Diurnal Wave

In the case of a diurnal wave, P = 86400s. Taking KH = 4.8 x 10-3cm2 s 1, an appropriate value for wet soil (see Appendix 4), we get from (9.7.5) and (9.7.6) the following values for the velocity and the wavelength:

During the day, a maximum temperature of about 45°C is reached around 2 p.m. and minimum of about 25 °C a little before sunrise at a land station in the tropics. These give the amplitude of the diurnal wave at the surface to be about 10°C (half of the daily range) which will decrease exponentially with depth at a rate given by the expression

Using this expression, it is easy to show that the amplitude will fall off to a fraction of 0.42 at 10 cm, 0.076 at 30 cm, 1.8 x 10~4 at 100 cm, and so on. Thus, the amplitude of 10°C at the surface will be reduced to 4.2°C at 10 cm, 0.76 °C at 30 cm and about 0.0018 °C at 1 m. It will be almost imperceptible at greater depths.

Also, the time lag between the time of occurrence of a maximum or a minimum at the surface and that at a level below will increase with depth, according to (9.7.4), to 3.32 h at 10 cm, about 10h at 30 cm and about 33 h at 1 m.

People living in brick houses with concrete roofs must be aware of the diurnal variation of temperature in their rooms. The temperature is maximum at the roof top in the afternoon around 2 p.m., but it takes approximately 8 h or so for the wave maximum to travel through the roof slab which is usually about 25 cm thick to reach the rooms down below. This means that the temperature in the rooms is maximum late in the evening around 10 p.m. when outside is cooling down. Similarly, due to lag in the timing of the minimum, the coolest temperature inside the rooms is around noon when the outside is blazing hot. People in the tropics who are familiar with this diurnal cycle of temperatures in their homes take advantage of it by sleeping outside on the lawn at night and remaining indoors around noon during the hot summer months.

9.7.6 Annual Wave

In the annual cycle of temperatures at the earth's surface, the maximum is experienced during the summer and the minimum during the winter. For example, at New Delhi in India, the summer temperatures reach almost 50 °C in May-June, while the winter temperatures often drop to near freezing point in December-January. This gives amplitude of about 25°C at the surface and a period of 365/4 days. Taking a value of 0.0048 cm2 s—1 for the co-efficient of thermal diffusivity for wet soil we obtain the following values for the velocity and the wavelength of the annual wave from (9.7.5) and (9.7.6):

The results show that at a depth z = X/2 = 6.9m, the annual wave appears in the opposite phase, i.e., when it is summer at the surface, it is winter at this depth or vice versa. The wave appears in the same phase as at the surface at a depth of 13.8 m after 1 year. The amplitude and the time lag at different depths are given in Table 9.1.

Table 9.1 shows that the amplitude of the annual wave falls off rapidly with depth below a depth of about 10 m where it arrives about 8 days after occurrence at the

Table 9.1 The amplitude and time lag of the annual wave at different depths in wet soil at New Delhi (India)

surface. It should, however, be clarified that v as given by (9.7.5) is merely the velocity of the thermal wave and not the rate of actual penetration of heat energy into the soil or underground medium, which, inter alia, depends upon the physical and chemical properties of the underground material and its water content. In Appendix 6, we tabulate the experimental values of the density, specific heat, the co-efficient of thermal conductivity and the co-efficient of thermal diffusivity of a few common types of underground materials.

The Fourier equation (9.7.1) has been applied widely to study heat transfer in such diverse practical problems as determining the depth at which underground water pipes, electrical cables, etc., should be laid in areas subjected to frequent occurrence of severe heat and cold waves in order to protect them from damage and other undesirable effects, finding the thickness of different insulation materials in the manufacture of cold storages, furnaces, etc., estimating the age of the earth counting time from the moment its surface first started solidifying from fluid magma, and dealing with several other problems of geological, geophysical and astrophysical interest. Several of these applications are discussed in standard text-books on heat transfer.

9.8 Radiative Heat Flux into the Ocean

In the previous section, we studied heat transfer into the soil or crust below a land surface. We now look at the oceans which occupy more than two-thirds of the earth's surface. A difference to note here is that the solar radiation is incident at an interface between a gaseous and a liquid medium, in contrast to that between a gaseous and a solid medium. Physically, the difference is important, because while in the case of the land, only a small part of the radiation penetrates a thin layer of earth, in the oceans the incident radiation can penetrate to a much deeper level, producing diverse physical, chemical and biological effects for aquatic plant and animal life.

Numerous voyages of discovery and ocean explorations by scientists during the last several centuries have revealed a wealth of information about the oceans, a detailed description of which is beyond the scope of this book. For such information, the reader should consult a standard text-book on oceans. In what follows, we simply review a few salient aspects of the properties of ocean water and how it responds to the incoming solar radiation.

9.8.1 General Properties of Ocean Water

(a) Salinity and Density

Ocean water always contains a certain amount of dissolved salt, the proportion of which in a given sample of sea water, called salinity, usually varies between 33 and 37 parts per thousand with an average of about 35 parts per thousand. The salinity alters the usual properties of fresh water in several ways. For example, (i) it increases the density of fresh water by about 2.5%; (ii) the presence of salt and impurities in ocean water lowers the freezing point of pure water; (iii) the osmotic pressure and refractive index of water increases with salinity; and so on. In some coastal regions where sea water is diluted by influx of river water, or where precipitation exceeds evaporation, salinity can decrease considerably. However, it is the striking contrast between the properties of the atmosphere and the ocean that is of prime importance. Ocean water is about 800 times denser than air which has a density of about 1.2-1.3 kg m-3 near surface. Further, even though the oceans cover about 70% of the earth's surface and its average depth is only about 4 km, the global ocean has a mass which is about 280 times greater than that of the atmosphere which covers the whole surface of the earth and extends to almost unlimited height into space. The great difference between the densities of the ocean and the atmosphere makes the common boundary between them vertically very stable. The stability greatly restricts the vertical movement in the ocean as compared to that in the atmosphere. For example, the amplitude of an ocean wave hardly exceeds 1 m, whereas the buoyancy plumes in the atmosphere can rise to hundreds of metres. The density of ocean water varies with pressure, temperature and salinity.

(b) Pressure of ocean water

At the surface of the ocean, pressure is that of the overlying atmosphere which measures about 104kg m-2 and is called a bar. Since the mass of ocean water is nearly 103kg m-3 and the acceleration due to gravity is approximately 10m s-2, it follows from the hydrostatic approximation (2.3.4) that a column of ocean water 10 m deep would exert the same pressure as the whole atmosphere, i.e., 1 bar or 10 decibars (db). In other words, pressure increases with depth at the rate of 1 db per meter. At this rate, the pressure at the bottom of the ocean may be as high as 4000 db or even higher, if the ocean is deeper at a place. However, as we shall see later in this section, the density of sea water at times varies considerably with depth, especially in the surface layer.

(c) Specific heat and heat capacity

The specific heat of water is about 4 times that of air. This multiplied by high density endows the ocean water with a heat capacity which is about 1100 times greater than that of the atmosphere. So, a mere 2.5 m deep layer of the ocean has the same heat capacity as the whole depth of the atmosphere. In other words, the heat required to raise the temperature of 2.5 m of water by 1 K is the same as that required to raise the temperature of the whole atmosphere by 1 K. It is this great heat storage capacity of the ocean that maintains it more or less as a natural thermostat and allows only small diurnal and annual variations in the temperature of the air in direct contact with the ocean surface, as compared to the large variations that are observed over the continents (Monin, 1975).

9.8.2 Optical Properties of Ocean Water - Reflection and Refraction

When a beam of light of wavelength X and intensity I is incident upon an ocean surface at a point O (see Fig. 9.3) from a direction which makes an angle 9a with the outward normal to the surface, a fraction F of it is reflected from the surface, while the remainder R enters the body of the ocean where it is partly absorbed and partly transmitted to lower layers (see Fig. 9.3).

Now, if for a moment we neglect absorption and consider transmission only, the beam entering the water is refracted due to change in the refractive index of the medium from air to water in a direction which makes an angle 9w with the normal to the surface. Suppose, at some small depth at P, the refracted beam R meets a layer of particulate matter of different density and refractive index held in suspension in sea water. At P, a fraction I is reflected or scattered in a direction which makes an angle 9w with the normal to the surface at P, while the remainder is transmitted to lower layers. The reflected beam I on reaching the interface at Of from below will suffer reflection as well as refraction. The reflected part Ff re-enters the water making an angle 9w with the normal to the surface at Of, while the refracted beam R emerges into the air making an angle 9a with the local normal. Similar reflection and scattering may be expected to occur at myriads of points inside the water wherever particles intercept the radiation, followed by multiple total internal reflection at the interface. In this way, a large part of the solar energy is retained inside the body of the ocean to warm it up. The trapping of solar radiation in this manner leads to continual warming of the surface layer of the ocean.

However, it must be stated that the process of reflection, refraction and absorption of light radiation in the ocean is highly complex. The laws stated below follow from the electromagnetic theory of light (for details of the theory, reference may be made to any standard text-book on optics):

(i) The reflected and the refracted rays at a surface lie in the same plane as the incident ray and the normal to the surface;

(ii) The angle of reflection is equal to the angle of incidence; and

Fig. 9.3 Processes of reflection and refraction of solar radiation in the ocean

Fig. 9.3 Processes of reflection and refraction of solar radiation in the ocean

P

(iii) The product of refractive index of the medium of the incident ray and the sine of the angle of incidence is equal to the product of the refractive index of the medium of the refracted ray and the sine of the angle of refraction. In other words, nw sin 9w = na sin 9a, where n denotes the refractive index, 9 the angle and the subscripts w and a refer to water and air respectively. This is known as Snell's law.

The important point to note here is that as the angle of incidence increases, there is more of reflection into the same medium and less of transmission into the other medium. When this principle is applied to the interface at O' (Fig. 9.3), it means that for an angle of incidence 9w greater than a certain critical value 9w*, the beam I' will be totally reflected back into water. Such total internal reflection helps in retaining the solar radiation inside the water at O' and will not occur at O where, though the angle of incidence 9a can increase to n/2, the angle of refraction 9w has always a value less than 9w*.

Total internal reflection of light radiation of the kind described in the preceding para at multiple points along the ocean-atmosphere interface traps solar energy in the upper part of the ocean which leads to its warming This warming is in addition to that which results from direct absorption of the solar beam that enters the ocean from above. The increased warming of the ocean by total internal reflection of solar radiation in this manner appears to be somewhat analogous to the Greenhouse effect in the atmosphere, a brief description of which was given earlier in this chapter.

9.8.3 Absorption and Downward Penetration of Solar Radiation in the Ocean

Sverdrup et al. (1942) have shown that the depth to which light radiation penetrates into the ocean depends upon the wavelength of the radiation. Infrared part of the radiation is strongly absorbed by water and dissolved gases like CO2 in the surface layer allowing shorter waves only to penetrate further down. This is evident from a schematic representation of the energy spectrum of the radiation from the sun and the sky penetrating the sea surface, and of the energy spectra in pure water at depths of 0.1, 1, 10, and 100 m, presented by them in Fig. 9.4 of their book (not reproduced). Inset, they gave curves of percentages of total energy and of the energy in the visible part of the spectrum reaching different depths.

They show that radiation of wavelengths greater than 1| is almost totally absorbed by water within the first 10 cm of the surface. According to them, pure water is transparent for visible radiation between 0.35| and 0.75| only. The shorter the wavelength, the greater is the depth. In the visible part, it is only the shorter waves in the blue-green-yellow region between 0.4| and 0.6| which can reach a depth of about 100 m. The intensity of the transmitted beam, however, continually diminishes with depth.

9.8.4 Vertical Distribution of Temperature in the Ocean

The near-total absorption of solar radiation in the upper strata of the ocean together with a certain degree of mixing caused by wind-driven ocean currents near the surface produces a vertical profile of temperature in tropical oceans, which shows the following three distinct layers (see Fig. 9.4):

(i) A mixed or surface layer upto a depth of about 100 m in which there is little variation of temperature with depth,

(ii) A thermocline layer in which temperature drops steeply from a value of about 210 C to 260 C at 10 m to about 50 C at about 1000 m, and

(iii) A deep ocean layer, below about 1 km, in which there is little fall of temperature with depth. This layer constitutes the cold and dark region of the ocean.

Further, the depth of all the layers varies with latitude. For example, the mixed layer is rather shallow (< 100m) in low latitudes, compared to the midlatitudes, between about 300 and 500, where it may extend to a depth of about 300 m. The layer disappears beyond latitude about 50°. The depth of the main thermocline layer and the deep layer also appears to follow the same type of variation with latitude as the mixed layer.

While comparing the thermal structure of the ocean with that of the atmosphere, Defant (1961) has called the combined mixed-thermocline layer as the troposphere and the deep ocean as the stratosphere of the ocean. This analogy is often a useful one, especially when dealing with conditions in low latitudes.

9.9 The Thermohaline Circulation - Buoyancy Flux

Earlier in this chapter, we mentioned that the density of ocean water at a given pressure depends on both temperature and salinity. The surface layers of the ocean are subject to such physical processes as evaporation, precipitation, discharge from rivers, etc., as well as atmospheric temperature and the net effect of these processes may be either an increase or decrease of density. In the open ocean, the salinity increases when evaporation exceeds precipitation. The effect of a change in salinity on density may be in the same direction as that due to change of temperature, or in the opposite direction. When both the effects are in the same direction, they support each other in causing a large increase or decrease of density, but when they oppose each other the net effect may be no change or only a small change in density.

Now, it is well-known that both temperature and salinity usually vary with latitude. The temperature is maximum at the equator and decreases towards the poles. The temperature-induced density will, therefore, be minimum at the equator and increase towards the poles. Normally, a high temperature at the equator will produce high evaporation but its effect is offset by precipitation exceeding evaporation in equatorial latitudes. So the net effect of both temperature and salinity at the equator is to produce a lowering of surface water density. Compare this with conditions over the subtropical belt where the temperature may be lower than at the equator but where evaporation exceeds precipitation. Here both temperature and salinity combine to produce a relatively large increase in density. The effect of these changes of density between the equator and the subtropical belt is to force a meridional circulation in the ocean called the thermohaline circulation, in which denser water over the subtropical belt will sink under the force of gravity to a depth where the density difference with the environment disappears and then move equatorward at a subsurface level to rise at the equator. At the surface, the equatorial waters will move towards the subtropical belt to replace the sinking water.

Poleward of the subtropical belt also there will be a thermohaline circulation but it will be a weak one, because in the higher latitudes while density will increase on account of lower temperature, it will decrease due to precipitation being in excess of evaporation in the polar belt.

Agafonova and Monin (1972) have constructed a quasi-climatic map of buoyancy flux (divided by g) at the ocean surface (generated by changes in temperature and salinity) as a driving term for the thermohaline circulation of the ocean.

A pure thermohaline circulation is, however, difficult to observe in the real ocean on account of the prevalence of strong wind-driven ocean currents which most often

Fig. 9.5 Isolines of the annual buoyancy flux (divided by g) (in grams per cm2 per year) at the surface of the World Ocean-the atmospheric forcing function for thermohaline circulation (Agafonova and Monin, 1972, their Fig. 1)

are too strong for it to develop. Density changes on account of net heating or cooling and excess evaporation or precipitation, however, do occur which lead to buoyancy fluxes in the upper ocean. Surface water the density of which has been increased by excess cooling or evaporation will then sink until it meets water of the same density. Reversely, when surface density decreases on account of excess heating or precipitation, water from a subsurface level will rise to the surface.

9.10 Photosynthesis in the Ocean: Chemical and Biological Processes

The sunlight that enters the ocean plays a very important role for life in the ocean, by promoting what is known as greenplant photosynthesis in which molecules of carbon dioxide dissolved in sea water chemically combine with molecules of water in the presence of sunlight to produce carbohydrates which form the building blocks of plant bodies and release oxygen. The process is reversible and in the respiratory cycle in which the released oxygen is consumed, the energy is released. The chemical reaction may be expressed by the reversible equation:

Thus, photosynthesis is the chemical-biological process in which water molecules are split with the energy of sunlight and oxygen is released. In to-day's ocean, green plants, single-celled phytoplankton (free-floating organisms), especially chlorophyll - containing bacteria, all perform oxygenic photosynthesis. However, it is well-known that the reverse process of respiration does not remove all the oxygen produced, since a small fraction (0.1%) of carbon gets buried in sediments and escapes oxidation. It follows from Eq. (9.10.1) that a burial of 1 mole of organic carbon will generate one mole of oxygen. Oxygen is also generated by several other chemical and biological processes in the ocean. It is believed that the transition from the ancient atmosphere which had no oxygen to the oxygen-rich modern atmosphere commenced only when life appeared on earth more than 2.3 billions of years ago and that in this transformation, greenplant and bacterial photosynthesis played a key role.