 So, last time we have looked at the seasonal variation of the direction of winds associated with the monsoon and we also looked at the pressure pattern. Now to understand the relationship between rainfall which is what we focused on in the first two lectures, the wind on the basis of which monsoon regional monsoonal regions were defined and pressure and so on one needs a little bit of a background. So, that is what I am going to prepare in this talk. So, to begin with you know the basic source of energy for atmospheric circulation is the radiation from the sun. Now the sun is extremely hot as you know with temperatures around 6000 k that wavelength of maximum emission is inversely proportional to the temperature of the radiating body. So, the incoming solar radiation is short wave. Now in turn the earth atmosphere system emits radiation at long wavelengths that is with a peak of around 10 microns because it is much cooler right it is about 257 k also. So, the associated net radiative cooling of the atmosphere is about 1.5 degrees a day. So, the atmospheric circulation is driven by the solar energy which comes in short waves and the earth atmosphere system in turn emits long wave radiation. Now, since the atmosphere is almost transparent to the incoming short wave radiation it gets absorbed at the surface of the earth be it land or ocean. So, although the basic source is far away you know it is the sun. In fact, the atmosphere is heated from below because the solar energy is absorbed at the surface. So, the atmosphere is heated from below. Hence, the temperature of the atmosphere decreases with height up to the tropopause or so. Now in the next slide I will show you temperature measurements which are actually taken by scientist from our center over the Bay of Bengal and Arabian Sea during the Bob-Mex Bay of Bengal monsoon experiment and the Arabian Sea monsoon experiment. Now this is the vertical variation of temperature with height. What you see is that temperature decreases with height steadily up to about maybe 15 or 16 kilometers or so and then it begins to increase with height. This is the stratospheric increase of temperature that I talked about when I quoted Lorenz as not being unant not being anticipated at all by the meteorological theories. So, this is the tropopause then up to the tropopause we have the troposphere in which we have a decrease of temperature with elevation. Above the tropopause is the stratosphere in which it actually increases but we will mostly focus on the troposphere because that is where all the action is in terms of events whether or climate events. Now this is another profile this is from the Bay of Bengal and this is from the Arabian Sea again very similar you see that the tropopause is around 16 kilometers or so. So, the temperature decreases with height because the atmosphere is heated from below. Now we have seen that above the tropopause in the stratosphere the temperature actually increases with height. Now why does that happen? This is because in the stratosphere we have ozone. Ozone in fact primarily occurs in the stratosphere and ozone can absorb suns ultraviolet rays. So, ultraviolet radiation absorption by ozone creates warming in the stratosphere and that is why in the stratosphere temperature increases with height. So, this is how the temperature varies in the atmosphere. Now consider the pressure another very important climatic element. Under the influence of the earth's gravitational field the entire mass of the atmosphere exerts a force on the surface of the earth known as pressure. Usually pressure is expressed as force per unit area and atmospheric pressure is expressed in units of millibars which is the older unit with 1 millibar being equal to 1000 dynes per centimeter square dynes being of course a unit of force. So, force per unit area is dynes per centimeter square and 1 millibar is 1000 dynes per centimeter square. Now recently meteorologists have begun to use another unit which is called Pascal named after the French physicist and Pascal is defined so that 1 millibar is 100 Pascal's or 1 hectopascal. So, the pressure that supports a column of 76 centimeters that is the whole of the atmosphere is close to 1000 HPA. Now we have all seen this in school the parameter with the mercury column of about 76 centimeters being supported by the atmosphere and this is the pressure at the surface of the earth and this is around 1000 HPA. The corresponding weight of the whole atmosphere is only 1 kilogram per centimeter square so you can see how light air is. Now how does the pressure vary with height? The atmosphere is almost in hydrostatic balance. What does that mean? This means that the pressure at any point is actually simply given by the weight of the air column above that point. It is simply the weight of the air column above the point. So naturally as we go higher and higher the height of the air column above decreases and so the pressure decreases. So, this is how the pressure varies with height and for your reference you can see Mount Everest is around here and there is a rapid decrease in pressure and we will in fact often come across various levels of pressure so that 850 is around 1.5 kilometers and so on and so forth and 500 millibar or HPA is around 6 kilometers or so above the atmosphere and this is the mid troposphere and above this is the upper troposphere. Now this is how pressure varies with height. Now we have to consider density. Now if we had an incompressible fluid like water and this is relevant for the ocean then the pressure would decrease with height at a uniform rate. Why is that? Because the density is the same. So as you go above you get less and less fluid left so it will just decrease at a uniform rate. However the atmosphere is highly compressible so it expands with decreasing pressure and becomes compressed with increasing pressure. What does that mean? The density which is defined as the mass of the atmosphere per unit volume therefore decreases with a lowering of the pressure. So as you go higher the pressure is lower and which means the density is also less. So this means that the density decreases with height in the atmosphere thus the atmosphere is stably stratified. Now this concept of stability is going to come again and again in this set of lectures because the special features of atmospheric weather is that many of the processes we are interested in you know the cloud systems that give us rain such as depression, hurricane and so on and even the systems that give rain in the mid latitude system or what is called weather are often the product of instabilities in the atmosphere. So it is important to have under our belt the concept of stability. So I will come to this again and again but right now let me just define stability for you a system is said to be stable if when perturbed it returns to its original state. So you create a small perturbation it will return to its original state. So we used to have a toy when we were small which used to be a doll with a very heavy bottom and no matter how much you pushed it it will always stand up vertical again. I do not remember the English word for it and there is no point in telling you the Marathi word for it. So this is a example of a very stable system that you can give perturbations to it but the perturbations die out in time and the system returns to its original state. On the other hand consider an egg standing on its head you touch it a little bit and it will immediately fall this is an unstable system. So any perturbation you give to an unstable system actually will grow with time. Now why do I say that the atmosphere is stably stratified because we have what does it mean we have said the density decreases as you go higher and higher that means heavy air is below light air that means even if you create some perturbations it is not going to turn upside down right because the perturbations are going to die because if you displace a parcel of air vertically upward for example it is going to find itself in a surrounding in which the air is less dense around it and this particle is more dense. So buoyancy forces will imply that it goes back to its original position. So perturbations to such an atmosphere will die and therefore we consider that the atmosphere is stably stratified. Now because the density decreases with height pressure decreases at a lesser and lesser rate the further we go from the surface of the earth why is that because the amount of air in that column decreases because the density decreases. So the weight of the air above also decreases and so the pressure decreases at a lesser and lesser rate the further we go and in fact we could have seen it in the earlier slide here see it is decreasing more and more slowly as we go here. Now we are interested in the relationship between winds and pressure. So let us consider first the relationship between winds and pressure patterns. Let us see what we have seen earlier already these are the mean pressure and surface winds for July and these are the mean pressure and surface winds for November and remember I explained last time that the winds are south westerly that is coming from the south west in July what does the pressure look like? You can see that the pressure is decreasing from south to north this is the lowest pressure region here and these are what we call isobars. Isobars are lines of constant pressure. So these are isobars and isobars are more or less east west and as you go from south to north the pressure is decreasing as you can see from these isobars. So we have a pressure gradient which is such that high pressure is here and low pressure is here and yet the winds are not going from here to here right. So as I mentioned as one moves northward from the tip of the Indian peninsula the surface pressure decreases till the latitude of the trough. This region where the pressure is minimum is called the trough. So the pressure actually decreases as we go. So there is a north south pressure gradient over a large part of the Indian region and this pressure gradient in fact persists up to a few kilometers from the surface. Now we know that water always flows down a pressure gradient right. So in the kind of fluids we experience in a laboratory for example we would expect that if there is a pressure gradient in the north south direction right. So that as you go northward the pressure is decreasing you would have expected the flow to be from south to north right towards the low pressure. Why instead are the winds from the south west? Now to understand this we have to note two things. First of all the winds we measure here are relative to the earth relative to the surface of the earth and the earth is itself rotating with reference to the inertial frame or the frame of the fixed stars. So we have a we are measuring velocities or winds or currents relative to a rotating system okay and we also note that the spatial scale of the system involved is very large. For example this is 70 degrees this is 80 degrees so this is about 100 each degree is about 100 kilometers this is 10 degrees. So this is about 1000 kilometers. So this is a system which is characterized by a spatial scale of thousands of kilometers very very large scale okay. So when we have systems with spatial scale which is very large then the fact that we are measuring these winds relative to a rotating earth makes a difference okay. Rotation of the earth becomes important. Now how is the earth rotating? We all know that the earth rotates about an axis across from south pole to north pole in this direction okay. Now another thing we have to notice is the following that the oceans and the atmosphere are a thin layer of fluid over the earth with typical depth of the oceans of about only about 5 kilometers okay and you saw that troposphere is typically up to about 16 kilometers or so 15 or 16 kilometers while the radius of the earth is 7000 kilometers. So while the radius is 7000 kilometers so you can see that the radius of the earth is about 7000 on that there is a very thin layer of the atmosphere which is only 16 kilometers. So you can see 16 versus 7000. So it is a extremely thin layer that we have and similarly oceans. Now for flows with spatial scales which are much larger than the vertical extent of these systems that is to say for flows which have spatial scales much larger than few kilometers which is most of the systems we are interested in the monsoon system or the depressions and so on that we talked about only the component of rotation about the local vertical is important and this is something that I am not going to get into at this point this is something that we can look at and show by looking at the equations of motion governing a fluid which is on a rotating earth okay. But what matters the main result is the following. So suppose you are at this latitude okay then this is a tangential plane and this is the local vertical okay whereas this is the axis of rotation of the earth. So what really matters is what the projection of this on the local vertical that is what is relevant when we are looking at the flow of a thin fluid over the earth okay. Now in rotating fluids an additional force called the Coriolis force has to be incorporated in the equations of motion. Coriolis force is proportional to the wind velocity and acts at right angles to it and furthermore which way it acts right angles could have been to the right or to the left of the wind but which way it acts depends on the on how the system is rotating. So for the earth in the northern hemisphere the Coriolis force is to the right of the wind vector. Now effects of rotation of the earth are strong in fluid flow in which the velocity relative to the rotating earth is not large which means most of the flows we are interested in because at the equator the velocity of rotation is 440 meters per second it is huge this is the basic rotation of the earth while the relative velocity of the wind we measure is at most 40. So certainly the relative velocity is an order of magnitude smaller than the basic velocity. Now the parameter and this is again something we will run into again and again when we are trying to assess which of the many terms in the equation are important for a specific phenomena or which of the forces are really dominating that phenomena what we do is to assess how large the different terms are. So if you want to assess how large is the friction you try and assess how large is the friction vis-a-vis the acceleration and so on and so forth. So in this case the important and the way by taking those ratios you form non-dimensional parameters and it is how large these non-dimensional parameters are which will determine which flow regime we are in is it a regime in which rotation is important is it a regime in which friction is important and so on and so forth. So for rotation the critical parameter is what is called the Ross v number which is the wind divided by the rate of rotation into the spatial scale. You can just see that it is non-dimensional because wind has dimensions of say meters per second and rate of rotation is 1 over something over second and length is again that. So length over second in this case and this is also length over second. So it is actually a non-dimensional parameter and Ross v number defined as this is the definition of the Ross v number. Now when the Ross v number is small and when frictional forces are unimportant it is the rotation which is the most important term and then the basic balance is between the pressure gradient and the Coriolis force. Look at it another way that when we write down the full equations which we will do much later on there are acceleration terms in the laws of motion which involves conservation of momentum. There are acceleration terms that involve u and then there is the Coriolis term which involves f and when Ross v number is small it is the Coriolis term which dominates the local acceleration. This is why this is why when the Ross v number is small the main basic balance is between pressure gradient and Coriolis force. Now this balance is called geostrophy and the associate winds or currents are called geostrophic winds or currents. Now let us understand what is the relationship between pressure grade pressure patterns and winds when you have a geostrophic balance and to do so I am going to consider a very simple example. Let us assume that actually all the isobars are you know along the latitude circles if you wish I consider this as a longitude and this as a latitude. So this is increasing latitude this is longitude and they are independent of longitude. In other words we have actually pressure decreasing from 996, 994, 992 to 990. So we have a steady linear decrease of pressure from here to here and we want to know how the wind would be. In a non-rotating system of course the wind would be simply coming from south to north. Now if we assume that the wind was the same in this rotating system what would happen? If the wind were to go from south to north then the Coriolis force is to its right. So it would be this way right and the pressure gradient is this way. So the Coriolis force cannot balance the pressure gradient. So the only way the two can be balanced is if we have this kind of a situation. We have wind vectors parallel to the isobars wind blowing this way then what will happen then the Coriolis force as I said is to the right in the northern hemisphere. So it is this way and the pressure gradient is this way. So when you have wind like this it is possible for the pressure gradient to be balanced by Coriolis force. In other words when rotating when we consider rotating systems in which rotation is very very important that is to say the spatial scales are large. In those systems in fact you get a balance between pressure gradient and Coriolis force and in those systems you do not expect flow or winds to be down the pressure gradient but rather along the isobars. Now this is a very striking difference between rotating and non-rotating systems. So as I explained here earlier if the flow were down the pressure gradient then the Coriolis force to the right cannot be balanced by the pressure gradient. The only way geostrophic balance can be achieved is if the flow is from the west that is westerly. Metrologists call flow from the south southerly flow from the west westerly and so on. This is something that I will keep using. Then the Coriolis force is from north to south and can balance the pressure gradient as we have seen. Thus geostrophic flow is along isobars. Hence with pressure decreasing with latitude over most of the Indian region during July which we saw the geostrophic winds are westerly from the west. So what do we expect in terms of winds given that the pressure over Indian region during our summer monsoon decreases from south to north. We expect winds to be westerly. Now let us consider but the problem is that the picture I showed you of the winds earlier were winds at the surface and as I will come to in a minute near the surface you know one more force becomes important the frictional force. We are geostrophic balance occurs away from boundaries that is to say away from regions in which friction is important. So we should now look in fact I will show you the flow pattern over India at a height of 850 hpa which is about 1.5 kilometers above the surface above the sea level. Now at this height frictional effects are not important and what we find is that in fact these are you can consider these as isobars if you wish and you find that in fact the arrows are essentially parallel to the isobars. Now I must also mention that these are not actually isobars because what this shows is the level of the 850 millibar surface or 850 hpa surface. So this is low level and this is higher level. So rather than saying what is the pressure at a specific level like we did in the simple example here we are asking the question what is the level of a certain pressure surface but it comes to the same thing. These are lines of equal height for the pressure surface and we get low pressure here and high pressure here and what you see is that indeed way above the frictional way above the place where friction effects are important. In fact geostrophy prevails. Now we have to see what happens near the surface of the earth. Now why do we have to worry about friction at all? Now we have to remember that actually air and water the viscosity is very small see water is very different from honey for example which is a very viscous fluid. Air and water the viscosity is very small the kinematic viscosity at atmospheric pressure and about 20 degrees centigrade for glycerin is 6.4, engine oil much more viscous 10.4, water is 0.01 and air is 0.15 centimeter square per second. This is just to give you a feel for how viscous air is. So now let us consider the simple problem of flow of air past a flat plate. Why do I say flow of air? Because I want to consider a fluid with low viscosity. Now however small the air viscosity real fluids like air cannot slip past the plate right. If you have a plate here and you have a flow like this this is the wind if you wish and this is the surface of the earth a flat plate. Then add the surface of the earth surely the air cannot flow go past it the there cannot be a slip. So the boundary condition here is of no slip and frictional effects become important in a layer near the surface called the boundary layer and the whole purpose of the boundary layer is to satisfy the conditions at the surface of no slip. So within the boundary layer the velocity in fact decreases from what it was well above the boundary layer to the no slip or zero velocity at the surface. So how thick this boundary layer is depends on how viscous the fluid is. This is the region in which viscosity viscous effects become important and this is a region where viscous effects are not important. The velocity has increased slowly and has in fact may come to the free flow velocity around here. Now note this is a picture of what happens in our lab in a non-rotating fluid. So in a non-rotating fluid friction becomes important in a layer whose thickness depends on the viscosity and above that the friction is not important and within the frictional layer the velocity rapidly decreases with distance from the plate to become 0 at the plate. Now since the viscosity of air and water is small over a large part of the atmosphere and ocean away from solid boundaries viscous that is frictional effects can be neglected. Thus in the presence of pressure gradients large scale winds and currents are geostrophic in what is called the interior of the fluid where the frictional effects are neglected. However near the surface frictional effects become important and they become important in the boundary layer. Now we already saw what a boundary layer in a non-rotating fluid looks like. How do boundary layers in rotating fluids look? Now this is some work done way in the last century in the early years 1905 by Ekman and so these boundary layers are called Ekman layers after this great geophysical fluid dynamics is Ekman. Now within the boundary layer of the rotating system the balance of forces involves Coriolis force, pressure gradient remember these two are important away from the boundaries also that is the geostrophic balance. So Coriolis force is important pressure gradient is important and in addition frictional force comes into being. Now in which direction is the frictional force? Frictional force acts in a direction opposite to the wind. So what is the balance like? The balance is suppose we go back to the old example where the pressure decrease this way so that the pressure gradient is like this and earlier you remember if there was no friction the wind would be in this direction and the Coriolis force would balance it. Now if the wind continued to be in this direction it would be slowed down by frictional force. So it cannot balance the pressure gradient term therefore what happens is you get a wind in a direction like this the Coriolis force is in this direction the friction is in this direction and the two together then can balance the pressure gradient. So when you have frictional forces come into play the wind is no longer along isobars but you get another component which is down the pressure gradient this wind comprises a component along the isobars like the geostrophic component and also one down the pressure gradient and this down the pressure gradient is called cross isobar component. So this cross isobar component comes into play within the frictional boundary layer and this is what you see here that you saw the profile earlier suppose this is the velocity way above the frictional boundary layer you have a wind going this way then the velocity decreases within the boundary layer and here the boundary layer is taken to be about 1 kilometer a realistic assessment for the atmosphere and here the u velocity is going down but what you find is that v velocity comes up. So this is exactly what I showed earlier that see this wind now has a u component as well as a v component right that is what you see here that both u and v go to 0 at the plate as they must at the plate but within the Ekman layer or within the boundary layer in fact you see that there is a cross isobar flow. So as this is decreasing this is increasing this is increasing and it in fact peaks around halfway through the layer and then decreases in fact I will not have much time to go into it but that kind of thing leads to a very famous diagram called the Ekman spiral. So if you consider this as the wind of the free flow then it slowly spirals down and goes to 0 so very beautiful image here. Now let us look at the atmospheric boundary layer. So in the boundary layer near the surface frictional force which acts in a direction opposite to the wind also becomes important. Atmospheric boundary layer is turbulent and hence its vertical extent is determined not by the molecular viscosity but by what is called eddy viscosity. The atmospheric boundary layer extends to about 1 kilometer from the surface. Now because of the cross isobar component the component of wind down the pressure gradient if the pressure decreases from south to north not only will you have a geostrophic component which goes from the west to the east in addition to that you will have a component which goes from south to north. So the wind becomes southwesterly wind from the south west. So this is again an idealized picture. Suppose you had a trough here okay this is the line of minimum pressure. So to the south of the trough the pressure is decreasing as you go this way. So the cross isobar component is towards the north and you have a geostrophic component to the west so you have southwest flow. But look at what happens north of the trough. If you go to the north of the trough in fact now here pressure is decreasing from here to here. So the cross isobar component is this way from north to south and the geostrophic component is from east to west. So what you get here is northeasterly winds and here southwesterly winds okay. Now this is more or less what we see in July that you have a trough around here to the south or southwesterly winds to the north or northeasterly winds. In November when the trough has moved to here you will still have southwest winds to the south and northeast winds to the north. So actually there has not been a substantive change in the system itself. What has happened is that the system is shifted and earlier only a little region to the north was under the sway of northeast winds. Now the entire region has come to the under the sway of the north winds. This is why I think that the name southwest and northeast for this are somewhat misleading because they give the impression that the entire system has changed but there is actually just a movement of the system. I will come back to this later. So then to summarize thus the meridional pressure gradient in July over a large part of India and surrounding seas south of the trough implies that the geostrophic winds that is above the frictional boundary layer would be westerly and the winds within the boundary layer would be southwestally. In November the pressure decreases from north to south that is pressure gradient reverses. This implies that the surface winds would be northeasterly and winds above the boundary layer would be easterly over a large part of India. Thus the seasonal variation in the direction of winds is associated with the seasonal variation in the location of the trough, trough being the region where the pressure is minimum. So this is important to see. So we have now understood why the wind direction is the way it is but in a way all we are saying is it is that way because the trough moves. So now the ball is in the court of what creates the movement of the trough which we will come to. But there is another very important feature of boundary layers in rotating fluids which we have to understand and this has very important implications for genesis of clouds and so on and so forth. So before I can consider that I have to introduce one of the most important facets of fluid flow in rotating system. Now this is something some of you may already know this is the vorticity. So what is the vorticity? Vorticity is defined as the curl of the velocity and is related to the rotation of the flow. It is del cross v curl of the velocity. Now to get a physical feel for what is vorticity suppose that an infinitesimally small sphere of fluid is instantaneously solidified made rigid without any change in momentum, angular momentum or mass distribution. As it is this is a thought experiment as it is suppose you solidify a sphere which was a fluid before without any change in momentum, angular momentum or mass distribution. Then the sphere will start rotating with an angular velocity which is half the vorticity of the flow. So if the flow has vorticity then such a sphere will start rotating and it will start rotating with an angular velocity which is half the vorticity of the flow. So you can see vorticity is related to the basic rotation in the fluid. Now there is a very simple way of deciding whether a particular flow has vorticity or not and that is suppose you take a cross and this can be done very easily with water flow for example in streams. Suppose you make a cross out of 2 wooden sticks so that it is at right angles to one another and let the cross float with the stream. Then suppose we have flow that is parallel but velocity here is high, velocity decreases, velocity decreases here this is called a shear flow. In such a case then what will happen to this cross as it proceeds along it will in fact rotate because you can see that a will go faster than b will. So at this point of time for example a has come much further and b is lagging behind. So what you see effectively is a rotation in the counter clockwise direction. So the cross will start rotating counter clockwise because that is how the shear flow is, this is how the velocity pattern is. So in this case it rotates counter clockwise. So this means that such a flow does have vorticity and it is counter clockwise. Now if you have a flow like suppose you have a low pressure and you have a flow around like this then also if I placed a cross here it will rotate with the flow in this direction. So the rotation of the earth related to which we observe winds is counter clockwise in the northern hemisphere. So meteorologists call that rotation or vorticity cyclonic. So when the isobars are closed as in a low or a depression so in what happens when the isobars are closed lowest pressure is here and this is the next isobar. In that case geostrophic flow will be along the isobars like this and that means geostrophic flow will be counter clockwise that is to say it will be cyclonic. So this is a way of seeing if the flow has vorticity. Now there is a very special characteristic of boundary layers in rotating fluid. In a rotating system when the flow above the surface boundary layer that is in the interior of the fluid where viscous effects are negligible like say at 1.5 kilometers or so above the surface of the earth. If the flow has cyclonic vorticity that is rotation is in the same sense of the earth then there is convergence of air in the boundary layer and ascent of air above the boundary layer. So let me just show this as an example. Imagine this is the earth okay this is rotating with a velocity omega angular velocity omega. Now above in the interior of the fluid you have vorticity which is the same sign of as the earth. So you in effect if we went to the inertial system this is rotating with a angular velocity of omega plus delta omega. This is what happens when you have a cyclonic vorticity above the frictional layer. So in that case what is happening is this fluid is spinning faster than this one and this leads in fact to convergence of air this is the surface air and once it converges it has to go somewhere and it goes in fact in the interior of the fluid. Now what happens when the vorticity is anti-cyclonic okay opposite sign what happens when it is anti-cyclonic is that in fact you have divergence of air here okay. So more and more air leaves this place and the continuity is maintained or conservation of mass is maintained by having descent of air from above. So what we have seen is that when the air above the boundary layer has cyclonic vorticity there is convergence of air in the boundary layer giving rise to ascent of air above the boundary layer here and on the other hand when the vorticity in the interior is anti-cyclonic the earth rotates faster than the air above the boundary layer air diverges in the boundary layer leading to descent of air from the interior to the boundary layer. So the vertical velocity at the top of the boundary layer is proportional to the in fact one can show this mathematically that the vertical velocity at the top of the layer is proportional to this relative vorticity okay and derived from the winds measured relative to the earth. In this way the effect of friction in the boundary layer is communicated directly to the free atmosphere through a force secondary circulation rather than indirectly by slow process of viscous diffusion. Now this is very important and because of this rotating fluids can spin up much faster than non rotating fluids because of this dynamic if you wish dynamic boundary layer a boundary layer which communicates directly with the interior of the fluid I am not going to go into it right now okay. So now what have we seen we have seen that the mean winds above the boundary layer are in this direction westerly here and easterly here. So this means the velocity is cyclonic it is anticlockwise or cyclonic okay so mean July winds above the boundary layer are westerly south of the trough and easterly north and the vorticity associated with this wind pattern is counterclockwise or cyclonic okay. On the other hand if we go way above to the upper troposphere 200 millibars then this is the winds are like this and you can see that this is clockwise right. So it is anti-cyclonic this has anti-cyclonic vorticity okay. Now when we consider systems that give us rainfall we will see that perhaps the most important feature of synoptic and planetary scale systems which are large enough for the rotation of the earth to become important in their dynamics is the cyclonic vorticity above the boundary layer which is associated with convergence of moisture near the surface. So we have now learnt so far that because although the radiation although the atmospheric circulation the main source of energy is solar radiation because most of it is absorbed at the surface of the earth the atmosphere is heated from the bottom because of that the temperature decreases with height and temperature decreases with height throughout the troposphere and above the tropopause begins the stratosphere in the stratosphere though the temperature increases with height because of ozone which absorbs ultraviolet radiation. So temperature variation in the atmosphere involves decrease of temperature in the troposphere and increase in the stratosphere. How does the pressure vary? Pressure decreases as we go higher and higher basically because pressure just depends on the weight of the air column above that level okay. Now it so happens that the density of the atmosphere also decreases with height. So we say that atmosphere is stably stratified because we have light air overlying heavy air. Then we came to the major difference between a rotating and a non-rotating system and that difference is in how in the relationship between wind and pressure gradient. In a non-rotating system the wind will blow from high pressure to low pressure or the current will flow from high pressure to low pressure water in our taps flows from high pressure to low pressure okay. But in a rotating system on spatial scales for which rotation is important that is large scales of the earth which feel the earth's rotation. In fact what happens is Coriolis force is an important force that has to be incorporated then the basic balance is between the Coriolis force and the pressure gradient and in that situation what you get is flow along isobars or along lines of equal pressure. So whereas in a non-rotating system the flow is essentially across isobars or cross isobar flow from high to low pressure in a rotating system the flow is along isobars provided the frictional effects are not important. Now where are frictional effects important see although air and water are fluids of very low viscosity in comparison with things like honey or engine oil or something like that even then you see frictional effects become important because even though they have very low viscosity these fluids cannot slip past the surface. So if you consider a flow past a flat plate the flow has to become 0 at the plate because the fluid cannot slip over the plate. So this no slip condition has to be satisfied and what this means is that frictional effects become very important in a layer very near the surface where the boundary conditions have to be satisfied how thick the layer is depends on the viscosity. So in that layer frictional effects become important again we said that frictional effects lead to another dimension in the relationship between wind and pressure gradient whereas when frictional effects were not important in a rotating system we had flow along isobars. Once frictional effects become important we also get a cross isobar component to the wind and this leads to a very beautiful spiraling wind in an idealist case and this is the Ekman spiral. Now even more important than the fact that this cross isobar flow in fact implies convergence or divergence of air. So you have convergence or divergence of air in the frictional boundary layer and furthermore there is another important property of the boundary layers in rotating fluids that is something that depends on the vorticity of the flow and we defined what was vorticity of the flow. If the flow in the interior is such that it has vorticity which is cyclonic that is same sign as the rotating earth beneath then it becomes a problem of a faster rotating fluid in the layer above the frictional layer and a slower rotating boundary namely the earth. In that case actually there is convergence in the boundary layer and this surface air ascends into the interior. So the boundary layer directly supplies moist surface air to the interior of the fluid. Now this phenomena has very very important impacts on the genesis of clouds and rainfall as we will see later. If on the other hand the vorticity in the interior happens to be anti-cyclonic then in fact there is divergence in the boundary layer and descent of air from the boundary layer to the interior. So this is something that all these features have very very important implications to clouds and rainfall and that is what I am going to consider in the next lecture. Thank you.