You have probably seen the picture of people floating on their backs in the Dead Sea, reading a newspaper or a book. But do you know why they are floating?
You need:
2 large plastic containers
Water and a lot of salt
Different kinds of vegetables and fruits (or other things you might want to experiment with)
Mix a lot of salt with the water (salt dissolves more easily if the water is warm!) in one of the plastic containers to represent the Dead Sea, and fill the second container with tub water at the same temperature as your “Dead Sea”. In the Dead Sea, the salinity is 33,7%, that means to reproduce that you need ca 1 kg salt for 4 liters of water!
Now look at all your fruits and vegetables. Which, do you think, will float in the “Dead Sea”? Which will sink? Does your answer change if you look at your second container with tub water?
Does the coconut float? Fra Forskningsdagene i Bergen. Foto: UNI research
When heading down for dinner earlier today I glanced out through my window and all I saw was a white “wall”. A white wall of ice extending to the right and the left for as far as I could see (which admittedly wasn’t very far, since it was snowing and a light mist caused the horizon to disappear). We are in front of the Dotson ice shelf, one of the smaller ice shelves in the Amundsen Sea. The biologists had a station right at the ice shelf front, and one of the plankton nets just went down into the water. How high is the wall? Ten meters? Twenty? Thirty? There was a lively discussion around the dinner table and there were plenty of guesses – but no answer, so when the dinner (squid, sweet potatoes and rice) was finished we all headed up to the bridge and asked the captain if we could borrow the sextant (Google or Wikipedia will do a better job explaining what it is than I’d do). We had a look at the radar screen while one of the deck hands searched in the cupboard for the sextant. The wall was half a nautical mile (1 nm=1852 m) away. Before we the sextant was located (and before we’d learnt how to use it) the plankton net was back on deck and we were heading to the next station. When we finally managed to measure the angle (0.77 degrees) the wall was 1.5 nm away. Now, how high was the wall? If you want to do it correctly, you also need to know that the bridge is 16.7m above sea level and the sextant was 1.5m above the floor. But does it matter if you do it “correctly”? The difference between the “correct” solution and the simplified solution is surprisingly small!
When Araon stops again the “wall” is still there, we are still along the front of the Dotson ice shelf. The CTD is going into the water. The
Korean oceanographers are working in shifts and there is always someone on guard in the CTD-room. This time it is Ta-wan who is placed in front of the big CTD-screen while the deck hands are preparing the winch and the CTD outside. It is snowing and the wind is rather chilly, so I decide to stay inside with Ta-wan. The radio calls for attention and I hear a few short sentences in Korean – at the same time, the screen comes to live in front of Ta-wan. The CTD has gone into the water. We wait with the CTD just below the surface until the pump has started and everything is working as it should. Then, down she goes! The data collected by the CTD is displayed “live” on the screen in front of us, and the lines grows longer as the CTD sinks down. During the first 30-40 meters the water is relatively fresh (33.9) and the temperature between 0C and 0.5C; this is the surface layer – mixed by the wind, warmed by the sun and freshened because it’s been diluted by meltwater from melting sea ice and ice bergs. When we go deeper, the salinity increases to 34.2 and the temperature sinks to -1.5C, and it then remains roughly constant for several hundreds of meters. This is “winter water”, water that has been cooled down during winter.
Back to the screen; the pressure sensor shows us that we’ve reached down to 400 m depth and the temperature and the salinity has started to increase. The blue line that shows the temperature is heading out of the figure, off the scale. While Ta-wan searches through the menus on the side to change the scale, the rest of us places bets on the maximum temperature. When the scale is changed and the blue line is back on the screen we learn that the winner isŠ Karen and the University of Gothenburg! The warmest water reaching the front of the ice shelf was 0.64C – this is the water we are here to study, the “circumpolar deep water” that has found its way onto the continental shelf and southward towards the ice shelf through the Dotson trough, a deep trough that the ice has carved a long time ago when the climate was colder and the Antarctic ice sheet was bigger and thicker than it is today.
The CTD has reached the bottom and we see three layers of water on the screen. Three layers, or water masses, as we oceanographer would call them. The water with the lowest density is floating on top – just like the light oil floats on top of the heavier water – and the water with the highest density at the bottom.
But enough oceanography for today – the clock has just struck eight and I leave Ta-wan and the others in the CTD-room to head to the training room and the ping-pong table. Povl ( a Danish oceanographer working at British Antarctic Survey in Cambridge, UK) and I have been challenged by Monsieur Park and Isabelle from L’Ocean in Paris, so we’ll have to stand up to defend the Scandinavian colors.
One of the most beautiful ice shelfs. (Photo: Elin Darelius Chiche)
Ps – while we were up playing tabletennis Nicole (from Rutgers University,US) deployed her glider. The glider can change its volume (and hence its density) and using it swings it can fly up and down through the water carrying with it a bunch of sensors – an autonomous CTD! While at the surface, it sends home data, position via satellites, and at the same time it receives new orders about where to swim, how deep to dive, what sensors to turn on etc. If you visit www.marine.rutgers.edu/cool/auvs and look for glider RU25 you can see what her glider is up to!
Nicole’s glider dives into the water (the wings are not mounted yet)(Photo: Elin Darelius Chiche)
Beautiful waves in Antarctica! Photo: Elin Darelius Chiche
Oceanographers like me often talk about «water masses», that is water with different origin that therefore has different salinity and temperature. We talk about “Atlantic water”, which is warm and salty, about Antarctic surface water which is fresh and col or about Antarctic shelf water which is cold and salty. The salinity and temperature of the water will determine its density; cold water is denser than warm water, fresh water is lighter than saline water.
The properties of the water masses are to a large extent set by the atmosphere. Where it is warm, the water is heated up and where it is cold the water is cooled down. The salinity is determined by evaporation, freshwater input (from rivers or precipitation) and by the formation of sea ice. When ice is formed during the winter, it is the water molecules that freeze. Most of the salt is rejected, and the salinity in the water below the ice thus increases. In shallow areas where a lot of ice is formed – for example in some parts of the continental shelf surrounding Antarctica – the water can become very saline and hence very dense.
The exercise below is about Circumpolar Deep Water, CDW. CDW is actually a mixture of several water masses, amongst other water that orinates as far away as the North Atlantic. CDW has a temperature between 1-2 degrees and a salinity between 34.62 and 34.73. Strangely enough, salinity does not have any unit, but is approximately permil so if the salinity is 1 there is about 1 gram of salt per kilo water. The salinity in the ocean is typically about 35, or 3.5%.
In a TS-diagram (a graph with salinity on one axis and temperature on the other axis, see below) a water mass is a point or a small box – if we mix two water masses the mixture will lie on a straight line between the two water masses.
TS-diagram showing the temperature and salinity of WW and CDW. The dashed lines are ispycnals – all watermasses on a line have the same density. The black line shows the freezing point of the water.
Exercise 1
You have two bottles A and B where \(S_A\)=33.2, \(T_A\)=4C and \(S_B\)=34.8, \(T_B\)=1C. Mark them in a TS-diagram
What is the salinity and temperature of a mixture that is made of 50% A and 50% B?
What is the salinity and temperature of a mixture that is made of 10% A and 90 % B?
What is the salinity and temperature of a mixture that is made of 73% A and 27% B?
Plot your mixtures in the TS-diagram. What do you see?
If you have a third water mass \(S_C\)=33.7, \(T_A\)=0C – which mixtures can you get then?
Exercise 2
Import and plot salinity and temperature from the mooring S4, 320 m depth as a function of time (the file is named ENG_Riggdata_S4_TS).
Time is given as days since 1 january, 2012. What day was the mooring deployed? Recovered?
What is the average temperature /salinity and standard deviation?
Is there a seasonal signal? Can you describe it with a sinus function? Why / why not?
Plot temperature versus salinity in a TS-diagram – what do you see? Can you describe the relationship between salinity and temperature with a linear regression?
An instrument in the vicinity of the mooring measured S=34.25, S=34.6 and S=33.9. What do you think the temperature was?
Are your answers to the exercise above reasonable? Sea water freezes at -1.9C. For what salinities are your regression valid?
The observations show that the mooring is surrounded by a mixture of CDW (Circumpolar Deep Water) and WW (Winter Water). What are the salinity/temperature of our CDW? WW normally has a temperature of -1.9C. Do we observe pure WW at our mooring? Use your regression to determine the salinity of the WW.
You now have determined the properties (S and T) of WW and CDW. What is the temperature and salinity in a mixtruer of 10% CDW and 90%WW? 75% CDW abd 25% WW?
What would be the termeprature of water with a salinity of 34.45? What fraction of the water is CDW?
Exercise 3
The density of seawater depends on its salinity and temperature. Cold water is denser than warm fresh water is lighter than saline water. The relationship between S, T and density is complicated, but for small changes in salinity and temperature the relationship is approximately linear.
In the expression above \(S\) is salinity, \(T\) is temperature, \(\beta\) is the haline coefficient and \(\alpha\) is the thermal coefficient. \(S_0\) och \(T_0\) are reference values that you can choose freely and \(\rho_0=\rho(S_0,T_0)\). The values of \(\alpha\) and \(\beta\) depends on what values you chopse forr \(S_0\) and \(T_0\). If we chose \(S_0\)=34.6 and \(T_0=\)=0.5C then \(\rho_0=\rho(S_0,T_0)\)=1027,8 kg/m\(^3\), \(\alpha \approx \) 5.77*10\(^{-5}\) C\(^{-1}\) and \(\beta \approx 7.84*10^{-4}\).
Use the linearisation to calculate density profiles based on the temperature and salinity profiles from the Amundsen Sea (file ENG_CTDdata_Amundsenhavet). What do they look like compared with the salinity and temperature profiles?
Chose one of the profiles? Where is the density largest? Smallest? Why is it like that?
How big is the density difference between the bottom and the surface? How much more saline must the water in the surface be to be as dene as the water at the bottom?
The density must increase with depth, otherwise the water column I unstable: dense water is lying on top of light water. The dense water then will sink down to “its” level (this is called convection)
If we cool down the water in the surface to the freezing point (-1.9C), what will happen?
Strong wind can mix the upper layer so that we get a homogenous layer (constant salinity and temperature). The salinity is then equal to the mean salinity.
What is the mean salinity of the upper 100 m?
How heavy would the homogenous surface layer be if it was cooled down to the freezing point (-1.9C)
By how much do we have to increase the salinity for the water in the surface to be as heavy as the water at the bottom? (How can this happen in Antarctica? In the Mediterranean Sea?)
Exercise 4
When the temperature increase the density decrease – that means that1 kg of warm water occupies a larger space than 1 kg of cold water. A large part of the sea level rise that we are observing today (and that we will see in the future) is caused by the increase in temperature of water at depth in the ocean. If water which is 4000m deep (with \(S_0\), \(T_0\), \(\rho_0\),\(\beta\) and \(\alpha\) as given in exercise 3) is heated by 1C, how much will the sea level then rise?
Exercise 5
It is the water molecules that forms crystals when sea water freezes – the salt is rejected by the growing ice and mixes with the sea water below. The salinity* of freshely frozen ice is typically 7-10**. Since the salinity has such a large influence on the density, we want to find out how much the salinity in the water increases (\(\Delta S\)) when ice of a certain thickness (\(h_{ice}\)) and salinity (\(S_{ice}\)) is formed. We can do that using the formula:
\(\Delta S= \frac{h_{ice}(S-S_{ice})}{H_{water}}\) where \(H_{water}\) is the thickness of the layer that the salt mixes into.
By how much does the salinity increase of we freeze (i) 10 cm (ii) 1 m of ice over a 100 m thick layer where S=34.5 and \(S_{ice}\) =7?
By how much does the salinity increase of we freeze (i) 10 cm (ii) 1 m of ice over a 1000 m thick layer where S=34.5 and \(S_{ice}\) =7?
By how much does the density increase in a-b? (Set T=T\(_f\) (See exercize 3).
How much ice do we have to freeze for the water in 3h to be as heavy as the water on the bottom? (Let H=100 m, the thickness of the layer that the storm mixed) Is that realistic?
*You determine the salinity of ice by melting it down and measureing the salinity of the melt water.
**For old ice in the Arctic the salinity can be almost zero!
Warm water needs more space than cold water — check it out in this experiment!
You will need:
1 small plastic bottle
1 drinking straw
modelling clay / play dough
Food dye (not strictly necessary, but more fun)
A large, high container in which the small plastic bottle can stand
cold and warm water
Fill the bottle with cold water (and add a couple of food dye if you like). The bottle should be completely full, so full that it is almost overflowing.
Place the straw in the bottle and lock the bottle with modelling clay. At least 10 cm of the straw should be left above the lock! Test that the lock is water tight by slightly pressing on the bottle. Water should now be rising in the straw, but not spilling out of the lock! It is not easy to get the lock completely watertight, you might need several attempts.
Now place the bottle in the larger container and fill the container with hot water (careful – don’t hurt yourself!). Wait a couple of minutes and observe what is happening. How high is the water rising in the straw?
Now put really cold water in the larger container instead of the hot water. What happens?
Try this for different water temperatures – lukewarm, really hot, medium hot, cold, etc. What happens now?
Researchers have found out that the water in the deep ocean is slowly warming. What do you think the consequences will be?
Can you think of a way to measure the salinity of the sea water? There are many possibilities to figure out how much salt there is in sea water! How would you go do it?
When you fetch your sea water, take a little more than you need and put it in a bowl or glass somewhere where it can sit without being disturbed (maybe on top of a cupboard?). As water evaporates, what happens? Check occasionally on your glass with sea water, and look at how much water vanished since you last checked. What is happening in the glass? At what point can you notice salt crystals forming? How long does it take until all the water is gone?
The Amundsen Sea – we are finally here! The viw outside our round windows has changed – it is no longer only grey and blue. Between us and the horizon there’s the odd iceberg bobbing about and every now and then some sea ice and maybe a lonely snow petrell or a seal… but no penguins, just yet!
We are now quite precisely 15711 km from Bergen and home – and you proabably want to know why we came here.
The water in the Amundsen Sea is of course just as blue as the water outside Bergen – but on our oceanographic charts we tend to color it red. Red because it is (relatively) warm, red because the ice shelves are melting faster here than in most other places around Antarctica. This is not a coincidence – the ice shelves, i.e. the floating extension of the ice sheet covering the continent, are melting because the warm water is entering the cavity beneath them. And you all know what happens when you put ice in warm water.
Undocking of a buoy. (Photo: Povl Abrahamsen)
Melting ice shelves are a big concern in the chapter of the IPCC-report that discussed sea level rise. It is a concern, because the consequences if they are to melt are so large, but the ice shelves also represent a big question mark, because we know so little about how the work and about how they are affected by (and affect) the ocean around them. The ice shelf itself is floating, so the sea level is not affected when it melts, but when it thins, it tends to speed up and the glacier or ice sheet feeding it will follow. Ice is then moved from land to the ocean – and the sea level rises.
During our weeks at sea will do measurements and install instrument – both in the sea and up on the ice shelves – to better understand what is happening, and to measure the amount of heat that the ocean is transporting towards the ice shelf and how the ice shelf is responding.
A lot of the time on board is used to do “CTD-stations”. CTD stands for “Conductivity-Temperature-Depth, and it is a bunch of sensors mounted on a frame (most of the time with a number of bottles attached to it) that we lower down to the ocean using a big winch. On its way down to the bottom the CTD is continuously measuring and sending the data back to us. On the screen in front of us a profiles show how salinity and temperature is changing as the instrument moves downward. The “bottles” on the frame are open in both ends so the water is flowing through them and when the CTD is returning up to the surface we stop it every now and then to close one of the bottles – in that way we can bring water from different depths up, that we (or the biologists onboard) can analyze.
There is a lot of equipment at the lab. (Photo: Povl Abrahamsen)
A few hours ago we took the first CTD-station and the instrument was sent down to the bottom 3450 m below us. We are still above deep water, and we will continue to do CTD-stations on our way in towards the shallow continental shelf. Down in the deep there is plenty of “warm” water, the big question is how much of it that makes it up on the continental shelf, in towards the floating ice.
We are now getting used to life onboard… we’ve learnt what buttons to press to make the Korean laundry machine start, I’ve learnt to stay away from the red (and thus spicy) food and we’ve made the bread baking a routine! My colleague Anna (from Gothenburg University) has been onboard Araon on previous expeditions, and after spending eight weeks at sea with no real bread last time she was on board, she decided to bring a bread machine (and 25 kilos of flour!). The Koreans normally don’t eat bread, but when the smell of freshly baked bread is spreading in the corridors they are eager to come and taste!
An historical moment! We cut up the first bread baked on Araon. (Photo: Povl Abrahamsen)Korean barbecue on the menu on saturdays (Photo: Povl Abrahamsen)
The ice shelves in the Amundsen Sea are melting relatively quickly since warm water is entering the cavity beneath the ice. We thus want to know how much heat the water on the continental shelf contains, and how much heat that is entering the ice shelf cavity. The heat content is given relative to a reference temeprature \(T_{ref}\). What you calculate, is how much heat you have to remove before the temperature of the water is \(T_{ref}\). If you have to add heat for the water to reach \(T_{ref}\), then the heat content is negative.
We can find the heat content \(H\) in the water from a CTD-profile (observations of temperature, and salinity from the surface to the bottom):
\(\rho\) is the density of the water (about 1027 kg/m\(^3\) and \(c_p=4\times10^3\)J/kg/C is its heat capacity.
You are free to choose the reference temperature – but since sea water freezes and -1.9C it is practical to choose \(T_{ref}\)=-1.9C. The heat content is then the energy one can remove from the water before it freezes. \(H\) is the heat conent per square meter.
When warm water is in contact with ice the heat will be used to melt ice. To melt a kilo of ice you need approximately 330 kJ (or a bit more if the ice is cold).
The CTD about to dive down into the cold Antarctic water. Sensors for temperature, conductivity, pressure and other parameters are hidden between the bottles.
Exercise 1
Import the data from the CTD-profiles from the Amundsen Sea (you’ll find them one after each other in the file ENG_CTDdata_Amundsenhavet in Geogebra. Plot a few of the profiles and calculated the heat content
How much of the heat is found in the upper 200 m? below 200 m depth?
We are mostly interested in the heat at depth. Do you know why?
Make a table where you note the heat content (in the upper and lower layer separately) and the temperature at the bottom. (You may well cooperate in groups!)
My colleagues argue that there is a direct relationship between the bottom temperature and the heat content, so that all we’d need to measure is the temperature at the bottom. What does it look like in your data? Can you draw a conclusion based on the data at hand? Discuss!
If you want to add more points to your table, you can download data from the entire cruise in 2010 from NODC, a large data bank where we scientist send our data so that other researchers (and you!) can use them!
Exercise 2
How much ice (per square meter) can we melt with the heat from the profiles above?
The melt below the ice shelf in the Amundsen Sea is about 400 Gton per year. How much heat is that?
Exercise 3
If the West Antarctic Ice sheet were to collapse, the sea level would increase with three meters – how many cubic meters of ice does that correspond to?
How much heat is needed to melt that ice? (Does it have to melt for the sea level to rice?)
A wind turbine typically produce 2 MW – how long time would it take for the wind turbine to produce the energy needed to melt the ice?
The earth receives about 0.5 W/m\(^2\) more energy (through radiation) from the sun than what is given off – how long time would it take to melt the ice if all of the energy was used to melt ice?
A Norwegian uses about 30 000 kWh per person per year –how many cubic meters of melted ice does that correspond to?
[slr-infobox]
Radius of the Earth: 6371 km
Density, ice: 900 kg/m\(^3\)
Density, snow: 900 kg/m\(^3\)
Density, sea water: 1027 kg/m\(^3\)
Percentage of the Earth that is water: 70%
[/slr-infobox]
Mix the food dye and water, put it the ice cube tray, put the ice cube tray in the freezer and wait… Now you have colored ice cubes!
Fill the two glasses with tap water. Take one of the glasses and mix in salt until the water tastes like sea water. Then, put one ice cube in each of the glasses and watch what happens. Where does the ice melt fastest? And why?
For advanced oceanographers: you can also use “clear” (not dyed) ice cubes, then seeing what happens is a little more difficult (and a little more exciting :-))
You can read about what happens – and why – on my friend’s and former colleague Mirjam’s blog “Adventures in oceanography and teaching“. There you can find many more exciting experiments, too!
It’s early in the morning and I’m alone out on the deck. Far away the blue sea mixes with the grey sky and forms a blurry horizon. It doesn’t matter in what direction I look, it is all the same: grey and blue. Araon that appeared so large back in the harbor is now a small red dot in a seemingly eternal blue ocean. Araon is a Korean icebreaker that during this expedition to Antarctica and the Amundsen Sea brings along about 40 scientist: biologist, chemists, meteorologists and a group of physical oceanographers. I belong to the latter; I’m a physical oceanographer. That means that I try to find out how the ocean works – where do the currents go and why? In a way it’s like meteorology, but in the ocean. I boarded Araon more than a week ago in Christchurch, new Zealand in order to – when we finally get there – deploy instruments on the continental shelf around Antarctica.
Araon in the harobur of Christchurch, Nya Zealand. Our stay here was prolonged due to trubble with the engines.
We were supposed to be down there by now, in the ice – but an hour or so before we were set out on New year’s eve they discovered a leak in the engine so the departure was delayed and we couldn’t do much but hang out and wait for the technician’s to repair and fix the problem.
Most of the ice cover around Antarctica is seasonal, that is it grows during winter and melts away during summer – compared to the Arctic there is very little ice that survives the summer (You can read more about the differences between sea-ice in the Arctic and Antarctica here: https://nsidc.org/cryosphere/seaice/characteristics/difference.html, but close to the continents the ice remains. You can see how much ice there is around Antarctica here: http://www.iup.uni-bremen.de:8084/amsr2/ (The pictures from Antarctica is at the bottom of the page Antarctic).
Sea ice is not only beautiful but also important. It is crucial for the marine biology (everything from large seals to small algae lives on or in it), for the ocean below it (it isolates the ocean from the cold atmosphere and influences the properties of the seawater below by separating the fresh water from the salt) and for our climate, since the white ice will reflect the incoming solar radiation while the dark ocean absorbs it.
But the best thing about ice (at least in the opinion of a sea sick oceanographer), is that it effectively “kills” the waves… right now, there are quite big waves and the ship is rolling back and forth, back and forth, back and forth. We are crossing over the Southern ocean, and there is a reason why one tend to talk about “the roaring forties, the furious fifties (where we are now) and the screaming sixties… All equipment has to be secured and tied down, if not it would be flying around. I was up more than once this night to pick up things that were rolling around on the floor. My stomach is also “rolling”, and I didn’t manage to eat very much of the Korean breakfast: soup, fried small (3-4 cm long, you eat the head and everything!) fish and egg, and then off course rice. The breakfast looks much like lunch and dinner!
My room the next seven weeks. I share cabin with Isabell from France.
On our way to the Amundsen Sea we will make a detour for our French colleagues who are studying the Antarctic circumpolar current- that is the strongest current in the world! Next week I’ll tell you more about why we are going to the Amundsen Sea and what we will do there… but until then, try to do the exercises and learn more about how the ice grows. I hear it is cold back in Bergen, so maybe you’ve got more ice around than I do…
Map of the Antarctic region. New Zealand at the bottom to the right!
Pancake ice! If there are waves when the ice is freezing on the sea, you’ll typically see “pancake ice” being formed. Photo: Elin Darelius Chiche.
Ice, ice, ice! There is sea ice everywhere! Large floes, small floes and the odd iceberg. It is all white, and all beautiful, and it puts a definitive end to waves and seasickness!
When heat is removed from water, the water will cool and it will continue to do so until it reaches its freezingpoint. If we continue to remove heat, the water will freeze. The heat that we remove is then the latent heat. Normally it is not “we” who remove heat, but the atmosphere. When the air above is colder than the ocean below, heat will move from the water up into the air: the colder it is, the faster the heat moves. That is, the colder it is, the faster the ice grows. But the ice is a good isolator; it will isolate the water from the cold atmosphere above. Just like your jacket isolates you when it is cold outside and makes you keep the warmth inside, the ice causes the water to loose heat more slowly, since the heat must be conducted through the ice in order to be lost to the atmosphere. The thicker the ice is, the more slowly is the heat conducted through the ice, since the heatflux (\(F_{ice}\), i.e. the amount of heat that is conducted through the ice per unit of time) is proportional to the temperature gradient:
\(k_{ice}=2\,W\,m^{-1}\,^{\circ}C^{-1}\) is the heat conductivity of ice and \(H\) is the thickness of the ice.
\(T_{atm}\) is the temperature at the top of the ice (which we assume to be equal to the temperature of the air) and \(T_f=-1.9^\circ C\) is the temperature at the bottom of the ice, that is, the freezingpoint of sea water.
The latent heat that is released (per square meter) when the ice is growing a little bit\(dH\) is \(\rho_{ice}LdH\). If that happens during a short time \(dt\), then the latent heat flux is:
\(F_{latent}=\rho_{ice}L\frac{dH}{dt}\)
\(\rho_{ice}=900\,kg\,m^{-3}\) is the density of ice and
Ice on the sea. The black lines show the temperature gradient in the ice and the red Arrows the heat flux. When the air above is cold (or if the ice is thin) the gradients and the heat flux is large and the ice grows quickly. When the temperature difference between the air and the water is small the gradient and the heat flux is small.
\(L=3.3*10^5J\,kg^{-1}\) is the latent heat of fusion.
The ice will grow exactly as fast as the latent heat can be conducted up through the ice, i.e. so that
\(F_{latent}=F_{ice}\)
When combining the two equations we get a differential equation, that we can solve to get an expression for how the ice thickness increase in time, \(H(t)\).
Exercise 1
a) Set up the differential equation and show that the solution \(H(t)\) is
Hint: Use the chain rule \(\frac{dH^2}{dt}=2H\frac{dH}{dt}\).
b) Let \(H_0=0\) and plot the function for different \(T_{atm}\)!When does the ice grow fastest? Why?
c) Use the equation from (a) to calculate the thickness of the ice ten hours after it started freezing if the temperature outside is (i) -20C (ii) -2C.
d) When the ice is 1 m thick, how long is it before it grow another 10cm?
e) What do you think will happen if there is snow falling on the ice? \(\kappa_{\textit{snow}}\) is typically between 0.15 and 0.4\(W\,m^{-1}\,^{\circ}C^{-1}\). What is the better isolator? Snow or ice?
f) All heat that is conducted up through the ice has to be conducted through the snow as well. Where is the temperature gradient largest? In the snow or in the ice? Make a sketch!
Exercise 2
The temperature varies from day to day and from year to year. The file ENG_Temperatur gives temperature data from the Amundsen Sea from March 2014 to March 2015.
a) Find the mean temperature for each month and plot it. Find the standard deviation and add it to your graph. What month is coldest? Warmest? When is the temperature most variable?
b) When does the ice stop to grow?
c) Find out how much the ice thickness increase everyt month? What value should you use for \(H_0\)?
d) Plot the (i) the ice thickness and (ii) the ice growth as a function of time. When is the ice growing fastest? Is this when it is coldest? Why? Why not?
If it is calm and no Wind when the ice freezes there are no pancakes but socalled “nilas”: thinice that looks almost black as one sees the dark open beneath. The thin icefloes can easily slide on top of ar below each other.
Exercise 3
If an ice flow is 30 cm thick, 2 m wide and 5 m long – how much of the ice floe is then above water? \(\rho_{ice}=900kg m^{-3}\)
How many scientist can stand on the ice flow (in the middle)without getting their feet wet?
How much snow can fall on the ice before the ice floe is submerged? \(\rho_{snow}\approx 300kg m^{-3}\)
Exercise 4
The ice in Antarctica is relatively thin and it often snows so much that the ice is submerged. Then we’ll have a layer of slush (snow + seawater) on top of the ice. When the slush freezes, we get what is often called “snow ice”. Estimations suggests that as much as 40% of the ice in the Amundsen Sea is snow ice!
It is quicker to freeze snow ice than regular sea ice – can you explain why? How far does the heat have to be conducted when freezing snow ice? Does the snow have to freeze?
