---
title: "The Layered Ocean"
book: "High School Earth and Space Sciences"
subject: earth
language: en
chapter: 6
exercises: 15
source: https://one-course.com/books/earth/2/en/chapter/6-the-layered-ocean
license: CC-BY-NC-SA-4.0
credit: "One Earth and Space Sciences Book, One Course (one-course.com)"
---

# Chapter 6 — The Layered Ocean

On a summer day you swim out from a beach into water that is pleasantly warm. Then you let your legs hang down — and your feet find water that is suddenly cold, a couple of metres below the surface. The sea is not mixed from top to bottom: it is made of layers, warm and light above, cold and dense below. In the open ocean the same layering reaches down kilometres, and it decides where the sea is a desert and where it teems with life. This chapter looks at the ocean in depth: how it is measured, how its temperature and salinity change downwards, why the layers are stable, and where cold deep water comes back up to the surface.

**You already know.**

Seawater contains dissolved salts: its salinity, about 35 grams of salt per kilogram of seawater on average, varies from sea to sea. Winds drive the surface currents and the great circular gyres; deep currents of cold, salty water move slowly along the ocean floor (Book 1, grade 8). Density is mass divided by volume (the physics books). The phytoplankton, microscopic algae, need light and mineral nutrients to grow by photosynthesis, and they feed the rest of the ocean’s food chains (the biology books).

## 6.1 Measuring the ocean

The ocean covers about $362$ million $\mathrm{km}^{2}$ and is on average $3682\,\mathrm{m}$ deep: some $1.33$ billion $\mathrm{km}^{3}$ of water. Most of it lies far below the reach of light, and it can only be measured by sending instruments down.

From a ship, oceanographers lower on a cable a frame carrying sensors that measure the conductivity of the water (from which its salinity is computed), its temperature and the pressure (hence the depth), surrounded by a ring of bottles that are closed at chosen depths to bring water samples back on board. Since the year 2000 a fleet of robotic floats has added millions of profiles: each float drifts with the currents at a depth of $1000\,\mathrm{m}$, sinks every ten days or so to $2000\,\mathrm{m}$, then rises to the surface measuring temperature and salinity on the way, and sends its profile by satellite.

**Figures as of 2026.**

The international Argo array counts close to 4000 active floats; its three millionth profile was collected in July 2024.

![Left: a rosette of sampling bottles around its sensors, hauled back up beside a research ship in the Arctic, 2008 (photograph: Pablo Clemente-Colon, NOAA Photo Library). Right: a profiling float is launched from a research ship (photograph: NOAA Global Ocean Monitoring and Observing Program). Both public domain.](https://one-course.com/images/onecourse/chapters/earth-2/g10-layered-ocean/img-537c658ab146.jpg)

![Left: a rosette of sampling bottles around its sensors, hauled back up beside a research ship in the Arctic, 2008 (photograph: Pablo Clemente-Colon, NOAA Photo Library). Right: a profiling float is launched from a research ship (photograph: NOAA Global Ocean Monitoring and Observing Program). Both public domain.](https://one-course.com/images/onecourse/chapters/earth-2/g10-layered-ocean/img-cc88aba21e2d.jpg)

*Left: a rosette of sampling bottles around its sensors, hauled back up beside a research ship in the Arctic, 2008 (photograph: Pablo Clemente-Colon, NOAA Photo Library). Right: a profiling float is launched from a research ship (photograph: NOAA Global Ocean Monitoring and Observing Program). Both public domain.*

Averaged over decades of measurements, these profiles give a picture of the ocean in depth. The profiles of this chapter are such averages, from the *World Ocean Atlas 2023* of the NOAA National Centers for Environmental Information.

## 6.2 Temperature with depth

![Average temperature against depth at three sites (depth increases downwards). Data: World Ocean Atlas 2023, annual averages, NOAA NCEI.](https://one-course.com/images/onecourse/chapters/earth-2/g10-layered-ocean/fig-bc6f11beb2f9.svg)

*Average temperature against depth at three sites (depth increases downwards). Data: World Ocean Atlas 2023, annual averages, NOAA NCEI.*

Sunlight heats the ocean from above, in its surface layer. The wind and the waves stir this warm water into a layer of almost uniform temperature. Below it, the temperature falls quickly over a few hundred metres; deeper still, it falls slowly to the cold water that fills the ocean basins.

**Definition 6.1 (Mixed layer).**

The *mixed layer* is the surface layer of the ocean, stirred by the wind and the waves, in which temperature and salinity hardly change with depth.

**Definition 6.2 (Thermocline; halocline; pycnocline; deep ocean).**

The *thermocline* is the layer below the [mixed layer](#def-g10-layered-ocean-mixed-layer) in which the temperature falls quickly with depth. The layer in which the salinity changes quickly with depth is a *halocline*; the layer in which the density increases quickly with depth is the *pycnocline*. Below them lies the *deep ocean*, cold and slowly changing.

In the tropical Pacific the [mixed layer](#def-g10-layered-ocean-mixed-layer) is at $29.2{}^{\circ}\mathrm{C}$ and some $60\,\mathrm{m}$ thick; between $70\,\mathrm{m}$ and $300\,\mathrm{m}$ the temperature drops by nearly nineteen degrees, and at $1000\,\mathrm{m}$ it is down to $4.5{}^{\circ}\mathrm{C}$. In the North Atlantic the surface is cooler and the fall more gradual. In the Arctic Ocean the whole column stays within two degrees of $0{}^{\circ}\mathrm{C}$: there is no warm surface layer to speak of.

**Method 6.3 (Reading an ocean profile).**

1. Find the axes: depth increases downwards, the measured quantity is read along the top.
2. The [mixed layer](#def-g10-layered-ocean-mixed-layer) is the upper part where the curve is nearly vertical; its depth is where the curve starts to bend away (a common rule: where the temperature has fallen $0.5{}^{\circ}\mathrm{C}$ below its surface value).
3. The [thermocline](#def-g10-layered-ocean-thermocline) is where the curve is closest to horizontal: the largest change for the smallest depth.
4. Below, read the deep values and compare sites at the same depth.

The [mixed layer](#def-g10-layered-ocean-mixed-layer) changes with the seasons. In winter the surface loses heat, storms stir the sea, and the [mixed layer](#def-g10-layered-ocean-mixed-layer) deepens; in summer the sun warms a thin surface layer that the gentler winds cannot mix downwards, and a *seasonal [thermocline](#def-g10-layered-ocean-thermocline)* forms near the surface — the cold water that the swimmer’s feet find.

![Winter and summer in the North Atlantic (40.5°N, 30.5°W): monthly average temperatures for February and August. In February the mixed layer reaches about 170\, m; in August a warm layer about 15\, m thick lies on a seasonal thermocline. Data: World Ocean Atlas 2023, NOAA NCEI.](https://one-course.com/images/onecourse/chapters/earth-2/g10-layered-ocean/fig-66c1c7b5abc0.svg)

*Winter and summer in the North Atlantic (40.5°N, 30.5°W): monthly average temperatures for February and August. In February the [mixed layer](#def-g10-layered-ocean-mixed-layer) reaches about $170\,\mathrm{m}$; in August a warm layer about $15\,\mathrm{m}$ thick lies on a seasonal [thermocline](#def-g10-layered-ocean-thermocline). Data: World Ocean Atlas 2023, NOAA NCEI.*

## 6.3 Salinity and density

The density of seawater depends on its temperature and on its salinity. It is computed from an internationally agreed formula, the equation of state of seawater, fitted to laboratory measurements.

**Proposition 6.4 (Density of seawater).**

The density of seawater increases with its salinity and decreases as its temperature rises. At the pressure of the surface, seawater of salinity 35 has a density of $1028.1\,\mathrm{kg}/\mathrm{m}^{3}$ at $0{}^{\circ}\mathrm{C}$ and $1023.3\,\mathrm{kg}/\mathrm{m}^{3}$ at $25{}^{\circ}\mathrm{C}$; pure water at $4{}^{\circ}\mathrm{C}$ has a density of $1000.0\,\mathrm{kg}/\mathrm{m}^{3}$.

![The density of seawater at the pressure of the surface, against its temperature, for three salinities (computed from the international equation of state of seawater).](https://one-course.com/images/onecourse/chapters/earth-2/g10-layered-ocean/fig-633813fe3ea5.svg)

*The density of seawater at the pressure of the surface, against its temperature, for three salinities (computed from the international equation of state of seawater).*

Two things show on the chart. One unit of salinity adds about $0.8\,\mathrm{kg}/\mathrm{m}^{3}$. One degree of warming removes about $0.31\,\mathrm{kg}/\mathrm{m}^{3}$ at $25{}^{\circ}\mathrm{C}$, $0.18\,\mathrm{kg}/\mathrm{m}^{3}$ at $10{}^{\circ}\mathrm{C}$, but only $0.06\,\mathrm{kg}/\mathrm{m}^{3}$ near $0{}^{\circ}\mathrm{C}$: in warm seas temperature controls the density, in cold seas salinity does.

**Remark 6.5.**

The densities of this chapter are computed at the pressure of the surface. The pressure of the water above compresses seawater a little, by about $4\,\mathrm{kg}/\mathrm{m}^{3}$ per kilometre of depth; oceanographers compare water masses at the same pressure, so that only temperature and salinity count.

![Salinity (left) and density at the pressure of the surface (right) against depth, at the three sites of the temperature profiles. At every site the density increases downwards. Data: World Ocean Atlas 2023, NOAA NCEI; densities from the international equation of state of seawater.](https://one-course.com/images/onecourse/chapters/earth-2/g10-layered-ocean/fig-fd89f2261a94.svg)

*Salinity (left) and density at the pressure of the surface (right) against depth, at the three sites of the temperature profiles. At every site the density increases downwards. Data: World Ocean Atlas 2023, NOAA NCEI; densities from the international equation of state of seawater.*

In the tropical Pacific the [pycnocline](#def-g10-layered-ocean-thermocline) coincides with the [thermocline](#def-g10-layered-ocean-thermocline). In the Arctic Ocean the temperature hardly changes, but the salinity rises from 28 at the surface, freshened by rivers and melting ice, to 34.8 at $500\,\mathrm{m}$: the [halocline](#def-g10-layered-ocean-thermocline) is the [pycnocline](#def-g10-layered-ocean-thermocline). In each case the density increases downwards.

**Definition 6.6 (Stratification).**

The ocean is *stratified* when its density increases with depth: lighter water lies on denser water, in layers.

A [stratified](#def-g10-layered-ocean-stratification) ocean is stable. A parcel of water pushed down into denser water is lighter than its surroundings and floats back up; a parcel pushed up sinks back. To mix the layers, the wind must work against this, and the stronger the [pycnocline](#def-g10-layered-ocean-thermocline), the harder it is: the [thermocline](#def-g10-layered-ocean-thermocline) is a lid that separates the surface from the [deep ocean](#def-g10-layered-ocean-thermocline). The [deep ocean](#def-g10-layered-ocean-thermocline) is filled with water that sank long ago from the cold polar seas, where surface water becomes dense enough to sink (Book 1, grade 8).

## 6.4 Upwelling

**Definition 6.7 (Upwelling).**

*Upwelling* is the rise of cold water from below the surface layer, to replace surface water that the wind pushes away. It occurs along some coasts and in the open ocean.

Along a coast, the wind blowing parallel to the shore drags the surface water; because of the Earth’s rotation the water does not simply follow the wind but is turned away from it, to the right in the Northern Hemisphere and to the left in the Southern Hemisphere (how this works is the subject of the university volumes). Off Peru the wind blows along the shore towards the equator, and the surface water is pushed out to sea; cold water rises near the coast to take its place. [Upwelling](#def-g10-layered-ocean-upwelling) also takes place along the equator, where the trade winds drive the surface water away from it on both sides.

![Coastal upwelling off Peru (schematic cross-section from west to east, not to scale): the wind blows along the shore towards the equator, northward, into the page; the surface water is turned to its left and pushed out to sea; cold water from below the thermocline rises near the coast to replace it.](https://one-course.com/images/onecourse/chapters/earth-2/g10-layered-ocean/fig-2e1f29e17a94.svg)

*Coastal [upwelling](#def-g10-layered-ocean-upwelling) off Peru (schematic cross-section from west to east, not to scale): the wind blows along the shore towards the equator, northward, into the page; the surface water is turned to its left and pushed out to sea; cold water from below the [thermocline](#def-g10-layered-ocean-thermocline) rises near the coast to replace it.*

The water that rises is not only cold. Below the sunlit surface layer, the remains of dead plankton that sink and decay release the mineral nutrients that the phytoplankton need. Brought back into the light, these nutrients make the [upwelling](#def-g10-layered-ocean-upwelling) regions the most productive waters of the ocean, with the richest fishing grounds. Where the ocean is strongly [stratified](#def-g10-layered-ocean-stratification) and nothing brings deep water up, the sunlit layer runs out of nutrients: the centres of the subtropical gyres are the deserts of the ocean.

![The chlorophyll of the phytoplankton seen from space, averaged over 2002–2010: from dark blue (very little) through light blue to yellow (a lot); land in grey. The coast of Peru and the band along the equator in the Pacific stand out; the gyres are deep blue. Image: Jesse Allen and Robert Simmon, NASA Earth Observatory (public domain).](https://one-course.com/images/onecourse/chapters/earth-2/g10-layered-ocean/img-29e52896608e.jpg)

*The chlorophyll of the phytoplankton seen from space, averaged over 2002–2010: from dark blue (very little) through light blue to yellow (a lot); land in grey. The coast of Peru and the band along the equator in the Pacific stand out; the gyres are deep blue. Image: Jesse Allen and Robert Simmon, NASA Earth Observatory (public domain).*

![Off Peru, the cold water comes close to the surface: water at 15 C (dashed line) lies at about 65\, m, against nearly 300\, m in the middle of the South Pacific gyre, which is farther from the equator. Data: World Ocean Atlas 2023, annual averages, NOAA NCEI.](https://one-course.com/images/onecourse/chapters/earth-2/g10-layered-ocean/fig-c75d958f9034.svg)

*Off Peru, the cold water comes close to the surface: water at $15{}^{\circ}\mathrm{C}$ (dashed line) lies at about $65\,\mathrm{m}$, against nearly $300\,\mathrm{m}$ in the middle of the South Pacific gyre, which is farther from the equator. Data: World Ocean Atlas 2023, annual averages, NOAA NCEI.*

## 6.5 Exercises

**Exercise 6.1 ★.**

Define the [mixed layer](#def-g10-layered-ocean-mixed-layer) and the [thermocline](#def-g10-layered-ocean-thermocline). What stirs the [mixed layer](#def-g10-layered-ocean-mixed-layer)?

**Solution of Exercise 6.1.**

The [mixed layer](#def-g10-layered-ocean-mixed-layer) is the surface layer of the ocean in which temperature and salinity hardly change with depth; the [thermocline](#def-g10-layered-ocean-thermocline) is the layer below it in which the temperature falls quickly with depth. The wind and the waves stir the [mixed layer](#def-g10-layered-ocean-mixed-layer) (helped in winter by the cooling of the surface).

**Exercise 6.2 ★.**

Define [upwelling](#def-g10-layered-ocean-upwelling). Why are the waters of [upwelling](#def-g10-layered-ocean-upwelling) regions rich in life?

**Solution of Exercise 6.2.**

[Upwelling](#def-g10-layered-ocean-upwelling) is the rise of cold water from below the surface layer, replacing surface water pushed away by the wind. The rising water brings mineral nutrients into the sunlit layer, where the phytoplankton use them to grow; the phytoplankton feed the rest of the food chain.

**Exercise 6.3 ★.**

Using the temperature profiles of the three sites, give the temperature at the surface and at $1000\,\mathrm{m}$ in the tropical Pacific and in the Arctic Ocean.

**Solution of Exercise 6.3.**

Tropical Pacific: about $29{}^{\circ}\mathrm{C}$ at the surface and $4.5{}^{\circ}\mathrm{C}$ at $1000\,\mathrm{m}$. Arctic Ocean: about $-1.4{}^{\circ}\mathrm{C}$ at the surface and close to $0{}^{\circ}\mathrm{C}$ at $1000\,\mathrm{m}$.

**Exercise 6.4 ★.**

Which is denser, seawater of salinity 35 at $25{}^{\circ}\mathrm{C}$ or at $0{}^{\circ}\mathrm{C}$? Seawater of salinity 35 or pure water, at the same temperature? Use the values of the chapter.

**Solution of Exercise 6.4.**

At $0{}^{\circ}\mathrm{C}$ ($1028.1\,\mathrm{kg}/\mathrm{m}^{3}$ against $1023.3\,\mathrm{kg}/\mathrm{m}^{3}$ at $25{}^{\circ}\mathrm{C}$). Seawater: at $4{}^{\circ}\mathrm{C}$ pure water has a density of $1000.0\,\mathrm{kg}/\mathrm{m}^{3}$, seawater of salinity 35 about $1027.8\,\mathrm{kg}/\mathrm{m}^{3}$ (read on the chart).

**Exercise 6.5 ★.**

Explain how a profiling float measures a profile of the ocean, and why floats are useful where ships rarely go.

**Solution of Exercise 6.5.**

The float drifts at $1000\,\mathrm{m}$, sinks to $2000\,\mathrm{m}$, then rises to the surface measuring temperature, salinity (from the conductivity) and pressure on the way; at the surface it sends its profile by satellite and sinks again. Floats drift with the currents all over the ocean and work for years, in all seasons, far from the ship routes.

**Exercise 6.6 ★★.**

The ocean covers $361.84$ million $\mathrm{km}^{2}$ with a mean depth of $3682\,\mathrm{m}$. Compute its volume in cubic kilometres. What fraction of its depth does the top $100\,\mathrm{m}$ represent?

**Solution of Exercise 6.6.**

$361.84\times10^6 \times 3.682 \approx 1.33 \times 10^{9}\,\mathrm{km}^{3}$, about $1.33$ billion cubic kilometres. $100/3682 \approx 0.027$: under $3\,\%$ of the mean depth.

**Exercise 6.7 ★★.**

In the North Atlantic profile of August, the temperature is $22.7{}^{\circ}\mathrm{C}$ at the surface, $22.2{}^{\circ}\mathrm{C}$ at $15\,\mathrm{m}$, $21.8{}^{\circ}\mathrm{C}$ at $20\,\mathrm{m}$ and $17.3{}^{\circ}\mathrm{C}$ at $50\,\mathrm{m}$. Using the rule of the method, estimate the depth of the [mixed layer](#def-g10-layered-ocean-mixed-layer). What is the average rate of fall of temperature between $20\,\mathrm{m}$ and $50\,\mathrm{m}$, in degrees per metre?

**Solution of Exercise 6.7.**

$22.7 - 0.5 = 22.2{}^{\circ}\mathrm{C}$, reached at $15\,\mathrm{m}$: the [mixed layer](#def-g10-layered-ocean-mixed-layer) is about $15\,\mathrm{m}$ deep. Between $20\,\mathrm{m}$ and $50\,\mathrm{m}$: $(21.8 - 17.3)/30 = 0.15{}^{\circ}\mathrm{C}$ per metre.

**Exercise 6.8 ★★.**

At the same North Atlantic site the surface is at $15.3{}^{\circ}\mathrm{C}$ in February and $22.7{}^{\circ}\mathrm{C}$ in August, while at $300\,\mathrm{m}$ it is at $13.5{}^{\circ}\mathrm{C}$ in both months. Explain why the deep water does not follow the seasons, and why the winter [mixed layer](#def-g10-layered-ocean-mixed-layer) is much deeper than the summer one.

**Solution of Exercise 6.8.**

The sun heats only the surface layer, and the seasonal heating and cooling are spread only through the [mixed layer](#def-g10-layered-ocean-mixed-layer): below the [thermocline](#def-g10-layered-ocean-thermocline) the water is cut off from them. In winter the surface cools, becomes denser and sinks into the water below, and the storms stir the sea: the mixing goes deep. In summer the sun warms a light surface layer that floats on the colder water; the gentler winds cannot push it down, and the [mixed layer](#def-g10-layered-ocean-mixed-layer) stays thin.

**Exercise 6.9 ★★.**

Near $10{}^{\circ}\mathrm{C}$, one unit of salinity adds $0.78\,\mathrm{kg}/\mathrm{m}^{3}$ to the density and one degree of warming removes $0.18\,\mathrm{kg}/\mathrm{m}^{3}$. How many degrees of warming cancel one unit of salinity? Answer the same question near $0{}^{\circ}\mathrm{C}$, where one degree removes only $0.06\,\mathrm{kg}/\mathrm{m}^{3}$. What do you conclude for the polar seas?

**Solution of Exercise 6.9.**

$0.78/0.18 \approx 4.3$ degrees near $10{}^{\circ}\mathrm{C}$; $0.78/0.06 = 13$ degrees near $0{}^{\circ}\mathrm{C}$. In the cold polar seas small changes of salinity matter far more for the density than changes of temperature: there, salinity controls the layering.

**Exercise 6.10 ★★.**

In the Arctic Ocean the water at the surface is at $-1.4{}^{\circ}\mathrm{C}$ with a salinity of 28.1, and at $200\,\mathrm{m}$ at $-1.4{}^{\circ}\mathrm{C}$ with a salinity of 33.3. Their densities are $1022.6\,\mathrm{kg}/\mathrm{m}^{3}$ and $1026.8\,\mathrm{kg}/\mathrm{m}^{3}$. What makes the deeper water denser? Name the layer between them.

**Solution of Exercise 6.10.**

The temperature is the same: the deeper water is denser because it is saltier (33.3 against 28.1). The layer between them, where the salinity changes quickly with depth, is a [halocline](#def-g10-layered-ocean-thermocline); here it is also the [pycnocline](#def-g10-layered-ocean-thermocline).

**Exercise 6.11 ★★.**

Explain why a [stratified](#def-g10-layered-ocean-stratification) ocean is stable, using a parcel of surface water pushed down by a wave.

**Solution of Exercise 6.11.**

Pushed down, the parcel keeps its temperature and salinity, so its density. Surrounded by denser water, it is lighter than the water it displaces: the buoyancy pushes it back up to its own level. A parcel pushed up would be denser than its new surroundings and sink back. The layers are stable.

**Exercise 6.12 ★★★.**

A litre of seawater of salinity 35 at $0{}^{\circ}\mathrm{C}$ is warmed to $25{}^{\circ}\mathrm{C}$. Using the densities of the chapter, compute its mass, then its new volume. By how much has it expanded, in millilitres? A layer of ocean $700\,\mathrm{m}$ thick warms in the same proportion: how much does its thickness grow? (This is a large exaggeration of real ocean warming, used here only to show the effect.)

**Solution of Exercise 6.12.**

Mass: $0.001 \times 1028.1 = 1.0281\,\mathrm{kg}$. New volume: $1.0281/1023.3
\approx 0.001\,004\,7\,\mathrm{m}^{3}$, about $1004.7\,\mathrm{mL}$: it has expanded by about $4.7\,\mathrm{mL}$, $0.47\,\%$. The layer of $700\,\mathrm{m}$ would thicken by $700 \times 0.0047 \approx 3.3\,\mathrm{m}$.

**Exercise 6.13 ★★★.**

In the tropical Pacific the density is $1021.6\,\mathrm{kg}/\mathrm{m}^{3}$ at $50\,\mathrm{m}$ and $1026.0\,\mathrm{kg}/\mathrm{m}^{3}$ at $200\,\mathrm{m}$; in the North Atlantic in February the temperature hardly changes over the top $150\,\mathrm{m}$. In which of the two would a storm find it easier to stir the water down to $150\,\mathrm{m}$? Explain.

**Solution of Exercise 6.13.**

In the North Atlantic in February. There the top $150\,\mathrm{m}$ has almost the same temperature, hence almost the same density: stirring it costs little. In the tropical Pacific the density rises by $1026.0 - 1021.6 =
4.4\,\mathrm{kg}/\mathrm{m}^{3}$ between $50\,\mathrm{m}$ and $200\,\mathrm{m}$: a strong [pycnocline](#def-g10-layered-ocean-thermocline), and the storm would have to push light water down into much denser water.

**Exercise 6.14 ★★★.**

On the chlorophyll map, find two regions of high chlorophyll in the open ocean far from any coast, and one large region of very low chlorophyll. Using the chapter, explain each.

**Solution of Exercise 6.14.**

High chlorophyll far from coasts: the band along the equator in the Pacific (and in the Atlantic), where the trade winds drive an [upwelling](#def-g10-layered-ocean-upwelling); and the high latitudes, such as the North Atlantic, where the winter [mixed layer](#def-g10-layered-ocean-mixed-layer) reaches deep and brings nutrients up. Very low chlorophyll: the centres of the subtropical gyres, strongly [stratified](#def-g10-layered-ocean-stratification), where nothing brings deep water up and the sunlit layer has run out of nutrients.

**Exercise 6.15 ★★★.**

Suppose that a float sinks from $1000\,\mathrm{m}$ to $2000\,\mathrm{m}$ in six hours, then rises to the surface in ten hours. Compute its average vertical speed in each phase, in centimetres per second. If it measured every $2\,\mathrm{s}$ while rising, how many measurements does a profile contain, and what depth separates two of them on average?

**Solution of Exercise 6.15.**

Sinking: $1000/(6 \times 3600) \approx 0.046\,\mathrm{m}/\mathrm{s}$, about $4.6\,\mathrm{cm}/\mathrm{s}$. Rising: $2000/(10 \times 3600) \approx 0.056\,\mathrm{m}/\mathrm{s}$, about $5.6\,\mathrm{cm}/\mathrm{s}$. $36\,000/2 = 18\,000$ measurements, on average $2000/18\,000 \approx 0.11\,\mathrm{m}$ apart.

## 6.6 Problem: A Cast off Peru

**Problem 6.1.**

Weekend problem — two profiles of the South Pacific

The table gives the average temperature and salinity, and the density computed at the pressure of the surface, at two places of the South Pacific: off Peru ($13.5{}^{\circ}\mathrm{S}$, $77.5{}^{\circ}\mathrm{W}$) and in the middle of the subtropical gyre ($20.5{}^{\circ}\mathrm{S}$, $110.5{}^{\circ}\mathrm{W}$).

|  | off Peru | gyre |
| --- | --- | --- |
| depth ($\mathrm{m}$) | ${}^{\circ}\mathrm{C}$ | salinity | $\mathrm{kg}/\mathrm{m}^{3}$ | ${}^{\circ}\mathrm{C}$ | salinity | $\mathrm{kg}/\mathrm{m}^{3}$ |
| 0 | 19.0 | 35.08 | 1025.08 | 24.0 | 36.41 | 1024.71 |
| 25 | 17.4 | 35.06 | 1025.47 | 23.9 | 36.39 | 1024.73 |
| 50 | 15.8 | 35.03 | 1025.83 | 23.6 | 36.38 | 1024.80 |
| 100 | 13.7 | 34.93 | 1026.20 | 22.6 | 36.27 | 1025.02 |
| 200 | 12.4 | 34.89 | 1026.44 | 20.3 | 35.80 | 1025.30 |
| 300 | 11.1 | 34.80 | 1026.62 | 14.4 | 34.76 | 1025.92 |
| 500 | 7.9 | 34.60 | 1026.97 | 7.1 | 34.39 | 1026.92 |

**Part I — Reading the profiles.**

1. Which site is warmer at the surface, and by how much?
2. Which site is farther from the equator? Is the difference of surface temperature what you would expect from the latitudes alone?
3. Using the rule of the method, estimate the depth of the [mixed layer](#def-g10-layered-ocean-mixed-layer) in the gyre.
4. Is there a [mixed layer](#def-g10-layered-ocean-mixed-layer) off Peru? Describe the top $100\,\mathrm{m}$ .
5. Between which depths does the temperature fall fastest in the gyre? Give the rate, in degrees per hundred metres.
6. At what depth, roughly, is the water at $15{}^{\circ}\mathrm{C}$ at each site?

**Part II — Densities.**

7. Check that the density increases with depth at both sites. What does this tell you about their stability?
8. In the gyre, the surface water is saltier than off Peru. Should this make it denser or lighter? Is it denser?
9. Explain which of the two effects wins.
10. Compute the increase in density from the surface to $200\,\mathrm{m}$ off Peru.
11. Compute the same increase in the gyre.

**Part III — Stratification compared.**

12. In the gyre, where is most of the density increase of the top $500\,\mathrm{m}$ found: above or below $200\,\mathrm{m}$ ?
13. Off Peru, where is it found?
14. At $500\,\mathrm{m}$ , compare the two sites. What does this suggest about the deep water below both?
15. Explain in a few sentences how the [thermocline](#def-g10-layered-ocean-thermocline) off Peru has been lifted towards the surface.
16. The phytoplankton live in the top few tens of metres. At which site is nutrient-rich water from below the [thermocline](#def-g10-layered-ocean-thermocline) within reach of the wind’s stirring? Explain.

**Part IV — Why the Peruvian waters are productive.**

17. What would the surface water off Peru be like if the wind along the shore stopped blowing for months?
18. Using the chlorophyll map, compare the two sites.
19. Explain why the gyre is called a desert of the ocean although it is full of sunlight.
20. Compute the ratio of the density increases from the surface to $200\,\mathrm{m}$ off Peru and in the gyre, and say what it shows.

**Solution of Problem 6.1.**

**1.** The gyre, by $24.0 - 19.0 = 5.0{}^{\circ}\mathrm{C}$.

**2.** The gyre ($20.5{}^{\circ}\mathrm{S}$ against $13.5{}^{\circ}\mathrm{S}$). Farther from the equator, it should be the cooler one: the latitudes alone cannot explain why it is $5{}^{\circ}\mathrm{C}$ warmer.

**3.** $24.0 - 0.5 = 23.5{}^{\circ}\mathrm{C}$, reached between $50\,\mathrm{m}$ (23.6) and $100\,\mathrm{m}$ (22.6), at about $50 + 50 \times
0.1/1.0 = 55\,\mathrm{m}$.

**4.** No: the temperature falls steadily from the surface, by $1.6{}^{\circ}\mathrm{C}$ in the first $25\,\mathrm{m}$ and $5.3{}^{\circ}\mathrm{C}$ in the first $100\,\mathrm{m}$; the [thermocline](#def-g10-layered-ocean-thermocline) starts at the surface.

**5.** Between $200\,\mathrm{m}$ and $300\,\mathrm{m}$: $20.3 - 14.4 =
5.9{}^{\circ}\mathrm{C}$ per hundred metres.

**6.** Off Peru, between $50\,\mathrm{m}$ and $100\,\mathrm{m}$: about $70\,\mathrm{m}$ by interpolation (the full profile gives $65\,\mathrm{m}$). In the gyre, between $200\,\mathrm{m}$ and $300\,\mathrm{m}$: about $200 + 100 \times 5.3/5.9
\approx 290\,\mathrm{m}$.

**7.** Yes, at every level of both columns: lighter water lies on denser water, and both columns are stable.

**8.** Saltier water should be denser; yet the gyre’s surface water is lighter: $1024.71\,\mathrm{kg}/\mathrm{m}^{3}$ against $1025.08\,\mathrm{kg}/\mathrm{m}^{3}$.

**9.** The gyre’s water is about 1.3 units saltier, which adds about $1.3 \times 0.8 \approx 1.0\,\mathrm{kg}/\mathrm{m}^{3}$; it is $5{}^{\circ}\mathrm{C}$ warmer, which removes about $5 \times 0.27 \approx 1.4\,\mathrm{kg}/\mathrm{m}^{3}$ at these temperatures. The temperature wins.

**10.** $1026.44 - 1025.08 = 1.36\,\mathrm{kg}/\mathrm{m}^{3}$.

**11.** $1025.30 - 1024.71 = 0.59\,\mathrm{kg}/\mathrm{m}^{3}$.

**12.** From the surface to $500\,\mathrm{m}$ the density rises by $1026.92 - 1024.71 = 2.21\,\mathrm{kg}/\mathrm{m}^{3}$, of which only $0.59\,\mathrm{kg}/\mathrm{m}^{3}$ above $200\,\mathrm{m}$: most of it, $1.62\,\mathrm{kg}/\mathrm{m}^{3}$, lies below $200\,\mathrm{m}$, in the [thermocline](#def-g10-layered-ocean-thermocline) between $200\,\mathrm{m}$ and $500\,\mathrm{m}$.

**13.** Off Peru the density rises by $1026.97 - 1025.08 =
1.89\,\mathrm{kg}/\mathrm{m}^{3}$ from the surface to $500\,\mathrm{m}$, of which $1.36\,\mathrm{kg}/\mathrm{m}^{3}$ in the top $200\,\mathrm{m}$: most of it is near the surface.

**14.** At $500\,\mathrm{m}$ the two sites are almost alike ($7.9{}^{\circ}\mathrm{C}$ and $7.1{}^{\circ}\mathrm{C}$, $1026.97\,\mathrm{kg}/\mathrm{m}^{3}$ and $1026.92\,\mathrm{kg}/\mathrm{m}^{3}$): the same cold water lies beneath both; the difference is how close it comes to the surface.

**15.** The wind blowing along the shore towards the equator pushes the surface water out to sea; water from below rises near the coast to take its place. The cold water of the [thermocline](#def-g10-layered-ocean-thermocline) is drawn up, so the [thermocline](#def-g10-layered-ocean-thermocline) slopes up towards the coast and reaches almost to the surface.

**16.** Off Peru: water at $13{}^{\circ}\mathrm{C}$ to $15{}^{\circ}\mathrm{C}$, from below the [thermocline](#def-g10-layered-ocean-thermocline), lies within the top $100\,\mathrm{m}$, within reach of the wind’s stirring and of the light. In the gyre it lies below $250\,\mathrm{m}$, under a warm, light layer that the wind cannot stir that deep.

**17.** The [upwelling](#def-g10-layered-ocean-upwelling) would stop: the surface water would warm in the sun, a warm light layer would form on top, and the supply of nutrients to the sunlit layer would dwindle.

**18.** The coast of Peru is light blue to yellow (much chlorophyll); the middle of the South Pacific gyre is among the darkest blue regions of the map (very little).

**19.** Phytoplankton need nutrients as well as light. In the gyre the strong [stratification](#def-g10-layered-ocean-stratification) keeps the deep, nutrient-rich water far below the sunlit layer, and the nutrients of the surface layer have long been used up.

**20.** $1.36/0.59 \approx 2.3$: **the density increase over the top $200\,\mathrm{m}$ is about 2.3 times larger off Peru than in the gyre**. The [pycnocline](#def-g10-layered-ocean-thermocline), with the cold, nutrient-rich water beneath it, has been lifted into the top $200\,\mathrm{m}$ off Peru, while in the gyre it lies deeper, below $200\,\mathrm{m}$.