So the heat capacities for ideal gases, at least the ideal gases that we've been able to understand using the 3D particle in a box model, have turned out to be fairly simple. So the internal energy of an ideal gas as predicted by the 3D particle in a box model is three-halves RT. The enthalpy per mole of that same gas would be five-halves RT. If I take the derivative with respect to temperature to find the heat capacities, the constant volume heat capacity, three-halves RT becomes three-halves R. The constant pressure heat capacity, if I take the HDT, five-halves RT becomes five-halves R. So those are the expressions we've seen for the constant volume molar heat capacity and constant pressure molar heat capacity for a gas predicted by the 3D particle in a box. Those expressions are fairly remarkable. They make a prediction that says it doesn't matter what the gas is, doesn't matter whether it's argon gas or nitrogen gas or water, steam, vapor, doesn't matter what the gas is, doesn't matter what the temperature is, these are the heat capacities of those gases. If I want a numerical value, if I take the gas constant 8.314 and I multiply by one-and-a-half, predicts that the heat capacity, the constant volume heat capacity of every gas is 12-and-a-half joules per mole Kelvin. If I multiply the gas constant by five-and-a-half, that I'll have to remind myself of what the calculator tells me. That's 20.79 joules per mole Kelvin for the heat capacity. So again, same prediction for every gas. Does it actually work that way? We can see. What's if I bring up a table of numbers here that give us the heat capacities for a bunch of different gases? Here are the experimentally determined heat capacities, molar heat capacities for a bunch of different gases. Do they all equal 20.79? Well, some of them do. Helium, neon, argon, the heat capacities of all those gases are exactly 20.79. So the 3D particle in a box is making pretty good predictions. And I can color code these values to make it clear what the patterns are. So clearly the first three, helium, neon, argon, the prediction is pretty good for the 3D particle in a box model. But the rest of these are not. 29, these numbers I've colored orange, values near 29, that's nothing like 20.79. CO2 and H2O, those are even worse. Those values are much higher than 20.79. And we can see some patterns here. We can see that for the monatomic gases, helium, neon, argon, are just gases that are composed of a single atom. Those predictions are perfect. Carbon monoxide, hydrogen gas, nitrogen gas, oxygen gas, those are diatomic gases. The prediction is much less good for them. But all of those values are pretty close to each other. So it seems like there's a different value that's a reasonable estimate for diatomic gases. For these triatomic gases, carbon dioxide and water, again, it's a completely different value. And this prediction is even worse. So clearly something has gone wrong with the 3D particle in a box model. And it's actually even worse than what these data show. Because the heat capacity here, again, doesn't depend on what the molecule is. Also, it doesn't depend on the conditions like the temperature. So we would make the prediction that these heat capacities are the same regardless of what the conditions are. And we can see whether that's true or not if we pull up a graph over here. So what I'm plotting now is the heat capacity of the gas as a function of the temperature. So room temperature is down here somewhere around 300 Kelvin. And for argon gas, again, monatomic ideal gas, monatomic gas that behaves fairly ideally, things are fine. The value is 20.79 exactly as we predicted with the 3D particle in a box model. And that value does not change very much at all as the temperature changes. But if I pull up the data for another gas, like nitrogen gas, we can see that the value at room temperature, which we saw was about 29 and changed at room temperature. If I change the temperature, the prediction gets even worse. So at 500 Kelvin or 1,000 Kelvin or 2,000 Kelvin, the value is not well predicted by the 3D particle in a box model. And it also keeps changing. So pretty clearly, the heat capacity for some gases, at least, is dependent on the temperature, has some dependence on the temperature. So that's going to complicate things a little bit. We can take two approaches. We can take the empirical approach and say, well, now that we know that heat capacities are different for every gas, we can just look up those values or look up a graph of those values and see how they vary. And one way to do that would be to say, for every gas, to handle the temperature dependence, a pretty common thing to do is to use an empirical equation like this one. In fact, this equation has a name. We use the Schoemait equation to come up with an equation. So essentially, this is a polynomial that describes how the heat capacity is depending on the temperature. So with this linear term, quadratic term, cubic term, and a 1 over T squared term, that allows us to do a pretty good job of predicting the variation in the heat capacity as the temperature goes on at the cost of, however, having these five empirical parameters. So we could look up the values of A and B and C and D and E for a gas like nitrogen and use that equation to predict the heat capacity. And sometimes we'll have occasion to do that. In fact, as we go forward, we'll have better ways to predict, more accurately, exactly what these coefficients should be or exactly what the heat capacity of a gas should be under different conditions. But for now, the important point is the 3D particle in a box model that has been working so well for us so far works great for monatomic ideal gases. It's pretty clear that it's left something out for the diatomic and triatomic gases. And so one approach and the one that we'll take next is to take a step backwards, look at the quantum mechanics again, and say, OK, what have we left out of our model for a diatomic molecule that we didn't include in the 3D particle in a box model that might help us make a better prediction about properties like the heat capacity? So that's what we'll tackle next.


Now, in the last lecture, we have looked at the hypothesis. First hypothesis proposed for the basic system responsible for the monsoon which said that the primary cause of the monsoon is the land ocean contrast in surface temperatures. And we showed that that hypothesis is not tenable and is inconsistent with the observed variability in space and time of the monsoon. Now, today we will consider the second hypothesis which looks at monsoon as a manifestation of seasonal variation of tropical circulation and rainfall. So, according to the second hypothesis, the monsoon is a manifestation of the seasonal variation of tropical circulation in response to the seasonal variation of the solar radiation. Now, to understand this hypothesis, it is necessary to first get a background on tropical circulation itself. So, I will consider that first in this lecture. So, we first consider tropical circulation. Now, we have noted before that the energy that drives the atmospheric circulation comes from the sun. Since the atmosphere is almost transparent to the shortwave radiation, most of it gets absorbed at the surface of the earth be it land or ocean. So, the annual average of the solar radiation reaching the surface which is here is in fact, maximum in the equatorial region. So, this is the annually average solar radiation reaching the surface of the earth in watts per meter square. And you can see that it is very large in the equatorial region. So, it is maximum in the equatorial regions of the earth. Thus, the atmosphere is heated from below with the maximum heating over the equatorial region for the annual average. So, if we look for simplicity first at the annual average, then the atmosphere is heated from below with heating being maximum at around the equatorial region and decreasing as you go poleward on either side. Now, this implies that the surface temperature also behaves in the same way. This is the annual mean surface air temperature and shaded regions are where it is very warm. And you see that in the annual mean also the surface temperature is maximum in the equatorial regions and decreases as you go poleward. So, we have a situation in which the radiation incident at the surface is also maximum in the equatorial region and the surface temperature is also maximum in the equatorial region if we look at the annual average. Now, so in response to this the annual average sea level pressure distribution also shows a presence of a low pressure belt or trough over the equatorial region. So, this is the annual mean sea level pressure distribution. And what you see is again this is where the low pressure region is or the trough is and that is also roughly in the equatorial region. So, the incident solar radiation as well as the temperature at the surface as well as the pressure have extrema near the equatorial region radiation and temperature being maximum and pressure being minimum around the equatorial region. Now, if we look at annual mean rainfall annual mean precipitation in millimeters per day that also is maximum in the equatorial region this is the belt rain belt if we look at the annual average. So, so the annual average sea level pressure distribution also shows the presence of a low pressure belt or trough over the equatorial region and the annual mean precipitation distribution shows the heaviest rainfall occurs over the equatorial region. So, the if you look at the annual average then the entire action is over the equatorial region where there is maximum temperature there is a trough and also maximum rainfall. Now, to understand the annual average of tropical temperature pressure and precipitation distribution one needs to consider the response of a fluid to heating from below which varies with latitude. So, we expect the annual average tropical circulation in the meridional that is to say north south and vertical plane to be rather similar to the Bernard convection we looked at in the last lecture. This is this if you remember Rayleigh number measures how much the heating is we saw with the viscous effects and effects of conduction and large Rayleigh numbers means viscous effects are relatively less and this is what happens to a fluid. Now, we are assuming in this case the fluid is non-rotating when it is heated over this region what you get is a circulation which with ascent here and descent in the surrounding region and these are the temperature contours. So, you get hot region here and it becomes successively colder as you go up and notice that the as the Rayleigh number increases that is to say the viscous effects become less and less important we get a very narrow zone of strong ascent and a broad zone of slow descent this is Bernard convection. So, the atmospheric circulation near the surface would. So, this is what we would get when the atmosphere is heated from below with the heating being maximum at the equatorial region you expect to get ascent over the heated region over the trough region and descent in the surrounding region. Now, the atmospheric circulation near the surface involves winds from the north of the equatorial trough converging with the winds from the south of the trough in the trough zone. So, if you remember when we looked at the pressure distribution if we have a trough zone around here around the equatorial region in this trough zone you will get winds coming from the north in the northern hemisphere and from the south in the southern hemisphere and remember we are looking at a very large scale system extending over thousands of kilometers. So, for such a system then Coriolis force will also become important. So, because these are large scale systems rotation of the earth is important and due to the Coriolis force both these winds the wind coming from the north in the northern hemisphere the northern winds as well as the winds coming from the south in the southern hemisphere. So, the wind will acquire an easterly component thus the winds will be from the northeast in the northern hemisphere and from the southeast in the southern hemisphere. So, an idealized picture of annual average circulation in the tropics would be as follows that there would be an equatorial trough here this is the region of low pressure around the equator where the heating is maximum and the temperature is maximum and into this low pressure you will get winds at the surface, but because of the Coriolis force they will get an easterly component because now the wind that tries to go this way will have a Coriolis force acting to its right in the northern hemisphere and to its left in the southern hemisphere. So, both these winds will get components from the east and the net result then is that the surface winds towards the equatorial trough will be from the northeast in the northern hemisphere and from the southeast in the southern hemisphere these are the northeast and southeast trades and they emanate from the high pressure regions here in the subtropical region. Now, the moisture converging in the surface layer over the trough ascends this results in deep convection and heavy rainfall. So, at high levels above the trough the air diverges and the circulation is completed by descent in the region surrounding the trough this is called a Hadley cell. So, in fact, this rising limb of this Hadley cell which is located over the trough has been called equatorial trough by Reel. Now, Reel is one of the great contributors to our understanding of tropical metrology and he called it the equatorial trough. So, here is a schematic picture of the tropical circulation in this is remember it is an annual average and so this trough region is over the equatorial region and what you get is trade winds converging into the trough ascending here and ascending throughout the troposphere diverging at high levels and then descending around this. So, this is the Hadley cell which is the circulation in the north south this is the north south and vertical plane if you look at the annual average. So, this is an idealized circulation that you have and the rising limb of this cell this is the rising limb of the Hadley cell. This rising limb in fact, involves deep convection or deep clouds and rainfall and this is called the equatorial trough by Reel and also the ITCG by Charney and we will come to that. Now, Reel has also shown what the pressure distribution relative to the equatorial trough at different levels is. So, now this is pressure distribution relative to the equatorial trough which is supposed to be at this latitude 0. So, near the surface and up to even 2 kilometers or more there is a low pressure belt here this is the equatorial trough and above say at the height of these are actually in 100 millibar. So, around say 200 millibar or so what you see is a high over lying a low and air will diverge from this and then descend in the surrounding regions. So, this is the vertical structure of the pressure distribution around the equatorial trough. Now, since convergence of air from northern and southern hemisphere is an important feature of the rising limb of the Hadley cell it is also been called the intertropical convergence zone because it is characterized by convergence of air from the 2 hemispheres northern and southern hemisphere. So, it has also been called ITCZ by Charney. Now, an idealized picture of axisymmetric component which is to say averaged over all the longitudes of the general circulation of the earth looks like this. So, we have a case this is an idealized picture of circulation which is averaged over all the longitudes mind you these are the tropics. This is the equatorial trough and you have the northeast and the southeast trails actually in reality this cell the Hadley cell is restricted to the tropics and north of the Hadley cell is a mid latitude cell here which you can see. So, it also has a descending limb here and an ascending limb north of 60 north or so and a similar one here and then there is a polar cell. Now, why we get 3 cells and not just a single cell with the Hadley cell extending to the pole is a question I will not consider in this lecture, but it really depends on various parameters such as the rotation of the rate of rotation of the earth the heating that comes from the sun and so on and so forth. The parameters for the present earth atmosphere system which is driven by the given solar radiation are such that in fact the circulation the solution for the circulation breaks up into these 3 cells and it is only in the tropics that we see a direct circulation of rising about the heating and sinking in the subtropical highs these are the subtropical highs that I mentioned. So, this is the picture these are the polar regions and these are the mid latitudes here. Now, this is the same picture which shows the surface winds much more colourfully perhaps and this is the ITCG you see the north east trade winds south east trade winds converging in the ITCG which also can be called the equatorial trough and these are the mid latitude westerlies these are the subtropical highs which are also called horse latitudes and these are the polar this is the polar circulation that you have. So, this then is the Hadley cell we talked about with rising in the equatorial region low pressure here and diverging at high levels and sinking in the surrounding region. So, this is an idealized picture of the general circulation of the earth. Now, it is important to note that the ITCG as Chani called it and the equatorial trough as real called it are not only characterized by convergence in the lower troposphere. In fact, the word convergence comes also in the name ITCG that Chani and others before him have referred to this system as. So, not only is there convergence in the lower troposphere, but they are also associated with cyclonic vorticity above the boundary layer strong ascent of this air and deep convection with heavy precipitation. So, the important attributes of features of this ITCG are that there is strong cyclonic vorticity above the boundary layer convergence within the boundary layer towards this region. So, it is a zone of convergence there is strong cyclonic vorticity above the boundary layer there is strong upward velocity or ascent of air above the boundary layer. And this ascent in fact extends almost throughout the troposphere until about 200 millibar or so at which point there is anti cyclonic vorticity and the air diverges and then the circulation is completed with descent in the surrounding region. So, intense convergence in the boundary layer cyclonic vorticity above the boundary layer deep convection and heavy precipitation are considered to be very important attributes of the ITCG by Chani. Now, let us consider you know the case of what I can call a canonical ITCG or the intertropical convergence zone over the oceanic region of the Pacific and let us consider it over the region east of the dateline this is the mean July rainfall and you see a very coherent zone zonal band of rain belt here and this is believed to be associated with the equatorial trough or the ITCG. So, let us see what it looks like. Now, what you see here is actually the vertical velocity above the boundary layer this is omega at 850 hPa and this is the relative vorticity above the boundary layer and what you can see is this band here of yellows and reds corresponds to cyclonic vorticity and corresponding to this band of cyclonic vorticity you see that there is ascent at the level above the boundary layer. So, this is you know what we expected from Ekman layer theory that if we had cyclonic vorticity above the boundary layer there will be ascent of this moisture at the level above the boundary layer and this is what we had expected. So, the correspondence between cyclonic vorticity above the boundary layer and upward velocity at this level is clearly seen this is what we just saw. Now, in fact over this classical ITCG there is also a correspondence between now this is the rainfall over the region this is mean for July and this is omega at 850 or the upward velocity at 850 above the boundary layer and you see that there is a very very close correspondence between the upward velocity just above the boundary layer at 850 and rainfall for the classical ITCG. And you remember that this was the basis of the sixth theory that Chani proposed that this cyclonic vorticity by having convergence in the boundary layer can create upward velocity here. This is the ascent that is required for clouds to form and then the clouds form heat the region intensify the trough and actually give rainfall here. So, the basic elements of this what happens in a rotating fluid in the presence of a cyclonic vorticity are actually now here seen to be in operation for a classic ITCG which is over the eastern Pacific. Now, let us see what happens on the daily scale first we have to understand what the canonical ITCG or equatorial trough as real calls it looks like. So, on the daily scale it appears as a bright zonal meaning east west cloud band in satellite imagery we have actually seen many many instances of such and you see one here. Now, this is actually from reals book and what you see here is this is the Pacific region here and this is the band zonal band you know over eastern Pacific and what you see here is a cyclone taking off. Now, this is a case that we saw last time about interaction between the planetary scale and synoptic scale how all cyclones are born as cloud blobs or lows within the ITCG and then they start intensifying and take off and this is such a picture. So, this really is a canonical ITCG a picture of the canonical ITCG over the Pacific ocean next picture is again from real and this is over south Indian ocean. In fact, you can see Madagascar here. So, this is over south Indian ocean on 18th February 1977 and what you see here is this nice band of cloud this is the ITCG from it two cyclones were born and they have taken off. So, you see that equatorial trough for ITCG over south Indian ocean and two band two blobs of cloud which shows two tropical cyclones on that region. Now, this is another example of ITCG over southern equatorial Indian ocean and you see a very coherent band of clouds and notice that almost in every picture of the ITCG the intensity of the clouds is not uniform throughout rather the cloud band comprises blobs which are sort of synoptic scale blobs which are embedded in this larger planetary scale. So, this is again a typical picture of a canonical ITCG taken by satellite and it happens to be taken this year 6th March 2012. So, let us see if you know this argument about cyclonic vorticity coinciding, cyclonic vorticity above the boundary layer coinciding with the rain belt or with the cloud band is actually seen in this as well and in fact, what it is here what you see here is the cyclonic vorticity for the same region this is equator and this is 20 south and you see a band of cyclonic vorticity here and below is shown the outgoing long wave radiation and the colors indicate where the outgoing long wave radiation is very low which means we have very tall clouds clouds with very very high tops. So, these are the deep convection areas of this which actually look as bright look like bright white clouds in the imagery I showed you and you see that there is a correspondence between the cyclonic vorticity above the boundary layer and this OLR. So, for a canonical ITCG on a daily or a monthly scale we see that cyclonic vorticity above the boundary layer is associated with upward velocity at that is associated with upward velocity at that level and rainfall. So, this is consistent with what is expected from boundary layers in rotating systems and cooperative interaction between cloud scale and synoptic and larger scale. So, we see that for a canonical ITCG on a daily scale and I will show later that this is also true on a monthly scale in fact, we have seen it on a monthly scale for the Pacific. So, for daily as well as monthly scale we see that cyclonic vorticity above the boundary layer is associated with upward velocity at that level and rainfall. So, this is all consistent with whatever we had developed as background material the boundary layers in rotating system the special feature of boundary layers in rotating system which imply that there is convergence in the boundary layer when this cyclonic vorticity above the boundary layer and cooperative interaction between cloud scale and large synoptic and larger scale. Now, so now we have so far focused on the annual picture right and the annual picture comprises this trough region the Hadley cell with the trough region and ascending over the trough region descending in the surrounding region and convergence in the boundary layer whereas, divergence at the higher level this is the annual average picture. Now, next we have to look at how it varies in which season. So, we now consider seasonal variation now why do we have variation with season at all. So, let us revise a little bit of our basic geography now you know that the earth revolves around the sun with a period of one year the axis around which the earth rotates once in a day is in fact not perpendicular to this plane. So, this is the plane ecliptic plane in which the earth is rotating revolving rather around the sun and it takes 365 and 1 4 days to complete one revolution, but the earth in addition to revolving around the sun is rotating about an axis and the axis this angle that this axis of rotation of the earth makes with the perpendicular to the ecliptic plane is 23.5 degrees. So, the earth revolves around the sun with a period of one year the axis around which the earth rotates once in a day is not perpendicular to the orbital plane, but at an angle 23.5 degrees to this direction this is what you have seen. So, the earth is rotating around this axis and is revolving around an axis which is perpendicular to this plane. So, there is a variation in the latitude at which the sun is overhead with the season and that is seen here. So, you have the sun here and this is the north pole of the earth and this is the south pole and this is the situation in the summer. So, in the summer the sun is overhead over this tropic 23 0.5 degrees north which is the tropic of cancer. So, this is the summer solstice as we call it in the northern hemisphere on June 21st 22nd the sun is overhead over the tropic of cancer then comes the equinox which is actually the September 22nd 23rd this is when the sun is overhead over the equator and then comes the what we call winter solstice which is the summer solstice of the southern hemisphere when the sun is overhead over the tropic of Capricorn which is the tropic in the southern hemisphere and then in March again it is overhead over the equator. So, this declination of the axis around which the earth rotates to the orbital plane leads to this kind of a story that in the northern hemisphere in the northern hemisphere summer which is in June the peak of the summer as far as the radiation is concerned is in June in that at that time the sun is overhead over the tropic of cancer and in our winter which is December it is overhead over the tropic of Capricorn. So, the sun is overhead over the equator at equinox which is March 21st 22nd and September 22nd 23rd over the tropic of Capricorn in the southern hemisphere at 23.5 degrees south in the on 21st 22nd December and over the tropic of cancer on June 21st 22nd this is what we have seen. Now, what does this mean this means that the net solar radiation actually varies with season as you can see this is from January to December and this is the latitude now southern pole to the northern pole 90 south to 90 north. What you see is that the maximum net radiation is always in the equatorial region, but the latitude at which it is maximum goes from the southern hemisphere in December it starts moving northward in June it is in the northern hemisphere and then again moves southward. So, this is the seasonal migration of the latitude of at which the net solar radiation is maximum. So, this is the seasonal migration of this latitude. So, the net solar radiation at the top of the atmosphere when it is zonally average as a function of latitude and month shows very clearly the seasonal migration of the belt of the region where it is high which is this migration here and the maximum is shown by the dashed line which you can see going from the southern hemisphere to the northern hemisphere in June and returning to the southern hemisphere in December. So, this is the seasonal variation of the radiation which actually drives the atmospheric circulation. So, the latitude at which the net solar radiation on top of the atmosphere is maximum varies from the tropic of Capricorn at the southern summer solstice to the tropic of Cancer at the northern summer solstice. On the equator the solar radiation has only a few percent of variation with a mean value of 425 watts per meter square and the sun is overhead twice a year at the equator. So, the sun is overhead at this time as well as this time at the equator and so you have so at the equator the solar radiation has very little variation. So, you can see by and large at the equator there is very very little variation of the solar radiation see it is around it is more than 400 watts throughout the year. Now, some of the solar radiation is directly reflected back to space. So, the earth atmosphere system receives radiation from the sun and in turn radiates energy back to space because otherwise it would keep on heating up equilibrium is there only because the earth atmosphere system radiates energy back to space. Now, the net gain or loss of energy as a function of latitude we see here. So, this is net gain or loss of energy this is the balance of what you get from the sun the incoming solar radiation and what is all emitted by the earth atmosphere system and you see here that this is net gain here in this region again this is beginning with January here and it this is the our winter when the net gain maximum gain is in the southern hemisphere this belt of maximum gain actually moves north is in the northern hemisphere in our summer and then retreats to the southern region in our winter. So, this is the seasonal march of the net gain in heat. So, now in response to this seasonal march how does the surface temperature change we have seen that the there is maximum gain in the northern hemisphere in our summer and in the southern hemisphere in our winter. So, this is the surface temperature for typical month in our summer July and what you see is that the maximum temperature is in fact also in the northern hemisphere in July which is not a surprise because that is where the net gain in heat is maximum. So, this is the maximum temperature here and in January the maximum temperature is in the southern hemisphere. So, hence the maximum heating and temperature at the surface is over the summer hemisphere this is the summer hemisphere northern hemisphere is the summer hemisphere in July southern hemisphere is the summer hemisphere in January, but you also notice another feature that given the same latitude the land gets much hotter than the ocean. This is something to be noted you see here also in Australia is much much hotter than the ocean at the same latitude which receives the same radiation. Now, this is the sea surface temperature what we saw earlier was the surface air temperature this is the sea surface temperature and in the sea surface temperature also you see that the maximum sea surface temperature is in the northern hemisphere in our summer in July and shifts to the southern hemisphere in January which is the southern hemisphere summer. And what you see here is the difference between July and January and you see that the there is a lot of heating of the northern hemisphere in July related to January the SST or the sea surface temperature is much warmer here in July than January. Now, in response to this what does the equatorial trough do remember that for the annual average the maximum heating was the equator and the trough was also in over the equatorial region. Now, the maximum heating the latitude of maximum heating is changing with the season in July it is in the northern hemisphere in January it is in the southern hemisphere. So, what happens to the location of the equatorial trough? So, mean sea level pressure with latitude for January and July is shown here this is again average over all longitudes. So, if you look at July then you find of course, high pressure here the higher latitudes and the minimum pressure is around 15 degrees north in January it is nearer the equator. So, there is a seasonal variation in the location of the minimum of surface pressure that is seen which is consistent with the seasonal variation of temperature. So, now this is an idealized picture again annual march of the sun's genital position position or the latitude over which the sun is vertically above sun is overhead and of the equatorial trough. So, we have the surface trough equatorial trough which moves north in the summer and comes south in the winter this is January and this is March. So, the equatorial trough comes south and this is in response to the sun which in fact has its southernmost location in December and the northernmost location in June. So, in response to the seasonal variation of the heating we have a seasonal variation of the location of the surface trough note that the amplitude of the response is smaller than the heating itself that actually the region over which the equatorial trough varies the latitudinal extent or the amplitude of the equatorial trough variation with season is smaller than the latitudinal extent of variation of the sun itself. And secondly notice that there is a lag which again we expect because the atmosphere does not respond instantaneously. So, there is a lag between the forcing by the sun and the equatorial trough. So, the equatorial trough gets its southernmost position about 2 months after the sun has got its southernmost position and similarly here also there is a lag of about 2 months and this is primarily from the oceans because the sea surface temperature you know takes time to respond the ocean is somewhat sluggish and it is only after the sea surface temperature attains the maximum latitude that the equatorial trough moves there. So, first and foremost that the equatorial trough follows the seasonal march of the sun, but with a lag of 2 months and the amplitude of variation of the equatorial trough in terms of latitude is less than that of the sun which is forcing it. So, now relative to the equatorial trough what do the different distributions look like first is just the pressure surface pressure and obviously, since we have made the equatorial trough as 0 latitude obviously, the pressure will increase both in January and July north and south of the trough. Now, these are the meridional velocity or the north south velocity. So, from the south of the trough the velocity is towards the trough or southerly from north of the trough the velocity is northerly or towards the trough and this is true both for January and July what you see here is convergence or divergence and so this is a zone of convergence around the equatorial trough zone. So, this is a zone in which convergence occur this is why it is called ITCG or intertropical convergence zone intertropical because the convergence is coming by winds from both the hemisphere and this is the convergence zone. So, what do the surface streamlines look like these are the surface streamlines and pressure and what you see here is that in fact you can see this is India around here and the winds in January are sort of from the northeast but since the trough is in the south they actually turn here and these are the southeast trades these are the northeast trades and here you see very clearly over a classical region how convergence occurs between northeast trades and southeast trades and this is the surface pressure. And you can see that the surface pressure trough in fact moves from the southern hemisphere to the northern hemisphere as we go from January to July. So, there is a seasonal migration which we saw earlier in the zonal average also of the trough from the southern hemisphere to the northern hemisphere this is over our region which is the monsoonal region it does not move as much over this specific as you can see it is roughly at the same location. So, the amplitude of seasonal variation is not the same over all longitudes it is more over some longitudes and less over other longitudes. So, in fact you can see this depicted here that it is over continents that the amplitude of the variation is largest this is African and this is the Asian region whereas over the oceanic region the amplitude of variation is very small. Now, let us look at precipitation. So, we have rainfall for July and you can see that the rain belt is in the northern hemisphere this is the rain and you also see a second mode if you wish in the equatorial region in July and then this is the rainfall in January. So, if you subtract from July the rainfall in January you will see that in fact the rain increases in July throughout the northern hemisphere here, but the signal is very very large over our region here and it decreases here this in fact this change in sign across for the difference just signifies the shift of the system from here to here or when you go from January to July the rain belt shifts from here to here that is why you see an intensification here and a decrease in rain here. Now, the seasonal variation of the winds and rainfall occurs in association with that of the surface trough which is a response to the seasonal variation of the incident radiation from the sun. Now, the seasonal variation of the winds and the rainfall associated with the monsoon can therefore be considered as a manifestation of this response to the seasonal variation of the solar radiation. So, you see we have now looked at very simple picture of how the tropical circulation arises due to the incident solar radiation being maximum at the equatorial region and decreasing as you go poleward in either hemisphere then we have also noted the fact that actually this incident radiation varies with season and you have maximum incident radiation in the northern hemisphere in the northern hemispheric summer maximum solar radiation in the southern hemisphere in the southern hemispheric summer as a result of that the net radiation gain also is maximum in the southern hemisphere in the summer this is the net from what we get from the sun minus what the earth atmosphere system emits back to space. So, that is also maximum in the northern hemisphere in the northern hemispheric summer and in the southern hemisphere in the southern hemispheric summer. So, there is a seasonal variation in the location of where the heating is maximum in response to that there is a seasonal variation of the temperature this is the temperature of the ocean which is sea surface temperature and the temperature of the land as well. So, overall the temperature at the surface of air actually is maximum in the summer hemisphere it is maximum in the northern hemisphere in our summer which is June, July, August and it is maximum in the southern hemisphere in our winter or the southern hemispheric summer which is December, January, February. So, now with the maximum temperature varying the location of the maximum temperature or heating varying from the southern hemisphere to the northern hemisphere as we go from our winter to our summer the pressure distribution also responds and so the equatorial trough as we will call it or the surface pressure trough actually goes from the southern hemisphere in December, January, February to be located in the northern hemisphere in our summer and we see the surface trough over all the longitudes including the our own monsoonal regions or Indian monsoon region and this trough in fact comes over India in our summer monsoon time. Now, in association with the seasonal variation of the trough will be seasonal variation in the direction of winds. So, the seasonal variation of the winds and rainfall associated with the monsoon can thus be considered as a manifestation of this response to the seasonal variation of the solar radiation. So, now we have to consider the implications of the monsoon. Let me just go back for a minute into what we are saying now. So, the second hypothesis says that the system which gives us rain which is responsible for the monsoon which in fact leads to the seasonal variation of winds by which Arabs define the monsoon and also leads to seasonal variation of rainfall which we observe over our region and this system according to the second hypothesis is nothing other than the intertropical conversion zone or equatorial trough which gives rain in other parts of the tropics. So, whereas the first hypothesis said that the monsoon arises because of land ocean contrast. So, they actually attributed the monsoon to a system which is special to the monsoonal regions of the world which arises there because of the land ocean contrast. The second hypothesis which is a fallout of all the analysis that was done by Charney and Riel and so on actually says that the system that gives us rain in the monsoon or that the seasonal variation of winds and rain which we associate with the monsoon is simply a manifestation of the arrival of the system on to our region, arrival of the ITCZ on to our region during the summer and then the system retreats from our region to the winter hemisphere in our winter. So, it retreats from our region to the southern hemisphere in our winter. Now, this is actually totally different approach to seeing it because if the system is special to our region then we have to figure out what is going to be the variability associated with it. Why is it important to first of all identify what is the basic system responsible for the monsoon? As we saw in the critique of the land ocean contrast as the primary source primary forcing of the monsoon that Simpson talked about he said that you know actually the land ocean contrast is minimum when the rain is maximum and where the rain is maximum remember he pointed out that when India is at its hottest in May there is no rain and when it cools down in July there is plenty of rain. So, this is opposite to what one would expect from the land ocean contrast being the primary driving force of the monsoon. Similarly, he mentioned that actually the rain is least where the temperature is hottest this is over Rajasthan if you look at the mean picture. We have maximum rain over the eastern part of the monsoon zone Orissa and eastern UP and so on and so forth. Whereas the western part of the monsoon zone towards the north west which actually tapers into the Rajasthan desert that is the reason where the temperature is highest. So, for that reason the land ocean contrast would be highest, but that is not where most of the rain occurs that is where the rain is minimum. And he also pointed out that if we compare seasons rainfall seasons in which we get a lot of rain we saw the seasons in which we have droughts like we had a recent drought in 2009 and we had very good rains in various years 1998 1975 and so on and so forth. If we compare those two seasons then with land ocean contrast theory we would have expected that actually land would be hotter in those years in which the rain is more, but opposite is seen and this was shown very nicely by Kothavalli and Rupkumar that if we compare years of extremes that is droughts we saw we excess rainfall season then systematically what we see is that at the surface in fact the air temperature is colder for excess monsoon seasons and warmer for droughts. So, the land ocean contrast is actually less for good rain seasons then it is for poor rain seasons. So, this again goes against the theory that suggests that in fact it is a system which is primarily driven by land ocean contrast. On the other hand what we are now saying is that the monsoon is a manifestation of the annual visit to a region of the ITCZ the intertropical conversion zone or the equatorial trough as real called it. So, it is a region it is in fact a annual visit of the system which gives rain all over the tropics it is the same system that gives rain over specific that we saw. The second hypothesis says it is the same dynamically the same system that actually comes over us in our summer and leads to the seasonal variation in winds and the seasonality of rainfall that we experience. So, the two hypothesis are totally different and we have to now consider the implications for the monsoon oops. So, this is the January and July pattern. So, now next we are going to consider what are the implications of saying that the system that gives us the monsoon is not a system which is special to the monsoonal regions of the world driven by primarily by land ocean contrast, but rather is a system that is responsible for the rainfall all over the tropics which comes to visit us every monsoon season. So, according to the first hypothesis monsoon is considered a gigantic land sea breeze driven primarily by the differential heating between land and the surrounding ocean and according to the second hypothesis the critical factor is the latitudinal variation of heating at the surface induced by that of the radiation of the sun. So, the system according to the second hypothesis is driven by the latitudinal variation in the heating of the sun at the surface and the seasonal variation of this heating. So, the second hypothesis says that the critical factor is latitudinal variation of the heating and seasonality of the latitudinal variation of the heating from the sun. Thus the monsoon is considered to be a manifestation of the seasonal variation of the tropical circulation and rainfall in response to the seasonal variation of the incoming radiation. Now, the implications in terms of variability and so on are very different. A lot of work has been done on the intertropical convergence zone on the oceans and what we are now saying is that the basic feedbacks that operate the basic mechanisms which lead to the variability of the intertropical convergence zone the classical canonical intertropical convergence zone that we see over the Pacific will also in fact be operating over the monsoonal region when the ITCC visits us. So, the hypothesis to explain the variability of the monsoon will be very different because now we are saying that the system is the same one that we see over the tropical oceans only thing is now it has come over land and that would mean that other factors will also become important when it comes over land. But the insight gained into the dynamics of the ITCC over the years over various studies can now be used to gain an insight into the variability of the monsoon. So, now in the next lecture we will actually see what are the implications of assuming this and why do we believe that the monsoon is just a manifestation of the seasonal variation of tropical circulation and rainfall or there have been you know this has been asserted by me at this point. But we need to actually show that the system is indeed the same as the one that gives rain over the tropics and that is what I will show you in the next lecture. Thank you.


In addition to fields, a class can have zero or more methods. What is a method? Well, it's basically just a function. In object-oriented programming, the term method is preferred over function, though really you can use them interchangeably. Some pedants will insist that you only use the term method in C sharp, but a lot of programmers will just loosely say function when they need method. So here in this class cat, we have this method foo, which returns a string and has a single parameter a of type string, and this method bar, which returns nothing and has no parameters. But the special thing about these methods is that implicitly, their first parameter is a special parameter called this, which has the same type as the class which contains the methods. So these methods are inside cat. So their first parameter implicitly is this parameter called this, which is of type cat. And then same thing for bar. It implicitly has this parameter this of type cat. So implicitly, this is how these methods are defined, but we don't actually write this parameter. We just leave an implicit. It exists implicitly. Otherwise, this special parameter is like any other parameter, but for one restriction, normally our parameters are like variables and we can assign to them like we do any other variable inside a method. So we can hear assigned to a just any string, and this would be valid. But we can't ever assign to this. So this in this method will be of type cat. So normally with a cat variable or parameter, we can assign it some cats, but the compiler does allows this. The reason for this restriction is not from some technical limitation. It's just a language trying to force broad notions of how objectory code is supposed to be structured. Otherwise, we can use this parameter like any other. And in this case, especially this parameter will be of type cat. So we can set its name to be some string. And this is a valid operation. When we call foo, the first argument will be some cat. The reference to that cat, the address of the cat will be stored in this. And then we can do whatever we want with it like any other cat reference. And understand nothing actually obligates us to in any way use this special parameter. Here in the bar method, the this parameter exists, it's there. We're just not using it. We're just ignoring it. So again, this line here is a compilation here, I'll get rid of that. So now imagine elsewhere in code in some method somewhere. We want to call the methods of cat. Well, we need a cat instance to call those methods. We'll create a variable C of type cat to assign it a cat instance. Here we're calling bar passing in the reference to the cat, which is assigned to the special this parameter, though that's then ignored in the method. And then here we're calling foo also passing in the cat, which is assigned to the this parameter which is here used in this set operation. And we also pass in the string high, which is assigned to this parameter a for normal reference type parameters, like say the string parameter here, it's perfectly fine to pass in null. When we call the method, like say here, instead of passing the string, if we make this null, this is still a perfectly valid call. That's if we call a method and pass null to the special this parameter, that trigger is an exception a runtime error. So here if we made C null and then try to call bar and foo at runtime, the language that object that this can't be null, it'll trigger an exception on this call. The idea of a method is that it's supposed to be an operation enacted upon instances of the class that contains them. These are the things that we want to do with our cats. So it doesn't really make sense to invoke one of these methods when we don't have an actual cat. And also be clear that these are runtime errors. You might assume that the compiler could look at this and say, well, obviously when we get down here, C is going to have the value null. So the compiler in this case could analyze their code and figure out that, yeah, this is going to be null. So it's going to be a bad call. But it doesn't actually do that. Because in this case, yes, it could figure out that the value of C is going to be null, but in many, many other cases, most of the cases, it couldn't figure out what the value of our variable is going to be. Like say if we just had some condition here, some condition that depended upon user input. And now if we conditionally assign C the value null, when we get down here, the compiler just can't possibly know if C is going to be null or not. Sometimes it will be, sometimes it won't. So the compiler never presumes to know what the actual value of any variable is. It only knows the type, not the actual value. So that's why whether this is null is checked only at runtime, never compile time. Now, when the compiler looks at our method calls, it determines which method is being called, of course, by the name. But it also goes by the type of the first argument. That is what determines which method we're calling. So say if I happen to have some class dog, which also has a method called bar, taking nothing, returning nothing. I was just saying it prints a wolf. Well, the compiler here when we call bar knows that we're invoking the method bar of cat because it knows that this thing here is a cat. So it must be the cat method we're invoking. Whereas if we were to create a variable of type dog, let's just create a new dog instance, and now we were to call bar passing in D. The compiler looks at this and knows that this is a call to bar of dog, not cat, because we're passing in a dog instance as the first argument. So so far, which method being called is always a runtime choice. So whereas in Pigeon, we can only have one function of a particular name. In C sharp, we can have multiple methods of the same name, if they're in separate classes. But in fact, even within one class, we can have multiple methods of the same name, as long as the compiler can distinguish between calls to one method and another. And what makes calls distinguishable is if they have different numbers of parameters or different types of parameters in different orders. So here, if I have a method bar, and it doesn't matter what it returns, it can turn a string or just let's just say nothing. But now if I give it a parameter, a type integer. Well now, we can't return a thing, excuse me, we'll just print out that value. Sure, whatever. Now when I call bar here, it knows which bar I'm talking about. Well, first off, because C is a cat, it's bar within the cat class. And because there's no arguments, it must be this bar. Whereas if I had an int argument, well now the compiler can look and say, it matches up with this bar. So this is the method being called. The fact that both these methods have the name bar really is just incidental. There's no necessary relationship between these two methods. They can do entirely different things. We could open files and read them in here. We could launch missiles from this bar. They can do entirely different things. Language doesn't care. It just needs to be able to distinguish between calls to this bar and calls to this bar based on the parameters. And understand the order can matter too. So here, if I have AI and another parameter be type string, and here, this bar is a, well, it doesn't matter what the names are, just the types. So if I just reverse the order, this is still fine too. Same types of parameters, but in different order. And so the compiler could distinguish between calls to one bar and calls to the other. So now if I do seven and then a string here, it knows it's this one, because this is the one where it's integer and then string rather than the other way around. So this is called overloading. Within a single class, we're defining methods of the same name, distinguished by having different parameter types or least parameter types in different order. Sometimes stylistically, this is a nice thing to have because maybe there's some operation to perform on your cat class, but there are variations, same basic idea, but taking different inputs. So it makes sense to give those methods the same name and distinguish between them just by their types of inputs. Be clear, as so far described at least, every time we call a method, the choice of which method to call is entirely a compile time decision. The compiler looks first and says what type of instances that determines the class. And then within the class, it looks for a method of the same name, with the parameter types matching the arguments. The normal fields of our classes are called instance fields, because every instance of the class has its own copy of that field. Every cat instance we create has its own name, age, and weight. A static field, in contrast, is a field which exists only once for the whole class. And in fact, it exists independent of any of the instances of the class. What it really is, is just a global variable. So here in class cat, we have the static field x of type i, of type integer. And this exists at the start of our program and persists throughout the lifetime of the program. And the way we access it is with the get and set operator specifying the cat type name itself, rather than an instance of cat. So here if we set x cat to three, that's setting this static field to the value three, and if we get x cat, that's retrieving the value of the static field, which again is really just a global variable. The frankly odd and unnecessary thing in my opinion is that we have to put our global variables in one class or another. We can't have a global variable existing outside of any class. We have to create static fields, interclasses, and those are global variables. Our classes can also have static methods. Here a static method named alex, which returns an int and takes in a string. And unlike our instance methods here bar and foo, our instance methods, these static methods do not have the special this parameter. So when I call this method alex, the way I do so, here I'll just do so from this method bar inside dog. The way I do it is I write the name of the method, specify the class name, your cat, and then pass in the arguments, in this case just a string. So what is a static method? Well, it's just a method where we don't have to have an instance of the class. Honestly, much like static fields are really just global variables, these static methods are really just like ordinary functions. The odd thing though is that we have to decide which class to put them in. We can't just have them outside of our classes. We have to put them in one class or another. And then when we call them, we specify the class in which they are contained. And we do that because well, we could also have static methods named alex in any other class. So we have to specify which classes alex were talking about. And in fact, within a class, we can have multiple overloads of our static methods, just like we do with our instance methods. And the compiler will distinguish between them based on their parameter types. Which reminds me, I'm not sure I made this explicit, but just keep in mind, when you overload methods, the compiler will object to get a compilation error if you have two methods where the parameters are the same. Like here, we can't have two methods bar taking the arguments because then the compiler couldn't distinguish a call to this bar versus a call to that bar. So the compiler will make sure that you don't have any two overloads that conflict. Class can also have special methods called constructors. And these are methods that are implicitly called when we use the new operator. Here, this class cat has two constructed methods. Both of them have the implicit this parameter as their first parameter. And here, when we call new cat with no arguments, it matches this constructor, this overload. And inside, we're simply just setting the weight to 12.3. And in the call, the newly instantiated cat is passed into this parameter, we're then setting its weight to 12.3. And then always with the new operator returns is the new instance. So in fact, inside constructors, you can have return statements, but you never specify any value to return. It's just always implicitly returning the new instance. So you never put a value here in your return statements. But of course, we don't need that return statement at the end. It just implicitly returns at the end of the method. And then here in this new operation, we have three arguments 9.8, a float, a string, and an integer. And that matches this constructor signature. So this is the constructor that's called, and we're setting its weight to the weight parameter, the age to the nth parameter, and the name to the string parameter. So effectively, these are the initial values for the weight, name, and age. They'll understand it'd be perfectly fine if these had the same name as the fields they're being assigned to, and these get updated accordingly. So now this is age and name. And be clear in the set operation where we're setting the field of a class, well, it determines what the type of this instance is. In this case, it's gonna be an instance of cat. So it's looking here for the name of one of the fields. There's not an expression. This is not some variable or anything. It's just a name that has to match one of these names here of the fields. But then here, this is just anything which is an expression. In this case, it's a float variable, which happens to have the same name as the field, but that's just coincidence.  And the fact that the name here is the same as the field, the compiler is not confused by that because it knows that when it looks here, it's not looking at variables, it's just looking at the fields of the class. So in fact, the common style with constructors is if when you are setting fields from parameters, you just give the parameters the same name as the field which they're being assigned to. Now, in these constructor examples, I'm not doing anything interesting other than just setting the initial values of certain fields. But understand in these methods, we could do whatever we want. Otherwise, they're really just like any other method. You could launch missiles in these constructors. Though arguably that's a very surprising thing to do inside a constructor. And so probably not something you should do. In general, constructors are really just for setting up our instances with initial values. But do understand that aside from how they get called, these constructors really are just methods. Last thing about constructors here is that if you create a class with no constructors, well then it only has a so-called default constructor, constructor that takes no arguments and does nothing. But as soon as you give your class a constructor, it no longer has that default constructor. So if I were to take away this constructor, because I have this constructor defined, now there's no default constructor. And so this new operation is invalid because we don't have a cat constructor taking no arguments.