Convection and Weather

This morning I guided the upper-graders at Peregrine School through a
set of weather-related activities.

First, we reviewed what we had learned previously about energy in the
Earth-Sun system.  Briefly, although the Earth's core is very hot and
slowly cooling off due to heat flowing outward through the surface,
the vast majority of heat that we experience comes from the Sun.  How
could we figure that out from everyday observations? Julia nailed it:
the surface temperature varies quite a bit from pole to equator and
from day to night, which is indicative of the Sun rather than of a
constant flow of heat outward in all directions from the Earth's core.
We also reviewed how the Sun heats the ground, not the air (because
air is transparent to visible light); air near the ground is heated by
the ground and that heat then gets mixed throughout the atmosphere.
Whenever something is heated from the bottom, as our atmosphere is,
you get convection (one of the three forms of heat transport we had
discussed earlier).

Convection is the reason we have weather. Hot air rises, cool air
sinks, and so air is always in motion.  To assess the solidity of
their understanding of convection, I immersed a shot-glass full of hot
water (dyed red) into a big container of cool water (dyed ever so
slightly yellow to provide contrast), but first, I asked them to make
predictions about what would happen.  This is a really nice, really
simple experiment or demo.  You can see the hot fluid rising in wisps;
eventually all the red collects on the top half of the large
container.  But the true test of understanding is predicting what
happens when I immerse a shot-glass full of cool water into a big
container of warm water.  The kids showed a good understanding by
predicting that the cool water would not rise at all, and just stay in
the shot-glass (and the bit of cool water which might spill in the
process of setting the shot glass down in the large container would
also settle on the bottom of the large container).  In weather, this
is called an inversion: if cold air gets under a layer of warm air, it
is trapped there, and among other things air pollution can build up in
a city where there's an inversion. (The Wikipedia article on inversion
has some decent pictures, and a Google image search on "weather
inversion" also yields some nice pics.)

Convection transports heat in the oceans as well as in the atmosphere.
There are ocean currents which circulate warm equatorial water toward
northern regions and bring cold water from the north back down toward
the equator to get warmed up again.  The sea off California's coast is
rather cold because the current here comes from Alaska.

But the takeaway message of this part of the day (which took probably
only 20-25 minutes) is that the Sun provides the energy for moving air
around, which makes weather happen.  Because of the way the Sun's
energy hits Earth, hot air must rise from equatorial regions and cold
air must sink near the poles.  But the only way for this to be
sustainable is with a "conveyor belt": hot air which rises from
equatorial regions moves toward the poles, where it cools, sinks, and
moves along the surface back toward the equator.  This creates wind
and weather patterns.  Our next activity was designed to add more
nuance to this general idea.

Before proceeding to the next activity, I presented the class with a
lava lamp for long-term loan.  This will constantly remind them of
convection even when I'm not there!

Climate Change

Yesterday we tied together California (Grade 6) Science Standards 6
(resources), 3 (Heat), and 4 (Energy in the Earth System).  We'd
already done quite a bit of 3 and 4, so we started with a discussion
of resources.  The consequences of using resources (6a) led naturally to
the greenhouse effect, which builds on our previous understanding of
heat flow in the Earth-Sun system.  We had previously calculated a
rough temperature that Earth "should" be at, ie the stable temperature
at which Earth should radiate just as much heat into space (in the
form of infrared light) as it gets from the Sun (mostly in the form of
visible light).  This temperature was just below freezing, and it
turns out that a natural greenhouse effect makes Earth livable.

We started with this video, which is a nice short demo of how carbon
dioxide absorbs infrared light.  C02 is by no means the only
greenhouse gas; water vapor is also very important, and methane
absorbs much more infrared light on a gram-for-gram basis, but there
is not enough methane in the atmosphere to make it the most important
greenhouse gas overall.  We also watched a short clip of another
video, which demonstrated how the temperature of a bottle of carbon
dioxide increased more than a bottle of air when both were heated by a
lamp.  This latter experiment requires only basic equipment and a
teacher might consider having the kids do the experiment, but I
suspect the experiment could be finicky in real life: you will have to
make sure there are no leaks in the C02 bottle, etc.

The kids were ahead of me on this one. They had already made the leap
to climate change, but I wanted to do at least a quick review to fill
in the logic.  The atmosphere is basically transparent to visible
light, the form in which we get energy from the Sun; if it's not
transparent to infrared light, the form in which Earth gets rid of its
heat, then Earth must heat up.  As stated above, we need a certain
amount of natural greenhouse effect to avoid freezing over, but there
can be too much of a good thing.  We spent the rest of the time in
small groups, playing with a computer simulation of all this. This
simulation is really good, so I encourage you to click Run Now (it
takes a minute to load and start).  You can adjust the level of
greenhouse gases from none (to see our previous calculation in action)
to lots.  As I circulated around the groups, we discussed the effect
of clouds (keep us cooler during the day but warmer at night) vs
greenhouse gases (always keep us warmer).  We also looked at the
Photon Absorption tab, which shows what's going on microscopically.
You can shoot visible or infrared photons (the smallest unit of light)
at a variety of molecules to see which are greenhouse gases.  In the
main (Greenhouse Effect) tab, the view is too zoomed out to see what
the photons are interacting with when they bounce around.  This was a
successful activity: students learned something as they explored, and
some students worked into their recess break to finish answering the
questions on the worksheet.

(Maven alert: it's common to say that greenhouse gases "trap" heat,
but this is not technically correct. It's more accurate to say that
they impede the flow of energy.  I didn't correct the kids when they
said "trap", but teachers should be aware of this.  Saying "trap" as a
teacher leaves you open to refutation.)

After the recess break, we discussed feedback loops and the
physics/engineering definition of positive and negative feedback
(which have nothing to do with psychological concepts such as negative
reinforcement or positive attitude).  I asked them to classify 11
different situations as positive or negative feedback (eg, foxes
provide negative feedback on the rabbit population), and they did very
well, so the concept is possibly less challenging than I imagined.  We
briefly discussed how confusing it is to have delayed feedback (eg
Alice says something to Bob and three days later he raises his voice).
Psychological experiments have shown that when feedback is delayed a
long time, people get very confused as to what causes what: they think
their actions have no effect, or the opposite effect.  (For more on
this, I recommend the book The Logic of Failure.)

So it is with climate change.  Scientists knew of CO2's heat
"trapping" properties more than a century ago and predicted rising
temperatures as we dumped more CO2 into the atmosphere, but it takes
so long for the heat to build up that it's easy to ignore.  By the
time we really see the temperature rise in a very convincing way, we
have dumped so much C02 into the atmosphere that temperatures will
rise much more even if we take immediate action.  Compounding this is
variability: if you just pay attention to the temperatures in your
neighborhood, there is so much variability from day to day and season
to season that it's impossible to notice a change in the average
temperature.  To see the change, you have to average together many
thousands of temperature measurements.

Even after getting people to accept that line of reasoning, they will be
unimpressed by the global average change so far: 1.4 degrees Fahrenheit.
What's a degree or two between friends?  But the change has been much
larger in some regions (the Arctic) and even 1.4 degrees results in a lot of
dislocation and expense: species have to adjust their ranges all over the world,
malaria may be able to move further from tropical regions, etc.  Won't Canada
and the northern US be happy to be a little bit warmer? Maybe, but it's not that
simple. Rain patterns may shift, so farmers in Canada may not be so happy after
all.  And northern forests are being destroyed at a rapid rate now that certain
kinds of beetles can survive the winter further north; beetles are mobile, but trees
are not, and the northern trees will be destroyed before they have time to
adapt to the beetle.  And areas which do gain from climate change may
be overrun with refugees from areas which lose big-time.

Anyway, the delayed-feedback idea led into the carbon cycle.  Over
tens of thousands of years the carbon cycle will remove excess carbon
from the atmosphere, so the Earth will not get hotter without limit
(thus answering an earlier question from a student). 

Our final activity was looking at this interactive flood map.  Seas
rise because the ocean heats up and expands (a very slow process) and
because of melting glaciers (not as slow, but still not easy to
predict).  The standard prediction for the year 2100 (when these
students will be old, but quite possibly still alive) is about 1 meter
of sea level rise, so I asked the students to dial in 1 meter and
answer a few questions about impacts on their house and on nearby
areas.  But the slowness of the ocean expansion means that the impact
of the current amount of carbon is further down the road, and has been
estimated to be 21 meters.  So I asked the students to dial in 21
meters and answer a few more questions.  This was another successful
activity combining student exploration with learning; I urge readers
of this blog to try the interactive flood map as well. Twenty-one
meters seems insane, so some kids need to be reassured that it will be
slow, over hundreds of years and perhaps a thousand years, so people
will have time to evacuate and adjust.  Still, evacuation and
adjustment are costly financially and emotionally so it may be better
to prevent the need for so much evacuation and adjustment in the first
place.

I didn't have time for a few things I wanted to show, but I can link to them here.
First, a quick Google image search for "glacier comparison" shows how fast most
glaciers are melting.  It is astounding*.  Second 30 seconds from this story about the
documentary Chasing Ice provide another dramatic look at glacier melting. (Sorry,
you will probably have to watch an ad to see this, but I couldn't find a better link.)

P.S.: Another important point for teachers of this subject is to emphasize that
"global warming" doesn't mean "every part of the Earth warms all of the time."
There is a model behind the predictions, a model with moving parts which affect
each other so that the predictions are richer than a novice imagines. For example,
a warmer atmosphere will also be a more humid atmosphere, so many areas will
get more precipitation and more intense storms.  If you live in a place where it's
cool enough to snow occasionally, then yes, global warming predicts that you can
get more snow.  People who think a big snowstorm contradicts predictions of
climate models simply haven't taken the time to get familiar with what climate
models really predict.  A scientific model should make a rich set of nuanced
predictions: that makes it easier to set up stringent experimental tests of the model.
This nuance does mean that scientists must work harder to educate the public.  If
any scientists are reading this, I plead with you to put in that hard work.  Society
needs you.

*Climate change deniers have recently made a big deal about a study showing that glaciers in some parts of the Himalayas are actually growing.  Note the qualified phrase "some parts of the Himalayas."  This is NOT what's happening to most glaciers around the world.  As noted above, climate change may have some "winners" as well as losers.  But I doubt the "winners" will feel very secure with so much dislocation in the world.

Heat, Earth, and Sun

Friday I started earth science with the 5-7 graders at Peregrine
School. We started half an hour late because of the all-school
discussion of the meteor strike over Russia.  So I squeezed a lot into
35 minutes before a shortened recess break.  We reviewed the structure
of the Earth and then we talked about the three different ways heat
flows: conduction, convection, and radiation (which in this context is
just another word for light; it does not mean ionizing radiation,
which is what you need to protect your DNA from).  I brought a torch
and a saucepan to make the discussion of conduction more concrete:
cookware designers want the bottom to conduct heat very well so that
the food is heated evenly, but they want the handle to conduct heat
poorly so that you don't burn yourself.  Then I added water to segue
to convection.  Because hot fluids rise, convection occurs whenever a
fluid is heated from below, which occurs in very diverse contexts:
boiling water on the stove, fluid rock in Earth's mantle, and the
movement of air in the atmosphere.

Next, I drew a Sun far from our diagram of Earth, and I asked how heat
gets from the Sun to the Earth.  It can't be conduction or convection,
because empty space can't do either of these.  It's radiation (light).
So we observed thermal radiation (the light emitted by an object by
virtue of its temperature), noting the brightness and color of a light
bulb at different temperatures (achieved by changing the voltage).  We
analyzed the color in detail by looking through diffraction gratings
to make rainbows from the white light, and noting which color in the
rainbow was brightest.  The pattern that emerges is: raising the
temperature makes the light bluer, and makes it much brighter.  We
think of red hot as being about the hottest temperature we ever
encounter, but really white hot is even hotter (the light is a mixture
of red, green, and blue), and blue hot is even hotter than that.  (The
ocean and sky are blue because they scatter the blue light from the
Sun, not because they are emitting light.)  Even objects at room
temperature emit thermal radiation, but that light is "redder than
red" or infrared.  These kids had played with an infrared camera
before, so I didn't bring one, but we discussed their IR camera
experience in this new light.  (Read this post to get the basics of
the IR camera experience.)

The last point I made before recess break: Earth's temperature is a
balance between the energy it gets from the Sun and the energy
(infrared light) it emits into space.  To maintain a roughly stable
temperature, it must emit as much as it gets.  We would examine that
balance in more detail after the break.  During the break, I had a
trick to keep them thinking about this subject: I brought a parabolic
mirror, pointed it at the Sun, and we entertained ourselves setting
things on fire.

After the break, before moving on, I felt they needed more practice with
conduction, convection, and radiation, so I had them work in groups to design
thermoses.  We put together ideas from the different groups to arrive at a
consensus design which minimizes conduction, convection, and radiation.

Back to the main thread: I noted how the parabolic mirror gathered energy from
the Sun over a largish area and concentrated it on a small area.  If we
measured the power (energy per second) falling over one square meter
(about twice the area of the mirror), we would find that it's about
one kilowatt, or 1 kW.  I brought a 1 kW hair dryer to make that more
concrete.  We then talked about night vs day, and how the Sun is
fairly low in the sky during part of the day, and concluded that the
average power from the Sun on 1 square meter of Earth would be more
like 300 W.  So each square meter of Earth should emit about 300 W of
infrared light in order to maintain a stable temperature.

Recall that power emitted ("brightness") increases strongly as the
temperature of an object increases.  So if the temperature of that
square meter of Earth is low, it will emit less than it absorbs, and
that will raise its temperature.  But if the temperature goes up very
high, it will emit more than it absorbs, and the temp will come down.
We ought to be able to calculate the temp which is just right so that
it emits exactly 300 W.  This is where we returned to the computer
programming that the kids are loving so much.  Most of these kids are
not familiar with algebra, but they can (with lots of guidance from
me) write a loop over a range of plausible temperatures and print out
the power emitted at each temperature.

To do this, I had to give them the equation for power (in watts)
emitted as a function of temperature: 0.0000000567 T⁴, where T is in
Kelvins.  That led to a discussion of Fahrenheit vs Celsius vs Kelvin.
Fahrenheit is defined so that water freezes at 32 degrees and boils at
212, a 180-degree difference; Celsius is defined so that water freezes
at 0 degrees and boils at 100.  Therefore, each Celsius degree is
"bigger" by 180/100 or 9/5.  Therefore Fahrenheit = 9/5 Celsius + 32.
Kelvin = Celsius + 273 (I explained about absolute zero), so
Fahrenheit = 9/5 (Kelvin-273) + 32.  Admittedly, most students didn't
follow all these steps, but at least one did, and I told the others to
just use this to convert while focusing on the logical steps needed to
carry out their program.

So each group wrote a Python script to check from 1 to 1000 Kelvins,
at each step printing out the power emitted and the Fahrenheit
temperature.  It turns out that 26 F is the right temperature for 300
W.  Is this a reasonable answer?  We discussed the approximations
involved (primarily albedo, using snow as an example).  Then we tried
representing this information graphically.  Instead of scanning a list
of numbers to find the right temperature, I taught them how to make a
graph of power emitted vs temperature.  We then added a horizontal
line at 300 W, and the temp at which the line intersects the curve is
the "right" temp.  I really want to work on graph-making and
-interpreting skills, so we discussed the labels we should put on each
axis, and how to summarize the plot in words.

As a teaser for next week, a slightly more rigorous calculation shows
that Earth's global average temperature should be even colder than 26
F.  The reason we are not in fact that cold is that our atmosphere
intercepts some of the outgoing infrared light and turns it back to
the surface: the greenhouse effect.  There is a natural greenhouse
effect which makes our planet livable.  The kids had of course heard
of the greenhouse effect and global warming, so they were able to see
right away that the problem is not the greenhouse effect per se; it is
that we are adding to the natural greenhouse effect, resulting in too
much of a good thing.  More on that next week.

The original plot we made:

and a zoom in to the important part: