distribution of data. Of necessity, observations are concentrated along shipping lanes, and until recently, some regions- especially in the Pacific- were completely devoid of reliable data.
Nevertheless, useful empirical relationships have been derived using those variables that are regularly determined, especially mean cloudiness, relative humidity immediately above the surface of the water, and the surface temperature. Figure 6.6 illustrates the empirically determined relationship between these last two variables and Qb.
Figure 6.6 Curves showing how the net back- radiation, O b (in W m-2), from the sea-surface to a clear sky, varies as a function of the sea- surface temperature and the relative humidity at an altitude of a few metres. Relative humidity is a measure of the degree of saturation of the air. It is defined as: (actual water vapour pressure)/
(saturation water vapour pressure at the ambient temperature), expressed as a percentage.
At first sight, no: according to Figure 6.6, for a given relative humidity Qb decreases with temperature. The explanation for this apparent anomaly lies in the fact that the warmer the air over the oceans, the more water it can hold before becoming saturated. Thus, a given relative humidity value at high temperature corresponds to a greater atmospheric water vapour content than the same relative humidity at a lower temperature. The more water vapour there is in the atmosphere, the more long-wave radiation is absorbed by it, and the more is radiated back to the sea-surface, thus decreasing the net loss of long-wave energy from the sea-surface. Global patterns of outgoing long-wave radiation (often referred to as OLR), compiled from satellite observations, are extremely useful climatological tools.
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Figure 6.9 The variation with latitude of the mean values (per unit area) for heat-budget terms relating to heat transfer across the air- sea interface. In each case, the full curve is for January and the broken curve is for July.
(a) The terms for radiative gain and loss (Qs and Qb);
(b) the terms relating to the 'turbulent fluxes', Qh (sensible heat, brick-red curve) and Qe (latent heat, blue curve);
(c) the net heat loss/gain, Qnet.
The first factor is that in the Northern Hemisphere large amounts of heat are lost as Qe from the warm western boundary currents (cf. Question 6.3) (this warm water moving polewards also accounts for high values of Qb in the same regions). The second marked difference is that Qh plays a much greater role in winter cooling of the ocean in the Northern Hemisphere than in the Southern Hemisphere (cf. Figures 6.7 and 6.9(b)) - this is a consequence of outbreaks of extremely cold air from the continents passing over relatively warm surface waters.
So far in this discussion of the oceanic heat budget, we have been ignoring Qt on the assumption that for any given latitude band, the heat gained is equal to the heat lost - i.e. on average, Qt = 0 - at least over periods of several years.
Figure 6.9 also does not include the Q,. term for heat transport within the oceans. As discussed in earlier Chapters, ocean currents transport heat from low to high latitudes; the advective loss of heat from low-latitude regions ensures they do not continually heat up, while the advective gain of heat by high-latitude regions ensures they do not continually cool down. For the
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Figure 6.10 The global distribution of
Qnet (W m-2), the net heat loss/gain at the
sea-surface, for (a) July and (b) January.
Red, orange and yellow indicate the areas where there is the greatest net gain of heat by the sea; darker blues and purple indicate the areas where there is the greatest net loss of heat from the sea.
purposes of heat-budget calculations, it may therefore be assumed that at any location, over periods of a few years (so global warming may be ignored), the mean temperature of the water remains constant and Qt is zero.
As a result of the poleward transport of heat in warm currents, the surface of the sea is generally above the freezing point of seawater (--- - 1 . 9 ~ except at very high latitudes. If sea-ice does form, however, the radiation balance is changed dramatically. The a l b e d o of the surface - i.e. the percentage of incoming radiation that is reflected - increases, perhaps to as much as 80-90c~. Thus Q~ is greatly reduced: however, Qb for ice is much the same as it is for water, so Q~ - Qb is also significantly decreased. Once ice has formed, therefore, it tends to be maintained. On the other hand, it has been estimated that the balance in the Arctic Sea is fairly fine, so that if the ice cover in a particular area were to n~elt, the resulting increase in Q~ - Q b
might well keep the sea ice-free. Because of the positive feedback loop between decreasing ice/snow c o v e r ( o n both land and sea) and decreasing albedo, climatologists believe that the effects of global warming will develop more rapidly in the Arctic than elsewhere. In this context, we have space only to note that over the last decade or so, pack ice in the Arctic Sea has become thinner, and open water has been observed at the North Pole in summer.
However, it is not a simple task to work out what effect local ice-melting or ice-formation will have on the overall heat budget. For example, when ice cover increases, heat losses by conduction/convection (Qh) and by evaporation (Q~) are reduced, but the temperature of surface waters is still likely to be lowered until a new heat balance is attained. During this period, the input of heat from adjacent parts of the ocean (Q,) is likely to increase substantially. A small initial decrease in surface temperature in regions that are already close to freezing point can therefore have a considerable effect on the heat budget, not only of the overlying atmosphere but also of a very much wider area of ocean. In Section 6.3, you will see that the interaction between atmosphere, ocean and ice is further complicated by the important role played by the ocean's salt content.
In considering the heat budget of the ocean, we have assumed that, over periods of several years at least, the Earth's heat supply - incoming solar radiation - remains constant, and that as a result the ocean is neither heating up nor cooling down. We have in effect been applying the principle of conservation of energy. In Section 4.2.3, we introduced the principle of continuity, which is another way of expressing the principle of conservation of mass which, because seawater is nearly incompressible, in turn
approximates to the conservation of volume. Another conservation principle that is very important in oceanography is the principle of conservation of salt.
The principle that the amount of salt in the oceans remains constant may, at first sight, appear to be seriously flawed, because salt is being continually added by rivers, at a rate of about 3.6 x 10 9 tonnes a year. However, there is a consensus among marine scientists that the rates of input of dissolved substances to the oceans are balanced by their rates of removal to the sediments, so that the oceans are in a steady state. The salt content of the oceans, and hence the average salinity of seawater, therefore change little with time. So, for all practical purposes, the principle of conservation of salt is a valid one.
Of course, at a given location in the ocean, the salinity may be changed.
Within the oceans, this occurs through the mixing together of waters with different salinities to produce water with an intermediate salinity. At the surface of the ocean, salinity is increased by evaporation, and decreased as a result of dilution by rain and snow and, occasionally, by condensation on the sea-surface. Figure 6.11 (a) shows the distribution of the mean surface salinity and Figure 6.1 l(b) demonstrates the correlation between surface salinity and the balance between evaporation and precipitation ( E - P).
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Figure 6.11 (a) The mean annual distribution of surface salinity. Note that although they are effectively parts per thousand by weight, salinity values have no units because the salinity of a water sample is determined as the ratio of the electrical conductivity of the sample to the electrical conductivity of a standard. These salinity values are sometimes quoted as 'p.s.u.' or practical salinity units.
(b) Average values of salinity, S (black line), and the difference between average annual evaporation and precipitation ( E - P) (blue line), plotted against latitude.
The difference in surface salinities between the Pacific and the Atlantic is reflected in the marked difference between the average salinities of the two oceans as a whole: about 34.9 for the Atlantic and about 34.6 for the Pacific.
Awareness of the global variations of such factors as sea-surface salinity, local evaporation-precipitation b a l a n c e s - and indeed of the various heat- budget terms - is essential if we are to quantify fluxes of water (and heat) across the ocean-atmosphere boundary. The redistribution of salt and heat within the ocean is studied by monitoring the movement of bodies of water with characteristic combinations of temperature and salinity. These
identifiable bodies of water are the subject of Section 6.3.
First, however, let us see how the principle of conservation of salt may be applied on a relatively small scale.
6.2.1 PRACTICAL APPLICATION OF THE PRINCIPLES OF CONSERVATION AND