Today, we are going to talk about a very very important facet of the variation of the monsoon within the season, what we call the sub-seasonal or inter-seasonal variation of the monsoon. Namely, active and weak spells and breaks in the monsoon. The fluctuation between active spells and weak spells or what are known as breaks in the monsoon, that is what we will talk about today. You know, although the summer monsoon season is the rainy season over most of the Indian region, we all know that it does not rain every day at any place during the season. Naturally, on the all India scale also, there are fluctuations in the quantum of the daily rainfall as we see in the next slide. So, this is the all India average daily rainfall that you see for two years. One is 2009, which turned out to be a drought and another is 2010. And these sticks represent the daily rainfall and this is the climatological average over long period. So, you can see that year after year, there are fluctuations between what we call active spells, where you see a spell which sustained high rainfall like this one or this one and so on and weak spells such as these and you see them all the time. So, even in a normal monsoon year like 2010, you see fluctuations between the active spells and the weak spells here. Now, in a drought, sometimes these weak spells become very intense. They can also become intense without there being a drought. So, these intense long weak spells have been called bricks. Now, you can see that in 2009, there was a weak spell here and even the onset was delayed to a large extent that is why this weak spell occurred. Even in the peak monsoon months, there was a very intense weak spell here. Such weak spells in the intense monsoon, such intense weak spells in the peak monsoon months have been traditionally known as bricks and that is what we are going to talk about today. So, let us recall how the advance of the monsoon in the onset phase takes place. We know that the onset occurs over Kerala around 1st June or so. Even while onset has also already occurred over the other months around 20th May. Now, this branch moves northward. So, you have the onset here around 5th June, this is 10th June. This branch is also moving. So, around 10th June, the onset has occurred all over here. Then continued northward progression here and westward progression here leads to the almost the entire country being under the sway of the monsoon by 1st of July. By 15 July, it has reached here. So, this is the advance of the monsoon. By 1st of July, the CTCG gets established in the monsoon zone here. Now, at the end of the onset phase of the monsoon around the beginning of July, the CTCG gets established over the monsoon zone. Now, during the peak monsoon months of July and August, the large scale rainfall occurs primarily over the monsoon zone. This is the monsoon zone just to remind you. So, during the peak monsoon months, most of the time, CTCG is located over the monsoon zone. And now, we consider the fluctuations between active spells and weak spells of brick. So, even in the peak monsoon months of July and August, it does not rain every day over the monsoon zone. Rather, there are fluctuations between active spells with continuous rainfall for several days interspersed with weak spells with little rainfall, often lasting several days. So, this is a phenomena which is observed year after year. The fluctuations between active spells and weak spells for rainfall over the monsoon zone during the peak monsoon months. Let me just remind you that during the peak monsoon months of July and August, the CTCG fluctuates primarily over the monsoon zone. Now, these fluctuations between active spells and weak spells. On the super synoptic time scales, these are synoptic would be of a few days. They are characteristic of the kind of genesis of lows or depressions and propagation. Those are the synoptic scale systems and synoptic time scale. Super synoptic would be few days up to weeks and on the super synoptic time scales, we see these fluctuations on active and weak spells and it is a very, very important feature of the sub seasonal or the inter seasonal variation of the monsoon. It is interesting how rich the literature is vis-a-vis the various important facets of the monsoon. Now, perhaps the first illustration of a fluctuation between active and weak spells over monsoon zone came from Ramdas which we will see here. And this is the 1917 remember now rainfall is in inches and Ramdas has depicted variation of the weekly rainfall from May to October over what was then called central provinces and central India. So, this is over the central part of India and what you see is that there are active spells and weak spells and you can see this is on the weekly time scale and still they are clear. This is what one means by super synoptic time scale. So, even in 1917 which was a good monsoon year, you do get active spells and weak spells fluctuations and in 1918 which was turned out to be a very severe drought, you get a very, very long intense weak spell here. This is a brick in fact. So, this is one of the first illustrations that I could find of the active weak fluctuations over the central region of India. So, this is the first illustration perhaps of such a fluctuation which shows how the very weakly rainfall over the region known as central provinces central India varies and we saw a long dry spell is seen to occur during the drought season of 1918. This is the long dry spell here. Now, the variation of daily rainfall over a central part of the monsoon zone which is 75 to 85 degrees east and 15 to 25 degrees north during the drought of 72 and excess monsoon season of 75 is what we see here. This is a picture that Krishnamurti and Balmep first had and what you see again here is a daily rainfall between 75 to 85 and 15 to 25. So, this is the central portion of the monsoon zone and you can again see active spells and weak spells. In 75 they are just active spells and weak spells no long intense weak spells, but in 72 we have active spells and in addition to that an intense dry spell here and this is a brick. So, Landford first described this fluctuation in the rainfall over the monsoon trough zone as he called it between spells during the height of rains and intervals of drought. So he talked of active spells as spells during the height of rains and weak spells as or breaks as intervals of drought and he in fact elicited the nature of the circulation and pressure distribution associated with these phases of contrasting rainfall conditions. So, Landford talks of what happens during height of rains in active spells and what happens in intervals of drought which are weak spells or breaks if they are intense. Now, how did Landford put it? He said the normal meeting place of the eastern and western branches of the monsoon is indicated by the trough of low pressure which runs down from the Punjab to the southeast. The westerly branch prevailing to the southwest of this trough and the easterly branch more frequently in the gadgetic plane to the northeast. So, we see that in the slide here this is the trough at the surface and you have westerly winds to the south and easterly winds to the north. So, this is the trough that he describes here that this is the normal meeting place or the convergence zone if you wish of the winds of the westerly and easterly type here. So, this is the normal meeting place is the way he put it this is the normal meeting place of the eastern and western branches is this low pressure zone which you see stretching across is this low pressure region stretching across which is also known as the monsoon trough, but it is actually a surface trough. Now, then he says this is the what happens normally. So, what you saw earlier was actually the mean surface wind and pressure pattern for July. So, this is the mean July situation. Now, in intervals of drought or read it as weak spells or intense weak spells and breaks when north westerly and westerly winds interrupt the monsoon in north western and central India it meaning the trough of low pressure is pushed northward to the foot of the hills. To this day this remains the definition of break monsoon as we shall see in the literature and this is a typical break monsoon day this is the surface chart of a typical break monsoon day and what has happened is that the low pressure region has now just been pushed northward to the foot of the Himalayas remember it was here before the eastern end was in the head bay this was the mean location. Now, that end has been pushed here. So, you the surface low pressure is here and what you see is all westerly winds are penetrating here there are no easterly at all. So, this is the surface chart of a typical break day which Blanford himself described earlier. Now, let us contrast it to what happens during what Blanford called the height of rains. He says during height of rains at certain intervals trough cyclonic vortices with closed isobars that is barometric minima are formed on the on or in the intermediate immediate neighborhood of this trough this is the way he describes it and this is a situation this is a sea level chart for a typical active day typical active day and what you see here these are the vortices and in fact they happen to be depressions these are the cyclonic vortices you see which are embedded in the trough actually which are along the trough and these of course cause a lot of rain. So, on a typical active day then at certain intervals true cyclonic vortices with closed isobars which is what you saw are formed on or in the immediate neighborhood of this trough. So, this is a typical active day here and you see these vortices formed here. Now, we have to define what we mean by breaks and active spells and that is what we will now look at how do we define this. So, Blanford's intervals of droughts during which the large scale rainfall over the monsoon zone is interrupted for several days in the peak monsoon months of july august have been called as breaks in the monsoon by Indian meteorologists for over a 100 years. So, it is as if a break has occurred after the monsoon has been established over the monsoon zone when suddenly it stops raining and that condition persists for several days they call it a break as if the monsoon has broken in the middle. So, this is the origin of the term breaks which is used by has been used by monsoon meteorologists for a long time. So, traditionally intense weak spells in july august are referred to as breaks because a break is associated with a lull in the monsoon rainfall after the CTCG is established over the monsoon zone at the end of the onset phase. So, this is how the term break monsoon has been traditionally applied. Now, active spells of the monsoon are spells characterized by what Blanford called height of rains over the monsoon zone during the peak monsoon months of july and august. Now, how have breaks been defined? Actually the first comprehensive study of breaks was by Ram Murthy in 1969 and he studied breaks during 1888 to 1967 and how did he define breaks? Although we talked of breaks as lull in the monsoon and cessation of rains in the middle of the season and so on. Actually break was defined by something else that Blanford described in his classic treatise namely the fact that the trough moves to the foothills of the Himalayas and therefore, there are no easterlies anymore over the Indian region. So, the break situation was defined as one in which the trough of low pressure was not seen on the surface chart and easterlies were practically absent. So, this is the similar to the synoptic situation described by Blanford. Now, subsequent to Ram Murthy's classic work Day et al have identified breaks during 68 to 97. So, data on breaks based on this definition absence of easterlies in the chart or the surface trough moving to the foothills of the Himalayas are available for a well errone period 1888 to 1997. So, let us now first consider what we know about this traditionally defined breaks as we saw this is the monsoon trough going to the foothills and total absence of easterlies in the surface chart. This is what defines the break note the absence of easterlies on the surface chart and secondly, note also that there is a ridge present here over the western part which you can see at the surface. We will come back to this Simpson specifically referred to it while talking of monsoon, but there is a ridge over western part here. Now, let us see the circulation of this day which is 7th august 65 at different levels in the atmosphere. So, this is at 0.6 kilometers, 0.9 kilometers, 1.5 and 3 kilometers. So, right from very near the surface you see here, easterlies pervade the entire region there are no easterlies at all and furthermore you can also see that the vorticity is anti-cyclonic because maximum of the winds are occurring here same story at 0.9 same story above the boundary layer. So, very clearly the entire region in the break is coming under the sway of anti-cyclonic vorticity here and note that at 3 kilometers also the situation is the same. There is no trough over the monsoon zone. There is a trough at best can be drawn near the foothills of the Himalayas. So, there are no easterlies up to 3 kilometers in a break situation. Now, for the same day there are records of how much it rained and what is the pressure departure. So, this is the rain and you can see there is hardly any rain over the monsoon zone here. There is rain over the foothills of the Himalayas and there is also some rain over this Tamil Nadu region southeast corner of the peninsula. This is a pattern of the rainfall for that typical break day that I showed you in August 65. Now, what are the pressure departure from normal? This means pressure anomaly. This is the pressure away from the mean pressure and what you see is that there is a very big region of high pressure departure from normal here. So, over the entire monsoon zone the pressure is higher than average and this has certain implications. So, large positive pressure anomalies are seen over the monsoon zone and whereas, for a typical active day what happens? Typical active day you have cyclonic vortices here and you get rainfall which is very well distributed across the monsoon zone. So, this is a typical active day and you can see the pressure departure is negative over the entire monsoon zone. So, these are two opposite sides totally mirror images if you wish or opposite phases of the fluctuation of the monsoon. These are the break phases and the active phases and now this is for the same day active day and what you see is very clearly Easterlies here and that the vorticity is cyclonic over most of the region. The maximum Westerlies are here and you get cyclonic vorticity over the entire region. So, Ram Murthy identified breaks as spells in which the trough of low pressure was not seen in the surface chart and Easterlies were practically absent in the lower tropospheric levels up to 1.5 kilometers above the sea level provided they were three days or longer. So, such spells were called breaks only if they were three days or longer one day or two day kind of spell in which these conditions were satisfied were not considered as breaks. So, he had in mind that these were longer time scale phenomena then one or two days and so provided they were three days or longer he called situation in which there were no Easterlies on the surface chart and practically up to 1.5 kilometer he called them breaks. Now, till about 1932 identification of breaks was done mainly with reference to surface charts only after that some upper wind charts became available and they were consulted. So, what Ram Murthy did is having defined breaks in a very specific way by saying they were days when no Easterlies were seen on the surface charts or up to about 3 kilometers impact. He then went on to describe the morphology of breaks in terms of the surface pressure patterns rainfall distribution and lower middle and upper tropospheric wind circulation associated with breaks and compare them with those characteristic of active spells. So, what he did was that he identified the breaks and active spells over a large period for which he had data and then he made composites of them to see what is a break composite and active composite for surface pressure patterns rainfall distribution as well as circulation patterns. That is how he got the morphology of the breaks and breaks are in fact characterized by particularly large positive pressure departure that is departure from normal and a large suppression of rainfall over the monsoon zone whereas, active spells are characterized by very high rainfall over the monsoon zone. So, now this is a typical pattern for a break. Now, this remember is an average over several breaks and what you see is that the pressure departure from normal in this composite is more than 2 millibers which is a huge pressure departure over this region over the monsoon zone and it is in fact positive over almost the entire Indian region except for the foothills of Himalayas and the southeastern peninsula. So, this kind of pressure departure is what is characteristic of a break. Now, what this implies is see you know that in the normal you have a low pressure belt here. Now, when you have a departure which is positive pressure anomaly here this means the low pressure has become less intense. So, this low pressure belt that you have has become less intense because of this positive pressure departure which is occurring right over here and so this means that the north south pressure gradient that exists between the southern hemispheric highs and this low pressure is going to be weaker during the breaks. Now, what is the mean departure of rainfall during breaks this again Ramurthy computed this is based on subdivisional rainfall and actually about 80 percent deficit occurs here towards the north western part of the monsoon zone 60 percent here. So, there are huge rainfall departures and they are in fact negative over most of the region please notice that even over west coast there is a huge deficit in rain because 40 percent and 27 percent and 41 percent is very large amount of deficit in terms of quantum of rainfall because the mean rainfall here is very very high. So, it appears that breaks are characterized of course by large deficit in rainfall over the monsoon zone, but associated with it are also deficit in rainfall over the west coast. Now, this is all from Ramurthy and if we look at the subdivisions which is what he used the data for then in fact you see that this is 80 percent and so on and so forth 84. So, very very large departure as we noted in this end of the thing and very large departures also over the west coast, but not as large as over the north western part of the trough zone here. So, the largest anomalies occur over this region in the breaks. Now, what are the winds like in the breaks and this is again a very interesting composite here this is a break situation and this is an active situation this is 850 millibar this is 700 millibar or HPA as we call it now. So, this is 850 HPA and 700 HPA for break situation and this is the same for an active situation. Let us see first what happens as at 850 millibar for a break situation you can see that the winds are westerly throughout and further more they are very very high here relative to here. So, the vorticity is clockwise or anti-cyclonic over the entire region as far as the pressure is concerned you see in fact there is a ridge here over the western part at 850 millibar and this presence of the ridge again will be mentioned in subsequent analysis of break situation and so please note it here. Now, 700 millibar also there is no trough here at all in fact the entire region is still anti-cyclonic vorticity as it is at 850. Now, look at the opposite case active monsoon active monsoon in fact the trough is here and we have a 700 millibar trough here. So, very active trough over the Indian region here and you have strong westerlies and relatively strong easterlies which means a high cyclonic vorticity above the boundary layer here. So, remember this now high cyclonic vorticity above the boundary layer is associated with large scale convergence and large scale ascent and can lead to heavy precipitation because of the deep clouds. Now, you see at 700 millibar a very clear trace of that trough here and this is why 700 millibar is considered a very key level to look at the system which is associated with moist convection in the tropics. So, these are the contrasting cases which were presented by Ram Murthy. So, Ram Murthy's composites for breaks clearly show anti-cyclonic vorticity at 850 millibar that is above the boundary layer whereas, that for active spells is cyclonic. In the break composite of 850 HPA a ridge is seen over the western part of the monsoon zone and such a ridge is also seen in the surface chart of a typical break day. See this is the ridge we are talking about. So, there is a ridge seen over the western part which is also seen for a typical break day we had seen it earlier. Now, as I pointed out at 700 HPA a trough is clearly seen in the composite for active spells, but not in that of break spells. So, you have a trough very clearly seen here in the active spell, but there is no trough over this entire region in the break spell. Now, it is interesting that although we defined breaks by Ram Murthy's criteria because Ram Murthy was the first to do a very detailed study of break monsoon. Actually even before Ram Murthy various people have written about breaks and in particular interesting or observations made by our friend Simpson about whom we talked because he had a theory of the basic system responsible for the monsoon. He also shot down the land sea breeze model for the monsoon. So, in that same paper in fact Simpson talks about breaks as well. And what is very interesting is that even in that era because the paper was published in 1921 even in that era people were keen to look at what is happening around on the oceans around the region. So, Simpson says that for the period 1893 to 99 the IMD collected observations taken on the ships in the Indian Ocean as far south as 8 degrees south and from these prepared daily weather map for the whole area. So, for a 7 year period IMD had taken the trouble to collect observations from the ships and these were all ships of opportunity and actually prepared daily weather maps for the whole area that is including Indian Ocean up to 8 degrees south. Now, using these maps Simpson showed that on a typical break day namely 18th August 1899 the conditions were very similar to those in May. He showed that on the break day the winds over the southeast Arabian sea blow against the southeast trails. Now, this is very interesting because now he is talking of winds over the ocean. So, far in the definition we were only talking of winds over land, but he showed that in association with the break situation over land on the break day the winds over southeast Arabian sea blow against southeast trails and in consequence. So, what happens is that there is a convergence between winds over the southeast Arabian sea blowing towards the southeast trails. So, there is a convergence over the equatorial region this is what he pointed out and so in consequence he says the weather is cloudy and rainy over the equator and dry over the Indian region except for the northeastern parts. So, this is very interesting he points out with perhaps the first analysis of observations on the Indian Ocean that during breaks it is cloudy and rainy over the equatorial region. We will come back to this later on. He also pointed out that the pressure gradient between the south of the Indian Ocean and Arabian sea is small as a consequence of the relatively high pressure over western India. We have seen this from Ram Murthy's analysis and in his view one of the most frequent causes of breaks is the establishment of an area of relatively high pressure over western India. Remember we I pointed out to you the ridge over western India which is seen in surface charts as well as 850 HPA on typical break days and is also seen very clearly in Ram Murthy's composite of break monsoon. So, he says this is one of the most frequent causes of breaks this presence of the ridge and in fact this is what I show here again this presence of the ridge in Ram Murthy's composite which he is talking about. Now, there is another very interesting study by Koteswaram who has shown the presence of lows in low latitudes during the breaks in the monsoon. So, Koteswaram had also suggested that during the breaks in the monsoon the equatorial convergence zone becomes more active or the equatorial rain belt gets more rain. Now, this is again consistent with Simpson's observation about whether being cloudy and rainy over the equator during breaks. So, now we have to distinguish between active spells weak spells and breaks as I have tried to show active spells and weak spells occur in every monsoon season and we have seen that before and let me go back. In fact, during weak spells what happens is that the strength of the cyclonic vorticity and rainfall over the monsoon zone is much less than during active spells. So, it is not that the nature of the circulation changes, but the magnitude of the cyclonic vorticity above the boundary layer magnitude of the large scale convergence and rainfall decreases during weak spells we survey active spells. So, fluctuations between active spells and weak spells of rainfall occur year after year. Now, break is a special case of a weak spell with well defined circulation characteristics which does not occur in every monsoon season. So, breaks as we have Ramurthy defined them and as are traditionally defined actually do not occur each and every year, but fluctuations between active weak spells are seen year after year. Now, what are active spells? You may recall that Blanford also remarked on how there is frequent generation of cyclonic vortices during what he called the height of the monsoon rains. So, Murakami says active spells are characterized by a sequence of time clustering partly overlapping this development of monsoon disturbances cyclonic vorticity above the boundary layer. So, naturally these disturbances are associated with cyclonic vorticity above the boundary layer. So, active spells you have a series of disturbances which are actually generated and which move along the monsoon zone. So, this is the definition of active spells. On the other hand the break spell is characterized by a marked change in the lower tropospheric circulation over the monsoon zone with vorticity above the boundary layer becoming anti-cyclonic. Now, this again you have seen from Ramurthy's composite. Now, there is another interesting way to look at these things and this is by looking at the mean meridional velocity because this gives an idea of the circulation in the latitude height dimension. These are the remember we talked of the Hadley cell which involved rising of air in the ITCG and spreading towards higher latitudes and sinking beyond the ITCG and then returning at low level to the ITCG. So, this is one cell this is the Hadley cell. Now, we try and see how cells are modified during active and break conditions. So, let us see in the next one. Now, this is actually from Ramurthy this is the active monsoon case and you know in those days what they did was to get an idea of how things vary with latitude they would look very carefully at data at various stations going all the way from Trivandrum to Srinagar here. So, this is roughly along say 75 or 80 degrees east. So, this is roughly along the central Indian longitudes and they do not worry about differences that arise from east west displacement rather they take the data of all these stations and then draw maps for active monsoon and break monsoon. How does the wind which is going north or coming from the north in which places does it occur and what you see is over the Indian region which begins from Trivandrum, but from Vizag onwards you have Sutherleys. In other words wind is flowing from the south to the north in an active monsoon day and these Sutherleys are very deep. In fact, even at 300 millibar you see the winds are coming from the south. So, there is a very deep layer in which winds are coming to the north to the monsoon trough zone and air rises here and in fact returns to equatorial latitudes only up in the upper levels that is beyond 200 millibar or so. So, you have a deep cell in which this is the at the lower levels air is going towards the north towards the monsoon trough and at the higher levels it is coming from the north to the south. So, this is a very deep circulation cell it is similar to what we conceived of as a Hadley cell with the rising limb of the Hadley cell being here. This is the active monsoon situation, but look what happens in the break monsoon. What happens in the break monsoon is very interesting the belt of Sutherleys here is restricted to only a very low level it does not even reach 700 millibar. So, the belt of Sutherleys is up to about 2 kilometers or so. So, air is moving north here and it is actually returning to the equatorial region here. So, you are getting a very shallow cell in the break monsoon which is totally different from the deep cell that characterizes the active monsoon. So, now let us look at the again what we do now is to see what we have seen here is this is the break monsoon slide and in fact, this circulation looks very much like the heat law that I described earlier heat law circulation remember actually the ascent never goes beyond 700 millibar and actually at 700 millibar and above there is descent and there is divergence. So, the air is the cell is completed by circulation at 700 millibar towards the south and ascent only up to 2 kilometers or so. This is a typical heat law kind of circulation and what we do is in the next slide compare these two. So, what you see here is the break monsoon slide that you saw this is the same one this is the shallow cell, but what you see here is now with modern data what we have plotted here is the latitude height section of meridional wind climatology. So, this is the mean for July for 60 to 70 east remember the heat law is located in this region the heat law over the northwestern India. So, take those longitudes and we look at the meridional circulation in fact, what we find is that the circulation is very similar very similar to what we see in the break monsoon that you are getting south southerly flow only up to over 2 kilometers or so and at 700 millibar in fact, there is a return flow already. So, the ascent is restricted to below 700 millibar and you have a return flow here. So, this is the heat law circulation in the mean July pattern and this is the break monsoon. So, the mean meridional velocity pattern of a break monsoon is very very similar to the heat law on the other hand the mean meridional velocity distribution for active spells is found to be rather similar to that of the mean July patterns as well as the mean pattern along 80 degrees east. So, let us see now in the next one. So, this is the active monsoon remember that is the deep cell with southerly is extending way beyond 500 millibar also and ascent of air here and northerly is that is the return current at this high levels here. Now, this is the latitude height section of 78 to 88 remember this is mean for July and this is where the CTCG axis is. So, this is the characteristic of the CTCG and what you see is in fact a very very deep cell with southerly is here and northerly is beyond 300 millibar also. In fact, this is the mean July picture again from IMD and that is similar to the July picture here. So, active monsoon is the cell is very typical this is again like a Hadley cell and typical of the CTCG whereas, break monsoon this meridional cell is very much like a heat low. Now, let us see what is the special feature of intense long breaks during intense long breaks in the monsoon the surface temperature increases rapidly and a heat trough type of circulation gets established over the monsoon zone with subsidence over most of the troposphere and the prominent trough at 700 HPA associated with large scale rainfall disappears. This heat was first pointed out by Raghavan in 73 and what we are saying is anyway the meridional circulation in the vertical plane for a break is like a heat low. Now, what happens in for intense breaks is and this is an example of the intense break that occurred in 2002 and what you see here is the average temperature anomaly for 12 July to 15 July and all the reds and yellows and so on are positive and what you see is that entire monsoon zone region has positive anomalies. In fact, very large positive anomalies and these are also positive anomalies but are not as large. So, entire region has positive anomalies and this is something we experience whenever there is a dry spell things become very hot because of the clouds free skies the incident radiation heats up the land. So, this is a case in which you have a genuine heat low with very large heating here sensible heating here and also structure like that of a heat low. So, now we actually look at the structure what we had seen earlier was from break monsoon of Ramurthy which was with earlier data now with modern data we can look at again at the meridional circulation for the break of 2002 and what you see here is very interesting 11 to 19 July you see the shallow cell here and active monsoon again 1 to 9 August in 2002 you see a very deep cell here. So, this is very interesting that you get a transition from a heat low situation to a T C T C G situation when you go from break to active. So, this is a very major transition that occurs. So, on the other hand during the active spell the meridional cell is deep with northerly seen only above 300 HPA. So, this is comparable to the dynamic low in the July mean pattern. So, this is comparable to the dynamic low in the July mean pattern this is the active situation and remember over the same region this is the break situation. So, this is the C T C G and this is the heat low that you see. So, this is comparable to the dynamical low. Now, the occurrence of a heat trough type circulation over the monsoon zone in place of a T C G in the peak monsoon months of July August implies a very major transition. Now, revival from such breaks involves a transition to a moist convective regime with convergence up to the mid troposphere and northerly is allowed which is similar to the transition that takes place in the onset phase of the monsoon. Now, as we see for before the onset also in May there is a heat trough over the Indian region and the transition to having a C T C G over the Indian region takes place during the onset phase. So, revival from breaks such as these when you have a heat trough again established over the Indian region involves a similar transition to that which is seen in the onset phase. Now, we come to revival from breaks and this again it is amazing how comprehensive study of Ram Murthy has been in terms of looking at every facet of break not only describing the morphology, but also describing the transitions. In other words how does the monsoon revive from breaks because remember breaks occur in the mid season. So, it is not as if the monsoon has withdrawn for good it has to revive and it has been suggested that revival of breaks occurs with the formation of a low or a depression over the north bay of Bengal. This is what was traditionally believed, but Ram Murthy meticulously looked at all the breaks and how they were terminated and he said that only 45 to 50 percent of the breaks were terminated in this manner. So, only about half the breaks were terminated by having a genesis of a system over the north bay of Bengal which then moves across the monsoon zone and revives the rain. In fact, Sikhar and Gargil's analysis showed that out of 22 occasions on which the C T C G disappeared from the monsoon zone for several days and this analysis is for 73 to 77 only 9 cases the revival occurred by this process in the other 13 cases revival occurred with the northward propagation of T C G from the equatorial Indian ocean. So, this is very interesting and so what are the important features of the traditionally defined breaks and active spells emerging from the large number of studies over several decades. And the first of course is the way breaks are defined by Ram Murthy and IMD definition of breaks also is the same thing. So, absence of easterlies on the surface chart that is movement of the surface trough to the Himalayan foothills this is the traditional definition of breaks. Then we have seen another characteristic is of course, large positive surface pressure anomalies over the monsoon zone with a ridge over the western parts of the monsoon zone at the surface and 850 HPA absence of a trough at 700 HPA this is a very important feature because this also indicates that there is no moist convection during break periods over the monsoon zone. Now, anti cyclonic vorticity at 850 HPA above the boundary layer. So, this implies that they would not be ascent at the top edge of the boundary layer and large negative rainfall anomalies over the monsoon zone negative anomalies also over the west coast, but positive anomalies over south eastern part of the peninsula and Himalayan foothills. So, this is the signature of the breaks we have also seen that the meridional circulation for breaks is a shallow layer of southerlies over the monsoon zone suggesting a shallow vertical circulation cell similar to that observed in a heat low and in fact, in prolonged breaks the surface temperature anomaly becomes large and positive over the monsoon zone and a heat trough occurs over the region. So, these are the major features of the breaks and so far we have been talking of breaks as defined by absence of easterlies on the surface weather charts. Now, all the interruption of monsoon rainfall is recognized as the most important feature of the break the criteria used by India Med Department and by several meteorologists for identifying a break is the synoptic situation associated with such a rainfall anomaly because although Blanford talks of height of rains he does not talk of a synoptic situation and intervals of drought. So, he is talking of rainfall and we all associated break monsoon with a major negative rainfall anomaly, but the way break is defined it is on the basis of winds the synoptic situation associated with such a rainfall anomaly. It is implicitly assumed that a rainfall anomaly pattern of the Ramurthi break type will always be associated with such a distribution of rain pressure. Now, clearly it would be useful to have a definition of break monsoon and active monsoon on the basis of rainfall and its distribution rather than in terms of circulation and pressure distribution. So, a definition of break and active monsoon in terms of rainfall distribution and hence convection. So, we can also talk in terms of how the OLR anomalies would be can also facilitate analysis of teleconnection with convection over other parts of the tropics since global data and satellite derived convection are now readily available for over 3D kids. However, since a great deal is known about the traditionally defined breaks the criteria for the definition on the basis of rainfall should be chosen. So, that the breaks based on rainfall which we can call rain breaks have a large overlap with the traditional breaks. Now, this actually has been accomplished in two recent studies one is by Gadgil and Joseph in 2003 and another by Rajiv and others in 2010. So, this is the paper on breaks of the Indian monsoon by Gadgil and Joseph in 2003 and this is the paper that appeared in the same journal in 2010 active and break spells of the Indian summer monsoon. Now, Gadgil and Joseph have defined breaks on the basis of rainfall over monsoon zone remember we have emphasized that traditional definition really involves conditions primarily over the monsoon zone. So, they have also defined breaks on the basis of rainfall over the monsoon zone on the basis of rainfall criteria which are chosen. So, as to ensure maximum overlap with the traditional breaks documented by Ramurthy and Day. See between Ramurthy and Day traditional breaks have been documented from 1888 to 1997. So, if we use rainfall data then we should be able to check to what extent breaks defined using rainfall with criteria that has chosen overlap with those of Ramurthy and Day and in fact that is what they have done and in fact this at this point I am going to stop this lecture and from the next lecture we will look at what we will look at what happens when we define breaks in terms of rainfall and we will also confirm that the characteristics morphology that was identified by Ramurthy and others to what extent is it also the morphology of the rain breaks and so on and then look at a large number of breaks defined a large number of definition of breaks by many scientists. Because for some reason the word break monsoon or breaks has become extremely popular since the eighties and everybody seems to have their own definition of breaks we will look at implication of that we saw either in breaks also in the next lecture. Thank you.


again one way to do it is to transition everyone into groups okay so offer just group training and offer one-on-one as well but you make it you make sure that the one-on-one is obviously a premium type of service and that if any parent wants to do it you let them know right this is the price if you want to work with me one-on-one but we have this alternative option which is a little bit more affordable which is our group and it's still a private experience because our groups are you know four to eight players so your child's still going to get a lot of personal attention but there's a lot of benefits to the small group is that we can do more game realistic training they're also developing the social skills and they also get to play with playing train with different players that they wouldn't be training in their club teams as well okay because sometimes what a lot of coaches do is they're so and I and I speak to a lot a lot of coaches and they're afraid of doing the groups because they feel that yeah parents aren't going to do it because they already get group training with their team but we've got to find ways to add more value so that parents see that right okay even though it's still group training with coach Katie but coach Katie is doing this she's offering this she's offering this and she's offering this and this is something we're not getting with with our team okay so a lot of a few things it might be you get them to do homework you set them homework every week that they have to do and they have to stay accountable and you can offer zoom sessions either technical training on zoom or you can do like mindset training where all your players are coming on a set they set time during the week once a week or once a month and you talk to them about nutrition confidence and how to get recruited you can do a session on that okay and then you can offer a lot of other things which the team doesn't offer and that's


Welcome back to our lecture series Math 1050, College Algebra for Students at Southern Utah University. As usual, I'll be a professor today, Dr. Andrew Missildine. We've now arrived upon the last lecture, number 36 in our Chapter 5 unit about algebraic functions, that is rational functions, radical functions, and these other algebraically generated functions more complicated than just polynomials. This will be the seventh lecture in that chapter, which admittedly, if I'm going to keep up the Star Wars pun, I probably need at least two more lectures and admittedly, I have no idea how many Star Wars movie Disney is going to make here, so I think we'll leave it at seven right here. And so what I want to do in this very last section is introduce a technique called partial fraction decompositions that have to do with rational functions in the following way. We're probably very familiar with the algebraic problem that if we had two rational expressions to these two algebraic fractions, take like for example, 3 over x plus 4 plus 2 over x minus 3, how do you add these things together and simplify? Well, the first thing to do is we have to find a common denominator, right? So you investigate x plus 4 and x minus 3, they don't have common denominators. So in order to add them together, we have to find that common denominator, which the least common denominator here would simply just be x plus 4 times x minus 3. We've talked about that before. So we're going to reproportion things. We're going to take the 3 over x plus 4 over the times top and bottom by x minus 3 so that the denominator now agrees, okay? And we're going to do the same thing with the 2 over x minus 3. We need to times the top and bottom by x plus 4. And so now we have this common denominator in play. We can add the numerators together. We'll distribute it and we get 3x and a negative 9, like so, distribute the 2 here, we get 2x and an 8. Because we have a common denominator, we can now add these together.  We then get the rational function, the numerator then. And in the denominator, if you want to, I actually abhor multiplying out denominators of a rational function, but oftentimes we're trying to do that for the worst reasons ever. x plus 4 times x minus 3, if you were to foil that out, you get x squared minus 3x plus 4x minus 12, which combines to be x squared plus x minus 12. That's great. And so this is how we can add together fractions, these rational functions. So we have these two fractions right here and we add them together to get this one right here. What if we wanted to reverse the process? What if we don't know any of this? We can't see it now, right? What if we started off with the rational function 5x minus 1 over x squared plus x minus 12? What if we took this fraction, this rational function? What if we wanted to decompose it into simpler fractions? That is fractions with simpler denominators. The term we use are partial fractions because it's fraction, which is a part of the original one. How could we break this rational function up into these partial fractions right here? How could we go from this more complicated fraction to these two right here? It's not as simple as it seems, but it's a very important skill to do algebraically. It's a purely algebraic skill, but it's very helpful. For example, in calculus when you learn about integrals and such, and so I wanna talk about in this lecture how we can compute the partial fraction decomposition. How do you find these simpler fractions? And the way we're gonna break this up is we're gonna break it up between so-called improper fractions and proper fractions. You're used to this with like integer fractions, right? If you take three-fifths, this is what we call a proper fraction because the numerator is smaller than the denominator, right? On the other hand, if you take something like seven-fifths, this is an improper fraction because you could rewrite it as a mixed number so we could write this as one and two-fifths. Or if you take like five-fifths itself or like 10-fifths, these are also improper fractions because we could simplify them, right? So whenever the numerator on top is greater than or equal to the denominator, we say it's improper. If the numerator is smaller than the denominator, we call it proper. The same thing can be done for rational functions as well. So we say that the rational expression px over qx is improper if the numerator has a degree greater than or equal to the denominator's degree. So when we say that the top is bigger than the bottom, we're talking about the degree of the polynomial. If the top has a smaller degree than the denominator, then we say it's a proper fraction. So the first step when it comes to a partial fraction decomposition is to determine whether the fraction and play is proper or not. If it's a proper fraction, we can move on to the next step of the decomposition process. If it is an improper fraction, then we have to do polynomial division. So take as an example here, r of x here, it will be 4x over x squared minus three. Notice the numerator is degree x, that is it's degree one, it's a linear polynomial, the bottom is a degree two polynomial. Previously in this series, this is what we would call a bottom heavy fraction. Bottom heavy fractions are what we mean by proper fractions, that's what we want here. So this one is proper, so we would proceed to do the next step, which we haven't talked about yet. Okay, we don't have to worry about anything there. Now if you look at the next example, this one actually is an improper fraction, right? You'll notice that the numerator has degree three, the denominator has degree one, three is bigger than one, so this is an improper fraction. So what we have to then do is we wanna convert our improper fraction into a mixed number, so to speak. And how does this process work? Well, five goes into seven, right? Five goes into seven once, we subtract the five, we get a remainder of two, right? And so here's the quotient, here's the remainder. We do the same thing for polynomials, that's what long division's all about here. So we're gonna take the numerator, x cubed plus three, and we're gonna divide it by the divisor, the denominator x minus one. Now admittedly this one, since the denominator's x minus one, we could use synthetic division, but I'm just gonna do long division, because that's generally what you have to do here. So x goes into x cubed x squared times, if we take x squared and times it by x minus one, you're gonna end up with x cubed minus x squared. If you distribute a negative one through that, you're gonna get negative x cubed plus x squared. So x cubed minus x squared, those cancel out, we're gonna bring down the x, so we get x squared plus x, and so we repeat the process, x divides into x squared, x many times, because I'm just taking x squared divided by x here to get x, that's what that is. So then, we then are gonna take x times x minus one, that gives us x squared minus x times that by negative one, we then subtract that from below right here, x squared plus x, we see that the x squared's canceled, the x is actually double up, so we get a two x, there's nothing to bring down, so it's just a zero. So then we repeat the process one more time, how many times does x divide into two x? That'll give us two times, right? Two times x minus one is gonna be two x minus two, which when we subtract that, we're gonna get two x plus two, the two x is canceled, we have a remainder of two. So with this remainder of two right here, we can then write the rational function, the improper rational function, x cubed plus x over x minus one, we can write that as the quotient x squared plus x plus two, and then we have a proper rational function part, this is now proper, this rational function could sit with the queen, in which case we have two over x minus one. And so the first step when it comes to a partial fraction decomposition is make sure the rational function is proper. If it's an improper fraction, do long division, you'll get a polynomial plus a proper rational part.