GG 140: The Atmosphere, the Ocean, and Environmental Change

Lecture 13.?Global Climate and the Coriolis Force

https://oyc.yale.edu/geology-and-geophysics/gg-140/lecture-13

Three-Cell Circulation Model of the Earth’s Atmosphere [00:00:00]

We're talking about the general circulation of the atmosphere. In its most basic form, you're just putting more heat in near the equator, and taking more heat out near the pole, and the differential heating causes a circulation.?But the nature of that circulation becomes rather complicated because?of the spherical geometry of the Earth, the fact that the Earth is spinning, which distributes the solar heat pretty well zonally around the equator, but then the other big thing is the Coriolis force. We're going to be talking about Coriolis force today in some detail.

Now of these three cells, the one that is the easiest to see, in day to day weather, in satellite images, is the Hadley cell. So if you're not going to memorize everything on this, be sure you know the Hadley cell. That represents the rising air near the equator, poleward air moving aloft, and then sinking and then returning towards the equator at the surface of the earth in a kind of a symmetric way around the equator. It's a double kind of a circulation pattern driven by the excess heat put in from the sun along the equator.?

The Ferrel cell is less easy to see in the data, and so is the Polar cell, but what's easy to see are these westerlies. Here you have easterly flow near the surface, here westerlies, and we'll talk about that, as well as this being the belt of storms, which I'll define for you in just a moment.

Geostationary Satellite Images of Clouds [00:02:28]

There are several satellites in orbit of a type called geostationary satellites. If you put a satellite in orbit, approximately this far from Earth, about 42,000 kilometers, the time it takes to go once around in its orbit just happens to be 24 hours. Then it looks like the Earth is just fixed, and you can see all the cloud motions beautifully. In fact there are several of these geostationary satellites in orbit at the present time. The United States has two, the Europeans have one, the Indians have one, the Japanese have one, all generally in their part of the world. With a little bit of computer wizardry, you can stitch those movies together, and make something like this.

We're not looking at reflected sunlight. Notice that the full globe seems to be illuminated. How could that be? There's always a day side and a night side, so you could never have a situation like that. We're looking at emitted radiation in the thermal infrared, the TIR. The wavelengths being used here are roughly in the range of eight to twelve microns. There happens to be in atmospheric window there which allows those photons to move through the atmosphere without being strongly absorbed. And therefore, what we're seeing is the intensity of that radiation emitted by the earth reaching the satellite. In the areas where there are no clouds, we're seeing radiation emitted from the land, and the land is hot. So the radiation is strong. In other areas where there are high clouds, those cloud tops are cold.

So we're trying to play a trick on all of us?by coding that emitted radiation to make it look a little bit like clouds are white and land is dark and ocean is dark. So don't be fooled by that, this is really emitted radiation. So it's a temperature map, but we can easily find these high clouds because they are higher up in the troposphere.?

You're seeing clouds generally along in the equatorial region. These are high, deep, convective clouds with heavy rain under them, and they're generally moving from east to west. We'll see in just a minute that they're moving along with the easterly trade winds in those latitudes. You're also?seeing these comma shaped clouds, notice they're upside down in the south, so the commas look like this in the north, but they're kind of reversed in the south?due to the?sign of the Coriolis force. And they're generally moving from west to east because this is a belt of westerlies. Westerly winds, or winds moving from west to east, and they're carrying those storms eastward. In between, there are belts where there are fewer clouds,?less rain as well, so this happens to be the belt of deserts, for example, the Sahara Desert lies in that range, and so does some deserts in Argentina, and Africa, and Australia.

And then I'll move on to the next, which is very similar, except it's taken in a different wavelength. Instead of near 10 microns, it's about 6.7 microns, which is not a window. It's not a wavelength for which the atmosphere is transparent. It's actually a wavelength for which the atmosphere is rather opaque. It's opaque because water vapor absorbs at that particular wavelength. So we call this a water vapor image, because the radiation you're seeing there is coming from water vapor molecules in the atmosphere.

Climate Terminology [00:11:40]

First of all, I've broken this into kind of zones at various latitudes. And the first one I want to talk about is what's called the equatorial zone. It's the zone going around the Earth east to west,?from five degrees north to five degrees south.?Some of the things that goes on in that zone is that at least part of the year, that's where the Intertropical Convergence Zone is. That's where the northeast and the southeast trade winds converge at low levels, and cause rising air.?And in there somewhere will be the belt of rainforest, because it's that rain that produces that kind of ecology, that forest that's adapted to receiving a whole lot of rain every year.

This word doldrums,?it refers to a region over the oceans where the winds are usually very weak. And that's because you're right in between these two trade wind zones. So in the early days, when the sailors were trying to travel across the equator, they would often become becalmed in this zone, and then the name doldrums came from that experience.

Then as we go north and south a little bit more, north or south, we enter what's called the tropics. I've defined it as being five degrees to 23 degrees.?I'm referring to both the northern and southern hemisphere tropics.

Now I'm sure you know where that 23 comes from, actually should be 23 1/2 degrees. The tilt of the Earth is 23 1/2 degrees from normal to the plane of the ecliptic, and based on that we define the so-called Tropics of Cancer and Capricorn. It's not so precise when we're applying it to meteorology and climate. It's more of an astronomical definition of the tropics than it is a climatological definition.?In this?region is where you have these steady easterly trade winds, and the Hadley cell is operating in both hemispheres, generally in that range of latitudes.?

Well, the subtropics then,?I'm going to take it 23 to 35.?Florida would be in the sub tropics. Generally you've got high pressure, slightly higher average pressure around the globe in that belt. So it's called sometimes the STHP, the Subtropical High Pressure, it's also the belt of deserts, it's where the air in the Hadley cell is descending. When air descends, it compresses adiabatically, it warms, and the relative humidity decreases. That air becomes drier and drier in the sense of relative humidity, so you're unlikely to get clouds and precipitation in any area where the air is descending, therefore that's the belt of deserts.

Over the oceans, it has a special name, sometimes it's called the horse latitudes. That too is a reversal point, because you've got easterly trade winds equatorward of that, and westerlies poleward of that, so there's a zone, again, where the average winds are very weak.?

Then we get into mid latitudes. That's where we live. New Haven's latitude is about 41 degrees north.?Generally it's a zone of westerlies, it's the belt of frontal storms, remember all those little comma clouds we saw zipping from west to east.?That really characterizes this part of the world. The jet stream is here, and the so-called polar front, which is a boundary between colder air to the north and warmer air to the south in the northern hemisphere is found in the mid-latitude zone.?

Dynamics that Drive Atmospheric Motion [00:18:11]

Now, the general circulation is pretty complicated. I'm simply calling atmospheric dynamics, it's kind of a box diagram that tries to point out some of the causality. And this applies?not only to the general circulation, but to really every type of atmospheric motion, including sea breezes and thunderstorms.

Differential heating is the ultimate cause of all the atmospheric motion on our planet. And of course, it would cause temperature differences. It would heat up some parts of the Earth more than others, the air in that region would become warmer or cooler relative to other regions. Now, the temperature differences generally cause density differences. We can understand that partially through the perfect gas law. There are three variables in the perfect gas law, not just two. But generally, temperature differences give rise to density differences.?Density differences give rise to pressure differences, not so much through the perfect gas law, but through the hydrostatic law. In other words, if I have cold, dense air here, hydrostatically, it's going to have higher pressure beneath it. If I have warm, less dense air over here, hydrostatically, it's going to have lower pressure beneath it. So it's largely through the hydrostatic law that we develop pressure differences on a horizontal plane, so called sea level pressure differences, or pressure differences at other horizontal levels.

The pressure differences want to make the air move. In this case, however, the law that controls that to a first approximation, is the geostrophic law.?And then it loops back on itself, because the wind will have an influence back on the temperature of the air. It does that in two ways. If I've got cold air here, and the wind is blowing, it's going to carry that cold air to a different location. Last time we talked about if air moves, heat moves too. Air will advect from one place to another, carrying its temperature field with it, so that's going to cause a change in some region's temperature.

And the other thing, if air converges horizontally, and air rises, then you get adiabatic cooling. Or if air descends, you get adiabatic warming. So, there's a couple of ways in which the wind can influence the temperature, and then the loop just continues. So, in order to understand atmospheric dynamics, one has to understand how all of these things work together in a system.

Coriolis Force [00:22:38]

We can't go any further in atmospheric dynamics without knowing about the Coriolis force.?There's always a question of whether there is some reference frame, some ultimate Newtonian reference frame, from which one can measure such things as the rotation of the Earth. If you look at the most distant stars and use that as a reference frame, and measure the rotation of the Earth relative to that, I think we've convinced ourselves that that is the absolute rotation of the Earth. We can take those distant stars as zero rotating inertial reference frame. So when I say rotation of the Earth, that's what I'm referring to.

It's only?acting?when you get up to larger scale systems, such as the atmosphere and the ocean that it turns out to be important. And not just important, but actually, in some ways dominant.?It has the odd characteristic, of always being a deflecting force. In other words, whatever motion you already have with your object, it doesn't try to speed you up or slow you down, it just tries to turn you. So it's always just a deflecting force. It acts at right angles to the motion vector.?

A?Foucault pendulum?is?a remarkable way to see the action of the Coriolis force.?Turns out that if you can design a pendulum that will--of course, that would probably damp out in half an hour and we wouldn't see any motion. But if it's a massive enough bob, that weight on the end of the pendulum's called a bob, it might keep going for several hours, or even a day or so. And if you did that, you’d begin to notice that the plane of that oscillation would begin to rotate.

And this is why, because we're looking down now at the pendulum, so it's swinging back and forth like this, and when it's moving in this direction, this is a Coriolis force, it's acting to deflect it to the right of the motion. Well that's going to put it probably over onto this trajectory, but then when it's swinging back in the other direction, again the Coriolis force acts to the right of the motion, the motion has reversed, and so has the Coriolis force. So that's going to rotate the plane of that oscillation even more. So you can see, slowly through time the plane of that oscillation is going to rotate, in this case I've drawn the Coriolis force acting to the right of the motion vector. So indeed, this one must be in the Northern hemisphere, because it is processing in the clockwise direction.?It would go opposite in the Southern Hemisphere, it would go in a counterclockwise direction.

The magnitude of the Coriolis force is given by the mass of the object, times 2 times the speed of the object. I'm using capital Greek letter Omega to represent the rotation rate of the Earth and the sine of the latitude. Rotation rate of the Earth once around is 2 pi radians. It takes one day to do that, so if I express that in SI units, that'll be units of radians per second, or just inverse seconds, and the value is this. U is?the speed of the object.?Phi is the latitude that you're at. So that tells you about the magnitude of it.?In the Northern hemisphere, it acts to the right of the motion vector. In the Southern hemisphere, it acts to the left of the motion vector. Remember, there always has to be motion, if there's no motion, there's no Coriolis force. So there always has to be the Coriolis force only acts on moving objects.

Geostrophic Balance [00:33:07]

Now, here's where it comes in to the atmospheric application. Very often, we find that air is moving along, around the atmosphere, in the atmosphere, in a state of geostrophic balance. Geostrophic balance is a particular kind of force balance. Remember hydrostatic balance was a kind of force balance, it's a balance between weight and the vertical pressure gradient force. Well, this is more of a force balance in the horizontal.?Pressure gradient force and the Coriolis force, when they come into balance, we call that geostrophic, geo meaning Earth, stroph coming from a root meaning turning.?

It results in some very odd things that I'll show you, as we move through this section. For example, the wind blows parallel to the isobars instead of across them. And the speed of the wind is related to the isobar spacing. I would say maybe 90 or 95% of the time, when you're above the boundary layer, the air is moving along at a pretty good state of geostrophic force balance.?It is invalid, however, you do not have geostrophic force balance down in the frictional boundary layer, where there's a lot of turbulence, or in strong storms or other disturbances. So it's not universally applicable, but it's widely applicable.

If there happens to be high pressure to the south on this particular day, and low pressure to the north, then there's going to be a pressure gradient force acting on a parcel of air sitting here from high to low.?If I've got an object, no matter how small it is, if there's slightly higher pressure on one side and lower pressure on the other side, there's going to be a net force on that. That net force is what we call the pressure gradient force. We call it a pressure gradient force because it arises because there is a gradient. Gradient means a change in pressure with position.

If it's in geostrophic balance, it has to have a Coriolis force that is equal and opposite to that. This is a vector balance, so the speed and--the magnitude and the direction have to be exactly opposite to that. And here's how the reasoning goes. If the force must be like that, then what must the air be doing, how must it be moving. It must be moving, then, from west to east, so that the Coriolis force which is at right angles to it, has the orientation given by the green vector. So this is the only consistent--once I draw in that pressure gradient force, than that vector and that vector are locked in, that's the only way I can draw them if that's air parcel is to be in geostrophic balance.

These lines of constant pressure are called isobars, and you could label them with a pressure, 1,020, 1,010, 1,000, 990; those are just lines of constant pressure drawn on a map called isobars. And so, you'll notice that in this circumstance, instead of the air blowing from high pressure to low, like you would have expected, because of the Coriolis force, it moves along the isobars, not across them. On a larger scale, where the Coriolis force plays a role, it's more like this. Air moves along the isobars rather than across them.?

So mathematically,?first of all, I need a formula for the pressure gradient force, and that's given by the pressure gradient times the volume of the object. The pressure gradient is defined as the rate at which pressure changes with position, as units of pascals per meter. And the volume is just the volume of the object in cubic meters. The mass of any object would be given by its mass density times its volume. On the left, is the pressure gradient force given by this, and on the right, is the Coriolis force, given here on the board still. But for mass, I've put in the product of the density and the volume of the air parcel that's being considered.?

We're trying to come up with a geostrophic balance formula for a chunk of air and rho is the density of that air, volume, 2UΩ sin(φ). Now, the volumes are going to cancel out from the left and right, and I can solve this formula for u, I'll put a subsequent geostrophic on it, it's given by the pressure gradient divided by 2ρΩ sine of the latitude. It says if you know something about the pressure field, I can tell you something about the wind. It's a relationship between spatial variations in pressure and the wind speed and direction, called the geostrophic formula.

So, if I were to imagine another isobar pattern that was in the form of a circle, or a bullseye, whenever you have an isolated low pressure region with high pressure all the way around, it you normally refer to that in meteorology as a cyclone. Sometimes the word cyclone has other connotations. It may imply some kind of severe storm, or a tornado, or something like that. In meteorology, it has somewhat broader and less dangerous meaning. It's just a low pressure center with a high pressure around it.

So, there's high pressure here, and low pressure there, so the pressure gradient force is going to be from high to low, so the red arrow's going to be the pressure gradient force, PGF. If it's to be in geostrophic balance, the Coriolis force must be equal and opposite to that. And the only way, given the properties of the Coriolis force, the only way it can have a Coriolis force in that direction is if the wind velocity was to the north. Because then, the Coriolis force is to the right of the motion vector.?So I conclude, by that reasoning, that the air must be moving northwards, or I could say it's a southerly wind at that location. The air must be going around the cyclone in a counterclockwise direction, if we're in the Northern hemisphere. So, low pressure, cyclone, Northern hemisphere, air goes around counterclockwise. We say that's the cyclonic direction, the air is moving cyclonically around that low pressure zone.

Here's the equator. So Northern hemisphere, Southern hemisphere. There's the problem I just worked out, there's the low pressure, and that's called a cyclone. I'm going to introduce an anticyclone in the Northern hemisphere. And then in the Southern hemisphere, I'm going to have a cyclone and an anticyclone. And we're going to understand what way the wind blows around each of these systems. In the Northern hemisphere, with high pressure in the center, the pressure gradient forces it outwards, so the Coriolis force must be inwards, so the air must go around this way. It must go around in the clockwise direction. Around an anticyclone in the Northern hemisphere.

In the Southern hemisphere, we've got the low pressure in the center again, because it's a cyclone, but now, the pressure gradient force is again in towards the center. But because the Coriolis force acts to the left of the motion vector, we end up with just the opposite circulation, direction to the circulation. It's clockwise here, and counterclockwise around the anticyclone.

So, this is a weather map taken from yesterday. At 500 millibars, so about five kilometers up in the atmosphere, you can consider these black lines to be the isobars. And they're from individual balloon launches. Every place there's a balloon launch, they've picked off the wind speed and direction, and put a wind barb at the location of that balloon launch. And notice first of all, that the wind vectors kind of parallel the isobars. There's high pressure down here, low pressure up there, you might expect the wind to be blowing from high to low, but no, it blows along the isobars instead. And that's what we expect from geostrophic balance.

Notice also that the wind is stronger here, it's getting up to be 70 or 80 knots, where the isobars are packed closely together. But where the isobars are far apart, the wind is very weak. We'll take a look at this formula, this example we did for a minute. If those isobars were further apart, then the L would be greater. If L is greater, the pressure gradient is less, and putting the pressure gradient into the geostrophic formula, I get a weaker wind. So directly, whenever you have closely spaced isobars, you have strong winds. Whenever the isobars are far apart, you have weak winds. That follows directly from the geostrophic formula. For example, here's a map, and no winds are given. This is a sea level pressure map. No winds are given. What can you conclude from this? Well, a lot, now that you know the geostrophic law. Because you know that around the anticyclone, the winds are generally going in this direction. And because those isobars are spaced out quite a bit, there's a rather weak wind blowing around here. Here near this low pressure, near this cyclone, with closely spaced isobars, there are very strong winds going around in a counterclockwise direction.?