Answer key · Unit 22

Water and oceans.

Each lesson’s practice questions, their correct answers and the mistakes they spot. Answers read off the Scene use the same setting the learner sees.

Misconception catalogue

Answer key 5

Lesson 1 of 5 · About 25 minutes

The water cycle

The Sun evaporates water from the sea, the wind carries it inland, and a mountain lifts the air until it cools to its dew point. Work out the cloud base from the cooling rate, find the freezing level, and see why there is desert behind mountains.

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The 6 steps and their answers

Step 1 of 6
Open this step
The Sun lifts water
Practice · Choose
Question
Every day about 1000 km³ of water evaporates from the oceans. Where does the energy come from that turns all that water into vapour?

Correct answer
- Correct From sunlight, which warms the sea’s surface
Setup, choices and feedback
The Scene at this step
Sea temperature
288.1 K
Height of the mountains
2500 m
Follow the water
Evaporation
Choices
Shown in a random order.
- Correct From sunlight, which warms the sea’s surface
- Wrong No energy is needed: water only evaporates where the sea boils
  Misconception: Thinks water only turns to vapour when it boils, so a cool sea hardly evaporates.
  Feedback from the catalogue
  Water evaporates at every temperature, not only at 100 °C. At any moment some molecules at the surface are faster than average, and one that is fast enough escapes into the air. Boiling is just the state in which vapour also forms inside the water, as bubbles. The warmer the water, the more molecules are fast enough, so a warm sea evaporates far more than a cold one, but a sea at 4 °C evaporates too.
- Wrong From the wind, which tears the water into vapour
  Feedback
  The wind helps: it clears away the damp air above the water and brings dry air. But it does not supply the energy a molecule needs to break free of the water.
- Wrong From the heat of the Earth’s interior, rising through the sea floor
  Feedback
  The heat rising from the Earth’s interior is about $3000$ ⁠ times smaller than the heat arriving from the Sun. It matters for tectonics, not for the water cycle.
Feedback for a right answer
The Sun. It supplies the latent heat, and that heat is released again in the cloud.

Worked solution
1. For a water molecule to leave the liquid for the air it needs energy: the latent heat of evaporation, about 2.5 MJ per kilogram of water.
2. That energy comes from sunlight absorbed by the sea’s surface, warming it.
3. The energy is not lost: it travels with the vapour, and is released again as heat when the vapour condenses into cloud.
So the water cycle is also a machine that carries heat from the sea’s surface into the air above it.
Step 2 of 6
Open this step
A warmer sea
Practice · Predict, then look
Question
Sea temperature is now 4 °C, a cold sea. Predict: what will happen to evaporation if the sea warms to 28 °C, a tropical sea?

Correct answer
- Correct It will grow several times over, almost fivefold
Setup, choices and feedback
The Scene at this step
Sea temperature
277.1 K
Height of the mountains
2500 m
Follow the water
Evaporation
Choices
- Correct It will grow several times over, almost fivefold
- Wrong It will hardly change: at 28 °C the water is still far from boiling
  Misconception: Thinks water only turns to vapour when it boils, so a cool sea hardly evaporates.
  Feedback from the catalogue
  Water evaporates at every temperature, not only at 100 °C. At any moment some molecules at the surface are faster than average, and one that is fast enough escapes into the air. Boiling is just the state in which vapour also forms inside the water, as bubbles. The warmer the water, the more molecules are fast enough, so a warm sea evaporates far more than a cold one, but a sea at 4 °C evaporates too.
- Wrong It will fall, because warm air is already full of vapour
  Feedback
  Warm air can hold more vapour, not less, so it lets evaporation carry on.
Once the prediction is locked in, the Scene changes
Sea temperature
301.1 K
The Scene then shows: 4.549 · Water evaporating from the sea/nodes/land/outputs/evaporation
A prediction is never marked as a failure: the learner sees the outcome and the explanation either way.
Feedback for a right answer
Almost fivefold: from about 1 mm to about 4.5 mm a day.

Worked solution
1. The saturation vapour pressure roughly doubles every 10 °C: from 8 hPa at 4 °C to about 38 hPa at 28 °C.
2. The air over the sea is 80% saturated, and evaporation grows with the difference between the vapour at the water’s surface and the vapour in the air, so it grows almost in the same proportion.
3. In the Scene: about 0.95 mm a day from a cold sea, and about 4.5 mm a day from a tropical one.
That is why the air over a tropical sea is so humid, and why the world’s heaviest rain falls in the warm regions.
Step 3 of 6
Open this step
The cloud base
Practice · Calculate
Question
Sea temperature is locked at 15 °C. The air over the sea is 80% saturated with vapour, so its dew point is about 11.6 °C. Rising, the air cools by 9.8 °C every kilometre, and its dew point falls by 1.8 °C every kilometre. At what height does the air reach its dew point: how high is the cloud base?

Correct answer
422.9 m ± 5%
Setup, choices and feedback
The Scene at this step
Sea temperature
288.1 Kfixed
Height of the mountains
2500 m
Follow the water
Cloud
Accepted within
± 5%
Computed from the Scene at this step’s setting
Height where the rising air reaches its dew point/nodes/land/outputs/cloudBase
Any unit of the same quantity is accepted; it is converted before checking.
Wrong answers it recognises
- 347 m ± 3%
  Misconception: Works out the cloud base from the dry cooling rate alone, as if the dew point stayed fixed as the air rises.
  Feedback from the catalogue
  The air’s dew point falls too as it rises, because the pressure drops and the vapour spreads through a larger volume: by about 1.8 °C per kilometre. The air cools by 9.8 °C per kilometre, so the gap between its temperature and its dew point closes by only 8 °C per kilometre, one degree every 125 m. Working with 9.8 °C alone gives too low a cloud base.
Feedback for a right answer
About 425 m: one degree of gap every 125 m.

Hint
The gap between the air’s temperature and its dew point starts at 3.4 °C. By how many degrees does it close each kilometre?

Worked solution
1. The gap at the start: $15 - 11.6 = 3.4$ ⁠ degrees.
2. Each kilometre the air cools by $9.8$ ⁠ degrees and its dew point falls by $1.8$ ⁠, so the gap closes by $9.8 - 1.8 = 8$ ⁠ degrees per kilometre.
3. $h = \dfrac{3.4}{8}\ \mathrm{km} \approx 0.43\ \mathrm{km} = 425\ \mathrm{m}$ ⁠.
This is a forecaster’s rule of thumb: the cloud base lies about 125 m above the ground for each degree between the temperature and the dew point. Working with 9.8 °C alone, as if the dew point stayed fixed, gives about 350 m, too low.
Step 4 of 6
Open this step
Rain or snow
Practice · Reach the target
Question
Height of the mountains is locked at 2500 m, and the droplet we are following comes down on the slope as rain. Change Sea temperature until it lands as snow, and press Check.

Goal
- 1 ± 0.1
  At the start of the step: 0
Setup, choices and feedback
The Scene at this step
Sea temperature
288.1 K
Height of the mountains
2500 mfixed
Follow the water
Rain or snow
Read from the Scene at
1 when the followed droplet lands as snow, else 0/nodes/land/outputs/snowLanding
One setting that reaches it
Sea temperature
275.1 K
Feedback for a right answer
Snow. The freezing level has dropped below the middle of the slope.

Feedback for a wrong answer
Still rain. Cool the sea further, so the freezing level comes down.

Hint
Snow falls above the freezing level. The colder the sea, the lower the air rising from it reaches 0 °C.

Worked solution
1. Air rising from the sea cools as it climbs, and at the freezing level it reaches 0 °C. Above it, what falls is snow.
2. Over a 15 °C sea the freezing level is about 2400 m, just below the summit, so most of what falls on the slope is still rain.
3. As the sea cools, the freezing level drops: at about 9.5 °C it is already about 1300 m, and more than half the precipitation falls as snow, our droplet with it.
Any temperature of 9.5 °C or below works. That is how high mountains are white in winter while the valleys at their feet stay green.
Step 5 of 6
Open this step
Higher mountains
Practice · Predict, then look
Question
The mountains are now 800 m hills. Predict: what will happen to the rain on the windward slope if Height of the mountains rises to 4200 m?

Correct answer
- Correct It will grow several times over: the air will climb higher, cool more and lose more water
Setup, choices and feedback
The Scene at this step
Sea temperature
288.1 K
Height of the mountains
800 m
Follow the water
Rain or snow
Choices
- Correct It will grow several times over: the air will climb higher, cool more and lose more water
- Wrong It will stay about the same: the air brings the same amount of vapour from the sea
  Feedback
  The air does bring the same vapour, but only part of it falls: what the air can no longer hold. The higher it climbs and the more it cools, the larger that part.
- Wrong It will fall: the clouds will not get over so high a mountain and will break up
  Misconception: Thinks the far side of a mountain is dry because the mountain blocks the clouds like a wall.
  Feedback from the catalogue
  The air is not stopped by the mountain: it rises over it and carries on. What stays behind is the water. Rising, the air cools, and vapour it can no longer hold condenses and falls as rain on the windward slope. Sinking on the far side, the air is compressed and warms, its remaining cloud droplets evaporate, and it arrives below warm and dry. That is the rain shadow: it is how the Judean Desert lies dry behind the Jerusalem hills.
Once the prediction is locked in, the Scene changes
Height of the mountains
4200 m
The Scene then shows: 40.55 · Rain and snow on the windward slope/nodes/land/outputs/rain
A prediction is never marked as a failure: the learner sees the outcome and the explanation either way.
Feedback for a right answer
About eightfold: a high mountain wrings far more water out of the air.

Worked solution
1. The air arrives from the sea with about 8.5 g of vapour in each kilogram, whatever the height of the mountains.
2. Over an 800 m summit it can still hold about 7.8 g, so only about 0.7 g condenses.
3. Over 4200 m it is so cold that it holds only about 2.6 g: about 6 g condenses, some eight times as much.
4. In the Scene the rain on the slope rises from about 5 mm to about 40 mm a day.
That is why the world’s wettest places are often the slopes of high ranges facing a warm sea, like the Himalaya facing the monsoon.
Step 6 of 6
Open this step
Back to the sea
Practice · Choose
Question
On the far side of the mountains, in the rain shadow, almost no rain falls, though the very same wind passes over it. Why?

Correct answer
- Correct The air left most of its water on the windward slope, and as it sinks it warms and dries
Setup, choices and feedback
The Scene at this step
Sea temperature
288.1 K
Height of the mountains
2500 m
Follow the water
Runoff
Choices
Shown in a random order.
- Correct The air left most of its water on the windward slope, and as it sinks it warms and dries
- Wrong The mountain stops the clouds like a wall, and they never reach the far side
  Misconception: Thinks the far side of a mountain is dry because the mountain blocks the clouds like a wall.
  Feedback from the catalogue
  The air is not stopped by the mountain: it rises over it and carries on. What stays behind is the water. Rising, the air cools, and vapour it can no longer hold condenses and falls as rain on the windward slope. Sinking on the far side, the air is compressed and warms, its remaining cloud droplets evaporate, and it arrives below warm and dry. That is the rain shadow: it is how the Judean Desert lies dry behind the Jerusalem hills.
- Wrong The far side is far from the sea, so less water evaporates there
  Feedback
  Rain on land does not come from evaporation on the spot, but from the vapour the wind brings. And the wind does get there, only without its water.
Feedback for a right answer
The water stayed behind, on the slope. The air itself crosses the mountain.

Worked solution
1. Climbing the slope, the air cools, the vapour it can no longer hold condenses, and part of it falls as rain or snow.
2. Over the summit the air holds only what it can hold at that cold height.
3. Sinking on the far side, the pressure rises, the air is compressed and warms, and its remaining cloud droplets evaporate.
4. The air arrives below warm, dry and cloudless.
The water that fell on the slope runs down the river to the sea, and the cycle closes. In Israel it is the difference between Jerusalem, with about 550 mm of rain a year, and the Dead Sea, with less than 100 mm.

Lesson 2 of 5 · About 35 minutes

Groundwater and aquifers

Under your feet, between the grains of sand, there is water. Use Darcy’s law to work out how slowly it creeps, find how much a well can give before it runs dry, and see what drought and over-pumping do to an aquifer.

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The 9 steps and their answers

Step 1 of 9
Open this step
Under the ground
Practice · Choose
Question
Cut into the ground has taken away the dry sand above the water table. Where exactly is the groundwater?

Correct answer
- Correct In the gaps between the sand grains, which below the water table are all full of water
Setup, choices and feedback
The Scene at this step
Rainfall
800 mm per year
Pumping rate
0 m³ per day
Cut into the ground
Water table
Choices
Shown in a random order.
- Correct In the gaps between the sand grains, which below the water table are all full of water
- Wrong In a large underground lake beneath the layer of sand
  Misconception: Thinks groundwater lies mostly in underground lakes and rivers.
  Feedback from the catalogue
  Most groundwater is not in underground lakes or rivers. It fills the pores, the tiny gaps between grains of sand, gravel or cracked rock, like water in a sponge. Below the water table every such gap is full. Caves with water do exist, mostly in limestone, but they are the exception.
- Wrong In underground rivers flowing in channels between the well and the streams
  Misconception: Thinks groundwater lies mostly in underground lakes and rivers.
  Feedback from the catalogue
  Most groundwater is not in underground lakes or rivers. It fills the pores, the tiny gaps between grains of sand, gravel or cracked rock, like water in a sponge. Below the water table every such gap is full. Caves with water do exist, mostly in limestone, but they are the exception.
Feedback for a right answer
In the pores. An aquifer is wet sand, not a lake.

Worked solution
1. Sand is made of grains with gaps between them: pores. In fine sand about a third of the volume is gaps.
2. Water soaking down from above sinks to a layer it cannot pass, here clay, and fills the gaps from the bottom up.
3. The water table is the top of the saturated part. Above it the gaps hold air too.
4. A layer like this, which holds water and lets it through, is an aquifer.
Israel has two large aquifers: the Coastal Aquifer, in the sand and sandstone of the coastal plain, and the Mountain Aquifer, in the limestone of the Judean and Samarian hills.
Step 2 of 9
Open this step
Rain and the water table
Practice · Predict, then look
Question
With no pumping, the rain raises the water table into a mound between the two streams. Predict: what will happen to that mound if Rainfall drops from 800 mm a year to a drought of 100 mm?

Correct answer
- Correct It will sink and flatten towards the level of the streams
Setup, choices and feedback
The Scene at this step
Rainfall
800 mm per year
Pumping rate
0 m³ per day
Cut into the ground
Water table
Choices
- Correct It will sink and flatten towards the level of the streams
- Wrong It will not change: groundwater is a fixed store that does not depend on any one year’s rain
  Misconception: Thinks a well draws from an endless store, so it gives the same water whatever the rain.
  Feedback from the catalogue
  A well does not draw from an endless underground lake. It pulls water from the sand around it, and every drop it gives over time came there in the end from rain that soaked in. When the rain falls off, the water table drops, the cone round the well deepens, and if the water falls to the pump, the well can no longer give what it is asked for.
- Wrong It will vanish, and the sand will dry out down to the clay
  Feedback
  The streams hold the water table at least at their own level, and the water below that level has nowhere to flow. The sand beneath it stays saturated.
Once the prediction is locked in, the Scene changes
Rainfall
100 mm per year
The Scene then shows: 20.84 m · Height of the water table above the clay under the well, without pumping/nodes/ground/outputs/natural
A prediction is never marked as a failure: the learner sees the outcome and the explanation either way.
Feedback for a right answer
It sinks towards the streams’ level: less rain, less water to push.

Worked solution
1. Groundwater flows all the time from the mound to the streams, and the rain soaking in refills it: about a quarter of the rain reaches the water table.
2. In a steady state the mound stands just high enough for the flow to the streams to match what soaks in.
3. When less soaks in, a gentler slope is enough: the mound sinks. In the middle it drops from about 26 m above the clay to about 21 m, almost down to the streams’ level, 20 m.
In reality this takes years: groundwater responds slowly, so a single drought shows in it only after a while.
Step 3 of 9
Open this step
Darcy’s law
Practice · Calculate
Question
Rainfall is locked at 800 mm a year, with no pumping. In the middle the water table stands about 6 m above the streams, which are 1000 m away. The fine sand’s hydraulic conductivity is $K = 2$ ⁠ metres a day, and its porosity is $n = 0.3$ ⁠. How long does the water take to creep from the middle to the stream?

Correct answer
25160 d ± 5%
Setup, choices and feedback
The Scene at this step
Rainfall
800 mm per yearfixed
Pumping rate
0 m³ per day
Cut into the ground
Water table
Accepted within
± 5%
Computed from the Scene at this step’s setting
Time for groundwater to creep 1 km, from the middle to a stream, at the seepage speed/nodes/ground/outputs/travelTime
Any unit of the same quantity is accepted; it is converted before checking.
Wrong answers it recognises
- 83330 d ± 5%
  Misconception: Takes the Darcy flux, K times the slope, as the speed of the water itself.
  Feedback from the catalogue
  Darcy’s law, $q = K\,i$ ⁠, gives how much water passes through each square metre of the whole cross-section of the aquifer, sand and water together. But the water passes only through the gaps between the grains, a small part of the cross-section: the porosity $n$ ⁠, here $0.3$ ⁠. The same water squeezed through a smaller area moves faster: $v = \dfrac{q}{n}$ ⁠. Without dividing by $n$ ⁠ the journey comes out three and a third times too long.
Feedback for a right answer
About $25{,}000$ ⁠ days, some 70 years: four centimetres a day.

Hint
Darcy’s law: $q = K \dfrac{\Delta h}{L}$ ⁠. The water itself passes only through the gaps, so its speed is $v = \dfrac{q}{n}$ ⁠.

Worked solution
1. The hydraulic gradient: $i = \dfrac{\Delta h}{L} = \dfrac{6}{1000} = 0.006$ ⁠.
2. Darcy’s law: $q = K\,i = 2 \cdot 0.006 = 0.012$ ⁠ metres a day. That is the water passing through each square metre of cross-section.
3. The water passes only through the pores: $v = \dfrac{q}{n} = \dfrac{0.012}{0.3} = 0.04$ ⁠ metres a day, four centimetres.
4. $t = \dfrac{L}{v} = \dfrac{1000}{0.04} = 25{,}000$ ⁠ days, about $69$ ⁠ years.
A raindrop soaking in at the middle today will reach the stream only two generations from now. Without dividing by $n$ ⁠ you get about $83{,}000$ ⁠ days: that is the average flow over the whole cross-section, not the speed of the water.
Step 4 of 9
Open this step
A cone round the well
Practice · Reach the target
Question
Rainfall is locked at 800 mm a year. Raise Pumping rate to the most the well gives without running dry, to within 12 m³ a day, and press Check.

Goal
- 0 ± 0.1
  At the start of the step: 0
- 450 m³ ± 12 m³
  At the start of the step: 0 m³
Setup, choices and feedback
The Scene at this step
Rainfall
800 mm per yearfixed
Pumping rate
0 m³ per day
Cut into the ground
Water table
Read from the Scene at
1 when the pump asks for more than the well can give, else 0/nodes/ground/outputs/dry
Read from the Scene at
The water the well actually gives each day, at most what it is asked for/nodes/ground/outputs/pumpedDaily
One setting that reaches it
Pumping rate
440 m³ per day
Feedback for a right answer
Close to the limit: about 460 m³ a day, water for a small town.

Feedback for a wrong answer
Not yet. If the well is running dry, lower the pumping; if not, try raising it.

Hint
Raise the pumping in steps and watch the label over the well. The moment it says the well is running dry, go back a step.

Worked solution
1. Pumping pulls the water table round the well down into a cone. The more you pump, the deeper the cone.
2. The pump sits 3 m above the clay. When the water in the well falls to it, no more can be drawn.
3. With 800 mm of rain this happens at about 460 m³ a day: up to 460 the well gives all it is asked for, and from 470 it runs dry.
In a drought the limit is lower: the cone starts from a lower water table, so it reaches the pump sooner.
Step 5 of 9
Open this step
A drought
Practice · Predict, then look
Question
The town pumps 400 m³ a day, and the well gives all of it. Predict: what will happen if Rainfall drops to a drought of 100 mm a year and the town keeps asking for the same?

Correct answer
- Correct The well will run dry and give only part of what it is asked for
Setup, choices and feedback
The Scene at this step
Rainfall
800 mm per year
Pumping rate
400 m³ per day
Cut into the ground
Water table
Choices
- Correct The well will run dry and give only part of what it is asked for
- Wrong The well will keep giving 400 m³ a day: it draws on a big store that does not depend on the rain
  Misconception: Thinks a well draws from an endless store, so it gives the same water whatever the rain.
  Feedback from the catalogue
  A well does not draw from an endless underground lake. It pulls water from the sand around it, and every drop it gives over time came there in the end from rain that soaked in. When the rain falls off, the water table drops, the cone round the well deepens, and if the water falls to the pump, the well can no longer give what it is asked for.
- Wrong The well will give more, because dry sand passes water faster
  Feedback
  Water flows only through wet sand. When the water table drops, there is less saturated sand for it to flow through to the well, not more.
Once the prediction is locked in, the Scene changes
Rainfall
100 mm per year
The Scene then shows: 295.4 m³ · The water the well actually gives each day, at most what it is asked for/nodes/ground/outputs/pumpedDaily
A prediction is never marked as a failure: the learner sees the outcome and the explanation either way.
Feedback for a right answer
It runs dry: about 300 m³ a day instead of 400.

Worked solution
1. In a drought less water soaks in, and the water table in the middle drops from about 26 m to about 21 m above the clay.
2. The cone round the well starts from a lower level, and pumping 400 m³ a day now draws the water down to the pump.
3. The well gives only what the sand round it can pass to it: about 300 m³ a day.
Over time a well can give only what the rain puts back. Pumping more than that is over-pumping: the water table falls year after year.
Step 6 of 9
Open this step
Over-pumping
Practice · Choose
Question
Israel’s Coastal Aquifer meets the Mediterranean. Under the shore, the fresh groundwater floats on salty, heavier sea water. What happened where it was over-pumped for years?

Correct answer
- Correct Sea water pushed into the aquifer, and wells near the shore turned salty
Setup, choices and feedback
The Scene at this step
Rainfall
100 mm per year
Pumping rate
800 m³ per day
Cut into the ground
Water table
Choices
Shown in a random order.
- Correct Sea water pushed into the aquifer, and wells near the shore turned salty
- Wrong Nothing: the aquifer refills from the sea itself, so it cannot be emptied
  Feedback
  The sea does fill what is pumped, but with salt water. That is exactly the harm.
- Wrong The water table rose, because the sea water pushed the fresh water up
  Feedback
  The water table fell, not rose, and sea water took the place of the fresh water pumped out.
Feedback for a right answer
Sea water got in. Fresh water lasts only as long as you pump what the rain puts back.

Worked solution
1. Fresh water is lighter than sea water, so it floats on it like a lens. The boundary between them holds as long as the fresh water stands high enough.
2. Over-pumping lowers the water table, and the boundary moves inland, under the land.
3. Sea water reaches the wells near the shore, and their water turns salty and undrinkable.
That is why Israel watches its aquifer levels, and since the 2000s desalination has supplied much of the drinking water, letting the aquifers recover.
Step 7 of 9
Open this step
A wet year
Practice · Calculate
Question
Rainfall is locked at 1600 mm a year, a very wet year, with no pumping. In the middle the water table stands 10.8 m above the streams, which are 1000 m away. What is the hydraulic gradient, $i = \dfrac{\Delta h}{L}$ ⁠?

Correct answer
0.01079 ± 3%
Setup, choices and feedback
The Scene at this step
Rainfall
1600 mm per yearfixed
Pumping rate
0 m³ per dayfixed
Cut into the ground
Water table
Accepted within
± 3%
Computed from the Scene at this step’s setting
The natural water table’s average fall from the middle to a stream, metres per metre (the hydraulic gradient)/nodes/ground/outputs/slope
Wrong answers it recognises
- 10.8 ± 3%
  Misconception: Divides a height in metres by a distance in kilometres, or forgets to divide at all.
  Feedback from the catalogue
  A gradient is a ratio of two lengths, so both must be in the same units. 10.8 m over 1000 m is $0.0108$ ⁠, about a centimetre for every metre.
Feedback for a right answer
About $0.0108$ ⁠: almost twice an ordinary year’s, so the flow to the streams nearly doubles too.

Hint
Divide the height by the distance, in the same units.

Worked solution
1. $\Delta h = 10.8$ ⁠ metres, $L = 1000$ ⁠ metres.
2. $i = \dfrac{10.8}{1000} \approx 0.0108$ ⁠.
In an ordinary year, 800 mm, the gradient was $0.006$ ⁠. By Darcy’s law, $q = K i$ ⁠, the water now flows to the streams almost twice as fast: the extra rain leaves the way it came in.
Step 8 of 9
Open this step
Pumping harder
Practice · Predict, then look
Question
The Pumping rate is 200 m³ a day, and the water in the well has dropped 6.3 m. Predict: by how much will the water in the well drop when the town pumps twice as much, 400 m³ a day?

Correct answer
- Correct More than twice as much
Setup, choices and feedback
The Scene at this step
Rainfall
800 mm per yearfixed
Pumping rate
200 m³ per day
Cut into the ground
Water table
Choices
- Wrong Less than twice as much, because the aquifer refills the well faster
  No feedback of its own; the learner sees the standard message
  Not yet. Look again and try once more.
- Wrong Exactly twice as much, 12.6 m, because the drop goes with the pumping
  Misconception: Thinks the drop in a well grows in step with the pumping rate.
  Feedback from the catalogue
  Near a pumping well the water flows through the saturated sand, and that layer gets thinner as the level drops. Less sand carries the water, so every extra cubic metre needs a bigger drop. Twice the pumping, more than twice the drop.
- Correct More than twice as much
Once the prediction is locked in, the Scene changes
Pumping rate
400 m³ per day
The Scene then shows: 16.06 m · How far pumping lowers the water in the well/nodes/ground/outputs/drawdown
A prediction is never marked as a failure: the learner sees the outcome and the explanation either way.
Feedback for a right answer
About 16 m, two and a half times: the emptier the well, the thinner the layer that feeds it.

Hint
The water flows to the well through the saturated layer of sand. What happens to that layer near the well as the level there drops?

Worked solution
1. To pump more, the groundwater needs a steeper slope towards the well, so the level in the well drops.
2. But as the level drops, the saturated layer near the well gets thinner, and less sand carries the water in.
3. So each extra cubic metre needs a bigger drop still: at 400 m³ a day the drop is about 16 m, more than two and a half times.
That is why a well working near its limit suddenly runs dry when the pumping is raised a little.
Step 9 of 9
Open this step
Above the pump
Practice · Reach the target
Question
Rainfall is locked at 800 mm a year. The pump hangs 15 m above the clay layer. Raise the Pumping rate until exactly 15 m of water stand in the well above the clay, and press Check.

Goal
- 15 ± 0.5
  At the start of the step: 25.96
Setup, choices and feedback
The Scene at this step
Rainfall
800 mm per yearfixed
Pumping rate
0 m³ per day
Cut into the ground
Water table
Read from the Scene at
Height of the water in the well above the clay/nodes/ground/outputs/wellLevel
One setting that reaches it
Pumping rate
310 m³ per day
Feedback for a right answer
At about 310 m³ a day: a drop of about 11 m from the level with no pumping.

Hint
With no pumping the water in the well is about 26 m above the clay. Every cubic metre a day lowers it further.

Worked solution
1. With no pumping the water in the well stands about 26 m high.
2. It has to drop about 11 m.
3. That happens at about 300–320 m³ a day.
Any more, and the pump starts sucking air. That is why a well is planned with room to spare: for the pumping rate in a drought, not in an ordinary year.

Lesson 3 of 5 · About 25 minutes

Ocean currents

The wind turns the sea’s surface, and density drives a deep loop round the world. Find out which water sinks, find how much salt it takes, and see what meltwater does to the current that warms Europe.

Open the lesson

The 6 steps and their answers

Step 1 of 6
Open this step
Gyres
Practice · Choose
Question
On the surface of every ocean the water turns in a huge loop, a gyre, like the Gulf Stream running up the coast of America. What drives these surface currents?

Correct answer
- Correct The steady winds, which drag the surface water, with the Earth’s spin bending it into a loop
Setup, choices and feedback
The Scene at this step
Water temperature
274.1 K
Salinity
35 g/kg
Follow the deep loop
Surface currents
Choices
Shown in a random order.
- Correct The steady winds, which drag the surface water, with the Earth’s spin bending it into a loop
- Wrong The tides, which pull the water back and forth
  Feedback
  The tide moves the water back and forth twice a day, but on average it carries it nowhere. A current that always flows the same way needs a force that always pushes the same way.
- Wrong The rivers, which flow into the sea and push its water along
  Feedback
  All the world’s rivers together pour about 1 Sv into the sea, a million cubic metres a second. The Gulf Stream alone carries a hundred times that.
Feedback for a right answer
The wind. It drives the top layer, and the Earth’s spin and the continents shape the loop.

Worked solution
1. The trade winds blow from east to west near the equator, and the westerlies blow from west to east at middle latitudes.
2. They drag the top few tens of metres of water along by friction.
3. The Earth’s spin bends each current, to the right in the northern hemisphere and to the left in the southern, and the continents close the way.
4. So every ocean gets a loop, with a narrow, fast current on its western side, like the Gulf Stream.
Step 2 of 6
Open this step
Heavy water
Practice · Choose
Question
Dense water sinks below lighter water. Which water is densest?

Correct answer
- Correct Cold, salty water
Setup, choices and feedback
The Scene at this step
Water temperature
274.1 K
Salinity
35 g/kg
Follow the deep loop
Sinking
Choices
Shown in a random order.
- Correct Cold, salty water
- Wrong Cold, fresh water, like a glacier’s meltwater
  Misconception: Thinks colder water always sinks, whatever its salt.
  Feedback from the catalogue
  What sinks is water denser than the water below it, and density depends on salt as well as temperature. Very cold but fairly fresh water, like meltwater, is lighter than the salty deep water and stays on top, like a lid. It is cold and salty water that is densest.
- Wrong Warm, salty water, like the Mediterranean in summer
  Feedback
  Salt does add density, but warmth takes it away: warm water expands. Water at 25 °C is about 5 kg/m³ lighter than water at 2 °C of the same salinity.
Feedback for a right answer
Cold and salty. Both add density.

Worked solution
1. Water shrinks as it cools, so cold water is denser.
2. Dissolved salt adds mass with almost no added volume, so salty water is denser: about 0.8 kg/m³ for each gram of salt per kilogram.
3. Both together: the densest is the cold and salty.
Flow driven by differences of temperature and salt is called the thermohaline circulation, from the Greek for heat and salt.
Step 3 of 6
Open this step
The Gulf Stream
Practice · Predict, then look
Question
In winter, in the Greenland Sea, the surface water is at about 1 °C with a salinity of 35 g/kg, and it sinks. Predict: what will happen if Water temperature there rises to 18 °C, as in the Gulf Stream?

Correct answer
- Correct The water will stay on top: it will be lighter than the deep water
Setup, choices and feedback
The Scene at this step
Water temperature
274.1 K
Salinity
35 g/kg
Follow the deep loop
Sinking
Choices
- Correct The water will stay on top: it will be lighter than the deep water
- Wrong It will sink faster, because warm water is saltier
  Feedback
  The salinity stayed at 35 g/kg: only the temperature changed. And warmth lowers the density.
- Wrong Nothing will change: what sinks is the salt, not the water
  Feedback
  The salt is dissolved in the water and moves with it. What sinks is water denser than what lies below it, and density depends on temperature too.
Once the prediction is locked in, the Scene changes
Water temperature
291.1 K
The Scene then shows: -2.465 · Surface density minus deep density; above 0 it sinks/nodes/ocean/outputs/excess
A prediction is never marked as a failure: the learner sees the outcome and the explanation either way.
Feedback for a right answer
It stays on top: warm water is too light to sink.

Worked solution
1. The deep water of the North Atlantic is at about 4 °C with a salinity of 34.9 g/kg: a density of about 1027.8 kg/m³.
2. At 1 °C and 35 g/kg the surface water is a little denser, about 1028.1 kg/m³, so it sinks.
3. At 18 °C it expands, and its density falls to about 1025.3 kg/m³: lighter than the deep water, so it stays on top.
That is why the Gulf Stream flows north on the surface: only after it gives its heat to the air, near Greenland, does its water become heavy enough to sink.
Step 4 of 6
Open this step
How much salt it takes
Practice · Reach the target
Question
Water temperature is locked at 4 °C, a mild winter, and Salinity is at 33 g/kg, meltwater: the water does not sink. Raise Salinity until the water in the north sinks strongly, and press Check.

Goal
- 2 ± 0.1
  At the start of the step: 0
Setup, choices and feedback
The Scene at this step
Water temperature
277.1 Kfixed
Salinity
33 g/kg
Follow the deep loop
Sinking
Read from the Scene at
0 none, 1 weak (under 8 Sv), 2 strong/nodes/ocean/outputs/sinking
One setting that reaches it
Salinity
35.1 g/kg
Feedback for a right answer
The water sinks: a little more salt is enough when the temperature matches the deep.

Feedback for a wrong answer
Not yet. Add salt until the water is saltier than the deep water.

Hint
At 4 °C the water must be a little saltier than the deep water, 34.9 g/kg, to be denser than it.

Worked solution
1. At 4 °C the surface water is at the same temperature as the deep water, so only the salt decides.
2. As long as it is fresher than 34.9 g/kg, it is lighter and stays on top.
3. At 35 g/kg it already sinks, but slowly; from about 35.1 g/kg the sinking is strong.
So the two work together: water that is less cold must be saltier to sink.
Step 5 of 6
Open this step
Meltwater
Practice · Predict, then look
Question
The deep loop is running: water sinks in the north, and a warm current comes up from the south to take its place. Predict: what will happen if Greenland’s ice melts and the Salinity of the surface water there drops to 33 g/kg?

Correct answer
- Correct The sinking will stop, the Atlantic loop will stall, and less warm water will flow north
Setup, choices and feedback
The Scene at this step
Water temperature
274.1 K
Salinity
35 g/kg
Follow the deep loop
The deep loop
Choices
- Correct The sinking will stop, the Atlantic loop will stall, and less warm water will flow north
- Wrong The sinking will strengthen, because meltwater is very cold
  Misconception: Thinks colder water always sinks, whatever its salt.
  Feedback from the catalogue
  What sinks is water denser than the water below it, and density depends on salt as well as temperature. Very cold but fairly fresh water, like meltwater, is lighter than the salty deep water and stays on top, like a lid. It is cold and salty water that is densest.
- Wrong Nothing will change: the wind drives the currents, not the salt
  Feedback
  The wind drives the surface currents, but the deep loop is driven by the sinking in the north. With no sinking, there is no space for the warm current to fill.
Once the prediction is locked in, the Scene changes
Salinity
33 g/kg
The Scene then shows: 0 · 0 none, 1 weak (under 8 Sv), 2 strong/nodes/ocean/outputs/sinking
A prediction is never marked as a failure: the learner sees the outcome and the explanation either way.
Feedback for a right answer
The loop stalls: fresh water is too light to sink.

Worked solution
1. At 1 °C and 33 g/kg the surface water is about 1.2 kg/m³ lighter than the deep water, so it stays on top, like a lid.
2. With no sinking in the north, no water leaves the surface, and no warm water is needed to replace it.
3. The Atlantic loop stalls, and the heat it carried north, about 1.2 petawatts, almost vanishes.
At the end of the last ice age, about $12{,}900$ ⁠ years ago, fresh water released from ice sheets probably stalled the loop, and Europe went back into a hard cold for about a thousand years.
Step 6 of 6
Open this step
Round the world
Practice · Choose
Question
The water that sank near Greenland creeps south through the deep, round Antarctica and into the Indian and Pacific Oceans, where it slowly rises back to the surface. How long does a drop take to complete this loop?

Correct answer
- Correct About a thousand years
Setup, choices and feedback
The Scene at this step
Water temperature
274.1 K
Salinity
35 g/kg
Follow the deep loop
The deep loop
Choices
Shown in a random order.
- Correct About a thousand years
- Wrong A few months, like the Gulf Stream
  Feedback
  The Gulf Stream is fast, about 2 m/s, but in the deep the water creeps at a few centimetres a second or less, over tens of thousands of kilometres.
- Wrong About a million years
  Feedback
  Slow, but not that slow. The carbon-14 in deep water shows that the oldest water, in the North Pacific, left the air about one to two thousand years ago.
Feedback for a right answer
About a thousand years: the way is long, and the deep water creeps.

Worked solution
1. The way is very long: tens of thousands of kilometres, from the North Atlantic through the Southern Ocean to the North Pacific.
2. In the deep the water moves very slowly, a few centimetres a second or less, and the rise back to the surface is slower still.
3. Carbon-14 measurements in deep water give an order of a thousand years.
So the deep loop is the climate’s long memory: water that sank in the Middle Ages is surfacing now.

Lesson 4 of 5 · About 25 minutes

El Niño

The trade winds have piled warm water in the western Pacific. Weaken them and watch the water and rain move east, strengthen them for a La Niña, and see how sea and air strengthen each other.

Open the lesson

The 6 steps and their answers

Step 1 of 6
Open this step
A normal year
Practice · Choose
Question
In a normal year the sea near Indonesia is about 5 °C warmer than the sea near the Galápagos, though both lie on the equator. Why?

Correct answer
- Correct The trade winds push the warm surface water west, and it piles up there
Setup, choices and feedback
The Scene at this step
Trade winds
5 m/s
Show ocean and air
Sea and sky
Choices
Shown in a random order.
- Correct The trade winds push the warm surface water west, and it piles up there
- Wrong The Sun is stronger over the western Pacific
  Misconception: Thinks the western Pacific is warmer because the Sun shines more strongly there.
  Feedback from the catalogue
  Both ends of the Pacific lie on the equator and get almost the same sunshine. The difference is the wind: the trade winds blow from east to west, drag the warm surface water west and pile it up there. In the east, in place of the water dragged away, cold water wells up from below.
- Wrong Indonesia’s volcanoes warm the sea
  Feedback
  The heat rising from volcanoes is negligible next to the sunlight on a whole ocean.
Feedback for a right answer
The wind. It has piled the warm water in the west.

Worked solution
1. The trade winds blow along the equator from east to west, about 5 m/s.
2. They drag the warm top layer west, and it piles up near Indonesia: there the sea stands about half a metre higher than off South America.
3. In the east, in place of the water dragged away, cold water wells up from below.
So the west has a warm pool with heavy rain, and the east a tongue of cold water under dry skies.
Step 2 of 6
Open this step
The thermocline
Practice · Choose
Question
Show ocean and air shows the ocean’s temperature at depth. What cools the sea’s surface in the east, off South America?

Correct answer
- Correct Cold water rising from below the thermocline, which lies close to the surface there
Setup, choices and feedback
The Scene at this step
Trade winds
5 m/s
Show ocean and air
Ocean temperature
Choices
Shown in a random order.
- Correct Cold water rising from below the thermocline, which lies close to the surface there
- Wrong The cold air above, which cools the sea
  Feedback
  It is the other way round: over an ocean, the sea sets the air’s temperature. Water stores thousands of times more heat than the same volume of air.
- Wrong The ocean is deeper in the east, so it is colder
  Feedback
  The ocean floor does not set the surface temperature. What matters is how close to the surface the cold water comes.
Feedback for a right answer
Upwelling: the thermocline is close, and the wind pulls away the water above it.

Worked solution
1. The thermocline is the boundary between the warm top layer and the cold water beneath it.
2. In the west, under the warm pool, it is deep: about 160 m. In the east, where the warm water was dragged from, it is only about 60 m.
3. The wind pulls the surface water aside, and cold water from below the thermocline wells up to replace it.
The upwelling water is rich in nutrients, which is why the sea off Peru is one of the richest fisheries in the world.
Step 3 of 6
Open this step
The wind weakens
Practice · Predict, then look
Question
Predict: what will happen if Trade winds weaken from 5 m/s to 2 m/s?

Correct answer
- Correct The warm water will slide back east, and the rain will move with it
Setup, choices and feedback
The Scene at this step
Trade winds
5 m/s
Show ocean and air
Sea and sky
Choices
- Correct The warm water will slide back east, and the rain will move with it
- Wrong Almost nothing: an ocean is too big for a wind to change it
  Feedback
  A whole ocean does respond to the wind over months: the warm water piled in the west slides back when the wind no longer holds it.
- Wrong The whole ocean will cool, because less wind means less heat
  Feedback
  The wind brings no heat to the ocean: it only moves it about. Without it, the east actually warms.
Once the prediction is locked in, the Scene changes
Trade winds
2 m/s
The Scene then shows: 28.65 °C · Sea-surface temperature at 90° W/nodes/pacific/outputs/eastTemperature
A prediction is never marked as a failure: the learner sees the outcome and the explanation either way.
Feedback for a right answer
The warm water and the rain move east: that is El Niño.

Worked solution
1. When the wind weakens, it no longer holds the warm water piled in the west, and it slides back east.
2. The thermocline in the east sinks, and the water welling up there is no longer cold: the sea near the Galápagos warms from about 24 °C to almost 29 °C.
3. Air rises, and rain falls, over the warmest water, so the rain moves east too: a sharp drop over Indonesia, and rain on the coast of Peru.
That is El Niño. Peru’s fishermen named the warming that came around Christmas “the boy”.
Step 4 of 6
Open this step
La Niña
Practice · Reach the target
Question
A La Niña year is one in which the sea in the Niño 3.4 region, in the middle of the ocean, is at least 0.5 °C colder than normal. Change Trade winds until there is a La Niña, and press Check.

Goal
- 0 ± 0.1
  At the start of the step: 1
Setup, choices and feedback
The Scene at this step
Trade winds
5 m/s
Show ocean and air
Ocean temperature
Read from the Scene at
0 La Niña (Niño 3.4 at least 0.5 °C below normal), 1 neutral, 2 El Niño (at least 0.5 °C above)/nodes/pacific/outputs/regime
One setting that reaches it
Trade winds
5.6 m/s
Feedback for a right answer
La Niña: a strong wind, a long cold tongue.

Feedback for a wrong answer
Not yet. To cool the middle of the ocean you need more cold water welling up.

Hint
El Niño comes from a weak wind. What will do the opposite?

Worked solution
1. A stronger wind pushes even more warm water west, and the thermocline in the east rises.
2. More cold water wells up, and the cold tongue reaches further west, into the middle of the ocean.
3. From about 5.6 m/s the sea in the Niño 3.4 region is half a degree or more below normal: La Niña, “the girl”.
In La Niña the rain gathers in the far west: floods in Australia and Indonesia, and drought on the coast of South America.
Step 5 of 6
Open this step
The air’s loop
Practice · Choose
Question
Show ocean and air now shows the air’s loop over the ocean, in an El Niño year. Why does an El Niño that has started tend to grow stronger still, for months?

Correct answer
- Correct The warming east shrinks the temperature difference across the ocean, which weakens the trade winds further
Setup, choices and feedback
The Scene at this step
Trade winds
2 m/s
Show ocean and air
Air loop
Choices
Shown in a random order.
- Correct The warming east shrinks the temperature difference across the ocean, which weakens the trade winds further
- Wrong In El Niño years the Sun is stronger
  Misconception: Thinks the western Pacific is warmer because the Sun shines more strongly there.
  Feedback from the catalogue
  Both ends of the Pacific lie on the equator and get almost the same sunshine. The difference is the wind: the trade winds blow from east to west, drag the warm surface water west and pile it up there. In the east, in place of the water dragged away, cold water wells up from below.
- Wrong The ocean keeps sliding east on its own, whatever the wind does
  Feedback
  The warm water slides east only as long as the wind is too weak to hold it. What keeps the wind weak is the ocean itself.
Feedback for a right answer
Feedback: a warm east, a weak wind, a warmer east still.

Worked solution
1. The trade winds are the lower part of the Walker circulation: air rises over the warm water in the west, flows east high up, sinks over the cold sea and returns west along the surface.
2. The difference between the warm west and the cold east is what drives this circulation.
3. When the east warms, the difference shrinks, the circulation weakens, and the wind weakens further. A weaker wind warms the east more.
This is positive feedback, found by the meteorologist Jacob Bjerknes in the 1960s: sea and air strengthen each other until the system swings back after a year or two.
Step 6 of 6
Open this step
Far from the Pacific
Practice · Choose
Question
In a strong El Niño year, which of these happen? Choose all the correct answers.

Correct answer
- Correct Drought and fires in Indonesia and Australia
- Correct Rain and floods in the desert on the coast of Peru
- Correct The fishery off Peru collapses
Setup, choices and feedback
The Scene at this step
Trade winds
2 m/s
Show ocean and air
Sea and sky
Choices
Shown in a random order. More than one choice is correct: every one must be selected.
- Correct Drought and fires in Indonesia and Australia
- Correct Rain and floods in the desert on the coast of Peru
- Correct The fishery off Peru collapses
- Wrong The year is colder on the world average
  Feedback
  The opposite: El Niño releases ocean heat into the air, and El Niño years are often among the warmest on the world average, like 1998, 2016 and 2023.
Feedback for a right answer
Three: drought in the west, rain in the east, and a collapsing fishery.

Worked solution
1. The rain moves east with the warm water: air sinks over Indonesia, and the rain there stops. Hence drought and fires.
2. Over the warming east the air rises, and rain falls on the coastal desert of Peru and Ecuador.
3. The water welling up off Peru is no longer cold and rich in nutrients: the plankton dwindles, and the fish with it.
4. The ocean gives heat to the air, so the world average rises.
The effects reach far beyond the Pacific, through changes in the air’s circulation.

Lesson 5 of 5 · About 35 minutes

Tsunamis

A quake lifts the sea floor, and the wave it makes travels at $\sqrt{g d}$, set by the depth alone. Work out how fast it crosses an ocean, find why the shallow water takes most of the time, and use Green’s law for how much it grows near the coast.

Open the lesson

The 9 steps and their answers

Step 1 of 9
Open this step
The jolt
Practice · Choose
Question
An earthquake under the sea floor. What exactly makes the tsunami?

Correct answer
- Correct The sea floor jumps all at once and lifts the whole column of water above it, up to the surface
Setup, choices and feedback
The Scene at this step
Ocean depth
4 km
Sea-floor jump
3 m
Labels
ondefault
Time
0.025 (Earthquake → Flood drains)
Choices
Shown in a random order.
- Correct The sea floor jumps all at once and lifts the whole column of water above it, up to the surface
- Wrong A storm the quake stirs up, whose winds build huge waves
  Feedback
  A wind wave moves only the top few tens of metres of water, and is metres to hundreds of metres long. A tsunami moves the whole water column, kilometres deep, and is hundreds of kilometres long.
- Wrong The shaking of the sea floor, which stirs ripples that grow on the way
  Feedback
  Shaking back and forth moves almost no water on average. What makes the tsunami is a lasting shift of the sea floor, up or down, along hundreds of kilometres.
Feedback for a right answer
The floor lifts the whole water column. The tsunami starts as a rise of the sea’s surface, but kilometres of water move beneath it.

Worked solution
1. In a great quake at a trench, one plate is stuck beneath another and the upper plate bends. When it lets go, the sea floor jumps up by a few metres, along hundreds of kilometres.
2. Water hardly compresses, so the whole column above moves with it, and the sea’s surface rises in the same shape.
3. The hump splits into two waves: one heads for the open ocean, the other for the coast.
Underwater landslides and volcanic eruptions make tsunamis the same way: they move a vast amount of water all at once.
Step 2 of 9
Open this step
A long wave
Practice · Calculate
Question
Ocean depth is locked at 4 km. A long wave, far longer than the water is deep, travels at $v = \sqrt{g d}$ ⁠. What is the tsunami’s speed in the open ocean, in kilometres an hour?

Correct answer
713.1 km/h ± 2%
Setup, choices and feedback
The Scene at this step
Ocean depth
4 kmfixed
Sea-floor jump
3 m
Labels
ondefault
Time
Earthquake
Accepted within
± 2%
Computed from the Scene at this step’s setting
The wave’s speed over the open-ocean basin, √(g · depth)/nodes/sea/outputs/oceanSpeed
Any unit of the same quantity is accepted; it is converted before checking.
Wrong answers it recognises
- 22.5 km/h ± 5%
  Misconception: Puts the depth into √(g d) in kilometres instead of metres.
  Feedback from the catalogue
  In $v = \sqrt{g d}$ ⁠, $g$ ⁠ is in m/s², so $d$ ⁠ must be in metres too: 4 km is $4000\ \mathrm{m}$ ⁠. With $d = 4$ ⁠ you get $\sqrt{39}$ ⁠, about 6 m/s, a cyclist’s speed, $\sqrt{1000} \approx 32$ ⁠ times too small.
Feedback for a right answer
About 713 km/h, like an airliner.

Hint
Put $d$ ⁠ in metres, and multiply the result by $3.6$ ⁠ to go from m/s to km/h.

Worked solution
1. $d = 4\ \mathrm{km} = 4000\ \mathrm{m}$ ⁠.
2. $v = \sqrt{g d} = \sqrt{9.81 \cdot 4000} = \sqrt{39{,}240} \approx 198\ \mathrm{m/s}$ ⁠.
3. $198 \cdot 3.6 \approx 713\ \mathrm{km/h}$ ⁠.
A jet airliner’s speed. With $d = 4$ ⁠, in kilometres, you get about 6 m/s: that is the common slip.
Step 3 of 9
Open this step
Height and speed
Practice · Predict, then look
Question
Sea-floor jump is now 1 m, as in a magnitude $7.5$ ⁠ quake. Predict: if the floor jumps 5 m, as in magnitude $9$ ⁠, will the wave cross the ocean faster?

Correct answer
- Correct No: it will be taller, but cross in the same time
Setup, choices and feedback
The Scene at this step
Ocean depth
4 km
Sea-floor jump
1 m
Labels
ondefault
Time
0.246 (Earthquake → Flood drains)
Choices
- Correct No: it will be taller, but cross in the same time
- Wrong Yes: a taller wave carries more energy, so it moves faster
  Misconception: Thinks a bigger earthquake sends a faster tsunami.
  Feedback from the catalogue
  A tsunami is a long wave: hundreds of kilometres long, far longer than the water is deep. Such a wave travels at $v = \sqrt{g d}$ ⁠, which depends only on the depth $d$ ⁠, not on the wave’s height or the strength of the quake. A stronger quake makes a taller wave, which arrives with more water, but at the same time.
- Wrong No, the opposite: a heavier wave moves more slowly
  Feedback
  The water in a taller wave follows the same law, $v = \sqrt{g d}$ ⁠: the speed does not depend on the height.
Once the prediction is locked in, the Scene changes
Sea-floor jump
5 m
The Scene then shows: 14.3 min · Time for the crest to cross the deep basin, 170 km, to the foot of the continental slope/nodes/sea/outputs/basinTime
A prediction is never marked as a failure: the learner sees the outcome and the explanation either way.
Feedback for a right answer
The same time. The depth sets the speed, and the quake sets the height.

Worked solution
1. A long wave’s speed is set by the depth alone: $v = \sqrt{g d}$ ⁠. There is no height in the formula.
2. The depth has not changed, so the wave crosses the deep basin in the same time, about $14$ ⁠ minutes.
3. What has changed is the height: each of the two waves leaves with half the jump, 2.5 m instead of 0.5 m, and brings five times as much water to the coast.
That is why a tsunami’s arrival time can be forecast right after the quake, before anyone knows how tall it is: a map of the sea’s depth is enough.
Step 4 of 9
Open this step
Crossing the basin
Practice · Calculate
Question
Ocean depth is locked at 4 km. The crest sets off 30 km from the fault, and the deep basin ends 200 km from the fault, at the foot of the continental slope. How many minutes does the crest take to cross the basin?

Correct answer
14.3 min ± 3%
Setup, choices and feedback
The Scene at this step
Ocean depth
4 kmfixed
Sea-floor jump
3 m
Labels
ondefault
Time
Earthquake
Accepted within
± 3%
Computed from the Scene at this step’s setting
Time for the crest to cross the deep basin, 170 km, to the foot of the continental slope/nodes/sea/outputs/basinTime
Any unit of the same quantity is accepted; it is converted before checking.
Feedback for a right answer
About $14$ ⁠ minutes: 170 km at an airliner’s speed.

Hint
The way is $200 - 30$ ⁠ kilometres, and the speed is the one you found, $\sqrt{g d}$ ⁠.

Worked solution
1. The way: $s = 200 - 30 = 170\ \mathrm{km} = 170{,}000\ \mathrm{m}$ ⁠.
2. The speed: $v = \sqrt{9.81 \cdot 4000} \approx 198\ \mathrm{m/s}$ ⁠.
3. $t = \dfrac{s}{v} = \dfrac{170{,}000}{198} \approx 858\ \mathrm{s} \approx 14.3$ ⁠ minutes.
A quarter of an hour for $170$ ⁠ kilometres. Counting the whole $200$ ⁠ kilometres gives about $17$ ⁠ minutes, but the wave does not start at the fault itself.
Step 5 of 9
Open this step
The shelf
Practice · Predict, then look
Question
The crest has crossed 170 km of deep ocean in about $14$ ⁠ minutes. 80 km remain: the continental slope, a shallow shelf and the coast. Predict: how long will this part take?

Correct answer
- Correct Much longer: about three times the basin crossing
Setup, choices and feedback
The Scene at this step
Ocean depth
4 km
Sea-floor jump
3 m
Labels
ondefault
Time
0.41 (Earthquake → Flood drains)
Choices
- Correct Much longer: about three times the basin crossing
- Wrong Less: the way is almost half as long, so about seven minutes
  Misconception: Thinks a tsunami keeps its open-ocean speed all the way to the shore, so the short shallow part takes little time.
  Feedback from the catalogue
  The wave’s speed is set by the depth where it is: $v = \sqrt{g d}$ ⁠. Over 4 km of water it moves at about 700 km/h, but over a 100 m shelf only about 110 km/h, and in a few metres of water like a car. So the last, shallow kilometres take most of the time.
- Wrong The wave will stop at the slope and never reach the coast
  Feedback
  The wave slows on the slope, but does not stop: its energy carries on, and in shallow water it only grows.
Once the prediction is locked in, the Scene changes
Time
Flood drains
The Scene then shows: 61.35 min · Time from the quake until the crest reaches the beach/nodes/sea/outputs/landfall
A prediction is never marked as a failure: the learner sees the outcome and the explanation either way.
Feedback for a right answer
About $47$ ⁠ minutes: the shallow water takes most of the time.

Worked solution
1. The speed is set by the depth where the wave is: over the shelf, 120 m of water, it is $\sqrt{9.81 \cdot 120} \approx 34\ \mathrm{m/s}$ ⁠, about 120 km/h.
2. The shallower the water, the slower the wave, and in the last few metres it moves at a car’s speed.
3. So the last 80 km take about $47$ ⁠ minutes, more than three times the 170 km of deep ocean. The crest reaches the beach about an hour after the quake.
That hour is all the people on the coast have. In Japan in 2011 the wave reached some coasts in under half an hour.
Step 6 of 9
Open this step
The wave grows
Practice · Calculate
Question
Ocean depth is locked at 4 km and Sea-floor jump at 3 m, so the wave sets off 1.5 m high. As the wave slows, the energy it carries stays, and its height grows by Green’s law: $a \propto d^{-1/4}$ ⁠. The wave breaks where the water is about 8.7 m deep. How tall is it there?

Correct answer
6.949 m ± 3%
Setup, choices and feedback
The Scene at this step
Ocean depth
4 kmfixed
Sea-floor jump
3 mfixed
Labels
ondefault
Time
0.574 (Earthquake → Flood drains)
Accepted within
± 3%
Computed from the Scene at this step’s setting
The wave’s height where it breaks near the beach, grown by Green’s law/nodes/sea/outputs/coastHeight
Any unit of the same quantity is accepted; it is converted before checking.
Feedback for a right answer
About 7 m: four and a half times its height in the ocean.

Hint
$a_2 = a_1 \left(\dfrac{d_1}{d_2}\right)^{1/4}$ ⁠. A fourth root is the square root of a square root.

Worked solution
1. The ratio of depths: $\dfrac{d_1}{d_2} = \dfrac{4000}{8.7} \approx 460$ ⁠.
2. $460^{1/4} = \sqrt{\sqrt{460}} \approx \sqrt{21.4} \approx 4.6$ ⁠.
3. $a_2 = 1.5 \cdot 4.6 \approx 7\ \mathrm{m}$ ⁠.
The wave that was too low in the open ocean for a ship to notice reaches the coast as a seven-metre wall of water, and carries on inland as a flood. Green’s law does not depend on the wave’s length, so it holds for any long wave running into shallow water.
Step 7 of 9
Open this step
Landfall
Practice · Choose
Question
Just before the crest arrives, the sea draws back from the beach, leaving the sea floor bare and fish flapping. What should someone standing on the beach do?

Correct answer
- Correct Run at once to high ground, or high up in a strong building
Setup, choices and feedback
The Scene at this step
Ocean depth
4 km
Sea-floor jump
3 m
Labels
ondefault
Time
0.738 (Earthquake → Flood drains)
Choices
Shown in a random order.
- Correct Run at once to high ground, or high up in a strong building
- Wrong There is no danger: the tsunami has already passed far out at sea, which is why the water drew back
  Misconception: Thinks a sea that drains away from the beach means the danger has passed.
  Feedback from the catalogue
  When the sea suddenly drains from the beach, it is the tsunami’s trough, which sometimes arrives before the crest. The crest follows within minutes. It is the last warning: in 2004 people walked out to gather fish on the bared sea floor and were caught by the wave. When the sea draws back, run for high ground at once.
- Wrong Wait on the beach to see how tall the wave is before deciding
  Feedback
  By the time you see the wave it is too late: it moves at a car’s speed, and behind it a flood runs hundreds of metres inland.
Feedback for a right answer
Run at once. The retreating sea is the trough, and the crest comes after it.

Worked solution
1. The quake lifted the sea floor in one place and dropped it in another, so a tsunami has both a trough and a crest.
2. Here the trough reaches the coast first: the sea draws back.
3. The crest follows within minutes, and usually more waves after it, sometimes taller than the first.
So a sudden retreat of the sea, or a strong earthquake near the coast, is the signal to run at once, without waiting for a siren.
Step 8 of 9
Open this step
Both ways
Practice · Calculate
Question
Sea-floor jump is locked at 3 m: the sea floor lifts the whole column of water above it at once. The hump on the surface splits into two waves, one each way. How high is each of them as it sets off?

Correct answer
1.5 m ± 3%
Setup, choices and feedback
The Scene at this step
Ocean depth
4 km
Sea-floor jump
3 mfixed
Labels
ondefault
Time
0.025 (Earthquake → Flood drains)
Accepted within
± 3%
Computed from the Scene at this step’s setting
Height of each half of the wave as it leaves: half the sea-floor jump/nodes/sea/outputs/startHeight
Any unit of the same quantity is accepted; it is converted before checking.
Wrong answers it recognises
- 3 m ± 3%
  Misconception: Thinks the tsunami sets off as high as the sea floor jumped.
  Feedback from the catalogue
  The floor lifts a hump of water as high as the jump, but it splits at once into two waves moving opposite ways, each half as high. Only one of them heads for the coast.
Feedback for a right answer
1.5 m each: half the jump. One heads for the coast, the other for the open ocean.

Hint
The hump splits into two equal halves, like a stone dropped into a narrow channel.

Worked solution
1. The floor jumps 3 m, and the surface above it rises by almost as much.
2. The hump cannot stay where it is: it falls apart into two equal waves moving opposite ways.
3. Each of them is $\dfrac{3}{2} = 1.5$ ⁠ metres high.
A wave a metre and a half high and tens of kilometres long is not felt at all on a ship in the open ocean. It grows only near the coast.
Step 9 of 9
Open this step
Where it breaks
Practice · Predict, then look
Question
Sea-floor jump is at 3 m, and the wave breaks where the water is about 8.7 m deep. Predict: when the floor jumps only 1 m, where will the wave break?

Correct answer
- Correct In shallower water, nearer the coast
Setup, choices and feedback
The Scene at this step
Ocean depth
4 km
Sea-floor jump
3 m
Labels
ondefault
Time
0.697 (Earthquake → Flood drains)
Choices
- Wrong In deeper water, farther from the coast
  No feedback of its own; the learner sees the standard message
  Not yet. Look again and try once more.
- Wrong At the same depth, because breaking depends only on the sea floor
  No feedback of its own; the learner sees the standard message
  Not yet. Look again and try once more.
- Correct In shallower water, nearer the coast
Once the prediction is locked in, the Scene changes
Sea-floor jump
1 m
The Scene then shows: 3.607 m · Depth of water where the wave breaks into a bore and stops growing/nodes/sea/outputs/breakDepth
A prediction is never marked as a failure: the learner sees the outcome and the explanation either way.
Feedback for a right answer
In shallower water, about 3.6 m: a low wave has to come nearer the coast to grow tall enough to break.

Hint
A wave breaks when its height reaches a good part of the water’s depth, about eight tenths. A lower wave has to travel farther in to grow that tall.

Worked solution
1. A wave breaks when its height is about $0.8$ ⁠ of the water’s depth: its trough then almost touches the floor, and its front falls forward.
2. A wave that sets off three times lower grows by Green’s law at the same rate, but stays three times lower at every depth.
3. It reaches $0.8$ ⁠ of the depth only in shallower water: about 3.6 m.
A low wave too breaks at last into a wall of water, but nearer the coast and lower.

Across the unit · 15 misconceptions

Misconception catalogue

Each common mistake this unit recognises, in a few words. Open one for what the learner reads when an answer matches it, and where it is asked.

Index

The water cycle

The Sun lifts water

Question

Correct answer

The Scene at this step

Choices

Worked solution

A warmer sea

Question

Correct answer

The Scene at this step

Choices

Once the prediction is locked in, the Scene changes

Worked solution

The cloud base

Question

Correct answer

The Scene at this step

Wrong answers it recognises

Hint

Worked solution

Rain or snow

Question

Goal

The Scene at this step

One setting that reaches it

Hint

Worked solution

Higher mountains

Question

Correct answer

The Scene at this step

Choices

Once the prediction is locked in, the Scene changes

Worked solution

Back to the sea

Question

Correct answer

The Scene at this step

Choices

Worked solution

Groundwater and aquifers

Under the ground

Question

Correct answer

The Scene at this step

Choices

Worked solution

Rain and the water table

Question

Correct answer

The Scene at this step

Choices

Once the prediction is locked in, the Scene changes

Worked solution

Darcy’s law

Question

Correct answer

The Scene at this step

Wrong answers it recognises

Hint

Worked solution

A cone round the well

Question

Goal

The Scene at this step

One setting that reaches it

Hint

Worked solution

A drought

Question

Correct answer

The Scene at this step

Choices

Once the prediction is locked in, the Scene changes

Worked solution

Over-pumping

Question

Correct answer

The Scene at this step