Density, the effects of depth and upwelling

Density as mass per unit volume

Density is the mass of a substance per unit volume: how much matter is packed into a given amount of space. You must be able to recall and use the formula density = mass / volume. Because mass is measured in kilograms and volume in cubic metres, a density worked out this way is in kg/m3. In the laboratory the samples are small, so mass is measured in grams and volume in cubic centimetres, which gives g/cm3. One gram per cubic centimetre is exactly 1 000 kilograms per cubic metre, so a density of 1.026 g/cm3 is 1 026 kg/m3 - the same water, described in two sets of units.

Density is a property of the water itself, not of how much of it you have. A bucket of sea water and a swimming pool of sea water at the same temperature and salinity have the same density, because the mass and the volume rise together in proportion. That is what makes density so useful in marine science: it lets you compare a sample from the surface with a sample from 1 000 m down, and it tells you straight away which one would sink beneath the other.

Worked example 1. A 250 cm3 sample of sea water has a mass of 256.5 g. density = mass / volume = 256.5 / 250 = 1.026 g/cm3, which is 1 026 kg/m3. Write the unit every time - an answer of 1.026 on its own is not a density.

Worked example 2 - rearranging the formula. A volume of 0.50 m3 of sea water has a density of 1 027 kg/m3. mass = density x volume = 1 027 x 0.50 = 513.5 kg. To find a volume instead, divide the mass by the density: 513.5 / 1 027 = 0.50 m3. Learn the triangle mass on top, density and volume beneath, and you can rearrange it in your head.

Worked example 3 - the same volume of two different waters. Take 2.0 m3 of fresh water of density 1 000 kg/m3 and 2.0 m3 of sea water of density 1 025 kg/m3. The fresh water has a mass of 2 000 kg and the sea water 2 050 kg. The volumes are identical, so the sea water holds 50 kg more mass in the same space, which is exactly what the dissolved salts add.

• Formula: density = mass / volume. Rearranged: mass = density x volume, volume = mass / density.
• Units: kg/m3 for metres and kilograms, g/cm3 for centimetres and grams. 1 g/cm3 = 1 000 kg/m3.
• Density is independent of the size of the sample: it depends on what the water contains, not on how much you collected.
• Typical values: fresh water about 1 000 kg/m3, sea water of ordinary salinity about 1 025 kg/m3.
• Always give the unit, and check that mass and volume are in matching units before you divide.

Temperature and density: what the particles are doing

Water is made of particles in constant motion, and temperature is a measure of their average kinetic energy. Heat a sample and its particles gain energy: they move faster, they vibrate and slide past one another more vigorously, and on average they push further apart. The water therefore takes up more space - its volume increases. Nothing has been added or taken away, so the mass stays exactly the same, and the same mass spread through a larger volume is a lower density.

Cool the water and the reverse happens. The particles lose kinetic energy, move less, and the attractions between them pull them closer together, so the water contracts into a smaller volume and the density rises. This is why the coldest water in a region, at a given salinity, is also the densest.

Worked example 4. 1.00 m3 of sea water of density 1 025 kg/m3 is warmed and expands by 0.2 per cent. The new volume is 1.002 m3 and the mass is still 1 025 kg, so the new density is 1 025 / 1.002 = 1 023 kg/m3 to three significant figures. The change looks tiny, and in absolute terms it is - a few kilograms per cubic metre - but convection is driven by differences in density, not by their absolute size, so a difference of that order is enough to make water sink or rise.

Investigating it (practical). Fill a density bottle or measuring cylinder with the same water sample, stand it in a water bath at a chosen temperature, let it settle, then measure the mass and the volume, or find the density directly with a hydrometer, which floats lower in a less dense liquid. Repeat at four or five temperatures, cover the container to prevent evaporation, read the meniscus at eye level and take the reading at the same point each time, then plot density on the y-axis against temperature on the x-axis. You expect a smooth downward line. The controls are the same sample, the same container, the same balance and no loss by evaporation - if the water evaporates, the mass falls as well and your result is meaningless.

Salinity and density, and the two effects together

Dissolving a salt adds mass to the water. The dissolved ions fit into the gaps between the water molecules, so the volume increases only slightly, while the mass increases by the full mass of the salt. More mass in almost the same volume means a higher density. This is why sea water, at about 35 parts per thousand of dissolved salts, has a density near 1 025 kg/m3 while fresh water at the same temperature is close to 1 000 kg/m3. Each additional part per thousand of dissolved salt raises the density by a little less than 1 kg/m3, so the effect is close to linear and easy to plot.

Salinity itself was defined earlier in this area as the concentration of dissolved salts, measured in parts per thousand (ppt): 35 g of dissolved salts in 1 000 g of sea water is a salinity of 35 ppt. That definition matters here, because it is the mass of salt per mass of water that adds mass without adding volume.

Investigating it (practical). Weigh 100 cm3 of distilled water, then weigh 100 cm3 of water to which increasing masses of salt have been added and stirred until fully dissolved - for example 1 g, 2 g, 3.5 g and 7 g per 100 cm3. Keep the volume and the temperature the same, dry the outside of the measuring cylinder before weighing, and use the same balance each time. Calculate the density of each and plot density against the mass of salt added: the points should lie close to a straight line rising to the right. The temperature must be held constant, otherwise you are measuring two effects at once and cannot tell which one caused the change.

The two effects together. Density rises as temperature falls and as salinity rises. So the densest water in the ocean is cold and salty and the least dense is warm and fresh. Cold polar water is dense because of its temperature; the water left behind when sea ice forms is dense because the salt has been concentrated into it; and warm tropical surface water is light because it is both warm and, in rainy regions, relatively fresh. That simple ranking explains nearly everything that follows about sinking, stratification and convection.

Convection, and why colder water lies beneath warmer water

Whenever a liquid has denser material sitting above less dense material, the arrangement is unstable. Gravity pulls the denser liquid down, the less dense liquid is pushed up out of its way, and the result is a convection current: a continuous circulation in which dense liquid sinks and light liquid rises. The current stops when the liquid has sorted itself out, with the densest at the bottom.

You can see this in a beaker heated at one side. The water next to the heat source warms, expands, becomes less dense and rises; cooler, denser water from the far side flows in along the bottom to replace it; that water is then heated in turn. The loop that forms carries heat through the whole beaker far faster than conduction alone, which is why water heats more evenly when it is stirred or when the heat is applied at the bottom. In the sea the same mechanism operates over thousands of kilometres. Surface water that is cooled at high latitudes contracts, becomes denser and sinks; warmer surface water flows in to take its place. When sea ice forms, the salt it leaves behind makes the water beneath even denser, which strengthens the sinking. The water that goes down spreads at depth and eventually returns towards the surface somewhere else, carrying heat, salt, dissolved oxygen and nutrients with it.

Why colder water generally lies beneath warmer water. At the same salinity, colder water is denser, so gravity pulls it below the warmer water, which floats on top. That is why the surface of the sea is warm and the deep ocean is cold, and why the boundary between the two resists being mixed: to stir warm water down you have to lift denser cold water up, which takes energy, and the wind rarely supplies enough.

The word generally is there for a reason. Salinity can outweigh temperature. Warm, very salty water can be denser than cooler, fresher water, which is why the warm, salty water flowing out of the Mediterranean sinks beneath the cooler, fresher Atlantic water at the Strait of Gibraltar. The one case where colder material lies on top is ice: water expands as it freezes, so solid ice is less dense than the liquid water it floats in.

Sketching it. If you are asked to sketch a convection current, draw the container, mark the heat source, draw a closed loop with an arrow rising on the warm side and falling on the cool side, and label the warm water 'less dense, rises' and the cool water 'denser, sinks'. Labels carry the marks, not the neatness of the arrows.

Light penetration and the Secchi disc

Sunlight entering the sea is absorbed by the water and by the substances dissolved in it, and it is scattered by anything suspended in it. Both processes remove light, so the intensity of light falls rapidly with depth, and the deeper you go the darker it gets. How fast it falls depends mainly on turbidity - the amount of suspended sediment and plankton - and also on the angle of the sun, on reflection at the surface and on the water itself. Clear open-ocean water lets useful light reach tens of metres; the muddy water of an estuary may be dark within a metre or two.

This has an obvious biological consequence: photosynthesis can only happen in the upper, sunlit layer. Phytoplankton must stay near the surface, and seaweeds and seagrasses are confined to shallow water where light reaches the bottom. Below the sunlit layer there is not enough light for plants to grow, so the animals living there depend on food sinking from above, or on each other. The syllabus only asks you to describe how light penetration changes with depth - the different wavelengths are absorbed at different rates, but the details of which colour is absorbed where are not required.

Using a Secchi disc (practical). A Secchi disc is a white disc, usually about 30 cm across with black quarters, attached to a marked line. Lower it on the shaded side of the boat until it just disappears from view, and record that depth. Then raise it until it reappears and record that depth too. The average of the two is the Secchi depth, a simple index of water clarity. Repeat at each site, and compare sites on the same day and at the same time of day so that the sun is at the same angle. A small Secchi depth means turbid, murky water; a large one means clear water.

Getting it right. Measure on the shaded side to avoid glare and surface reflection, keep the line vertical, lower the disc slowly, use the same observer when comparing sites (eyesight and judgement differ), note the sea state because waves make the disc flick in and out of view, keep the disc clean, and record the depth to the nearest 0.1 m. Take repeat readings and average them. These precautions are where the marks are: the disc is easy to use, and the skill being tested is controlling the variables that would otherwise make your comparison unfair.

Pressure: why it rises steadily with depth

Pressure is force per unit area, measured in pascals (Pa), where 1 Pa = 1 N/m2. The pressure at any point in the sea is caused by the weight of the water above that point pressing down, plus the pressure of the atmosphere on the surface. It acts in every direction, not just downwards, which is why a fish is not squashed flat and why a diver feels the pressure inside the ears as well as on the chest.

Water is almost incompressible: squeezing it hardly changes its volume, so its density stays nearly constant with depth. Because each extra metre adds the same weight of water, pressure increases steadily and in proportion to depth. The useful rule is that every 10 m of sea water adds about 1 atmosphere, roughly 1.0 x 10^5 Pa. That gives 1 atm at the surface (the air), 2 atm at 10 m, 4 atm at 30 m, 6 atm at 50 m and 11 atm at 100 m.

Worked example 5. Find the total pressure at 20 m. The pressure from the water is depth x density x gravitational field strength = 20 x 1 025 x 9.8 = 200 900 Pa, about 2.0 x 10^5 Pa. Add the atmosphere at the surface, 1.0 x 10^5 Pa, and the total is about 3.0 x 10^5 Pa, or 3 atmospheres. The 10 m rule comes from the same sum: 10 x 1 025 x 9.8 = 100 450 Pa, which is about one atmosphere.

Explain it in one sentence. Double the depth and you double the weight of water above, so the pressure from the water doubles - and because the atmosphere at the surface is a fixed extra term, the total pressure rises steadily rather than sharply. The shape of the container and the temperature of the water make almost no difference: only the depth of water above the point matters.

Pressure matters to organisms because gases compress and liquids do not. A fish has no large gas-filled spaces, so the pressure inside it matches the pressure outside and it is not crushed; a diver breathes air at the surrounding pressure, so the gas in the lungs is squeezed as they descend and expands as they rise, which is why they must never hold their breath while ascending.

Temperature with depth: mixed layer and thermocline

The surface of the sea is heated by the sun. Wind and waves stir the top layer, so its temperature is almost the same from the surface down for tens of metres: this is the mixed layer. Beneath it the temperature falls quickly through a zone called the thermocline, and below the thermocline lies the deep water, which is cold - commonly around 2 to 4 °C - and whose temperature changes very little however much deeper you go.

The pattern depends on latitude. In low latitudes there is a strong, permanent thermocline, because the surface is warm and the deep water is cold and the two rarely mix. In high latitudes the thermocline is weak or absent, because the surface water is cold anyway and storms mix the water deeply, so the temperature is nearly uniform from top to bottom. In temperate seas a seasonal thermocline forms in summer as the surface warms and the water stratifies, and is destroyed in autumn and winter when storms and cooling mix it away.

The layering is stable because warm water is less dense than cold water. The warm surface water floats on the cold deep water, and the thermocline is therefore also a density boundary - a pycnocline - which resists mixing. To stir warm surface water down you would have to lift dense cold water up, and the wind rarely has the energy. That is why the deep ocean stays cold even in the tropics, and why the thermocline is such a strong barrier to nutrients and oxygen moving between the surface and the deep.

Describing a profile. If you are asked to sketch a temperature profile, put depth on the vertical axis with 0 at the top and increasing downwards, temperature on the horizontal axis increasing to the right, then draw a line that runs nearly vertical through the mixed layer, bends sharply to the left through the thermocline, and runs nearly vertical again in the cold deep water. Label the three parts. The shape is the answer; the exact numbers are not.

Dissolved oxygen, and the summary of conditions with depth

Oxygen enters the surface water from the air by diffusion across the sea surface, and it is also produced there by photosynthesis of phytoplankton in the sunlit layer. Wind and waves mix that oxygen downwards, so the highest concentrations are normally found near the surface.

Below the sunlit layer, photosynthesis stops, but oxygen is still being used: by the respiration of animals, including zooplankton and fish, and by bacteria decomposing dead organisms and faecal material that sink from above. Once production has stopped and consumption continues, the concentration must fall, so dissolved oxygen decreases with depth. Where productivity at the surface is high, so much material sinks that consumption at depth is intense, and a distinct oxygen minimum layer forms a few hundred metres down.

Deeper still, the concentration often rises again, for two reasons. The deep water is cold, and cold water can hold more dissolved gas than warm water - the same solubility rule that applies to oxygen and carbon dioxide. And that deep water sank from the surface at high latitudes, where it was cold and in contact with the atmosphere and with well-mixed, oxygen-rich surface water, so it carried a good supply down with it.

The shape of the profile therefore depends on the balance between supply and demand. In well-mixed water, such as the Southern Ocean or a shallow sea in winter, oxygen is fairly uniform from top to bottom. In strongly stratified water the surface layer is well supplied and the water below the pycnocline is cut off from the air, so oxygen falls sharply and can become very low. Upwelled water can also be low in oxygen, because it has spent time below the sunlit layer where oxygen was being used up rather than added.

The five conditions, side by side. The syllabus asks you to state the conditions that change with depth and then to describe each one, so learn them as a set, with the reason for each.

Upwelling and El Nino

Upwelling is the rise of water from below the surface to replace surface water that has been moved away. Wind does the moving: where a steady wind blows across the sea, it drags the surface water with it. Where the wind blows along a coast or offshore, the surface water is pushed away from the coast, and water from below rises to fill the gap. The same thing happens along the equator, where the trade winds push surface water westwards and deeper water rises to replace it.

The water that rises is cold, because it comes from below the sunlit, wind-mixed layer and has never been warmed by the sun. It is also nutrient-rich. Nutrients such as nitrate and phosphate are released at depth by the decay of dead organisms that sank from the surface; in the sunlit surface layer they are quickly used up by phytoplankton, and because the thermocline is a density barrier they cannot easily be mixed back up. Upwelling takes that store of nutrients from below the barrier into the sunlight, where phytoplankton can use them, so productivity explodes and the food chain above it supports enormous numbers of fish, seabirds and marine mammals.

Upwelling of this kind is concentrated on the eastern side of ocean basins, where the winds blow along the coast towards the equator: off Peru and Chile in the Humboldt Current, off Namibia and South Africa in the Benguela system, off north-west Africa in the Canary Current, and off California. These are among the most productive waters in the world, which is why they carry major fisheries - and why they are so vulnerable when the wind changes. Upwelled water may also be low in dissolved oxygen, because it has spent time below the sunlit layer where oxygen was being used rather than produced.

El Nino. Normally the trade winds blow strongly from east to west across the Pacific, piling warm surface water up in the west and allowing upwelling to continue off South America. In an El Nino, the trade winds weaken or reverse. The warm surface water then spreads eastwards, or the boundary between warm and cold water deepens in the east, and the surface water of the eastern Pacific becomes warmer than usual. Because the wind has weakened, upwelling is reduced, so far less nutrient-rich water reaches the surface. Phytoplankton production falls, the small fish that feed on it - the anchoveta off Peru is the classic case - decline or move away, and the fishery and the seabirds that depend on it collapse. Warm water also drives strong convection and heavy rain over the eastern Pacific, bringing floods to Peru and Ecuador, while the western Pacific has descending air instead, so Indonesia, Papua New Guinea and eastern Australia get drought and the conditions for bushfires.

Discussing the local effects. Keep to the three effects the syllabus names. Water temperature: the eastern Pacific surface warms by a few degrees, while the west is slightly cooler than usual. Nutrient availability: upwelling and the supply of nutrients fall in the east, so productivity and fish catches drop. Rainfall: the east - Peru and Ecuador - gets far more rain and floods, while Australia and Asia get far less, with drought and fire risk. The effects last from a few months to about a year, and they matter economically because they hit fishing communities and farmers, not just the plankton.