02 February 2010

Snowflakes and climate






jg said...

This is a delightful anology, but the image will be hard to share with others here in Southern California who haven't seen it snow. However, I have seen mist droplets do the same thing.

Penguindreams said...


Yes, mist droplets. Also ash and sparks rising from a bonfire or forest fire. Or, go down to a river and watch bubbles eddy around. Although in each case there is a normal flow, you will also see some of the ash, sparks, bubbles, droplets, ... moving opposite to the main flow.

Mike Coombes said...

Can I offer another analogy? I came up with this when reading various blogs lamenting how people read too much into short term trends.

This analogy is on temperature trends. Imagine the earth as a bathtub with the level of the water standing in for the average global temperature. There is a faucet and drain that you can't see. The faucet may be open different amounts or closed. The drain may be open different amounts or closed. If you want to see whether the faucet or drain has the bigger effect (warming or cooling), stick an upright ruler in the tub and measure the height versus time. The trend will be obvious over a short time.

Now stick a small splashing child in the tub (the child is the internal variability of the system). Now you will see ups and downs that have no bearing on the whether the drain or faucet is the main effect on water level. However given sufficient time, the effect of the child should average out to zero and you can tease out the trend as you showed with previous posts.

Anonymous said...

I was thinking about climate, temperature, choas and variability and came up with a rather different analogy.

Think of a lake, the mean level of the lake is controlled by the equilibrium of water flowing in versus water flowing out. Snow melt or storm will temporarily raise the level of the lake. Block the outlet, and the level rises. The flow of water through the lake may or may not be chaotic, waves an currents within the lake are almost certainly chaotic. The mean level of the lake is not chaotic, it is dependent only on the inflow and outflow.

So is climate chaotic, maybe. Is the earths mean temperature chaotic, no. It depends what you are measuring Climate is in some ways not a precise enough term to answer the question. Temperature is a different matter.

Kooiti MASUDA said...

Incidentally we had a fairly hard snow too around Tokyo yesterday.

It reminded me of a story I wrote before
which seems to be somewhat related to yours, if not directly.

Certainly Nakaya also wrote essays about actual behavior of falling snow crystals, but unfortunately I cannot give examples now.

Penguindreams said...

Nice picture.

I'm not sure I agree about the lake levels, etc.. The thing is, in order to decide whether something is chaotic or not, you need to understand that specific system, and do so carefully. A different issue is that something can be chaotic (the earth's orbit is) but still be pretty well-behaved (as the earth's orbit is).

For climate, I'm not sure whether global mean temperature is chaotic or not. And if it's chaotic, I'm not sure whether it's of the well-behave sort (like the earth's orbit) or the badly-behaved sort (like weather).

Thank you for the story about Nakaya. I encountered his work on ice crystals when I was studying cloud physics. I've always liked the idea of being able to catch ice crystals on my coat sleeve and be able to tell what the conditions are in the part of the cloud they came from. The Panda's Thumb has a nice rendition of the Nakaya diagram and some comments on more recent work.

Anonymous said...


In general systems require some level of feedback to be chaotic. This occurs in gravitational mechanics, or fluid flows or even flocks of birds.

I can't see any feedback in the Earth "energy in" v "energy out" balance. I'm not even sure it would really qualify as a non-linear system.

Penguindreams said...

Energy in vs. energy out is entirely capable of producing chaos. In fact, if you go to the source paper on meteorological chaos (Lorenz, 1963 in Tellus), you'll discover that what we now know of as the Lorenz oscillator was derived by looking at exactly that. More specifically, it was a simplified model of convection -- where heat is coming in at the bottom and leaving at the top of a layer of fluid.

You can see a breakdown to chaos on a stove top. Put a thin, few mm, layer of cooking oil on a pan. Then put pan on a stove at low heat. It works best with a silvery pan (as opposed to cast iron or other dark surfaces) because you can see the fluid motion better. At a very low heat, you'll see a regular pattern of cells. Turn the heat up more, and it breaks down -- chaotically.

Coming back to the original post ... if you look more carefully, you'll see that in terms of area, most of the fluid is moving upwards. Since you can't have all the oil leap out of the pot, some moves down too. But in terms of area, these sinking plumes are small. Again, most of the fluid, most of the time is doing what we expect (climate). But some is flowing against our expectation (weather over-riding the climate tendency)