Physical Oceanography...

The ocean is a fluid in turbulent motion, ie it is characterised by the presence of turbulent eddies with velocities often larger than the velocities of the mean flow. As the atmosphere is also a fluid in turbulent motion it can be expected that the two media, the study objects of physical oceanography and meteorology, show similar behaviour and are governed by the same balance of forces and that it is therefore advantageous to study both together. To demonstrate the similarity, and show examples of eddies in the atmosphere and in the ocean. Note the difference in scale: Atmospheric eddies are typically some 2,000 km in diameter, while oceanic eddy diameter are typically 200 km. A movie sequence of images taken from the weather satellite or from the ocean model would show that atmospheric time scales are also different: At any given location, atmospheric eddies pass at a rate of one eddy every 5 - 7 days (experienced as the passage of fronts), while oceanic eddy movement is such that the passage of an eddy takes 50 - 70 days. The aim of oceanography is an understanding of the oceanic circulation and the distribution of heat in the ocean, how the ocean interacts with the atmosphere, and what role the ocean plays in maintaining our climate.

Tools and Prerequisites for Physical Oceanography...

Projections...

An important tool in oceanography (as in all other earth sciences) is the atlas. People are used to looking up items of interest in an atlas, but few realise the importance of the correct choice of projections used for the maps. A projection widely used in physical oceanography is the Mercator projection. It was developed in the 16^th century at a time of colonial exploration and expanded sea travel. Columbus had discovered America and Magellan's ships had circled the globe. One problem faced by these mariners was the uncertainty involved in navigation away from the coast. In the 16^th century a navigator had to sail between two points along a rhumb line (a line of constant compass bearing) because it was not practical to do otherwise. Mercator developed a projection that showed the earth's surface in such a way that a straight line on the resulting plane anywhere and in any direction was a rhumb line. Thus a mariner with a knowledge of the starting position could draw a straight line to the destination and read off the correct bearing.

As a result, Mercator's projection has become the standard projection for navigation. It is, however, not an equidistant or equal area projection and therefore unsuitable for mapping over large areas. It is a conformal map, i.e. small circles of equal area on the earth are represented as circles on the map but increase in size towards the poles. The poles cannot be shown in a Mercator projection, since distances near the poles grow to infinity. In principle, representation of a curved surface on a plane always involves some "stretching" or "shrinking" resulting in distortions, or some "tearing" resulting in interruption of the surface. No projection can satisfy all three desirable properties ; (1) Equidistance : correct representations of distances, (2) Conformality (Orthomorphism) : correct representation of shapes and (3) Equivalency : correct representation of areas. The three criteria are basic but mutually exclusive. All other properties are of a secondary nature. Most projections with the property of fidelity of area achieve area conservation through the use of a curved longitude grid and therefore require a grid drawn over the map surface to enable determination of geographical location coordinates . The Gall/Peters projection, which was developed by Gall in 1855 and rediscovered again independently by Peters in the 1970s, combines fidelity of area with a rectangular latitude/longitude grid. It is ideal for mapping large ocean regions.

Topographic Features of the Oceans...

The surface of the earth varies in height from 8,848 m (Mount Everest) to a depth of 11,022 m (Vitiaz deep in the Mariana Trench, western North Pacific Ocean). On a geological time scale the position of the coastline depends on the amount of water available, which is mainly determined by the amount of ice and snow bound in Antarctica and in the Arctic Ocean, and to some degree by the temperature of the water in the ocean (water expands when warmed, so sea level rises during periods of warm climate). A characteristic of the land/water distribution of today, which has important ramifications for the climate, is that the area covered by water increases continuously from 70°N to 60°S. Water coverage of the earth : northern hemisphere 61%, southern hemisphere 81%, global average 71%. "Land hemisphere" 53% (pole off the Loire river in France), , "water hemisphere" 89% (pole near New Zealand). The present distribution of land and sea and the various depth levels is shown in the so-called hypsographic curve . Average elevation - 2,440 m; mean land elevation + 840 m, average ocean floor level - 3,795 m. The major oceans are structured into continental margins, mid- ocean ridges and deep sea basins . Each structural feature occupies about one third of the ocean floor.

Scales of Graphs...

As noted the average depth of the oceans is just under 4 km. This is quite deep. Or is it? If you use a divider and a very sharp pencil to draw a circle of 15 cm radius and take it to represent the earth then the pencil line would be thick enough to represent the crust of the Earth under continents (30 km) but much too thick for the oceanic crust (10 km). Irregularities in the line would be more than enough to represent the variation in the relief of the solid earth. So the ocean is really only a thin film of fluid - if the earth was a basketball, one would notice that much if its surface was damp. There is no way of showing the oceans on a scale that preserves the aspect ratio of horizontal vs. vertical length. So how are we going to map ocean properties such as temperature, salinity or currents that vary considerably with depth? Compared to the ocean's vertical extent, horizontal distances are so large that the only way to produce a meaningful representation of the data is to distort the scales. A given distance on a diagram will thus represent several hundred times as much in real distance in the horizontal as in the vertical. A typical ratio is 500:1. This should be kept in mind when looking at oceanographic sections.

Objects of Study in Physical Oceanography...

Physical oceanography studies all forms of motion in the ocean. It relates observations of motion to physical laws, such as Newton's Law that if a force F acts on a body of mass m, it undergoes an acceleration a such that F = (m) (a). For the mathematically inclined, bold characters in this and all following lectures indicate vectors, characters in italics stand for scalars. If you do not know what that means, don't despair; it is more a matter of using the correct notation than a matter of practical importance for this topic.

The Geographical and Atmospheric Framework...

The prevailing wind system is the major driving force for ocean currents. shows that in the open ocean winds are nearly zonal (blowing east-west). The Trade Winds are easterly winds in the tropics and subtropics (between 30°N and 30°S). They are regions of extremely uniform wind conditions, where the wind blows steadily from the same direction with moderate strength throughout the year. Their strength increases slightly in winter. The Trade Winds of the two hemispheres are separated by the Doldrums, a region of weak and variable winds near 5°N. Between 30° and 65° are the Westerlies. They are stronger in winter than in summer and are regions of frequent storms. Poleward of 65° the wind direction reverses again, and the Polar Easterlies blow from east to west.

Deviations from zonal wind direction occur near continents. This is particularly noticeable along the east coast of the oceans in the tropics and subtropics where the winds blow parallel to the coast towards the equator. The present configuration of the distribution between land and water determines the ocean's response to the winds. It defines the major subdivisions of the world ocean, the Pacific, Indian and Atlantic Oceans. Their southern region around Antarctica is also known as the Southern Ocean.

is a map of surface currents. The combined action of the Trade Winds and the Westerlies produces large gyres, with clockwise rotation in the northern hemisphere, anti-clockwise rotation in the southern hemisphere, known as the subtropical gyres. A subpolar gyre is produced in the north Pacific Ocean by the combined action of the Westerlies and the Polar Easterlies; it consists of the Oyashio, North Pacific Current and Alaskan Current. An indication of a subpolar gyre is also seen in the north Atlantic Ocean (anti-clockwise rotation in the current system that includes the North Atlantic, East Greenland and Labrador Currents). The subpolar region of the southern hemisphere does not have land barriers and therefore is dominated by the Antarctic Circumpolar Current.

The convention for indicating the direction of ocean currents differs from the convention used for wind directions. A "westerly" wind is a wind which blows from the west and goes to the east; a "westward" current is a current which comes from the east and flows towards west. This can cause confusion to people who rarely, if ever, go to sea; but it is easily understood and remembered when related to practical experience with winds and ocean currents. On land, it is important to know from where the wind blows: any windbreak must be erected in this direction. Where the wind goes is of no consequence. At sea, the important information is where the current goes: a ship exposed to current drift has to stay well clear from obstacles downstream. Where the water comes from is irrelevant.

A feature to note is that as a general rule currents along the western coasts of ocean basins are much narrower and stronger than currents in the remainder of the ocean. Typical current velocities at the surface in the open ocean are 0.2 - 0.5 m / s (about 1 km / h). In western boundary currents velocities are closer to 2 m / s (about 7 km / h). These differences in current strength do not come out in most surface current maps.

The Indian Ocean is dominated by seasonal wind reversal (the Monsoons) and a corresponding reversal of surface currents. shows the situation during the Southwest Monsoon season when the Equatorial Countercurrent is suppressed and the circulation in the northern Indian Ocean differs significantly from that of the other ocean basins. Just as in the atmosphere, where wind systems are linked to atmospheric pressure patterns, ocean currents are linked to pressure patterns in the ocean. Pressure at any depth in the ocean is determined by the weight of the water above, which is determined by the density of the water, which in turn depends on the water's temperature and salinity. It follows that ocean currents can be determined by measuring temperature and salinity, a task infinitely easier than direct current measurement. It is therefore appropriate to turn to a discussion of the basic properties of seawater before proceeding with a discussion of the oceanic circulation and the physical laws that govern it.

Properties of Seawater...

Sea water is a mixture of 96.5% pure water and 3.5% other material, such as salts, dissolved gases, organic substances, and undissolved particles. Its physical properties are mainly determined by the 96.5% pure water. The physical properties of pure water will therefore be discussed first. Pure water, when compared with fluids of similar composition, displays most uncommon properties. This is the result of the particular structure of the water molecule H₂O : The hydrogen atoms carry one positive charge, the oxygen atom two negative charges, but the atom arrangement in the water molecule is such that the charges are not neutralized. See ; the charges would be neutralized if the angle were 180° rather than 105°.

The major consequences of the molecular structure of pure water are ; (1) The water molecule is an electric dipole, forming aggregations of molecules (polymers), of on average 6 molecules at 20°C. Therefore, water reacts slower to changes than individual molecules; for example the boiling point is shifted from -80°C to 100°C, the freezing point from -110°C to 0°C. (2) Water has an unusually strong disassociative power, i.e. it splits dissolved material into electrically charged ions ( ). As a consequence, dissolved material greatly increases the electrical conductivity of water. The conductivity of pure water is relatively low, but that of sea water is midway between pure water and copper. At 20°C, the resistance of sea water of 3.5% salt content over 1.3 km roughly equals that of pure water over 1 mm. (3) The angle 105° is close to the angle of a tetrahedron, i.e. a structure with four arms emanating from a centre at equal angles (109° 28´). As a result, oxygen atoms in water try to have four hydrogen atoms attached to them in a tetrahedral arrangement ( ). This is called a "hydrogen bond", in contrast to the (ionic) molecular bond and covalent bonding. Hydrogen bonds need a bonding energy 10 to 100 times smaller than molecular bonds, so water is very flexible in its reaction to changing chemical conditions. (4) Tetrahedrons are of a more wide-meshed nature than the molecular closest packing arrangement. They form aggregates of single, two, four and eight molecules. At high temperatures the one and two molecule aggregates dominate; as the temperature falls the larger clusters begin to dominate ( ). The larger clusters occupy more space than the same number of molecules in smalles clusters. As a result, the density of water shows a maximum at 4°C.

Physical properties of most substances show uniform variation with temperature. In contrast, most physical properties of pure water show a minimum at some intermediate temperature. Sound velocity shows a maximum at 74°C.

A list of some minimum temperatures (the physical property is given first, followed by the temperature in °C at which the minimum occurs)
Oxygen solubility	80
Specific volume	4
Specific heat	34
Hydrogen solubility	37
Compressibility	44
Speed of light	- 1
Speed of sound (max)	74

When freezing, all water molecules form tetrahedrons. This leads to a sudden expansion in volume, ie a decrease in density. The solid phase of water is therefore lighter than the liquid phase, which is a rare property. Some important consequences are ; (1) Ice floats. This is important for life in freswater lakes, since the ice acts as an insulator against further heat loss, preventing the water to freeze from the surface to the bottom. (2) Density shows a rapid decrease as the freezing point is approached. The resulting expansion during freezing is a major cause for the weathering of rocks. (3) The freezing point decreases under pressure. As a consequence, melting occurs at the base of glaciers, which facilitates glacier flow. (4) Hydrogen bonds give way under pressure, i.e. ice under pressure becomes plastic. As a consequence, the inland ice of the Antarctic and the Arctic flows, shedding icebergs at the outer rims. Without this process all water would eventually end up as ice in the polar regions.

The Concept of Salinity...

As mentioned before, sea water contains 3.5% salts, dissolved gasses, organic substances and undissolved particulate matter. The presence of these additions influences most physical properties of sea water (density, compressibility, freezing point, temperature of the density maximum) to some degree but does not determine them. Some properties (viscosity, light absorbtion) are not significantly affected by salinity. Two properties which are determined by the amount of salt in the sea are conductivity and osmotic pressure. Ideally, salinity should be the sum of all dissolved salts in grams per kilogram of sea water. In practice, this is difficult to measure. The observation that - no matter how much salt is in the sea - the various components contribute in a fixed ratio, helps overcome the difficulty. It allows determination of salt content through the measurement of a substitution quantity and calculation of the total of all material making up the salinity from that measurement.

Determination of salinity could thus be made through its most important component, chloride. Chloride content was defined in 1902 as the total amount in grams of chlorine ions contained in one kilogram of sea water if all the halogens are replaced by chlorides. The definition reflects the chemical titration process for the determination of chloride content and is still of importance when dealing with historical data. Salinity was defined in 1902 as the total amount in grams of dissolved substances contained in one kilogram of sea water if all carbonates are converted into oxides, all bromides and iodides into chlorides, and all organic substances oxidized. The relationship between salinity and chloride was determined through a series of fundamental laboratory measurements based on sea water samples from all regions of the world ocean and was given as ;

S (o/oo) = 0.03 + 1.805 Cl (o/oo)

The symbol o/oo stands for "parts per thousand" or "per mil"; a salt content of 3.5% is equivalent to 35 o/oo, or 35 grams of salt per kilogram of sea water. The fact that the equation of 1902 gives a salinity of 0.03 o/oo for zero chlorinity is a cause for concern. It indicates a problem in the laboratory measurements. The United Nations Scientific, Education and Cultural Organization (UNESCO) decided to repeat the base determination of the relation between chlorinity and salinity and introduced a new definition, known as absolute salinity,

S (o/oo) = 1.80655 Cl (o/oo)

The definitions of 1902 and 1969 give identical results at a salinity of 35 o/oo and do not differ significantly for most applications. The definition of salinity was reviewed again when techniques to determine salinity from measurements of conductivity, temperature and pressure were developed. Since 1978, the "Practical Salinity Scale" defines salinity in terms of a conductivity ratio : "The practical salinity, symbol S, of a sample of sea water, is defined in terms of the ratio K of the electrical conductivity of a sea water sample of 15°C and the pressure of one standard atmosphere, to that of a potassium chloride (KCl) solution, in which the mass fraction of KCl is 0.0324356, at the same temperature and pressure. The K value exactly equal to one corresponds, by definition, to a practical salinity equal to 35". The corresponding formula is :

S = 0.0080 - 0.1692 K^1/2 + 25.3853 K + 14.0941 K^3/2 - 7.0261 K² + 2.7081 K^5/2

Note that in this definition, (o/oo) is no longer used, but an old value of 35 o/oo corresponds to a new value of 35. Again, minute differences occur between the old definitions and the new Practical Salinity Scale, but they are usually negligible.

Electrical Conductivity...

The conductivity of sea water depends on the number of dissolved ions per volume (i.e. salinity) and the mobility of the ions (i.e. temperature and pressure). Its units are mS / cm (milli-Siemens per centimetre). Conductivity increases by the same amount with a salinity increase of 0.01, a temperature increase of 0.01°C, and a depth (ie pressure) increase of 20 m. In most practical oceanographic applications the change of conductivity is dominated by temperature.

Density...

Density is one of the most important parameters in the study of the oceans' dynamics. Small horizontal density differences (caused for example by differences in surface heating) can produce very strong currents. The determination of density has therefore been one of the most important tasks in oceanography. The symbol for density is the Greek letter r (rho). The density of sea water depends on temperature T, salinity S and pressure p. This dependence is known as the Equation of State of Sea Water. The equation of state for an ideal gas was is given by ;

p = (r) (R) (T)

where ; R is the gas constant. Seawater is not an ideal gas, but over small temperature ranges it comes very close to one. The exact equation for the entire range of temperatures, salinities and pressures encountered in the ocean ;

r = r (T,S,p)

(where ; S is salinity) is the result of many careful laboratory determinations. The first fundamental determinations to establish the equation were made in 1902 by Knundsen and Ekman. Their equation expressed r in g / cm³. New fundamental determinations, based on data over a larger pressure and salinity range, resulted in a new density equation, known as the "International Equation of State (1980)". This equation uses temperature in °C, salinity from the Practical Salinity Scale and pressure in dbar (1 dbar = 10,000 pascal = 10,000 N / m²) and gives density in kg / m³. Thus, a density of 1.025 g / cm³ in the old formula corresponds to a density of 1,025 kg / m³ in the International Equation of State.

Density increases with an increase in salinity and a decrease in temperature, except at temperatures below the density maximum ( ). Oceanic density is usually close to 1,025 kg / m³ (In freshwater it is close to 1,000 kg / m³). Oceanographers usually use the symbol st (the Greek letter sigma with a subscript t) for density, which they pronounce "sigma-t". This quantity is defined as st = r - 1000 and does not usually carry units (it should carry the same units as r). A typical seawater density is thus st = 25 ( ). A useful rule of thumb is that st changes by the same amount if T changes by 1°C, S by 0.1, and p by the equivalent of a 50 m depth change.

Notice that the density maximum is above the freezing point for salinities below 24.7 but below the freezing point for salinities above 24.7. This affects the thermal convection ; (1) S < 24.7 : The water cools until it reaches maximum density; then, when the surface water becomes lighter (ie after the density maximum has been passed) cooling is restricted to the wind-mixed layer, which eventually freezes over. The deep basins are filled with water of maximum density. (2) S > 24.7 : Convection always reaches the entire water body. Cooling is slowed down because a large amount of heat is stored in the water body. This is because the water reaches freezing point before the maximum density is attained.