[MUSIC] The aim of this session is to give you some basic notions, about what drives the wind and how the atmosphere moves around the globe. So we will go through the following topics. What is it that sets the atmosphere in motion? This will lead us to describe the vertical structure of the atmosphere, how it is layered. Then, we will resume with the analysis with the equations of motion. And from a simple scaling, we will see what the dominant terms are and suggest a good approximation for the wind. With that, we will be able to give an overview of the general circulation of the atmosphere and show the main flow features in mid latitudes. Ready? So what is it that sets the atmosphere in motion? One could imagine that the atmosphere could simply be in solid body rotation at the same rate as the earth. As you know it's not, and this is because of the heating due to the incoming radiation from the sun, this heating is in homogeneous in space and this results in motions. So let's be more precise. First, there is a horizontal originating. Because the surface in the tropics is more heated than the surface in the high latitudes. Here, I sketched two tubes of with the same cross section. So there is the same flux of energy through both of them. See how this flux and the tube with high latitudes spreads out over a much wider area, implying that there is much less energy arriving per square meter at the Earth's surface. So the main driver of atmospheric motions is the differential heating between the tropics and the high latitudes. Atmospheric motions and oceanic motions too redistribute this energy. This is well confirmed by satellite observations of the outgoing long way radiation at the top of the atmosphere. I'll come back to this point in a minute. But before that, let's make just one small parenthesis. In what I've described above, I focus on the main aspect, and I have simplified things. As you know, the rotation axis of the Earth is tilted. And this leads to seasons. The differential heating between the low and high latitude is strongest in winter when there is the polar light and the winter polar. Let's leave that aside from now. So, another aspect that could require more discussion concerns the wave length of the incoming solar radiation. In what I just said, I took for granted that the solar radiation simply goes through the atmosphere and heats the surface. Now, here's a spectrum of the incoming solar radiation. See how close it is to that expected for blackbody radiation at the temperature between 5,000 and 6,000 Kelvin. Most of the energy corresponds to visible light, wavelengths between 400 and 800 nanometers. And indeed, it is not very much attenuated as it goes through the atmosphere. There's no absorption bands. So, most of the solar radiation reaches the surface heating the atmosphere from below and in space with strong latitudinal gradients. So let's first consider the in the vertical now. This is an example of a vertical profile of atmospheric temperature in the mid latitudes measured by radiosonde carried by a balloon. Quite logically, the temperature maximum is at the surface. The temperature decreases with height at a nearly concentrate for about ten kilometers. It is possible to have cold air above warmer air because the pressure decreases in the vertical, but only up to a point. When too much heat is received at the surface, the temperature profile may become unstable. And a column of a turns. This happens, and with water involved, this leads to the formation of clouds. And this is called moist convection. The layer of such meteorological phenomenal occur is called the troposphere. Up to about ten kilometers in the extra tropics, and up to 15 kilometers in the tropics. At the time of troposphere, the temperature is between 200 and 50 exc bas cal about 10 kilometer, and about 100 activex cal that's about 15 kilometers. Above the troposphere, there's the stratosphere, roughly between 15 and 50 kilometers. There the temperatures increase with height because of the absorption of the ultraviolet component of solarization by the ozone layer. Higher up, there is the mesosphere. And then beyond 100 kilometers, the atmosphere is no longer well-mixed, and ions become important. Wind energy today only concerns the lower most layers down close to the surface. It comes down only at very tiny fractions of the troposphere. The first couple 100 meters, we try and contact with the surface, and which are part of what we call the boundary layer. Nonetheless, I have to start with this more general picture because what goes on in the boundary layer depends on the motion above in the free troposphere. Hence, the order of magnitude of the vertical scale, let's call it h, of the atmospheric motions involved in the general circulation is about, say, ten kilometers. In the horizontal, the relevant scale, say, l, is a few thousand kilometers. Remember, there's 10,000 kilometers from the equator to the pole. So in other words, we are talking about motions in a very, very thin layer like the skin of an apple. So evidently, horizontal motions will be much greater than vertical motions. Let's have a look now at the equations of motion. We won't go into all the equations and into details. My purpose is just to extract what to expect for large scale motions. That we will do by analyzing the orders of magnitude of the different terms. Our starting point is Newton's second law, stating that mass times the acceleration is equal to the forces acting on the body considered. On the left hand side it is the derivative of the velocity that is written. This is necessary because Newton's law applies to entire system. So we need to follow through along it's movement to apply it. Now, on the right on side we have the pressure forces, gravity and near the surface at one point who will need to come for friction, but not today. To describe atmospheric motions, we naturally want to use the Earth as our reference frame and the Earth is not a Galilean referential, it's a rotating frame of reference. This rotation is conventionally expressed using the rotation vector omega. It is aligned with the axis of rotation and the amplitude is the rotation rate in per second. So the rotation, the red arrow on the figure application given by the vector R is the product of omega and R. In the frame rotating with the earth, two traditional terms in the acceleration need to be taken into account. They're called forces but they are just part of the acceleration really. They are the Coriolis force and the Centrifugal force. The centrifugal force is always present, even for fluid at rest. It is the green arrow on the graph. In fact, we can incorporate it into gravity and switch from a spherical planet to a planet which is likely an ellipsoid. And then we get rid of this term. Now, for the Coriolis force, it has an amplitude proportional to the velocity. It does no work as it is normal to the velocity. So how is this Coriolis force going to effect the motions? Is it going to be important, or could we neglect it? That's for the next session.