clouds

Air raising

Small waves seen from Lindisfarne

How do clouds form? How does temperature vary with altitude, and what does coffee have to do with any of it?

You put a drop of alcohol on your hand and feel your hand get cooler as the alcohol evaporates, but what has this to do with coffee, climate and physics?

Erasmus Darwin (1731-1802) was the grandfather of Charles of “Origin of the Species” fame. As a member of the Lunar Society (so-called because the members used to meet on evenings on which there was a full moon so that they could continue their discussions into the night and still see their way home) he would conduct all sorts of scientific experiments and propose various imaginative inventions. Other members of the Lunar Society included Matthew Boulton, Josiah Wedgwood and Joseph Priestley. The society was a great example of what can happen when a group of people who are interested in how things work get together and investigate things, partly just for the sake of it.

One of the things that Darwin had noticed was that when ether* evaporates from your hand, it cools it down, just as alcohol does. Darwin considered that in order to evaporate, the ether (or alcohol or even water) needed the heat that was provided by his hand, hence his hand started to feel cooler. But then he considered the corollary, if water (ether or alcohol) were to condense, would it not give off heat? He started to form an explanation of how clouds form: As moist air rises, it cools and expands until the moisture in the air starts to condense into droplets, clouds.

hole in water alcohol

There are several cool things you can notice with evaporating alcohol. Here a hole has been created in a thin layer of coffee by evaporating some gin. You can see the video of the effect here.

As with many such ideas, we can do a ‘back of the envelope’ calculation to see if Darwin could be correct, which is where we could also bring in coffee. The arabica growing regions are in the “bean belt” between 25 °N and 30 °S. In the sub-tropical region of that belt, between about 16-24°, the arabica is best grown at an altitude between 550-1100 m (1800-3600 ft). In the more equatorial regions (< 10º), the arabica is grown between 1100-1920m (3600-6300 ft). It makes sense that in the hotter, equatorial regions, the arabica needs to be grown at higher altitude so that the air is cooler, but can we calculate how much cooler it should be and then compare to how much cooler it is?

We do this by assuming that we can define a parcel of air that we will allow to rise (in our rough calculation of what is going on)¹. We assume that the parcel stays intact as it rises but that its temperature and pressure can vary as they would for an ideal gas. Assuming that the air parcel does not encounter friction as it rises (so we have a reversible process), what we are left with is that the rate of change of temperature with height (dT/dz) is given by the ratio of the gravitational acceleration (g) to the specific heat of the air at constant pressure (Cp) or, to express it mathematically:

dT/dz = -g/Cp = Γa

Γa is known as the adiabatic lapse rate and because it only depends on the gravitational acceleration and the specific heat of the gas at constant pressure (which we know/can measure), we can calculate it exactly. For dry air, the rate of change of temperature with height for an air parcel is -9.8 Kelvin/Km.

contrail, sunset

Contrails are caused by condensing water droplets behind aeroplanes.

So, a difference in mountain height of 1000 m would lead to a temperature drop of 9.8 ºC. Does this explain why coffee grows in the hills of Mexico at around 1000 m but the mountains of Columbia at around 1900 m? Not really. If you take the mountains of Columbia as an example, the average temperature at 1000 m is about 24ºC all year, but climb to 2000 m and the temperature only drops to 17-22ºC. How can we reconcile this with our calculation?

Firstly of course we have not considered microclimate and the heating effects of the sides or plateaus of the mountains together with the local weather patterns that will form in different regions of the world. But we have also missed something slightly more fundamental in our calculation, and something that will take us back to Erasmus Darwin: the air is not dry.

Specific heat is the amount of energy that is required to increase the temperature of a substance by one degree. Dry air has a different specific heat to that of air containing water vapour and so the adiabatic lapse rate (g/Cp) will be different. Additionally however we have Erasmus Darwin’s deduction from his ether: water vapour that condenses into water droplets will release heat. Condensing water vapour out of moist air will therefore affect the adiabatic lapse rate and, because there are now droplets of water in our air parcel, there will be clouds. When we calculate the temperature variation with height for water-saturated air, it is as low as 0.5 ºC/100 m (or 5 K/Km), more in keeping with the variations that we observe in the coffee growing regions†.

We have gone from having our head in the clouds and arrived back at our observations of evaporating liquids. It is fascinating what Erasmus Darwin was able to deduce about the way the world worked from what he noticed in his every-day life. Ideas that he could then either calculate, or experiment with to test. We have very varied lives and very varied approaches to coffee brewing. What will you notice? What will you deduce? How can you test it?

 

*ether could refer to a number of chemicals but given that Erasmus Darwin was a medical doctor, is it possible that the ether he refers to was the ether that is used as an anaesthetic?

†Though actually we still haven’t accounted for microclimate/weather patterns and so it is still very much a ‘rough’ calculation. The calculation would be far better tested by using weather balloons etc. as indeed it has been.

¹The calculation can be found in “Introduction to Atmospheric Physics”, David Andrews, Cambridge University Press

 

 

Stirring up some climate science

Everything is connected. At least, that is part of the premise of Bean Thinking, where the physics of a coffee cup is used to explore the physics of the wider world. So it was great to stumble upon a new connection that I had not previously appreciated¹.

vortices in coffee

Like the vortices behind a spoon dragged through coffee….

The connection is between climate science and that wonderful pastime of pulling a spoon through coffee and watching the vortices form behind it. Yet the research that revealed this connection was not looking for links between coffee and the atmosphere. Instead the researchers were interested in something seemingly (and hopefully) very far from a coffee cup: rogue waves.

Rogue waves are rare and extremely large waves that have been the subject of mariners tales for many years. Nonetheless, it is only relatively recently that they have become the subject of scientific research, partly because they are so rare and so outside our usual experience that they were thought to be the stuff of myth rather than of science. So it is only now that we are developing an understanding of how it can be that, in amongst a number of smaller waves, a massive wave of 20m height can suddenly appear, apparently out of nowhere. One of the groups looking at this problem investigated the effect of a particular sort of (known) instability on a series of waves in water. However, unlike other research groups, this particular study included the effect of the air above the water as well as the waves themselves.

Small waves seen from Lindisfarne

Rogue waves seem to come out of nowhere. A rogue wave can be 2 or 3 times the height of the other waves in the water at the time. How and why do they form?

Although this sounds a simple idea, modelling water waves in air is actually extremely complex. To do so, the authors of the study had to use a computer simulation of the air-water interface. It is not the sort of problem that can be solved analytically, instead the computer has to crunch through the numerical solutions. In order to start to see what was going on with the rogue waves, the authors had to simulate multiple waves of different amplitudes. Each simulation took weeks to perform. Given that this was only a few years ago (the study was published in 2013), you can start to see why people had previously been approximating water waves as waves in water (without worrying too much about the air interface).

Now here is where the link with coffee comes in. The group modelled waves as a function of steepness and found that, above a critical steepness, the wave breaking caused significant interaction between the air and the water layers. In addition to the bubbles that form when waves break, the movement of the air over the breaking wave formed into a vortex which, when it interacted with the back of the wave created an opposite vortex: a vortex dipole “much like the vortices that form behind a spoon dragged through a cup of coffee“.

Rayleigh Benard cells in clouds

The water droplets that form clouds are often ‘seeded’ by particles of salt or dust, such as the aerosols distributed by the vortices in this wave study. Image shows clouds above the Pacific. Image NASA image by Jeff Schmaltz, LANCE/EOSDIS Rapid Response

Just as with the vortices in the coffee cup, vortices were forming in the air behind the wave crest (which acted as the spoon) and travelled upwards through the atmosphere and away from the waves. As each wave broke, a train of vortex dipoles were produced that twirled off into the sky. Imagine a coffee bath and multiple spoons rather than a coffee cup. The authors suggested that these vortices could carry aerosols from the sea (salt, water droplets etc) into the atmosphere. Travelling within the vortices, these tiny particles could travel far further and far higher than we may have expected otherwise. Such aerosols can be critical for cloud formation and so the effect of these breaking waves could be important for climate modelling.

While an undergraduate, I had an opportunity to study a course in atmospheric physics. I remember the lecturer lamenting that while we (as a community, but not really as the students sitting in the lecture theatre at that time) understood atmospheric modelling quite well and that we understood how to model the oceans fairly well, we got problems when we tried to put the two sets of models together. It was clear that something wasn’t quite right. Years later, it seems that at least past of the reason for that is linked to those vortices that you see as you pull your spoon through your coffee cup.

Everything is connected indeed.

A summary of the study can be found here. The abstract (and link to the pdf) of the published paper can be found here. If you do not have access to the journal through a library, an early, but free, version of the paper is here – note though that this version may not include the amendments included after peer review.

 

¹A quote attributed to Jean-Baptiste Biot (1774-1862), is perhaps relevant here “Nothing is so easy to see than what has been found yesterday, and nothing more difficult than what will be found tomorrow.”

Coffee and Pluto

Three billion miles away, on an object formerly known as the planet Pluto (now sadly demoted to the dwarf planet Pluto), there exists a plain of polygonal cells 10-40 km across, extending over a region of about 1200 km diameter. Last year, the New Horizons mission photographed this region and these strange shapes (see photo) as the probe flew past Pluto and its moon Charon. But what could have caused them, and perhaps more importantly for this website, can we see the same thing closer to home and specifically in a cup of coffee? Well, the answer to those questions are yes and probably, so what on Earth is happening on Pluto?

Plutonian polygons

What is causing these strange polygons on the surface of Pluto. Image © NASA

Pluto moves in an highly elliptical orbit with an average distance to the Sun of 5.9 billion km (3.7 billion miles). Each Pluto year is 248 Earth years but one day on Pluto is only 6½ Earth days. As it is so far from the Sun, it is very cold on Pluto’s surface, somewhere between -238 to -218 ºC. The polygons that were photographed by New Horizons are in the ‘Sputnik Planum’ basin where the temperatures are at the lower end of that scale, somewhere around -238 ºC. At this temperature, nitrogen gas (which makes up 78% of the Earth’s own atmosphere) has not just liquified, it has solidified; turned into nitrogen ice. These polygons are made of solid nitrogen.

But solid nitrogen is a very odd type of solid and in fact, at the temperatures on Pluto’s surface, solid nitrogen is expected to flow with a very high viscosity (like an extremely gloopy liquid). And it is this fact that is the clue to the origin of the odd polygons (and the link to fluids like coffee). Pluto is not just a cold dead rock circling the Sun, but instead it has a warm interior, heated by the radioactive decay of elements in the rocks making up Pluto. This means that the base of the nitrogen ice in the Sputnik Planum basin is being heated and, as two groups writing earlier this summer in Nature showed, this leads to the nitrogen ice in the basin forming convection currents. The warmer nitrogen ‘ice’ at the bottom of the basin flows towards the surface forming convection patterns. It is these nitrogen convection cells that appear as the polygons on the surface of Pluto.

Rayleigh Benard cells in clouds

Rayleigh-Benard cells in cloud structures above the Pacific showing both closed and open cell structures. Image © NASA image by Jeff Schmaltz, LANCE/EOSDIS Rapid Response

Of course, convection occurs in coffee too, we can see it when we add milk to the coffee and watch the patterns form or by observing the dancing caustics in a cup of tea. So why is it that we see stable polygons of nitrogen on the surface of Pluto but not coffee polygons on the surface of our coffee? The first point to note is the time-scale. Although the polygons on Pluto are moving, they are doing so much more slowly than the liquid movement in a cup of tea or coffee, at a rate of only a few cm per year. But secondly, the type of convection may be different. Although both of the papers in Nature attributed the polygons on Pluto to convection, they differed in the type of convection that they considered was happening. McKinnon et al., suggest that the viscosity of the nitrogen on Pluto is much greater on the surface of the basin than in the warmer interior and so the surface flows far more slowly. This leads to cells that are much wider than they are deep. We would not expect such a drastic change in the viscosity of the coffee between the (cool) top and (warm) bottom of the cup! In contrast, Trowbridge et al., think that the cells are Rayleigh-Bénard convection cells,  circular convection cells that form such that the cells are as wide as they are deep. This sort of convection is seen in a coffee cup as well as in the sky on cloudy days: On the Earth, clouds often form at the top (or bottom) of Rayleigh-Benard cells, where hot humid air meets cold dry air (more info here). But to form cells that you can see in your coffee (such as are on the surface of Pluto) you would need the coffee to be in a fairly thin layer and heated from below. You would also need some way of visualising the cells, either with an infra-red camera or with powder suspended in the liquid, it would be hard I think to see it in coffee alone. However, you can see these cells in cooking oil as this video shows:

As well as providing the link to the coffee, the different types of convection on the surface of Pluto hypothesised by Trowbridge and McKinnon have consequences for our understanding of the geology of Pluto. If the cells are formed through Rayleigh-Bénard convection (Trowbridge), the basin has to be as deep as the cells are wide (meaning the basin has to be 10-40km deep with nitrogen ice). If McKinnon is correct on the other hand, the basin only needs to be 3-6 km deep. It is easy to imagine that an impact crater could cause a shallow crater such as that needed for McKinnon’s mechanism. A deeper crater would create another puzzle.

If you do manage to heat coffee (or tea) from below and form some lovely Rayleigh-Bénard cells while doing so I’d love to see the photos or video. Please do contact me either by email, Facebook or Twitter. Otherwise, if you just enjoy watching the patterns form on your coffee, it’s worth remembering that there could be an entire cosmos in that cup.

Clouds in my coffee

clouds over Lindisfarne

How do clouds form?

Does your coffee appear to steam more next to a polluted road than in the countryside?

This is a question that has been bothering me for some time. Perhaps it seems an odd question and maybe it is, but it is all about how clouds form. Maybe as you read this you can glance out the window where you will see blue skies and fluffy white clouds. Each cloud consists of millions, billions, of water droplets. Indeed, according to the Met Office, just one cubic metre of a cloud contains 1 hundred million water droplets. We know something about the size of these droplets because the clouds appear white which is due to the way that particles, including water droplets, scatter sunlight. Clouds appear white because the water droplets scatter the sunlight in all directions. In contrast, the particles in a cloudless sky scatter blue light (from the Sun) more than they scatter red. Consequently, from our viewpoint, the scattered light from the clouds appears white while the sky appears blue. The sort of directionless light scattering that comes from the clouds happens when the scattering sites (ie. the water droplets) are of a size that is comparable to, or larger than, the wavelength of light. This means that the water droplets in a cloud have to be larger than about 700 nm in diameter (or approximately just less than a tenth of the size of the smallest particle in an espresso grind). The particles in the atmosphere on the other hand scatter blue light more than they scatter red light because they are smaller than the wavelength of the blue light. You can find out more about light scattering, blue skies and cloudy days, with a simple experiment involving a glass of milk, more details can be found here.

glass of milk, sky, Mie scattering

A glass of (diluted) milk can provide clues as to the colours of the clouds in the sky as well as the sky itself

So each of the one hundred million water droplets in a cubic metre of cloud is at least about a micron in diameter. We can then estimate how many water molecules make up one droplet by dividing the mass of a droplet of this size by the mass of one water molecule. This turns out to be more than 1000 million water molecules that are needed to make up one droplet of cloud. So, 1000 million water molecules are needed for each of the 100 million drops that make up one, just one, cubic metre of cloud. These numbers are truly huge.

But can so many molecules just spontaneously form into so many water droplets? Unlike a snowball, the water droplet in a cloud cannot start very small and accumulate more water, getting larger and larger until it forms a droplet of about a micron in size. Water droplets that are much smaller than about a micron are unstable because the water molecules in the drop evaporate out of it before they get a chance to form into a cloud (precise details depend on the exact atmospheric conditions). Water droplets need to come ‘ready formed’ to make the clouds which seems unlikely. So how is it that clouds can form?

Condensation on mug in CGaF

Look carefully at the rim of the mug. Do you see the condensation?

It turns out that the water droplets form by the water condensing onto something in the atmosphere. That something could be dust, or salt or one of the many other sorts of aerosol that are floating around in our skies. Just as with a cold mug filled with hot coffee, the dust in the air gives the water molecules a cold surface onto which they can condense. This sort of water droplet can ‘snowball’ into the bigger droplets that form clouds because the water is now condensing onto something and so does not evaporate off again so easily. At the heart of each water droplet in a cloud is a bit of dust or a tiny crystal of salt. Which brings me back to my question. It is much more dusty along a polluted road  than it is in the clean air of the countryside. Is this going to be enough of an effect to affect the probability of cloud formation? Does your coffee steam more as you cross the road than when you walk through the park?

It is a question that demands an experiment (and associated video). Last year, the Met Office suggested this simple experiment for observing clouds in a bottle. Unfortunately however, I have yet to make this experiment work in a way that would allow me to test whether polluted air produces thicker clouds than cleaner air. If you have any suggestions as to a good experiment (that will work on camera!) please let me know either in the comments section, by emailing me, or on Facebook. In the meanwhile, I’d be interested to know what you think, so if you think this post is about you, please let me know.

 

 

Coffee & Contrails (I)

contrail, sunset

A set of criss-crossing contrails taken in the evening.

If you gaze up at the sky on a clear day, you will often see a few contrails tracing their way across the blue. Formed as a result of water in the atmosphere condensing onto exhaust particles from aeroplanes, contrails are a regular feature of the skies in our modern life. There are at least two ways that I can think of, in which the physics of the contrail is connected to the physics of the coffee cup, so, there will be two Daily Grind articles about them. This first one, about the physics of how we see them, and a second post (scheduled for 10th June) about interesting effects that we can see in them.

Perhaps now would be a good point to go and make a cup of coffee before coming back to this post. Make sure that you notice how the steam clouds form above the kettle spout as the water boils. Do you see the steam at the spout itself, or just a few centimetres above it? With the cup next to you, notice the steam rising above it. Does the steam seem more obvious on some days than others? For example, the coffee always seems to me to steam more on cold damp days in winter than on warm-ish days in late spring. Both of these observations (about where and when we see the steam clouds) are mirrored in the contrails, it’s time to take a closer look at the coffee.

V60 from Leyas

The clouds above a coffee cup are a rough indicator of the relative humidity.

The difference in the day to day visibility of the steam above the coffee cup is an indicator of the relative humidity of the atmosphere. If we prepare our cup of coffee on a day when the relative humidity is already high, adding that extra bit of water vapour from the cup leads to clouds of steam above the mug, as the water condenses into droplets of liquid water and forms clouds. If our coffee was instead prepared on a day with low relative humidity, the water vapour above the coffee cup is less likely to condense into clouds. Contrails are formed high in the atmosphere when the relative humidity is quite high. Exhaust particles from the engines of the plane offer a surface onto which the water in the surrounding (humid) atmosphere can condense to form clouds. We know that it is mostly the atmospheric moisture that is forming the contrails (rather than water from the exhaust itself) because of research done by NASA. In research flights, the amount of water vapour leaving the aeroplane engine was 1.7 grammes per metre of travel while the mass of water in the contrail was estimated to be between 20.7 and 41.2 kilograms per metre. This means that contrails can give a clue as to the weather: on dry days, contrails will not form because the water in the atmosphere is likely to remain a gas and therefore invisible to us, it is only when the air is already quite humid that contrails are likely to form and persist.

glass of milk, sky, Mie scattering

A glass of (diluted) milk can provide clues as to the colours of the clouds in the sky as well as the sky itself

Then there is the question of why we see them at all. Contrails appear as white clouds trailing behind the plane. We see them as white because of an optical effect caused by the size of the condensed droplets of water (actually ice) in the contrail. Objects appear as having different colours either as a result of light absorption by chemicals in the object (leaves are green because of chlorophyll) or as a result of light scattering from the object. A water droplet is colourless and so the colour we see coming from the droplet must be purely a consequence of light scattering rather than a light absorption effect. Clouds appear white because the water droplets within the cloud are as large, or larger than, the wavelength of visible light (0.7 μm). Droplets this size will scatter all wavelengths of visible light and so appear white. If the droplets were much smaller than the wavelength of light they would scatter different wavelengths by different amounts. It is because the atmosphere is full of such tiny particles (and molecules) that blue light is scattered more than red light in the atmosphere and so the sky appears blue to us from our vantage point on the Earth’s surface. Milk is composed of large fat droplets (which will scatter a white light) and smaller molecules which will preferentially scatter blue light, just as the sky. This is why you can mimic the colours of the sky in a glass of milk. It is because the water droplets have formed a few cm above the kettle spout that you can see them scattering the light. For exactly the same reason, the contrails in the sky appear as white clouds.

contrails

A hot air balloon in a sky full of contrails

Contrails can persist in the sky for anything from a few minutes to a few days. Just like clouds, contrails affect the way that light (and heat) is reflected from the Sun or back towards the Earth. However, unlike normal clouds they are entirely man-made, another factor that could have an unknown effect on our climate. A few years ago, a volcano eruption in Iceland caused the closure of UK airspace (as well as the airspace of much of Europe). I remember being in the queue to buy a cup of coffee in the physics department and hearing the excited conversation of two atmospheric physicists behind me. For the first time they were able to study some particular atmospheric effects without the influence of any contrails. In effect they could start to understand the influence of contrails by this unique opportunity of taking measurements during their absence. What was a major pain in the neck for so many travellers in 2010 meant a lot of extra (but presumably very interesting) work for them.

Coffee & Contrails (II), on 10 June 2015, will be about the structures you can sometimes see within the contrail. If you can think of any other connections between coffee and contrails (or coffee and clouds) why not let us know in the comments section below.