 We have seen that most of the cloud systems that give us rain over the Indian region are in fact, born over the surrounding oceans. So, we have already seen that most of the cloud systems that give rain over land are actually born over the oceans around us or you can say Bay of Bengal equatorial Indian ocean. So, naturally the variability of monsoon rainfall is linked to the variability of the cloud systems or the organized convection or rainfall over the tropical oceans. So, and it is very important to understand what determines the variability of organized deep convection that is cloud systems over tropical oceans. Now, we have seen that clouds are generated when water vapor in the air condenses to form liquid water. So, clearly a critical element is the amount of water vapor in the air. The source of water vapor as we all know is evaporation from the oceans. Now, when we let us consider evaporation from a liquid or water specifically, the average energy of the particles in a liquid is governed by the temperature. The higher the temperature, the higher the average energy. But within that average, some particles have energies higher than the average and others have energies lower than the average. Some of the more energetic particles on the surface of the liquid can be moving fast enough to escape from the attractive forces holding the liquid together. They evaporate and occur in gaseous form in the air above. So, this is the water vapor that we see. So, we have all these particles of water here and some of the energetic ones as you can see are escaping from the water surface and evaporating into the air above and this is what constitutes the vapor. Now, like other gases, water vapor also exerts pressure and this is called vapor pressure. As the gaseous particles bounce around, some of them will hit the surface of the liquid again and be trapped there. So, you know you have all these particles moving around in liquid and in air above and as the gaseous particles in the air bounce around, some of them will hit the liquid surface and get trapped there. So, when the space above the liquid is saturated with vapor particles, the pressure exerted by the water vapor is the saturation vapor pressure. So, when the space above the water surface is saturated with vapor particles, the pressure exerted by the water vapor is called the saturation vapor pressure. In this case that is to say when the air above is saturated with water vapor, there is an equilibrium in which the number of particles leaving the surface is exactly balanced by the numbers rejoining it. So, you have a water surface here and the number of particles leaving the water surface is exactly equal to the numbers rejoining it. So, there is an equilibrium maintained and thus the change from liquid to vapor is balanced exactly by the change from vapor to liquid. Now, the forward change which is liquid to vapor is endothermic. It needs heat to convert liquid into vapor. Now, according to Lesch et alia, increasing the temperature of a system in a dynamic equilibrium favours the endothermic change. That means that increasing the temperature increases the amount of vapor present and so increases the saturated vapor pressure. As you increase the temperature, the particles in the liquid have more energy, more can escape and the equilibrium shifts to a larger amount of water vapor in the air. So, it turns out that the saturation vapor pressure is highly sensitive to the variation of the temperature. So, it is a non-linear function of the temperature as we will see. Now, the nature of the variation of the saturation vapor pressure with the temperature is governed by the Clausius-Clapeyron relation. I will just briefly mention what it is. It says DES by DT that is to say the variation of ES is the saturation vapor pressure above a liquid surface. L is the latent heat of vaporization, T is the temperature. So, this is saying what is the slope of the saturation pressure curve versus temperature. And that slope is equal to L over T, T is the temperature and alpha represents the specific volume of the vapor alpha V and alpha L is of the liquid. So, alpha is the specific volume, alpha V is of the vapor, alpha L of the liquid. Now for this is the equation Clausius-Clapeyron relation that governs the rate of change of saturation vapor pressure with temperature. And you can see that it is inversely proportionate to the temperature. Now, this is what makes it highly non-linear. For terrestrial conditions, a 1 percent change in temperature say about 3 degrees centigrade or Kelvin implies a 20 percent change in the saturation vapor pressure. So, this is what I meant when I said that the saturation vapor pressure is a highly sensitive function of temperature. Now, the fractional change in the specific humidity at saturation which is Q star. The specific humidity is the mass of water vapor per unit volume. So, it is related to the fractional change of temperature by delta Q star by Q star again proportional to delta T by T. Now, this is a plot of how the saturation vapor pressure which is on the y axis varies with temperature. And you can see that it is a highly non-linear curve. This is the temperature in degree centigrade and this is the specific humidity grams per unit of air. So, this is how the specific humidity varies and you can see that around 20 degrees or so 25 degrees it is a very very rapid increase in saturation vapor pressure with temperature. Now, so far we have been talking about the temperature of air. Since the temperature of air at or near the sea surface is close to the sea surface temperature SST, we expect the quantity of water vapor in the surface air to be also sensitive to the SST. Hence, the saturated vapor pressure also varies non-linearly with SST. And in fact, the sea surface temperature or SST is the most popular candidate for explaining the variation of tropical convection. So, it is widely believed that a critical parameter which determines the variation of tropical convection is the sea surface over tropical oceans is the sea surface temperature SST. Now, the question that is to be addressed is how is the organized moist convection on the scale of a few hundred kilometers or more related to SST. So, this is what we will look at in this lecture. Now, this also has a long history half a century ago, Parman suggested that SST has to be above a threshold of 26.5 degrees centigrade for tropical disturbances to intensify to tropical cyclones or hurricanes. So, this is something that Parman suggested from observations that unless the SST is above 26.5, the tropical disturbances that you get over tropical oceans will not intensify to hurricanes. Next came a pioneering study by Birkness in 1969 which showed that the variation of monthly rainfall over Canton Island in the Central Equatorial Pacific could actually be attributed to variations in SST. And this is a picture from his classic paper and what you see here is the rainfall is given here below. This is the rainfall and you can see these are the units of rainfall and this is sea surface temperature is in solid and air temperature is in dashed. So, let us focus on the sea surface temperature. Note that generally the monthly rainfall is less than 10 centimeters. So, this is rainfall in millimeters. Generally the rainfall is less than this 10 centimeters or so. But every now and then you get these high rainfall events or episodes which last for several months, 2 months here but several months here. And these are invariably associated with SST above a threshold of about 27.8 or 28 somewhere around 28. So, if the solid line is above that then you get these peaks in rainfall. When it is below that what you get is these very very small peaks and rainfall generally not exceeding 10 centimeters. So, this is what this was for 1950 to 67. So, that generally the monthly rainfall is less than 10 centimeters. However, there were periods when the monthly rainfall was sustained at a high level that is well over 10 to 50 centimeters for several months when the SST was above 28 degrees. This is shown by Birkenness. Now actually the problem was how does one assess rainfall over the oceans or convection over the oceans? So, systematic investigation of the variation of convection and its relationships with the SST became possible only after the availability of satellite data because through this eye in the sky one could actually see the cloud systems on a day to day basis. This is why systematic investigation of the relationship of convection with SST became possible once satellites were available. In the first such study the relationship between monthly cloudiness intensity determined from cloudiness index derived from satellite imagery over the equatorial Indian Ocean Bay of Bengal and Arabian Sea and the SST was investigated. So, this was the first study of SST convection relationship and this was done by Gadgil et al. And what we did then was the following the data used were the following. First is daily values of a cloudiness index ranging from 1 to 9 each 2.5 at each 2.5 degree squares over the tropics based on operational neph analysis prepared by Ness and Nova and compiled by Sadler and Associates. So, this was the basic data that was used and this was this is what we call the Sadler data and this was in fact neph analysis is you know subjective assessment of satellite imagery. So, subjective assessment of satellite imagery gave rise to these values of cloudiness index again which were prepared by Sadler and others the basic satellite imagery and basic neph analysis was provided by Ness and Nova. So, this was the basic data set it is important to remember that at the time of this study digital data from satellite like outgoing long wave radiation etcetera were not available. So, the best digital data we could get was actually these values of cloudiness index derived from an assessment of satellite imagery. Monthly SST over oceanic regions were available and this is because one of the co-authors of the study was in India Med Department PV Joseph and he had actually compiled he and Pillai had compiled SST data for 5 degree latitude longitude grids from 40 to 100 degrees east that is entire Indian Ocean north of 10 south. And these data were available and they were originally collected from voluntary observational fleet of over 40 maritime nations and stored at the national data center of the India Med Department and Joseph was working at that time in the India Med Department and he and Pillai had actually generated a data set of monthly SST using these voluntary observational fleet data that was with IMD. Now, a comparison of the daily distribution of the Sadler index with the hemispheric mosaics analyzed by Sikha and Gadgil and we have seen a lot of those in the last lecture showed that synoptic and large scale convection such as the TCG Tropical Convergence Zone is associated with Sadler index of 6 or larger. So we subjectively decided by comparison with satellite imagery that Sadler index of for cloudiness of 6 or larger implied deep organized clouds. In this study the cloudiness intensity hence for CI at any grid point at for any month was calculated as the sum of the Sadler index for that for the days on which it was 6 or larger. So at every grid point you will have some value of cloudiness index and there are absolutely no clouds it will be 0 otherwise it will range from 1 to 9. So at every grid point for every month what we did is calculate the number of days on which CI the cloudiness index was 6 or larger. Now at each grid point for each month of the summer monsoon season we therefore had a pair of values one was the cloudiness intensity which is now available on monthly scale and SST available from 7 seasons of let me just mention that it is important to remember that cloudiness index is not simply the number of days on which the Sadler index was 6 or larger rather it is the sum of the Sadler index for the number of days on which it was 6 or larger. So if on some days it was 7, 8 or 9 that day was counted as more than one value right. So one day it would be 9, one day it would be 6 and you would sum over all these days for which the index was 6 or larger. So there was a measure of also intensity involved in this. So at each grid point then we had values for the cloudiness intensity CI and SST and they were available for the 7 seasons of 66 and 72. Now there are 58 grid points each 5 degree latitude by 5 degree longitude in the study area thus there are more than 1600 pairs of values of CI and SST. Now remember that the original Sadler data was on a higher resolution than the SST data. So we had to make it coarser. We had to average over the SST grids to get the oil to get the cloudiness intensity. So we had several values 16 more than 1600 pairs of values of a cloudiness index and co-located SST right. Cloudiness index of the clouds above is a grid point and the SST of that same grid point. Now we are interested in deriving the relationship between cloudiness index and SST and we have the 1600 pairs of values. So the most straightforward way of depicting the relationship between CI and SST is a scatter plot with the frequency of the points in each SST CI bin indicated. So what you see here is a scatter plot this is the cloudiness intensity this is SST and we have bins of SST here and each bin of SST and cloudiness index you either see a blank or you see a dot and the size of dot tells you that how many points there are and in fact that is indicated here 1 to 4 is the smallest dot 5 to 9 is bigger and greater than 10 is the biggest. So most of the points are where the big dots are in this. So this is a very nice way to look at a relationship between two variables it is a scatter plot and it has the information of the total region and the total number of months you have what is the relationship between cloudiness and SST. The most remarkable feature of this distribution is the restriction of the points to the right of the lines of A, B and B, C. Now you see here these are first of all you see that all the cloudiness points are to the right of this curve here. So that is to say to the left of these two lines there are hardly any points at all. So given SST you have a restriction see below this there is absolutely no cloudiness then given an SST of 24 the cloudiness intensity is rather small restricted to less than 10 given an SST of 26 also it is restricted to 50 and so with this line you see that the minimum cloudiness associated cloudiness intensity associated with an SST is actually increasing sorry maximum cloudiness intensity is actually increasing. It is increasing from a very low value to something rather large over 100 by the time you come to about 28 degrees or 27.5 degrees interestingly after this it can be anywhere after this it does not really show any steady increase rather it is just at a high level everywhere. So the maximum cloudiness intensity first increases with SST and then becomes flat. Now look at the minimum cloudiness intensity interestingly the minimum cloudiness intensity is 0 up to about 28 beyond 28 degree centigrade the minimum starts to increase. Until it comes to about this point and this is the point after that there are no points at all with clouds. So this is a very very interesting pattern. So what have we seen the most remarkable feature of this distribution is the restriction of the points to the right of the lines A, B and B, C. A given level of C, I occurs only if the SST above a specific value which is clearly a necessary condition for organized convection. For SST below 28 there is a well defined value for the maximum C, I which increases linearly with SST whereas above 28 it seems to become independent of SST. We have also seen this up to about 28 the minimum C, I is 0. So let us go back and see that we have already seen that up to about 28 the minimum C, I is 0 above that it increases with SST. About SST being a necessary condition is here that unless SST is above 26 you will not get intensities of the level of 100. See this is what one means by SST being above a specific value for a given level of C, I to occur. So it is a necessary condition for organized convection. These are very very interesting features that we have seen how the maximum depend up to the threshold the maximum depends on maximum C, I depends on SST. Beyond below the threshold the minimum is independent of SST above the threshold the minimum starts increasing with SST but above the threshold the maximum becomes independent of SST. Now another way of looking at this variation is what is the probability of different values of C, I for given SST ranges. Now if we go back to this graph suppose we specify an SST range somewhere here then you can see that largest number of points are at 0. So maximum number of points are at 0 and then slowly you will have some number of points as you go higher and higher C, I. Now here if you see the probability say at 28 then the maximum number of points seem to have some cloudiness intensity somewhere between 50 and 100 and so or so. And so one can talk of probability of occurrence of different cloudiness intensity levels for a specific range of SST and that is what is plotted in the next diagram here. So what we see here is we go from 24.5 to 25.5. So these are 1 degree specified limits of SST and what you see here is frequency of cloudiness intensity. How often did this cloudiness and the cloudiness intensity is on the x axis? This is 0, this is 30, 60, 90 and so on 120. So these are monthly values of cloudiness intensity and over very cold oceans you can see the most likely is that you will have no clouds at all. Then possibility of having 10 CAI becomes little bit is a little bit may be around 20 or so and so on and then higher becomes very very small. Same pattern you see as you go to somewhat warmer seas that is 25.5 to 26.5. But now you can see that the probability of getting high CAI is slightly more than it was earlier. And again for somewhat higher 26.5 to 27.5 you see actually that this mode has now become shorter whereas it 60 percent chance of no zero CAI was there. Now it is much more like less than 30 percent and chance of getting other values of CAI probability of getting other values of CAI has increased and you have got somewhat long tail here. Then as you cross 27.5 and go to 27.5 to 28.5 there is a remarkable change in pattern notice that all along here the mode or the most likely CAI was at zero. Now suddenly the mode of the distribution or where the peak is or the most likely CAI has shifted from zero to somewhere around 30 between 30 and 60 and that is how it remains for SSD is beyond this. So there is indeed a very remarkable change across this 27.5 here in which the likelihood of zero cloudiness is much less than the likelihood of substantive cloudiness between 30 and 60 above the threshold whereas likelihood of zero cloudiness is the maximum likelihood below the threshold. So you see across 27.5 which I kept calling the threshold in fact 27.5 turns out to be a threshold below the threshold the distribution is like this above the threshold the mode has shifted. And if we go back to the scatter plot there also we have seen 28 as a limit we could see that below 28 you had a certain kind of distribution where you had actually the maximum CAI determined by SSD and above 28 there is a huge spread of CAI given any kind of specific SSD range. So we said the propensity of convection the propensity of convection is very high above the threshold of about 28 or 27.5 and below the threshold the propensity of convection is low and the mode shifts across the threshold from zero here you can see the mode is zero to some substantive cloudiness intensity once you cross the threshold. So this is what we have seen now and so the frequency distribution so the probability of different values of CAI for a given SSD ranges which we saw also shows a market change across 28. So whereas the most probable CAI that is the mode is zero for SSD below 28 it shifts to about 40 units above this SSD. So Gadgettall concluded that SSD of 28 degrees so is a threshold for active generation of organized convection. The propensity of convection is high for SSD above the threshold and for SSD below the threshold convection tends to get suppressed. So far we have been talking of studies using cloudiness intensity but now this paper was published in 84 in Nature subsequent to this digitized data on outgoing long wave radiation or OLR became available and Graham and Barnett revisited the same problem what is the relationship between SSD and convection using actually OLR outgoing long wave radiation as a measure of convection. And using this much better data set digital data set in fact they found that the relationship that was discovered using cloudiness intensity actually remains the same even if you use these better data set. So what did Graham and Barnett use they use 5 degree by 5 degree average of OLR for 5 day periods and they actually filtered the 40 to 60 day Madden Julian oscillation from these data but we will see that later on just by using raw OLR data also it makes no difference to the results. Now the scatter plot indicating the number of grid points with SSD OLR values in each bin based on co-located SSD and OLR at 20 sites in the tropical Indian and Pacific ocean is shown here and this is from Graham and Barnett you see the features are very similar to what we had seen here this is the threshold that they get they get around 27.5 and what you see is that for SSD now this is OLR you must remember that low values of OLR correspond to high cloud tops and therefore more convection. So this OLR axis is shown in a reverse way maximum OLR is 300 is here and minimum is up there and 240 watts per meter square is considered as a limit. So OLR should be for monthly scales OLR should be below 240 for the clouds to be considered sufficiently deep to represent deep convection. So 240 below 240 is what we have to look at and these are the clouds here you see and propensity of these deep clouds becomes higher once the threshold is crossed again in the same way you know the minimum convection that increases with SSD here. So, the major problem and above the threshold you can see that there is a very large variation of OLR given the SSD. So there is hardly any relationship between SSD and convection once the threshold is crossed. So these all these features were what we had seen earlier with cloudiness index. So values of monthly OLR below 240 are generally associated with deep convection it is seen that over cold oceans that is below the palm and threshold there are hardly any points with OLR less than 240 watts per square meter suggesting that convection organized on the scale of 250 by 250 is very rare for such low SSD. Now as for CI as I mentioned this when SSD increases beyond the threshold maximum OLR decreases with SSD that is to say the minimum convection increases with SSD. The value of OLR with maximum chance of occurrence that is the mode shifts towards lower values of OLR as SSD increases but remains higher than 240 watts per meter square for SSD less than 20 that is to say SSD below the threshold. Now in addition to pooling all the points together as we saw Graham and Barnett actually present data also for individual points and they select two points one is A at the point A and I will mention where it is located the SSD at that individual point is always above the threshold and what do we expect in that case that there will be no relationship between convection and SSD whereas if the SSD variation is across the threshold that is to say at a point B again I will just show the plot then the scatter plot we get is what is a mini version of what we had seen earlier. So A is in the Bay of Bengal 90 degrees east and 5 degrees north SSD is always maintained above the threshold and the OLR is independent of SSD. So you are always in this part of the scatter plot on the other hand if we look at 50 east and 15 south then we have an SSD variation going all the way from almost 24 to beyond 28 and what you see is that no convection below 28 and above convection above 28 convection has become independent of SSD. So SSD varies from 24 to above the threshold OLR is above 240 when SSD is below the threshold but varies between 210 to 260 watts per meter square similar when it is above the threshold. So this is very similar this is like a mini version of the scatter plot you had seen earlier which was here. So what you get in the case of that point B is just this part here but a mini version of the entire one. So these relationships hold now the not only when you consider a large region together where space time variation is mixed up but also where you consider the temporal variation at fixed points in space. So what are the major results now from cloudiness intensity and OLR relationship to SSD. High propensity for organized convection over warm oceans with SSD above about 27.5 or 28 degrees centigrade called the threshold. Second is when the SSD is above the threshold the cloudiness intensity or OLR varies over a large range from almost no convection to intense deep convection. The scatter plot for co-located SSD and OLR over the Indian ocean based on July data is also rather similar. So one does not have to do the filtering that they did of 30 to 40 to 60 day mode and what you see here is for the Indian ocean 15th out to 20 north 60 degrees east to 100 degrees east. Again the size and intensity of the stars show how many points there are and what you see is exactly the same shape and you know this total enormous scatter once you cross about 28 or 27.5. So this is similar and again once is percentage of grids in different OLR ranges for specified SSD again same story you see. You see that SSD is 24.5 again it has now increased to 25.5 and this is 26.5, 27.5 and so on and so forth. Now here the only difference is that a mode has shifted a little bit even before the threshold. Now consider next the variation with SSD of the mean OLR and the standard deviation of OLR for each SSD for July for the Indian ocean. Now so here what we are saying is at each range of SSD we derive the mean and also the standard deviation and what you see here is plotted variation of mean OLR versus SSD and what you see is that there is a very sharp increase in mean OLR across the threshold you see from about here may be 27 to about 28.5 or so there is a sharp increase in the mean and after that it remains flat and the standard deviation becomes very large from about 27.5 or so. So this is what we see and it is seen that the mean OLR decreases rapidly from about 26 to about 29 degree centigrade and remains more or less constant for higher SSD. The standard deviation is large for SSD higher than about 27.5. Now so far we have seen that when we used OLR the relationship is very similar. Now Wallis are actually used one more data set which was the so called HRC data set. Let me first of all explain to you what this is. See so far I have considered only the satellite derived outgoing long wave radiation OLR and low values of OLR are associated with a high radiating surface that is to say a high cloud top and high cloud tops are associated with deep clouds as well as serious clouds that is the problem. You can have thin clouds that you see on top you know very near the top of our troposphere and those clouds are not deep convective clouds but the radiating surface is high. So they will also have low values. Now hence it is believed that high value of reflectivity or Albedo may be a better index for assessment of deep clouds. But actually one needs both Albedo and OLR one has to make sure that a lot of light gets reflected from the cloud that is to say it is deep and also that its top is high enough. So OLR also has to be low. Now relationship of the frequency of highly reflective clouds to HR that is to say HRC to SST was investigated by Walliser. Now highly reflective clouds again this is all done by subjective analysis highly reflective clouds are identified by using visible satellite mosaics and then the lower and medium level clouds amongst them were filtered out with the use of infrared mosaics by Garcia. So this is the way of using bispectral information both visible and infrared visible to first filter out which is the regions with highly reflective clouds and then from that regions those regions remove the clouds which are whose tops are not sufficiently high by using you know infrared which is what we use by OLR. So this is similar to the bispectral algorithms use later. So these dataset comprises of values 0 or 1 on a 1 degree by 1 degree grid from which deep organized tropical convective systems extending at least 200 kilometers horizontally can be verified identified. The HRC dataset is for 25 south to 25 north round the globe. So now using that dataset for the entire global tropical oceans what Walliser shows is the following. This is again the mean and this time he shows the standard deviation by shading. So what you see here is just the number of points corresponding to each SST range and what you can see interestingly is that beyond 29 the number of points with SST higher than 29 decreases very rapidly with SST. But now let us go to SST HRC relationship what you see is that the mean is very flat mean is almost 0 very close to 0 until a certain point about 26 which is the palm and threshold then the mean begins to increase up to 29 which is what we had seen in OLR as well and then it decreases. Now this decrease is something that was first pointed out by Walliser although the decrease becomes little less reliable because the sample of points also become much less than they were in the earlier part. But Walliser showed that the decrease was real when we compare with OLR mean then this is the OLR mean for global tropical oceans and it appears that actually the convection is decreasing with SST as you go here. But this is not the correct this is not due to convection decreasing rather it is true that OLR is increasing as you go here and here but this has to this has to do so OLR is decreasing with SST here right and that is simply because there are no clouds but the ocean surface is cooler so the OLR is less. So this this decrease in OLR is due to decrease of the SST itself it has nothing to do with clouds and when we look at HRC we see that below 26 or so actually there is no change in HRC it is very very close to 0. Now above this the patterns are very very similar as you can see there is an increase from about 26 to about 29 and a decrease after that. So the new feature that Walliser found was that convection is a decreasing function of SST beyond 29.5 thus the maximum SST does not occur over the warmest oceans rather the warmest oceans occur under clear skies. See we are looking at SST convection relationship but always in the back of meteorologist mind is that somehow SST is the cause and convection is the effect. But in fact what Walliser pointed out is true more SST means more water vapor which may increase the propensity of convection but the highest SST you get under cloud free skies because radiation directly goes to heat the tropical ocean. So this is an important point to remember. Now in fact it turns out that the basic relationship we have seen from the scatter plots of cloudiness intensity versus SST as well as from OLR versus SST HRC versus SST the same pattern is faithfully shown by all the later day and better assessments of clouds. So there is a very special satellite called cloud set from where you can get dependence on the vertical distribution of clouds on SST from clouds at measurements and this is from some work done by Rajeev et al and this is for 30 to 120, 30 south to 30 north Indian subcontinent and period June to February. So it includes actually all the months of the year and what you see is that the shift in the mode you see from about 0 till 27 and by 28 the entire mode has shifted to deep clouds. This is where clouds have reached very high. So note the shift in the mode from shallow to deep clouds around SST of 28 degrees and this is a result from Rajeevan studies and again you see the same thing cloud and this is the cloud ice water content cloud ice water path and cloud liquid water path these are also from cloud set integrated over different layers and what you see again is that you get very deep presence of liquid water and ice beyond 28. So this threshold story is borne out and again when you look at scatter plots over different regions again the same story appears that you have a kind of a exactly similar in nature about 28 suddenly you start getting a huge spread in the values of cloud liquid water. Thus the relationship of organized convection over tropical oceans to SST first elucidated by use of cloudiness intensity has withstood the test of time and studies with better indices such as OLR HRC and vertical distribution of clouds or cloud liquid water path and ice water path have yielded the same basic features. Now Walliser has also shown that okay so this is as far as the relationship is concerned but the value of the threshold need not be exactly the same from one region to another and this was very elegantly shown by Walliser. What he did was plot the same curves but now for different regions so you have North Indian, West Pacific, ITCG and Equatorial Pacific and Atlantic ITCG and what you see is that actually there are major differences see this is the Equatorial Pacific and you can see that for it the threshold is around 28 that is also true for West Pacific West Pacific actually the convection tends to be more but again the threshold is 28 or so but when he talks of the ITCG Equatorial Pacific is we have seen West Pacific we have seen then there is the Atlantic this is the now this is the West Pacific Atlantic is the dashed curve so Atlantic should be this one and Atlantic you see that the threshold is somewhat lower it is 27.5 so this is an important point that Walliser made and you can see it also very clearly here that you see Atlantic it is flattening out or after 27.5 whereas for some of the other ones it can be even larger it appears that for West Pacific and so on the mean seems to be increasing almost till 29 so there is some variation from region to region in the actual value of the threshold. Now let us see so far we have been talking only of clouds it is also important to see how the rainfall varies and this is again from a study by Rajendra and others 2012 and what you see here is scatter plots of the same kind but now you have rainfall on the y axis since of convection measures SST on the x axis and the number of points is given here from blue to gray it increases very much this is for the entire Indian ocean which you have seen before what you see here is also plot of the mean and you can see mean increasing and then beyond 28 or so becoming flat this is the 90 percentile and this is the standard deviation standard deviation also behaves very similarly as the mean. Now let us go to the central Pacific and the importance of this region this region will come clear to you once we talk about the El Nino Southern Oscillation and so on this is the central Pacific notice that central Pacific there is a large variation across the threshold large number of points are below the threshold and not that many above the threshold and there is actually a considerable variation across the threshold in that case you see that the mean is very sensitive to SST beyond 26 mean in fact varies linearly with SST. So, depending on the region depending on how the SST is distributed in the region you get different kind of characteristics of the mean and this is tropical way specific a region like the point A in Graham and Barnett it is always maintained above the threshold and there is no relationship at all between this you can see here in fact this is the Indian Ocean SST distribution and you can see the mode is above the threshold for Nino 3.4 which is the central Pacific region in fact it is spread out here and for WPO it is here. So, you get entirely different patterns now correlation of the rainfall with local SST note that for a region such as tropical west Pacific for which the SST is always maintained above the threshold there is hardly any relationship between the rainfall and SST with a large range of the variation of rainfall for each SST on the other hand for the Nino 3.4 region of the central Pacific the rainfall varies across the threshold and mean rainfall does increase with SST. In fact in the Gargil et al paper itself we had shown that when if we restrict our attention to SSTs beyond a certain value if we take entire region so SST beyond 24.5 the correlation is 0.5 or so, but as we go increase to higher and higher SSTs then at 20 beyond 28 it has already dropped to 183 and beyond 28.5 it has become insignificant. So, the correlation decreases and this is because the spread of the sea eye increases enormously. In fact Graham and Barnett have pointed out that one might be tempted to fit a sharp looking curve to the distribution which suggests a strong dependence of convection on SST. However, associations between SSTs and OLR for SSTs above 28 degrees at applicable locations suggests that the dependence of the level of convection in this temperature range is usually slight. They further suggested that when the SST is maintained above the threshold convection is determined by the low level convergence. Thus above the threshold the SST is no longer the limiting resource for convection, but dynamics can be and this is a very important point to remember because it is important to bear this observed lack of relationship between rainfall and SST when the latter is always above the threshold and the correlation coefficients between rainfall and SST should not be used when comparing with the results of atmospheric and climate models with observations. Unfortunately, meteorologists have done that and come to wrong conclusions. Now, let us see what are the implications of this SST convection relationship and what we can see here this is the rainfall pattern here and you can see higher rain means from green to red basically. This is the SST and SST coloring is such that this is above 27.5 their shades of yellow. And what you can see very nicely you look at this region this is June, July, August and look at this region and you find most of the region the SST is below the threshold and you get hardly any rain here. This is June, July I am sorry this is this is December, January, February I am sorry and in December, January, February you would have expected that in the southern hemisphere you should get a tropical convergence on, but southern hemisphere is extremely cold and there is no such TCC. In fact, there is a little bit of warm water here and little bit of rain to the north, but you can see that SST being below the threshold has completely suppressed you know the possibility of having a TCC over the southern hemisphere in equatorial is specific. Now, we go to the summer and summer thing should be in the north and they are, but you see here this is our Arabian say this is Madagascar region and you can see that there is no rain here at all and that is the region which coincides with all the blues in SST. So, SST is so cold here this is because of the upwelling that you cannot have rainfall in this region. So, this implication of the relationships we have talked about are these that when SST is below the threshold you cannot have organized convection. Now, the implications also are there for variability of convection and that is the most important thing because we began with saying what is the variability, how is the variability of convection related to SST and what we find is that in fact this is the central pacific I am sorry this is the central pacific and in the central pacific now what you can see here is this is the SST and this is the rainfall here and you can see whenever SST is larger than about 27.5 or 28 these are these big red things here and that is when you get rain events. So, there is a one to one correspondence between the SST and rain here because SST is varying across the threshold you know it may be above it may be below, but it is varying across the threshold you take on the other end Indian Ocean equatorial Indian Ocean where SST is perpetually above and in that case there is hardly any relationship between rainfall and SST. So, this relationship between SST and convection is a very interesting relationship and it has very important implications for our understanding of the variation of organized convection over tropical oceans and eventually thereby of our understanding of monsoon variability and its links to variation of convection over tropical oceans. Thank you.