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Posts Tagged ‘Orders of magnitude in weather’

Why does humid air rise?

How can the addition of water vapor make it lighter? When I take a dishrag and wet it, it gets heavier; how can I take a parcel of air, add water, and thereby make it lighter? This is all nonsense!

(I suppose this lesson should have come before the one about phase change, but better late than never.)

Yes, if you add liquid water to a parcel of air it will be heavier, but humidity is not about liquid water; it is about water vapor. We confuse the two because a fog is obviously heavy and since the droplets in fog are so small as to be invisible, we think of them as vapor. This is an understandable mistake; we can’t see fog droplets and we understand that the air is saturated in a fog, so we think that the fog is the vapor. Besides, in poetry, fog is called vapor.

But for scientific purposes, (and in sci-speak) vapor has a specific meaning; and fog is not vapor.

Fog and cloud droplets, for all that they are very small, are enormous compared to a molecule of water – and true water vapor means water floating in molecular form. Fog forms when saturated air cools and some of the water condenses. The remaining air is still saturated, and would be so even if you took away all the water droplets. The saturation is about vapor, not about droplets, however tiny.

How big is a water molecule?

Can a water molecule really be much smaller than a cloud droplet?

If the water droplets of an evaporating fog are a few 1/100ths of a millimeter wide, they are still a good five orders of magnitude larger than a molecule of water which is a few Ångstroms wide. Five orders of magnitude… That means like the difference between a softball and a city; the difference between a single grain of dandelion pollen and your kitchen table; between a beetle and a freight train, between a kitten and a thunderhead. The difference is simply enormous.

Look closely at the steam coming out of your teapot. Notice that right by the spout, the steam is invisible. An inch or two away, it is white. Right out of the spout, it is vapor; a short distance away, it has condensed into tiny droplets.

Avogadro:

Now that we have an idea of what we mean by humid air – air full of water vapor – we can say something else which we learned from the research of a fellow named Avogadro and those who followed his lead; it is this:

Every parcel of gas, every volume of gas, holds the exact same number of molecules, no matter what kind of molecules they are. Well, that’s not quite right: of course a gas that is hotter expands and has fewer molecules in a specific volume; or a gas can have a wrapping around it such as a balloon and be squashed so more molecules fit into a specific volume. But if we have an imaginary box of gas of any precise size, then every other box of that size that has the same temperature and the same pressure has the same number of molecules, and it doesn’t matter whether the molecules are water, oxygen, nitrogen, carbon dioxide, or even much larger molecules such as vanillin or cinnamaldehyde. It will always be the same total number of molecules if the box size, the temperature, and the pressure are the same.

We don’t imagine this would be true, because we think of atoms and molecules as balls of different sizes, and we would certainly not get as many beach balls as we would marbles into any box. But the point about gases is that they are balls in motion, all banging against each other and bouncing away, and – this is the crucial point – the little ones move faster. Of course they move faster. Wouldn’t you move faster if a bear bumped into you as opposed to a rabbit or a fly? Because the little ones move faster, they effectively take up as much room as the big ones that move more slowly, and the sum of it is that a given volume of gas always has the same number of molecules. Some may be little speeding molecules that would condense into something quite small; others may be big galumphing ones that would condense into something moderately large. But if you count them, the number is the same.

And if you have 22.4 liters of cold gas down by the sea, you have precisely 6.02 x 1023 molecules in your box. That’s a famous number, called Avogadro’s number, and you can ask your chemistry teacher why they chose 22.4 liters instead of something more obvious. (There is always an interesting reason for such things.)

But always having the same number of molecules means that some gases are heavier than others. The heavy gases don’t take up any more room; they are just heavier. It follows that they are more gravity-challenged; they fall while others rise.

Saturated air rises:

So let us get back to the air with its water vapor. When water vapor gets mixed into the air, the oxygen and nitrogen have to move over to make room because only 6,02 x 1023 bits can fit into the box; ultimately, when you are out-of-doors, the gases move up, because all the space around is already filled with oxygen, nitrogen, argon, and the other components of air, and “up” is the only place where there is more room. But the water molecule is actually lighter than the oxygen molecule and also lighter than the nitrogen molecule.

Some airy weights:

Basically, you get the weight of a molecule by counting the protons and neutrons in its atoms:

That makes O2 have a weight of 16 + 16 = 32

It makes N2 have a weight of 14 + 14 = 28

Carbon dioxide (CO2) has a weight of 12 + 16 + 16 = 44

Argon is an atom that has a weight close to 40

Finally, water H2O has have a weight of 1 + 1 + 16 = 18

See how light the water is? It is amazing that it doesn’t float away altogether and become lost in space.

Anyway, you can see that a box of gas that is part water vapor will be lighter than one that is only oxygen and nitrogen. So it will rise.

In conclusion

When people talk about dry air soaking up water like a sponge, then, it’s not really like a sponge that gets heavier as it soaks up water. It’s more like potting soil that gets lighter (per cubic foot) as you add Styrofoam (or whatever that white stuff is).  So saturated air – air holding all the water vapor it can – naturally rises.

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So we’ve gone down-size and up-size looking at the sizes of things that produce weather effects on Earth. Now let’s get larger again:

[5] Weather forms in the 60-mile (or 100 km) range include such things as:

  • Simple roll clouds such as we often see crossing the sky. When the sky is too full of clouds to allow free convection up the center of each cloud and down the outside, the clouds combine in long sausage-type rolls which can cross the entire sky, visible for a distance of 60-80 miles. Convection takes air up one one side of the roll and down the other.
  • Lakes such as the Finger Lakes of New York State lie in this size range and definitely affect the weather nearby since tbey produce clouds differently from land, many times bringing rain and snow to lakeside areas.
  • New Zealand has a Maori name that means “land of the long white cloud.” Undoubtedly the first men to arrive in New Zealand from the Micronesian islands to the west found this island because, long before they could see it over the horizon, they could see the clouds that formed above its hills and mountains.

[6] Are there single weather forms in the size range of 1,000 miles?

  • Of course! Hurricanes by whatever name — cyclones or typhoons. These are generally at least a few hundred miles wide, and they can grow to over 1000 miles across.
  • Besides that, the segments of jet stream wind that are over 60 miles an hour are often in the range of 1000 miles across. If you remember that the US is 3,000 miles across, you can readily recognize this size range in the jet stream images.
  • The Sahara desert, 1000 from north to south and three times that from east to west, is the birthplace of the winds that become hurricanes as they cross the Atlantic.
  • The Sahara and other large deserts mark the meeting place of Hadley and Ferrel cells, of which see more below.
  • The Moon, which pulls the tides and in turn gives an impetus to coastal weather, is in this size range.

[7] Our home planet, Earth, is about 8,000 miles in diameter on the large end of the seventh size range (the seventh order of magnitude) which is centered on 6,000 miles.

  • Six massive circulation cells encircle the globe — The northern and southern Hadley cells starting near the equator, the northern and southern Ferrell cells in the middle latitudes, north and south, and the two Polar cells.
  • Between the Polar and Ferrell cells, the world-encircling jet stream journeys on its sinuous path.
  • Of course the oceans fill the atmosphere with the water needed for rain and snow, so they are part of weather.

[8] The size range of our larger neighbor Jupiter is around ten times that of Earth.

  • I don’t suppose you imagine that Jupiter affects our weather, but it might; at least it might have. Because of its large size, it attracts various objects as they enter the solar system, and along with Saturn it protects Earth from most potential invasions by comets and things. When comets do get here, it’s pretty explosive; dust gets into the atmosphere, and clouds and rain follow.It would be fair to say that Jupiter affects the weather by protecting us from more explosive visitations from outer space.
  • But we don’t have to go to Jupiter to find things ten times the size of Earth, for our own magnetic field, particularly as expressed by the Van Allen Belts, is in this size range. The Aurora Borealis is one expression of this belt.
  • Solar flares are in this size range, and seem to be responsible for the massive “winds” of ionized particles that visit Earth when there are sunspots. These not only cause auroras, but the new supply of ionized particles help seed rain clouds. Times of more sunspots and therefore of more flares seem to be related (historically) to warmer times on earth.

[9] The ninth order of magnitude is 100 times the diameter of our earthly home. Nothing that big affects us, right?

  • Except the sun. That’s a weather producer; that’s the weather producer. It builds the Hadley and other major wind cells, evaporates the oceans, heats the deserts, shifts air back and forth between water and land; the sun does everything to keep air and water in motion, and that’s what weather is.

It’s strange to think that such large and distant objects are concerned in the weather in your back yard; do you suppose that anything larger, or from the farther reaches of the universe, affects Earthly weather?

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In the post about the size of a raindrop, we began a consideration of the magnitudes of the objects studied in meteorology. Today we continue, but we are going the opposite direction — not down to the objects smaller than a raindrop, but upwards in size, through some of the cloud forms.
Just to get oriented, we begin once more with [0] — the consideration of things that are one meter or so in length, width, or height. We might have said: anything from 1/3 or a meter to 3 meters or so. A child, a young scientist, standing in a puddle with an umbrella wondering whether he will be the lucky one to find a weather balloon would be a display of some weather objects in this size range.
When I was in college, I used to ride a bike to Mass in the morning in Florida, and there would be miniature fogs about 4 feet off the ground, and just a few feet wide. I’ve never seen that sort of fog body since.
Tendrils of sea smoke can be in this size range, possibly smaller.

[1] Ten meters is the next size range: about the size of a house or a mature maple tree.

  • Let us consider that right above our young meteorologist, the smallest of the fair weather clouds are barely beginning to form. They form, float away from their sources, and quickly die.
  • But on a different kind of day, only the curled edges of a cloud would be in the size range of his house, though they seem smaller because of their distance.
  • Before the sky is entirely caught into gray sheets, a few small gray shreds still float by at the size of small establishments such as houses, stores, and small yards. Because of the immense distance of the sun, its rays arrive on earth so close to parallel that as long as there is some sun, our meteorologist can verify the sizes of small clouds by the sizes of their shadows.
  • Little drifts of fog form in the evening near creeks or low places in a field.
  • Widths of tornadoes are generally in this size range.
  • Typical waterspouts are here.

[2] But as weather systems build, 100 meter items, the size of football fields, quickly turn up.

  • Small clouds are readily incorporated into larger ones.
  • If it’s evening, gathering fogs are likely to appear in small valleys and fields, or to wind along creeks for great distances.
  • In the tree-covered mountains of New England, roads may be marked after a summer rain because the mist rises above their hot pavements.
  • This is the usual tornado diameter.
  • Destructive waterspouts can be in this size range, though their sizes very quite a bit. Here’s a list of historic and destructive waterspouts.
    • All of us have seen the little whirlwinds of snow that sculpt our drifts all winter. But snonados can get a little larger. Here’s an interesting view from You tube, just by way of reminding us that the physics of the wind is the same everywhere. It’s what heat adds to it that makes the most intense forms of weather. Never much heat in a snowdrift.

    [3] Here we are at 1000 meters, one kilometer.

    • Low, fair-weather cloud heights might be as little as a kilometer.
    • As the sky fills, many cloud-bases will be one or a few kilometers above the ground.
    • A cumulus congestus is likely to be a kilometer wide and high.
    • Larger clouds come in many shapes and at many heights. It’s hard to judge the width of a cloud, but you can learn to do it. When you drive along, notice how far you have to drive to actually pass a cloud. Bring your cloud viewers in the car and watch the odometer — don’t do this when you’re the driver, of course. In time, you’ll get used to what you are seeing.
    • In the tree-covered mountains of New England, roads may be marked after a summer rain because the mist rises above their hot pavements and hovers above the treetops.
    • The pannus clouds that form on the front end of a storm are only as deep as a field or two but may roil along in lines that are a few kilometers long.

    [4] What features of weather are 6 miles tall, wide, or long? This is about 10 kilometers?

  • Cumulonimbus clouds with their anvil tops can be 3 miles or more in height, (not counting rom the ground, but from the base of the cloud) so they belong to this order of size. (order of magnitude, right?).
  • Since they already begin a mile or two up in the atmosphere thunderheads may reach to the top of the troposphere, that 6-10 mile veneer of atmosphere which covers the earth and houses most of our weather.
  • An average storm cell consists of a cumulonimbus cloud and a few of its associates moving in. When an entire front moves in, the storm cells are spaced a few miles apart because they are pulling in the air from some distance around.
  • Of course there are many other such objects that might have been listed. If I left out your favorite, drop me a line.  We’ll extend the size range next time. Meantime, ask yourself, what is the largest object you can think of which makes a contribution to weather on Earth? And what is the smallest?

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