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The oceans
The oceans

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3.2 The density of fresh water and seawater

Fresh water and seawater have very different physical properties. Imagine a freshwater lake in winter. As the air temperature falls the temperature of the water at the surface decreases and its density changes (Figure 4).

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Figure 4 The density of fresh water plotted against temperature.
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Figure 4

This is a line graph showing the change in density with temperature.

The horizontal axis is labelled 'temperature/°C' and is marked from 0 °C to 10 °C in intervals of 1°.

The vertical axis is labelled 'density of freshwater/kg m−3' and is marked from 999.6 kg m−3 to 1000.0 kg m−3 in intervals of 0.1 kg m−3.

There are horizontal and vertical gridlines at the marked axes points.

The density data are represented by a solid green line.

The pattern in the line is an asymmetric inverted 'U' shape.

The density is approximately 999.86 kg m−3 at 0° and then increases steadily to a maximum of almost 1000.0 kg m−3 at approximately 4°.

The density then decreases steadily to 999.73 at 10°.

Figure 4 The density of fresh water plotted against temperature.

  • What is the temperature at maximum density?

  • The maximum density is at ~4 °C (Figure 4). At both lower and higher temperatures than this the water is less dense.

While it is hard to see on the scale in Figure 4, the maximum density is at 3.98 °C. As a lake cools to this temperature in winter the surface waters will sink through convection and warmer water rises to the surface. With continued cooling this warmer surface water also becomes dense and sinks. As the surface water is being cooled the lake will become stratified. That is, the density will increase with depth to 1000 kg m−3, and the deep water will have a temperature of 3.98 °C. Imagine the convection continuing until all the water has reached 3.98 °C.

  • What will happen to the water in the lake when all the water is cooled below to 3.98 °C?

  • The water at the surface of the lake will cool and become less dense. This means that it will not sink away from the surface. So the lake will end up with a cool surface layer with warmer, denser water beneath.

Eventually the surface layer of water will be cooled to the freezing point (0 °C) and ice will form on the surface. At this point the temperature and density of the water will have a structure like that shown in Figure 5.

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Figure 5 (a) Section through a lake showing ice on the surface. (b) Temperature structure throughout the lake: there are three layers: a cold surface layer, an intermediate layer and a warm deeper layer. (c) Density structure mirroring the shape of the temperature profile in (b).
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Figure 5

This is a series of 3 diagrams that show the change in temperature and density with depth in a lake and within designated layers within the depth profile of the lake.

Figure (a) is on the far left and is labelled 'side view of lake'

This diagram shows the depth profile of the lake along with 4 identified layers to this profile.

The top layer is labelled 'ice', is the narrowest of the 4 layers and is shaded very pale blue.

The layer below this is labelled 'surface layer at 0 °C', is the third narrowest of the 4 layers and shaded very pale blue.

The layer below that is labelled 'intermediate layer', is the second narrowest of the 4 layers and is shaded in slightly darker shade of blue than the top 2 layers.

The layer at the bottom is labelled 'deep layer at 3.98 °C', is the widest of the layers and is shaded in the darker blue.

Figure (b), in the middle, presents temperature data as a line graph. It has the same colour and layering as Figure (a), except there are no labels and the top 2 layers (ice and surface layer at 0 °C) have been merged into one layer.

The horizontal axis is located at the top of the figure and is labelled 'temperature/°C' and is marked from −1 °C to 5 °C in intervals of 1 °C.

The vertical axis is labelled 'depth increasing' with no quantitative markings. There is black directional arrow head pointing downward at the lower end of the axis.

There is a red line indicating the temperature. The red line runs vertically, at a temperature of 0 °C from the top of the graph to the top of the intermediate layer. In the intermediate layer the red line shows an linear increase in temperature with depth from 0 °C to approximately 4 °C. The red line then runs vertically down through the bottom layer at approximately 4 °C.

Figure (c), on the right presents density data as a line graph. It has the same colour and layering as Figure (a), except there are no labels and the top 2 layers (ice and surface layer at 0 °C) have been merged into one layer.

The horizontal axis is located at the top of the figure and is labelled 'density/kg m−3' and is marked from 999.8 kg m−3 to 1000 kg m−3 in intervals of 0.1 kg m−3.

The vertical axis is labelled 'depth increasing' with no quantitative markings. There is black directional arrow head pointing downward at the lower end of the axis.

There is a green line indicating the density. The green line shows the same pattern of change as the red temperature line in Figure (b). The density starts at approximately 999.82 kg m−3 at the surface and remains at that value down to the top of the intermediate layer. In the intermediate layer the green line shows a linear increase in density with depth from 999.82 kg m−3 to approximately 999.98 kg m−3. The green line them runs vertically down through the bottom layer at approximately 999.98 kg m−3.

Figure 5 (a) Section through a lake showing ice on the surface. (b) Temperature structure throughout the lake: there are three layers: a ...

Figures 5b and c show that the temperature and the density increase with depth from the surface to the bottom layer, where the temperature is 3.98 °C and density is at its maximum.

Let us think about this a little more.

Usually when a liquid is heated the molecules acquire more energy and become more widely spaced, so in the same volume, the density decreases. In fresh water the opposite may happen, depending on the temperature. When fresh water at 3.97 °C (Figure 4) is cooled the density will decrease. You know from the lake (Figure 5) that ice (i.e. solid water) is less dense and floats. But cooling a liquid usually packs the molecules more closely, which increases the density. This means that below 3.98 °C cooling results in the water molecules spacing out and both the liquid and the solid water below this temperature expand. This is an amazing physical property and is why pipes burst and water in cracks shatters rocks in cold temperatures. The molecular structure of a water molecule is shown in Figure 6.

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Figure 6 A molecule of water, H2O, with the hydrogen and the oxygen atoms sharing electrons.
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Figure 6

This is a schematic diagram of a water molecule.

The oxygen atom is represented by a circle, shaded red and labelled 'O'.

The hydrogen atoms are represented by a circle, shaded grey and labelled 'H'.

1 oxygen atom is connected to 2 hydrogen atoms and the connection is shown by an narrow elongated rectangle shaded pale orange.

The water molecule has an 'L' shape with the oxygen atom at the corner and the 2 hydrogen atoms radiating out from this corner.

There is a dashed black line that radiates from the oxygen atom to each of the hydrogen atoms, along the connecting rectangle.

These dashed lines extend past the hydrogen atoms and they are then connected by a solid black line in the shape of an arc with directional arrow heads at either end.

The arc represents the angle of the 'L' shape or the angle between the two hydrogen atoms and is labelled '105°'.

Figure 6 A molecule of water, H2O, with the hydrogen and the oxygen atoms sharing electrons.

In H2O, the oxygen and the hydrogen atoms share electrons, and the angle between the two hydrogen atoms is 105°. This results in a small net negative charge on the oxygen side of the molecule, and a small net positive charge on the hydrogen side. This is a polar structure in which molecules are weakly attracted to each other and form weak 'hydrogen bonds'. At low temperatures a more ordered packing of water molecules develops and the density is reduced. If the temperature is increased but is

Seawater is saline and the salt affects the density. Figure 7 shows the vertical structure of the temperature, salinity, and density at latitude 20° S in the Atlantic Ocean over an abyssal plain almost 5300 m deep.

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Figure 7 The physical properties of seawater at 20° S in the Atlantic Ocean against depth. (a) Temperature; (b) salinity; (c) density.
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Figure 7

A series of three line graphs to show the change in temperature, salinity and density with depth in the Atlantic ocean.

All three graphs share the same vertical axis. The scale is the same for all three graphs and there are major and minor axis ticks on the left and right aides of each graph. However, the axis is only labelled and numbered on Figure (a) on the left. Here the vertical axis is labelled 'depth/m' and goes down from 0 m to 5300 m, with minor axis ticks at intervals of 200 m, but only the major axis ticks are numbered, from 0 m to 5000 m in intervals of 1000 m.

In all three graphs the horizontal axis is labelled and marked at the top of the graph, and the major and minor axis tick marks are also shown, unlabelled, at the bottom of the graph.

Figure (a), on the left, shows the temperature data with a red line.

The horizontal axis is labelled 'temperature/°C'. It is marked from 0 °C to 30 °C in intervals of 5 °C with unlabelled minor ticks at intervals of 1 °C.

The red line starts at 29 °C at the surface and temperature decreases rapidly to approximately 4 °C at 1000 m depth. From there the temperature drops more slowly as seen by an almost linearly change with depth to 1 °C at 5100 m.

Figure (b), in the middle, shows the salinity data with a blue line.

The horizontal axis is labelled 'salinity'. It is marked from 34 to 38 in intervals of 1 with unlabelled minor ticks at intervals of 0.2. No units are indicated.

The blue line starts at 37.2 at the surface and salinity decreases rapidly to approximately 34.2 at 800 m depth. From there the salinity increases slightly to 35 at a depth of 1800 m and then decreases slowly to 34.8 at 5100 m.

Figure (c ), on the right, shows the density data with a green line.

The horizontal axis is labelled 'density/kg m−3'. The axis scale is from range 1023.2 kg m−3to 1028.8 kg m−3 with unnumbered minor tick marks at intervals 0.4 kg m−3. The major tick marks are numbered from 1024 kg m−3 to 1028 kg m−3 in intervals of 2 kg m−3.

The green line starts at 1024 kg m−3 at the surface and density increases steadily with depth to approximately 1027.2 kg m−3 at 600 m depth. From there the density increases slowly to 1028 kg m−3 at 5100 m.

Figure 7 The physical properties of seawater at 20° S in the Atlantic Ocean against depth. (a) Temperature; (b) salinity; (c) density.

Figure 7a shows 28 °C temperature at the surface to below 1 °C at the sea floor. The variation in salinity in 7b clearly affects the temperature of maximum density shown in 7c. The seawater density ranges from 1024 to 1028 kg m−3, ~24-28 kg m−3 denser than fresh water (Figure 4), and density increases with depth and the water is stratified all the way to the sea floor (although >3 000 m depth there is only a small increase). Because seawater is typically 1024-1028 kg m−3 there is a density anomaly, σt (pronounced 'sigma t') given by:

σt = (ρ - 1000) kg m−3
Equation label: (Eqn 1)

where ρ is the density of water.

  • What is the range of σt for typical seawater?

  • The density anomaly for typical seawater is in the range 24-28 kg m−3.

Box 1 explains how the physical properties shown in Figure 7 are measured.

Box 1 Measuring the physical properties of the ocean

Much of our knowledge about how the oceans circulate is based on measuring the various parameters such as temperature and salinity from the surface to the sea floor. The water which makes up this range is called the water column. The most important instrument used by oceanographers is called a CTD (Figure 8), which measures the conductivity and temperature of the seawater and depth (pressure).

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Figure 8 A CTD: the bottles on the side of the instrument collect samples of water and can be closed by the operator at any chosen depth.
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The photo shows the instrument sitting on the wooden deck of a ship. The deck is wet, so it's probably just been winched out of the water. The instrument is within a cylindrical frame about 2.5 metres high and 1.5 metres in diameter. The collection bottles are dark grey, about a metre long and thin, and lie within the top third of the instrument. There are about 20-25 of them arranged vertically in a concentric pattern.

Figure 8 A CTD: the bottles on the side of the instrument collect samples of water and can be closed by the operator at any chosen depth.

Because pressure in the ocean is proportional to the weight of the water above, it is given by the hydrostatic equation:

p = -g ρ z
Equation label: (Eqn 2)

where p is pressure, z is a change in depth and g is the acceleration due to gravity. The minus sign indicates that the vertical coordinate z (depth) is positive in an upwards direction. So by measuring pressure, Equation 2 can be arranged to get depth.

Other parameters can also be measured, such as sediment particle density, the amount of chlorophyll present (in algae), and so on. A CTD is lowered from a ship on a winch at a rate of ~60 m min−1. If the ocean is 5300 m deep, as in Figure 7, a round trip is 10 600 m and one profile can take almost three hours.