The styrofoam cup experiment & aspects of ocean mass, pressure, and heat

A humpback whale fluke with ''angel slides'' from sun rays poking through the clouds, as seen from the south Scotia Sea region of the Southern Ocean on the JC Ross research ship.

An overcast sky let the sun peak through the clouds for most of the day.  The sea state has been relatively mild this past week, a result of the modest (less than 20knot) winds for most of the time (though it blew above 30knots last night).  We have thus made further progress on oceanographic measurements in the Orkney Passage region of the Southern Ocean.  In particular, the auto-sub Boaty McBoatface completed its final mission, this one for three days in the Orkney Passage.  In addition, we have taken many more CTD and VMP measurements, and we have seen some interesting signals in the high resolution CTD measurements taken from the tow-yos. 

Although we have seen modest winds, we do have signs of the approaching winter, with the air temperature dipping down to -13C yesterday.  With colder temperatures, the humidity (nearly 100% for much of the past week) has reduced to around 70%, thus making the colder air less bone chilling than it would be with the 100% humidity.  Nonetheless, it is still quite cold, particularly for those working outside.

Whales remain frequent companions, with both southern right and humpbacks often following the ship. Humpback whales offer a bit more of a show than southern rights, with humpbacks often found extending their flippers and splashing around. They also generally swim in packs of two or more.  Indeed, on some days with a reasonably clear sky, we can see a horizon full of a number of blow hole vapour trails.  Any kind of whale sighting remains a joy, even after having seen heaps thus far on this cruise.

Two humpback whales (mother and child?) swimming near the ship in the Scotia Sea.

 

The styrofoam cup experiment and the immense pressures of the deep ocean 

Upon roaming through my cabin when first arriving onboard in Chile, I was puzzled why the previous scientist using my cabin left a bag of styrofoam cups in one of the desk drawers.  The ship does not use styrofoam cups, for good reason as they contribute to the exponentially growing problem of plastic pollution in the ocean.  So what are these cups doing here?

My puzzle was resolved when I recalled the experiment (first described to me by Jennifer MacKinnon of Scripps in La Jolla, California) of placing a styrofoam cup on the rosette wheel to illustrate the incredibly large pressures in the deep ocean. I thus brought the bag to the UIC, at which point others on board, particularly the graduate students Jack and Nikki, became excited about performing the experiment as well.

Here is how the experiment works.  Draw some designs or such on the side of a styrofoam cup.  Then place the cup in a sock and tie it to the rosette wheel, letting it travel into the abyss during a CTD cast.  What returns from the CTD cast is a wonderful example of how pressure works to compress objects on all sides.

Styrofoam cup on the right, before going into the deep ocean.  Note my amazing artistic skills (joke!),  meant to show waves, penguins, a sun behind clouds, and single star (seen just the other morning by the night watch!), and some birds. The mug on the left is for size comparison.

Styrofoam cup on the right after going into the deep ocean.  The mug on the left is roughly the same size as the blue mug above (I could not find the blue mug when taking this photo).  Note how the cup deformed nearly uniformly.  To help in this uniform compression, Jack stuffed some paper towels into the cup. 

Jack prompted the experiment yesterday (22 April) when he came on shift at 4pm.  We each drew on our cups with some Sharpees, trying to channel our inner artist.  I then took a photo of the cup to record the "before" state. I gave him one of my socks to tie onto the next CTD cast, which was planned for late night when I was sleeping.

The next morning (today), Nikki gave me the cup after it had gone to near 4000 m depth.  I expected it to be a crumpled ball with little to recognize. What I saw was something far different and much more pleasing.  It was a "mini-me" version of the cup.  Upon reflection, and after being chided by others for my naivety, I understood what had happened.

The cup is a very small object relative to the depth scales over which pressure changes.  So pressure acts on all parts of the cup in roughly the same manner. Hence, one side of a cup wall feels a pressure force just as on the other side.  As a result, pressure forces compress each and every piece of styrofoam in roughly the same proportion, ensuring that the cup does not merely collapse into a crumpled ball.  Instead, pressure compresses the cup into a mini version of its original self by squeezing out the air within the styrofoam pores. Because the styrofoam has a "memory", when returning to the surface it retains its compressed state. I hope to bring this cup home in one piece to show my family and to place on my office desk! 

Eleanor, Alberto, and Kurt during an animated science discussion in the UIC on a recent morning.

 

Some numbers to help understand ocean mass and pressure

The ocean is really massive, which in turn produces huge pressure forces when descending into the abyss. Eleanor, in her post about Boaty’s second mission on 19 April, already mentioned the difficulties of engineering ocean measurement devices to withstand these pressures. The styrofoam cup experiment offers a vivid illustration. It is also useful to consider some numbers to garner a more quantitative understanding of the scales.

Our bodies have adapted to pressure from the weight of the atmosphere.  At sea level, the mass of atmosphere per unit horizontal area is roughly 10^4 kg/m2.  That is, for every square metre of earth surface at sea level, there is about ten thousand kilograms of atmosphere above.  When multiplied by the gravitational acceleration at the earth's surface, that atmospheric mass leads to about 10^5 Newtons per square metre of pressure acting on our bodies.  This pressure is known as ''sea level pressure'' for obvious reasons.  

Our bodies have evolved to withstand atmospheric pressure at sea level as well as in higher elevations (where pressure is less due to the reduced atmospheric mass at higher elevations), maintaining its integrity even as the atmosphere presses on our bodies. However, consider an alien from the moon who visits the earth.  This moon being lives on an object with far less gravitational acceleration than the earth (since the moon is far less massive than the earth), and with nearly zero atmospheric pressure (since the moon has basically no atmosphere).  So this moon being would be compressed in the absence of an "earth suit" to protect against pressures felt at sea level on the earth.

Now what about when we dive into water?  Most people have jumped into a swimming pool deep enough to notice the increased pressure on the ears.  Even more compression is felt when scuba diving down a few tens of metres.  For such dives into a swimming pool or ocean, we can perform an inner ear equilibration to adjust to the increased pressure. Likewise, we can adjust our inner ear when riding in a car that climbs to the top of a mountain, where there is less atmospheric pressure acting on our ears. However, note the huge differences in scales. Namely, we must adjust our inner ear pressure when diving to the bottom of a 10 metre pool, but we have no such need when climbing to the top of a 10 metre tree. The difference is related to the huge difference in density between air and water.

Air density is roughly 1.2 kg/m^3, whereas seawater density is roughly 1030 kg/m^3.  Ever try to lift the water out of your full rain barrel?  This density difference means that upon reaching 10 m into the ocean, we have accumulated a full atmosphere's worth of pressure just from the 10 metres of water over our heads. Hence, at 10 m depth in the ocean, we feel the pressure equal to two full earth atmospheres (one from the atmosphere itself, and the second from the 10 m of seawater).  In turn, at 4000 m in the ocean abyss, there is roughly 400+1 earth atmospheres of pressure.  That pressure produces a huge force on any object at this depth.  

In particular, marine life in the abyss must withstand pressures of the ocean water. Even marine life living in the upper ocean, say just a few tens of metres deep, must adapt a body structure quite distinct from terrestrial beings feeling only a single atmosphere's worth of pressure. In turn, it can be lethal for marine life to rise to the surface ocean too fast, without allowing sufficient time for their body to equilibrate to the lower pressure.

Back deck of the JR Ross on 23 April.  Note the snowman on top of a mooring float on the right.  The blue sky has been quite a treat this day, as well as the very cold yet somewhat drier air.

 

A few facts about ocean heat 

Another facet of seawater concerns its ability to absorb and to store a huge amount of heat.  This property is due to the very large mass of the ocean as well as its large heat capacity. Let’s again consider some numbers. 

The atmosphere is warming through human-induced climate change arising from increases in greenhouse gases that change the earth's radiation balance ("anthropogenic climate change"). Measurements of the planetary heat budget indicate that more than 90% of the extra heat from greenhouse gas pollution (from burning fossil fuels) is absorbed by the ocean.  This ocean warming contributes to sea level rise through thermal expansion (warm water expands) and melting of ice shelves that are exposed to the warmer water. 

Ocean measurements estimate that roughly 2.4 x 10^{23} Joules of heat accumulated in the ocean during the past 40 years.  The surface area of the oceans is roughly 3.6 x 10^{14} m^2.  When dividing the net heat accumulated (2.4 x 10^{23} Joules) by 40 years (time it took to accumulate this heat) and dividing by 3.6 x 10^{14} m^2 (surface area of the ocean), we find an averaged surface heat flux of roughly 0.5 Watts per square meter entering the ocean.  That is, for each square metre of surface ocean, there is, when globally averaged, about one-half a Watt entering that square due to anthropogenic warming.  This heat flux is quite small when compared to, say, the heat flux generated by a 60 Watt light crossing its glass bulb.  But consider this heat flux in comparison to something more planetary in scale, and something far more dramatic.

The amount of energy released from one Hiroshima bomb was roughly 6.3 x 10^{13} Joules. Assume there is one such bomb exploded each second, and distribute the released heat energy over the area of the ocean. Crunching through the numbers reveals that one Hiroshima's worth of energy per second, spread over the ocean surface, corresponds to 0.17 Watts/m^2 heat flux. Hence, the observed ocean warming during the past 40 years, due to increases in greenhouse gas pollution, is equivalent to the amount of heat released by exploding three Hiroshima bombs every second for 40 years.  When measured in this manner, we see that the magnitude of ocean heating is thus very large indeed.

As a means to understand the role of the ocean for the climate system, consider an earth without an ocean. Instead of sequestering 2.4 x 10^{23} Joules of heat in the ocean, we instead let it remain in the atmosphere where it originated.  Given the mass of the atmosphere and its heat capacity, and assuming the added heat is mixed uniformly throughout the atmosphere, the average temperature of the atmosphere would rise about 40 degrees Celsius.  This is an incredibly large increase in atmospheric temperature. The ocean thus performs a huge "climate service" to those of us who live on land. Indeed, one of the biggest questions of climate science is how long the ocean will continue to absorb the extra heat produced by increases in greenhouse gases that alter the earth's energy budget.

The day watch on 23 April: Eleanor Frajka-Williams from Southampton University, Paul Anker from British Antarctic Survey (BAS), Stephen Griffies from NOAA/Geophysical Fluid Dynamics Lab and Princeton University, and Christian Buckingham from BAS. Weeks of close work has made us quite a team indeed!