The waters of the ocean are continually m o v i n g - in powerful currents like the Gulf Stream, in large gyres, in features visible from space (Figure 1.1), and in smaller swirls and eddies ranging in size down to a centimetre across or less.
Figure 1.1 These spiral eddies in the central Mediterranean Sea (made visible through the phenomenon of 'sun glint') were photographed from the Space Shuttle Challenger. Measuring some 12-15 km across, they are only one example of the wide range of gyral motions occurring in the oceans.
The short answer is: energy from the Sun, and the rotation of the Earth.
The most obvious way in which the Sun drives the oceanic circulation is through the circulation of the atmosphere - that is, winds. Energy is transferred from winds to the upper layers of the ocean through frictional coupling between the ocean and the atmosphere at the sea-surface.
The Sun also drives ocean circulation by causing variations in the temperature and salinity of seawater which in turn control its density.
Changes in temperature are caused by fluxes of heat across the air-sea boundary; changes in salinity are brought about by addition or removal of freshwater, mainly through evaporation and precipitation, but also, in polar regions, by the freezing and melting of ice. All of these processes are linked directly or indirectly to the effect of solar radiation.
If surface water becomes denser than the underlying water, the situation is unstable and the denser surface water sinks. Vertical, density-driven circulation that results from cooling and/or increase in salinity - i.e.
changes in the content of heat and/or s a l t - is known as therrnohaline circulation. The large-scale thermohaline circulation of the ocean will be discussed in Chapter 6.
Except for a relatively thin layer close to the solid Earth, frictional coupling between moving water and the Earth is weak, and the same is true for air masses. In the extreme case of a projectile moving above the surface of the Earth, the frictional coupling is effectively zero. Consider, for instance, a missile fired northwards from a rocket launcher positioned on the Equator (Figure 1.2(a)). As it leaves the launcher, the missile is moving eastwards at the same velocity as the Earth's surface as well as moving northwards at its firing velocity. As the missile travels north, the Earth is turning eastwards beneath it. Initially, because it has the same eastward velocity as the surface of the Earth, the missile appears to travel in a straight line.
However, the eastward velocity at the surface of the Earth is greatest at the Equator and decreases towards the poles, so as the missile travels
progressively northwards, the eastward velocity of the Earth beneath becomes less and less. As a result, in relation to the Earth, the missile is moving not only northwards but also eastwards, at a progressively greater rate (Figure 1.2(b)). This apparent deflection of objects that are moving over the surface of the Earth without being frictionally bound to it - be they missiles, parcels of water or parcels of a i r - is explained in terms of an apparent force known as the Coriolis force.
Figure 1.2 (a) A missile launched from the Equator has not only its northward firing velocity but also the same eastward velocity as the surface of the Earth at the Equator. The resultant velocity of the missile is therefore a combination of these two, as shown by the double arrow.
(b) The path taken by the missile in relation to the surface of the Earth. In time interval 7"1, the missile has moved eastwards to/1/I1, and the Earth to G1;in the time interval T2, the missile has moved to M2, and the Earth to G2. Note that the apparent deflection attributed to the Coriolis force (the difference between M~ and G~ and M2 and G2)increases with increasing latitude. The other blue curves show possible paths for missiles or any other bodies moving over the surface of the Earth without being strongly bound to it by friction.
Figure 1.3 Diagram of a hypothetical cylindrical Earth, for use with Question 1.1.
The example given above, of a missile fired northwards from the Equator, was chosen because of its simplicity. In fact, the rotation of the (spherical) Earth about its axis causes deflection of currents, winds and projectiles, irrespective of their initial direction (Figure 1.2(b)). Why this occurs will be explained in Chapter 4, but for now you need only be aware of the
following important points:
1 The magnitude of the Coriolis force increases from zero at the Equator to a maximum at the poles.
2 The Coriolis force acts at right angles to the direction of motion, so as to cause deflection to the right in the Northern Hemisphere and to the left in the Southern Hemisphere.
How these factors affect the direction of current flow in the oceans, and of winds in the atmosphere, is illustrated by the blue arrows in Figure 1.2(b).
When missile trajectories are determined, the effect of the Coriolis force is included in the calculations, but the allowance that has to be made for it is relatively small. This is because a missile travels at high speed and the amount that the Earth has 'turned beneath' it during its short period of travel is small. Winds and ocean currents, on the other hand, are relatively slow moving, and so are significantly affected by the Coriolis force. Consider, for example, a current flowing with a speed of 0.5 m s -1 (,~ 1 knot) at about 45 ~ of latitude. Water in the current will travel approximately 1800 metres in an hour, and during that hour the Coriolis force will have deflected it about 300 m from its original path (assuming that no other forces are acting to oppose it).
Deflection by the Coriolis force is sometimes said to be cum sole (pronounced 'cum so-lay'), or 'with the Sun'. This is because deflection occurs in the same direction as that in which the Sun appears to move across the sky - towards the right in the Northern Hemisphere and towards the left in the Southern Hemisphere.
The Coriolis force thus has the visible effect of deflecting ocean currents.
It must also be considered in any study of ocean circulation for another, less obvious, reason. Although it is not a real force in the fixed framework of space, it is real enough from the point of view of anything moving in relation to the Earth. We can study, and make predictions about, currents and winds within which the Coriolis force is balanced by horizontal forces resulting from pressure gradients, and for which there is no deflection. Such flows are described as geostrophic (meaning 'turned by the Earth') and will be discussed in Chapters 2 and 3.
Because solar heating, directly and indirectly, is the fundamental cause of atmospheric and oceanic circulation, the second half of this introductory Chapter will be devoted to the radiation balance of planet Earth.
The solid red curves in Figure 1.4(a)(i) and (ii) show the incoming solar radiation reaching the Earth and atmosphere, as a function of latitude, for the northern summer and the southern summer, respectively. The intensity of incoming solar radiation is greatest for mid-latitudes in the hemisphere experiencing summer, while for high latitudes in the winter hemisphere, the oblique angle of the Sun's rays, combined with the long periods of winter darkness, results in amounts of radiation received being low.
However, the Earth not only receives short-wave radiation from the Sun, it also re-emits radiation, of a longer wavelength. Little of this long-wave radiation is radiated directly into space; most of it is absorbed by the
Figure 1.4 (a) The radiation balance at the top of the atmosphere plotted against latitude (scaled according to the Earth's surface area) for (i) the northern summer and (ii) the southern summer. The red solid line is the intensity of incoming solar radiation and the red dashed line is the intensity of radiation lost to space (both determined using satellite-borne radiometer).
(b) The average temperature of surface waters at different latitudes. At a given latitude, there will be surface waters whose annual mean temperatures are higher or lower than shown by the curve; this range is represented by the thickness of the pink envelope.
15 atmosphere, particularly by carbon dioxide, water vapour and cloud
droplets. Thus, the atmosphere is heated from beneath by the Earth and itself re-emits long-wave radiation into space. This generally occurs from the top of the cloud cover where temperatures are surprisingly similar at all latitudes. The intensity of the radiation emitted into space therefore does not vary greatly with latitude, although as can be seen from the dashed curves in Figure 1.4(a), it is highest for the subtropics and lowest for high latitudes in the hemisphere experiencing winter.
In Figure 1.4(a), the two areas labelled 'net surplus' are together about equal to those labelled 'net loss'. This suggests that the radiation budget for the Earth-ocean-atmosphere system as a whole is in balance, i.e. that over the course of a year the system is not gaining more radiation energy than it is losing (or vice versa). Note that this use of areas under curves only works here because the horizontal axis is increasingly compressed towards higher latitudes to compensate for the decreasing area of the globe within given latitude bands. Note also that the temperature at the top of the atmosphere is not directly related to the global temperature in general so plots such as those in Figure 1.4(a) do not allow us to determine whether the 'enhanced greenhouse effect' resulting from increasing concentrations of atmospheric CO2 is leading to global warming.
The positive radiation balance at low latitudes, and the negative one at high latitudes, results in a net transfer of heat energy from low to high latitudes, by means of wind systems in the atmosphere and current systems in the ocean.
There has been much debate about the relative importance of the atmosphere and ocean in the poleward transport of heat. Figure 1.5 shows estimates of poleward heat transport, based on satellite observations of the upper atmosphere, and measurements within the atmosphere, published in 1985. Positive values correspond to northward transport and negative values to southward transport.
Wind systems redistribute heat partly by the advection of warm air masses into cooler regions (and vice versa), and partly by the transfer of latent heat which is taken up when water is converted into water vapour, and released when the water vapour condenses in a cooler environment. The tropical storms known as cyclones or hurricanes are dramatic manifestations of the transfer of energy from ocean to atmosphere in the form of latent heat. The generation of cyclones, and their role in carrying heat away from the tropical oceans, will be described in Chapter 2.
Figure 1.5 Estimates of the contributions to poleward heat transport (red curve) by the ocean (solid blue curve) and the atmosphere (dashed blue curve). Positive values are northward heat transport, negative values are southward heat transport. The total heat transport was derived from satellite measurements at the top of the atmosphere, heat transported by the atmosphere was estimated using measurements of
atmospheric heat fluxes, and the heat transported by the ocean was calculated as the difference between the two.
0 c/') c---
t - " -
1 Circulation in both the oceans and the atmosphere is driven by energy from the Sun and modified by the Earth's rotation.
2 The radiation balance of the Earth-ocean-atmosphere system is positive at low latitudes and negative at high latitudes. Heat is redistributed from low to high latitudes by means of wind systems in the atmosphere and current systems in the ocean. There are two principal components of the ocean circulation: wind-driven surface currents and the density-driven (thermohaline) deep circulation.
3 Air and water masses moving over the surface of the Earth are only weakly bound to it by friction and so are subject to the Coriolis force. The Coriolis force acts at right angles to the direction of motion, so as to deflect winds and currents to the right in the Northern Hemisphere and to the left in the Southern Hemisphere; the deflections are significant because winds and currents travel relatively slowly. The Coriolis force is zero at the Equator and increases to a maximum at the poles.
Now try the following questions to consolidate your understanding of this Chapter.
Anyone who has seen images of the Earth from space, like that in Figure 2.1, will have been struck by how much of our planet is ocean, and will have wondered about the swirling cloud patterns. In fact, the atmosphere and the ocean form one system and, if either is to be understood properly, must be considered together. What occurs in one affects the other, and the two are linked by complex feedback loops.
Figure 2.1 The Earth as seen from a geostationary satellite positioned over the Equator.
The height of the satellite (about 35 800 km) is such that almost half of the Earth's surface may be seen at once. The outermost part of the image is extremely foreshortened, as can be seen from the apparent position of the British Isles. Colours have been constructed using digital image-processing to simulate natural colours.
The underlying theme of this Chapter is the redistribution of heat by, and within, the atmosphere. We first consider the large-scale atmospheric circulation of the atmosphere, and then move on to consider the smaller- scale phenomena that characterize the moist atmosphere over the oceans.
Figure 2.2(a) shows what the global wind system would be if the Earth were completely covered with water. As you will see later, the existence of large land masses significantly disturbs this theoretical pattern, but the features shown may all be found in the real atmosphere to greater or lesser extents.
In the lower atmosphere, pressure is low along the Equator, and warm air converges here, rises, and moves polewards. Because the Earth is spherical, air moving polewards in the upper part of the troposphere is forced to converge, as lines of longitude converge. As a result, at about 30 ~ N and S there is a 'piling up' of air aloft, which results in raised atmospheric
pressure at the Earth's surface below.* There is therefore a pressure gradient from the subtropical highs (where air is subsiding) towards the equatorial low (Figure 2.2(a)) and, as winds blow from areas of high pressure to areas of low pressure, equatorward winds result. These are the Trade Winds.
The answer, of course, is because of the Coriolis force. Away from the Equator, the Coriolis force acts to deflect winds and currents to the right in the Northern Hemisphere and to the left in the Southern Hemisphere.
Note that the Trade Winds are named the South-East and North-East Trades because they come from the south-east and north-east. However, whereas winds are always described in terms of where they are blowing from, currents are described in terms of where they are flowing towards. Thus, a southerly current flows towards the south and a southerly wind blows from the south. To avoid confusion, we will generally use southward rather than souther/y (for example) when describing current direction.
The Trade Winds form part of the atmospheric circulation known as the Hadley circulation, or Hadley ceils, which can be seen in Figure 2.2(a) and (b).
Strictly speaking, the term 'Hadley cell' refers only to the north-south component of the circulation. Because the flow is deflected by the Coriolis force, in three dimensions the circulation follows an approximately spiral pattern (Figure 2.2(c)).
Figure 2.3(a) and (b) (p. 20) show the prevailing winds at the Earth's surface for July and January, along with the average positions of the main regions of high and low pressure for these months of the year. Figure 2.3(c) shows the surface winds over the Pacific and Atlantic for one particular day in 1999.
*Generally, atmospheric pressure at sea-level is determined by the weight of the column of air above, even if that air is gently rising or subsiding in regions of low or high pressure. Only in intense thunderstorms, cyclones and tornadoes, where the air has an appreciable upward acceleration~ is atmospheric pressure directly affected by the vertical motion of the air.
Figure 2.2 (a) Wind system for a hypothetical water-covered Earth, showing major winds and zones of low and high pressure systems. Vertical air movements and circulation cells are shown in exaggerated profile either side, with
characteristic surface conditions given on the right. Note that convergence of air at low levels and divergence at high levels results in air rising, while the converse results in air sinking. The two north-south cells on either side of the Equator make up the Hadley circulation. ITCZ = Intertropical Convergence Zone, the zone along which the wind systems of the Northern and Southern Hemispheres meet. (This and other details are discussed further in the text.) (b) Section through the atmosphere, from polar regions to the Equator, showing the general circulation, the relationship of the polar jet stream to the polar front, and regions of tropical cloud formation. Note that much of the poleward return flow takes place in the upper part of the troposphere (the part of the atmosphere in which the temperature decreases with distance above the Earth); the tropopause is the top of the troposphere and the base of the stratosphere.
(c) Schematic diagram to show the spiral circulation patterns of which the Trade Winds form the surface expression; the north-south component of this spiral circulation (see right- hand side)is known as the Hadley circulation or 'Hadley cells' (also shown on Figure 2.2(a)).
Figure 2.3 The prevailing winds at the Earth's surface, and the average position of the Intertropical Convergence Zone for (a) July (northern summer/southern winter) and (b) January (southern summer/northern winter). Also shown are the positions of the main regions of high and low atmospheric pressure (red/pink for high pressure, blue for low). Note that as these maps represent conditions averaged over a long period, they show simpler patterns of highs and lows, and of wind flow, than would be observed on any one day (cf. the more complicated patterns in (c)).
Extreme conditions are not represented, as they have been 'averaged out' (which is not the case in (c), above).
(c) Surface winds over the Pacific and Atlantic Oceans for one day in 1999 (to be used later, in Question 2.6). Green/pale blue -- lowest wind speeds, yellow = highest wind speeds. The maps have been obtained using a satellite-borne 'scatterometer' which measures microwave radar back-scattered from the sea-surface (wind speed is calculated from the estimated roughness of the sea-surface, and wind direction determined from the inferred orientation of wave crests). Note the complexity of the flow pattern, and localized extreme conditions, which do not show up in the maps of averaged data in Figure 2.3(a) and (b).
In general, not that closely, although the actual and hypothetical winds a r e
very similar over large areas of ocean, away from the land. You may also have noticed that the simple arrangement of high pressure systems in the subtropics and low pressure in subpolar regions is more clearly seen in the Southern Hemisphere, which is largely ocean.
If you compare Figure 2.3(a) and (b), you will see that the greatest seasonal change occurs in the region of the Eurasian land mass. During the northern winter, the direction of prevailing winds is outwards from the Eurasian land mass;
by the summer, the winds have reversed and are generally blowing in towards the land mass. This is because continental masses cool down and heat up faster than the oceans (their thermal capacity is lower than that of the oceans) and so in winter they are colder than the oceans, and in summer they are warmer. Thus, in winter the air above the Eurasian land mass is cooled and becomes denser, so that a large shallow high pressure area develops, from which winds blow out towards regions of lower pressure. In the summer, the situation is reversed: air over the Eurasian land mass heats up, and becomes less dense. There is a region of warm rising air and low pressure which winds blow t o w a r d s . The oceanic regions most affected by these seasonal changes are the Indian Ocean and the western tropical Pacific, where the seasonally reversing winds are known as the monsoons.
The distribution of ocean and continent also influences the position of the zone along which the wind systems of the two hemispheres converge. The zone of convergence - known as the I n t e r t r o p i c a l C o n v e r g e n c e Zone or I T C Z - is generally associated with the zone of highest surface temperature. Because the continental masses heat up faster than the ocean in summer and cool faster in winter, the ITCZ tends to be distorted southwards over land in the southern summer and northwards over land in the northern summer (Figure 2.3).
Figure 2.4 Simple atmospheric convection system for a hypothetical non-rotating Earth.
Heat is transported to higher latitudes by the atmosphere both directly and indirectly. If you look at Figure 2.2(a) and (b), you will see that motion in the upper troposphere is generally polewards. Air moving equatorwards over the surface of the Earth takes up heat from the oceans and continents.
When it later moves polewards, after rising at regions of low atmospheric pressure such as the Equator, heat is also transported polewards. Thus, any mechanism that transfers heat from the surface of the Earth to the
atmosphere also contributes to the poleward transport of heat. The most spectacular example of heat transfer from ocean to atmosphere is the generation of tropical cyclones, which will be discussed in Section 2.3.1.
The Hadley cells, of which the Trade Winds are the surface expressions, may be seen as simple convection cells, in the upper limbs of which heat is transported polewards. How heat is carried polewards at higher latitudes is not quite so obvious.
2.2.1 ATMOSPHERIC CIRCULATION IN MID-LATITUDES
Like the Hadley cells, the low and high pressure centres characteristic of mid-latitudes are a manifestation of the need for heat to be moved
polewards, to compensate for the radiation imbalance between low and high latitudes (Figure 1.4). Though less spectacular than tropical cyclones, mid- latitude weather systems transfer enormous amounts of h e a t - a single travelling depression may be transferring 10-100 times the amount of heat transported by a tropical cyclone.
If, in the long term, no given latitude zone is to heat up, heat must be transported polewards at all latitudes. On an idealized, non-rotating Earth, this could be achieved by a simple atmospheric circulation pattern in which surface winds blew from the polar high to the equatorial low, and the warmed air rose at the Equator and returned to the poles at the top of the troposphere to complete the convection cell (see Figure 2.4).
However, because the Earth is rotating, and moving fluids tend to form eddies, this simple system cannot operate. The Coriolis force causes equatorward winds to be deflected to the fight in the Northern Hemisphere and to the left in the Southern Hemisphere, so acquiring an easterly component in both
hemispheres- as we have seen, the Trade Winds blow towards the Equator from the south-east and north-east. But the Coriolis force increases with latitude, from zero at the Equator to a maximum at the poles, so while winds are deflected relatively little at low latitudes, at higher latitudes the degree of deflection is much greater. The Coriolis force and the inherent instability of air flow together lead to the generation of atmospheric vortices. These are the depressions and anticyclones so familiar to those who live in temperate regions. Their predominantly near-horizontal, or slantwise, circulatory patterns contrast with the near-vertical Hadley circulation of low latitudes.
Before proceeding further, we should briefly summarize the conventions used in describing atmospheric vortices. Circulations around low pressure centres, whether in the Northern Hemisphere (where they are anticlockwise) or in the Southern Hemisphere (where they are clockwise), are known as cyclones (or lows, or depressions). The way in which air spirals in and up in cyclonic circulation is shown schematically in Figure 2.5(a). Circulations around high pressure centres (clockwise in the Northern Hemisphere,
Figure 2.5 Schematic diagrams to illustrate how (a) air spirals inwards and upwards in low pressure areas (cyclones) and (b) air spirals downwards and outwards in high pressure areas (anticyclones) (drawn for Northern Hemisphere situations). The contours are isebars (lines connecting points of equal atmospheric pressure) and the numbers give typical pressures at ground level, in millibars. Note that here the angle at which the air flow crosses the isobars is somewhat exaggerated. Within ~ 1 km of the Earth's surface, the air flow would cross the isobars at small angles, while above that it would follow the isobars quite closely.
anticlockwise in the Southern Hemisphere), in which air spirals downwards and outwards, are known as anticyclones (Figure 2.5(b)).
If you study Figure 2.5(a), you will see that the direction of air flow is such that the pressure gradient (acting from higher to lower pressure, at right angles to the isobars) is to the left of the flow direction, in the opposite direction to the Coriolis force, which (as this is the Northern Hemisphere) is to the right of the flow direction. The same is true in the case of the
anticyclone in Figure 2.5(b), although here the pressure gradient is acting outwards and the Coriolis force inwards. If the balance between pressure gradient force and Coriolis force were exact, the winds would blow along the isobars. As mentioned in Chapter 1, this type of fluid flow is known as geostrophic. If you study weather charts, you will see that, away from the centres of cyclones and anticyclones, air flow is often geostrophic, or almost so, with the wind arrows either parallel to the isobars or crossing them at small angles. Geostrophic flow is also important in the oceans, as will become clear in Chapter 3.
Figure 2.6 Highly schematic diagram to show the poleward transport of heat in the atmosphere by means of mid-latitude vortices (cyclones and anticyclones).
Moving air masses mix with adjacent air masses and heat is exchanged between them. For example, air moving northwards around a Northern Hemisphere cyclone or anticyclone will be transporting relatively warm air polewards, while the air that returns equatorwards will have been cooled. This may be likened to the stirring of bath water to encourage the effect of hot water from the tap to reach the far end of the bath, and is shown schematically in Figure 2.6.
Mixing occurs on a variety of scales. Between the warm westerlies and the polar easterlies, there is a more or less permanent boundary region known as the Polar Front (Figure 2.2(b)). Flowing at high level along the polar limit of the westerlies is the fast air current known as the polar jet stream.
For days or weeks at a time, this may simply travel eastwards around the globe, but it tends to develop large-scale undulations. As a result, tongues of warm air may be allowed to penetrate to high latitudes, and cold polar air masses may be isolated at relatively low latitudes (Figure 2.7(a)).
Figure 2.7 (a) Schematic diagram showing later stages (1,2)in the development of undulations in the northern polar jet stream, which flows near the tropopause at heights of 10 km or more, cf. Figure 2.2(b)). Meanwhile, cyclones (or depressions, shown here as swirls of cloud) form beneath the poleward-flowing parts of the jet stream, and anticyclones (not shown) form below the equatorward-flowing parts.
For clarity, we have omitted the subtropical high pressure regions in mid-latitudes and the Hadley circulation at low latitudes.
(b) Satellite photomosaic of the Southern Hemisphere showing cloud cover for one day in April 1983 (i.e. during the southern winter). The cyclonic storms that develop below the poleward-trending sections of the jet stream mean that its undulating path is shown up by the cloud pattern. In comparing the cloud swirls with the path of the polar jet stream shown in (a), remember that in the Southern Hemisphere air moves clockwise around subpolar lows.
Figure 2.8 (a) Stages in the development of a mid-latitude cyclone (depression)in the Northern Hemisphere, showing how it contributes to the poleward transport of heat.
The pale purple band represents the sloping frontal boundary, where warm air overlies a wedge of cold air (as in Figure 2.2(b)). Frontal boundaries can be anything from 50 km to more than 200 km across. That part of the front where cold air is advancing is known as a cold front, and that part where warm air is advancing, as a warm front. Where they combine, an occluded front results.
(b) Typical weather chart for the northern Atlantic/north-west Europe (for 31 October 1999), showing waves in the polar front developing into low pressure systems. The heavy lines are where the warm and cold air masses meet, and the symbols on these lines indicate whether the front is warm or cold (cf. (a)), or a combination (i.e. occluded).
25 The undulations that develop in the polar jet stream are known as Rossby waves, and they always travel ~'estwards around the globe. For reasons that will become clear later (Chapter 5), small-scale waves in the polar front tend to develop into anticyclones below equatorward-flowing parts of the jet stream, and into cyclones (indicated by the cloud spirals in Figure 2.7(a)) below poleward-trending parts of the stream. Often referred to as
depressions, these low pressure systems are common features of weather charts of the north-east Atlantic region. The overall effect is that heat is transported polewards (Figure 2.8).
polar air easterlies
tropical air westerlies
(i) ~ (ii)
(iii) (iv) --.---~" ... ~ (v)
24 ooo :
i ' ' 10 ~ " ""-' ~ o
40 ~ 30 ~ 20 ~
(b) Key coldfront 9 9 w a r m f r o n t ~ occluded front 9 9
We now move on to consider how heat is redistributed within the atmosphere, by means of predominantly vertical motions.
2.2.2 VERTICAL CONVECTION IN THE ATMOSPHERE
Processes occurring at the air-sea interface are greatly affected by the degree of turbulent convection that can occur in the atmosphere above the sea-surface. This in turn is dependent on the degree of stability of the air, i.e. on the extent to which, once displaced upwards, it tends to continue rising.
Two ways in which density may vary with height in a fluid are illustrated in Figure 2.9. Situation (a), in which density increases with height, is unstable, and fluid higher up will tend to sink and fluid lower down will tend to rise.
Situation (b), in which density decreases with height, is stable" a parcel of fluid (at, say, position O) that is displaced upwards will be denser than its surroundings and will sink back to its original position.
Figure 2.9 Possible variations of fluid density with height, leading to (a) unstable and (b) stable conditions.
E3r) . E
( J .E_
(a) density increasing (b) density increasing
The density of air depends on its pressure and its temperature. It also depends on the amount of water vapour it contains - water vapour is less dense than a i r - but for most practical purposes water vapour content has a negligible effect on density. Thus, the variation of density with height in a column of air is determined by the variation in temperature with height.
The variation in temperature with height in the atmosphere is complicated.
For one thing, air, like all fluids, is compressible. When a fluid is compressed, the internal energy it possesses per unit volume by virtue of the motions of its constituent atoms, and which determines its temperature, is increased.
Conversely, when a fluid expands, its internal energy decreases. Thus, a fluid heats up when compressed (a well-known example of this is the air in a bicycle pump), and cools when it expands. Changes in temperature that result from changes in volume/density and internal energy, and not because of gain or loss of heat from or to the surroundings, are described as adiabatic.
Adiabatic temperature changes have a much greater effect on the behaviour of air masses than do other mechanisms for gaining or losing energy (absorbing or emitting radiation, or mixing with other air masses).
Imagine a parcel of air above a warm sea-surface moving upwards in random, turbulent eddying motions. As it rises, it is subjected to decreasing atmospheric pressure and so expands and becomes less dense; this results in an adiabatic decrease in temperature, which for dry air is 9.8 ~ per
kilometre increase in altitude (black line on Figure 2.10). If the adiabatic
Figure 2.10 (a) Graph to illustrate that the rate at which dry air cools adiabatically (black line)is greater than the rate at which saturated air cools adiabatically (blue curve).
Unlike the 'dry' lapse rate, the reduced adiabatic lapse rate for air saturated with water vapour varies with temperature; this is because a small decrease in temperature at high temperatures will result in more condensation than a similar decrease at low temperatures. In the example shown, the air has a temperature of 10 ~ at ground level. (As discussed in the text, in practice, it is atmospheric pressure rather than height as such that is important.)
(b) The implications of the 'dry' and 'saturated' adiabatic lapse rates for the stability of columns of air with various different temperature profiles (dashed red lines).
27 decrease in temperature of a rising parcel of air is less than the local
decrease of temperature with height in the atmosphere, the rising parcel of air will be warmer than the surrounding air and will continue to rise. In other words, this is an unstable situation, conducive to upward convection of air. If, on the other hand, the adiabatic cooling of the rising parcel of air is sufficient to reduce its temperature to a value below that of the surrounding air, it will sink back to its original l e v e l - i.e. conditions will be stable.
However, the situation is further complicated by the presence of water vapour in the air. Water vapour has a high latent heat content, with the result that the constant 'dry' adiabatic lapse rate of 9.8 ~ per km is of limited relevance.
If rising air is saturated with water v a p o u r - or becomes saturated as a result of adiabatic cooling - its continued rise and associated adiabatic cooling results in the condensation of water vapour (onto atmospheric nuclei, such as salt or dust particles), to form water droplets. Condensation releases latent heat of evaporation, which partly offsets the adiabatic cooling, so the rate at which air containing water vapour cools on rising (blue 'saturated' lapse rate in Figure 2.10(a)) is less than the rate for dry air.
The implications of the 'dry' and 'saturated' adiabatic lapse rate for the stability of various columns of air with various different temperature-height profiles is shown in Figure 2.10(b). Over most of the oceans, particularly in winter when the sea-surface is warmer than the overlying air, the variation of temperature with height in the atmosphere, and the water content of the air, are such that conditions are unstable, air rises, and convection occurs.
Convection is further promoted by turbulence resulting from strong winds blowing over the sea-surface. When turbulence is a more effective cause of upward movement of air than the buoyancy forces causing instability, convection is said to be forced. The cumulus clouds characteristic of oceanic regions within the Trade Wind belts are a result of such forced convection (Figure 2.11 (a)).
Figure 2.11 (a) Cumulus clouds over the ocean in the Trade Wind belt.
(b) Cumulonimbus and, at lower levels, cumulus clouds, in the Intertropical Convergence Zone over the Java Sea. Like cumulus,
cumulonimbus form where moist air rises and cools, so that the water vapour it contains condenses to form droplets. However,
cumulonimbus generally extend to much greater heights than cumulus, and their upper parts consist of ice crystals.
As illustrated in Figure 2.2(b), upward development of the Trade Wind cumulus clouds is inhibited by the subsidence of warm air from above. This leads to an increase of temperature with height, or a temperature inversion (Figure 2.12). Rising air encountering a temperature inversion is no longer warmer than its surroundings and ceases its ascent. The warmer air therefore acts as a 'ceiling' as far as upward convection is concerned.
Along the Intertropical Convergence Zone, the 'ceiling' is the tropopause, so the vigorous convection in the ITCZ can extend much higher than that associated with cumulus formation (Figure 2.2(b)). The towering
cumulonimbus that result (Figure 2.11 (b)) allow the ITCZ to be easily seen on images obtained via satellites (Figure 2.13). Convection in the ITCZ is the main way that heat becomes distributed throughout the troposphere in low latitudes.
Figure 2.12 Typical variation of temperature with height in the Trade Wind zone, at about 5 ~ of latitude, showing the temperature inversion (here at an altitude of ~2 km).
Figure 2.13 The ITCZ over the tropical Pacific, clearly marked out by cumulonimbus clouds.
(This is an infra-red image, obtained from the GEOS satellite. The area shown is between
~40 ~ N and ~40 ~ S.)
As discussed in the previous Section, the ocean influences the atmosphere by affecting its moisture content and hence its stability. Intimately related to this is the effect of sea-surface temperature on the atmospheric circulation.
For example, sea-surface temperatures influence the intensity of the Hadley circulation and (as mentioned earlier) the position of the ITCZ generally corresponds to the zone where sea-surface temperatures are highest.
The surface of the sea is usually warmer than the overlying air, and the higher the temperature of the sea-surface, the more heat may be transferred from the upper ocean to the lower atmosphere. Warmer air is less dense and rises, allowing more air to flow in laterally to take its place. Thus, an area of exceptionally high surface temperature in the vicinity of the Equator could lead to an increase in the intensity of the Trade Winds and the Hadley circulation. The position of the ITCZ will also be related to the vigorous convection and low pressure zones associated with high sea-surface
temperatures; and the warmer the sea-surface, the more buoyancy is supplied to the lower atmosphere, and the more vigorous the vertical convection.
As discussed in the previous Section, this effect is enhanced by the fact that the atmosphere over the ocean contains a large amount of water vapour.
In the next Section, you will see a striking example of the influence of sea- surface temperature on the atmosphere.
2.3.1 EASTERLY WAVES AND TROPICAL CYCLONES
A large amount of heat is transported away from low latitudes by strong tropical c y c l o n e s - also known as hurricanes and typhoons. Tropical cyclones only develop over oceans and so it is difficult to study the atmospheric conditions associated with their formation. It is known, however, that they are triggered by small low pressure centres, as may occur in small vortices associated with the ITCZ, or in small depressions that have moved in from higher latitudes. Cyclones may also be triggered by linear low pressure areas that form at right angles to the direction of the Trade Winds and travel with them (Figure 2.14). These linear low pressure regions ('troughs') produce wave-like disturbances in the isobaric patterns, with wavelengths of the order of 2500 km; because they move with the easterly Trade Winds, they are known as e a s t e r l y wa~'es.
Easterly waves usually develop in the western parts of the large ocean basins, between about 5 ~ and 20 ~ N. They occur most frequently when the Trade Wind temperature inversion (Figures 2.2(b) and 2.12) is weakest, i.e.
during the late summer, when the sea-surface, and hence the lower atmosphere in the Trade Wind belt, are at their warmest.
Figure 2.14 Schematic diagram of an easterly wave in the Northern Hemisphere. The black lines are isobars, with sea-level atmospheric pressure given in millibars. Wind direction is shown by the blue arrows. As the wave itself moves slowly westward, lower level air ahead of the 'axis' diverges, and dry air sinking from above to replace it leads to particularly fine weather. Behind the axis, moist air converges and rises, generating showers and thunderstorms (the main rainfall area is shown in greyish-blue).
Ahead of the easterly wave's 'axis', the air flow at low level diverges, so air above sinks, strengthening and lowering the Trade Wind inversion and leading to particularly fine weather. Behind the axis (the 'trough' in
atmospheric pressure), moist air converges and rises, temporarily destroying the Trade Wind inversion and generating showers and thunderstorms.
Although only a small proportion of easterly waves give rise to cyclones, they are important because they bring large amounts of rainfall to areas that remain generally dry as long as air flow in the Trade Winds is unperturbed.
Figure 2.15 Satellite image of Hurricane 'Andrew' moving across the Gulf of Mexico in August 1992.
31 Intense tropical cyclones are not generated within about 5 ~ of the Equator.
Cyclonic (and anticyclonic) weather systems can only form where flow patterns result from an approximate balance between a horizontal pressure gradient force and the Coriolis force (Section 2.2.1) and, as mentioned earlier, the Coriolis force is zero at the Equator and very small within about 5 ~ of it.
Poleward of about 5 ~ of latitude, positive feedback between the ocean and the atmosphere can transform a low pressure area into a powerful tropical cyclone, characterized by closely packed isobars encircling a centre of very low pressure (typically about 950 mbar). Large pressure gradients near the centre of the cyclone cause air to spiral rapidly in towards the low pressure region (anticlockwise in the Northern Hemisphere, clockwise in the Southern Hemisphere), and wind speeds commonly reach 100-200 km hr -1 ( - 3 0 - 6 0 m s -j, see Table 2.2). Violent upward convection of warm humid air results in bands of cumulonimbus and thunderstorms, which spiral in to the core or 'eye' of the c y c l o n e - an area of light winds and little cloud, surrounded by a wall of towering cumulonimbus (see Figures 2.15 and 2.16).
The energy that drives the cyclone comes from the release of latent heat as the water vapour in the rising air condenses into clouds and rain; the resultant warming of the air around the central region of the cyclone causes it to become less dense and to rise yet more, intensifying the divergent anticyclonic flow of air in the upper troposphere that is necessary for the cyclone to be maintained (Figure 2.16). Given their source of energy, it is not surprising that tropical cyclones occur only over relatively large areas of ocean where the surface water temperature is high.
anticyclonic divergent flow at the top of the troposphere
Figure 2.16 Schematic diagram of a tropical cyclone. Moist air spirals inwards and upwards at high speed, forming cumulonimbus clouds arranged in spiral bands which encircle the 'eye'. Meanwhile, in the eye itself (and between the bands), air subsides, warming adiabatically (red arrows), and there are light winds and little cloud.
In practice, the critical sea-surface temperature needed to generate the increased vertical convection which leads to extensive cumulonimbus development and rain and/or cyclone formation is about 27-29 ~ Why should this value be critical? One factor seems to be that the higher the temperature of an air mass the more moisture it can hold, and the greater the upward transfer of latent heat that can occur. Given the positive feedback of the system, a rise in temperature from 27 to 29 ~ has a much greater effect on the overlying atmosphere than a rise from, say, 19 to 21 ~ The full answer to this question is, however, as yet unknown. Furthermore, because the local sea-surface temperature- strictly, the heat content of the uppermost 60 m of ocean - has such a marked effect on the rate of development of a tropical cyclone, predicting the intensity of such a system as it moves across expanses of ocean towards land is extremely difficult.
Figure 2.17 The effect of a cyclone on the surface ocean. Near the centre of the storm - in fact, somewhat to the rear, as it is moving - surface water diverges and upwelling of deeper, cooler water occurs; some distance from the centre, the surface water that has travelled outwards converges with the surrounding ocean surface water and downwelling, or sinking, occurs. In between the zones of upwelling and downwelling, the displaced surface water mixes with cooler subsurface water. (How cyclonic winds lead to upwelling of subsurface water will be explained in Chapter 3.)
Tropical cyclones also occur more often in the western than the eastern parts of the Atlantic and Pacific Oceans. This is because sea-surface temperatures are higher there, for reasons that will become clear in later Chapters.
The violent winds of tropical cyclones generate very large waves on the sea- surface. These waves travel outwards from the central region and as the cyclone progresses the sea becomes very rough and confused. The region where the winds are blowing in the same direction as that in which the cyclone is travelling is particularly dangerous because here the waves have effectively been blowing over a greater distance (i.e. they have a greater fetch). Furthermore, ships in this region are in danger of being blown into the cyclone's path.
Cyclones also affect the deeper structure of the ocean over which they pass.
For reasons that will be explained in Chapter 3, the action of the wind causes the surface waters to diverge so that deeper, cooler water upwells to replace it (Figure 2.17). Thus not only are cyclones affected by sea-surface temperature, but they also modify it, so that their tracks are marked out by surface water with anomalously low temperatures, perhaps as much as 5 ~ below that of the surrounding water.
Characteristic tracks followed by tropical cyclones as they move away from their sites of generation are shown in Figure 2.18. The path of a newly
generated cyclone is relatively easy to predict, because it is largely determined by the general air flow in the surrounding atmosphere - compare the paths in Figure 2.18 with the average winds (for summer) in Figure 2.3. The fact that cyclones nearly always move polewards enhances the contribution that they make to the transport of heat from the tropics to higher latitudes.
If they move over extensive areas of land they begin to die away, as the energy conversion system needed to drive them can no longer operate. Their decay over land may be hastened by increased surface friction and the resulting increased variation of wind velocity with height (vertical wind shear) which inhibits the maintenance of atmospheric vortices. The lower temperatures of land masses (especially at night) may also play a part in their decay. The average lifespan of a tropical cyclone is about a week.
There is great interannual variation in the frequency of tropical cyclones. Over the past few decades there seems to have been an increase in their occurrence, but it is not clear whether this is a genuine long-term increase or part of a cyclical variation. Information about the number of cyclones occurring annually in the various oceanic regions over a 20-year period is given in Table 2.1.
Figure 2.18 Characteristic tracks followed by tropical cyclones, commonly called hurricanes (Atlantic and eastern North Pacific), typhoons (western North Pacific) or cyclones (India and Australia). Initially they move westwards, but then generally curve polewards and eastwards around the subtropical high pressure centres.
The pink regions are those areas where the sea-surface temperature exceeds 27 ~ in summer (mean values for September and March.
in the Northern and Southern Hemispheres, respectively).
Cyclones have a great impact on life in the tropics. They are largely responsible for late summer or autumn rainfall maxima in many tropical areas. The strong winds and large waves associated with them may cause severe damage to natural environments such as reefs; indeed, these catastrophic events play a major role in determining the patterns of distribution of species and life forms within such communities. They may lead to great loss of human life, particularly where there are large populations living near to sea- level, on the flood plains of major rivers or on islands. Quite apart from the high seas caused by the winds, the low atmospheric pressures within a cyclone may cause a storm surge - a local rise in sea-level of up to 5 m or more (see Table 2.2, overleaf). Storm surges can lead to widespread flooding of low-lying areas, and deaths from drowning, post-flood disruption and disease greatly exceed those caused by the winds. A storm surge contributed to the havoc caused by tropical cyclones in Orissa, on the north-west of the Bay of Bengal, in October-November 1999, and the cyclonic disaster which devastated the delta region of the Bay in May 1985 was largely the result of a storm surge further amplified by the occurrence of high tides.
Table 2.1 Numbers of tropical cyclones (> 33 m s -! sustained wind speed) occurring annually during a 20-year period (from 1968/69 to 1989/90) in various oceanic regions.
Maximum Minimum Mean
Atlantic, including Caribbean 12 2 5.4
NE Pacific 14 4 8.9
NW Pacific 24 11 16.0
Northern Indian Ocean 6 0 2.5
SW Indian Ocean 10 0 4.4
SE Indian Ocean/NW of Australia 7 0 3.4
SW Pacific/NE of Australia 11 2 4.3
Global total 65 34 44.9
While sea-surface temperature plays a highly significant role in the climate and weather of tropical regions, its effect at higher latitudes cannot be ignored. For example, the 'hurricane' that struck southern England and parts of continental Europe in October 1987 was generated above a patch of anomalously warm water in the Bay of Biscay.
Table 2.2 The Saffir-Simpson scale for potential cyclone damage.
Category Central Wind speeds Height of
pressure (m s -!) (knots) storm surge
l > 980 33--42 64-82 - 1.5
2 965-979 42--48 83-95 - 2.0-2.5
3 945-964 49-58 96-113 - 2.5--4.0
4 920-944 58--69 114-135 -4.0-5.5
5 < 920 > 70 > 135 > 5.5
Damage mainly to trees, shrubbery and unanchored mobile homes
Some trees blown down
Major damage to exposed mobile homes Some damage to roofs of buildings
Foliage removed from trees: large trees blown down Mobile homes destroyed
Some structural damage to small buildings All signs blown down
Extensive damage to roofs, windows and doors Complete destruction of mobile homes Flooding inland as far as 10 km
Major damage to lower floors of structures near shore Severe damage to windows and doors
Extensive damage to roofs of homes and industrial buildings Small buildings overturned and blown away
Major damage to lower floors of all structures less than 4.5 m above sea-level within 500 m of the shore
Figure 2.19 A water spout near Lower Malecumbe Key, Florida.
Water spouts are similar to cyclones, in that they are funnel-shaped vortices of air with very low pressures at their centres, so that air and water spiral rapidly inwards and upwards. The funnels extend from the sea-surface to the 'parent' clouds that travel with them (see Figure 2.19). They whip up a certain amount of spray from the sea-surface but are visible mainly because the reduction of pressure within them leads to adiabatic expansion and cooling which causes atmospheric water vapour to condense.
Water spouts are much smaller-scale phenomena than cyclones. They range from a few metres to a few hundred metres in diameter, and they rarely last more than fifteen minutes. Unlike cyclones they are not confined to the tropics, although they occur most frequently there, usually in the spring and early summer. They are particularly common over the Bay of Bengal and the Gulf of Mexico, and also occur frequently in the Mediterranean.
2.3.2 A BRIEF LOOK AHEAD
In the previous Section, we concentrated on phenomena resulting from atmosphere-ocean interaction in the tropics, where the two fluid systems are most closely 'coupled'. The interaction of enormous expanses of warm tropical oceans and a readily convecting atmosphere inevitably has a profound effect on climate, and not just at low latitudes. Because the atmosphere-ocean system is dynamic, it has natural oscillations, and the most famous of these, seated in the tropics, but also affecting higher latitudes, is the phenomenon of El Nifio. This and other large-scale atmosphere-ocean oscillations will be discussed in Chapters 4 and 5. A completely different kind of interaction between atmosphere and ocean occurs at high latitudes. As you will see in Chapter 6, this also has a profound effect on the world's climate, over much longer time-scales.
1 The global wind system acts to redistribute heat between low and high latitudes.
2 Winds blow from regions of high pressure to regions of low pressure, but they are also affected by the Coriolis force, to an extent that increases with increasing latitude. Because of the differing thermal capacities of continental masses and oceans, wind patterns are greatly influenced by the geographical distribution of land and sea.
3 In mid-latitudes, the predominant weather systems are cyclones (low pressure centres or depressions) and anticyclones (high pressure centres).
At low latitudes, the atmospheric circulation consists essentially of the spiral Hadley cells, of which the Trade Winds form the lowermost limb.
The Intertropical Convergence Zone, where the wind systems of the two hemispheres meet, is generally associated with the zone of maximum sea-surface temperature in the vicinity of the Equator.
4 Heat is transported polewards in the atmosphere as a result of warm air moving into cooler latitudes. It is also transported as latent heat: heat used to convert water to water vapour is released when the water vapour condenses (e.g. in cloud formation) in a cooler environment. Over the tropical oceans, turbulent atmospheric convection transports large amounts of heat from the sea-surface high into the atmosphere, leading to the formation of cumulus and (especially) cumulonimbus clouds. An extreme expression of this convection of moisture-laden air is the generation of tropical cyclones.
5 Interaction between the atmosphere and the overlying ocean is most intense- i.e. atmosphere-ocean 'coupling' is closest- in the tropics.
Now try' the following questions to consolidate your understanding of this Chapter.
Figure 2.20 Satellite image of the Earth, constructed using the 'water vapour' channel (wavelength 6000 nm); the colour is artificial.
This image and that in Figure 2.1 show the same view of the Earth and are for 26 March 1982.
In Chapter 2, we saw how the atmospheric circulation transports heat from low to high latitudes. Figure 3.1 shows how the same is true in the oceans, where surface currents warmed in low latitudes carry heat polewards, while currents cooled at high latitudes flow equatorwards.
Figure 3.1 Highly generalized representation of the global surface current system. Cool currents are shown by dashed arrows; warm currents are shown by solid arrows. The map shows average conditions for summer months in the Northern Hemisphere. There are local differences in the winter, particularly in regions affected by monsoonal circulations (those parts of the tropics where there are large seasonal changes in the position of the ITCZ, cf. Figure 2.3).
As far as the transport of heat is concerned, the 'warm' and 'cool' surface currents shown in Figure 3.1 are only part of the story. In certain high- latitude regions, water that has been subjected to extreme cooling sinks and flows equatorwards in the thermohaline circulation (Chapter 1). In order to know the net poleward heat transport in the oceans at any location, we would need to know the direction and speed of flow of water, and its temperature, at all depths. In fact, the three-dimensional current structure of the oceans is complex and has only relatively recently begun to be
If you compare Figures 2.3 and 3. l, you will see immediately that the surface wind field and the surface current system have a general similarity.
The most obvious difference is that because the flow of ocean currents is constrained by coastal boundaries, the tendency for circular or gyral motion seen in the atmospheric circulation is even more noticeable in the oceans.
However, the way in which ocean currents are driven by the atmospheric circulation is not as obvious as it might at first appear, and in this Chapter we consider some of the mechanisms involved.
Figure 3.2 The paths of drifting derelict sailing vessels (and a few drifting buoys) over the period 1883-1902. This chart was produced using data from the monthly Pilot Charts of the US Navy Hydrographic Office, which is why the paths are shown as straight lines between points. The paths are extremely convoluted and cross one another, but the general large-scale anticyclonic circulation of the North Atlantic may just be distinguished.
This is perhaps a suitable point to emphasize that maps like Figures 2.3(a) and (b) and 3.1 represent average conditions. If you were to observe the wind and current at, for instance, a locality in the region labelled 'Gulf Stream' on Figure 3.1, you might well find that the wind and/or current directions were quite different from those shown by the arrows in Figures 2.3 and 3.1, perhaps even in the opposite direction. Moreover, currents should not be regarded as river-like. Even powerful, relatively well-defined currents like the Gulf Stream continually shift and change their position to greater or lesser extents, forming meanders and eddies, or splitting into filaments. The actual spatial and temporal variations in velocity (speed and direction) are much more complex than could be shown by the most detailed series of current charts. The drift paths in Figure 3.2 convey something of the variability of surface currents in the North Atlantic, while the satellite image on the book cover shows the complexity of the Gulf Stream flow pattern at one moment in time.
Despite the complex and variable nature of the marine environment, certain key theoretical ideas have been developed about the causes and nature of current flow in the ocean, and have been shown to be reasonable approximations to reality, at least under certain circumstances. The most fundamental of these are introduced in Sections 3.1 to 3.4.
direction of wave propagation
Figure 3.3 In a surface wave, water particles make orbits in the vertical plane. The particles advance slightly further in the crest (the top of the orbit) than they retreat in the trough (bottom of the orbit), so a small net forward motion (known as 'wave drift') results. In deep water, this motion may be of the order of several millimetres to several centimetres per second.
When wind blows over the ocean, energy is transferred from the wind to the surface layers. Some of this energy is expended in the generation of surface gravity waves (which lead to a small net movement of water in the direction of wave propagation; see Figure 3.3) and some is expended in driving currents. The processes whereby energy is transferred between waves and currents are complex; it is not a simple task to discover, for example, how much of the energy of a breaking wave is dissipated and how much is transferred to the surface current.
Nevertheless, it is still possible to make some general statements and predictions about the action of wind on the sea. The greater the speed of the wind, the greater the frictional force acting on the sea-surface, and the stronger the surface current generated. The frictional force acting on the sea-surface as a result of the wind blowing over it is known as the wind stress. Wind stress, which is usually given the symbol 1: (Greek 'tau'), has been found by experiment to be proportional to the square of the wind speed, W. Thus:
z = c W 2 (3.1)
where the value of c depends on the prevailing atmospheric conditions. The more turbulent the atmosphere overlying the sea-surface (Section 2.2.2), the higher the value of c.
The value of c will increase with increasing wind speed, which not only increases the amount of turbulent convection in the atmosphere over the sea (Section 2.2.2) but also increases the roughness of the sea-surface.
Because of friction with the sea-surface, wind speed decreases with increasing proximity to the sea, and so the value of c to be used also depends critically on the h e i g h t at which the wind speed is measured; this is commonly about 10 m, the height of the deck or bridge of a ship. As a rough guide, we can say that a wind which has a speed of 10 m s -1 (nearly 20 knots) 5-10 m above the sea-surface, will give rise to wind stress on the sea-surface of the order of 0.2 N m -2 (1 newton = 1 kg m s-Z).
It is important to remember that, for the reasons given above, c is not constant. Nevertheless, a value of c of about 2 x 10 -3 gives values of I: that are accurate to within a factor of 2, and often considerably better than that.
Another useful empirical observation is that the surface current speed is typically about 3% of the wind speed, so that a 1 0 m s -~ wind might be expected to give rise to a surface current of about 0.3 m s -~. Again, this is only a rough 'rule of thumb', for reasons that should become clear shortly.